LMFDB - Embedded newform 300.2.w.a.103.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.9
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.723992 - 1.21484i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-0.951672 + 1.75907i) q^{4} +(-1.94762 - 1.09854i) q^{5} +(-0.905121 - 1.08663i) q^{6} +(-2.52433 - 2.52433i) q^{7} +(2.82599 - 0.117421i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.723992 - 1.21484i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-0.951672 + 1.75907i) q^{4} +(-1.94762 - 1.09854i) q^{5} +(-0.905121 - 1.08663i) q^{6} +(-2.52433 - 2.52433i) q^{7} +(2.82599 - 0.117421i) q^{8} +(0.951057 - 0.309017i) q^{9} +(0.0755097 + 3.16138i) q^{10} +(-1.68955 - 0.548967i) q^{11} +(-0.664777 + 1.88629i) q^{12} +(-1.62677 + 3.19271i) q^{13} +(-1.23906 + 4.89425i) q^{14} +(-2.09549 - 0.780339i) q^{15} +(-2.18864 - 3.34811i) q^{16} +(0.815187 - 5.14689i) q^{17} +(-1.06396 - 0.931656i) q^{18} +(-6.47859 + 4.70697i) q^{19} +(3.78590 - 2.38054i) q^{20} +(-2.88815 - 2.09836i) q^{21} +(0.556310 + 2.44998i) q^{22} +(-3.63061 - 7.12548i) q^{23} +(2.77283 - 0.558057i) q^{24} +(2.58643 + 4.27907i) q^{25} +(5.05640 - 0.335234i) q^{26} +(0.891007 - 0.453990i) q^{27} +(6.84281 - 2.03813i) q^{28} +(2.24828 - 3.09449i) q^{29} +(0.569128 + 3.11064i) q^{30} +(-2.52195 - 3.47117i) q^{31} +(-2.48286 + 5.08285i) q^{32} +(-1.75462 - 0.277905i) q^{33} +(-6.84283 + 2.73598i) q^{34} +(2.14336 + 7.68951i) q^{35} +(-0.361512 + 1.96706i) q^{36} +(4.07246 + 2.07502i) q^{37} +(10.4087 + 4.46264i) q^{38} +(-1.10729 + 3.40789i) q^{39} +(-5.63294 - 2.87577i) q^{40} +(1.90439 + 5.86111i) q^{41} +(-0.458179 + 5.02783i) q^{42} +(6.90605 - 6.90605i) q^{43} +(2.57356 - 2.44959i) q^{44} +(-2.19176 - 0.442926i) q^{45} +(-6.02779 + 9.56940i) q^{46} +(-0.113466 - 0.716398i) q^{47} +(-2.68545 - 2.96451i) q^{48} +5.74450i q^{49} +(3.32583 - 6.24010i) q^{50} -5.21104i q^{51} +(-4.06805 - 5.90001i) q^{52} +(-0.150417 - 0.949696i) q^{53} +(-1.19661 - 0.753745i) q^{54} +(2.68753 + 2.92521i) q^{55} +(-7.43014 - 6.83732i) q^{56} +(-5.66249 + 5.66249i) q^{57} +(-5.38704 - 0.490913i) q^{58} +(-0.117276 - 0.360938i) q^{59} +(3.36689 - 2.94348i) q^{60} +(3.14261 - 9.67197i) q^{61} +(-2.39104 + 5.57686i) q^{62} +(-3.18084 - 1.62072i) q^{63} +(7.97242 - 0.663661i) q^{64} +(6.67564 - 4.43111i) q^{65} +(0.932722 + 2.33279i) q^{66} +(13.5463 + 2.14552i) q^{67} +(8.27793 + 6.33212i) q^{68} +(-4.70059 - 6.46980i) q^{69} +(7.78975 - 8.17097i) q^{70} +(0.772327 - 1.06302i) q^{71} +(2.65139 - 0.984953i) q^{72} +(0.731193 - 0.372562i) q^{73} +(-0.427607 - 6.44968i) q^{74} +(3.22398 + 3.82178i) q^{75} +(-2.11439 - 15.8758i) q^{76} +(2.87920 + 5.65075i) q^{77} +(4.94171 - 1.12210i) q^{78} +(-5.19452 - 3.77404i) q^{79} +(0.584601 + 8.92515i) q^{80} +(0.809017 - 0.587785i) q^{81} +(5.74154 - 6.55692i) q^{82} +(0.109993 - 0.694468i) q^{83} +(6.43973 - 3.08349i) q^{84} +(-7.24173 + 9.12865i) q^{85} +(-13.3897 - 3.38982i) q^{86} +(1.73651 - 3.40809i) q^{87} +(-4.83910 - 1.35299i) q^{88} +(-4.92819 - 1.60126i) q^{89} +(1.04873 + 2.98331i) q^{90} +(12.1660 - 3.95296i) q^{91} +(15.9894 + 0.394626i) q^{92} +(-3.03391 - 3.03391i) q^{93} +(-0.788160 + 0.656510i) q^{94} +(17.7886 - 2.05039i) q^{95} +(-1.65716 + 5.40868i) q^{96} +(8.43146 - 1.33541i) q^{97} +(6.97865 - 4.15897i) q^{98} -1.77649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.723992	−	1.21484i	−0.511939	−	0.859022i
$2$	−0.723992	−	1.21484i	−0.511939	−	0.859022i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$3$	0.987688	−	0.156434i	0.570242	−	0.0903175i
$4$	−0.951672	+	1.75907i	−0.475836	+	0.879534i
$5$	−1.94762	−	1.09854i	−0.871001	−	0.491281i
$5$	−1.94762	−	1.09854i	−0.871001	−	0.491281i
$6$	−0.905121	−	1.08663i	−0.369514	−	0.443613i
$7$	−2.52433	−	2.52433i	−0.954108	−	0.954108i	0.0448845	−	0.998992i	$-0.485708\pi$
$7$	−2.52433	−	2.52433i	−0.954108	−	0.954108i	−0.998992	+	0.0448845i	$0.985708\pi$
$8$	2.82599	−	0.117421i	0.999138	−	0.0415146i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	0.0755097	+	3.16138i	0.0238783	+	0.999715i
$11$	−1.68955	−	0.548967i	−0.509417	−	0.165520i	0.0430199	−	0.999074i	$-0.486302\pi$
$11$	−1.68955	−	0.548967i	−0.509417	−	0.165520i	−0.552437	+	0.833554i	$0.686302\pi$
$12$	−0.664777	+	1.88629i	−0.191905	+	0.544524i
$13$	−1.62677	+	3.19271i	−0.451184	+	0.885499i	0.547625	+	0.836724i	$0.315532\pi$
$13$	−1.62677	+	3.19271i	−0.451184	+	0.885499i	−0.998810	+	0.0487756i	$0.984468\pi$
$14$	−1.23906	+	4.89425i	−0.331154	+	1.30804i
$15$	−2.09549	−	0.780339i	−0.541053	−	0.201483i
$16$	−2.18864	−	3.34811i	−0.547160	−	0.837028i
$17$	0.815187	−	5.14689i	0.197712	−	1.24830i	−0.666626	−	0.745392i	$-0.732262\pi$
$17$	0.815187	−	5.14689i	0.197712	−	1.24830i	0.864338	−	0.502911i	$-0.167738\pi$
$18$	−1.06396	−	0.931656i	−0.250779	−	0.219593i
$19$	−6.47859	+	4.70697i	−1.48629	+	1.07985i	−0.510828	+	0.859683i	$0.670661\pi$
$19$	−6.47859	+	4.70697i	−1.48629	+	1.07985i	−0.975462	+	0.220170i	$0.929339\pi$
$20$	3.78590	−	2.38054i	0.846552	−	0.532305i
$21$	−2.88815	−	2.09836i	−0.630245	−	0.457900i
$22$	0.556310	+	2.44998i	0.118606	+	0.522337i
$23$	−3.63061	−	7.12548i	−0.757035	−	1.48577i	−0.870471	−	0.492220i	$-0.836185\pi$
$23$	−3.63061	−	7.12548i	−0.757035	−	1.48577i	0.113435	−	0.993545i	$-0.463815\pi$
