LMFDB - Embedded newform 225.2.q.a.196.1

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			196.1
Character	$\chi$	$=$	225.196
Dual form			225.2.q.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.83613 - 2.03923i) q^{2} +(-0.676463 - 1.59449i) q^{3} +(-0.578024 + 5.49953i) q^{4} +(-2.11223 - 0.733812i) q^{5} +(-2.00946 + 4.30715i) q^{6} +(-0.931182 + 1.61286i) q^{7} +(7.83615 - 5.69329i) q^{8} +(-2.08480 + 2.15723i) q^{9} +(2.38192 + 5.65469i) q^{10} +(1.84882 + 2.05333i) q^{11} +(9.15995 - 2.79857i) q^{12} +(1.13315 - 1.25849i) q^{13} +(4.99875 - 1.06252i) q^{14} +(0.258789 + 3.86433i) q^{15} +(-15.1801 - 3.22664i) q^{16} +(-5.11464 + 3.71600i) q^{17} +(8.22703 + 0.290429i) q^{18} +(1.23445 - 0.896882i) q^{19} +(5.25654 - 11.1921i) q^{20} +(3.20159 + 0.393724i) q^{21} +(0.792522 - 7.54034i) q^{22} +(-0.478689 + 0.101749i) q^{23} +(-14.3788 - 8.64335i) q^{24} +(3.92304 + 3.09996i) q^{25} -4.64695 q^{26} +(4.84996 + 1.86490i) q^{27} +(-8.33169 - 6.05333i) q^{28} +(1.65287 - 0.735904i) q^{29} +(7.40507 - 7.62313i) q^{30} +(-2.49743 - 1.11193i) q^{31} +(11.6068 + 20.1036i) q^{32} +(2.02335 - 4.33693i) q^{33} +(16.9689 + 3.60685i) q^{34} +(3.15040 - 2.72341i) q^{35} +(-10.6587 - 12.7123i) q^{36} +(1.30318 + 4.01076i) q^{37} +(-4.09556 - 0.870538i) q^{38} +(-2.77318 - 0.955473i) q^{39} +(-20.7296 + 6.27529i) q^{40} +(-2.54252 + 2.82375i) q^{41} +(-5.07564 - 7.25170i) q^{42} +(-5.30871 + 9.19495i) q^{43} +(-12.3610 + 8.98078i) q^{44} +(5.98657 - 3.02671i) q^{45} +(1.08642 + 0.789333i) q^{46} +(-5.86186 + 2.60987i) q^{47} +(5.12396 + 26.3873i) q^{48} +(1.76580 + 3.05845i) q^{49} +(-0.881677 - 13.6919i) q^{50} +(9.38499 + 5.64150i) q^{51} +(6.26611 + 6.95922i) q^{52} +(4.80881 + 3.49380i) q^{53} +(-5.10219 - 13.3144i) q^{54} +(-2.39838 - 5.69379i) q^{55} +(1.88558 + 17.9401i) q^{56} +(-2.26513 - 1.36161i) q^{57} +(-4.53555 - 2.01936i) q^{58} +(-6.79693 + 7.54876i) q^{59} +(-21.4016 - 0.810453i) q^{60} +(4.87810 + 5.41768i) q^{61} +(2.31813 + 7.13448i) q^{62} +(-1.53797 - 5.37124i) q^{63} +(10.0928 - 31.0624i) q^{64} +(-3.31697 + 1.82670i) q^{65} +(-12.5591 + 3.83709i) q^{66} +(-7.98812 - 3.55654i) q^{67} +(-17.4799 - 30.2760i) q^{68} +(0.486052 + 0.694436i) q^{69} +(-11.3382 - 1.42386i) q^{70} +(2.74292 + 1.99285i) q^{71} +(-4.05504 + 28.7737i) q^{72} +(4.80018 - 14.7734i) q^{73} +(5.78606 - 10.0218i) q^{74} +(2.28907 - 8.35226i) q^{75} +(4.21888 + 7.30732i) q^{76} +(-5.03331 + 1.06986i) q^{77} +(3.14349 + 7.40952i) q^{78} +(-11.7217 + 5.21885i) q^{79} +(29.6962 + 17.9548i) q^{80} +(-0.307250 - 8.99475i) q^{81} +10.4267 q^{82} +(0.0919281 + 0.874638i) q^{83} +(-4.01589 + 17.3797i) q^{84} +(13.5301 - 4.09587i) q^{85} +(28.4981 - 6.05745i) q^{86} +(-2.29149 - 2.13767i) q^{87} +(26.1778 + 5.56427i) q^{88} +(1.51233 - 4.65447i) q^{89} +(-17.1643 - 6.65055i) q^{90} +(0.974593 + 2.99949i) q^{91} +(-0.282875 - 2.69138i) q^{92} +(-0.0835387 + 4.73431i) q^{93} +(16.0852 + 7.16161i) q^{94} +(-3.26559 + 0.988565i) q^{95} +(24.2034 - 32.1063i) q^{96} +(-3.46928 + 1.54462i) 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} - 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}+ \cdots - 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

Character values

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

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

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 $

$2$	−1.83613	−	2.03923i	−1.29834	−	1.44195i	−0.829331	−	0.558758i	$-0.811278\pi$
$2$	−1.83613	−	2.03923i	−1.29834	−	1.44195i	−0.469009	−	0.883194i	$-0.655389\pi$
$3$	−0.676463	−	1.59449i	−0.390556	−	0.920579i
$3$	−0.676463	−	1.59449i	−0.390556	−	0.920579i
$4$	−0.578024	+	5.49953i	−0.289012	+	2.74976i
$5$	−2.11223	−	0.733812i	−0.944618	−	0.328171i
$5$	−2.11223	−	0.733812i	−0.944618	−	0.328171i
$6$	−2.00946	+	4.30715i	−0.820357	+	1.75839i
$7$	−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
$9$	−2.08480	+	2.15723i	−0.694932	+	0.719075i
$10$	2.38192	+	5.65469i	0.753229	+	1.78817i
$11$	1.84882	+	2.05333i	0.557441	+	0.619101i	0.954326	−	0.298767i	$-0.0965755\pi$
$11$	1.84882	+	2.05333i	0.557441	+	0.619101i	−0.396885	+	0.917868i	$0.629909\pi$
$12$	9.15995	−	2.79857i	2.64425	−	0.807878i
$13$	1.13315	−	1.25849i	0.314279	−	0.349042i	−0.565222	−	0.824939i	$-0.691210\pi$
$13$	1.13315	−	1.25849i	0.314279	−	0.349042i	0.879501	+	0.475896i	$0.157876\pi$
$14$	4.99875	−	1.06252i	1.33597	−	0.283970i
$15$	0.258789	+	3.86433i	0.0668191	+	0.997765i
$16$	−15.1801	−	3.22664i	−3.79503	−	0.806659i
$17$	−5.11464	+	3.71600i	−1.24048	+	0.901263i	−0.997630	−	0.0688008i	$-0.978083\pi$
$17$	−5.11464	+	3.71600i	−1.24048	+	0.901263i	−0.242851	+	0.970064i	$0.578083\pi$
$18$	8.22703	+	0.290429i	1.93913	+	0.0684547i
$19$	1.23445	−	0.896882i	0.283203	−	0.205759i	−0.437110	−	0.899408i	$-0.643998\pi$
$19$	1.23445	−	0.896882i	0.283203	−	0.205759i	0.720313	+	0.693649i	$0.243998\pi$
$20$	5.25654	−	11.1921i	1.17540	−	2.50263i
$21$	3.20159	+	0.393724i	0.698645	+	0.0859177i
$22$	0.792522	−	7.54034i	0.168966	−	1.60761i
$23$	−0.478689	+	0.101749i	−0.0998136	+	0.0212160i	−0.257548	−	0.966266i	$-0.582914\pi$
$23$	−0.478689	+	0.101749i	−0.0998136	+	0.0212160i	0.157734	+	0.987482i	$0.449581\pi$
$24$	−14.3788	−	8.64335i	−2.93505	−	1.76432i
$25$	3.92304	+	3.09996i	0.784608	+	0.619992i
$26$	−4.64695			−0.911343
$27$	4.84996	+	1.86490i	0.933376	+	0.358901i
$28$	−8.33169	−	6.05333i	−1.57454	−	1.14397i
$29$	1.65287	−	0.735904i	0.306930	−	0.136654i	−0.247492	−	0.968890i	$-0.579606\pi$
$29$	1.65287	−	0.735904i	0.306930	−	0.136654i	0.554421	+	0.832236i	$0.312940\pi$
$30$	7.40507	−	7.62313i	1.35198	−	1.39179i
$31$	−2.49743	−	1.11193i	−0.448552	−	0.199708i	0.170013	−	0.985442i	$-0.445619\pi$
$31$	−2.49743	−	1.11193i	−0.448552	−	0.199708i	−0.618565	+	0.785734i	$0.712286\pi$
$32$	11.6068	+	20.1036i	2.05182	+	3.55385i
$33$	2.02335	−	4.33693i	0.352219	−	0.754962i
$34$	16.9689	+	3.60685i	2.91014	+	0.618570i
$35$	3.15040	−	2.72341i	0.532516	−	0.460340i
$36$	−10.6587	−	12.7123i	−1.77644	−	2.11872i
$37$	1.30318	+	4.01076i	0.214241	+	0.659366i	0.999207	+	0.0398264i	$0.0126805\pi$
$37$	1.30318	+	4.01076i	0.214241	+	0.659366i	−0.784966	+	0.619539i	$0.787319\pi$
$38$	−4.09556	−	0.870538i	−0.664387	−	0.141220i
$39$	−2.77318	−	0.955473i	−0.444064	−	0.152998i
$40$	−20.7296	+	6.27529i	−3.27763	+	0.992210i
$41$	−2.54252	+	2.82375i	−0.397075	+	0.440996i	−0.908217	−	0.418500i	$-0.862556\pi$
$41$	−2.54252	+	2.82375i	−0.397075	+	0.440996i	0.511142	+	0.859496i	$0.329223\pi$
$42$	−5.07564	−	7.25170i	−0.783188	−	1.11896i
$43$	−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
$45$	5.98657	−	3.02671i	0.892425	−	0.451195i
$46$	1.08642	+	0.789333i	0.160184	+	0.116381i
$47$	−5.86186	+	2.60987i	−0.855040	+	0.380688i	−0.786969	−	0.616992i	$-0.788351\pi$
$47$	−5.86186	+	2.60987i	−0.855040	+	0.380688i	−0.0680708	+	0.997680i	$0.521684\pi$
$48$	5.12396	+	26.3873i	0.739579	+	3.80868i
$49$	1.76580	+	3.05845i	0.252257	+	0.436922i
$50$	−0.881677	−	13.6919i	−0.124688	−	1.93633i
$51$	9.38499	+	5.64150i	1.31416	+	0.789968i
$52$	6.26611	+	6.95922i	0.868953	+	0.965070i
$53$	4.80881	+	3.49380i	0.660540	+	0.479911i	0.866845	−	0.498577i	$-0.166144\pi$
$53$	4.80881	+	3.49380i	0.660540	+	0.479911i	−0.206305	+	0.978488i	$0.566144\pi$
$54$	−5.10219	−	13.3144i	−0.694321	−	1.81186i
$55$	−2.39838	−	5.69379i	−0.323398	−	0.767750i
$56$	1.88558	+	17.9401i	0.251971	+	2.39734i
$57$	−2.26513	−	1.36161i	−0.300024	−	0.180350i
$58$	−4.53555	−	2.01936i	−0.595547	−	0.265155i
$59$	−6.79693	+	7.54876i	−0.884885	+	0.982764i	−0.999944	−	0.0105943i	$-0.996628\pi$
$59$	−6.79693	+	7.54876i	−0.884885	+	0.982764i	0.115059	+	0.993359i	$0.463294\pi$
$60$	−21.4016	−	0.810453i	−2.76293	−	0.104629i
$61$	4.87810	+	5.41768i	0.624577	+	0.693663i	0.969534	−	0.244955i	$-0.0787732\pi$
$61$	4.87810	+	5.41768i	0.624577	+	0.693663i	−0.344957	+	0.938618i	$0.612107\pi$
$62$	2.31813	+	7.13448i	0.294403	+	0.906079i
$63$	−1.53797	−	5.37124i	−0.193766	−	0.676713i
$64$	10.0928	−	31.0624i	1.26160	−	3.88280i
$65$	−3.31697	+	1.82670i	−0.411419	+	0.226574i
$66$	−12.5591	+	3.83709i	−1.54592	+	0.472313i
$67$	−7.98812	−	3.55654i	−0.975904	−	0.434500i	−0.144096	−	0.989564i	$-0.546027\pi$
$67$	−7.98812	−	3.55654i	−0.975904	−	0.434500i	−0.831808	+	0.555063i	$0.812694\pi$
$68$	−17.4799	−	30.2760i	−2.11975	−	3.67151i
$69$	0.486052	+	0.694436i	0.0585138	+	0.0836002i
$70$	−11.3382	−	1.42386i	−1.35517	−	0.170184i
$71$	2.74292	+	1.99285i	0.325524	+	0.236507i	0.738529	−	0.674222i	$-0.235521\pi$
$71$	2.74292	+	1.99285i	0.325524	+	0.236507i	−0.413005	+	0.910729i	$0.635521\pi$
$72$	−4.05504	+	28.7737i	−0.477892	+	3.39101i
$73$	4.80018	−	14.7734i	0.561818	−	1.72910i	−0.115403	−	0.993319i	$-0.536816\pi$
