LMFDB - Embedded newform 176.2.w.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,2,Mod(5,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("176.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	176.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.40536707557$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	176.5
Dual form			176.2.w.a.141.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.779948 + 1.17970i) q^{2} +(1.33374 - 0.211244i) q^{3} +(-0.783362 - 1.84020i) q^{4} +(0.141837 - 0.0722696i) q^{5} +(-0.791046 + 1.73817i) q^{6} +(1.45574 + 2.00365i) q^{7} +(2.78186 + 0.511133i) q^{8} +(-1.11893 + 0.363561i) q^{9} +(-0.0253694 + 0.223691i) q^{10} +(2.80267 - 1.77343i) q^{11} +(-1.43353 - 2.28887i) q^{12} +(5.97781 + 3.04584i) q^{13} +(-3.49909 + 0.154583i) q^{14} +(0.173908 - 0.126351i) q^{15} +(-2.77269 + 2.88309i) q^{16} +(0.997950 - 3.07138i) q^{17} +(0.443813 - 1.60355i) q^{18} +(-7.96492 + 1.26152i) q^{19} +(-0.244101 - 0.204396i) q^{20} +(2.36483 + 2.36483i) q^{21} +(-0.0938250 + 4.68948i) q^{22} -3.93241i q^{23} +(3.81826 + 0.0940686i) q^{24} +(-2.92403 + 4.02458i) q^{25} +(-8.25555 + 4.67639i) q^{26} +(-5.02512 + 2.56042i) q^{27} +(2.54675 - 4.24843i) q^{28} +(0.321711 - 2.03120i) q^{29} +(0.0134171 + 0.303705i) q^{30} +(-1.33069 - 4.09543i) q^{31} +(-1.23862 - 5.51959i) q^{32} +(3.36341 - 2.95735i) q^{33} +(2.84494 + 3.57279i) q^{34} +(0.351280 + 0.178986i) q^{35} +(1.54555 + 1.77425i) q^{36} +(1.07714 + 0.170602i) q^{37} +(4.72402 - 10.3801i) q^{38} +(8.61627 + 2.79960i) q^{39} +(0.431510 - 0.128546i) q^{40} +(3.33302 - 4.58751i) q^{41} +(-4.63423 + 0.945337i) q^{42} +(-4.85094 - 4.85094i) q^{43} +(-5.45898 - 3.76823i) q^{44} +(-0.132431 + 0.132431i) q^{45} +(4.63905 + 3.06708i) q^{46} +(-4.29363 - 3.11950i) q^{47} +(-3.08901 + 4.43101i) q^{48} +(0.267678 - 0.823828i) q^{49} +(-2.46719 - 6.58843i) q^{50} +(0.682199 - 4.30723i) q^{51} +(0.922181 - 13.3864i) q^{52} +(-3.26044 + 6.39897i) q^{53} +(0.898808 - 7.92510i) q^{54} +(0.269357 - 0.454086i) q^{55} +(3.02552 + 6.31794i) q^{56} +(-10.3567 + 3.36508i) q^{57} +(2.14528 + 1.96375i) q^{58} +(-9.97559 - 1.57998i) q^{59} +(-0.368745 - 0.221046i) q^{60} +(3.72256 + 7.30593i) q^{61} +(5.86923 + 1.62442i) q^{62} +(-2.35731 - 1.71269i) q^{63} +(7.47749 + 2.84380i) q^{64} +1.06800 q^{65} +(0.865485 + 6.27437i) q^{66} +(2.66050 - 2.66050i) q^{67} +(-6.43371 + 0.569569i) q^{68} +(-0.830699 - 5.24482i) q^{69} +(-0.485130 + 0.274804i) q^{70} +(0.0749414 + 0.0243499i) q^{71} +(-3.29852 + 0.439456i) q^{72} +(3.33103 + 4.58477i) q^{73} +(-1.04137 + 1.13764i) q^{74} +(-3.04973 + 5.98544i) q^{75} +(8.56087 + 13.6688i) q^{76} +(7.63328 + 3.03391i) q^{77} +(-10.0229 + 7.98103i) q^{78} +(1.23948 + 3.81473i) q^{79} +(-0.184910 + 0.609310i) q^{80} +(-3.30589 + 2.40187i) q^{81} +(2.81228 + 7.50996i) q^{82} +(1.99285 + 3.91118i) q^{83} +(2.49925 - 6.20430i) q^{84} +(-0.0804208 - 0.507757i) q^{85} +(9.50611 - 1.93915i) q^{86} -2.77706i q^{87} +(8.70308 - 3.50090i) q^{88} -12.8156i q^{89} +(-0.0529389 - 0.259517i) q^{90} +(2.59931 + 16.4114i) q^{91} +(-7.23644 + 3.08050i) q^{92} +(-2.63993 - 5.18115i) q^{93} +(7.02887 - 2.63212i) q^{94} +(-1.03855 + 0.754553i) q^{95} +(-2.81797 - 7.10005i) q^{96} +(-2.40325 - 7.39643i) q^{97} +(0.763091 + 0.958322i) q^{98} +(-2.49123 + 3.00328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 6 q^{2} - 6 q^{3} - 10 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{8} - 16 q^{10} - 12 q^{11} - 6 q^{13} - 12 q^{15} + 14 q^{16} - 12 q^{17} - 44 q^{18} - 6 q^{19} + 2 q^{20} - 28 q^{21} + 50 q^{22} - 38 q^{24}+ \cdots + 92 q^{99}+O(q^{100}) $ 176 * q - 6 * q^2 - 6 * q^3 - 10 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^8 - 16 * q^10 - 12 * q^11 - 6 * q^13 - 12 * q^15 + 14 * q^16 - 12 * q^17 - 44 * q^18 - 6 * q^19 + 2 * q^20 - 28 * q^21 + 50 * q^22 - 38 * q^24 - 68 * q^26 - 18 * q^27 - 46 * q^28 - 22 * q^29 + 26 * q^30 - 12 * q^31 - 16 * q^32 - 16 * q^33 + 12 * q^34 - 26 * q^35 - 22 * q^36 + 18 * q^37 - 34 * q^38 + 14 * q^40 - 10 * q^42 - 40 * q^43 + 2 * q^44 - 24 * q^45 + 38 * q^46 - 12 * q^47 - 26 * q^48 + 8 * q^49 - 62 * q^50 + 6 * q^51 + 74 * q^52 - 30 * q^53 - 52 * q^54 - 96 * q^56 - 26 * q^58 + 10 * q^59 + 118 * q^60 - 6 * q^61 - 42 * q^62 - 28 * q^63 - 106 * q^64 - 32 * q^65 + 6 * q^66 + 24 * q^67 + 116 * q^68 + 12 * q^69 + 52 * q^70 - 98 * q^72 + 96 * q^74 - 46 * q^75 + 112 * q^76 - 14 * q^77 + 44 * q^78 - 52 * q^79 - 28 * q^80 + 66 * q^82 + 54 * q^83 + 120 * q^84 + 14 * q^85 + 86 * q^86 + 142 * q^88 + 228 * q^90 - 122 * q^91 + 146 * q^92 + 6 * q^93 + 56 * q^94 + 52 * q^95 + 86 * q^96 - 12 * q^97 + 140 * q^98 + 92 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.779948	+	1.17970i	−0.551507	+	0.834171i
$2$	−0.779948	+	1.17970i	−0.551507	+	0.834171i
$3$	1.33374	−	0.211244i	0.770036	−	0.121962i	0.240959	−	0.970535i	$-0.422538\pi$
$3$	1.33374	−	0.211244i	0.770036	−	0.121962i	0.529077	+	0.848574i	$0.322538\pi$
$4$	−0.783362	−	1.84020i	−0.391681	−	0.920101i
$5$	0.141837	−	0.0722696i	0.0634315	−	0.0323200i	−0.421987	−	0.906602i	$-0.638667\pi$
$5$	0.141837	−	0.0722696i	0.0634315	−	0.0323200i	0.485419	+	0.874282i	$0.338667\pi$
$6$	−0.791046	+	1.73817i	−0.322943	+	0.709604i
$7$	1.45574	+	2.00365i	0.550217	+	0.757308i	0.990042	−	0.140775i	$-0.0449595\pi$
$7$	1.45574	+	2.00365i	0.550217	+	0.757308i	−0.439825	+	0.898083i	$0.644960\pi$
$8$	2.78186	+	0.511133i	0.983536	+	0.180713i
$9$	−1.11893	+	0.363561i	−0.372975	+	0.121187i
$10$	−0.0253694	+	0.223691i	−0.00802252	+	0.0707374i
$11$	2.80267	−	1.77343i	0.845036	−	0.534710i
$11$	2.80267	−	1.77343i	0.845036	−	0.534710i
$12$	−1.43353	−	2.28887i	−0.413826	−	0.660741i
$13$	5.97781	+	3.04584i	1.65795	+	0.844765i	0.995407	+	0.0957377i	$0.0305210\pi$
$13$	5.97781	+	3.04584i	1.65795	+	0.844765i	0.662539	+	0.749028i	$0.269479\pi$
$14$	−3.49909	+	0.154583i	−0.935172	+	0.0413141i
$15$	0.173908	−	0.126351i	0.0449028	−	0.0326238i
$16$	−2.77269	+	2.88309i	−0.693172	+	0.720772i
$17$	0.997950	−	3.07138i	0.242039	−	0.744918i	−0.754071	−	0.656793i	$-0.771913\pi$
$17$	0.997950	−	3.07138i	0.242039	−	0.744918i	0.996109	−	0.0881250i	$-0.0280875\pi$
$18$	0.443813	−	1.60355i	0.104608	−	0.377960i
$19$	−7.96492	+	1.26152i	−1.82728	+	0.289413i	−0.973069	−	0.230515i	$-0.925959\pi$
$19$	−7.96492	+	1.26152i	−1.82728	+	0.289413i	−0.854210	+	0.519928i	$0.825959\pi$
$20$	−0.244101	−	0.204396i	−0.0545826	−	0.0457043i
$21$	2.36483	+	2.36483i	0.516049	+	0.516049i
$22$	−0.0938250	+	4.68948i	−0.0200036	+	0.999800i
$23$		−	3.93241i		−	0.819965i	−0.912093	−	0.409982i	$-0.865535\pi$
$23$		−	3.93241i		−	0.819965i	0.912093	−	0.409982i	$-0.134465\pi$
$24$	3.81826	+	0.0940686i	0.779398	+	0.0192017i
$25$	−2.92403	+	4.02458i	−0.584806	+	0.804917i
$26$	−8.25555	+	4.67639i	−1.61905	+	0.917116i
$27$	−5.02512	+	2.56042i	−0.967084	+	0.492754i
$28$	2.54675	−	4.24843i	0.481290	−	0.802878i
$29$	0.321711	−	2.03120i	0.0597401	−	0.377184i	−0.939646	−	0.342148i	$-0.888845\pi$
$29$	0.321711	−	2.03120i	0.0597401	−	0.377184i	0.999386	−	0.0350360i	$-0.0111546\pi$
$30$	0.0134171	+	0.303705i	0.00244962	+	0.0554488i
$31$	−1.33069	−	4.09543i	−0.238999	−	0.735562i	−0.996566	−	0.0828047i	$-0.973612\pi$
$31$	−1.33069	−	4.09543i	−0.238999	−	0.735562i	0.757567	−	0.652757i	$-0.226388\pi$
$32$	−1.23862	−	5.51959i	−0.218958	−	0.975734i
$33$	3.36341	−	2.95735i	0.585494	−	0.514808i
$34$	2.84494	+	3.57279i	0.487903	+	0.612729i
$35$	0.351280	+	0.178986i	0.0593772	+	0.0302542i
$36$	1.54555	+	1.77425i	0.257592	+	0.295708i
$37$	1.07714	+	0.170602i	0.177081	+	0.0280468i	0.244345	−	0.969688i	$-0.421427\pi$
$37$	1.07714	+	0.170602i	0.177081	+	0.0280468i	−0.0672643	+	0.997735i	$0.521427\pi$
$38$	4.72402	−	10.3801i	0.766337	−	1.68388i
$39$	8.61627	+	2.79960i	1.37971	+	0.448294i
$40$	0.431510	−	0.128546i	0.0682278	−	0.0203250i
$41$	3.33302	−	4.58751i	0.520530	−	0.716448i	−0.465120	−	0.885247i	$-0.653989\pi$
$41$	3.33302	−	4.58751i	0.520530	−	0.716448i	0.985650	+	0.168799i	$0.0539889\pi$
$42$	−4.63423	+	0.945337i	−0.715078	+	0.145869i
$43$	−4.85094	−	4.85094i	−0.739761	−	0.739761i	0.232771	−	0.972532i	$-0.425221\pi$
$43$	−4.85094	−	4.85094i	−0.739761	−	0.739761i	−0.972532	+	0.232771i	$0.925221\pi$
$44$	−5.45898	−	3.76823i	−0.822972	−	0.568083i
$45$	−0.132431	+	0.132431i	−0.0197416	+	0.0197416i
$46$	4.63905	+	3.06708i	0.683991	+	0.452216i
$47$	−4.29363	−	3.11950i	−0.626290	−	0.455026i	0.228823	−	0.973468i	$-0.426512\pi$
$47$	−4.29363	−	3.11950i	−0.626290	−	0.455026i	−0.855113	+	0.518442i	$0.826512\pi$
$48$	−3.08901	+	4.43101i	−0.445861	+	0.639561i
$49$	0.267678	−	0.823828i	0.0382397	−	0.117690i
$50$	−2.46719	−	6.58843i	−0.348913	−	0.931745i
$51$	0.682199	−	4.30723i	0.0955269	−	0.603133i
$52$	0.922181	−	13.3864i	0.127884	−	1.85636i
$53$	−3.26044	+	6.39897i	−0.447856	+	0.878967i	0.551151	+	0.834406i	$0.314189\pi$
$53$	−3.26044	+	6.39897i	−0.447856	+	0.878967i	−0.999007	+	0.0445610i	$0.985811\pi$
$54$	0.898808	−	7.92510i	0.122312	−	1.07847i
$55$	0.269357	−	0.454086i	0.0363201	−	0.0612290i
$56$	3.02552	+	6.31794i	0.404302	+	0.844271i
$57$	−10.3567	+	3.36508i	−1.37177	+	0.445716i
$58$	2.14528	+	1.96375i	0.281689	+	0.257853i
$59$	−9.97559	−	1.57998i	−1.29871	−	0.205696i	−0.531483	−	0.847069i	$-0.678365\pi$
$59$	−9.97559	−	1.57998i	−1.29871	−	0.205696i	−0.767229	+	0.641373i	$0.778365\pi$
$60$	−0.368745	−	0.221046i	−0.0476047	−	0.0285370i
$61$	3.72256	+	7.30593i	0.476624	+	0.935428i	0.996690	+	0.0813015i	$0.0259077\pi$
$61$	3.72256	+	7.30593i	0.476624	+	0.935428i	−0.520065	+	0.854127i	$0.674092\pi$
$62$	5.86923	+	1.62442i	0.745393	+	0.206302i
$63$	−2.35731	−	1.71269i	−0.296993	−	0.215778i
