LMFDB - Embedded newform 348.2.t.a.35.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.12
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18856 + 0.766379i) q^{2} +(0.725197 + 1.57292i) q^{3} +(0.825327 - 1.82177i) q^{4} +(-2.26138 - 1.80339i) q^{5} +(-2.06739 - 1.31373i) q^{6} +(-0.188704 - 0.0430704i) q^{7} +(0.415217 + 2.79778i) q^{8} +(-1.94818 + 2.28136i) q^{9} +O(q^{10})$	\(q+(-1.18856 + 0.766379i) q^{2} +(0.725197 + 1.57292i) q^{3} +(0.825327 - 1.82177i) q^{4} +(-2.26138 - 1.80339i) q^{5} +(-2.06739 - 1.31373i) q^{6} +(-0.188704 - 0.0430704i) q^{7} +(0.415217 + 2.79778i) q^{8} +(-1.94818 + 2.28136i) q^{9} +(4.06986 + 0.410356i) q^{10} +(-2.39142 - 4.96583i) q^{11} +(3.46403 - 0.0229638i) q^{12} +(-1.87573 + 0.903302i) q^{13} +(0.257293 - 0.0934270i) q^{14} +(1.19665 - 4.86480i) q^{15} +(-2.63767 - 3.00711i) q^{16} -7.51186 q^{17} +(0.567132 - 4.20456i) q^{18} +(-0.569639 - 2.49575i) q^{19} +(-5.15174 + 2.63132i) q^{20} +(-0.0691009 - 0.328051i) q^{21} +(6.64803 + 4.06943i) q^{22} +(0.845248 + 1.05991i) q^{23} +(-4.09959 + 2.68205i) q^{24} +(0.749022 + 3.28168i) q^{25} +(1.53713 - 2.51114i) q^{26} +(-5.00122 - 1.40990i) q^{27} +(-0.234207 + 0.308227i) q^{28} +(5.33452 - 0.736842i) q^{29} +(2.30599 + 6.69917i) q^{30} +(3.82574 - 4.79733i) q^{31} +(5.43960 + 1.55266i) q^{32} +(6.07662 - 7.36272i) q^{33} +(8.92826 - 5.75693i) q^{34} +(0.349059 + 0.437706i) q^{35} +(2.54822 + 5.43199i) q^{36} +(-3.33194 + 6.91884i) q^{37} +(2.58974 + 2.52978i) q^{38} +(-2.78110 - 2.29530i) q^{39} +(4.10654 - 7.07566i) q^{40} +1.63085 q^{41} +(0.333542 + 0.336949i) q^{42} +(-4.34091 - 5.44332i) q^{43} +(-11.0203 + 0.258173i) q^{44} +(8.51976 - 1.64570i) q^{45} +(-1.81691 - 0.611978i) q^{46} +(3.88922 + 8.07606i) q^{47} +(2.81712 - 6.32960i) q^{48} +(-6.27303 - 3.02093i) q^{49} +(-3.40527 - 3.32642i) q^{50} +(-5.44758 - 11.8156i) q^{51} +(0.0975189 + 4.16266i) q^{52} +(-3.72859 - 2.97345i) q^{53} +(7.02474 - 2.15708i) q^{54} +(-3.54743 + 15.5423i) q^{55} +(0.0421486 - 0.545836i) q^{56} +(3.51253 - 2.70591i) q^{57} +(-5.77567 + 4.96404i) q^{58} +8.45247 q^{59} +(-7.87490 - 6.19507i) q^{60} +(-4.15912 - 0.949292i) q^{61} +(-0.870534 + 8.63385i) q^{62} +(0.465888 - 0.346592i) q^{63} +(-7.65519 + 2.32338i) q^{64} +(5.87074 + 1.33996i) q^{65} +(-1.57977 + 13.4080i) q^{66} +(-0.507966 + 1.05480i) q^{67} +(-6.19974 + 13.6849i) q^{68} +(-1.05418 + 2.09815i) q^{69} +(-0.750324 - 0.252726i) q^{70} +(-0.0620979 + 0.0299048i) q^{71} +(-7.19167 - 4.50332i) q^{72} +(-3.58145 + 2.85611i) q^{73} +(-1.34226 - 10.7770i) q^{74} +(-4.61865 + 3.55802i) q^{75} +(-5.01682 - 1.02206i) q^{76} +(0.237389 + 1.04007i) q^{77} +(5.06456 + 0.596720i) q^{78} +(-2.21794 - 1.06810i) q^{79} +(0.541790 + 11.5570i) q^{80} +(-1.40920 - 8.88899i) q^{81} +(-1.93835 + 1.24985i) q^{82} +(-1.33167 - 5.83443i) q^{83} +(-0.654664 - 0.144864i) q^{84} +(16.9872 + 13.5468i) q^{85} +(9.33105 + 3.14291i) q^{86} +(5.02757 + 7.85643i) q^{87} +(12.9003 - 8.75256i) q^{88} +(-10.3727 + 13.0069i) q^{89} +(-8.86498 + 8.48537i) q^{90} +(0.392862 - 0.0896682i) q^{91} +(2.62851 - 0.665075i) q^{92} +(10.3202 + 2.53859i) q^{93} +(-10.8119 - 6.61822i) q^{94} +(-3.21265 + 6.67113i) q^{95} +(1.50257 + 9.68206i) q^{96} +(-2.07275 + 0.473091i) q^{97} +(9.77102 - 1.21697i) q^{98} +(15.9877 + 4.21864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.18856	+	0.766379i	−0.840435	+	0.541912i
$2$	−1.18856	+	0.766379i	−0.840435	+	0.541912i
$3$	0.725197	+	1.57292i	0.418693	+	0.908128i
$3$	0.725197	+	1.57292i	0.418693	+	0.908128i
$4$	0.825327	−	1.82177i	0.412663	−	0.910884i
$5$	−2.26138	−	1.80339i	−1.01132	−	0.806502i	−0.0301310	−	0.999546i	$-0.509592\pi$
$5$	−2.26138	−	1.80339i	−1.01132	−	0.806502i	−0.981190	+	0.193044i	$0.938164\pi$
$6$	−2.06739	−	1.31373i	−0.844009	−	0.536328i
$7$	−0.188704	−	0.0430704i	−0.0713233	−	0.0162791i	0.186710	−	0.982415i	$-0.440217\pi$
$7$	−0.188704	−	0.0430704i	−0.0713233	−	0.0162791i	−0.258034	+	0.966136i	$0.583075\pi$
$8$	0.415217	+	2.79778i	0.146801	+	0.989166i
$9$	−1.94818	+	2.28136i	−0.649393	+	0.760453i
$10$	4.06986	+	0.410356i	1.28700	+	0.129766i
$11$	−2.39142	−	4.96583i	−0.721039	−	1.49725i	−0.861821	−	0.507212i	$-0.830676\pi$
$11$	−2.39142	−	4.96583i	−0.721039	−	1.49725i	0.140782	−	0.990041i	$-0.455038\pi$
$12$	3.46403	−	0.0229638i	0.999978	−	0.00662909i
$13$	−1.87573	+	0.903302i	−0.520233	+	0.250531i	−0.675524	−	0.737338i	$-0.736083\pi$
$13$	−1.87573	+	0.903302i	−0.520233	+	0.250531i	0.155291	+	0.987869i	$0.450368\pi$
$14$	0.257293	−	0.0934270i	0.0687645	−	0.0249694i
$15$	1.19665	−	4.86480i	0.308974	−	1.25609i
$16$	−2.63767	−	3.00711i	−0.659418	−	0.751777i
$17$	−7.51186			−1.82189			−0.910947	−	0.412523i	$-0.864647\pi$
$17$	−7.51186			−1.82189			−0.910947	+	0.412523i	$0.864647\pi$
$18$	0.567132	−	4.20456i	0.133674	−	0.991025i
$19$	−0.569639	−	2.49575i	−0.130684	−	0.572565i	−0.997290	−	0.0735713i	$-0.976560\pi$
$19$	−0.569639	−	2.49575i	−0.130684	−	0.572565i	0.866606	−	0.498993i	$-0.166297\pi$
$20$	−5.15174	+	2.63132i	−1.15196	+	0.588382i
$21$	−0.0691009	−	0.328051i	−0.0150791	−	0.0715866i
$22$	6.64803	+	4.06943i	1.41737	+	0.867605i
$23$	0.845248	+	1.05991i	0.176246	+	0.221006i	0.862106	−	0.506728i	$-0.169145\pi$
$23$	0.845248	+	1.05991i	0.176246	+	0.221006i	−0.685860	+	0.727734i	$0.740574\pi$
$24$	−4.09959	+	2.68205i	−0.836825	+	0.547471i
$25$	0.749022	+	3.28168i	0.149804	+	0.656336i
$26$	1.53713	−	2.51114i	0.301456	−	0.492475i
$27$	−5.00122	−	1.40990i	−0.962485	−	0.271336i
$28$	−0.234207	+	0.308227i	−0.0442609	+	0.0582495i
$29$	5.33452	−	0.736842i	0.990595	−	0.136828i
$29$	5.33452	−	0.736842i	0.990595	−	0.136828i
$30$	2.30599	+	6.69917i	0.421015	+	1.22310i
$31$	3.82574	−	4.79733i	0.687123	−	0.861625i	−0.308865	−	0.951106i	$-0.599949\pi$
$31$	3.82574	−	4.79733i	0.687123	−	0.861625i	0.995989	+	0.0894806i	$0.0285207\pi$
$32$	5.43960	+	1.55266i	0.961595	+	0.274474i
$33$	6.07662	−	7.36272i	1.05780	−	1.28168i
$34$	8.92826	−	5.75693i	1.53118	−	0.987306i
$35$	0.349059	+	0.437706i	0.0590017	+	0.0739857i
$36$	2.54822	+	5.43199i	0.424704	+	0.905332i
$37$	−3.33194	+	6.91884i	−0.547768	+	1.13745i	0.424898	+	0.905241i	$0.360310\pi$
$37$	−3.33194	+	6.91884i	−0.547768	+	1.13745i	−0.972666	+	0.232210i	$0.925404\pi$
$38$	2.58974	+	2.52978i	0.420111	+	0.410384i
$39$	−2.78110	−	2.29530i	−0.445332	−	0.367542i
$40$	4.10654	−	7.07566i	0.649301	−	1.11876i
$41$	1.63085			0.254696			0.127348	−	0.991858i	$-0.459354\pi$
$41$	1.63085			0.254696			0.127348	+	0.991858i	$0.459354\pi$
$42$	0.333542	+	0.336949i	0.0514666	+	0.0519924i
$43$	−4.34091	−	5.44332i	−0.661982	−	0.830099i	0.331575	−	0.943429i	$-0.392420\pi$
$43$	−4.34091	−	5.44332i	−0.661982	−	0.830099i	−0.993557	+	0.113330i	$0.963848\pi$
$44$	−11.0203	+	0.258173i	−1.66137	+	0.0389211i
$45$	8.51976	−	1.64570i	1.27005	−	0.245326i
$46$	−1.81691	−	0.611978i	−0.267889	−	0.0902313i
$47$	3.88922	+	8.07606i	0.567302	+	1.17801i	0.965425	+	0.260682i	$0.0839474\pi$
$47$	3.88922	+	8.07606i	0.567302	+	1.17801i	−0.398123	+	0.917332i	$0.630338\pi$
$48$	2.81712	−	6.32960i	0.406616	−	0.913599i
$49$	−6.27303	−	3.02093i	−0.896147	−	0.431562i
$50$	−3.40527	−	3.32642i	−0.481577	−	0.470427i
$51$	−5.44758	−	11.8156i	−0.762814	−	1.65451i
$52$	0.0975189	+	4.16266i	0.0135234	+	0.577256i
$53$	−3.72859	−	2.97345i	−0.512161	−	0.408435i	0.333016	−	0.942921i	$-0.391934\pi$
$53$	−3.72859	−	2.97345i	−0.512161	−	0.408435i	−0.845177	+	0.534486i	$0.820505\pi$
$54$	7.02474	−	2.15708i	0.955946	−	0.293542i
$55$	−3.54743	+	15.5423i	−0.478335	+	2.09572i
$56$	0.0421486	−	0.545836i	0.00563234	−	0.0729404i
$57$	3.51253	−	2.70591i	0.465246	−	0.358407i
$58$	−5.77567	+	4.96404i	−0.758382	+	0.651810i
$59$	8.45247			1.10042			0.550209	−	0.835027i	$-0.314548\pi$
$59$	8.45247			1.10042			0.550209	+	0.835027i	$0.314548\pi$
$60$	−7.87490	−	6.19507i	−1.01665	−	0.799780i
$61$	−4.15912	−	0.949292i	−0.532521	−	0.121544i	−0.0521990	−	0.998637i	$-0.516623\pi$
$61$	−4.15912	−	0.949292i	−0.532521	−	0.121544i	−0.480322	+	0.877092i	$0.659480\pi$
$62$	−0.870534	+	8.63385i	−0.110558	+	1.09650i
$63$	0.465888	−	0.346592i	0.0586963	−	0.0436665i
$64$	−7.65519	+	2.32338i	−0.956899	+	0.290422i
$65$	5.87074	+	1.33996i	0.728176	+	0.166201i
$66$	−1.57977	+	13.4080i	−0.194456	+	1.65041i
$67$	−0.507966	+	1.05480i	−0.0620579	+	0.128865i	−0.929691	−	0.368341i	$-0.879926\pi$
$67$	−0.507966	+	1.05480i	−0.0620579	+	0.128865i	0.867633	+	0.497205i	$0.165640\pi$
$68$	−6.19974	+	13.6849i	−0.751829	+	1.65953i
$69$	−1.05418	+	2.09815i	−0.126909	+	0.252588i
$70$	−0.750324	−	0.252726i	−0.0896808	−	0.0302066i
$71$	−0.0620979	+	0.0299048i	−0.00736967	+	0.00354904i	−0.437565	−	0.899187i	$-0.644159\pi$
$71$	−0.0620979	+	0.0299048i	−0.00736967	+	0.00354904i	0.430195	+	0.902736i	$0.358445\pi$
$72$	−7.19167	−	4.50332i	−0.847546	−	0.530722i
$73$	−3.58145	+	2.85611i	−0.419177	+	0.334282i	−0.810257	−	0.586074i	$-0.800673\pi$
$73$	−3.58145	+	2.85611i	−0.419177	+	0.334282i	0.391081	+	0.920356i	$0.372101\pi$
$74$	−1.34226	−	10.7770i	−0.156035	−	1.25280i
$75$	−4.61865	+	3.55802i	−0.533315	+	0.410845i
$76$	−5.01682	−	1.02206i	−0.575468	−	0.117238i
$77$	0.237389	+	1.04007i	0.0270530	+	0.118527i
$78$	5.06456	+	0.596720i	0.573448	+	0.0675652i
$79$	−2.21794	−	1.06810i	−0.249538	−	0.120171i	0.304934	−	0.952373i	$-0.401366\pi$
