LMFDB - Embedded newform 552.2.bb.a.85.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.11
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11564 - 0.869107i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.489306 + 1.93922i) q^{4} +(-0.756543 + 0.345502i) q^{5} +(0.127979 - 1.40841i) q^{6} +(-3.66239 + 1.07537i) q^{7} +(1.13950 - 2.58873i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.11564 - 0.869107i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.489306 + 1.93922i) q^{4} +(-0.756543 + 0.345502i) q^{5} +(0.127979 - 1.40841i) q^{6} +(-3.66239 + 1.07537i) q^{7} +(1.13950 - 2.58873i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(1.14431 + 0.272061i) q^{10} +(2.56240 - 2.22033i) q^{11} +(-1.36684 + 1.46005i) q^{12} +(0.635317 - 2.16369i) q^{13} +(5.02052 + 1.98328i) q^{14} +(-0.699673 - 0.449652i) q^{15} +(-3.52116 + 1.89775i) q^{16} +(-1.05713 + 7.35248i) q^{17} +(1.25402 - 0.653782i) q^{18} +(-5.92823 + 0.852351i) q^{19} +(-1.04019 - 1.29805i) q^{20} +(-2.88470 - 2.49960i) q^{21} +(-4.78842 + 0.250092i) q^{22} +(2.22141 - 4.25034i) q^{23} +(2.79384 - 0.440965i) q^{24} +(-2.82132 + 3.25597i) q^{25} +(-2.58926 + 1.86174i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(-3.87742 - 6.57599i) q^{28} +(-6.91690 - 0.994501i) q^{29} +(0.389787 + 1.10974i) q^{30} +(-5.48418 - 3.52447i) q^{31} +(5.57769 + 0.943061i) q^{32} +(3.25320 + 0.955225i) q^{33} +(7.56947 - 7.28397i) q^{34} +(2.39921 - 2.07893i) q^{35} +(-1.96724 - 0.360493i) q^{36} +(-6.41059 - 2.92762i) q^{37} +(7.35456 + 4.20135i) q^{38} +(2.16369 - 0.635317i) q^{39} +(0.0323299 + 2.35219i) q^{40} +(-2.34435 - 5.13341i) q^{41} +(1.04586 + 5.29577i) q^{42} +(-0.890424 - 1.38553i) q^{43} +(5.55951 + 3.88263i) q^{44} -0.831702i q^{45} +(-6.17229 + 2.81121i) q^{46} -6.67219 q^{47} +(-3.50017 - 1.93619i) q^{48} +(6.36787 - 4.09238i) q^{49} +(5.97737 - 1.18047i) q^{50} +(-6.75683 + 3.08574i) q^{51} +(4.50674 + 0.173313i) q^{52} +(2.73892 + 9.32791i) q^{53} +(1.22797 + 0.701489i) q^{54} +(-1.17144 + 2.56509i) q^{55} +(-1.38944 + 10.7063i) q^{56} +(-3.92209 - 4.52633i) q^{57} +(6.85245 + 7.12103i) q^{58} +(1.99171 - 6.78314i) q^{59} +(0.529621 - 1.57684i) q^{60} +(-2.08206 + 3.23975i) q^{61} +(3.05523 + 8.69838i) q^{62} +(0.543216 - 3.77815i) q^{63} +(-5.40308 - 5.89973i) q^{64} +(0.266914 + 1.85643i) q^{65} +(-2.79921 - 3.89306i) q^{66} +(-0.672017 - 0.582306i) q^{67} +(-14.7754 + 1.54761i) q^{68} +(4.77659 - 0.429140i) q^{69} +(-4.48347 + 0.234165i) q^{70} +(-1.95680 + 2.25827i) q^{71} +(1.88143 + 2.11192i) q^{72} +(1.68986 + 11.7532i) q^{73} +(4.60750 + 8.83765i) q^{74} +(-4.26442 - 0.613131i) q^{75} +(-4.55362 - 11.0791i) q^{76} +(-6.99681 + 10.8872i) q^{77} +(-2.96606 - 1.17169i) q^{78} +(5.10875 + 1.50006i) q^{79} +(2.00823 - 2.65229i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.84603 + 7.76454i) q^{82} +(4.72400 + 2.15738i) q^{83} +(3.43579 - 6.81714i) q^{84} +(-1.74053 - 5.92771i) q^{85} +(-0.210778 + 2.31962i) q^{86} +(-2.90293 - 6.35654i) q^{87} +(-2.82799 - 9.16343i) q^{88} +(14.8089 - 9.51710i) q^{89} +(-0.722838 + 0.927881i) q^{90} +8.60748i q^{91} +(9.32929 + 2.22808i) q^{92} -6.51906i q^{93} +(7.44376 + 5.79885i) q^{94} +(4.19048 - 2.69305i) q^{95} +(2.22217 + 5.20211i) q^{96} +(7.16690 + 15.6933i) q^{97} +(-10.6610 - 0.968735i) q^{98} +(0.955225 + 3.25320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.11564	−	0.869107i	−0.788877	−	0.614551i
$2$	−1.11564	−	0.869107i	−0.788877	−	0.614551i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$3$	0.540641	+	0.841254i	0.312139	+	0.485698i
$4$	0.489306	+	1.93922i	0.244653	+	0.969611i
$5$	−0.756543	+	0.345502i	−0.338336	+	0.154513i	−0.577336	−	0.816507i	$-0.695908\pi$
$5$	−0.756543	+	0.345502i	−0.338336	+	0.154513i	0.239000	+	0.971020i	$0.423180\pi$
$6$	0.127979	−	1.40841i	0.0522471	−	0.574981i
$7$	−3.66239	+	1.07537i	−1.38425	+	0.406453i	−0.887247	−	0.461295i	$-0.847385\pi$
$7$	−3.66239	+	1.07537i	−1.38425	+	0.406453i	−0.497005	+	0.867748i	$0.665567\pi$
$8$	1.13950	−	2.58873i	0.402874	−	0.915255i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	1.14431	+	0.272061i	0.361862	+	0.0860333i
$11$	2.56240	−	2.22033i	0.772592	−	0.669455i	−0.176554	−	0.984291i	$-0.556495\pi$
$11$	2.56240	−	2.22033i	0.772592	−	0.669455i	0.949146	+	0.314836i	$0.101950\pi$
$12$	−1.36684	+	1.46005i	−0.394572	+	0.421481i
$13$	0.635317	−	2.16369i	0.176205	−	0.600100i	−0.823268	−	0.567653i	$-0.807852\pi$
$13$	0.635317	−	2.16369i	0.176205	−	0.600100i	0.999473	−	0.0324473i	$-0.0103301\pi$
$14$	5.02052	+	1.98328i	1.34179	+	0.530053i
$15$	−0.699673	−	0.449652i	−0.180655	−	0.116100i
$16$	−3.52116	+	1.89775i	−0.880290	+	0.474437i
$17$	−1.05713	+	7.35248i	−0.256391	+	1.78324i	0.301643	+	0.953421i	$0.402465\pi$
$17$	−1.05713	+	7.35248i	−0.256391	+	1.78324i	−0.558034	+	0.829818i	$0.688444\pi$
$18$	1.25402	−	0.653782i	0.295576	−	0.154098i
$19$	−5.92823	+	0.852351i	−1.36003	+	0.195543i	−0.783428	−	0.621482i	$-0.786531\pi$
$19$	−5.92823	+	0.852351i	−1.36003	+	0.195543i	−0.576602	+	0.817025i	$0.695622\pi$
$20$	−1.04019	−	1.29805i	−0.232593	−	0.290252i
$21$	−2.88470	−	2.49960i	−0.629493	−	0.545458i
$22$	−4.78842	+	0.250092i	−1.02089	+	0.0533198i
$23$	2.22141	−	4.25034i	0.463195	−	0.886256i
$23$	2.22141	−	4.25034i	0.463195	−	0.886256i
$24$	2.79384	−	0.440965i	0.570290	−	0.0900117i
$25$	−2.82132	+	3.25597i	−0.564264	+	0.651195i
$26$	−2.58926	+	1.86174i	−0.507796	+	0.365118i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	−3.87742	−	6.57599i	−0.732763	−	1.24275i
$29$	−6.91690	−	0.994501i	−1.28444	−	0.184674i	−0.533925	−	0.845532i	$-0.679284\pi$
$29$	−6.91690	−	0.994501i	−1.28444	−	0.184674i	−0.750511	+	0.660857i	$0.770193\pi$
$30$	0.389787	+	1.10974i	0.0711650	+	0.202610i
$31$	−5.48418	−	3.52447i	−0.984988	−	0.633013i	−0.0541837	−	0.998531i	$-0.517256\pi$
$31$	−5.48418	−	3.52447i	−0.984988	−	0.633013i	−0.930804	+	0.365518i	$0.880892\pi$
$32$	5.57769	+	0.943061i	0.986006	+	0.166711i
$33$	3.25320	+	0.955225i	0.566309	+	0.166283i
$34$	7.56947	−	7.28397i	1.29815	−	1.24919i
$35$	2.39921	−	2.07893i	0.405541	−	0.351403i
$36$	−1.96724	−	0.360493i	−0.327874	−	0.0600822i
$37$	−6.41059	−	2.92762i	−1.05389	−	0.481297i	−0.188335	−	0.982105i	$-0.560309\pi$
$37$	−6.41059	−	2.92762i	−1.05389	−	0.481297i	−0.865559	+	0.500807i	$0.833036\pi$
$38$	7.35456	+	4.20135i	1.19307	+	0.681549i
$39$	2.16369	−	0.635317i	0.346468	−	0.101732i
$40$	0.0323299	+	2.35219i	0.00511181	+	0.371913i
$41$	−2.34435	−	5.13341i	−0.366126	−	0.801705i	−0.999609	−	0.0279481i	$-0.991103\pi$
$41$	−2.34435	−	5.13341i	−0.366126	−	0.801705i	0.633483	−	0.773756i	$-0.281625\pi$
$42$	1.04586	+	5.29577i	0.161380	+	0.817155i
$43$	−0.890424	−	1.38553i	−0.135788	−	0.211291i	0.766699	−	0.642006i	$-0.221898\pi$
$43$	−0.890424	−	1.38553i	−0.135788	−	0.211291i	−0.902488	+	0.430715i	$0.858261\pi$
$44$	5.55951	+	3.88263i	0.838128	+	0.585329i
$45$		−	0.831702i		−	0.123983i
$46$	−6.17229	+	2.81121i	−0.910054	+	0.414490i
$47$	−6.67219			−0.973239			−0.486619	−	0.873614i	$-0.661770\pi$
$47$	−6.67219			−0.973239			−0.486619	+	0.873614i	$0.661770\pi$
$48$	−3.50017	−	1.93619i	−0.505206	−	0.279465i
$49$	6.36787	−	4.09238i	0.909696	−	0.584626i
$50$	5.97737	−	1.18047i	0.845327	−	0.166944i
$51$	−6.75683	+	3.08574i	−0.946145	+	0.432090i
$52$	4.50674	+	0.173313i	0.624972	+	0.0240341i
$53$	2.73892	+	9.32791i	0.376220	+	1.28129i	0.902395	+	0.430911i	$0.141808\pi$
$53$	2.73892	+	9.32791i	0.376220	+	1.28129i	−0.526175	+	0.850376i	$0.676374\pi$
$54$	1.22797	+	0.701489i	0.167106	+	0.0954605i
$55$	−1.17144	+	2.56509i	−0.157956	+	0.345876i
$56$	−1.38944	+	10.7063i	−0.185671	+	1.43069i
$57$	−3.92209	−	4.52633i	−0.519493	−	0.599527i
$58$	6.85245	+	7.12103i	0.899771	+	0.935038i
$59$	1.99171	−	6.78314i	0.259298	−	0.883089i	−0.722211	−	0.691673i	$-0.756874\pi$
$59$	1.99171	−	6.78314i	0.259298	−	0.883089i	0.981509	−	0.191416i	$-0.0613079\pi$
$60$	0.529621	−	1.57684i	0.0683738	−	0.203569i
$61$	−2.08206	+	3.23975i	−0.266581	+	0.414807i	−0.948576	−	0.316549i	$-0.897476\pi$
$61$	−2.08206	+	3.23975i	−0.266581	+	0.414807i	0.681996	+	0.731356i	$0.261112\pi$
$62$	3.05523	+	8.69838i	0.388015	+	1.10470i
$63$	0.543216	−	3.77815i	0.0684388	−	0.476002i
$64$	−5.40308	−	5.89973i	−0.675384	−	0.737466i
$65$	0.266914	+	1.85643i	0.0331066	+	0.230262i
$66$	−2.79921	−	3.89306i	−0.344558	−	0.479203i
$67$	−0.672017	−	0.582306i	−0.0820999	−	0.0711400i	0.612844	−	0.790204i	$-0.290025\pi$
$67$	−0.672017	−	0.582306i	−0.0820999	−	0.0711400i	−0.694944	+	0.719064i	$0.744571\pi$
$68$	−14.7754	+	1.54761i	−1.79177	+	0.187676i
$69$	4.77659	−	0.429140i	0.575034	−	0.0516624i
$70$	−4.48347	+	0.234165i	−0.535877	+	0.0279881i
$71$	−1.95680	+	2.25827i	−0.232230	+	0.268007i	−0.859889	−	0.510481i	$-0.829468\pi$
$71$	−1.95680	+	2.25827i	−0.232230	+	0.268007i	0.627660	+	0.778488i	$0.284013\pi$
$72$	1.88143	+	2.11192i	0.221728	+	0.248893i
$73$	1.68986	+	11.7532i	0.197783	+	1.37561i	0.810700	+	0.585462i	$0.199087\pi$
$73$	1.68986	+	11.7532i	0.197783	+	1.37561i	−0.612917	+	0.790147i	$0.710004\pi$
$74$	4.60750	+	8.83765i	0.535611	+	1.02736i
$75$	−4.26442	−	0.613131i	−0.492413	−	0.0707983i
$76$	−4.55362	−	11.0791i	−0.522336	−	1.27086i
$77$	−6.99681	+	10.8872i	−0.797360	+	1.24072i
