LMFDB - Embedded newform 552.2.bb.a.13.37

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			13.37
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01903 - 0.980598i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(0.0768558 - 1.99852i) q^{4} +(0.756543 + 0.345502i) q^{5} +(0.274001 + 1.38742i) q^{6} +(-3.66239 - 1.07537i) q^{7} +(-1.88143 - 2.11192i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(1.01903 - 0.980598i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(0.0768558 - 1.99852i) q^{4} +(0.756543 + 0.345502i) q^{5} +(0.274001 + 1.38742i) q^{6} +(-3.66239 - 1.07537i) q^{7} +(-1.88143 - 2.11192i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(1.10974 - 0.389787i) q^{10} +(-2.56240 - 2.22033i) q^{11} +(1.63971 + 1.14514i) q^{12} +(-0.635317 - 2.16369i) q^{13} +(-4.78660 + 2.49549i) q^{14} +(-0.699673 + 0.449652i) q^{15} +(-3.98819 - 0.307196i) q^{16} +(-1.05713 - 7.35248i) q^{17} +(-1.31530 - 0.519590i) q^{18} +(5.92823 + 0.852351i) q^{19} +(0.748638 - 1.48541i) 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} +(-2.76912 - 1.58188i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-2.43063 + 7.23671i) q^{28} +(6.91690 - 0.994501i) q^{29} +(-0.272061 + 1.14431i) q^{30} +(-5.48418 + 3.52447i) q^{31} +(-4.36533 + 3.59776i) q^{32} +(3.25320 - 0.955225i) q^{33} +(-8.28708 - 6.45580i) q^{34} +(-2.39921 - 2.07893i) q^{35} +(-1.84985 + 0.760306i) q^{36} +(6.41059 - 2.92762i) q^{37} +(6.87688 - 4.94464i) q^{38} +(2.16369 + 0.635317i) q^{39} +(-0.693708 - 2.24780i) q^{40} +(-2.34435 + 5.13341i) q^{41} +(0.488495 - 5.37591i) q^{42} +(0.890424 - 1.38553i) q^{43} +(-4.63432 + 4.95036i) q^{44} -0.831702i q^{45} +(6.43156 + 2.15293i) q^{46} -6.67219 q^{47} +(2.41461 - 3.18899i) q^{48} +(6.36787 + 4.09238i) q^{49} +(-6.06782 - 0.551367i) q^{50} +(6.75683 + 3.08574i) q^{51} +(-4.37301 + 1.10340i) q^{52} +(-2.73892 + 9.32791i) q^{53} +(1.14821 - 0.825593i) q^{54} +(-1.17144 - 2.56509i) q^{55} +(4.61941 + 9.75792i) q^{56} +(-3.92209 + 4.52633i) q^{57} +(6.07335 - 7.79613i) q^{58} +(-1.99171 - 6.78314i) q^{59} +(0.844866 + 1.43287i) q^{60} +(2.08206 + 3.23975i) q^{61} +(-2.13247 + 8.96933i) q^{62} +(0.543216 + 3.77815i) q^{63} +(-0.920454 + 7.94687i) q^{64} +(0.266914 - 1.85643i) q^{65} +(2.37842 - 4.16348i) 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} +(-1.13950 + 2.58873i) q^{72} +(1.68986 - 11.7532i) q^{73} +(3.66178 - 9.26955i) q^{74} +(4.26442 - 0.613131i) q^{75} +(2.15906 - 11.7822i) q^{76} +(6.99681 + 10.8872i) q^{77} +(2.82786 - 1.47430i) q^{78} +(5.10875 - 1.50006i) q^{79} +(-2.91110 - 1.61033i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(2.64484 + 7.52998i) q^{82} +(-4.72400 + 2.15738i) q^{83} +(-4.77381 - 5.95724i) q^{84} +(1.74053 - 5.92771i) q^{85} +(-0.451273 - 2.28505i) q^{86} +(-2.90293 + 6.35654i) q^{87} +(0.131797 + 9.58898i) q^{88} +(14.8089 + 9.51710i) q^{89} +(-0.815566 - 0.847532i) q^{90} +8.60748i q^{91} +(8.66512 - 4.11287i) q^{92} -6.51906i q^{93} +(-6.79918 + 6.54274i) q^{94} +(4.19048 + 2.69305i) q^{95} +(-0.666557 - 5.61745i) q^{96} +(7.16690 - 15.6933i) q^{97} +(10.5021 - 2.07405i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	1.01903	−	0.980598i	0.720565	−	0.693387i
$2$	1.01903	−	0.980598i	0.720565	−	0.693387i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$4$	0.0768558	−	1.99852i	0.0384279	−	0.999261i
$5$	0.756543	+	0.345502i	0.338336	+	0.154513i	0.577336	−	0.816507i	$-0.304092\pi$
$5$	0.756543	+	0.345502i	0.338336	+	0.154513i	−0.239000	+	0.971020i	$0.576820\pi$
$6$	0.274001	+	1.38742i	0.111860	+	0.566410i
$7$	−3.66239	−	1.07537i	−1.38425	−	0.406453i	−0.497005	−	0.867748i	$-0.665567\pi$
$7$	−3.66239	−	1.07537i	−1.38425	−	0.406453i	−0.887247	+	0.461295i	$0.847385\pi$
$8$	−1.88143	−	2.11192i	−0.665185	−	0.746678i
$9$	−0.415415	−	0.909632i	−0.138472	−	0.303211i
$10$	1.10974	−	0.389787i	0.350931	−	0.123261i
$11$	−2.56240	−	2.22033i	−0.772592	−	0.669455i	0.176554	−	0.984291i	$-0.443505\pi$
$11$	−2.56240	−	2.22033i	−0.772592	−	0.669455i	−0.949146	+	0.314836i	$0.898050\pi$
$12$	1.63971	+	1.14514i	0.473344	+	0.330573i
$13$	−0.635317	−	2.16369i	−0.176205	−	0.600100i	−0.999473	−	0.0324473i	$-0.989670\pi$
$13$	−0.635317	−	2.16369i	−0.176205	−	0.600100i	0.823268	−	0.567653i	$-0.192148\pi$
$14$	−4.78660	+	2.49549i	−1.27927	+	0.666947i
$15$	−0.699673	+	0.449652i	−0.180655	+	0.116100i
$16$	−3.98819	−	0.307196i	−0.997047	−	0.0767991i
$17$	−1.05713	−	7.35248i	−0.256391	−	1.78324i	−0.558034	−	0.829818i	$-0.688444\pi$
$17$	−1.05713	−	7.35248i	−0.256391	−	1.78324i	0.301643	−	0.953421i	$-0.402465\pi$
$18$	−1.31530	−	0.519590i	−0.310020	−	0.122468i
$19$	5.92823	+	0.852351i	1.36003	+	0.195543i	0.783428	−	0.621482i	$-0.213469\pi$
$19$	5.92823	+	0.852351i	1.36003	+	0.195543i	0.576602	+	0.817025i	$0.304378\pi$
$20$	0.748638	−	1.48541i	0.167400	−	0.332149i
$21$	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
$26$	−2.76912	−	1.58188i	−0.543069	−	0.310232i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	−2.43063	+	7.23671i	−0.459347	+	1.36761i
$29$	6.91690	−	0.994501i	1.28444	−	0.184674i	0.533925	−	0.845532i	$-0.320716\pi$
$29$	6.91690	−	0.994501i	1.28444	−	0.184674i	0.750511	+	0.660857i	$0.229807\pi$
$30$	−0.272061	+	1.14431i	−0.0496714	+	0.208921i
$31$	−5.48418	+	3.52447i	−0.984988	+	0.633013i	−0.930804	−	0.365518i	$-0.880892\pi$
$31$	−5.48418	+	3.52447i	−0.984988	+	0.633013i	−0.0541837	+	0.998531i	$0.517256\pi$
$32$	−4.36533	+	3.59776i	−0.771688	+	0.636001i
$33$	3.25320	−	0.955225i	0.566309	−	0.166283i
$34$	−8.28708	−	6.45580i	−1.42122	−	1.10716i
$35$	−2.39921	−	2.07893i	−0.405541	−	0.351403i
$36$	−1.84985	+	0.760306i	−0.308308	+	0.126718i
$37$	6.41059	−	2.92762i	1.05389	−	0.481297i	0.188335	−	0.982105i	$-0.439691\pi$
$37$	6.41059	−	2.92762i	1.05389	−	0.481297i	0.865559	+	0.500807i	$0.166964\pi$
$38$	6.87688	−	4.94464i	1.11558	−	0.802126i
$39$	2.16369	+	0.635317i	0.346468	+	0.101732i
$40$	−0.693708	−	2.24780i	−0.109685	−	0.355408i
$41$	−2.34435	+	5.13341i	−0.366126	+	0.801705i	0.633483	+	0.773756i	$0.281625\pi$
$41$	−2.34435	+	5.13341i	−0.366126	+	0.801705i	−0.999609	+	0.0279481i	$0.991103\pi$
$42$	0.488495	−	5.37591i	0.0753764	−	0.829521i
$43$	0.890424	−	1.38553i	0.135788	−	0.211291i	−0.766699	−	0.642006i	$-0.778102\pi$
$43$	0.890424	−	1.38553i	0.135788	−	0.211291i	0.902488	+	0.430715i	$0.141739\pi$
$44$	−4.63432	+	4.95036i	−0.698649	+	0.746296i
$45$		−	0.831702i		−	0.123983i
$46$	6.43156	+	2.15293i	0.948281	+	0.317432i
$47$	−6.67219			−0.973239			−0.486619	−	0.873614i	$-0.661770\pi$
$47$	−6.67219			−0.973239			−0.486619	+	0.873614i	$0.661770\pi$
$48$	2.41461	−	3.18899i	0.348518	−	0.460291i
$49$	6.36787	+	4.09238i	0.909696	+	0.584626i
$50$	−6.06782	−	0.551367i	−0.858119	−	0.0779750i
$51$	6.75683	+	3.08574i	0.946145	+	0.432090i
$52$	−4.37301	+	1.10340i	−0.606428	+	0.153014i
$53$	−2.73892	+	9.32791i	−0.376220	+	1.28129i	0.526175	+	0.850376i	$0.323626\pi$
$53$	−2.73892	+	9.32791i	−0.376220	+	1.28129i	−0.902395	+	0.430911i	$0.858192\pi$
$54$	1.14821	−	0.825593i	0.156252	−	0.112349i
$55$	−1.17144	−	2.56509i	−0.157956	−	0.345876i
$56$	4.61941	+	9.75792i	0.617295	+	1.30396i
$57$	−3.92209	+	4.52633i	−0.519493	+	0.599527i
$58$	6.07335	−	7.79613i	0.797470	−	1.02368i
$59$	−1.99171	−	6.78314i	−0.259298	−	0.883089i	−0.981509	−	0.191416i	$-0.938692\pi$
$59$	−1.99171	−	6.78314i	−0.259298	−	0.883089i	0.722211	−	0.691673i	$-0.243126\pi$
$60$	0.844866	+	1.43287i	0.109072	+	0.184983i
$61$	2.08206	+	3.23975i	0.266581	+	0.414807i	0.948576	−	0.316549i	$-0.102524\pi$
$61$	2.08206	+	3.23975i	0.266581	+	0.414807i	−0.681996	+	0.731356i	$0.738888\pi$
$62$	−2.13247	+	8.96933i	−0.270824	+	1.13911i
$63$	0.543216	+	3.77815i	0.0684388	+	0.476002i
$64$	−0.920454	+	7.94687i	−0.115057	+	0.993359i
$65$	0.266914	−	1.85643i	0.0331066	−	0.230262i
$66$	2.37842	−	4.16348i	0.292764	−	0.512489i
$67$	0.672017	−	0.582306i	0.0820999	−	0.0711400i	−0.612844	−	0.790204i	$-0.709975\pi$
$67$	0.672017	−	0.582306i	0.0820999	−	0.0711400i	0.694944	+	0.719064i	$0.255429\pi$
$68$	−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	0.627660	−	0.778488i	$-0.284013\pi$
$71$	−1.95680	−	2.25827i	−0.232230	−	0.268007i	−0.859889	+	0.510481i	$0.829468\pi$
$72$	−1.13950	+	2.58873i	−0.134291	+	0.305085i
$73$	1.68986	−	11.7532i	0.197783	−	1.37561i	−0.612917	−	0.790147i	$-0.710004\pi$
$73$	1.68986	−	11.7532i	0.197783	−	1.37561i	0.810700	−	0.585462i	$-0.199087\pi$
$74$	3.66178	−	9.26955i	0.425674	−	1.07756i
$75$	4.26442	−	0.613131i	0.492413	−	0.0707983i
$76$	2.15906	−	11.7822i	0.247661	−	1.35151i
$77$	6.99681	+	10.8872i	0.797360	+	1.24072i
$78$	2.82786	−	1.47430i	0.320192	−	0.166932i
$79$	5.10875	−	1.50006i	0.574779	−	0.168770i	0.0185914	−	0.999827i	$-0.494082\pi$