$79$	−2.21794	−	1.06810i	−0.249538	−	0.120171i	−0.554472	+	0.832202i	$0.687080\pi$
$80$	0.541790	+	11.5570i	0.0605740	+	1.29211i
$81$	−1.40920	−	8.88899i	−0.156578	−	0.987666i
$82$	−1.93835	+	1.24985i	−0.214055	+	0.138023i
$83$	−1.33167	−	5.83443i	−0.146170	−	0.640411i	−0.993928	−	0.110029i	$-0.964906\pi$
$83$	−1.33167	−	5.83443i	−0.146170	−	0.640411i	0.847759	−	0.530382i	$-0.177952\pi$
$84$	−0.654664	−	0.144864i	−0.0714297	−	0.0158059i
$85$	16.9872	+	13.5468i	1.84252	+	1.46936i
$86$	9.33105	+	3.14291i	1.00619	+	0.338909i
$87$	5.02757	+	7.85643i	0.539012	+	0.842298i
$88$	12.9003	−	8.75256i	1.37518	−	0.933026i
$89$	−10.3727	+	13.0069i	−1.09950	+	1.37873i	−0.180921	+	0.983498i	$0.557908\pi$
$89$	−10.3727	+	13.0069i	−1.09950	+	1.37873i	−0.918580	+	0.395234i	$0.870664\pi$
$90$	−8.86498	+	8.48537i	−0.934451	+	0.894436i
$91$	0.392862	−	0.0896682i	0.0411831	−	0.00939978i
$92$	2.62851	−	0.665075i	0.274041	−	0.0693388i
$93$	10.3202	+	2.53859i	1.07016	+	0.263240i
$94$	−10.8119	−	6.61822i	−1.11516	−	0.682617i
$95$	−3.21265	+	6.67113i	−0.329611	+	0.684444i
$96$	1.50257	+	9.68206i	0.153356	+	0.988171i
$97$	−2.07275	+	0.473091i	−0.210455	+	0.0480351i	−0.326449	−	0.945215i	$-0.605852\pi$
$97$	−2.07275	+	0.473091i	−0.210455	+	0.0480351i	0.115993	+	0.993250i	$0.462995\pi$
$98$	9.77102	−	1.21697i	0.987022	−	0.122933i
$99$	15.9877	+	4.21864i	1.60683	+	0.423989i
$100$	6.59665	+	1.34392i	0.659665	+	0.134392i
$101$	3.86123	+	4.84183i	0.384207	+	0.481780i	0.935899	−	0.352268i	$-0.114589\pi$
$101$	3.86123	+	4.84183i	0.384207	+	0.481780i	−0.551693	+	0.834047i	$0.686018\pi$
$102$	15.5300	+	9.86857i	1.53770	+	0.977134i
$103$	6.31542	+	13.1141i	0.622277	+	1.29217i	0.939086	+	0.343682i	$0.111674\pi$
$103$	6.31542	+	13.1141i	0.622277	+	1.29217i	−0.316809	+	0.948489i	$0.602612\pi$
$104$	−3.30608	−	4.87281i	−0.324188	−	0.477818i
$105$	−0.435341	+	0.866465i	−0.0424850	+	0.0845584i
$106$	6.71042	+	0.676598i	0.651774	+	0.0657170i
$107$	−5.28071	−	2.54306i	−0.510506	−	0.245847i	0.160854	−	0.986978i	$-0.448575\pi$
$107$	−5.28071	−	2.54306i	−0.510506	−	0.245847i	−0.671360	+	0.741132i	$0.734289\pi$
$108$	−6.69615	+	7.94742i	−0.644337	+	0.764741i
$109$	2.95265	−	12.9364i	0.282812	−	1.23908i	−0.611357	−	0.791355i	$-0.709376\pi$
$109$	2.95265	−	12.9364i	0.282812	−	1.23908i	0.894170	−	0.447728i	$-0.147767\pi$
$110$	−7.69497	−	21.1915i	−0.733687	−	2.02053i
$111$	−13.2991	−	0.223362i	−1.26230	−	0.0212006i
$112$	0.368221	+	0.681058i	0.0347936	+	0.0643539i
$113$	1.64844	−	7.22231i	0.155073	−	0.679418i	−0.836292	−	0.548284i	$-0.815281\pi$
$113$	1.64844	−	7.22231i	0.155073	−	0.679418i	0.991365	−	0.131133i	$-0.0418616\pi$
$114$	−2.10108	+	5.90805i	−0.196784	+	0.553340i
$115$		−	3.92117i		−	0.365651i
$116$	3.06037	−	10.3264i	0.284148	−	0.958780i
$117$	1.59349	−	6.03900i	0.147318	−	0.558306i
$118$	−10.0462	+	6.47780i	−0.924831	+	0.596330i
$119$	1.41752	+	0.323539i	0.129944	+	0.0296588i
$120$	14.1075	+	1.32802i	1.28783	+	0.121231i
$121$	−12.0822	+	15.1506i	−1.09838	+	1.37732i
$122$	5.67086	−	2.05918i	0.513416	−	0.186429i
$123$	1.18269	+	2.56520i	0.106639	+	0.231296i
$124$	−5.58212	−	10.9290i	−0.501290	−	0.981450i
$125$	−2.05053	+	4.25797i	−0.183405	+	0.380844i
$126$	−0.288112	+	0.768990i	−0.0256671	+	0.0685071i
$127$	−6.79080	+	3.27028i	−0.602586	+	0.290190i	−0.710197	−	0.704003i	$-0.751394\pi$
$127$	−6.79080	+	3.27028i	−0.602586	+	0.290190i	0.107611	+	0.994193i	$0.465680\pi$
$128$	7.31803	−	8.62824i	0.646828	−	0.762636i
$129$	5.41392	−	10.7754i	0.476669	−	0.948721i
$130$	−8.00462	+	2.90660i	−0.702051	+	0.254925i
$131$	−16.0182	+	12.7741i	−1.39952	+	1.11608i	−0.421670	+	0.906750i	$0.638556\pi$
$131$	−16.0182	+	12.7741i	−1.39952	+	1.11608i	−0.977846	+	0.209327i	$0.932873\pi$
$132$	−8.39796	−	17.1468i	−0.730948	−	1.49244i
$133$			0.495492i			0.0429646i
$134$	−0.204632	−	1.64298i	−0.0176775	−	0.141932i
$135$	8.76706	+	12.2075i	0.754548	+	1.05065i
$136$	−3.11905	−	21.0166i	−0.267457	−	1.80216i
$137$	−8.73610	−	4.20709i	−0.746376	−	0.359436i	0.0217256	−	0.999764i	$-0.493084\pi$
$137$	−8.73610	−	4.20709i	−0.746376	−	0.359436i	−0.768101	+	0.640328i	$0.778798\pi$
$138$	−0.355026	−	3.30167i	−0.0302218	−	0.281057i
$139$	10.9954	−	8.76853i	0.932617	−	0.743737i	−0.0341448	−	0.999417i	$-0.510871\pi$
$139$	10.9954	−	8.76853i	0.932617	−	0.743737i	0.966761	+	0.255680i	$0.0822993\pi$
$140$	1.08549	−	0.274653i	0.0917402	−	0.0232124i
$141$	−9.88257	+	11.9742i	−0.832262	+	1.00841i
$142$	0.0508884	−	0.0831340i	0.00427046	−	0.00697645i
$143$	8.97128	+	7.15436i	0.750216	+	0.598277i
$144$	11.9989	−	0.159095i	0.999912	−	0.0132579i
$145$	−13.3922	−	7.95395i	−1.11216	−	0.660539i
$146$	2.06789	−	6.13939i	0.171139	−	0.508099i
$147$	0.202513	−	12.0578i	0.0167030	−	0.994508i
$148$	9.85458	+	11.7803i	0.810042	+	0.968337i
$149$	4.17225	−	0.952289i	0.341804	−	0.0780146i	−0.0481732	−	0.998839i	$-0.515340\pi$
$149$	4.17225	−	0.952289i	0.341804	−	0.0780146i	0.389977	+	0.920824i	$0.372483\pi$
$150$	2.76272	−	7.76854i	0.225575	−	0.634298i
$151$	5.66388	−	4.51680i	0.460920	−	0.367572i	−0.365327	−	0.930879i	$-0.619043\pi$
$151$	5.66388	−	4.51680i	0.460920	−	0.367572i	0.826247	+	0.563308i	$0.190471\pi$
$152$	6.74605	−	2.63001i	0.547177	−	0.213322i
$153$	14.6344	−	17.1373i	1.18312	−	1.38546i
$154$	−1.07924	−	1.05425i	−0.0869674	−	0.0849538i
$155$	−17.3029	+	3.94928i	−1.38980	+	0.317214i
$156$	−6.47682	+	3.17213i	−0.518561	+	0.253974i
$157$		−	19.0238i		−	1.51826i	−0.650938	−	0.759131i	$-0.725624\pi$
$157$		−	19.0238i		−	1.51826i	0.650938	−	0.759131i	$-0.274376\pi$
$158$	3.45472	−	0.430283i	0.274843	−	0.0342314i
$159$	1.97305	−	8.02112i	0.156473	−	0.636116i
$160$	−9.50097	−	13.3209i	−0.751118	−	1.05311i
$161$	−0.113851	−	0.236414i	−0.00897270	−	0.0186320i
$162$	8.48725	+	9.48507i	0.666821	+	0.745218i
$163$	17.4483	−	8.40267i	1.36666	−	0.658148i	0.400547	−	0.916276i	$-0.368820\pi$
$163$	17.4483	−	8.40267i	1.36666	−	0.658148i	0.966111	+	0.258128i	$0.0831057\pi$
$164$	1.34598	−	2.97103i	0.105104	−	0.231998i
$165$	−27.0194	+	5.69139i	−2.10346	+	0.443074i
$166$	6.05414	+	5.91397i	0.469893	+	0.459013i
$167$	3.36261	−	14.7325i	0.260206	−	1.14004i	−0.660822	−	0.750543i	$-0.729792\pi$
$167$	3.36261	−	14.7325i	0.260206	−	1.14004i	0.921028	−	0.389496i	$-0.127351\pi$
$168$	0.889124	−	0.329542i	0.0685974	−	0.0254247i
$169$	−5.40297	+	6.77512i	−0.415613	+	0.521163i
$170$	−30.5722	−	3.08253i	−2.34478	−	0.236420i
$171$	6.80346	+	3.56262i	0.520274	+	0.272440i
$172$	−13.4991	+	3.41560i	−1.02930	+	0.260437i
$173$		−	2.16043i		−	0.164254i	−0.996622	−	0.0821272i	$-0.973829\pi$
$173$		−	2.16043i		−	0.164254i	0.996622	−	0.0821272i	$-0.0261714\pi$
$174$	−11.9965	−	5.48478i	−0.909456	−	0.415800i
$175$		−	0.651526i		−	0.0492508i
$176$	−8.62500	+	20.2895i	−0.650134	+	1.52938i
$177$	6.12971	+	13.2951i	0.460737	+	0.999321i
$178$	2.36027	−	23.4089i	0.176909	−	1.75457i
$179$	11.7506	−	14.7347i	0.878278	−	1.10133i	−0.115867	−	0.993265i	$-0.536965\pi$
$179$	11.7506	−	14.7347i	0.878278	−	1.10133i	0.994144	−	0.108061i	$-0.0344641\pi$
$180$	4.03352	−	16.8793i	0.300640	−	1.25811i
$181$	−0.363424	+	1.59227i	−0.0270131	+	0.118352i	−0.986637	−	0.162935i	$-0.947904\pi$
$181$	−0.363424	+	1.59227i	−0.0270131	+	0.118352i	0.959624	+	0.281287i	$0.0907612\pi$
$182$	−0.398218	+	0.407657i	−0.0295179	+	0.0302175i
$183$	−1.52302	−	7.23040i	−0.112585	−	0.534487i
$184$	−2.61443	+	2.80491i	−0.192738	+	0.206781i
$185$	20.0122	−	9.63736i	1.47132	−	0.708553i
$186$	−14.2117	+	4.89196i	−1.04205	+	0.358696i
$187$	17.9640	+	37.3026i	1.31366	+	2.72784i
$188$	17.9226	−	0.419874i	1.30714	−	0.0306224i
$189$	0.883023	+	0.481458i	0.0642305	+	0.0350209i
$190$	−1.29421	−	10.3911i	−0.0938915	−	0.753851i
$191$			3.85967i			0.279276i	0.990203	+	0.139638i	$0.0445939\pi$
$191$			3.85967i			0.279276i	−0.990203	+	0.139638i	$0.955406\pi$
$192$	−9.20601	−	10.3561i	−0.664387	−	0.747389i
$193$	5.23935	−	1.19585i	0.377137	−	0.0860791i	−0.0297504	−	0.999557i	$-0.509471\pi$
$193$	5.23935	−	1.19585i	0.377137	−	0.0860791i	0.406887	+	0.913478i	$0.366614\pi$
$194$	2.10101	−	2.15080i	0.150843	−	0.154419i
$195$	2.14979	+	10.2060i	0.153950	+	0.730864i
$196$	−10.6807	+	8.93474i	−0.762909	+	0.638196i
$197$	16.9363	−	13.5063i	1.20666	−	0.962283i	0.206794	−	0.978384i	$-0.433697\pi$
$197$	16.9363	−	13.5063i	1.20666	−	0.962283i	0.999870	+	0.0161018i	$0.00512557\pi$
$198$	−22.2354	+	7.23858i	−1.58020	+	0.514423i
$199$	−16.0810	+	3.67039i	−1.13995	+	0.260187i	−0.750508	−	0.660862i	$-0.770191\pi$
$199$	−16.0810	+	3.67039i	−1.13995	+	0.260187i	−0.389447	+	0.921049i	$0.627334\pi$
$200$	−8.87043	+	3.45821i	−0.627234	+	0.244533i
$201$	−2.02750	−	0.0340523i	−0.143009	−	0.00240187i
$202$	−8.29996	−	2.79562i	−0.583983	−	0.196699i
$203$	−1.03838	−	0.0907149i	−0.0728799	−	0.00636694i
$204$	−26.0213	+	0.172501i	−1.82185	+	0.0120775i
$205$	−3.68797	−	2.94106i	−0.257579	−	0.205413i
$206$	−17.5566	−	10.7468i	−1.22323	−	0.748767i
$207$	−4.06472	−	0.136575i	−0.282518	−	0.00949259i
$208$	7.66387	+	3.25789i	0.531394	+	0.225894i
$209$	−11.0312	+	8.79711i	−0.763046	+	0.608509i
$210$	−0.146614	−	1.36348i	−0.0101173	−	0.0940889i
$211$	4.06013	+	1.95526i	0.279511	+	0.134605i	0.568387	−	0.822761i	$-0.307567\pi$
$211$	4.06013	+	1.95526i	0.279511	+	0.134605i	−0.288877	+	0.957366i	$0.593282\pi$