$78$	−2.96606	−	1.17169i	−0.335840	−	0.132668i
$79$	5.10875	+	1.50006i	0.574779	+	0.168770i	0.556187	−	0.831057i	$-0.312264\pi$
$79$	5.10875	+	1.50006i	0.574779	+	0.168770i	0.0185914	+	0.999827i	$0.494082\pi$
$80$	2.00823	−	2.65229i	0.224527	−	0.296535i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−1.84603	+	7.76454i	−0.203860	+	0.857449i
$83$	4.72400	+	2.15738i	0.518526	+	0.236803i	0.657447	−	0.753500i	$-0.271636\pi$
$83$	4.72400	+	2.15738i	0.518526	+	0.236803i	−0.138921	+	0.990303i	$0.544363\pi$
$84$	3.43579	−	6.81714i	0.374875	−	0.743811i
$85$	−1.74053	−	5.92771i	−0.188787	−	0.642950i
$86$	−0.210778	+	2.31962i	−0.0227288	+	0.250131i
$87$	−2.90293	−	6.35654i	−0.311227	−	0.681492i
$88$	−2.82799	−	9.16343i	−0.301464	−	0.976825i
$89$	14.8089	−	9.51710i	1.56974	−	1.00881i	0.590274	−	0.807203i	$-0.299020\pi$
$89$	14.8089	−	9.51710i	1.56974	−	1.00881i	0.979466	−	0.201607i	$-0.0646165\pi$
$90$	−0.722838	+	0.927881i	−0.0761938	+	0.0978072i
$91$			8.60748i			0.902309i
$92$	9.32929	+	2.22808i	0.972646	+	0.232293i
$93$		−	6.51906i		−	0.675995i
$94$	7.44376	+	5.79885i	0.767766	+	0.598105i
$95$	4.19048	−	2.69305i	0.429934	−	0.276302i
$96$	2.22217	+	5.20211i	0.226800	+	0.530938i
$97$	7.16690	+	15.6933i	0.727689	+	1.59342i	0.802805	+	0.596242i	$0.203340\pi$
$97$	7.16690	+	15.6933i	0.727689	+	1.59342i	−0.0751161	+	0.997175i	$0.523933\pi$
$98$	−10.6610	−	0.968735i	−1.07692	−	0.0978570i
$99$	0.955225	+	3.25320i	0.0960037	+	0.326959i
$100$	−7.69454	−	3.87799i	−0.769454	−	0.387799i
$101$	14.2756	+	6.51947i	1.42048	+	0.648712i	0.969784	−	0.243966i	$-0.0784484\pi$
$101$	14.2756	+	6.51947i	1.42048	+	0.648712i	0.450696	+	0.892677i	$0.351176\pi$
$102$	10.2200	+	2.42983i	1.01193	+	0.240589i
$103$	9.56910	+	11.0433i	0.942871	+	1.08813i	0.995983	+	0.0895426i	$0.0285405\pi$
$103$	9.56910	+	11.0433i	0.942871	+	1.08813i	−0.0531120	+	0.998589i	$0.516914\pi$
$104$	−4.87727	−	4.11019i	−0.478256	−	0.403038i
$105$	3.04602	+	0.894391i	0.297261	+	0.0872836i
$106$	5.05130	−	12.7870i	0.490626	−	1.24198i
$107$	−4.80748	+	7.48058i	−0.464756	+	0.723175i	−0.991958	−	0.126565i	$-0.959605\pi$
$107$	−4.80748	+	7.48058i	−0.464756	+	0.723175i	0.527202	+	0.849740i	$0.323241\pi$
$108$	−0.760306	−	1.84985i	−0.0731605	−	0.178002i
$109$	−17.1764	−	2.46959i	−1.64520	−	0.236544i	−0.743446	−	0.668796i	$-0.766810\pi$
$109$	−17.1764	−	2.46959i	−1.64520	−	0.236544i	−0.901753	+	0.432252i	$0.857719\pi$
$110$	3.53624	−	1.84361i	0.337167	−	0.175782i
$111$	−1.00296	−	6.97572i	−0.0951965	−	0.662106i
$112$	10.8551	−	10.7368i	1.02571	−	1.01454i
$113$	1.40284	−	1.61896i	0.131968	−	0.152299i	−0.685920	−	0.727677i	$-0.740600\pi$
$113$	1.40284	−	1.61896i	0.131968	−	0.152299i	0.817887	+	0.575379i	$0.195145\pi$
$114$	0.441774	+	8.45847i	0.0413759	+	0.792208i
$115$	−0.212091	+	3.98306i	−0.0197776	+	0.371422i
$116$	−1.45593	−	13.9000i	−0.135180	−	1.29058i
$117$	1.70424	+	1.47673i	0.157557	+	0.136524i
$118$	−8.11730	+	5.83653i	−0.747258	+	0.537296i
$119$	−4.03506	−	28.0644i	−0.369893	−	2.57266i
$120$	−1.96131	+	1.29889i	−0.179042	+	0.118572i
$121$	0.0705523	−	0.490702i	0.00641385	−	0.0446093i
$122$	5.13852	−	1.80486i	0.465220	−	0.163405i
$123$	3.05105	−	4.74753i	0.275104	−	0.428070i
$124$	4.15128	−	12.3596i	0.372796	−	1.10992i
$125$	2.18109	−	7.42812i	0.195083	−	0.664391i
$126$	−3.88965	+	3.74294i	−0.346518	+	0.333448i
$127$	−4.73588	−	5.46550i	−0.420241	−	0.484984i	0.505669	−	0.862727i	$-0.331246\pi$
$127$	−4.73588	−	5.46550i	−0.420241	−	0.484984i	−0.925910	+	0.377743i	$0.876700\pi$
$128$	0.900395	+	11.2778i	0.0795844	+	0.996828i
$129$	0.684180	−	1.49815i	0.0602387	−	0.131904i
$130$	1.31565	−	2.30308i	0.115391	−	0.201994i
$131$	−4.86383	−	16.5647i	−0.424955	−	1.44726i	−0.842544	−	0.538628i	$-0.818943\pi$
$131$	−4.86383	−	16.5647i	−0.424955	−	1.44726i	0.417589	−	0.908636i	$-0.362875\pi$
$132$	−0.260583	+	6.77607i	−0.0226808	+	0.589781i
$133$	20.7949	−	9.49671i	1.80315	−	0.823469i
$134$	0.243643	+	1.23370i	0.0210475	+	0.106575i
$135$	0.699673	−	0.449652i	0.0602182	−	0.0386999i
$136$	17.8290	+	11.1148i	1.52883	+	0.953085i
$137$	0.262237			0.0224044			0.0112022	−	0.999937i	$-0.496434\pi$
$137$	0.262237			0.0224044			0.0112022	+	0.999937i	$0.496434\pi$
$138$	−5.70193	−	3.67260i	−0.485380	−	0.312633i
$139$		−	8.64728i		−	0.733453i	−0.930329	−	0.366727i	$-0.880478\pi$
$139$		−	8.64728i		−	0.733453i	0.930329	−	0.366727i	$-0.119522\pi$
$140$	5.20545	+	3.63537i	0.439941	+	0.307245i
$141$	−3.60726	−	5.61300i	−0.303786	−	0.472700i
$142$	4.14576	−	0.818746i	0.347905	−	0.0687077i
$143$	−3.17617	−	6.95485i	−0.265605	−	0.581594i
$144$	−0.263509	−	3.99131i	−0.0219591	−	0.332609i
$145$	5.57654	−	1.63742i	0.463106	−	0.135980i
$146$	8.32953	−	14.5810i	0.689357	−	1.20673i
$147$	6.88546	+	3.14449i	0.567904	+	0.259353i
$148$	2.54056	−	13.8641i	0.208833	−	1.13962i
$149$	−4.04268	+	3.50300i	−0.331189	+	0.286977i	−0.804542	−	0.593896i	$-0.797589\pi$
$149$	−4.04268	+	3.50300i	−0.331189	+	0.286977i	0.473353	+	0.880873i	$0.343044\pi$
$150$	4.22468	+	4.39027i	0.344944	+	0.358464i
$151$	4.83500	+	1.41968i	0.393466	+	0.115532i	0.472480	−	0.881341i	$-0.343359\pi$
$151$	4.83500	+	1.41968i	0.393466	+	0.115532i	−0.0790136	+	0.996874i	$0.525177\pi$
$152$	−4.54872	+	16.3179i	−0.368950	+	1.32355i
$153$	−6.24891	−	4.01593i	−0.505194	−	0.324669i
$154$	17.2681	−	6.06527i	1.39150	−	0.488754i
$155$	5.36673	+	0.771619i	0.431066	+	0.0619780i
$156$	2.29073	+	3.88501i	0.183405	+	0.311050i
$157$	8.36861	−	1.20322i	0.667888	−	0.0960278i	0.199973	−	0.979801i	$-0.435914\pi$
$157$	8.36861	−	1.20322i	0.667888	−	0.0960278i	0.467915	+	0.883774i	$0.345005\pi$
$158$	−4.39581	−	6.11358i	−0.349712	−	0.486370i
$159$	−6.36636	+	7.34718i	−0.504886	+	0.582669i
$160$	−4.54559	+	1.21364i	−0.359361	+	0.0959463i
$161$	−3.56495	+	17.9552i	−0.280957	+	1.41507i
$162$	0.0737618	+	1.41229i	0.00579527	+	0.110960i
$163$	−14.7262	−	12.7603i	−1.15344	−	0.999464i	−0.999936	−	0.0113159i	$-0.996398\pi$
$163$	−14.7262	−	12.7603i	−1.15344	−	0.999464i	−0.153506	−	0.988148i	$-0.549057\pi$
$164$	8.80772	−	7.05803i	0.687767	−	0.551139i
$165$	−2.79122	+	0.401316i	−0.217296	+	0.0312424i
$166$	−3.39529	−	6.51252i	−0.263526	−	0.505469i
$167$	−1.76517	+	12.2771i	−0.136593	+	0.950027i	0.800098	+	0.599870i	$0.204781\pi$
$167$	−1.76517	+	12.2771i	−0.136593	+	0.950027i	−0.936691	+	0.350157i	$0.886128\pi$
$168$	−9.75792	+	4.61941i	−0.752840	+	0.356395i
$169$	6.65837	+	4.27907i	0.512182	+	0.329159i
$170$	−3.21001	+	8.12590i	−0.246196	+	0.623228i
$171$	1.68735	−	5.74659i	0.129035	−	0.439453i
$172$	2.25115	−	2.40468i	0.171649	−	0.183355i
$173$	−2.44138	+	2.11547i	−0.185615	+	0.160836i	−0.742712	−	0.669612i	$-0.766461\pi$
$173$	−2.44138	+	2.11547i	−0.185615	+	0.160836i	0.557097	+	0.830447i	$0.311915\pi$
$174$	−2.28588	+	9.61457i	−0.173292	+	0.728879i
$175$	6.83137	−	14.9586i	0.516403	−	1.13076i
$176$	−4.80899	+	12.6809i	−0.362491	+	0.955860i
$177$	6.78314	−	1.99171i	0.509852	−	0.149706i
$178$	−24.7928	−	2.25286i	−1.85830	−	0.168859i
$179$	−6.52201	+	2.97850i	−0.487478	+	0.222624i	−0.643963	−	0.765057i	$-0.722711\pi$
$179$	−6.52201	+	2.97850i	−0.487478	+	0.222624i	0.156485	+	0.987680i	$0.449984\pi$
$180$	1.61285	−	0.406957i	0.120215	−	0.0303328i
$181$	11.4807	+	17.8643i	0.853351	+	1.32784i	0.943316	+	0.331895i	$0.107688\pi$
$181$	11.4807	+	17.8643i	0.853351	+	1.32784i	−0.0899653	+	0.995945i	$0.528676\pi$
$182$	7.48082	−	9.60285i	0.554515	−	0.711810i
$183$	−3.85110			−0.284681
$184$	−8.47169	−	10.5939i	−0.624541	−	0.780992i
$185$	5.86138			0.430937
$186$	−5.66576	+	7.27293i	−0.415434	+	0.533277i
$187$	13.6162	+	21.1872i	0.995712	+	1.54936i
$188$	−3.26474	−	12.9389i	−0.238106	−	0.943663i
$189$	3.47207	−	1.58564i	0.252556	−	0.115338i
$190$	−7.01562	−	0.637491i	−0.508966	−	0.0462484i
$191$	−17.5987	+	5.16744i	−1.27340	+	0.373903i	−0.847465	−	0.530852i	$-0.821872\pi$
$191$	−17.5987	+	5.16744i	−1.27340	+	0.373903i	−0.425933	+	0.904755i	$0.640054\pi$
$192$	2.04204	−	7.73499i	0.147372	−	0.558225i
$193$	−6.63210	+	14.5223i	−0.477389	+	1.04534i	0.505784	+	0.862660i	$0.331203\pi$
$193$	−6.63210	+	14.5223i	−0.477389	+	1.04534i	−0.983173	+	0.182676i	$0.941524\pi$
$194$	5.64350	−	23.7369i	0.405179	−	1.70421i
$195$	−1.41742	+	1.22820i	−0.101504	+	0.0879535i
$196$	11.0519	+	10.3463i	0.789420	+	0.739020i
$197$	2.52274	−	8.59165i	0.179737	−	0.612130i	−0.819500	−	0.573079i	$-0.805749\pi$
$197$	2.52274	−	8.59165i	0.179737	−	0.612130i	0.999237	−	0.0390501i	$-0.0124332\pi$
$198$	1.76169	−	4.45959i	0.125198	−	0.316929i
$199$	−3.10991	−	1.99861i	−0.220455	−	0.141678i	0.425752	−	0.904840i	$-0.360010\pi$
$199$	−3.10991	−	1.99861i	−0.220455	−	0.141678i	−0.646207	+	0.763162i	$0.723646\pi$
$200$	5.21395	+	11.0138i	0.368682	+	0.778795i
$201$	0.126547	−	0.880155i	0.00892595	−	0.0620813i
$202$	−10.2604	−	19.6804i	−0.721917	−	1.38471i
$203$	26.4018	−	3.79601i	1.85305	−	0.266428i
$204$	−9.29009	−	11.5931i	−0.650437	−	0.811680i
$205$	3.54721	+	3.07367i	0.247748	+	0.214675i
$206$	−1.07784	−	20.6369i	−0.0750965	−	1.43784i
$207$	2.94344	+	3.78632i	0.204583	+	0.263167i
$208$	1.86908	+	8.82437i	0.129598	+	0.611860i
$209$	−13.2980	+	15.3467i	−0.919841	+	1.06155i
$210$	−2.62094	−	3.64513i	−0.180862	−	0.251538i
$211$	−12.4883	+	1.79554i	−0.859729	+	0.123610i	−0.558058	−	0.829802i	$-0.688453\pi$