$64$	7.47749	+	2.84380i	0.934686	+	0.355475i
$65$	1.06800			0.132469
$66$	0.865485	+	6.27437i	0.106534	+	0.772322i
$67$	2.66050	−	2.66050i	0.325031	−	0.325031i	−0.525662	−	0.850693i	$-0.676182\pi$
$67$	2.66050	−	2.66050i	0.325031	−	0.325031i	0.850693	+	0.525662i	$0.176182\pi$
$68$	−6.43371	+	0.569569i	−0.780202	+	0.0690704i
$69$	−0.830699	−	5.24482i	−0.100004	−	0.631403i
$70$	−0.485130	+	0.274804i	−0.0579841	+	0.0328453i
$71$	0.0749414	+	0.0243499i	0.00889391	+	0.00288981i	0.313461	−	0.949601i	$-0.398512\pi$
$71$	0.0749414	+	0.0243499i	0.00889391	+	0.00288981i	−0.304567	+	0.952491i	$0.598512\pi$
$72$	−3.29852	+	0.439456i	−0.388735	+	0.0517904i
$73$	3.33103	+	4.58477i	0.389868	+	0.536607i	0.958165	−	0.286217i	$-0.0923977\pi$
$73$	3.33103	+	4.58477i	0.389868	+	0.536607i	−0.568297	+	0.822823i	$0.692398\pi$
$74$	−1.04137	+	1.13764i	−0.121057	+	0.132248i
$75$	−3.04973	+	5.98544i	−0.352153	+	0.691139i
$76$	8.56087	+	13.6688i	0.982000	+	1.56792i
$77$	7.63328	+	3.03391i	0.869893	+	0.345746i
$78$	−10.0229	+	7.98103i	−1.13487	+	0.903674i
$79$	1.23948	+	3.81473i	0.139453	+	0.429191i	0.996256	−	0.0864522i	$-0.0275530\pi$
$79$	1.23948	+	3.81473i	0.139453	+	0.429191i	−0.856803	+	0.515643i	$0.827553\pi$
$80$	−0.184910	+	0.609310i	−0.0206736	+	0.0681230i
$81$	−3.30589	+	2.40187i	−0.367321	+	0.266874i
$82$	2.81228	+	7.50996i	0.310564	+	0.829337i
$83$	1.99285	+	3.91118i	0.218743	+	0.429308i	0.974135	−	0.225965i	$-0.0725536\pi$
$83$	1.99285	+	3.91118i	0.218743	+	0.429308i	−0.755392	+	0.655273i	$0.772554\pi$
$84$	2.49925	−	6.20430i	0.272691	−	0.676944i
$85$	−0.0804208	−	0.507757i	−0.00872286	−	0.0550739i
$86$	9.50611	−	1.93915i	1.02507	−	0.209104i
$87$		−	2.77706i		−	0.297732i
$88$	8.70308	−	3.50090i	0.927752	−	0.373197i
$89$		−	12.8156i		−	1.35845i	−0.733929	−	0.679226i	$-0.762316\pi$
$89$		−	12.8156i		−	1.35845i	0.733929	−	0.679226i	$-0.237684\pi$
$90$	−0.0529389	−	0.259517i	−0.00558025	−	0.0273555i
$91$	2.59931	+	16.4114i	0.272481	+	1.72038i
$92$	−7.23644	+	3.08050i	−0.754451	+	0.321165i
$93$	−2.63993	−	5.18115i	−0.273748	−	0.537261i
$94$	7.02887	−	2.63212i	0.724973	−	0.271483i
$95$	−1.03855	+	0.754553i	−0.106553	+	0.0774155i
$96$	−2.81797	−	7.10005i	−0.287608	−	0.724646i
$97$	−2.40325	−	7.39643i	−0.244013	−	0.750994i	−0.995797	−	0.0915850i	$-0.970807\pi$
$97$	−2.40325	−	7.39643i	−0.244013	−	0.750994i	0.751785	−	0.659409i	$-0.229193\pi$
$98$	0.763091	+	0.958322i	0.0770839	+	0.0968051i
$99$	−2.49123	+	3.00328i	−0.250378	+	0.301841i
$100$	9.69662	+	2.22810i	0.969662	+	0.222810i
$101$	−6.90027	+	13.5425i	−0.686603	+	1.34753i	0.239734	+	0.970839i	$0.422940\pi$
$101$	−6.90027	+	13.5425i	−0.686603	+	1.34753i	−0.926337	+	0.376695i	$0.877060\pi$
$102$	4.54914	+	4.16420i	0.450432	+	0.412318i
$103$	−1.33107	−	1.83206i	−0.131154	−	0.180518i	0.738389	−	0.674375i	$-0.235587\pi$
$103$	−1.33107	−	1.83206i	−0.131154	−	0.180518i	−0.869543	+	0.493857i	$0.835587\pi$
$104$	15.0726	+	11.5286i	1.47799	+	1.13047i
$105$	0.506327	+	0.164516i	0.0494125	+	0.0160551i
$106$	−5.00587	−	8.83719i	−0.486213	−	0.858344i
$107$	1.99306	+	12.5837i	0.192676	+	1.21651i	0.874512	+	0.485005i	$0.161182\pi$
$107$	1.99306	+	12.5837i	0.192676	+	1.21651i	−0.681835	+	0.731506i	$0.738818\pi$
$108$	8.64819	+	7.24149i	0.832172	+	0.696813i
$109$	−9.48803	+	9.48803i	−0.908789	+	0.908789i	−0.996175	−	0.0873857i	$-0.972149\pi$
$109$	−9.48803	+	9.48803i	−0.908789	+	0.908789i	0.0873857	+	0.996175i	$0.472149\pi$
$110$	0.325599	+	0.671923i	0.0310446	+	0.0640653i
$111$	1.47267			0.139779
$112$	−9.81300	−	1.35847i	−0.927241	−	0.128364i
$113$	0.886226	+	0.643881i	0.0833692	+	0.0605712i	0.628689	−	0.777657i	$-0.283592\pi$
$113$	0.886226	+	0.643881i	0.0833692	+	0.0605712i	−0.545320	+	0.838228i	$0.683592\pi$
$114$	4.10789	−	14.8423i	0.384739	−	1.39011i
$115$	−0.284194	−	0.557762i	−0.0265012	−	0.0520116i
$116$	−3.98984	+	0.999153i	−0.370447	+	0.0927691i
$117$	−7.79607	−	1.23478i	−0.720747	−	0.114155i
$118$	9.64434	−	10.5359i	0.887833	−	0.969905i
$119$	7.60671	−	2.47157i	0.697306	−	0.226568i
$120$	0.548369	−	0.262602i	0.0500590	−	0.0239721i
$121$	4.70988	−	9.94068i	0.428171	−	0.903698i
$122$	−11.5222	−	1.30676i	−1.04317	−	0.118309i
$123$	3.47630	−	6.82263i	0.313448	−	0.615176i
$124$	−6.49402	+	5.65694i	−0.583180	+	0.508008i
$125$	−0.248393	+	1.56829i	−0.0222170	+	0.140272i
$126$	3.85903	−	1.44510i	0.343789	−	0.128740i
$127$	3.00883	−	9.26021i	0.266990	−	0.821711i	−0.724238	−	0.689550i	$-0.757808\pi$
$127$	3.00883	−	9.26021i	0.266990	−	0.821711i	0.991228	−	0.132161i	$-0.0421916\pi$
$128$	−9.18687	+	6.60314i	−0.812012	+	0.583641i
$129$	−7.49463	−	5.44517i	−0.659865	−	0.479420i
$130$	−0.832982	+	1.25991i	−0.0730574	+	0.110502i
$131$	5.04787	−	5.04787i	0.441034	−	0.441034i	−0.451325	−	0.892359i	$-0.649049\pi$
$131$	5.04787	−	5.04787i	0.441034	−	0.441034i	0.892359	+	0.451325i	$0.149049\pi$
$132$	−8.07688	−	3.87268i	−0.703002	−	0.337073i
$133$	−14.1225	−	14.1225i	−1.22457	−	1.22457i
$134$	1.06353	+	5.21362i	0.0918747	+	0.450389i
$135$	−0.527707	+	0.726327i	−0.0454178	+	0.0625122i
$136$	4.34604	−	8.03405i	0.372670	−	0.688914i
$137$	−11.6541	−	3.78666i	−0.995679	−	0.323516i	−0.234541	−	0.972106i	$-0.575359\pi$
$137$	−11.6541	−	3.78666i	−0.995679	−	0.323516i	−0.761138	+	0.648590i	$0.775359\pi$
$138$	6.83520	+	3.11072i	0.581851	+	0.264802i
$139$	6.32049	+	1.00107i	0.536097	+	0.0849094i	0.418612	−	0.908165i	$-0.362517\pi$
$139$	6.32049	+	1.00107i	0.536097	+	0.0849094i	0.117485	+	0.993075i	$0.462517\pi$
$140$	0.0541912	−	0.786638i	0.00457999	−	0.0664830i
$141$	−6.38557	−	3.25361i	−0.537762	−	0.274003i
$142$	−0.0871759	+	0.0694163i	−0.00731564	+	0.00582529i
$143$	22.1554	−	2.06474i	1.85273	−	0.172663i
$144$	2.05425	−	4.23401i	0.171188	−	0.352834i
$145$	−0.101164	−	0.311350i	−0.00840118	−	0.0258562i
$146$	−8.00666	+	0.353719i	−0.662636	+	0.0292740i
$147$	0.182985	−	1.15532i	0.0150923	−	0.0952891i
$148$	−0.529848	−	2.11580i	−0.0435533	−	0.173918i
$149$	20.3554	−	10.3716i	1.66758	−	0.849673i	0.673721	−	0.738985i	$-0.264695\pi$
$149$	20.3554	−	10.3716i	1.66758	−	0.849673i	0.993855	−	0.110687i	$-0.0353052\pi$
$150$	−4.68236	−	8.26609i	−0.382313	−	0.674923i
$151$	−6.26771	+	8.62676i	−0.510059	+	0.702036i	−0.983929	−	0.178559i	$-0.942857\pi$
$151$	−6.26771	+	8.62676i	−0.510059	+	0.702036i	0.473870	+	0.880595i	$0.342857\pi$
$152$	−22.8021	−	0.561765i	−1.84950	−	0.0455651i
$153$			3.79946i			0.307168i
$154$	−9.53265	+	6.63865i	−0.768163	+	0.534958i
$155$	−0.484716	−	0.484716i	−0.0389334	−	0.0389334i
$156$	−1.59784	−	18.0488i	−0.127929	−	1.44506i
$157$	8.30576	−	1.31550i	0.662872	−	0.104989i	0.184072	−	0.982913i	$-0.441072\pi$
$157$	8.30576	−	1.31550i	0.662872	−	0.104989i	0.478800	+	0.877924i	$0.341072\pi$
$158$	−5.46696	−	1.51308i	−0.434928	−	0.120374i
$159$	−2.99684	+	9.22333i	−0.237665	+	0.731458i
$160$	−0.574580	−	0.693368i	−0.0454246	−	0.0548156i
$161$	7.87918	−	5.72456i	0.620966	−	0.451158i
$162$	−0.255052	−	5.77327i	−0.0200388	−	0.453591i
$163$	3.40270	+	1.73376i	0.266520	+	0.135799i	0.582144	−	0.813086i	$-0.302214\pi$
$163$	3.40270	+	1.73376i	0.266520	+	0.135799i	−0.315624	+	0.948884i	$0.602214\pi$
$164$	−11.0529	−	2.53975i	−0.863087	−	0.198321i
$165$	0.263330	−	0.662534i	0.0205002	−	0.0515782i
$166$	−6.16832	−	0.699566i	−0.478754	−	0.0542968i
$167$	1.76401	−	0.573161i	0.136503	−	0.0443525i	−0.239969	−	0.970781i	$-0.577137\pi$
$167$	1.76401	−	0.573161i	0.136503	−	0.0443525i	0.376472	+	0.926428i	$0.377137\pi$
$168$	5.36989	+	7.78738i	0.414296	+	0.600810i
$169$	18.8158	+	25.8977i	1.44737	+	1.99213i
$170$	0.661722	+	0.301152i	0.0507518	+	0.0230973i
$171$	8.45352	−	4.30728i	0.646457	−	0.329386i
$172$	−5.12666	+	12.7267i	−0.390904	+	0.970405i
$173$	−10.6104	+	1.68053i	−0.806697	+	0.127768i	−0.546144	−	0.837691i	$-0.683905\pi$
$173$	−10.6104	+	1.68053i	−0.806697	+	0.127768i	−0.260553	+	0.965459i	$0.583905\pi$
$174$	3.27608	+	2.16596i	0.248359	+	0.164201i
$175$	−12.3205			−0.931340
$176$	−2.65796	+	12.9975i	−0.200351	+	0.979724i
$177$	−13.6386			−1.02514
$178$	15.1185	+	9.99551i	1.13318	+	0.749195i
$179$	9.71848	−	1.53926i	0.726393	−	0.115049i	0.217723	−	0.976011i	$-0.430137\pi$
$179$	9.71848	−	1.53926i	0.726393	−	0.115049i	0.508671	+	0.860961i	$0.330137\pi$
$180$	0.347441	+	0.139958i	0.0258967	+	0.0104319i
$181$	16.1603	−	8.23410i	1.20119	−	0.612036i	0.265242	−	0.964182i	$-0.414548\pi$
$181$	16.1603	−	8.23410i	1.20119	−	0.612036i	0.935945	+	0.352146i	$0.114548\pi$
$182$	−21.3877	−	9.73363i	−1.58536	−	0.721504i
$183$	6.50826	+	8.95785i	0.481105	+	0.662184i
$184$	2.00999	−	10.9394i	0.148178	−	0.806465i
$185$	0.165108	−	0.0536468i	0.0121390	−	0.00394419i
$186$	8.17119	+	0.926718i	0.599141	+	0.0679502i
$187$	−2.64995	−	10.3778i	−0.193784	−	0.758903i
$188$	−2.37705	+	10.3448i	−0.173364	+	0.754475i
$189$	−12.4454	−	6.34127i	−0.905272	−	0.461259i
$190$	−0.0801252	−	1.81369i	−0.00581289	−	0.131579i
$191$	5.58712	−	4.05928i	0.404270	−	0.293719i	−0.367008	−	0.930218i	$-0.619618\pi$
$191$	5.58712	−	4.05928i	0.404270	−	0.293719i	0.771278	+	0.636499i	$0.219618\pi$
$192$	10.5738	+	2.21332i	0.763096	+	0.159733i
$193$	−1.12019	+	3.44759i	−0.0806330	+	0.248163i	−0.983244	−	0.182294i	$-0.941648\pi$
$193$	−1.12019	+	3.44759i	−0.0806330	+	0.248163i	0.902611	+	0.430457i	$0.141648\pi$
$194$	10.5999	+	2.93373i	0.761031	+	0.210630i
$195$	1.42443	−	0.225608i	0.102006	−	0.0161561i
$196$	−1.72570	+	0.152774i	−0.123264	+	0.0109124i
$197$	3.75105	+	3.75105i	0.267252	+	0.267252i	0.827992	−	0.560740i	$-0.189483\pi$
$197$	3.75105	+	3.75105i	0.267252	+	0.267252i	−0.560740	+	0.827992i	$0.689483\pi$
$198$	−1.59993	−	5.28129i	−0.113702	−	0.375325i