$24$	2.77283	−	0.558057i	0.566001	−	0.113913i
$25$	2.58643	+	4.27907i	0.517285	+	0.855813i
$26$	5.05640	−	0.335234i	0.991642	−	0.0657448i
$27$	0.891007	−	0.453990i	0.171474	−	0.0873705i
$28$	6.84281	−	2.03813i	1.29317	−	0.385171i
$29$	2.24828	−	3.09449i	0.417494	−	0.574631i	−0.547532	−	0.836785i	$-0.684433\pi$
$29$	2.24828	−	3.09449i	0.417494	−	0.574631i	0.965026	+	0.262153i	$0.0844326\pi$
$30$	0.569128	+	3.11064i	0.103908	+	0.567923i
$31$	−2.52195	−	3.47117i	−0.452956	−	0.623440i	0.520074	−	0.854121i	$-0.325905\pi$
$31$	−2.52195	−	3.47117i	−0.452956	−	0.623440i	−0.973029	+	0.230681i	$0.925905\pi$
$32$	−2.48286	+	5.08285i	−0.438912	+	0.898530i
$33$	−1.75462	−	0.277905i	−0.305441	−	0.0483770i
$34$	−6.84283	+	2.73598i	−1.17354	+	0.469217i
$35$	2.14336	+	7.68951i	0.362293	+	1.29976i
$36$	−0.361512	+	1.96706i	−0.0602520	+	0.327843i
$37$	4.07246	+	2.07502i	0.669508	+	0.341131i	0.755485	−	0.655166i	$-0.227401\pi$
$37$	4.07246	+	2.07502i	0.669508	+	0.341131i	−0.0859772	+	0.996297i	$0.527401\pi$
$38$	10.4087	+	4.46264i	1.68851	+	0.723936i
$39$	−1.10729	+	3.40789i	−0.177308	+	0.545699i
$40$	−5.63294	−	2.87577i	−0.890645	−	0.454699i
$41$	1.90439	+	5.86111i	0.297416	+	0.915351i	0.982399	+	0.186793i	$0.0598092\pi$
$41$	1.90439	+	5.86111i	0.297416	+	0.915351i	−0.684984	+	0.728558i	$0.740191\pi$
$42$	−0.458179	+	5.02783i	−0.0706986	+	0.775811i
$43$	6.90605	−	6.90605i	1.05316	−	1.05316i	0.0546581	−	0.998505i	$-0.482593\pi$
$43$	6.90605	−	6.90605i	1.05316	−	1.05316i	0.998505	−	0.0546581i	$-0.0174069\pi$
$44$	2.57356	−	2.44959i	0.387979	−	0.369290i
$45$	−2.19176	−	0.442926i	−0.326728	−	0.0660275i
$46$	−6.02779	+	9.56940i	−0.888749	+	1.41093i
$47$	−0.113466	−	0.716398i	−0.0165508	−	0.104497i	0.978030	−	0.208464i	$-0.0668465\pi$
$47$	−0.113466	−	0.716398i	−0.0165508	−	0.104497i	−0.994581	+	0.103967i	$0.966846\pi$
$48$	−2.68545	−	2.96451i	−0.387612	−	0.427891i
$49$			5.74450i			0.820643i
$50$	3.32583	−	6.24010i	0.470343	−	0.882483i
$51$		−	5.21104i		−	0.729692i
$52$	−4.06805	−	5.90001i	−0.564137	−	0.818185i
$53$	−0.150417	−	0.949696i	−0.0206614	−	0.130451i	0.975202	−	0.221318i	$-0.0710360\pi$
$53$	−0.150417	−	0.949696i	−0.0206614	−	0.130451i	−0.995863	+	0.0908676i	$0.971036\pi$
$54$	−1.19661	−	0.753745i	−0.162838	−	0.102572i
$55$	2.68753	+	2.92521i	0.362386	+	0.394435i
$56$	−7.43014	−	6.83732i	−0.992895	−	0.913676i
$57$	−5.66249	+	5.66249i	−0.750015	+	0.750015i
$58$	−5.38704	−	0.490913i	−0.707353	−	0.0644600i
$59$	−0.117276	−	0.360938i	−0.0152680	−	0.0469901i	0.943132	−	0.332418i	$-0.107864\pi$
$59$	−0.117276	−	0.360938i	−0.0152680	−	0.0469901i	−0.958400	+	0.285428i	$0.907864\pi$
