LMFDB - Embedded newform 225.2.q.a.106.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.28
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.68409 + 0.570520i) q^{2} +(-1.72549 + 0.150630i) q^{3} +(5.05174 + 2.24918i) q^{4} +(0.420615 - 2.19615i) q^{5} +(-4.71730 - 0.580123i) q^{6} +(-0.931182 + 1.61286i) q^{7} +(7.83615 + 5.69329i) q^{8} +(2.95462 - 0.519820i) q^{9} +O(q^{10})$	\(q+(2.68409 + 0.570520i) q^{2} +(-1.72549 + 0.150630i) q^{3} +(5.05174 + 2.24918i) q^{4} +(0.420615 - 2.19615i) q^{5} +(-4.71730 - 0.580123i) q^{6} +(-0.931182 + 1.61286i) q^{7} +(7.83615 + 5.69329i) q^{8} +(2.95462 - 0.519820i) q^{9} +(2.38192 - 5.65469i) q^{10} +(-2.70264 - 0.574464i) q^{11} +(-9.05552 - 3.11999i) q^{12} +(-1.65646 + 0.352091i) q^{13} +(-3.41954 + 3.79779i) q^{14} +(-0.394961 + 3.85279i) q^{15} +(10.3844 + 11.5331i) q^{16} +(-5.11464 - 3.71600i) q^{17} +(8.22703 + 0.290429i) q^{18} +(1.23445 + 0.896882i) q^{19} +(7.06438 - 10.1484i) q^{20} +(1.36380 - 2.92323i) q^{21} +(-6.92639 - 3.08383i) q^{22} +(0.327461 - 0.363683i) q^{23} +(-14.3788 - 8.64335i) q^{24} +(-4.64617 - 1.84747i) q^{25} -4.64695 q^{26} +(-5.01986 + 1.34200i) q^{27} +(-8.33169 + 6.05333i) q^{28} +(-0.189122 - 1.79938i) q^{29} +(-3.25821 + 10.1159i) q^{30} +(0.285758 - 2.71880i) q^{31} +(11.6068 + 20.1036i) q^{32} +(4.74991 + 0.584133i) q^{33} +(-11.6081 - 12.8921i) q^{34} +(3.15040 + 2.72341i) q^{35} +(16.0952 + 4.01948i) q^{36} +(1.30318 - 4.01076i) q^{37} +(2.80169 + 3.11159i) q^{38} +(2.80516 - 0.857041i) q^{39} +(15.7993 - 14.8147i) q^{40} +(3.71670 - 0.790010i) q^{41} +(5.32832 - 7.06812i) q^{42} +(-5.30871 + 9.19495i) q^{43} +(-12.3610 - 8.98078i) q^{44} +(0.101155 - 6.70744i) q^{45} +(1.08642 - 0.789333i) q^{46} +(0.670718 + 6.38145i) q^{47} +(-19.6554 - 18.3360i) q^{48} +(1.76580 + 3.05845i) q^{49} +(-11.4167 - 7.60951i) q^{50} +(9.38499 + 5.64150i) q^{51} +(-9.15992 - 1.94700i) q^{52} +(4.80881 - 3.49380i) q^{53} +(-14.2394 + 0.738105i) q^{54} +(-2.39838 + 5.69379i) q^{55} +(-16.4793 + 7.33707i) q^{56} +(-2.26513 - 1.36161i) q^{57} +(0.518961 - 4.93758i) q^{58} +(9.93588 - 2.11194i) q^{59} +(-10.6609 + 18.5750i) q^{60} +(-7.13090 - 1.51572i) q^{61} +(2.31813 - 7.13448i) q^{62} +(-1.91290 + 5.24942i) q^{63} +(10.0928 + 31.0624i) q^{64} +(0.0765136 + 3.78593i) q^{65} +(12.4159 + 4.27779i) q^{66} +(0.914005 - 8.69618i) q^{67} +(-17.4799 - 30.2760i) q^{68} +(-0.510249 + 0.676856i) q^{69} +(6.90220 + 9.10724i) q^{70} +(2.74292 - 1.99285i) q^{71} +(26.1123 + 12.7481i) q^{72} +(4.80018 + 14.7734i) q^{73} +(5.78606 - 10.0218i) q^{74} +(8.29519 + 2.48794i) q^{75} +(4.21888 + 7.30732i) q^{76} +(3.44318 - 3.82404i) q^{77} +(8.01827 - 0.699970i) q^{78} +(1.34121 + 12.7607i) q^{79} +(29.6962 - 17.9548i) q^{80} +(8.45957 - 3.07174i) q^{81} +10.4267 q^{82} +(-0.803423 + 0.357707i) q^{83} +(13.4644 - 11.7000i) q^{84} +(-10.3122 + 9.66951i) q^{85} +(-19.4950 + 21.6513i) q^{86} +(0.597368 + 3.07632i) q^{87} +(-17.9077 - 19.8885i) q^{88} +(1.51233 + 4.65447i) q^{89} +(4.09824 - 17.9456i) q^{90} +(0.974593 - 2.99949i) q^{91} +(2.47224 - 1.10071i) q^{92} +(-0.0835387 + 4.73431i) q^{93} +(-1.84048 + 17.5110i) q^{94} +(2.48892 - 2.33380i) q^{95} +(-23.0557 - 32.9402i) q^{96} +(0.396958 + 3.77680i) q^{97} +(2.99465 + 9.21658i) q^{98} +(-8.28390 - 0.292436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.68409	+	0.570520i	1.89794	+	0.403419i	0.999372	−	0.0354233i	$-0.0112779\pi$
$2$	2.68409	+	0.570520i	1.89794	+	0.403419i	0.898564	+	0.438842i	$0.144611\pi$
$3$	−1.72549	+	0.150630i	−0.996211	+	0.0869662i
$3$	−1.72549	+	0.150630i	−0.996211	+	0.0869662i
$4$	5.05174	+	2.24918i	2.52587	+	1.12459i
$5$	0.420615	−	2.19615i	0.188105	−	0.982149i
$5$	0.420615	−	2.19615i	0.188105	−	0.982149i
$6$	−4.71730	−	0.580123i	−1.92583	−	0.236834i
$7$	−0.931182	+	1.61286i	−0.351954	+	0.609602i	−0.986592	−	0.163208i	$-0.947816\pi$
$7$	−0.931182	+	1.61286i	−0.351954	+	0.609602i	0.634638	+	0.772810i	$0.281149\pi$
$8$	7.83615	+	5.69329i	2.77050	+	2.01288i
$9$	2.95462	−	0.519820i	0.984874	−	0.173273i
$10$	2.38192	−	5.65469i	0.753229	−	1.78817i
$11$	−2.70264	−	0.574464i	−0.814878	−	0.173208i	−0.218423	−	0.975854i	$-0.570091\pi$
$11$	−2.70264	−	0.574464i	−0.814878	−	0.173208i	−0.596455	+	0.802647i	$0.703424\pi$
$12$	−9.05552	−	3.11999i	−2.61410	−	0.900664i
$13$	−1.65646	+	0.352091i	−0.459419	+	0.0976525i	−0.431807	−	0.901966i	$-0.642124\pi$
$13$	−1.65646	+	0.352091i	−0.459419	+	0.0976525i	−0.0276122	+	0.999619i	$0.508790\pi$
$14$	−3.41954	+	3.79779i	−0.913911	+	1.01500i
$15$	−0.394961	+	3.85279i	−0.101978	+	0.994787i
$16$	10.3844	+	11.5331i	2.59610	+	2.88327i
$17$	−5.11464	−	3.71600i	−1.24048	−	0.901263i	−0.242851	−	0.970064i	$-0.578083\pi$
$17$	−5.11464	−	3.71600i	−1.24048	−	0.901263i	−0.997630	+	0.0688008i	$0.978083\pi$
$18$	8.22703	+	0.290429i	1.93913	+	0.0684547i
$19$	1.23445	+	0.896882i	0.283203	+	0.205759i	0.720313	−	0.693649i	$-0.243998\pi$
$19$	1.23445	+	0.896882i	0.283203	+	0.205759i	−0.437110	+	0.899408i	$0.643998\pi$
$20$	7.06438	−	10.1484i	1.57964	−	2.26924i
$21$	1.36380	−	2.92323i	0.297606	−	0.637900i
$22$	−6.92639	−	3.08383i	−1.47671	−	0.657474i
$23$	0.327461	−	0.363683i	0.0682804	−	0.0758331i	−0.708037	−	0.706176i	$-0.750419\pi$
$23$	0.327461	−	0.363683i	0.0682804	−	0.0758331i	0.776317	+	0.630343i	$0.217086\pi$
$24$	−14.3788	−	8.64335i	−2.93505	−	1.76432i
$25$	−4.64617	−	1.84747i	−0.929233	−	0.369494i
$26$	−4.64695			−0.911343
$27$	−5.01986	+	1.34200i	−0.966073	+	0.258268i
$28$	−8.33169	+	6.05333i	−1.57454	+	1.14397i
$29$	−0.189122	−	1.79938i	−0.0351191	−	0.334136i	−0.997948	−	0.0640249i	$-0.979606\pi$
$29$	−0.189122	−	1.79938i	−0.0351191	−	0.334136i	0.962829	−	0.270111i	$-0.0870604\pi$
$30$	−3.25821	+	10.1159i	−0.594864	+	1.84690i
$31$	0.285758	−	2.71880i	0.0513236	−	0.488312i	−0.938424	−	0.345485i	$-0.887714\pi$
$31$	0.285758	−	2.71880i	0.0513236	−	0.488312i	0.989748	−	0.142826i	$-0.0456190\pi$
$32$	11.6068	+	20.1036i	2.05182	+	3.55385i
$33$	4.74991	+	0.584133i	0.826853	+	0.101685i
$34$	−11.6081	−	12.8921i	−1.99077	−	2.21097i
$35$	3.15040	+	2.72341i	0.532516	+	0.460340i
$36$	16.0952	+	4.01948i	2.68253	+	0.669913i
$37$	1.30318	−	4.01076i	0.214241	−	0.659366i	−0.784966	−	0.619539i	$-0.787319\pi$
$37$	1.30318	−	4.01076i	0.214241	−	0.659366i	0.999207	−	0.0398264i	$-0.0126805\pi$
$38$	2.80169	+	3.11159i	0.454494	+	0.504766i
$39$	2.80516	−	0.857041i	0.449186	−	0.137236i
$40$	15.7993	−	14.8147i	2.49809	−	2.34241i
$41$	3.71670	−	0.790010i	0.580452	−	0.123379i	0.0916768	−	0.995789i	$-0.470777\pi$
$41$	3.71670	−	0.790010i	0.580452	−	0.123379i	0.488775	+	0.872410i	$0.337444\pi$
$42$	5.32832	−	7.06812i	0.822178	−	1.09063i
$43$	−5.30871	+	9.19495i	−0.809571	+	1.40222i	0.103591	+	0.994620i	$0.466967\pi$
$43$	−5.30871	+	9.19495i	−0.809571	+	1.40222i	−0.913162	+	0.407597i	$0.866367\pi$
$44$	−12.3610	−	8.98078i	−1.86349	−	1.35390i
$45$	0.101155	−	6.70744i	0.0150793	−	0.999886i
$46$	1.08642	−	0.789333i	0.160184	−	0.116381i
$47$	0.670718	+	6.38145i	0.0978342	+	0.930831i	0.927816	+	0.373039i	$0.121684\pi$
$47$	0.670718	+	6.38145i	0.0978342	+	0.930831i	−0.829981	+	0.557791i	$0.811649\pi$
$48$	−19.6554	−	18.3360i	−2.83702	−	2.64657i
$49$	1.76580	+	3.05845i	0.252257	+	0.436922i
$50$	−11.4167	−	7.60951i	−1.61456	−	1.07615i
$51$	9.38499	+	5.64150i	1.31416	+	0.789968i
$52$	−9.15992	−	1.94700i	−1.27025	−	0.270000i
$53$	4.80881	−	3.49380i	0.660540	−	0.479911i	−0.206305	−	0.978488i	$-0.566144\pi$
$53$	4.80881	−	3.49380i	0.660540	−	0.479911i	0.866845	+	0.498577i	$0.166144\pi$
$54$	−14.2394	+	0.738105i	−1.93774	+	0.100443i
$55$	−2.39838	+	5.69379i	−0.323398	+	0.767750i
$56$	−16.4793	+	7.33707i	−2.20214	+	0.980458i
$57$	−2.26513	−	1.36161i	−0.300024	−	0.180350i
$58$	0.518961	−	4.93758i	0.0681429	−	0.648336i
$59$	9.93588	−	2.11194i	1.29354	−	0.274951i	0.490797	−	0.871274i	$-0.336706\pi$
$59$	9.93588	−	2.11194i	1.29354	−	0.274951i	0.802744	+	0.596323i	$0.203372\pi$
$60$	−10.6609	+	18.5750i	−1.37631	+	2.39802i
$61$	−7.13090	−	1.51572i	−0.913019	−	0.194068i	−0.272630	−	0.962119i	$-0.587893\pi$
$61$	−7.13090	−	1.51572i	−0.913019	−	0.194068i	−0.640389	+	0.768051i	$0.721227\pi$
$62$	2.31813	−	7.13448i	0.294403	−	0.906079i
$63$	−1.91290	+	5.24942i	−0.241002	+	0.661365i
$64$	10.0928	+	31.0624i	1.26160	+	3.88280i
$65$	0.0765136	+	3.78593i	0.00949034	+	0.469587i
$66$	12.4159	+	4.27779i	1.52829	+	0.526559i
$67$	0.914005	−	8.69618i	0.111664	−	1.06241i	−0.784939	−	0.619572i	$-0.787306\pi$
$67$	0.914005	−	8.69618i	0.111664	−	1.06241i	0.896603	−	0.442835i	$-0.146027\pi$
$68$	−17.4799	−	30.2760i	−2.11975	−	3.67151i
$69$	−0.510249	+	0.676856i	−0.0614268	+	0.0814839i
$70$	6.90220	+	9.10724i	0.824971	+	1.08852i
$71$	2.74292	−	1.99285i	0.325524	−	0.236507i	−0.413005	−	0.910729i	$-0.635521\pi$
$71$	2.74292	−	1.99285i	0.325524	−	0.236507i	0.738529	+	0.674222i	$0.235521\pi$
$72$	26.1123	+	12.7481i	3.07737	+	1.50238i
$73$	4.80018	+	14.7734i	0.561818	+	1.72910i	0.677221	+	0.735780i	$0.263184\pi$
$73$	4.80018	+	14.7734i	0.561818	+	1.72910i	−0.115403	+	0.993319i	$0.536816\pi$
$74$	5.78606	−	10.0218i	0.672616	−	1.16501i
$75$	8.29519	+	2.48794i	0.957846	+	0.287282i
$76$	4.21888	+	7.30732i	0.483939	+	0.838207i
$77$	3.44318	−	3.82404i	0.392387	−	0.435790i