$73$	4.80018	−	14.7734i	0.561818	−	1.72910i	0.677221	−	0.735780i	$-0.263184\pi$
$74$	5.78606	−	10.0218i	0.672616	−	1.16501i
$75$	2.28907	−	8.35226i	0.264319	−	0.964435i
$76$	4.21888	+	7.30732i	0.483939	+	0.838207i
$77$	−5.03331	+	1.06986i	−0.573599	+	0.121922i
$78$	3.14349	+	7.40952i	0.355930	+	0.838963i
$79$	−11.7217	+	5.21885i	−1.31880	+	0.587166i	−0.940901	−	0.338682i	$-0.890019\pi$
$79$	−11.7217	+	5.21885i	−1.31880	+	0.587166i	−0.377896	+	0.925848i	$0.623352\pi$
$80$	29.6962	+	17.9548i	3.32014	+	2.00740i
$81$	−0.307250	−	8.99475i	−0.0341389	−	0.999417i
$82$	10.4267			1.15143
$83$	0.0919281	+	0.874638i	0.0100904	+	0.0960040i	0.998408	−	0.0564046i	$-0.0179637\pi$
$83$	0.0919281	+	0.874638i	0.0100904	+	0.0960040i	−0.988318	+	0.152409i	$0.951297\pi$
$84$	−4.01589	+	17.3797i	−0.438170	+	1.89628i
$85$	13.5301	−	4.09587i	1.46755	−	0.444259i
$86$	28.4981	−	6.05745i	3.07303	−	0.653192i
$87$	−2.29149	−	2.13767i	−0.245674	−	0.229182i
$88$	26.1778	+	5.56427i	2.79057	+	0.593153i
$89$	1.51233	−	4.65447i	0.160306	−	0.493372i	−0.838353	−	0.545127i	$-0.816481\pi$
$89$	1.51233	−	4.65447i	0.160306	−	0.493372i	0.998660	+	0.0517547i	$0.0164814\pi$
$90$	−17.1643	−	6.65055i	−1.80927	−	0.701029i
$91$	0.974593	+	2.99949i	0.102165	+	0.314432i
$92$	−0.282875	−	2.69138i	−0.0294918	−	0.280595i
$93$	−0.0835387	+	4.73431i	−0.00866256	+	0.490925i
$94$	16.0852	+	7.16161i	1.65907	+	0.738664i
$95$	−3.26559	+	0.988565i	−0.335042	+	0.101425i
$96$	24.2034	−	32.1063i	2.47025	−	3.27684i
$97$	−3.46928	+	1.54462i	−0.352252	+	0.156833i	−0.575232	−	0.817990i	$-0.695088\pi$
$97$	−3.46928	+	1.54462i	−0.352252	+	0.156833i	0.222980	+	0.974823i	$0.428422\pi$
$98$	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	$0.0591146\pi$
$102$	−5.72774	−	29.4967i	−0.567131	−	2.92060i
$103$	0.160690	−	1.52886i	0.0158332	−	0.150643i	−0.983749	−	0.179550i	$-0.942536\pi$
$103$	0.160690	−	1.52886i	0.0158332	−	0.150643i	0.999582	+	0.0289066i	$0.00920255\pi$
$104$	1.71457	−	16.3131i	0.168128	−	1.59963i
$105$	−6.47358	−	3.18100i	−0.631757	−	0.310434i
$106$	−1.70493	−	16.2213i	−0.165597	−	1.57555i
$107$	−14.6327			−1.41460			−0.707299	−	0.706914i	$-0.750087\pi$
$107$	−14.6327			−1.41460			−0.707299	+	0.706914i	$0.750087\pi$
$108$	−13.0595	+	25.5945i	−1.25665	+	2.46284i
$109$	0.620591	+	1.90998i	0.0594418	+	0.182943i	0.976368	−	0.216113i	$-0.0693379\pi$
$109$	0.620591	+	1.90998i	0.0594418	+	0.182943i	−0.916927	+	0.399056i	$0.869338\pi$
$110$	−7.20718	+	15.3454i	−0.687178	+	1.46312i
$111$	5.51357	−	4.79103i	0.523325	−	0.454745i
$112$	19.3396	−	21.4788i	1.82742	−	2.02955i
$113$	−8.93496	+	9.92328i	−0.840530	+	0.933503i	−0.998545	−	0.0539335i	$-0.982824\pi$
$113$	−8.93496	+	9.92328i	−0.840530	+	0.933503i	0.158014	+	0.987437i	$0.449491\pi$
$114$	1.38243	+	7.11921i	0.129476	+	0.666775i
$115$	1.08577	+	0.136352i	0.101248	+	0.0127149i
$116$	3.09173	+	9.51536i	0.287060	+	0.883479i
$117$	0.352462	+	5.06815i	0.0325851	+	0.468551i
$118$	27.8737			2.56598
$119$	−1.23071	−	11.7094i	−0.112819	−	1.07340i
$120$	24.0287	+	28.8081i	2.19351	+	2.62981i
$121$	0.351813	−	3.34727i	0.0319830	−	0.304298i
$122$	2.09106	−	19.8951i	0.189316	−	1.80122i
$123$	6.22237	+	2.14386i	0.561052	+	0.193305i
$124$	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	−0.855026	−	0.518585i	$-0.826459\pi$
$127$	1.59486	−	4.90847i	0.141521	−	0.435556i	0.996547	+	0.0830282i	$0.0264591\pi$
$128$	−39.4615	+	17.5694i	−3.48794	+	1.55293i
$129$	18.2524	+	2.24464i	1.60703	+	0.197629i
$130$	9.81544	+	3.40999i	0.860871	+	0.299076i
$131$	−10.9163	−	4.86025i	−0.953761	−	0.424642i	−0.129959	−	0.991519i	$-0.541485\pi$
$131$	−10.9163	−	4.86025i	−0.953761	−	0.424642i	−0.823802	+	0.566878i	$0.808151\pi$
$132$	22.6815	+	13.6343i	1.97417	+	1.18671i
$133$	0.297041	+	2.82615i	0.0257567	+	0.245058i
$134$	7.41462	+	22.8199i	0.640526	+	1.97134i
$135$	−8.87575	−	7.49807i	−0.763903	−	0.645331i
$136$	−18.9228	+	58.2383i	−1.62261	+	4.99389i
$137$	4.23928	+	0.901088i	0.362187	+	0.0769851i	0.385411	−	0.922745i	$-0.374060\pi$
$137$	4.23928	+	0.901088i	0.362187	+	0.0769851i	−0.0232241	+	0.999730i	$0.507393\pi$
$138$	0.523658	−	2.26625i	0.0445767	−	0.192916i
$139$	−13.0288	+	2.76935i	−1.10508	+	0.234893i	−0.724105	−	0.689690i	$-0.757747\pi$
$139$	−13.0288	+	2.76935i	−1.10508	+	0.234893i	−0.380980	+	0.924583i	$0.624413\pi$
$140$	13.1565	+	18.8999i	1.11192	+	1.59734i
$141$	8.12674	+	7.58120i	0.684395	+	0.638452i
$142$	−0.972483	−	9.25256i	−0.0816090	−	0.776457i
$143$	4.67908			0.391284
$144$	38.6081	−	26.0201i	3.21734	−	2.16834i
$145$	−4.03125	+	0.341505i	−0.334777	+	0.0283604i
$146$	−38.9401	+	17.3373i	−3.22271	+	1.43484i
$147$	3.68218	−	4.88448i	0.303701	−	0.402865i
$148$	−22.8106	+	4.84854i	−1.87502	+	0.398547i
$149$	−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	$0.870640\pi$
$150$	−21.2352	+	10.6679i	−1.73384	+	0.871029i
$151$	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
$153$	2.64672	−	18.7805i	0.213975	−	1.51832i
$154$	11.4235	+	8.29965i	0.920531	+	0.668805i
$155$	4.45921	+	4.18130i	0.358172	+	0.335850i
$156$	6.85762	−	14.6989i	0.549049	−	1.17685i
$157$	−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	$-0.362665\pi$
$158$	32.1650	+	14.3208i	2.55891	+	1.13930i
$159$	2.31785	−	10.0310i	0.183818	−	0.795512i
$160$	−9.76402	−	50.9807i	−0.771914	−	4.03038i
$161$	0.281641	−	0.866803i	0.0221964	−	0.0683136i
$162$	−17.7782	+	17.1421i	−1.39679	+	1.34681i
$163$	2.58162	+	7.94542i	0.202208	+	0.622333i	0.999816	+	0.0191571i	$0.00609828\pi$
$163$	2.58162	+	7.94542i	0.202208	+	0.622333i	−0.797608	+	0.603176i	$0.793902\pi$
$164$	−14.0597	−	15.6149i	−1.09788	−	1.21932i
$165$	−7.45627	+	7.67583i	−0.580469	+	0.597563i
$166$	1.61479	−	1.79341i	0.125332	−	0.139196i
$167$	10.3354	+	4.60161i	0.799776	+	0.356083i	0.765587	−	0.643332i	$-0.222449\pi$
$167$	10.3354	+	4.60161i	0.799776	+	0.356083i	0.0341890	+	0.999415i	$0.489115\pi$
$168$	27.3297	−	15.1423i	2.10853	−	1.16826i
$169$	1.05910	+	10.0767i	0.0814693	+	0.775129i
$170$	−33.1955	−	20.0705i	−2.54598	−	1.53934i
$171$	−0.638803	+	4.53281i	−0.0488505	+	0.346632i
$172$	−47.4993	−	34.5103i	−3.62179	−	2.63139i
$173$	4.25476	+	4.72538i	0.323483	+	0.359264i	0.882849	−	0.469656i	$-0.155622\pi$
$173$	4.25476	+	4.72538i	0.323483	+	0.359264i	−0.559366	+	0.828921i	$0.688955\pi$
$174$	−0.151713	+	8.59791i	−0.0115014	+	0.651806i
$175$	−8.65285	+	3.44066i	−0.654094	+	0.260090i
$176$	−21.4400	−	37.1352i	−1.61610	−	2.79917i
$177$	16.6343	+	5.73118i	1.25031	+	0.430782i
$178$	−12.2683	+	5.46222i	−0.919551	+	0.409411i
$179$	5.40088	+	3.92397i	0.403681	+	0.293291i	0.771039	−	0.636788i	$-0.219738\pi$
$179$	5.40088	+	3.92397i	0.403681	+	0.293291i	−0.367358	+	0.930080i	$0.619738\pi$
$180$	13.1851	+	34.6728i	0.982759	+	2.58436i
$181$	5.85623	−	4.25480i	0.435290	−	0.316257i	−0.348470	−	0.937320i	$-0.613299\pi$
$181$	5.85623	−	4.25480i	0.435290	−	0.316257i	0.783761	+	0.621063i	$0.213299\pi$
$182$	4.32716	−	7.49486i	0.320751	−	0.555556i
$183$	5.33859	−	11.4430i	0.394640	−	0.845887i
$184$	−3.17179	+	3.52263i	−0.233828	+	0.259692i
$185$	0.190539	−	9.42795i	0.0140087	−	0.693157i
$186$	9.80772	−	8.52245i	0.719137	−	0.624896i
$187$	−17.0862	−	3.63179i	−1.24947	−	0.265583i
$188$	−10.9647	−	33.7460i	−0.799686	−	2.46118i
$189$	−7.52402	+	6.08572i	−0.547292	+	0.442671i
$190$	8.01195	+	4.84415i	0.581248	+	0.351431i
$191$	−1.11059	−	0.236063i	−0.0803593	−	0.0170809i	0.167557	−	0.985862i	$-0.446412\pi$
$191$	−1.11059	−	0.236063i	−0.0803593	−	0.0170809i	−0.247916	+	0.968782i	$0.579746\pi$
$192$	−56.3561	+	4.91972i	−4.06715	+	0.355050i
$193$	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	$0.798034\pi$
$194$	9.51989	+	4.23853i	0.683488	+	0.304309i
$195$	5.15646	+	4.05317i	0.369262	+	0.290254i
$196$	−17.8407	+	7.94320i	−1.27434	+	0.567372i
$197$	18.8592	+	13.7020i	1.34366	+	0.976227i	0.999301	+	0.0373893i	$0.0119042\pi$
$197$	18.8592	+	13.7020i	1.34366	+	0.976227i	0.344360	+	0.938838i	$0.388096\pi$
$198$	14.6140	+	17.4297i	1.03857	+	1.23868i
$199$	−18.6167			−1.31970			−0.659851	−	0.751396i	$-0.729381\pi$
$199$	−18.6167			−1.31970			−0.659851	+	0.751396i	$0.729381\pi$
$200$	48.3905	+	1.95674i	3.42173	+	0.138363i
$201$	−0.267201	+	15.1428i	−0.0188469	+	1.06809i
$202$	−17.8838	+	3.80133i	−1.25830	+	0.267460i
$203$	−0.352214	+	3.35110i	−0.0247206	+	0.235201i
$204$	−36.4503	+	48.3521i	−2.55203	+	3.38532i
$205$	7.44250	−	4.09869i	0.519806	−	0.286265i
$206$	−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
$209$	4.12387	+	0.876556i	0.285254	+	0.0606326i
$210$	5.39954	+	19.0418i	0.372603	+	1.31401i
$211$	11.2610	−	2.39359i	0.775237	−	0.164782i	0.196728	−	0.980458i	$-0.436968\pi$
$211$	11.2610	−	2.39359i	0.775237	−	0.164782i	0.578509	+	0.815676i	$0.303635\pi$
