LMFDB - Embedded newform 378.2.bf.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	378.5
Dual form			378.2.bf.a.227.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(0.801094 - 1.53566i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.703607 - 3.99035i) q^{5} +(-0.522259 + 1.65144i) q^{6} +(2.53004 + 0.773898i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.71650 - 2.46041i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(0.801094 - 1.53566i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.703607 - 3.99035i) q^{5} +(-0.522259 + 1.65144i) q^{6} +(2.53004 + 0.773898i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.71650 - 2.46041i) q^{9} +4.05191i q^{10} +(5.22149 - 0.920690i) q^{11} +(0.227556 - 1.71704i) q^{12} +(-3.27929 + 3.90811i) q^{13} +(-2.62599 - 0.322804i) q^{14} +(-5.56417 - 4.27715i) q^{15} +(0.766044 - 0.642788i) q^{16} -0.0707799 q^{17} +(2.11767 + 2.12497i) q^{18} +1.23359i q^{19} +(-0.703607 - 3.99035i) q^{20} +(3.21524 - 3.26531i) q^{21} +(-4.98229 + 1.81340i) q^{22} +(-2.58415 + 3.07967i) q^{23} +(0.0740617 + 1.73047i) q^{24} +(-10.7294 - 3.90518i) q^{25} +(2.55083 - 4.41818i) q^{26} +(-5.15343 + 0.664930i) q^{27} +(2.64214 - 0.138098i) q^{28} +(4.30832 + 5.13446i) q^{29} +(6.22235 + 3.24596i) q^{30} +(-1.27820 - 3.51183i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(2.76904 - 8.75599i) q^{33} +(0.0697046 - 0.0122908i) q^{34} +(4.86828 - 9.55122i) q^{35} +(-2.45449 - 1.72496i) q^{36} +(1.80485 + 3.12609i) q^{37} +(-0.214210 - 1.21485i) q^{38} +(3.37450 + 8.16663i) q^{39} +(1.38584 + 3.80755i) q^{40} +(-6.51665 - 5.46812i) q^{41} +(-2.59938 + 3.77402i) q^{42} +(4.48570 + 1.63266i) q^{43} +(4.59170 - 2.65102i) q^{44} +(-11.0257 + 5.11827i) q^{45} +(2.01011 - 3.48161i) q^{46} +(1.49865 + 0.545464i) q^{47} +(-0.373429 - 1.69132i) q^{48} +(5.80217 + 3.91598i) q^{49} +(11.2445 + 1.98271i) q^{50} +(-0.0567013 + 0.108694i) q^{51} +(-1.74487 + 4.79400i) q^{52} +(3.11372 - 1.79771i) q^{53} +(4.95968 - 1.54971i) q^{54} -21.4834i q^{55} +(-2.57802 + 0.594803i) q^{56} +(1.89437 + 0.988221i) q^{57} +(-5.13446 - 4.30832i) q^{58} +(-5.72162 - 4.80101i) q^{59} +(-6.69148 - 2.11615i) q^{60} +(-0.497181 + 1.36599i) q^{61} +(1.86861 + 3.23652i) q^{62} +(-2.43869 - 7.55333i) q^{63} +(0.500000 - 0.866025i) q^{64} +(13.2874 + 15.8353i) q^{65} +(-1.20651 + 9.10380i) q^{66} +(-0.233472 + 1.32409i) q^{67} +(-0.0665113 + 0.0242081i) q^{68} +(2.65917 + 6.43547i) q^{69} +(-3.13576 + 10.2515i) q^{70} +(-9.55283 - 5.51533i) q^{71} +(2.71674 + 1.27253i) q^{72} +(6.81728 + 3.93596i) q^{73} +(-2.32027 - 2.76519i) q^{74} +(-14.5923 + 13.3483i) q^{75} +(0.421912 + 1.15919i) q^{76} +(13.9231 + 1.71152i) q^{77} +(-4.74135 - 7.45659i) q^{78} +(2.90676 + 16.4851i) q^{79} +(-2.02596 - 3.50906i) q^{80} +(-3.10728 + 8.44659i) q^{81} +(7.36718 + 4.25344i) q^{82} +(-8.74491 + 7.33785i) q^{83} +(1.90454 - 4.16806i) q^{84} +(-0.0498012 + 0.282437i) q^{85} +(-4.70106 - 0.828923i) q^{86} +(11.3361 - 2.50293i) q^{87} +(-4.06160 + 3.40809i) q^{88} -1.56656 q^{89} +(9.96938 - 6.95509i) q^{90} +(-11.3212 + 7.34981i) q^{91} +(-1.37500 + 3.77777i) q^{92} +(-6.41693 - 0.850425i) q^{93} +(-1.57060 - 0.276939i) q^{94} +(4.92246 + 0.867962i) q^{95} +(0.661450 + 1.60078i) q^{96} +(-0.436616 + 1.19959i) q^{97} +(-6.39402 - 2.84895i) q^{98} +(-11.2279 - 11.2667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) $ 144 * q + 18 * q^6 - 12 * q^9	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	0.801094	−	1.53566i	0.462512	−	0.886613i
$3$	0.801094	−	1.53566i	0.462512	−	0.886613i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	0.703607	−	3.99035i	0.314663	−	1.78454i	−0.259442	−	0.965759i	$-0.583539\pi$
$5$	0.703607	−	3.99035i	0.314663	−	1.78454i	0.574105	−	0.818782i	$-0.305350\pi$
$6$	−0.522259	+	1.65144i	−0.213211	+	0.674196i
$7$	2.53004	+	0.773898i	0.956264	+	0.292506i
$7$	2.53004	+	0.773898i	0.956264	+	0.292506i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−1.71650	−	2.46041i	−0.572166	−	0.820138i
$10$			4.05191i			1.28133i
$11$	5.22149	−	0.920690i	1.57434	−	0.277598i	0.682821	−	0.730585i	$-0.260753\pi$
$11$	5.22149	−	0.920690i	1.57434	−	0.277598i	0.891517	+	0.452987i	$0.149642\pi$
$12$	0.227556	−	1.71704i	0.0656897	−	0.495666i
$13$	−3.27929	+	3.90811i	−0.909511	+	1.08391i	0.0866378	+	0.996240i	$0.472388\pi$
$13$	−3.27929	+	3.90811i	−0.909511	+	1.08391i	−0.996149	+	0.0876736i	$0.972057\pi$
$14$	−2.62599	−	0.322804i	−0.701824	−	0.0862730i
$15$	−5.56417	−	4.27715i	−1.43666	−	1.10436i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.0707799			−0.0171666			−0.00858332	−	0.999963i	$-0.502732\pi$
$17$	−0.0707799			−0.0171666			−0.00858332	+	0.999963i	$0.502732\pi$
$18$	2.11767	+	2.12497i	0.499139	+	0.500860i
$19$			1.23359i			0.283005i	0.989938	+	0.141502i	$0.0451933\pi$
$19$			1.23359i			0.283005i	−0.989938	+	0.141502i	$0.954807\pi$
$20$	−0.703607	−	3.99035i	−0.157331	−	0.892270i
$21$	3.21524	−	3.26531i	0.701623	−	0.712549i
$22$	−4.98229	+	1.81340i	−1.06223	+	0.386619i
$23$	−2.58415	+	3.07967i	−0.538832	+	0.642155i	−0.964925	−	0.262524i	$-0.915445\pi$
$23$	−2.58415	+	3.07967i	−0.538832	+	0.642155i	0.426093	+	0.904679i	$0.359890\pi$
$24$	0.0740617	+	1.73047i	0.0151178	+	0.353230i
$25$	−10.7294	−	3.90518i	−2.14588	−	0.781037i
$26$	2.55083	−	4.41818i	0.500260	−	0.866476i
$27$	−5.15343	+	0.664930i	−0.991779	+	0.127966i
$28$	2.64214	−	0.138098i	0.499318	−	0.0260980i
$29$	4.30832	+	5.13446i	0.800035	+	0.953444i	0.999651	−	0.0264298i	$-0.00841384\pi$
$29$	4.30832	+	5.13446i	0.800035	+	0.953444i	−0.199616	+	0.979874i	$0.563969\pi$
$30$	6.22235	+	3.24596i	1.13604	+	0.592629i
$31$	−1.27820	−	3.51183i	−0.229572	−	0.630743i	0.770405	−	0.637555i	$-0.220054\pi$
$31$	−1.27820	−	3.51183i	−0.229572	−	0.630743i	−0.999977	+	0.00681139i	$0.997832\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	2.76904	−	8.75599i	0.482028	−	1.52422i
$34$	0.0697046	−	0.0122908i	0.0119542	−	0.00210785i
$35$	4.86828	−	9.55122i	0.822889	−	1.61445i
$36$	−2.45449	−	1.72496i	−0.409082	−	0.287493i
$37$	1.80485	+	3.12609i	0.296715	+	0.513926i	0.975382	−	0.220520i	$-0.0707755\pi$
$37$	1.80485	+	3.12609i	0.296715	+	0.513926i	−0.678667	+	0.734446i	$0.737442\pi$
$38$	−0.214210	−	1.21485i	−0.0347495	−	0.197074i
$39$	3.37450	+	8.16663i	0.540352	+	1.30771i
$40$	1.38584	+	3.80755i	0.219120	+	0.602027i
$41$	−6.51665	−	5.46812i	−1.01773	−	0.853977i	−0.0283894	−	0.999597i	$-0.509038\pi$
$41$	−6.51665	−	5.46812i	−1.01773	−	0.853977i	−0.989341	+	0.145620i	$0.953482\pi$
$42$	−2.59938	+	3.77402i	−0.401093	+	0.582344i
$43$	4.48570	+	1.63266i	0.684062	+	0.248978i	0.660591	−	0.750746i	$-0.270306\pi$
$43$	4.48570	+	1.63266i	0.684062	+	0.248978i	0.0234715	+	0.999725i	$0.492528\pi$
$44$	4.59170	−	2.65102i	0.692225	−	0.399656i
$45$	−11.0257	+	5.11827i	−1.64361	+	0.762986i
$46$	2.01011	−	3.48161i	0.296375	−	0.513336i
$47$	1.49865	+	0.545464i	0.218601	+	0.0795641i	0.448999	−	0.893532i	$-0.351781\pi$
$47$	1.49865	+	0.545464i	0.218601	+	0.0795641i	−0.230398	+	0.973096i	$0.574003\pi$
$48$	−0.373429	−	1.69132i	−0.0538998	−	0.244120i
$49$	5.80217	+	3.91598i	0.828881	+	0.559425i
$50$	11.2445	+	1.98271i	1.59022	+	0.280398i
$51$	−0.0567013	+	0.108694i	−0.00793977	+	0.0152202i
$52$	−1.74487	+	4.79400i	−0.241970	+	0.664808i
$53$	3.11372	−	1.79771i	0.427703	−	0.246934i	−0.270665	−	0.962674i	$-0.587244\pi$
$53$	3.11372	−	1.79771i	0.427703	−	0.246934i	0.698367	+	0.715739i	$0.253910\pi$
$54$	4.95968	−	1.54971i	0.674926	−	0.210889i
$55$		−	21.4834i		−	2.89682i
$56$	−2.57802	+	0.594803i	−0.344503	+	0.0794839i
$57$	1.89437	+	0.988221i	0.250916	+	0.130893i
$58$	−5.13446	−	4.30832i	−0.674187	−	0.565710i
$59$	−5.72162	−	4.80101i	−0.744892	−	0.625038i	0.189255	−	0.981928i	$-0.439393\pi$
$59$	−5.72162	−	4.80101i	−0.744892	−	0.625038i	−0.934147	+	0.356890i	$0.883837\pi$
$60$	−6.69148	−	2.11615i	−0.863866	−	0.273194i
$61$	−0.497181	+	1.36599i	−0.0636575	+	0.174898i	−0.967443	−	0.253087i	$-0.918554\pi$
$61$	−0.497181	+	1.36599i	−0.0636575	+	0.174898i	0.903786	+	0.427985i	$0.140776\pi$
$62$	1.86861	+	3.23652i	0.237313	+	0.411039i
$63$	−2.43869	−	7.55333i	−0.307246	−	0.951630i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	13.2874	+	15.8353i	1.64810	+	1.96413i
$66$	−1.20651	+	9.10380i	−0.148511	+	1.12060i
$67$	−0.233472	+	1.32409i	−0.0285232	+	0.161763i	−0.995742	−	0.0921800i	$-0.970616\pi$
$67$	−0.233472	+	1.32409i	−0.0285232	+	0.161763i	0.967219	+	0.253943i	$0.0817276\pi$
$68$	−0.0665113	+	0.0242081i	−0.00806568	+	0.00293567i
$69$	2.65917	+	6.43547i	0.320127	+	0.774740i
$70$	−3.13576	+	10.2515i	−0.374796	+	1.22529i
$71$	−9.55283	−	5.51533i	−1.13371	−	0.654549i	−0.188846	−	0.982007i	$-0.560475\pi$
$71$	−9.55283	−	5.51533i	−1.13371	−	0.654549i	−0.944866	+	0.327458i	$0.893808\pi$
$72$	2.71674	+	1.27253i	0.320171	+	0.149969i
$73$	6.81728	+	3.93596i	0.797902	+	0.460669i	0.842737	−	0.538326i	$-0.180943\pi$
$73$	6.81728	+	3.93596i	0.797902	+	0.460669i	−0.0448351	+	0.998994i	$0.514276\pi$
$74$	−2.32027	−	2.76519i	−0.269726	−	0.321447i
$75$	−14.5923	+	13.3483i	−1.68497	+	1.54133i
$76$	0.421912	+	1.15919i	0.0483967	+	0.132969i
$77$	13.9231	+	1.71152i	1.58668	+	0.195046i
$78$	−4.74135	−	7.45659i	−0.536852	−	0.844292i