$78$	8.01827	−	0.699970i	0.907890	−	0.0792560i
$79$	1.34121	+	12.7607i	0.150898	+	1.43570i	0.763757	+	0.645503i	$0.223352\pi$
$79$	1.34121	+	12.7607i	0.150898	+	1.43570i	−0.612860	+	0.790192i	$0.709981\pi$
$80$	29.6962	−	17.9548i	3.32014	−	2.00740i
$81$	8.45957	−	3.07174i	0.939953	−	0.341305i
$82$	10.4267			1.15143
$83$	−0.803423	+	0.357707i	−0.0881871	+	0.0392634i	−0.450356	−	0.892849i	$-0.648703\pi$
$83$	−0.803423	+	0.357707i	−0.0881871	+	0.0392634i	0.362169	+	0.932112i	$0.382036\pi$
$84$	13.4644	−	11.7000i	1.46909	−	1.27657i
$85$	−10.3122	+	9.66951i	−1.11851	+	1.04881i
$86$	−19.4950	+	21.6513i	−2.10219	+	2.33472i
$87$	0.597368	+	3.07632i	0.0640446	+	0.329816i
$88$	−17.9077	−	19.8885i	−1.90897	−	2.12012i
$89$	1.51233	+	4.65447i	0.160306	+	0.493372i	0.998660	−	0.0517547i	$-0.0164814\pi$
$89$	1.51233	+	4.65447i	0.160306	+	0.493372i	−0.838353	+	0.545127i	$0.816481\pi$
$90$	4.09824	−	17.9456i	0.431993	−	1.89164i
$91$	0.974593	−	2.99949i	0.102165	−	0.314432i
$92$	2.47224	−	1.10071i	0.257749	−	0.114757i
$93$	−0.0835387	+	4.73431i	−0.00866256	+	0.490925i
$94$	−1.84048	+	17.5110i	−0.189831	+	1.80613i
$95$	2.48892	−	2.33380i	0.255358	−	0.239443i
$96$	−23.0557	−	32.9402i	−2.35311	−	3.36195i
$97$	0.396958	+	3.77680i	0.0403049	+	0.383476i	0.996016	+	0.0891705i	$0.0284216\pi$
$97$	0.396958	+	3.77680i	0.0403049	+	0.383476i	−0.955711	+	0.294305i	$0.904912\pi$
$98$	2.99465	+	9.21658i	0.302505	+	0.931015i
$99$	−8.28390	−	0.292436i	−0.832564	−	0.0293910i
$100$	−19.3159	−	19.7830i	−1.93159	−	1.97830i
$101$	3.33145	−	5.77025i	0.331492	−	0.574161i	−0.651313	−	0.758810i	$-0.725781\pi$
$101$	3.33145	−	5.77025i	0.331492	−	0.574161i	0.982805	+	0.184648i	$0.0591146\pi$
$102$	21.9715	+	20.4966i	2.17551	+	2.02947i
$103$	−1.40438	−	0.625269i	−0.138377	−	0.0616096i	0.336380	−	0.941726i	$-0.390797\pi$
$103$	−1.40438	−	0.625269i	−0.138377	−	0.0616096i	−0.474757	+	0.880117i	$0.657464\pi$
$104$	−14.9848	−	6.67167i	−1.46938	−	0.654211i
$105$	−5.84621	−	4.22467i	−0.570532	−	0.412285i
$106$	14.9005	−	6.63415i	1.44727	−	0.644366i
$107$	−14.6327			−1.41460			−0.707299	−	0.706914i	$-0.750087\pi$
$107$	−14.6327			−1.41460			−0.707299	+	0.706914i	$0.750087\pi$
$108$	−28.3775	−	4.51115i	−2.73062	−	0.434086i
$109$	0.620591	−	1.90998i	0.0594418	−	0.182943i	−0.916927	−	0.399056i	$-0.869338\pi$
$109$	0.620591	−	1.90998i	0.0594418	−	0.182943i	0.976368	+	0.216113i	$0.0693379\pi$
$110$	−9.68590	+	13.9143i	−0.923514	+	1.32668i
$111$	−1.64447	+	7.11683i	−0.156087	+	0.675499i
$112$	−28.2709	+	6.00918i	−2.67135	+	0.567814i
$113$	13.0613	−	2.77626i	1.22870	−	0.261169i	0.452565	−	0.891732i	$-0.350509\pi$
$113$	13.0613	−	2.77626i	1.22870	−	0.261169i	0.776138	+	0.630563i	$0.217176\pi$
$114$	−5.30298	−	4.94699i	−0.496669	−	0.463328i
$115$	−0.660967	−	0.872125i	−0.0616355	−	0.0813261i
$116$	3.09173	−	9.51536i	0.287060	−	0.883479i
$117$	−4.71118	+	1.90136i	−0.435549	+	0.175780i
$118$	27.8737			2.56598
$119$	10.7560	−	4.78889i	0.986004	−	0.438997i
$120$	−25.0300	+	27.9424i	−2.28492	+	2.55078i
$121$	−3.07473	−	1.36896i	−0.279521	−	0.124451i
$122$	−18.2752	−	8.13665i	−1.65456	−	0.736658i
$123$	−6.29413	+	1.92300i	−0.567523	+	0.173391i
$124$	7.55865	−	13.0920i	0.678787	−	1.17569i
$125$	−6.01157	+	9.42661i	−0.537692	+	0.843142i
$126$	−8.12928	+	12.9986i	−0.724214	+	1.15800i
$127$	1.59486	+	4.90847i	0.141521	+	0.435556i	0.996547	−	0.0830282i	$-0.0264591\pi$
$127$	1.59486	+	4.90847i	0.141521	+	0.435556i	−0.855026	+	0.518585i	$0.826459\pi$
$128$	4.51521	+	42.9594i	0.399092	+	3.79711i
$129$	7.77508	−	16.6654i	0.684558	−	1.46731i
$130$	−1.95458	+	10.2054i	−0.171428	+	0.895074i
$131$	1.24905	−	11.8839i	0.109130	−	1.03830i	−0.793701	−	0.608307i	$-0.791849\pi$
$131$	1.24905	−	11.8839i	0.109130	−	1.03830i	0.902831	−	0.429995i	$-0.141485\pi$
$132$	22.6815	+	13.6343i	1.97417	+	1.18671i
$133$	−2.59604	+	1.15583i	−0.225105	+	0.100223i
$134$	7.41462	−	22.8199i	0.640526	−	1.97134i
$135$	0.835799	+	11.5888i	0.0719342	+	0.997409i
$136$	−18.9228	−	58.2383i	−1.62261	−	4.99389i
$137$	−2.90001	−	3.22078i	−0.247764	−	0.275170i	0.606415	−	0.795148i	$-0.292607\pi$
$137$	−2.90001	−	3.22078i	−0.247764	−	0.275170i	−0.854180	+	0.519978i	$0.825940\pi$
$138$	−1.75571	+	1.52563i	−0.149456	+	0.129870i
$139$	8.91270	−	9.89856i	0.755966	−	0.839585i	−0.235237	−	0.971938i	$-0.575587\pi$
$139$	8.91270	−	9.89856i	0.755966	−	0.839585i	0.991203	+	0.132353i	$0.0422533\pi$
$140$	9.78959	+	20.8438i	0.827372	+	1.76162i
$141$	−2.11855	−	10.9101i	−0.178414	−	0.918796i
$142$	8.49919	−	3.78408i	0.713236	−	0.317553i
$143$	4.67908			0.391284
$144$	36.6771	+	28.6778i	3.05643	+	2.38982i
$145$	−4.03125	−	0.341505i	−0.334777	−	0.0283604i
$146$	4.45555	+	42.3918i	0.368744	+	3.50837i
$147$	−3.50756	−	5.01134i	−0.289299	−	0.413329i
$148$	15.6042	−	17.3303i	1.28266	−	1.42454i
$149$	−1.42735	−	2.47225i	−0.116933	−	0.202535i	0.801618	−	0.597837i	$-0.203973\pi$
$149$	−1.42735	−	2.47225i	−0.116933	−	0.202535i	−0.918551	+	0.395303i	$0.870640\pi$
$150$	20.8456	+	11.4104i	1.70204	+	0.931657i
$151$	5.61232	−	9.72082i	0.456724	−	0.791069i	−0.542062	−	0.840339i	$-0.682356\pi$
$151$	5.61232	−	9.72082i	0.456724	−	0.791069i	0.998786	+	0.0492697i	$0.0156894\pi$
$152$	4.56713	+	14.0562i	0.370443	+	1.14011i
$153$	−17.0435	−	8.32068i	−1.37788	−	0.672688i
$154$	11.4235	−	8.29965i	0.920531	−	0.668805i
$155$	−5.85071	−	1.77114i	−0.469940	−	0.142261i
$156$	16.0986	+	1.97977i	1.28892	+	0.158508i
$157$	−7.23692	−	12.5347i	−0.577569	−	1.00038i	−0.995757	−	0.0920188i	$-0.970668\pi$
$157$	−7.23692	−	12.5347i	−0.577569	−	1.00038i	0.418188	−	0.908360i	$-0.362665\pi$
$158$	−3.68034	+	35.0161i	−0.292792	+	2.78573i
$159$	−7.77127	+	6.75287i	−0.616302	+	0.535537i
$160$	49.0326	−	17.0345i	3.87637	−	1.34669i
$161$	0.281641	+	0.866803i	0.0221964	+	0.0683136i
$162$	24.4587	−	3.41847i	1.92166	−	0.268580i
$163$	2.58162	−	7.94542i	0.202208	−	0.622333i	−0.797608	−	0.603176i	$-0.793902\pi$
$163$	2.58162	−	7.94542i	0.202208	−	0.622333i	0.999816	−	0.0191571i	$-0.00609828\pi$
$164$	20.5527	+	4.36861i	1.60490	+	0.341131i
$165$	3.28073	−	10.1858i	0.255405	−	0.792966i
$166$	−2.36054	+	0.501747i	−0.183213	+	0.0389432i
$167$	−1.18258	+	11.2515i	−0.0915109	+	0.870668i	0.848425	+	0.529316i	$0.177551\pi$
$167$	−1.18258	+	11.2515i	−0.0915109	+	0.870668i	−0.939936	+	0.341352i	$0.889115\pi$
$168$	27.3297	−	15.1423i	2.10853	−	1.16826i
$169$	−9.25621	+	4.12113i	−0.712016	+	0.317010i
$170$	−33.1955	+	20.0705i	−2.54598	+	1.53934i
$171$	4.11355	+	2.00825i	0.314571	+	0.153575i
$172$	−47.4993	+	34.5103i	−3.62179	+	2.63139i
$173$	−6.21968	−	1.32203i	−0.472874	−	0.100512i	−0.0346904	−	0.999398i	$-0.511045\pi$
$173$	−6.21968	−	1.32203i	−0.472874	−	0.100512i	−0.438183	+	0.898886i	$0.644378\pi$
$174$	−0.151713	+	8.59791i	−0.0115014	+	0.651806i
$175$	7.30613	−	5.77326i	0.552291	−	0.436417i
$176$	−21.4400	−	37.1352i	−1.61610	−	2.79917i
$177$	−16.8261	+	5.14076i	−1.26473	+	0.386403i
$178$	1.40375	+	13.3558i	0.105216	+	1.00106i
$179$	5.40088	−	3.92397i	0.403681	−	0.293291i	−0.367358	−	0.930080i	$-0.619738\pi$
$179$	5.40088	−	3.92397i	0.403681	−	0.293291i	0.771039	+	0.636788i	$0.219738\pi$
$180$	15.5973	−	33.6567i	1.16255	−	2.50863i
$181$	5.85623	+	4.25480i	0.435290	+	0.316257i	0.783761	−	0.621063i	$-0.213299\pi$
$181$	5.85623	+	4.25480i	0.435290	+	0.316257i	−0.348470	+	0.937320i	$0.613299\pi$
$182$	4.32716	−	7.49486i	0.320751	−	0.555556i
$183$	12.5326	+	1.54123i	0.926437	+	0.113931i
$184$	4.63659	−	0.985537i	0.341814	−	0.0726547i
$185$	−8.26011	−	4.54896i	−0.607295	−	0.334446i
$186$	−2.92524	+	12.6596i	−0.214489	+	0.928250i
$187$	11.6883	+	12.9812i	0.854735	+	0.949280i
$188$	−10.9647	+	33.7460i	−0.799686	+	2.46118i
$189$	2.50996	−	9.34596i	0.182573	−	0.679818i
$190$	8.01195	−	4.84415i	0.581248	−	0.351431i
$191$	0.759730	+	0.843766i	0.0549721	+	0.0610527i	0.770004	−	0.638039i	$-0.220254\pi$
$191$	0.759730	+	0.843766i	0.0549721	+	0.0610527i	−0.715032	+	0.699092i	$0.753588\pi$
$192$	−22.0939	−	52.0776i	−1.59449	−	3.75837i
$193$	1.53746	+	2.66296i	0.110669	+	0.191684i	0.916040	−	0.401087i	$-0.131367\pi$
$193$	1.53746	+	2.66296i	0.110669	+	0.191684i	−0.805371	+	0.592771i	$0.798034\pi$
$194$	−1.08927	+	10.3637i	−0.0782052	+	0.744073i
$195$	−0.702297	−	6.52105i	−0.0502926	−	0.466982i
$196$	2.04135	+	19.4221i	0.145811	+	1.38729i
$197$	18.8592	−	13.7020i	1.34366	−	0.976227i	0.344360	−	0.938838i	$-0.388096\pi$
$197$	18.8592	−	13.7020i	1.34366	−	0.976227i	0.999301	−	0.0373893i	$-0.0119042\pi$
$198$	−22.0679	−	5.51106i	−1.56830	−	0.391654i
$199$	−18.6167			−1.31970			−0.659851	−	0.751396i	$-0.729381\pi$
$199$	−18.6167			−1.31970			−0.659851	+	0.751396i	$0.729381\pi$
$200$	−25.8898	−	40.9290i	−1.83069	−	2.89412i
$201$	−0.267201	+	15.1428i	−0.0188469	+	1.06809i
$202$	12.2340	−	13.5872i	0.860778	−	0.955991i
$203$	3.07824	+	1.37052i	0.216050	+	0.0961917i
$204$	34.7218	+	49.6079i	2.43101	+	3.47325i
$205$	−0.171679	−	8.49473i	−0.0119905	−	0.593298i
$206$	−3.41274	−	2.47950i	−0.237777	−	0.172755i
$207$	0.778475	−	1.24477i	0.0541077	−	0.0865172i
$208$	−21.2620	−	15.4478i	−1.47426	−	1.07111i
$209$	−2.82106	−	3.13310i	−0.195136	−	0.216721i
$210$	−13.2815	−	14.6748i	−0.916510	−	1.01265i
$211$	−7.70340	+	8.55549i	−0.530324	+	0.588984i	−0.947466	−	0.319857i	$-0.896365\pi$