$212$	−21.9939	+	24.4267i	−1.51054	+	1.67763i
$213$	1.32209	−	5.72164i	0.0905882	−	0.392040i
$214$	26.8676	+	29.8395i	1.83663	+	2.03978i
$215$	17.9606	−	15.5263i	1.22490	−	1.05888i
$216$	48.6225	−	12.9986i	3.30834	−	0.884443i
$217$	4.11894	−	2.99259i	0.279612	−	0.203150i
$218$	2.75541	−	4.77250i	0.186620	−	0.323235i
$219$	−26.8032	+	2.33984i	−1.81119	+	0.158112i
$220$	32.6995	−	9.89884i	2.20460	−	0.667380i
$221$	−1.11910	+	10.6475i	−0.0752786	+	0.716228i
$222$	−19.8936	−	2.44647i	−1.33517	−	0.164197i
$223$	−1.36992	−	1.52145i	−0.0917364	−	0.101884i	0.695529	−	0.718498i	$-0.255170\pi$
$223$	−1.36992	−	1.52145i	−0.0917364	−	0.101884i	−0.787265	+	0.616615i	$0.788504\pi$
$224$	−43.2323			−2.88858
$225$	−14.8661	+	2.00009i	−0.991070	+	0.133340i
$226$	36.6416			2.43736
$227$	10.1691	+	11.2940i	0.674949	+	0.749607i	0.979181	−	0.202991i	$-0.0650663\pi$
$227$	10.1691	+	11.2940i	0.674949	+	0.749607i	−0.304231	+	0.952598i	$0.598400\pi$
$228$	8.79753	−	11.6701i	0.582631	−	0.772871i
$229$	0.0219935	−	0.209254i	0.00145337	−	0.0138279i	−0.993771	−	0.111440i	$-0.964454\pi$
$229$	0.0219935	−	0.209254i	0.00145337	−	0.0138279i	0.995225	+	0.0976120i	$0.0311204\pi$
$230$	−1.71555	−	2.46448i	−0.113120	−	0.162503i
$231$	5.11073	+	7.30183i	0.336261	+	0.480425i
$232$	8.76239	−	15.1769i	0.575279	−	0.996413i
$233$	−13.5683	+	9.85792i	−0.888887	+	0.645814i	−0.935587	−	0.353095i	$-0.885129\pi$
$233$	−13.5683	+	9.85792i	−0.888887	+	0.645814i	0.0467009	+	0.998909i	$0.485129\pi$
$234$	9.68795	−	10.0245i	0.633321	−	0.655324i
$235$	14.2968	−	1.21114i	0.932617	−	0.0790060i
$236$	−37.5858	−	41.7433i	−2.44663	−	2.71726i
$237$	16.2507	+	15.1598i	1.05560	+	0.984736i
$238$	−21.6185	+	24.0098i	−1.40132	+	1.55632i
$239$	24.1536	−	5.13400i	1.56237	−	0.332091i	0.656058	−	0.754710i	$-0.272223\pi$
$239$	24.1536	−	5.13400i	1.56237	−	0.332091i	0.906307	+	0.422619i	$0.138889\pi$
$240$	8.54033	−	59.4960i	0.551276	−	3.84045i
$241$	2.97638	+	0.632648i	0.191725	+	0.0407524i	0.302773	−	0.953063i	$-0.402087\pi$
$241$	2.97638	+	0.632648i	0.191725	+	0.0407524i	−0.111048	+	0.993815i	$0.535421\pi$
$242$	−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
$245$	−1.48544	−	7.75593i	−0.0949016	−	0.495508i
$246$	−7.05326	−	16.6252i	−0.449699	−	1.05999i
$247$	0.270102	−	2.56984i	0.0171862	−	0.163515i
$248$	−25.9008	+	5.50538i	−1.64470	+	0.349592i
$249$	1.33242	−	0.738238i	0.0844384	−	0.0467840i
$250$	−8.18498	+	29.5674i	−0.517664	+	1.87001i
$251$	−24.9480			−1.57470			−0.787352	−	0.616504i	$-0.788548\pi$
$251$	−24.9480			−1.57470			−0.787352	+	0.616504i	$0.788548\pi$
$252$	30.4283	−	5.35339i	1.91680	−	0.337232i
$253$	−1.09393	−	0.794789i	−0.0687750	−	0.0499680i
$254$	−12.9379	+	5.76031i	−0.811793	+	0.361434i
$255$	−15.6835	−	18.8030i	−0.982136	−	1.17749i
$256$	48.6099	+	21.6425i	3.03812	+	1.35266i
$257$	−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	$0.876209\pi$
$258$	−28.9364	−	41.3423i	−1.80150	−	2.57386i
$259$	−7.68228	−	1.63292i	−0.477353	−	0.101465i
$260$	−8.12871	−	19.2976i	−0.504121	−	1.19679i
$261$	−1.85838	+	5.09982i	−0.115031	+	0.315671i
$262$	10.1326	+	31.1849i	0.625992	+	1.92661i
$263$	12.5266	+	2.66260i	0.772421	+	0.164183i	0.577229	−	0.816582i	$-0.304134\pi$
$263$	12.5266	+	2.66260i	0.772421	+	0.164183i	0.195191	+	0.980765i	$0.437467\pi$
$264$	−8.83615	−	45.5043i	−0.543828	−	2.80060i
$265$	−7.59351	−	10.9085i	−0.466466	−	0.670102i
$266$	5.21776	−	5.79491i	0.319922	−	0.355309i
$267$	−8.44453	+	0.737182i	−0.516797	+	0.0451148i
$268$	24.1766	−	41.8751i	1.47682	−	2.55793i
$269$	16.3393	−	11.8712i	0.996227	−	0.723801i	0.0349513	−	0.999389i	$-0.488872\pi$
$269$	16.3393	−	11.8712i	0.996227	−	0.723801i	0.961276	+	0.275588i	$0.0888724\pi$
$270$	1.00676	+	31.8671i	0.0612693	+	1.93937i
$271$	6.40204	+	4.65136i	0.388897	+	0.282550i	0.765003	−	0.644027i	$-0.222737\pi$
$271$	6.40204	+	4.65136i	0.388897	+	0.282550i	−0.376107	+	0.926576i	$0.622737\pi$
$272$	89.6311	−	39.9063i	5.43468	−	2.41968i
$273$	4.12338	−	3.58302i	0.249558	−	0.216854i
$274$	−5.94635	−	10.2994i	−0.359232	−	0.622208i
$275$	0.887772	+	13.7866i	0.0535347	+	0.831360i
$276$	−4.10002	+	2.27166i	−0.246792	+	0.136738i
$277$	0.120461	+	0.133786i	0.00723780	+	0.00803839i	0.746753	−	0.665102i	$-0.231612\pi$
$277$	0.120461	+	0.133786i	0.00723780	+	0.00803839i	−0.739515	+	0.673140i	$0.764945\pi$
$278$	29.5698	+	21.4837i	1.77348	+	1.28851i
$279$	7.60532	−	3.06938i	0.455318	−	0.183759i
$280$	9.18186	−	39.2772i	0.548721	−	2.34726i
$281$	0.170074	+	1.61814i	0.0101457	+	0.0965302i	0.998423	−	0.0561402i	$-0.0178794\pi$
$281$	0.170074	+	1.61814i	0.0101457	+	0.0965302i	−0.988277	+	0.152670i	$0.951213\pi$
$282$	0.538049	−	30.4923i	0.0320403	−	1.81579i
$283$	−3.34093	−	1.48748i	−0.198598	−	0.0884214i	0.305028	−	0.952343i	$-0.401334\pi$
$283$	−3.34093	−	1.48748i	−0.198598	−	0.0884214i	−0.503626	+	0.863922i	$0.668001\pi$
$284$	−12.5452	+	13.9328i	−0.744420	+	0.826762i
$285$	3.78531	+	4.53822i	0.224222	+	0.268821i
$286$	−8.59139	−	9.54171i	−0.508020	−	0.564213i
$287$	−2.18676	−	6.73015i	−0.129080	−	0.397268i
$288$	−67.5659	−	16.8734i	−3.98136	−	0.994274i
$289$	7.09756	−	21.8440i	0.417503	−	1.28494i
$290$	8.09831	+	7.59360i	0.475549	+	0.445911i
$291$	4.80973	+	4.48686i	0.281951	+	0.263024i
$292$	78.4722	+	34.9381i	4.59224	+	2.04460i
$293$	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	$0.579714\pi$
$294$	−16.7215	+	1.45974i	−0.975219	+	0.0851336i
$295$	19.8961	−	10.9570i	1.15839	−	0.637944i
$296$	33.0463	+	24.0096i	1.92078	+	1.39553i
$297$	5.13747	+	13.4064i	0.298106	+	0.777920i
$298$	−2.42067	+	7.45007i	−0.140226	+	0.431571i
$299$	−0.414377	+	0.717721i	−0.0239640	+	0.0415069i
$300$	44.6103	+	17.4166i	2.57558	+	1.00555i
$301$	−9.88675	−	17.1244i	−0.569863	−	0.987032i
$302$	−30.1279	+	6.40388i	−1.73367	+	0.368502i
$303$	−11.4542	−	1.40861i	−0.658027	−	0.0809227i
$304$	−21.6331	+	9.63166i	−1.24074	+	0.552413i
$305$	−6.32812	−	15.0230i	−0.362347	−	0.860215i
$306$	−43.1575	+	29.0862i	−2.46715	+	1.66275i
$307$	3.80945			0.217417			0.108708	−	0.994074i	$-0.465329\pi$
$307$	3.80945			0.217417			0.108708	+	0.994074i	$0.465329\pi$
$308$	−2.97437	−	28.2992i	−0.169480	−	1.61250i
$309$	−2.54646	+	0.778000i	−0.144863	+	0.0442589i
$310$	0.338936	−	16.7707i	0.0192503	−	0.952514i
$311$	24.6629	−	5.24225i	1.39850	−	0.297261i	0.553868	−	0.832604i	$-0.313151\pi$
$311$	24.6629	−	5.24225i	1.39850	−	0.297261i	0.844634	+	0.535344i	$0.179818\pi$
$312$	−27.1708	+	8.30131i	−1.53825	+	0.469969i
$313$	−25.3750	−	5.39362i	−1.43428	−	0.304865i	−0.575748	−	0.817627i	$-0.695289\pi$
$313$	−25.3750	−	5.39362i	−1.43428	−	0.304865i	−0.858531	+	0.512762i	$0.828622\pi$
$314$	−12.2732	+	37.7731i	−0.692618	+	2.13166i
$315$	−0.692942	+	12.4739i	−0.0390428	+	0.702824i
$316$	−21.9258	−	67.4806i	−1.23342	−	3.79608i
$317$	2.39991	+	22.8336i	0.134792	+	1.28246i	0.827591	+	0.561331i	$0.189711\pi$
$317$	2.39991	+	22.8336i	0.134792	+	1.28246i	−0.692799	+	0.721131i	$0.743623\pi$
$318$	−24.7114	+	13.6916i	−1.38575	+	0.767788i
$319$	4.56691	+	2.03332i	0.255698	+	0.113844i
$320$	−44.1123	+	58.2048i	−2.46595	+	3.25375i
$321$	9.89849	+	23.3317i	0.552480	+	1.30225i
$322$	−2.28474	+	1.01723i	−0.127323	+	0.0566880i
$323$	−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
$327$	2.62564	−	2.28156i	0.145198	−	0.126170i
$328$	−3.84710	+	36.6027i	−0.212420	+	2.02104i
$329$	1.24912	−	11.8846i	0.0688663	−	0.655219i
$330$	29.3434	+	1.11120i	1.61530	+	0.0611697i
$331$	−0.643087	−	6.11857i	−0.0353473	−	0.336307i	−0.997877	−	0.0651299i	$-0.979254\pi$
$331$	−0.643087	−	6.11857i	−0.0353473	−	0.336307i	0.962530	−	0.271177i	$-0.0874128\pi$
$332$	−4.86323			−0.266904
$333$	−11.3690	−	5.55038i	−0.623016	−	0.304159i
$334$	−9.59337	−	29.5254i	−0.524926	−	1.61556i
$335$	14.2629	+	13.3740i	0.779266	+	0.730700i
$336$	−47.3302	−	16.3072i	−2.58207	−	0.889629i
$337$	−10.0778	+	11.1925i	−0.548972	+	0.609695i	−0.952227	−	0.305393i	$-0.901212\pi$
$337$	−10.0778	+	11.1925i	−0.548972	+	0.609695i	0.403254	+	0.915088i	$0.367879\pi$
$338$	18.6040	−	20.6618i	1.01192	−	1.12385i
$339$	21.8667	+	7.53397i	1.18764	+	0.409189i
$340$	14.7046	+	76.7769i	0.797469	+	4.16381i
$341$	−2.33416	−	7.18380i	−0.126402	−	0.389024i
$342$	10.4164	−	7.02015i	0.563252	−	0.379606i
$343$	−19.6137			−1.05904
$344$	10.7498	+	102.277i	0.579588	+	5.51441i
$345$	−0.517069	−	1.82348i	−0.0278381	−	0.0981729i
$346$	1.82386	−	17.3528i	0.0980511	−	0.932894i
$347$	1.75900	−	16.7357i	0.0944278	−	0.898421i	−0.840076	−	0.542468i	$-0.817490\pi$
$347$	1.75900	−	16.7357i	0.0944278	−	0.898421i	0.934504	−	0.355953i	$-0.115844\pi$
$348$	13.0807	−	11.3665i	0.701199	−	0.609309i
$349$	−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