$212$	−8.49424	+	4.33855i	−0.583387	+	0.297973i
$213$	−0.0920712	−	0.0759884i	−0.00630861	−	0.00520664i
$214$	8.22536	−	1.02446i	0.562274	−	0.0700308i
$215$			20.1378i			1.37339i
$216$	1.86801	−	14.5777i	0.127102	−	0.991890i
$217$	−0.928554	+	0.740497i	−0.0630344	+	0.0502682i
$218$	6.40480	+	17.6385i	0.433788	+	1.19463i
$219$	−7.08970	−	3.56210i	−0.479077	−	0.240705i
$220$	25.3866	+	19.2901i	1.71157	+	1.30054i
$221$	14.0902	−	6.78548i	0.947809	−	0.456441i
$222$	15.9779	−	9.92669i	1.07237	−	0.666236i
$223$	−2.68618	+	5.57790i	−0.179880	+	0.373524i	−0.971339	−	0.237698i	$-0.923607\pi$
$223$	−2.68618	+	5.57790i	−0.179880	+	0.373524i	0.791460	+	0.611222i	$0.209322\pi$
$224$	−0.959600	−	0.527278i	−0.0641159	−	0.0352302i
$225$	−8.94592	−	4.68451i	−0.596395	−	0.312301i
$226$	3.57576	+	9.84745i	0.237856	+	0.655042i
$227$	16.3970	−	20.5612i	1.08831	−	1.36470i	0.162497	−	0.986709i	$-0.448045\pi$
$227$	16.3970	−	20.5612i	1.08831	−	1.36470i	0.925811	−	0.377986i	$-0.123383\pi$
$228$	−2.03056	−	8.63227i	−0.134477	−	0.571686i
$229$	19.6235	+	4.47895i	1.29676	+	0.295977i	0.814558	−	0.580083i	$-0.196980\pi$
$229$	19.6235	+	4.47895i	1.29676	+	0.295977i	0.482203	+	0.876060i	$0.339837\pi$
$230$	3.00510	+	4.66053i	0.198151	+	0.307306i
$231$	−1.46380	+	1.12765i	−0.0963107	+	0.0741939i
$232$	4.27651	+	14.6189i	0.280767	+	0.959776i
$233$			2.95736i			0.193743i	0.995297	+	0.0968715i	$0.0308836\pi$
$233$			2.95736i			0.193743i	−0.995297	+	0.0968715i	$0.969116\pi$
$234$	2.73421	+	8.39890i	0.178741	+	0.549053i
$235$	5.76928	−	25.2768i	0.376346	−	1.64888i
$236$	6.97605	−	15.3984i	0.454102	−	1.00235i
$237$	0.0716022	−	4.26324i	0.00465106	−	0.276927i
$238$	−1.93275	+	0.701811i	−0.125282	+	0.0454916i
$239$	4.28374	−	18.7683i	0.277092	−	1.21402i	−0.624358	−	0.781138i	$-0.714639\pi$
$239$	4.28374	−	18.7683i	0.277092	−	1.21402i	0.901450	−	0.432882i	$-0.142503\pi$
$240$	−17.7853	+	9.23328i	−1.14804	+	0.596006i
$241$	3.42220	+	1.64804i	0.220443	+	0.106160i	0.540846	−	0.841121i	$-0.318104\pi$
$241$	3.42220	+	1.64804i	0.220443	+	0.106160i	−0.320403	+	0.947281i	$0.603818\pi$
$242$	2.74925	−	27.2668i	0.176729	−	1.75278i
$243$	12.9598	−	8.66283i	0.831369	−	0.555721i
$244$	−5.16202	+	6.79347i	−0.330465	+	0.434908i
$245$	8.73779	+	18.1442i	0.558237	+	1.15919i
$246$	−3.37160	−	2.14250i	−0.214966	−	0.136601i
$247$	3.32290	+	4.16679i	0.211431	+	0.265126i
$248$	15.0104	+	8.71166i	0.953161	+	0.553191i
$249$	8.21138	−	6.32572i	0.520375	−	0.400876i
$250$	−0.826050	−	6.63231i	−0.0522440	−	0.419464i
$251$	−25.0568	+	5.71904i	−1.58157	+	0.360983i	−0.920932	−	0.389722i	$-0.872571\pi$
$251$	−25.0568	+	5.71904i	−1.58157	+	0.360983i	−0.660637	+	0.750705i	$0.729714\pi$
$252$	−0.246901	−	1.13479i	−0.0155533	−	0.0714851i
$253$	3.24198	−	6.73203i	0.203821	−	0.423239i
$254$	5.56497	−	9.09123i	0.349177	−	0.570435i
$255$	−8.98908	+	36.5437i	−0.562918	+	2.28845i
$256$	−2.08538	+	15.8635i	−0.130336	+	0.991470i
$257$	−10.4950	+	2.39541i	−0.654658	+	0.149421i	−0.536933	−	0.843625i	$-0.680417\pi$
$257$	−10.4950	+	2.39541i	−0.654658	+	0.149421i	−0.117725	+	0.993046i	$0.537560\pi$
$258$	1.82329	+	16.9563i	0.113513	+	1.05565i
$259$	0.926747	−	1.16210i	0.0575853	−	0.0722096i
$260$	7.28637	−	9.58922i	0.451882	−	0.594698i
$261$	−8.71159	+	13.6054i	−0.539234	+	0.842156i
$262$	9.24872	−	27.4587i	0.571388	−	1.69640i
$263$	−3.26282	−	2.60201i	−0.201194	−	0.160447i	0.517710	−	0.855556i	$-0.326785\pi$
$263$	−3.26282	−	2.60201i	−0.201194	−	0.160447i	−0.718904	+	0.695109i	$0.755356\pi$
$264$	23.1224	+	13.9439i	1.42309	+	0.858190i
$265$	3.06947	+	13.4482i	0.188556	+	0.826117i
$266$	−0.379735	−	0.588920i	−0.0232830	−	0.0361090i
$267$	−27.9811	−	6.88285i	−1.71242	−	0.421223i
$268$	1.50237	+	1.79595i	0.0917716	+	0.109705i
$269$	−12.0916	−	5.82300i	−0.737236	−	0.355034i	0.0272893	−	0.999628i	$-0.491312\pi$
$269$	−12.0916	−	5.82300i	−0.737236	−	0.355034i	−0.764526	+	0.644593i	$0.777027\pi$
$270$	−19.7757	−	7.79038i	−1.20351	−	0.474107i
$271$	−3.70693	−	16.2411i	−0.225180	−	0.986578i	−0.953512	−	0.301354i	$-0.902561\pi$
$271$	−3.70693	−	16.2411i	−0.225180	−	0.986578i	0.728332	−	0.685224i	$-0.240296\pi$
$272$	19.8138	+	22.5890i	1.20139	+	1.36966i
$273$	0.425944	+	0.552915i	0.0257793	+	0.0334639i
$274$	13.6076	−	1.69481i	0.822063	−	0.102387i
$275$	14.5050	−	11.5674i	0.874686	−	0.697539i
$276$	2.95230	+	3.65214i	0.177708	+	0.219833i
$277$	−18.3723	+	8.84763i	−1.10388	+	0.531602i	−0.894878	−	0.446312i	$-0.852737\pi$
$277$	−18.3723	+	8.84763i	−1.10388	+	0.531602i	−0.209006	+	0.977914i	$0.567023\pi$
$278$	−6.34861	+	18.8485i	−0.380764	+	1.13046i
$279$	3.49120	+	18.0739i	0.209013	+	1.08206i
$280$	−1.07967	+	1.15833i	−0.0645226	+	0.0692237i
$281$	−1.12585	+	2.33785i	−0.0671624	+	0.139464i	−0.931847	−	0.362850i	$-0.881804\pi$
$281$	−1.12585	+	2.33785i	−0.0671624	+	0.139464i	0.864685	+	0.502314i	$0.167518\pi$
$282$	2.56922	−	21.8058i	0.152995	−	1.29851i
$283$	0.627232	+	0.143162i	0.0372851	+	0.00851007i	0.241123	−	0.970495i	$-0.422484\pi$
$283$	0.627232	+	0.143162i	0.0372851	+	0.00851007i	−0.203838	+	0.979005i	$0.565341\pi$
$284$	0.00322847	+	0.137809i	0.000191574	+	0.00817747i
$285$	−12.8230	−	0.215365i	−0.759568	−	0.0127571i
$286$	−16.1458	−	1.62795i	−0.954722	−	0.0962626i
$287$	−0.307747	−	0.0702413i	−0.0181657	−	0.00414621i
$288$	−14.1395	+	9.38483i	−0.833177	+	0.553006i
$289$	39.4281			2.31930
$290$	22.0131	−	0.809795i	1.29265	−	0.0475528i
$291$	−2.24728	−	2.91719i	−0.131738	−	0.171009i
$292$	2.24730	+	8.88179i	0.131513	+	0.519767i
$293$	3.02980	−	13.2744i	0.177003	−	0.775500i	−0.806001	−	0.591914i	$-0.798372\pi$
$293$	3.02980	−	13.2744i	0.177003	−	0.775500i	0.983004	−	0.183586i	$-0.0587705\pi$
$294$	9.00012	+	14.4865i	0.524898	+	0.844871i
$295$	−19.1143	−	15.2431i	−1.11288	−	0.887489i
$296$	−20.7409	−	6.44922i	−1.20554	−	0.374853i
$297$	4.95866	+	28.2068i	0.287731	+	1.63673i
$298$	−4.22914	+	4.32937i	−0.244987	+	0.250794i
$299$	−2.54287	−	1.22458i	−0.147058	−	0.0708194i
$300$	2.66999	+	11.3506i	0.154152	+	0.655329i
$301$	0.584699	+	1.21414i	0.0337015	+	0.0699819i
$302$	−3.27026	+	9.70914i	−0.188182	+	0.558698i
$303$	−4.81567	+	9.58470i	−0.276653	+	0.550627i
$304$	−6.00247	+	8.29594i	−0.344265	+	0.475805i
$305$	7.69342	+	9.64724i	0.440524	+	0.552399i
$306$	−4.26022	+	31.5841i	−0.243540	+	1.80554i
$307$	−13.0516			−0.744893			−0.372447	−	0.928054i	$-0.621481\pi$
$307$	−13.0516			−0.744893			−0.372447	+	0.928054i	$0.621481\pi$
$308$	2.09069	+	0.425929i	0.119128	+	0.0242696i
$309$	−16.0476	+	19.4440i	−0.912914	+	1.10613i
$310$	17.5388	−	17.9545i	0.996139	−	1.01975i
$311$	1.65153	−	3.42944i	0.0936498	−	0.194466i	−0.848882	−	0.528583i	$-0.822724\pi$
$311$	1.65153	−	3.42944i	0.0936498	−	0.194466i	0.942532	+	0.334117i	$0.108438\pi$
$312$	5.26700	−	8.73395i	0.298185	−	0.494463i
$313$	−3.19319	−	4.00414i	−0.180490	−	0.226327i	0.683353	−	0.730088i	$-0.260521\pi$
$313$	−3.19319	−	4.00414i	−0.180490	−	0.226327i	−0.863843	+	0.503761i	$0.831949\pi$
$314$	14.5794	+	22.6108i	0.822764	+	1.27600i
$315$	−1.67859	−	0.0564007i	−0.0945779	−	0.00317782i
$316$	−3.77636	+	3.15904i	−0.212437	+	0.177710i
$317$	0.965320	−	1.21047i	0.0542178	−	0.0679870i	−0.753983	−	0.656894i	$-0.771870\pi$
$317$	0.965320	−	1.21047i	0.0542178	−	0.0679870i	0.808201	+	0.588907i	$0.200441\pi$
$318$	3.80214	+	11.0456i	0.213213	+	0.619409i
$319$	−16.4161	−	24.7282i	−0.919124	−	1.38451i
$320$	21.5013	+	8.55127i	1.20196	+	0.478030i
$321$	0.170478	−	10.1504i	0.00951516	−	0.566539i
$322$	0.316500	+	0.193738i	0.0176379	+	0.0107966i
$323$	4.27905	+	18.7477i	0.238093	+	1.04315i
$324$	−17.3567	−	4.76909i	−0.964262	−	0.264949i
$325$	−4.36931	−	5.47894i	−0.242366	−	0.303917i
$326$	−14.2987	+	23.3591i	−0.791930	+	1.29374i
$327$	22.4892	−	4.73715i	1.24366	−	0.261965i
$328$	0.677157	+	4.56276i	0.0373897	+	0.251936i
$329$	−0.386072	−	1.69149i	−0.0212848	−	0.0932550i
$330$	27.7523	−	27.4716i	1.52771	−	1.51226i
$331$	−21.9313			−1.20545			−0.602726	−	0.797948i	$-0.705919\pi$
$331$	−21.9313			−1.20545			−0.602726	+	0.797948i	$0.705919\pi$
$332$	−11.7280	−	2.38932i	−0.643659	−	0.131131i
$333$	−9.29316	−	21.0805i	−0.509262	−	1.15520i
$334$	7.29407	+	20.0875i	0.399114	+	1.09914i
$335$	3.05093	−	1.46925i	0.166690	−	0.0802736i
$336$	−0.804219	+	1.07308i	−0.0438738	+	0.0585416i
$337$	0.488031	+	1.01341i	0.0265847	+	0.0552037i	0.913838	−	0.406078i	$-0.133104\pi$
$337$	0.488031	+	1.01341i	0.0265847	+	0.0552037i	−0.887254	+	0.461282i	$0.847390\pi$
$338$	1.22943	−	12.1933i	0.0668721	−	0.663229i
$339$	12.5556	−	2.64472i	0.681926	−	0.143641i
$340$	38.6992	−	19.7661i	2.09876	−	1.07197i
$341$	−32.9716	−	7.52556i	−1.78551	−	0.407532i
$342$	−10.8166	+	0.979663i	−0.584895	+	0.0529741i
$343$	2.11293	+	1.68501i	0.114088	+	0.0909818i
$344$	13.4268	−	14.4051i	0.723926	−	0.776670i
$345$	6.16770	−	2.84362i	0.332058	−	0.153095i
$346$	1.65571	+	2.56779i	0.0890114	+	0.138045i
$347$	−22.8542			−1.22688			−0.613439	−	0.789742i	$-0.710214\pi$
$347$	−22.8542			−1.22688			−0.613439	+	0.789742i	$0.710214\pi$
$348$	18.4620	−	2.67494i	0.989666	−	0.143392i
$349$	−25.5713			−1.36880			−0.684399	−	0.729108i	$-0.739935\pi$
$349$	−25.5713			−1.36880			−0.684399	+	0.729108i	$0.739935\pi$
$350$	0.499316	+	0.774375i	0.0266896	+	0.0413921i