$211$	−7.70340	+	8.55549i	−0.530324	+	0.588984i	0.417142	+	0.908841i	$0.363032\pi$
$212$	32.1510	−	6.83391i	2.20814	−	0.469355i
$213$	−4.43269	+	3.85180i	−0.303723	+	0.263921i
$214$	−39.2755	−	8.34827i	−2.68482	−	0.570676i
$215$	17.9606	+	15.5263i	1.22490	+	1.05888i
$216$	−46.9768	−	18.0635i	−3.19637	−	1.22906i
$217$	4.11894	+	2.99259i	0.279612	+	0.203150i
$218$	2.75541	−	4.77250i	0.186620	−	0.323235i
$219$	−10.5080	−	24.7683i	−0.710063	−	1.67369i
$220$	−24.9224	+	23.3691i	−1.68027	+	1.57555i
$221$	9.78055	+	4.35458i	0.657911	+	0.292921i
$222$	−8.47421	+	18.1640i	−0.568752	+	1.21909i
$223$	2.00257	+	0.425659i	0.134102	+	0.0285043i	0.274474	−	0.961595i	$-0.411496\pi$
$223$	2.00257	+	0.425659i	0.134102	+	0.0285043i	−0.140372	+	0.990099i	$0.544830\pi$
$224$	−43.2323			−2.88858
$225$	−14.6880	−	3.04340i	−0.979201	−	0.202894i
$226$	36.6416			2.43736
$227$	−14.8654	−	3.15974i	−0.986653	−	0.209720i	−0.313795	−	0.949491i	$-0.601600\pi$
$227$	−14.8654	−	3.15974i	−0.986653	−	0.209720i	−0.672858	+	0.739771i	$0.734934\pi$
$228$	−8.38034	−	11.9732i	−0.555001	−	0.792945i
$229$	−0.192216	−	0.0855802i	−0.0127020	−	0.00565530i	0.400376	−	0.916351i	$-0.368880\pi$
$229$	−0.192216	−	0.0855802i	−0.0127020	−	0.00565530i	−0.413078	+	0.910696i	$0.635546\pi$
$230$	−1.27653	−	2.71796i	−0.0841718	−	0.179217i
$231$	−5.36515	+	7.11698i	−0.353001	+	0.468263i
$232$	8.76239	−	15.1769i	0.575279	−	0.996413i
$233$	−13.5683	−	9.85792i	−0.888887	−	0.645814i	0.0467009	−	0.998909i	$-0.485129\pi$
$233$	−13.5683	−	9.85792i	−0.888887	−	0.645814i	−0.935587	+	0.353095i	$0.885129\pi$
$234$	−13.7300	+	2.41558i	−0.897557	+	0.157911i
$235$	14.2968	+	1.21114i	0.932617	+	0.0790060i
$236$	54.9436	+	11.6786i	3.57653	+	0.760214i
$237$	−4.23639	−	21.8165i	−0.275183	−	1.41713i
$238$	31.6023	−	6.71727i	2.04847	−	0.435416i
$239$	−16.5230	+	18.3506i	−1.06878	+	1.18700i	−0.0871544	+	0.996195i	$0.527777\pi$
$239$	−16.5230	+	18.3506i	−1.06878	+	1.18700i	−0.981627	+	0.190808i	$0.938889\pi$
$240$	−48.5359	+	35.4539i	−3.13298	+	2.28854i
$241$	−2.03608	−	2.26129i	−0.131155	−	0.145663i	0.673990	−	0.738741i	$-0.264579\pi$
$241$	−2.03608	−	2.26129i	−0.131155	−	0.145663i	−0.805145	+	0.593078i	$0.797913\pi$
$242$	−7.47183	−	5.42860i	−0.480307	−	0.348964i
$243$	−14.1342	+	6.57452i	−0.906709	+	0.421756i
$244$	−32.6144	−	23.6957i	−2.08792	−	1.51696i
$245$	7.45955	−	2.59153i	0.476573	−	0.165567i
$246$	−17.9911	+	1.57057i	−1.14707	+	0.100136i
$247$	−2.36060	−	1.05101i	−0.150201	−	0.0668740i
$248$	17.7182	−	19.6780i	1.12511	−	1.24956i
$249$	1.33242	−	0.738238i	0.0844384	−	0.0467840i
$250$	−21.5137	+	21.8721i	−1.36064	+	1.38331i
$251$	−24.9480			−1.57470			−0.787352	−	0.616504i	$-0.788548\pi$
$251$	−24.9480			−1.57470			−0.787352	+	0.616504i	$0.788548\pi$
$252$	−21.4704	+	22.2163i	−1.35251	+	1.39949i
$253$	−1.09393	+	0.794789i	−0.0687750	+	0.0499680i
$254$	1.48036	+	14.0847i	0.0928859	+	0.883751i
$255$	16.3371	−	18.2380i	1.02307	−	1.14211i
$256$	−5.56198	+	52.9187i	−0.347624	+	3.30742i
$257$	−2.15283	−	3.72881i	−0.134290	−	0.232597i	0.791036	−	0.611770i	$-0.209542\pi$
$257$	−2.15283	−	3.72881i	−0.134290	−	0.232597i	−0.925326	+	0.379172i	$0.876209\pi$
$258$	30.3770	−	40.2957i	1.89119	−	2.50870i
$259$	5.25529	+	5.83659i	0.326548	+	0.362668i
$260$	−8.12871	+	19.2976i	−0.504121	+	1.19679i
$261$	−1.49414	−	5.21817i	−0.0924848	−	0.322996i
$262$	10.1326	−	31.1849i	0.625992	−	1.92661i
$263$	−8.56916	−	9.51702i	−0.528397	−	0.586844i	0.418566	−	0.908186i	$-0.362533\pi$
$263$	−8.56916	−	9.51702i	−0.528397	−	0.586844i	−0.946963	+	0.321342i	$0.895866\pi$
$264$	33.8954	+	31.6200i	2.08611	+	1.94608i
$265$	−5.65026	−	12.0304i	−0.347093	−	0.739023i
$266$	−7.62742	+	1.62126i	−0.467667	+	0.0994058i
$267$	−3.31061	−	7.80343i	−0.202606	−	0.477562i
$268$	24.1766	−	41.8751i	1.47682	−	2.55793i
$269$	16.3393	+	11.8712i	0.996227	+	0.723801i	0.961276	−	0.275588i	$-0.0888724\pi$
$269$	16.3393	+	11.8712i	0.996227	+	0.723801i	0.0349513	+	0.999389i	$0.488872\pi$
$270$	−4.36832	+	31.5823i	−0.265847	+	1.92204i
$271$	6.40204	−	4.65136i	0.388897	−	0.282550i	−0.376107	−	0.926576i	$-0.622737\pi$
$271$	6.40204	−	4.65136i	0.388897	−	0.282550i	0.765003	+	0.644027i	$0.222737\pi$
$272$	−10.2556	−	97.5760i	−0.621840	−	5.91641i
$273$	−1.22984	+	5.32238i	−0.0744331	+	0.322125i
$274$	−5.94635	−	10.2994i	−0.359232	−	0.622208i
$275$	11.4956	+	7.66211i	0.693212	+	0.462043i
$276$	−4.10002	+	2.27166i	−0.246792	+	0.136738i
$277$	−0.176092	−	0.0374296i	−0.0105804	−	0.00224892i	0.202618	−	0.979258i	$-0.435055\pi$
$277$	−0.176092	−	0.0374296i	−0.0105804	−	0.00224892i	−0.213199	+	0.977009i	$0.568388\pi$
$278$	29.5698	−	21.4837i	1.77348	−	1.28851i
$279$	−0.568983	−	8.18158i	−0.0340641	−	0.489818i
$280$	9.18186	+	39.2772i	0.548721	+	2.34726i
$281$	−1.48639	+	0.661783i	−0.0886705	+	0.0394786i	−0.450593	−	0.892730i	$-0.648787\pi$
$281$	−1.48639	+	0.661783i	−0.0886705	+	0.0394786i	0.361922	+	0.932208i	$0.382121\pi$
$282$	0.538049	−	30.4923i	0.0320403	−	1.81579i
$283$	0.382272	−	3.63707i	0.0227237	−	0.216201i	−0.977268	−	0.212010i	$-0.931999\pi$
$283$	0.382272	−	3.63707i	0.0227237	−	0.216201i	0.999991	−	0.00419159i	$-0.00133423\pi$
$284$	18.3388	−	3.89803i	1.08821	−	0.231305i
$285$	−3.94306	+	4.40185i	−0.233567	+	0.260743i
$286$	12.5591	+	2.66951i	0.742633	+	0.157851i
$287$	−2.18676	+	6.73015i	−0.129080	+	0.397268i
$288$	44.7441	+	53.3651i	2.63657	+	3.14457i
$289$	7.09756	+	21.8440i	0.417503	+	1.28494i
$290$	−10.6254	−	3.21654i	−0.623945	−	0.188882i
$291$	−1.25384	−	6.45703i	−0.0735017	−	0.378518i
$292$	−8.97884	+	85.4280i	−0.525447	+	4.99929i
$293$	12.2406	+	21.2013i	0.715101	+	1.23859i	0.962921	+	0.269785i	$0.0869525\pi$
$293$	12.2406	+	21.2013i	0.715101	+	1.23859i	−0.247820	+	0.968806i	$0.579714\pi$
$294$	−6.55553	−	15.4520i	−0.382326	−	0.901180i
$295$	−0.458949	−	22.7090i	−0.0267210	−	1.32217i
$296$	33.0463	−	24.0096i	1.92078	−	1.39553i
$297$	14.3378	−	0.743208i	0.831965	−	0.0431253i
$298$	−2.42067	−	7.45007i	−0.140226	−	0.431571i
$299$	−0.414377	+	0.717721i	−0.0239640	+	0.0415069i
$300$	36.3093	+	31.2258i	2.09632	+	1.80282i
$301$	−9.88675	−	17.1244i	−0.569863	−	0.987032i
$302$	20.6099	−	22.8896i	1.18597	−	1.31715i
$303$	−4.87921	+	10.4583i	−0.280304	+	0.600814i
$304$	2.47527	+	23.5506i	0.141966	+	1.35072i
$305$	−6.32812	+	15.0230i	−0.362347	+	0.860215i
$306$	−40.9990	−	32.0571i	−2.34376	−	1.83258i
$307$	3.80945			0.217417			0.108708	−	0.994074i	$-0.465329\pi$
$307$	3.80945			0.217417			0.108708	+	0.994074i	$0.465329\pi$
$308$	25.9950	−	11.5737i	1.48120	−	0.659474i
$309$	2.51742	+	0.867354i	0.143211	+	0.0493420i
$310$	−14.6934	−	8.09184i	−0.834526	−	0.459586i
$311$	−16.8714	+	18.7375i	−0.956687	+	1.06251i	0.0413039	+	0.999147i	$0.486849\pi$
$311$	−16.8714	+	18.7375i	−0.956687	+	1.06251i	−0.997991	+	0.0633616i	$0.979818\pi$
$312$	26.8611	+	9.25472i	1.52071	+	0.523945i
$313$	17.3585	+	19.2786i	0.981161	+	1.08969i	0.995960	+	0.0897989i	$0.0286224\pi$
$313$	17.3585	+	19.2786i	0.981161	+	1.08969i	−0.0147991	+	0.999890i	$0.504711\pi$
$314$	−12.2732	−	37.7731i	−0.692618	−	2.13166i
$315$	10.7239	+	6.40900i	0.604225	+	0.361106i
$316$	−21.9258	+	67.4806i	−1.23342	+	3.79608i
$317$	−20.9744	+	9.33841i	−1.17804	+	0.524497i	−0.899923	−	0.436050i	$-0.856377\pi$
$317$	−20.9744	+	9.33841i	−1.17804	+	0.524497i	−0.278118	+	0.960547i	$0.589711\pi$
$318$	−24.7114	+	13.6916i	−1.38575	+	0.767788i
$319$	−0.522549	+	4.97172i	−0.0292571	+	0.278363i
$320$	72.4630	−	9.09997i	4.05080	−	0.508704i
$321$	25.2486	−	2.20413i	1.40924	−	0.123022i
$322$	0.261421	+	2.48726i	0.0145684	+	0.138609i
$323$	−2.98096	−	9.17445i	−0.165865	−	0.510480i
$324$	49.6445	+	3.50945i	2.75803	+	0.194969i
$325$	8.34666	+	1.42438i	0.462989	+	0.0790106i
$326$	11.4623	−	19.8533i	0.634839	−	1.09957i
$327$	−0.783122	+	3.38913i	−0.0433068	+	0.187420i
$328$	33.6224	+	14.9697i	1.85649	+	0.826561i
$329$	−10.9169	−	4.86053i	−0.601869	−	0.267969i
$330$	14.6170	−	25.4679i	0.804639	−	1.40196i
$331$	5.62038	−	2.50235i	0.308924	−	0.137542i	−0.246419	−	0.969163i	$-0.579254\pi$
$331$	5.62038	−	2.50235i	0.308924	−	0.137542i	0.555343	+	0.831622i	$0.312587\pi$
$332$	−4.86323			−0.266904
$333$	1.76552	−	12.5277i	0.0967497	−	0.686514i
$334$	−9.59337	+	29.5254i	−0.524926	+	1.61556i
$335$	−18.7137	−	5.66504i	−1.02244	−	0.309514i
$336$	47.8760	−	14.6272i	2.61185	−	0.797980i
$337$	14.7319	−	3.13136i	0.802498	−	0.170576i	0.211636	−	0.977349i	$-0.432121\pi$
$337$	14.7319	−	3.13136i	0.802498	−	0.170576i	0.590862	+	0.806772i	$0.298788\pi$
$338$	−27.1957	+	5.78061i	−1.47925	+	0.314424i
$339$	−22.1189	+	6.75783i	−1.20133	+	0.367035i
$340$	−73.8430	+	25.6539i	−4.00470	+	1.39128i
$341$	−2.33416	+	7.18380i	−0.126402	+	0.389024i
$342$	9.89539	+	7.73719i	0.535082	+	0.418380i
$343$	−19.6137			−1.05904
$344$	−93.9494	+	41.8290i	−5.06541	+	2.25527i
$345$	1.27186	+	1.40528i	0.0684746	+	0.0756578i
$346$	−15.9399	−	7.09691i	−0.856935	−	0.381532i
$347$	−15.3731	−	6.84453i	−0.825269	−	0.367434i	−0.0497533	−	0.998762i	$-0.515844\pi$
$347$	−15.3731	−	6.84453i	−0.825269	−	0.367434i	−0.775516	+	0.631328i	$0.782510\pi$
$348$	−3.90144	+	16.8843i	−0.209139	+	0.905096i
$349$	−7.75462	+	13.4314i	−0.415096	+	0.718967i	−0.995438	−	0.0954057i	$-0.969585\pi$
