LMFDB - Embedded newform 99.2.p.a.74.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(2,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.p (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			74.1
Character	$\chi$	$=$	99.74
Dual form			99.2.p.a.95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.281588 - 2.67913i) q^{2} +(1.33430 - 1.10437i) q^{3} +(-5.14217 + 1.09300i) q^{4} +(1.43896 + 0.151241i) q^{5} +(-3.33448 - 3.26380i) q^{6} +(-1.07283 + 0.965979i) q^{7} +(2.71136 + 8.34470i) q^{8} +(0.560727 - 2.94713i) q^{9} -3.89775i q^{10} +(2.66871 + 1.96926i) q^{11} +(-5.65413 + 7.13726i) q^{12} +(-1.21080 + 2.71950i) q^{13} +(2.89008 + 2.60224i) q^{14} +(2.08703 - 1.38735i) q^{15} +(11.9880 - 5.33739i) q^{16} +(-3.35854 - 2.44012i) q^{17} +(-8.05365 - 0.672385i) q^{18} +(-1.19136 + 0.387096i) q^{19} +(-7.56469 + 0.795081i) q^{20} +(-0.364678 + 2.47371i) q^{21} +(4.52444 - 7.70435i) q^{22} +(5.02939 - 2.90372i) q^{23} +(12.8334 + 8.14001i) q^{24} +(-2.84300 - 0.604299i) q^{25} +(7.62685 + 2.47811i) q^{26} +(-2.50655 - 4.55162i) q^{27} +(4.46085 - 6.13983i) q^{28} +(-0.0651453 - 0.0723511i) q^{29} +(-4.30457 - 5.20078i) q^{30} +(3.73471 + 1.66280i) q^{31} +(-8.90112 - 15.4172i) q^{32} +(5.73566 - 0.319656i) q^{33} +(-5.59169 + 9.68509i) q^{34} +(-1.68985 + 1.22775i) q^{35} +(0.337866 + 15.7675i) q^{36} +(-3.08635 + 9.49880i) q^{37} +(1.37255 + 3.08281i) q^{38} +(1.38777 + 4.96581i) q^{39} +(2.63948 + 12.4178i) q^{40} +(-3.05835 + 3.39664i) q^{41} +(6.73009 + 0.280454i) q^{42} +(-1.84140 - 1.06313i) q^{43} +(-15.8754 - 7.20937i) q^{44} +(1.25259 - 4.15600i) q^{45} +(-9.19566 - 12.6567i) q^{46} +(1.50921 - 7.10026i) q^{47} +(10.1011 - 20.3609i) q^{48} +(-0.513854 + 4.88899i) q^{49} +(-0.818442 + 7.78695i) q^{50} +(-7.17611 + 0.453215i) q^{51} +(3.25372 - 15.3075i) q^{52} +(-0.197492 - 0.271824i) q^{53} +(-11.4886 + 7.99706i) q^{54} +(3.54233 + 3.23731i) q^{55} +(-10.9696 - 6.33332i) q^{56} +(-1.16214 + 1.83221i) q^{57} +(-0.175494 + 0.194906i) q^{58} +(0.629292 + 2.96059i) q^{59} +(-9.21552 + 9.41510i) q^{60} +(0.129468 + 0.290790i) q^{61} +(3.40321 - 10.4740i) q^{62} +(2.24530 + 3.70342i) q^{63} +(-17.5657 + 12.7622i) q^{64} +(-2.15359 + 3.73013i) q^{65} +(-2.47150 - 15.2766i) q^{66} +(-1.71828 - 2.97615i) q^{67} +(19.9373 + 8.87664i) q^{68} +(3.50394 - 9.42875i) q^{69} +(3.76515 + 4.18162i) q^{70} +(-5.38901 + 7.41734i) q^{71} +(26.1133 - 3.31163i) q^{72} +(-6.75113 - 2.19358i) q^{73} +(26.3176 + 5.59399i) q^{74} +(-4.46080 + 2.33342i) q^{75} +(5.70308 - 3.29267i) q^{76} +(-4.76533 + 0.465238i) q^{77} +(12.9133 - 5.11632i) q^{78} +(9.96549 - 1.04742i) q^{79} +(18.0574 - 5.86722i) q^{80} +(-8.37117 - 3.30507i) q^{81} +(9.96124 + 7.23727i) q^{82} +(5.44872 - 2.42593i) q^{83} +(-0.828533 - 13.1188i) q^{84} +(-4.46376 - 4.01919i) q^{85} +(-2.32976 + 5.23272i) q^{86} +(-0.166826 - 0.0245938i) q^{87} +(-9.19707 + 27.6090i) q^{88} -5.11584i q^{89} +(-11.4872 - 2.18558i) q^{90} +(-1.32800 - 4.08716i) q^{91} +(-22.6882 + 20.4285i) q^{92} +(6.81957 - 1.90583i) q^{93} +(-19.4475 - 2.04402i) q^{94} +(-1.77286 + 0.376834i) q^{95} +(-28.9031 - 10.7411i) q^{96} +(-0.631450 - 6.00784i) q^{97} +13.2430 q^{98} +(7.30009 - 6.76082i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.281588	−	2.67913i	−0.199113	−	1.89443i	−0.402631	−	0.915362i	$-0.631904\pi$
$2$	−0.281588	−	2.67913i	−0.199113	−	1.89443i	0.203518	−	0.979071i	$-0.434762\pi$
$3$	1.33430	−	1.10437i	0.770360	−	0.637609i
$3$	1.33430	−	1.10437i	0.770360	−	0.637609i
$4$	−5.14217	+	1.09300i	−2.57109	+	0.546501i
$5$	1.43896	+	0.151241i	0.643523	+	0.0676370i	0.420668	−	0.907215i	$-0.361796\pi$
$5$	1.43896	+	0.151241i	0.643523	+	0.0676370i	0.222855	+	0.974852i	$0.428462\pi$
$6$	−3.33448	−	3.26380i	−1.36130	−	1.33244i
$7$	−1.07283	+	0.965979i	−0.405491	+	0.365106i	−0.846493	−	0.532401i	$-0.821290\pi$
$7$	−1.07283	+	0.965979i	−0.405491	+	0.365106i	0.441001	+	0.897506i	$0.354623\pi$
$8$	2.71136	+	8.34470i	0.958610	+	2.95030i
$9$	0.560727	−	2.94713i	0.186909	−	0.982377i
$10$		−	3.89775i		−	1.23258i
$11$	2.66871	+	1.96926i	0.804646	+	0.593755i
$11$	2.66871	+	1.96926i	0.804646	+	0.593755i
$12$	−5.65413	+	7.13726i	−1.63221	+	2.06035i
$13$	−1.21080	+	2.71950i	−0.335815	+	0.754253i	0.664163	+	0.747588i	$0.268788\pi$
$13$	−1.21080	+	2.71950i	−0.335815	+	0.754253i	−0.999978	+	0.00666518i	$0.997878\pi$
$14$	2.89008	+	2.60224i	0.772407	+	0.695479i
$15$	2.08703	−	1.38735i	0.538870	−	0.358211i
$16$	11.9880	−	5.33739i	2.99699	−	1.33435i
$17$	−3.35854	−	2.44012i	−0.814566	−	0.591817i	0.100585	−	0.994928i	$-0.467929\pi$
$17$	−3.35854	−	2.44012i	−0.814566	−	0.591817i	−0.915151	+	0.403112i	$0.867929\pi$
$18$	−8.05365	−	0.672385i	−1.89826	−	0.158483i
$19$	−1.19136	+	0.387096i	−0.273317	+	0.0888059i	−0.442468	−	0.896784i	$-0.645897\pi$
$19$	−1.19136	+	0.387096i	−0.273317	+	0.0888059i	0.169152	+	0.985590i	$0.445897\pi$
$20$	−7.56469	+	0.795081i	−1.69152	+	0.177785i
$21$	−0.364678	+	2.47371i	−0.0795793	+	0.539808i
$22$	4.52444	−	7.70435i	0.964613	−	1.64257i
$23$	5.02939	−	2.90372i	1.04870	−	0.605467i	0.126414	−	0.991978i	$-0.459653\pi$
$23$	5.02939	−	2.90372i	1.04870	−	0.605467i	0.922285	+	0.386511i	$0.126320\pi$
$24$	12.8334	+	8.14001i	2.61961	+	1.66157i
$25$	−2.84300	−	0.604299i	−0.568601	−	0.120860i
$26$	7.62685	+	2.47811i	1.49575	+	0.485998i
$27$	−2.50655	−	4.55162i	−0.482385	−	0.875959i
$28$	4.46085	−	6.13983i	0.843021	−	1.16032i
$29$	−0.0651453	−	0.0723511i	−0.0120972	−	0.0134353i	0.737066	−	0.675821i	$-0.236211\pi$
$29$	−0.0651453	−	0.0723511i	−0.0120972	−	0.0134353i	−0.749163	+	0.662386i	$0.769544\pi$
$30$	−4.30457	−	5.20078i	−0.785903	−	0.949529i
$31$	3.73471	+	1.66280i	0.670773	+	0.298647i	0.713721	−	0.700430i	$-0.247008\pi$
$31$	3.73471	+	1.66280i	0.670773	+	0.298647i	−0.0429482	+	0.999077i	$0.513675\pi$
$32$	−8.90112	−	15.4172i	−1.57351	−	2.72540i
$33$	5.73566	−	0.319656i	0.998451	−	0.0556450i
$34$	−5.59169	+	9.68509i	−0.958967	+	1.66098i
$35$	−1.68985	+	1.22775i	−0.285637	+	0.207528i
$36$	0.337866	+	15.7675i	0.0563111	+	2.62792i
$37$	−3.08635	+	9.49880i	−0.507392	+	1.56159i	0.289319	+	0.957233i	$0.406571\pi$
$37$	−3.08635	+	9.49880i	−0.507392	+	1.56159i	−0.796711	+	0.604360i	$0.793429\pi$
$38$	1.37255	+	3.08281i	0.222658	+	0.500098i
$39$	1.38777	+	4.96581i	0.222220	+	0.795166i
$40$	2.63948	+	12.4178i	0.417338	+	1.96342i
$41$	−3.05835	+	3.39664i	−0.477634	+	0.530466i	−0.933018	−	0.359829i	$-0.882835\pi$
$41$	−3.05835	+	3.39664i	−0.477634	+	0.530466i	0.455385	+	0.890295i	$0.349502\pi$
$42$	6.73009	+	0.280454i	1.03848	+	0.0432749i
$43$	−1.84140	−	1.06313i	−0.280811	−	0.162126i	0.352980	−	0.935631i	$-0.385168\pi$
$43$	−1.84140	−	1.06313i	−0.280811	−	0.162126i	−0.633790	+	0.773505i	$0.718502\pi$
$44$	−15.8754	−	7.20937i	−2.39330	−	1.08685i
$45$	1.25259	−	4.15600i	0.186725	−	0.619540i
$46$	−9.19566	−	12.6567i	−1.35583	−	1.86614i
$47$	1.50921	−	7.10026i	0.220141	−	1.03568i	−0.719758	−	0.694225i	$-0.755747\pi$
$47$	1.50921	−	7.10026i	0.220141	−	1.03568i	0.939898	−	0.341454i	$-0.110920\pi$
$48$	10.1011	−	20.3609i	1.45797	−	2.93884i
$49$	−0.513854	+	4.88899i	−0.0734077	+	0.698428i
$50$	−0.818442	+	7.78695i	−0.115745	+	1.10124i
$51$	−7.17611	+	0.453215i	−1.00486	+	0.0634627i
$52$	3.25372	−	15.3075i	0.451209	−	2.12277i
$53$	−0.197492	−	0.271824i	−0.0271276	−	0.0373379i	0.795238	−	0.606298i	$-0.207346\pi$
$53$	−0.197492	−	0.271824i	−0.0271276	−	0.0373379i	−0.822365	+	0.568960i	$0.807346\pi$
$54$	−11.4886	+	7.99706i	−1.56340	+	1.08826i
$55$	3.54233	+	3.23731i	0.477648	+	0.436518i
$56$	−10.9696	−	6.33332i	−1.46588	−	0.846325i
$57$	−1.16214	+	1.83221i	−0.153929	+	0.242682i
$58$	−0.175494	+	0.194906i	−0.0230435	+	0.0255924i
$59$	0.629292	+	2.96059i	0.0819268	+	0.385435i	0.999938	−	0.0111187i	$-0.00353925\pi$
$59$	0.629292	+	2.96059i	0.0819268	+	0.385435i	−0.918011	+	0.396554i	$0.870206\pi$
$60$	−9.21552	+	9.41510i	−1.18972	+	1.21548i
$61$	0.129468	+	0.290790i	0.0165767	+	0.0372319i	0.921644	−	0.388036i	$-0.126846\pi$
$61$	0.129468	+	0.290790i	0.0165767	+	0.0372319i	−0.905067	+	0.425268i	$0.860180\pi$
$62$	3.40321	−	10.4740i	0.432208	−	1.33020i
$63$	2.24530	+	3.70342i	0.282882	+	0.466587i
$64$	−17.5657	+	12.7622i	−2.19571	+	1.59527i
$65$	−2.15359	+	3.73013i	−0.267120	+	0.462666i
$66$	−2.47150	−	15.2766i	−0.304220	−	1.88042i
$67$	−1.71828	−	2.97615i	−0.209922	−	0.363595i	0.741768	−	0.670657i	$-0.233988\pi$
$67$	−1.71828	−	2.97615i	−0.209922	−	0.363595i	−0.951690	+	0.307062i	$0.900654\pi$
$68$	19.9373	+	8.87664i	2.41775	+	1.07645i
$69$	3.50394	−	9.42875i	0.421825	−	1.13509i
$70$	3.76515	+	4.18162i	0.450021	+	0.499799i
$71$	−5.38901	+	7.41734i	−0.639558	+	0.880276i	−0.998592	−	0.0530483i	$-0.983106\pi$
$71$	−5.38901	+	7.41734i	−0.639558	+	0.880276i	0.359034	+	0.933325i	$0.383106\pi$
$72$	26.1133	−	3.31163i	3.07748	−	0.390279i
$73$	−6.75113	−	2.19358i	−0.790160	−	0.256739i	−0.113988	−	0.993482i	$-0.536363\pi$
$73$	−6.75113	−	2.19358i	−0.790160	−	0.256739i	−0.676172	+	0.736743i	$0.736363\pi$
$74$	26.3176	+	5.59399i	3.05936	+	0.650288i
$75$	−4.46080	+	2.33342i	−0.515089	+	0.269440i
$76$	5.70308	−	3.29267i	0.654188	−	0.377695i
$77$	−4.76533	+	0.465238i	−0.543060	+	0.0530188i
$78$	12.9133	−	5.11632i	1.46214	−	0.579309i