$79$	5.10875	−	1.50006i	0.574779	−	0.168770i	0.556187	+	0.831057i	$0.312264\pi$
$80$	−2.91110	−	1.61033i	−0.325471	−	0.180041i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	2.64484	+	7.52998i	0.292074	+	0.831548i
$83$	−4.72400	+	2.15738i	−0.518526	+	0.236803i	−0.657447	−	0.753500i	$-0.728364\pi$
$83$	−4.72400	+	2.15738i	−0.518526	+	0.236803i	0.138921	+	0.990303i	$0.455637\pi$
$84$	−4.77381	−	5.95724i	−0.520866	−	0.649989i
$85$	1.74053	−	5.92771i	0.188787	−	0.642950i
$86$	−0.451273	−	2.28505i	−0.0486621	−	0.246403i
$87$	−2.90293	+	6.35654i	−0.311227	+	0.681492i
$88$	0.131797	+	9.58898i	0.0140496	+	1.02219i
$89$	14.8089	+	9.51710i	1.56974	+	1.00881i	0.979466	+	0.201607i	$0.0646165\pi$
$89$	14.8089	+	9.51710i	1.56974	+	1.00881i	0.590274	+	0.807203i	$0.299020\pi$
$90$	−0.815566	−	0.847532i	−0.0859682	−	0.0893377i
$91$			8.60748i			0.902309i
$92$	8.66512	−	4.11287i	0.903401	−	0.428796i
$93$		−	6.51906i		−	0.675995i
$94$	−6.79918	+	6.54274i	−0.701282	+	0.674832i
$95$	4.19048	+	2.69305i	0.429934	+	0.276302i
$96$	−0.666557	−	5.61745i	−0.0680301	−	0.573328i
$97$	7.16690	−	15.6933i	0.727689	−	1.59342i	−0.0751161	−	0.997175i	$-0.523933\pi$
$97$	7.16690	−	15.6933i	0.727689	−	1.59342i	0.802805	−	0.596242i	$-0.203340\pi$
$98$	10.5021	−	2.07405i	1.06087	−	0.209511i
$99$	−0.955225	+	3.25320i	−0.0960037	+	0.326959i
$100$	−6.72397	+	5.38823i	−0.672397	+	0.538823i
$101$	−14.2756	+	6.51947i	−1.42048	+	0.648712i	−0.969784	−	0.243966i	$-0.921552\pi$
$101$	−14.2756	+	6.51947i	−1.42048	+	0.648712i	−0.450696	+	0.892677i	$0.648824\pi$
$102$	9.91130	−	3.48126i	0.981365	−	0.344696i
$103$	9.56910	−	11.0433i	0.942871	−	1.08813i	−0.0531120	−	0.998589i	$-0.516914\pi$
$103$	9.56910	−	11.0433i	0.942871	−	1.08813i	0.995983	−	0.0895426i	$-0.0285405\pi$
$104$	−3.37425	+	5.41257i	−0.330872	+	0.530746i
$105$	3.04602	−	0.894391i	0.297261	−	0.0872836i
$106$	6.35588	+	12.1912i	0.617337	+	1.18412i
$107$	4.80748	+	7.48058i	0.464756	+	0.723175i	0.991958	−	0.126565i	$-0.0403953\pi$
$107$	4.80748	+	7.48058i	0.464756	+	0.723175i	−0.527202	+	0.849740i	$0.676759\pi$
$108$	0.360493	−	1.96724i	0.0346885	−	0.189298i
$109$	17.1764	−	2.46959i	1.64520	−	0.236544i	0.743446	−	0.668796i	$-0.233190\pi$
$109$	17.1764	−	2.46959i	1.64520	−	0.236544i	0.901753	+	0.432252i	$0.142281\pi$
$110$	−3.70905	−	1.46520i	−0.353644	−	0.139701i
$111$	−1.00296	+	6.97572i	−0.0951965	+	0.662106i
$112$	14.2759	+	5.41386i	1.34895	+	0.511562i
$113$	1.40284	+	1.61896i	0.131968	+	0.152299i	0.817887	−	0.575379i	$-0.195145\pi$
$113$	1.40284	+	1.61896i	0.131968	+	0.152299i	−0.685920	+	0.727677i	$0.740600\pi$
$114$	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
$118$	−8.68114	−	4.95917i	−0.799164	−	0.456529i
$119$	−4.03506	+	28.0644i	−0.369893	+	2.57266i
$120$	2.26602	+	0.631667i	0.206858	+	0.0576631i
$121$	0.0705523	+	0.490702i	0.00641385	+	0.0446093i
$122$	5.29858	+	1.25975i	0.479711	+	0.114052i
$123$	−3.05105	−	4.74753i	−0.275104	−	0.428070i
$124$	6.62224	+	11.2311i	0.594695	+	1.00859i
$125$	−2.18109	−	7.42812i	−0.195083	−	0.664391i
$126$	4.25840	+	3.31738i	0.379369	+	0.295536i
$127$	−4.73588	+	5.46550i	−0.420241	+	0.484984i	−0.925910	−	0.377743i	$-0.876700\pi$
$127$	−4.73588	+	5.46550i	−0.420241	+	0.484984i	0.505669	+	0.862727i	$0.331246\pi$
$128$	6.85471	+	9.00072i	0.605877	+	0.795559i
$129$	0.684180	+	1.49815i	0.0602387	+	0.131904i
$130$	−1.54842	−	2.15350i	−0.135805	−	0.188874i
$131$	4.86383	−	16.5647i	0.424955	−	1.44726i	−0.417589	−	0.908636i	$-0.637125\pi$
$131$	4.86383	−	16.5647i	0.424955	−	1.44726i	0.842544	−	0.538628i	$-0.181057\pi$
$132$	−1.65901	−	6.57500i	−0.144398	−	0.572281i
$133$	−20.7949	−	9.49671i	−1.80315	−	0.823469i
$134$	0.113799	−	1.25237i	0.00983076	−	0.108188i
$135$	0.699673	+	0.449652i	0.0602182	+	0.0386999i
$136$	−13.5390	+	16.0657i	−1.16096	+	1.37763i
$137$	0.262237			0.0224044			0.0112022	−	0.999937i	$-0.496434\pi$
$137$	0.262237			0.0224044			0.0112022	+	0.999937i	$0.496434\pi$
$138$	−5.28832	+	4.24661i	−0.450172	+	0.361495i
$139$		−	8.64728i		−	0.733453i	−0.930329	−	0.366727i	$-0.880478\pi$
$139$		−	8.64728i		−	0.733453i	0.930329	−	0.366727i	$-0.119522\pi$
$140$	−4.33918	+	4.63510i	−0.366727	+	0.391737i
$141$	3.60726	−	5.61300i	0.303786	−	0.472700i
$142$	−4.20850	−	0.382415i	−0.353169	−	0.0320916i
$143$	−3.17617	+	6.95485i	−0.265605	+	0.581594i
$144$	1.37732	+	3.75540i	0.114776	+	0.312950i
$145$	5.57654	+	1.63742i	0.463106	+	0.135980i
$146$	−9.80316	−	13.6340i	−0.811315	−	1.12836i
$147$	−6.88546	+	3.14449i	−0.567904	+	0.259353i
$148$	−5.35822	−	13.0367i	−0.440443	−	1.07161i
$149$	4.04268	+	3.50300i	0.331189	+	0.286977i	0.804542	−	0.593896i	$-0.202411\pi$
$149$	4.04268	+	3.50300i	0.331189	+	0.286977i	−0.473353	+	0.880873i	$0.656956\pi$
$150$	3.74435	−	4.80648i	0.305725	−	0.392448i
$151$	4.83500	−	1.41968i	0.393466	−	0.115532i	−0.0790136	−	0.996874i	$-0.525177\pi$
$151$	4.83500	−	1.41968i	0.393466	−	0.115532i	0.472480	+	0.881341i	$0.343359\pi$
$152$	−9.35345	−	14.1236i	−0.758665	−	1.14558i
$153$	−6.24891	+	4.01593i	−0.505194	+	0.324669i
$154$	17.8060	+	4.23341i	1.43485	+	0.341138i
$155$	−5.36673	+	0.771619i	−0.431066	+	0.0619780i
$156$	1.43599	−	4.27536i	0.114971	−	0.342303i
$157$	−8.36861	−	1.20322i	−0.667888	−	0.0960278i	−0.199973	−	0.979801i	$-0.564086\pi$
$157$	−8.36861	−	1.20322i	−0.667888	−	0.0960278i	−0.467915	+	0.883774i	$0.654995\pi$
$158$	3.73502	−	6.53824i	0.297142	−	0.520154i
$159$	−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	0.153506	−	0.988148i	$-0.450943\pi$
$163$	14.7262	−	12.7603i	1.15344	−	0.999464i	0.999936	−	0.0113159i	$-0.00360204\pi$
$164$	10.0791	+	5.07977i	0.787043	+	0.396664i
$165$	2.79122	+	0.401316i	0.217296	+	0.0312424i
$166$	−2.69839	+	6.83078i	−0.209436	+	0.530172i
$167$	−1.76517	−	12.2771i	−0.136593	−	0.950027i	−0.936691	−	0.350157i	$-0.886128\pi$
$167$	−1.76517	−	12.2771i	−0.136593	−	0.950027i	0.800098	−	0.599870i	$-0.204781\pi$
$168$	−10.7063	−	1.38944i	−0.826011	−	0.107197i
$169$	6.65837	−	4.27907i	0.512182	−	0.329159i
$170$	−4.03904	−	7.74729i	−0.309780	−	0.594190i
$171$	−1.68735	−	5.74659i	−0.129035	−	0.439453i
$172$	−2.70057	−	1.88602i	−0.205917	−	0.143808i
$173$	2.44138	+	2.11547i	0.185615	+	0.160836i	0.742712	−	0.669612i	$-0.233539\pi$
$173$	2.44138	+	2.11547i	0.185615	+	0.160836i	−0.557097	+	0.830447i	$0.688085\pi$
$174$	3.27502	+	9.32413i	0.248279	+	0.706861i
$175$	6.83137	+	14.9586i	0.516403	+	1.13076i
$176$	9.53724	+	9.64225i	0.718897	+	0.726812i
$177$	6.78314	+	1.99171i	0.509852	+	0.149706i
$178$	24.4232	−	4.82333i	1.83060	−	0.361524i
$179$	6.52201	+	2.97850i	0.487478	+	0.222624i	0.643963	−	0.765057i	$-0.277289\pi$
$179$	6.52201	+	2.97850i	0.487478	+	0.222624i	−0.156485	+	0.987680i	$0.550016\pi$
$180$	−1.66218	−	0.0639212i	−0.123891	−	0.00476440i
$181$	−11.4807	+	17.8643i	−0.853351	+	1.32784i	0.0899653	+	0.995945i	$0.471324\pi$
$181$	−11.4807	+	17.8643i	−0.853351	+	1.32784i	−0.943316	+	0.331895i	$0.892312\pi$
$182$	8.44047	+	8.77130i	0.625649	+	0.650172i
$183$	−3.85110			−0.284681
$184$	4.79698	−	12.6881i	0.353638	−	0.935382i
$185$	5.86138			0.430937
$186$	−6.39258	−	6.64314i	−0.468726	−	0.487098i
$187$	−13.6162	+	21.1872i	−0.995712	+	1.54936i
$188$	−0.512797	+	13.3345i	−0.0373995	+	0.972520i
$189$	−3.47207	−	1.58564i	−0.252556	−	0.115338i
$190$	6.91104	−	1.36486i	0.501379	−	0.0990173i
$191$	−17.5987	−	5.16744i	−1.27340	−	0.373903i	−0.425933	−	0.904755i	$-0.640054\pi$
$191$	−17.5987	−	5.16744i	−1.27340	−	0.373903i	−0.847465	+	0.530852i	$0.821872\pi$
$192$	−6.18770	−	5.07074i	−0.446559	−	0.365949i
$193$	−6.63210	−	14.5223i	−0.477389	−	1.04534i	−0.983173	−	0.182676i	$-0.941524\pi$
$193$	−6.63210	−	14.5223i	−0.477389	−	1.04534i	0.505784	−	0.862660i	$-0.331203\pi$
$194$	−8.08554	−	23.0199i	−0.580508	−	1.65273i
$195$	1.41742	+	1.22820i	0.101504	+	0.0879535i
$196$	8.66813	−	12.4118i	0.619152	−	0.886558i
$197$	−2.52274	−	8.59165i	−0.179737	−	0.612130i	−0.999237	−	0.0390501i	$-0.987567\pi$
$197$	−2.52274	−	8.59165i	−0.179737	−	0.612130i	0.819500	−	0.573079i	$-0.194251\pi$
$198$	2.21667	+	4.25181i	0.157532	+	0.302163i
$199$	−3.10991	+	1.99861i	−0.220455	+	0.141678i	−0.646207	−	0.763162i	$-0.723646\pi$
$199$	−3.10991	+	1.99861i	−0.220455	+	0.141678i	0.425752	+	0.904840i	$0.360010\pi$
$200$	−1.56827	+	12.0843i	−0.110893	+	0.854489i
$201$	0.126547	+	0.880155i	0.00892595	+	0.0620813i
$202$	−8.15438	+	20.6422i	−0.573740	+	1.45238i
$203$	−26.4018	−	3.79601i	−1.85305	−	0.266428i
$204$	6.68622	−	13.2665i	0.468129	−	0.928842i
$205$	−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
$210$	2.22695	−	3.89833i	0.153674	−	0.269010i
$211$	12.4883	+	1.79554i	0.859729	+	0.123610i	0.558058	−	0.829802i	$-0.311547\pi$