$353$	8.58398	−	3.82183i	0.456879	−	0.203416i	−0.165375	−	0.986231i	$-0.552884\pi$
$353$	8.58398	−	3.82183i	0.456879	−	0.203416i	0.622254	+	0.782815i	$0.286217\pi$
$354$	−18.8555	−	44.4443i	−1.00216	−	2.36219i
$355$	−4.33130	−	6.22214i	−0.229882	−	0.330237i
$356$	24.7232	+	11.0075i	1.31033	+	0.583395i
$357$	−17.8381	+	9.88336i	−0.944090	+	0.523083i
$358$	−1.91485	−	18.2185i	−0.101203	−	0.962880i
$359$	−2.47394	−	7.61399i	−0.130569	−	0.401851i	0.864305	−	0.502968i	$-0.167759\pi$
$359$	−2.47394	−	7.61399i	−0.130569	−	0.401851i	−0.994875	+	0.101116i	$0.967759\pi$
$360$	29.6797	−	57.8010i	1.56426	−	3.04638i
$361$	−5.15185	+	15.8558i	−0.271150	+	0.834514i
$362$	−19.4293	−	4.12983i	−1.02118	−	0.217059i
$363$	−5.57518	+	1.70334i	−0.292621	+	0.0894024i
$364$	−17.0591	+	3.62602i	−0.894140	+	0.190055i
$365$	−20.9800	+	27.6825i	−1.09814	+	1.44897i
$366$	−33.1371	+	10.1241i	−1.73210	+	0.529197i
$367$	−2.76047	−	26.2641i	−0.144095	−	1.37098i	−0.792589	−	0.609757i	$-0.791267\pi$
$367$	−2.76047	−	26.2641i	−0.144095	−	1.37098i	0.648493	−	0.761220i	$-0.275399\pi$
$368$	7.59487			0.395910
$369$	−0.790842	−	11.3717i	−0.0411696	−	0.591989i
$370$	−19.5756	+	16.9224i	−1.01769	+	0.879752i
$371$	−10.1129	+	4.50254i	−0.525034	+	0.233760i
$372$	−25.9882	−	3.19597i	−1.34742	−	0.165703i
$373$	20.3189	−	4.31891i	1.05207	−	0.223625i	0.350749	−	0.936469i	$-0.385927\pi$
$373$	20.3189	−	4.31891i	1.05207	−	0.223625i	0.701322	+	0.712845i	$0.252594\pi$
$374$	23.9665	+	41.5111i	1.23928	+	2.14649i
$375$	−10.9640	+	15.9621i	−0.566180	+	0.824282i
$376$	−31.0756	+	53.8246i	−1.60260	+	2.77579i
$377$	0.946817	−	2.91400i	0.0487636	−	0.150079i
$378$	26.2252	+	4.16902i	1.34888	+	0.214431i
$379$	15.5059	+	11.2657i	0.796485	+	0.578680i	0.909881	−	0.414870i	$-0.136173\pi$
$379$	15.5059	+	11.2657i	0.796485	+	0.578680i	−0.113396	+	0.993550i	$0.536173\pi$
$380$	−3.54905	−	18.5306i	−0.182063	−	0.950601i
$381$	−8.90537	+	0.777412i	−0.456236	+	0.0398280i
$382$	1.55780	+	2.69818i	0.0797038	+	0.138051i
$383$	−22.0779	−	9.82970i	−1.12813	−	0.502274i	−0.244118	−	0.969746i	$-0.578498\pi$
$383$	−22.0779	−	9.82970i	−1.12813	−	0.502274i	−0.884008	+	0.467471i	$0.845165\pi$
$384$	54.7085	+	51.0360i	2.79183	+	2.60442i
$385$	11.4166	+	1.43371i	0.581843	+	0.0730684i
$386$	2.60740	−	8.02476i	0.132713	−	0.408449i
$387$	−8.76802	−	30.6217i	−0.445704	−	1.55659i
$388$	−6.48938	−	19.9722i	−0.329448	−	1.01394i
$389$	−25.2326	−	28.0236i	−1.27934	−	1.42086i	−0.857747	−	0.514072i	$-0.828137\pi$
$389$	−25.2326	−	28.0236i	−1.27934	−	1.42086i	−0.421596	−	0.906784i	$-0.638530\pi$
$390$	−1.20258	−	17.9574i	−0.0608951	−	0.909306i
$391$	2.07022	−	2.29922i	0.104696	−	0.116276i
$392$	31.2497	+	13.9133i	1.57835	+	0.702727i
$393$	−0.365148	+	20.6937i	−0.0184193	+	1.04386i
$394$	−6.68640	−	63.6168i	−0.336856	−	3.20497i
$395$	28.5887	−	2.42187i	1.43845	−	0.121857i
$396$	6.39655	−	45.3885i	0.321439	−	2.28086i
$397$	22.7545	+	16.5321i	1.14202	+	0.829724i	0.987399	−	0.158251i	$-0.0505855\pi$
$397$	22.7545	+	16.5321i	1.14202	+	0.829724i	0.154618	+	0.987974i	$0.450585\pi$
$398$	34.1827	+	37.9637i	1.71342	+	1.90295i
$399$	4.30533	−	2.38542i	0.215536	−	0.119420i
$400$	−49.5498	−	59.7161i	−2.47749	−	2.98580i
$401$	−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	$-0.366898\pi$
$402$	31.3703	−	27.2593i	1.56461	−	1.35957i
$403$	−4.22931	+	1.88301i	−0.210677	+	0.0937995i
$404$	29.8080	+	21.6568i	1.48300	+	1.07746i
$405$	−5.95148	+	19.2245i	−0.295731	+	0.955271i
$406$	7.48036	−	5.43480i	0.371244	−	0.269725i
$407$	−5.82606	+	10.0910i	−0.288787	+	0.500194i
$408$	105.661	−	9.22387i	5.23099	−	0.456650i
$409$	7.03120	−	7.80894i	0.347670	−	0.386127i	−0.543793	−	0.839219i	$-0.683012\pi$
$409$	7.03120	−	7.80894i	0.347670	−	0.386127i	0.891464	+	0.453092i	$0.149679\pi$
$410$	−22.0235	−	7.65122i	−1.08767	−	0.377867i
$411$	−1.43094	−	7.36905i	−0.0705832	−	0.363488i
$412$	8.31513	+	1.76744i	0.409657	+	0.0870753i
$413$	−5.84587	−	17.9917i	−0.287656	−	0.885315i
$414$	−3.96774	+	0.698063i	−0.195004	+	0.0343079i
$415$	0.447647	−	1.91490i	0.0219741	−	0.0939985i
$416$	38.4525	+	8.17332i	1.88529	+	0.400730i
$417$	13.2292	+	18.9009i	0.647835	+	0.925579i
$418$	−5.78446	−	10.0190i	−0.282927	−	0.490045i
$419$	8.64814	+	3.85040i	0.422489	+	0.188104i	0.606958	−	0.794734i	$-0.292390\pi$
$419$	8.64814	+	3.85040i	0.422489	+	0.188104i	−0.184468	+	0.982838i	$0.559056\pi$
$420$	21.2359	−	33.7629i	1.03621	−	1.64746i
$421$	−6.18495	+	2.75372i	−0.301436	+	0.134208i	−0.551881	−	0.833923i	$-0.686090\pi$
$421$	−6.18495	+	2.75372i	−0.301436	+	0.134208i	0.250445	+	0.968131i	$0.419423\pi$
$422$	−25.5577	−	18.5687i	−1.24413	−	0.903912i
$423$	6.59071	−	18.0864i	0.320451	−	0.879391i
$424$	57.5737			2.79603
$425$	−31.5844	−	1.27716i	−1.53207	−	0.0619515i
$426$	−14.0953	+	7.80963i	−0.682918	+	0.378378i
$427$	−13.2803	+	2.82282i	−0.642681	+	0.136606i
$428$	8.45806	−	80.4730i	0.408836	−	3.88981i
$429$	−3.16522	−	7.46074i	−0.152818	−	0.360208i
$430$	−64.6396	−	8.11750i	−3.11720	−	0.391461i
$431$	−20.0354	+	14.5565i	−0.965069	+	0.701164i	−0.954322	−	0.298779i	$-0.903421\pi$
$431$	−20.0354	+	14.5565i	−0.965069	+	0.701164i	−0.0107465	+	0.999942i	$0.503421\pi$
$432$	−67.6057	−	43.9586i	−3.25268	−	2.11496i
$433$	5.18591	−	3.76779i	0.249219	−	0.181068i	−0.456162	−	0.889897i	$-0.650776\pi$
$433$	5.18591	−	3.76779i	0.249219	−	0.181068i	0.705381	+	0.708829i	$0.250776\pi$
$434$	−13.6655	−	2.90469i	−0.655964	−	0.139429i
$435$	3.27152	+	6.19678i	0.156857	+	0.297113i
$436$	−10.8627	+	2.30894i	−0.520230	+	0.110578i
$437$	−0.499662	+	0.554931i	−0.0239021	+	0.0265460i
$438$	53.9856	+	50.3616i	2.57953	+	2.40637i
$439$	−0.171740	−	0.190736i	−0.00819669	−	0.00910335i	0.739033	−	0.673670i	$-0.235283\pi$
$439$	−0.171740	−	0.190736i	−0.00819669	−	0.00910335i	−0.747229	+	0.664566i	$0.768616\pi$
$440$	−51.2105	−	30.9626i	−2.44136	−	1.47609i
$441$	−10.2791	−	2.56702i	−0.489481	−	0.122239i
$442$	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	$0.0534759\pi$
$444$	23.1614	+	33.0914i	1.09919	+	1.57045i
$445$	−6.60989	+	8.72154i	−0.313339	+	0.413441i
$446$	−0.587233	+	5.58714i	−0.0278063	+	0.264559i
$447$	−2.97643	+	3.94829i	−0.140780	+	0.186748i
$448$	40.7009	+	45.2030i	1.92294	+	2.13564i
$449$	15.5412			0.733436			0.366718	−	0.930332i	$-0.380481\pi$
$449$	15.5412			0.733436			0.366718	+	0.930332i	$0.380481\pi$
$450$	31.3746	+	26.6428i	1.47901	+	1.25596i
$451$	−10.4988			−0.494367
$452$	−49.4087	−	54.8739i	−2.32399	−	2.58105i
$453$	−19.2963	−	2.37301i	−0.906618	−	0.111494i
$454$	4.35913	−	41.4744i	0.204584	−	1.94649i
$455$	0.142496	−	7.05078i	0.00668032	−	0.330546i
$456$	−25.5020	+	2.22624i	−1.19424	+	0.104253i
$457$	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
$459$	−31.7358	+	8.48417i	−1.48130	+	0.396007i
$460$	−1.37747	+	5.89239i	−0.0642248	+	0.274734i
$461$	2.20165	+	2.44518i	0.102541	+	0.113883i	0.792231	−	0.610222i	$-0.208920\pi$
$461$	2.20165	+	2.44518i	0.102541	+	0.113883i	−0.689690	+	0.724105i	$0.742253\pi$
$462$	5.50615	−	23.8291i	0.256169	−	1.10863i
$463$	−25.5921	+	28.4229i	−1.18936	+	1.32092i	−0.254013	+	0.967201i	$0.581751\pi$
$463$	−25.5921	+	28.4229i	−1.18936	+	1.32092i	−0.935351	+	0.353721i	$0.884916\pi$
$464$	−27.4652	+	5.83792i	−1.27504	+	0.271019i
$465$	3.65055	−	9.93865i	0.169290	−	0.460894i
$466$	45.0156	+	9.56837i	2.08531	+	0.443246i
$467$	4.63677	−	3.36881i	0.214564	−	0.155890i	−0.475312	−	0.879817i	$-0.657665\pi$
$467$	4.63677	−	3.36881i	0.214564	−	0.155890i	0.689876	+	0.723927i	$0.257665\pi$
$468$	−28.0762	−	0.991138i	−1.29782	−	0.0458154i
$469$	13.1746	−	9.57189i	0.608345	−	0.441989i
$470$	−28.7205	−	26.9305i	−1.32478	−	1.24221i
$471$	−15.0910	+	20.0185i	−0.695355	+	0.922402i
$472$	−10.2845	+	97.8501i	−0.473381	+	4.50392i
$473$	−28.6951	+	6.09933i	−1.31940	+	0.280448i
$474$	1.07591	−	60.9743i	0.0494184	−	2.80064i
$475$	7.62310	+	0.308252i	0.349772	+	0.0141436i
$476$	65.1078			2.98421
$477$	−17.5623	+	3.08982i	−0.804123	+	0.141473i
$478$	−54.8185	−	39.8280i	−2.50734	−	1.82169i
$479$	−12.3081	+	5.47992i	−0.562371	+	0.250384i	−0.668176	−	0.744003i	$-0.732925\pi$
$479$	−12.3081	+	5.47992i	−0.562371	+	0.250384i	0.105805	+	0.994387i	$0.466258\pi$
$480$	−74.6833	+	50.0552i	−3.40881	+	2.28470i
$481$	6.52420	+	2.90476i	0.297478	+	0.132446i
$482$	−4.17490	−	7.23113i	−0.190161	−	0.329369i
$483$	−1.57263	+	0.137286i	−0.0715570	+	0.00624671i
$484$	18.2051	+	3.86961i	0.827503	+	0.175891i
$485$	8.46139	−	0.716801i	0.384212	−	0.0325483i
$486$	39.3592	+	16.7512i	1.78537	+	0.759849i
$487$	−8.88128	−	27.3338i	−0.402449	−	1.23861i	−0.923006	−	0.384785i	$-0.874276\pi$
$487$	−8.88128	−	27.3338i	−0.402449	−	1.23861i	0.520557	−	0.853827i	$-0.325724\pi$
$488$	69.0700	+	14.6813i	3.12665	+	0.664590i