$351$	10.6545	−	1.87302i	0.568694	−	0.0999745i
$352$	−5.29812	−	30.7252i	−0.282391	−	1.63766i
$353$	12.5836	+	10.0351i	0.669756	+	0.534113i	0.898279	−	0.439426i	$-0.144818\pi$
$353$	12.5836	+	10.0351i	0.669756	+	0.534113i	−0.228523	+	0.973539i	$0.573390\pi$
$354$	−17.4746	−	11.1043i	−0.928763	−	0.590186i
$355$	0.194357	+	0.0443608i	0.0103154	+	0.00235442i
$356$	15.1347	+	29.6316i	0.802140	+	1.57047i
$357$	0.519077	+	2.46427i	0.0274724	+	0.130423i
$358$	−2.67380	+	26.5184i	−0.141315	+	1.40154i
$359$	2.82011	+	5.85601i	0.148839	+	0.309068i	0.962037	−	0.272920i	$-0.0879893\pi$
$359$	2.82011	+	5.85601i	0.148839	+	0.309068i	−0.813197	+	0.581988i	$0.802275\pi$
$360$	8.14185	+	23.1531i	0.429113	+	1.22028i
$361$	11.2141	−	5.40044i	0.590217	−	0.284233i
$362$	−0.788329	−	2.17102i	−0.0414337	−	0.114106i
$363$	−32.5926	−	8.01719i	−1.71067	−	0.420793i
$364$	0.160885	−	0.789709i	0.00843267	−	0.0413920i
$365$	13.2497			0.693521
$366$	7.35142	+	7.42653i	0.384265	+	0.388191i
$367$	4.04703	+	17.7312i	0.211253	+	0.925562i	0.963717	+	0.266928i	$0.0860085\pi$
$367$	4.04703	+	17.7312i	0.211253	+	0.925562i	−0.752463	+	0.658634i	$0.771134\pi$
$368$	0.957768	−	5.33744i	0.0499271	−	0.278233i
$369$	−3.17718	+	3.72055i	−0.165398	+	0.193684i
$370$	−16.3997	+	26.7914i	−0.852581	+	1.39282i
$371$	0.575531	+	0.721693i	0.0298801	+	0.0374684i
$372$	13.1423	−	16.7059i	0.681396	−	0.866161i
$373$	−4.79105	−	20.9909i	−0.248071	−	1.08687i	−0.933457	−	0.358690i	$-0.883224\pi$
$373$	−4.79105	−	20.9909i	−0.248071	−	1.08687i	0.685386	−	0.728180i	$-0.259634\pi$
$374$	−49.9391	−	30.5690i	−2.58229	−	1.58068i
$375$	−8.18450	−	0.137461i	−0.422646	−	0.00709844i
$376$	−20.9802	+	14.2345i	−1.08197	+	0.734090i
$377$	−9.34050	+	6.20079i	−0.481060	+	0.319357i
$378$	−1.41850	+	0.104491i	−0.0729598	+	0.00537444i
$379$	−5.04324	+	6.32402i	−0.259054	+	0.324843i	−0.894301	−	0.447466i	$-0.852327\pi$
$379$	−5.04324	+	6.32402i	−0.259054	+	0.324843i	0.635247	+	0.772309i	$0.280898\pi$
$380$	9.50176	+	11.3586i	0.487430	+	0.582682i
$381$	−10.0686	−	8.30982i	−0.515828	−	0.425725i
$382$	−2.95797	−	4.58743i	−0.151343	−	0.234713i
$383$	−2.29238	−	2.87455i	−0.117135	−	0.146883i	0.719807	−	0.694174i	$-0.244230\pi$
$383$	−2.29238	−	2.87455i	−0.117135	−	0.146883i	−0.836942	+	0.547292i	$0.815659\pi$
$384$	18.8786	+	5.25353i	0.963393	+	0.268093i
$385$	1.33883	−	2.78010i	0.0682329	−	0.141687i
$386$	−5.31079	+	5.43666i	−0.270312	+	0.276719i
$387$	20.8750	+	0.701401i	1.06114	+	0.0356542i
$388$	−0.848832	+	4.16651i	−0.0430929	+	0.211523i
$389$	12.8465			0.651345			0.325673	−	0.945483i	$-0.394409\pi$
$389$	12.8465			0.651345			0.325673	+	0.945483i	$0.394409\pi$
$390$	−10.3768	−	10.4828i	−0.525449	−	0.530817i
$391$	−6.34938	−	7.96188i	−0.321102	−	0.402649i
$392$	5.84724	−	18.8049i	0.295330	−	0.949792i
$393$	−31.7090	−	15.9317i	−1.59951	−	0.803646i
$394$	−9.77885	+	29.0326i	−0.492651	+	1.46264i
$395$	3.08940	+	6.41521i	0.155445	+	0.322784i
$396$	20.8805	−	25.6442i	1.04928	−	1.28867i
$397$	9.59209	+	4.61931i	0.481413	+	0.231836i	0.658819	−	0.752301i	$-0.271056\pi$
$397$	9.59209	+	4.61931i	0.481413	+	0.231836i	−0.177406	+	0.984138i	$0.556771\pi$
$398$	16.3003	−	16.6866i	0.817060	−	0.836426i
$399$	−0.779372	+	0.359330i	−0.0390174	+	0.0179890i
$400$	7.89269	−	10.9084i	0.394635	−	0.545419i
$401$	−1.55058	−	1.23654i	−0.0774322	−	0.0617501i	0.584009	−	0.811747i	$-0.301483\pi$
$401$	−1.55058	−	1.23654i	−0.0774322	−	0.0617501i	−0.661441	+	0.749997i	$0.730055\pi$
$402$	2.43589	−	1.51336i	0.121491	−	0.0754795i
$403$	−2.84261	+	12.4543i	−0.141600	+	0.620391i
$404$	12.0075	−	3.03817i	0.597393	−	0.151155i
$405$	−12.8436	+	22.6428i	−0.638204	+	1.12513i
$406$	1.30369	−	0.687972i	0.0647012	−	0.0341435i
$407$	42.3258			2.09801
$408$	30.7955	−	20.1472i	1.52461	−	0.997434i
$409$	−7.70101	−	1.75771i	−0.380791	−	0.0869130i	0.0278410	−	0.999612i	$-0.491137\pi$
$409$	−7.70101	−	1.75771i	−0.380791	−	0.0869130i	−0.408632	+	0.912699i	$0.633994\pi$
$410$	6.63733	+	0.669228i	0.327794	+	0.0330508i
$411$	0.282029	−	16.7922i	0.0139115	−	0.828298i
$412$	29.1031	−	0.681802i	1.43381	−	0.0335900i
$413$	−1.59501	−	0.364051i	−0.0784855	−	0.0179138i
$414$	4.93582	−	2.95279i	0.242582	−	0.145122i
$415$	−7.51034	+	15.5954i	−0.368668	+	0.765548i
$416$	−11.6057	+	2.00124i	−0.569017	+	0.0981190i
$417$	21.7661	+	10.9360i	1.06589	+	0.535538i
$418$	6.36930	−	18.9099i	0.311533	−	0.924916i
$419$	17.9680	−	8.65296i	0.877797	−	0.422725i	0.0599774	−	0.998200i	$-0.480897\pi$
$419$	17.9680	−	8.65296i	0.877797	−	0.422725i	0.817819	+	0.575475i	$0.195183\pi$
$420$	1.21920	+	1.50821i	0.0594908	+	0.0735930i
$421$	−8.71006	+	6.94604i	−0.424502	+	0.338529i	−0.812325	−	0.583205i	$-0.801799\pi$
$421$	−8.71006	+	6.94604i	−0.424502	+	0.338529i	0.387823	+	0.921734i	$0.373227\pi$
$422$	−6.32415	+	0.787669i	−0.307855	+	0.0383431i
$423$	−26.0013	−	6.86088i	−1.26423	−	0.333588i
$424$	6.77089	−	11.6664i	0.328824	−	0.566571i
$425$	−5.62655	−	24.6515i	−0.272928	−	1.19578i
$426$	0.167668	+	0.0197551i	0.00812352	+	0.000957135i
$427$	0.743955	+	0.358270i	0.0360025	+	0.0173379i
$428$	−8.99117	+	7.52137i	−0.434605	+	0.363559i
$429$	−4.74731	+	19.2995i	−0.229202	+	0.931787i
$430$	−15.4332	−	23.9349i	−0.744254	−	1.15424i
$431$	5.22018	+	22.8711i	0.251447	+	1.10166i	0.930130	+	0.367231i	$0.119694\pi$
$431$	5.22018	+	22.8711i	0.251447	+	1.10166i	−0.678682	+	0.734432i	$0.737449\pi$
$432$	8.95184	+	18.7581i	0.430696	+	0.902497i
$433$	7.45244	+	5.94313i	0.358142	+	0.285608i	0.785986	−	0.618244i	$-0.212156\pi$
$433$	7.45244	+	5.94313i	0.358142	+	0.285608i	−0.427845	+	0.903852i	$0.640727\pi$
$434$	0.536136	−	1.59175i	0.0257354	−	0.0764063i
$435$	2.79897	−	26.8331i	0.134200	−	1.28655i
$436$	−21.1302	−	16.0558i	−1.01195	−	0.768933i
$437$	2.16378	−	2.71329i	0.103508	−	0.129794i
$438$	11.1564	−	1.19964i	0.533074	−	0.0573209i
$439$	19.2623	−	4.39650i	0.919342	−	0.209834i	0.263436	−	0.964677i	$-0.415144\pi$
$439$	19.2623	−	4.39650i	0.919342	−	0.209834i	0.655905	+	0.754843i	$0.272287\pi$
$440$	−44.9569	−	3.47150i	−2.14324	−	0.165497i
$441$	19.1128	−	8.42572i	0.910134	−	0.401225i
$442$	−11.5467	+	18.8633i	−0.549222	+	0.897238i
$443$	13.0232	−	27.0429i	0.618750	−	1.28485i	−0.322318	−	0.946631i	$-0.604462\pi$
$443$	13.0232	−	27.0429i	0.618750	−	1.28485i	0.941068	−	0.338217i	$-0.109824\pi$
$444$	−11.3830	+	24.0436i	−0.540215	+	1.14106i
$445$	46.9132	−	10.7076i	2.22390	−	0.507590i
$446$	−1.08212	−	8.68828i	−0.0512398	−	0.411402i
$447$	4.52358	+	5.87204i	0.213958	+	0.277738i
$448$	1.54463	−	0.108718i	0.0729770	−	0.00513644i
$449$	−11.2275	−	14.0788i	−0.529858	−	0.664421i	0.442812	−	0.896615i	$-0.353981\pi$
$449$	−11.2275	−	14.0788i	−0.529858	−	0.664421i	−0.972670	+	0.232194i	$0.925410\pi$
$450$	14.2228	−	1.28817i	0.670471	−	0.0607247i
$451$	−3.90004	−	8.09851i	−0.183646	−	0.381344i
$452$	−11.7969	−	8.96385i	−0.554878	−	0.421624i
$453$	11.2120	+	5.63329i	0.526786	+	0.264675i
$454$	−3.73108	+	37.0045i	−0.175108	+	1.73670i
$455$	−1.05012	−	0.505710i	−0.0492303	−	0.0237081i
$456$	9.02901	+	8.70375i	0.422822	+	0.407590i
$457$	−1.32496	+	5.80504i	−0.0619791	+	0.271548i	−0.996417	−	0.0845784i	$-0.973046\pi$
$457$	−1.32496	+	5.80504i	−0.0619791	+	0.271548i	0.934438	+	0.356127i	$0.115903\pi$
$458$	−26.7562	+	9.71559i	−1.25024	+	0.453980i
$459$	37.5685	+	10.5910i	1.75355	+	0.494345i
$460$	−7.14346	−	3.23625i	−0.333065	−	0.150891i
$461$	−3.79640	+	16.6331i	−0.176816	+	0.774682i	0.806271	+	0.591546i	$0.201482\pi$
$461$	−3.79640	+	16.6331i	−0.176816	+	0.774682i	−0.983088	+	0.183136i	$0.941375\pi$
$462$	0.875595	−	2.46210i	0.0407364	−	0.114547i
$463$		−	33.1708i		−	1.54158i	−0.637090	−	0.770789i	$-0.719862\pi$
$463$		−	33.1708i		−	1.54158i	0.637090	−	0.770789i	$-0.280138\pi$
$464$	−16.2865	−	14.0979i	−0.756080	−	0.654479i
$465$	−18.7599	−	24.3522i	−0.869972	−	1.12931i
$466$	−2.26646	−	3.51499i	−0.104992	−	0.162829i
$467$	−22.0101	−	5.02366i	−1.01850	−	0.232467i	−0.319502	−	0.947586i	$-0.603516\pi$
$467$	−22.0101	−	5.02366i	−1.01850	−	0.232467i	−0.699003	+	0.715119i	$0.746373\pi$
$468$	−9.68650	−	7.88712i	−0.447758	−	0.364582i
$469$	0.141286	−	0.177167i	0.00652397	−	0.00818080i
$470$	12.5145	+	34.4644i	0.577253	+	1.58972i
$471$	29.9229	−	13.7960i	1.37878	−	0.635685i
$472$	3.50961	+	23.6482i	0.161543	+	1.08850i
$473$	−16.6497	+	34.5734i	−0.765553	+	1.58969i
$474$	3.18215	+	5.12197i	0.146161	+	0.235260i
$475$	7.76359	−	3.73875i	0.356218	−	0.171546i
$476$	1.75933	−	2.31536i	0.0806386	−	0.106124i
$477$	14.0475	−	2.71344i	0.643189	−	0.124240i
$478$	9.29216	+	25.5901i	0.425014	+	1.17047i
$479$	−5.78260	+	4.61147i	−0.264214	+	0.210704i	−0.746632	−	0.665238i	$-0.768330\pi$
$479$	−5.78260	+	4.61147i	−0.264214	+	0.210704i	0.482418	+	0.875941i	$0.339759\pi$
$480$	14.0627	−	24.6046i	0.641870	−	1.12304i
$481$		−	15.9876i		−	0.728972i
$482$	−5.33050	+	0.663909i	−0.242798	+	0.0302402i
$483$	0.289296	−	0.350525i	0.0131634	−	0.0159494i
$484$	17.6290	+	34.5150i	0.801320	+	1.56887i
$485$	5.54044	+	2.66813i	0.251578	+	0.121154i
$486$	−8.76437	+	20.2283i	−0.397560	+	0.917576i
$487$	−20.4925	+	16.3422i	−0.928605	+	0.740537i	−0.965940	−	0.258765i	$-0.916684\pi$
$487$	−20.4925	+	16.3422i	−0.928605	+	0.740537i	0.0373356	+	0.999303i	$0.488113\pi$
$488$	0.928975	−	12.0305i	0.0420527	−	0.544594i