$79$	2.90676	+	16.4851i	0.327036	+	1.85472i	0.494960	+	0.868916i	$0.335183\pi$
$79$	2.90676	+	16.4851i	0.327036	+	1.85472i	−0.167923	+	0.985800i	$0.553706\pi$
$80$	−2.02596	−	3.50906i	−0.226509	−	0.392325i
$81$	−3.10728	+	8.44659i	−0.345253	+	0.938510i
$82$	7.36718	+	4.25344i	0.813569	+	0.469714i
$83$	−8.74491	+	7.33785i	−0.959879	+	0.805434i	−0.980933	−	0.194344i	$-0.937742\pi$
$83$	−8.74491	+	7.33785i	−0.959879	+	0.805434i	0.0210545	+	0.999778i	$0.493298\pi$
$84$	1.90454	−	4.16806i	0.207802	−	0.454773i
$85$	−0.0498012	+	0.282437i	−0.00540170	+	0.0306346i
$86$	−4.70106	−	0.828923i	−0.506928	−	0.0893851i
$87$	11.3361	−	2.50293i	1.21536	−	0.268342i
$88$	−4.06160	+	3.40809i	−0.432968	+	0.363303i
$89$	−1.56656			−0.166055			−0.0830275	−	0.996547i	$-0.526459\pi$
$89$	−1.56656			−0.166055			−0.0830275	+	0.996547i	$0.526459\pi$
$90$	9.96938	−	6.95509i	1.05087	−	0.733131i
$91$	−11.3212	+	7.34981i	−1.18678	+	0.770470i
$92$	−1.37500	+	3.77777i	−0.143353	+	0.393860i
$93$	−6.41693	−	0.850425i	−0.665405	−	0.0881849i
$94$	−1.57060	−	0.276939i	−0.161995	−	0.0285641i
$95$	4.92246	+	0.867962i	0.505033	+	0.0890510i
$96$	0.661450	+	1.60078i	0.0675089	+	0.163379i
$97$	−0.436616	+	1.19959i	−0.0443316	+	0.121800i	−0.959883	−	0.280401i	$-0.909533\pi$
$97$	−0.436616	+	1.19959i	−0.0443316	+	0.121800i	0.915551	+	0.402201i	$0.131755\pi$
$98$	−6.39402	−	2.84895i	−0.645894	−	0.287787i
$99$	−11.2279	−	11.2667i	−1.12845	−	1.13234i
$100$	−11.4180			−1.14180
$101$	10.6873	−	8.96772i	1.06343	−	0.892321i	0.0689861	−	0.997618i	$-0.478024\pi$
$101$	10.6873	−	8.96772i	1.06343	−	0.892321i	0.994441	+	0.105296i	$0.0335791\pi$
$102$	0.0369654	−	0.116889i	0.00366012	−	0.0115737i
$103$	12.2562	+	2.16110i	1.20764	+	0.212940i	0.740999	−	0.671506i	$-0.234352\pi$
$103$	12.2562	+	2.16110i	1.20764	+	0.212940i	0.466643	+	0.884446i	$0.345463\pi$
$104$	0.885896	−	5.02416i	0.0868692	−	0.492660i
$105$	−10.7675	−	15.1274i	−1.05080	−	1.47629i
$106$	−2.75425	+	2.31109i	−0.267516	+	0.224473i
$107$	−6.95855	−	4.01752i	−0.672708	−	0.388388i	0.124394	−	0.992233i	$-0.460301\pi$
$107$	−6.95855	−	4.01752i	−0.672708	−	0.388388i	−0.797102	+	0.603845i	$0.793635\pi$
$108$	−4.61522	+	2.38741i	−0.444100	+	0.229728i
$109$	2.70701	+	4.68868i	0.259284	+	0.449094i	0.966050	−	0.258354i	$-0.0831799\pi$
$109$	2.70701	+	4.68868i	0.259284	+	0.449094i	−0.706766	+	0.707447i	$0.749847\pi$
$110$	3.73055	+	21.1570i	0.355694	+	2.01724i
$111$	6.24646	−	0.267340i	0.592888	−	0.0253748i
$112$	2.43557	−	1.03344i	0.230140	−	0.0976505i
$113$	4.91116	+	13.4933i	0.462003	+	1.26934i	0.923977	+	0.382449i	$0.124919\pi$
$113$	4.91116	+	13.4933i	0.462003	+	1.26934i	−0.461974	+	0.886894i	$0.652859\pi$
$114$	−2.03719	−	0.644253i	−0.190801	−	0.0603398i
$115$	10.4707	+	12.4785i	0.976402	+	1.16363i
$116$	5.80458	+	3.35128i	0.538942	+	0.311158i
$117$	15.2445	+	1.36016i	1.40935	+	0.125747i
$118$	6.46838	+	3.73452i	0.595463	+	0.343791i
$119$	−0.179076	−	0.0547764i	−0.0164158	−	0.00502134i
$120$	6.95729	+	0.922036i	0.635110	+	0.0841700i
$121$	16.0797	−	5.85252i	1.46179	−	0.532047i
$122$	0.252425	−	1.43158i	0.0228535	−	0.129609i
$123$	−13.6176	+	5.62688i	−1.22786	+	0.507358i
$124$	−2.40223	−	2.86287i	−0.215727	−	0.257093i
$125$	−13.0026	+	22.5211i	−1.16298	+	2.01435i
$126$	3.71326	+	7.01510i	0.330804	+	0.624955i
$127$	−2.18596	−	3.78619i	−0.193972	−	0.335970i	0.752591	−	0.658489i	$-0.228804\pi$
$127$	−2.18596	−	3.78619i	−0.193972	−	0.335970i	−0.946563	+	0.322518i	$0.895471\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	6.10067	−	5.58059i	0.537134	−	0.491343i
$130$	−15.8353	−	13.2874i	−1.38885	−	1.16538i
$131$	−7.77729	−	6.52592i	−0.679505	−	0.570172i	0.236357	−	0.971666i	$-0.424047\pi$
$131$	−7.77729	−	6.52592i	−0.679505	−	0.570172i	−0.915862	+	0.401494i	$0.868491\pi$
$132$	−0.392678	−	9.17500i	−0.0341782	−	0.798582i
$133$	−0.954671	+	3.12102i	−0.0827805	+	0.270627i
$134$		−	1.34451i		−	0.116148i
$135$	−0.972684	+	21.0319i	−0.0837153	+	1.81014i
$136$	0.0612972	−	0.0353899i	0.00525619	−	0.00303466i
$137$	1.90159	−	5.22457i	0.162464	−	0.446366i	−0.831572	−	0.555416i	$-0.812559\pi$
$137$	1.90159	−	5.22457i	0.162464	−	0.446366i	0.994036	+	0.109051i	$0.0347811\pi$
$138$	−3.73628	−	5.87594i	−0.318054	−	0.500194i
$139$	−5.21406	−	0.919379i	−0.442251	−	0.0779807i	−0.0519111	−	0.998652i	$-0.516531\pi$
$139$	−5.21406	−	0.919379i	−0.442251	−	0.0779807i	−0.390340	+	0.920671i	$0.627642\pi$
$140$	1.30797	−	10.6403i	0.110544	−	0.899266i
$141$	2.03821	−	1.86445i	0.171648	−	0.157015i
$142$	10.3654	+	3.77271i	0.869847	+	0.316598i
$143$	−13.5246	+	23.4253i	−1.13099	+	1.95893i
$144$	−2.89644	−	0.781444i	−0.241370	−	0.0651203i
$145$	23.5197	−	13.5791i	1.95320	−	1.12768i
$146$	−7.39718	−	2.69235i	−0.612195	−	0.222821i
$147$	10.6617	−	5.77308i	0.879361	−	0.476156i
$148$	2.76519	+	2.32027i	0.227297	+	0.190725i
$149$	0.537796	+	1.47758i	0.0440579	+	0.121048i	0.959770	−	0.280786i	$-0.0905951\pi$
$149$	0.537796	+	1.47758i	0.0440579	+	0.121048i	−0.915712	+	0.401834i	$0.868373\pi$
$150$	12.0527	−	15.6794i	0.984098	−	1.28022i
$151$	−2.51881	−	14.2849i	−0.204978	−	1.16249i	−0.897474	−	0.441067i	$-0.854600\pi$
$151$	−2.51881	−	14.2849i	−0.204978	−	1.16249i	0.692496	−	0.721422i	$-0.256511\pi$
$152$	−0.616794	−	1.06832i	−0.0500286	−	0.0866521i
$153$	0.121493	+	0.174148i	0.00982216	+	0.0140790i
$154$	−14.0088	+	0.732199i	−1.12886	+	0.0590022i
$155$	−14.9128	+	2.62953i	−1.19783	+	0.211209i
$156$	5.96414	+	6.51998i	0.477514	+	0.522016i
$157$	0.680760	−	0.811298i	0.0543305	−	0.0647486i	−0.738195	−	0.674588i	$-0.764321\pi$
$157$	0.680760	−	0.811298i	0.0543305	−	0.0647486i	0.792525	+	0.609839i	$0.208766\pi$
$158$	−5.72521	−	15.7299i	−0.455473	−	1.25140i
$159$	−0.266283	−	6.22175i	−0.0211176	−	0.493417i
$160$	2.60452	+	3.10394i	0.205905	+	0.245388i
$161$	−8.92134	+	5.79181i	−0.703100	+	0.456458i
$162$	1.59334	−	8.85784i	0.125184	−	0.695937i
$163$	7.82998	−	13.5619i	0.613291	−	1.06225i	−0.377391	−	0.926054i	$-0.623179\pi$
$163$	7.82998	−	13.5619i	0.613291	−	1.06225i	0.990682	−	0.136197i	$-0.0434881\pi$
$164$	−7.99386	−	2.90953i	−0.624215	−	0.227196i
$165$	−32.9912	−	17.2102i	−2.56836	−	1.33981i
$166$	7.33785	−	8.74491i	0.569528	−	0.678737i
$167$	15.0730	−	5.48612i	1.16638	−	0.424528i	0.315009	−	0.949089i	$-0.397993\pi$
$167$	15.0730	−	5.48612i	1.16638	−	0.424528i	0.851373	+	0.524560i	$0.175770\pi$
$168$	−1.15183	+	4.43546i	−0.0888652	+	0.342203i
$169$	−2.26212	−	12.8291i	−0.174009	−	0.986856i
$170$		−	0.286794i		−	0.0219961i
$171$	3.03514	−	2.11745i	0.232103	−	0.161926i
$172$	4.77358			0.363982
$173$	−3.54928	+	2.97820i	−0.269847	+	0.226428i	−0.767662	−	0.640855i	$-0.778580\pi$
$173$	−3.54928	+	2.97820i	−0.269847	+	0.226428i	0.497816	+	0.867283i	$0.334136\pi$
$174$	−10.7293	+	4.43340i	−0.813385	+	0.336095i
$175$	−24.1236	−	18.1837i	−1.82357	−	1.37456i
$176$	3.40809	−	4.06160i	0.256894	−	0.306154i
$177$	−11.9563	+	4.94040i	−0.898688	+	0.371343i
$178$	1.54276	−	0.272030i	0.115635	−	0.0203895i
$179$		−	3.62945i		−	0.271278i	−0.990758	−	0.135639i	$-0.956691\pi$
$179$		−	3.62945i		−	0.271278i	0.990758	−	0.135639i	$-0.0433087\pi$
$180$	−8.61019	+	8.58060i	−0.641765	+	0.639560i
$181$	0.101409	−	0.0585484i	0.00753765	−	0.00435187i	−0.496226	−	0.868193i	$-0.665281\pi$
$181$	0.101409	−	0.0585484i	0.00753765	−	0.00435187i	0.503764	+	0.863841i	$0.331948\pi$
$182$	9.87292	−	9.20406i	0.731829	−	0.682250i
$183$	1.69941	+	1.85779i	0.125624	+	0.137332i
$184$	0.698104	−	3.95915i	0.0514649	−	0.291872i
$185$	13.7441	−	5.00244i	1.01049	−	0.367787i
$186$	6.46712	−	0.276784i	0.474192	−	0.0202948i
$187$	−0.369576	+	0.0651663i	−0.0270261	+	0.00476543i
$188$	1.59483			0.116315
$189$	−13.5530	−	2.30593i	−0.985833	−	0.167732i
$190$	−4.99839			−0.362622
$191$	17.1090	−	3.01677i	1.23796	−	0.218286i	0.483919	−	0.875113i	$-0.339213\pi$
$191$	17.1090	−	3.01677i	1.23796	−	0.218286i	0.754041	+	0.656827i	$0.228102\pi$
$192$	−0.929373	−	1.46160i	−0.0670717	−	0.105482i
$193$	7.96887	−	2.90043i	0.573612	−	0.208778i	−0.0388946	−	0.999243i	$-0.512384\pi$
$193$	7.96887	−	2.90043i	0.573612	−	0.208778i	0.612506	+	0.790466i	$0.290161\pi$
$194$	0.221676	−	1.25719i	0.0159154	−	0.0902607i
$195$	34.9621	−	7.71934i	2.50369	−	0.552794i
$196$	6.79160	+	1.69536i	0.485114	+	0.121097i
$197$	−2.04313	+	1.17960i	−0.145567	+	0.0840433i	−0.571015	−	0.820940i	$-0.693450\pi$
$197$	−2.04313	+	1.17960i	−0.145567	+	0.0840433i	0.425447	+	0.904983i	$0.360117\pi$
$198$	13.0138	+	9.14579i	0.924851	+	0.649963i
$199$		−	11.3089i		−	0.801669i	−0.916150	−	0.400835i	$-0.868720\pi$
$199$		−	11.3089i		−	0.801669i	0.916150	−	0.400835i	$-0.131280\pi$
$200$	11.2445	−	1.98271i	0.795108	−	0.140199i
$201$	1.84631	+	1.41925i	0.130229	+	0.100106i
$202$	−8.96772	+	10.6873i	−0.630966	+	0.751956i
$203$	6.92666	+	16.3246i	0.486156	+	1.14576i
$204$	−0.0161064	+	0.121532i	−0.00112767	+	0.00850892i
$205$	−26.4049	+	22.1563i	−1.84420	+	1.54747i
$206$	−12.4453			−0.867105
$207$	12.0129	+	1.07184i	0.834957	+	0.0744977i
$208$			5.10167i			0.353737i
$209$	1.13575	+	6.44117i	0.0785616	+	0.445545i
$210$	13.2307	+	13.0279i	0.913008	+	0.899008i
$211$	−2.86375	+	1.04232i	−0.197149	+	0.0717562i	−0.438707	−	0.898630i	$-0.644564\pi$