$489$	10.9225	−	9.49115i	0.493933	−	0.429205i
$490$	−13.0886	+	17.2700i	−0.591284	+	0.780181i
$491$	10.6856	−	11.8675i	0.482232	−	0.535573i	−0.452104	−	0.891965i	$-0.649327\pi$
$491$	10.6856	−	11.8675i	0.482232	−	0.535573i	0.934337	+	0.356392i	$0.115993\pi$
$492$	−15.3869	+	32.9809i	−0.693694	+	1.48689i
$493$	−5.71920	+	9.90594i	−0.257580	+	0.446141i
$494$	−5.73644	+	4.16777i	−0.258095	+	0.187517i
$495$	17.2829	+	6.69652i	0.776810	+	0.300986i
$496$	34.3236	+	24.9375i	1.54117	+	1.11973i
$497$	−5.76833	+	2.56823i	−0.258745	+	0.115201i
$498$	−3.95192	−	1.36160i	−0.177090	−	0.0610146i
$499$	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	$0.677615\pi$
$500$	55.3167	−	27.6120i	2.47384	−	1.23485i
$501$	0.345717	−	19.5925i	0.0154455	−	0.875328i
$502$	45.8077	+	50.8747i	2.04450	+	2.27065i
$503$	3.48380	+	2.53113i	0.155335	+	0.112857i	0.662738	−	0.748852i	$-0.269394\pi$
$503$	3.48380	+	2.53113i	0.155335	+	0.112857i	−0.507403	+	0.861709i	$0.669394\pi$
$504$	−42.6318	−	33.3338i	−1.89897	−	1.48480i
$505$	−11.2711	+	9.74344i	−0.501557	+	0.433577i
$506$	0.387847	+	3.69012i	0.0172419	+	0.164046i
$507$	15.3507	−	8.50522i	0.681749	−	0.377730i
$508$	26.0724	+	11.6082i	1.15678	+	0.515030i
$509$	28.2185	−	31.3398i	1.25076	−	1.38911i	0.361081	−	0.932535i	$-0.382408\pi$
$509$	28.2185	−	31.3398i	1.25076	−	1.38911i	0.889683	−	0.456579i	$-0.150925\pi$
$510$	−9.54669	+	66.5068i	−0.422734	+	2.94497i
$511$	19.3576	+	21.4987i	0.856328	+	0.951048i
$512$	−18.4234	−	56.7015i	−0.814209	−	2.50588i
$513$	7.65964	−	2.04771i	0.338181	−	0.0904086i
$514$	−3.65103	+	11.2367i	−0.161040	+	0.495630i
$515$	−1.46131	+	3.11139i	−0.0643931	+	0.137104i
$516$	−22.8948	+	99.0822i	−1.00789	+	4.36185i
$517$	−16.1964	−	7.21112i	−0.712319	−	0.317145i
$518$	10.7758	+	18.6642i	0.473460	+	0.820056i
$519$	4.65639	−	9.98071i	0.204393	−	0.438105i
$520$	−15.5923	+	33.1988i	−0.683767	+	1.45586i
$521$	−25.2789	−	18.3662i	−1.10749	−	0.804637i	−0.125222	−	0.992129i	$-0.539964\pi$
$521$	−25.2789	−	18.3662i	−1.10749	−	0.804637i	−0.982266	+	0.187491i	$0.939964\pi$
$522$	13.8119	−	5.57426i	0.604531	−	0.243979i
$523$	−11.4494	+	35.2378i	−0.500649	+	1.54084i	0.307314	+	0.951608i	$0.400570\pi$
$523$	−11.4494	+	35.2378i	−0.500649	+	1.54084i	−0.807964	+	0.589232i	$0.799430\pi$
$524$	33.0389	−	57.2251i	1.44331	−	2.49989i
$525$	11.3394	+	11.4694i	0.494894	+	0.500566i
$526$	−17.5707	−	30.4334i	−0.766120	−	1.32696i
$527$	16.9054	−	3.59335i	0.736410	−	0.156529i
$528$	−44.7084	+	59.3065i	−1.94568	+	2.58099i
$529$	−20.7928	+	9.25753i	−0.904033	+	0.402501i
$530$	−8.30220	+	35.5143i	−0.360625	+	1.54264i
$531$	−2.11416	−	30.4001i	−0.0917468	−	1.31925i
$532$	−15.7142			−0.681297
$533$	0.672611	+	6.39947i	0.0291340	+	0.277192i
$534$	17.0085	+	15.8668i	0.736031	+	0.686622i
$535$	30.9077	+	10.7377i	1.33626	+	0.464230i
$536$	−82.8445	+	17.6091i	−3.57834	+	0.760599i
$537$	2.60324	−	11.2661i	0.112338	−	0.486167i
$538$	−54.2093	−	11.5225i	−2.33713	−	0.496772i
$539$	−3.01535	+	9.28030i	−0.129880	+	0.399731i
$540$	46.3662	−	44.4784i	1.99528	−	1.91404i
$541$	−10.3961	−	31.9960i	−0.446965	−	1.37562i	−0.880314	−	0.474391i	$-0.842668\pi$
$541$	−10.3961	−	31.9960i	−0.446965	−	1.37562i	0.433350	−	0.901226i	$-0.357332\pi$
$542$	−2.26980	−	21.5957i	−0.0974963	−	0.927616i
$543$	−10.7458	−	6.45949i	−0.461145	−	0.277203i
$544$	−134.070	−	59.6917i	−5.74820	−	2.55926i
$545$	0.0907373	−	4.48972i	0.00388676	−	0.192319i
$546$	−14.8776	−	1.82962i	−0.636705	−	0.0783005i
$547$	5.08348	−	2.26331i	0.217354	−	0.0967722i	−0.295171	−	0.955444i	$-0.595377\pi$
$547$	5.08348	−	2.26331i	0.217354	−	0.0967722i	0.512525	+	0.858672i	$0.328710\pi$
$548$	−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
$552$	7.76240	+	2.67446i	0.330390	+	0.113833i
$553$	2.49782	−	23.7651i	0.106218	−	1.01060i
$554$	0.0516372	−	0.491295i	0.00219385	−	0.0208731i
$555$	−15.1617	+	6.07384i	−0.643577	+	0.257820i
$556$	−7.69917	−	73.2527i	−0.326518	−	3.10661i
$557$	37.0966			1.57183			0.785917	−	0.618332i	$-0.212191\pi$
$557$	37.0966			1.57183			0.785917	+	0.618332i	$0.212191\pi$
$558$	−20.2235	−	9.87319i	−0.856130	−	0.417966i
$559$	5.55619	+	17.1002i	0.235002	+	0.723262i
$560$	−56.6110	+	31.1765i	−2.39225	+	1.31745i
$561$	5.76734	+	29.7006i	0.243497	+	1.25396i
$562$	2.98748	−	3.31793i	0.126019	−	0.139959i
$563$	−14.3100	+	15.8928i	−0.603093	+	0.669802i	−0.964951	−	0.262431i	$-0.915476\pi$
$563$	−14.3100	+	15.8928i	−0.603093	+	0.669802i	0.361858	+	0.932233i	$0.382142\pi$
$564$	−46.3904	+	40.3111i	−1.95339	+	1.69740i
$565$	26.1545	−	14.4037i	1.10033	−	0.605967i
$566$	3.10107	+	9.54412i	0.130348	+	0.401169i
$567$	14.7933	+	7.88021i	0.621262	+	0.330938i
$568$	32.8398			1.37793
$569$	1.58549	+	15.0849i	0.0664672	+	0.632393i	0.976151	+	0.217092i	$0.0696571\pi$
$569$	1.58549	+	15.0849i	0.0664672	+	0.632393i	−0.909684	+	0.415301i	$0.863676\pi$
$570$	2.30416	−	16.0519i	0.0965105	−	0.672339i
$571$	−3.97913	+	37.8589i	−0.166522	+	1.58435i	0.518017	+	0.855370i	$0.326670\pi$
$571$	−3.97913	+	37.8589i	−0.166522	+	1.58435i	−0.684538	+	0.728977i	$0.739996\pi$
$572$	−2.70462	+	25.7327i	−0.113086	+	1.07594i
$573$	0.374872	+	1.93051i	0.0156605	+	0.0806481i
$574$	−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	−0.892482	−	0.451083i	$-0.851038\pi$
$577$	2.27456	−	7.00039i	0.0946913	−	0.291430i	0.987173	+	0.159653i	$0.0510377\pi$
$578$	−57.5770	+	25.6349i	−2.39489	+	1.06627i
$579$	3.20602	−	4.25285i	0.133238	−	0.176742i
$580$	0.452045	−	22.3674i	0.0187701	−	0.928755i
$581$	−1.49627	−	0.666181i	−0.0620756	−	0.0276378i
$582$	0.318439	−	18.0466i	0.0131997	−	0.748055i
$583$	1.71672	+	16.3335i	0.0710991	+	0.676463i
$584$	−46.4946	−	143.096i	−1.92396	−	5.92133i
$585$	2.97459	−	10.9637i	0.122984	−	0.453295i
$586$	20.7590	−	63.8895i	0.857545	−	2.63925i
$587$	24.3048	+	5.16615i	1.00317	+	0.213230i	0.680079	−	0.733139i	$-0.261945\pi$
$587$	24.3048	+	5.16615i	1.00317	+	0.213230i	0.323089	+	0.946369i	$0.395279\pi$
$588$	24.7339	+	23.0736i	1.02001	+	0.951538i
$589$	−4.08023	+	0.867279i	−0.168123	+	0.0357356i
$590$	−58.8756	−	20.4540i	−2.42387	−	0.842080i
$591$	9.09016	−	39.3397i	0.373919	−	1.61822i
$592$	−6.84111	−	65.0888i	−0.281168	−	2.67513i
$593$	43.3690			1.78095			0.890476	−	0.455030i	$-0.150371\pi$
$593$	43.3690			1.78095			0.890476	+	0.455030i	$0.150371\pi$
$594$	17.9057	−	35.0924i	0.734680	−	1.43986i
$595$	−5.99299	+	25.6362i	−0.245688	+	1.05098i
$596$	14.4213	−	6.42075i	0.590717	−	0.263004i
$597$	12.5935	+	29.6841i	0.515418	+	1.21489i
$598$	2.22445	−	0.472821i	0.0909644	−	0.0193351i
$599$	−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	$0.903569\pi$
$600$	−29.6144	−	78.4818i	−1.20900	−	3.20401i
$601$	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
$603$	24.3259	−	9.81752i	0.990625	−	0.399800i
$604$	50.2159	+	36.4840i	2.04325	+	1.48451i
$605$	−3.19938	+	6.81205i	−0.130073	+	0.276949i
$606$	18.1589	+	25.9441i	0.737656	+	1.05391i
$607$	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	$0.504339\pi$
$608$	32.3586	+	14.4070i	1.31232	+	0.584281i
$609$	5.58155	−	1.70529i	0.226176	−	0.0691018i
$610$	−19.0161	+	40.4887i	−0.769939	+	1.63934i
$611$	−3.35787	+	10.3345i	−0.135845	+	0.418087i
$612$	101.754	+	25.4113i	4.11317	+	1.02719i
$613$	13.3402	+	41.0570i	0.538806	+	1.65828i	0.735278	+	0.677766i	$0.237052\pi$
$613$	13.3402	+	41.0570i	0.538806	+	1.65828i	−0.196471	+	0.980510i	$0.562948\pi$
$614$	−6.99464	−	7.76833i	−0.282281	−	0.313504i
$615$	−11.5699	−	9.09437i	−0.466543	−	0.366720i
$616$	−33.3507	+	37.0397i	−1.34374	+	1.49237i
$617$	−34.5784	−	15.3953i	−1.39208	−	0.619792i	−0.432601	−	0.901586i	$-0.642404\pi$
$617$	−34.5784	−	15.3953i	−1.39208	−	0.619792i	−0.959475	+	0.281793i	$0.909071\pi$
$618$	6.26214	+	3.76429i	0.251900	+	0.151422i
$619$	1.66442	+	15.8359i	0.0668987	+	0.636499i	0.975676	+	0.219217i	$0.0703504\pi$
$619$	1.66442	+	15.8359i	0.0668987	+	0.636499i	−0.908777	+	0.417281i	$0.862983\pi$
$620$	−25.5727	+	22.1066i	−1.02702	+	0.887824i
$621$	−2.51138	−	0.399232i	−0.100778	−	0.0160206i
$622$	−55.9743	−	40.6677i	−2.24437	−	1.63063i
$623$	6.09873	+	6.77332i	0.244340	+	0.271367i
$624$	39.0143	+	23.4523i	1.56182	+	0.938842i
$625$	5.78047	+	24.3225i	0.231219	+	0.972902i
$626$	35.5929	+	61.6488i	1.42258	+	2.46398i
$627$	−1.39199	−	7.16843i	−0.0555906	−	0.286279i
$628$	73.1181	−	32.5543i	2.91773	−	1.29906i
$629$	−21.5693	−	15.6710i	−0.860024	−	0.624844i
$630$	26.7094	−	21.4906i	1.06413	−	0.856206i
$631$	−11.5984	+	8.42673i	−0.461725	+	0.335463i	−0.794208	−	0.607647i	$-0.792114\pi$
$631$	−11.5984	+	8.42673i	−0.461725	+	0.335463i	0.332483	+	0.943109i	$0.392114\pi$
$632$	−62.1407	+	107.631i	−2.47183	+	4.28133i
$633$	−11.4342	−	16.3363i	−0.454468	−	0.649311i