$489$	25.8702	+	21.3513i	1.16989	+	0.965539i
$490$	−24.2907	−	14.8689i	−1.09734	−	0.671710i
$491$	−21.3584	−	17.0328i	−0.963892	−	0.768678i	0.00899484	−	0.999960i	$-0.497137\pi$
$491$	−21.3584	−	17.0328i	−0.963892	−	0.768678i	−0.972887	+	0.231281i	$0.925708\pi$
$492$	5.64930	−	0.0374505i	0.254690	−	0.00168840i
$493$	−40.0721	+	5.53505i	−1.80476	+	0.249286i
$494$	−7.14279	−	2.40586i	−0.321370	−	0.108245i
$495$	−28.5465	−	38.3721i	−1.28307	−	1.72470i
$496$	−24.5171	+	1.14936i	−1.10085	+	0.0516078i
$497$	0.0130061	−	0.00296856i	0.000583404	−	0.000133158i
$498$	−4.91178	+	13.8115i	−0.220102	+	0.618908i
$499$	3.43190	−	2.73685i	0.153633	−	0.122518i	−0.543657	−	0.839308i	$-0.682961\pi$
$499$	3.43190	−	2.73685i	0.153633	−	0.122518i	0.697290	+	0.716789i	$0.254389\pi$
$500$	6.06467	+	7.24981i	0.271220	+	0.324221i
$501$	25.6117	−	5.39487i	1.14425	−	0.241025i
$502$	25.3984	−	26.0004i	1.13359	−	1.16045i
$503$	−15.1488	+	3.45761i	−0.675451	+	0.154167i	−0.546468	−	0.837480i	$-0.684028\pi$
$503$	−15.1488	+	3.45761i	−0.675451	+	0.154167i	−0.128982	+	0.991647i	$0.541171\pi$
$504$	1.16313	+	1.15954i	0.0518101	+	0.0516501i
$505$		−	17.9125i		−	0.797097i
$506$	1.30602	+	10.4860i	0.0580597	+	0.466158i
$507$	−14.5750	−	3.58517i	−0.647297	−	0.159223i
$508$	0.353054	+	15.0703i	0.0156642	+	0.668637i
$509$	7.45616	+	15.4829i	0.330489	+	0.686267i	0.998314	−	0.0580516i	$-0.0184888\pi$
$509$	7.45616	+	15.4829i	0.330489	+	0.686267i	−0.667825	+	0.744318i	$0.732775\pi$
$510$	−17.3223	−	50.3232i	−0.767044	−	2.22835i
$511$	0.798846	−	0.384704i	0.0353389	−	0.0170183i
$512$	−9.67887	−	20.4529i	−0.427750	−	0.903897i
$513$	−0.669875	+	13.2849i	−0.0295757	+	0.586544i
$514$	10.6381	−	10.8902i	0.469224	−	0.480346i
$515$	9.36830	−	41.0452i	0.412816	−	1.80867i
$516$	−15.1620	−	18.7561i	−0.667470	−	0.825693i
$517$	30.8035	−	38.6264i	1.35474	−	1.69879i
$518$	−0.210878	+	2.09146i	−0.00926545	+	0.0918936i
$519$	3.39819	−	1.56674i	0.149164	−	0.0687721i
$520$	−1.31128	+	16.9814i	−0.0575035	+	0.744685i
$521$		−	8.87672i		−	0.388896i	−0.980913	−	0.194448i	$-0.937708\pi$
$521$		−	8.87672i		−	0.388896i	0.980913	−	0.194448i	$-0.0622915\pi$
$522$	−0.0727230	−	22.8472i	−0.00318300	−	0.999995i
$523$		−	5.86667i		−	0.256532i	−0.991740	−	0.128266i	$-0.959059\pi$
$523$		−	5.86667i		−	0.256532i	0.991740	−	0.128266i	$-0.0409411\pi$
$524$	10.0512	+	39.7242i	0.439087	+	1.73536i
$525$	1.02480	−	0.472485i	0.0447260	−	0.0206209i
$526$	5.87216	+	0.592078i	0.256038	+	0.0258158i
$527$	−28.7384	+	36.0368i	−1.25187	+	1.56979i
$528$	−38.1686	+	1.14739i	−1.66107	+	0.0499336i
$529$	4.70902	−	20.6316i	0.204740	−	0.897025i
$530$	−13.9547	−	13.6316i	−0.606152	−	0.592118i
$531$	−16.4669	+	19.2831i	−0.714604	+	0.836817i
$532$	0.902672	+	0.408943i	0.0391358	+	0.0177299i
$533$	−3.05903	+	1.47315i	−0.132501	+	0.0638092i
$534$	38.5320	−	13.2635i	1.66744	−	0.573968i
$535$	7.35558	+	15.2740i	0.318009	+	0.660354i
$536$	−3.16202	−	0.983206i	−0.136579	−	0.0424680i
$537$	31.6981	+	7.79715i	1.36787	+	0.336472i
$538$	18.8341	−	2.34578i	0.811997	−	0.101134i
$539$			38.3751i			1.65293i
$540$	29.4749	−	5.89638i	1.26840	−	0.253740i
$541$	−16.2210	+	3.70234i	−0.697397	+	0.159176i	−0.556499	−	0.830848i	$-0.687856\pi$
$541$	−16.2210	+	3.70234i	−0.697397	+	0.159176i	−0.140897	+	0.990024i	$0.544999\pi$
$542$	16.8528	+	16.4626i	0.723888	+	0.707128i
$543$	−2.76807	+	0.583068i	−0.118789	+	0.0250218i
$544$	−40.8615	−	11.6633i	−1.75192	−	0.500062i
$545$	−30.0065	+	23.9294i	−1.28534	+	1.02502i
$546$	−0.930000	−	0.330736i	−0.0398003	−	0.0141542i
$547$	−12.4422	+	2.83984i	−0.531988	+	0.121423i	−0.480073	−	0.877229i	$-0.659390\pi$
$547$	−12.4422	+	2.83984i	−0.531988	+	0.121423i	−0.0519154	+	0.998651i	$0.516533\pi$
$548$	−14.8745	+	12.4429i	−0.635406	+	0.531535i
$549$	10.2684	−	7.63906i	0.438244	−	0.326027i
$550$	−8.37504	+	24.8648i	−0.357113	+	1.06024i
$551$	−4.87772	−	12.8939i	−0.207798	−	0.549298i
$552$	−6.30789	−	2.07818i	−0.268482	−	0.0884534i
$553$	0.372530	+	0.297083i	0.0158416	+	0.0126333i
$554$	15.0558	−	24.5960i	0.639662	−	1.04499i
$555$	29.6716	+	24.4887i	1.25949	+	1.03949i
$556$	−6.89943	−	27.2679i	−0.292601	−	1.15642i
$557$	−20.8330	+	16.6137i	−0.882722	+	0.703947i	−0.956001	−	0.293364i	$-0.905225\pi$
$557$	−20.8330	+	16.6137i	−0.882722	+	0.703947i	0.0732790	+	0.997311i	$0.476654\pi$
$558$	−18.0010	−	18.8063i	−0.762042	−	0.796134i
$559$	13.0593	+	6.28903i	0.552350	+	0.265998i
$560$	0.395526	−	2.20418i	0.0167140	−	0.0931436i
$561$	−45.6467	+	55.3077i	−1.92721	+	2.33509i
$562$	−0.453544	−	3.64148i	−0.0191316	−	0.153607i
$563$		−	8.59941i		−	0.362422i	−0.983444	−	0.181211i	$-0.941998\pi$
$563$		−	8.59941i		−	0.362422i	0.983444	−	0.181211i	$-0.0580016\pi$
$564$	13.6578	+	27.8864i	0.575098	+	1.17423i
$565$	−16.7524	+	13.3596i	−0.704780	+	0.562043i
$566$	−0.855215	+	0.310542i	−0.0359474	+	0.0130530i
$567$	−0.116931	+	1.73808i	−0.00491064	+	0.0729925i
$568$	−0.109451	−	0.161320i	−0.00459247	−	0.00676882i
$569$	−1.26006	+	0.606814i	−0.0528246	+	0.0254390i	−0.460110	−	0.887862i	$-0.652190\pi$
$569$	−1.26006	+	0.606814i	−0.0528246	+	0.0254390i	0.407285	+	0.913301i	$0.366476\pi$
$570$	15.4059	−	9.57129i	0.645281	−	0.400897i
$571$	2.90504	−	6.03237i	0.121572	−	0.252447i	−0.831297	−	0.555828i	$-0.812401\pi$
$571$	2.90504	−	6.03237i	0.121572	−	0.252447i	0.952869	+	0.303381i	$0.0981156\pi$
$572$	20.4378	−	10.4389i	0.854548	−	0.436472i
$573$	−6.07096	+	2.79902i	−0.253618	+	0.116931i
$574$	0.419606	−	0.152365i	0.0175140	−	0.00635961i
$575$	−2.84517	+	3.56773i	−0.118652	+	0.148785i
$576$	9.61322	−	21.9906i	0.400551	−	0.916275i
$577$	34.0653	+	7.77517i	1.41816	+	0.323685i	0.861795	−	0.507256i	$-0.169340\pi$
$577$	34.0653	+	7.77517i	1.41816	+	0.323685i	0.556360	+	0.830941i	$0.312197\pi$
$578$	−46.8624	+	30.2168i	−1.94922	+	1.25685i
$579$	5.68054	+	7.37388i	0.236075	+	0.306448i
$580$	−25.5432	+	17.8329i	−1.06062	+	0.740469i
$581$			1.15833i			0.0480558i
$582$	4.90669	+	1.74497i	0.203389	+	0.0723312i
$583$	−5.84903	+	25.6263i	−0.242242	+	1.06133i
$584$	−9.47785	−	8.83421i	−0.392196	−	0.365562i
$585$	−14.4942	+	10.7828i	−0.599261	+	0.445814i
$586$	6.57215	+	18.0994i	0.271493	+	0.747678i
$587$	−9.23619	+	40.4664i	−0.381218	+	1.67023i	0.312452	+	0.949934i	$0.398850\pi$
$587$	−9.23619	+	40.4664i	−0.381218	+	1.67023i	−0.693670	+	0.720293i	$0.744007\pi$
$588$	−21.7993	−	10.3205i	−0.898988	−	0.425611i
$589$	−14.1522	−	6.81535i	−0.583132	−	0.280822i
$590$	34.4004	+	3.46852i	1.41624	+	0.142797i
$591$	33.5265	+	16.8449i	1.37910	+	0.692905i
$592$	29.5943	−	8.23014i	1.21632	−	0.338257i
$593$	−15.6352	−	32.4669i	−0.642063	−	1.33326i	−0.927127	−	0.374748i	$-0.877729\pi$
$593$	−15.6352	−	32.4669i	−0.642063	−	1.33326i	0.285064	−	0.958508i	$-0.407985\pi$
$594$	−27.5108	−	29.7252i	−1.12878	−	1.21964i
$595$	−2.62208	−	3.28798i	−0.107495	−	0.134794i
$596$	1.70862	−	8.38682i	0.0699879	−	0.343538i
$597$	−17.4352	−	22.6325i	−0.713574	−	0.926286i
$598$	3.96083	−	0.493319i	0.161971	−	0.0201733i
$599$	44.6034	−	10.1804i	1.82245	−	0.415961i	0.832105	−	0.554618i	$-0.187136\pi$
$599$	44.6034	−	10.1804i	1.82245	−	0.415961i	0.990340	+	0.138657i	$0.0442786\pi$
$600$	−11.8723	−	11.4446i	−0.484685	−	0.467225i
$601$	−1.69777	+	3.52546i	−0.0692535	+	0.143806i	−0.932722	−	0.360597i	$-0.882573\pi$
$601$	−1.69777	+	3.52546i	−0.0692535	+	0.143806i	0.863468	+	0.504403i	$0.168287\pi$
$602$	−1.62544	−	0.994972i	−0.0662479	−	0.0405520i
$603$	−1.41677	−	3.21379i	−0.0576955	−	0.130876i
$604$	−3.55400	−	14.0461i	−0.144610	−	0.571528i
$605$	54.6448	−	12.4723i	2.22163	−	0.507072i
$606$	−1.62181	−	15.0826i	−0.0658817	−	0.612688i
$607$	−6.25330	+	7.84139i	−0.253814	+	0.318272i	−0.892371	−	0.451302i	$-0.850960\pi$
$607$	−6.25330	+	7.84139i	−0.253814	+	0.318272i	0.638558	+	0.769574i	$0.279531\pi$
$608$	0.776437	−	14.4603i	0.0314887	−	0.586444i
$609$	−0.610342	−	1.69908i	−0.0247323	−	0.0688501i
$610$	−16.5375	−	5.57021i	−0.669584	−	0.225531i
$611$	−14.5902	−	11.6353i	−0.590258	−	0.470715i
$612$	−19.1419	−	40.8044i	−0.773765	−	1.64942i
$613$	−5.36980	−	23.5266i	−0.216884	−	0.950232i	−0.959764	−	0.280807i	$-0.909398\pi$
$613$	−5.36980	−	23.5266i	−0.216884	−	0.950232i	0.742880	−	0.669425i	$-0.233459\pi$
$614$	15.5125	−	10.0025i	0.626035	−	0.403666i
$615$	1.95156	−	7.93375i	0.0786944	−	0.319920i
$616$	−2.81132	+	1.09602i	−0.113271	+	0.0441598i
$617$	−31.2217	−	15.0356i	−1.25694	−	0.605310i	−0.317575	−	0.948233i	$-0.602869\pi$
$617$	−31.2217	−	15.0356i	−1.25694	−	0.605310i	−0.939363	+	0.342923i	$0.888583\pi$
$618$	4.17196	−	35.4088i	0.167821	−	1.42435i
$619$	−7.54943	−	33.0762i	−0.303437	−	1.32945i	−0.864900	−	0.501944i	$-0.832618\pi$
$619$	−7.54943	−	33.0762i	−0.303437	−	1.32945i	0.561463	−	0.827502i	$-0.310239\pi$
$620$	−7.08590	+	34.7813i	−0.284577	+	1.39685i
$621$	−2.73290	−	6.49254i	−0.109668	−	0.260537i
$622$	0.665315	+	5.34178i	0.0266767	+	0.214186i
$623$	2.51758	−	2.00770i	0.100865	−	0.0804368i
$624$	0.433399	+	14.4173i	0.0173498	+	0.577154i
$625$	27.4795	−	13.2334i	1.09918	−	0.529337i
$626$	6.86397	+	2.31194i	0.274340	+	0.0924038i
$627$	−21.8370	−	10.9716i	−0.872085	−	0.438165i
$628$	−34.6569	−	15.7008i	−1.38296	−	0.626531i
$629$	25.0291	−	51.9734i	0.997974	−	2.07232i
$630$	2.03832	−	1.21940i	0.0812088	−	0.0485821i
$631$	1.54106	+	0.351736i	0.0613485	+	0.0140024i	0.253085	−	0.967444i	$-0.418555\pi$