$79$	9.96549	−	1.04742i	1.12121	−	0.117843i	0.474264	−	0.880383i	$-0.342714\pi$
$79$	9.96549	−	1.04742i	1.12121	−	0.117843i	0.646942	+	0.762539i	$0.276048\pi$
$80$	18.0574	−	5.86722i	2.01888	−	0.655975i
$81$	−8.37117	−	3.30507i	−0.930130	−	0.367230i
$82$	9.96124	+	7.23727i	1.10004	+	0.799222i
$83$	5.44872	−	2.42593i	0.598075	−	0.266280i	−0.0852911	−	0.996356i	$-0.527182\pi$
$83$	5.44872	−	2.42593i	0.598075	−	0.266280i	0.683366	+	0.730076i	$0.260515\pi$
$84$	−0.828533	−	13.1188i	−0.0904004	−	1.43138i
$85$	−4.46376	−	4.01919i	−0.484163	−	0.435942i
$86$	−2.32976	+	5.23272i	−0.251224	+	0.564259i
$87$	−0.166826	−	0.0245938i	−0.0178856	−	0.00263673i
$88$	−9.19707	+	27.6090i	−0.980411	+	2.94312i
$89$		−	5.11584i		−	0.542278i	−0.962540	−	0.271139i	$-0.912600\pi$
$89$		−	5.11584i		−	0.542278i	0.962540	−	0.271139i	$-0.0874004\pi$
$90$	−11.4872	−	2.18558i	−1.21086	−	0.230380i
$91$	−1.32800	−	4.08716i	−0.139212	−	0.428451i
$92$	−22.6882	+	20.4285i	−2.36541	+	2.12982i
$93$	6.81957	−	1.90583i	0.707157	−	0.197625i
$94$	−19.4475	−	2.04402i	−2.00586	−	0.210824i
$95$	−1.77286	+	0.376834i	−0.181892	+	0.0386623i
$96$	−28.9031	−	10.7411i	−2.94991	−	1.09625i
$97$	−0.631450	−	6.00784i	−0.0641140	−	0.610004i	−0.978655	−	0.205511i	$-0.934114\pi$
$97$	−0.631450	−	6.00784i	−0.0641140	−	0.610004i	0.914541	−	0.404493i	$-0.132552\pi$
$98$	13.2430			1.33774
$99$	7.30009	−	6.76082i	0.733687	−	0.679488i
$100$	15.2797			1.52797
$101$	−1.21696	−	11.5786i	−0.121092	−	1.15211i	−0.871246	−	0.490847i	$-0.836687\pi$
$101$	−1.21696	−	11.5786i	−0.121092	−	1.15211i	0.750154	−	0.661263i	$-0.229979\pi$
$102$	3.23493	+	19.0981i	0.320306	+	1.89100i
$103$	3.27668	−	0.696481i	0.322861	−	0.0686263i	−0.0436300	−	0.999048i	$-0.513892\pi$
$103$	3.27668	−	0.696481i	0.322861	−	0.0686263i	0.366491	+	0.930421i	$0.380559\pi$
$104$	−25.9763	−	2.73022i	−2.54719	−	0.267720i
$105$	−0.898883	+	3.50442i	−0.0877220	+	0.341996i
$106$	−0.672642	+	0.605650i	−0.0653328	+	0.0588259i
$107$	−2.92166	−	8.99195i	−0.282448	−	0.869285i	−0.987152	−	0.159784i	$-0.948920\pi$
$107$	−2.92166	−	8.99195i	−0.282448	−	0.869285i	0.704704	−	0.709501i	$-0.251080\pi$
$108$	17.8640	+	20.6655i	1.71897	+	1.98854i
$109$		−	4.11325i		−	0.393978i	−0.980406	−	0.196989i	$-0.936884\pi$
$109$		−	4.11325i		−	0.393978i	0.980406	−	0.196989i	$-0.0631163\pi$
$110$	7.67570	−	10.4020i	0.731849	−	0.991789i
$111$	6.37208	+	16.0828i	0.604811	+	1.52651i
$112$	−7.70523	+	17.3062i	−0.728076	+	1.63529i
$113$	−15.0282	−	13.5315i	−1.41374	−	1.27293i	−0.913377	−	0.407116i	$-0.866535\pi$
$113$	−15.0282	−	13.5315i	−1.41374	−	1.27293i	−0.500359	−	0.865818i	$-0.666799\pi$
$114$	5.23597	+	2.59759i	0.490394	+	0.243287i
$115$	7.67625	−	3.41769i	0.715814	−	0.318701i
$116$	0.414068	+	0.300838i	0.0384452	+	0.0279321i
$117$	7.33579	+	5.09328i	0.678194	+	0.470874i
$118$	7.75460	−	2.51962i	0.713869	−	0.231950i
$119$	5.96025	−	0.626447i	0.546375	−	0.0574263i
$120$	17.2357	+	13.6541i	1.57340	+	1.24644i
$121$	3.24402	+	10.5108i	0.294911	+	0.955525i
$122$	0.742609	−	0.428746i	0.0672327	−	0.0388168i
$123$	−0.329610	+	7.90969i	−0.0297199	+	0.713193i
$124$	−21.0219	−	4.46835i	−1.88783	−	0.401270i
$125$	−10.8799	−	3.53510i	−0.973131	−	0.316189i
$126$	9.28970	−	7.05831i	0.827592	−	0.628804i
$127$	−0.0604870	+	0.0832533i	−0.00536736	+	0.00738753i	−0.811692	−	0.584085i	$-0.801453\pi$
$127$	−0.0604870	+	0.0832533i	−0.00536736	+	0.00738753i	0.806325	+	0.591473i	$0.201453\pi$
$128$	15.3139	+	17.0078i	1.35357	+	1.50329i
$129$	−3.63108	+	0.615048i	−0.319698	+	0.0541520i
$130$	10.5999	+	4.71940i	0.929676	+	0.413919i
$131$	7.68267	+	13.3068i	0.671238	+	1.16262i	0.977553	+	0.210689i	$0.0675706\pi$
$131$	7.68267	+	13.3068i	0.671238	+	1.16262i	−0.306315	+	0.951930i	$0.599096\pi$
$132$	−29.1444	+	7.91282i	−2.53669	+	0.688722i
$133$	0.904197	−	1.56612i	0.0784039	−	0.135799i
$134$	−7.48966	+	5.44156i	−0.647008	+	0.470079i
$135$	−2.91843	−	6.92869i	−0.251179	−	0.596327i
$136$	11.2559	−	34.6421i	0.965185	−	2.97053i
$137$	−1.51448	−	3.40157i	−0.129391	−	0.290616i	0.837220	−	0.546867i	$-0.184179\pi$
$137$	−1.51448	−	3.40157i	−0.129391	−	0.290616i	−0.966610	+	0.256250i	$0.917513\pi$
$138$	−26.2475	−	6.73250i	−2.23434	−	0.573108i
$139$	−3.53785	−	16.6443i	−0.300077	−	1.41175i	−0.827174	−	0.561945i	$-0.810053\pi$
$139$	−3.53785	−	16.6443i	−0.300077	−	1.41175i	0.527097	−	0.849805i	$-0.323280\pi$
$140$	7.34758	−	8.16031i	0.620984	−	0.689672i
$141$	−5.82759	−	11.1406i	−0.490771	−	0.938210i
$142$	21.3895	+	12.3492i	1.79497	+	1.03633i
$143$	−8.58668	+	4.87317i	−0.718054	+	0.407515i
$144$	−9.00801	−	38.3230i	−0.750667	−	3.19358i
$145$	−0.0827990	−	0.113963i	−0.00687608	−	0.00946412i
$146$	−3.97584	+	18.7049i	−0.329043	+	1.54803i
$147$	4.71363	+	7.09088i	0.388774	+	0.584846i
$148$	5.48832	−	52.2178i	0.451137	−	4.29228i
$149$	−1.19705	+	11.3892i	−0.0980665	+	0.933040i	0.829279	+	0.558834i	$0.188751\pi$
$149$	−1.19705	+	11.3892i	−0.0980665	+	0.933040i	−0.927346	+	0.374206i	$0.877915\pi$
$150$	7.50764	+	11.2940i	0.612996	+	0.922153i
$151$	−0.221010	+	1.03977i	−0.0179855	+	0.0846153i	−0.986225	−	0.165409i	$-0.947105\pi$
$151$	−0.221010	+	1.03977i	−0.0179855	+	0.0846153i	0.968239	+	0.250025i	$0.0804388\pi$
$152$	−6.46040	−	8.89198i	−0.524008	−	0.721235i
$153$	−9.07459	+	8.52982i	−0.733637	+	0.689595i
$154$	2.58830	+	12.6360i	0.208571	+	1.01823i
$155$	5.12261	+	2.95754i	0.411458	+	0.237555i
$156$	−12.5638	−	24.0182i	−1.00591	−	1.92299i
$157$	−0.0571368	+	0.0634569i	−0.00456002	+	0.00506441i	−0.745421	−	0.666595i	$-0.767751\pi$
$157$	−0.0571368	+	0.0634569i	−0.00456002	+	0.00506441i	0.740861	+	0.671659i	$0.234418\pi$
$158$	−5.61233	−	26.4039i	−0.446493	−	2.10058i
$159$	−0.563709	−	0.144591i	−0.0447050	−	0.0114668i
$160$	−10.4766	−	23.5309i	−0.828252	−	1.86028i
$161$	−2.59074	+	7.97347i	−0.204179	+	0.628398i
$162$	−6.49751	+	23.3582i	−0.510493	+	1.83519i
$163$	−2.37021	+	1.72206i	−0.185650	+	0.134882i	−0.676728	−	0.736233i	$-0.736603\pi$
$163$	−2.37021	+	1.72206i	−0.185650	+	0.134882i	0.491079	+	0.871115i	$0.336603\pi$
$164$	12.0140	−	20.8089i	0.938136	−	1.62490i
$165$	8.30174	+	0.407494i	0.646289	+	0.0317233i
$166$	−8.03368	−	13.9147i	−0.623534	−	1.07999i
$167$	4.06863	+	1.81147i	0.314840	+	0.140176i	0.558072	−	0.829792i	$-0.311541\pi$
$167$	4.06863	+	1.81147i	0.314840	+	0.140176i	−0.243233	+	0.969968i	$0.578208\pi$
$168$	−21.6311	+	3.66398i	−1.66888	+	0.282682i
$169$	2.76906	+	3.07535i	0.213004	+	0.236565i
$170$	−9.51100	+	13.0908i	−0.729461	+	1.00402i
$171$	0.472796	+	3.72815i	0.0361556	+	0.285099i
$172$	10.6308	+	3.45415i	0.810590	+	0.263377i
$173$	−10.2220	−	2.17276i	−0.777166	−	0.165192i	−0.197781	−	0.980246i	$-0.563374\pi$
$173$	−10.2220	−	2.17276i	−0.777166	−	0.165192i	−0.579384	+	0.815055i	$0.696707\pi$
$174$	−0.0189137	+	0.453875i	−0.00143384	+	0.0344081i
$175$	3.63380	−	2.09797i	0.274689	−	0.158592i
$176$	42.5031	+	9.36351i	3.20379	+	0.705801i
$177$	4.10925	+	3.25535i	0.308870	+	0.244687i
$178$	−13.7060	+	1.44056i	−1.02731	+	0.107975i
$179$	9.58188	−	3.11334i	0.716183	−	0.232702i	0.0718157	−	0.997418i	$-0.477121\pi$
$179$	9.58188	−	3.11334i	0.716183	−	0.232702i	0.644368	+	0.764716i	$0.277121\pi$
$180$	−1.89852	+	22.7399i	−0.141507	+	1.69494i
$181$	12.5433	+	9.11327i	0.932339	+	0.677384i	0.946564	−	0.322515i	$-0.104528\pi$
$181$	12.5433	+	9.11327i	0.932339	+	0.677384i	−0.0142256	+	0.999899i	$0.504528\pi$
$182$	−10.5761	+	4.70879i	−0.783953	+	0.349038i
$183$	0.493890	+	0.245021i	0.0365094	+	0.0181125i
$184$	37.8671	+	34.0957i	2.79160	+	2.51357i
$185$	−5.87774	+	13.2016i	−0.432140	+	0.970602i
$186$	−7.02628	−	17.7339i	−0.515192	−	1.30031i
$187$	−4.15773	−	13.1258i	−0.304043	−	0.959855i
$188$			38.1603i			2.78313i
$189$	7.08586	+	2.46183i	0.515421	+	0.179072i
$190$	1.50881	+	4.64363i	0.109460	+	0.336884i
$191$	2.76063	−	2.48568i	0.199752	−	0.179857i	−0.563184	−	0.826331i	$-0.690424\pi$
$191$	2.76063	−	2.48568i	0.199752	−	0.179857i	0.762936	+	0.646474i	$0.223757\pi$
$192$	−9.34369	+	36.4276i	−0.674323	+	2.62894i
$193$	24.8007	+	2.60666i	1.78519	+	0.187631i	0.938692	−	0.344756i	$-0.112038\pi$
$193$	24.8007	+	2.60666i	1.78519	+	0.187631i	0.846501	+	0.532387i	$0.178705\pi$
$194$	−15.9180	+	3.38348i	−1.14285	+	0.242919i
$195$	1.24591	+	7.35549i	0.0892212	+	0.526737i
$196$	−2.70136	−	25.7017i	−0.192954	−	1.83583i
$197$	19.2214			1.36947			0.684733	−	0.728794i	$-0.259919\pi$
$197$	19.2214			1.36947			0.684733	+	0.728794i	$0.259919\pi$
$198$	−20.1688	−	17.6541i	−1.43333	−	1.25463i
$199$	−26.0126			−1.84399			−0.921993	−	0.387206i	$-0.873440\pi$
$199$	−26.0126			−1.84399			−0.921993	+	0.387206i	$0.873440\pi$
$200$	−2.66571	−	25.3625i	−0.188494	−	1.79340i
$201$	−5.57949	−	2.07347i	−0.393547	−	0.146251i
$202$	−30.6778	+	6.52077i	−2.15848	+	0.458800i
$203$	0.139779	+	0.0146914i	0.00981059	+	0.00103113i
$204$	36.4054	−	10.1740i	2.54889	−	0.712323i
$205$	−4.91455	+	4.42508i	−0.343247	+	0.309061i
$206$	−2.78864	−	8.58255i	−0.194294	−	0.597975i
$207$	−5.73752	−	16.4505i	−0.398785	−	1.14339i
$208$			39.0638i			2.70859i
$209$	−3.94168	−	1.31305i	−0.272652	−	0.0908256i
$210$	9.64191	+	1.42143i	0.665355	+	0.0980877i
$211$	−9.24806	+	20.7715i	−0.636663	+	1.42997i	0.250319	+	0.968163i	$0.419464\pi$
$211$	−9.24806	+	20.7715i	−0.636663	+	1.42997i	−0.886982	+	0.461804i	$0.847202\pi$