$349$	−7.75462	+	13.4314i	−0.415096	+	0.718967i	0.580343	+	0.814372i	$0.302919\pi$
$350$	22.9041	−	11.3276i	1.22427	−	0.605488i
$351$	7.84269	−	3.99041i	0.418612	−	0.212993i
$352$	−19.8203	−	61.0006i	−1.05643	−	3.25134i
$353$	−0.982184	−	9.34486i	−0.0522764	−	0.497377i	−0.989065	−	0.147481i	$-0.952884\pi$
$353$	−0.982184	−	9.34486i	−0.0522764	−	0.497377i	0.936789	−	0.349896i	$-0.113783\pi$
$354$	−48.0957	+	4.19861i	−2.55626	+	0.223154i
$355$	−3.22288	−	6.86209i	−0.171053	−	0.364202i
$356$	−2.82885	+	26.9147i	−0.149928	+	1.42647i
$357$	−17.8381	+	9.88336i	−0.944090	+	0.523083i
$358$	16.7351	−	7.45097i	0.884480	−	0.393796i
$359$	−2.47394	+	7.61399i	−0.130569	+	0.401851i	−0.994875	−	0.101116i	$-0.967759\pi$
$359$	−2.47394	+	7.61399i	−0.130569	+	0.401851i	0.864305	+	0.502968i	$0.167759\pi$
$360$	38.9801	−	51.9846i	2.05443	−	2.73983i
$361$	−5.15185	−	15.8558i	−0.271150	−	0.834514i
$362$	13.2912	+	14.7614i	0.698569	+	0.775840i
$363$	5.51162	+	1.89898i	0.289285	+	0.0996704i
$364$	11.6698	−	12.9606i	0.611663	−	0.679320i
$365$	34.4637	−	4.32799i	1.80391	−	0.226537i
$366$	32.7593	+	11.2869i	1.71236	+	0.589976i
$367$	24.1256	−	10.7414i	1.25935	−	0.560698i	0.334990	−	0.942222i	$-0.391267\pi$
$367$	24.1256	−	10.7414i	1.25935	−	0.560698i	0.924359	+	0.381524i	$0.124601\pi$
$368$	7.59487			0.395910
$369$	10.5708	−	4.26620i	0.550293	−	0.222089i
$370$	−19.5756	−	16.9224i	−1.01769	−	0.879752i
$371$	1.15712	+	11.0093i	0.0600747	+	0.571573i
$372$	−11.0703	+	23.7286i	−0.573970	+	1.23027i
$373$	−13.8997	+	15.4372i	−0.719700	+	0.799308i	−0.986381	−	0.164477i	$-0.947406\pi$
$373$	−13.8997	+	15.4372i	−0.719700	+	0.799308i	0.266681	+	0.963785i	$0.414073\pi$
$374$	23.9665	+	41.5111i	1.23928	+	2.14649i
$375$	8.95297	−	17.1710i	0.462330	−	0.886708i
$376$	−31.0756	+	53.8246i	−1.60260	+	2.77579i
$377$	0.946817	+	2.91400i	0.0487636	+	0.150079i
$378$	12.0690	−	23.6534i	0.620763	−	1.21660i
$379$	15.5059	−	11.2657i	0.796485	−	0.578680i	−0.113396	−	0.993550i	$-0.536173\pi$
$379$	15.5059	−	11.2657i	0.796485	−	0.578680i	0.909881	+	0.414870i	$0.136173\pi$
$380$	17.8225	−	6.19174i	0.914276	−	0.317629i
$381$	−3.49127	−	8.22928i	−0.178863	−	0.421599i
$382$	1.55780	+	2.69818i	0.0797038	+	0.138051i
$383$	2.52616	−	24.0348i	0.129081	−	1.22812i	−0.717765	−	0.696285i	$-0.754835\pi$
$383$	2.52616	−	24.0348i	0.129081	−	1.22812i	0.846846	−	0.531838i	$-0.178498\pi$
$384$	−14.2619	−	73.4458i	−0.727800	−	3.74802i
$385$	−6.94992	−	9.17020i	−0.354201	−	0.467357i
$386$	2.60740	+	8.02476i	0.132713	+	0.408449i
$387$	−10.9055	+	29.9272i	−0.554358	+	1.52128i
$388$	−6.48938	+	19.9722i	−0.329448	+	1.01394i
$389$	36.8855	+	7.84025i	1.87017	+	0.397517i	0.996096	−	0.0882786i	$-0.0281366\pi$
$389$	36.8855	+	7.84025i	1.87017	+	0.397517i	0.874073	+	0.485795i	$0.161470\pi$
$390$	1.83537	−	17.9037i	0.0929373	−	0.906591i
$391$	−3.02629	+	0.643258i	−0.153046	+	0.0325310i
$392$	−3.57561	+	34.0197i	−0.180596	+	1.71825i
$393$	−0.365148	+	20.6937i	−0.0184193	+	1.04386i
$394$	58.4370	−	26.0178i	2.94401	−	1.31076i
$395$	28.5887	+	2.42187i	1.43845	+	0.121857i
$396$	−41.1904	−	20.1093i	−2.06990	−	1.01053i
$397$	22.7545	−	16.5321i	1.14202	−	0.829724i	0.154618	−	0.987974i	$-0.450585\pi$
$397$	22.7545	−	16.5321i	1.14202	−	0.829724i	0.987399	+	0.158251i	$0.0505855\pi$
$398$	−49.9688	−	10.6212i	−2.50471	−	0.532393i
$399$	4.30533	−	2.38542i	0.215536	−	0.119420i
$400$	−26.9407	−	72.7694i	−1.34704	−	3.63847i
$401$	−11.7822	−	20.4073i	−0.588373	−	1.01909i	−0.994446	−	0.105251i	$-0.966435\pi$
$401$	−11.7822	−	20.4073i	−0.588373	−	1.01909i	0.406073	−	0.913841i	$-0.366898\pi$
$402$	−9.35649	+	40.4923i	−0.466659	+	2.01957i
$403$	0.483921	+	4.60420i	0.0241058	+	0.229351i
$404$	29.8080	−	21.6568i	1.48300	−	1.07746i
$405$	−3.18779	−	19.8705i	−0.158403	−	0.987375i
$406$	7.48036	+	5.43480i	0.371244	+	0.269725i
$407$	−5.82606	+	10.0910i	−0.288787	+	0.500194i
$408$	41.4234	+	97.6391i	2.05077	+	4.83386i
$409$	−10.2783	+	2.18473i	−0.508231	+	0.108028i	−0.454888	−	0.890548i	$-0.650321\pi$
$409$	−10.2783	+	2.18473i	−0.508231	+	0.108028i	−0.0533426	+	0.998576i	$0.516988\pi$
$410$	4.38562	−	22.8986i	0.216590	−	1.13088i
$411$	5.48908	+	5.12060i	0.270756	+	0.252581i
$412$	−5.68821	−	6.31740i	−0.280238	−	0.311236i
$413$	−5.84587	+	17.9917i	−0.287656	+	0.885315i
$414$	2.79966	−	2.89692i	0.137596	−	0.142376i
$415$	0.447647	+	1.91490i	0.0219741	+	0.0939985i
$416$	−26.3045	−	29.2141i	−1.28969	−	1.43234i
$417$	−13.8877	+	18.4224i	−0.680086	+	0.902147i
$418$	−5.78446	−	10.0190i	−0.282927	−	0.490045i
$419$	−0.989526	+	9.41471i	−0.0483415	+	0.459939i	0.943397	+	0.331665i	$0.107610\pi$
$419$	−0.989526	+	9.41471i	−0.0483415	+	0.459939i	−0.991739	+	0.128274i	$0.959056\pi$
$420$	−20.0315	−	34.4911i	−0.977439	−	1.68299i
$421$	0.707686	+	6.73319i	0.0344905	+	0.328155i	0.998139	+	0.0609816i	$0.0194231\pi$
$421$	0.707686	+	6.73319i	0.0344905	+	0.328155i	−0.963648	+	0.267174i	$0.913910\pi$
$422$	−25.5577	+	18.5687i	−1.24413	+	0.903912i
$423$	5.29893	+	18.5061i	0.257643	+	0.899799i
$424$	57.5737			2.79603
$425$	16.8982	+	26.7143i	0.819685	+	1.29583i
$426$	−14.0953	+	7.80963i	−0.682918	+	0.378378i
$427$	9.08481	−	10.0897i	0.439645	−	0.488275i
$428$	−73.9207	−	32.9116i	−3.57309	−	1.59084i
$429$	−8.07370	+	0.704809i	−0.389802	+	0.0340285i
$430$	39.3497	+	51.9208i	1.89761	+	2.50384i
$431$	−20.0354	−	14.5565i	−0.965069	−	0.701164i	−0.0107465	−	0.999942i	$-0.503421\pi$
$431$	−20.0354	−	14.5565i	−0.965069	−	0.701164i	−0.954322	+	0.298779i	$0.903421\pi$
$432$	−67.6057	−	43.9586i	−3.25268	−	2.11496i
$433$	5.18591	+	3.76779i	0.249219	+	0.181068i	0.705381	−	0.708829i	$-0.250776\pi$
$433$	5.18591	+	3.76779i	0.249219	+	0.181068i	−0.456162	+	0.889897i	$0.650776\pi$
$434$	9.34827	+	10.3823i	0.448731	+	0.498367i
$435$	7.00732	−	0.0179646i	0.335975	−	0.000861339i
$436$	7.43096	−	8.25292i	0.355879	−	0.395243i
$437$	0.730416	−	0.155255i	0.0349405	−	0.00742684i
$438$	−14.0735	−	72.4754i	−0.672457	−	3.46301i
$439$	0.251052	+	0.0533628i	0.0119821	+	0.00254687i	0.213899	−	0.976856i	$-0.431384\pi$
$439$	0.251052	+	0.0533628i	0.0119821	+	0.00254687i	−0.201917	+	0.979403i	$0.564717\pi$
$440$	−51.2105	+	30.9626i	−2.44136	+	1.47609i
$441$	6.80711	+	8.11867i	0.324148	+	0.386604i
$442$	23.7675	+	17.2681i	1.13050	+	0.821359i
$443$	7.32776	−	12.6920i	0.348152	−	0.603017i	−0.637769	−	0.770228i	$-0.720143\pi$
$443$	7.32776	−	12.6920i	0.348152	−	0.603017i	0.985921	+	0.167210i	$0.0534759\pi$
$444$	−24.3145	+	32.2536i	−1.15391	+	1.53069i
$445$	10.8580	−	1.36356i	0.514720	−	0.0646390i
$446$	5.13223	+	2.28501i	0.243018	+	0.108199i
$447$	2.83528	+	4.05084i	0.134104	+	0.191598i
$448$	−59.4974	−	12.6466i	−2.81099	−	0.597494i
$449$	15.5412			0.733436			0.366718	−	0.930332i	$-0.380481\pi$
$449$	15.5412			0.733436			0.366718	+	0.930332i	$0.380481\pi$
$450$	−37.6876	−	16.5486i	−1.77661	−	0.780107i
$451$	−10.4988			−0.494367
$452$	72.2266	+	15.3522i	3.39725	+	0.722108i
$453$	−8.21974	+	17.6185i	−0.386197	+	0.827791i
$454$	−38.0974	−	16.9621i	−1.78800	−	0.796069i
$455$	−6.17740	−	3.40198i	−0.289601	−	0.159487i
$456$	−9.99782	−	23.5659i	−0.468191	−	1.10357i
$457$	7.26861	−	12.5896i	0.340011	−	0.588916i	−0.644423	−	0.764669i	$-0.722903\pi$
$457$	7.26861	−	12.5896i	0.340011	−	0.588916i	0.984434	+	0.175752i	$0.0562358\pi$
$458$	−0.467100	−	0.339368i	−0.0218262	−	0.0158576i
$459$	30.6617	+	11.7900i	1.43116	+	0.550310i
$460$	−1.37747	−	5.89239i	−0.0642248	−	0.274734i
$461$	−3.21841	−	0.684094i	−0.149896	−	0.0318614i	0.132352	−	0.991203i	$-0.457747\pi$
$461$	−3.21841	−	0.684094i	−0.149896	−	0.0318614i	−0.282249	+	0.959341i	$0.591080\pi$
$462$	−18.4609	+	16.0417i	−0.858880	+	0.746326i
$463$	37.4109	−	7.95194i	1.73863	−	0.369558i	0.774007	−	0.633177i	$-0.218249\pi$
$463$	37.4109	−	7.95194i	1.73863	−	0.369558i	0.964627	+	0.263619i	$0.0849161\pi$
$464$	18.7884	−	20.8666i	0.872230	−	0.968709i
$465$	10.3621	+	2.17479i	0.480532	+	0.100853i
$466$	−30.7943	−	34.2005i	−1.42652	−	1.58431i
$467$	4.63677	+	3.36881i	0.214564	+	0.155890i	0.689876	−	0.723927i	$-0.257665\pi$
$467$	4.63677	+	3.36881i	0.214564	+	0.155890i	−0.475312	+	0.879817i	$0.657665\pi$
$468$	−28.0762	−	0.991138i	−1.29782	−	0.0458154i
$469$	13.1746	+	9.57189i	0.608345	+	0.441989i
$470$	37.6828	+	11.4074i	1.73818	+	0.526184i
$471$	14.3753	+	20.5384i	0.662380	+	0.946360i
$472$	89.8829	+	40.0184i	4.13720	+	1.84200i
$473$	19.6297	−	21.8010i	0.902576	−	1.00241i
$474$	1.07591	−	60.9743i	0.0494184	−	2.80064i
$475$	−4.07850	−	6.44767i	−0.187135	−	0.295840i
$476$	65.1078			2.98421
$477$	12.3921	−	12.8226i	0.567393	−	0.587105i
$478$	−54.8185	+	39.8280i	−2.50734	+	1.82169i
$479$	1.40830	+	13.3991i	0.0643469	+	0.612220i	0.978414	+	0.206656i	$0.0662581\pi$
$479$	1.40830	+	13.3991i	0.0643469	+	0.612220i	−0.914067	+	0.405564i	$0.867075\pi$
$480$	−82.0393	+	36.7786i	−3.74457	+	1.67870i
$481$	−0.746503	+	7.10250i	−0.0340376	+	0.323846i
$482$	−4.17490	−	7.23113i	−0.190161	−	0.329369i
$483$	−0.616535	−	1.45323i	−0.0280533	−	0.0661244i
$484$	−12.4537	−	13.8312i	−0.566078	−	0.628693i
$485$	8.46139	+	0.716801i	0.384212	+	0.0325483i
$486$	−41.6883	+	9.58275i	−1.89102	+	0.434682i
$487$	−8.88128	+	27.3338i	−0.402449	+	1.23861i	0.520557	+	0.853827i	$0.325724\pi$
$487$	−8.88128	+	27.3338i	−0.402449	+	1.23861i	−0.923006	+	0.384785i	$0.874276\pi$