$211$	−2.86375	+	1.04232i	−0.197149	+	0.0717562i	0.241559	+	0.970386i	$0.422341\pi$
$212$	2.31109	−	2.75425i	0.158726	−	0.189163i
$213$	−16.1224	+	10.2516i	−1.10469	+	0.702427i
$214$	7.55047	+	2.74815i	0.516139	+	0.187859i
$215$	9.67106	−	16.7508i	0.659561	−	1.14239i
$216$	4.13054	−	3.15256i	0.281048	−	0.214505i
$217$	−0.516100	−	9.87426i	−0.0350351	−	0.670308i
$218$	−3.48006	−	4.14738i	−0.235700	−	0.280896i
$219$	11.5056	−	7.31594i	0.777474	−	0.494365i
$220$	−7.34776	−	20.1878i	−0.495386	−	1.36106i
$221$	0.232108	−	0.276615i	0.0156133	−	0.0186072i
$222$	−6.10514	+	1.34796i	−0.409750	+	0.0904695i
$223$	−11.2251	+	1.97929i	−0.751688	+	0.132543i	−0.536349	−	0.843997i	$-0.680197\pi$
$223$	−11.2251	+	1.97929i	−0.751688	+	0.132543i	−0.215339	+	0.976539i	$0.569086\pi$
$224$	−2.21912	+	1.44067i	−0.148271	+	0.0962587i
$225$	8.80862	+	33.1020i	0.587241	+	2.20680i
$226$	−7.17963	−	12.4355i	−0.477582	−	0.827197i
$227$	0.149301	+	0.846726i	0.00990944	+	0.0561992i	0.989362	−	0.145478i	$-0.0464720\pi$
$227$	0.149301	+	0.846726i	0.00990944	+	0.0561992i	−0.979452	+	0.201677i	$0.935361\pi$
$228$	2.11812	+	0.280710i	0.140276	+	0.0185905i
$229$	0.674987	+	1.85451i	0.0446044	+	0.122549i	0.959995	−	0.280017i	$-0.0903403\pi$
$229$	0.674987	+	1.85451i	0.0446044	+	0.122549i	−0.915391	+	0.402567i	$0.868118\pi$
$230$	−12.4785	−	10.4707i	−0.822811	−	0.690420i
$231$	13.7820	−	20.0100i	0.906789	−	1.31656i
$232$	−6.29834	−	2.29241i	−0.413506	−	0.150504i
$233$	−2.65415	+	1.53237i	−0.173879	+	0.100389i	−0.584414	−	0.811456i	$-0.698675\pi$
$233$	−2.65415	+	1.53237i	−0.173879	+	0.100389i	0.410535	+	0.911845i	$0.365342\pi$
$234$	−15.2490	+	1.30767i	−0.996861	+	0.0854853i
$235$	3.23105	−	5.59635i	0.210771	−	0.365066i
$236$	−7.01861	−	2.55456i	−0.456872	−	0.166288i
$237$	27.6440	+	8.74230i	1.79567	+	0.567873i
$238$	0.185867	+	0.0228480i	0.0120480	+	0.00148102i
$239$	12.4097	+	2.18816i	0.802714	+	0.141540i	0.559930	−	0.828540i	$-0.310828\pi$
$239$	12.4097	+	2.18816i	0.802714	+	0.141540i	0.242784	+	0.970080i	$0.421939\pi$
$240$	−7.01170	+	0.300092i	−0.452603	+	0.0193708i
$241$	9.45391	−	25.9744i	0.608980	−	1.67316i	−0.123478	−	0.992347i	$-0.539405\pi$
$241$	9.45391	−	25.9744i	0.608980	−	1.67316i	0.732459	−	0.680812i	$-0.238373\pi$
$242$	−14.8191	+	8.55581i	−0.952608	+	0.549989i
$243$	10.4819	+	11.5382i	0.672411	+	0.740178i
$244$			1.45366i			0.0930611i
$245$	19.7086	−	20.3974i	1.25914	−	1.30314i
$246$	12.4336	−	7.90607i	0.792740	−	0.504072i
$247$	−4.82100	−	4.04530i	−0.306753	−	0.257396i
$248$	2.86287	+	2.40223i	0.181792	+	0.152542i
$249$	4.26294	+	19.3075i	0.270153	+	1.22356i
$250$	8.89428	−	24.4368i	0.562524	−	1.54552i
$251$	−7.38452	−	12.7904i	−0.466107	−	0.807320i	0.533144	−	0.846024i	$-0.321010\pi$
$251$	−7.38452	−	12.7904i	−0.466107	−	0.807320i	−0.999251	+	0.0387041i	$0.987677\pi$
$252$	−4.87501	−	6.26373i	−0.307097	−	0.394578i
$253$	−10.6577	+	18.4597i	−0.670043	+	1.16055i
$254$	2.81021	+	3.34908i	0.176328	+	0.210140i
$255$	0.393831	+	0.302736i	0.0246627	+	0.0189581i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−8.02332	+	2.92025i	−0.500481	+	0.182160i	−0.579910	−	0.814680i	$-0.696912\pi$
$257$	−8.02332	+	2.92025i	−0.500481	+	0.182160i	0.0794295	+	0.996840i	$0.474690\pi$
$258$	−5.03893	+	6.55517i	−0.313710	+	0.408107i
$259$	2.14706	+	9.30588i	0.133412	+	0.578239i
$260$	17.9021	+	10.3358i	1.11024	+	0.640997i
$261$	5.23767	−	19.4135i	0.324204	−	1.20167i
$262$	8.79235	+	5.07627i	0.543193	+	0.313613i
$263$	−4.16955	−	4.96908i	−0.257106	−	0.306407i	0.622016	−	0.783005i	$-0.286314\pi$
$263$	−4.16955	−	4.96908i	−0.257106	−	0.306407i	−0.879121	+	0.476598i	$0.841870\pi$
$264$	1.97994	+	8.96743i	0.121857	+	0.551907i
$265$	−4.98265	−	13.6897i	−0.306082	−	0.840953i
$266$	0.398208	−	3.23939i	0.0244157	−	0.198619i
$267$	−1.25496	+	2.40570i	−0.0768024	+	0.147227i
$268$	0.233472	+	1.32409i	0.0142616	+	0.0808816i
$269$	7.02738	+	12.1718i	0.428467	+	0.742126i	0.996737	−	0.0807155i	$-0.0257205\pi$
$269$	7.02738	+	12.1718i	0.428467	+	0.742126i	−0.568270	+	0.822842i	$0.692387\pi$
$270$	−2.69424	−	20.8813i	−0.163966	−	1.27079i
$271$	5.80719	+	3.35278i	0.352762	+	0.203667i	0.665901	−	0.746040i	$-0.268047\pi$
$271$	5.80719	+	3.35278i	0.352762	+	0.203667i	−0.313139	+	0.949707i	$0.601381\pi$
$272$	−0.0542205	+	0.0454964i	−0.00328760	+	0.00275863i
$273$	2.21747	+	23.2734i	0.134207	+	1.40857i
$274$	−0.965462	+	5.47541i	−0.0583257	+	0.330782i
$275$	−59.6189	−	10.5124i	−3.59516	−	0.633923i
$276$	4.69987	+	5.13788i	0.282899	+	0.309264i
$277$	−23.8217	+	19.9888i	−1.43131	+	1.20101i	−0.486376	+	0.873749i	$0.661682\pi$
$277$	−23.8217	+	19.9888i	−1.43131	+	1.20101i	−0.944934	+	0.327262i	$0.893874\pi$
$278$	5.29449			0.317543
$279$	−6.44653	+	9.17295i	−0.385944	+	0.549170i
$280$	0.559559	+	10.7057i	0.0334400	+	0.639790i
$281$	−8.53785	+	23.4575i	−0.509325	+	1.39936i	0.372609	+	0.927988i	$0.378463\pi$
$281$	−8.53785	+	23.4575i	−0.509325	+	1.39936i	−0.881935	+	0.471372i	$0.843759\pi$
$282$	−1.68348	+	2.19005i	−0.100250	+	0.130416i
$283$	−23.7156	−	4.18169i	−1.40974	−	0.248576i	−0.583603	−	0.812039i	$-0.698357\pi$
$283$	−23.7156	−	4.18169i	−1.40974	−	0.248576i	−0.826141	+	0.563464i	$0.809469\pi$
$284$	−10.8631	−	1.91545i	−0.644605	−	0.113661i
$285$	5.27624	−	6.86390i	0.312538	−	0.406582i
$286$	9.25139	−	25.4180i	0.547046	−	1.50300i
$287$	−12.2556	−	18.8778i	−0.723425	−	1.11432i
$288$	2.98813	+	0.266611i	0.176077	+	0.0157102i
$289$	−16.9950			−0.999705
$290$	−20.8044	+	17.4569i	−1.22167	+	1.02511i
$291$	1.49239	+	1.63148i	0.0874857	+	0.0956390i
$292$	7.75232	+	1.36694i	0.453670	+	0.0799943i
$293$	−4.30025	+	24.3879i	−0.251223	+	1.42476i	0.554361	+	0.832277i	$0.312963\pi$
$293$	−4.30025	+	24.3879i	−0.251223	+	1.42476i	−0.805584	+	0.592482i	$0.798148\pi$
$294$	−9.49723	+	7.53676i	−0.553889	+	0.439553i
$295$	−23.1835	+	19.4533i	−1.34980	+	1.13261i
$296$	−3.12609	−	1.80485i	−0.181700	−	0.104905i
$297$	−26.2964	+	8.21664i	−1.52587	+	0.476778i
$298$	−0.786205	−	1.36175i	−0.0455436	−	0.0788838i
$299$	−3.56150	−	20.1983i	−0.205967	−	1.16810i
$300$	−9.14688	+	17.5341i	−0.528096	+	1.01233i
$301$	10.0855	+	7.60216i	0.581316	+	0.438181i
$302$	4.96110	+	13.6305i	0.285479	+	0.784347i
$303$	−5.20982	−	23.5960i	−0.299296	−	1.35556i
$304$	0.792936	+	0.944984i	0.0454780	+	0.0541985i
$305$	5.10098	+	2.94505i	0.292081	+	0.168633i
$306$	−0.149888	−	0.150405i	−0.00856853	−	0.00859808i
$307$	16.0776	+	9.28239i	0.917596	+	0.529774i	0.882867	−	0.469623i	$-0.155610\pi$
$307$	16.0776	+	9.28239i	0.917596	+	0.529774i	0.0347286	+	0.999397i	$0.488943\pi$
$308$	13.6688	−	3.15367i	0.778851	−	0.179697i
$309$	13.1371	−	17.0901i	0.747344	−	0.972224i
$310$	14.2296	−	5.17916i	0.808189	−	0.294157i
$311$	−3.43225	+	19.4652i	−0.194625	+	1.10377i	0.718327	+	0.695705i	$0.244908\pi$
$311$	−3.43225	+	19.4652i	−0.194625	+	1.10377i	−0.912952	+	0.408067i	$0.866203\pi$
$312$	−7.00572	−	5.38526i	−0.396621	−	0.304880i
$313$	2.46602	+	2.93888i	0.139387	+	0.166115i	0.831222	−	0.555940i	$-0.187642\pi$
$313$	2.46602	+	2.93888i	0.139387	+	0.166115i	−0.691835	+	0.722056i	$0.743197\pi$
$314$	−0.529537	+	0.917185i	−0.0298835	+	0.0517597i
$315$	−31.8563	+	4.41666i	−1.79490	+	0.248851i
$316$	8.36969	+	14.4967i	0.470832	+	0.815505i
$317$	−11.3121	+	31.0797i	−0.635350	+	1.74561i	0.0305126	+	0.999534i	$0.490286\pi$
$317$	−11.3121	+	31.0797i	−0.635350	+	1.74561i	−0.665862	+	0.746075i	$0.731936\pi$
$318$	1.34263	+	6.08098i	0.0752911	+	0.341005i
$319$	27.2231	+	22.8429i	1.52420	+	1.27896i
$320$	−3.10394	−	2.60452i	−0.173516	−	0.145597i
$321$	−11.7440	+	7.46755i	−0.655486	+	0.416798i
$322$	7.78007	−	7.25299i	0.433566	−	0.404193i
$323$		−	0.0873132i		−	0.00485824i
$324$	−0.0309829	+	8.99995i	−0.00172127	+	0.499997i
$325$	50.4467	−	29.1254i	2.79828	−	1.61559i
$326$	−5.35602	+	14.7155i	−0.296642	+	0.815018i
$327$	9.36878	−	0.400972i	0.518095	−	0.0221738i
$328$	8.37765	+	1.47721i	0.462578	+	0.0815650i
$329$	3.36950	+	2.53984i	0.185767	+	0.140026i
$330$	35.4785	+	11.2199i	1.95303	+	0.617635i
$331$	−4.83490	−	1.75976i	−0.265750	−	0.0967250i	0.205709	−	0.978613i	$-0.434050\pi$
$331$	−4.83490	−	1.75976i	−0.265750	−	0.0967250i	−0.471459	+	0.881888i	$0.656272\pi$
$332$	−5.70784	+	9.88626i	−0.313258	+	0.542579i
$333$	4.59346	−	9.80659i	0.251720	−	0.537398i
$334$	−13.8913	+	8.02016i	−0.760100	+	0.438844i
$335$	5.11931	+	1.86328i	0.279698	+	0.101802i
$336$	0.364117	−	4.56809i	0.0198642	−	0.249210i
$337$	−20.1975	−	16.9477i	−1.10023	−	0.923200i	−0.102786	−	0.994703i	$-0.532776\pi$
$337$	−20.1975	−	16.9477i	−1.10023	−	0.923200i	−0.997440	+	0.0715039i	$0.977220\pi$
$338$	4.45551	+	12.2414i	0.242348	+	0.665845i
$339$	24.6554	+	3.26754i	1.33910	+	0.177468i
$340$	0.0498012	+	0.282437i	0.00270085	+	0.0153173i
$341$	−9.90743	−	17.1602i	−0.536517	−	0.929275i
$342$	−2.62134	+	2.61233i	−0.141746	+	0.141259i
$343$	11.6491	+	14.3978i	0.628993	+	0.777411i
$344$	−4.70106	+	0.828923i	−0.253464	+	0.0446925i
$345$	27.5508	−	6.08300i	1.48329	−	0.327498i
$346$	2.97820	−	3.54928i	0.160109	−	0.190810i
$347$	1.45017	+	3.98432i	0.0778494	+	0.213889i	0.972512	−	0.232853i	$-0.0748062\pi$
$347$	1.45017	+	3.98432i	0.0778494	+	0.213889i	−0.894662	+	0.446743i	$0.852584\pi$
$348$	9.79644	−	6.22917i	0.525144	−	0.333919i