$212$	1.31264	+	1.18191i	0.0901526	+	0.0811737i
$213$	1.00092	+	15.8484i	0.0685822	+	1.08592i
$214$	−23.2679	+	10.3596i	−1.59056	+	0.708165i
$215$	−2.48891	−	1.80830i	−0.169742	−	0.123325i
$216$	31.1857	−	33.2575i	2.12192	−	2.26288i
$217$	−5.61293	+	1.82375i	−0.381030	+	0.123804i
$218$	−11.0199	+	1.15824i	−0.746365	+	0.0784461i
$219$	−11.4306	+	4.52886i	−0.772407	+	0.306032i
$220$	−21.7537	−	12.7750i	−1.46663	−	0.861291i
$221$	10.7024	−	6.17905i	0.719923	−	0.415648i
$222$	41.2935	−	21.6004i	2.77144	−	1.44972i
$223$	22.2512	+	4.72965i	1.49005	+	0.316721i	0.879746	−	0.475444i	$-0.157712\pi$
$223$	22.2512	+	4.72965i	1.49005	+	0.316721i	0.610308	+	0.792164i	$0.291046\pi$
$224$	24.4421	+	7.94170i	1.63310	+	0.530627i
$225$	−3.37510	+	8.03986i	−0.225007	+	0.535991i
$226$	−32.0208	+	44.0729i	−2.13000	+	2.93169i
$227$	5.43847	+	6.04004i	0.360964	+	0.400891i	0.896084	−	0.443885i	$-0.146400\pi$
$227$	5.43847	+	6.04004i	0.360964	+	0.400891i	−0.535120	+	0.844776i	$0.679733\pi$
$228$	3.97330	−	10.6917i	0.263138	−	0.708077i
$229$	12.4183	+	5.52899i	0.820625	+	0.365366i	0.773715	−	0.633533i	$-0.218396\pi$
$229$	12.4183	+	5.52899i	0.820625	+	0.365366i	0.0469095	+	0.998899i	$0.485063\pi$
$230$	−11.3180	−	19.6033i	−0.746285	−	1.29260i
$231$	−5.84460	+	5.88347i	−0.384546	+	0.387104i
$232$	0.427117	−	0.739788i	0.0280416	−	0.0485694i
$233$	4.09157	−	2.97270i	0.268048	−	0.194748i	−0.445640	−	0.895212i	$-0.647024\pi$
$233$	4.09157	−	2.97270i	0.268048	−	0.194748i	0.713687	+	0.700464i	$0.247024\pi$
$234$	11.5799	−	21.0878i	0.757002	−	1.37855i
$235$	3.24554	−	9.98874i	0.211716	−	0.651594i
$236$	−6.47185	−	14.5360i	−0.421282	−	0.946214i
$237$	12.1402	−	12.4032i	0.788594	−	0.805673i
$238$	−3.35667	−	15.7919i	−0.217581	−	1.02364i
$239$	13.4937	−	14.9862i	0.872832	−	0.969378i	−0.126914	−	0.991914i	$-0.540507\pi$
$239$	13.4937	−	14.9862i	0.872832	−	0.969378i	0.999746	+	0.0225358i	$0.00717397\pi$
$240$	17.6145	−	27.7708i	1.13701	−	1.79260i
$241$	−24.5094	−	14.1505i	−1.57879	−	0.911516i	−0.995028	−	0.0995930i	$-0.968246\pi$
$241$	−24.5094	−	14.1505i	−1.57879	−	0.911516i	−0.583764	−	0.811923i	$-0.698421\pi$
$242$	27.2463	−	11.6509i	1.75146	−	0.748947i
$243$	−14.8197	+	4.83491i	−0.950684	+	0.310160i
$244$	−0.983581	−	1.35378i	−0.0629674	−	0.0866671i
$245$	−1.47883	+	6.95735i	−0.0944790	+	0.444489i
$246$	21.2839	−	1.34421i	1.35701	−	0.0857036i
$247$	0.389789	−	3.70860i	0.0248017	−	0.235972i
$248$	−3.74943	+	35.6734i	−0.238089	+	2.26527i
$249$	4.59112	−	9.25433i	0.290950	−	0.586469i
$250$	−6.40735	+	30.1442i	−0.405237	+	1.90649i
$251$	13.7475	+	18.9219i	0.867737	+	1.19434i	0.979669	+	0.200622i	$0.0642964\pi$
$251$	13.7475	+	18.9219i	0.867737	+	1.19434i	−0.111931	+	0.993716i	$0.535704\pi$
$252$	−15.5936	−	16.5895i	−0.982303	−	1.04504i
$253$	19.1401	+	2.15500i	1.20333	+	0.135483i
$254$	0.240079	+	0.138610i	0.0150639	+	0.00869715i
$255$	−10.3947	−	0.433163i	−0.650941	−	0.0271257i
$256$	12.1971	−	13.5463i	0.762319	−	0.846641i
$257$	0.0865878	+	0.407364i	0.00540120	+	0.0254106i	0.980766	−	0.195189i	$-0.0625320\pi$
$257$	0.0865878	+	0.407364i	0.00540120	+	0.0254106i	−0.975364	+	0.220599i	$0.929199\pi$
$258$	2.67027	+	9.55495i	0.166243	+	0.594865i
$259$	−5.86452	−	13.1719i	−0.364404	−	0.818464i
$260$	6.99709	−	21.5348i	0.433941	−	1.33553i
$261$	−0.249757	+	0.151422i	−0.0154596	+	0.00937281i
$262$	33.4873	−	24.3299i	2.06885	−	1.50311i
$263$	−14.0588	+	24.3505i	−0.866902	+	1.50152i	−0.00175644	+	0.999998i	$0.500559\pi$
$263$	−14.0588	+	24.3505i	−0.866902	+	1.50152i	−0.865146	+	0.501520i	$0.832774\pi$
$264$	18.2189	+	46.9957i	1.12129	+	2.89238i
$265$	−0.243072	−	0.421013i	−0.0149318	−	0.0258626i
$266$	−4.45045	−	1.98147i	−0.272874	−	0.121491i
$267$	−5.64979	−	6.82609i	−0.345762	−	0.417750i
$268$	12.0886	+	13.4258i	0.738431	+	0.820111i
$269$	7.97137	−	10.9716i	0.486023	−	0.668953i	−0.493625	−	0.869675i	$-0.664329\pi$
$269$	7.97137	−	10.9716i	0.486023	−	0.668953i	0.979648	+	0.200721i	$0.0643286\pi$
$270$	−17.7411	+	9.76991i	−1.07969	+	0.594578i
$271$	−10.5963	−	3.44294i	−0.643678	−	0.209144i	−0.0310533	−	0.999518i	$-0.509886\pi$
$271$	−10.5963	−	3.44294i	−0.643678	−	0.209144i	−0.612624	+	0.790374i	$0.709886\pi$
$272$	−53.2860	−	11.3263i	−3.23094	−	0.686757i
$273$	−6.28570	−	3.98691i	−0.380428	−	0.241299i
$274$	−8.68681	+	5.01533i	−0.524789	+	0.302987i
$275$	−6.39713	−	7.21132i	−0.385762	−	0.434859i
$276$	−7.71222	+	52.3140i	−0.464221	+	3.14894i
$277$	9.73067	−	1.02273i	0.584659	−	0.0614502i	0.192419	−	0.981313i	$-0.438367\pi$
$277$	9.73067	−	1.02273i	0.584659	−	0.0614502i	0.392240	+	0.919863i	$0.371700\pi$
$278$	−43.5961	+	14.1652i	−2.61472	+	0.849573i
$279$	6.99464	−	10.0743i	0.418758	−	0.603132i
$280$	−14.8270	−	10.7724i	−0.886083	−	0.643777i
$281$	11.1314	−	4.95603i	0.664046	−	0.295652i	−0.0468995	−	0.998900i	$-0.514934\pi$
$281$	11.1314	−	4.95603i	0.664046	−	0.295652i	0.710945	+	0.703247i	$0.248267\pi$
$282$	−28.2062	+	18.7500i	−1.67966	+	1.11654i
$283$	−11.4395	−	10.3001i	−0.680006	−	0.612280i	0.254988	−	0.966944i	$-0.417928\pi$
$283$	−11.4395	−	10.3001i	−0.680006	−	0.612280i	−0.934994	+	0.354664i	$0.884595\pi$
$284$	19.6041	−	44.0314i	1.16329	−	2.61278i
$285$	−1.94937	+	2.46071i	−0.115471	+	0.145760i
$286$	15.4738	+	21.6326i	0.914984	+	1.27916i
$287$		−	6.59831i		−	0.389486i
$288$	−50.4276	+	17.5879i	−2.97147	+	1.03638i
$289$	0.0723102	+	0.222548i	0.00425354	+	0.0130911i
$290$	−0.282007	+	0.253920i	−0.0165600	+	0.0149107i
$291$	−7.47744	−	7.31893i	−0.438335	−	0.429043i
$292$	37.1131	+	3.90074i	2.17188	+	0.228274i
$293$	26.6244	−	5.65919i	1.55541	−	0.330613i	0.651608	−	0.758556i	$-0.274095\pi$
$293$	26.6244	−	5.65919i	1.55541	−	0.330613i	0.903806	+	0.427943i	$0.140761\pi$
$294$	17.6701	−	14.6252i	1.03054	−	0.852956i
$295$	0.457765	+	4.35534i	0.0266521	+	0.253578i
$296$	−87.6328			−5.09356
$297$	2.27407	−	17.0830i	0.131955	−	0.991256i
$298$	30.8503			1.78711
$299$	1.80708	+	17.1932i	0.104506	+	0.994310i
$300$	20.3878	−	16.8745i	1.17709	−	0.974249i
$301$	3.00247	−	0.638194i	0.173059	−	0.0367849i
$302$	2.84792	+	0.299328i	0.163879	+	0.0172244i
$303$	−14.4108	−	14.1053i	−0.827880	−	0.810330i
$304$	−12.2159	+	10.9992i	−0.700630	+	0.630850i
$305$	0.142320	+	0.438016i	0.00814923	+	0.0250807i
$306$	25.4078	+	21.9101i	1.45247	+	1.25252i
$307$		−	31.0795i		−	1.77380i	−0.461960	−	0.886901i	$-0.652854\pi$
$307$		−	31.0795i		−	1.77380i	0.461960	−	0.886901i	$-0.347146\pi$
$308$	23.9956	−	7.60085i	1.36728	−	0.433099i
$309$	3.60291	−	4.54799i	0.204963	−	0.258726i
$310$	6.48118	−	14.5570i	0.368106	−	0.826780i
$311$	4.24667	+	3.82372i	0.240807	+	0.216823i	0.780693	−	0.624914i	$-0.214866\pi$
$311$	4.24667	+	3.82372i	0.240807	+	0.216823i	−0.539886	+	0.841738i	$0.681533\pi$
$312$	−37.6754	+	25.0446i	−2.13295	+	1.41787i
$313$	−24.1472	+	10.7510i	−1.36488	+	0.607685i	−0.952838	−	0.303479i	$-0.901852\pi$
$313$	−24.1472	+	10.7510i	−1.36488	+	0.607685i	−0.412044	+	0.911164i	$0.635185\pi$
$314$	0.186099	+	0.135209i	0.0105021	+	0.00763026i
$315$	2.67079	+	5.66865i	0.150482	+	0.319392i
$316$	−50.0994	+	16.2783i	−2.81831	+	0.915725i
$317$	−1.96901	+	0.206952i	−0.110591	+	0.0116236i	−0.159662	−	0.987172i	$-0.551040\pi$
$317$	−1.96901	+	0.206952i	−0.110591	+	0.0116236i	0.0490713	+	0.998795i	$0.484374\pi$
$318$	−0.228646	+	1.55097i	−0.0128218	+	0.0869739i
$319$	−0.0313755	−	0.321372i	−0.00175669	−	0.0179934i
$320$	−27.2064	+	15.7076i	−1.52089	+	0.878084i
$321$	−13.8288	−	8.77139i	−0.771851	−	0.489571i
$322$	22.0915	+	4.69570i	1.23111	+	0.261681i
$323$	4.94579	+	1.60698i	0.275191	+	0.0894150i
$324$	46.6584	+	7.84554i	2.59214	+	0.435864i
$325$	5.08570	−	6.99986i	0.282104	−	0.388283i
$326$	5.28106	+	5.86521i	0.292491	+	0.324844i
$327$	−4.54256	−	5.48832i	−0.251204	−	0.303505i
$328$	−36.6362	−	16.3115i	−2.02290	−	0.900651i
$329$	5.23958	+	9.07523i	0.288868	+	0.500333i
$330$	−1.24594	−	22.3562i	−0.0685868	−	1.23067i
$331$	2.03858	−	3.53093i	0.112051	−	0.194078i	−0.804546	−	0.593890i	$-0.797591\pi$
$331$	2.03858	−	3.53093i	0.112051	−	0.194078i	0.916597	+	0.399812i	$0.130925\pi$
$332$	−25.3667	+	18.4300i	−1.39218	+	1.01148i
$333$	26.2636	+	14.4221i	1.43924	+	0.790327i
$334$	3.70749	−	11.4105i	0.202865	−	0.624354i
$335$	−2.02242	−	4.54244i	−0.110497	−	0.248180i
$336$	8.83140	+	31.6012i	0.481792	+	1.72399i
$337$	5.93123	+	27.9042i	0.323095	+	1.52004i	0.777292	+	0.629140i	$0.216593\pi$
$337$	5.93123	+	27.9042i	0.323095	+	1.52004i	−0.454198	+	0.890901i	$0.650074\pi$
$338$	7.45954	−	8.28465i	0.405745	−	0.450626i
$339$	−34.9960	−	1.45834i	−1.90072	−	0.0792061i
$340$	27.3464	+	15.7885i	1.48307	+	0.856249i
$341$	6.69236	+	11.7921i	0.362412	+	0.638580i
$342$	9.85507	−	2.31649i	0.532901	−	0.125261i
$343$	−10.1112	−	13.9169i	−0.545954	−	0.751441i
$344$	3.87883	−	18.2484i	0.209132	−	0.983890i
$345$	6.46804	−	13.0377i	0.348228	−	0.701924i
$346$	−2.94271	+	27.9980i	−0.158201	+	1.50518i
$347$	1.08070	−	10.2822i	0.0580151	−	0.551976i	−0.926453	−	0.376411i	$-0.877158\pi$
$347$	1.08070	−	10.2822i	0.0580151	−	0.551976i	0.984468	−	0.175565i	$-0.0561753\pi$
$348$	0.884729	−	0.0558759i	0.0474265	−	0.00299527i
$349$	−3.83672	+	18.0504i	−0.205375	+	0.966213i	0.747830	+	0.663890i	$0.231096\pi$
$349$	−3.83672	+	18.0504i	−0.205375	+	0.966213i	−0.953205	+	0.302324i	$0.902238\pi$