$488$	−47.2494	−	52.4757i	−2.13888	−	2.37547i
$489$	−3.25774	+	14.0986i	−0.147320	+	0.637560i
$490$	21.5006	−	2.70007i	0.971299	−	0.121977i
$491$	−15.6203	+	3.32021i	−0.704936	+	0.149839i	−0.546412	−	0.837516i	$-0.684007\pi$
$491$	−15.6203	+	3.32021i	−0.704936	+	0.149839i	−0.158524	+	0.987355i	$0.550673\pi$
$492$	−36.1215	−	4.44214i	−1.62848	−	0.200267i
$493$	−5.71920	+	9.90594i	−0.257580	+	0.446141i
$494$	−5.73644	−	4.16777i	−0.258095	−	0.187517i
$495$	−4.12657	+	18.0697i	−0.185476	+	0.812173i
$496$	34.3236	−	24.9375i	1.54117	−	1.11973i
$497$	0.660016	+	6.27963i	0.0296058	+	0.281680i
$498$	3.99750	−	1.22133i	0.179132	−	0.0547290i
$499$	10.4973	+	18.1818i	0.469922	+	0.813929i	0.999409	−	0.0343894i	$-0.0109486\pi$
$499$	10.4973	+	18.1818i	0.469922	+	0.813929i	−0.529486	+	0.848318i	$0.677615\pi$
$500$	−51.5711	+	34.0997i	−2.30633	+	1.52498i
$501$	0.345717	−	19.5925i	0.0154455	−	0.875328i
$502$	−66.9626	−	14.2333i	−2.98869	−	0.635265i
$503$	3.48380	−	2.53113i	0.155335	−	0.112857i	−0.507403	−	0.861709i	$-0.669394\pi$
$503$	3.48380	−	2.53113i	0.155335	−	0.112857i	0.662738	+	0.748852i	$0.269394\pi$
$504$	−44.8762	+	30.2446i	−1.99895	+	1.34720i
$505$	−11.2711	−	9.74344i	−0.501557	−	0.433577i
$506$	−3.38966	+	1.50917i	−0.150689	+	0.0670909i
$507$	15.3507	−	8.50522i	0.681749	−	0.377730i
$508$	−2.98322	+	28.3835i	−0.132359	+	1.25931i
$509$	−41.2503	+	8.76803i	−1.82839	+	0.388636i	−0.988139	−	0.153562i	$-0.950925\pi$
$509$	−41.2503	+	8.76803i	−1.82839	+	0.388636i	−0.840251	+	0.542198i	$0.817592\pi$
$510$	54.2552	−	39.6316i	2.40246	−	1.75492i
$511$	−28.2972	−	6.01476i	−1.25180	−	0.266077i
$512$	−18.4234	+	56.7015i	−0.814209	+	2.50588i
$513$	−7.40039	−	2.84559i	−0.326735	−	0.125636i
$514$	−3.65103	−	11.2367i	−0.161040	−	0.495630i
$515$	−1.96389	+	2.82123i	−0.0865393	+	0.124318i
$516$	76.7613	−	66.7019i	3.37923	−	2.93639i
$517$	1.85321	−	17.6321i	0.0815040	−	0.775459i
$518$	10.7758	+	18.6642i	0.473460	+	0.820056i
$519$	10.9311	+	1.34428i	0.479823	+	0.0590075i
$520$	−20.9548	+	30.1027i	−0.918930	+	1.32009i
$521$	−25.2789	+	18.3662i	−1.10749	+	0.804637i	−0.982266	−	0.187491i	$-0.939964\pi$
$521$	−25.2789	+	18.3662i	−1.10749	+	0.804637i	−0.125222	+	0.992129i	$0.539964\pi$
$522$	−1.03332	−	14.8585i	−0.0452273	−	0.650337i
$523$	−11.4494	−	35.2378i	−0.500649	−	1.54084i	−0.807964	−	0.589232i	$-0.799430\pi$
$523$	−11.4494	−	35.2378i	−0.500649	−	1.54084i	0.307314	−	0.951608i	$-0.400570\pi$
$524$	33.0389	−	57.2251i	1.44331	−	2.49989i
$525$	−11.7370	+	11.0622i	−0.512245	+	0.482795i
$526$	−17.5707	−	30.4334i	−0.766120	−	1.32696i
$527$	−11.5646	+	12.8438i	−0.503763	+	0.559486i
$528$	42.5882	+	60.8469i	1.85341	+	2.64802i
$529$	2.37912	+	22.6358i	0.103440	+	0.984166i
$530$	−8.30220	−	35.5143i	−0.360625	−	1.54264i
$531$	28.2589	−	11.4048i	1.22633	−	0.494928i
$532$	−15.7142			−0.681297
$533$	−5.87841	+	2.61724i	−0.254622	+	0.113365i
$534$	−4.43394	−	22.8338i	−0.191875	−	0.988117i
$535$	−6.15475	+	32.1357i	−0.266093	+	1.38935i
$536$	56.6722	−	62.9408i	2.44787	−	2.71863i
$537$	−8.72809	+	7.58430i	−0.376645	+	0.327287i
$538$	37.0834	+	41.1853i	1.59878	+	1.77563i
$539$	−3.01535	−	9.28030i	−0.129880	−	0.399731i
$540$	−21.8432	+	60.4237i	−0.939980	+	2.60022i
$541$	−10.3961	+	31.9960i	−0.446965	+	1.37562i	0.433350	+	0.901226i	$0.357332\pi$
$541$	−10.3961	+	31.9960i	−0.446965	+	1.37562i	−0.880314	+	0.474391i	$0.842668\pi$
$542$	19.8373	−	8.83215i	0.852087	−	0.379374i
$543$	−10.7458	−	6.45949i	−0.461145	−	0.277203i
$544$	15.3404	−	145.954i	0.657712	−	6.25771i
$545$	−3.93358	−	2.16628i	−0.168496	−	0.0927933i
$546$	−6.33752	+	13.5841i	−0.271221	+	0.581346i
$547$	−0.581655	−	5.53408i	−0.0248698	−	0.236620i	−0.999895	−	0.0145239i	$-0.995377\pi$
$547$	−0.581655	−	5.53408i	−0.0248698	−	0.236620i	0.975025	−	0.222096i	$-0.0712899\pi$
$548$	−7.40596	−	22.7932i	−0.316367	−	0.973678i
$549$	−21.8570	−	0.771591i	−0.932835	−	0.0329307i
$550$	26.4839	+	27.1243i	1.12928	+	1.15658i
$551$	1.38037	−	2.39086i	0.0588056	−	0.101854i
$552$	−7.85193	+	2.39894i	−0.334200	+	0.102106i
$553$	−21.8301	−	9.71940i	−0.928312	−	0.413311i
$554$	−0.451293	−	0.200928i	−0.0191736	−	0.00853663i
$555$	14.9379	+	6.60496i	0.634080	+	0.280365i
$556$	67.2883	−	29.9587i	2.85366	−	1.27053i
$557$	37.0966			1.57183			0.785917	−	0.618332i	$-0.212191\pi$
$557$	37.0966			1.57183			0.785917	+	0.618332i	$0.212191\pi$
$558$	3.14056	−	22.2847i	0.132950	−	0.943386i
$559$	5.55619	−	17.1002i	0.235002	−	0.723262i
$560$	1.30587	+	64.6148i	0.0551829	+	2.73048i
$561$	−22.1234	−	20.6383i	−0.934052	−	0.871350i
$562$	−4.36716	+	0.928268i	−0.184217	+	0.0391566i
$563$	20.9186	−	4.44638i	0.881612	−	0.187392i	0.255203	−	0.966887i	$-0.417858\pi$
$563$	20.9186	−	4.44638i	0.881612	−	0.187392i	0.626408	+	0.779495i	$0.284524\pi$
$564$	13.8364	−	59.8800i	0.582617	−	2.52140i
$565$	−0.603315	−	29.8523i	−0.0253817	−	1.25590i
$566$	3.10107	−	9.54412i	0.130348	−	0.401169i
$567$	−2.92313	+	16.5044i	−0.122760	+	0.693120i
$568$	32.8398			1.37793
$569$	−13.8567	+	6.16939i	−0.580902	+	0.258634i	−0.676083	−	0.736826i	$-0.736324\pi$
$569$	−13.8567	+	6.16939i	−0.580902	+	0.258634i	0.0951807	+	0.995460i	$0.469657\pi$
$570$	−13.0949	+	9.56536i	−0.548483	+	0.400649i
$571$	34.7764	+	15.4834i	1.45535	+	0.647962i	0.973582	−	0.228339i	$-0.0733296\pi$
$571$	34.7764	+	15.4834i	1.45535	+	0.647962i	0.481764	+	0.876301i	$0.339996\pi$
$572$	23.6375	+	10.5241i	0.988333	+	0.440034i
$573$	−1.43800	−	1.34147i	−0.0600734	−	0.0560407i
$574$	−9.70913	+	16.8167i	−0.405251	+	0.701916i
$575$	−2.19333	+	1.08475i	−0.0914683	+	0.0452374i
$576$	45.9672	+	86.5312i	1.91530	+	3.60547i
$577$	2.27456	+	7.00039i	0.0946913	+	0.291430i	0.987173	−	0.159653i	$-0.0510377\pi$
$577$	2.27456	+	7.00039i	0.0946913	+	0.291430i	−0.892482	+	0.451083i	$0.851038\pi$
$578$	6.58800	+	62.6806i	0.274025	+	2.60717i
$579$	−3.05399	−	4.36331i	−0.126919	−	0.181333i
$580$	−19.5967	−	10.7922i	−0.813710	−	0.448122i
$581$	0.171204	−	1.62889i	0.00710273	−	0.0675779i
$582$	0.318439	−	18.0466i	0.0131997	−	0.748055i
$583$	−15.0036	+	6.68001i	−0.621384	+	0.276658i
$584$	−46.4946	+	143.096i	−1.92396	+	5.92133i
$585$	2.19407	+	11.1462i	0.0907137	+	0.460839i
$586$	20.7590	+	63.8895i	0.857545	+	2.63925i
$587$	−16.6264	−	18.4655i	−0.686247	−	0.762154i	0.294877	−	0.955535i	$-0.404721\pi$
$587$	−16.6264	−	18.4655i	−0.686247	−	0.762154i	−0.981124	+	0.193381i	$0.938055\pi$
$588$	−6.44787	−	33.2052i	−0.265906	−	1.36936i
$589$	2.79120	−	3.09994i	0.115009	−	0.127731i
$590$	11.7241	−	61.2148i	0.482673	−	2.52017i
$591$	−30.4774	+	26.4834i	−1.25367	+	1.08938i
$592$	59.7891	−	26.6198i	2.45732	−	1.09407i
$593$	43.3690			1.78095			0.890476	−	0.455030i	$-0.150371\pi$
$593$	43.3690			1.78095			0.890476	+	0.455030i	$0.150371\pi$
$594$	38.9080	+	6.18519i	1.59642	+	0.253781i
$595$	−5.99299	−	25.6362i	−0.245688	−	1.05098i
$596$	−1.65009	−	15.6995i	−0.0675903	−	0.643079i
$597$	32.1229	−	2.80423i	1.31470	−	0.114770i
$598$	−1.52170	+	1.69002i	−0.0622268	+	0.0691099i
$599$	−5.35663	−	9.27796i	−0.218866	−	0.379087i	0.735596	−	0.677421i	$-0.236902\pi$
$599$	−5.35663	−	9.27796i	−0.218866	−	0.379087i	−0.954462	+	0.298334i	$0.903569\pi$
$600$	50.8378	+	66.7228i	2.07544	+	2.72395i
$601$	8.90717	−	15.4277i	0.363331	−	0.629308i	−0.625176	−	0.780484i	$-0.714973\pi$
$601$	8.90717	−	15.4277i	0.363331	−	0.629308i	0.988507	+	0.151176i	$0.0483060\pi$
$602$	−16.7671	−	51.6039i	−0.683377	−	2.10322i
$603$	−1.81991	−	26.1690i	−0.0741125	−	1.06569i
$604$	50.2159	−	36.4840i	2.04325	−	1.48451i
$605$	−4.29972	+	6.17677i	−0.174808	+	0.251121i
$606$	−19.0629	+	25.2873i	−0.774378	+	1.02723i
$607$	21.1667	+	36.6618i	0.859129	+	1.48805i	0.872761	+	0.488148i	$0.162327\pi$
$607$	21.1667	+	36.6618i	0.859129	+	1.48805i	−0.0136324	+	0.999907i	$0.504339\pi$
$608$	−3.70250	+	35.2269i	−0.150156	+	1.42864i
$609$	−5.51791	−	1.90114i	−0.223597	−	0.0770382i
$610$	−25.5562	+	36.7128i	−1.03474	+	1.48646i
$611$	−3.35787	−	10.3345i	−0.135845	−	0.418087i
$612$	−67.3845	−	80.3678i	−2.72386	−	3.24868i
$613$	13.3402	−	41.0570i	0.538806	−	1.65828i	−0.196471	−	0.980510i	$-0.562948\pi$
$613$	13.3402	−	41.0570i	0.538806	−	1.65828i	0.735278	−	0.677766i	$-0.237052\pi$
$614$	10.2249	+	2.17337i	0.412643	+	0.0877100i
$615$	1.57579	+	14.6317i	0.0635420	+	0.590007i
$616$	48.7527	−	10.3627i	1.96430	−	0.417525i
$617$	3.95649	−	37.6435i	0.159282	−	1.51547i	−0.564496	−	0.825436i	$-0.690929\pi$
$617$	3.95649	−	37.6435i	0.159282	−	1.51547i	0.723778	−	0.690033i	$-0.242404\pi$
$618$	6.26214	+	3.76429i	0.251900	+	0.151422i
$619$	−14.5465	+	6.47652i	−0.584674	+	0.260313i	−0.677686	−	0.735351i	$-0.737017\pi$
$619$	−14.5465	+	6.47652i	−0.584674	+	0.260313i	0.0930123	+	0.995665i	$0.470350\pi$
$620$	−25.5727	−	22.1066i	−1.02702	−	0.887824i
$621$	−1.15575	+	2.26509i	−0.0463787	+	0.0908949i
$622$	−55.9743	+	40.6677i	−2.24437	+	1.63063i
$623$	−8.91523	−	1.89499i	−0.357181	−	0.0759212i
$624$	39.0143	+	23.4523i	1.56182	+	0.938842i
$625$	18.1737	+	17.1673i	0.726948	+	0.686692i
$626$	35.5929	+	61.6488i	1.42258	+	2.46398i
$627$	5.33964	+	4.98119i	0.213245	+	0.198930i
$628$	−8.36622	−	79.5993i	−0.333849	−	3.17636i
$629$	−21.5693	+	15.6710i	−0.860024	+	0.624844i
$630$	25.1275	+	23.3205i	1.00110	+	0.929113i