$60$	3.36689	−	2.94348i	0.434663	−	0.380001i
$61$	3.14261	−	9.67197i	0.402370	−	1.23837i	−0.520701	−	0.853739i	$-0.674329\pi$
$61$	3.14261	−	9.67197i	0.402370	−	1.23837i	0.923071	−	0.384629i	$-0.125671\pi$
$62$	−2.39104	+	5.57686i	−0.303663	+	0.708262i
$63$	−3.18084	−	1.62072i	−0.400749	−	0.204192i
$64$	7.97242	−	0.663661i	0.996553	−	0.0829576i
$65$	6.67564	−	4.43111i	0.828011	−	0.549612i
$66$	0.932722	+	2.33279i	0.114810	+	0.287146i
$67$	13.5463	+	2.14552i	1.65494	+	0.262116i	0.912883	−	0.408222i	$-0.133851\pi$
$67$	13.5463	+	2.14552i	1.65494	+	0.262116i	0.742056	+	0.670338i	$0.233851\pi$
$68$	8.27793	+	6.33212i	1.00385	+	0.767882i
$69$	−4.70059	−	6.46980i	−0.565884	−	0.778873i
$70$	7.78975	−	8.17097i	0.931053	−	0.976618i
$71$	0.772327	−	1.06302i	0.0916583	−	0.126157i	−0.760725	−	0.649074i	$-0.775156\pi$
$71$	0.772327	−	1.06302i	0.0916583	−	0.126157i	0.852383	+	0.522917i	$0.175156\pi$
$72$	2.65139	−	0.984953i	0.312469	−	0.116078i
$73$	0.731193	−	0.372562i	0.0855797	−	0.0436050i	−0.410677	−	0.911781i	$-0.634708\pi$
$73$	0.731193	−	0.372562i	0.0855797	−	0.0436050i	0.496257	+	0.868176i	$0.334708\pi$
$74$	−0.427607	−	6.44968i	−0.0497083	−	0.749760i
$75$	3.22398	+	3.82178i	0.372273	+	0.441301i
$76$	−2.11439	−	15.8758i	−0.242537	−	1.82107i
$77$	2.87920	+	5.65075i	0.328115	+	0.643963i
$78$	4.94171	−	1.12210i	0.559538	−	0.127053i
$79$	−5.19452	−	3.77404i	−0.584429	−	0.424612i	0.255889	−	0.966706i	$-0.417632\pi$
$79$	−5.19452	−	3.77404i	−0.584429	−	0.424612i	−0.840318	+	0.542094i	$0.817632\pi$
$80$	0.584601	+	8.92515i	0.0653604	+	0.997862i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	5.74154	−	6.55692i	0.634047	−	0.724090i
$83$	0.109993	−	0.694468i	0.0120733	−	0.0762278i	−0.980916	−	0.194432i	$-0.937714\pi$
$83$	0.109993	−	0.694468i	0.0120733	−	0.0762278i	0.992989	+	0.118204i	$0.0377137\pi$
$84$	6.43973	−	3.08349i	0.702632	−	0.336437i
$85$	−7.24173	+	9.12865i	−0.785475	+	0.990141i
$86$	−13.3897	−	3.38982i	−1.44385	−	0.365534i
$87$	1.73651	−	3.40809i	0.186174	−	0.365386i
$88$	−4.83910	−	1.35299i	−0.515850	−	0.144229i
$89$	−4.92819	−	1.60126i	−0.522387	−	0.169734i	0.0359415	−	0.999354i	$-0.488557\pi$
$89$	−4.92819	−	1.60126i	−0.522387	−	0.169734i	−0.558328	+	0.829620i	$0.688557\pi$
$90$	1.04873	+	2.98331i	0.110546	+	0.314469i
$91$	12.1660	−	3.95296i	1.27534	−	0.414383i
$92$	15.9894	+	0.394626i	1.66701	+	0.0411426i
$93$	−3.03391	−	3.03391i	−0.314602	−	0.314602i
$94$	−0.788160	+	0.656510i	−0.0812925	+	0.0677138i
$95$	17.7886	−	2.05039i	1.82507	−	0.210366i
$96$	−1.65716	+	5.40868i	−0.169133	+	0.552021i
$97$	8.43146	−	1.33541i	0.856085	−	0.135590i	0.287062	−	0.957912i	$-0.407322\pi$