$211$	12.4883	+	1.79554i	0.859729	+	0.123610i	0.301671	+	0.953412i	$0.402456\pi$
$212$	18.4315	+	6.19070i	1.26588	+	0.425179i
$213$	2.95770	−	0.425254i	0.202659	−	0.0291379i
$214$	12.2344	+	2.90875i	0.836327	+	0.198838i
$215$	1.15235	−	0.740568i	0.0785894	−	0.0505063i
$216$	−1.56172	−	2.35818i	−0.106262	−	0.160454i
$217$	23.8753	−	7.01043i	1.62076	−	0.475899i
$218$	15.0816	−	19.3597i	1.02146	−	1.31121i
$219$	8.97383	+	7.77587i	0.606395	+	0.525444i
$220$	−5.21642	+	2.14400i	−0.351691	+	0.144548i
$221$	−15.2369	+	6.95845i	−1.02494	+	0.468076i
$222$	5.81833	+	8.09198i	0.390501	+	0.543098i
$223$	−1.32004	−	0.387599i	−0.0883966	−	0.0259556i	0.237235	−	0.971452i	$-0.423759\pi$
$223$	−1.32004	−	0.387599i	−0.0883966	−	0.0259556i	−0.325632	+	0.945497i	$0.605577\pi$
$224$	19.8565	−	8.48204i	1.32672	−	0.566730i
$225$	−1.78972	+	3.91894i	−0.119315	+	0.261263i
$226$	3.01708	+	0.274154i	0.200693	+	0.0182365i
$227$	2.54285	−	3.95675i	0.168775	−	0.262619i	−0.746555	−	0.665324i	$-0.768294\pi$
$227$	2.54285	−	3.95675i	0.168775	−	0.262619i	0.915330	+	0.402705i	$0.131930\pi$
$228$	8.74454	+	8.18626i	0.579121	+	0.542148i
$229$			8.46102i			0.559120i	0.960128	+	0.279560i	$0.0901886\pi$
$229$			8.46102i			0.559120i	−0.960128	+	0.279560i	$0.909811\pi$
$230$	4.12191	+	3.85089i	0.271791	+	0.253920i
$231$	−12.9417			−0.851501
$232$	−15.1140	−	12.7369i	−0.992281	−	0.836219i
$233$	−10.2996	−	6.61916i	−0.674750	−	0.433635i	0.157885	−	0.987457i	$-0.449532\pi$
$233$	−10.2996	−	6.61916i	−0.674750	−	0.433635i	−0.832635	+	0.553822i	$0.813169\pi$
$234$	−0.288596	+	3.17602i	−0.0188661	+	0.207623i
$235$	−5.04780	−	2.30525i	−0.329282	−	0.150378i
$236$	−13.7093	+	3.45915i	−0.892401	+	0.225172i
$237$	−1.50006	+	5.10875i	−0.0974396	+	0.331849i
$238$	23.4081	+	32.5554i	1.51732	+	2.11025i
$239$	0.296939	+	0.650205i	0.0192074	+	0.0420583i	0.918993	−	0.394275i	$-0.129004\pi$
$239$	0.296939	+	0.650205i	0.0192074	+	0.0420583i	−0.899785	+	0.436333i	$0.856277\pi$
$240$	2.92856	−	1.57836i	0.189037	−	0.101883i
$241$	−9.71895	+	11.2163i	−0.626053	+	0.722503i	−0.976845	−	0.213950i	$-0.931367\pi$
$241$	−9.71895	+	11.2163i	−0.626053	+	0.722503i	0.350792	+	0.936453i	$0.385912\pi$
$242$	0.553077	+	0.430858i	0.0355531	+	0.0276966i
$243$	−0.281733	−	0.959493i	−0.0180732	−	0.0615515i
$244$	6.63473	−	3.91205i	0.424745	−	0.250443i
$245$	3.40365	+	5.29618i	0.217451	+	0.338360i
$246$	−7.76454	−	1.84603i	−0.495049	−	0.117699i
$247$	−1.92208	−	13.3684i	−0.122299	−	0.850609i
$248$	17.7615	+	4.95114i	1.12786	+	0.314398i
$249$	0.739085	−	5.14045i	0.0468376	−	0.325763i
$250$	−9.50660	−	5.43072i	−0.601250	−	0.343469i
$251$	−5.50873	+	4.77334i	−0.347708	+	0.301291i	−0.811152	−	0.584836i	$-0.801159\pi$
$251$	−5.50873	+	4.77334i	−0.347708	+	0.301291i	0.463444	+	0.886126i	$0.346614\pi$
$252$	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
$256$	15.8113	+	2.45031i	0.988204	+	0.153144i
$257$	−3.61032	+	25.1103i	−0.225206	+	1.56634i	0.492701	+	0.870199i	$0.336010\pi$
$257$	−3.61032	+	25.1103i	−0.225206	+	1.56634i	−0.717906	+	0.696140i	$0.754899\pi$
$258$	2.16628	+	0.855754i	0.134867	+	0.0532769i
$259$	−26.6263	+	3.82829i	−1.65448	+	0.237878i
$260$	−3.68960	−	0.676111i	−0.228819	−	0.0419306i
$261$	−3.77802	−	5.87871i	−0.233853	−	0.363883i
$262$	−11.2869	−	21.6494i	−0.697307	−	1.33751i
$263$	11.9550	−	3.51030i	0.737175	−	0.216454i	0.108472	−	0.994100i	$-0.465404\pi$
$263$	11.9550	−	3.51030i	0.737175	−	0.216454i	0.628703	+	0.777645i	$0.283586\pi$
$264$	−8.13802	−	5.07332i	−0.500861	−	0.312241i
$265$	−5.29492	+	6.11066i	−0.325264	+	0.375375i
$266$	−30.5031	+	10.7140i	−1.87027	+	0.656915i
$267$	−16.0126	+	7.31270i	−0.979955	+	0.447530i
$268$	−1.11210	−	1.38779i	−0.0679325	−	0.0847730i
$269$	−2.34812	+	7.99696i	−0.143167	+	0.487583i	−0.999588	−	0.0286950i	$-0.990865\pi$
$269$	−2.34812	+	7.99696i	−0.143167	+	0.487583i	0.856421	+	0.516278i	$0.172683\pi$
$270$	1.15392	−	0.227887i	0.0702252	−	0.0138688i
$271$	1.71209	−	3.74895i	0.104002	−	0.227732i	−0.850476	−	0.526014i	$-0.823686\pi$
$271$	1.71209	−	3.74895i	0.104002	−	0.227732i	0.954478	+	0.298281i	$0.0964134\pi$
$272$	1.95737	+	29.6478i	0.118683	+	1.79766i
$273$	−7.24107	−	4.65355i	−0.438249	−	0.281646i
$274$	0.267228	−	0.257149i	0.0161439	−	0.0155350i
$275$			14.6074i			0.880857i
$276$	−1.22475	+	9.51315i	−0.0737216	+	0.572624i
$277$		−	17.5330i		−	1.05346i	−0.850034	−	0.526728i	$-0.823419\pi$
$277$		−	17.5330i		−	1.05346i	0.850034	−	0.526728i	$-0.176581\pi$
$278$	−8.47951	−	8.81187i	−0.508567	−	0.528501i
$279$	5.48418	+	3.52447i	0.328329	+	0.211004i
$280$	0.123403	+	8.97830i	0.00737477	+	0.536556i
$281$	−9.36365	+	20.5035i	−0.558588	+	1.22314i	0.394066	+	0.919082i	$0.371068\pi$
$281$	−9.36365	+	20.5035i	−0.558588	+	1.22314i	−0.952654	+	0.304056i	$0.901659\pi$
$282$	−1.82818	−	9.25710i	−0.108867	−	0.551253i
$283$	0.270632	−	0.921689i	0.0160874	−	0.0547887i	−0.951058	−	0.309012i	$-0.900002\pi$
$283$	0.270632	−	0.921689i	0.0160874	−	0.0547887i	0.967146	+	0.254223i	$0.0818198\pi$
$284$	−4.66359	+	3.73715i	−0.276733	+	0.221759i
$285$	−4.53108	+	2.06928i	−0.268398	+	0.122573i
$286$	3.58329	+	10.2018i	0.211884	+	0.603243i
$287$	14.1063	−	16.2795i	0.832666	−	0.960948i
$288$	5.08606	+	2.47628i	0.299699	+	0.145916i
$289$	−36.6301	+	10.7556i	−2.15471	+	0.632681i
$290$	7.28833	−	3.79976i	0.427985	−	0.223129i
$291$	9.32735	+	14.5136i	0.546779	+	0.850805i
$292$	−23.3592	−	4.28052i	−1.36699	−	0.250499i
$293$	6.44045	−	0.925997i	0.376255	−	0.0540973i	0.0484068	−	0.998828i	$-0.484586\pi$
$293$	6.44045	−	0.925997i	0.376255	−	0.0540973i	0.327848	+	0.944730i	$0.393677\pi$
$294$	−3.93304	+	9.95621i	−0.229379	+	0.580658i
$295$	0.836771	−	5.81987i	0.0487187	−	0.338846i
$296$	−18.2440	−	8.03058i	−1.06041	−	0.466768i
$297$	−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
$302$	3.53488	−	6.18789i	0.203410	−	0.356073i
$303$	2.23347	−	15.5341i	0.128310	−	0.892413i
$304$	−23.3811	−	5.22047i	−1.34100	−	0.299414i
$305$	0.455830	+	3.17037i	0.0261007	+	0.181535i
$306$	−2.42983	+	10.2200i	−0.138904	+	0.584240i
$307$	15.4412	+	24.0269i	0.881275	+	1.37129i	0.928078	+	0.372386i	$0.121460\pi$
$307$	15.4412	+	24.0269i	0.881275	+	1.37129i	−0.0468032	+	0.998904i	$0.514903\pi$
$308$	22.2961	−	13.1465i	1.27044	−	0.749093i
$309$	4.11679	+	14.0205i	0.234196	+	0.797599i
$310$	−4.71223	+	6.04891i	−0.267636	+	0.343555i
$311$	−4.33322	+	5.00081i	−0.245715	+	0.283570i	−0.865188	−	0.501448i	$-0.832801\pi$
$311$	−4.33322	+	5.00081i	−0.245715	+	0.283570i	0.619473	+	0.785018i	$0.287346\pi$
$312$	−2.72909	−	5.76486i	−0.154504	−	0.326371i
$313$	−1.78234	−	3.90279i	−0.100744	−	0.220599i	0.852548	−	0.522649i	$-0.175056\pi$
$313$	−1.78234	−	3.90279i	−0.100744	−	0.220599i	−0.953292	+	0.302050i	$0.902329\pi$
$314$	−9.70777	+	6.98012i	−0.547841	+	0.393911i
$315$	−0.894391	+	3.04602i	−0.0503932	+	0.171624i
$316$	−2.60527	−	10.3252i	−0.146558	−	0.580840i
$317$	−0.275172	−	0.125667i	−0.0154552	−	0.00705816i	0.407672	−	0.913128i	$-0.366341\pi$
$317$	−0.275172	−	0.125667i	−0.0154552	−	0.00705816i	−0.423128	+	0.906070i	$0.639068\pi$
$318$	−13.6922	−	1.24417i	−0.767818	−	0.0697696i
$319$	−19.9320	−	12.8095i	−1.11598	−	0.717195i
$320$	−3.44202	+	5.69413i	−0.192415	+	0.318312i
$321$	−8.89218			−0.496313
$322$	−21.2396	−	14.8012i	−1.18364	−	0.824837i
$323$		−	44.4883i		−	2.47539i
$324$	1.46005	+	1.36684i	0.0811140	+	0.0759354i
$325$	−5.25249	+	8.17303i	−0.291356	+	0.453358i
$326$	2.49373	−	27.4436i	0.138115	−	1.51996i
$327$	−7.20870	+	15.7849i	−0.398642	+	0.872904i
$328$	15.2521	−	4.70706i	0.842157	−	0.259904i
$329$	24.4361	+	7.17510i	1.34721	+	0.395576i
$330$	3.23787	−	2.32811i	0.178239	−	0.128158i
$331$	−24.9427	+	11.3910i	−1.37098	+	0.626103i	−0.958559	−	0.284892i	$-0.908042\pi$
$331$	−24.9427	+	11.3910i	−1.37098	+	0.626103i	−0.412416	+	0.910996i	$0.635315\pi$
$332$	3.94850	+	9.60683i	0.216702	+	0.527243i
$333$	−5.32611	−	4.61510i	−0.291869	−	0.252906i
$334$	−13.8376	−	10.7798i	−0.757161	−	0.589844i
$335$	0.709597	−	0.208357i	0.0387694	−	0.0113837i
$336$	−12.2726	+	9.08272i	−0.669524	+	0.495503i
$337$	11.8272	−	7.60090i	0.644270	−	0.414047i	−0.177298	−	0.984157i	$-0.556736\pi$
$337$	11.8272	−	7.60090i	0.644270	−	0.414047i	0.821568	+	0.570110i	$0.193099\pi$
$338$	2.58904	−	10.8897i	0.140825	−	0.592321i
$339$	−2.12038	+	0.304865i	−0.115163	+	0.0165580i
$340$	−11.7129	−	3.93407i	−0.635221	−	0.213355i
$341$	21.8781	+	3.14560i	1.18477	+	0.170344i
$342$	−7.35456	−	4.20135i	−0.397689	−	0.227183i
$343$	−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	$-0.672478\pi$
$347$	4.82294	−	4.17910i	0.258909	−	0.224346i	0.774637	+	0.632407i	$0.217933\pi$
$348$	12.4806	+	6.29012i	0.669029	+	0.337186i
$349$	19.4886	+	2.80204i	1.04320	+	0.149990i	0.642552	−	0.766242i	$-0.277876\pi$