$631$	−11.5984	−	8.42673i	−0.461725	−	0.335463i	0.332483	−	0.943109i	$-0.392114\pi$
$631$	−11.5984	−	8.42673i	−0.461725	−	0.335463i	−0.794208	+	0.607647i	$0.792114\pi$
$632$	−62.1407	+	107.631i	−2.47183	+	4.28133i
$633$	12.0034	−	15.9228i	0.477093	−	0.632873i
$634$	−61.6249	+	13.0988i	−2.44744	+	0.520219i
$635$	11.4506	−	1.43797i	0.454402	−	0.0570643i
$636$	−54.4469	+	16.6347i	−2.15896	+	0.659611i
$637$	−4.00183	−	4.44448i	−0.158558	−	0.176097i
$638$	−4.23903	+	13.0464i	−0.167825	+	0.516512i
$639$	7.06836	−	7.31393i	0.279620	−	0.289335i
$640$	96.2445	+	8.15328i	3.80440	+	0.322287i
$641$	−15.0892	−	16.7583i	−0.595989	−	0.661913i	0.367387	−	0.930068i	$-0.380253\pi$
$641$	−15.0892	−	16.7583i	−0.595989	−	0.661913i	−0.963376	+	0.268156i	$0.913586\pi$
$642$	69.0269	+	8.48877i	2.72428	+	0.335025i
$643$	−21.0243	−	36.4152i	−0.829119	−	1.43608i	−0.898730	−	0.438502i	$-0.855509\pi$
$643$	−21.0243	−	36.4152i	−0.829119	−	1.43608i	0.0696109	−	0.997574i	$-0.477824\pi$
$644$	−0.526817	+	5.01232i	−0.0207595	+	0.197513i
$645$	−33.3295	−	24.0850i	−1.31235	−	0.948346i
$646$	−2.76695	−	26.3257i	−0.108864	−	1.03577i
$647$	9.23613	−	6.71044i	0.363110	−	0.263815i	−0.391238	−	0.920289i	$-0.627953\pi$
$647$	9.23613	−	6.71044i	0.363110	−	0.263815i	0.754348	+	0.656475i	$0.227953\pi$
$648$	83.7788	+	24.0922i	3.29114	+	0.946431i
$649$	−28.0664			−1.10170
$650$	21.5905	+	8.58511i	0.846850	+	0.336736i
$651$	−7.55796	−	4.54324i	−0.296220	−	0.178064i
$652$	30.9124	−	34.3317i	1.21062	−	1.34453i
$653$	7.83342	+	3.48766i	0.306545	+	0.136483i	0.554244	−	0.832354i	$-0.313008\pi$
$653$	7.83342	+	3.48766i	0.306545	+	0.136483i	−0.247698	+	0.968837i	$0.579674\pi$
$654$	−4.03554	+	8.64994i	−0.157802	+	0.338240i
$655$	−25.5735	−	7.74166i	−0.999239	−	0.302492i
$656$	47.7070	+	34.6612i	1.86265	+	1.35329i
$657$	21.8622	+	41.1546i	0.852927	+	1.60560i
$658$	−26.5289	−	19.2744i	−1.03421	−	0.751395i
$659$	−20.3348	−	22.5840i	−0.792130	−	0.879749i	0.202913	−	0.979197i	$-0.434959\pi$
$659$	−20.3348	−	22.5840i	−0.792130	−	0.879749i	−0.995043	+	0.0994474i	$0.968293\pi$
$660$	39.4832	−	44.0772i	1.53688	−	1.71570i
$661$	−14.3063	+	15.8887i	−0.556449	+	0.618000i	−0.954082	−	0.299545i	$-0.903165\pi$
$661$	−14.3063	+	15.8887i	−0.556449	+	0.618000i	0.397633	+	0.917545i	$0.369832\pi$
$662$	16.5132	−	3.51000i	0.641805	−	0.136420i
$663$	−17.5322	−	6.04054i	−0.680893	−	0.234595i
$664$	−8.33227	−	1.77108i	−0.323355	−	0.0687312i
$665$	1.44645	+	6.18746i	0.0560908	+	0.239939i
$666$	11.8861	−	32.6182i	0.460578	−	1.26393i
$667$	−0.716332	−	0.520446i	−0.0277365	−	0.0201517i
$668$	−31.2808	+	54.1799i	−1.21029	+	2.09628i
$669$	−3.51953	−	0.432823i	−0.136073	−	0.0167339i
$670$	−46.9972	−	25.8820i	−1.81566	−	0.999909i
$671$	18.4016	+	8.19290i	0.710384	+	0.316284i
$672$	74.5968	−	6.51208i	2.87764	−	0.251209i
$673$	−21.8048	−	4.63475i	−0.840513	−	0.178657i	−0.232513	−	0.972593i	$-0.574695\pi$
$673$	−21.8048	−	4.63475i	−0.840513	−	0.178657i	−0.608000	+	0.793937i	$0.708028\pi$
$674$	41.3282			1.59190
$675$	25.8024	+	3.03891i	0.993136	+	0.116968i
$676$	−56.0291			−2.15497
$677$	30.7046	+	6.52646i	1.18007	+	0.250832i	0.755862	−	0.654731i	$-0.227218\pi$
$677$	30.7046	+	6.52646i	1.18007	+	0.250832i	0.424211	+	0.905563i	$0.360551\pi$
$678$	−63.2246	+	5.51931i	−2.42813	+	0.211968i
$679$	−6.46107	−	2.87665i	−0.247953	−	0.110396i
$680$	−135.859	+	17.0613i	−5.20996	+	0.654273i
$681$	26.1261	+	3.21292i	1.00115	+	0.123120i
$682$	−10.3636	+	17.9503i	−0.396842	+	0.687351i
$683$	−41.1891	−	29.9257i	−1.57606	−	1.14507i	−0.921045	−	0.389457i	$-0.872663\pi$
$683$	−41.1891	−	29.9257i	−1.57606	−	1.14507i	−0.655014	−	0.755617i	$-0.727337\pi$
$684$	16.2637	+	19.3973i	0.621858	+	0.741674i
$685$	−8.29312	+	5.01414i	−0.316864	+	0.191581i
$686$	−52.6448	−	11.1900i	−2.00999	−	0.427236i
$687$	0.344558	+	0.118714i	0.0131457	+	0.00452923i
$688$	−161.174	+	34.2586i	−6.14470	+	1.30610i
$689$	−6.73545	+	7.48047i	−0.256600	+	0.284983i
$690$	2.61204	+	4.49752i	0.0994387	+	0.171218i
$691$	−4.76023	−	5.28677i	−0.181088	−	0.201118i	0.645766	−	0.763535i	$-0.276538\pi$
$691$	−4.76023	−	5.28677i	−0.181088	−	0.201118i	−0.826854	+	0.562417i	$0.809872\pi$
$692$	−28.4467	−	20.6678i	−1.08138	−	0.785670i
$693$	8.18548	−	13.0884i	0.310941	−	0.497188i
$694$	−37.3577	−	27.1420i	−1.41808	−	1.03029i
$695$	−17.9899	−	23.7371i	−0.682397	−	0.900401i
$696$	−12.8333	+	27.5075i	−0.486445	+	1.04267i
$697$	−21.9453	−	9.77066i	−0.831236	−	0.370090i
$698$	−28.4770	+	31.6269i	−1.07787	+	1.19710i
$699$	24.8968	+	14.9659i	0.941683	+	0.566064i
$700$	49.8938	−	12.7322i	1.88581	−	0.481232i
$701$	−42.2657			−1.59635			−0.798177	−	0.602423i	$-0.794202\pi$
$701$	−42.2657			−1.59635			−0.798177	+	0.602423i	$0.794202\pi$
$702$	23.3271	−	6.23620i	0.880424	−	0.235370i
$703$	5.20589	−	3.78230i	0.196344	−	0.142652i
$704$	−9.43295	−	89.7486i	−0.355518	−	3.38253i
$705$	−24.8513	+	0.0637112i	−0.935955	+	0.00239950i
$706$	2.69516	−	25.6428i	0.101434	−	0.965079i
$707$	6.20438	+	10.7463i	0.233340	+	0.404156i
$708$	−96.5638	−	11.8752i	−3.62909	−	0.446297i
$709$	6.41778	+	7.12767i	0.241025	+	0.267685i	0.851505	−	0.524346i	$-0.175690\pi$
$709$	6.41778	+	7.12767i	0.241025	+	0.267685i	−0.610480	+	0.792031i	$0.709024\pi$
$710$	−4.73553	−	20.2572i	−0.177721	−	0.760238i
$711$	10.5961	+	37.0060i	0.397383	+	1.38783i
$712$	−14.6484	+	45.0832i	−0.548973	+	1.68956i
$713$	−0.895207	−	0.994228i	−0.0335258	−	0.0372341i
$714$	−53.5176	+	16.3508i	−2.00284	+	0.611914i
$715$	1.96809	−	10.2760i	0.0736025	−	0.384299i
$716$	36.1096	−	7.67533i	1.34948	−	0.286840i
$717$	25.7460	−	34.1526i	0.961503	−	1.27545i
$718$	−10.9842	+	19.0252i	−0.409927	+	0.710014i
$719$	−35.1893	−	25.5666i	−1.31234	−	0.953472i	−0.999994	−	0.00350360i	$-0.998885\pi$
$719$	−35.1893	−	25.5666i	−1.31234	−	0.953472i	−0.312347	−	0.949968i	$-0.601115\pi$
$720$	78.4078	−	68.4863i	2.92209	−	2.55233i
$721$	2.31620	−	1.68282i	0.0862598	−	0.0626714i
$722$	−4.78198	−	45.4975i	−0.177967	−	1.69324i
$723$	3.85385	+	3.59514i	0.143326	+	0.133705i
$724$	20.0144	+	34.6659i	0.743828	+	1.28835i
$725$	−2.44560	+	8.70960i	−0.0908274	+	0.323466i
$726$	13.7103	+	8.24151i	0.508836	+	0.305871i
$727$	25.6825	+	5.45899i	0.952511	+	0.202463i	0.657858	−	0.753142i	$-0.271463\pi$
$727$	25.6825	+	5.45899i	0.952511	+	0.202463i	0.294653	+	0.955604i	$0.404796\pi$
$728$	24.7140	−	17.9558i	0.915962	−	0.665486i
$729$	23.3981	−	13.4733i	0.866596	−	0.499011i
$730$	94.9728	+	8.04556i	3.51510	+	0.297779i
$731$	61.3206	−	27.3017i	2.26802	−	1.00979i
$732$	59.8450	+	35.9740i	2.21193	+	1.32964i
$733$	−5.43558	+	51.7161i	−0.200768	+	1.91018i	0.176885	+	0.984231i	$0.443398\pi$
$733$	−5.43558	+	51.7161i	−0.200768	+	1.91018i	−0.377653	+	0.925947i	$0.623269\pi$
$734$	70.8836	−	15.0668i	2.61636	−	0.556124i
$735$	−12.4810	+	5.59529i	−0.460369	+	0.206385i
$736$	11.1121	+	2.36196i	0.409598	+	0.0870628i
$737$	−7.46588	+	22.9776i	−0.275009	+	0.846391i
$738$	30.8069	−	5.42000i	1.13402	−	0.199513i
$739$	−7.71260	−	23.7369i	−0.283712	−	0.873177i	−0.986782	−	0.162056i	$-0.948188\pi$
$739$	−7.71260	−	23.7369i	−0.283712	−	0.873177i	0.703069	−	0.711121i	$-0.251812\pi$
$740$	−31.4965	−	41.5587i	−1.15783	−	1.52773i
$741$	4.23150	+	1.45792i	0.155448	+	0.0535582i
$742$	−3.17520	+	30.2100i	−0.116565	+	1.10904i
$743$	−0.897873	−	1.55516i	−0.0329398	−	0.0570534i	0.849086	−	0.528255i	$-0.177154\pi$
$743$	−0.897873	−	1.55516i	−0.0329398	−	0.0570534i	−0.882025	+	0.471202i	$0.843820\pi$
$744$	−27.6084	+	36.6231i	−1.01217	+	1.34267i
$745$	−6.02980	+	2.09482i	−0.220915	+	0.0767483i
$746$	−46.1153	+	33.5047i	−1.68840	+	1.22669i
$747$	−2.18787	+	1.47452i	−0.0800498	+	0.0539500i
$748$	29.8493	+	91.8668i	1.09140	+	3.35898i
$749$	13.6257	−	23.6005i	0.497873	−	0.862342i
$750$	33.8270	−	40.9807i	1.23519	−	1.49640i
$751$	9.00025	+	15.5889i	0.328424	+	0.568846i	0.982199	−	0.187842i	$-0.0601493\pi$
$751$	9.00025	+	15.5889i	0.328424	+	0.568846i	−0.653776	+	0.756688i	$0.726816\pi$
$752$	−66.6327	+	74.0031i	−2.42984	+	2.69862i
$753$	43.0475	−	3.75791i	1.56874	−	0.136946i
$754$	0.878842	+	8.36162i	0.0320055	+	0.304512i
$755$	−18.9878	−	16.4142i	−0.691036	−	0.597375i
$756$	33.7004	−	41.5680i	1.22567	−	1.51181i
$757$	−9.03751			−0.328474			−0.164237	−	0.986421i	$-0.552516\pi$
$757$	−9.03751			−0.328474			−0.164237	+	0.986421i	$0.552516\pi$
$758$	48.0465	−	21.3917i	1.74513	−	0.776981i
$759$	1.76785	−	1.53618i	0.0641689	−	0.0557598i
$760$	32.7905	−	4.11787i	1.18944	−	0.149371i
$761$	26.4976	−	29.4286i	0.960539	−	1.06679i	−0.0371821	−	0.999309i	$-0.511838\pi$
$761$	26.4976	−	29.4286i	0.960539	−	1.06679i	0.997721	−	0.0674778i	$-0.0214952\pi$
$762$	−4.67591	−	24.0799i	−0.169390	−	0.872324i
$763$	2.50264	+	2.77947i	0.0906017	+	0.100623i
$764$	1.94018	+	5.97126i	0.0701932	+	0.216032i
$765$	−25.4422	+	33.9302i	−0.919866	+	1.22675i
$766$	20.4928	−	63.0704i	0.740435	−	2.27883i
$767$	−15.7148	+	6.99667i	−0.567428	+	0.252635i
$768$	1.62599	−	92.1484i	0.0586730	−	3.32512i
$769$	−3.52699	+	33.5571i	−0.127187	+	1.21010i	0.725703	+	0.688008i	$0.241515\pi$
$769$	−3.52699	+	33.5571i	−0.127187	+	1.21010i	−0.852890	+	0.522091i	$0.825152\pi$
$770$	−13.4224	−	28.5787i	−0.483710	−	1.02990i
$771$	4.27636	+	6.10975i	0.154009	+	0.220037i
$772$	1.77737	+	16.9106i	0.0639691	+	0.608625i