$631$	1.54106	+	0.351736i	0.0613485	+	0.0140024i	−0.191737	+	0.981446i	$0.561412\pi$
$632$	2.06740	−	6.64882i	0.0822367	−	0.264476i
$633$	−0.131074	+	7.80422i	−0.00520972	+	0.310190i
$634$	−0.219655	+	2.17852i	−0.00872362	+	0.0865199i
$635$	21.2542	+	4.85113i	0.843447	+	0.192511i
$636$	−12.9842	−	10.2145i	−0.514857	−	0.405031i
$637$	14.4953			0.574324
$638$	38.4626	+	16.8099i	1.52275	+	0.665509i
$639$	0.0527543	−	0.199927i	0.00208693	−	0.00790901i
$640$	−32.1090	+	6.31447i	−1.26922	+	0.249601i
$641$	−1.95701	+	8.57420i	−0.0772971	+	0.338661i	−0.998759	−	0.0498086i	$-0.984139\pi$
$641$	−1.95701	+	8.57420i	−0.0772971	+	0.338661i	0.921462	+	0.388469i	$0.126996\pi$
$642$	7.57641	+	12.1949i	0.299017	+	0.481296i
$643$	10.4831	+	8.35998i	0.413412	+	0.329685i	0.808010	−	0.589169i	$-0.200545\pi$
$643$	10.4831	+	8.35998i	0.413412	+	0.329685i	−0.394598	+	0.918854i	$0.629116\pi$
$644$	−0.524655	+	0.0122911i	−0.0206743	+	0.000484339i
$645$	−31.6752	+	14.6039i	−1.24721	+	0.575027i
$646$	−19.4538	−	19.0034i	−0.765398	−	0.747677i
$647$	−36.8516	−	17.7468i	−1.44879	−	0.697699i	−0.466402	−	0.884573i	$-0.654450\pi$
$647$	−36.8516	−	17.7468i	−1.44879	−	0.697699i	−0.982384	+	0.186874i	$0.940164\pi$
$648$	24.2844	−	7.63350i	0.953979	−	0.299872i
$649$	−20.2134	−	41.9735i	−0.793444	−	1.64760i
$650$	9.39211	+	3.16348i	0.368389	+	0.124082i
$651$	−1.83813	−	0.923539i	−0.0720420	−	0.0361963i
$652$	−0.907138	−	38.7217i	−0.0355263	−	1.51646i
$653$	3.57906	+	4.48800i	0.140059	+	0.175629i	0.846914	−	0.531730i	$-0.178458\pi$
$653$	3.57906	+	4.48800i	0.140059	+	0.175629i	−0.706855	+	0.707359i	$0.749886\pi$
$654$	−23.0992	+	22.8656i	−0.903252	+	0.894117i
$655$	59.2599			2.31548
$656$	−4.30164	−	4.90414i	−0.167951	−	0.191474i
$657$	0.461488	−	13.7348i	0.0180044	−	0.535845i
$658$	1.75519	+	1.71455i	0.0684245	+	0.0668403i
$659$	−14.7372	+	30.6021i	−0.574079	+	1.19209i	0.388592	+	0.921410i	$0.372962\pi$
$659$	−14.7372	+	30.6021i	−0.574079	+	1.19209i	−0.962670	+	0.270677i	$0.912753\pi$
$660$	−11.9315	+	53.9204i	−0.464432	+	2.09885i
$661$	30.3665	+	38.0783i	1.18112	+	1.48108i	0.841286	+	0.540590i	$0.181799\pi$
$661$	30.3665	+	38.0783i	1.18112	+	1.48108i	0.339833	+	0.940486i	$0.389630\pi$
$662$	26.0665	−	16.8077i	1.01310	−	0.653248i
$663$	20.8912	+	17.2420i	0.811347	+	0.669623i
$664$	15.7705	−	6.14828i	0.612015	−	0.238599i
$665$	0.893567	−	1.12050i	0.0346510	−	0.0434510i
$666$	27.2011	+	17.9333i	1.05402	+	0.694900i
$667$	5.28997	+	5.03128i	0.204829	+	0.194812i
$668$	−24.0640	−	18.2851i	−0.931065	−	0.707470i
$669$	−10.7216	−	0.180072i	−0.414522	−	0.00696200i
$670$	−2.50019	+	4.08445i	−0.0965909	+	0.157796i
$671$	5.23217	+	22.9236i	0.201986	+	0.884957i
$672$	0.133469	−	1.89176i	0.00514869	−	0.0729761i
$673$	10.9857	+	13.7756i	0.423468	+	0.531012i	0.947103	−	0.320931i	$-0.103996\pi$
$673$	10.9857	+	13.7756i	0.423468	+	0.531012i	−0.523635	+	0.851943i	$0.675424\pi$
$674$	−1.35670	−	0.830473i	−0.0522583	−	0.0319886i
$675$	0.880824	−	17.4685i	0.0339029	−	0.672361i
$676$	7.88346	+	15.4346i	0.303210	+	0.593640i
$677$	−5.79485	−	25.3889i	−0.222714	−	0.975775i	−0.955425	−	0.295234i	$-0.904602\pi$
$677$	−5.79485	−	25.3889i	−0.222714	−	0.975775i	0.732711	−	0.680540i	$-0.238255\pi$
$678$	−12.8962	+	12.7657i	−0.495274	+	0.490265i
$679$	0.411511			0.0157923
$680$	−30.8477	+	53.1514i	−1.18296	+	2.03826i
$681$	44.2323	+	10.8803i	1.69498	+	0.416935i
$682$	44.9560	−	16.3242i	1.72145	−	0.625086i
$683$	35.8981	−	17.2876i	1.37360	−	0.661493i	0.405979	−	0.913883i	$-0.366931\pi$
$683$	35.8981	−	17.2876i	1.37360	−	0.661493i	0.967626	+	0.252390i	$0.0812164\pi$
$684$	12.1053	−	9.45400i	0.462859	−	0.361483i
$685$	12.1686	+	25.2685i	0.464940	+	0.965458i
$686$	−3.80269	−	0.383417i	−0.145187	−	0.0146389i
$687$	7.18589	+	34.1145i	0.274159	+	1.30155i
$688$	−4.91877	+	27.4113i	−0.187526	+	1.04504i
$689$	9.67973	+	2.20934i	0.368768	+	0.0841690i
$690$	−5.15136	+	8.10660i	−0.196109	+	0.308613i
$691$	22.9112	+	18.2711i	0.871582	+	0.695064i	0.953441	−	0.301580i	$-0.0975141\pi$
$691$	22.9112	+	18.2711i	0.871582	+	0.695064i	−0.0818584	+	0.996644i	$0.526086\pi$
$692$	−3.93580	−	1.78306i	−0.149617	−	0.0677818i
$693$	−2.83525	−	1.48467i	−0.107702	−	0.0563980i
$694$	27.1635	−	17.5150i	1.03111	−	0.664860i
$695$	−40.6779			−1.54300
$696$	−19.8931	+	17.3282i	−0.754045	+	0.656823i
$697$	−12.2507			−0.464029
$698$	30.3929	−	19.5973i	1.15039	−	0.741768i
$699$	−4.65170	+	2.14467i	−0.175944	+	0.0811188i
$700$	−1.18693	−	0.537722i	−0.0448617	−	0.0203240i
$701$	−20.1532	−	16.0716i	−0.761175	−	0.607016i	0.164043	−	0.986453i	$-0.447546\pi$
$701$	−20.1532	−	16.0716i	−0.761175	−	0.607016i	−0.925218	+	0.379437i	$0.876118\pi$
$702$	−11.2280	+	10.3916i	−0.423773	+	0.392204i
$703$	19.1657	+	4.37445i	0.722849	+	0.164986i
$704$	29.8442	+	32.4582i	1.12480	+	1.22331i
$705$	43.9424	−	9.25606i	1.65497	−	0.348604i
$706$	−22.6469	−	2.28344i	−0.852329	−	0.0859386i
$707$	−0.520089	−	1.07998i	−0.0195600	−	0.0406167i
$708$	29.2796	−	0.194101i	1.10039	−	0.00729477i
$709$	−32.8678	+	15.8283i	−1.23438	+	0.594444i	−0.933280	−	0.359150i	$-0.883067\pi$
$709$	−32.8678	+	15.8283i	−1.23438	+	0.594444i	−0.301095	+	0.953594i	$0.597352\pi$
$710$	−0.265001	+	0.0962260i	−0.00994533	+	0.00361130i
$711$	6.75768	−	2.97906i	0.253433	−	0.111724i
$712$	−40.6975	−	23.6198i	−1.52520	−	0.885190i
$713$	8.31842			0.311527
$714$	−2.50552	−	2.53112i	−0.0937667	−	0.0947247i
$715$	−7.38538	−	32.3575i	−0.276198	−	1.21010i
$716$	−17.1452	−	33.5677i	−0.640746	−	1.25449i
$717$	32.6277	−	6.87271i	1.21850	−	0.256666i
$718$	−7.83977	−	4.79892i	−0.292578	−	0.179094i
$719$	20.1212	+	25.2311i	0.750393	+	0.940963i	0.999622	−	0.0274819i	$-0.00874885\pi$
$719$	20.1212	+	25.2311i	0.750393	+	0.940963i	−0.249230	+	0.968444i	$0.580177\pi$
$720$	−27.4211	−	21.2790i	−1.02192	−	0.793023i
$721$	−0.626914	−	2.74669i	−0.0233475	−	0.102292i
$722$	−9.18982	+	15.0130i	−0.342010	+	0.558725i
$723$	−0.110479	+	6.57801i	−0.00410877	+	0.244639i
$724$	2.60079	+	1.97621i	0.0966577	+	0.0734454i
$725$	6.41375	+	16.9543i	0.238201	+	0.629666i
$726$	44.8823	−	15.4494i	1.66574	−	0.573382i
$727$	−6.06095	+	7.60019i	−0.224788	+	0.281875i	−0.881417	−	0.472338i	$-0.843410\pi$
$727$	−6.06095	+	7.60019i	−0.224788	+	0.281875i	0.656629	+	0.754213i	$0.271982\pi$
$728$	0.413995	+	1.06191i	0.0153437	+	0.0393571i
$729$	23.0244	+	14.1024i	0.852754	+	0.522313i
$730$	−15.7480	+	10.1543i	−0.582860	+	0.375827i
$731$	32.6083	+	40.8895i	1.20606	+	1.51235i
$732$	−14.4291	−	3.19286i	−0.533315	−	0.118012i
$733$	−1.03991	+	2.15939i	−0.0384099	+	0.0797589i	−0.919291	−	0.393579i	$-0.871237\pi$
$733$	−1.03991	+	2.15939i	−0.0384099	+	0.0797589i	0.880881	+	0.473338i	$0.156951\pi$
$734$	−18.3990	−	17.9730i	−0.679118	−	0.663394i
$735$	−22.2028	+	26.9020i	−0.818964	+	0.992296i
$736$	2.95214	+	7.07785i	0.108817	+	0.260893i
$737$	6.45272			0.237689
$738$	0.924907	−	6.85701i	0.0340463	−	0.252410i
$739$	9.93564	+	12.4589i	0.365488	+	0.458308i	0.930239	−	0.366953i	$-0.119599\pi$
$739$	9.93564	+	12.4589i	0.365488	+	0.458308i	−0.564751	+	0.825261i	$0.691028\pi$
$740$	−1.04043	−	44.4115i	−0.0382471	−	1.63260i
$741$	−4.14428	+	8.24842i	−0.152244	+	0.303013i
$742$	−1.23714	−	0.416697i	−0.0454168	−	0.0152974i
$743$	17.3769	+	36.0834i	0.637496	+	1.32377i	0.930018	+	0.367515i	$0.119791\pi$
$743$	17.3769	+	36.0834i	0.637496	+	1.32377i	−0.292522	+	0.956259i	$0.594495\pi$
$744$	−2.81728	+	29.9279i	−0.103287	+	1.09721i
$745$	−11.1524	−	5.37072i	−0.408593	−	0.196768i
$746$	21.7814	+	21.2771i	0.797475	+	0.779011i
$747$	15.9048	+	8.32849i	0.581924	+	0.304723i
$748$	82.7828	−	1.93936i	3.02684	−	0.0709100i
$749$	0.886960	+	0.707327i	0.0324088	+	0.0258452i
$750$	9.83308	−	6.10905i	0.359053	−	0.223071i
$751$	−10.2217	+	44.7842i	−0.372995	+	1.63420i	0.345324	+	0.938484i	$0.387769\pi$
$751$	−10.2217	+	44.7842i	−0.372995	+	1.63420i	−0.718319	+	0.695714i	$0.755088\pi$
$752$	14.0271	−	32.9973i	0.511515	−	1.20329i
$753$	−27.1667	−	35.2650i	−0.990010	−	1.28513i
$754$	6.34954	−	14.5283i	0.231237	−	0.529091i
$755$	−20.9538			−0.762586
$756$	1.60589	−	1.21130i	0.0584056	−	0.0440547i
$757$	−7.43010	−	1.69587i	−0.270052	−	0.0616375i	0.0853506	−	0.996351i	$-0.472799\pi$
$757$	−7.43010	−	1.69587i	−0.270052	−	0.0616375i	−0.355402	+	0.934713i	$0.615656\pi$
$758$	1.14757	−	11.3815i	0.0416817	−	0.413394i
$759$	12.9400	+	0.217331i	0.469694	+	0.00788863i
$760$	−19.9983	−	6.21832i	−0.725416	−	0.225562i
$761$	−8.48527	−	1.93671i	−0.307591	−	0.0702056i	0.0659393	−	0.997824i	$-0.478996\pi$
$761$	−8.48527	−	1.93671i	−0.307591	−	0.0702056i	−0.373530	+	0.927618i	$0.621853\pi$
$762$	18.3355	+	2.16034i	0.664226	+	0.0782609i
$763$	−1.11435	+	2.31398i	−0.0403422	+	0.0837715i
$764$	7.03142	+	3.18549i	0.254388	+	0.115247i
$765$	−63.9993	+	12.3622i	−2.31390	+	0.446958i
$766$	4.92761	+	1.65973i	0.178042	+	0.0599685i
$767$	−15.8545	+	7.63514i	−0.572474	+	0.275689i
$768$	−26.4644	+	8.22403i	−0.954952	+	0.296759i
$769$	−5.05754	+	4.03325i	−0.182380	+	0.145443i	−0.710424	−	0.703774i	$-0.751497\pi$
$769$	−5.05754	+	4.03325i	−0.182380	+	0.145443i	0.528045	+	0.849217i	$0.322925\pi$
$770$	0.539342	+	4.33035i	0.0194365	+	0.156055i
$771$	−11.3787	−	14.7706i	−0.409794	−	0.531951i
$772$	2.14562	−	10.5319i	0.0772226	−	0.379050i