$634$	42.1563	−	46.8194i	1.67424	−	1.85943i
$635$	−6.97061	+	9.19750i	−0.276620	+	0.364992i
$636$	53.8261	+	18.5453i	2.13434	+	0.735368i
$637$	5.84994	+	1.24344i	0.231783	+	0.0492670i
$638$	−4.23903	−	13.0464i	−0.167825	−	0.516512i
$639$	−10.0174	+	1.76242i	−0.396284	+	0.0697201i
$640$	96.2445	−	8.15328i	3.80440	−	0.322287i
$641$	22.0577	+	4.68851i	0.871228	+	0.185185i	0.621769	−	0.783200i	$-0.286414\pi$
$641$	22.0577	+	4.68851i	0.871228	+	0.185185i	0.249458	+	0.968386i	$0.419747\pi$
$642$	29.4038	−	63.0253i	1.16048	−	2.48741i
$643$	−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	$-0.477824\pi$
$644$	4.60421	+	2.04993i	0.181431	+	0.0807784i
$645$	−36.9062	−	18.1350i	−1.45318	−	0.714066i
$646$	24.1822	−	10.7666i	0.951437	−	0.423607i
$647$	9.23613	+	6.71044i	0.363110	+	0.263815i	0.754348	−	0.656475i	$-0.227953\pi$
$647$	9.23613	+	6.71044i	0.363110	+	0.263815i	−0.391238	+	0.920289i	$0.627953\pi$
$648$	−53.6174	−	68.7349i	−2.10629	−	2.70016i
$649$	−28.0664			−1.10170
$650$	−18.2302	−	14.4054i	−0.715047	−	0.565026i
$651$	−7.55796	−	4.54324i	−0.296220	−	0.178064i
$652$	−45.1883	+	9.60506i	−1.76971	+	0.376163i
$653$	−0.896305	+	8.52777i	−0.0350751	+	0.333718i	0.962887	+	0.269906i	$0.0869925\pi$
$653$	−0.896305	+	8.52777i	−0.0350751	+	0.333718i	−0.997962	+	0.0638120i	$0.979674\pi$
$654$	−9.47364	−	1.16505i	−0.370448	−	0.0455569i
$655$	19.4912	+	18.2765i	0.761585	+	0.714121i
$656$	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
$659$	29.7257	+	6.31840i	1.15795	+	0.246130i	0.746553	−	0.665326i	$-0.231707\pi$
$659$	29.7257	+	6.31840i	1.15795	+	0.246130i	0.411397	+	0.911456i	$0.365041\pi$
$660$	−37.9036	−	45.4427i	−1.47539	−	1.76886i
$661$	20.9132	−	4.44523i	0.813428	−	0.172899i	0.217628	−	0.976032i	$-0.430168\pi$
$661$	20.9132	−	4.44523i	0.813428	−	0.172899i	0.595801	+	0.803132i	$0.296835\pi$
$662$	−11.2964	+	12.5459i	−0.439046	+	0.487609i
$663$	17.7344	−	5.41825i	0.688745	−	0.210427i
$664$	5.69993	+	6.33042i	0.221200	+	0.245668i
$665$	1.44645	−	6.18746i	0.0560908	−	0.239939i
$666$	9.55643	+	33.3752i	0.370304	+	1.29326i
$667$	−0.716332	+	0.520446i	−0.0277365	+	0.0201517i
$668$	−31.2808	+	54.1799i	−1.21029	+	2.09628i
$669$	−1.49923	+	3.21352i	−0.0579637	+	0.124242i
$670$	1.08410	−	53.6417i	0.0418824	−	2.07236i
$671$	−2.10552	+	20.0327i	−0.0812826	+	0.773353i
$672$	29.2450	+	68.9335i	1.12815	+	2.65917i
$673$	14.9162	+	16.5661i	0.574978	+	0.638577i	0.958547	−	0.284935i	$-0.0919720\pi$
$673$	14.9162	+	16.5661i	0.574978	+	0.638577i	−0.383569	+	0.923512i	$0.625305\pi$
$674$	41.3282			1.59190
$675$	13.2455	+	22.3508i	0.509818	+	0.860282i
$676$	−56.0291			−2.15497
$677$	−21.0044	−	23.3277i	−0.807264	−	0.896557i	0.189083	−	0.981961i	$-0.439449\pi$
$677$	−21.0044	−	23.3277i	−0.807264	−	0.896557i	−0.996346	+	0.0854038i	$0.972782\pi$
$678$	−24.7867	−	58.4246i	−0.951926	−	2.24378i
$679$	0.739280	−	7.03378i	0.0283710	−	0.269932i
$680$	82.7052	−	109.127i	3.17160	−	4.18483i
$681$	11.1291	−	23.8545i	0.426467	−	0.914107i
$682$	−10.3636	+	17.9503i	−0.396842	+	0.687351i
$683$	−41.1891	+	29.9257i	−1.57606	+	1.14507i	−0.655014	+	0.755617i	$0.727337\pi$
$683$	−41.1891	+	29.9257i	−1.57606	+	1.14507i	−0.921045	+	0.389457i	$0.872663\pi$
$684$	−24.5591	−	6.13319i	−0.939039	−	0.234508i
$685$	−8.29312	−	5.01414i	−0.316864	−	0.191581i
$686$	36.0132	+	39.9968i	1.37499	+	1.52708i
$687$	−0.348532	+	0.106484i	−0.0132973	+	0.00406263i
$688$	110.256	−	122.451i	4.20346	−	4.66842i
$689$	9.84601	−	2.09283i	0.375103	−	0.0797306i
$690$	−2.76909	+	4.40257i	−0.105417	+	0.167603i
$691$	6.95860	+	1.47910i	0.264718	+	0.0562674i	0.338358	−	0.941017i	$-0.390128\pi$
$691$	6.95860	+	1.47910i	0.264718	+	0.0562674i	−0.0736407	+	0.997285i	$0.523462\pi$
$692$	−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
$695$	29.5519	+	3.71116i	1.12097	+	0.140772i
$696$	−30.1269	−	3.70493i	−1.14196	−	0.140435i
$697$	2.51099	−	23.8905i	0.0951106	−	0.904917i
$698$	41.6282	−	8.84834i	1.57565	−	0.334915i
$699$	24.8968	+	14.9659i	0.941683	+	0.566064i
$700$	−13.9205	−	49.5754i	−0.526144	−	1.87377i
$701$	−42.2657			−1.59635			−0.798177	−	0.602423i	$-0.794202\pi$
$701$	−42.2657			−1.59635			−0.798177	+	0.602423i	$0.794202\pi$
$702$	−22.5376	−	8.66612i	−0.850625	−	0.327082i
$703$	5.20589	+	3.78230i	0.196344	+	0.142652i
$704$	82.4410	−	36.7051i	3.10711	−	1.38338i
$705$	−11.6024	−	21.9767i	−0.436971	−	0.827692i
$706$	−23.5549	−	10.4873i	−0.886499	−	0.394695i
$707$	6.20438	+	10.7463i	0.233340	+	0.404156i
$708$	−41.1338	+	88.1680i	−1.54590	+	3.31355i
$709$	−9.38163	−	1.99413i	−0.352335	−	0.0748910i	0.0283446	−	0.999598i	$-0.490976\pi$
$709$	−9.38163	−	1.99413i	−0.352335	−	0.0748910i	−0.380679	+	0.924707i	$0.624310\pi$
$710$	−4.73553	+	20.2572i	−0.177721	+	0.760238i
$711$	13.1792	−	36.1667i	0.494258	−	1.35636i
$712$	−14.6484	−	45.0832i	−0.548973	−	1.68956i
$713$	1.30863	+	0.278158i	0.0490086	+	0.0104171i
$714$	52.9074	+	18.2287i	1.98001	+	0.682193i
$715$	−9.88329	−	3.43357i	−0.369614	−	0.128408i
$716$	−24.7018	+	27.4341i	−0.923150	+	1.02526i
$717$	−24.5251	−	35.0397i	−0.915907	−	1.30858i
$718$	−10.9842	+	19.0252i	−0.409927	+	0.710014i
$719$	−35.1893	+	25.5666i	−1.31234	+	0.953472i	−0.312347	+	0.949968i	$0.601115\pi$
$719$	−35.1893	+	25.5666i	−1.31234	+	0.953472i	−0.999994	+	0.00350360i	$0.998885\pi$
$720$	−100.643	+	26.6294i	−3.75075	+	0.992419i
$721$	2.31620	+	1.68282i	0.0862598	+	0.0626714i
$722$	41.7930	−	18.6074i	1.55537	−	0.692497i
$723$	−1.00466	−	5.17376i	−0.0373636	−	0.192414i
$724$	20.0144	+	34.6659i	0.743828	+	1.28835i
$725$	8.76554	+	2.23685i	0.325544	+	0.0830744i
$726$	13.7103	+	8.24151i	0.508836	+	0.305871i
$727$	−17.5689	−	19.5122i	−0.651593	−	0.723668i	0.323311	−	0.946293i	$-0.395204\pi$
$727$	−17.5689	−	19.5122i	−0.651593	−	0.723668i	−0.974904	+	0.222625i	$0.928537\pi$
$728$	24.7140	+	17.9558i	0.915962	+	0.665486i
$729$	20.0443	+	18.0894i	0.742380	+	0.669979i
$730$	94.9728	−	8.04556i	3.51510	−	0.297779i
$731$	−7.01634	−	66.7560i	−0.259509	−	2.46906i
$732$	59.8450	+	35.9740i	2.21193	+	1.32964i
$733$	47.5053	+	21.1507i	1.75465	+	0.781219i	0.990720	+	0.135916i	$0.0433978\pi$
$733$	47.5053	+	21.1507i	1.75465	+	0.781219i	0.763927	+	0.645303i	$0.223269\pi$
$734$	−48.4900	+	53.8536i	−1.78980	+	1.98777i
$735$	−11.3619	+	7.61512i	−0.419090	+	0.280888i
$736$	−7.60158	−	8.44241i	−0.280198	−	0.311191i
$737$	−7.46588	−	22.9776i	−0.275009	−	0.846391i
$738$	−21.7375	+	22.4927i	−0.800168	+	0.827968i
$739$	−7.71260	+	23.7369i	−0.283712	+	0.873177i	0.703069	+	0.711121i	$0.251812\pi$
$739$	−7.71260	+	23.7369i	−0.283712	+	0.873177i	−0.986782	+	0.162056i	$0.948188\pi$
$740$	51.7391	+	6.49745i	1.90197	+	0.238851i
$741$	−4.28031	+	1.30773i	−0.157241	+	0.0480407i
$742$	27.7502	+	12.3552i	1.01874	+	0.453574i
$743$	−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	$0.843820\pi$
$744$	26.2992	+	37.5743i	0.964175	+	1.37754i
$745$	1.20073	+	6.26937i	0.0439915	+	0.229692i
$746$	−46.1153	−	33.5047i	−1.68840	−	1.22669i
$747$	−2.07844	−	1.62513i	−0.0760463	−	0.0594605i
$748$	29.8493	−	91.8668i	1.09140	−	3.35898i
$749$	13.6257	−	23.6005i	0.497873	−	0.862342i
$750$	52.6818	−	6.95041i	1.92367	−	0.253793i
$751$	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	$0.726816\pi$
$752$	97.4049	−	20.7041i	3.55199	−	0.754999i
$753$	16.8764	+	39.7793i	0.615010	+	1.44964i
$754$	−7.68080	+	3.41971i	−0.279718	+	0.124539i
$755$	−18.9878	+	16.4142i	−0.691036	+	0.597375i
$756$	−29.1195	−	44.8962i	−1.05907	−	1.63286i
$757$	−9.03751			−0.328474			−0.164237	−	0.986421i	$-0.552516\pi$
$757$	−9.03751			−0.328474			−0.164237	+	0.986421i	$0.552516\pi$
$758$	−5.49752	−	52.3054i	−0.199679	−	1.89982i
$759$	−0.527278	+	2.28191i	−0.0191390	+	0.0828282i
$760$	−19.9614	+	26.3385i	−0.724078	+	0.955398i
$761$	−38.7347	+	8.23332i	−1.40413	+	0.298458i	−0.846836	−	0.531855i	$-0.821495\pi$
$761$	−38.7347	+	8.23332i	−1.40413	+	0.298458i	−0.557298	+	0.830313i	$0.688162\pi$
$762$	17.9367	+	16.7327i	0.649779	+	0.606160i
$763$	−3.65841	−	0.777619i	−0.132443	−	0.0281517i
$764$	1.94018	−	5.97126i	0.0701932	−	0.216032i
$765$	−19.3719	+	37.7266i	−0.700391	+	1.36401i
$766$	20.4928	+	63.0704i	0.740435	+	2.27883i
$767$	1.79809	+	17.1077i	0.0649254	+	0.617724i
$768$	1.62599	−	92.1484i	0.0586730	−	3.32512i
$769$	30.8248	+	13.7241i	1.11157	+	0.494903i	0.878589	−	0.477579i	$-0.158485\pi$
$769$	30.8248	+	13.7241i	1.11157	+	0.494903i	0.232981	+	0.972481i	$0.425152\pi$
$770$	−18.0387	−	25.9135i	−0.650068	−	0.933857i
$771$	−4.48925	+	5.95507i	−0.161676	+	0.214467i
$772$	−15.5337	+	6.91604i	−0.559069	+	0.248914i
$773$	8.69380	−	26.7568i	0.312694	−	0.962374i	−0.663999	−	0.747734i	$-0.731142\pi$
$773$	8.69380	−	26.7568i	0.312694	−	0.962374i	0.976693	−	0.214640i	$-0.0688580\pi$