$349$	−12.6126	−	15.0311i	−0.675135	−	0.804594i	0.314338	−	0.949311i	$-0.398217\pi$
$349$	−12.6126	−	15.0311i	−0.675135	−	0.804594i	−0.989473	+	0.144717i	$0.953773\pi$
$350$	26.9146	+	13.7184i	1.43865	+	0.733282i
$351$	14.3010	−	22.3207i	0.763330	−	1.19139i
$352$	−2.65102	+	4.59170i	−0.141300	+	0.244739i
$353$	−14.8607	−	5.40885i	−0.790955	−	0.287884i	−0.0852220	−	0.996362i	$-0.527160\pi$
$353$	−14.8607	−	5.40885i	−0.790955	−	0.287884i	−0.705733	+	0.708478i	$0.749382\pi$
$354$	10.9167	−	6.94153i	0.580218	−	0.368938i
$355$	−28.7295	+	34.2385i	−1.52481	+	1.81719i
$356$	−1.47209	+	0.535795i	−0.0780204	+	0.0283971i
$357$	−0.227574	+	0.231118i	−0.0120445	+	0.0122321i
$358$	0.630248	+	3.57431i	0.0333096	+	0.188908i
$359$		−	20.2946i		−	1.07111i	−0.844502	−	0.535553i	$-0.820103\pi$
$359$		−	20.2946i		−	1.07111i	0.844502	−	0.535553i	$-0.179897\pi$
$360$	6.98937	−	9.94538i	0.368372	−	0.524168i
$361$	17.4783			0.919908
$362$	−0.0897013	+	0.0752683i	−0.00471460	+	0.00395602i
$363$	3.89385	−	29.3813i	0.204374	−	1.54212i
$364$	−8.12466	+	10.7786i	−0.425848	+	0.564954i
$365$	20.5025	−	24.4340i	1.07315	−	1.27893i
$366$	−1.99620	−	1.53447i	−0.104343	−	0.0802078i
$367$	15.7756	−	2.78167i	0.823482	−	0.145202i	0.253998	−	0.967205i	$-0.418254\pi$
$367$	15.7756	−	2.78167i	0.823482	−	0.145202i	0.569484	+	0.822003i	$0.307143\pi$
$368$			4.02022i			0.209569i
$369$	−2.26803	+	25.4197i	−0.118069	+	1.32330i
$370$	−12.6666	+	7.31308i	−0.658507	+	0.380189i
$371$	9.26907	−	2.13856i	0.481226	−	0.111029i
$372$	−6.32081	+	1.39558i	−0.327719	+	0.0723576i
$373$	−0.198779	+	1.12733i	−0.0102924	+	0.0583710i	−0.989521	−	0.144386i	$-0.953879\pi$
$373$	−0.198779	+	1.12733i	−0.0102924	+	0.0583710i	0.979229	+	0.202757i	$0.0649903\pi$
$374$	0.352646	−	0.128353i	0.0182349	−	0.00663695i
$375$	24.1685	+	38.0090i	1.24805	+	1.96278i
$376$	−1.57060	+	0.276939i	−0.0809975	+	0.0142821i
$377$	−34.1942			−1.76109
$378$	13.7475	−	0.0825483i	0.707094	−	0.00424583i
$379$	−24.3341			−1.24996			−0.624979	−	0.780642i	$-0.714892\pi$
$379$	−24.3341			−1.24996			−0.624979	+	0.780642i	$0.714892\pi$
$380$	4.92246	−	0.867962i	0.252517	−	0.0445255i
$381$	−7.56545	+	0.323792i	−0.387590	+	0.0165883i
$382$	−16.3252	+	5.94188i	−0.835268	+	0.304013i
$383$	3.04627	−	17.2762i	0.155657	−	0.882775i	−0.802526	−	0.596618i	$-0.796511\pi$
$383$	3.04627	−	17.2762i	0.155657	−	0.882775i	0.958183	−	0.286157i	$-0.0923780\pi$
$384$	1.16906	+	1.27801i	0.0596582	+	0.0652181i
$385$	16.6259	−	54.3538i	0.847337	−	2.77012i
$386$	−7.34415	+	4.24015i	−0.373807	+	0.215818i
$387$	−3.68266	−	13.8391i	−0.187200	−	0.703482i
$388$			1.27658i			0.0648085i
$389$	−30.8992	+	5.44835i	−1.56665	+	0.276243i	−0.888568	−	0.458745i	$-0.848299\pi$
$389$	−30.8992	+	5.44835i	−1.56665	+	0.276243i	−0.678081	+	0.734987i	$0.737188\pi$
$390$	−33.0905	+	13.6732i	−1.67560	+	0.692368i
$391$	0.182906	−	0.217978i	0.00924994	−	0.0110236i
$392$	−6.98281	−	0.490253i	−0.352685	−	0.0247615i
$393$	−16.2519	+	6.71539i	−0.819802	+	0.338747i
$394$	1.80726	−	1.51647i	0.0910483	−	0.0763986i
$395$	67.8265			3.41272
$396$	−14.4042	−	6.74702i	−0.723841	−	0.339051i
$397$			8.28248i			0.415686i	0.978162	+	0.207843i	$0.0666443\pi$
$397$			8.28248i			0.415686i	−0.978162	+	0.207843i	$0.933356\pi$
$398$	1.96378	+	11.1371i	0.0984352	+	0.558254i
$399$	4.02805	+	3.96628i	0.201655	+	0.198563i
$400$	−10.7294	+	3.90518i	−0.536470	+	0.195259i
$401$	17.8802	−	21.3088i	0.892893	−	1.06411i	−0.104681	−	0.994506i	$-0.533382\pi$
$401$	17.8802	−	21.3088i	0.892893	−	1.06411i	0.997575	−	0.0696032i	$-0.0221733\pi$
$402$	−2.06472	−	1.07708i	−0.102979	−	0.0537200i
$403$	17.9162	+	6.52096i	0.892470	+	0.324832i
$404$	6.97565	−	12.0822i	0.347051	−	0.601111i
$405$	31.5186	+	18.3422i	1.56617	+	0.911432i
$406$	−9.65616	−	14.8737i	−0.479227	−	0.738172i
$407$	12.3022	+	14.6611i	0.609795	+	0.726725i
$408$	−0.00524208	−	0.122482i	−0.000259522	−	0.00606377i
$409$	−3.73437	−	10.2601i	−0.184653	−	0.507329i	0.812481	−	0.582988i	$-0.198116\pi$
$409$	−3.73437	−	10.2601i	−0.184653	−	0.507329i	−0.997134	+	0.0756583i	$0.975894\pi$
$410$	22.1563	−	26.4049i	1.09422	−	1.30405i
$411$	−6.49981	−	7.10557i	−0.320612	−	0.350492i
$412$	12.2562	−	2.16110i	0.603821	−	0.106470i
$413$	−10.7604	−	16.5747i	−0.529486	−	0.815587i
$414$	−12.0166	+	1.03047i	−0.590582	+	0.0506450i
$415$	23.1277	+	40.0583i	1.13529	+	1.96638i
$416$	−0.885896	−	5.02416i	−0.0434346	−	0.246330i
$417$	−5.58880	+	7.27051i	−0.273685	+	0.356038i
$418$	−2.23700	−	6.14609i	−0.109415	−	0.300615i
$419$	−17.3720	−	14.5769i	−0.848679	−	0.712126i	0.110820	−	0.993841i	$-0.464652\pi$
$419$	−17.3720	−	14.5769i	−0.848679	−	0.712126i	−0.959498	+	0.281715i	$0.909097\pi$
$420$	−15.2920	−	10.5325i	−0.746173	−	0.513931i
$421$	11.4055	+	4.15128i	0.555872	+	0.202321i	0.604654	−	0.796489i	$-0.293312\pi$
$421$	11.4055	+	4.15128i	0.555872	+	0.202321i	−0.0487815	+	0.998809i	$0.515534\pi$
$422$	2.63925	−	1.52377i	0.128476	−	0.0741759i
$423$	−1.23036	−	4.62359i	−0.0598222	−	0.224806i
$424$	−1.79771	+	3.11372i	−0.0873044	+	0.151216i
$425$	0.759426	+	0.276408i	0.0368376	+	0.0134078i
$426$	14.0973	−	12.8955i	0.683015	−	0.624787i
$427$	−2.31503	+	3.07125i	−0.112032	+	0.148628i
$428$	−7.91297	−	1.39527i	−0.382488	−	0.0674429i
$429$	25.1388	+	39.5351i	1.21371	+	1.90877i
$430$	−6.61539	+	18.1756i	−0.319023	+	0.876507i
$431$	−24.5530	+	14.1757i	−1.18268	+	0.682818i	−0.956632	−	0.291299i	$-0.905912\pi$
$431$	−24.5530	+	14.1757i	−1.18268	+	0.682818i	−0.226043	+	0.974117i	$0.572579\pi$
$432$	−3.52035	+	3.82193i	−0.169373	+	0.183883i
$433$			0.872612i			0.0419350i	0.999780	+	0.0209675i	$0.00667466\pi$
$433$			0.872612i			0.0419350i	−0.999780	+	0.0209675i	$0.993325\pi$
$434$	2.22291	+	9.63462i	0.106703	+	0.462477i
$435$	−2.01138	−	46.9963i	−0.0964383	−	2.25330i
$436$	4.14738	+	3.48006i	0.198623	+	0.166665i
$437$	−3.79904	−	3.18778i	−0.181733	−	0.152492i
$438$	−10.0604	+	9.20272i	−0.480703	+	0.439723i
$439$	−11.8971	+	32.6871i	−0.567820	+	1.56007i	0.240081	+	0.970753i	$0.422826\pi$
$439$	−11.8971	+	32.6871i	−0.567820	+	1.56007i	−0.807900	+	0.589319i	$0.799396\pi$
$440$	10.7417	+	18.6052i	0.512090	+	0.886967i
$441$	−0.324471	−	20.9975i	−0.0154510	−	0.999881i
$442$	−0.180548	+	0.312718i	−0.00858778	+	0.0148745i
$443$	−20.9681	−	24.9888i	−0.996224	−	1.18725i	−0.982293	−	0.187351i	$-0.940010\pi$
$443$	−20.9681	−	24.9888i	−0.996224	−	1.18725i	−0.0139314	−	0.999903i	$-0.504435\pi$
$444$	5.77831	−	2.38763i	0.274227	−	0.113312i
$445$	−1.10224	+	6.25113i	−0.0522513	+	0.296332i
$446$	10.7109	−	3.89843i	0.507174	−	0.184596i
$447$	2.69989	+	0.357811i	0.127700	+	0.0169239i
$448$	1.93523	−	1.80413i	0.0914312	−	0.0852370i
$449$	−8.01682	−	4.62851i	−0.378337	−	0.218433i	0.298757	−	0.954329i	$-0.403428\pi$
$449$	−8.01682	−	4.62851i	−0.378337	−	0.218433i	−0.677094	+	0.735896i	$0.736761\pi$
$450$	−14.4229	−	31.0695i	−0.679902	−	1.46463i
$451$	−39.0611	−	22.5519i	−1.83931	−	1.06193i
$452$	9.22996	+	10.9998i	0.434141	+	0.517389i
$453$	−23.9546	−	7.57551i	−1.12548	−	0.355929i
$454$	−0.294065	−	0.807937i	−0.0138012	−	0.0379184i
$455$	21.3627	+	50.3470i	1.00150	+	2.36030i
$456$	−2.13468	+	0.0913617i	−0.0999658	+	0.00427840i
$457$	−3.10284	−	17.5971i	−0.145145	−	0.823156i	−0.967251	−	0.253822i	$-0.918312\pi$
$457$	−3.10284	−	17.5971i	−0.145145	−	0.823156i	0.822106	−	0.569334i	$-0.192799\pi$
$458$	−0.986764	−	1.70913i	−0.0461085	−	0.0798622i
$459$	0.364759	−	0.0470637i	0.0170255	−	0.00219674i
$460$	14.1072	+	8.14479i	0.657751	+	0.379753i
$461$	27.6538	−	23.2043i	1.28797	−	1.08073i	0.295874	−	0.955227i	$-0.404389\pi$
$461$	27.6538	−	23.2043i	1.28797	−	1.08073i	0.992093	−	0.125505i	$-0.0400552\pi$
$462$	−10.0979	+	22.0992i	−0.469798	+	1.02815i
$463$	1.33590	−	7.57624i	0.0620843	−	0.352098i	−0.937902	−	0.346900i	$-0.887234\pi$
$463$	1.33590	−	7.57624i	0.0620843	−	0.352098i	0.999986	−	0.00519778i	$-0.00165451\pi$
$464$	6.60073	+	1.16389i	0.306431	+	0.0540321i
$465$	−7.90850	+	25.0075i	−0.366748	+	1.15969i
$466$	2.34773	−	1.96998i	0.108757	−	0.0912576i
$467$	−5.67332			−0.262530			−0.131265	−	0.991347i	$-0.541904\pi$
$467$	−5.67332			−0.262530			−0.131265	+	0.991347i	$0.541904\pi$
$468$	14.7903	−	3.93578i	0.683682	−	0.181931i
$469$	−1.61540	+	3.16931i	−0.0745923	+	0.146345i
$470$	−2.21017	+	6.07240i	−0.101948	+	0.280099i
$471$	−0.700524	−	1.69534i	−0.0322784	−	0.0781172i
$472$	7.35557	+	1.29699i	0.338568	+	0.0596986i
$473$	24.9252	+	4.39498i	1.14606	+	0.202082i
$474$	−28.7422	−	3.80914i	−1.32017	−	0.174960i
$475$	4.81739	−	13.2357i	0.221037	−	0.607294i
$476$	−0.187011	+	0.00977452i	−0.00857162	+	0.000448015i
$477$	−9.76780	−	4.57528i	−0.447237	−	0.209488i
$478$	−12.6011			−0.576361
$479$	5.37405	−	4.50936i	0.245547	−	0.206038i	−0.511705	−	0.859161i	$-0.670986\pi$
$479$	5.37405	−	4.50936i	0.245547	−	0.206038i	0.757252	+	0.653123i	$0.226542\pi$
$480$	6.85306	−	1.51310i	0.312798	−	0.0690633i
$481$	−18.1357	−	3.19781i	−0.826917	−	0.145808i
$482$	−4.79988	+	27.2215i	−0.218628	+	1.23990i
$483$	1.74741	+	18.3399i	0.0795099	+	0.834495i
$484$	13.1083	−	10.9991i	0.595830	−	0.499961i
$485$	4.47959	+	2.58629i	0.203408	+	0.117438i
$486$	−12.3262	−	9.54278i	−0.559128	−	0.432869i
$487$	−1.07304	−	1.85856i	−0.0486240	−	0.0842193i	0.840689	−	0.541518i	$-0.182150\pi$