$349$	19.4886	+	2.80204i	1.04320	+	0.149990i	0.400649	+	0.916232i	$0.368785\pi$
$350$	21.6298	+	8.54449i	1.15616	+	0.456722i
$351$	−0.320925	−	2.23208i	−0.0171297	−	0.119140i
$352$	19.1739	+	0.473570i	1.02197	+	0.0252414i
$353$	−17.8735	+	11.4866i	−0.951311	+	0.611371i	−0.921581	−	0.388187i	$-0.873101\pi$
$353$	−17.8735	+	11.4866i	−0.951311	+	0.611371i	−0.0297309	+	0.999558i	$0.509465\pi$
$354$	8.86530	−	4.62191i	0.471185	−	0.245652i
$355$	−0.700169	−	2.38456i	−0.0371611	−	0.126559i
$356$	20.1583	−	28.8645i	1.06839	−	1.52981i
$357$	−21.4278	−	18.5673i	−1.13408	−	0.982685i
$358$	9.56686	−	3.36028i	0.505624	−	0.177596i
$359$	1.04838	+	2.29563i	0.0553315	+	0.121159i	0.935278	−	0.353913i	$-0.115149\pi$
$359$	1.04838	+	2.29563i	0.0553315	+	0.121159i	−0.879947	+	0.475072i	$0.842422\pi$
$360$	−1.75649	+	1.56479i	−0.0925753	+	0.0824716i
$361$	16.1871	+	4.75296i	0.851952	+	0.250156i
$362$	5.81848	+	29.4622i	0.305813	+	1.54850i
$363$	−0.450948	−	0.205941i	−0.0236687	−	0.0108091i
$364$	17.2022	+	0.661535i	0.901642	+	0.0346738i
$365$	5.33920	−	8.30796i	0.279467	−	0.434859i
$366$	−3.92440	+	3.77638i	−0.205131	+	0.197394i
$367$	−1.23586			−0.0645114			−0.0322557	−	0.999480i	$-0.510269\pi$
$367$	−1.23586			−0.0645114			−0.0322557	+	0.999480i	$0.510269\pi$
$368$	−7.55369	−	17.6335i	−0.393763	−	0.919212i
$369$	5.64340			0.293783
$370$	5.97294	−	5.74766i	0.310518	−	0.298807i
$371$	20.0620	−	31.2170i	1.04157	−	1.62071i
$372$	−13.0285	−	0.501028i	−0.675496	−	0.0259771i
$373$	2.12963	+	0.972570i	0.110268	+	0.0503578i	0.469785	−	0.882781i	$-0.344331\pi$
$373$	2.12963	+	0.972570i	0.110268	+	0.0503578i	−0.359517	+	0.933138i	$0.617059\pi$
$374$	6.90077	+	34.9424i	0.356830	+	1.80683i
$375$	7.42812	+	2.18109i	0.383586	+	0.112631i
$376$	12.5532	+	14.0912i	0.647384	+	0.726696i
$377$	−6.54622	−	14.3342i	−0.337147	−	0.738250i
$378$	−5.09303	+	1.78888i	−0.261957	+	0.0920102i
$379$	−6.58892	−	5.70933i	−0.338450	−	0.293268i	0.469008	−	0.883194i	$-0.344612\pi$
$379$	−6.58892	−	5.70933i	−0.338450	−	0.293268i	−0.807458	+	0.589926i	$0.799157\pi$
$380$	5.70419	−	8.16778i	0.292619	−	0.418998i
$381$	−2.03746	−	6.93894i	−0.104382	−	0.355493i
$382$	−23.0008	+	11.9915i	−1.17683	+	0.613536i
$383$	31.7682	−	20.4162i	1.62328	−	1.04322i	0.669458	−	0.742850i	$-0.266526\pi$
$383$	31.7682	−	20.4162i	1.62328	−	1.04322i	0.953823	−	0.300370i	$-0.0971100\pi$
$384$	−11.2778	+	0.900395i	−0.575519	+	0.0459481i
$385$	1.53183	+	10.6541i	0.0780690	+	0.542982i
$386$	−20.9988	−	8.29525i	−1.06881	−	0.422217i
$387$	−1.63022	−	0.234390i	−0.0828685	−	0.0119147i
$388$	−30.8127	−	15.5293i	−1.56428	−	0.788383i
$389$	18.2951	−	15.8528i	0.927598	−	0.803769i	−0.0532420	−	0.998582i	$-0.516955\pi$
$389$	18.2951	−	15.8528i	0.927598	−	0.803769i	0.980840	+	0.194813i	$0.0624100\pi$
$390$	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
$394$	−10.9957	−	6.28138i	−0.553955	−	0.316451i
$395$	4.38326	+	0.630218i	0.220546	+	0.0317097i
$396$	6.42817	+	2.15907i	0.323028	+	0.108497i
$397$	−28.0372	+	4.03113i	−1.40714	+	0.202317i	−0.803675	−	0.595069i	$-0.797125\pi$
$397$	−28.0372	+	4.03113i	−1.40714	+	0.202317i	−0.603470	+	0.797386i	$0.706216\pi$
$398$	−1.20926	+	5.08622i	−0.0606146	+	0.254949i
$399$	19.2317	−	12.3595i	0.962789	−	0.618747i
$400$	10.2517	+	13.8521i	0.512586	+	0.692606i
$401$	20.0199	−	5.87837i	0.999746	−	0.293552i	0.259394	−	0.965772i	$-0.416477\pi$
$401$	20.0199	−	5.87837i	0.999746	−	0.293552i	0.740352	+	0.672220i	$0.234659\pi$
$402$	0.992034	+	0.772815i	0.0494781	+	0.0385445i
$403$	11.1101	+	9.62692i	0.553431	+	0.479551i
$404$	11.9321	+	29.0313i	0.593646	+	1.44436i
$405$	−0.756543	+	0.345502i	−0.0375929	+	0.0171681i
$406$	−30.6267	+	22.0213i	−1.51998	+	1.09290i
$407$	−22.9268	−	6.73190i	−1.13644	−	0.333688i
$408$	−6.19564	−	20.0755i	−0.306730	−	0.993886i
$409$	−6.70333	+	14.6782i	−0.331458	+	0.725792i	−0.999837	−	0.0180283i	$-0.994261\pi$
$409$	−6.70333	+	14.6782i	−0.331458	+	0.725792i	0.668379	+	0.743821i	$0.266988\pi$
$410$	−0.600684	+	6.61055i	−0.0296657	+	0.326472i
$411$	−0.141776	+	0.220608i	−0.00699330	+	0.0108818i
$412$	−21.3349	−	19.9728i	−1.05109	−	0.983989i
$413$			26.9843i			1.32781i
$414$	−0.713394	−	6.74471i	−0.0350614	−	0.331484i
$415$	−4.31929			−0.212025
$416$	10.5578	+	7.15950i	0.517639	+	0.351023i
$417$	7.27456	+	4.67508i	0.356237	+	0.228939i
$418$	−28.6000	−	2.59881i	−1.39887	−	0.127112i
$419$	−7.69258	−	3.51308i	−0.375807	−	0.171625i	0.218552	−	0.975825i	$-0.429867\pi$
$419$	−7.69258	−	3.51308i	−0.375807	−	0.171625i	−0.594359	+	0.804200i	$0.702594\pi$
$420$	−1.55336	−	6.15627i	−0.0757960	−	0.300395i
$421$	9.50846	−	32.3828i	0.463414	−	1.57824i	−0.314109	−	0.949387i	$-0.601706\pi$
$421$	9.50846	−	32.3828i	0.463414	−	1.57824i	0.777522	−	0.628855i	$-0.216476\pi$
$422$	14.4867	−	10.4163i	0.705201	−	0.507056i
$423$	2.77173	+	6.06924i	0.134766	+	0.295096i
$424$	24.8529	−	11.7654i	1.20696	−	0.571378i
$425$	−20.9570	+	24.1857i	−1.01656	+	1.17318i
$426$	2.59699	−	3.33367i	0.125825	−	0.161517i
$427$	−4.14137	−	14.1042i	−0.200415	−	0.682551i
$428$	15.3196	−	9.03292i	0.740500	−	0.436623i
$429$	−4.13362	−	6.43204i	−0.199573	−	0.310542i
$430$	0.448079	−	1.88465i	0.0216083	−	0.0908860i
$431$	0.979740	+	6.81424i	0.0471924	+	0.328230i	0.999717	+	0.0237701i	$0.00756697\pi$
$431$	0.979740	+	6.81424i	0.0471924	+	0.328230i	−0.952525	+	0.304460i	$0.901524\pi$
$432$	−3.90387	−	0.871648i	−0.187825	−	0.0419372i
$433$	−1.02133	+	7.10349i	−0.0490819	+	0.341372i	0.950453	+	0.310869i	$0.100620\pi$
$433$	−1.02133	+	7.10349i	−0.0490819	+	0.341372i	−0.999535	+	0.0305030i	$0.990289\pi$
$434$	17.4553	−	30.5559i	0.837882	−	1.46673i
$435$	−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	0.795994	−	0.605305i	$-0.206949\pi$
$439$	1.75095	+	2.02070i	0.0835682	+	0.0964428i	−0.712426	+	0.701748i	$0.752403\pi$
$440$	−3.21330	+	7.30002i	−0.153188	+	0.348015i
$441$	1.07725	−	7.49246i	0.0512978	−	0.356784i
$442$	−8.70344	+	22.0322i	−0.413981	+	1.04796i
$443$	−20.5146	+	2.94956i	−0.974678	+	0.140138i	−0.611210	−	0.791469i	$-0.709317\pi$
$443$	−20.5146	+	2.94956i	−0.974678	+	0.140138i	−0.363469	+	0.931606i	$0.618408\pi$
$444$	13.8641	+	2.54056i	0.657959	+	0.120570i
$445$	7.91539	+	12.3166i	0.375226	+	0.583863i
$446$	−1.72525	+	0.899454i	−0.0816927	+	0.0425904i
$447$	−5.13255	+	1.50705i	−0.242761	+	0.0712812i
$448$	11.9169	−	28.1147i	0.563021	−	1.32829i
$449$	13.0936	−	15.1108i	0.617925	−	0.713123i	−0.357387	−	0.933957i	$-0.616332\pi$
$449$	13.0936	−	15.1108i	0.617925	−	0.713123i	0.975312	+	0.220833i	$0.0708776\pi$
$450$	2.01912	+	5.74853i	0.0951823	+	0.270988i
$451$	17.4050	−	7.94861i	0.819571	−	0.374286i
$452$	3.34334	−	2.67917i	0.157258	−	0.126018i
$453$	−1.41968	+	4.83500i	−0.0667025	+	0.227168i
$454$	−1.28873	−	6.52556i	−0.0604832	−	0.306260i
$455$	−2.97390	+	6.51193i	−0.139418	+	0.305284i
$456$	16.9384	−	0.232812i	0.793213	−	0.0109024i
$457$	−22.5392	−	14.4851i	−1.05434	−	0.677582i	−0.105846	−	0.994382i	$-0.533755\pi$
$457$	−22.5392	−	14.4851i	−1.05434	−	0.677582i	−0.948492	+	0.316800i	$0.897392\pi$
$458$	8.29686	+	8.62206i	0.387687	+	0.402882i
$459$		−	7.42809i		−	0.346714i
$460$	7.97654	−	0.117747i	0.371908	−	0.00548998i
$461$			24.1988i			1.12705i	0.826099	+	0.563525i	$0.190555\pi$
$461$			24.1988i			1.12705i	−0.826099	+	0.563525i	$0.809445\pi$
$462$	−13.1880	+	12.6906i	−0.613562	+	0.590420i
$463$	9.44766	+	6.07164i	0.439070	+	0.282173i	0.741442	−	0.671017i	$-0.234142\pi$
$463$	9.44766	+	6.07164i	0.439070	+	0.282173i	−0.302372	+	0.953190i	$0.597779\pi$
$464$	−27.8914	+	1.84141i	−1.29483	+	0.0854852i
$465$	2.25235	−	4.93195i	0.104450	−	0.228714i
$466$	−16.9864	+	3.35464i	−0.786878	+	0.155400i
$467$	−5.40475	+	18.4069i	−0.250102	+	0.851770i	0.734745	+	0.678344i	$0.237302\pi$
$467$	−5.40475	+	18.4069i	−0.250102	+	0.851770i	−0.984847	+	0.173426i	$0.944516\pi$
$468$	2.82031	+	3.51946i	0.130369	+	0.162687i
$469$	−3.08738	+	1.40996i	−0.142562	+	0.0651059i
$470$	−7.40440	+	2.60073i	−0.341539	+	0.119963i
$471$	5.53663	−	6.38961i	0.255115	−	0.294418i
$472$	−10.5782	+	16.9683i	−0.486902	+	0.781030i
$473$	−5.35795	+	1.57324i	−0.246359	+	0.0723375i
$474$	3.48101	+	6.67694i	0.159888	+	0.306682i
$475$	−13.9502	−	21.7069i	−0.640079	−	0.995982i
$476$	55.7773	+	10.2211i	2.55655	+	0.468482i
$477$	9.62275	−	1.38354i	0.440596	−	0.0633481i
$478$	0.940181	+	0.371403i	0.0430029	+	0.0169876i
$479$	−0.371521	+	2.58399i	−0.0169752	+	0.118065i	−0.996547	−	0.0830288i	$-0.973541\pi$
$479$	−0.371521	+	2.58399i	−0.0169752	+	0.118065i	0.979572	+	0.201094i	$0.0644497\pi$
$480$	1.43656	−	4.48014i	0.0655696	−	0.204489i
$481$	−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
$486$	−1.22797	−	0.701489i	−0.0557019	−	0.0318202i