$773$	9.91674	+	43.4481i	0.356680	+	1.56272i	0.761403	+	0.648279i	$0.224511\pi$
$773$	9.91674	+	43.4481i	0.356680	+	1.56272i	−0.404723	+	0.914439i	$0.632632\pi$
$774$	−25.3487	+	15.1645i	−0.911139	+	0.545078i
$775$	18.6089	+	8.96155i	0.668450	+	0.321909i
$776$	−2.18425	−	5.60266i	−0.0784098	−	0.201124i
$777$	2.49997	+	0.614948i	0.0896861	+	0.0220611i
$778$	−15.2688	+	9.84531i	−0.547414	+	0.352972i
$779$	−0.928995	−	4.07019i	−0.0332847	−	0.145830i
$780$	20.3672	+	4.50684i	0.729262	+	0.161371i
$781$	0.297004	+	0.236853i	0.0106276	+	0.00847525i
$782$	13.6484	+	4.59710i	0.488066	+	0.164392i
$783$	−27.7180	−	3.83604i	−0.990559	−	0.137089i
$784$	7.46192	+	26.8319i	0.266497	+	0.958282i
$785$	−34.3073	+	43.0200i	−1.22448	+	1.53545i
$786$	49.8976	−	5.36544i	1.77979	−	0.191379i
$787$	−14.4662	+	3.30182i	−0.515664	+	0.117697i	−0.472430	−	0.881368i	$-0.656623\pi$
$787$	−14.4662	+	3.30182i	−0.515664	+	0.117697i	−0.0432339	+	0.999065i	$0.513766\pi$
$788$	−10.6273	−	42.0012i	−0.378581	−	1.49623i
$789$	1.72658	−	7.01913i	0.0614678	−	0.249888i
$790$	−8.58841	−	5.25718i	−0.305562	−	0.187042i
$791$	−0.622135	+	1.29188i	−0.0221206	+	0.0459339i
$792$	−5.16445	+	46.4819i	−0.183511	+	1.65166i
$793$	8.65887	−	1.97633i	0.307485	−	0.0701815i
$794$	−14.9409	+	1.86087i	−0.530232	+	0.0660399i
$795$	−18.9270	+	14.5806i	−0.671273	+	0.517122i
$796$	−6.58552	+	32.3252i	−0.233417	+	1.14574i
$797$	−12.4200	−	15.5742i	−0.439939	−	0.551666i	0.511588	−	0.859231i	$-0.329057\pi$
$797$	−12.4200	−	15.5742i	−0.439939	−	0.551666i	−0.951527	+	0.307565i	$0.900486\pi$
$798$	0.650944	−	1.02438i	0.0230432	−	0.0362625i
$799$	−29.2153	−	60.6662i	−1.03356	−	2.14622i
$800$	−1.02094	+	19.0140i	−0.0360958	+	0.672247i
$801$	−9.46564	−	49.0036i	−0.334452	−	1.73146i
$802$	2.79061	+	0.281371i	0.0985398	+	0.00993557i
$803$	22.7477	+	10.9547i	0.802748	+	0.386583i
$804$	−1.73538	+	3.66552i	−0.0612023	+	0.129273i
$805$	−0.168886	+	0.739939i	−0.00595246	+	0.0260794i
$806$	−6.16609	−	16.9811i	−0.217191	−	0.598134i
$807$	0.390354	−	23.2419i	0.0137411	−	0.818155i
$808$	−11.9431	+	12.8133i	−0.420158	+	0.450770i
$809$	−4.18341	+	18.3287i	−0.147081	+	0.644403i	0.846607	+	0.532219i	$0.178642\pi$
$809$	−4.18341	+	18.3287i	−0.147081	+	0.644403i	−0.993687	+	0.112184i	$0.964215\pi$
$810$	−2.08760	−	36.7552i	−0.0733508	−	1.29145i
$811$		−	44.8418i		−	1.57461i	−0.616565	−	0.787304i	$-0.711476\pi$
$811$		−	44.8418i		−	1.57461i	0.616565	−	0.787304i	$-0.288524\pi$
$812$	−1.02226	+	1.81682i	−0.0358744	+	0.0637577i
$813$	22.8578	−	17.6087i	0.801658	−	0.617565i
$814$	−50.3066	+	32.4376i	−1.76324	+	1.13694i
$815$	−54.6106	−	12.4645i	−1.91293	−	0.436613i
$816$	−21.1618	+	47.5471i	−0.740811	+	1.66448i
$817$	−11.1124	+	13.9346i	−0.388775	+	0.487508i
$818$	10.5001	−	3.81276i	0.367129	−	0.133310i
$819$	−0.560800	+	1.07095i	−0.0195959	+	0.0374220i
$820$	−8.40171	+	4.29129i	−0.293400	+	0.149858i
$821$	22.6842	−	47.1043i	0.791685	−	1.64395i	0.0269224	−	0.999638i	$-0.491429\pi$
$821$	22.6842	−	47.1043i	0.791685	−	1.64395i	0.764762	−	0.644313i	$-0.222856\pi$
$822$	12.5340	+	20.1746i	0.437173	+	0.703670i
$823$	46.9835	−	22.6261i	1.63774	−	0.788695i	0.637916	−	0.770106i	$-0.279797\pi$
$823$	46.9835	−	22.6261i	1.63774	−	0.788695i	0.999827	−	0.0185892i	$-0.00591745\pi$
$824$	−34.0682	+	23.1144i	−1.18682	+	0.805228i
$825$	28.7136	+	14.4267i	0.999680	+	0.502273i
$826$	2.17476	−	0.789689i	0.0756697	−	0.0274768i
$827$	−4.22214	+	3.36704i	−0.146818	+	0.117083i	−0.694144	−	0.719836i	$-0.744217\pi$
$827$	−4.22214	+	3.36704i	−0.146818	+	0.117083i	0.547326	+	0.836919i	$0.315646\pi$
$828$	−3.60353	+	7.29226i	−0.125231	+	0.253424i
$829$			45.0353i			1.56414i	0.623191	+	0.782070i	$0.285836\pi$
$829$			45.0353i			1.56414i	−0.623191	+	0.782070i	$0.714164\pi$
$830$	−3.02552	−	24.2918i	−0.105017	−	0.843179i
$831$	−27.2402	−	22.4819i	−0.944951	−	0.779890i
$832$	12.2603	−	11.2730i	0.425050	−	0.390820i
$833$	47.1221	+	22.6928i	1.63268	+	0.786259i
$834$	−34.2513	+	3.68301i	−1.18602	+	0.127532i
$835$	−34.1727	+	27.2518i	−1.18260	+	0.943088i
$836$	6.92192	+	27.3568i	0.239399	+	0.946155i
$837$	−25.8971	+	18.5986i	−0.895135	+	0.642860i
$838$	−14.7246	+	24.0549i	−0.508652	+	0.830961i
$839$	−7.36053	−	5.86983i	−0.254114	−	0.202649i	0.488145	−	0.872763i	$-0.337674\pi$
$839$	−7.36053	−	5.86983i	−0.254114	−	0.202649i	−0.742258	+	0.670114i	$0.766245\pi$
$840$	−2.60494	−	0.858219i	−0.0898791	−	0.0296114i
$841$	27.9141	−	7.86139i	0.962556	−	0.271082i
$842$	5.02909	−	14.9310i	0.173314	−	0.514555i
$843$	−4.49371	−	0.0754731i	−0.154772	−	0.00259943i
$844$	6.91295	−	5.78289i	0.237954	−	0.199055i
$845$	24.4364	−	5.57745i	0.840637	−	0.191870i
$846$	36.1620	−	11.7723i	1.24328	−	0.404740i
$847$	2.93249	−	2.33858i	0.100762	−	0.0803546i
$848$	0.893308	+	19.0552i	0.0306763	+	0.654360i
$849$	0.229684	+	1.09041i	0.00788275	+	0.0374227i
$850$	25.5799	+	24.9876i	0.877383	+	0.857069i
$851$	−10.1496	+	2.31659i	−0.347925	+	0.0794117i
$852$	−0.214422	+	0.105017i	−0.00734598	+	0.00359782i
$853$			50.9128i			1.74322i	0.490198	+	0.871611i	$0.336925\pi$
$853$			50.9128i			1.74322i	−0.490198	+	0.871611i	$0.663075\pi$
$854$	−1.15880	+	0.144328i	−0.0396534	+	0.00493880i
$855$	−8.96044	−	20.3258i	−0.306440	−	0.695126i
$856$	4.92228	−	15.8302i	0.168240	−	0.541066i
$857$	9.51561	+	19.7594i	0.325047	+	0.674967i	0.997898	−	0.0648114i	$-0.0206446\pi$
$857$	9.51561	+	19.7594i	0.325047	+	0.674967i	−0.672851	+	0.739778i	$0.734930\pi$
$858$	−9.14825	−	26.5767i	−0.312316	−	0.907314i
$859$	−47.9128	+	23.0736i	−1.63476	+	0.787260i	−0.634870	+	0.772619i	$0.718946\pi$
$859$	−47.9128	+	23.0736i	−1.63476	+	0.787260i	−0.999893	+	0.0146413i	$0.995339\pi$
$860$	36.6864	+	16.6203i	1.25100	+	0.566746i
$861$	−0.112693	−	0.535002i	−0.00384057	−	0.0182328i
$862$	−23.7324	−	23.1829i	−0.808329	−	0.789614i
$863$	9.53690	−	41.7839i	0.324640	−	1.42234i	−0.504554	−	0.863380i	$-0.668343\pi$
$863$	9.53690	−	41.7839i	0.324640	−	1.42234i	0.829194	−	0.558960i	$-0.188800\pi$
$864$	−25.0155	−	15.4345i	−0.851046	−	0.525092i
$865$	−3.89610	+	4.88556i	−0.132471	+	0.166114i
$866$	−13.4123	−	1.35234i	−0.455769	−	0.0459543i
$867$	28.5931	+	62.0173i	0.971073	+	2.10622i
$868$	0.582653	+	2.30276i	0.0197765	+	0.0781608i
$869$			13.5682i			0.460269i
$870$	17.2376	+	34.0377i	0.584409	+	1.15399i
$871$		−	2.43736i		−	0.0825870i
$872$	37.4192	+	2.88946i	1.26718	+	0.0978493i
$873$	2.95879	−	5.65034i	0.100140	−	0.191235i
$874$	−0.492360	+	4.88317i	−0.0166543	+	0.165176i
$875$	0.570335	−	0.715178i	0.0192808	−	0.0241774i
$876$	−12.3406	+	9.97588i	−0.416951	+	0.337054i
$877$	9.21558	−	40.3761i	0.311188	−	1.36340i	−0.541376	−	0.840781i	$-0.682096\pi$
$877$	9.21558	−	40.3761i	0.311188	−	1.36340i	0.852564	−	0.522623i	$-0.175047\pi$
$878$	−19.5250	+	19.9877i	−0.658936	+	0.674554i
$879$	23.0769	−	4.86093i	0.778363	−	0.163955i
$880$	56.0943	−	30.3280i	1.89094	−	1.02236i
$881$	16.0114	−	7.71066i	0.539436	−	0.259779i	−0.144267	−	0.989539i	$-0.546082\pi$
$881$	16.0114	−	7.71066i	0.539436	−	0.259779i	0.683703	+	0.729760i	$0.260368\pi$
$882$	−16.2593	+	24.6621i	−0.547480	+	0.830416i
$883$	3.49636	+	7.26027i	0.117662	+	0.244328i	0.951479	−	0.307713i	$-0.0995636\pi$
$883$	3.49636	+	7.26027i	0.117662	+	0.244328i	−0.833817	+	0.552041i	$0.813849\pi$
$884$	−0.732549	−	31.2693i	−0.0246383	−	1.05170i
$885$	10.1147	−	41.1196i	0.340001	−	1.38222i
$886$	5.24635	+	42.1227i	0.176255	+	1.41514i
$887$		−	32.8310i		−	1.10236i	−0.834387	−	0.551179i	$-0.814178\pi$
$887$		−	32.8310i		−	1.10236i	0.834387	−	0.551179i	$-0.185822\pi$
$888$	−4.89711	−	37.3008i	−0.164336	−	1.25173i
$889$	1.42230	−	0.324631i	0.0477025	−	0.0108878i
$890$	−47.5528	+	48.6799i	−1.59397	+	1.63175i
$891$	−40.7712	+	28.2551i	−1.36589	+	0.946582i
$892$	7.94467	+	9.49718i	0.266007	+	0.317989i
$893$	17.9404	−	14.3070i	0.600352	−	0.478765i
$894$	−9.87673	−	3.51246i	−0.330327	−	0.117474i
$895$	−53.1450	+	12.1300i	−1.77644	+	0.405461i
$896$	−1.75256	+	1.31299i	−0.0585490	+	0.0438639i
$897$	0.0820919	−	4.88780i	0.00274097	−	0.163199i
$898$	24.1342	+	8.12895i	0.805369	+	0.271267i
$899$	16.8736	−	28.4104i	0.562766	−	0.947539i
$900$	−15.9174	+	12.4311i	−0.530580	+	0.414371i
$901$	28.0086	+	22.3361i	0.933103	+	0.744125i
$902$	10.8419	+	6.63662i	0.360997	+	0.220975i
$903$	−1.48573	+	1.80018i	−0.0494419	+	0.0599062i
$904$	20.8909	+	1.61316i	0.694822	+	0.0536531i
$905$	3.69332	−	2.94533i	0.122770	−	0.0979059i
$906$	−17.6433	+	1.89717i	−0.586160	+	0.0630293i
$907$	33.1323	+	15.9557i	1.10014	+	0.529799i	0.893702	−	0.448661i	$-0.148099\pi$
$907$	33.1323	+	15.9557i	1.10014	+	0.529799i	0.206437	+	0.978460i	$0.433813\pi$
$908$	−23.9248	−	46.8413i	−0.793973	−	1.55448i
$909$	−18.5683	−	0.623895i	−0.615872	−	0.0206933i
$910$	1.63569	−	0.203724i	0.0542226	−	0.00675338i
$911$		−	28.2738i		−	0.936753i	−0.883529	−	0.468377i	$-0.844839\pi$
$911$		−	28.2738i		−	0.936753i	0.883529	−	0.468377i	$-0.155161\pi$
$912$	−17.4019	−	3.42524i	−0.576233	−	0.113421i
$913$	−25.7882	+	20.5654i	−0.853464	+	0.680614i
$914$	−2.87407	−	7.91503i	−0.0950657	−	0.261806i
$915$	−9.59513	+	19.0973i	−0.317205	+	0.631338i
$916$	24.3554	−	32.0529i	0.804726	−	1.05906i
$917$	3.57288	−	1.72061i	0.117987	−	0.0568194i
$918$	−52.7689	+	16.2037i	−1.74163	+	0.534802i