$97$	8.43146	−	1.33541i	0.856085	−	0.135590i	0.569023	+	0.822322i	$0.307322\pi$
$98$	6.97865	−	4.15897i	0.704950	−	0.420120i
$99$	−1.77649			−0.178544
$100$	−9.98860	+	0.477429i	−0.998860	+	0.0477429i
$101$	−6.94087			−0.690643			−0.345321	−	0.938484i	$-0.612230\pi$
$101$	−6.94087			−0.690643			−0.345321	+	0.938484i	$0.612230\pi$
$102$	−6.33058	+	3.77275i	−0.626821	+	0.373558i
$103$	−14.8955	+	2.35922i	−1.46770	+	0.232461i	−0.838552	−	0.544822i	$-0.816597\pi$
$103$	−14.8955	+	2.35922i	−1.46770	+	0.232461i	−0.629151	+	0.777283i	$0.716597\pi$
$104$	−4.22234	+	9.21359i	−0.414034	+	0.903467i
$105$	3.31987	+	7.25954i	0.323986	+	0.708459i
$106$	−1.04483	+	0.870304i	−0.101483	+	0.0845314i
$107$	−4.92060	−	4.92060i	−0.475692	−	0.475692i	0.428059	−	0.903751i	$-0.359198\pi$
$107$	−4.92060	−	4.92060i	−0.475692	−	0.475692i	−0.903751	+	0.428059i	$0.859198\pi$
$108$	−0.0493461	+	1.99939i	−0.00474833	+	0.192392i
$109$	−0.895542	+	0.290979i	−0.0857773	+	0.0278707i	−0.351591	−	0.936154i	$-0.614359\pi$
$109$	−0.895542	+	0.290979i	−0.0857773	+	0.0278707i	0.265814	+	0.964024i	$0.414359\pi$
$110$	1.60791	−	5.38274i	0.153309	−	0.513224i
$111$	4.34692	+	1.41240i	0.412592	+	0.134059i
$112$	−2.92689	+	13.9766i	−0.276565	+	1.32066i
$113$	2.66129	−	5.22308i	0.250353	−	0.491346i	−0.731291	−	0.682065i	$-0.761082\pi$
$113$	2.66129	−	5.22308i	0.250353	−	0.491346i	0.981645	+	0.190719i	$0.0610821\pi$
$114$	10.9786	+	2.77942i	1.02824	+	0.260317i
$115$	−0.756571	+	17.8661i	−0.0705506	+	1.66602i
$116$	3.30379	+	6.89980i	0.306749	+	0.640631i
$117$	−0.560546	+	3.53915i	−0.0518225	+	0.327194i
$118$	−0.353575	+	0.403787i	−0.0325492	+	0.0371716i
$119$	−15.0503	+	10.9346i	−1.37965	+	1.00238i
$120$	−6.01345	−	1.95918i	−0.548951	−	0.178848i
$121$	−6.34599	−	4.61063i	−0.576908	−	0.419148i
$122$	−14.0251	+	3.18465i	−1.26977	+	0.288325i
$123$	2.79782	+	5.49103i	0.252271	+	0.495110i
$124$	8.50609	−	1.13287i	0.763870	−	0.101735i
$125$	−0.336646	−	11.1753i	−0.0301105	−	0.999547i
$126$	0.333988	+	5.03760i	0.0297540	+	0.448785i
$127$	−2.02791	+	1.03327i	−0.179948	+	0.0916881i	−0.541644	−	0.840608i	$-0.682198\pi$
$127$	−2.02791	+	1.03327i	−0.179948	+	0.0916881i	0.361696	+	0.932296i	$0.382198\pi$
$128$	−6.57821	−	9.20474i	−0.581437	−	0.813591i
$129$	5.74068	−	7.90137i	0.505439	−	0.695677i
$130$	−10.2162	−	4.90175i	−0.896020	−	0.429912i
$131$	7.97871	+	10.9818i	0.697103	+	0.959480i	0.999979	+	0.00645037i	$0.00205323\pi$
$131$	7.97871	+	10.9818i	0.697103	+	0.959480i	−0.302876	+	0.953030i	$0.597947\pi$
$132$	2.15868	−	2.82203i	0.187889	−	0.245626i
$133$	28.2360	+	4.47215i	2.44838	+	0.387785i