$487$	0.409020	−	2.84480i	0.0185345	−	0.128910i	−0.978453	−	0.206468i	$-0.933803\pi$
$487$	0.409020	−	2.84480i	0.0185345	−	0.128910i	0.996988	+	0.0775578i	$0.0247122\pi$
$488$	2.92486	−	10.4925i	0.132402	−	0.474974i
$489$	2.77308	+	19.2872i	0.125403	+	0.872196i
$490$	8.66184	+	2.05937i	0.391302	+	0.0930328i
$491$	−6.27959	−	9.77123i	−0.283394	−	0.440970i	0.670149	−	0.742227i	$-0.266230\pi$
$491$	−6.27959	−	9.77123i	−0.283394	−	0.440970i	−0.953543	+	0.301257i	$0.902594\pi$
$492$	−9.72253	+	5.73272i	−0.438326	+	0.258451i
$493$	−14.6241	−	49.8051i	−0.658636	−	2.24311i
$494$	−15.0677	−	11.7380i	−0.677926	−	0.528119i
$495$	−1.84665	+	2.13115i	−0.0830009	+	0.0957882i
$496$	22.9546	−	12.3715i	1.03069	−	0.555498i
$497$	4.73808	+	10.3749i	0.212532	+	0.465380i
$498$	−4.28756	−	5.96303i	−0.192130	−	0.267210i
$499$	−6.42345	+	21.8763i	−0.287553	+	0.979316i	0.681367	+	0.731942i	$0.261386\pi$
$499$	−6.42345	+	21.8763i	−0.287553	+	0.979316i	−0.968920	+	0.247374i	$0.920432\pi$
$500$	−15.0129	+	3.78807i	−0.671397	+	0.169408i
$501$	11.2824	+	5.15252i	0.504062	+	0.230197i
$502$	−0.932848	+	10.2660i	−0.0416350	+	0.458196i
$503$	−18.0183	−	11.5797i	−0.803397	−	0.516312i	0.0733256	−	0.997308i	$-0.476639\pi$
$503$	−18.0183	−	11.5797i	−0.803397	−	0.516312i	−0.876723	+	0.480996i	$0.840275\pi$
$504$	6.95715	−	8.25555i	0.309896	−	0.367731i
$505$	−13.0526			−0.580835
$506$	−11.7000	−	19.7968i	−0.520128	−	0.880077i
$507$			7.91482i			0.351509i
$508$	10.5589	+	9.88482i	0.468477	+	0.438568i
$509$	−6.40040	+	9.95922i	−0.283693	+	0.441435i	−0.953629	−	0.300984i	$-0.902685\pi$
$509$	−6.40040	+	9.95922i	−0.283693	+	0.441435i	0.669936	+	0.742419i	$0.266321\pi$
$510$	8.70111	+	0.790647i	0.385291	+	0.0350104i
$511$	−18.8280	+	41.2276i	−0.832902	+	1.82380i
$512$	18.5150	−	13.0075i	0.818254	−	0.574857i
$513$	5.74659	+	1.68735i	0.253718	+	0.0744984i
$514$	20.9441	+	29.1285i	0.923804	+	1.28480i
$515$	11.0549	−	5.04861i	0.487138	−	0.222468i
$516$	3.04666	−	1.25221i	0.134122	−	0.0551254i
$517$	17.0968	+	14.8145i	0.751917	+	0.651539i
$518$	−23.3791	+	30.0109i	−1.02722	+	1.31860i
$519$	−3.09955	+	0.910111i	−0.136055	+	0.0399494i
$520$	−4.42282	+	2.92903i	−0.193953	+	0.128447i
$521$	2.17658	−	1.39880i	0.0953578	−	0.0612827i	−0.492093	−	0.870543i	$-0.663768\pi$
$521$	2.17658	−	1.39880i	0.0953578	−	0.0612827i	0.587451	+	0.809260i	$0.300132\pi$
$522$	−9.61457	−	2.28588i	−0.420818	−	0.100050i
$523$	11.1116	−	1.59760i	0.485874	−	0.0698582i	0.104975	−	0.994475i	$-0.466524\pi$
$523$	11.1116	−	1.59760i	0.485874	−	0.0698582i	0.380899	+	0.924617i	$0.375615\pi$
$524$	−32.7311	−	10.9936i	−1.42986	−	0.480256i
$525$	−16.2773	−	2.34032i	−0.710399	−	0.102140i
$526$	8.74032	−	15.3001i	0.381096	−	0.667117i
$527$	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
$532$	−20.5776	+	40.8292i	−0.892152	+	1.77017i
$533$	12.5965	+	1.81111i	0.545616	+	0.0784477i
$534$	−9.14653	+	23.1538i	−0.395809	+	1.00196i
$535$	1.05251	+	7.32037i	0.0455040	+	0.316487i
$536$	−2.49414	−	0.323682i	−0.107730	−	0.0139809i
$537$	−6.03174	+	3.87637i	−0.260289	+	0.167278i
$538$	5.44899	+	10.4517i	0.234923	+	0.450606i
$539$	−7.23058	−	24.6251i	−0.311443	−	1.06068i
$540$	0.952414	−	1.36375i	0.0409854	−	0.0586866i
$541$	3.73329	+	3.23491i	0.160507	+	0.139080i	0.731411	−	0.681937i	$-0.238862\pi$
$541$	3.73329	+	3.23491i	0.160507	+	0.139080i	−0.570905	+	0.821016i	$0.693407\pi$
$542$	−1.93154	−	5.49917i	−0.0829666	−	0.236209i
$543$	−8.82146	−	19.3163i	−0.378565	−	0.828942i
$544$	31.0672	+	28.2927i	1.33200	+	1.21304i
$545$	13.8479	+	4.06612i	0.593180	+	0.174173i
$546$	−11.9422	+	2.35845i	−0.511077	+	0.100932i
$547$	31.4439	+	14.3599i	1.34444	+	0.613986i	0.952087	−	0.305827i	$-0.0989330\pi$
$547$	31.4439	+	14.3599i	1.34444	+	0.613986i	0.392356	+	0.919814i	$0.371660\pi$
$548$	0.0201545	−	0.524087i	0.000860956	−	0.0223879i
$549$	2.08206	−	3.23975i	0.0888602	−	0.138269i
$550$	14.3239	+	14.8854i	0.610775	+	0.634715i
$551$	41.8527			1.78298
$552$	8.08051	+	10.8952i	0.343929	+	0.463731i
$553$	−20.3233			−0.864236
$554$	−17.1928	−	17.8667i	−0.730452	−	0.759083i
$555$	−3.16890	+	4.93091i	−0.134512	+	0.209305i
$556$	−17.2818	−	0.664594i	−0.732911	−	0.0281851i
$557$	29.6855	+	13.5569i	1.25782	+	0.574425i	0.929039	−	0.369982i	$-0.120636\pi$
$557$	29.6855	+	13.5569i	1.25782	+	0.574425i	0.328777	+	0.944408i	$0.393363\pi$
$558$	9.04465	−	1.78623i	0.382891	−	0.0756170i
$559$	−3.56355	−	1.04635i	−0.150722	−	0.0442561i
$560$	8.92986	+	9.02818i	0.377355	+	0.381510i
$561$	−10.4623	−	22.9093i	−0.441719	−	0.967231i
$562$	10.5638	+	30.0757i	0.445609	+	1.26867i
$563$	17.2392	+	14.9379i	0.726546	+	0.629555i	0.937518	−	0.347937i	$-0.113118\pi$
$563$	17.2392	+	14.9379i	0.726546	+	0.629555i	−0.210972	+	0.977492i	$0.567663\pi$
$564$	−10.9405	−	7.64058i	−0.460677	−	0.321726i
$565$	0.501953	+	1.70949i	0.0211173	+	0.0719189i
$566$	−0.628023	−	1.20461i	−0.0263978	−	0.0506337i
$567$	3.21107	−	2.06363i	0.134852	−	0.0866642i
$568$	−1.08771	+	8.38139i	−0.0456394	+	0.351675i
$569$	−3.01328	−	20.9578i	−0.126323	−	0.878596i	−0.950159	−	0.311767i	$-0.899079\pi$
$569$	−3.01328	−	20.9578i	−0.126323	−	0.878596i	0.823835	−	0.566829i	$-0.191830\pi$
$570$	−2.58820	+	6.55183i	−0.108408	+	0.274426i
$571$	28.3459	+	4.07552i	1.18624	+	0.170555i	0.707055	−	0.707159i	$-0.250024\pi$
$571$	28.3459	+	4.07552i	1.18624	+	0.170555i	0.479184	+	0.877714i	$0.340933\pi$
$572$	13.6553	+	6.88218i	0.570957	+	0.287758i
$573$	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	0.877121	−	0.480270i	$-0.159461\pi$
$577$	6.65166	+	7.67643i	0.276912	+	0.319574i	−0.600209	+	0.799844i	$0.704916\pi$
$578$	−26.7804	+	46.8797i	−1.11392	+	1.94994i
$579$	15.8025	+	2.27206i	0.656729	+	0.0944234i
$580$	3.70101	−	11.0190i	0.153676	−	0.457539i
$581$	19.6211	−	2.82109i	0.814020	−	0.117038i
$582$	23.7369	+	5.64350i	0.983927	+	0.233930i
$583$	27.7292	−	17.8205i	1.14843	−	0.738050i
$584$	−28.0013	+	18.5440i	−1.15870	+	0.767355i
$585$	−1.79955	+	0.528395i	−0.0744021	+	0.0218464i
$586$	5.65500	−	7.25911i	0.233606	−	0.299871i
$587$	−14.3191	−	12.4076i	−0.591014	−	0.512116i	0.307218	−	0.951639i	$-0.400602\pi$
$587$	−14.3191	−	12.4076i	−0.591014	−	0.512116i	−0.898231	+	0.439523i	$0.855147\pi$
$588$	5.75514	+	14.0024i	0.237338	+	0.577450i
$589$	−35.5156	+	16.2194i	−1.46339	+	0.668310i
$590$	−4.85426	−	6.75118i	−0.199847	−	0.277942i
$591$	8.59165	+	2.52274i	0.353413	+	0.103771i
$592$	−26.4660	+	9.70658i	−1.08774	+	0.398938i
$593$	−9.35760	+	20.4903i	−0.384271	+	0.841435i	0.614355	+	0.789029i	$0.289416\pi$
$593$	−9.35760	+	20.4903i	−0.384271	+	0.841435i	−0.998626	+	0.0524056i	$0.983311\pi$
$594$	−4.77527	−	0.433916i	−0.195932	−	0.0178038i
$595$	−12.7490	+	19.8378i	−0.522658	+	0.813272i
$596$	7.31154	−	7.81017i	0.299492	−	0.319917i
$597$		−	3.69675i		−	0.151298i
$598$	0.572191	−	15.2837i	0.0233986	−	0.624996i
$599$	28.4392			1.16199			0.580997	−	0.813906i	$-0.302663\pi$
$599$	28.4392			1.16199			0.580997	+	0.813906i	$0.302663\pi$
$600$	−9.31809	−	7.85257i	−0.380409	−	0.320580i
$601$	37.1777	+	23.8927i	1.51651	+	0.974602i	0.992414	+	0.122944i	$0.0392334\pi$
$601$	37.1777	+	23.8927i	1.51651	+	0.974602i	0.524097	+	0.851659i	$0.324403\pi$
$602$	−0.804541	+	8.85401i	−0.0327906	+	0.360863i
$603$	−0.808850	−	0.369389i	−0.0329389	−	0.0150427i
$604$	−2.46567	−	9.77196i	−0.100327	−	0.397615i
$605$	−0.116163	+	0.395613i	−0.00472268	+	0.0160840i
$606$	−12.9568	−	18.0199i	−0.526332	−	0.732010i
$607$	−3.34591	−	7.32651i	−0.135806	−	0.297374i	0.829495	−	0.558515i	$-0.188629\pi$
$607$	−3.34591	−	7.32651i	−0.135806	−	0.297374i	−0.965301	+	0.261141i	$0.915901\pi$
$608$	−28.9452	+	17.6076i	−1.17388	+	0.714082i
$609$	17.4673	−	20.1584i	0.707812	−	0.816858i
$610$	3.57336	+	2.78372i	0.144681	+	0.112710i
$611$	4.23896	+	14.4366i	0.171490	+	0.584041i
$612$	7.54566	+	12.7972i	0.305015	+	0.517297i
$613$	3.79315	+	5.90226i	0.153204	+	0.238390i	0.909369	−	0.415991i	$-0.136565\pi$
$613$	3.79315	+	5.90226i	0.153204	+	0.238390i	−0.756164	+	0.654382i	$0.772929\pi$
$614$	39.2958	+	9.34266i	1.58585	+	0.377039i
$615$	−0.667973	−	4.64585i	−0.0269353	−	0.187339i
$616$	9.82905	−	35.2603i	0.396024	−	1.42068i
$617$	−1.50775	+	10.4866i	−0.0606997	+	0.422176i	0.936702	+	0.350129i	$0.113862\pi$
$617$	−1.50775	+	10.4866i	−0.0606997	+	0.422176i	−0.997401	+	0.0720469i	$0.977047\pi$
$618$	17.9436	+	10.2504i	0.721799	+	0.412333i
$619$	31.5068	−	27.3008i	1.26636	−	1.09731i	0.275663	−	0.961254i	$-0.411102\pi$
$619$	31.5068	−	27.3008i	1.26636	−	1.09731i	0.990701	−	0.136057i	$-0.0434430\pi$
$620$	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
$624$	−8.43403	−	3.19844i	−0.337632	−	0.128040i
$625$	−2.14932	+	14.9488i	−0.0859727	+	0.597953i
$626$	−5.64333	−	2.22931i	−0.225553	−	0.0891010i