$919$	14.1035	−	29.2862i	0.465232	−	0.966063i	−0.527927	−	0.849290i	$-0.677031\pi$
$919$	14.1035	−	29.2862i	0.465232	−	0.966063i	0.993159	−	0.116774i	$-0.0372552\pi$
$920$	10.9706	−	1.62814i	0.361689	−	0.0536781i
$921$	−9.46497	−	20.5291i	−0.311881	−	0.676458i
$922$	−8.23504	−	22.6789i	−0.271207	−	0.746889i
$923$	0.0894656	−	0.112186i	0.00294480	−	0.00369266i
$924$	0.846205	+	3.59737i	0.0278381	+	0.118345i
$925$	−25.2011	−	5.75200i	−0.828608	−	0.189124i
$926$	25.4214	+	39.4253i	0.835399	+	1.29560i
$927$	−42.2216	−	11.1409i	−1.38674	−	0.365914i
$928$	30.1617	+	4.27455i	0.990106	+	0.140319i
$929$		−	9.73088i		−	0.319260i	−0.987177	−	0.159630i	$-0.948970\pi$
$929$		−	9.73088i		−	0.319260i	0.987177	−	0.159630i	$-0.0510301\pi$
$930$	40.9602	+	14.5667i	1.34314	+	0.477660i
$931$	−3.96613	+	17.3768i	−0.129985	+	0.569500i
$932$	5.38762	+	2.44079i	0.176477	+	0.0799507i
$933$	6.59194	+	0.110713i	0.215810	+	0.00362459i
$934$	30.0102	−	10.8972i	0.981964	−	0.356566i
$935$	26.6478	−	116.752i	0.871475	−	3.81818i
$936$	17.5575	+	1.95075i	0.573883	+	0.0637623i
$937$	−20.1955	−	9.72566i	−0.659759	−	0.317723i	0.0738753	−	0.997267i	$-0.476463\pi$
$937$	−20.1955	−	9.72566i	−0.659759	−	0.317723i	−0.733635	+	0.679544i	$0.762178\pi$
$938$	−0.0321491	+	0.318851i	−0.00104970	+	0.0104108i
$939$	3.98251	−	7.92644i	0.129964	−	0.258670i
$940$	−41.2870	−	31.3719i	−1.34663	−	1.02324i
$941$	17.0910	+	35.4899i	0.557152	+	1.15694i	0.969314	+	0.245827i	$0.0790597\pi$
$941$	17.0910	+	35.4899i	0.557152	+	1.15694i	−0.412161	+	0.911111i	$0.635226\pi$
$942$	−24.9921	+	39.3296i	−0.814287	+	1.28143i
$943$	1.37847	+	1.72855i	0.0448892	+	0.0562893i
$944$	−22.2948	−	25.4175i	−0.725635	−	0.827269i
$945$	−1.12860	−	2.68120i	−0.0367132	−	0.0872194i
$946$	−6.70727	−	53.8524i	−0.218072	−	1.75089i
$947$	−23.3276	+	5.32437i	−0.758045	+	0.173019i	−0.584039	−	0.811726i	$-0.698528\pi$
$947$	−23.3276	+	5.32437i	−0.758045	+	0.173019i	−0.174006	+	0.984745i	$0.555671\pi$
$948$	−7.70754	−	3.64901i	−0.250329	−	0.118514i
$949$	4.13788	−	8.59240i	0.134321	−	0.278921i
$950$	−6.36216	+	10.3936i	−0.206416	+	0.337212i
$951$	2.60403	+	0.640544i	0.0844414	+	0.0207710i
$952$	−0.316614	+	4.10024i	−0.0102615	+	0.132890i
$953$	−35.9193	+	8.19834i	−1.16354	+	0.265570i	−0.760330	−	0.649537i	$-0.774963\pi$
$953$	−35.9193	+	8.19834i	−1.16354	+	0.265570i	−0.403210	+	0.915108i	$0.632106\pi$
$954$	−14.6167	+	13.9907i	−0.473232	+	0.452967i
$955$	6.96050	−	8.72819i	0.225236	−	0.282437i
$956$	−30.6560	−	23.2940i	−0.991485	−	0.753381i
$957$	26.9907	−	43.7540i	0.872484	−	1.41437i
$958$	3.33881	−	9.91266i	0.107872	−	0.320263i
$959$	1.46733	+	1.17016i	0.0473827	+	0.0377864i
$960$	2.14217	+	40.0212i	0.0691381	+	1.29168i
$961$	−1.47990	−	6.48387i	−0.0477388	−	0.209157i
$962$	12.2526	+	19.0021i	0.395038	+	0.612654i
$963$	16.0894	−	7.09287i	0.518474	−	0.228565i
$964$	5.82678	−	4.87427i	0.187668	−	0.156990i
$965$	−14.0048	−	6.74434i	−0.450830	−	0.217108i
$966$	−0.0752097	+	0.638329i	−0.00241983	+	0.0205379i
$967$	−2.13670	−	9.36148i	−0.0687115	−	0.301045i	0.928882	−	0.370375i	$-0.120771\pi$
$967$	−2.13670	−	9.36148i	−0.0687115	−	0.301045i	−0.997594	+	0.0693304i	$0.977914\pi$
$968$	−47.4047	−	27.5125i	−1.52364	−	0.884286i
$969$	−26.3856	+	20.3264i	−0.847628	+	0.652979i
$970$	−8.62992	+	1.07485i	−0.277090	+	0.0345113i
$971$	−31.6314	+	25.2252i	−1.01510	+	0.809515i	−0.981797	−	0.189931i	$-0.939174\pi$
$971$	−31.6314	+	25.2252i	−1.01510	+	0.809515i	−0.0333017	+	0.999445i	$0.510602\pi$
$972$	−5.08563	−	30.7593i	−0.163122	−	0.986606i
$973$	−2.45253	+	1.18108i	−0.0786247	+	0.0378636i
$974$	11.8321	−	35.1287i	0.379126	−	1.12560i
$975$	5.44935	−	10.8459i	0.174519	−	0.347347i
$976$	8.11577	+	15.0108i	0.259779	+	0.480485i
$977$	7.47728	−	15.5267i	0.239219	−	0.496744i	−0.746448	−	0.665444i	$-0.768242\pi$
$977$	7.47728	−	15.5267i	0.239219	−	0.496744i	0.985668	+	0.168699i	$0.0539567\pi$
$978$	−47.1114	−	5.55079i	−1.50646	−	0.177495i
$979$	89.3955	+	20.4039i	2.85709	+	0.652113i
$980$	40.2661	−	0.943317i	1.28625	−	0.0301332i
$981$	23.7603	+	31.9385i	0.758608	+	1.01972i
$982$	38.4392	+	3.87575i	1.22664	+	0.123680i
$983$	34.0630	+	7.77465i	1.08644	+	0.247973i	0.727998	−	0.685579i	$-0.240451\pi$
$983$	34.0630	+	7.77465i	1.08644	+	0.247973i	0.358442	+	0.933552i	$0.383308\pi$
$984$	−6.68581	+	4.37402i	−0.213136	+	0.139439i
$985$	−62.6567			−1.99641
$986$	43.3860	−	37.2892i	1.38169	−	1.18753i
$987$	2.38061	−	1.83393i	0.0757757	−	0.0583745i
$988$	10.3334	−	2.61459i	0.328749	−	0.0831813i
$989$	2.10028	−	9.20192i	0.0667849	−	0.292604i
$990$	63.3367	+	23.7299i	2.01297	+	0.754186i
$991$	16.8407	+	13.4300i	0.534964	+	0.426619i	0.853347	−	0.521343i	$-0.174569\pi$
$991$	16.8407	+	13.4300i	0.534964	+	0.426619i	−0.318384	+	0.947962i	$0.603140\pi$
$992$	28.2591	−	20.1555i	0.897227	−	0.639937i
$993$	−15.9045	−	34.4962i	−0.504714	−	1.09470i
$994$	−0.0131834	+	0.0134959i	−0.000418154	+	0.000428064i
$995$	42.9846	+	20.7003i	1.36270	+	0.656243i
$996$	−4.74692	−	20.1800i	−0.150412	−	0.639428i
$997$	−14.2580	−	29.6070i	−0.451554	−	0.937662i	−0.995155	−	0.0983181i	$-0.968654\pi$
$997$	−14.2580	−	29.6070i	−0.451554	−	0.937662i	0.543601	−	0.839344i	$-0.317061\pi$
$998$	−1.98154	+	5.88304i	−0.0627246	+	0.186224i
$999$	26.4186	−	29.9049i	0.835849	−	0.946150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.12	✓	336
3.2	odd	2	inner	348.2.t.a.35.45	yes	336
4.3	odd	2	inner	348.2.t.a.35.22	yes	336
12.11	even	2	inner	348.2.t.a.35.35	yes	336
29.5	even	14	inner	348.2.t.a.179.35	yes	336
87.5	odd	14	inner	348.2.t.a.179.22	yes	336
116.63	odd	14	inner	348.2.t.a.179.45	yes	336
348.179	even	14	inner	348.2.t.a.179.12	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.12	✓	336	1.1	even	1	trivial
348.2.t.a.35.22	yes	336	4.3	odd	2	inner
348.2.t.a.35.35	yes	336	12.11	even	2	inner
348.2.t.a.35.45	yes	336	3.2	odd	2	inner
348.2.t.a.179.12	yes	336	348.179	even	14	inner
348.2.t.a.179.22	yes	336	87.5	odd	14	inner
348.2.t.a.179.35	yes	336	29.5	even	14	inner
348.2.t.a.179.45	yes	336	116.63	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18856 + 0.766379i) q^{2} +(0.725197 + 1.57292i) q^{3} +(0.825327 - 1.82177i) q^{4} +(-2.26138 - 1.80339i) q^{5} +(-2.06739 - 1.31373i) q^{6} +(-0.188704 - 0.0430704i) q^{7} +(0.415217 + 2.79778i) q^{8} +(-1.94818 + 2.28136i) q^{9} +O(q^{10})\)	\(q+(-1.18856 + 0.766379i) q^{2} +(0.725197 + 1.57292i) q^{3} +(0.825327 - 1.82177i) q^{4} +(-2.26138 - 1.80339i) q^{5} +(-2.06739 - 1.31373i) q^{6} +(-0.188704 - 0.0430704i) q^{7} +(0.415217 + 2.79778i) q^{8} +(-1.94818 + 2.28136i) q^{9} +(4.06986 + 0.410356i) q^{10} +(-2.39142 - 4.96583i) q^{11} +(3.46403 - 0.0229638i) q^{12} +(-1.87573 + 0.903302i) q^{13} +(0.257293 - 0.0934270i) q^{14} +(1.19665 - 4.86480i) q^{15} +(-2.63767 - 3.00711i) q^{16} -7.51186 q^{17} +(0.567132 - 4.20456i) q^{18} +(-0.569639 - 2.49575i) q^{19} +(-5.15174 + 2.63132i) q^{20} +(-0.0691009 - 0.328051i) q^{21} +(6.64803 + 4.06943i) q^{22} +(0.845248 + 1.05991i) q^{23} +(-4.09959 + 2.68205i) q^{24} +(0.749022 + 3.28168i) q^{25} +(1.53713 - 2.51114i) q^{26} +(-5.00122 - 1.40990i) q^{27} +(-0.234207 + 0.308227i) q^{28} +(5.33452 - 0.736842i) q^{29} +(2.30599 + 6.69917i) q^{30} +(3.82574 - 4.79733i) q^{31} +(5.43960 + 1.55266i) q^{32} +(6.07662 - 7.36272i) q^{33} +(8.92826 - 5.75693i) q^{34} +(0.349059 + 0.437706i) q^{35} +(2.54822 + 5.43199i) q^{36} +(-3.33194 + 6.91884i) q^{37} +(2.58974 + 2.52978i) q^{38} +(-2.78110 - 2.29530i) q^{39} +(4.10654 - 7.07566i) q^{40} +1.63085 q^{41} +(0.333542 + 0.336949i) q^{42} +(-4.34091 - 5.44332i) q^{43} +(-11.0203 + 0.258173i) q^{44} +(8.51976 - 1.64570i) q^{45} +(-1.81691 - 0.611978i) q^{46} +(3.88922 + 8.07606i) q^{47} +(2.81712 - 6.32960i) q^{48} +(-6.27303 - 3.02093i) q^{49} +(-3.40527 - 3.32642i) q^{50} +(-5.44758 - 11.8156i) q^{51} +(0.0975189 + 4.16266i) q^{52} +(-3.72859 - 2.97345i) q^{53} +(7.02474 - 2.15708i) q^{54} +(-3.54743 + 15.5423i) q^{55} +(0.0421486 - 0.545836i) q^{56} +(3.51253 - 2.70591i) q^{57} +(-5.77567 + 4.96404i) q^{58} +8.45247 q^{59} +(-7.87490 - 6.19507i) q^{60} +(-4.15912 - 0.949292i) q^{61} +(-0.870534 + 8.63385i) q^{62} +(0.465888 - 0.346592i) q^{63} +(-7.65519 + 2.32338i) q^{64} +(5.87074 + 1.33996i) q^{65} +(-1.57977 + 13.4080i) q^{66} +(-0.507966 + 1.05480i) q^{67} +(-6.19974 + 13.6849i) q^{68} +(-1.05418 + 2.09815i) q^{69} +(-0.750324 - 0.252726i) q^{70} +(-0.0620979 + 0.0299048i) q^{71} +(-7.19167 - 4.50332i) q^{72} +(-3.58145 + 2.85611i) q^{73} +(-1.34226 - 10.7770i) q^{74} +(-4.61865 + 3.55802i) q^{75} +(-5.01682 - 1.02206i) q^{76} +(0.237389 + 1.04007i) q^{77} +(5.06456 + 0.596720i) q^{78} +(-2.21794 - 1.06810i) q^{79} +(0.541790 + 11.5570i) q^{80} +(-1.40920 - 8.88899i) q^{81} +(-1.93835 + 1.24985i) q^{82} +(-1.33167 - 5.83443i) q^{83} +(-0.654664 - 0.144864i) q^{84} +(16.9872 + 13.5468i) q^{85} +(9.33105 + 3.14291i) q^{86} +(5.02757 + 7.85643i) q^{87} +(12.9003 - 8.75256i) q^{88} +(-10.3727 + 13.0069i) q^{89} +(-8.86498 + 8.48537i) q^{90} +(0.392862 - 0.0896682i) q^{91} +(2.62851 - 0.665075i) q^{92} +(10.3202 + 2.53859i) q^{93} +(-10.8119 - 6.61822i) q^{94} +(-3.21265 + 6.67113i) q^{95} +(1.50257 + 9.68206i) q^{96} +(-2.07275 + 0.473091i) q^{97} +(9.77102 - 1.21697i) q^{98} +(15.9877 + 4.21864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more