$774$	−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
$777$	2.59310	+	13.3539i	0.0930270	+	0.479069i
$778$	−10.8163	+	102.910i	−0.387783	+	3.68950i
$779$	−0.606045	+	5.76613i	−0.0217138	+	0.206593i
$780$	−25.2711	+	26.0153i	−0.904851	+	0.931496i
$781$	0.979206	+	9.31652i	0.0350387	+	0.333371i
$782$	−8.48982			−0.303595
$783$	9.38873	−	0.486669i	0.335526	−	0.0173921i
$784$	−16.9365	−	52.1253i	−0.604877	−	1.86162i
$785$	6.08792	+	31.7868i	0.217287	+	1.13452i
$786$	42.8696	−	37.2517i	1.52911	−	1.32872i
$787$	20.6286	−	22.9104i	0.735332	−	0.816669i	−0.253242	−	0.967403i	$-0.581497\pi$
$787$	20.6286	−	22.9104i	0.735332	−	0.816669i	0.988574	+	0.150734i	$0.0481637\pi$
$788$	−86.2556	+	95.7965i	−3.07273	+	3.41261i
$789$	−4.22826	−	21.7746i	−0.150530	−	0.775197i
$790$	−57.4312	−	53.8519i	−2.04331	−	1.91597i
$791$	−7.68473	−	23.6512i	−0.273238	−	0.840939i
$792$	−66.5788	+	44.8711i	−2.36578	+	1.59443i
$793$	12.3457			0.438409
$794$	−8.06746	−	76.7568i	−0.286303	−	2.72400i
$795$	−12.2567	+	19.4870i	−0.434701	+	0.691131i
$796$	10.7609	−	102.383i	0.381410	−	3.62887i
$797$	−1.21380	+	11.5485i	−0.0429948	+	0.409069i	0.951765	+	0.306828i	$0.0992677\pi$
$797$	−1.21380	+	11.5485i	−0.0429948	+	0.409069i	−0.994760	+	0.102240i	$0.967399\pi$
$798$	−12.7696	−	4.39963i	−0.452037	−	0.155745i
$799$	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
$803$	39.2093	−	17.4571i	1.38367	−	0.616048i
$804$	−83.1240	−	10.2224i	−2.93156	−	0.360516i
$805$	−1.23096	+	1.62422i	−0.0433857	+	0.0572461i
$806$	11.6055	+	5.16708i	0.408785	+	0.182003i
$807$	−29.9815	−	18.0225i	−1.05540	−	0.634421i
$808$	−6.74595	−	64.1835i	−0.237322	−	2.25797i
$809$	11.6688	+	35.9129i	0.410254	+	1.26263i	0.916428	+	0.400200i	$0.131059\pi$
$809$	11.6688	+	35.9129i	0.410254	+	1.26263i	−0.506174	+	0.862432i	$0.668941\pi$
$810$	50.1307	−	23.1622i	1.76141	−	0.813836i
$811$	−1.37548	+	4.23331i	−0.0482998	+	0.148652i	−0.972298	−	0.233746i	$-0.924902\pi$
$811$	−1.37548	+	4.23331i	−0.0482998	+	0.148652i	0.923998	+	0.382398i	$0.124902\pi$
$812$	−18.2259	−	3.87402i	−0.639602	−	0.135952i
$813$	3.08580	−	13.3545i	0.108224	−	0.468362i
$814$	31.2753	−	6.64778i	1.09620	−	0.233004i
$815$	0.377462	−	18.6770i	0.0132219	−	0.654226i
$816$	−124.262	−	115.921i	−4.35005	−	4.05804i
$817$	1.69344	+	16.1120i	0.0592460	+	0.563688i
$818$	−28.8344			−1.00817
$819$	−8.50240	−	4.15090i	−0.297098	−	0.145044i
$820$	18.2389	+	43.2993i	0.636931	+	1.51208i
$821$	7.62642	−	3.39550i	0.266164	−	0.118504i	−0.269316	−	0.963052i	$-0.586798\pi$
$821$	7.62642	−	3.39550i	0.266164	−	0.118504i	0.535480	+	0.844548i	$0.320131\pi$
$822$	−12.3998	+	16.4485i	−0.432492	+	0.573709i
$823$	4.47531	−	0.951257i	0.156000	−	0.0331587i	−0.129250	−	0.991612i	$-0.541257\pi$
$823$	4.47531	−	0.951257i	0.156000	−	0.0331587i	0.285249	+	0.958453i	$0.407924\pi$
$824$	−7.44507	−	12.8952i	−0.259361	−	0.449227i
$825$	21.3820	−	10.7416i	0.744425	−	0.373976i
$826$	−25.9555	+	44.9562i	−0.903106	+	1.56423i
$827$	−2.49659	+	7.68370i	−0.0868148	+	0.267189i	−0.985034	−	0.172359i	$-0.944861\pi$
$827$	−2.49659	+	7.68370i	−0.0868148	+	0.267189i	0.898219	+	0.439547i	$0.144861\pi$
$828$	6.39565	+	5.00075i	0.222264	+	0.173788i
$829$	−14.9236	−	10.8426i	−0.518316	−	0.376579i	0.297653	−	0.954674i	$-0.403796\pi$
$829$	−14.9236	−	10.8426i	−0.518316	−	0.376579i	−0.815969	+	0.578095i	$0.803796\pi$
$830$	−4.72684	+	2.60314i	−0.164071	+	0.0903564i
$831$	0.131832	−	0.282575i	0.00457321	−	0.00980241i
$832$	−27.6551	−	47.9000i	−0.958767	−	1.66063i
$833$	−20.3966	−	9.08117i	−0.706702	−	0.314644i
$834$	14.2527	−	61.6817i	0.493531	−	2.13586i
$835$	−18.4540	−	17.3039i	−0.638627	−	0.598826i
$836$	−7.20434	+	22.1727i	−0.249167	+	0.766858i
$837$	−10.0388	−	10.0503i	−0.346992	−	0.347388i
$838$	−8.02726	−	24.7054i	−0.277297	−	0.853433i
$839$	−8.93605	−	9.92449i	−0.308507	−	0.342631i	0.568875	−	0.822424i	$-0.307379\pi$
$839$	−8.93605	−	9.92449i	−0.308507	−	0.342631i	−0.877382	+	0.479792i	$0.840712\pi$
$840$	−68.8383	+	11.9292i	−2.37515	+	0.411596i
$841$	−17.2144	+	19.1185i	−0.593599	+	0.659259i
$842$	16.9718	+	7.55635i	0.584888	+	0.260409i
$843$	2.46506	−	1.36579i	0.0849012	−	0.0470404i
$844$	6.65452	+	63.3135i	0.229058	+	2.17934i
$845$	5.15732	−	22.0614i	0.177417	−	0.758937i
$846$	−48.9837	+	19.7690i	−1.68409	+	0.679673i
$847$	5.07107	+	3.68435i	0.174244	+	0.126596i
$848$	−61.7251	−	68.5527i	−2.11965	−	2.35411i
$849$	−0.111754	+	6.33331i	−0.00383537	+	0.217359i
$850$	55.3886	+	66.7528i	1.89981	+	2.28960i
$851$	−1.03191	−	1.78731i	−0.0353733	−	0.0612683i
$852$	30.7021	+	10.5781i	1.05184	+	0.362401i
$853$	48.6704	−	21.6695i	1.66644	−	0.741948i	0.666450	−	0.745550i	$-0.267813\pi$
$853$	48.6704	−	21.6695i	1.66644	−	0.741948i	0.999994	+	0.00360148i	$0.00114639\pi$
$854$	30.1408	+	21.8986i	1.03140	+	0.749354i
$855$	4.67553	−	9.10557i	0.159900	−	0.311404i
$856$	−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	$0.207649\pi$
$858$	−9.40240	+	20.1535i	−0.320993	+	0.688029i
$859$	−16.0608	+	17.8373i	−0.547987	+	0.608602i	−0.951980	−	0.306161i	$-0.900956\pi$
$859$	−16.0608	+	17.8373i	−0.547987	+	0.608602i	0.403992	+	0.914762i	$0.367622\pi$
$860$	75.0055	+	107.749i	2.55767	+	3.67422i
$861$	−9.25189	+	8.03946i	−0.315304	+	0.273984i
$862$	66.4716	+	14.1290i	2.26403	+	0.481235i
$863$	−13.5353	−	41.6575i	−0.460748	−	1.41804i	−0.864252	−	0.503059i	$-0.832208\pi$
$863$	−13.5353	−	41.6575i	−0.460748	−	1.41804i	0.403504	−	0.914978i	$-0.367792\pi$
$864$	18.8014	+	119.147i	0.639636	+	4.05348i
$865$	−5.51948	−	13.1033i	−0.187668	−	0.445525i
$866$	−17.2054	−	3.65712i	−0.584663	−	0.124274i
$867$	−39.6313	+	3.45969i	−1.34595	+	0.117497i
$868$	14.0770	+	24.3820i	0.477804	+	0.827580i
$869$	−32.3874	−	14.4198i	−1.09867	−	0.489158i
$870$	6.62971	−	18.0495i	0.224768	−	0.611934i
$871$	−13.5276	+	6.02287i	−0.458365	+	0.204077i
$872$	15.7371	+	11.4337i	0.532927	+	0.387194i
$873$	3.90064	−	10.7043i	0.132017	−	0.362284i
$874$	2.04908			0.0693110
$875$	20.8016	−	0.917906i	0.703223	−	0.0310309i
$876$	2.62488	−	148.757i	0.0886866	−	5.02605i
$877$	25.2761	−	5.37260i	0.853514	−	0.181420i	0.239677	−	0.970853i	$-0.422959\pi$
$877$	25.2761	−	5.37260i	0.853514	−	0.181420i	0.613837	+	0.789433i	$0.289625\pi$
$878$	−0.0736185	+	0.700433i	−0.00248450	+	0.0236385i
$879$	25.5249	−	33.8593i	0.860934	−	1.14205i
$880$	18.0360	+	94.1712i	0.607994	+	3.17451i
$881$	−8.85610	+	6.43433i	−0.298369	+	0.216778i	−0.726890	−	0.686754i	$-0.759035\pi$
$881$	−8.85610	+	6.43433i	−0.298369	+	0.216778i	0.428520	+	0.903532i	$0.359035\pi$
$882$	13.6390	+	25.6748i	0.459250	+	0.864517i
$883$	34.4894	−	25.0580i	1.16066	−	0.843270i	0.170800	−	0.985306i	$-0.445365\pi$
$883$	34.4894	−	25.0580i	1.16066	−	0.843270i	0.989862	+	0.142036i	$0.0453648\pi$
$884$	−57.9093	−	12.3090i	−1.94770	−	0.413997i
$885$	−30.9298	−	24.3120i	−1.03970	−	0.817240i
$886$	−39.3367	+	8.36127i	−1.32154	+	0.280902i
$887$	37.5685	−	41.7241i	1.26143	−	1.40096i	0.382531	−	0.923943i	$-0.375052\pi$
$887$	37.5685	−	41.7241i	1.26143	−	1.40096i	0.878896	−	0.477014i	$-0.158281\pi$
$888$	15.9284	−	68.9336i	0.534522	−	2.31326i
$889$	6.43155	+	7.14296i	0.215707	+	0.239567i
$890$	29.9218	−	2.53481i	1.00298	−	0.0849669i
$891$	17.9011	−	17.2606i	0.599710	−	0.578251i
$892$	9.15908	−	6.65446i	0.306669	−	0.222808i
$893$	−4.89544	+	8.47915i	−0.163820	+	0.283744i
$894$	13.5166	−	1.17995i	0.452061	−	0.0394636i
$895$	−8.52845	−	12.2516i	−0.285075	−	0.409525i
$896$	8.40897	−	80.0060i	0.280924	−	2.67281i
$897$	1.42471	+	0.175208i	0.0475697	+	0.00585001i
$898$	−28.5357	−	31.6921i	−0.952249	−	1.05758i
$899$	−4.94620			−0.164965
$900$	−2.40664	−	82.9124i	−0.0802214	−	2.76375i
$901$	−37.5783			−1.25191
$902$	19.2771	+	21.4094i	0.641856	+	0.712853i
$903$	−20.6166	+	27.3483i	−0.686077	+	0.910095i
$904$	−13.5195	+	128.630i	−0.449652	+	4.27816i
$905$	−15.4919	+	4.68975i	−0.514970	+	0.155893i
$906$	30.5913	+	43.7067i	1.01633	+	1.45206i
$907$	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
$909$	5.50233	+	19.2165i	0.182501	+	0.637371i
$910$	−14.6398	+	12.6556i	−0.485304	+	0.419528i
$911$	−14.3799	−	15.9704i	−0.476426	−	0.529125i	0.456244	−	0.889854i	$-0.349194\pi$
$911$	−14.3799	−	15.9704i	−0.476426	−	0.529125i	−0.932670	+	0.360730i	$0.882528\pi$
$912$	29.9915	+	27.9782i	0.993119	+	0.926452i
$913$	−1.62596	+	1.80581i	−0.0538113	+	0.0597635i
$914$	−39.0192	+	8.29378i	−1.29064	+	0.274334i
$915$	−19.6733	+	20.2526i	−0.650379	+	0.669531i
$916$	1.13809	+	0.241908i	0.0376035	+	0.00799286i
$917$	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	−0.400202	−	0.916427i	$-0.631060\pi$
$919$	10.5406	−	7.65821i	0.347703	−	0.252621i	0.747905	+	0.663806i	$0.231060\pi$
$920$	9.28451	−	5.11311i	0.306101	−	0.168574i