$627$	20.0999	−	2.88993i	0.802713	−	0.115413i
$628$	−3.04785	+	16.6324i	−0.121622	+	0.663705i
$629$	−28.3021	−	44.0389i	−1.12848	−	1.75594i
$630$	2.07550	+	3.98103i	0.0826900	+	0.158608i
$631$	3.11870	−	0.915733i	0.124153	−	0.0364547i	−0.219066	−	0.975710i	$-0.570301\pi$
$631$	3.11870	−	0.915733i	0.124153	−	0.0364547i	0.343219	+	0.939255i	$0.388483\pi$
$632$	−12.7798	−	7.96703i	−0.508352	−	0.316911i
$633$	−8.26218	+	9.53507i	−0.328392	+	0.378985i
$634$	−0.403638	+	0.141775i	−0.0160305	+	0.00563059i
$635$	−5.47123	+	2.49863i	−0.217119	+	0.0991551i
$636$	−15.1728	+	12.1587i	−0.601640	+	0.482122i
$637$	4.80903	−	16.3781i	0.190541	−	0.648923i
$638$	−32.8723	+	6.49195i	−1.30143	+	0.257019i
$639$	−1.24131	+	2.71809i	−0.0491054	+	0.107526i
$640$	2.07612	+	9.17775i	0.0820659	+	0.362782i
$641$	3.34401	+	2.14907i	0.132081	+	0.0848831i	0.605013	−	0.796216i	$-0.293168\pi$
$641$	3.34401	+	2.14907i	0.132081	+	0.0848831i	−0.472932	+	0.881099i	$0.656804\pi$
$642$	−9.06142	+	8.71965i	−0.357626	+	0.344137i
$643$			10.5695i			0.416821i	0.978041	+	0.208410i	$0.0668290\pi$
$643$			10.5695i			0.416821i	−0.978041	+	0.208410i	$0.933171\pi$
$644$	−36.1579	+	5.74466i	−1.42482	+	0.226371i
$645$			1.36980i			0.0539357i
$646$	−43.6251	−	45.3350i	−1.71641	−	1.78368i
$647$	−12.0761	−	7.76084i	−0.474760	−	0.305110i	0.281291	−	0.959623i	$-0.409237\pi$
$647$	−12.0761	−	7.76084i	−0.474760	−	0.305110i	−0.756051	+	0.654513i	$0.772874\pi$
$648$	2.82816	−	0.0388720i	0.111101	−	0.00152704i
$649$	−9.95725	+	21.8033i	−0.390856	+	0.855856i
$650$	2.66200	+	13.4792i	0.104412	+	0.528697i
$651$	−7.01043	+	23.8753i	−0.274760	+	0.935747i
$652$	−24.3700	−	30.4113i	−0.954401	−	1.19100i
$653$	−17.3101	+	7.90526i	−0.677397	+	0.309357i	−0.724243	−	0.689545i	$-0.757810\pi$
$653$	−17.3101	+	7.90526i	−0.677397	+	0.309357i	0.0468455	+	0.998902i	$0.485083\pi$
$654$	8.13269	+	23.1541i	0.318013	+	0.905398i
$655$	9.40283	−	10.8514i	0.367399	−	0.424001i
$656$	10.9267	−	19.7528i	0.426615	−	0.771219i
$657$	−11.3931	+	3.34531i	−0.444487	+	0.130513i
$658$	31.9371	−	16.6504i	1.24504	−	0.649099i
$659$	2.64373	+	4.11372i	0.102985	+	0.160248i	0.888922	−	0.458059i	$-0.151455\pi$
$659$	2.64373	+	4.11372i	0.102985	+	0.160248i	−0.785937	+	0.618307i	$0.787819\pi$
$660$	1.01656	−	5.54746i	0.0395696	−	0.215935i
$661$	29.4921	−	4.24033i	1.14711	−	0.164930i	0.457568	−	0.889175i	$-0.348721\pi$
$661$	29.4921	−	4.24033i	1.14711	−	0.164930i	0.689543	+	0.724245i	$0.257812\pi$
$662$	−14.2475	+	36.0665i	−0.553745	+	1.40177i
$663$	2.38386	−	16.5801i	0.0925814	−	0.643918i
$664$	13.4441	+	5.91778i	0.521732	+	0.229654i
$665$	−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
$670$	0.518789	−	0.908152i	0.0200426	−	0.0350850i
$671$	1.85825	−	12.9244i	0.0717368	−	0.498941i
$672$	−3.59967	+	21.2901i	−0.138860	+	0.821282i
$673$	2.14696	+	14.9324i	0.0827592	+	0.575603i	0.988436	+	0.151635i	$0.0484540\pi$
$673$	2.14696	+	14.9324i	0.0827592	+	0.575603i	−0.905677	+	0.423968i	$0.860637\pi$
$674$	4.59891	−	19.3433i	0.177143	−	0.745077i
$675$	−2.32923	−	3.62435i	−0.0896520	−	0.139501i
$676$	−8.04009	−	13.6358i	−0.309234	−	0.524453i
$677$	4.21888	+	14.3682i	0.162145	+	0.552214i	0.999980	+	0.00629112i	$0.00200254\pi$
$677$	4.21888	+	14.3682i	0.162145	+	0.552214i	−0.837836	+	0.545923i	$0.816179\pi$
$678$	−1.86179	+	2.38991i	−0.0715017	+	0.0917840i
$679$	−43.1242	+	49.7680i	−1.65495	+	1.90992i
$680$	−15.7936	+	7.47669i	−0.605656	+	0.286718i
$681$	1.95386	+	4.27836i	0.0748721	+	0.163947i
$682$	25.3791	−	18.2482i	0.971817	−	0.698759i
$683$	2.40861	−	8.20297i	0.0921629	−	0.313878i	−0.900490	−	0.434877i	$-0.856792\pi$
$683$	2.40861	−	8.20297i	0.0921629	−	0.313878i	0.992653	+	0.120999i	$0.0386099\pi$
$684$	−11.6144	+	2.93055i	−0.444087	+	0.112052i
$685$	0.198394	+	0.0906034i	0.00758024	+	0.00346178i
$686$	−3.06161	−	0.278200i	−0.116893	−	0.0106217i
$687$	−7.11786	−	4.57437i	−0.271563	−	0.174523i
$688$	−3.97681	+	5.25221i	−0.151614	+	0.200238i
$689$	21.9228			0.835192
$690$	−5.46805	+	1.38562i	−0.208165	+	0.0527496i
$691$			6.72962i			0.256007i	0.991774	+	0.128003i	$0.0408568\pi$
$691$			6.72962i			0.256007i	−0.991774	+	0.128003i	$0.959143\pi$
$692$	4.41544	−	4.71657i	0.167850	−	0.179297i
$693$	6.99681	−	10.8872i	0.265787	−	0.413572i
$694$	0.816717	−	8.98801i	0.0310022	−	0.341180i
$695$	2.98765	−	6.54204i	0.113328	−	0.248154i
$696$	18.8862	−	5.82859i	0.715879	−	0.220932i
$697$	40.2216	+	11.8101i	1.52350	+	0.447341i
$698$	22.6072	−	16.2551i	0.855695	−	0.615265i
$699$	11.1368	−	5.08599i	0.421232	−	0.192370i
$700$	30.4201	−	12.5030i	1.14977	−	0.472568i
$701$	8.03903	+	6.96586i	0.303630	+	0.263097i	0.793327	−	0.608796i	$-0.208347\pi$
$701$	8.03903	+	6.96586i	0.303630	+	0.263097i	−0.489697	+	0.871893i	$0.662893\pi$
$702$	−2.51581	−	1.95987i	−0.0949531	−	0.0739704i
$703$	40.4988	−	11.8915i	1.52744	−	0.448497i
$704$	20.0032	−	18.3193i	0.753901	−	0.690436i
$705$	4.66835	−	3.00017i	0.175820	−	0.112993i
$706$	−6.94996	+	29.2320i	−0.261565	+	1.10016i
$707$	59.2938	−	8.52516i	2.22997	−	0.320622i
$708$	4.50180	−	13.4032i	0.169188	−	0.503722i
$709$	10.7071	+	1.53944i	0.402113	+	0.0578151i	0.340404	−	0.940279i	$-0.389436\pi$
$709$	10.7071	+	1.53944i	0.402113	+	0.0578151i	0.0617083	+	0.998094i	$0.480345\pi$
$710$	−3.05179	−	1.74336i	−0.114531	−	0.0654270i
$711$	−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
$716$	6.45386	−	12.8055i	0.241192	−	0.478563i
$717$	−0.707525	−	0.101727i	−0.0264230	−	0.00379905i
$718$	3.31943	+	1.31129i	0.123880	+	0.0489368i
$719$	0.202660	+	1.40953i	0.00755794	+	0.0525667i	0.993251	−	0.115981i	$-0.0370013\pi$
$719$	0.202660	+	1.40953i	0.00755794	+	0.0525667i	−0.985693	+	0.168548i	$0.946092\pi$
$720$	−0.255496	+	3.31698i	−0.00952177	+	0.123617i
$721$	−46.9214	+	30.1546i	−1.74745	+	1.12301i
$722$	21.1559	−	11.0296i	0.787341	−	0.410479i
$723$	−4.18126	−	14.2401i	−0.155503	−	0.529594i
$724$	34.8198	+	24.3173i	1.29407	+	0.903747i
$725$	−22.7529	−	19.7155i	−0.845020	−	0.732214i
$726$	−0.661477	+	0.232338i	−0.0245497	+	0.00862288i
$727$	−18.1118	−	39.6593i	−0.671729	−	1.47088i	−0.871175	−	0.490972i	$-0.836642\pi$
$727$	−18.1118	−	39.6593i	−0.671729	−	1.47088i	0.199446	−	0.979909i	$-0.436086\pi$
$728$	18.1783	−	16.1943i	0.673734	−	0.600202i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−2.70595	−	13.7017i	−0.100152	−	0.507123i
$731$	−11.1284	−	5.08215i	−0.411597	−	0.187970i
$732$	−0.295979	+	7.69651i	−0.0109397	+	0.284471i
$733$	6.68055	−	10.3951i	0.246752	−	0.383953i	−0.695680	−	0.718352i	$-0.744897\pi$
$733$	6.68055	−	10.3951i	0.246752	−	0.383953i	0.942432	+	0.334399i	$0.108533\pi$
$734$	−1.25938	+	1.21188i	−0.0464846	+	0.0447314i
$735$	−6.29558			−0.232216
$736$	−24.9889	−	10.5620i	−0.921102	−	0.389321i
$737$	−3.01489			−0.111055
$738$	5.75081	−	5.53390i	0.211690	−	0.203706i
$739$	26.1367	−	40.6695i	0.961455	−	1.49605i	0.0958075	−	0.995400i	$-0.469457\pi$
$739$	26.1367	−	40.6695i	0.961455	−	1.49605i	0.865648	−	0.500654i	$-0.166907\pi$
$740$	0.450481	−	11.7141i	0.0165600	−	0.430619i
$741$	12.2854	+	5.61053i	0.451314	+	0.206108i
$742$	−10.1676	−	51.4839i	−0.373263	−	1.89003i
$743$	−14.3370	−	4.20973i	−0.525974	−	0.154440i	0.00795634	−	0.999968i	$-0.497467\pi$
$743$	−14.3370	−	4.20973i	−0.525974	−	0.154440i	−0.533930	+	0.845528i	$0.679286\pi$
$744$	−13.7678	+	12.2651i	−0.504751	+	0.449662i
$745$	1.84817	+	4.04693i	0.0677117	+	0.148268i
$746$	3.12387	−	1.09723i	0.114373	−	0.0401725i
$747$	3.92484	+	3.40089i	0.143602	+	0.124432i
$748$	41.2965	+	28.8406i	1.50995	+	1.05452i
$749$	−9.56242	−	32.5666i	−0.349403	−	1.18996i
$750$	9.70827	−	5.06139i	0.354496	−	0.184816i
$751$	−10.9686	+	7.04907i	−0.400249	+	0.257224i	−0.725245	−	0.688491i	$-0.758273\pi$
$751$	−10.9686	+	7.04907i	−0.400249	+	0.257224i	0.324996	+	0.945715i	$0.394637\pi$
$752$	26.6099	+	2.04967i	0.970365	+	0.0747438i
$753$	−1.03735	−	7.21490i	−0.0378030	−	0.262926i
$754$	−20.7269	−	8.18783i	−0.754830	−	0.298183i
$755$	4.14839	+	0.596448i	0.150975	+	0.0217070i
$756$	−3.43579	+	6.81714i	−0.124958	+	0.247937i
$757$	−25.0027	+	21.6650i	−0.908738	+	0.787426i	−0.977659	−	0.210196i	$-0.932590\pi$
$757$	−25.0027	+	21.6650i	−0.908738	+	0.787426i	0.0689212	+	0.997622i	$0.478044\pi$
$758$	−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	0.530228	−	0.847855i	$-0.322106\pi$
$761$	−10.6057	−	12.2397i	−0.384457	−	0.443687i	−0.914685	+	0.404168i	$0.867561\pi$
$762$	−8.88055	−	5.07309i	−0.321708	−	0.183778i
$763$	−65.5623	−	9.42643i	−2.37351	−	0.341260i
$764$	−11.6798	+	34.7743i	−0.422561	+	1.25809i
$765$	−6.11508	+	0.879215i	−0.221091	+	0.0317881i
$766$	12.3528	−	51.9566i	0.446324	−	1.87727i
$767$	−13.4112	+	8.61888i	−0.484252	+	0.311210i
$768$	−10.6095	+	11.9765i	−0.382839	+	0.432166i