$487$	−1.07304	−	1.85856i	−0.0486240	−	0.0842193i	−0.889313	+	0.457299i	$0.848817\pi$
$488$	−0.252425	−	1.43158i	−0.0114268	−	0.0648044i
$489$	−14.5539	−	22.8885i	−0.658152	−	1.03506i
$490$	−15.8672	+	23.5099i	−0.716807	+	1.06207i
$491$	−0.239723	−	0.658633i	−0.0108185	−	0.0297237i	0.934166	−	0.356839i	$-0.116146\pi$
$491$	−0.239723	−	0.658633i	−0.0108185	−	0.0297237i	−0.944984	+	0.327116i	$0.893923\pi$
$492$	−10.8719	+	9.94503i	−0.490142	+	0.448357i
$493$	−0.304942	−	0.363416i	−0.0137339	−	0.0163674i
$494$	5.45021	+	3.14668i	0.245217	+	0.141576i
$495$	−52.8581	+	36.8762i	−2.37579	+	1.65746i
$496$	−3.23652	−	1.86861i	−0.145324	−	0.0839029i
$497$	−19.9007	−	21.3469i	−0.892668	−	0.957539i
$498$	−7.55089	−	18.2739i	−0.338364	−	0.818875i
$499$	27.0594	−	9.84882i	1.21135	−	0.440894i	0.344175	−	0.938905i	$-0.388159\pi$
$499$	27.0594	−	9.84882i	1.21135	−	0.440894i	0.867170	+	0.498012i	$0.165936\pi$
$500$	−4.51574	+	25.6101i	−0.201950	+	1.14532i
$501$	3.65007	−	27.5418i	0.163073	−	1.23048i
$502$	9.49335	+	11.3137i	0.423709	+	0.504957i
$503$	0.833126	−	1.44302i	0.0371473	−	0.0643409i	−0.846854	−	0.531825i	$-0.821506\pi$
$503$	0.833126	−	1.44302i	0.0371473	−	0.0643409i	0.884001	+	0.467484i	$0.154840\pi$
$504$	5.88863	+	5.32203i	0.262301	+	0.237062i
$505$	−28.2647	−	48.9559i	−1.25776	−	2.17851i
$506$	7.29029	−	20.0299i	0.324093	−	0.890438i
$507$	−21.5133	−	6.80349i	−0.955441	−	0.302154i
$508$	−3.34908	−	2.81021i	−0.148591	−	0.124683i
$509$	1.01373	+	0.850622i	0.0449329	+	0.0377031i	0.664978	−	0.746863i	$-0.268441\pi$
$509$	1.01373	+	0.850622i	0.0449329	+	0.0377031i	−0.620045	+	0.784566i	$0.712886\pi$
$510$	−0.440417	−	0.229749i	−0.0195020	−	0.0101734i
$511$	14.2019	+	15.2340i	0.628256	+	0.673912i
$512$			1.00000i			0.0441942i
$513$	−0.820251	−	6.35722i	−0.0362150	−	0.280678i
$514$	7.39433	−	4.26912i	0.326150	−	0.188303i
$515$	17.2471	−	47.3861i	0.759999	−	2.08808i
$516$	3.82408	−	7.33059i	0.168346	−	0.322711i
$517$	8.32739	+	1.46834i	0.366238	+	0.0645777i
$518$	−3.73039	−	8.79167i	−0.163904	−	0.386284i
$519$	1.73019	+	7.83630i	0.0759469	+	0.343975i
$520$	−19.4249	−	7.07008i	−0.851837	−	0.310043i
$521$	−2.44987	+	4.24330i	−0.107331	+	0.185902i	−0.914688	−	0.404160i	$-0.867564\pi$
$521$	−2.44987	+	4.24330i	−0.107331	+	0.185902i	0.807357	+	0.590063i	$0.200897\pi$
$522$	−1.78698	+	20.0281i	−0.0782138	+	0.876606i
$523$	−28.7406	+	16.5934i	−1.25674	+	0.725579i	−0.972439	−	0.233156i	$-0.925095\pi$
$523$	−28.7406	+	16.5934i	−1.25674	+	0.725579i	−0.284301	+	0.958735i	$0.591761\pi$
$524$	−9.54026	−	3.47237i	−0.416768	−	0.151691i
$525$	−47.2492	+	22.4787i	−2.06213	+	0.981051i
$526$	4.96908	+	4.16955i	0.216662	+	0.181801i
$527$	0.0904710	+	0.248567i	0.00394098	+	0.0108277i
$528$	−3.50703	−	8.48738i	−0.152624	−	0.369366i
$529$	1.18737	+	6.73394i	0.0516250	+	0.292780i
$530$	7.28415	+	12.6165i	0.316403	+	0.548027i
$531$	−1.99133	+	22.3185i	−0.0864164	+	0.968539i
$532$	0.170356	+	3.25932i	0.00738585	+	0.141309i
$533$	42.7400	−	7.53621i	1.85127	−	0.326430i
$534$	0.818151	−	2.58708i	0.0354048	−	0.111954i
$535$	−20.9274	+	24.9403i	−0.904771	+	1.07826i
$536$	−0.459851	−	1.26343i	−0.0198625	−	0.0545719i
$537$	−5.57360	−	2.90753i	−0.240519	−	0.125469i
$538$	−9.03423	−	10.7666i	−0.389493	−	0.464180i
$539$	33.9013	+	15.1052i	1.46023	+	0.650629i
$540$	6.27930	+	20.0962i	0.270218	+	0.864802i
$541$	11.7749	−	20.3948i	0.506244	−	0.876841i	−0.493730	−	0.869615i	$-0.664367\pi$
$541$	11.7749	−	20.3948i	0.506244	−	0.876841i	0.999974	−	0.00722531i	$-0.00229991\pi$
$542$	−6.30117	−	2.29344i	−0.270659	−	0.0985116i
$543$	−0.00867239	−	0.202632i	−0.000372168	−	0.00869577i
$544$	0.0454964	−	0.0542205i	0.00195064	−	0.00232469i
$545$	20.6142	−	7.50294i	0.883014	−	0.321391i
$546$	−6.22516	−	22.5348i	−0.266412	−	0.964398i
$547$	−1.64938	−	9.35408i	−0.0705223	−	0.399952i	−0.999552	−	0.0299454i	$-0.990467\pi$
$547$	−1.64938	−	9.35408i	−0.0705223	−	0.399952i	0.929029	−	0.370006i	$-0.120644\pi$
$548$		−	5.55988i		−	0.237506i
$549$	4.21432	−	1.12145i	0.179863	−	0.0478624i
$550$	60.5386			2.58138
$551$	−6.33381	+	5.31470i	−0.269829	+	0.226414i
$552$	−5.52065	−	4.24370i	−0.234974	−	0.180624i
$553$	−5.40354	+	43.9574i	−0.229782	+	1.86926i
$554$	19.9888	−	23.8217i	0.849243	−	1.01209i
$555$	3.32827	−	25.1137i	0.141277	−	1.06602i
$556$	−5.21406	+	0.919379i	−0.221125	+	0.0389904i
$557$			36.5737i			1.54968i	0.632160	+	0.774838i	$0.282169\pi$
$557$			36.5737i			1.54968i	−0.632160	+	0.774838i	$0.717831\pi$
$558$	4.75573	−	10.1530i	0.201326	−	0.429812i
$559$	−21.0905	+	12.1766i	−0.892033	+	0.515016i
$560$	−2.41009	−	10.4459i	−0.101845	−	0.441421i
$561$	−0.195992	+	0.619748i	−0.00827480	+	0.0261658i
$562$	4.33478	−	24.5838i	0.182852	−	1.03700i
$563$	−31.7158	+	11.5436i	−1.33666	+	0.486504i	−0.908759	−	0.417321i	$-0.862969\pi$
$563$	−31.7158	+	11.5436i	−1.33666	+	0.486504i	−0.427901	+	0.903826i	$0.640747\pi$
$564$	1.27761	−	2.44911i	0.0537970	−	0.103126i
$565$	57.2986	−	10.1033i	2.41057	−	0.425048i
$566$	24.0814			1.01222
$567$	−14.3983	+	18.9655i	−0.604672	+	0.796474i
$568$	11.0307			0.462836
$569$	−31.0929	+	5.48251i	−1.30348	+	0.229839i	−0.781922	−	0.623376i	$-0.785760\pi$
$569$	−31.0929	+	5.48251i	−1.30348	+	0.229839i	−0.521559	+	0.853215i	$0.674649\pi$
$570$	−4.00418	+	7.67583i	−0.167717	+	0.321505i
$571$	27.8692	−	10.1435i	1.16629	−	0.424494i	0.314948	−	0.949109i	$-0.398013\pi$
$571$	27.8692	−	10.1435i	1.16629	−	0.424494i	0.851340	+	0.524615i	$0.175791\pi$
$572$	−4.69705	+	26.6383i	−0.196394	+	1.11380i
$573$	9.07315	−	28.6902i	0.379036	−	1.19855i
$574$	15.3475	+	16.4628i	0.640592	+	0.687144i
$575$	39.7530	−	22.9514i	1.65782	−	0.957141i
$576$	−2.98903	+	0.256323i	−0.124543	+	0.0106801i
$577$			31.8403i			1.32553i	0.748828	+	0.662765i	$0.230617\pi$
$577$			31.8403i			1.32553i	−0.748828	+	0.662765i	$0.769383\pi$
$578$	16.7368	−	2.95115i	0.696159	−	0.122752i
$579$	1.92974	−	14.5610i	0.0801972	−	0.605134i
$580$	17.4569	−	20.8044i	0.724860	−	0.863854i
$581$	−27.8037	+	11.7974i	−1.15349	+	0.489437i
$582$	−1.75303	−	1.34754i	−0.0726652	−	0.0558574i
$583$	14.6031	−	12.2535i	0.604800	−	0.507487i
$584$	−7.87191			−0.325742
$585$	16.1536	−	59.8737i	0.667870	−	2.47547i
$586$		−	24.7642i		−	1.02300i
$587$	2.40587	+	13.6443i	0.0993008	+	0.563163i	0.993344	+	0.115183i	$0.0367453\pi$
$587$	2.40587	+	13.6443i	0.0993008	+	0.563163i	−0.894044	+	0.447980i	$0.852144\pi$
$588$	8.04420	−	9.07143i	0.331737	−	0.374100i
$589$	4.33216	−	1.57678i	0.178503	−	0.0649699i
$590$	19.4533	−	23.1835i	0.800879	−	0.954450i
$591$	0.174727	+	4.08253i	0.00718730	+	0.167933i
$592$	3.39200	+	1.23459i	0.139411	+	0.0507413i
$593$	14.1164	−	24.4503i	0.579691	−	1.00405i	−0.415824	−	0.909445i	$-0.636507\pi$
$593$	14.1164	−	24.4503i	0.579691	−	1.00405i	0.995515	−	0.0946085i	$-0.0301599\pi$
$594$	24.4701	−	12.6581i	1.00402	−	0.519369i
$595$	−0.344576	+	0.676034i	−0.0141262	+	0.0277147i
$596$	1.01073	+	1.20454i	0.0414009	+	0.0493397i
$597$	−17.3667	−	9.05952i	−0.710770	−	0.370781i
$598$	7.01478	+	19.2729i	0.286856	+	0.788129i
$599$	−12.7224	+	15.1620i	−0.519825	+	0.619503i	−0.960539	−	0.278144i	$-0.910281\pi$
$599$	−12.7224	+	15.1620i	−0.519825	+	0.619503i	0.440714	+	0.897647i	$0.354725\pi$
$600$	5.96315	−	18.8561i	0.243445	−	0.769797i
$601$	8.84391	−	1.55942i	0.360751	−	0.0636100i	0.00966459	−	0.999953i	$-0.496924\pi$
$601$	8.84391	−	1.55942i	0.360751	−	0.0636100i	0.351086	+	0.936343i	$0.385813\pi$
$602$	−11.2523	−	5.73534i	−0.458611	−	0.233755i
$603$	3.65856	−	1.69835i	0.148988	−	0.0691623i
$604$	−7.25264	−	12.5619i	−0.295106	−	0.511138i
$605$	−12.0399	−	68.2815i	−0.489490	−	2.77604i
$606$	9.22808	+	22.3329i	0.374865	+	0.907212i
$607$	3.73104	+	10.2509i	0.151438	+	0.416073i	0.992094	−	0.125497i	$-0.0400525\pi$
$607$	3.73104	+	10.2509i	0.151438	+	0.416073i	−0.840656	+	0.541570i	$0.817830\pi$
$608$	−0.944984	−	0.792936i	−0.0383242	−	0.0321578i
$609$	30.6179	+	2.44051i	1.24070	+	0.0988946i
$610$	−5.53489	−	2.01453i	−0.224101	−	0.0815661i
$611$	−7.04624	+	4.06815i	−0.285060	+	0.164580i
$612$	0.173729	+	0.122092i	0.00702256	+	0.00493528i
$613$	−16.9110	+	29.2908i	−0.683030	+	1.18304i	0.291021	+	0.956717i	$0.406005\pi$
$613$	−16.9110	+	29.2908i	−0.683030	+	1.18304i	−0.974052	+	0.226326i	$0.927328\pi$
$614$	−17.4452	−	6.34953i	−0.704031	−	0.256246i
$615$	12.8718	+	58.2982i	0.519040	+	2.35081i
$616$	−12.9135	+	5.47932i	−0.520300	+	0.220768i
$617$	−21.9771	−	3.87515i	−0.884764	−	0.156008i	−0.287240	−	0.957859i	$-0.592738\pi$
$617$	−21.9771	−	3.87515i	−0.884764	−	0.156008i	−0.597524	+	0.801851i	$0.703849\pi$
$618$	−9.96985	+	19.1117i	−0.401046	+	0.768786i
$619$	−4.11926	+	11.3176i	−0.165567	+	0.454892i	−0.994535	−	0.104405i	$-0.966706\pi$
$619$	−4.11926	+	11.3176i	−0.165567	+	0.454892i	0.828968	+	0.559296i	$0.188929\pi$
$620$	−13.1141	+	7.57143i	−0.526675	+	0.304076i
$621$	11.2695	−	17.5891i	0.452228	−	0.705828i
$622$		−	19.7655i		−	0.792525i
$623$	−3.96345	−	1.21236i	−0.158792	−	0.0485721i
$624$	7.83442	+	4.08692i	0.313628	+	0.163608i
$625$	36.9851	+	31.0341i	1.47940	+	1.24137i
$626$	−2.93888	−	2.46602i	−0.117461	−	0.0985618i
$627$	10.8013	+	3.41586i	0.431362	+	0.136416i
$628$	0.362225	−	0.995204i	0.0144543	−	0.0397130i