$199$			8.19027i			0.580593i	0.956937	+	0.290296i	$0.0937539\pi$
$199$			8.19027i			0.580593i	−0.956937	+	0.290296i	$0.906246\pi$
$200$	−10.1913	+	9.70126i	−0.720637	+	0.685983i
$201$	2.98640	−	4.11043i	0.210645	−	0.289927i
$202$	−10.5942	−	18.7027i	−0.745407	−	1.31592i
$203$	4.53814	−	2.31230i	0.318515	−	0.162291i
$204$	−8.46059	+	2.11874i	−0.592360	+	0.148342i
$205$	0.141208	−	0.891555i	0.00986243	−	0.0622689i
$206$	3.19944	−	0.141345i	0.222915	−	0.00984797i
$207$	1.42967	+	4.40008i	0.0993691	+	0.305827i
$208$	−25.3560	+	8.78938i	−1.75812	+	0.609434i
$209$	−20.0858	+	17.6609i	−1.38936	+	1.22163i
$210$	−0.588987	+	0.468998i	−0.0406440	+	0.0323639i
$211$	−17.9667	−	9.15449i	−1.23688	−	0.630221i	−0.291617	−	0.956535i	$-0.594193\pi$
$211$	−17.9667	−	9.15449i	−1.23688	−	0.630221i	−0.945262	+	0.326314i	$0.894193\pi$
$212$	14.3295	+	0.987154i	0.984155	+	0.0677980i
$213$	0.105096	+	0.0166456i	0.00720108	+	0.00114054i
$214$	−16.3994	−	7.46341i	−1.12104	−	0.510188i
$215$	−1.03862	−	0.337468i	−0.0708332	−	0.0230151i
$216$	−15.2879	+	4.55424i	−1.04021	+	0.309877i
$217$	6.26868	−	8.62810i	0.425546	−	0.585714i
$218$	−3.79282	−	18.5932i	−0.256882	−	1.25929i
$219$	5.41124	+	5.41124i	0.365658	+	0.365658i
$220$	−1.04661	−	0.139957i	−0.0705627	−	0.00943592i
$221$	15.3205	−	15.3205i	1.03057	−	1.03057i
$222$	−1.14860	+	1.73730i	−0.0770892	+	0.116600i
$223$	4.79796	+	3.48592i	0.321295	+	0.233435i	0.736728	−	0.676189i	$-0.236370\pi$
$223$	4.79796	+	3.48592i	0.321295	+	0.233435i	−0.415433	+	0.909624i	$0.636370\pi$
$224$	9.25621	−	10.5168i	0.618457	−	0.702684i
$225$	1.80859	−	5.56628i	0.120573	−	0.371085i
$226$	−1.45079	+	0.543283i	−0.0965054	+	0.0361387i
$227$	−2.25789	+	14.2558i	−0.149862	+	0.946189i	0.792081	+	0.610416i	$0.208998\pi$
$227$	−2.25789	+	14.2558i	−0.149862	+	0.946189i	−0.941943	+	0.335773i	$0.891002\pi$
$228$	14.3055	+	16.4223i	0.947402	+	1.08759i
$229$	−4.37818	+	8.59267i	−0.289318	+	0.567819i	−0.989223	−	0.146417i	$-0.953226\pi$
$229$	−4.37818	+	8.59267i	−0.289318	+	0.567819i	0.699905	+	0.714236i	$0.253226\pi$
$230$	0.879646	+	0.0997631i	0.0580022	+	0.00657819i
$231$	10.8217	+	2.43397i	0.712017	+	0.160144i
$232$	1.93317	−	5.48608i	0.126919	−	0.360179i
$233$	−9.52594	+	3.09517i	−0.624065	+	0.202771i	−0.603944	−	0.797027i	$-0.706405\pi$
$233$	−9.52594	+	3.09517i	−0.624065	+	0.202771i	−0.0201207	+	0.999798i	$0.506405\pi$
$234$	7.53719	−	8.23393i	0.492722	−	0.538269i
$235$	−0.834441	−	0.132163i	−0.0544330	−	0.00862133i
$236$	4.90702	+	19.5948i	0.319420	+	1.27551i
$237$	2.45899	+	4.82604i	0.159728	+	0.313485i
$238$	−3.01714	+	10.9013i	−0.195572	+	0.706626i
$239$	11.7305	+	8.52269i	0.758782	+	0.551287i	0.898536	−	0.438899i	$-0.144631\pi$
$239$	11.7305	+	8.52269i	0.758782	+	0.551287i	−0.139755	+	0.990186i	$0.544631\pi$
$240$	−0.117909	+	0.851724i	−0.00761102	+	0.0549785i
$241$	22.2506			1.43329			0.716643	−	0.697440i	$-0.245678\pi$
$241$	22.2506			1.43329			0.716643	+	0.697440i	$0.245678\pi$
$242$	8.05351	+	13.3094i	0.517699	+	0.855563i
$243$	8.06204	−	8.06204i	0.517180	−	0.517180i
$244$	10.5283	−	12.5734i	0.674004	−	0.804932i
$245$	−0.0215711	−	0.136194i	−0.00137813	−	0.00870114i
$246$	5.33729	+	9.42228i	0.340293	+	0.600743i
$247$	−51.4552	−	16.7188i	−3.27401	−	1.06379i
$248$	−1.60847	−	12.0731i	−0.102138	−	0.766642i
$249$	3.48415	+	4.79553i	0.220799	+	0.303904i
$250$	−1.65637	−	1.51621i	−0.104758	−	0.0958938i
$251$	2.69578	−	5.29076i	0.170156	−	0.333950i	−0.790143	−	0.612922i	$-0.789994\pi$
$251$	2.69578	−	5.29076i	0.170156	−	0.333950i	0.960299	+	0.278973i	$0.0899939\pi$
$252$	−1.30506	+	5.67958i	−0.0822111	+	0.357780i
$253$	−6.97387	−	11.0212i	−0.438443	−	0.692900i
$254$	8.57750	+	10.7720i	0.538200	+	0.675894i
$255$	−0.214521	−	0.660228i	−0.0134338	−	0.0413451i
$256$	−0.624412	−	15.9878i	−0.0390257	−	0.999238i
$257$	6.25605	−	4.54529i	0.390242	−	0.283527i	−0.375313	−	0.926898i	$-0.622465\pi$
$257$	6.25605	−	4.54529i	0.390242	−	0.283527i	0.765555	+	0.643371i	$0.222465\pi$
$258$	12.2691	−	4.59443i	0.763838	−	0.286037i
$259$	1.22620	+	2.40656i	0.0761927	+	0.149537i
$260$	−0.836629	−	1.96533i	−0.0518855	−	0.121885i
$261$	0.378495	+	2.38972i	0.0234283	+	0.147920i
$262$	2.01787	+	9.89202i	0.124664	+	0.611131i
$263$		−	29.2018i		−	1.80066i	−0.435210	−	0.900329i	$-0.643326\pi$
$263$		−	29.2018i		−	1.80066i	0.435210	−	0.900329i	$-0.356674\pi$
$264$	10.8681	−	6.50777i	0.668887	−	0.400526i
$265$			1.14324i			0.0702289i
$266$	27.6750	−	5.64542i	1.69686	−	0.346143i
$267$	−2.70722	−	17.0927i	−0.165679	−	1.04606i
$268$	−6.97998	−	2.81172i	−0.426370	−	0.171753i
$269$	10.5530	+	20.7115i	0.643429	+	1.26280i	0.950385	+	0.311077i	$0.100690\pi$
$269$	10.5530	+	20.7115i	0.643429	+	1.26280i	−0.306956	+	0.951724i	$0.599310\pi$
$270$	−0.445260	−	1.18903i	−0.0270977	−	0.0723621i
$271$	−23.7344	+	17.2440i	−1.44176	+	1.04750i	−0.454088	+	0.890957i	$0.650035\pi$
$271$	−23.7344	+	17.2440i	−1.44176	+	1.04750i	−0.987671	+	0.156542i	$0.949965\pi$
$272$	6.08805	+	11.3931i	0.369142	+	0.690811i
$273$	6.93361	+	21.3394i	0.419641	+	1.29152i
$274$	13.5567	−	10.7949i	0.818991	−	0.652145i
$275$	−1.05776	+	16.4651i	−0.0637853	+	0.992885i
$276$	−9.00080	+	5.63725i	−0.541784	+	0.339323i
$277$	4.71319	−	9.25015i	0.283188	−	0.555788i	−0.704968	−	0.709239i	$-0.749039\pi$
$277$	4.71319	−	9.25015i	0.283188	−	0.555788i	0.988156	+	0.153451i	$0.0490388\pi$
$278$	−6.11061	+	6.67547i	−0.366490	+	0.400368i
$279$	2.97788	+	4.09870i	0.178281	+	0.245383i
$280$	0.885727	+	0.677466i	0.0529323	+	0.0404863i
$281$	−7.37905	−	2.39760i	−0.440197	−	0.143029i	0.0805294	−	0.996752i	$-0.474339\pi$
$281$	−7.37905	−	2.39760i	−0.440197	−	0.143029i	−0.520727	+	0.853723i	$0.674339\pi$
$282$	8.81868	−	4.99538i	0.525145	−	0.297471i
$283$	0.671306	+	4.23846i	0.0399050	+	0.251950i	0.999574	−	0.0291817i	$-0.00929014\pi$
$283$	0.671306	+	4.23846i	0.0399050	+	0.251950i	−0.959669	+	0.281132i	$0.909290\pi$
$284$	−0.0138975	−	0.156982i	−0.000824662	−	0.00931518i
$285$	−1.22577	+	1.22577i	−0.0726081	+	0.0726081i
$286$	−14.8443	+	27.7470i	−0.877761	+	1.64072i
$287$	14.0438			0.828976
$288$	3.39263	+	5.72570i	0.199912	+	0.337390i
$289$	5.31585	+	3.86219i	0.312697	+	0.227188i
$290$	0.446200	+	0.123494i	0.0262018	+	0.00725183i
$291$	−4.76776	−	9.35726i	−0.279491	−	0.548532i
$292$	5.82750	−	9.72130i	0.341029	−	0.568896i
$293$	1.73540	+	0.274861i	0.101383	+	0.0160575i	0.206920	−	0.978358i	$-0.433656\pi$
$293$	1.73540	+	0.274861i	0.101383	+	0.0160575i	−0.105537	+	0.994415i	$0.533656\pi$
$294$	1.22021	+	1.11696i	0.0711639	+	0.0651421i
$295$	−1.52909	+	0.496833i	−0.0890273	+	0.0289267i
$296$	2.90925	+	1.02515i	0.169097	+	0.0595858i
$297$	−9.54299	+	16.0877i	−0.553740	+	0.933504i
$298$	−3.64083	+	32.1024i	−0.210907	+	1.85964i
$299$	11.9775	−	23.5072i	0.692678	−	1.35946i
$300$	13.4035	+	0.923359i	0.773849	+	0.0533102i
$301$	2.65789	−	16.7813i	0.153198	−	0.967256i
$302$	−5.28846	−	14.1224i	−0.304317	−	0.812653i
$303$	−6.34240	+	19.5199i	−0.364361	+	1.12139i
$304$	18.4472	−	26.4614i	1.05802	−	1.51766i
$305$	1.05599	+	0.767224i	0.0604660	+	0.0439311i
$306$	−4.48220	−	2.96338i	−0.256230	−	0.169405i
$307$	9.33324	−	9.33324i	0.532676	−	0.532676i	−0.388692	−	0.921368i	$-0.627073\pi$
$307$	9.33324	−	9.33324i	0.532676	−	0.532676i	0.921368	+	0.388692i	$0.127073\pi$
$308$	−0.396612	−	16.4234i	−0.0225991	−	0.935811i
$309$	−2.16231	−	2.16231i	−0.123010	−	0.123010i
$310$	0.949871	−	0.193764i	0.0539491	−	0.0110051i
$311$	−13.7800	+	18.9665i	−0.781392	+	1.07549i	0.213735	+	0.976892i	$0.431437\pi$
$311$	−13.7800	+	18.9665i	−0.781392	+	1.07549i	−0.995127	+	0.0986016i	$0.968563\pi$
$312$	22.5383	+	12.1921i	1.27598	+	0.690244i
$313$	−8.95972	−	2.91119i	−0.506434	−	0.164550i	0.0446461	−	0.999003i	$-0.485784\pi$
$313$	−8.95972	−	2.91119i	−0.506434	−	0.164550i	−0.551080	+	0.834453i	$0.685784\pi$
$314$	−4.92617	+	10.8243i	−0.278000	+	0.610850i
$315$	−0.458129	−	0.0725605i	−0.0258127	−	0.00408832i
$316$	6.04892	−	5.26922i	0.340278	−	0.296417i
$317$	−22.7920	−	11.6131i	−1.28012	−	0.652256i	−0.324234	−	0.945977i	$-0.605106\pi$
$317$	−22.7920	−	11.6131i	−1.28012	−	0.652256i	−0.955891	+	0.293721i	$0.905106\pi$
$318$	−8.54334	−	10.7291i	−0.479087	−	0.601657i
$319$	−2.70055	−	6.26331i	−0.151202	−	0.350678i
$320$	1.26611	−	0.137039i	0.0707775	−	0.00766069i
$321$	5.31645	+	16.3624i	0.296735	+	0.913258i
$322$	0.607885	+	13.7599i	0.0338761	+	0.766808i
$323$	−4.07400	+	25.7222i	−0.226683	+	1.43122i
$324$	7.00963	+	4.20197i	0.389424	+	0.233443i
$325$	−29.7376	+	15.1520i	−1.64954	+	0.840484i
$326$	−4.69923	+	2.66190i	−0.260267	+	0.147429i
$327$	−10.6503	+	14.6589i	−0.588963	+	0.810638i
$328$	11.6168	−	11.0582i	0.641432	−	0.610586i
$329$		−	13.1441i		−	0.724658i
$330$	0.576205	+	0.827391i	0.0317190	+	0.0455464i
$331$	−1.87938	−	1.87938i	−0.103300	−	0.103300i	0.653568	−	0.756868i	$-0.273271\pi$
$331$	−1.87938	−	1.87938i	−0.103300	−	0.103300i	−0.756868	+	0.653568i	$0.773271\pi$
$332$	5.63624	−	6.73111i	0.309329	−	0.369418i
$333$	−1.26726	+	0.200715i	−0.0694457	+	0.0109991i
$334$	−0.699679	+	2.52803i	−0.0382847	+	0.138327i
$335$	0.185084	−	0.569630i	0.0101122	−	0.0311222i
$336$	−13.3750	+	0.261084i	−0.729665	+	0.0142433i
$337$	−15.9627	+	11.5976i	−0.869544	+	0.631761i	−0.930465	−	0.366382i	$-0.880596\pi$
$337$	−15.9627	+	11.5976i	−0.869544	+	0.631761i	0.0609205	+	0.998143i	$0.480596\pi$
$338$	−45.2268	+	1.99803i	−2.46001	+	0.108679i
$339$	1.31801	+	0.671561i	0.0715847	+	0.0364742i
$340$	−0.871376	+	0.545748i	−0.0472570	+	0.0295973i
$341$	−10.9924	−	9.11826i	−0.595274	−	0.493781i
$342$	−1.51202	+	13.3320i	−0.0817609	+	0.720914i
$343$	18.5283	−	6.02022i	1.00044	−	0.325062i