$769$	−10.9513	+	3.21560i	−0.394914	+	0.115957i	−0.473159	−	0.880977i	$-0.656887\pi$
$769$	−10.9513	+	3.21560i	−0.394914	+	0.115957i	0.0782450	+	0.996934i	$0.475068\pi$
$770$	12.0083	+	9.35475i	0.432751	+	0.337122i
$771$	−19.1723	−	16.6129i	−0.690472	−	0.598298i
$772$	−29.5328	+	12.1383i	−1.06291	+	0.436866i
$773$	−7.85729	+	3.58830i	−0.282607	+	0.129062i	−0.551676	−	0.834059i	$-0.686011\pi$
$773$	−7.85729	+	3.58830i	−0.282607	+	0.129062i	0.269069	+	0.963121i	$0.413284\pi$
$774$	−1.89109	+	1.35974i	−0.0679737	+	0.0488747i
$775$	26.9482	+	7.91271i	0.968008	+	0.284233i
$776$	−46.6272	+	14.3899i	−1.67382	+	0.516568i
$777$	11.1747	−	24.4692i	0.400891	−	0.877829i
$778$	3.09809	−	34.0947i	0.111072	−	1.22235i
$779$	−18.2733	+	28.4339i	−0.654710	+	1.01875i
$780$	2.56353	−	2.73836i	0.0917891	−	0.0980489i
$781$			10.1313i			0.362528i
$782$	9.03038	−	49.5638i	0.322926	−	1.77240i
$783$	6.98803			0.249732
$784$	−24.1391	−	18.2774i	−0.862111	−	0.652763i
$785$	−5.91550	−	3.80166i	−0.211133	−	0.135687i
$786$	24.3148	+	2.20942i	0.867281	+	0.0788075i
$787$	−33.2499	−	15.1847i	−1.18523	−	0.541277i	−0.277458	−	0.960738i	$-0.589492\pi$
$787$	−33.2499	−	15.1847i	−1.18523	−	0.541277i	−0.907774	+	0.419460i	$0.862219\pi$
$788$	−17.3645	+	4.38143i	−0.618584	+	0.156082i
$789$	−3.51030	+	11.9550i	−0.124970	+	0.425608i
$790$	5.08468	−	3.65600i	0.180905	−	0.130075i
$791$	−3.39674	−	7.43782i	−0.120774	−	0.264459i
$792$	8.66770	−	4.10329i	0.307993	−	0.145804i
$793$	5.68705	−	6.56320i	0.201953	−	0.233066i
$794$	−24.6179	+	31.6010i	−0.873655	+	1.12148i
$795$	−2.27797	−	7.75804i	−0.0807912	−	0.275149i
$796$	3.75526	+	6.36882i	0.133102	+	0.225737i
$797$	−26.3407	−	40.9870i	−0.933037	−	1.45183i	−0.891668	−	0.452690i	$-0.850465\pi$
$797$	−26.3407	−	40.9870i	−0.933037	−	1.45183i	−0.0413685	−	0.999144i	$-0.513172\pi$
$798$	7.47807	−	31.4533i	0.264721	−	1.11343i
$799$	7.05336	+	49.0572i	0.249530	+	1.73552i
$800$	24.0302	+	4.06296i	0.849596	+	0.143647i
$801$	2.50522	−	17.4242i	0.0885176	−	0.615654i
$802$	14.6366	−	25.6217i	0.516837	−	0.904734i
$803$	−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
$808$	40.6272	+	17.8832i	1.42926	+	0.629128i
$809$	−3.24940	+	22.6001i	−0.114243	+	0.794576i	0.849470	+	0.527636i	$0.176922\pi$
$809$	−3.24940	+	22.6001i	−0.114243	+	0.794576i	−0.963713	+	0.266940i	$0.913988\pi$
$810$	−0.432144	+	1.09394i	−0.0151840	+	0.0384372i
$811$	−28.1714	+	4.05044i	−0.989232	+	0.142230i	−0.617889	−	0.786266i	$-0.712012\pi$
$811$	−28.1714	+	4.05044i	−0.989232	+	0.142230i	−0.371343	+	0.928496i	$0.621103\pi$
$812$	−9.61555	+	52.4729i	−0.337440	+	1.84144i
$813$	2.22819	+	3.46713i	0.0781461	+	0.121598i
$814$	−29.9644	+	15.6219i	−1.05025	+	0.547547i
$815$	15.5497	−	4.56580i	0.544682	−	0.159933i
$816$	−25.9996	−	14.3822i	−0.910167	−	0.503477i
$817$	6.45960	−	7.45478i	0.225993	−	0.260810i
$818$	7.56254	+	21.5309i	0.264418	+	0.752810i
$819$	7.82963	−	3.57567i	0.273590	−	0.124944i
$820$	5.87018	+	7.32540i	0.204996	+	0.255814i
$821$	−11.7705	+	40.0866i	−0.410793	+	1.39903i	0.451341	+	0.892352i	$0.350946\pi$
$821$	−11.7705	+	40.0866i	−0.410793	+	1.39903i	−0.862134	+	0.506681i	$0.830872\pi$
$822$	0.0718532	+	0.363832i	0.00250617	+	0.0126901i
$823$	−22.3354	+	48.9078i	−0.778564	+	1.70482i	−0.0717444	+	0.997423i	$0.522857\pi$
$823$	−22.3354	+	48.9078i	−0.778564	+	1.70482i	−0.706819	+	0.707394i	$0.749871\pi$
$824$	−41.3262	+	0.568014i	−1.43967	+	0.0197877i
$825$	−12.2885	−	7.89733i	−0.427830	−	0.274950i
$826$	26.4607	+	27.4979i	0.920687	+	0.956774i
$827$		−	18.2798i		−	0.635650i	−0.948149	−	0.317825i	$-0.897048\pi$
$827$		−	18.2798i		−	0.635650i	0.948149	−	0.317825i	$-0.102952\pi$
$828$	−7.34082	−	6.17353i	−0.255111	−	0.214545i
$829$			18.6361i			0.647259i	0.946184	+	0.323629i	$0.104903\pi$
$829$			18.6361i			0.647259i	−0.946184	+	0.323629i	$0.895097\pi$
$830$	−4.40149	+	4.23548i	−0.152778	+	0.147016i
$831$	14.7497	+	9.47905i	0.511661	+	0.328825i
$832$	17.7794	−	3.05720i	0.616388	−	0.105989i
$833$	23.3575	−	51.1459i	0.809290	−	1.77210i
$834$	11.9974	−	2.36936i	0.415435	−	0.0820443i
$835$	2.90631	−	9.89799i	0.100577	−	0.342534i
$836$	−31.6928	+	25.3969i	−1.09612	+	0.878369i
$837$	−5.92995	+	2.70812i	−0.204969	+	0.0936062i
$838$	−11.2839	+	3.96338i	−0.389796	+	0.136913i
$839$	12.5944	−	14.5347i	0.434808	−	0.501795i	−0.495483	−	0.868618i	$-0.665009\pi$
$839$	12.5944	−	14.5347i	0.434808	−	0.501795i	0.930291	+	0.366823i	$0.119554\pi$
$840$	−7.61975	−	4.75022i	−0.262906	−	0.163898i
$841$	19.0292	−	5.58749i	0.656181	−	0.192672i
$842$	−22.0651	−	42.3231i	−0.760414	−	1.45855i
$843$	−12.1863	−	18.9622i	−0.419718	−	0.653094i
$844$	4.54823	−	24.8201i	0.156557	−	0.854344i
$845$	6.51577	−	0.936826i	0.224149	−	0.0322278i
$846$	8.77596	+	3.46680i	0.301724	+	0.119191i
$847$	0.269298	−	1.87301i	0.00925320	−	0.0643574i
$848$	13.7888	−	36.3601i	0.473510	−	1.24861i
$849$	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	$-0.748100\pi$
$853$	−2.88640	+	2.50108i	−0.0988283	+	0.0856352i	0.604045	+	0.796950i	$0.293555\pi$
$854$	−18.0507	−	10.3116i	−0.617684	−	0.352857i
$855$	0.708903	−	4.93053i	0.0242440	−	0.168620i
$856$	6.75350	−	24.2272i	0.230830	−	0.828069i
$857$	−0.636559	−	4.42737i	−0.0217445	−	0.151236i	0.976057	−	0.217517i	$-0.0697957\pi$
$857$	−0.636559	−	4.42737i	−0.0217445	−	0.151236i	−0.997801	+	0.0662809i	$0.978887\pi$
$858$	−10.5195	−	2.50104i	−0.359131	−	0.0853841i
$859$	−8.66434	−	13.4820i	−0.295623	−	0.459999i	0.661390	−	0.750042i	$-0.269967\pi$
$859$	−8.66434	−	13.4820i	−0.295623	−	0.459999i	−0.957014	+	0.290043i	$0.906330\pi$
$860$	−1.39148	−	2.35991i	−0.0474490	−	0.0804722i
$861$	6.06876	+	20.6683i	0.206823	+	0.704374i
$862$	7.68041	+	5.98320i	0.261596	+	0.203789i
$863$	−3.99224	+	4.60730i	−0.135898	+	0.156834i	−0.819619	−	0.572909i	$-0.805815\pi$
$863$	−3.99224	+	4.60730i	−0.135898	+	0.156834i	0.683721	+	0.729743i	$0.260360\pi$
$864$	−4.83291	+	2.93989i	−0.164419	+	0.100017i
$865$	1.11611	+	2.44394i	0.0379489	+	0.0830965i
$866$	5.92490	+	8.24020i	0.201336	+	0.280013i
$867$	10.7556	−	36.6301i	0.365278	−	1.24402i
$868$	−12.1755	−	48.2542i	−0.413265	−	1.63785i
$869$	−16.4213	−	7.49935i	−0.557054	−	0.254398i
$870$	−0.743807	+	8.18563i	−0.0252174	+	0.277519i
$871$	−1.68687	−	1.08409i	−0.0571575	−	0.0367329i
$872$	−37.5317	−	31.6289i	−1.27098	−	1.07109i
$873$	−17.2524			−0.583905
$874$	36.2927	+	18.2450i	1.22762	+	0.617146i
$875$			29.5501i			0.998977i
$876$	16.2299	−	17.3368i	0.548359	−	0.585755i
$877$	7.45059	−	11.5933i	0.251588	−	0.391479i	−0.692370	−	0.721542i	$-0.743434\pi$
$877$	7.45059	−	11.5933i	0.251588	−	0.391479i	0.943959	+	0.330063i	$0.107070\pi$
$878$	3.76577	+	0.342185i	0.127088	+	0.0115482i
$879$	−2.70297	+	5.91868i	−0.0911690	+	0.199632i
$880$	3.88392	+	10.5899i	0.130927	+	0.356986i
$881$	−33.4258	−	9.81471i	−1.12615	−	0.330666i	−0.334954	−	0.942235i	$-0.608721\pi$
$881$	−33.4258	−	9.81471i	−1.12615	−	0.330666i	−0.791192	+	0.611568i	$0.790539\pi$
$882$	−6.24933	−	8.69141i	−0.210426	−	0.292655i
$883$	41.4593	−	18.9338i	1.39522	−	0.637174i	0.431014	−	0.902345i	$-0.358156\pi$
$883$	41.4593	−	18.9338i	1.39522	−	0.637174i	0.964201	+	0.265171i	$0.0854285\pi$
$884$	12.7356	+	30.9861i	0.428344	+	1.04217i
$885$	4.44360	+	3.85040i	0.149370	+	0.129430i
$886$	−18.0127	+	23.1223i	−0.605149	+	0.776808i
$887$	−35.3915	+	10.3919i	−1.18833	+	0.348926i	−0.815380	−	0.578926i	$-0.803472\pi$
$887$	−35.3915	+	10.3919i	−1.18833	+	0.348926i	−0.372951	+	0.927851i	$0.621654\pi$
$888$	16.6192	−	11.0061i	0.557703	−	0.369342i
$889$	23.2221	−	14.9239i	0.778843	−	0.500532i
$890$	20.1437	+	4.78920i	0.675217	+	0.160534i
$891$	3.35603	−	0.482524i	0.112431	−	0.0161652i
$892$	−0.876079	+	2.60835i	−0.0293333	+	0.0873339i
$893$	−39.5543	−	5.68705i	−1.32363	−	0.190310i
$894$	−3.75243	+	6.56871i	−0.125500	+	0.219690i
$895$	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
$900$	7.69454	+	3.87799i	0.256485	+	0.129266i
$901$	71.4787	+	10.2771i	2.38130	+	0.342379i
$902$	9.94191	−	25.1672i	0.331029	−	0.837977i
$903$	−0.894666	−	6.22254i	−0.0297726	−	0.207073i
$904$	0.779784	−	6.00864i	0.0259352	−	0.199844i
$905$	−14.8577	+	9.54849i	−0.493888	+	0.317403i
$906$	3.29448	+	6.31916i	0.109452	+	0.209940i
$907$	−3.70455	−	12.6165i	−0.123008	−	0.418925i	0.874847	−	0.484400i	$-0.160962\pi$
$907$	−3.70455	−	12.6165i	−0.123008	−	0.418925i	−0.997854	+	0.0654745i	$0.979144\pi$
$908$	−7.71222	−	5.38604i	−0.255939	−	0.178742i
$909$	11.8606	+	10.2773i	0.393393	+	0.340877i
$910$	3.35508	+	9.55206i	0.111220	+	0.316648i
$911$	16.6699	+	36.5020i	0.552299	+	1.20937i	0.955700	+	0.294343i	$0.0951009\pi$
$911$	16.6699	+	36.5020i	0.552299	+	1.20937i	−0.403400	+	0.915024i	$0.632172\pi$
$912$	17.0325	−	16.8470i	0.564002	−	0.557860i