$629$	−0.127747	−	0.221264i	−0.00509360	−	0.00882238i
$630$	30.6054	−	9.88136i	1.21935	−	0.393683i
$631$	−10.1141	+	17.5182i	−0.402637	+	0.697387i	−0.994043	−	0.108986i	$-0.965240\pi$
$631$	−10.1141	+	17.5182i	−0.402637	+	0.697387i	0.591406	+	0.806374i	$0.298573\pi$
$632$	−10.7599	−	12.8231i	−0.428005	−	0.510076i
$633$	−0.693485	+	5.23274i	−0.0275636	+	0.207983i
$634$	5.74329	−	32.5718i	0.228095	−	1.29359i
$635$	−16.6463	+	6.05876i	−0.660588	+	0.240434i
$636$	−2.37819	−	5.75546i	−0.0943012	−	0.228219i
$637$	−34.3310	+	9.83385i	−1.36025	+	0.389631i
$638$	−30.7761	−	17.7686i	−1.21844	−	0.703466i
$639$	2.82741	+	32.9710i	0.111850	+	1.30431i
$640$	3.50906	+	2.02596i	0.138708	+	0.0800829i
$641$	20.2359	+	24.1162i	0.799268	+	0.952531i	0.999630	−	0.0271910i	$-0.00865623\pi$
$641$	20.2359	+	24.1162i	0.799268	+	0.952531i	−0.200362	+	0.979722i	$0.564212\pi$
$642$	10.2689	−	9.39342i	0.405279	−	0.370729i
$643$	−4.81327	−	13.2243i	−0.189817	−	0.521517i	0.807880	−	0.589347i	$-0.200615\pi$
$643$	−4.81327	−	13.2243i	−0.189817	−	0.521517i	−0.997697	+	0.0678295i	$0.978393\pi$
$644$	−6.40240	+	8.49379i	−0.252290	+	0.334702i
$645$	−17.9760	−	28.2704i	−0.707806	−	1.11315i
$646$	0.0151618	+	0.0859868i	0.000596532	+	0.00338310i
$647$	−19.4744	−	33.7306i	−0.765617	−	1.32609i	−0.939920	−	0.341396i	$-0.889100\pi$
$647$	−19.4744	−	33.7306i	−0.765617	−	1.32609i	0.174302	−	0.984692i	$-0.444233\pi$
$648$	−1.53231	−	8.86860i	−0.0601949	−	0.348391i
$649$	−34.2956	−	19.8006i	−1.34622	−	0.777241i
$650$	−44.6227	+	37.4429i	−1.75025	+	1.46863i
$651$	−15.5769	−	7.11765i	−0.610508	−	0.278963i
$652$	2.71932	−	15.4220i	0.106497	−	0.603974i
$653$	31.1453	+	5.49177i	1.21881	+	0.214909i	0.745814	−	0.666154i	$-0.232061\pi$
$653$	31.1453	+	5.49177i	1.21881	+	0.214909i	0.472998	+	0.881064i	$0.343172\pi$
$654$	−9.15682	+	2.02175i	−0.358060	+	0.0790567i
$655$	−31.5129	+	26.4425i	−1.23131	+	1.03319i
$656$	−8.50688			−0.332138
$657$	−2.01775	−	23.5294i	−0.0787199	−	0.917969i
$658$	−3.75935	−	1.91615i	−0.146555	−	0.0746993i
$659$	−3.14185	+	8.63215i	−0.122389	+	0.336261i	−0.985724	−	0.168371i	$-0.946149\pi$
$659$	−3.14185	+	8.63215i	−0.122389	+	0.336261i	0.863335	+	0.504632i	$0.168372\pi$
$660$	−36.8878	−	4.88867i	−1.43586	−	0.190291i
$661$	24.1411	+	4.25673i	0.938982	+	0.165568i	0.622136	−	0.782909i	$-0.286265\pi$
$661$	24.1411	+	4.25673i	0.938982	+	0.165568i	0.316846	+	0.948477i	$0.397376\pi$
$662$	5.06702	+	0.893453i	0.196935	+	0.0347250i
$663$	−0.238846	−	0.578033i	−0.00927603	−	0.0224489i
$664$	3.90439	−	10.7272i	0.151520	−	0.416297i
$665$	11.7823	+	6.00545i	0.456897	+	0.232881i
$666$	−2.82077	+	10.4553i	−0.109303	+	0.405133i
$667$	−26.9458			−1.04334
$668$	12.2876	−	10.3105i	0.475422	−	0.398926i
$669$	−5.95284	+	18.8235i	−0.230150	+	0.727759i
$670$	−5.36509	−	0.946010i	−0.207271	−	0.0365475i
$671$	−1.33837	+	7.59027i	−0.0516672	+	0.293019i
$672$	0.434655	+	4.56192i	0.0167672	+	0.175980i
$673$	−20.1082	+	16.8728i	−0.775113	+	0.650397i	−0.942013	−	0.335577i	$-0.891069\pi$
$673$	−20.1082	+	16.8728i	−0.775113	+	0.650397i	0.166900	+	0.985974i	$0.446624\pi$
$674$	22.8336	+	13.1830i	0.879516	+	0.507789i
$675$	57.8899	+	12.9908i	2.22818	+	0.500016i
$676$	−6.51352	−	11.2817i	−0.250520	−	0.433913i
$677$	−0.815379	−	4.62424i	−0.0313375	−	0.177724i	0.965122	−	0.261802i	$-0.0843167\pi$
$677$	−0.815379	−	4.62424i	−0.0313375	−	0.177724i	−0.996459	+	0.0840778i	$0.973206\pi$
$678$	−24.8482	+	1.06347i	−0.954291	+	0.0408424i
$679$	−2.03302	+	2.69712i	−0.0780200	+	0.103506i
$680$	−0.0980892	−	0.269498i	−0.00376155	−	0.0103348i
$681$	1.41989	+	0.449033i	0.0544102	+	0.0172070i
$682$	12.7367	+	15.1791i	0.487715	+	0.581236i
$683$	18.2209	+	10.5198i	0.697204	+	0.402531i	0.806305	−	0.591500i	$-0.201464\pi$
$683$	18.2209	+	10.5198i	0.697204	+	0.402531i	−0.109101	+	0.994031i	$0.534797\pi$
$684$	2.12789	−	3.02783i	0.0813618	−	0.115772i
$685$	−19.5099	−	11.2641i	−0.745436	−	0.430378i
$686$	−13.9723	−	12.1563i	−0.533465	−	0.464128i
$687$	3.38862	+	0.449088i	0.129284	+	0.0171338i
$688$	4.48570	−	1.63266i	0.171016	−	0.0622446i
$689$	−3.18516	+	18.0640i	−0.121345	+	0.688182i
$690$	−26.0760	+	10.7747i	−0.992695	+	0.410187i
$691$	−26.8939	−	32.0509i	−1.02309	−	1.21927i	−0.975407	−	0.220412i	$-0.929260\pi$
$691$	−26.8939	−	32.0509i	−1.02309	−	1.21927i	−0.0476858	−	0.998862i	$-0.515185\pi$
$692$	−2.31663	+	4.01252i	−0.0880649	+	0.152533i
$693$	−19.6879	−	37.1944i	−0.747880	−	1.41290i
$694$	−2.12001	−	3.67197i	−0.0804746	−	0.139386i
$695$	−7.33730	+	20.1591i	−0.278320	+	0.764677i
$696$	−8.56592	+	7.83567i	−0.324690	+	0.297010i
$697$	0.461248	+	0.387033i	0.0174710	+	0.0146599i
$698$	15.0311	+	12.6126i	0.568934	+	0.477392i
$699$	0.226980	+	5.30344i	0.00858519	+	0.200595i
$700$	−28.8879	−	8.83635i	−1.09186	−	0.333983i
$701$			47.6053i			1.79803i	0.437922	+	0.899013i	$0.355715\pi$
$701$			47.6053i			1.79803i	−0.437922	+	0.899013i	$0.644285\pi$
$702$	−10.2078	+	24.4649i	−0.385268	+	0.923368i
$703$	−3.85631	+	2.22644i	−0.145443	+	0.0839718i
$704$	1.81340	−	4.98229i	0.0683453	−	0.187777i
$705$	−6.00571	−	9.44500i	−0.226188	−	0.355719i
$706$	15.5742	+	2.74615i	0.586141	+	0.103353i
$707$	33.9794	−	14.4178i	1.27793	−	0.542236i
$708$	−9.54550	+	8.73174i	−0.358742	+	0.328159i
$709$	16.1197	+	5.86710i	0.605389	+	0.220344i	0.626485	−	0.779434i	$-0.284493\pi$
$709$	16.1197	+	5.86710i	0.605389	+	0.220344i	−0.0210954	+	0.999777i	$0.506715\pi$
$710$	22.3476	−	38.7072i	0.838691	−	1.45266i
$711$	35.5707	−	35.4484i	1.33400	−	1.32942i
$712$	1.35668	−	0.783280i	0.0508438	−	0.0293547i
$713$	14.1183	+	5.13866i	0.528736	+	0.192444i
$714$	0.183984	−	0.267125i	0.00688541	−	0.00999689i
$715$	83.9594	+	70.4503i	3.13990	+	2.63469i
$716$	−1.24135	−	3.41057i	−0.0463913	−	0.127459i
$717$	13.3016	−	17.3041i	0.496756	−	0.646233i
$718$	3.52411	+	19.9862i	0.131519	+	0.745880i
$719$	−1.74594	−	3.02405i	−0.0651125	−	0.112778i	0.831631	−	0.555328i	$-0.187407\pi$
$719$	−1.74594	−	3.02405i	−0.0651125	−	0.112778i	−0.896744	+	0.442550i	$0.854074\pi$
$720$	−5.15619	+	11.0080i	−0.192160	+	0.410243i
$721$	29.3362	+	14.9527i	1.09254	+	0.556869i
$722$	−17.2127	+	3.03507i	−0.640591	+	0.112954i
$723$	−32.3144	−	35.3259i	−1.20178	−	1.31379i
$724$	0.0752683	−	0.0897013i	0.00279733	−	0.00333372i
$725$	−26.1747	−	71.9144i	−0.972104	−	2.67083i
$726$	1.26732	+	29.6111i	0.0470345	+	1.09897i
$727$	9.00353	+	10.7300i	0.333922	+	0.397953i	0.906713	−	0.421749i	$-0.138584\pi$
$727$	9.00353	+	10.7300i	0.333922	+	0.397953i	−0.572790	+	0.819702i	$0.694139\pi$
$728$	6.12954	−	12.0257i	0.227176	−	0.445703i
$729$	26.1157	−	6.85335i	0.967249	−	0.253828i
$730$	−15.9481	+	27.6230i	−0.590267	+	1.02237i
$731$	−0.317497	−	0.115559i	−0.0117430	−	0.00427412i
$732$	2.23233	+	1.16452i	0.0825092	+	0.0430418i
$733$	23.0196	−	27.4337i	0.850249	−	1.01329i	−0.149451	−	0.988769i	$-0.547750\pi$
$733$	23.0196	−	27.4337i	0.850249	−	1.01329i	0.999699	−	0.0245179i	$-0.00780506\pi$
$734$	−15.0529	+	5.47882i	−0.555614	+	0.202227i
$735$	−15.5350	−	46.6059i	−0.573017	−	1.71908i
$736$	−0.698104	−	3.95915i	−0.0257325	−	0.145936i
$737$			7.12867i			0.262588i
$738$	−2.18051	−	25.4273i	−0.0802656	−	0.935993i
$739$	−0.281407			−0.0103517			−0.00517587	−	0.999987i	$-0.501648\pi$
$739$	−0.281407			−0.0103517			−0.00517587	+	0.999987i	$0.501648\pi$
$740$	11.2043	−	9.40152i	0.411878	−	0.345607i
$741$	−10.0743	+	4.16274i	−0.370087	+	0.152922i
$742$	−8.75689	+	3.71563i	−0.321476	+	0.136405i
$743$	11.3742	−	13.5553i	0.417279	−	0.497294i	−0.515928	−	0.856632i	$-0.672553\pi$
$743$	11.3742	−	13.5553i	0.417279	−	0.497294i	0.933208	+	0.359338i	$0.116997\pi$
$744$	5.98244	−	2.47198i	0.219327	−	0.0906271i
$745$	6.27447	−	1.10636i	0.229879	−	0.0405338i
$746$		−	1.14472i		−	0.0419113i
$747$	33.0648	+	8.92071i	1.20978	+	0.326392i
$748$	−0.325000	+	0.187639i	−0.0118832	+	0.00686076i
$749$	−14.4962	−	15.5497i	−0.529681	−	0.568173i
$750$	−30.4015	−	33.2348i	−1.11011	−	1.21356i
$751$	5.32935	−	30.2243i	0.194471	−	1.10290i	−0.718699	−	0.695321i	$-0.755262\pi$
$751$	5.32935	−	30.2243i	0.194471	−	1.10290i	0.913170	−	0.407578i	$-0.133627\pi$
$752$	1.49865	−	0.545464i	0.0546501	−	0.0198910i
$753$	−25.5573	+	1.09382i	−0.931361	+	0.0398610i
$754$	33.6747	−	5.93777i	1.22636	−	0.216241i
$755$	−58.7741			−2.13901
$756$	−13.5243	+	2.46852i	−0.491874	+	0.0897792i
$757$	−10.2813			−0.373681			−0.186840	−	0.982390i	$-0.559825\pi$
$757$	−10.2813			−0.373681			−0.186840	+	0.982390i	$0.559825\pi$
$758$	23.9644	−	4.22557i	0.870426	−	0.153480i
$759$	19.8099	+	31.1545i	0.719055	+	1.13084i
$760$	−4.69695	+	1.70955i	−0.170376	+	0.0620119i
$761$	−6.74059	+	38.2278i	−0.244346	+	1.38576i	0.577660	+	0.816278i	$0.303966\pi$
$761$	−6.74059	+	38.2278i	−0.244346	+	1.38576i	−0.822006	+	0.569479i	$0.807145\pi$
$762$	7.39429	−	1.63260i	0.267867	−	0.0591428i
$763$	3.22028	+	13.9575i	0.116582	+	0.505294i
$764$	15.0454	−	8.68644i	0.544322	−	0.314264i
$765$	0.780395	−	0.362270i	0.0282152	−	0.0130979i
$766$			17.5428i			0.633846i
$767$	37.5257	−	6.61680i	1.35497	−	0.238919i
$768$	−1.37322	−	1.05559i	−0.0495518	−	0.0380902i
$769$	9.28268	−	11.0627i	0.334742	−	0.398930i	−0.572249	−	0.820080i	$-0.693929\pi$
$769$	9.28268	−	11.0627i	0.334742	−	0.398930i	0.906991	+	0.421150i	$0.138373\pi$