$344$	−11.0152	−	15.9741i	−0.593897	−	0.861266i
$345$	−0.496865	−	0.683877i	−0.0267503	−	0.0368187i
$346$	6.29308	−	13.8278i	0.338318	−	0.743388i
$347$	13.3651	−	6.80984i	0.717475	−	0.365572i	−0.0568306	−	0.998384i	$-0.518099\pi$
$347$	13.3651	−	6.80984i	0.717475	−	0.365572i	0.774305	+	0.632812i	$0.218099\pi$
$348$	−5.11035	+	2.17544i	−0.273943	+	0.116616i
$349$	−1.61382	+	0.255604i	−0.0863857	+	0.0136821i	−0.199478	−	0.979902i	$-0.563925\pi$
$349$	−1.61382	+	0.255604i	−0.0863857	+	0.0136821i	0.113092	+	0.993585i	$0.463925\pi$
$350$	9.60933	−	14.5344i	0.513640	−	0.776896i
$351$	−37.8378			−2.01963
$352$	−13.2600	−	13.2730i	−0.706762	−	0.707451i
$353$	2.37657			0.126492			0.0632460	−	0.997998i	$-0.479855\pi$
$353$	2.37657			0.126492			0.0632460	+	0.997998i	$0.479855\pi$
$354$	10.6374	−	16.0894i	0.565373	−	0.855143i
$355$	0.0123892	−	0.00196226i	0.000657552	−	0.000104146i
$356$	−23.5833	+	10.0393i	−1.24991	+	0.532080i
$357$	9.62328	−	4.90331i	0.509318	−	0.259511i
$358$	−5.76406	+	12.6654i	−0.304640	+	0.669386i
$359$	−10.9510	−	15.0728i	−0.577974	−	0.795512i	0.415498	−	0.909594i	$-0.363607\pi$
$359$	−10.9510	−	15.0728i	−0.577974	−	0.795512i	−0.993471	+	0.114082i	$0.963607\pi$
$360$	−0.436094	+	0.300714i	−0.0229842	+	0.0158490i
$361$	43.7785	−	14.2245i	2.30413	−	0.748658i
$362$	−2.89049	+	25.4864i	−0.151921	+	1.33954i
$363$	4.18186	−	14.2532i	0.219491	−	0.748101i
$364$	28.1640	−	17.6393i	1.47620	−	0.924550i
$365$	0.803803	+	0.409558i	0.0420730	+	0.0214373i
$366$	−15.6436	+	0.691106i	−0.817706	+	0.0361247i
$367$	9.67041	−	7.02596i	0.504791	−	0.366752i	−0.306053	−	0.952015i	$-0.599008\pi$
$367$	9.67041	−	7.02596i	0.504791	−	0.366752i	0.810844	+	0.585262i	$0.199008\pi$
$368$	11.3375	+	10.9034i	0.591008	+	0.568377i
$369$	−2.06156	+	6.34484i	−0.107321	+	0.330299i
$370$	−0.0654887	+	0.236619i	−0.00340459	+	0.0123012i
$371$	−17.5676	+	2.78244i	−0.912066	+	0.144457i
$372$	−7.46635	+	8.91672i	−0.387112	+	0.462311i
$373$	22.0000	+	22.0000i	1.13912	+	1.13912i	0.988609	+	0.150506i	$0.0480903\pi$
$373$	22.0000	+	22.0000i	1.13912	+	1.13912i	0.150506	+	0.988609i	$0.451910\pi$
$374$	14.3095	+	4.96804i	0.739927	+	0.256891i
$375$			2.14417i			0.110724i
$376$	−10.3498	−	10.8726i	−0.533750	−	0.560713i
$377$	8.10984	−	11.1622i	0.417678	−	0.574885i
$378$	17.1876	−	9.73596i	0.884032	−	0.500764i
$379$	−13.1907	+	6.72102i	−0.677563	+	0.345236i	−0.758675	−	0.651469i	$-0.774153\pi$
$379$	−13.1907	+	6.72102i	−0.677563	+	0.345236i	0.0811120	+	0.996705i	$0.474153\pi$
$380$	2.20209	+	1.32006i	0.112965	+	0.0677176i
$381$	2.05683	−	12.9863i	0.105375	−	0.665310i
$382$	0.431051	+	9.75712i	0.0220545	+	0.499218i
$383$	−3.23826	−	9.96634i	−0.165467	−	0.509256i	0.833603	−	0.552364i	$-0.186274\pi$
$383$	−3.23826	−	9.96634i	−0.165467	−	0.509256i	−0.999070	+	0.0431077i	$0.986274\pi$
$384$	−10.8580	+	10.7476i	−0.554097	+	0.548459i
$385$	1.30194	−	0.121333i	0.0663531	−	0.00618370i
$386$	−3.19341	−	4.01042i	−0.162541	−	0.204125i
$387$	7.19145	+	3.66423i	0.365562	+	0.186263i
$388$	−11.7283	+	10.2165i	−0.595415	+	0.518666i
$389$	12.0447	+	1.90769i	0.610691	+	0.0967239i	0.454117	−	0.890942i	$-0.349955\pi$
$389$	12.0447	+	1.90769i	0.610691	+	0.0967239i	0.156574	+	0.987666i	$0.449955\pi$
$390$	−0.844835	+	1.85636i	−0.0427799	+	0.0940004i
$391$	−12.0779	−	3.92435i	−0.610807	−	0.198463i
$392$	1.16573	−	2.15496i	0.0588782	−	0.108842i
$393$	5.66622	−	7.79888i	0.285823	−	0.393401i
$394$	−7.35073	+	1.49947i	−0.370324	+	0.0755424i
$395$	0.451494	+	0.451494i	0.0227171	+	0.0227171i
$396$	7.47817	+	2.23170i	0.375792	+	0.112147i
$397$	−9.05147	+	9.05147i	−0.454280	+	0.454280i	−0.896772	−	0.442492i	$-0.854094\pi$
$397$	−9.05147	+	9.05147i	−0.454280	+	0.454280i	0.442492	+	0.896772i	$0.354094\pi$
$398$	−9.66203	−	6.38799i	−0.484314	−	0.320201i
$399$	−21.8190	−	15.8524i	−1.09232	−	0.793615i
$400$	−3.49581	−	19.5892i	−0.174791	−	0.979458i
$401$	1.05777	−	3.25549i	0.0528227	−	0.162572i	−0.921165	−	0.389172i	$-0.872761\pi$
$401$	1.05777	−	3.25549i	0.0528227	−	0.162572i	0.973988	+	0.226600i	$0.0727612\pi$
$402$	2.51982	+	6.72897i	0.125677	+	0.335610i
$403$	4.51947	−	28.5348i	0.225131	−	1.42142i
$404$	30.3264	+	2.08918i	1.50880	+	0.103940i
$405$	−0.295316	+	0.579589i	−0.0146743	+	0.0288000i
$406$	−0.811706	+	7.15709i	−0.0402843	+	0.355200i
$407$	3.32142	−	1.43209i	0.164637	−	0.0709862i
$408$	4.09935	−	11.6334i	0.202948	−	0.575940i
$409$	−31.6863	+	10.2955i	−1.56678	+	0.509079i	−0.958610	−	0.284724i	$-0.908098\pi$
$409$	−31.6863	+	10.2955i	−1.56678	+	0.509079i	−0.608175	+	0.793803i	$0.708098\pi$
$410$	0.941628	+	0.861950i	0.0465037	+	0.0425687i
$411$	−16.3435	−	2.58856i	−0.806166	−	0.127684i
$412$	−2.32865	+	3.88460i	−0.114724	+	0.191381i
$413$	−11.3561	−	22.2876i	−0.558798	−	1.09670i
$414$	−6.30582	−	1.74526i	−0.309914	−	0.0857746i
$415$	0.565319	+	0.410728i	0.0277504	+	0.0201619i
$416$	9.40760	−	36.7677i	0.461245	−	1.80268i
$417$	8.64137			0.423170
$418$	−5.16856	−	37.4697i	−0.252803	−	1.83270i
$419$	−19.1225	+	19.1225i	−0.934195	+	0.934195i	−0.997965	−	0.0637693i	$-0.979688\pi$
$419$	−19.1225	+	19.1225i	−0.934195	+	0.934195i	0.0637693	+	0.997965i	$0.479688\pi$
$420$	−0.0938955	−	1.06062i	−0.00458163	−	0.0517529i
$421$	−4.41552	−	27.8785i	−0.215199	−	1.35871i	−0.824539	−	0.565805i	$-0.808565\pi$
$421$	−4.41552	−	27.8785i	−0.215199	−	1.35871i	0.609340	−	0.792909i	$-0.291435\pi$
$422$	24.8126	−	14.0552i	1.20786	−	0.684197i
$423$	5.93838	+	1.92950i	0.288734	+	0.0938154i
$424$	−12.3408	+	16.1345i	−0.599323	+	0.783562i
$425$	9.44297	+	12.9971i	0.458051	+	0.630454i
$426$	−0.101606	+	0.110999i	−0.00492284	+	0.00537791i
$427$	−9.21945	+	18.0942i	−0.446161	+	0.875639i
$428$	21.5952	−	13.5252i	1.04384	−	0.653766i
$429$	29.1134	−	7.43403i	1.40561	−	0.358918i
$430$	1.20818	−	0.962046i	0.0582635	−	0.0463940i
$431$	−0.498521	−	1.53429i	−0.0240129	−	0.0739041i	0.938332	−	0.345736i	$-0.112371\pi$
$431$	−0.498521	−	1.53429i	−0.0240129	−	0.0739041i	−0.962345	+	0.271832i	$0.912371\pi$
$432$	6.55114	−	21.5871i	0.315192	−	1.03861i
$433$	−10.6595	+	7.74461i	−0.512265	+	0.372182i	−0.813682	−	0.581310i	$-0.802540\pi$
$433$	−10.6595	+	7.74461i	−0.512265	+	0.372182i	0.301417	+	0.953492i	$0.402540\pi$
$434$	5.28929	+	14.1246i	0.253894	+	0.678003i
$435$	−0.200697	−	0.393890i	−0.00962268	−	0.0188856i
$436$	24.8925	+	10.0273i	1.19213	+	0.480222i
$437$	4.96082	+	31.3214i	0.237308	+	1.49830i
$438$	−10.6041	+	2.16313i	−0.506683	+	0.103358i
$439$			14.5049i			0.692280i	0.938183	+	0.346140i	$0.112508\pi$
$439$			14.5049i			0.692280i	−0.938183	+	0.346140i	$0.887492\pi$
$440$	0.981412	−	1.12553i	0.0467870	−	0.0536574i
$441$			1.01912i			0.0485295i
$442$	6.12432	+	30.0227i	0.291304	+	1.42803i
$443$	−0.156773	−	0.989826i	−0.00744851	−	0.0470281i	0.983684	−	0.179904i	$-0.0575788\pi$
$443$	−0.156773	−	0.989826i	−0.00744851	−	0.0470281i	−0.991133	+	0.132876i	$0.957579\pi$
$444$	−1.15363	−	2.71000i	−0.0547489	−	0.128611i
$445$	−0.926179	−	1.81773i	−0.0439051	−	0.0861686i
$446$	−7.85449	+	2.94130i	−0.371921	+	0.139274i
$447$	24.9579	−	18.1330i	1.18047	−	0.857659i
$448$	5.18727	+	19.1221i	0.245075	+	0.903433i
$449$	1.44395	+	4.44403i	0.0681443	+	0.209727i	0.979330	−	0.202270i	$-0.0648317\pi$
$449$	1.44395	+	4.44403i	0.0681443	+	0.209727i	−0.911186	+	0.411996i	$0.864832\pi$
$450$	5.15590	+	6.47499i	0.243052	+	0.305234i
$451$	1.20571	−	18.7681i	0.0567747	−	0.883757i
$452$	0.490635	−	2.13523i	0.0230775	−	0.100433i
$453$	−6.53715	+	12.8299i	−0.307142	+	0.602801i
$454$	−15.0564	−	13.7824i	−0.706633	−	0.646839i
$455$	1.55472	+	2.13989i	0.0728865	+	0.100320i
$456$	−30.5308	+	4.06756i	−1.42974	+	0.190481i
$457$	18.4893	+	6.00752i	0.864891	+	0.281020i	0.707670	−	0.706543i	$-0.249746\pi$
$457$	18.4893	+	6.00752i	0.864891	+	0.281020i	0.157221	+	0.987563i	$0.449746\pi$
$458$	−6.72197	−	11.8668i	−0.314097	−	0.554497i
$459$	2.84921	+	17.9892i	0.132990	+	0.839664i
$460$	−0.803768	+	0.959904i	−0.0374759	+	0.0447558i
$461$	−4.87332	+	4.87332i	−0.226973	+	0.226973i	−0.811427	−	0.584454i	$-0.801309\pi$
$461$	−4.87332	+	4.87332i	−0.226973	+	0.226973i	0.584454	+	0.811427i	$0.301309\pi$
$462$	−11.3117	+	10.8680i	−0.526269	+	0.505623i
$463$	4.34716			0.202030			0.101015	−	0.994885i	$-0.467791\pi$
$463$	4.34716			0.202030			0.101015	+	0.994885i	$0.467791\pi$
$464$	4.96413	+	6.55940i	0.230454	+	0.304513i
$465$	−0.748880	−	0.544093i	−0.0347285	−	0.0252317i
$466$	3.77838	−	13.6518i	0.175030	−	0.632406i
$467$	8.02822	+	15.7563i	0.371502	+	0.729113i	0.998764	−	0.0496945i	$-0.0158248\pi$
$467$	8.02822	+	15.7563i	0.371502	+	0.729113i	−0.627263	+	0.778808i	$0.715825\pi$
$468$	3.83491	+	15.3136i	0.177269	+	0.707873i
$469$	9.20368	+	1.45772i	0.424987	+	0.0673112i
$470$	0.806732	−	0.881307i	0.0372118	−	0.0406516i
$471$	10.7998	−	3.50908i	0.497631	−	0.161690i
$472$	−26.9431	−	9.49414i	−1.24016	−	0.437003i
$473$	−22.1984	−	4.99275i	−1.02068	−	0.229567i
$474$	−7.61114	−	0.863200i	−0.349591	−	0.0396481i
$475$	18.2126	−	35.7442i	0.835651	−	1.64006i
$476$	−10.5070	−	12.0617i	−0.481587	−	0.552849i
$477$	1.32177	−	8.34535i	0.0605198	−	0.382107i
$478$	−19.2033	+	7.19114i	−0.878341	+	0.328915i
$479$	−6.71859	+	20.6777i	−0.306980	+	0.944788i	0.671950	+	0.740596i	$0.265457\pi$
$479$	−6.71859	+	20.6777i	−0.306980	+	0.944788i	−0.978931	+	0.204192i	$0.934543\pi$
$480$	−0.912811	−	0.803397i	−0.0416640	−	0.0366699i
$481$	5.91931	+	4.30063i	0.269897	+	0.196092i
$482$	−17.3543	+	26.2489i	−0.790466	+	1.19560i
$483$	9.29951	−	9.29951i	0.423142	−	0.423142i
$484$	−21.9824	−	0.879981i	−0.999200	−	0.0399991i
$485$	−0.875407	−	0.875407i	−0.0397502	−	0.0397502i
$486$	3.22278	+	15.7987i	0.146188	+	0.716645i