$134$	−7.20092	−	18.0099i	−0.622064	−	1.55582i
$135$	−2.23407	−	0.0946055i	−0.192278	−	0.00814235i
$136$	1.69936	−	14.6408i	0.145719	−	1.25544i
$137$	−17.2164	−	8.77220i	−1.47090	−	0.749460i	−0.479158	−	0.877729i	$-0.659058\pi$
$137$	−17.2164	−	8.77220i	−1.47090	−	0.749460i	−0.991739	+	0.128269i	$0.959058\pi$
$138$	−4.45659	+	10.3945i	−0.379370	+	0.884842i
$139$	−4.07647	+	12.5461i	−0.345761	+	1.06414i	0.615414	+	0.788204i	$0.288989\pi$
$139$	−4.07647	+	12.5461i	−0.345761	+	1.06414i	−0.961175	+	0.275940i	$0.911011\pi$
$140$	−15.5661	−	3.54758i	−1.31558	−	0.299826i
$141$	−0.224139	−	0.689828i	−0.0188759	−	0.0580940i
$142$	−1.85055	−	0.168638i	−0.155295	−	0.0141518i
$143$	4.50119	−	4.50119i	0.376409	−	0.376409i
$144$	−3.11614	−	2.50792i	−0.259679	−	0.208993i
$145$	−7.77819	+	3.55705i	−0.645944	+	0.295397i
$146$	−0.981980	−	0.618551i	−0.0812693	−	0.0511917i
$147$	0.898638	+	5.67378i	0.0741184	+	0.467965i
$148$	−7.52575	+	5.18899i	−0.618613	+	0.426532i
$149$			10.7792i			0.883069i	0.897244	+	0.441535i	$0.145566\pi$
$149$			10.7792i			0.883069i	−0.897244	+	0.441535i	$0.854434\pi$
$150$	2.30872	−	6.68355i	0.188506	−	0.545709i
$151$			5.33464i			0.434127i	0.976158	+	0.217063i	$0.0696478\pi$
$151$			5.33464i			0.434127i	−0.976158	+	0.217063i	$0.930352\pi$
$152$	−17.7557	+	14.0626i	−1.44018	+	1.14062i
$153$	−0.815187	−	5.14689i	−0.0659039	−	0.416101i
$154$	4.78024	−	7.58886i	0.385203	−	0.611528i
$155$	1.09858	+	9.53097i	0.0882403	+	0.765546i
$156$	−4.94093	−	5.19099i	−0.395591	−	0.415612i
$157$	2.71002	−	2.71002i	0.216283	−	0.216283i	−0.590647	−	0.806930i	$-0.701127\pi$
$157$	2.71002	−	2.71002i	0.216283	−	0.216283i	0.806930	+	0.590647i	$0.201127\pi$
$158$	−0.824065	+	9.04288i	−0.0655591	+	0.719413i
$159$	−0.297130	−	0.914473i	−0.0235640	−	0.0725224i
$160$	10.4194	−	7.17193i	0.823724	−	0.566991i
$161$	−8.82221	+	27.1520i	−0.695287	+	2.13987i
$162$	−1.29979	−	0.557275i	−0.102121	−	0.0437836i
$163$	−11.6794	−	5.95093i	−0.914798	−	0.466113i	−0.0677942	−	0.997699i	$-0.521596\pi$
$163$	−11.6794	−	5.95093i	−0.914798	−	0.466113i	−0.847004	+	0.531586i	$0.821596\pi$
$164$	−12.1224	−	2.22790i	−0.946603	−	0.173970i
$165$	3.11204	+	2.46877i	0.242272	+	0.192194i
$166$	−0.923302	+	0.369165i	−0.0716621	+	0.0286528i
$167$	10.3967	+	1.64667i	0.804517	+	0.127423i	0.545131	−	0.838351i	$-0.316480\pi$
$167$	10.3967	+	1.64667i	0.804517	+	0.127423i	0.259386	+	0.965774i	$0.416480\pi$
$168$	−8.40826	−	5.59081i	−0.648711	−	0.431341i
$169$	0.0941679	+	0.129611i	0.00724368	+	0.00997007i
$170$	16.3328	+	2.18847i	1.25267	+	0.167848i
$171$	−4.70697	+	6.47859i	−0.359951	+	0.495430i