$770$	−6.93493	+	56.4151i	−0.249918	+	2.03306i
$771$	−1.94293	+	14.6605i	−0.0699727	+	0.527984i
$772$	6.49628	−	5.45103i	0.233806	−	0.196187i
$773$	27.5601			0.991269			0.495634	−	0.868531i	$-0.334936\pi$
$773$	27.5601			0.991269			0.495634	+	0.868531i	$0.334936\pi$
$774$	6.02985	+	12.9894i	0.216739	+	0.466894i
$775$			42.6715i			1.53280i
$776$	−0.221676	−	1.25719i	−0.00795770	−	0.0451303i
$777$	16.0107	+	4.15774i	0.574379	+	0.149158i
$778$	29.4836	−	10.7312i	1.05704	−	0.384731i
$779$	6.74541	−	8.03887i	0.241679	−	0.288022i
$780$	30.2134	−	19.2115i	1.08181	−	0.687884i
$781$	−54.9579	−	20.0030i	−1.96655	−	0.715765i
$782$	−0.142275	+	0.246428i	−0.00508776	+	0.00881225i
$783$	−25.6167	−	23.5953i	−0.915466	−	0.843229i
$784$	6.96186	−	0.729747i	0.248638	−	0.0260624i
$785$	−2.75838	−	3.28731i	−0.0984507	−	0.117329i
$786$	14.8389	−	9.43549i	0.529287	−	0.336553i
$787$	−4.98038	−	13.6835i	−0.177531	−	0.487764i	0.818727	−	0.574182i	$-0.194680\pi$
$787$	−4.98038	−	13.6835i	−0.177531	−	0.487764i	−0.996259	+	0.0864187i	$0.972458\pi$
$788$	−1.51647	+	1.80726i	−0.0540220	+	0.0643809i
$789$	−10.9710	+	2.42231i	−0.390578	+	0.0862365i
$790$	−66.7961	+	11.7780i	−2.37650	+	0.419041i
$791$	1.98298	+	37.9393i	0.0705066	+	1.34897i
$792$	15.3570	+	4.14325i	0.545688	+	0.147224i
$793$	−3.70805	−	6.42253i	−0.131677	−	0.228071i
$794$	−1.43824	−	8.15665i	−0.0510412	−	0.289469i
$795$	−25.0143	−	3.31510i	−0.887167	−	0.117575i
$796$	−3.86788	−	10.6269i	−0.137093	−	0.376661i
$797$	20.3609	+	17.0848i	0.721218	+	0.605174i	0.927722	−	0.373272i	$-0.121764\pi$
$797$	20.3609	+	17.0848i	0.721218	+	0.605174i	−0.206504	+	0.978446i	$0.566209\pi$
$798$	−4.65559	−	3.20656i	−0.164806	−	0.113511i
$799$	−0.106074	−	0.0386079i	−0.00375264	−	0.00136585i
$800$	9.88827	−	5.70900i	0.349603	−	0.201843i
$801$	2.68900	+	3.85439i	0.0950110	+	0.136188i
$802$	−13.9083	+	24.0899i	−0.491119	+	0.850644i
$803$	39.2201	+	14.2750i	1.38405	+	0.503752i
$804$	2.22038	+	0.702185i	0.0783068	+	0.0247642i
$805$	16.8342	+	39.6745i	0.593329	+	1.39834i
$806$	−18.7764	−	3.31078i	−0.661369	−	0.116617i
$807$	24.3213	−	1.04092i	0.856150	−	0.0366421i
$808$	−4.77162	+	13.1099i	−0.167865	+	0.461206i
$809$	40.6092	−	23.4457i	1.42774	−	0.824308i	0.430800	−	0.902447i	$-0.358231\pi$
$809$	40.6092	−	23.4457i	1.42774	−	0.824308i	0.996942	+	0.0781397i	$0.0248980\pi$
$810$	−34.2248	−	12.5904i	−1.20254	−	0.442382i
$811$			53.2892i			1.87124i	0.353015	+	0.935618i	$0.385157\pi$
$811$			53.2892i			1.87124i	−0.353015	+	0.935618i	$0.614843\pi$
$812$	12.0923	+	12.9710i	0.424355	+	0.455193i
$813$	9.80084	−	6.23197i	0.343730	−	0.218565i
$814$	−14.6611	−	12.3022i	−0.513872	−	0.431190i
$815$	−48.6076	−	40.7866i	−1.70265	−	1.42869i
$816$	0.0264312	+	0.119711i	0.000925279	+	0.00419073i
$817$	−2.01403	+	5.53350i	−0.0704620	+	0.193593i
$818$	5.45929	+	9.45576i	0.190879	+	0.330613i
$819$	37.5164	+	15.2389i	1.31093	+	0.532490i
$820$	−17.2346	+	29.8512i	−0.601857	+	1.04245i
$821$	−0.976000	−	1.16315i	−0.0340626	−	0.0405943i	0.748744	−	0.662859i	$-0.230657\pi$
$821$	−0.976000	−	1.16315i	−0.0340626	−	0.0405943i	−0.782807	+	0.622265i	$0.786213\pi$
$822$	7.63494	+	5.86894i	0.266299	+	0.204703i
$823$	7.32354	−	41.5339i	0.255283	−	1.44778i	−0.540064	−	0.841624i	$-0.681600\pi$
$823$	7.32354	−	41.5339i	0.255283	−	1.44778i	0.795346	−	0.606155i	$-0.207289\pi$
$824$	−11.6948	+	4.25654i	−0.407406	+	0.148284i
$825$	−63.9039	+	83.1329i	−2.22485	+	2.89432i
$826$	13.4751	+	14.4543i	0.468859	+	0.502931i
$827$	26.6429	+	15.3823i	0.926464	+	0.534894i	0.885691	−	0.464275i	$-0.153685\pi$
$827$	26.6429	+	15.3823i	0.926464	+	0.534894i	0.0407722	+	0.999168i	$0.487018\pi$
$828$	11.6551	−	3.10147i	0.405041	−	0.107784i
$829$	−39.4570	−	22.7805i	−1.37040	−	0.791201i	−0.379421	−	0.925224i	$-0.623877\pi$
$829$	−39.4570	−	22.7805i	−1.37040	−	0.791201i	−0.990978	+	0.134023i	$0.957210\pi$
$830$	−29.7323	−	35.4336i	−1.03202	−	1.22992i
$831$	11.6125	+	52.5950i	0.402835	+	1.82450i
$832$	1.74487	+	4.79400i	0.0604926	+	0.166202i
$833$	−0.410676	−	0.277172i	−0.0142291	−	0.00960345i
$834$	4.24139	−	8.13054i	0.146867	−	0.281537i
$835$	−11.2861	−	64.0066i	−0.390571	−	2.21504i
$836$	3.27027	+	5.66427i	0.113105	+	0.195903i
$837$	8.92225	+	17.2481i	0.308398	+	0.596180i
$838$	19.6393	+	11.3388i	0.678430	+	0.391692i
$839$	−2.58975	+	2.17305i	−0.0894080	+	0.0750222i	−0.686396	−	0.727228i	$-0.740808\pi$
$839$	−2.58975	+	2.17305i	−0.0894080	+	0.0750222i	0.596988	+	0.802250i	$0.296364\pi$
$840$	16.8886	+	7.71701i	0.582713	+	0.266262i
$841$	−2.76522	+	15.6823i	−0.0953523	+	0.540770i
$842$	−11.9531	−	2.10766i	−0.411932	−	0.0726347i
$843$	29.1832	+	31.9029i	1.00512	+	1.09880i
$844$	−2.33455	+	1.95892i	−0.0803585	+	0.0674288i
$845$	−52.7844			−1.81584
$846$	2.01455	+	4.33969i	0.0692615	+	0.149202i
$847$	45.2114	−	2.36307i	1.55348	−	0.0811962i
$848$	1.22970	−	3.37859i	0.0422282	−	0.116021i
$849$	−25.4200	+	33.0691i	−0.872414	+	1.13493i
$850$	−0.795886	−	0.140336i	−0.0272987	−	0.00481349i
$851$	−14.2913	−	2.51994i	−0.489900	−	0.0863826i
$852$	−11.6438	+	15.1475i	−0.398911	+	0.518945i
$853$	−8.77758	+	24.1162i	−0.300539	+	0.825723i	0.693868	+	0.720102i	$0.255905\pi$
$853$	−8.77758	+	24.1162i	−0.300539	+	0.825723i	−0.994406	+	0.105621i	$0.966317\pi$
$854$	1.74654	−	3.42659i	0.0597653	−	0.117255i
$855$	−6.31384	−	13.6011i	−0.215929	−	0.465149i
$856$	8.03504			0.274632
$857$	28.9926	−	24.3277i	0.990367	−	0.831017i	0.00474649	−	0.999989i	$-0.498489\pi$
$857$	28.9926	−	24.3277i	0.990367	−	0.831017i	0.985621	+	0.168972i	$0.0540447\pi$
$858$	−31.6221	−	34.5692i	−1.07956	−	1.18017i
$859$	−13.4720	−	2.37548i	−0.459659	−	0.0810503i	−0.0609762	−	0.998139i	$-0.519421\pi$
$859$	−13.4720	−	2.37548i	−0.459659	−	0.0810503i	−0.398683	+	0.917089i	$0.630532\pi$
$860$	3.35872	−	19.0483i	0.114532	−	0.649541i
$861$	−38.8077	+	3.69756i	−1.32256	+	0.126012i
$862$	21.7184	−	18.2239i	0.739731	−	0.620708i
$863$	13.4949	+	7.79127i	0.459371	+	0.265218i	0.711780	−	0.702403i	$-0.247889\pi$
$863$	13.4949	+	7.79127i	0.459371	+	0.265218i	−0.252409	+	0.967621i	$0.581223\pi$
$864$	2.80320	−	4.37517i	0.0953667	−	0.148846i
$865$	9.38677	+	16.2584i	0.319160	+	0.552801i
$866$	−0.151527	−	0.859355i	−0.00514911	−	0.0292021i
$867$	−13.6146	+	26.0985i	−0.462376	+	0.886352i
$868$	−3.86217	−	9.10225i	−0.131091	−	0.308950i
$869$	30.3553	+	83.4004i	1.02973	+	2.82917i
$870$	10.1416	+	45.9330i	0.343834	+	1.55728i
$871$	−4.40905	−	5.25450i	−0.149395	−	0.178042i
$872$	−4.68868	−	2.70701i	−0.158779	−	0.0916709i
$873$	3.70095	−	0.984841i	0.125258	−	0.0333318i
$874$	4.29488	+	2.47965i	0.145276	+	0.0838754i
$875$	−50.3260	+	46.9166i	−1.70133	+	1.58607i
$876$	8.30950	−	10.8099i	0.280752	−	0.365232i
$877$	−32.9777	+	12.0029i	−1.11358	+	0.405309i	−0.832305	−	0.554318i	$-0.812979\pi$
$877$	−32.9777	+	12.0029i	−1.11358	+	0.405309i	−0.281273	+	0.959628i	$0.590757\pi$
$878$	6.04034	−	34.2565i	0.203852	−	1.15610i
$879$	34.0066	+	26.1407i	1.14702	+	0.881705i
$880$	−13.8093	−	16.4572i	−0.465510	−	0.554773i
$881$	25.8689	−	44.8063i	0.871546	−	1.50956i	0.0111491	−	0.999938i	$-0.496451\pi$
$881$	25.8689	−	44.8063i	0.871546	−	1.50956i	0.860397	−	0.509624i	$-0.170216\pi$
$882$	3.96572	+	20.6222i	0.133533	+	0.694384i
$883$	−4.21906	−	7.30763i	−0.141983	−	0.245921i	0.786260	−	0.617895i	$-0.212014\pi$
$883$	−4.21906	−	7.30763i	−0.141983	−	0.245921i	−0.928243	+	0.371974i	$0.878681\pi$
$884$	0.123502	−	0.339319i	0.00415382	−	0.0114125i
$885$	11.3014	+	51.1859i	0.379893	+	1.72059i
$886$	24.9888	+	20.9681i	0.839515	+	0.704437i
$887$	−31.1003	−	26.0962i	−1.04425	−	0.876226i	−0.0517685	−	0.998659i	$-0.516486\pi$
$887$	−31.1003	−	26.0962i	−1.04425	−	0.876226i	−0.992477	+	0.122433i	$0.960930\pi$
$888$	−5.27592	+	3.35475i	−0.177048	+	0.112578i
$889$	−2.60043	−	11.2709i	−0.0872156	−	0.378014i
$890$		−	6.34757i		−	0.212771i
$891$	−8.44793	+	46.9646i	−0.283016	+	1.57337i
$892$	−9.87118	+	5.69913i	−0.330511	+	0.190821i
$893$	−0.672878	+	1.84872i	−0.0225170	+	0.0618650i
$894$	−2.72100	+	0.116455i	−0.0910039	+	0.00389485i
$895$	−14.4828	−	2.55371i	−0.484106	−	0.0853610i
$896$	−1.59255	+	2.11277i	−0.0532033	+	0.0705826i
$897$	−33.8707	−	10.7115i	−1.13091	−	0.357645i
$898$	8.69876	+	3.16609i	0.290281	+	0.105654i
$899$	12.5244	−	21.6930i	0.417713	−	0.723501i
$900$	19.5989	+	28.0930i	0.653298	+	0.936433i
$901$	−0.220389	+	0.127242i	−0.00734221	+	0.00423903i
$902$	42.3837	+	15.4264i	1.41122	+	0.513644i
$903$	19.7537	−	9.39779i	0.657363	−	0.312739i
$904$	−10.9998	−	9.22996i	−0.365849	−	0.306984i
$905$	−0.162277	−	0.445852i	−0.00539427	−	0.0148206i
$906$	24.9061	+	3.30076i	0.827450	+	0.109660i
$907$	−4.42686	−	25.1059i	−0.146991	−	0.833629i	−0.965747	−	0.259487i	$-0.916447\pi$
$907$	−4.42686	−	25.1059i	−0.146991	−	0.833629i	0.818755	−	0.574143i	$-0.194664\pi$
$908$	0.429894	+	0.744599i	0.0142665	+	0.0247104i
$909$	−40.4090	−	10.9022i	−1.34028	−	0.361602i
$910$	−29.7808	−	45.8725i	−0.987224	−	1.52066i
$911$	−7.89479	+	1.39206i	−0.261566	+	0.0461211i	−0.302893	−	0.953025i	$-0.597953\pi$
$911$	−7.89479	+	1.39206i	−0.261566	+	0.0461211i	0.0413271	+	0.999146i	$0.486841\pi$
$912$	2.08639	−	0.460658i	0.0690872	−	0.0152539i
$913$	−38.9056	+	46.3659i	−1.28759	+	1.53449i