$487$	8.83346	−	12.1582i	0.400282	−	0.550941i	−0.560532	−	0.828132i	$-0.689403\pi$
$487$	8.83346	−	12.1582i	0.400282	−	0.550941i	0.960815	+	0.277191i	$0.0894035\pi$
$488$	6.62133	+	22.2268i	0.299733	+	1.00616i
$489$	4.90456	+	1.59359i	0.221792	+	0.0720646i
$490$	0.177492	+	0.0807773i	0.00801828	+	0.00364914i
$491$	−21.6392	−	3.42732i	−0.976565	−	0.154673i	−0.352301	−	0.935887i	$-0.614601\pi$
$491$	−21.6392	−	3.42732i	−0.976565	−	0.154673i	−0.624263	+	0.781214i	$0.714601\pi$
$492$	−15.2782	−	1.05251i	−0.688796	−	0.0474508i
$493$	−5.91753	−	3.01513i	−0.266512	−	0.135795i
$494$	59.8555	−	47.6616i	2.69302	−	2.14440i
$495$	−0.136302	+	0.606017i	−0.00612634	+	0.0272384i
$496$	15.4971	+	7.51887i	0.695840	+	0.337607i
$497$	0.0603062	+	0.185603i	0.00270510	+	0.00832545i
$498$	−8.37472	+	0.369979i	−0.375280	+	0.0165792i
$499$	−2.72183	+	17.1849i	−0.121846	+	0.769303i	0.848787	+	0.528736i	$0.177334\pi$
$499$	−2.72183	+	17.1849i	−0.121846	+	0.769303i	−0.970632	+	0.240568i	$0.922666\pi$
$500$	3.08056	−	0.771448i	0.137767	−	0.0345002i
$501$	2.23165	−	1.13708i	0.0997030	−	0.0508012i
$502$	4.13892	+	7.30671i	0.184729	+	0.326114i
$503$	17.4767	−	24.0547i	0.779249	−	1.07254i	−0.216115	−	0.976368i	$-0.569339\pi$
$503$	17.4767	−	24.0547i	0.779249	−	1.07254i	0.995364	−	0.0961769i	$-0.0306614\pi$
$504$	−5.68229	−	5.96935i	−0.253110	−	0.265896i
$505$			2.41952i			0.107667i
$506$	18.4410	+	0.368959i	0.819801	+	0.0164022i
$507$	30.5662	+	30.5662i	1.35749	+	1.35749i
$508$	−19.3977	+	1.71725i	−0.860632	+	0.0761908i
$509$	−32.1858	+	5.09773i	−1.42661	+	0.225953i	−0.821509	−	0.570196i	$-0.806867\pi$
$509$	−32.1858	+	5.09773i	−1.42661	+	0.225953i	−0.605101	+	0.796149i	$0.706867\pi$
$510$	0.946183	+	0.261874i	0.0418977	+	0.0115960i
$511$	−4.33717	+	13.3484i	−0.191865	+	0.590500i
$512$	19.3478	+	11.7330i	0.855058	+	0.518532i
$513$	36.7946	−	26.7329i	1.62452	−	1.18029i
$514$	0.482660	+	10.9253i	0.0212892	+	0.481895i
$515$	−0.321197	−	0.163658i	−0.0141536	−	0.00721164i
$516$	−4.14920	+	18.0572i	−0.182658	+	0.794923i
$517$	−17.5658	−	1.12847i	−0.772545	−	0.0496301i
$518$	−3.79539	−	0.430445i	−0.166760	−	0.0189127i
$519$	−13.7966	+	4.48279i	−0.605603	+	0.196772i
$520$	2.97102	+	0.545889i	0.130288	+	0.0239388i
$521$	19.2421	+	26.4845i	0.843013	+	1.16031i	0.985359	+	0.170491i	$0.0545355\pi$
$521$	19.2421	+	26.4845i	0.843013	+	1.16031i	−0.142346	+	0.989817i	$0.545464\pi$
$522$	−3.11435	−	1.41735i	−0.136312	−	0.0620358i
$523$	−7.94459	+	4.04797i	−0.347393	+	0.177005i	−0.618977	−	0.785409i	$-0.712453\pi$
$523$	−7.94459	+	4.04797i	−0.347393	+	0.177005i	0.271584	+	0.962415i	$0.412453\pi$
$524$	−13.2434	−	5.33478i	−0.578541	−	0.233051i
$525$	−16.4323	+	2.60263i	−0.717166	+	0.113588i
$526$	34.4492	+	22.7759i	1.50206	+	0.993074i
$527$	−13.9066			−0.605780
$528$	−0.799380	+	17.8968i	−0.0347886	+	0.778858i
$529$	7.53612			0.327658
$530$	−1.34868	−	0.891670i	−0.0585829	−	0.0387317i
$531$	11.7364	−	1.85886i	0.509315	−	0.0806676i
$532$	−14.9252	+	37.0512i	−0.647089	+	1.60637i
$533$	33.8970	−	17.2714i	1.46824	−	0.748106i
$534$	22.2757	+	10.1377i	0.963963	+	0.438703i
$535$	1.19211	+	1.64080i	0.0515393	+	0.0709378i
$536$	8.76100	−	6.04126i	0.378417	−	0.260943i
$537$	12.6368	−	4.10594i	0.545318	−	0.177184i
$538$	−32.6640	−	3.70452i	−1.40825	−	0.159713i
$539$	−0.710791	−	2.78362i	−0.0306159	−	0.119899i
$540$	1.74997	+	0.402111i	0.0753069	+	0.0173041i
$541$	41.0034	+	20.8923i	1.76287	+	0.898228i	0.947798	+	0.318871i	$0.103304\pi$
$541$	41.0034	+	20.8923i	1.76287	+	0.898228i	0.815074	+	0.579357i	$0.196696\pi$
$542$	−1.83113	−	41.4487i	−0.0786536	−	1.78038i
$543$	19.8143	−	14.3959i	0.850313	−	0.617789i
$544$	−18.1888	−	1.70402i	−0.779838	−	0.0730592i
$545$	−0.660059	+	2.03145i	−0.0282738	+	0.0870179i
$546$	−30.5819	−	8.46412i	−1.30878	−	0.362231i
$547$	28.6257	−	4.53386i	1.22395	−	0.193854i	0.489185	−	0.872180i	$-0.337294\pi$
$547$	28.6257	−	4.53386i	1.22395	−	0.193854i	0.734761	+	0.678326i	$0.237294\pi$
$548$	2.16119	+	24.4123i	0.0923215	+	1.04284i
$549$	−6.82142	−	6.82142i	−0.291131	−	0.291131i
$550$	−18.5988	−	14.0898i	−0.793058	−	0.600790i
$551$			16.5842i			0.706511i
$552$	0.369916	−	15.0150i	0.0157447	−	0.639079i
$553$	−5.83903	+	8.03673i	−0.248301	+	0.341757i
$554$	7.23632	+	12.7748i	0.307442	+	0.542747i
$555$	0.208879	−	0.106429i	0.00886641	−	0.00451766i
$556$	−3.10907	−	12.4152i	−0.131854	−	0.526521i
$557$	−5.47429	+	34.5633i	−0.231953	+	1.46449i	0.546852	+	0.837229i	$0.315826\pi$
$557$	−5.47429	+	34.5633i	−0.231953	+	1.46449i	−0.778806	+	0.627265i	$0.784174\pi$
$558$	−7.15781	+	0.316218i	−0.303014	+	0.0133866i
$559$	−14.2228	−	43.7732i	−0.601559	−	1.85141i
$560$	−1.49002	+	0.516500i	−0.0629650	+	0.0218261i
$561$	−5.72661	−	13.2816i	−0.241778	−	0.560748i
$562$	8.58371	−	6.83503i	0.362082	−	0.288318i
$563$	1.44158	+	0.734522i	0.0607554	+	0.0309564i	0.484104	−	0.875010i	$-0.339146\pi$
$563$	1.44158	+	0.734522i	0.0607554	+	0.0309564i	−0.423349	+	0.905967i	$0.639146\pi$
$564$	−0.985086	+	14.2995i	−0.0414796	+	0.602117i
$565$	0.172233	+	0.0272790i	0.00724589	+	0.00114764i
$566$	−5.52367	−	2.51384i	−0.232177	−	0.105665i
$567$	−9.62500	−	3.12735i	−0.404212	−	0.131336i
$568$	0.196030	+	0.106043i	0.00822525	+	0.00444947i
$569$	2.43584	−	3.35264i	0.102116	−	0.140550i	−0.754901	−	0.655839i	$-0.772315\pi$
$569$	2.43584	−	3.35264i	0.102116	−	0.140550i	0.857017	+	0.515288i	$0.172315\pi$
$570$	−0.489997	−	2.40207i	−0.0205237	−	0.100611i
$571$	21.9987	+	21.9987i	0.920615	+	0.920615i	0.997073	−	0.0764577i	$-0.0243610\pi$
$571$	21.9987	+	21.9987i	0.920615	+	0.920615i	−0.0764577	+	0.997073i	$0.524361\pi$
$572$	−21.1552	−	39.1530i	−0.884545	−	1.63707i
$573$	6.59428	−	6.59428i	0.275480	−	0.275480i
$574$	−10.9534	+	16.5673i	−0.457186	+	0.691508i
$575$	15.8263	+	11.4985i	0.660004	+	0.479521i
$576$	−9.40065	−	0.463480i	−0.391694	−	0.0193117i
$577$	1.31161	−	4.03673i	0.0546032	−	0.168051i	−0.920036	−	0.391834i	$-0.871841\pi$
$577$	1.31161	−	4.03673i	0.0546032	−	0.168051i	0.974639	+	0.223783i	$0.0718406\pi$
$578$	−8.70229	+	3.25877i	−0.361968	+	0.135547i
$579$	−0.765761	+	4.83483i	−0.0318239	+	0.200929i
$580$	−0.493698	+	0.430061i	−0.0204997	+	0.0178573i
$581$	−4.93557	+	9.68661i	−0.204762	+	0.401868i
$582$	14.7573	+	1.67367i	0.611711	+	0.0693758i
$583$	2.21022	+	23.7164i	0.0915378	+	0.982231i
$584$	6.92303	+	14.4568i	0.286477	+	0.598226i
$585$	−1.19501	+	0.388282i	−0.0494076	+	0.0160535i
$586$	−1.67778	+	1.83287i	−0.0693083	+	0.0757151i
$587$	−28.7878	−	4.55955i	−1.18820	−	0.188193i	−0.469130	−	0.883129i	$-0.655432\pi$
$587$	−28.7878	−	4.55955i	−1.18820	−	0.188193i	−0.719071	+	0.694936i	$0.755432\pi$
$588$	−2.26936	+	0.568305i	−0.0935870	+	0.0234365i
$589$	15.7653	+	30.9411i	0.649598	+	1.27491i
$590$	0.606503	−	2.19137i	0.0249693	−	0.0902172i
$591$	5.79533	+	4.21055i	0.238388	+	0.173199i
$592$	−3.47843	+	2.63247i	−0.142963	+	0.108194i
$593$	−18.3132			−0.752031			−0.376016	−	0.926613i	$-0.622706\pi$
$593$	−18.3132			−0.752031			−0.376016	+	0.926613i	$0.622706\pi$
$594$	−11.5356	−	23.8054i	−0.473310	−	0.976747i
$595$	0.900295	−	0.900295i	0.0369085	−	0.0369085i
$596$	−35.0314	−	29.3333i	−1.43494	−	1.20154i
$597$	1.73015	+	10.9237i	0.0708101	+	0.447078i
$598$	18.3895	+	32.4642i	0.752003	+	1.32756i
$599$	37.8357	+	12.2936i	1.54593	+	0.502302i	0.953004	−	0.302958i	$-0.0979743\pi$
$599$	37.8357	+	12.2936i	1.54593	+	0.502302i	0.592922	+	0.805260i	$0.297974\pi$
$600$	−11.5433	+	15.0918i	−0.471253	+	0.616122i
$601$	−7.85107	−	10.8061i	−0.320252	−	0.440789i	0.618292	−	0.785948i	$-0.287825\pi$
$601$	−7.85107	−	10.8061i	−0.320252	−	0.440789i	−0.938544	+	0.345159i	$0.887825\pi$
$602$	17.7238	+	16.2240i	0.722366	+	0.661241i
$603$	−2.00965	+	3.94415i	−0.0818391	+	0.160618i
$604$	20.7849	+	4.77597i	0.845724	+	0.194331i
$605$	−0.0503731	−	1.75034i	−0.00204796	−	0.0711614i
$606$	−18.0808	−	22.7066i	−0.734482	−	0.922393i
$607$	13.2472	+	40.7707i	0.537687	+	1.65483i	0.737771	+	0.675051i	$0.235878\pi$
$607$	13.2472	+	40.7707i	0.537687	+	1.65483i	−0.200084	+	0.979779i	$0.564122\pi$
$608$	16.8285	+	42.4006i	0.682488	+	1.71957i
$609$	5.56425	−	4.04266i	0.225475	−	0.163817i
$610$	−1.72871	+	0.647356i	−0.0699934	+	0.0262107i
$611$	−16.1650	−	31.7255i	−0.653964	−	1.28348i
$612$	6.99177	−	2.97635i	0.282626	−	0.120312i
$613$	−3.84479	−	24.2751i	−0.155290	−	0.980460i	−0.935084	−	0.354425i	$-0.884677\pi$
$613$	−3.84479	−	24.2751i	−0.155290	−	0.980460i	0.779795	−	0.626035i	$-0.215323\pi$
$614$	3.73094	+	18.2898i	0.150568	+	0.738117i
$615$		−	1.21893i		−	0.0491522i
$616$	19.6840	+	12.3415i	0.793090	+	0.497255i
$617$		−	37.5228i		−	1.51061i	−0.655373	−	0.755306i	$-0.727488\pi$
$617$		−	37.5228i		−	1.51061i	0.655373	−	0.755306i	$-0.272512\pi$
$618$	4.23736	−	0.864379i	0.170452	−	0.0347704i
$619$	3.31406	+	20.9241i	0.133203	+	0.841012i	0.960303	+	0.278958i	$0.0899889\pi$
$619$	3.31406	+	20.9241i	0.133203	+	0.841012i	−0.827100	+	0.562055i	$0.810011\pi$
$620$	−0.512268	+	1.27168i	−0.0205732	+	0.0510721i
$621$	10.0686	+	19.7608i	0.404041	+	0.792975i
$622$	−11.6271	−	31.0491i	−0.466202	−	1.24496i
$623$	25.6780	−	18.6561i	1.02877	−	0.747443i
$624$	−31.9617	+	17.0791i	−1.27949	+	0.683710i
$625$	−7.60816	−	23.4155i	−0.304327	−	0.936621i
$626$	10.4224	−	8.29917i	0.416564	−	0.331701i
$627$	−23.0585	+	27.7980i	−0.920869	+	1.11015i
$628$	−8.92721	−	14.2538i	−0.356234	−	0.568787i
$629$	1.59892	−	3.13805i	0.0637530	−	0.125122i
$630$	0.442916	−	0.483859i	0.0176462	−	0.0192774i
$631$	1.68406	+	2.31792i	0.0670415	+	0.0922747i	0.841221	−	0.540691i	$-0.181837\pi$
$631$	1.68406	+	2.31792i	0.0670415	+	0.0922747i	−0.774180	+	0.632966i	$0.781837\pi$
$632$	1.49823	+	11.2456i	0.0595963	+	0.447326i