$211$	−12.4883	+	1.79554i	−0.859729	+	0.123610i	−0.301671	+	0.953412i	$0.597544\pi$
$212$	−16.7487	+	9.87558i	−1.15031	+	0.678258i
$213$	−2.95770	−	0.425254i	−0.202659	−	0.0291379i
$214$	11.8648	−	4.16742i	0.811063	−	0.284879i
$215$	1.15235	+	0.740568i	0.0785894	+	0.0505063i
$216$	−0.759487	+	2.72455i	−0.0516766	+	0.185382i
$217$	23.8753	+	7.01043i	1.62076	+	0.475899i
$218$	17.0163	+	17.6833i	1.15249	+	1.19766i
$219$	−8.97383	+	7.77587i	−0.606395	+	0.525444i
$220$	−5.54746	−	1.01656i	−0.374010	−	0.0685365i
$221$	15.2369	+	6.95845i	1.02494	+	0.468076i
$222$	−4.94371	+	8.65407i	−0.331800	+	0.580823i
$223$	−1.32004	+	0.387599i	−0.0883966	+	0.0259556i	−0.325632	−	0.945497i	$-0.605577\pi$
$223$	−1.32004	+	0.387599i	−0.0883966	+	0.0259556i	0.237235	+	0.971452i	$0.423759\pi$
$224$	−21.4418	+	2.54425i	−1.43264	+	0.169995i
$225$	−1.78972	−	3.91894i	−0.119315	−	0.261263i
$226$	−2.97211	+	0.586961i	−0.197702	+	0.0390441i
$227$	−2.54285	−	3.95675i	−0.168775	−	0.262619i	0.746555	−	0.665324i	$-0.231706\pi$
$227$	−2.54285	−	3.95675i	−0.168775	−	0.262619i	−0.915330	+	0.402705i	$0.868070\pi$
$228$	6.85846	−	9.82056i	0.454212	−	0.650382i
$229$			8.46102i			0.559120i	0.960128	+	0.279560i	$0.0901886\pi$
$229$			8.46102i			0.559120i	−0.960128	+	0.279560i	$0.909811\pi$
$230$	3.69832	−	4.25933i	0.243860	−	0.280852i
$231$	−12.9417			−0.851501
$232$	−10.4563	+	16.7728i	−0.686491	+	1.10119i
$233$	−10.2996	+	6.61916i	−0.674750	+	0.433635i	−0.832635	−	0.553822i	$-0.813169\pi$
$233$	−10.2996	+	6.61916i	−0.674750	+	0.433635i	0.157885	+	0.987457i	$0.449532\pi$
$234$	−0.617881	−	3.12867i	−0.0403922	−	0.204528i
$235$	5.04780	−	2.30525i	0.329282	−	0.150378i
$236$	14.1286	+	0.543332i	0.919691	+	0.0353679i
$237$	1.50006	+	5.10875i	0.0974396	+	0.331849i
$238$	−19.8893	+	34.8167i	−1.28923	+	2.25683i
$239$	0.296939	−	0.650205i	0.0192074	−	0.0420583i	−0.899785	−	0.436333i	$-0.856277\pi$
$239$	0.296939	−	0.650205i	0.0192074	−	0.0420583i	0.918993	+	0.394275i	$0.129004\pi$
$240$	3.31698	+	0.255496i	0.214110	+	0.0164922i
$241$	−9.71895	−	11.2163i	−0.626053	−	0.722503i	0.350792	−	0.936453i	$-0.385912\pi$
$241$	−9.71895	−	11.2163i	−0.626053	−	0.722503i	−0.976845	+	0.213950i	$0.931367\pi$
$242$	−0.505184	+	0.486130i	−0.0324744	+	0.0312496i
$243$	0.281733	−	0.959493i	0.0180732	−	0.0615515i
$244$	−7.30136	−	2.45235i	−0.467421	−	0.156995i
$245$	−3.40365	+	5.29618i	−0.217451	+	0.338360i
$246$	−7.52998	+	2.64484i	−0.480094	+	0.168629i
$247$	−1.92208	+	13.3684i	−0.122299	+	0.850609i
$248$	−15.3731	+	10.1809i	−0.976195	+	0.646491i
$249$	0.739085	+	5.14045i	0.0468376	+	0.325763i
$250$	−8.88914	+	6.39150i	−0.562199	+	0.404234i
$251$	5.50873	+	4.77334i	0.347708	+	0.301291i	0.811152	−	0.584836i	$-0.198841\pi$
$251$	5.50873	+	4.77334i	0.347708	+	0.301291i	−0.463444	+	0.886126i	$0.653386\pi$
$252$	7.59247	−	0.795257i	0.478281	−	0.0500965i
$253$	−3.74503	−	15.8233i	−0.235448	−	0.994803i
$254$	0.533437	+	10.2135i	0.0334708	+	0.640853i
$255$	4.04570	−	4.66899i	0.253352	−	0.292384i
$256$	8.79712	−	13.3645i	0.549820	−	0.835283i
$257$	−3.61032	−	25.1103i	−0.225206	−	1.56634i	−0.717906	−	0.696140i	$-0.754899\pi$
$257$	−3.61032	−	25.1103i	−0.225206	−	1.56634i	0.492701	−	0.870199i	$-0.336010\pi$
$258$	−2.06535	+	1.07677i	−0.128583	+	0.0670365i
$259$	26.6263	+	3.82829i	1.65448	+	0.237878i
$260$	−3.46942	+	1.42597i	−0.215164	+	0.0884348i
$261$	3.77802	−	5.87871i	0.233853	−	0.363883i
$262$	−8.97020	+	22.7074i	−0.554181	+	1.40287i
$263$	11.9550	+	3.51030i	0.737175	+	0.216454i	0.628703	−	0.777645i	$-0.283586\pi$
$263$	11.9550	+	3.51030i	0.737175	+	0.216454i	0.108472	+	0.994100i	$0.465404\pi$
$264$	6.17984	−	7.33318i	0.380343	−	0.451326i
$265$	−5.29492	−	6.11066i	−0.325264	−	0.375375i
$266$	−31.4533	−	7.47807i	−1.92852	−	0.458510i
$267$	16.0126	+	7.31270i	0.979955	+	0.447530i
$268$	0.800398	−	1.58812i	0.0488921	−	0.0970096i
$269$	2.34812	+	7.99696i	0.143167	+	0.487583i	0.999588	−	0.0286950i	$-0.00913517\pi$
$269$	2.34812	+	7.99696i	0.143167	+	0.487583i	−0.856421	+	0.516278i	$0.827317\pi$
$270$	−1.17138	−	0.106440i	−0.0712878	−	0.00647774i
$271$	1.71209	+	3.74895i	0.104002	+	0.227732i	0.954478	−	0.298281i	$-0.0964134\pi$
$271$	1.71209	+	3.74895i	0.104002	+	0.227732i	−0.850476	+	0.526014i	$0.823686\pi$
$272$	−10.2308	−	27.8954i	−0.620335	−	1.69141i
$273$	−7.24107	+	4.65355i	−0.438249	+	0.281646i
$274$	−0.292563	−	0.227912i	−0.0176743	−	0.0137687i
$275$			14.6074i			0.880857i
$276$	3.16941	+	9.05289i	0.190776	+	0.544920i
$277$		−	17.5330i		−	1.05346i	−0.850034	−	0.526728i	$-0.823419\pi$
$277$		−	17.5330i		−	1.05346i	0.850034	−	0.526728i	$-0.176581\pi$
$278$	−7.51541	+	9.64726i	−0.450745	+	0.578604i
$279$	5.48418	−	3.52447i	0.328329	−	0.211004i
$280$	−2.64789	−	8.57985i	−0.158241	−	0.512744i
$281$	−9.36365	−	20.5035i	−0.558588	−	1.22314i	−0.952654	−	0.304056i	$-0.901659\pi$
$281$	−9.36365	−	20.5035i	−0.558588	−	1.22314i	0.394066	−	0.919082i	$-0.371068\pi$
$282$	−0.853898	+	9.39719i	−0.0508489	+	0.559594i
$283$	−0.270632	−	0.921689i	−0.0160874	−	0.0547887i	0.951058	−	0.309012i	$-0.0999984\pi$
$283$	−0.270632	−	0.921689i	−0.0160874	−	0.0547887i	−0.967146	+	0.254223i	$0.918180\pi$
$284$	−5.33676	−	2.68969i	−0.316678	−	0.159604i
$285$	4.53108	+	2.06928i	0.268398	+	0.122573i
$286$	−2.50104	+	10.5195i	−0.147890	+	0.622034i
$287$	14.1063	+	16.2795i	0.832666	+	0.960948i
$288$	−3.17490	+	4.68188i	−0.187082	+	0.275883i
$289$	−36.6301	−	10.7556i	−2.15471	−	0.632681i
$290$	−7.64450	−	3.01984i	−0.448901	−	0.177331i
$291$	−9.32735	+	14.5136i	−0.546779	+	0.850805i
$292$	−21.9652	+	9.02793i	−1.28542	+	0.528320i
$293$	−6.44045	−	0.925997i	−0.376255	−	0.0540973i	−0.0484068	−	0.998828i	$-0.515414\pi$
$293$	−6.44045	−	0.925997i	−0.376255	−	0.0540973i	−0.327848	+	0.944730i	$0.606323\pi$
$294$	−4.94881	−	9.49232i	−0.288620	−	0.553603i
$295$	0.836771	+	5.81987i	0.0487187	+	0.338846i
$296$	−14.8837	+	13.2593i	−0.865097	+	0.770680i
$297$	−2.22033	+	2.56240i	−0.128837	+	0.148685i
$298$	7.55466	−	0.394569i	0.437630	−	0.0228568i
$299$	−7.78512	−	7.50674i	−0.450225	−	0.434126i
$300$	−0.897611	−	8.56966i	−0.0518236	−	0.494770i
$301$	4.75104	+	4.11680i	0.273845	+	0.237288i
$302$	−4.16026	−	5.78598i	−0.239396	−	0.332946i
$303$	2.23347	+	15.5341i	0.128310	+	0.892413i
$304$	19.2567	−	14.2515i	1.10445	−	0.817382i
$305$	0.455830	−	3.17037i	0.0261007	−	0.181535i
$306$	3.48126	+	9.91130i	0.199010	+	0.566591i
$307$	−15.4412	+	24.0269i	−0.881275	+	1.37129i	0.0468032	+	0.998904i	$0.485097\pi$
$307$	−15.4412	+	24.0269i	−0.881275	+	1.37129i	−0.928078	+	0.372386i	$0.878540\pi$
$308$	−24.5364	−	8.24116i	−1.39809	−	0.469584i
$309$	−4.11679	+	14.0205i	−0.234196	+	0.797599i
$310$	−5.31672	−	5.52511i	−0.301969	−	0.313805i
$311$	−4.33322	−	5.00081i	−0.245715	−	0.283570i	0.619473	−	0.785018i	$-0.287346\pi$
$311$	−4.33322	−	5.00081i	−0.245715	−	0.283570i	−0.865188	+	0.501448i	$0.832801\pi$
$312$	0.820862	−	6.32516i	0.0464721	−	0.358092i
$313$	−1.78234	+	3.90279i	−0.100744	+	0.220599i	−0.953292	−	0.302050i	$-0.902329\pi$
$313$	−1.78234	+	3.90279i	−0.100744	+	0.220599i	0.852548	+	0.522649i	$0.175056\pi$
$314$	−10.3821	−	5.93085i	−0.585895	−	0.334697i
$315$	0.894391	+	3.04602i	0.0503932	+	0.171624i
$316$	−0.409213	+	10.6410i	−0.0230200	+	0.598602i
$317$	0.275172	−	0.125667i	0.0154552	−	0.00705816i	−0.407672	−	0.913128i	$-0.633659\pi$
$317$	0.275172	−	0.125667i	0.0154552	−	0.00705816i	0.423128	+	0.906070i	$0.360932\pi$
$318$	13.4881	−	2.66375i	0.756372	−	0.149376i
$319$	−19.9320	+	12.8095i	−1.11598	+	0.717195i
$320$	6.12602	+	2.59663i	0.342455	+	0.145156i
$321$	−8.89218			−0.496313
$322$	19.5822	−	16.9332i	1.09127	−	0.943653i
$323$		−	44.4883i		−	2.47539i
$324$	1.14514	−	1.63971i	0.0636188	−	0.0910952i
$325$	5.25249	+	8.17303i	0.291356	+	0.453358i
$326$	5.33904	+	27.0345i	0.295702	+	1.49730i
$327$	−7.20870	−	15.7849i	−0.398642	−	0.872904i
$328$	−15.9604	+	0.219370i	−0.881267	+	0.0121127i
$329$	24.4361	−	7.17510i	1.34721	−	0.395576i
$330$	3.46278	+	1.97814i	0.190620	+	0.108893i
$331$	24.9427	+	11.3910i	1.37098	+	0.626103i	0.958559	−	0.284892i	$-0.0919579\pi$
$331$	24.9427	+	11.3910i	1.37098	+	0.626103i	0.412416	+	0.910996i	$0.364685\pi$
$332$	−1.87215	+	10.2165i	−0.102748	+	0.560703i
$333$	5.32611	−	4.61510i	0.291869	−	0.252906i
$334$	12.6394	−	12.1626i	0.691596	−	0.665511i
$335$	0.709597	+	0.208357i	0.0387694	+	0.0113837i
$336$	14.9011	+	3.32708i	0.812921	+	0.181507i
$337$	11.8272	+	7.60090i	0.644270	+	0.414047i	0.821568	−	0.570110i	$-0.193099\pi$
$337$	11.8272	+	7.60090i	0.644270	+	0.414047i	−0.177298	+	0.984157i	$0.556736\pi$
$338$	−3.70937	−	10.5607i	−0.201763	−	0.574428i
$339$	2.12038	+	0.304865i	0.115163	+	0.0165580i
$340$	10.6435	−	6.27574i	0.577224	−	0.340350i
$341$	−21.8781	+	3.14560i	−1.18477	+	0.170344i
$342$	−6.87688	+	4.94464i	−0.371859	+	0.267375i
$343$	−1.42354	+	1.64285i	−0.0768639	+	0.0887056i
$344$	−4.60140	+	0.726261i	−0.248091	+	0.0391574i
$345$	−3.46543	+	1.97498i	−0.186572	+	0.106330i
$346$	4.56227	−	0.238281i	0.245269	−	0.0128100i
$347$	−4.82294	−	4.17910i	−0.258909	−	0.224346i	0.515727	−	0.856753i	$-0.327522\pi$
$347$	−4.82294	−	4.17910i	−0.258909	−	0.224346i	−0.774637	+	0.632407i	$0.782067\pi$
$348$	10.9063	−	8.73973i	0.584640	−	0.468498i