$350$	−6.64399	−	9.14466i	−0.355136	−	0.488803i
$351$	15.4130	−	1.30546i	0.822687	−	0.0696805i
$352$	6.60597	−	58.6726i	0.352100	−	3.12726i
$353$	−11.5976	−	6.69588i	−0.617279	−	0.356386i	0.158530	−	0.987354i	$-0.449324\pi$
$353$	−11.5976	−	6.69588i	−0.617279	−	0.356386i	−0.775809	+	0.630968i	$0.782658\pi$
$354$	7.56439	−	11.9259i	0.402043	−	0.633855i
$355$	−8.87638	+	9.85822i	−0.471109	+	0.523220i
$356$	5.59163	+	26.3065i	0.296356	+	1.39424i
$357$	7.26094	−	7.41820i	0.384290	−	0.392613i
$358$	−11.0392	−	24.7945i	−0.583440	−	1.31043i
$359$	1.92854	−	5.93545i	0.101785	−	0.313261i	−0.887178	−	0.461428i	$-0.847337\pi$
$359$	1.92854	−	5.93545i	0.101785	−	0.313261i	0.988962	+	0.148167i	$0.0473373\pi$
$360$	38.0768	−	0.815909i	2.00682	−	0.0430022i
$361$	−14.1018	+	10.2456i	−0.742202	+	0.539241i
$362$	20.8836	−	36.1715i	1.09762	−	1.90113i
$363$	15.9363	+	10.4419i	0.836439	+	0.548060i
$364$	11.2961	+	19.5654i	0.592075	+	1.02550i
$365$	−9.38285	−	4.17752i	−0.491121	−	0.218661i
$366$	0.517371	−	1.39219i	0.0270434	−	0.0727711i
$367$	−5.15250	−	5.72243i	−0.268958	−	0.298708i	0.593503	−	0.804832i	$-0.297745\pi$
$367$	−5.15250	−	5.72243i	−0.268958	−	0.298708i	−0.862461	+	0.506124i	$0.831078\pi$
$368$	44.7939	−	61.6535i	2.33504	−	3.21391i
$369$	8.29544	+	10.9179i	0.431843	+	0.568365i
$370$	37.0240	+	12.0298i	1.92479	+	0.625401i
$371$	0.474451	+	0.100848i	0.0246323	+	0.00523575i
$372$	−32.9843	+	17.2539i	−1.71016	+	0.894573i
$373$	18.2379	−	10.5296i	0.944321	−	0.545204i	0.0530086	−	0.998594i	$-0.483119\pi$
$373$	18.2379	−	10.5296i	0.944321	−	0.545204i	0.891312	+	0.453390i	$0.149786\pi$
$374$	−33.9951	+	14.8352i	−1.75784	+	0.767110i
$375$	−18.4212	+	7.29859i	−0.951266	+	0.376897i
$376$	63.3416	−	6.65747i	3.26659	−	0.343333i
$377$	0.275637	−	0.0895598i	0.0141960	−	0.00461256i
$378$	4.60028	−	19.6772i	0.236613	−	1.01209i
$379$	24.0003	+	17.4372i	1.23281	+	0.895691i	0.997098	−	0.0761314i	$-0.0242568\pi$
$379$	24.0003	+	17.4372i	1.23281	+	0.895691i	0.235715	+	0.971822i	$0.424257\pi$
$380$	8.70449	−	3.87549i	0.446531	−	0.198808i
$381$	0.0112345	+	0.177885i	0.000575562	+	0.00911333i
$382$	−7.43682	−	6.69615i	−0.380501	−	0.342605i
$383$	1.08521	−	2.43741i	0.0554515	−	0.124546i	−0.883695	−	0.468064i	$-0.844952\pi$
$383$	1.08521	−	2.43741i	0.0554515	−	0.124546i	0.939146	+	0.343518i	$0.111618\pi$
$384$	39.2162	+	5.78132i	2.00124	+	0.295027i
$385$	−6.92749	−	0.0512539i	−0.353057	−	0.00261214i
$386$		−	67.1784i		−	3.41929i
$387$	−4.16571	+	4.83072i	−0.211755	+	0.245559i
$388$	9.81361	+	30.2032i	0.498210	+	1.53333i
$389$	−0.473711	+	0.426531i	−0.0240181	+	0.0216260i	−0.681052	−	0.732235i	$-0.738477\pi$
$389$	−0.473711	+	0.426531i	−0.0240181	+	0.0216260i	0.657034	+	0.753861i	$0.271811\pi$
$390$	19.3555	−	5.40917i	0.980104	−	0.273904i
$391$	−23.9768	−	2.52007i	−1.21256	−	0.127445i
$392$	−42.1904	+	8.96785i	−2.13094	+	0.452945i
$393$	24.9466	+	9.27075i	1.25839	+	0.467647i
$394$	−5.41251	−	51.4966i	−0.272678	−	2.59436i
$395$	14.4984			0.729492
$396$	−30.1487	+	42.7443i	−1.51503	+	2.14798i
$397$	−25.2145			−1.26548			−0.632741	−	0.774364i	$-0.718070\pi$
$397$	−25.2145			−1.26548			−0.632741	+	0.774364i	$0.718070\pi$
$398$	7.32485	+	69.6913i	0.367162	+	3.49331i
$399$	−0.523101	−	3.08824i	−0.0261878	−	0.154605i
$400$	−37.3072	+	7.92990i	−1.86536	+	0.396495i
$401$	−29.0104	−	3.04912i	−1.44871	−	0.152266i	−0.652731	−	0.757590i	$-0.726377\pi$
$401$	−29.0104	−	3.04912i	−1.44871	−	0.152266i	−0.795979	+	0.605324i	$0.793044\pi$
$402$	−3.98397	+	15.5321i	−0.198703	+	0.774668i
$403$	−9.04396	+	8.14322i	−0.450512	+	0.405642i
$404$	18.9132	+	58.2088i	0.940966	+	2.89600i
$405$	−11.5459	−	6.02193i	−0.573721	−	0.299232i
$406$		−	0.378625i		−	0.0187908i
$407$	−26.9422	+	19.2717i	−1.33547	+	0.955263i
$408$	−23.2389	−	58.6537i	−1.15050	−	2.90379i
$409$	6.75518	−	15.1724i	0.334022	−	0.750226i	−0.665969	−	0.745979i	$-0.731982\pi$
$409$	6.75518	−	15.1724i	0.334022	−	0.750226i	0.999991	−	0.00424629i	$-0.00135164\pi$
$410$	13.2393	+	11.9207i	0.653841	+	0.588721i
$411$	−5.77737	−	2.86618i	−0.284977	−	0.141378i
$412$	−16.0880	+	7.16284i	−0.792599	+	0.352888i
$413$	−3.53499	−	2.56832i	−0.173945	−	0.126379i
$414$	−42.4573	+	20.0038i	−2.08666	+	0.983136i
$415$	8.20739	−	2.66674i	0.402885	−	0.130905i
$416$	52.7045	−	5.53947i	2.58405	−	0.271595i
$417$	−23.1020	−	18.3014i	−1.13131	−	0.896224i
$418$	−2.40791	+	10.9300i	−0.117775	+	0.534606i
$419$	−8.11793	+	4.68689i	−0.396587	+	0.228969i	−0.685010	−	0.728534i	$-0.740202\pi$
$419$	−8.11793	+	4.68689i	−0.396587	+	0.228969i	0.288423	+	0.957503i	$0.406869\pi$
$420$	0.791877	−	19.0028i	0.0386396	−	0.927241i
$421$	3.23871	+	0.688408i	0.157845	+	0.0335510i	0.286156	−	0.958183i	$-0.407622\pi$
$421$	3.23871	+	0.688408i	0.157845	+	0.0335510i	−0.128311	+	0.991734i	$0.540956\pi$
$422$	58.2537	+	18.9278i	2.83575	+	0.921390i
$423$	−20.0792	−	8.42914i	−0.976282	−	0.409839i
$424$	1.73282	−	2.38502i	0.0841532	−	0.115827i
$425$	8.07378	+	8.96685i	0.391636	+	0.434956i
$426$	42.1783	−	7.14435i	2.04354	−	0.346145i
$427$	−0.419794	−	0.186904i	−0.0203153	−	0.00904494i
$428$	24.8519	+	43.0448i	1.20126	+	2.08065i
$429$	−6.07543	+	15.9852i	−0.293325	+	0.771771i
$430$	−4.14383	+	7.17732i	−0.199833	+	0.346121i
$431$	−1.72195	+	1.25107i	−0.0829434	+	0.0602619i	−0.628484	−	0.777822i	$-0.716324\pi$
$431$	−1.72195	+	1.25107i	−0.0829434	+	0.0602619i	0.545541	+	0.838084i	$0.316324\pi$
$432$	−54.3422	−	41.1862i	−2.61454	−	1.98157i
$433$	−4.76068	+	14.6519i	−0.228784	+	0.704124i	0.769102	+	0.639126i	$0.220704\pi$
$433$	−4.76068	+	14.6519i	−0.228784	+	0.704124i	−0.997885	+	0.0649975i	$0.979296\pi$
$434$	6.46661	+	14.5242i	0.310407	+	0.697186i
$435$	−0.236336	−	0.0606203i	−0.0113315	−	0.00290652i
$436$	4.49579	+	21.1510i	0.215309	+	1.01295i
$437$	−4.86779	+	5.40623i	−0.232858	+	0.258615i
$438$	15.3521	+	29.3488i	0.733554	+	1.40234i
$439$	31.0083	+	17.9026i	1.47995	+	0.854447i	0.999742	−	0.0227105i	$-0.00722958\pi$
$439$	31.0083	+	17.9026i	1.47995	+	0.854447i	0.480203	+	0.877157i	$0.340563\pi$
$440$	−17.4098	+	38.3372i	−0.829981	+	1.82765i
$441$	14.1204	+	4.25579i	0.672399	+	0.202656i
$442$	−19.5682	−	26.9333i	−0.930764	−	1.28109i
$443$	2.49445	−	11.7354i	0.118515	−	0.557568i	−0.878321	−	0.478072i	$-0.841336\pi$
$443$	2.49445	−	11.7354i	0.118515	−	0.557568i	0.996835	−	0.0794956i	$-0.0253310\pi$
$444$	−50.3448	−	75.7355i	−2.38926	−	3.59425i
$445$	0.773725	−	7.36150i	0.0366781	−	0.348968i
$446$	6.40567	−	60.9459i	0.303317	−	2.88587i
$447$	10.9807	+	16.5186i	0.519368	+	0.781305i
$448$	6.51692	−	30.6597i	0.307896	−	1.44853i
$449$	15.0088	+	20.6578i	0.708307	+	0.974901i	0.999832	+	0.0183378i	$0.00583742\pi$
$449$	15.0088	+	20.6578i	0.708307	+	0.974901i	−0.291525	+	0.956563i	$0.594163\pi$
$450$	22.4903	+	6.77841i	1.06020	+	0.319537i
$451$	−14.8507	+	3.04196i	−0.699292	+	0.143240i
$452$	92.0676	+	53.1552i	4.33050	+	2.50021i
$453$	0.853399	+	1.63145i	0.0400962	+	0.0766520i
$454$	14.6507	−	16.2712i	0.687589	−	0.763645i
$455$	−1.29279	−	6.08211i	−0.0606071	−	0.285134i
$456$	−18.4402	−	4.72991i	−0.863541	−	0.221498i
$457$	0.414845	+	0.931757i	0.0194056	+	0.0435857i	0.922988	−	0.384828i	$-0.125739\pi$
$457$	0.414845	+	0.931757i	0.0194056	+	0.0435857i	−0.903583	+	0.428414i	$0.859073\pi$
$458$	11.3160	−	34.8272i	0.528764	−	1.62737i
$459$	−2.68816	+	21.4031i	−0.125472	+	0.999010i
$460$	−35.7370	+	25.9645i	−1.66625	+	1.21060i
$461$	2.26202	−	3.91794i	0.105353	−	0.182477i	−0.808529	−	0.588456i	$-0.799736\pi$
$461$	2.26202	−	3.91794i	0.105353	−	0.182477i	0.913882	+	0.405979i	$0.133069\pi$
$462$	17.4084	+	14.0018i	0.809910	+	0.651420i
$463$	4.22594	+	7.31953i	0.196396	+	0.340168i	0.947357	−	0.320179i	$-0.103743\pi$
$463$	4.22594	+	7.31953i	0.196396	+	0.340168i	−0.750961	+	0.660346i	$0.770410\pi$
$464$	−1.16713	−	0.519638i	−0.0541825	−	0.0241236i
$465$	10.1013	−	1.71101i	0.468438	−	0.0793462i
$466$	−9.11640	−	10.1248i	−0.422309	−	0.469022i
$467$	3.64591	−	5.01817i	0.168713	−	0.232213i	−0.716286	−	0.697807i	$-0.754159\pi$
$467$	3.64591	−	5.01817i	0.168713	−	0.232213i	0.884998	+	0.465594i	$0.154159\pi$
$468$	−43.2889	−	18.1725i	−2.00103	−	0.840023i
$469$	4.71832	+	1.53308i	0.217872	+	0.0707909i
$470$	−27.6751	−	5.88252i	−1.27656	−	0.271340i
$471$	−0.00615786	+	0.147771i	−0.000283739	+	0.00680893i
$472$	−22.9990	+	13.2785i	−1.05861	+	0.611191i
$473$	−2.82057	−	6.46338i	−0.129690	−	0.297187i
$474$	−36.6483	−	29.0328i	−1.68331	−	1.33352i
$475$	3.62096	−	0.380578i	0.166141	−	0.0174621i
$476$	−29.9639	+	9.73586i	−1.37339	+	0.446242i
$477$	−0.911841	+	0.429615i	−0.0417503	+	0.0196707i
$478$	−43.9497	−	31.9314i	−2.01021	−	1.46051i
$479$	−20.3778	+	9.07278i	−0.931085	+	0.414546i	−0.815504	−	0.578752i	$-0.803540\pi$
$479$	−20.3778	+	9.07278i	−0.931085	+	0.414546i	−0.115582	+	0.993298i	$0.536873\pi$
$480$	−39.9659	−	19.8273i	−1.82419	−	0.904987i
$481$	−22.0950	−	19.8945i	−1.00745	−	0.907109i
$482$	−31.0096	+	69.6487i	−1.41245	+	3.17241i
$483$	5.34885	+	13.5002i	0.243381	+	0.614279i
$484$	−28.1696	−	50.5025i	−1.28044	−	2.29557i
$485$		−	8.74055i		−	0.396888i
$486$	17.1264	+	38.3425i	0.776871	+	1.73925i
$487$	10.5290	+	32.4051i	0.477117	+	1.46841i	0.843082	+	0.537786i	$0.180739\pi$
$487$	10.5290	+	32.4051i	0.477117	+	1.46841i	−0.365965	+	0.930629i	$0.619261\pi$