$633$	−25.8968	−	8.41437i	−1.02930	−	0.334441i
$634$	31.4765	−	17.8300i	1.25009	−	0.708119i
$635$	−0.242469	−	1.53089i	−0.00962209	−	0.0607515i
$636$	19.3204	−	1.71041i	0.766104	−	0.0678223i
$637$	4.10938	−	4.10938i	0.162820	−	0.162820i
$638$	9.49508	+	1.69923i	0.375914	+	0.0672732i
$639$	−0.0927066			−0.00366742
$640$	−0.825833	+	1.60050i	−0.0326439	+	0.0632654i
$641$	−38.4922	−	27.9662i	−1.52035	−	1.10460i	−0.961314	−	0.275455i	$-0.911172\pi$
$641$	−38.4922	−	27.9662i	−1.52035	−	1.10460i	−0.559035	−	0.829144i	$-0.688828\pi$
$642$	−23.4492	−	6.49000i	−0.925464	−	0.256140i
$643$	−5.43046	−	10.6579i	−0.214156	−	0.420306i	0.758790	−	0.651335i	$-0.225791\pi$
$643$	−5.43046	−	10.6579i	−0.214156	−	0.420306i	−0.972947	+	0.231029i	$0.925791\pi$
$644$	−16.7066	−	10.0149i	−0.658332	−	0.394641i
$645$	−1.45654	−	0.230693i	−0.0573511	−	0.00908352i
$646$	−27.1669	−	24.8681i	−1.06887	−	0.978421i
$647$	−15.6500	+	5.08501i	−0.615267	+	0.199912i	−0.600038	−	0.799972i	$-0.704848\pi$
$647$	−15.6500	+	5.08501i	−0.615267	+	0.199912i	−0.0152290	+	0.999884i	$0.504848\pi$
$648$	−10.4242	+	4.99191i	−0.409501	+	0.196101i
$649$	−30.7602	+	13.2629i	−1.20745	+	0.520614i
$650$	5.31895	−	46.8991i	0.208627	−	1.83953i
$651$	6.53817	−	12.8319i	0.256251	−	0.502921i
$652$	0.524926	−	7.61981i	0.0205577	−	0.298415i
$653$	4.53897	−	28.6579i	0.177624	−	1.12147i	−0.724271	−	0.689516i	$-0.757823\pi$
$653$	4.53897	−	28.6579i	0.177624	−	1.12147i	0.901894	−	0.431956i	$-0.142177\pi$
$654$	−8.98633	−	23.9973i	−0.351393	−	0.938368i
$655$	0.351167	−	1.08078i	0.0137212	−	0.0422297i
$656$	3.98478	+	22.3291i	0.155579	+	0.871806i
$657$	−5.39402	−	3.91899i	−0.210441	−	0.152894i
$658$	15.5060	+	10.2517i	0.604488	+	0.399653i
$659$	−0.387867	+	0.387867i	−0.0151091	+	0.0151091i	−0.714621	−	0.699512i	$-0.753401\pi$
$659$	−0.387867	+	0.387867i	−0.0151091	+	0.0151091i	0.699512	+	0.714621i	$0.253401\pi$
$660$	−1.42548	+	0.0344241i	−0.0554867	+	0.00133996i
$661$	−16.3188	−	16.3188i	−0.634727	−	0.634727i	0.314523	−	0.949250i	$-0.398156\pi$
$661$	−16.3188	−	16.3188i	−0.634727	−	0.634727i	−0.949250	+	0.314523i	$0.898156\pi$
$662$	3.68291	−	0.751277i	0.143140	−	0.0291992i
$663$	17.1972	−	23.6699i	0.667885	−	0.919264i
$664$	3.54468	+	11.8990i	0.137560	+	0.461769i
$665$	−3.02372	−	0.982465i	−0.117255	−	0.0380984i
$666$	0.751618	−	1.65153i	0.0291246	−	0.0639956i
$667$	−7.98752	−	1.26510i	−0.309278	−	0.0489848i
$668$	−2.43659	−	2.79714i	−0.0942744	−	0.108225i
$669$	7.13563	+	3.63578i	0.275879	+	0.140567i
$670$	0.527634	+	0.662625i	0.0203843	+	0.0255994i
$671$	23.3896	+	13.8744i	0.902947	+	0.535614i
$672$	10.1238	−	15.9820i	0.390534	−	0.616520i
$673$	−13.7011	−	42.1678i	−0.528140	−	1.62545i	−0.758021	−	0.652230i	$-0.773834\pi$
$673$	−13.7011	−	42.1678i	−0.528140	−	1.62545i	0.229880	−	0.973219i	$-0.426166\pi$
$674$	−1.23154	−	27.8766i	−0.0474370	−	1.07377i
$675$	4.38895	−	27.7108i	0.168931	−	1.06659i
$676$	32.9175	−	54.9122i	1.26606	−	2.11201i
$677$	4.16492	−	2.12214i	0.160071	−	0.0815603i	−0.372120	−	0.928185i	$-0.621369\pi$
$677$	4.16492	−	2.12214i	0.160071	−	0.0815603i	0.532191	+	0.846624i	$0.321369\pi$
$678$	−1.82022	+	1.03107i	−0.0699051	+	0.0395981i
$679$	11.3214	−	15.5825i	0.434474	−	0.598002i
$680$	0.0358120	−	1.45361i	0.00137333	−	0.0557435i
$681$			19.4905i			0.746877i
$682$	19.3303	−	5.85597i	0.740195	−	0.224237i
$683$	16.8305	+	16.8305i	0.644000	+	0.644000i	0.951536	−	0.307536i	$-0.0995045\pi$
$683$	16.8305	+	16.8305i	0.644000	+	0.644000i	−0.307536	+	0.951536i	$0.599504\pi$
$684$	−14.5484	−	12.1820i	−0.556274	−	0.465791i
$685$	−1.92665	+	0.305151i	−0.0736134	+	0.0116592i
$686$	−7.34911	+	26.5533i	−0.280590	+	1.01381i
$687$	−4.02422	+	12.3853i	−0.153533	+	0.472527i
$688$	27.4358	−	0.535555i	1.04598	−	0.0204179i
$689$	−38.9806	+	28.3210i	−1.48504	+	1.07895i
$690$	1.19430	−	0.0527617i	0.0454660	−	0.00200860i
$691$	−4.53260	−	2.30947i	−0.172428	−	0.0878565i	0.365646	−	0.930754i	$-0.380848\pi$
$691$	−4.53260	−	2.30947i	−0.172428	−	0.0878565i	−0.538074	+	0.842897i	$0.680848\pi$
$692$	11.4043	+	18.2089i	0.433528	+	0.692199i
$693$	−9.64408	−	0.619559i	−0.366348	−	0.0235351i
$694$	−2.39052	+	21.0780i	−0.0907429	+	0.800111i
$695$	0.968827	−	0.314791i	0.0367497	−	0.0119407i
$696$	1.41945	−	7.72538i	0.0538039	−	0.292830i
$697$	−10.7638	−	14.8151i	−0.407707	−	0.561160i
$698$	0.957160	−	2.10317i	0.0362290	−	0.0796062i
$699$	−12.0513	+	6.14045i	−0.455822	+	0.232253i
$700$	9.65139	+	22.6722i	0.364788	+	0.856927i
$701$	3.04952	−	0.482997i	0.115179	−	0.0182425i	−0.0985789	−	0.995129i	$-0.531430\pi$
$701$	3.04952	−	0.482997i	0.115179	−	0.0182425i	0.213758	+	0.976887i	$0.431430\pi$
$702$	29.5115	−	44.6371i	1.11384	−	1.68472i
$703$	−8.79456			−0.331693
$704$	26.0002	−	5.29058i	0.979919	−	0.199396i
$705$	−1.14085			−0.0429668
$706$	−1.85360	+	2.80363i	−0.0697612	+	0.105516i
$707$	−37.1795	+	5.88865i	−1.39828	+	0.221466i
$708$	10.6840	+	25.0978i	0.401529	+	0.943234i
$709$	−5.41094	+	2.75701i	−0.203212	+	0.103542i	−0.552635	−	0.833423i	$-0.686378\pi$
$709$	−5.41094	+	2.75701i	−0.203212	+	0.103542i	0.349423	+	0.936965i	$0.386378\pi$
$710$	−0.00734809	+	0.0161460i	−0.000275769	+	0.000605948i
$711$	−2.77378	−	3.81778i	−0.104025	−	0.143178i
$712$	6.55048	−	35.6512i	0.245490	−	1.33609i
$713$	−16.1049	+	5.23281i	−0.603135	+	0.195970i
$714$	−1.72125	+	15.1769i	−0.0644162	+	0.567980i
$715$	2.99324	−	1.89402i	0.111941	−	0.0708323i
$716$	−10.4456	−	16.6782i	−0.390372	−	0.623293i
$717$	17.4458	+	8.88908i	0.651526	+	0.331969i
$718$	26.3226	−	1.16288i	0.982349	−	0.0433983i
$719$	26.8101	−	19.4787i	0.999849	−	0.726433i	0.0377932	−	0.999286i	$-0.487967\pi$
$719$	26.8101	−	19.4787i	0.999849	−	0.726433i	0.962056	+	0.272853i	$0.0879672\pi$
$720$	−0.0146207	−	0.748999i	−0.000544881	−	0.0279136i
$721$	1.73312	−	5.33399i	0.0645447	−	0.198648i
$722$	−17.3644	+	62.7397i	−0.646236	+	2.33493i
$723$	29.6765	−	4.70030i	1.10368	−	0.174806i
$724$	−27.8118	−	23.2880i	−1.03362	−	0.865491i
$725$	7.23405	+	7.23405i	0.268666	+	0.268666i
$726$	13.5528	+	16.0501i	0.502993	+	0.595675i
$727$			23.2021i			0.860520i	0.902705	+	0.430260i	$0.141578\pi$
$727$			23.2021i			0.860520i	−0.902705	+	0.430260i	$0.858422\pi$
$728$	−1.15749	+	46.9827i	−0.0428995	+	1.74130i
$729$	16.2552	−	22.3734i	0.602046	−	0.828645i
$730$	−1.11008	+	0.628809i	−0.0410859	+	0.0232733i
$731$	−19.7400	+	10.0581i	−0.730112	+	0.372011i
$732$	11.3859	−	18.9938i	0.420836	−	0.702030i
$733$	0.540579	−	3.41308i	0.0199667	−	0.126065i	−0.975692	−	0.219148i	$-0.929672\pi$
$733$	0.540579	−	3.41308i	0.0199667	−	0.126065i	0.995658	+	0.0930831i	$0.0296722\pi$
$734$	0.746080	+	16.8880i	0.0275383	+	0.623348i
$735$	−0.0575405	−	0.177091i	−0.00212241	−	0.00653212i
$736$	−21.7053	+	4.87075i	−0.800068	+	0.179538i
$737$	2.73828	−	12.1747i	0.100866	−	0.448461i
$738$	−5.87706	−	7.38066i	−0.216338	−	0.271686i
$739$	−1.84129	−	0.938186i	−0.0677331	−	0.0345117i	0.419796	−	0.907619i	$-0.362102\pi$
$739$	−1.84129	−	0.938186i	−0.0677331	−	0.0345117i	−0.487529	+	0.873107i	$0.662102\pi$
$740$	−0.228060	−	0.261807i	−0.00838366	−	0.00962421i
$741$	−72.1597	−	11.4290i	−2.65085	−	0.419854i
$742$	10.4194	−	22.8946i	0.382509	−	0.840488i
$743$	−8.24128	−	2.67776i	−0.302343	−	0.0982373i	0.153917	−	0.988084i	$-0.450811\pi$
$743$	−8.24128	−	2.67776i	−0.302343	−	0.0982373i	−0.456260	+	0.889847i	$0.650811\pi$
$744$	−4.69565	−	15.7626i	−0.172151	−	0.577885i
$745$	2.13760	−	2.94215i	0.0783155	−	0.107792i
$746$	−43.1121	+	8.79443i	−1.57845	+	0.321987i
$747$	−3.65180	−	3.65180i	−0.133612	−	0.133612i
$748$	−17.0214	+	13.0061i	−0.622366	+	0.475548i
$749$	−22.3119	+	22.3119i	−0.815259	+	0.815259i
$750$	−2.52947	−	1.67234i	−0.0923631	−	0.0610652i
$751$	16.2775	+	11.8263i	0.593975	+	0.431548i	0.843735	−	0.536760i	$-0.180352\pi$
$751$	16.2775	+	11.8263i	0.593975	+	0.431548i	−0.249761	+	0.968308i	$0.580352\pi$
$752$	20.8987	−	3.72951i	0.762097	−	0.136001i
$753$	2.47783	−	7.62597i	0.0902971	−	0.277906i
$754$	6.84279	+	18.2731i	0.249200	+	0.665468i
$755$	−0.265541	+	1.67656i	−0.00966403	+	0.0610163i
$756$	−1.91993	+	27.8696i	−0.0698270	+	1.01361i
$757$	6.82722	−	13.3992i	0.248140	−	0.487002i	−0.733018	−	0.680209i	$-0.761889\pi$
$757$	6.82722	−	13.3992i	0.248140	−	0.487002i	0.981158	+	0.193207i	$0.0618890\pi$
$758$	2.35934	−	20.8031i	0.0856950	−	0.755603i
$759$	−11.6295	−	13.2263i	−0.422124	−	0.480085i
$760$	−3.27478	+	1.56822i	−0.118789	+	0.0568853i
$761$	−19.8864	+	6.46149i	−0.720882	+	0.234229i	−0.646406	−	0.762994i	$-0.723729\pi$
$761$	−19.8864	+	6.46149i	−0.720882	+	0.234229i	−0.0744766	+	0.997223i	$0.523729\pi$
$762$	13.7157	+	12.5551i	0.496867	+	0.454823i
$763$	−32.8228	−	5.19861i	−1.18826	−	0.188202i
$764$	−11.8466	−	7.10154i	−0.428596	−	0.256925i
$765$	0.274585	+	0.538904i	0.00992766	+	0.0194841i
$766$	14.2829	+	3.95307i	0.516063	+	0.142830i
$767$	−54.8198	−	39.8289i	−1.97943	−	1.43814i
$768$	−4.21013	−	21.1917i	−0.151920	−	0.764690i
$769$	−3.47076			−0.125159			−0.0625794	−	0.998040i	$-0.519933\pi$
$769$	−3.47076			−0.125159			−0.0625794	+	0.998040i	$0.519933\pi$
$770$	−0.872311	+	1.63053i	−0.0314359	+	0.0587602i
$771$	7.38379	−	7.38379i	0.265921	−	0.265921i
$772$	7.22177	−	0.639336i	0.259917	−	0.0230102i
$773$	3.72949	+	23.5471i	0.134141	+	0.846930i	0.959374	+	0.282138i	$0.0910436\pi$
$773$	3.72949	+	23.5471i	0.134141	+	0.846930i	−0.825233	+	0.564792i	$0.808956\pi$
$774$	−9.93163	+	5.62581i	−0.356985	+	0.202216i
$775$	20.3734	+	6.61972i	0.731834	+	0.237787i
$776$	−2.90493	−	21.8042i	−0.104281	−	0.782726i
$777$	2.14381	+	2.95071i	0.0769089	+	0.105856i
$778$	−11.6447	+	12.7212i	−0.417484	+	0.456076i
$779$	−20.7600	+	40.7438i	−0.743805	+	1.45980i