$921$	−2.57695	−	6.07413i	−0.0849134	−	0.200149i
$922$	0.943765	−	8.97932i	0.0310812	−	0.295718i
$923$	5.61611	−	1.19374i	0.184857	−	0.0392925i
$924$	−43.1108	+	23.8860i	−1.41824	+	0.785790i
$925$	−7.32081	+	19.7742i	−0.240707	+	0.650171i
$926$	104.951			3.44890
$927$	2.96310	+	3.53401i	0.0973208	+	0.116072i
$928$	33.9789	+	24.6871i	1.11541	+	0.810394i
$929$	−21.8726	+	9.73830i	−0.717616	+	0.319503i	−0.732859	−	0.680380i	$-0.761815\pi$
$929$	−21.8726	+	9.73830i	−0.717616	+	0.319503i	0.0152427	+	0.999884i	$0.495148\pi$
$930$	−26.9700	+	10.8043i	−0.884383	+	0.354289i
$931$	4.92286	+	2.19180i	0.161340	+	0.0718334i
$932$	−46.3711	−	80.3172i	−1.51894	−	2.63088i
$933$	−25.0422	−	35.7785i	−0.819846	−	1.17134i
$934$	−15.3835	−	3.26986i	−0.503363	−	0.106993i
$935$	33.4250	+	20.2092i	1.09311	+	0.660913i
$936$	31.6164	+	37.7081i	1.03341	+	1.23253i
$937$	5.43437	+	16.7253i	0.177533	+	0.546390i	0.999740	−	0.0227980i	$-0.00725746\pi$
$937$	5.43437	+	16.7253i	0.177533	+	0.546390i	−0.822207	+	0.569188i	$0.807257\pi$
$938$	−43.7095	−	9.29074i	−1.42717	−	0.303353i
$939$	8.56516	+	44.1087i	0.279514	+	1.43943i
$940$	−1.60317	+	79.3255i	−0.0522895	+	2.58731i
$941$	9.42586	−	10.4685i	0.307274	−	0.341262i	−0.569653	−	0.821885i	$-0.692923\pi$
$941$	9.42586	−	10.4685i	0.307274	−	0.341262i	0.876928	+	0.480622i	$0.159589\pi$
$942$	68.5312	−	5.98256i	2.23287	−	0.194922i
$943$	0.929764	−	1.61040i	0.0302773	−	0.0524418i
$944$	127.535	−	92.6599i	4.15093	−	3.01582i
$945$	20.3582	−	7.33323i	0.662254	−	0.238550i
$946$	65.1258	+	47.3167i	2.11742	+	1.53840i
$947$	−20.1930	+	8.99050i	−0.656184	+	0.292152i	−0.707693	−	0.706521i	$-0.750264\pi$
$947$	−20.1930	+	8.99050i	−0.656184	+	0.292152i	0.0515084	+	0.998673i	$0.483597\pi$
$948$	−92.7651	+	80.6085i	−3.01287	+	2.61804i
$949$	−13.1529	−	22.7815i	−0.426961	−	0.739517i
$950$	−13.3684	−	16.1112i	−0.433728	−	0.522717i
$951$	34.7845	−	19.2727i	1.12796	−	0.624960i
$952$	−76.3093	−	84.7501i	−2.47320	−	2.74677i
$953$	−25.0086	−	18.1698i	−0.810108	−	0.588578i	0.103754	−	0.994603i	$-0.466915\pi$
$953$	−25.0086	−	18.1698i	−0.810108	−	0.588578i	−0.913862	+	0.406025i	$0.866915\pi$
$954$	38.5475	+	30.1402i	1.24802	+	0.975826i
$955$	2.17259	+	1.31358i	0.0703034	+	0.0425065i
$956$	14.2732	+	135.801i	0.461630	+	4.39211i
$957$	0.152762	−	8.65735i	0.00493810	−	0.279852i
$958$	33.7741	+	15.0372i	1.09119	+	0.485829i
$959$	−5.40087	+	5.99827i	−0.174403	+	0.193694i
$960$	122.647	+	30.9632i	3.95842	+	0.999334i
$961$	−15.7423	−	17.4836i	−0.507815	−	0.563986i
$962$	−6.05580	−	18.6378i	−0.195247	−	0.600908i
$963$	30.5062	−	31.5661i	0.983050	−	1.01720i
$964$	−5.19968	+	16.0030i	−0.167470	+	0.515421i
$965$	−1.29336	−	6.75298i	−0.0416346	−	0.217386i
$966$	3.16750	+	2.95487i	0.101913	+	0.0950715i
$967$	−23.5362	−	10.4790i	−0.756873	−	0.336981i	−0.00823972	−	0.999966i	$-0.502623\pi$
$967$	−23.5362	−	10.4790i	−0.756873	−	0.336981i	−0.748633	+	0.662985i	$0.769289\pi$
$968$	−16.3002	−	28.2327i	−0.523907	−	0.907433i
$969$	16.6451	−	1.45306i	0.534717	−	0.0466791i
$970$	−16.9979	−	15.9386i	−0.545771	−	0.511757i
$971$	27.8824	+	20.2577i	0.894787	+	0.650101i	0.937122	−	0.349002i	$-0.113479\pi$
$971$	27.8824	+	20.2577i	0.894787	+	0.650101i	−0.0423344	+	0.999103i	$0.513479\pi$
$972$	−27.9869	−	81.5317i	−0.897679	−	2.61513i
$973$	7.66559	−	23.5923i	0.245748	−	0.756333i
$974$	−39.4326	+	68.2993i	−1.26350	+	2.18845i
$975$	−7.91737	−	12.3451i	−0.253559	−	0.395360i
$976$	−56.5694	−	97.9811i	−1.81074	−	3.13630i
$977$	−6.09683	+	1.29592i	−0.195055	+	0.0414602i	−0.304403	−	0.952543i	$-0.598457\pi$
$977$	−6.09683	+	1.29592i	−0.195055	+	0.0414602i	0.109348	+	0.994004i	$0.465124\pi$
$978$	−39.4098	−	4.84652i	−1.26019	−	0.154975i
$979$	12.3532	−	5.49998i	0.394809	−	0.175780i
$980$	43.5125	−	3.68613i	1.38996	−	0.117749i
$981$	−5.41407	−	2.64317i	−0.172858	−	0.0843899i
$982$	−43.8206			−1.39837
$983$	0.211716	+	2.01434i	0.00675268	+	0.0642475i	0.997379	−	0.0723502i	$-0.0230499\pi$
$983$	0.211716	+	2.01434i	0.00675268	+	0.0642475i	−0.990627	+	0.136598i	$0.956383\pi$
$984$	60.9650	−	18.6262i	1.94349	−	0.593781i
$985$	−29.7803	−	42.7809i	−0.948878	−	1.36311i
$986$	30.7016	−	6.52584i	0.977740	−	0.207825i
$987$	−19.7948	+	6.04777i	−0.630077	+	0.192503i
$988$	13.9768	+	2.97086i	0.444661	+	0.0945157i
$989$	1.60565	−	4.94168i	0.0510566	−	0.157136i
$990$	−18.0779	−	47.5395i	−0.574555	−	1.51090i
$991$	−0.263346	−	0.810497i	−0.00836547	−	0.0257463i	0.946787	−	0.321862i	$-0.104309\pi$
$991$	−0.263346	−	0.810497i	−0.00836547	−	0.0257463i	−0.955152	+	0.296116i	$0.904309\pi$
$992$	−6.63348	−	63.1134i	−0.210613	−	2.00385i
$993$	−9.32097	+	5.16438i	−0.295792	+	0.163887i
$994$	15.8286	+	7.04734i	0.502053	+	0.223528i
$995$	39.3228	+	13.6612i	1.24662	+	0.433088i
$996$	3.28980	+	7.75437i	0.104241	+	0.245707i
$997$	−52.6273	+	23.4312i	−1.66672	+	0.742073i	−0.999995	−	0.00322852i	$-0.998972\pi$
$997$	−52.6273	+	23.4312i	−1.66672	+	0.742073i	−0.666728	+	0.745301i	$0.732306\pi$
$998$	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.196.1	yes	224
3.2	odd	2		675.2.r.a.46.28		224
9.4	even	3	inner	225.2.q.a.121.28	yes	224
9.5	odd	6		675.2.r.a.496.1		224
25.6	even	5	inner	225.2.q.a.106.28	yes	224
75.56	odd	10		675.2.r.a.181.1		224
225.31	even	15	inner	225.2.q.a.31.1	✓	224
225.131	odd	30		675.2.r.a.631.28		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.1	✓	224	225.31	even	15	inner
225.2.q.a.106.28	yes	224	25.6	even	5	inner
225.2.q.a.121.28	yes	224	9.4	even	3	inner
225.2.q.a.196.1	yes	224	1.1	even	1	trivial
675.2.r.a.46.28		224	3.2	odd	2
675.2.r.a.181.1		224	75.56	odd	10
675.2.r.a.496.1		224	9.5	odd	6
675.2.r.a.631.28		224	225.131	odd	30

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+(-1.83613 - 2.03923i) q^{2} +(-0.676463 - 1.59449i) q^{3} +(-0.578024 + 5.49953i) q^{4} +(-2.11223 - 0.733812i) q^{5} +(-2.00946 + 4.30715i) q^{6} +(-0.931182 + 1.61286i) q^{7} +(7.83615 - 5.69329i) q^{8} +(-2.08480 + 2.15723i) q^{9} +(2.38192 + 5.65469i) q^{10} +(1.84882 + 2.05333i) q^{11} +(9.15995 - 2.79857i) q^{12} +(1.13315 - 1.25849i) q^{13} +(4.99875 - 1.06252i) q^{14} +(0.258789 + 3.86433i) q^{15} +(-15.1801 - 3.22664i) q^{16} +(-5.11464 + 3.71600i) q^{17} +(8.22703 + 0.290429i) q^{18} +(1.23445 - 0.896882i) q^{19} +(5.25654 - 11.1921i) q^{20} +(3.20159 + 0.393724i) q^{21} +(0.792522 - 7.54034i) q^{22} +(-0.478689 + 0.101749i) q^{23} +(-14.3788 - 8.64335i) q^{24} +(3.92304 + 3.09996i) q^{25} -4.64695 q^{26} +(4.84996 + 1.86490i) q^{27} +(-8.33169 - 6.05333i) q^{28} +(1.65287 - 0.735904i) q^{29} +(7.40507 - 7.62313i) q^{30} +(-2.49743 - 1.11193i) q^{31} +(11.6068 + 20.1036i) q^{32} +(2.02335 - 4.33693i) q^{33} +(16.9689 + 3.60685i) q^{34} +(3.15040 - 2.72341i) q^{35} +(-10.6587 - 12.7123i) q^{36} +(1.30318 + 4.01076i) q^{37} +(-4.09556 - 0.870538i) q^{38} +(-2.77318 - 0.955473i) q^{39} +(-20.7296 + 6.27529i) q^{40} +(-2.54252 + 2.82375i) q^{41} +(-5.07564 - 7.25170i) q^{42} +(-5.30871 + 9.19495i) q^{43} +(-12.3610 + 8.98078i) q^{44} +(5.98657 - 3.02671i) q^{45} +(1.08642 + 0.789333i) q^{46} +(-5.86186 + 2.60987i) q^{47} +(5.12396 + 26.3873i) q^{48} +(1.76580 + 3.05845i) q^{49} +(-0.881677 - 13.6919i) q^{50} +(9.38499 + 5.64150i) q^{51} +(6.26611 + 6.95922i) q^{52} +(4.80881 + 3.49380i) q^{53} +(-5.10219 - 13.3144i) q^{54} +(-2.39838 - 5.69379i) q^{55} +(1.88558 + 17.9401i) q^{56} +(-2.26513 - 1.36161i) q^{57} +(-4.53555 - 2.01936i) q^{58} +(-6.79693 + 7.54876i) q^{59} +(-21.4016 - 0.810453i) q^{60} +(4.87810 + 5.41768i) q^{61} +(2.31813 + 7.13448i) q^{62} +(-1.53797 - 5.37124i) q^{63} +(10.0928 - 31.0624i) q^{64} +(-3.31697 + 1.82670i) q^{65} +(-12.5591 + 3.83709i) q^{66} +(-7.98812 - 3.55654i) q^{67} +(-17.4799 - 30.2760i) q^{68} +(0.486052 + 0.694436i) q^{69} +(-11.3382 - 1.42386i) q^{70} +(2.74292 + 1.99285i) q^{71} +(-4.05504 + 28.7737i) q^{72} +(4.80018 - 14.7734i) q^{73} +(5.78606 - 10.0218i) q^{74} +(2.28907 - 8.35226i) q^{75} +(4.21888 + 7.30732i) q^{76} +(-5.03331 + 1.06986i) q^{77} +(3.14349 + 7.40952i) q^{78} +(-11.7217 + 5.21885i) q^{79} +(29.6962 + 17.9548i) q^{80} +(-0.307250 - 8.99475i) q^{81} +10.4267 q^{82} +(0.0919281 + 0.874638i) q^{83} +(-4.01589 + 17.3797i) q^{84} +(13.5301 - 4.09587i) q^{85} +(28.4981 - 6.05745i) q^{86} +(-2.29149 - 2.13767i) q^{87} +(26.1778 + 5.56427i) q^{88} +(1.51233 - 4.65447i) q^{89} +(-17.1643 - 6.65055i) q^{90} +(0.974593 + 2.99949i) q^{91} +(-0.282875 - 2.69138i) q^{92} +(-0.0835387 + 4.73431i) q^{93} +(16.0852 + 7.16161i) q^{94} +(-3.26559 + 0.988565i) q^{95} +(24.2034 - 32.1063i) q^{96} +(-3.46928 + 1.54462i) q^{97} +(2.99465 - 9.21658i) q^{98} +(-8.28390 - 0.292436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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