$773$	8.69380	+	26.7568i	0.312694	+	0.962374i	0.976693	+	0.214640i	$0.0688580\pi$
$773$	8.69380	+	26.7568i	0.312694	+	0.962374i	−0.663999	+	0.747734i	$0.731142\pi$
$774$	−46.3454	+	74.1054i	−1.66585	+	2.66366i
$775$	−6.35059	+	12.1041i	−0.228120	+	0.434791i
$776$	−18.3918	+	31.8556i	−0.660228	+	1.14355i
$777$	−9.94710	−	9.27936i	−0.356850	−	0.332895i
$778$	94.5309	+	42.0879i	3.38910	+	1.50892i
$779$	5.29664	+	2.35821i	0.189772	+	0.0844918i
$780$	11.1192	−	34.5223i	0.398131	−	1.23610i
$781$	−8.55795	+	3.81024i	−0.306227	+	0.136341i
$782$	−8.48982			−0.303595
$783$	3.36413	+	8.77883i	0.120224	+	0.313730i
$784$	−16.9365	+	52.1253i	−0.604877	+	1.86162i
$785$	−30.5721	+	10.6211i	−1.09117	+	0.379083i
$786$	−12.7863	+	55.3354i	−0.456071	+	1.97375i
$787$	−30.1553	+	6.40972i	−1.07492	+	0.228482i	−0.711174	−	0.703016i	$-0.751836\pi$
$787$	−30.1553	+	6.40972i	−1.07492	+	0.228482i	−0.363748	+	0.931498i	$0.618503\pi$
$788$	126.090	−	26.8013i	4.49177	−	0.954755i
$789$	16.2195	+	15.1307i	0.577431	+	0.538668i
$790$	75.3527	+	22.8109i	2.68093	+	0.811576i
$791$	−7.68473	+	23.6512i	−0.273238	+	0.840939i
$792$	−63.2490	−	49.4543i	−2.24745	−	1.75728i
$793$	12.3457			0.438409
$794$	70.5070	−	31.3918i	2.50220	−	1.11405i
$795$	11.5616	+	19.9072i	0.410048	+	0.706037i
$796$	−94.0467	−	41.8723i	−3.33340	−	1.48412i
$797$	10.6082	+	4.72307i	0.375761	+	0.167300i	0.585923	−	0.810367i	$-0.300732\pi$
$797$	10.6082	+	4.72307i	0.375761	+	0.167300i	−0.210161	+	0.977667i	$0.567399\pi$
$798$	12.9168	−	3.94638i	0.457251	−	0.139700i
$799$	20.2830	−	35.1312i	0.717561	−	1.24285i
$800$	−16.7864	−	114.848i	−0.593489	−	4.06049i
$801$	6.88784	+	12.9660i	0.243370	+	0.458133i
$802$	−19.9816	−	61.4969i	−0.705574	−	2.17153i
$803$	−4.48636	−	42.6848i	−0.158320	−	1.50631i
$804$	−35.4088	+	75.8967i	−1.24877	+	2.67667i
$805$	2.02209	−	0.253936i	0.0712694	−	0.00895008i
$806$	−1.32790	+	12.6342i	−0.0467734	+	0.445019i
$807$	−29.9815	−	18.0225i	−1.05540	−	0.634421i
$808$	58.9575	−	26.2496i	2.07412	−	0.923456i
$809$	11.6688	−	35.9129i	0.410254	−	1.26263i	−0.506174	−	0.862432i	$-0.668941\pi$
$809$	11.6688	−	35.9129i	0.410254	−	1.26263i	0.916428	−	0.400200i	$-0.131059\pi$
$810$	2.78024	−	55.1529i	0.0976876	−	1.93788i
$811$	−1.37548	−	4.23331i	−0.0482998	−	0.148652i	0.923998	−	0.382398i	$-0.124902\pi$
$811$	−1.37548	−	4.23331i	−0.0482998	−	0.148652i	−0.972298	+	0.233746i	$0.924902\pi$
$812$	12.4679	+	13.8470i	0.437539	+	0.485936i
$813$	−10.3460	+	8.99020i	−0.362851	+	0.315300i
$814$	−21.3948	+	23.7613i	−0.749887	+	0.832834i
$815$	−16.3635	−	9.01160i	−0.573187	−	0.315663i
$816$	32.3939	+	166.821i	1.13401	+	5.83992i
$817$	−14.8001	+	6.58944i	−0.517791	+	0.230535i
$818$	−28.8344			−1.00817
$819$	1.32036	−	9.36896i	0.0461370	−	0.327378i
$820$	18.2389	−	43.2993i	0.636931	−	1.51208i
$821$	−0.872620	−	8.30242i	−0.0304546	−	0.289757i	−0.999140	−	0.0414649i	$-0.986798\pi$
$821$	−0.872620	−	8.30242i	−0.0304546	−	0.289757i	0.968685	−	0.248292i	$-0.0798691\pi$
$822$	11.8118	+	16.8758i	0.411982	+	0.588610i
$823$	−3.06147	+	3.40010i	−0.106716	+	0.118520i	−0.794136	−	0.607740i	$-0.792076\pi$
$823$	−3.06147	+	3.40010i	−0.106716	+	0.118520i	0.687420	+	0.726260i	$0.258743\pi$
$824$	−7.44507	−	12.8952i	−0.259361	−	0.449227i
$825$	−20.9897	−	11.4893i	−0.730768	−	0.400006i
$826$	−25.9555	+	44.9562i	−0.903106	+	1.56423i
$827$	−2.49659	−	7.68370i	−0.0868148	−	0.267189i	0.898219	−	0.439547i	$-0.144861\pi$
$827$	−2.49659	−	7.68370i	−0.0868148	−	0.267189i	−0.985034	+	0.172359i	$0.944861\pi$
$828$	6.73236	−	4.53730i	0.233966	−	0.157682i
$829$	−14.9236	+	10.8426i	−0.518316	+	0.376579i	−0.815969	−	0.578095i	$-0.803796\pi$
$829$	−14.9236	+	10.8426i	−0.518316	+	0.376579i	0.297653	+	0.954674i	$0.403796\pi$
$830$	0.109036	+	5.39514i	0.00378468	+	0.187268i
$831$	0.309483	+	0.0380595i	0.0107358	+	0.00132027i
$832$	−27.6551	−	47.9000i	−0.958767	−	1.66063i
$833$	2.33380	−	22.2046i	0.0808613	−	0.769344i
$834$	−47.7863	+	41.5240i	−1.65470	+	1.43786i
$835$	24.2126	+	7.32969i	0.837912	+	0.253654i
$836$	−7.20434	−	22.1727i	−0.249167	−	0.766858i
$837$	2.21416	+	14.0315i	0.0765327	+	0.485000i
$838$	−8.02726	+	24.7054i	−0.277297	+	0.853433i
$839$	13.0629	+	2.77660i	0.450981	+	0.0958589i	0.427802	−	0.903872i	$-0.359288\pi$
$839$	13.0629	+	2.77660i	0.450981	+	0.0958589i	0.0231787	+	0.999731i	$0.492621\pi$
$840$	−21.7595	−	66.3893i	−0.750775	−	2.29065i
$841$	25.1643	−	5.34884i	0.867734	−	0.184443i
$842$	−1.94193	+	18.4762i	−0.0669233	+	0.636732i
$843$	2.46506	−	1.36579i	0.0849012	−	0.0470404i
$844$	−58.1584	+	25.8938i	−2.00189	+	0.891301i
$845$	5.15732	+	22.0614i	0.177417	+	0.758937i
$846$	3.66466	+	52.6952i	0.125994	+	1.81170i
$847$	5.07107	−	3.68435i	0.174244	−	0.126596i
$848$	90.2309	+	19.1792i	3.09854	+	0.658615i
$849$	−0.111754	+	6.33331i	−0.00383537	+	0.217359i
$850$	30.1153	+	81.3443i	1.03295	+	2.79009i
$851$	−1.03191	−	1.78731i	−0.0353733	−	0.0612683i
$852$	−31.0562	+	9.48837i	−1.06397	+	0.325066i
$853$	−5.56890	−	52.9846i	−0.190676	−	1.81416i	−0.503116	−	0.864219i	$-0.667813\pi$
$853$	−5.56890	−	52.9846i	−0.190676	−	1.81416i	0.312440	−	0.949937i	$-0.398854\pi$
$854$	30.1408	−	21.8986i	1.03140	−	0.749354i
$855$	6.14065	−	8.18929i	0.210006	−	0.280068i
$856$	−114.664	−	83.3084i	−3.91914	−	2.84742i
$857$	−3.75868	+	6.51022i	−0.128394	+	0.222385i	−0.923054	−	0.384669i	$-0.874316\pi$
$857$	−3.75868	+	6.51022i	−0.128394	+	0.222385i	0.794661	+	0.607054i	$0.207649\pi$
$858$	−22.0726	−	2.71444i	−0.753547	−	0.0926694i
$859$	23.4780	−	4.99040i	0.801058	−	0.170270i	0.210847	−	0.977519i	$-0.432378\pi$
$859$	23.4780	−	4.99040i	0.801058	−	0.170270i	0.590211	+	0.807249i	$0.299044\pi$
$860$	55.8109	+	118.831i	1.90314	+	4.05211i
$861$	2.75946	−	11.9422i	0.0940423	−	0.406988i
$862$	−45.4718	−	50.5016i	−1.54878	−	1.72009i
$863$	−13.5353	+	41.6575i	−0.460748	+	1.41804i	0.403504	+	0.914978i	$0.367792\pi$
$863$	−13.5353	+	41.6575i	−0.460748	+	1.41804i	−0.864252	+	0.503059i	$0.832208\pi$
$864$	−85.2437	−	85.3411i	−2.90005	−	2.90336i
$865$	−5.51948	+	13.1033i	−0.187668	+	0.445525i
$866$	11.7698	+	13.0717i	0.399956	+	0.444196i
$867$	−15.5371	−	36.6225i	−0.527668	−	1.24377i
$868$	14.0770	+	24.3820i	0.477804	+	0.827580i
$869$	3.70579	−	35.2582i	0.125710	−	1.19605i
$870$	18.8185	+	3.94960i	0.638007	+	0.133904i
$871$	1.54784	+	14.7267i	0.0524464	+	0.498994i
$872$	15.7371	−	11.4337i	0.532927	−	0.387194i
$873$	3.13612	+	10.9527i	0.106141	+	0.370692i
$874$	2.04908			0.0693110
$875$	−9.60588	−	18.4737i	−0.324738	−	0.624525i
$876$	2.62488	−	148.757i	0.0886866	−	5.02605i
$877$	−17.2909	+	19.2035i	−0.583871	+	0.648454i	−0.960621	−	0.277860i	$-0.910375\pi$
$877$	−17.2909	+	19.2035i	−0.583871	+	0.648454i	0.376750	+	0.926315i	$0.377041\pi$
$878$	0.643402	+	0.286461i	0.0217138	+	0.00966759i
$879$	−24.3145	−	34.7387i	−0.820107	−	1.17171i
$880$	−90.5726	+	31.4659i	−3.05320	+	1.06072i
$881$	−8.85610	−	6.43433i	−0.298369	−	0.216778i	0.428520	−	0.903532i	$-0.359035\pi$
$881$	−8.85610	−	6.43433i	−0.298369	−	0.216778i	−0.726890	+	0.686754i	$0.759035\pi$
$882$	13.6390	+	25.6748i	0.459250	+	0.864517i
$883$	34.4894	+	25.0580i	1.16066	+	0.843270i	0.989862	−	0.142036i	$-0.0453648\pi$
$883$	34.4894	+	25.0580i	1.16066	+	0.843270i	0.170800	+	0.985306i	$0.445365\pi$
$884$	39.6146	+	43.9965i	1.33238	+	1.47976i
$885$	4.21257	+	39.1150i	0.141604	+	1.31484i
$886$	26.9094	−	29.8859i	0.904039	−	1.00404i
$887$	−54.9183	+	11.6733i	−1.84398	+	0.391949i	−0.991423	−	0.130690i	$-0.958281\pi$
$887$	−54.9183	+	11.6733i	−1.84398	+	0.391949i	−0.852554	+	0.522639i	$0.824948\pi$
$888$	−53.4045	+	46.4060i	−1.79214	+	1.55728i
$889$	−9.40176	−	1.99841i	−0.315325	−	0.0670244i
$890$	29.9218	+	2.53481i	1.00298	+	0.0849669i
$891$	−24.6278	+	3.44210i	−0.825063	+	0.115315i
$892$	9.15908	+	6.65446i	0.306669	+	0.222808i
$893$	−4.89544	+	8.47915i	−0.163820	+	0.283744i
$894$	5.29905	+	12.4904i	0.177227	+	0.417741i
$895$	−6.34594	−	13.5116i	−0.212121	−	0.451644i
$896$	−73.4917	−	32.7206i	−2.45519	−	1.09312i
$897$	0.606892	−	1.30084i	0.0202635	−	0.0434337i
$898$	41.7140	+	8.86659i	1.39201	+	0.295882i
$899$	−4.94620			−0.164965
$900$	−67.3549	−	48.4105i	−2.24516	−	1.61368i
$901$	−37.5783			−1.25191
$902$	−28.1796	−	5.98975i	−0.938277	−	0.199437i
$903$	19.6389	+	28.0586i	0.653542	+	0.933733i
$904$	118.156	+	52.6066i	3.92982	+	1.74967i
$905$	11.8074	−	11.0715i	0.392492	−	0.368030i
$906$	−32.1143	+	42.6002i	−1.06692	+	1.41530i
$907$	19.3181	−	33.4600i	0.641448	−	1.11102i	−0.343662	−	0.939093i	$-0.611667\pi$
$907$	19.3181	−	33.4600i	0.641448	−	1.11102i	0.985110	−	0.171927i	$-0.0549992\pi$
$908$	−67.9895	−	49.3972i	−2.25631	−	1.63931i
$909$	6.84369	−	18.7807i	0.226991	−	0.622915i
$910$	−14.6398	−	12.6556i	−0.485304	−	0.419528i
$911$	21.0207	+	4.46810i	0.696448	+	0.148035i	0.542514	−	0.840047i	$-0.317472\pi$
$911$	21.0207	+	4.46810i	0.696448	+	0.148035i	0.153934	+	0.988081i	$0.450806\pi$
$912$	−7.81847	−	40.2635i	−0.258896	−	1.33326i
$913$	2.37685	−	0.505216i	0.0786624	−	0.0167202i
$914$	26.6922	−	29.6447i	0.882900	−	0.980559i
$915$	8.65619	−	26.8752i	0.286165	−	0.888468i
$916$	−0.778542	−	0.864658i	−0.0257237	−	0.0285691i
$917$	18.0039	+	13.0806i	0.594542	+	0.431960i
$918$	75.5721	+	49.1385i	2.49425	+	1.62181i