$780$	−1.53101	−	2.44451i	−0.0548190	−	0.0875275i
$781$	0.253219	−	0.0646587i	0.00906088	−	0.00231367i
$782$	14.0497	−	11.1875i	0.502416	−	0.400063i
$783$	3.58410	+	11.0307i	0.128085	+	0.394206i
$784$	1.63298	+	3.05596i	0.0583208	+	0.109141i
$785$	1.08299	−	0.786841i	0.0386537	−	0.0280836i
$786$	4.78095	+	12.7671i	0.170531	+	0.455389i
$787$	7.90584	+	15.5161i	0.281813	+	0.553089i	0.987910	−	0.155026i	$-0.0495460\pi$
$787$	7.90584	+	15.5161i	0.281813	+	0.553089i	−0.706098	+	0.708115i	$0.749546\pi$
$788$	3.96426	−	9.84113i	0.141221	−	0.350576i
$789$	−6.16870	−	38.9476i	−0.219611	−	1.38657i
$790$	−0.884767	+	0.180484i	−0.0314786	+	0.00642132i
$791$			2.71301i			0.0964634i
$792$	−8.46532	+	7.08135i	−0.300802	+	0.251625i
$793$			55.0117i			1.95352i
$794$	−3.61830	−	17.7376i	−0.128409	−	0.629485i
$795$	0.241503	+	1.52479i	0.00856524	+	0.0540788i
$796$	15.0718	−	6.41595i	0.534204	−	0.227407i
$797$	13.5746	+	26.6417i	0.480837	+	0.943696i	0.996231	+	0.0867423i	$0.0276457\pi$
$797$	13.5746	+	26.6417i	0.480837	+	0.943696i	−0.515394	+	0.856953i	$0.672354\pi$
$798$	35.7188	−	13.3757i	1.26443	−	0.473495i
$799$	−13.8660	+	10.0742i	−0.490544	+	0.356401i
$800$	25.8358	+	11.1545i	0.913433	+	0.394372i
$801$	4.65926	+	14.3397i	0.164627	+	0.506669i
$802$	3.01548	+	3.78697i	0.106480	+	0.133722i
$803$	17.4665	+	6.94223i	0.616381	+	0.244986i
$804$	−9.90346	−	2.27563i	−0.349268	−	0.0802552i
$805$	0.703848	−	1.38138i	0.0248074	−	0.0486872i
$806$	30.1374	+	27.5872i	1.06154	+	0.971719i
$807$	18.4502	+	25.3945i	0.649477	+	0.893929i
$808$	−26.1176	+	34.1465i	−0.918815	+	1.20127i
$809$	−47.7962	−	15.5299i	−1.68042	−	0.546003i	−0.695430	−	0.718594i	$-0.744786\pi$
$809$	−47.7962	−	15.5299i	−1.68042	−	0.546003i	−0.984994	+	0.172591i	$0.944786\pi$
$810$	−0.453408	−	0.800432i	−0.0159311	−	0.0281243i
$811$	3.83527	+	24.2150i	0.134675	+	0.850302i	0.958839	+	0.283951i	$0.0916454\pi$
$811$	3.83527	+	24.2150i	0.134675	+	0.850302i	−0.824164	+	0.566351i	$0.808355\pi$
$812$	−7.81010	−	6.53972i	−0.274081	−	0.229499i
$813$	−28.0128	+	28.0128i	−0.982452	+	0.982452i
$814$	−0.901098	+	5.03522i	−0.0315835	+	0.176484i
$815$	0.607927			0.0212948
$816$	10.5266	+	13.9095i	0.368505	+	0.486928i
$817$	44.7569	+	32.5178i	1.56585	+	1.13765i
$818$	12.5681	−	45.4101i	0.439433	−	1.58773i
$819$	−8.87497	−	17.4181i	−0.310116	−	0.608638i
$820$	−1.75126	+	0.438559i	−0.0611566	+	0.0153151i
$821$	−13.1888	−	2.08890i	−0.460292	−	0.0729030i	−0.0780175	−	0.996952i	$-0.524859\pi$
$821$	−13.1888	−	2.08890i	−0.460292	−	0.0729030i	−0.382274	+	0.924049i	$0.624859\pi$
$822$	15.8008	−	17.2614i	0.551116	−	0.602061i
$823$	15.8547	−	5.15150i	0.552660	−	0.179570i	−0.0193559	−	0.999813i	$-0.506162\pi$
$823$	15.8547	−	5.15150i	0.552660	−	0.179570i	0.572016	+	0.820243i	$0.306162\pi$
$824$	−2.76642	−	5.77688i	−0.0963728	−	0.201247i
$825$	2.06738	+	22.1837i	0.0719770	+	0.772337i
$826$	35.1498	+	3.98643i	1.22302	+	0.138706i
$827$	0.863809	−	1.69532i	0.0300376	−	0.0589521i	−0.875500	−	0.483218i	$-0.839468\pi$
$827$	0.863809	−	1.69532i	0.0300376	−	0.0589521i	0.905538	+	0.424266i	$0.139468\pi$
$828$	6.97708	−	6.07774i	0.242470	−	0.211216i
$829$	7.07315	−	44.6581i	0.245661	−	1.55104i	−0.488805	−	0.872393i	$-0.662567\pi$
$829$	7.07315	−	44.6581i	0.245661	−	1.55104i	0.734465	−	0.678646i	$-0.237433\pi$
$830$	−0.925454	+	0.346557i	−0.0321230	+	0.0120292i
$831$	4.33214	−	13.3329i	0.150280	−	0.462515i
$832$	36.0372	+	39.7750i	1.24936	+	1.37895i
$833$	−2.26316	−	1.64428i	−0.0784137	−	0.0569709i
$834$	−6.73982	+	10.1942i	−0.233381	+	0.352996i
$835$	0.208780	−	0.208780i	0.00722512	−	0.00722512i
$836$	48.2340	+	23.1271i	1.66821	+	0.799867i
$837$	17.1729	+	17.1729i	0.593583	+	0.593583i
$838$	−7.64417	−	37.4733i	−0.264063	−	1.29449i
$839$	−14.2650	+	19.6341i	−0.492482	+	0.677843i	−0.980843	−	0.194798i	$-0.937595\pi$
$839$	−14.2650	+	19.6341i	−0.492482	+	0.677843i	0.488361	+	0.872641i	$0.337595\pi$
$840$	1.32444	+	0.716460i	0.0456976	+	0.0247202i
$841$	23.5584	+	7.65458i	0.812357	+	0.263951i
$842$	36.3320	+	16.5348i	1.25208	+	0.569827i
$843$	−10.3482	−	1.63900i	−0.356412	−	0.0564501i
$844$	−2.77168	+	40.2336i	−0.0954051	+	1.38490i
$845$	4.54040	+	2.31345i	0.156194	+	0.0795850i
$846$	−6.90785	+	5.50058i	−0.237497	+	0.189114i
$847$	26.7740	−	5.03405i	0.919964	−	0.172972i
$848$	−9.40864	−	27.1425i	−0.323094	−	0.932077i
$849$	1.79070	+	5.51120i	0.0614566	+	0.189144i
$850$	−22.6977	+	1.00274i	−0.778524	+	0.0343937i
$851$	0.670879	−	4.23576i	0.0229974	−	0.145200i
$852$	−0.0516972	−	0.206438i	−0.00177112	−	0.00707245i
$853$	1.05435	−	0.537218i	0.0361003	−	0.0183940i	−0.435847	−	0.900021i	$-0.643551\pi$
$853$	1.05435	−	0.537218i	0.0361003	−	0.0183940i	0.471947	+	0.881627i	$0.343551\pi$
$854$	−14.1549	−	24.9887i	−0.484372	−	0.855095i
$855$	0.887738	−	1.22187i	0.0303600	−	0.0417869i
$856$	−0.887525	+	36.0248i	−0.0303350	+	1.23130i
$857$		−	54.3532i		−	1.85667i	−0.371744	−	0.928335i	$-0.621240\pi$
$857$		−	54.3532i		−	1.85667i	0.371744	−	0.928335i	$-0.378760\pi$
$858$	−13.9371	+	40.1431i	−0.475803	+	1.37046i
$859$	−38.2734	−	38.2734i	−1.30587	−	1.30587i	−0.924368	−	0.381502i	$-0.875407\pi$
$859$	−38.2734	−	38.2734i	−1.30587	−	1.30587i	−0.381502	−	0.924368i	$-0.624593\pi$
$860$	0.192606	+	2.17563i	0.00656781	+	0.0741883i
$861$	18.7307	−	2.96666i	0.638342	−	0.101103i
$862$	2.19882	+	0.608563i	0.0748919	+	0.0207278i
$863$	−8.56138	+	26.3492i	−0.291433	+	0.896938i	0.692964	+	0.720973i	$0.256305\pi$
$863$	−8.56138	+	26.3492i	−0.291433	+	0.896938i	−0.984396	+	0.175965i	$0.943695\pi$
$864$	20.3567	+	24.5652i	0.692548	+	0.835724i
$865$	−1.38350	+	1.00517i	−0.0470406	+	0.0341770i
$866$	−0.822393	−	18.6154i	−0.0279460	−	0.632577i
$867$	7.90583	+	4.02822i	0.268496	+	0.136806i
$868$	−20.7881	−	4.77671i	−0.705594	−	0.162132i
$869$	10.2390	+	8.49329i	0.347335	+	0.288115i
$870$	0.621203	+	0.0704524i	0.0210608	+	0.00238856i
$871$	24.0074	−	7.80047i	0.813459	−	0.264309i
$872$	−31.2440	+	21.5447i	−1.05806	+	0.729597i
$873$	5.37811	+	7.40233i	0.182021	+	0.250531i
$874$	−40.8189	−	18.5768i	−1.38072	−	0.628369i
$875$	−3.50390	+	1.78533i	−0.118454	+	0.0603551i
$876$	5.71881	−	14.1967i	0.193221	−	0.479663i
$877$	19.6968	−	3.11967i	0.665114	−	0.105344i	0.185257	−	0.982690i	$-0.440688\pi$
$877$	19.6968	−	3.11967i	0.665114	−	0.105344i	0.479858	+	0.877346i	$0.340688\pi$
$878$	−17.1113	−	11.3131i	−0.577480	−	0.381797i
$879$	2.37264			0.0800272
$880$	0.562329	+	2.03562i	0.0189561	+	0.0686207i
$881$	−14.2973			−0.481687			−0.240844	−	0.970564i	$-0.577424\pi$
$881$	−14.2973			−0.481687			−0.240844	+	0.970564i	$0.577424\pi$
$882$	−1.20225	−	0.794861i	−0.0404819	−	0.0267643i
$883$	4.66376	−	0.738667i	0.156948	−	0.0248581i	−0.0774659	−	0.996995i	$-0.524683\pi$
$883$	4.66376	−	0.738667i	0.156948	−	0.0248581i	0.234414	+	0.972137i	$0.424683\pi$
$884$	−40.1943	−	16.1913i	−1.35188	−	0.544572i
$885$	−1.93446	+	0.985659i	−0.0650263	+	0.0331326i
$886$	1.28997	+	0.587069i	0.0433373	+	0.0197230i
$887$	−8.91345	−	12.2683i	−0.299284	−	0.411929i	0.632718	−	0.774382i	$-0.281939\pi$
$887$	−8.91345	−	12.2683i	−0.299284	−	0.411929i	−0.932002	+	0.362453i	$0.881939\pi$
$888$	4.09675	+	0.752728i	0.137478	+	0.0252599i
$889$	22.9343	−	7.45180i	0.769191	−	0.249925i
$890$	2.86674	+	0.325125i	0.0960933	+	0.0108982i
$891$	−5.00575	+	12.5944i	−0.167699	+	0.421928i
$892$	2.65626	−	11.5600i	0.0889382	−	0.387056i
$893$	38.1337	+	19.4301i	1.27610	+	0.650204i
$894$	1.92552	+	43.5855i	0.0643991	+	1.45772i
$895$	1.26720	−	0.920675i	0.0423578	−	0.0307748i
$896$	−26.6040	−	8.79483i	−0.888778	−	0.293815i
$897$	11.0092	−	33.8827i	0.367585	−	1.13131i
$898$	−6.36881	−	1.76269i	−0.212530	−	0.0588216i
$899$	−8.74675	+	1.38535i	−0.291720	+	0.0462040i
$900$	−11.6599	+	1.03223i	−0.388662	+	0.0344078i
$901$	16.3999	+	16.3999i	0.546360	+	0.546360i
$902$	21.2003	+	16.0605i	0.705893	+	0.534758i
$903$		−	22.9433i		−	0.763506i
$904$	2.13625	+	2.24417i	0.0710506	+	0.0746399i
$905$	1.69706	−	2.33580i	0.0564122	−	0.0776447i
$906$	−10.0367	−	17.7185i	−0.333448	−	0.588658i
$907$	51.7942	−	26.3904i	1.71980	−	0.876280i	0.740985	−	0.671522i	$-0.234359\pi$
$907$	51.7942	−	26.3904i	1.71980	−	0.876280i	0.978813	−	0.204758i	$-0.0656409\pi$
$908$	28.0022	−	7.01245i	0.929287	−	0.232716i
$909$	2.79735	−	17.6618i	0.0927823	−	0.585804i
$910$	−3.73702	+	0.165094i	−0.123881	+	0.00547283i
$911$	4.43753	+	13.6573i	0.147022	+	0.452487i	0.997265	−	0.0739025i	$-0.0235453\pi$
$911$	4.43753	+	13.6573i	0.147022	+	0.452487i	−0.850243	+	0.526390i	$0.823545\pi$
$912$	19.0140	−	39.1895i	0.629615	−	1.29769i
$913$	12.5215	+	7.42756i	0.414401	+	0.245816i
$914$	−21.5077	+	17.1261i	−0.711412	+	0.566482i
$915$	1.57049	+	0.800207i	0.0519189	+	0.0264540i
$916$	19.2419	+	1.32557i	0.635772	+	0.0437980i
$917$	17.4625	+	2.76579i	0.576663	+	0.0913344i
$918$	−23.4440	−	10.6694i	−0.773768	−	0.352144i
$919$	26.0616	+	8.46791i	0.859691	+	0.279331i	0.705500	−	0.708710i	$-0.250723\pi$
$919$	26.0616	+	8.46791i	0.859691	+	0.279331i	0.154192	+	0.988041i	$0.450723\pi$
$920$	−0.505497	−	1.69688i	−0.0166658	−	0.0559444i
$921$	10.4765	−	14.4197i	0.345214	−	0.475146i
$922$	−1.94810	−	9.54998i	−0.0641572	−	0.314512i
$923$	0.373819	+	0.373819i	0.0123044	+	0.0123044i
$924$	−3.99833	−	21.8208i	−0.131535	−	0.717852i
$925$	−3.83620	+	3.83620i	−0.126133	+	0.126133i
$926$	−3.39056	+	5.12833i	−0.111421	+	0.168527i
$927$	2.15543	+	1.56601i	0.0707937	+	0.0514346i
$928$	−11.6099	+	0.740168i	−0.381112	+	0.0242972i
$929$	6.51508	−	20.0514i	0.213753	−	0.657864i	−0.785487	−	0.618878i	$-0.787587\pi$
$929$	6.51508	−	20.0514i	0.213753	−	0.657864i	0.999240	−	0.0389855i	$-0.0124126\pi$