$349$	−19.4886	+	2.80204i	−1.04320	+	0.149990i	−0.642552	−	0.766242i	$-0.722124\pi$
$349$	−19.4886	+	2.80204i	−1.04320	+	0.149990i	−0.400649	+	0.916232i	$0.631215\pi$
$350$	−20.6220	+	10.7512i	−1.10229	+	0.574678i
$351$	−0.320925	+	2.23208i	−0.0171297	+	0.119140i
$352$	16.3862	−	9.96782i	0.873386	−	0.531286i
$353$	−17.8735	−	11.4866i	−0.951311	−	0.611371i	−0.0297309	−	0.999558i	$-0.509465\pi$
$353$	−17.8735	−	11.4866i	−0.951311	−	0.611371i	−0.921581	+	0.388187i	$0.873101\pi$
$354$	−9.29855	−	3.67324i	−0.494212	−	0.195231i
$355$	0.700169	−	2.38456i	0.0371611	−	0.126559i
$356$	25.7019	+	24.0610i	1.36220	+	1.27523i
$357$	21.4278	−	18.5673i	1.13408	−	0.982685i
$358$	9.86486	+	2.34539i	0.521374	+	0.123958i
$359$	1.04838	−	2.29563i	0.0553315	−	0.121159i	−0.879947	−	0.475072i	$-0.842422\pi$
$359$	1.04838	−	2.29563i	0.0553315	−	0.121159i	0.935278	+	0.353913i	$0.115149\pi$
$360$	−2.15306	−	0.947726i	−0.113476	−	0.0499495i
$361$	16.1871	−	4.75296i	0.851952	−	0.250156i
$362$	2.71766	−	29.9080i	0.142837	−	1.57193i
$363$	0.450948	−	0.205941i	0.0236687	−	0.0108091i
$364$	−16.6918	+	4.21169i	−0.874888	+	0.220753i
$365$	−5.33920	−	8.30796i	−0.279467	−	0.434859i
$366$	4.29644	+	3.34702i	0.224579	+	0.174951i
$367$	−1.23586			−0.0645114			−0.0322557	−	0.999480i	$-0.510269\pi$
$367$	−1.23586			−0.0645114			−0.0322557	+	0.999480i	$0.510269\pi$
$368$	0.244139	+	19.1818i	0.0127266	+	0.999919i
$369$	5.64340			0.293783
$370$	−6.53919	−	5.09417i	−0.339957	−	0.264833i
$371$	−20.0620	−	31.2170i	−1.04157	−	1.62071i
$372$	12.6419	−	3.18982i	0.655452	−	0.165384i
$373$	−2.12963	+	0.972570i	−0.110268	+	0.0503578i	−0.469785	−	0.882781i	$-0.655669\pi$
$373$	−2.12963	+	0.972570i	−0.110268	+	0.0503578i	0.359517	+	0.933138i	$0.382941\pi$
$374$	3.22317	−	35.4711i	0.166666	−	1.83417i
$375$	7.42812	−	2.18109i	0.383586	−	0.112631i
$376$	−7.60297	+	17.2725i	−0.392093	+	0.890762i
$377$	−6.54622	+	14.3342i	−0.337147	+	0.738250i
$378$	−5.25167	−	1.24859i	−0.270117	−	0.0642207i
$379$	6.58892	−	5.70933i	0.338450	−	0.293268i	−0.469008	−	0.883194i	$-0.655388\pi$
$379$	6.58892	−	5.70933i	0.338450	−	0.293268i	0.807458	+	0.589926i	$0.200843\pi$
$380$	7.27286	+	6.80853i	0.373090	+	0.349270i
$381$	2.03746	−	6.93894i	0.104382	−	0.355493i
$382$	24.1249	+	9.53014i	1.23434	+	0.487605i
$383$	31.7682	+	20.4162i	1.62328	+	1.04322i	0.953823	+	0.300370i	$0.0971100\pi$
$383$	31.7682	+	20.4162i	1.62328	+	1.04322i	0.669458	+	0.742850i	$0.266526\pi$
$384$	−9.00072	+	6.85471i	−0.459316	+	0.349803i
$385$	1.53183	−	10.6541i	0.0780690	−	0.542982i
$386$	20.0204	−	10.4376i	1.01901	−	0.531261i
$387$	1.63022	−	0.234390i	0.0828685	−	0.0119147i
$388$	−26.9260	+	21.5771i	−1.36696	+	1.09541i
$389$	−18.2951	−	15.8528i	−0.927598	−	0.803769i	0.0532420	−	0.998582i	$-0.483045\pi$
$389$	−18.2951	−	15.8528i	−0.927598	−	0.803769i	−0.980840	+	0.194813i	$0.937590\pi$
$390$	2.64877	−	0.138342i	0.134126	−	0.00700520i
$391$	28.9022	+	20.8260i	1.46165	+	1.05322i
$392$	−3.33789	−	21.1480i	−0.168589	−	1.06814i
$393$	11.3055	−	13.0473i	0.570288	−	0.658147i
$394$	−10.2815	+	7.39266i	−0.517976	+	0.372437i
$395$	−4.38326	+	0.630218i	−0.220546	+	0.0317097i
$396$	−5.84127	+	3.44420i	−0.293535	+	0.173078i
$397$	28.0372	+	4.03113i	1.40714	+	0.202317i	0.803675	−	0.595069i	$-0.202875\pi$
$397$	28.0372	+	4.03113i	1.40714	+	0.202317i	0.603470	+	0.797386i	$0.293784\pi$
$398$	1.73253	+	4.93258i	0.0868437	+	0.247248i
$399$	19.2317	+	12.3595i	0.962789	+	0.618747i
$400$	3.75529	−	16.8189i	0.187765	−	0.840947i
$401$	20.0199	+	5.87837i	0.999746	+	0.293552i	0.740352	−	0.672220i	$-0.234659\pi$
$401$	20.0199	+	5.87837i	0.999746	+	0.293552i	0.259394	+	0.965772i	$0.416477\pi$
$402$	−0.906130	+	0.871953i	−0.0451936	+	0.0434891i
$403$	−11.1101	+	9.62692i	−0.553431	+	0.479551i
$404$	−5.65753	+	30.8737i	−0.281473	+	1.53602i
$405$	0.756543	+	0.345502i	0.0375929	+	0.0171681i
$406$	−32.7541	−	18.7110i	−1.62556	−	0.928613i
$407$	−22.9268	+	6.73190i	−1.13644	+	0.333688i
$408$	0.288745	+	21.0078i	0.0142950	+	1.04004i
$409$	−6.70333	−	14.6782i	−0.331458	−	0.725792i	0.668379	−	0.743821i	$-0.266988\pi$
$409$	−6.70333	−	14.6782i	−0.331458	−	0.725792i	−0.999837	+	0.0180283i	$0.994261\pi$
$410$	−1.28606	−	6.51201i	−0.0635138	−	0.321605i
$411$	0.141776	+	0.220608i	0.00699330	+	0.0108818i
$412$	−16.7332	+	23.9602i	−0.824387	+	1.18043i
$413$			26.9843i			1.32781i
$414$	0.00689642	−	6.78233i	0.000338941	−	0.333333i
$415$	−4.31929			−0.212025
$416$	5.58409	−	11.4693i	0.273783	−	0.562326i
$417$	7.27456	−	4.67508i	0.356237	−	0.228939i
$418$	28.1737	−	5.56402i	1.37802	−	0.272145i
$419$	7.69258	−	3.51308i	0.375807	−	0.171625i	−0.218552	−	0.975825i	$-0.570133\pi$
$419$	7.69258	−	3.51308i	0.375807	−	0.171625i	0.594359	+	0.804200i	$0.297406\pi$
$420$	−0.243987	+	6.34453i	−0.0119054	+	0.309581i
$421$	−9.50846	−	32.3828i	−0.463414	−	1.57824i	−0.777522	−	0.628855i	$-0.783524\pi$
$421$	−9.50846	−	32.3828i	−0.463414	−	1.57824i	0.314109	−	0.949387i	$-0.398294\pi$
$422$	15.4930	+	8.85047i	0.754185	+	0.430834i
$423$	2.77173	−	6.06924i	0.134766	−	0.295096i
$424$	27.2685	+	3.53883i	1.32427	+	0.171861i
$425$	−20.9570	−	24.1857i	−1.01656	−	1.17318i
$426$	2.93014	+	3.04499i	0.141966	+	0.147530i
$427$	4.14137	−	14.1042i	0.200415	−	0.682551i
$428$	−16.8588	−	5.66247i	−0.814902	−	0.273706i
$429$	4.13362	−	6.43204i	0.199573	−	0.310542i
$430$	−0.641971	−	1.82772i	−0.0309586	−	0.0881405i
$431$	0.979740	−	6.81424i	0.0471924	−	0.328230i	−0.952525	−	0.304460i	$-0.901524\pi$
$431$	0.979740	−	6.81424i	0.0471924	−	0.328230i	0.999717	−	0.0237701i	$-0.00756697\pi$
$432$	3.21524	−	2.37954i	0.154693	−	0.114486i
$433$	−1.02133	−	7.10349i	−0.0490819	−	0.341372i	−0.999535	−	0.0305030i	$-0.990289\pi$
$433$	−1.02133	−	7.10349i	−0.0490819	−	0.341372i	0.950453	−	0.310869i	$-0.100620\pi$
$434$	−20.5435	−	28.5713i	−0.986117	−	1.37147i
$435$	4.39239	+	3.80603i	0.210599	+	0.182485i
$436$	−3.61543	−	34.5172i	−0.173148	−	1.65307i
$437$	−9.54623	+	27.0904i	−0.456658	+	1.29591i
$438$	16.7696	−	0.875853i	0.801284	−	0.0418499i
$439$	1.75095	−	2.02070i	0.0835682	−	0.0964428i	−0.712426	−	0.701748i	$-0.752403\pi$
$439$	1.75095	−	2.02070i	0.0835682	−	0.0964428i	0.795994	+	0.605305i	$0.206949\pi$
$440$	5.30547	+	5.95546i	0.252929	+	0.283915i
$441$	1.07725	+	7.49246i	0.0512978	+	0.356784i
$442$	−10.9512	−	21.0056i	−0.520898	−	0.999135i
$443$	20.5146	+	2.94956i	0.974678	+	0.140138i	0.611210	−	0.791469i	$-0.290683\pi$
$443$	20.5146	+	2.94956i	0.974678	+	0.140138i	0.363469	+	0.931606i	$0.381592\pi$
$444$	13.0367	−	5.35822i	0.618695	−	0.254290i
$445$	−7.91539	+	12.3166i	−0.375226	+	0.583863i
$446$	1.80956	+	0.714836i	0.0856850	+	0.0338485i
$447$	−5.13255	−	1.50705i	−0.242761	−	0.0712812i
$448$	26.1326	+	15.7968i	1.23465	+	0.746327i
$449$	13.0936	+	15.1108i	0.617925	+	0.713123i	0.975312	−	0.220833i	$-0.0708776\pi$
$449$	13.0936	+	15.1108i	0.617925	+	0.713123i	−0.357387	+	0.933957i	$0.616332\pi$
$450$	−1.40929	+	5.92759i	−0.0664348	+	0.279429i
$451$	−17.4050	−	7.94861i	−0.819571	−	0.374286i
$452$	3.82593	+	1.92824i	0.179957	+	0.0906969i
$453$	1.41968	+	4.83500i	0.0667025	+	0.227168i
$454$	−0.601934	+	6.62431i	−0.0282502	+	0.310894i
$455$	−2.97390	−	6.51193i	−0.139418	−	0.305284i
$456$	−16.1867	+	4.99548i	−0.758011	+	0.233935i
$457$	−22.5392	+	14.4851i	−1.05434	+	0.677582i	−0.948492	−	0.316800i	$-0.897392\pi$
$457$	−22.5392	+	14.4851i	−1.05434	+	0.677582i	−0.105846	+	0.994382i	$0.533755\pi$
$458$	7.35353	−	9.43945i	0.343608	−	0.441077i
$459$		−	7.42809i		−	0.346714i
$460$	−7.82782	+	1.53765i	−0.364974	+	0.0716931i
$461$			24.1988i			1.12705i	0.826099	+	0.563525i	$0.190555\pi$
$461$			24.1988i			1.12705i	−0.826099	+	0.563525i	$0.809445\pi$
$462$	14.4383	+	11.2477i	0.671729	+	0.523291i
$463$	9.44766	−	6.07164i	0.439070	−	0.282173i	−0.302372	−	0.953190i	$-0.597779\pi$
$463$	9.44766	−	6.07164i	0.439070	−	0.282173i	0.741442	+	0.671017i	$0.234142\pi$
$464$	26.2428	−	9.62474i	1.21829	−	0.446817i
$465$	2.25235	+	4.93195i	0.104450	+	0.228714i
$466$	17.2434	+	1.56686i	0.798786	+	0.0725835i
$467$	5.40475	+	18.4069i	0.250102	+	0.851770i	0.984847	+	0.173426i	$0.0554837\pi$
$467$	5.40475	+	18.4069i	0.250102	+	0.851770i	−0.734745	+	0.678344i	$0.762698\pi$
$468$	−2.02982	+	4.02748i	−0.0938284	+	0.186170i
$469$	3.08738	+	1.40996i	0.142562	+	0.0651059i
$470$	−7.63504	−	1.81524i	−0.352178	−	0.0837310i
$471$	5.53663	+	6.38961i	0.255115	+	0.294418i
$472$	−15.2902	−	12.8854i	−0.703787	−	0.593098i
$473$	−5.35795	−	1.57324i	−0.246359	−	0.0723375i
$474$	2.76652	−	7.00324i	0.127070	−	0.321669i
$475$	13.9502	−	21.7069i	0.640079	−	0.995982i
$476$	52.4488	−	21.5570i	2.40399	−	0.988063i
$477$	−9.62275	−	1.38354i	−0.440596	−	0.0633481i
$478$	−0.896375	+	0.467324i	−0.0409992	+	0.0213749i
$479$	−0.371521	−	2.58399i	−0.0169752	−	0.118065i	0.979572	−	0.201094i	$-0.0644497\pi$
$479$	−0.371521	−	2.58399i	−0.0169752	−	0.118065i	−0.996547	+	0.0830288i	$0.973541\pi$
$480$	−3.47851	−	3.16786i	−0.158771	−	0.144592i
$481$	−10.4072	+	12.0106i	−0.474528	+	0.547635i
$482$	1.09472	+	20.9601i	0.0498630	+	0.954708i
$483$	−17.0322	+	6.70830i	−0.774994	+	0.305238i
$484$	0.986102	−	0.103287i	0.0448228	−	0.00469487i
$485$	−10.8441	−	9.39650i	−0.492407	−	0.426673i
$486$	−1.14821	+	0.825593i	−0.0520841	+	0.0374497i