$913$	16.8949	+	4.96078i	0.559138	+	0.164178i
$914$	−37.1722	+	7.34113i	−1.22955	+	0.242823i
$915$	−2.91352	−	1.33056i	−0.0963180	−	0.0439870i
$916$	16.9095	+	0.650279i	0.558707	+	0.0214858i
$917$	−35.6265	+	55.4359i	−1.17649	+	1.83065i
$918$	−7.28397	−	7.56947i	−0.240407	−	0.249830i
$919$	−57.3329			−1.89124			−0.945619	−	0.325276i	$-0.894543\pi$
$919$	−57.3329			−1.89124			−0.945619	+	0.325276i	$0.894543\pi$
$920$	8.01289	−	7.94177i	0.264177	−	0.261832i
$921$	−28.5609			−0.941113
$922$	23.7293	+	24.6593i	0.781482	+	0.812112i
$923$	−3.64301	+	5.66863i	−0.119911	+	0.186585i
$924$	−0.994644	+	25.8643i	−0.0327214	+	0.850872i
$925$	−27.6186	−	12.6130i	−0.908092	−	0.414712i
$926$	15.5813	−	3.07715i	0.512034	−	0.101121i
$927$	−14.0205	−	4.11679i	−0.460494	−	0.135213i
$928$	−26.6166	+	29.2267i	−0.873732	+	0.959414i
$929$	8.16755	+	17.8844i	0.267969	+	0.586769i	0.995004	−	0.0998301i	$-0.0318299\pi$
$929$	8.16755	+	17.8844i	0.267969	+	0.586769i	−0.727036	+	0.686599i	$0.759103\pi$
$930$	−2.54104	−	7.23446i	−0.0833241	−	0.237227i
$931$	34.2621	+	29.6883i	1.12289	+	0.972994i
$932$	−14.0201	+	20.0753i	−0.459244	+	0.657588i
$933$	−1.86423	−	6.34898i	−0.0610321	−	0.207856i
$934$	12.5421	+	24.0571i	0.410391	+	0.787173i
$935$	−17.6214	+	11.3246i	−0.576282	+	0.370354i
$936$	6.32516	+	0.820862i	0.206744	+	0.0268307i
$937$	−6.13515	−	42.6709i	−0.200427	−	1.39400i	−0.803021	−	0.595951i	$-0.796775\pi$
$937$	−6.13515	−	42.6709i	−0.200427	−	1.39400i	0.602594	−	0.798048i	$-0.294134\pi$
$938$	−1.76354	+	4.46428i	−0.0575816	+	0.145764i
$939$	4.24684	+	0.610603i	0.138590	+	0.0199263i
$940$	−4.99505	+	9.91097i	−0.162921	+	0.323260i
$941$	12.0127	−	10.4091i	0.391604	−	0.339327i	−0.436698	−	0.899608i	$-0.643852\pi$
$941$	12.0127	−	10.4091i	0.391604	−	0.339327i	0.828303	+	0.560281i	$0.189307\pi$
$942$	−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
$946$	−3.91721	+	6.85717i	−0.127360	+	0.222946i
$947$	41.2174	+	5.92616i	1.33938	+	0.192574i	0.774489	−	0.632588i	$-0.218007\pi$
$947$	41.2174	+	5.92616i	1.33938	+	0.192574i	0.564896	+	0.825162i	$0.308916\pi$
$948$	10.0947	+	3.39055i	0.327859	+	0.110120i
$949$	−26.5039	+	3.81069i	−0.860353	+	0.123700i
$950$	−35.5015	−	8.44054i	−1.15182	−	0.273847i
$951$	0.254487	−	0.163549i	0.00825231	−	0.00530344i
$952$	66.8617	−	44.2795i	2.16700	−	1.43511i
$953$	12.0623	−	3.54182i	0.390738	−	0.114731i	−0.0804616	−	0.996758i	$-0.525639\pi$
$953$	12.0623	−	3.54182i	0.390738	−	0.114731i	0.471199	+	0.882027i	$0.343821\pi$
$954$	8.44920	−	10.8459i	0.273553	−	0.351150i
$955$	−11.5288	−	9.98977i	−0.373064	−	0.323262i
$956$	1.32227	−	0.543467i	0.0427653	−	0.0175770i
$957$	21.5521	−	9.84251i	0.696680	−	0.318163i
$958$	2.15526	+	2.99748i	0.0696333	+	0.0968442i
$959$	−0.960415	−	0.282003i	−0.0310134	−	0.00910636i
$960$	−2.92931	−	5.97409i	−0.0945431	−	0.192813i
$961$	4.77650	−	10.4591i	0.154081	−	0.337389i
$962$	−22.3828	−	2.03387i	−0.721651	−	0.0655746i
$963$	4.80748	−	7.48058i	0.154919	−	0.241058i
$964$	21.6690	+	20.2856i	0.697912	+	0.653355i
$965$		−	13.2781i		−	0.427438i
$966$	23.9346	−	9.86580i	0.770082	−	0.317427i
$967$	−8.05730			−0.259105			−0.129553	−	0.991573i	$-0.541354\pi$
$967$	−8.05730			−0.259105			−0.129553	+	0.991573i	$0.541354\pi$
$968$	0.903587	−	1.07222i	0.0290424	−	0.0344625i
$969$	37.4259	+	24.0522i	1.20229	+	0.772667i
$970$	1.83635	−	20.2091i	0.0589616	−	0.648875i
$971$	6.33218	+	2.89181i	0.203209	+	0.0928026i	0.514420	−	0.857538i	$-0.328007\pi$
$971$	6.33218	+	2.89181i	0.203209	+	0.0928026i	−0.311211	+	0.950341i	$0.600735\pi$
$972$	−1.93922	+	0.489306i	−0.0622006	+	0.0156945i
$973$	−9.29906	+	31.6697i	−0.298114	+	1.01528i
$974$	−2.37280	−	3.30002i	−0.0760293	−	0.105740i
$975$	−4.03588	−	8.83735i	−0.129252	−	0.283022i
$976$	−7.30841	−	13.5603i	−0.233936	−	0.434055i
$977$	14.8737	−	17.1652i	0.475853	−	0.549164i	−0.466177	−	0.884691i	$-0.654369\pi$
$977$	14.8737	−	17.1652i	0.475853	−	0.549164i	0.942030	+	0.335528i	$0.108915\pi$
$978$	21.7388	+	16.9350i	0.695131	+	0.541521i
$979$	−16.8152	−	57.2672i	−0.537415	−	1.83027i
$980$	10.8461	−	6.39522i	0.346466	−	0.204288i
$981$	−9.38175	−	14.5983i	−0.299536	−	0.466087i
$982$	−15.9808	−	3.79945i	−0.509966	−	0.121245i
$983$	−2.73122	−	18.9960i	−0.0871123	−	0.605880i	−0.985880	−	0.167454i	$-0.946445\pi$
$983$	−2.73122	−	18.9960i	−0.0871123	−	0.605880i	0.898768	−	0.438425i	$-0.144464\pi$
$984$	−4.28609	+	15.3757i	−0.136635	+	0.490160i
$985$	1.05987	−	7.37156i	0.0337703	−	0.234877i
$986$	−63.7412	−	36.4127i	−2.02993	−	1.15962i
$987$	−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	0.894015	−	0.448037i	$-0.147877\pi$
$991$	10.1777	+	11.7457i	0.323306	+	0.373115i	−0.570709	+	0.821153i	$0.693331\pi$
$992$	11.2600	−	35.1163i	0.357507	−	1.11494i
$993$	3.90237	−	27.1416i	0.123838	−	0.861311i
$994$	15.0019	+	5.92626i	0.475832	+	0.187970i
$995$	−3.04330	+	0.437561i	−0.0964792	+	0.0138716i
$996$	−10.2165	−	1.87215i	−0.323722	−	0.0593214i
$997$	−21.6845	−	33.7418i	−0.686755	−	1.06861i	−0.993166	−	0.116713i	$-0.962764\pi$
$997$	−21.6845	−	33.7418i	−0.686755	−	1.06861i	0.306410	−	0.951900i	$-0.400872\pi$
$998$	14.9061	+	28.5915i	0.471845	+	0.905047i
$999$	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.13.37	yes	480
8.5	even	2	inner	552.2.bb.a.13.11	✓	480
23.16	even	11	inner	552.2.bb.a.85.11	yes	480
184.85	even	22	inner	552.2.bb.a.85.37	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.11	✓	480	8.5	even	2	inner
552.2.bb.a.13.37	yes	480	1.1	even	1	trivial
552.2.bb.a.85.11	yes	480	23.16	even	11	inner
552.2.bb.a.85.37	yes	480	184.85	even	22	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)

\(f(q)\)	\(=\)	\(q+(1.01903 - 0.980598i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(0.0768558 - 1.99852i) q^{4} +(0.756543 + 0.345502i) q^{5} +(0.274001 + 1.38742i) q^{6} +(-3.66239 - 1.07537i) q^{7} +(-1.88143 - 2.11192i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(1.01903 - 0.980598i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(0.0768558 - 1.99852i) q^{4} +(0.756543 + 0.345502i) q^{5} +(0.274001 + 1.38742i) q^{6} +(-3.66239 - 1.07537i) q^{7} +(-1.88143 - 2.11192i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(1.10974 - 0.389787i) q^{10} +(-2.56240 - 2.22033i) q^{11} +(1.63971 + 1.14514i) q^{12} +(-0.635317 - 2.16369i) q^{13} +(-4.78660 + 2.49549i) q^{14} +(-0.699673 + 0.449652i) q^{15} +(-3.98819 - 0.307196i) q^{16} +(-1.05713 - 7.35248i) q^{17} +(-1.31530 - 0.519590i) q^{18} +(5.92823 + 0.852351i) q^{19} +(0.748638 - 1.48541i) 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} +(-2.76912 - 1.58188i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-2.43063 + 7.23671i) q^{28} +(6.91690 - 0.994501i) q^{29} +(-0.272061 + 1.14431i) q^{30} +(-5.48418 + 3.52447i) q^{31} +(-4.36533 + 3.59776i) q^{32} +(3.25320 - 0.955225i) q^{33} +(-8.28708 - 6.45580i) q^{34} +(-2.39921 - 2.07893i) q^{35} +(-1.84985 + 0.760306i) q^{36} +(6.41059 - 2.92762i) q^{37} +(6.87688 - 4.94464i) q^{38} +(2.16369 + 0.635317i) q^{39} +(-0.693708 - 2.24780i) q^{40} +(-2.34435 + 5.13341i) q^{41} +(0.488495 - 5.37591i) q^{42} +(0.890424 - 1.38553i) q^{43} +(-4.63432 + 4.95036i) q^{44} -0.831702i q^{45} +(6.43156 + 2.15293i) q^{46} -6.67219 q^{47} +(2.41461 - 3.18899i) q^{48} +(6.36787 + 4.09238i) q^{49} +(-6.06782 - 0.551367i) q^{50} +(6.75683 + 3.08574i) q^{51} +(-4.37301 + 1.10340i) q^{52} +(-2.73892 + 9.32791i) q^{53} +(1.14821 - 0.825593i) q^{54} +(-1.17144 - 2.56509i) q^{55} +(4.61941 + 9.75792i) q^{56} +(-3.92209 + 4.52633i) q^{57} +(6.07335 - 7.79613i) q^{58} +(-1.99171 - 6.78314i) q^{59} +(0.844866 + 1.43287i) q^{60} +(2.08206 + 3.23975i) q^{61} +(-2.13247 + 8.96933i) q^{62} +(0.543216 + 3.77815i) q^{63} +(-0.920454 + 7.94687i) q^{64} +(0.266914 - 1.85643i) q^{65} +(2.37842 - 4.16348i) 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} +(-1.13950 + 2.58873i) q^{72} +(1.68986 - 11.7532i) q^{73} +(3.66178 - 9.26955i) q^{74} +(4.26442 - 0.613131i) q^{75} +(2.15906 - 11.7822i) q^{76} +(6.99681 + 10.8872i) q^{77} +(2.82786 - 1.47430i) q^{78} +(5.10875 - 1.50006i) q^{79} +(-2.91110 - 1.61033i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(2.64484 + 7.52998i) q^{82} +(-4.72400 + 2.15738i) q^{83} +(-4.77381 - 5.95724i) q^{84} +(1.74053 - 5.92771i) q^{85} +(-0.451273 - 2.28505i) q^{86} +(-2.90293 + 6.35654i) q^{87} +(0.131797 + 9.58898i) q^{88} +(14.8089 + 9.51710i) q^{89} +(-0.815566 - 0.847532i) q^{90} +8.60748i q^{91} +(8.66512 - 4.11287i) q^{92} -6.51906i q^{93} +(-6.79918 + 6.54274i) q^{94} +(4.19048 + 2.69305i) q^{95} +(-0.666557 - 5.61745i) q^{96} +(7.16690 - 15.6933i) q^{97} +(10.5021 - 2.07405i) 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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