$930$	1.22595	−	0.459086i	0.0402005	−	0.0150540i
$931$	−1.09276	+	6.89941i	−0.0358137	+	0.226119i
$932$	13.1580	+	15.1050i	0.431004	+	0.494781i
$933$	−14.3724	+	28.2074i	−0.470531	+	0.923469i
$934$	−24.8492	−	2.81822i	−0.813090	−	0.0922149i
$935$	−1.12586	−	1.28045i	−0.0368197	−	0.0418753i
$936$	−21.0564	−	7.41981i	−0.688252	−	0.242524i
$937$	5.61906	−	1.82574i	0.183567	−	0.0596444i	−0.215791	−	0.976440i	$-0.569233\pi$
$937$	5.61906	−	1.82574i	0.183567	−	0.0596444i	0.399358	+	0.916795i	$0.369233\pi$
$938$	−8.89806	+	9.72059i	−0.290532	+	0.317389i
$939$	−12.5649	−	1.99009i	−0.410041	−	0.0649441i
$940$	0.410464	+	1.63907i	0.0133879	+	0.0534606i
$941$	−3.71379	−	7.28872i	−0.121066	−	0.237605i	0.822518	−	0.568740i	$-0.192569\pi$
$941$	−3.71379	−	7.28872i	−0.121066	−	0.237605i	−0.943584	+	0.331134i	$0.892569\pi$
$942$	−4.28367	+	15.4774i	−0.139569	+	0.504282i
$943$	−18.0400	−	13.1068i	−0.587462	−	0.426816i
$944$	32.2144	−	24.3797i	1.04849	−	0.793493i
$945$	−2.22351			−0.0723307
$946$	23.2035	−	22.2932i	0.754411	−	0.724815i
$947$	−18.6039	+	18.6039i	−0.604545	+	0.604545i	−0.941515	−	0.336970i	$-0.890598\pi$
$947$	−18.6039	+	18.6039i	−0.604545	+	0.604545i	0.336970	+	0.941515i	$0.390598\pi$
$948$	6.95460	−	8.30557i	0.225875	−	0.269752i
$949$	5.94776	+	37.5527i	0.193072	+	1.21901i
$950$	27.9624	+	49.3640i	0.907221	+	1.60158i
$951$	−32.8518	−	10.6742i	−1.06529	−	0.346135i
$952$	22.4241	−	2.98752i	0.726769	−	0.0968261i
$953$	−13.9844	−	19.2479i	−0.453000	−	0.623501i	0.520039	−	0.854143i	$-0.325918\pi$
$953$	−13.9844	−	19.2479i	−0.453000	−	0.623501i	−0.973039	+	0.230642i	$0.925918\pi$
$954$	8.81405	+	8.06823i	0.285366	+	0.261219i
$955$	0.499098	−	0.979535i	0.0161504	−	0.0316970i
$956$	6.49426	−	28.2628i	0.210039	−	0.914085i
$957$	−4.92492	−	7.78316i	−0.159200	−	0.251594i
$958$	−19.1532	−	24.0534i	−0.618813	−	0.777131i
$959$	−9.37820	−	28.8631i	−0.302838	−	0.932040i
$960$	1.65971	−	0.450231i	0.0535669	−	0.0145312i
$961$	10.0777	−	7.32186i	0.325086	−	0.236189i
$962$	−9.69019	+	3.62871i	−0.312424	+	0.116994i
$963$	−6.80502	−	13.3556i	−0.219289	−	0.430378i
$964$	−17.4303	−	40.9456i	−0.561391	−	1.31877i
$965$	0.0902715	+	0.569952i	0.00290594	+	0.0183474i
$966$	3.71745	+	18.2237i	0.119607	+	0.586339i
$967$		−	31.5924i		−	1.01594i	−0.861374	−	0.507972i	$-0.830395\pi$
$967$		−	31.5924i		−	1.01594i	0.861374	−	0.507972i	$-0.169605\pi$
$968$	18.1832	−	25.2462i	0.584431	−	0.811443i
$969$			35.1674i			1.12974i
$970$	1.71549	−	0.349942i	0.0550809	−	0.0112359i
$971$	2.23710	+	14.1245i	0.0717919	+	0.453276i	0.997230	+	0.0743778i	$0.0236971\pi$
$971$	2.23710	+	14.1245i	0.0717919	+	0.453276i	−0.925438	+	0.378899i	$0.876303\pi$
$972$	−21.1513	−	8.52029i	−0.678428	−	0.273288i
$973$	7.19518	+	14.1213i	0.230667	+	0.452709i
$974$	7.45335	+	19.9036i	0.238821	+	0.637752i
$975$	−36.4614	+	26.4908i	−1.16770	+	0.848384i
$976$	−31.3851	−	9.52459i	−1.00461	−	0.304875i
$977$	0.195885	+	0.602873i	0.00626693	+	0.0192876i	0.954141	−	0.299357i	$-0.0967722\pi$
$977$	0.195885	+	0.602873i	0.00626693	+	0.0192876i	−0.947874	+	0.318645i	$0.896772\pi$
$978$	−5.70526	+	4.54298i	−0.182434	+	0.145268i
$979$	−22.7276	−	35.9179i	−0.726378	−	1.14794i
$980$	−0.233727	+	0.146385i	−0.00746614	+	0.00467609i
$981$	7.16693	−	14.0659i	0.228822	−	0.449089i
$982$	20.9207	−	22.8546i	0.667605	−	0.729318i
$983$	−11.8628	−	16.3278i	−0.378366	−	0.520775i	0.576785	−	0.816896i	$-0.304307\pi$
$983$	−11.8628	−	16.3278i	−0.378366	−	0.520775i	−0.955151	+	0.296120i	$0.904307\pi$
$984$	13.1579	−	17.2027i	0.419457	−	0.548404i
$985$	0.803126	+	0.260952i	0.0255897	+	0.00831461i
$986$	8.17230	−	4.62924i	0.260259	−	0.147425i
$987$	−2.77661	−	17.5308i	−0.0883805	−	0.558013i
$988$	9.54207	+	107.785i	0.303574	+	3.42909i
$989$	−19.0759	+	19.0759i	−0.606578	+	0.606578i
$990$	−0.608606	−	0.633457i	−0.0193428	−	0.0201326i
$991$	−27.5697			−0.875779			−0.437890	−	0.899029i	$-0.644274\pi$
$991$	−27.5697			−0.875779			−0.437890	+	0.899029i	$0.644274\pi$
$992$	−20.9569	+	12.4175i	−0.665382	+	0.394256i
$993$	−2.90361	−	2.10960i	−0.0921434	−	0.0669461i
$994$	−0.265991	−	0.0736180i	−0.00843672	−	0.00233502i
$995$	0.591908	+	1.16168i	0.0187647	+	0.0368279i
$996$	6.09538	−	10.1682i	0.193140	−	0.322191i
$997$	41.0242	+	6.49760i	1.29925	+	0.205781i	0.767461	−	0.641095i	$-0.221520\pi$
$997$	41.0242	+	6.49760i	1.29925	+	0.205781i	0.531790	+	0.846876i	$0.321520\pi$
$998$	−18.1501	−	16.6143i	−0.574532	−	0.525916i
$999$	−5.84957	+	1.90064i	−0.185072	+	0.0601336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.2.w.a.5.7	✓	176
4.3	odd	2		704.2.be.a.49.6		176
11.9	even	5	inner	176.2.w.a.53.21	yes	176
16.3	odd	4		704.2.be.a.401.6		176
16.13	even	4	inner	176.2.w.a.93.21	yes	176
44.31	odd	10		704.2.be.a.625.6		176
176.141	even	20	inner	176.2.w.a.141.7	yes	176
176.163	odd	20		704.2.be.a.273.6		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.w.a.5.7	✓	176	1.1	even	1	trivial
176.2.w.a.53.21	yes	176	11.9	even	5	inner
176.2.w.a.93.21	yes	176	16.13	even	4	inner
176.2.w.a.141.7	yes	176	176.141	even	20	inner
704.2.be.a.49.6		176	4.3	odd	2
704.2.be.a.273.6		176	176.163	odd	20
704.2.be.a.401.6		176	16.3	odd	4
704.2.be.a.625.6		176	44.31	odd	10

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	176.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.779948 + 1.17970i) q^{2} +(1.33374 - 0.211244i) q^{3} +(-0.783362 - 1.84020i) q^{4} +(0.141837 - 0.0722696i) q^{5} +(-0.791046 + 1.73817i) q^{6} +(1.45574 + 2.00365i) q^{7} +(2.78186 + 0.511133i) q^{8} +(-1.11893 + 0.363561i) q^{9} +(-0.0253694 + 0.223691i) q^{10} +(2.80267 - 1.77343i) q^{11} +(-1.43353 - 2.28887i) q^{12} +(5.97781 + 3.04584i) q^{13} +(-3.49909 + 0.154583i) q^{14} +(0.173908 - 0.126351i) q^{15} +(-2.77269 + 2.88309i) q^{16} +(0.997950 - 3.07138i) q^{17} +(0.443813 - 1.60355i) q^{18} +(-7.96492 + 1.26152i) q^{19} +(-0.244101 - 0.204396i) q^{20} +(2.36483 + 2.36483i) q^{21} +(-0.0938250 + 4.68948i) q^{22} -3.93241i q^{23} +(3.81826 + 0.0940686i) q^{24} +(-2.92403 + 4.02458i) q^{25} +(-8.25555 + 4.67639i) q^{26} +(-5.02512 + 2.56042i) q^{27} +(2.54675 - 4.24843i) q^{28} +(0.321711 - 2.03120i) q^{29} +(0.0134171 + 0.303705i) q^{30} +(-1.33069 - 4.09543i) q^{31} +(-1.23862 - 5.51959i) q^{32} +(3.36341 - 2.95735i) q^{33} +(2.84494 + 3.57279i) q^{34} +(0.351280 + 0.178986i) q^{35} +(1.54555 + 1.77425i) q^{36} +(1.07714 + 0.170602i) q^{37} +(4.72402 - 10.3801i) q^{38} +(8.61627 + 2.79960i) q^{39} +(0.431510 - 0.128546i) q^{40} +(3.33302 - 4.58751i) q^{41} +(-4.63423 + 0.945337i) q^{42} +(-4.85094 - 4.85094i) q^{43} +(-5.45898 - 3.76823i) q^{44} +(-0.132431 + 0.132431i) q^{45} +(4.63905 + 3.06708i) q^{46} +(-4.29363 - 3.11950i) q^{47} +(-3.08901 + 4.43101i) q^{48} +(0.267678 - 0.823828i) q^{49} +(-2.46719 - 6.58843i) q^{50} +(0.682199 - 4.30723i) q^{51} +(0.922181 - 13.3864i) q^{52} +(-3.26044 + 6.39897i) q^{53} +(0.898808 - 7.92510i) q^{54} +(0.269357 - 0.454086i) q^{55} +(3.02552 + 6.31794i) q^{56} +(-10.3567 + 3.36508i) q^{57} +(2.14528 + 1.96375i) q^{58} +(-9.97559 - 1.57998i) q^{59} +(-0.368745 - 0.221046i) q^{60} +(3.72256 + 7.30593i) q^{61} +(5.86923 + 1.62442i) q^{62} +(-2.35731 - 1.71269i) q^{63} +(7.47749 + 2.84380i) q^{64} +1.06800 q^{65} +(0.865485 + 6.27437i) q^{66} +(2.66050 - 2.66050i) q^{67} +(-6.43371 + 0.569569i) q^{68} +(-0.830699 - 5.24482i) q^{69} +(-0.485130 + 0.274804i) q^{70} +(0.0749414 + 0.0243499i) q^{71} +(-3.29852 + 0.439456i) q^{72} +(3.33103 + 4.58477i) q^{73} +(-1.04137 + 1.13764i) q^{74} +(-3.04973 + 5.98544i) q^{75} +(8.56087 + 13.6688i) q^{76} +(7.63328 + 3.03391i) q^{77} +(-10.0229 + 7.98103i) q^{78} +(1.23948 + 3.81473i) q^{79} +(-0.184910 + 0.609310i) q^{80} +(-3.30589 + 2.40187i) q^{81} +(2.81228 + 7.50996i) q^{82} +(1.99285 + 3.91118i) q^{83} +(2.49925 - 6.20430i) q^{84} +(-0.0804208 - 0.507757i) q^{85} +(9.50611 - 1.93915i) q^{86} -2.77706i q^{87} +(8.70308 - 3.50090i) q^{88} -12.8156i q^{89} +(-0.0529389 - 0.259517i) q^{90} +(2.59931 + 16.4114i) q^{91} +(-7.23644 + 3.08050i) q^{92} +(-2.63993 - 5.18115i) q^{93} +(7.02887 - 2.63212i) q^{94} +(-1.03855 + 0.754553i) q^{95} +(-2.81797 - 7.10005i) q^{96} +(-2.40325 - 7.39643i) q^{97} +(0.763091 + 0.958322i) q^{98} +(-2.49123 + 3.00328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 6 q^{2} - 6 q^{3} - 10 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{8} - 16 q^{10} - 12 q^{11} - 6 q^{13} - 12 q^{15} + 14 q^{16} - 12 q^{17} - 44 q^{18} - 6 q^{19} + 2 q^{20} - 28 q^{21} + 50 q^{22} - 38 q^{24}+ \cdots + 92 q^{99}+O(q^{100}) \) 176 * q - 6 * q^2 - 6 * q^3 - 10 * q^4 - 6 * q^5 - 6 * q^6 - 6 * q^8 - 16 * q^10 - 12 * q^11 - 6 * q^13 - 12 * q^15 + 14 * q^16 - 12 * q^17 - 44 * q^18 - 6 * q^19 + 2 * q^20 - 28 * q^21 + 50 * q^22 - 38 * q^24 - 68 * q^26 - 18 * q^27 - 46 * q^28 - 22 * q^29 + 26 * q^30 - 12 * q^31 - 16 * q^32 - 16 * q^33 + 12 * q^34 - 26 * q^35 - 22 * q^36 + 18 * q^37 - 34 * q^38 + 14 * q^40 - 10 * q^42 - 40 * q^43 + 2 * q^44 - 24 * q^45 + 38 * q^46 - 12 * q^47 - 26 * q^48 + 8 * q^49 - 62 * q^50 + 6 * q^51 + 74 * q^52 - 30 * q^53 - 52 * q^54 - 96 * q^56 - 26 * q^58 + 10 * q^59 + 118 * q^60 - 6 * q^61 - 42 * q^62 - 28 * q^63 - 106 * q^64 - 32 * q^65 + 6 * q^66 + 24 * q^67 + 116 * q^68 + 12 * q^69 + 52 * q^70 - 98 * q^72 + 96 * q^74 - 46 * q^75 + 112 * q^76 - 14 * q^77 + 44 * q^78 - 52 * q^79 - 28 * q^80 + 66 * q^82 + 54 * q^83 + 120 * q^84 + 14 * q^85 + 86 * q^86 + 142 * q^88 + 228 * q^90 - 122 * q^91 + 146 * q^92 + 6 * q^93 + 56 * q^94 + 52 * q^95 + 86 * q^96 - 12 * q^97 + 140 * q^98 + 92 * q^99

Introduction

L-functions

Modular forms

Varieties

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