$488$	−2.07552	+	1.86881i	−0.0939545	+	0.0845970i
$489$	−1.26079	+	4.91535i	−0.0570148	+	0.222280i
$490$	19.0561	+	2.00288i	0.860867	+	0.0904807i
$491$	18.4134	−	3.91389i	0.830985	−	0.176631i	0.227270	−	0.973832i	$-0.427020\pi$
$491$	18.4134	−	3.91389i	0.830985	−	0.176631i	0.603715	+	0.797201i	$0.293687\pi$
$492$	−6.95040	−	41.0333i	−0.313348	−	1.84992i
$493$	0.0422474	+	0.401957i	0.00190273	+	0.0181032i
$494$	−10.0456			−0.451972
$495$	11.5271	−	8.62448i	0.518102	−	0.387642i
$496$	53.6466			2.40880
$497$	−1.38351	−	13.1632i	−0.0620588	−	0.590450i
$498$	−26.0864	−	9.69431i	−1.16896	−	0.434412i
$499$	−7.43187	+	1.57969i	−0.332696	+	0.0707167i	−0.371231	−	0.928541i	$-0.621064\pi$
$499$	−7.43187	+	1.57969i	−0.332696	+	0.0707167i	0.0385350	+	0.999257i	$0.487731\pi$
$500$	59.8103	+	6.28632i	2.67480	+	0.281133i
$501$	7.42931	−	2.07623i	0.331917	−	0.0927590i
$502$	46.8231	−	42.1597i	2.08982	−	1.88168i
$503$	−8.18033	−	25.1765i	−0.364743	−	1.12256i	−0.950142	−	0.311818i	$-0.899062\pi$
$503$	−8.18033	−	25.1765i	−0.364743	−	1.12256i	0.585399	−	0.810745i	$-0.300938\pi$
$504$	−24.8161	+	28.7777i	−1.10540	+	1.28186i
$505$		−	16.8451i		−	0.749599i
$506$	0.383884	−	51.8858i	0.0170657	−	2.30661i
$507$	7.09109	+	1.04538i	0.314926	+	0.0464269i
$508$	0.220039	−	0.494215i	0.00976264	−	0.0219272i
$509$	−9.47468	−	8.53104i	−0.419958	−	0.378132i	0.431885	−	0.901929i	$-0.357849\pi$
$509$	−9.47468	−	8.53104i	−0.419958	−	0.378132i	−0.851843	+	0.523797i	$0.824515\pi$
$510$	1.76652	+	27.9707i	0.0782228	+	1.23856i
$511$	9.36176	−	4.16812i	0.414140	−	0.184387i
$512$	−2.69612	−	1.95884i	−0.119153	−	0.0865695i
$513$	4.74811	+	4.45234i	0.209634	+	0.196575i
$514$	1.06700	−	0.346689i	0.0470633	−	0.0152918i
$515$	4.82035	−	0.506640i	0.212410	−	0.0223252i
$516$	17.9994	−	7.13146i	0.792378	−	0.313945i
$517$	18.0099	−	15.9765i	0.792075	−	0.702646i
$518$	−33.6380	+	19.4209i	−1.47797	+	0.853305i
$519$	−16.0388	+	8.38979i	−0.704025	+	0.368271i
$520$	−36.9660	−	7.85736i	−1.62106	−	0.344568i
$521$	−6.80629	−	2.21150i	−0.298189	−	0.0968875i	0.156102	−	0.987741i	$-0.450107\pi$
$521$	−6.80629	−	2.21150i	−0.298189	−	0.0968875i	−0.454291	+	0.890854i	$0.650107\pi$
$522$	0.476010	+	0.626494i	0.0208344	+	0.0274209i
$523$	18.1933	−	25.0410i	0.795539	−	1.09497i	−0.197857	−	0.980231i	$-0.563398\pi$
$523$	18.1933	−	25.0410i	0.795539	−	1.09497i	0.993396	−	0.114734i	$-0.0366017\pi$
$524$	−54.0500	−	60.0286i	−2.36118	−	2.62236i
$525$	2.53164	−	6.81239i	0.110490	−	0.297317i
$526$	69.1972	+	30.8086i	3.01714	+	1.34332i
$527$	−8.48573	−	14.6977i	−0.369644	−	0.640243i
$528$	67.0528	−	34.4455i	2.91810	−	1.49905i
$529$	5.36315	−	9.28924i	0.233180	−	0.403880i
$530$	−1.05950	+	0.769775i	−0.0460219	+	0.0334369i
$531$	9.07810	−	0.194525i	0.393956	−	0.00844168i
$532$	−2.93777	+	9.04152i	−0.127368	+	0.392000i
$533$	−5.53411	−	12.4298i	−0.239709	−	0.538395i
$534$	−16.6971	+	17.0587i	−0.722553	+	0.738202i
$535$	−2.84421	−	13.3809i	−0.122966	−	0.578508i
$536$	20.1762	−	22.4080i	0.871480	−	0.967876i
$537$	9.34684	−	14.7361i	0.403346	−	0.635909i
$538$	−31.6392	−	18.2669i	−1.36406	−	0.787541i
$539$	−10.9990	+	12.0354i	−0.473762	+	0.518401i
$540$	22.5802	+	32.4386i	0.971695	+	1.39594i
$541$	25.5272	+	35.1352i	1.09750	+	1.51058i	0.838656	+	0.544661i	$0.183342\pi$
$541$	25.5272	+	35.1352i	1.09750	+	1.51058i	0.258845	+	0.965919i	$0.416658\pi$
$542$	−6.24030	+	29.3583i	−0.268044	+	1.26105i
$543$	26.8010	−	1.69265i	1.15014	−	0.0726384i
$544$	−7.72506	+	73.4991i	−0.331209	+	3.15125i
$545$	0.622091	−	5.91881i	0.0266475	−	0.253534i
$546$	−8.91148	+	17.9629i	−0.381376	+	0.768741i
$547$	−1.55388	+	7.31045i	−0.0664392	+	0.312572i	−0.998801	−	0.0489546i	$-0.984411\pi$
$547$	−1.55388	+	7.31045i	−0.0664392	+	0.312572i	0.932362	+	0.361527i	$0.117744\pi$
$548$	11.5056	+	15.8361i	0.491496	+	0.676487i
$549$	0.929593	−	0.218506i	0.0396741	−	0.00932560i
$550$	−17.5187	+	19.1694i	−0.747001	+	0.817386i
$551$	0.105618	+	0.0609787i	0.00449949	+	0.00259778i
$552$	88.1805	+	3.67462i	3.75321	+	0.156402i
$553$	−9.67948	+	10.7502i	−0.411613	+	0.457143i
$554$	−5.48008	−	25.7818i	−0.232826	−	1.09536i
$555$	6.73681	+	24.1062i	0.285962	+	1.02325i
$556$	36.3845	+	81.7209i	1.54305	+	3.46574i
$557$	−8.26967	+	25.4514i	−0.350397	+	1.07841i	0.608233	+	0.793758i	$0.291879\pi$
$557$	−8.26967	+	25.4514i	−0.350397	+	1.07841i	−0.958631	+	0.284653i	$0.908121\pi$
$558$	−28.9600	−	15.9028i	−1.22597	−	0.673218i
$559$	5.12075	−	3.72044i	0.216585	−	0.157358i
$560$	−13.7049	+	23.7376i	−0.579139	+	1.00310i
$561$	−20.0435	−	12.9221i	−0.846235	−	0.545573i
$562$	−16.4124	−	28.4270i	−0.692314	−	1.19912i
$563$	−21.3311	−	9.49724i	−0.899000	−	0.400261i	−0.0954063	−	0.995438i	$-0.530415\pi$
$563$	−21.3311	−	9.49724i	−0.899000	−	0.400261i	−0.803594	+	0.595178i	$0.797082\pi$
$564$	42.1432	+	50.9174i	1.77455	+	2.14401i
$565$	−19.5785	−	21.7441i	−0.823674	−	0.914782i
$566$	−24.3742	+	33.5483i	−1.02453	+	1.41014i
$567$	12.1735	−	4.54060i	0.511237	−	0.190687i
$568$	−76.5070	−	24.8586i	−3.21016	−	1.04305i
$569$	5.31206	+	1.12911i	0.222693	+	0.0473349i	0.317907	−	0.948122i	$-0.397020\pi$
$569$	5.31206	+	1.12911i	0.222693	+	0.0473349i	−0.0952135	+	0.995457i	$0.530353\pi$
$570$	7.14149	+	4.52972i	0.299124	+	0.189729i
$571$	8.79380	−	5.07710i	0.368009	−	0.212470i	−0.304579	−	0.952487i	$-0.598516\pi$
$571$	8.79380	−	5.07710i	0.368009	−	0.212470i	0.672588	+	0.740017i	$0.265183\pi$
$572$	38.8278	−	34.4439i	1.62347	−	1.44017i
$573$	0.938397	−	6.36540i	0.0392021	−	0.265918i
$574$	−17.6778	+	1.85801i	−0.737855	+	0.0775517i
$575$	−16.0533	+	5.21603i	−0.669468	+	0.217523i
$576$	27.7623	+	58.9244i	1.15676	+	2.45518i
$577$	17.0075	+	12.3566i	0.708029	+	0.514414i	0.882537	−	0.470242i	$-0.155833\pi$
$577$	17.0075	+	12.3566i	0.708029	+	0.514414i	−0.174508	+	0.984656i	$0.555833\pi$
$578$	0.575874	−	0.256396i	0.0239532	−	0.0106647i
$579$	35.9704	−	23.9111i	1.49488	−	0.993712i
$580$	0.550328	+	0.495518i	0.0228511	+	0.0205753i
$581$	−3.50215	+	7.86595i	−0.145294	+	0.326335i
$582$	−17.5028	+	22.0940i	−0.725515	+	0.915825i
$583$	0.00824453	−	1.11433i	0.000341453	−	0.0461510i
$584$		−	62.2837i		−	2.57732i
$585$	9.78561	+	8.43850i	0.404585	+	0.348889i
$586$	−22.6588	−	69.7367i	−0.936028	−	2.88080i
$587$	32.4155	−	29.1870i	1.33793	−	1.20468i	0.377550	−	0.925989i	$-0.376767\pi$
$587$	32.4155	−	29.1870i	1.33793	−	1.20468i	0.960381	−	0.278689i	$-0.0898999\pi$
$588$	−31.9886	−	31.3105i	−1.31919	−	1.29122i
$589$	−5.09304	−	0.535300i	−0.209855	−	0.0220567i
$590$	11.5396	−	2.45283i	0.475079	−	0.100981i
$591$	25.6471	−	21.2275i	1.05498	−	0.873184i
$592$	13.6998	+	130.344i	0.563056	+	5.35712i
$593$	−37.0300			−1.52064			−0.760319	−	0.649549i	$-0.774958\pi$
$593$	−37.0300			−1.52064			−0.760319	+	0.649549i	$0.774958\pi$
$594$	−46.4080	−	1.28217i	−1.90414	−	0.0526082i
$595$	8.67130			0.355489
$596$	−6.29297	−	59.8736i	−0.257770	−	2.45252i
$597$	−34.7087	+	28.7276i	−1.42053	+	1.17574i
$598$	45.5541	−	9.68282i	1.86285	−	0.395960i
$599$	−23.9622	−	2.51853i	−0.979068	−	0.102904i	−0.398546	−	0.917148i	$-0.630485\pi$
$599$	−23.9622	−	2.51853i	−0.979068	−	0.102904i	−0.580522	+	0.814244i	$0.697152\pi$
$600$	−31.5665	−	30.8973i	−1.28870	−	1.26138i
$601$	13.8822	−	12.4996i	0.566268	−	0.509870i	−0.335529	−	0.942030i	$-0.608915\pi$
$601$	13.8822	−	12.4996i	0.566268	−	0.509870i	0.901797	+	0.432160i	$0.142248\pi$
$602$	−2.55527	−	7.86431i	−0.104145	−	0.320525i
$603$	−9.73460	+	3.39519i	−0.396424	+	0.138263i
$604$		−	5.58824i		−	0.227382i
$605$	3.07836	+	15.6152i	0.125153	+	0.634849i
$606$	−33.7322	+	42.5804i	−1.37028	+	1.72971i
$607$	−10.0075	+	22.4773i	−0.406193	+	0.912324i	0.588409	+	0.808563i	$0.299754\pi$
$607$	−10.0075	+	22.4773i	−0.406193	+	0.912324i	−0.994602	+	0.103761i	$0.966912\pi$
$608$	16.5724	+	14.9218i	0.672098	+	0.605160i
$609$	0.202733	−	0.134766i	0.00821515	−	0.00546098i
$610$	1.13343	−	0.504635i	0.0458912	−	0.0204321i
$611$	17.4818	+	12.7013i	0.707238	+	0.513839i
$612$	37.3400	−	53.7803i	1.50938	−	2.17394i
$613$	21.4976	−	6.98501i	0.868282	−	0.282122i	0.159199	−	0.987247i	$-0.449109\pi$
$613$	21.4976	−	6.98501i	0.868282	−	0.282122i	0.709083	+	0.705125i	$0.249109\pi$
$614$	−83.2662	+	8.75163i	−3.36035	+	0.353187i
$615$	−1.67056	+	11.3319i	−0.0673636	+	0.456946i
$616$	−16.8028	−	38.5038i	−0.677004	−	1.55136i
$617$	8.17258	−	4.71844i	0.329016	−	0.189957i	−0.326388	−	0.945236i	$-0.605832\pi$
$617$	8.17258	−	4.71844i	0.329016	−	0.189957i	0.655404	+	0.755278i	$0.272498\pi$
$618$	−13.1992	−	8.37203i	−0.530950	−	0.336772i
$619$	13.0960	+	2.78364i	0.526373	+	0.111884i	0.463431	−	0.886133i	$-0.346618\pi$
$619$	13.0960	+	2.78364i	0.526373	+	0.111884i	0.0629422	+	0.998017i	$0.479952\pi$
$620$	−29.5739	−	9.60915i	−1.18772	−	0.385913i
$621$	−25.8230	−	15.6135i	−1.03624	−	0.626549i
$622$	9.04845	−	12.4541i	0.362810	−	0.499365i
$623$	4.94180	+	5.48842i	0.197989	+	0.219889i
$624$	43.1409	+	52.1229i	1.72702	+	2.08659i
$625$	−1.84495	−	0.821424i	−0.0737980	−	0.0328570i
$626$	35.6031	+	61.6663i	1.42298	+	2.46468i
$627$	−6.70950	+	2.60108i	−0.267951	+	0.103877i
$628$	0.224449	−	0.388757i	0.00895648	−	0.0155131i
$629$	33.5439	−	24.3710i	1.33748	−	0.971737i
$630$	14.4350	−	8.75164i	0.575105	−	0.348674i