$487$	0.409020	+	2.84480i	0.0185345	+	0.128910i	0.996988	−	0.0775578i	$-0.0247122\pi$
$487$	0.409020	+	2.84480i	0.0185345	+	0.128910i	−0.978453	+	0.206468i	$0.933803\pi$
$488$	6.01434	+	9.08160i	0.272256	+	0.411105i
$489$	2.77308	−	19.2872i	0.125403	−	0.872196i
$490$	8.40019	−	2.95049i	0.379482	−	0.133290i
$491$	6.27959	−	9.77123i	0.283394	−	0.440970i	−0.670149	−	0.742227i	$-0.733770\pi$
$491$	6.27959	−	9.77123i	0.283394	−	0.440970i	0.953543	+	0.301257i	$0.0974062\pi$
$492$	10.6994	+	3.59367i	0.482366	+	0.162015i
$493$	14.6241	−	49.8051i	0.658636	−	2.24311i
$494$	13.7629	−	13.2438i	0.619222	−	0.595867i
$495$	−1.84665	−	2.13115i	−0.0830009	−	0.0957882i
$496$	25.9992	+	2.00263i	1.16740	+	0.0899208i
$497$	4.73808	−	10.3749i	0.212532	−	0.465380i
$498$	3.64305	−	6.37723i	0.163249	−	0.285771i
$499$	6.42345	+	21.8763i	0.287553	+	0.979316i	0.968920	+	0.247374i	$0.0795677\pi$
$499$	6.42345	+	21.8763i	0.287553	+	0.979316i	−0.681367	+	0.731942i	$0.738614\pi$
$500$	15.4720	+	0.594996i	0.691928	+	0.0266090i
$501$	−11.2824	+	5.15252i	−0.504062	+	0.230197i
$502$	−1.99722	−	10.1130i	−0.0891401	−	0.451365i
$503$	−18.0183	+	11.5797i	−0.803397	+	0.516312i	−0.876723	−	0.480996i	$-0.840275\pi$
$503$	−18.0183	+	11.5797i	−0.803397	+	0.516312i	0.0733256	+	0.997308i	$0.476639\pi$
$504$	−9.16163	−	5.71145i	−0.408091	−	0.254408i
$505$	−13.0526			−0.580835
$506$	−9.57404	+	20.9079i	−0.425618	+	0.929471i
$507$			7.91482i			0.351509i
$508$	8.28151	−	11.8582i	0.367433	−	0.526123i
$509$	6.40040	+	9.95922i	0.283693	+	0.441435i	0.953629	−	0.300984i	$-0.0973150\pi$
$509$	6.40040	+	9.95922i	0.283693	+	0.441435i	−0.669936	+	0.742419i	$0.733679\pi$
$510$	−8.57140	+	1.69277i	−0.379548	+	0.0749569i
$511$	−18.8280	−	41.2276i	−0.832902	−	1.82380i
$512$	−21.4296	+	7.26437i	−0.947065	+	0.321043i
$513$	5.74659	−	1.68735i	0.253718	−	0.0744984i
$514$	−17.7957	+	31.1518i	−0.784936	+	1.37405i
$515$	−11.0549	−	5.04861i	−0.487138	−	0.222468i
$516$	3.24001	+	0.593725i	0.142633	+	0.0261373i
$517$	−17.0968	+	14.8145i	−0.751917	+	0.651539i
$518$	−26.3782	−	27.4121i	−1.15899	−	1.20442i
$519$	−3.09955	−	0.910111i	−0.136055	−	0.0399494i
$520$	5.10995	+	1.42443i	0.224086	+	0.0624655i
$521$	2.17658	+	1.39880i	0.0953578	+	0.0612827i	0.587451	−	0.809260i	$-0.300132\pi$
$521$	2.17658	+	1.39880i	0.0953578	+	0.0612827i	−0.492093	+	0.870543i	$0.663768\pi$
$522$	−9.32413	+	3.27502i	−0.408106	+	0.143344i
$523$	−11.1116	−	1.59760i	−0.485874	−	0.0698582i	−0.104975	−	0.994475i	$-0.533476\pi$
$523$	−11.1116	−	1.59760i	−0.485874	−	0.0698582i	−0.380899	+	0.924617i	$0.624385\pi$
$524$	29.7427	−	17.5373i	1.29932	−	0.766119i
$525$	16.2773	−	2.34032i	0.710399	−	0.102140i
$526$	−10.2866	−	14.3064i	−0.448518	−	0.623788i
$527$	31.7111	−	36.5965i	1.38136	−	1.59417i
$528$	−13.2678	+	2.81025i	−0.577407	+	0.122300i
$529$	−13.1307	−	18.8834i	−0.570901	−	0.821019i
$530$	0.596406	+	11.4192i	0.0259062	+	0.496016i
$531$	5.34277	+	4.62954i	0.231857	+	0.200905i
$532$	28.5913	+	35.6791i	1.23959	+	1.54688i
$533$	−12.5965	+	1.81111i	−0.545616	+	0.0784477i
$534$	−11.5088	−	22.0750i	−0.498033	−	0.955279i
$535$	1.05251	−	7.32037i	0.0455040	−	0.316487i
$536$	−2.27320	+	1.07613i	−0.0981872	+	0.0464819i
$537$	−6.03174	−	3.87637i	−0.260289	−	0.167278i
$538$	4.33056	−	10.9625i	0.186704	−	0.472627i
$539$	7.23058	−	24.6251i	0.311443	−	1.06068i
$540$	1.21433	+	1.13680i	0.0522564	+	0.0489202i
$541$	−3.73329	+	3.23491i	−0.160507	+	0.139080i	−0.731411	−	0.681937i	$-0.761138\pi$
$541$	−3.73329	+	3.23491i	−0.160507	+	0.139080i	0.570905	+	0.821016i	$0.306593\pi$
$542$	1.34816	−	5.67046i	0.0579086	−	0.243567i
$543$	−8.82146	+	19.3163i	−0.378565	+	0.828942i
$544$	−12.8302	+	40.0129i	−0.550089	+	1.71554i
$545$	13.8479	−	4.06612i	0.593180	−	0.174173i
$546$	12.1229	+	1.10157i	0.518811	+	0.0471430i
$547$	−31.4439	+	14.3599i	−1.34444	+	0.613986i	−0.952087	−	0.305827i	$-0.901067\pi$
$547$	−31.4439	+	14.3599i	−1.34444	+	0.613986i	−0.392356	+	0.919814i	$0.628340\pi$
$548$	0.128314	+	0.508536i	0.00548132	+	0.0217236i
$549$	−2.08206	−	3.23975i	−0.0888602	−	0.138269i
$550$	12.6954	−	16.2966i	0.541332	−	0.694887i
$551$	41.8527			1.78298
$552$	4.33200	−	12.8543i	0.184382	−	0.547117i
$553$	−20.3233			−0.864236
$554$	−15.2380	+	19.5605i	−0.647402	+	0.831046i
$555$	3.16890	+	4.93091i	0.134512	+	0.209305i
$556$	16.7690	−	4.23117i	0.711164	−	0.179442i
$557$	−29.6855	+	13.5569i	−1.25782	+	0.574425i	−0.929039	−	0.369982i	$-0.879364\pi$
$557$	−29.6855	+	13.5569i	−1.25782	+	0.574425i	−0.328777	+	0.944408i	$0.606637\pi$
$558$	−9.18151	−	0.834300i	−0.388685	−	0.0353187i
$559$	−3.56355	+	1.04635i	−0.150722	+	0.0442561i
$560$	−4.50272	+	11.8733i	−0.190275	+	0.501740i
$561$	−10.4623	+	22.9093i	−0.441719	+	0.967231i
$562$	−7.37329	+	31.0126i	−0.311024	+	1.30819i
$563$	−17.2392	+	14.9379i	−0.726546	+	0.629555i	−0.937518	−	0.347937i	$-0.886882\pi$
$563$	−17.2392	+	14.9379i	−0.726546	+	0.629555i	0.210972	+	0.977492i	$0.432337\pi$
$564$	9.11980	−	9.74175i	0.384013	−	0.410202i
$565$	−0.501953	+	1.70949i	−0.0211173	+	0.0719189i
$566$	−0.499118	+	1.26348i	−0.0209795	+	0.0531081i
$567$	3.21107	+	2.06363i	0.134852	+	0.0866642i
$568$	3.61628	+	7.63894i	0.151736	+	0.320523i
$569$	−3.01328	+	20.9578i	−0.126323	+	0.878596i	0.823835	+	0.566829i	$0.191830\pi$
$569$	−3.01328	+	20.9578i	−0.126323	+	0.878596i	−0.950159	+	0.311767i	$0.899079\pi$
$570$	−3.25664	−	6.24656i	−0.136406	−	0.261640i
$571$	−28.3459	+	4.07552i	−1.18624	+	0.170555i	−0.707055	−	0.707159i	$-0.749976\pi$
$571$	−28.3459	+	4.07552i	−1.18624	+	0.170555i	−0.479184	+	0.877714i	$0.659067\pi$
$572$	11.9329	−	9.56235i	0.498938	−	0.399822i
$573$	−13.8617	−	12.0112i	−0.579081	−	0.501777i
$574$	−1.58889	−	30.4219i	−0.0663191	−	1.26979i
$575$	7.57169	+	19.2244i	0.315761	+	0.801712i
$576$	7.61110	−	2.46398i	0.317129	−	0.102666i
$577$	6.65166	−	7.67643i	0.276912	−	0.319574i	−0.600209	−	0.799844i	$-0.704916\pi$
$577$	6.65166	−	7.67643i	0.276912	−	0.319574i	0.877121	+	0.480270i	$0.159461\pi$
$578$	31.5183	+	43.8348i	1.31099	+	1.82329i
$579$	−15.8025	+	2.27206i	−0.656729	+	0.0944234i
$580$	5.90395	+	10.0129i	0.245148	+	0.415765i
$581$	−19.6211	−	2.82109i	−0.814020	−	0.117038i
$582$	23.0199	−	8.08554i	0.954204	−	0.335156i
$583$	27.7292	+	17.8205i	1.14843	+	0.738050i
$584$	32.3515	+	9.01821i	1.33872	+	0.373176i
$585$	−1.79955	−	0.528395i	−0.0744021	−	0.0218464i
$586$	6.38043	+	6.63052i	0.263573	+	0.273904i
$587$	14.3191	−	12.4076i	0.591014	−	0.512116i	−0.307218	−	0.951639i	$-0.599398\pi$
$587$	14.3191	−	12.4076i	0.591014	−	0.512116i	0.898231	+	0.439523i	$0.144853\pi$
$588$	−2.72875	+	14.8911i	−0.112532	+	0.614097i
$589$	35.5156	+	16.2194i	1.46339	+	0.668310i
$590$	4.12456	−	7.22013i	0.169805	−	0.297248i
$591$	8.59165	−	2.52274i	0.353413	−	0.103771i
$592$	28.1286	−	1.85706i	1.15608	−	0.0763249i
$593$	−9.35760	−	20.4903i	−0.384271	−	0.841435i	−0.998626	−	0.0524056i	$-0.983311\pi$
$593$	−9.35760	−	20.4903i	−0.384271	−	0.841435i	0.614355	−	0.789029i	$-0.289416\pi$
$594$	4.70409	−	0.929010i	0.193011	−	0.0381177i
$595$	12.7490	+	19.8378i	0.522658	+	0.813272i
$596$	−8.77121	−	6.12561i	−0.359283	−	0.250915i
$597$		−	3.69675i		−	0.151298i
$598$	2.16122	+	15.1409i	0.0883791	+	0.619158i
$599$	28.4392			1.16199			0.580997	−	0.813906i	$-0.302663\pi$
$599$	28.4392			1.16199			0.580997	+	0.813906i	$0.302663\pi$
$600$	−6.44654	+	10.3408i	−0.263179	+	0.422161i
$601$	37.1777	−	23.8927i	1.51651	−	0.974602i	0.524097	−	0.851659i	$-0.324403\pi$
$601$	37.1777	−	23.8927i	1.51651	−	0.974602i	0.992414	−	0.122944i	$-0.0392334\pi$
$602$	−1.72251	−	8.72203i	−0.0702043	−	0.355483i
$603$	0.808850	−	0.369389i	0.0329389	−	0.0150427i
$604$	−0.387285	+	10.0708i	−0.0157584	+	0.409775i
$605$	0.116163	+	0.395613i	0.00472268	+	0.0160840i
$606$	11.0091	−	19.2716i	0.447213	−	0.782856i
$607$	−3.34591	+	7.32651i	−0.135806	+	0.297374i	−0.965301	−	0.261141i	$-0.915901\pi$
$607$	−3.34591	+	7.32651i	−0.135806	+	0.297374i	0.829495	+	0.558515i	$0.188629\pi$
$608$	−33.8697	−	0.836535i	−1.37360	−	0.0339260i
$609$	17.4673	+	20.1584i	0.707812	+	0.816858i
$610$	−3.26393	+	3.14082i	−0.132153	+	0.127168i
$611$	−4.23896	+	14.4366i	−0.171490	+	0.584041i
$612$	4.73015	−	14.0830i	0.191205	−	0.569273i
$613$	−3.79315	+	5.90226i	−0.153204	+	0.238390i	−0.909369	−	0.415991i	$-0.863435\pi$
$613$	−3.79315	+	5.90226i	−0.153204	+	0.238390i	0.756164	+	0.654382i	$0.227071\pi$
$614$	38.1088	−	13.3854i	1.53795	−	0.540190i
$615$	−0.667973	+	4.64585i	−0.0269353	+	0.187339i
$616$	20.2113	+	30.5189i	0.814336	+	1.22964i
$617$	−1.50775	−	10.4866i	−0.0606997	−	0.422176i	−0.997401	−	0.0720469i	$-0.977047\pi$
$617$	−1.50775	−	10.4866i	−0.0606997	−	0.422176i	0.936702	−	0.350129i	$-0.113862\pi$
$618$	16.7782	−	12.0639i	0.674917	−	0.485282i
$619$	−31.5068	−	27.3008i	−1.26636	−	1.09731i	−0.990701	−	0.136057i	$-0.956557\pi$
$619$	−31.5068	−	27.3008i	−1.26636	−	1.09731i	−0.275663	−	0.961254i	$-0.588898\pi$
$620$	1.12963	+	10.7848i	0.0453672	+	0.433129i
$621$	−1.59391	+	4.52321i	−0.0639614	+	0.181510i
$622$	0.488083	+	9.34514i	0.0195703	+	0.374706i
$623$	−44.0015	+	50.7804i	−1.76288	+	2.03447i
$624$	−6.41303	+	6.34319i	−0.256727	+	0.253931i
$625$	−2.14932	−	14.9488i	−0.0859727	−	0.597953i
$626$	5.38039	−	2.80506i	0.215044	−	0.112113i
$627$	−20.0999	−	2.88993i	−0.802713	−	0.115413i