$919$	10.5406	+	7.65821i	0.347703	+	0.252621i	0.747905	−	0.663806i	$-0.231060\pi$
$919$	10.5406	+	7.65821i	0.347703	+	0.252621i	−0.400202	+	0.916427i	$0.631060\pi$
$920$	−0.214169	−	10.5972i	−0.00706094	−	0.349379i
$921$	−6.57316	+	0.573817i	−0.216593	+	0.0189079i
$922$	−8.24821	−	3.67234i	−0.271640	−	0.120942i
$923$	−3.84187	+	4.26682i	−0.126457	+	0.140444i
$924$	−43.1108	+	23.8860i	−1.41824	+	0.785790i
$925$	−13.4645	+	16.2271i	−0.442711	+	0.533544i
$926$	104.951			3.44890
$927$	−4.47443	−	1.11741i	−0.146960	−	0.0367006i
$928$	33.9789	−	24.6871i	1.11541	−	0.810394i
$929$	2.50268	+	23.8114i	0.0821101	+	0.781226i	0.955656	+	0.294484i	$0.0951479\pi$
$929$	2.50268	+	23.8114i	0.0821101	+	0.781226i	−0.873546	+	0.486741i	$0.838185\pi$
$930$	26.5721	+	11.7491i	0.871333	+	0.385269i
$931$	−0.563277	+	5.35923i	−0.0184607	+	0.175642i
$932$	−46.3711	−	80.3172i	−1.51894	−	2.63088i
$933$	26.2889	−	34.8727i	0.860660	−	1.14168i
$934$	10.5235	+	11.6876i	0.344340	+	0.382429i
$935$	33.4250	−	20.2092i	1.09311	−	0.660913i
$936$	−47.7425	−	11.9228i	−1.56051	−	0.389710i
$937$	5.43437	−	16.7253i	0.177533	−	0.546390i	−0.822207	−	0.569188i	$-0.807257\pi$
$937$	5.43437	−	16.7253i	0.177533	−	0.546390i	0.999740	+	0.0227980i	$0.00725746\pi$
$938$	29.9008	+	33.2082i	0.976294	+	1.08428i
$939$	−32.8558	−	30.6502i	−1.07221	−	1.00023i
$940$	69.4994	+	38.2743i	2.26682	+	1.24837i
$941$	−13.7789	+	2.92879i	−0.449179	+	0.0954759i	−0.426947	−	0.904277i	$-0.640411\pi$
$941$	−13.7789	+	2.92879i	−0.449179	+	0.0954759i	−0.0222325	+	0.999753i	$0.507077\pi$
$942$	26.8671	+	63.3283i	0.875376	+	2.06335i
$943$	0.929764	−	1.61040i	0.0302773	−	0.0524418i
$944$	127.535	+	92.6599i	4.15093	+	3.01582i
$945$	−19.4694	−	9.44331i	−0.633340	−	0.307191i
$946$	65.1258	−	47.3167i	2.11742	−	1.53840i
$947$	2.31050	+	21.9829i	0.0750810	+	0.714348i	0.965711	+	0.259619i	$0.0835971\pi$
$947$	2.31050	+	21.9829i	0.0750810	+	0.714348i	−0.890630	+	0.454729i	$0.849736\pi$
$948$	27.6681	−	119.740i	0.898617	−	3.88896i
$949$	−13.1529	−	22.7815i	−0.426961	−	0.739517i
$950$	−7.26853	−	19.6330i	−0.235822	−	0.636978i
$951$	34.7845	−	19.2727i	1.12796	−	0.624960i
$952$	111.550	+	23.7108i	3.61537	+	0.768471i
$953$	−25.0086	+	18.1698i	−0.810108	+	0.588578i	−0.913862	−	0.406025i	$-0.866915\pi$
$953$	−25.0086	+	18.1698i	−0.810108	+	0.588578i	0.103754	+	0.994603i	$0.466915\pi$
$954$	40.5769	−	27.3470i	1.31373	−	0.885392i
$955$	2.17259	−	1.31358i	0.0703034	−	0.0425065i
$956$	−124.744	+	55.5394i	−4.03450	+	1.79627i
$957$	0.152762	−	8.65735i	0.00493810	−	0.279852i
$958$	−3.86445	+	36.7678i	−0.124855	+	1.18791i
$959$	7.89509	−	1.67815i	0.254946	−	0.0541904i
$960$	−123.663	+	26.6170i	−3.99121	+	0.859059i
$961$	23.0123	+	4.89142i	0.742334	+	0.157788i
$962$	−6.05580	+	18.6378i	−0.195247	+	0.600908i
$963$	−43.2341	+	7.60638i	−1.39320	+	0.245112i
$964$	−5.19968	−	16.0030i	−0.167470	−	0.515421i
$965$	6.49493	−	2.25641i	0.209079	−	0.0726364i
$966$	−0.825734	−	4.25235i	−0.0265676	−	0.136817i
$967$	2.69303	−	25.6224i	0.0866019	−	0.823962i	−0.861876	−	0.507119i	$-0.830711\pi$
$967$	2.69303	−	25.6224i	0.0866019	−	0.823962i	0.948478	−	0.316843i	$-0.102623\pi$
$968$	−16.3002	−	28.2327i	−0.523907	−	0.907433i
$969$	6.52556	+	15.3814i	0.209631	+	0.494121i
$970$	22.3022	+	6.75135i	0.716079	+	0.216773i
$971$	27.8824	−	20.2577i	0.894787	−	0.650101i	−0.0423344	−	0.999103i	$-0.513479\pi$
$971$	27.8824	−	20.2577i	0.894787	−	0.650101i	0.937122	+	0.349002i	$0.113479\pi$
$972$	−86.1896	+	1.42243i	−2.76453	+	0.0456245i
$973$	7.66559	+	23.5923i	0.245748	+	0.756333i
$974$	−39.4326	+	68.2993i	−1.26350	+	2.18845i
$975$	−14.6166	−	1.20050i	−0.468106	−	0.0384469i
$976$	−56.5694	−	97.9811i	−1.81074	−	3.13630i
$977$	4.17072	−	4.63205i	0.133433	−	0.148192i	−0.672725	−	0.739892i	$-0.734876\pi$
$977$	4.17072	−	4.63205i	0.133433	−	0.148192i	0.806158	+	0.591700i	$0.201543\pi$
$978$	−16.7876	+	35.9832i	−0.536808	+	1.15062i
$979$	−1.41346	−	13.4481i	−0.0451743	−	0.429804i
$980$	43.5125	+	3.68613i	1.38996	+	0.117749i
$981$	0.840764	−	5.96587i	0.0268435	−	0.190476i
$982$	−43.8206			−1.39837
$983$	−1.85033	+	0.823819i	−0.0590163	+	0.0262757i	−0.436033	−	0.899931i	$-0.643617\pi$
$983$	−1.85033	+	0.823819i	−0.0590163	+	0.0262757i	0.377016	+	0.926207i	$0.376950\pi$
$984$	−60.2699	−	20.7654i	−1.92133	−	0.661978i
$985$	−22.1592	−	47.1809i	−0.706051	−	1.50331i
$986$	−21.0024	+	23.3255i	−0.668852	+	0.742835i
$987$	19.5692	+	6.74237i	0.622893	+	0.214612i
$988$	−9.56125	−	10.6188i	−0.304184	−	0.337830i
$989$	1.60565	+	4.94168i	0.0510566	+	0.157136i
$990$	−21.3852	+	46.1464i	−0.679667	+	1.46663i
$991$	−0.263346	+	0.810497i	−0.00836547	+	0.0257463i	−0.955152	−	0.296116i	$-0.904309\pi$
$991$	−0.263346	+	0.810497i	−0.00836547	+	0.0257463i	0.946787	+	0.321862i	$0.104309\pi$
$992$	57.9745	−	25.8119i	1.84069	−	0.819530i
$993$	−9.32097	+	5.16438i	−0.295792	+	0.163887i
$994$	−1.81112	+	17.2316i	−0.0574452	+	0.546554i
$995$	−7.83047	+	40.8851i	−0.248243	+	1.29614i
$996$	8.39145	−	0.732548i	0.265893	−	0.0232117i
$997$	6.02165	+	57.2921i	0.190707	+	1.81446i	0.502793	+	0.864407i	$0.332306\pi$
$997$	6.02165	+	57.2921i	0.190707	+	1.81446i	−0.312086	+	0.950054i	$0.601028\pi$
$998$	17.8025	+	54.7904i	0.563528	+	1.73436i
$999$	−1.15933	+	21.8824i	−0.0366796	+	0.692327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.28	yes	224
3.2	odd	2		675.2.r.a.181.1		224
9.4	even	3	inner	225.2.q.a.31.1	✓	224
9.5	odd	6		675.2.r.a.631.28		224
25.21	even	5	inner	225.2.q.a.196.1	yes	224
75.71	odd	10		675.2.r.a.46.28		224
225.121	even	15	inner	225.2.q.a.121.28	yes	224
225.221	odd	30		675.2.r.a.496.1		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.1	✓	224	9.4	even	3	inner
225.2.q.a.106.28	yes	224	1.1	even	1	trivial
225.2.q.a.121.28	yes	224	225.121	even	15	inner
225.2.q.a.196.1	yes	224	25.21	even	5	inner
675.2.r.a.46.28		224	75.71	odd	10
675.2.r.a.181.1		224	3.2	odd	2
675.2.r.a.496.1		224	225.221	odd	30
675.2.r.a.631.28		224	9.5	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.68409 + 0.570520i) q^{2} +(-1.72549 + 0.150630i) q^{3} +(5.05174 + 2.24918i) q^{4} +(0.420615 - 2.19615i) q^{5} +(-4.71730 - 0.580123i) q^{6} +(-0.931182 + 1.61286i) q^{7} +(7.83615 + 5.69329i) q^{8} +(2.95462 - 0.519820i) q^{9} +O(q^{10})\)	\(q+(2.68409 + 0.570520i) q^{2} +(-1.72549 + 0.150630i) q^{3} +(5.05174 + 2.24918i) q^{4} +(0.420615 - 2.19615i) q^{5} +(-4.71730 - 0.580123i) q^{6} +(-0.931182 + 1.61286i) q^{7} +(7.83615 + 5.69329i) q^{8} +(2.95462 - 0.519820i) q^{9} +(2.38192 - 5.65469i) q^{10} +(-2.70264 - 0.574464i) q^{11} +(-9.05552 - 3.11999i) q^{12} +(-1.65646 + 0.352091i) q^{13} +(-3.41954 + 3.79779i) q^{14} +(-0.394961 + 3.85279i) q^{15} +(10.3844 + 11.5331i) q^{16} +(-5.11464 - 3.71600i) q^{17} +(8.22703 + 0.290429i) q^{18} +(1.23445 + 0.896882i) q^{19} +(7.06438 - 10.1484i) q^{20} +(1.36380 - 2.92323i) q^{21} +(-6.92639 - 3.08383i) q^{22} +(0.327461 - 0.363683i) q^{23} +(-14.3788 - 8.64335i) q^{24} +(-4.64617 - 1.84747i) q^{25} -4.64695 q^{26} +(-5.01986 + 1.34200i) q^{27} +(-8.33169 + 6.05333i) q^{28} +(-0.189122 - 1.79938i) q^{29} +(-3.25821 + 10.1159i) q^{30} +(0.285758 - 2.71880i) q^{31} +(11.6068 + 20.1036i) q^{32} +(4.74991 + 0.584133i) q^{33} +(-11.6081 - 12.8921i) q^{34} +(3.15040 + 2.72341i) q^{35} +(16.0952 + 4.01948i) q^{36} +(1.30318 - 4.01076i) q^{37} +(2.80169 + 3.11159i) q^{38} +(2.80516 - 0.857041i) q^{39} +(15.7993 - 14.8147i) q^{40} +(3.71670 - 0.790010i) q^{41} +(5.32832 - 7.06812i) q^{42} +(-5.30871 + 9.19495i) q^{43} +(-12.3610 - 8.98078i) q^{44} +(0.101155 - 6.70744i) q^{45} +(1.08642 - 0.789333i) q^{46} +(0.670718 + 6.38145i) q^{47} +(-19.6554 - 18.3360i) q^{48} +(1.76580 + 3.05845i) q^{49} +(-11.4167 - 7.60951i) q^{50} +(9.38499 + 5.64150i) q^{51} +(-9.15992 - 1.94700i) q^{52} +(4.80881 - 3.49380i) q^{53} +(-14.2394 + 0.738105i) q^{54} +(-2.39838 + 5.69379i) q^{55} +(-16.4793 + 7.33707i) q^{56} +(-2.26513 - 1.36161i) q^{57} +(0.518961 - 4.93758i) q^{58} +(9.93588 - 2.11194i) q^{59} +(-10.6609 + 18.5750i) q^{60} +(-7.13090 - 1.51572i) q^{61} +(2.31813 - 7.13448i) q^{62} +(-1.91290 + 5.24942i) q^{63} +(10.0928 + 31.0624i) q^{64} +(0.0765136 + 3.78593i) q^{65} +(12.4159 + 4.27779i) q^{66} +(0.914005 - 8.69618i) q^{67} +(-17.4799 - 30.2760i) q^{68} +(-0.510249 + 0.676856i) q^{69} +(6.90220 + 9.10724i) q^{70} +(2.74292 - 1.99285i) q^{71} +(26.1123 + 12.7481i) q^{72} +(4.80018 + 14.7734i) q^{73} +(5.78606 - 10.0218i) q^{74} +(8.29519 + 2.48794i) q^{75} +(4.21888 + 7.30732i) q^{76} +(3.44318 - 3.82404i) q^{77} +(8.01827 - 0.699970i) q^{78} +(1.34121 + 12.7607i) q^{79} +(29.6962 - 17.9548i) q^{80} +(8.45957 - 3.07174i) q^{81} +10.4267 q^{82} +(-0.803423 + 0.357707i) q^{83} +(13.4644 - 11.7000i) q^{84} +(-10.3122 + 9.66951i) q^{85} +(-19.4950 + 21.6513i) q^{86} +(0.597368 + 3.07632i) q^{87} +(-17.9077 - 19.8885i) q^{88} +(1.51233 + 4.65447i) q^{89} +(4.09824 - 17.9456i) q^{90} +(0.974593 - 2.99949i) q^{91} +(2.47224 - 1.10071i) q^{92} +(-0.0835387 + 4.73431i) q^{93} +(-1.84048 + 17.5110i) q^{94} +(2.48892 - 2.33380i) q^{95} +(-23.0557 - 32.9402i) q^{96} +(0.396958 + 3.77680i) q^{97} +(2.99465 + 9.21658i) q^{98} +(-8.28390 - 0.292436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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