$914$	6.11140	+	16.7909i	0.202147	+	0.555395i
$915$	8.60896	−	5.47410i	0.284603	−	0.180968i
$916$	1.26856	+	1.51181i	0.0419144	+	0.0499516i
$917$	−14.6264	−	22.5296i	−0.483007	−	0.743994i
$918$	−0.351045	+	0.109688i	−0.0115862	+	0.00362026i
$919$	−3.60711	+	6.24770i	−0.118988	+	0.206093i	−0.919367	−	0.393402i	$-0.871298\pi$
$919$	−3.60711	+	6.24770i	−0.118988	+	0.206093i	0.800379	+	0.599494i	$0.204632\pi$
$920$	−15.3072	−	5.57137i	−0.504663	−	0.183682i
$921$	27.1342	−	17.2536i	0.894104	−	0.568526i
$922$	−23.2043	+	27.6538i	−0.764193	+	0.910730i
$923$	52.8810	−	19.2471i	1.74060	−	0.633526i
$924$	6.10702	−	23.5170i	0.200906	−	0.773652i
$925$	−7.15699	−	40.5893i	−0.235320	−	1.33457i
$926$			7.69311i			0.252811i
$927$	−15.7206	−	33.8649i	−0.516331	−	1.11227i
$928$	−6.70256			−0.220022
$929$	22.9179	−	19.2304i	0.751911	−	0.630928i	−0.184097	−	0.982908i	$-0.558936\pi$
$929$	22.9179	−	19.2304i	0.751911	−	0.630928i	0.936008	+	0.351980i	$0.114491\pi$
$930$	3.44585	−	26.0009i	0.112994	−	0.852602i
$931$	−4.83071	+	7.15749i	−0.158320	+	0.234577i
$932$	−1.96998	+	2.34773i	−0.0645289	+	0.0769025i
$933$	27.1424	+	20.8642i	0.888603	+	0.683065i
$934$	5.58713	−	0.985161i	0.182816	−	0.0322355i
$935$			1.52059i			0.0497287i
$936$	−13.8822	+	6.44429i	−0.453753	+	0.210638i
$937$	32.6011	−	18.8222i	1.06503	−	0.614896i	0.138211	−	0.990403i	$-0.455865\pi$
$937$	32.6011	−	18.8222i	1.06503	−	0.614896i	0.926820	+	0.375507i	$0.122531\pi$
$938$	1.04052	−	3.40167i	0.0339741	−	0.111068i
$939$	6.48863	−	1.43264i	0.211748	−	0.0467523i
$940$	1.12213	−	6.36394i	0.0366000	−	0.207569i
$941$	−50.3890	+	18.3401i	−1.64263	+	0.597870i	−0.987497	−	0.157641i	$-0.949611\pi$
$941$	−50.3890	+	18.3401i	−1.64263	+	0.597870i	−0.655137	+	0.755510i	$0.727389\pi$
$942$	0.984274	+	1.54794i	0.0320694	+	0.0504346i
$943$	33.6800	−	5.93869i	1.09677	−	0.193390i
$944$	−7.46905			−0.243097
$945$	−18.7374	+	52.4586i	−0.609529	+	1.70648i
$946$	−25.3097			−0.822889
$947$	−29.7269	+	5.24165i	−0.965994	+	0.170331i	−0.634326	−	0.773065i	$-0.718722\pi$
$947$	−29.7269	+	5.24165i	−0.965994	+	0.170331i	−0.331668	+	0.943396i	$0.607611\pi$
$948$	28.9669	−	1.23975i	0.940803	−	0.0402651i
$949$	−37.7380	+	13.7355i	−1.22503	+	0.445873i
$950$	−2.44585	+	13.8711i	−0.0793540	+	0.450039i
$951$	38.6658	+	42.2692i	1.25382	+	1.37067i
$952$	0.182472	−	0.0421001i	0.00591396	−	0.00136447i
$953$	1.65341	−	0.954599i	0.0535593	−	0.0309225i	−0.472981	−	0.881073i	$-0.656822\pi$
$953$	1.65341	−	0.954599i	0.0535593	−	0.0309225i	0.526541	+	0.850150i	$0.323489\pi$
$954$	10.4139	+	2.80962i	0.337162	+	0.0909647i
$955$		−	70.3934i		−	2.27788i
$956$	12.4097	−	2.18816i	0.401357	−	0.0707701i
$957$	56.8871	−	23.5061i	1.83890	−	0.759844i
$958$	−4.50936	+	5.37405i	−0.145691	+	0.173628i
$959$	8.85438	−	11.7467i	0.285923	−	0.379322i
$960$	−6.48620	+	2.68014i	−0.209341	+	0.0865010i
$961$	13.0482	−	10.9488i	0.420910	−	0.353186i
$962$	18.4155			0.593739
$963$	2.05956	+	24.0170i	0.0663685	+	0.773936i
$964$		−	27.6414i		−	0.890269i
$965$	−5.96679	−	33.8394i	−0.192078	−	1.08933i
$966$	−4.90555	−	17.7579i	−0.157834	−	0.571350i
$967$	21.8040	−	7.93602i	0.701170	−	0.255205i	0.0332598	−	0.999447i	$-0.489411\pi$
$967$	21.8040	−	7.93602i	0.701170	−	0.255205i	0.667910	+	0.744242i	$0.267189\pi$
$968$	−10.9991	+	13.1083i	−0.353526	+	0.421316i
$969$	−0.134083	−	0.0699461i	−0.00430738	−	0.00224699i
$970$	−4.86064	−	1.76913i	−0.156066	−	0.0568033i
$971$	−2.68551	+	4.65144i	−0.0861821	+	0.149272i	−0.905894	−	0.423504i	$-0.860800\pi$
$971$	−2.68551	+	4.65144i	−0.0861821	+	0.149272i	0.819712	+	0.572776i	$0.194133\pi$
$972$	13.7960	+	7.25738i	0.442508	+	0.232781i
$973$	−12.4803	−	6.36121i	−0.400098	−	0.203931i
$974$	1.37947	+	1.64399i	0.0442011	+	0.0526768i
$975$	−4.31416	−	100.801i	−0.138164	−	3.22822i
$976$	0.497181	+	1.36599i	0.0159144	+	0.0437244i
$977$	−23.0978	+	27.5269i	−0.738964	+	0.880663i	−0.996325	−	0.0856527i	$-0.972702\pi$
$977$	−23.0978	+	27.5269i	−0.738964	+	0.880663i	0.257361	+	0.966315i	$0.417147\pi$
$978$	18.3074	+	20.0136i	0.585405	+	0.639963i
$979$	−8.17978	+	1.44232i	−0.261427	+	0.0460966i
$980$	11.5437	−	25.9080i	0.368750	−	0.827601i
$981$	6.88952	−	14.7085i	0.219965	−	0.469605i
$982$	0.350451	+	0.607000i	0.0111834	+	0.0193701i
$983$	7.41521	+	42.0538i	0.236509	+	1.34131i	0.839413	+	0.543494i	$0.182899\pi$
$983$	7.41521	+	42.0538i	0.236509	+	1.34131i	−0.602905	+	0.797813i	$0.705990\pi$
$984$	8.97976	−	11.6818i	0.286264	−	0.372403i
$985$	3.26947	+	8.98280i	0.104174	+	0.286216i
$986$	0.363416	+	0.304942i	0.0115735	+	0.00971134i
$987$	6.59962	−	3.13976i	0.210068	−	0.0999395i
$988$	−5.91383	−	2.15246i	−0.188144	−	0.0684788i
$989$	−16.6198	+	9.59542i	−0.528477	+	0.305117i
$990$	45.6515	−	45.4947i	1.45090	−	1.44592i
$991$	28.2157	−	48.8710i	0.896301	−	1.55244i	0.0641139	−	0.997943i	$-0.479578\pi$
$991$	28.2157	−	48.8710i	0.896301	−	1.55244i	0.832187	−	0.554496i	$-0.187089\pi$
$992$	3.51183	+	1.27820i	0.111501	+	0.0405830i
$993$	−6.57559	+	6.01502i	−0.208670	+	0.190881i
$994$	23.3052	+	17.5669i	0.739196	+	0.557187i
$995$	−45.1267	−	7.95705i	−1.43061	−	0.252255i
$996$	10.6094	+	16.6851i	0.336172	+	0.528688i
$997$	−14.3699	+	39.4811i	−0.455100	+	1.25038i	0.473992	+	0.880529i	$0.342813\pi$
$997$	−14.3699	+	39.4811i	−0.455100	+	1.25038i	−0.929092	+	0.369849i	$0.879410\pi$
$998$	−24.9381	+	14.3980i	−0.789401	+	0.455761i
$999$	−11.3798	−	14.9100i	−0.360041	−	0.471731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.5.8	yes	144
7.3	odd	6		378.2.ba.a.59.24	✓	144
27.11	odd	18		378.2.ba.a.173.24	yes	144
189.38	even	18	inner	378.2.bf.a.227.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.59.24	✓	144	7.3	odd	6
378.2.ba.a.173.24	yes	144	27.11	odd	18
378.2.bf.a.5.8	yes	144	1.1	even	1	trivial
378.2.bf.a.227.8	yes	144	189.38	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.801094 - 1.53566i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.703607 - 3.99035i) q^{5} +(-0.522259 + 1.65144i) q^{6} +(2.53004 + 0.773898i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.71650 - 2.46041i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.801094 - 1.53566i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.703607 - 3.99035i) q^{5} +(-0.522259 + 1.65144i) q^{6} +(2.53004 + 0.773898i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.71650 - 2.46041i) q^{9} +4.05191i q^{10} +(5.22149 - 0.920690i) q^{11} +(0.227556 - 1.71704i) q^{12} +(-3.27929 + 3.90811i) q^{13} +(-2.62599 - 0.322804i) q^{14} +(-5.56417 - 4.27715i) q^{15} +(0.766044 - 0.642788i) q^{16} -0.0707799 q^{17} +(2.11767 + 2.12497i) q^{18} +1.23359i q^{19} +(-0.703607 - 3.99035i) q^{20} +(3.21524 - 3.26531i) q^{21} +(-4.98229 + 1.81340i) q^{22} +(-2.58415 + 3.07967i) q^{23} +(0.0740617 + 1.73047i) q^{24} +(-10.7294 - 3.90518i) q^{25} +(2.55083 - 4.41818i) q^{26} +(-5.15343 + 0.664930i) q^{27} +(2.64214 - 0.138098i) q^{28} +(4.30832 + 5.13446i) q^{29} +(6.22235 + 3.24596i) q^{30} +(-1.27820 - 3.51183i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(2.76904 - 8.75599i) q^{33} +(0.0697046 - 0.0122908i) q^{34} +(4.86828 - 9.55122i) q^{35} +(-2.45449 - 1.72496i) q^{36} +(1.80485 + 3.12609i) q^{37} +(-0.214210 - 1.21485i) q^{38} +(3.37450 + 8.16663i) q^{39} +(1.38584 + 3.80755i) q^{40} +(-6.51665 - 5.46812i) q^{41} +(-2.59938 + 3.77402i) q^{42} +(4.48570 + 1.63266i) q^{43} +(4.59170 - 2.65102i) q^{44} +(-11.0257 + 5.11827i) q^{45} +(2.01011 - 3.48161i) q^{46} +(1.49865 + 0.545464i) q^{47} +(-0.373429 - 1.69132i) q^{48} +(5.80217 + 3.91598i) q^{49} +(11.2445 + 1.98271i) q^{50} +(-0.0567013 + 0.108694i) q^{51} +(-1.74487 + 4.79400i) q^{52} +(3.11372 - 1.79771i) q^{53} +(4.95968 - 1.54971i) q^{54} -21.4834i q^{55} +(-2.57802 + 0.594803i) q^{56} +(1.89437 + 0.988221i) q^{57} +(-5.13446 - 4.30832i) q^{58} +(-5.72162 - 4.80101i) q^{59} +(-6.69148 - 2.11615i) q^{60} +(-0.497181 + 1.36599i) q^{61} +(1.86861 + 3.23652i) q^{62} +(-2.43869 - 7.55333i) q^{63} +(0.500000 - 0.866025i) q^{64} +(13.2874 + 15.8353i) q^{65} +(-1.20651 + 9.10380i) q^{66} +(-0.233472 + 1.32409i) q^{67} +(-0.0665113 + 0.0242081i) q^{68} +(2.65917 + 6.43547i) q^{69} +(-3.13576 + 10.2515i) q^{70} +(-9.55283 - 5.51533i) q^{71} +(2.71674 + 1.27253i) q^{72} +(6.81728 + 3.93596i) q^{73} +(-2.32027 - 2.76519i) q^{74} +(-14.5923 + 13.3483i) q^{75} +(0.421912 + 1.15919i) q^{76} +(13.9231 + 1.71152i) q^{77} +(-4.74135 - 7.45659i) q^{78} +(2.90676 + 16.4851i) q^{79} +(-2.02596 - 3.50906i) q^{80} +(-3.10728 + 8.44659i) q^{81} +(7.36718 + 4.25344i) q^{82} +(-8.74491 + 7.33785i) q^{83} +(1.90454 - 4.16806i) q^{84} +(-0.0498012 + 0.282437i) q^{85} +(-4.70106 - 0.828923i) q^{86} +(11.3361 - 2.50293i) q^{87} +(-4.06160 + 3.40809i) q^{88} -1.56656 q^{89} +(9.96938 - 6.95509i) q^{90} +(-11.3212 + 7.34981i) q^{91} +(-1.37500 + 3.77777i) q^{92} +(-6.41693 - 0.850425i) q^{93} +(-1.57060 - 0.276939i) q^{94} +(4.92246 + 0.867962i) q^{95} +(0.661450 + 1.60078i) q^{96} +(-0.436616 + 1.19959i) q^{97} +(-6.39402 - 2.84895i) q^{98} +(-11.2279 - 11.2667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) 144 * q + 18 * q^6 - 12 * q^9	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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