$628$	6.42813	+	15.6398i	0.256511	+	0.624098i
$629$	28.3021	−	44.0389i	1.12848	−	1.75594i
$630$	1.64949	−	4.17558i	0.0657174	−	0.166359i
$631$	3.11870	+	0.915733i	0.124153	+	0.0364547i	0.343219	−	0.939255i	$-0.388483\pi$
$631$	3.11870	+	0.915733i	0.124153	+	0.0364547i	−0.219066	+	0.975710i	$0.570301\pi$
$632$	9.70468	−	11.5159i	0.386032	−	0.458076i
$633$	−8.26218	−	9.53507i	−0.328392	−	0.378985i
$634$	−0.416211	−	0.0989550i	−0.0165299	−	0.00393001i
$635$	5.47123	+	2.49863i	0.217119	+	0.0991551i
$636$	−17.3629	−	8.75077i	−0.688484	−	0.346991i
$637$	−4.80903	−	16.3781i	−0.190541	−	0.648923i
$638$	33.3698	+	3.03222i	1.32112	+	0.120047i
$639$	−1.24131	−	2.71809i	−0.0491054	−	0.107526i
$640$	−4.57769	−	8.22107i	−0.180949	−	0.324966i
$641$	3.34401	−	2.14907i	0.132081	−	0.0848831i	−0.472932	−	0.881099i	$-0.656804\pi$
$641$	3.34401	−	2.14907i	0.132081	−	0.0848831i	0.605013	+	0.796216i	$0.293168\pi$
$642$	9.92047	+	7.72826i	0.391530	+	0.305010i
$643$			10.5695i			0.416821i	0.978041	+	0.208410i	$0.0668290\pi$
$643$			10.5695i			0.416821i	−0.978041	+	0.208410i	$0.933171\pi$
$644$	−36.5635	+	1.87238i	−1.44080	+	0.0737821i
$645$			1.36980i			0.0539357i
$646$	−38.6651	+	49.6329i	−1.52126	+	1.95278i
$647$	−12.0761	+	7.76084i	−0.474760	+	0.305110i	−0.756051	−	0.654513i	$-0.772874\pi$
$647$	−12.0761	+	7.76084i	−0.474760	+	0.305110i	0.281291	+	0.959623i	$0.409237\pi$
$648$	−2.70265	+	0.834082i	−0.106170	+	0.0327658i
$649$	−9.95725	−	21.8033i	−0.390856	−	0.855856i
$650$	1.24335	−	13.6831i	0.0487682	−	0.536697i
$651$	7.01043	+	23.8753i	0.274760	+	0.935747i
$652$	17.5394	−	34.8010i	0.686897	−	1.36291i
$653$	17.3101	+	7.90526i	0.677397	+	0.309357i	0.724243	−	0.689545i	$-0.242190\pi$
$653$	17.3101	+	7.90526i	0.677397	+	0.309357i	−0.0468455	+	0.998902i	$0.514917\pi$
$654$	−5.67641	+	23.8753i	−0.221965	+	0.933600i
$655$	9.40283	+	10.8514i	0.367399	+	0.424001i
$656$	17.9968	+	13.6266i	0.702655	+	0.532029i
$657$	−11.3931	−	3.34531i	−0.444487	−	0.130513i
$658$	−33.4979	−	13.2328i	−1.30588	−	0.515868i
$659$	−2.64373	+	4.11372i	−0.102985	+	0.160248i	−0.888922	−	0.458059i	$-0.848545\pi$
$659$	−2.64373	+	4.11372i	−0.102985	+	0.160248i	0.785937	+	0.618307i	$0.212181\pi$
$660$	−2.14400	−	5.21642i	−0.0834551	−	0.203049i
$661$	−29.4921	−	4.24033i	−1.14711	−	0.164930i	−0.457568	−	0.889175i	$-0.651279\pi$
$661$	−29.4921	−	4.24033i	−1.14711	−	0.164930i	−0.689543	+	0.724245i	$0.742188\pi$
$662$	−17.9271	−	34.3861i	−0.696758	−	1.33645i
$663$	2.38386	+	16.5801i	0.0925814	+	0.643918i
$664$	10.9679	−	9.77084i	0.425636	−	0.379182i
$665$	−12.4511	+	14.3693i	−0.482833	+	0.557219i
$666$	−9.95304	+	0.519833i	−0.385672	+	0.0201431i
$667$	−19.5922	+	27.1900i	−0.758614	+	1.05280i
$668$	−24.6716	+	2.58418i	−0.954574	+	0.0999848i
$669$	−1.03974	−	0.900938i	−0.0401986	−	0.0348323i
$670$	−0.610571	−	0.849167i	−0.0235884	−	0.0328062i
$671$	1.85825	+	12.9244i	0.0717368	+	0.498941i
$672$	−13.7327	−	16.6625i	−0.529749	−	0.642769i
$673$	2.14696	−	14.9324i	0.0827592	−	0.575603i	−0.905677	−	0.423968i	$-0.860637\pi$
$673$	2.14696	−	14.9324i	0.0827592	−	0.575603i	0.988436	−	0.151635i	$-0.0484540\pi$
$674$	−6.58894	−	18.7590i	−0.253796	−	0.722569i
$675$	2.32923	−	3.62435i	0.0896520	−	0.139501i
$676$	−5.04009	+	15.0058i	−0.193850	+	0.577147i
$677$	−4.21888	+	14.3682i	−0.162145	+	0.552214i	0.837836	+	0.545923i	$0.183821\pi$
$677$	−4.21888	+	14.3682i	−0.162145	+	0.552214i	−0.999980	+	0.00629112i	$0.997997\pi$
$678$	−2.10063	−	2.18296i	−0.0806740	−	0.0838361i
$679$	−43.1242	−	49.7680i	−1.65495	−	1.90992i
$680$	−17.3286	−	2.24886i	−0.664521	−	0.0862397i
$681$	1.95386	−	4.27836i	0.0748721	−	0.163947i
$682$	27.1420	+	15.5051i	1.03932	+	0.593720i
$683$	−2.40861	−	8.20297i	−0.0921629	−	0.313878i	0.900490	−	0.434877i	$-0.143208\pi$
$683$	−2.40861	−	8.20297i	−0.0921629	−	0.313878i	−0.992653	+	0.120999i	$0.961390\pi$
$684$	11.9695	+	0.460305i	0.457667	+	0.0176002i
$685$	−0.198394	+	0.0906034i	−0.00758024	+	0.00346178i
$686$	3.01597	−	0.595624i	0.115150	−	0.0227410i
$687$	−7.11786	+	4.57437i	−0.271563	+	0.174523i
$688$	5.76471	+	3.18886i	0.219777	+	0.121574i
$689$	21.9228			0.835192
$690$	5.58264	+	0.808458i	0.212528	+	0.0307775i
$691$			6.72962i			0.256007i	0.991774	+	0.128003i	$0.0408568\pi$
$691$			6.72962i			0.256007i	−0.991774	+	0.128003i	$0.959143\pi$
$692$	−5.29694	−	3.69926i	−0.201359	−	0.140625i
$693$	−6.99681	−	10.8872i	−0.265787	−	0.413572i
$694$	1.74858	+	8.85403i	0.0663752	+	0.336094i
$695$	2.98765	+	6.54204i	0.113328	+	0.248154i
$696$	−19.7633	+	0.271639i	−0.749125	+	0.0102964i
$697$	40.2216	−	11.8101i	1.52350	−	0.447341i
$698$	24.1775	+	13.8116i	0.915133	+	0.522777i
$699$	−11.1368	−	5.08599i	−0.421232	−	0.192370i
$700$	32.3507	+	5.92819i	1.22274	+	0.224065i
$701$	−8.03903	+	6.96586i	−0.303630	+	0.263097i	−0.793327	−	0.608796i	$-0.791653\pi$
$701$	−8.03903	+	6.96586i	−0.303630	+	0.263097i	0.489697	+	0.871893i	$0.337107\pi$
$702$	2.29796	−	2.21128i	0.0867307	−	0.0834595i
$703$	40.4988	+	11.8915i	1.52744	+	0.448497i
$704$	−26.9442	−	3.12083i	−1.01550	−	0.117621i
$705$	4.66835	+	3.00017i	0.175820	+	0.112993i
$706$	9.95732	+	28.3489i	0.374749	+	1.06693i
$707$	−59.2938	−	8.52516i	−2.22997	−	0.320622i
$708$	7.18139	+	12.1794i	0.269893	+	0.457732i
$709$	−10.7071	+	1.53944i	−0.402113	+	0.0578151i	−0.340404	−	0.940279i	$-0.610564\pi$
$709$	−10.7071	+	1.53944i	−0.402113	+	0.0578151i	−0.0617083	+	0.998094i	$0.519655\pi$
$710$	−2.85357	+	2.05179i	−0.107093	+	0.0770021i
$711$	−3.48676	+	4.02393i	−0.130764	+	0.150909i
$712$	−7.76248	−	49.1810i	−0.290911	−	1.84314i
$713$	−27.1628	+	15.4803i	−1.01725	+	0.579743i
$714$	−40.0427	+	2.09137i	−1.49856	+	0.0782676i
$715$	4.80582	+	4.16427i	0.179728	+	0.155735i
$716$	−8.96724	−	11.1902i	−0.335121	−	0.418198i
$717$	0.707525	−	0.101727i	0.0264230	−	0.00379905i
$718$	−3.16477	+	1.64995i	−0.118108	+	0.0615755i
$719$	0.202660	−	1.40953i	0.00755794	−	0.0525667i	−0.985693	−	0.168548i	$-0.946092\pi$
$719$	0.202660	−	1.40953i	0.00755794	−	0.0525667i	0.993251	+	0.115981i	$0.0370013\pi$
$720$	1.57836	+	2.92856i	0.0588220	+	0.109141i
$721$	−46.9214	−	30.1546i	−1.74745	−	1.12301i
$722$	−22.1898	−	8.76572i	−0.825818	−	0.326226i
$723$	4.18126	−	14.2401i	0.155503	−	0.529594i
$724$	−29.0252	+	31.0046i	−1.07871	+	1.15228i
$725$	22.7529	−	19.7155i	0.845020	−	0.732214i
$726$	−0.682081	−	0.162166i	−0.0253144	−	0.00601855i
$727$	−18.1118	+	39.6593i	−0.671729	+	1.47088i	0.199446	+	0.979909i	$0.436086\pi$
$727$	−18.1118	+	39.6593i	−0.671729	+	1.47088i	−0.871175	+	0.490972i	$0.836642\pi$
$728$	22.2825	+	9.80823i	0.825843	+	0.363517i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	−1.26388	+	13.9090i	−0.0467782	+	0.514797i
$731$	11.1284	−	5.08215i	0.411597	−	0.187970i
$732$	−1.88437	−	7.46813i	−0.0696482	−	0.276030i
$733$	−6.68055	−	10.3951i	−0.246752	−	0.383953i	0.695680	−	0.718352i	$-0.255103\pi$
$733$	−6.68055	−	10.3951i	−0.246752	−	0.383953i	−0.942432	+	0.334399i	$0.891467\pi$
$734$	1.37878	+	1.07409i	0.0508915	+	0.0396456i
$735$	−6.29558			−0.232216
$736$	16.3986	−	21.6121i	0.604462	−	0.796634i
$737$	−3.01489			−0.111055
$738$	−6.29600	−	4.90471i	−0.231759	−	0.180545i
$739$	−26.1367	−	40.6695i	−0.961455	−	1.49605i	−0.865648	−	0.500654i	$-0.833093\pi$
$739$	−26.1367	−	40.6695i	−0.961455	−	1.49605i	−0.0958075	−	0.995400i	$-0.530543\pi$
$740$	2.86801	+	11.3665i	0.105430	+	0.417842i
$741$	−12.2854	+	5.61053i	−0.451314	+	0.206108i
$742$	−4.74900	+	52.2630i	−0.174341	+	1.91864i
$743$	−14.3370	+	4.20973i	−0.525974	+	0.154440i	−0.533930	−	0.845528i	$-0.679286\pi$
$743$	−14.3370	+	4.20973i	−0.525974	+	0.154440i	0.00795634	+	0.999968i	$0.497467\pi$
$744$	−16.8761	−	7.42847i	−0.618708	−	0.272341i
$745$	1.84817	−	4.04693i	0.0677117	−	0.148268i
$746$	3.22117	+	0.765839i	0.117935	+	0.0280394i
$747$	−3.92484	+	3.40089i	−0.143602	+	0.124432i
$748$	−34.4241	+	36.7718i	−1.25867	+	1.34451i
$749$	9.56242	−	32.5666i	0.349403	−	1.18996i
$750$	−10.1827	−	4.02251i	−0.371820	−	0.146881i
$751$	−10.9686	−	7.04907i	−0.400249	−	0.257224i	0.324996	−	0.945715i	$-0.394637\pi$
$751$	−10.9686	−	7.04907i	−0.400249	−	0.257224i	−0.725245	+	0.688491i	$0.758273\pi$
$752$	23.4938	−	12.6621i	0.856732	−	0.461740i
$753$	−1.03735	+	7.21490i	−0.0378030	+	0.262926i
$754$	19.7612	−	10.3025i	0.719660	−	0.375194i
$755$	−4.14839	+	0.596448i	−0.150975	+	0.0217070i
$756$	4.77381	+	5.95724i	0.173622	+	0.216663i
$757$	25.0027	+	21.6650i	0.908738	+	0.787426i	0.977659	−	0.210196i	$-0.0674102\pi$
$757$	25.0027	+	21.6650i	0.908738	+	0.787426i	−0.0689212	+	0.997622i	$0.521956\pi$
$758$	−12.3129	+	0.643084i	−0.447224	+	0.0233579i
$759$	11.2867	−	11.7052i	0.409681	−	0.424873i
$760$	−2.19655	−	13.9168i	−0.0796772	−	0.504814i
$761$	−10.6057	+	12.2397i	−0.384457	+	0.443687i	−0.914685	−	0.404168i	$-0.867561\pi$
$761$	−10.6057	+	12.2397i	−0.384457	+	0.443687i	0.530228	+	0.847855i	$0.322106\pi$
$762$	−8.30375	+	5.97060i	−0.300813	+	0.216292i
$763$	65.5623	−	9.42643i	2.37351	−	0.341260i
$764$	−18.6320	−	31.5993i	−0.674081	−	1.14322i
$765$	6.11508	+	0.879215i	0.221091	+	0.0317881i
$766$	−17.6981	−	50.3871i	−0.639457	−	1.82056i
$767$	−13.4112	−	8.61888i	−0.484252	−	0.311210i
$768$	15.9990	+	0.175194i	0.577316	+	0.00632177i
$769$	−10.9513	−	3.21560i	−0.394914	−	0.115957i	0.0782450	−	0.996934i	$-0.475068\pi$