$631$	−3.99811	+	12.3049i	−0.159162	+	0.489851i	−0.998559	−	0.0536685i	$-0.982909\pi$
$631$	−3.99811	+	12.3049i	−0.159162	+	0.489851i	0.839397	+	0.543519i	$0.182909\pi$
$632$	35.7604	+	80.3191i	1.42247	+	3.19492i
$633$	10.5997	+	37.9287i	0.421301	+	1.50753i
$634$	1.10890	+	5.21698i	0.0440402	+	0.207193i
$635$	−0.0996297	+	0.110650i	−0.00395369	+	0.00439101i
$636$	3.05673	+	0.127379i	0.121207	+	0.00505089i
$637$	−12.6734	−	7.31701i	−0.502140	−	0.289911i
$638$	−0.852164	+	0.174554i	−0.0337375	+	0.00691065i
$639$	18.8381	+	20.0412i	0.745224	+	0.792819i
$640$	19.4638	+	26.7896i	0.769373	+	1.05895i
$641$	−2.07714	+	9.77218i	−0.0820421	+	0.385978i	−0.999941	−	0.0108359i	$-0.996551\pi$
$641$	−2.07714	+	9.77218i	−0.0820421	+	0.385978i	0.917899	+	0.396814i	$0.129884\pi$
$642$	−19.6057	+	39.5192i	−0.773774	+	1.55970i
$643$	1.32573	−	12.6135i	0.0522817	−	0.497428i	−0.936779	−	0.349921i	$-0.886209\pi$
$643$	1.32573	−	12.6135i	0.0522817	−	0.497428i	0.989061	−	0.147507i	$-0.0471248\pi$
$644$	4.60700	−	43.8326i	0.181541	−	1.72725i
$645$	−5.31799	+	0.335863i	−0.209396	+	0.0132246i
$646$	2.91265	−	13.7029i	0.114597	−	0.539135i
$647$	−19.3401	−	26.6193i	−0.760337	−	1.04651i	−0.997186	−	0.0749678i	$-0.976115\pi$
$647$	−19.3401	−	26.6193i	−0.760337	−	1.04651i	0.236849	−	0.971547i	$-0.423885\pi$
$648$	4.88261	−	78.8161i	0.191807	−	3.09619i
$649$	−4.15077	+	9.14018i	−0.162932	+	0.358784i
$650$	−20.1856	−	11.6542i	−0.791746	−	0.457115i
$651$	−5.47525	+	8.63219i	−0.214592	+	0.338322i
$652$	10.3058	−	11.4458i	0.403608	−	0.448252i
$653$	−4.44155	−	20.8959i	−0.173811	−	0.817718i	−0.975504	−	0.219982i	$-0.929400\pi$
$653$	−4.44155	−	20.8959i	−0.173811	−	0.817718i	0.801693	−	0.597736i	$-0.203933\pi$
$654$	−13.4248	+	13.7156i	−0.524952	+	0.536321i
$655$	9.04253	+	20.3099i	0.353321	+	0.793572i
$656$	−18.5342	+	57.0424i	−0.723639	+	2.22713i
$657$	−10.2503	+	18.6665i	−0.399902	+	0.728249i
$658$	22.8383	−	16.5930i	0.890331	−	0.646863i
$659$	5.34609	−	9.25969i	0.208254	−	0.360706i	−0.742911	−	0.669391i	$-0.766555\pi$
$659$	5.34609	−	9.25969i	0.208254	−	0.360706i	0.951165	+	0.308684i	$0.0998886\pi$
$660$	−43.1343	+	6.97841i	−1.67900	+	0.271634i
$661$	−14.6301	−	25.3401i	−0.569045	−	0.985615i	−0.996661	−	0.0816544i	$-0.973980\pi$
$661$	−14.6301	−	25.3401i	−0.569045	−	0.985615i	0.427616	−	0.903961i	$-0.359354\pi$
$662$	−10.0339	−	4.46737i	−0.389978	−	0.173629i
$663$	7.45631	−	20.0642i	0.289579	−	0.779228i
$664$	35.0171	+	38.8904i	1.35893	+	1.50924i
$665$	1.53796	−	2.11683i	0.0596397	−	0.0820870i
$666$	31.2432	−	74.4248i	1.21065	−	2.88390i
$667$	−0.537728	−	0.174718i	−0.0208209	−	0.00676512i
$668$	−22.9015	−	4.86786i	−0.886086	−	0.188343i
$669$	34.9132	−	18.2629i	1.34982	−	0.706083i
$670$	−11.6003	+	6.69744i	−0.448159	+	0.258745i
$671$	−0.227129	+	1.03099i	−0.00876822	+	0.0398010i
$672$	41.3837	−	16.3965i	1.59641	−	0.632508i
$673$	41.5078	−	4.36264i	1.60001	−	0.168168i	0.737906	−	0.674904i	$-0.235815\pi$
$673$	41.5078	−	4.36264i	1.60001	−	0.168168i	0.862101	+	0.506736i	$0.169148\pi$
$674$	73.0890	−	23.7481i	2.81528	−	0.914741i
$675$	4.37559	+	14.4550i	0.168417	+	0.556372i
$676$	−17.6003	−	12.7874i	−0.676935	−	0.491822i
$677$	−27.1757	+	12.0994i	−1.04445	+	0.465017i	−0.855951	−	0.517057i	$-0.827028\pi$
$677$	−27.1757	+	12.0994i	−1.04445	+	0.465017i	−0.188495	+	0.982074i	$0.560361\pi$
$678$	5.94737	+	94.1695i	0.228407	+	3.61656i
$679$	6.48089	+	5.83542i	0.248714	+	0.223943i
$680$	21.4361	−	48.1462i	0.822036	−	1.84632i
$681$	13.9270	+	2.05314i	0.533684	+	0.0786766i
$682$	29.7082	−	21.2503i	1.13759	−	0.813714i
$683$			27.9122i			1.06803i	0.845475	+	0.534015i	$0.179317\pi$
$683$			27.9122i			1.06803i	−0.845475	+	0.534015i	$0.820683\pi$
$684$	−6.50607	−	18.6540i	−0.248766	−	0.713254i
$685$	−1.66482	−	5.12378i	−0.0636094	−	0.195770i
$686$	−34.4380	+	31.0081i	−1.31485	+	1.18390i
$687$	22.6758	−	6.33708i	0.865137	−	0.241775i
$688$	−27.7490	−	2.91654i	−1.05792	−	0.111192i
$689$	0.978349	−	0.207954i	0.0372721	−	0.00792243i
$690$	−36.7509	−	13.6575i	−1.39908	−	0.519932i
$691$	−0.134166	−	1.27650i	−0.00510390	−	0.0485604i	0.991674	−	0.128777i	$-0.0411053\pi$
$691$	−0.134166	−	1.27650i	−0.00510390	−	0.0485604i	−0.996777	+	0.0802171i	$0.974439\pi$
$692$	54.9382			2.08844
$693$	−1.30093	+	14.3049i	−0.0494184	+	0.543400i
$694$	−27.8516			−1.05723
$695$	−2.57353	−	24.4855i	−0.0976197	−	0.928790i
$696$	−0.247098	−	1.45880i	−0.00936621	−	0.0552955i
$697$	18.5598	−	3.94501i	0.703003	−	0.149428i
$698$	49.4397	+	5.19632i	1.87132	+	0.196684i
$699$	2.17643	−	8.48509i	0.0823201	−	0.320936i
$700$	−16.3925	+	14.7599i	−0.619579	+	0.557871i
$701$	9.82030	+	30.2238i	0.370908	+	1.14154i	0.946198	+	0.323588i	$0.104889\pi$
$701$	9.82030	+	30.2238i	0.370908	+	1.14154i	−0.575290	+	0.817949i	$0.695111\pi$
$702$	−7.83764	−	40.9260i	−0.295813	−	1.54465i
$703$		−	12.5112i		−	0.471869i
$704$	−72.0097	−	0.532773i	−2.71397	−	0.0200796i
$705$	−6.70075	−	16.9123i	−0.252365	−	0.636954i
$706$	−14.6734	+	32.9570i	−0.552241	+	1.24035i
$707$	12.4902	+	11.2463i	0.469744	+	0.422959i
$708$	−24.6886	−	12.2481i	−0.927853	−	0.460313i
$709$	0.437717	−	0.194884i	0.0164388	−	0.00731903i	−0.398501	−	0.917168i	$-0.630469\pi$
$709$	0.437717	−	0.194884i	0.0164388	−	0.00731903i	0.414940	+	0.909849i	$0.363803\pi$
$710$	28.9110	+	21.0050i	1.08501	+	0.788305i
$711$	2.50105	−	29.9569i	0.0937967	−	1.12347i
$712$	42.6902	−	13.8709i	1.59988	−	0.519833i
$713$	23.6116	−	2.48168i	0.884260	−	0.0929395i
$714$	−21.9189	−	17.3642i	−0.820296	−	0.649837i
$715$	−13.0929	+	5.71365i	−0.489647	+	0.213678i
$716$	−45.8688	+	26.4823i	−1.71420	+	0.989692i
$717$	1.45426	−	34.8982i	0.0543104	−	1.30330i
$718$	−16.4449	−	3.49548i	−0.613719	−	0.130450i
$719$	−22.0526	−	7.16534i	−0.822425	−	0.267222i	−0.132574	−	0.991173i	$-0.542324\pi$
$719$	−22.0526	−	7.16534i	−0.822425	−	0.267222i	−0.689851	+	0.723951i	$0.742324\pi$
$720$	−7.16617	−	56.5076i	−0.267067	−	2.10591i
$721$	−2.84253	+	3.91241i	−0.105862	+	0.145706i
$722$	31.4202	+	34.8957i	1.16934	+	1.29868i
$723$	−48.3305	+	8.18644i	−1.79743	+	0.304457i
$724$	−74.4608	−	33.1521i	−2.76731	−	1.23209i
$725$	0.141487	+	0.245062i	0.00525468	+	0.00910137i
$726$	23.4879	−	45.6358i	0.871718	−	1.69370i
$727$	−19.7219	+	34.1593i	−0.731444	+	1.26690i	0.224822	+	0.974400i	$0.427820\pi$
$727$	−19.7219	+	34.1593i	−0.731444	+	1.26690i	−0.956266	+	0.292498i	$0.905513\pi$
$728$	30.5055	−	22.1635i	1.13061	−	0.821435i
$729$	−14.4344	+	22.8177i	−0.534608	+	0.845100i
$730$	−8.55002	+	26.3143i	−0.316450	+	0.973934i
$731$	3.59024	+	8.06381i	0.132790	+	0.298251i
$732$	−2.80748	−	0.720118i	−0.103767	−	0.0266163i
$733$	−2.03269	−	9.56304i	−0.0750790	−	0.353219i	0.924532	−	0.381104i	$-0.124456\pi$
$733$	−2.03269	−	9.56304i	−0.0750790	−	0.353219i	−0.999611	+	0.0278852i	$0.991123\pi$
$734$	−13.8803	+	15.4156i	−0.512330	+	0.569000i
$735$	5.71029	+	10.9164i	0.210627	+	0.402657i
$736$	−89.5343	−	51.6927i	−3.30028	−	1.90542i
$737$	1.27523	−	11.3262i	0.0469735	−	0.417207i
$738$	26.9147	−	25.2990i	0.990744	−	0.931268i
$739$	−14.0478	−	19.3351i	−0.516757	−	0.711255i	0.468284	−	0.883578i	$-0.344873\pi$
$739$	−14.0478	−	19.3351i	−0.516757	−	0.711255i	−0.985040	+	0.172324i	$0.944873\pi$
$740$	15.7949	−	74.3093i	0.580633	−	2.73167i
$741$	−3.57557	−	5.37886i	−0.131352	−	0.197597i
$742$	0.136585	−	1.29952i	0.00501418	−	0.0477067i
$743$	−3.84917	+	36.6224i	−0.141212	+	1.34355i	0.662738	+	0.748851i	$0.269394\pi$
$743$	−3.84917	+	36.6224i	−0.141212	+	1.34355i	−0.803951	+	0.594696i	$0.797273\pi$
$744$	34.3939	+	51.7399i	1.26094	+	1.89688i
$745$	−3.44503	+	16.2076i	−0.126216	+	0.593799i
$746$	−33.3459	−	45.8967i	−1.22088	−	1.68040i
$747$	−4.09428	−	17.4184i	−0.149802	−	0.637305i
$748$	35.7263	+	62.9508i	1.30628	+	2.30171i
$749$	11.8205	+	6.82456i	0.431911	+	0.249364i
$750$	24.7411	+	47.2976i	0.903417	+	1.72707i
$751$	−20.5430	+	22.8153i	−0.749625	+	0.832543i	−0.990428	−	0.138031i	$-0.955923\pi$
$751$	−20.5430	+	22.8153i	−0.749625	+	0.832543i	0.240803	+	0.970574i	$0.422589\pi$
$752$	−19.8045	−	93.1730i	−0.722197	−	3.39767i
$753$	39.2402	+	10.0651i	1.42999	+	0.366793i
$754$	−0.317559	−	0.713249i	−0.0115648	−	0.0259750i
$755$	−0.475281	+	1.46276i	−0.0172972	+	0.0532354i
$756$	−39.1275	−	4.91429i	−1.42305	−	0.178731i
$757$	−34.5971	+	25.1362i	−1.25745	+	0.913592i	−0.998630	−	0.0523331i	$-0.983334\pi$
$757$	−34.5971	+	25.1362i	−1.25745	+	0.913592i	−0.258822	+	0.965925i	$0.583334\pi$
$758$	39.9585	−	69.2101i	1.45136	−	2.51383i
$759$	27.9187	−	18.2624i	1.01338	−	0.662884i
$760$	−7.95143	−	13.7723i	−0.288429	−	0.499573i
$761$	24.6757	+	10.9863i	0.894493	+	0.398254i	0.801906	−	0.597451i	$-0.203820\pi$
$761$	24.6757	+	10.9863i	0.894493	+	0.398254i	0.0925874	+	0.995705i	$0.470486\pi$
$762$	0.473415	−	0.0801892i	0.0171500	−	0.00290495i
$763$	3.97331	+	4.41281i	0.143844	+	0.159755i
$764$	−11.4788	+	15.7991i	−0.415287	+	0.571593i
$765$	−14.3480	+	10.9016i	−0.518754	+	0.394149i
$766$	−6.83574	−	2.22107i	−0.246985	−	0.0802504i
$767$	−8.81326	−	1.87332i	−0.318228	−	0.0676415i
$768$	1.31453	−	31.5449i	0.0474340	−	1.13828i
$769$	−41.9099	+	24.1967i	−1.51131	+	0.872555i	−0.511396	+	0.859345i	$0.670871\pi$
$769$	−41.9099	+	24.1967i	−1.51131	+	0.872555i	−0.999913	+	0.0132095i	$0.995795\pi$
$770$	1.81338	+	18.5741i	0.0653498	+	0.669364i