$769$	−10.9513	−	3.21560i	−0.394914	−	0.115957i	−0.473159	+	0.880977i	$0.656887\pi$
$770$	−10.9685	+	10.5548i	−0.395277	+	0.380368i
$771$	19.1723	−	16.6129i	0.690472	−	0.598298i
$772$	−31.4070	−	5.75527i	−1.13036	−	0.207137i
$773$	7.85729	+	3.58830i	0.282607	+	0.129062i	0.551676	−	0.834059i	$-0.313989\pi$
$773$	7.85729	+	3.58830i	0.282607	+	0.129062i	−0.269069	+	0.963121i	$0.586716\pi$
$774$	−2.02244	−	1.15534i	−0.0726952	−	0.0415277i
$775$	26.9482	−	7.91271i	0.968008	−	0.284233i
$776$	48.7925	−	0.670635i	1.75155	−	0.0240744i
$777$	11.1747	+	24.4692i	0.400891	+	0.877829i
$778$	6.63298	+	33.5864i	0.237804	+	1.20413i
$779$	18.2733	+	28.4339i	0.654710	+	1.01875i
$780$	−3.07531	−	2.14773i	−0.110114	−	0.0769010i
$781$			10.1313i			0.362528i
$782$	−14.1445	−	48.3534i	−0.505805	−	1.72912i
$783$	6.98803			0.249732
$784$	−14.6560	+	26.4945i	−0.523428	+	0.946234i
$785$	−5.91550	+	3.80166i	−0.211133	+	0.135687i
$786$	−23.9524	+	4.73035i	−0.854352	+	0.168726i
$787$	33.2499	−	15.1847i	1.18523	−	0.541277i	0.277458	−	0.960738i	$-0.410508\pi$
$787$	33.2499	−	15.1847i	1.18523	−	0.541277i	0.907774	+	0.419460i	$0.137781\pi$
$788$	17.8955	+	0.688195i	0.637501	+	0.0245159i
$789$	3.51030	+	11.9550i	0.124970	+	0.425608i
$790$	5.43787	+	3.10643i	0.193471	+	0.110522i
$791$	−3.39674	+	7.43782i	−0.120774	+	0.264459i
$792$	9.51014	+	1.23420i	0.337928	+	0.0438554i
$793$	5.68705	+	6.56320i	0.201953	+	0.233066i
$794$	−27.7759	−	28.8646i	−0.985730	−	1.02437i
$795$	2.27797	−	7.75804i	0.0807912	−	0.275149i
$796$	2.35406	−	7.00873i	0.0834375	−	0.248418i
$797$	26.3407	−	40.9870i	0.933037	−	1.45183i	0.0413685	−	0.999144i	$-0.486828\pi$
$797$	26.3407	−	40.9870i	0.933037	−	1.45183i	0.891668	−	0.452690i	$-0.149535\pi$
$798$	−10.7140	−	30.5031i	−0.379270	−	1.07980i
$799$	7.05336	−	49.0572i	0.249530	−	1.73552i
$800$	−18.8070	+	15.5001i	−0.664929	+	0.548013i
$801$	2.50522	+	17.4242i	0.0885176	+	0.615654i
$802$	−17.2261	−	23.9576i	−0.608274	−	0.845971i
$803$	30.4261	+	26.3644i	1.07371	+	0.930378i
$804$	1.76874	−	0.185262i	0.0623785	−	0.00653370i
$805$	−3.50652	−	14.8156i	−0.123589	−	0.522181i
$806$	20.7616	−	1.08435i	0.731298	−	0.0381946i
$807$	−5.45798	+	6.29885i	−0.192130	+	0.221730i
$808$	33.1443	−	29.5269i	1.16601	−	1.03875i
$809$	−3.24940	−	22.6001i	−0.114243	−	0.794576i	−0.963713	−	0.266940i	$-0.913988\pi$
$809$	−3.24940	−	22.6001i	−0.114243	−	0.794576i	0.849470	−	0.527636i	$-0.176922\pi$
$810$	−0.543752	−	1.04297i	−0.0191055	−	0.0366463i
$811$	28.1714	+	4.05044i	0.989232	+	0.142230i	0.617889	−	0.786266i	$-0.287988\pi$
$811$	28.1714	+	4.05044i	0.989232	+	0.142230i	0.371343	+	0.928496i	$0.378897\pi$
$812$	20.2799	+	49.3416i	0.711685	+	1.73155i
$813$	−2.22819	+	3.46713i	−0.0781461	+	0.121598i
$814$	31.4288	+	12.4154i	1.10158	+	0.435160i
$815$	15.5497	+	4.56580i	0.544682	+	0.159933i
$816$	17.9359	−	23.6881i	0.627883	−	0.829250i
$817$	6.45960	+	7.45478i	0.225993	+	0.260810i
$818$	−5.27846	+	22.2015i	−0.184557	+	0.776259i
$819$	−7.82963	−	3.57567i	−0.273590	−	0.124944i
$820$	−4.22486	+	8.38278i	−0.147538	+	0.292740i
$821$	11.7705	+	40.0866i	0.410793	+	1.39903i	0.862134	+	0.506681i	$0.169128\pi$
$821$	11.7705	+	40.0866i	0.410793	+	1.39903i	−0.451341	+	0.892352i	$0.649054\pi$
$822$	0.0335608	−	0.369338i	0.00117057	−	0.0128821i
$823$	−22.3354	−	48.9078i	−0.778564	−	1.70482i	−0.706819	−	0.707394i	$-0.749871\pi$
$823$	−22.3354	−	48.9078i	−0.778564	−	1.70482i	−0.0717444	−	0.997423i	$-0.522857\pi$
$824$	39.4922	−	12.1880i	1.37578	−	0.424587i
$825$	−12.2885	+	7.89733i	−0.427830	+	0.274950i
$826$	23.4522	−	30.1048i	0.816008	−	1.04748i
$827$		−	18.2798i		−	0.635650i	−0.948149	−	0.317825i	$-0.897048\pi$
$827$		−	18.2798i		−	0.635650i	0.948149	−	0.317825i	$-0.102952\pi$
$828$	−5.90226	+	7.56064i	−0.205118	+	0.262750i
$829$			18.6361i			0.647259i	0.946184	+	0.323629i	$0.104903\pi$
$829$			18.6361i			0.647259i	−0.946184	+	0.323629i	$0.895097\pi$
$830$	4.81877	+	3.75392i	0.167262	+	0.130301i
$831$	14.7497	−	9.47905i	0.511661	−	0.328825i
$832$	−16.1978	+	7.94239i	−0.561559	+	0.275353i
$833$	23.3575	+	51.1459i	0.809290	+	1.77210i
$834$	−12.1789	−	1.10667i	−0.421722	−	0.0383208i
$835$	−2.90631	−	9.89799i	−0.100577	−	0.342534i
$836$	−36.2674	−	18.2785i	−1.25434	−	0.632176i
$837$	5.92995	+	2.70812i	0.204969	+	0.0936062i
$838$	−11.6354	−	2.76634i	−0.401938	−	0.0955615i
$839$	12.5944	+	14.5347i	0.434808	+	0.501795i	0.930291	−	0.366823i	$-0.119554\pi$
$839$	12.5944	+	14.5347i	0.434808	+	0.501795i	−0.495483	+	0.868618i	$0.665009\pi$
$840$	5.78628	−	6.86616i	0.199646	−	0.236905i
$841$	19.0292	+	5.58749i	0.656181	+	0.192672i
$842$	−17.5361	+	44.3914i	−0.604335	+	1.52983i
$843$	12.1863	−	18.9622i	0.419718	−	0.653094i
$844$	−9.59255	−	23.3390i	−0.330189	−	0.803361i
$845$	−6.51577	−	0.936826i	−0.224149	−	0.0322278i
$846$	−8.36707	+	4.36216i	−0.287666	+	0.149974i
$847$	0.269298	+	1.87301i	0.00925320	+	0.0643574i
$848$	−27.3462	−	27.6473i	−0.939072	−	0.949411i
$849$	0.629060	−	0.725973i	0.0215893	−	0.0249153i
$850$	2.36054	+	45.1964i	0.0809659	+	1.55022i
$851$	−26.6839	+	20.7437i	−0.914711	+	0.711086i
$852$	−0.622562	−	5.94372i	−0.0213286	−	0.203629i
$853$	2.88640	+	2.50108i	0.0988283	+	0.0856352i	0.702874	−	0.711315i	$-0.251900\pi$
$853$	2.88640	+	2.50108i	0.0988283	+	0.0856352i	−0.604045	+	0.796950i	$0.706445\pi$
$854$	−16.8783	+	12.1359i	−0.577565	+	0.415283i
$855$	0.708903	+	4.93053i	0.0242440	+	0.168620i
$856$	13.8871	+	20.9694i	0.474651	+	0.716719i
$857$	−0.636559	+	4.42737i	−0.0217445	+	0.151236i	−0.997801	−	0.0662809i	$-0.978887\pi$
$857$	−0.636559	+	4.42737i	−0.0217445	+	0.151236i	0.976057	+	0.217517i	$0.0697957\pi$
$858$	−10.2018	+	3.58329i	−0.348283	+	0.122331i
$859$	8.66434	−	13.4820i	0.295623	−	0.459999i	−0.661390	−	0.750042i	$-0.730033\pi$
$859$	8.66434	−	13.4820i	0.295623	−	0.459999i	0.957014	+	0.290043i	$0.0936696\pi$
$860$	−0.872275	+	2.59702i	−0.0297443	+	0.0885576i
$861$	−6.06876	+	20.6683i	−0.206823	+	0.704374i
$862$	−7.01534	+	6.75074i	−0.238943	+	0.229931i
$863$	−3.99224	−	4.60730i	−0.135898	−	0.156834i	0.683721	−	0.729743i	$-0.260360\pi$
$863$	−3.99224	−	4.60730i	−0.135898	−	0.156834i	−0.819619	+	0.572909i	$0.805815\pi$
$864$	−5.65513	−	0.139674i	−0.192391	−	0.00475181i
$865$	1.11611	−	2.44394i	0.0379489	−	0.0830965i
$866$	−5.03426	+	8.81258i	−0.171071	+	0.299464i
$867$	−10.7556	−	36.6301i	−0.365278	−	1.24402i
$868$	−1.91242	+	49.7298i	−0.0649119	+	1.68794i
$869$	16.4213	−	7.49935i	0.557054	−	0.254398i
$870$	−1.59248	−	8.06361i	−0.0539902	−	0.273382i
$871$	−1.68687	+	1.08409i	−0.0571575	+	0.0367329i
$872$	−25.9656	+	41.6510i	−0.879307	+	1.41048i
$873$	−17.2524			−0.583905
$874$	34.1946	−	21.9264i	1.15665	−	0.741673i
$875$			29.5501i			0.998977i
$876$	−19.4701	−	13.5975i	−0.657833	−	0.459416i
$877$	−7.45059	−	11.5933i	−0.251588	−	0.391479i	0.692370	−	0.721542i	$-0.256566\pi$
$877$	−7.45059	−	11.5933i	−0.251588	−	0.391479i	−0.943959	+	0.330063i	$0.892930\pi$
$878$	−3.70963	+	0.732615i	−0.125194	+	0.0247246i
$879$	−2.70297	−	5.91868i	−0.0911690	−	0.199632i
$880$	−0.743073	−	11.2552i	−0.0250490	−	0.379412i
$881$	−33.4258	+	9.81471i	−1.12615	+	0.330666i	−0.791192	−	0.611568i	$-0.790539\pi$
$881$	−33.4258	+	9.81471i	−1.12615	+	0.330666i	−0.334954	+	0.942235i	$0.608721\pi$
$882$	5.30992	−	9.29514i	0.178794	−	0.312984i
$883$	−41.4593	−	18.9338i	−1.39522	−	0.637174i	−0.431014	−	0.902345i	$-0.641844\pi$
$883$	−41.4593	−	18.9338i	−1.39522	−	0.637174i	−0.964201	+	0.265171i	$0.914571\pi$
$884$	−6.03848	+	32.9525i	−0.203096	+	1.10831i
$885$	−4.44360	+	3.85040i	−0.149370	+	0.129430i
$886$	−20.3234	−	21.1200i	−0.682779	−	0.709541i
$887$	−35.3915	−	10.3919i	−1.18833	−	0.348926i	−0.372951	−	0.927851i	$-0.621654\pi$
$887$	−35.3915	−	10.3919i	−1.18833	−	0.348926i	−0.815380	+	0.578926i	$0.803472\pi$
$888$	−19.2011	−	5.35245i	−0.644348	−	0.179616i
$889$	23.2221	+	14.9239i	0.778843	+	0.500532i
$890$	19.5352	−	6.86156i	0.654820	−	0.230000i
$891$	−3.35603	−	0.482524i	−0.112431	−	0.0161652i
$892$	−1.39755	−	2.37020i	−0.0467933	−	0.0793601i
$893$	39.5543	−	5.68705i	1.32363	−	0.190310i
$894$	4.41629	+	6.14207i	0.147703	+	0.205421i
$895$	3.90511	−	4.50673i	0.130533	−	0.150643i
$896$	−15.4255	−	40.3355i	−0.515329	−	1.34751i
$897$	2.10612	−	10.6077i	0.0703214	−	0.354181i
$898$	−1.47483	−	28.2380i	−0.0492157	−	0.942313i
$899$	34.4285	+	29.8324i	1.14825	+	0.994968i
$900$	6.72397	−	5.38823i	0.224132	−	0.179608i
$901$	−71.4787	+	10.2771i	−2.38130	+	0.342379i
$902$	12.5096	+	23.9946i	0.416523	+	0.798934i
$903$	−0.894666	+	6.22254i	−0.0297726	+	0.207073i
$904$	−2.59252	−	5.47637i	−0.0862259	−	0.182141i
$905$	−14.8577	−	9.54849i	−0.493888	−	0.317403i
$906$	2.61827	−	6.62797i	0.0869863	−	0.220200i
$907$	3.70455	−	12.6165i	0.123008	−	0.418925i	−0.874847	−	0.484400i	$-0.839038\pi$
$907$	3.70455	−	12.6165i	0.123008	−	0.418925i	0.997854	+	0.0654745i	$0.0208561\pi$
$908$	6.42878	−	6.86720i	0.213346	−	0.227896i
$909$	−11.8606	+	10.2773i	−0.393393	+	0.340877i
$910$	−2.34176	+	9.84960i	−0.0776286	+	0.326511i
$911$	16.6699	−	36.5020i	0.552299	−	1.20937i	−0.403400	−	0.915024i	$-0.632172\pi$
$911$	16.6699	−	36.5020i	0.552299	−	1.20937i	0.955700	−	0.294343i	$-0.0951009\pi$
$912$	22.4001	+	8.49480i	0.741742	+	0.281291i