$771$	0.565415	+	0.447921i	0.0203629	+	0.0161315i
$772$	−130.379	+	13.7033i	−4.69242	+	0.493194i
$773$	−33.6456	+	10.9321i	−1.21015	+	0.393201i	−0.843485	−	0.537152i	$-0.819500\pi$
$773$	−33.6456	+	10.9321i	−1.21015	+	0.393201i	−0.366664	+	0.930354i	$0.619500\pi$
$774$	14.1152	+	9.80023i	0.507359	+	0.352262i
$775$	−9.61296	−	6.98422i	−0.345308	−	0.250881i
$776$	48.4216	−	21.5587i	1.73823	−	0.773911i
$777$	−22.3718	−	11.0987i	−0.802582	−	0.398165i
$778$	1.27613	+	1.14903i	0.0457513	+	0.0411947i
$779$	2.32876	−	5.23049i	0.0834366	−	0.187402i
$780$	−14.4462	−	36.4614i	−0.517258	−	1.30553i
$781$	−28.9884	+	9.18235i	−1.03729	+	0.328570i
$782$			64.9467i			2.32249i
$783$	−0.166025	+	0.477868i	−0.00593325	+	0.0170776i
$784$	19.9344	+	61.3518i	0.711943	+	2.19113i
$785$	−0.0918149	+	0.0826705i	−0.00327701	+	0.00295064i
$786$	17.8129	−	69.4459i	0.635365	−	2.47705i
$787$	−25.6484	−	2.69576i	−0.914267	−	0.0960933i	−0.364302	−	0.931281i	$-0.618692\pi$
$787$	−25.6484	−	2.69576i	−0.914267	−	0.0960933i	−0.549965	+	0.835188i	$0.685359\pi$
$788$	−98.8396	+	21.0090i	−3.52101	+	0.748415i
$789$	8.13336	+	48.0171i	0.289555	+	1.70945i
$790$	−4.08257	−	38.8430i	−0.145251	−	1.38197i
$791$	29.1938			1.03801
$792$	76.2102	+	42.5861i	2.70801	+	1.51323i
$793$	−0.947564			−0.0336490
$794$	7.10012	+	67.5531i	0.251974	+	2.39737i
$795$	−0.789287	−	0.293317i	−0.0279931	−	0.0104029i
$796$	133.761	−	28.4319i	4.74105	−	1.00774i
$797$	16.9653	+	1.78313i	0.600943	+	0.0631617i	0.400115	−	0.916465i	$-0.368970\pi$
$797$	16.9653	+	1.78313i	0.600943	+	0.0631617i	0.200828	+	0.979627i	$0.435637\pi$
$798$	−8.12651	+	2.27107i	−0.287676	+	0.0803950i
$799$	−22.3943	+	20.1639i	−0.792252	+	0.713347i
$800$	15.9893	+	49.2101i	0.565308	+	1.73984i
$801$	−15.0771	−	2.86859i	−0.532722	−	0.101357i
$802$			78.5813i			2.77480i
$803$	−13.6971	−	19.1488i	−0.483360	−	0.675745i
$804$	30.9570	+	4.56372i	1.09177	+	0.160950i
$805$	−4.93388	+	11.0817i	−0.173897	+	0.390578i
$806$	24.3634	+	21.9369i	0.858165	+	0.772696i
$807$	−1.48056	−	23.4429i	−0.0521181	−	0.825227i
$808$	93.3200	−	41.5487i	3.28299	−	1.46168i
$809$	−38.7684	−	28.1669i	−1.36302	−	0.990295i	−0.998246	−	0.0592001i	$-0.981145\pi$
$809$	−38.7684	−	28.1669i	−1.36302	−	0.990295i	−0.364778	−	0.931095i	$-0.618855\pi$
$810$	−12.8824	+	32.6288i	−0.452640	+	1.14646i
$811$	45.0299	−	14.6311i	1.58121	−	0.513768i	0.618845	−	0.785513i	$-0.287601\pi$
$811$	45.0299	−	14.6311i	1.58121	−	0.513768i	0.962369	+	0.271745i	$0.0876009\pi$
$812$	−0.734827	+	0.0772334i	−0.0257874	+	0.00271036i
$813$	−17.9409	+	7.10830i	−0.629215	+	0.249299i
$814$	59.2181	+	66.7550i	2.07559	+	2.33976i
$815$	−3.67109	+	2.11951i	−0.128593	+	0.0742430i
$816$	−83.6081	+	43.7348i	−2.92687	+	1.53103i
$817$	2.60530	+	0.553774i	0.0911480	+	0.0193741i
$818$	−42.5510	−	13.8257i	−1.48776	−	0.483403i
$819$	−12.7901	+	1.62201i	−0.446921	+	0.0566775i
$820$	20.4348	−	28.1261i	0.713615	−	0.982207i
$821$	−11.7622	−	13.0632i	−0.410503	−	0.455910i	0.502068	−	0.864828i	$-0.332573\pi$
$821$	−11.7622	−	13.0632i	−0.410503	−	0.455910i	−0.912571	+	0.408918i	$0.865906\pi$
$822$	−6.05204	+	16.2854i	−0.211089	+	0.568020i
$823$	26.1285	+	11.6332i	0.910784	+	0.405507i	0.807990	−	0.589196i	$-0.200555\pi$
$823$	26.1285	+	11.6332i	0.910784	+	0.405507i	0.102793	+	0.994703i	$0.467222\pi$
$824$	14.6962	+	25.4545i	0.511966	+	0.886751i
$825$	−16.4997	−	2.55727i	−0.574445	−	0.0890328i
$826$	−5.88546	+	10.1939i	−0.204781	+	0.354691i
$827$	−13.0031	+	9.44733i	−0.452163	+	0.328516i	−0.790449	−	0.612527i	$-0.790153\pi$
$827$	−13.0031	+	9.44733i	−0.452163	+	0.328516i	0.338286	+	0.941043i	$0.390153\pi$
$828$	47.4837	+	78.3199i	1.65017	+	2.72181i
$829$	0.324003	−	0.997179i	0.0112531	−	0.0346335i	−0.945272	−	0.326282i	$-0.894204\pi$
$829$	0.324003	−	0.997179i	0.0112531	−	0.0346335i	0.956525	+	0.291649i	$0.0942039\pi$
$830$	−9.45567	−	21.2378i	−0.328211	−	0.737174i
$831$	11.8542	−	12.1109i	0.411217	−	0.420123i
$832$	−13.4383	−	63.2222i	−0.465889	−	2.19184i
$833$	13.6555	−	15.1660i	0.473137	−	0.525471i
$834$	−42.5267	+	67.0469i	−1.47258	+	2.32165i
$835$	5.58062	+	3.22197i	0.193125	+	0.111501i
$836$	21.7040	+	2.44366i	0.750648	+	0.0845158i
$837$	−1.79280	−	21.1668i	−0.0619683	−	0.731633i
$838$	14.8427	+	20.4292i	0.512733	+	0.705716i
$839$	4.36460	−	20.5338i	0.150683	−	0.708907i	−0.836325	−	0.548234i	$-0.815300\pi$
$839$	4.36460	−	20.5338i	0.150683	−	0.708907i	0.987008	−	0.160673i	$-0.0513664\pi$
$840$	−31.6805	+	2.00081i	−1.09308	+	0.0690346i
$841$	3.03033	−	28.8317i	0.104494	−	0.994197i
$842$	0.932356	−	8.87077i	0.0321311	−	0.305707i
$843$	9.37940	−	18.9061i	0.323044	−	0.651160i
$844$	24.8518	−	116.919i	0.855435	−	4.02451i
$845$	3.51944	+	4.84410i	0.121073	+	0.166642i
$846$	−16.9287	+	56.1683i	−0.582022	+	1.93111i
$847$	−13.6335	−	8.14260i	−0.468451	−	0.279783i
$848$	−3.81836	−	2.20453i	−0.131123	−	0.0757039i
$849$	−26.6389	−	1.11009i	−0.914244	−	0.0380980i
$850$	21.7499	−	24.1557i	0.746015	−	0.828534i
$851$	12.0594	+	56.7350i	0.413391	+	1.94485i
$852$	−22.4693	−	80.4014i	−0.769786	−	2.75451i
$853$	−2.15268	−	4.83501i	−0.0737065	−	0.165547i	0.872935	−	0.487837i	$-0.162214\pi$
$853$	−2.15268	−	4.83501i	−0.0737065	−	0.165547i	−0.946641	+	0.322290i	$0.895547\pi$
$854$	−0.382533	+	1.17732i	−0.0130900	+	0.0402869i
$855$	0.116486	+	5.43616i	0.00398374	+	0.185913i
$856$	67.1135	−	48.7608i	2.29389	−	1.66661i
$857$	−3.88021	+	6.72072i	−0.132545	+	0.229575i	−0.924657	−	0.380801i	$-0.875648\pi$
$857$	−3.88021	+	6.72072i	−0.132545	+	0.229575i	0.792112	+	0.610376i	$0.208982\pi$
$858$	44.5372	+	11.7757i	1.52047	+	0.402014i
$859$	24.3358	+	42.1508i	0.830326	+	1.43817i	0.897780	+	0.440445i	$0.145179\pi$
$859$	24.3358	+	42.1508i	0.830326	+	1.43817i	−0.0674537	+	0.997722i	$0.521488\pi$
$860$	14.7749	+	6.57820i	0.503819	+	0.224315i
$861$	−7.28698	−	8.80414i	−0.248340	−	0.300044i
$862$	3.83666	+	4.26105i	0.130677	+	0.145132i
$863$	8.87079	−	12.2096i	0.301965	−	0.415619i	−0.630889	−	0.775873i	$-0.717310\pi$
$863$	8.87079	−	12.2096i	0.301965	−	0.415619i	0.932854	+	0.360253i	$0.117310\pi$
$864$	−47.8620	+	79.1584i	−1.62830	+	2.69302i
$865$	−14.3805	−	4.67250i	−0.488951	−	0.158870i
$866$	40.5949	+	8.62871i	1.37947	+	0.293215i
$867$	0.342259	+	0.217089i	0.0116237	+	0.00737273i
$868$	26.8693	−	15.5130i	0.912002	−	0.526545i
$869$	28.6576	+	16.8294i	0.972144	+	0.570899i
$870$	−0.0958604	+	0.650247i	−0.00324997	+	0.0220454i
$871$	10.1741	−	1.06934i	0.344737	−	0.0362334i
$872$	34.3238	−	11.1525i	1.16235	−	0.377671i
$873$	−18.0600	−	1.50780i	−0.611238	−	0.0510311i
$874$	15.8547	+	11.5191i	0.536294	+	0.389640i
$875$	15.0871	−	6.71723i	0.510038	−	0.227084i
$876$	53.8279	−	35.7818i	1.81868	−	1.20896i
$877$	−16.4615	−	14.8220i	−0.555866	−	0.500504i	0.342639	−	0.939467i	$-0.388679\pi$
$877$	−16.4615	−	14.8220i	−0.555866	−	0.500504i	−0.898505	+	0.438963i	$0.855346\pi$
$878$	39.2320	−	88.1166i	1.32402	−	2.97379i
$879$	29.2752	−	36.9543i	0.987426	−	1.24644i
$880$	59.7442	+	19.9019i	2.01398	+	0.670894i
$881$		−	18.8235i		−	0.634180i	−0.948395	−	0.317090i	$-0.897294\pi$
$881$		−	18.8235i		−	0.634180i	0.948395	−	0.317090i	$-0.102706\pi$
$882$	7.42569	−	39.0288i	0.250036	−	1.31417i
$883$	−11.7223	−	36.0776i	−0.394488	−	1.21411i	−0.929360	−	0.369175i	$-0.879640\pi$
$883$	−11.7223	−	36.0776i	−0.394488	−	1.21411i	0.534872	−	0.844933i	$-0.320360\pi$
$884$	−48.2800	+	43.4715i	−1.62383	+	1.46211i
$885$	5.42071	+	5.30580i	0.182215	+	0.178353i
$886$	−32.1432	−	3.37839i	−1.07987	−	0.113499i
$887$	−28.4769	+	6.05295i	−0.956161	+	0.203238i	−0.659466	−	0.751734i	$-0.729218\pi$
$887$	−28.4769	+	6.05295i	−0.956161	+	0.203238i	−0.296694	+	0.954972i	$0.595884\pi$
$888$	−116.929	+	96.7792i	−3.92387	+	3.24770i
$889$	−0.0155287	−	0.147746i	−0.000520816	−	0.00495523i
$890$	−19.9403			−0.668401
$891$	−15.8317	−	25.3053i	−0.530381	−	0.847760i
$892$	−119.589			−4.00414
$893$	0.950476	+	9.04317i	0.0318065	+	0.302618i
$894$	41.1636	−	34.0702i	1.37672	−	1.13948i
$895$	14.2588	−	3.03080i	0.476619	−	0.101309i
$896$	−32.8583	−	3.45355i	−1.09772	−	0.115375i
$897$	21.3989	+	20.9453i	0.714489	+	0.699343i
$898$	51.1187	−	46.0275i	1.70585	−	1.53596i
$899$	−0.122993	−	0.378534i	−0.00410205	−	0.0126248i
$900$	8.56775	−	45.0313i	0.285592	−	1.50104i
$901$			1.39484i			0.0464688i
$902$	12.3316	+	38.9305i	0.410597	+	1.29624i
$903$	3.30140	−	4.16738i	0.109864	−	0.138682i
$904$	72.1692	−	162.095i	2.40031	−	5.39119i
$905$	16.6711	+	15.0107i	0.554165	+	0.498972i
$906$	4.13055	−	2.74577i	0.137228	−	0.0912219i
$907$	−16.9502	+	7.54671i	−0.562822	+	0.250584i	−0.668369	−	0.743830i	$-0.733007\pi$
$907$	−16.9502	+	7.54671i	−0.562822	+	0.250584i	0.105547	+	0.994414i	$0.466341\pi$
$908$	−34.5673	−	25.1146i	−1.14716	−	0.833458i
$909$	−34.8059	−	2.90588i	−1.15444	−	0.0963821i
$910$	−15.9308	+	5.17622i	−0.528100	+	0.171590i
$911$	33.0374	−	3.47238i	1.09458	−	0.115045i	0.460012	−	0.887913i	$-0.347845\pi$
$911$	33.0374	−	3.47238i	1.09458	−	0.115045i	0.634567	+	0.772868i	$0.281178\pi$
$912$	−4.15245	+	28.1672i	−0.137501	+	0.932710i
$913$	19.3183	+	4.25586i	0.639344	+	0.140848i
$914$	2.37949	−	1.37380i	0.0787064	−	0.0454411i
$915$	0.673631	+	0.427272i	0.0222696	+	0.0141252i
$916$	−69.9002	−	14.8578i	−2.30957	−	0.490914i
$917$	−21.0963	−	6.85459i	−0.696660	−	0.226359i