$913$	16.8949	−	4.96078i	0.559138	−	0.164178i
$914$	37.7347	+	3.42885i	1.24815	+	0.113416i
$915$	2.91352	−	1.33056i	0.0963180	−	0.0439870i
$916$	−16.4078	+	4.14003i	−0.542129	+	0.136790i
$917$	35.6265	+	55.4359i	1.17649	+	1.83065i
$918$	−6.45580	+	8.28708i	−0.213073	+	0.273514i
$919$	−57.3329			−1.89124			−0.945619	−	0.325276i	$-0.894543\pi$
$919$	−57.3329			−1.89124			−0.945619	+	0.325276i	$0.894543\pi$
$920$	10.0694	+	5.08775i	0.331978	+	0.167738i
$921$	−28.5609			−0.941113
$922$	21.0313	−	26.9971i	0.692630	−	0.889103i
$923$	3.64301	+	5.66863i	0.119911	+	0.186585i
$924$	−6.33245	−	25.0968i	−0.208322	−	0.825624i
$925$	27.6186	−	12.6130i	0.908092	−	0.414712i
$926$	−15.8171	−	1.43726i	−0.519782	−	0.0472312i
$927$	−14.0205	+	4.11679i	−0.460494	+	0.135213i
$928$	−37.6425	−	12.0701i	−1.23567	−	0.396220i
$929$	8.16755	−	17.8844i	0.267969	−	0.586769i	−0.727036	−	0.686599i	$-0.759103\pi$
$929$	8.16755	−	17.8844i	0.267969	−	0.586769i	0.995004	+	0.0998301i	$0.0318299\pi$
$930$	1.77358	−	7.45981i	0.0581581	−	0.244617i
$931$	−34.2621	+	29.6883i	−1.12289	+	0.972994i
$932$	−17.8757	−	16.7344i	−0.585537	−	0.548154i
$933$	1.86423	−	6.34898i	0.0610321	−	0.207856i
$934$	9.96780	−	25.2328i	0.326156	−	0.825642i
$935$	−17.6214	−	11.3246i	−0.576282	−	0.370354i
$936$	5.76486	−	2.72909i	0.188430	−	0.0892030i
$937$	−6.13515	+	42.6709i	−0.200427	+	1.39400i	0.602594	+	0.798048i	$0.294134\pi$
$937$	−6.13515	+	42.6709i	−0.200427	+	1.39400i	−0.803021	+	0.595951i	$0.796775\pi$
$938$	−2.21900	−	4.25627i	−0.0724530	−	0.138972i
$939$	−4.24684	+	0.610603i	−0.138590	+	0.0199263i
$940$	6.94032	+	8.66083i	0.226368	+	0.282485i
$941$	−12.0127	−	10.4091i	−0.391604	−	0.339327i	0.436698	−	0.899608i	$-0.356148\pi$
$941$	−12.0127	−	10.4091i	−0.391604	−	0.339327i	−0.828303	+	0.560281i	$0.810693\pi$
$942$	−0.623632	−	11.9404i	−0.0203190	−	0.389040i
$943$	−27.0265	−	1.43911i	−0.880104	−	0.0468639i
$944$	5.85955	+	27.6643i	0.190712	+	0.900395i
$945$	−2.07893	+	2.39921i	−0.0676275	+	0.0780463i
$946$	4.61023	+	6.41180i	0.149892	+	0.208465i
$947$	−41.2174	+	5.92616i	−1.33938	+	0.192574i	−0.774489	−	0.632588i	$-0.781993\pi$
$947$	−41.2174	+	5.92616i	−1.33938	+	0.192574i	−0.564896	+	0.825162i	$0.691084\pi$
$948$	−9.17300	+	5.40870i	−0.297925	+	0.175666i
$949$	26.5039	+	3.81069i	0.860353	+	0.123700i
$950$	−34.4290	+	12.0929i	−1.11703	+	0.392346i
$951$	0.254487	+	0.163549i	0.00825231	+	0.00530344i
$952$	−77.2493	−	21.5338i	−2.50366	−	0.697914i
$953$	12.0623	+	3.54182i	0.390738	+	0.114731i	0.471199	−	0.882027i	$-0.343821\pi$
$953$	12.0623	+	3.54182i	0.390738	+	0.114731i	−0.0804616	+	0.996758i	$0.525639\pi$
$954$	9.53308	+	9.90674i	0.308645	+	0.320743i
$955$	11.5288	−	9.98977i	0.373064	−	0.323262i
$956$	1.40619	+	0.257681i	0.0454793	+	0.00833399i
$957$	−21.5521	−	9.84251i	−0.696680	−	0.318163i
$958$	−1.83128	+	3.20569i	−0.0591659	+	0.103571i
$959$	−0.960415	+	0.282003i	−0.0310134	+	0.00910636i
$960$	1.12756	+	6.55738i	0.0363918	+	0.211639i
$961$	4.77650	+	10.4591i	0.154081	+	0.337389i
$962$	22.0492	−	4.35449i	0.710894	−	0.140394i
$963$	−4.80748	−	7.48058i	−0.154919	−	0.241058i
$964$	16.9953	−	24.3354i	0.547381	−	0.783790i
$965$		−	13.2781i		−	0.427438i
$966$	24.8321	+	7.31879i	0.798959	+	0.235478i
$967$	−8.05730			−0.259105			−0.129553	−	0.991573i	$-0.541354\pi$
$967$	−8.05730			−0.259105			−0.129553	+	0.991573i	$0.541354\pi$
$968$	−1.18990	−	0.741797i	−0.0382449	−	0.0238423i
$969$	37.4259	−	24.0522i	1.20229	−	0.772667i
$970$	3.93160	+	19.9078i	0.126236	+	0.639202i
$971$	−6.33218	+	2.89181i	−0.203209	+	0.0928026i	−0.514420	−	0.857538i	$-0.671993\pi$
$971$	−6.33218	+	2.89181i	−0.203209	+	0.0928026i	0.311211	+	0.950341i	$0.399265\pi$
$972$	1.99852	+	0.0768558i	0.0641026	+	0.00246515i
$973$	9.29906	+	31.6697i	0.298114	+	1.01528i
$974$	2.01611	−	3.52925i	0.0646004	−	0.113085i
$975$	−4.03588	+	8.83735i	−0.129252	+	0.283022i
$976$	1.18304	−	15.3589i	0.0378683	−	0.491626i
$977$	14.8737	+	17.1652i	0.475853	+	0.549164i	0.942030	−	0.335528i	$-0.108915\pi$
$977$	14.8737	+	17.1652i	0.475853	+	0.549164i	−0.466177	+	0.884691i	$0.654369\pi$
$978$	−19.8564	+	19.1075i	−0.634937	+	0.610989i
$979$	16.8152	−	57.2672i	0.537415	−	1.83027i
$980$	−11.9359	−	4.00897i	−0.381278	−	0.128062i
$981$	9.38175	−	14.5983i	0.299536	−	0.466087i
$982$	−15.4980	+	5.44354i	−0.494561	+	0.173710i
$983$	−2.73122	+	18.9960i	−0.0871123	+	0.605880i	0.898768	+	0.438425i	$0.144464\pi$
$983$	−2.73122	+	18.9960i	−0.0871123	+	0.605880i	−0.985880	+	0.167454i	$0.946445\pi$
$984$	−8.81340	−	13.3082i	−0.280961	−	0.424249i
$985$	1.05987	+	7.37156i	0.0337703	+	0.234877i
$986$	−59.6012	+	42.8547i	−1.89809	+	1.36477i
$987$	19.2473	+	16.6778i	0.612647	+	0.530861i
$988$	−26.8647	+	2.81389i	−0.854681	+	0.0895217i
$989$	−7.86695	+	0.706785i	−0.250154	+	0.0224744i
$990$	0.208002	+	3.98254i	0.00661075	+	0.126573i
$991$	10.1777	−	11.7457i	0.323306	−	0.373115i	−0.570709	−	0.821153i	$-0.693331\pi$
$991$	10.1777	−	11.7457i	0.323306	−	0.373115i	0.894015	+	0.448037i	$0.147877\pi$
$992$	−27.2653	−	24.8303i	−0.865674	−	0.788363i
$993$	3.90237	+	27.1416i	0.123838	+	0.861311i
$994$	−14.3029	+	7.45681i	−0.453662	+	0.236516i
$995$	3.04330	+	0.437561i	0.0964792	+	0.0138716i
$996$	−9.60683	+	3.94850i	−0.304404	+	0.125113i
$997$	21.6845	−	33.7418i	0.686755	−	1.06861i	−0.306410	−	0.951900i	$-0.599128\pi$
$997$	21.6845	−	33.7418i	0.686755	−	1.06861i	0.993166	−	0.116713i	$-0.0372357\pi$
$998$	11.8466	−	29.9887i	0.374996	−	0.949276i
$999$	6.76198	+	1.98550i	0.213940	+	0.0628183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.11	yes	480
8.5	even	2	inner	552.2.bb.a.85.37	yes	480
23.13	even	11	inner	552.2.bb.a.13.37	yes	480
184.13	even	22	inner	552.2.bb.a.13.11	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.11	✓	480	184.13	even	22	inner
552.2.bb.a.13.37	yes	480	23.13	even	11	inner
552.2.bb.a.85.11	yes	480	1.1	even	1	trivial
552.2.bb.a.85.37	yes	480	8.5	even	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11564 - 0.869107i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.489306 + 1.93922i) q^{4} +(-0.756543 + 0.345502i) q^{5} +(0.127979 - 1.40841i) q^{6} +(-3.66239 + 1.07537i) q^{7} +(1.13950 - 2.58873i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.11564 - 0.869107i) q^{2} +(0.540641 + 0.841254i) q^{3} +(0.489306 + 1.93922i) q^{4} +(-0.756543 + 0.345502i) q^{5} +(0.127979 - 1.40841i) q^{6} +(-3.66239 + 1.07537i) q^{7} +(1.13950 - 2.58873i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(1.14431 + 0.272061i) q^{10} +(2.56240 - 2.22033i) q^{11} +(-1.36684 + 1.46005i) q^{12} +(0.635317 - 2.16369i) q^{13} +(5.02052 + 1.98328i) q^{14} +(-0.699673 - 0.449652i) q^{15} +(-3.52116 + 1.89775i) q^{16} +(-1.05713 + 7.35248i) q^{17} +(1.25402 - 0.653782i) q^{18} +(-5.92823 + 0.852351i) q^{19} +(-1.04019 - 1.29805i) q^{20} +(-2.88470 - 2.49960i) q^{21} +(-4.78842 + 0.250092i) q^{22} +(2.22141 - 4.25034i) q^{23} +(2.79384 - 0.440965i) q^{24} +(-2.82132 + 3.25597i) q^{25} +(-2.58926 + 1.86174i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(-3.87742 - 6.57599i) q^{28} +(-6.91690 - 0.994501i) q^{29} +(0.389787 + 1.10974i) q^{30} +(-5.48418 - 3.52447i) q^{31} +(5.57769 + 0.943061i) q^{32} +(3.25320 + 0.955225i) q^{33} +(7.56947 - 7.28397i) q^{34} +(2.39921 - 2.07893i) q^{35} +(-1.96724 - 0.360493i) q^{36} +(-6.41059 - 2.92762i) q^{37} +(7.35456 + 4.20135i) q^{38} +(2.16369 - 0.635317i) q^{39} +(0.0323299 + 2.35219i) q^{40} +(-2.34435 - 5.13341i) q^{41} +(1.04586 + 5.29577i) q^{42} +(-0.890424 - 1.38553i) q^{43} +(5.55951 + 3.88263i) q^{44} -0.831702i q^{45} +(-6.17229 + 2.81121i) q^{46} -6.67219 q^{47} +(-3.50017 - 1.93619i) q^{48} +(6.36787 - 4.09238i) q^{49} +(5.97737 - 1.18047i) q^{50} +(-6.75683 + 3.08574i) q^{51} +(4.50674 + 0.173313i) q^{52} +(2.73892 + 9.32791i) q^{53} +(1.22797 + 0.701489i) q^{54} +(-1.17144 + 2.56509i) q^{55} +(-1.38944 + 10.7063i) q^{56} +(-3.92209 - 4.52633i) q^{57} +(6.85245 + 7.12103i) q^{58} +(1.99171 - 6.78314i) q^{59} +(0.529621 - 1.57684i) q^{60} +(-2.08206 + 3.23975i) q^{61} +(3.05523 + 8.69838i) q^{62} +(0.543216 - 3.77815i) q^{63} +(-5.40308 - 5.89973i) q^{64} +(0.266914 + 1.85643i) q^{65} +(-2.79921 - 3.89306i) q^{66} +(-0.672017 - 0.582306i) q^{67} +(-14.7754 + 1.54761i) q^{68} +(4.77659 - 0.429140i) q^{69} +(-4.48347 + 0.234165i) q^{70} +(-1.95680 + 2.25827i) q^{71} +(1.88143 + 2.11192i) q^{72} +(1.68986 + 11.7532i) q^{73} +(4.60750 + 8.83765i) q^{74} +(-4.26442 - 0.613131i) q^{75} +(-4.55362 - 11.0791i) q^{76} +(-6.99681 + 10.8872i) q^{77} +(-2.96606 - 1.17169i) q^{78} +(5.10875 + 1.50006i) q^{79} +(2.00823 - 2.65229i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.84603 + 7.76454i) q^{82} +(4.72400 + 2.15738i) q^{83} +(3.43579 - 6.81714i) q^{84} +(-1.74053 - 5.92771i) q^{85} +(-0.210778 + 2.31962i) q^{86} +(-2.90293 - 6.35654i) q^{87} +(-2.82799 - 9.16343i) q^{88} +(14.8089 - 9.51710i) q^{89} +(-0.722838 + 0.927881i) q^{90} +8.60748i q^{91} +(9.32929 + 2.22808i) q^{92} -6.51906i q^{93} +(7.44376 + 5.79885i) q^{94} +(4.19048 - 2.69305i) q^{95} +(2.22217 + 5.20211i) q^{96} +(7.16690 + 15.6933i) q^{97} +(-10.6610 - 0.968735i) q^{98} +(0.955225 + 3.25320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

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