$918$	58.0987	+	1.17508i	1.91754	+	0.0387834i
$919$	−10.8277	+	14.9031i	−0.357173	+	0.491606i	−0.949358	−	0.314195i	$-0.898265\pi$
$919$	−10.8277	+	14.9031i	−0.357173	+	0.491606i	0.592185	+	0.805802i	$0.298265\pi$
$920$	49.3326	+	54.7894i	1.62645	+	1.80635i
$921$	−34.3233	−	41.4695i	−1.13099	−	1.36647i
$922$	−11.1336	−	4.95702i	−0.366667	−	0.163251i
$923$	−13.6464	−	23.6363i	−0.449178	−	0.777999i
$924$	23.6233	−	36.6419i	0.777149	−	1.20543i
$925$	14.5146	−	25.1401i	0.477238	−	0.826600i
$926$	18.4200	−	13.3829i	0.605320	−	0.439791i
$927$	−0.215295	−	10.0474i	−0.00707120	−	0.329998i
$928$	−0.535586	+	1.64836i	−0.0175815	+	0.0541102i
$929$	11.9113	+	26.7533i	0.390798	+	0.877747i	0.996620	+	0.0821472i	$0.0261777\pi$
$929$	11.9113	+	26.7533i	0.390798	+	0.877747i	−0.605822	+	0.795600i	$0.707156\pi$
$930$	−7.42845	−	26.5810i	−0.243588	−	0.871626i
$931$	−1.28033	−	6.02346i	−0.0419610	−	0.197411i
$932$	−17.7904	+	19.7582i	−0.582743	+	0.647202i
$933$	9.88916	+	0.412097i	0.323756	+	0.0134915i
$934$	−14.4710	−	8.35483i	−0.473505	−	0.273378i
$935$	−3.99765	−	19.5164i	−0.130737	−	0.638253i
$936$	−22.6119	+	75.0247i	−0.739095	+	2.45226i
$937$	−9.28756	−	12.7832i	−0.303411	−	0.417610i	0.629901	−	0.776675i	$-0.283095\pi$
$937$	−9.28756	−	12.7832i	−0.303411	−	0.417610i	−0.933312	+	0.359066i	$0.883095\pi$
$938$	2.77869	−	13.0727i	0.0907275	−	0.426839i
$939$	−20.3466	+	41.0127i	−0.663985	+	1.33840i
$940$	−5.77140	+	54.9112i	−0.188242	+	1.79101i
$941$	−0.865821	+	8.23774i	−0.0282250	+	0.268543i	0.971304	+	0.237843i	$0.0764403\pi$
$941$	−0.865821	+	8.23774i	−0.0282250	+	0.268543i	−0.999529	+	0.0306999i	$0.990226\pi$
$942$	0.397632	−	0.0251129i	0.0129556	−	0.000818221i
$943$	−5.51873	+	25.9636i	−0.179715	+	0.845490i
$944$	23.3457	+	32.1326i	0.759839	+	1.04583i
$945$	9.82395	+	4.61415i	0.319573	+	0.150098i
$946$	−16.5220	+	9.37671i	−0.537178	+	0.304863i
$947$	−4.25424	−	2.45619i	−0.138244	−	0.0798154i	0.429283	−	0.903170i	$-0.358766\pi$
$947$	−4.25424	−	2.45619i	−0.138244	−	0.0798154i	−0.567527	+	0.823355i	$0.692100\pi$
$948$	−48.8705	+	77.0485i	−1.58724	+	2.50242i
$949$	14.1397	−	15.7037i	0.458994	−	0.509764i
$950$	−2.03924	−	9.59388i	−0.0661617	−	0.311266i
$951$	−2.39871	+	2.45066i	−0.0777835	+	0.0794681i
$952$	21.3879	+	48.0379i	0.693185	+	1.55692i
$953$	1.81366	−	5.58186i	0.0587501	−	0.180814i	−0.917375	−	0.398025i	$-0.869696\pi$
$953$	1.81366	−	5.58186i	0.0587501	−	0.180814i	0.976125	+	0.217211i	$0.0696958\pi$
$954$	1.40776	+	2.32197i	0.0455779	+	0.0751765i
$955$	4.34837	−	3.15927i	0.140710	−	0.102232i
$956$	−53.0067	+	91.8103i	−1.71436	+	2.96936i
$957$	−0.396779	−	0.394158i	−0.0128260	−	0.0127413i
$958$	30.0453	+	52.0401i	0.970721	+	1.68134i
$959$	4.91062	+	2.18635i	0.158572	+	0.0706009i
$960$	−18.9545	+	51.0048i	−0.611755	+	1.64617i
$961$	−9.55992	−	10.6174i	−0.308384	−	0.342496i
$962$	−47.0782	+	64.7976i	−1.51786	+	2.08916i
$963$	−28.1387	+	3.56849i	−0.906758	+	0.114993i
$964$	141.498	+	45.9756i	4.55735	+	1.48077i
$965$	35.2930	+	7.50176i	1.13612	+	0.241490i
$966$	34.6626	−	18.1318i	1.11525	−	0.583380i
$967$	−15.1909	+	8.77049i	−0.488507	+	0.282040i	−0.723955	−	0.689847i	$-0.757678\pi$
$967$	−15.1909	+	8.77049i	−0.488507	+	0.282040i	0.235448	+	0.971887i	$0.424344\pi$
$968$	−78.9135	+	55.5688i	−2.53638	+	1.78605i
$969$	8.37389	−	3.31779i	0.269008	−	0.106583i
$970$	−23.4171	+	2.46124i	−0.751878	+	0.0790255i
$971$	46.6836	−	15.1684i	1.49815	−	0.486778i	0.558672	−	0.829389i	$-0.311311\pi$
$971$	46.6836	−	15.1684i	1.49815	−	0.486778i	0.939478	+	0.342610i	$0.111311\pi$
$972$	70.9209	−	41.0599i	2.27479	−	1.31700i
$973$	19.8735	+	14.4390i	0.637117	+	0.462892i
$974$	83.8527	−	37.3336i	2.68681	−	1.19625i
$975$	−0.944589	−	14.9564i	−0.0302511	−	0.478989i
$976$	3.10412	+	2.79496i	0.0993605	+	0.0894646i
$977$	5.10387	−	11.4635i	0.163287	−	0.366749i	−0.813308	−	0.581833i	$-0.802336\pi$
$977$	5.10387	−	11.4635i	0.163287	−	0.366749i	0.976596	+	0.215084i	$0.0690025\pi$
$978$	13.5239	+	1.99371i	0.432447	+	0.0637520i
$979$	10.0744	−	13.6527i	0.321980	−	0.436342i
$980$		−	37.3923i		−	1.19445i
$981$	−12.1223	−	2.30641i	−0.387035	−	0.0736381i
$982$	−15.6708	−	48.2298i	−0.500076	−	1.53908i
$983$	−15.6637	+	14.1037i	−0.499594	+	0.449837i	−0.879994	−	0.474986i	$-0.842453\pi$
$983$	−15.6637	+	14.1037i	−0.499594	+	0.449837i	0.380399	+	0.924822i	$0.375787\pi$
$984$	−66.8977	+	18.6955i	−2.13262	+	0.595991i
$985$	27.6588	+	2.90706i	0.881282	+	0.0926265i
$986$	1.06500	−	0.226373i	0.0339165	−	0.00720917i
$987$	17.0136	+	6.32265i	0.541549	+	0.201252i
$988$	2.04914	+	19.4963i	0.0651919	+	0.620259i
$989$	−12.3481			−0.392648
$990$	−26.3520	−	28.4540i	−0.837522	−	0.904326i
$991$	60.3045			1.91564			0.957818	−	0.287375i	$-0.0927826\pi$
$991$	60.3045			1.91564			0.957818	+	0.287375i	$0.0927826\pi$
$992$	−7.60738	−	72.3794i	−0.241535	−	2.29805i
$993$	−1.17937	−	6.96269i	−0.0374262	−	0.220954i
$994$	−34.8764	+	7.41321i	−1.10621	+	0.235133i
$995$	−37.4311	−	3.93417i	−1.18665	−	0.124722i
$996$	−13.4933	+	52.6055i	−0.427552	+	1.66687i
$997$	−41.7692	+	37.6091i	−1.32284	+	1.19109i	−0.356365	+	0.934347i	$0.615984\pi$
$997$	−41.7692	+	37.6091i	−1.32284	+	1.19109i	−0.966479	+	0.256747i	$0.917349\pi$
$998$	6.32493	+	19.4661i	0.200212	+	0.616190i
$999$	50.9710	−	9.76134i	1.61265	−	0.308835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.p.a.74.1	yes	80
3.2	odd	2		297.2.t.a.8.10		80
9.2	odd	6		891.2.k.a.404.20		80
9.4	even	3		297.2.t.a.206.10		80
9.5	odd	6	inner	99.2.p.a.41.1	yes	80
9.7	even	3		891.2.k.a.404.1		80
11.7	odd	10	inner	99.2.p.a.29.1	✓	80
33.29	even	10		297.2.t.a.62.10		80
99.7	odd	30		891.2.k.a.161.20		80
99.29	even	30		891.2.k.a.161.1		80
99.40	odd	30		297.2.t.a.260.10		80
99.95	even	30	inner	99.2.p.a.95.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.1	✓	80	11.7	odd	10	inner
99.2.p.a.41.1	yes	80	9.5	odd	6	inner
99.2.p.a.74.1	yes	80	1.1	even	1	trivial
99.2.p.a.95.1	yes	80	99.95	even	30	inner
297.2.t.a.8.10		80	3.2	odd	2
297.2.t.a.62.10		80	33.29	even	10
297.2.t.a.206.10		80	9.4	even	3
297.2.t.a.260.10		80	99.40	odd	30
891.2.k.a.161.1		80	99.29	even	30
891.2.k.a.161.20		80	99.7	odd	30
891.2.k.a.404.1		80	9.7	even	3
891.2.k.a.404.20		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281588 - 2.67913i) q^{2} +(1.33430 - 1.10437i) q^{3} +(-5.14217 + 1.09300i) q^{4} +(1.43896 + 0.151241i) q^{5} +(-3.33448 - 3.26380i) q^{6} +(-1.07283 + 0.965979i) q^{7} +(2.71136 + 8.34470i) q^{8} +(0.560727 - 2.94713i) q^{9} -3.89775i q^{10} +(2.66871 + 1.96926i) q^{11} +(-5.65413 + 7.13726i) q^{12} +(-1.21080 + 2.71950i) q^{13} +(2.89008 + 2.60224i) q^{14} +(2.08703 - 1.38735i) q^{15} +(11.9880 - 5.33739i) q^{16} +(-3.35854 - 2.44012i) q^{17} +(-8.05365 - 0.672385i) q^{18} +(-1.19136 + 0.387096i) q^{19} +(-7.56469 + 0.795081i) q^{20} +(-0.364678 + 2.47371i) q^{21} +(4.52444 - 7.70435i) q^{22} +(5.02939 - 2.90372i) q^{23} +(12.8334 + 8.14001i) q^{24} +(-2.84300 - 0.604299i) q^{25} +(7.62685 + 2.47811i) q^{26} +(-2.50655 - 4.55162i) q^{27} +(4.46085 - 6.13983i) q^{28} +(-0.0651453 - 0.0723511i) q^{29} +(-4.30457 - 5.20078i) q^{30} +(3.73471 + 1.66280i) q^{31} +(-8.90112 - 15.4172i) q^{32} +(5.73566 - 0.319656i) q^{33} +(-5.59169 + 9.68509i) q^{34} +(-1.68985 + 1.22775i) q^{35} +(0.337866 + 15.7675i) q^{36} +(-3.08635 + 9.49880i) q^{37} +(1.37255 + 3.08281i) q^{38} +(1.38777 + 4.96581i) q^{39} +(2.63948 + 12.4178i) q^{40} +(-3.05835 + 3.39664i) q^{41} +(6.73009 + 0.280454i) q^{42} +(-1.84140 - 1.06313i) q^{43} +(-15.8754 - 7.20937i) q^{44} +(1.25259 - 4.15600i) q^{45} +(-9.19566 - 12.6567i) q^{46} +(1.50921 - 7.10026i) q^{47} +(10.1011 - 20.3609i) q^{48} +(-0.513854 + 4.88899i) q^{49} +(-0.818442 + 7.78695i) q^{50} +(-7.17611 + 0.453215i) q^{51} +(3.25372 - 15.3075i) q^{52} +(-0.197492 - 0.271824i) q^{53} +(-11.4886 + 7.99706i) q^{54} +(3.54233 + 3.23731i) q^{55} +(-10.9696 - 6.33332i) q^{56} +(-1.16214 + 1.83221i) q^{57} +(-0.175494 + 0.194906i) q^{58} +(0.629292 + 2.96059i) q^{59} +(-9.21552 + 9.41510i) q^{60} +(0.129468 + 0.290790i) q^{61} +(3.40321 - 10.4740i) q^{62} +(2.24530 + 3.70342i) q^{63} +(-17.5657 + 12.7622i) q^{64} +(-2.15359 + 3.73013i) q^{65} +(-2.47150 - 15.2766i) q^{66} +(-1.71828 - 2.97615i) q^{67} +(19.9373 + 8.87664i) q^{68} +(3.50394 - 9.42875i) q^{69} +(3.76515 + 4.18162i) q^{70} +(-5.38901 + 7.41734i) q^{71} +(26.1133 - 3.31163i) q^{72} +(-6.75113 - 2.19358i) q^{73} +(26.3176 + 5.59399i) q^{74} +(-4.46080 + 2.33342i) q^{75} +(5.70308 - 3.29267i) q^{76} +(-4.76533 + 0.465238i) q^{77} +(12.9133 - 5.11632i) q^{78} +(9.96549 - 1.04742i) q^{79} +(18.0574 - 5.86722i) q^{80} +(-8.37117 - 3.30507i) q^{81} +(9.96124 + 7.23727i) q^{82} +(5.44872 - 2.42593i) q^{83} +(-0.828533 - 13.1188i) q^{84} +(-4.46376 - 4.01919i) q^{85} +(-2.32976 + 5.23272i) q^{86} +(-0.166826 - 0.0245938i) q^{87} +(-9.19707 + 27.6090i) q^{88} -5.11584i q^{89} +(-11.4872 - 2.18558i) q^{90} +(-1.32800 - 4.08716i) q^{91} +(-22.6882 + 20.4285i) q^{92} +(6.81957 - 1.90583i) q^{93} +(-19.4475 - 2.04402i) q^{94} +(-1.77286 + 0.376834i) q^{95} +(-28.9031 - 10.7411i) q^{96} +(-0.631450 - 6.00784i) q^{97} +13.2430 q^{98} +(7.30009 - 6.76082i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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