$172$	5.57592	+	18.7205i	0.425160	+	1.42743i
$173$	−16.5463	+	8.43077i	−1.25799	+	0.640979i	−0.950545	−	0.310586i	$-0.899475\pi$
$173$	−16.5463	+	8.43077i	−1.25799	+	0.640979i	−0.307447	+	0.951565i	$0.599475\pi$
$174$	−5.39751	+	0.357849i	−0.409184	+	0.0271285i
$175$	4.27279	−	17.3308i	0.322992	−	1.31008i
$176$	1.85981	+	6.85828i	0.140188	+	0.516962i
$177$	−0.172295	−	0.338148i	−0.0129505	−	0.0254168i
$178$	1.62269	+	7.14626i	0.121625	+	0.535635i
$179$	−8.42724	−	6.12275i	−0.629882	−	0.457636i	0.226477	−	0.974016i	$-0.427279\pi$
$179$	−8.42724	−	6.12275i	−0.629882	−	0.457636i	−0.856359	+	0.516380i	$0.827279\pi$
$180$	2.86497	−	3.43394i	0.213543	−	0.255951i
$181$	11.7201	−	8.51513i	0.871146	−	0.632925i	−0.0597480	−	0.998213i	$-0.519030\pi$
$181$	11.7201	−	8.51513i	0.871146	−	0.632925i	0.930894	+	0.365289i	$0.119030\pi$
$182$	−13.6103	−	11.9178i	−1.00886	−	0.883406i
$183$	1.59089	−	10.0445i	0.117602	−	0.742511i
$184$	−11.0968	−	19.7102i	−0.818064	−	1.45306i
$185$	−5.65210	−	8.51510i	−0.415550	−	0.626042i
$186$	−1.48919	+	5.88224i	−0.109193	+	0.431307i
$187$	−4.20277	+	8.24839i	−0.307337	+	0.603182i
$188$	1.36818	+	0.482181i	0.0997845	+	0.0351667i
$189$	−3.39522	−	1.10317i	−0.246966	−	0.0802441i
$190$	−15.3697	−	20.1258i	−1.11503	−	1.46008i
$191$	12.7629	−	4.14693i	0.923494	−	0.300061i	0.191595	−	0.981474i	$-0.438634\pi$
$191$	12.7629	−	4.14693i	0.923494	−	0.300061i	0.731899	+	0.681413i	$0.238634\pi$
$192$	7.77045	−	1.90265i	0.560784	−	0.137312i
$193$	−1.91194	−	1.91194i	−0.137625	−	0.137625i	0.634938	−	0.772563i	$-0.281026\pi$
$193$	−1.91194	−	1.91194i	−0.137625	−	0.137625i	−0.772563	+	0.634938i	$0.781026\pi$
$194$	−7.72661	−	9.27604i	−0.554739	−	0.665981i
$195$	5.90027	−	5.42086i	0.422527	−	0.388196i
$196$	−10.1050	−	5.46688i	−0.721783	−	0.390492i
$197$	−0.592792	+	0.0938891i	−0.0422347	+	0.00668932i	−0.177516	−	0.984118i	$-0.556806\pi$
$197$	−0.592792	+	0.0938891i	−0.0422347	+	0.00668932i	0.135281	+	0.990807i	$0.456806\pi$
$198$	1.28617	+	2.15816i	0.0914039	+	0.153373i
$199$	13.4831			0.955790			0.477895	−	0.878417i	$-0.341400\pi$
$199$	13.4831			0.955790			0.477895	+	0.878417i	$0.341400\pi$
$200$	7.81166	+	11.7889i	0.552368	+	0.833601i
$201$	13.7151			0.967389
$202$	5.02513	+	8.43205i	0.353567	+	0.593277i
$203$	−13.4869	+	2.13611i	−0.946595	+	0.149926i
$204$	9.16658	+	4.95921i	0.641789	+	0.347214i
$205$	2.72963	−	13.5072i	0.190646	−	0.943386i
$206$	13.6503	+	16.3877i	0.951064	+	1.14178i
$207$	−5.65481	−	5.65481i	−0.393037	−	0.393037i
$208$	14.2500	−	1.54110i	0.988058	−	0.106856i
$209$	13.5298	−	4.39611i	0.935879	−	0.304085i
$210$	6.41562	−	9.28896i	0.442720	−	0.640999i
$211$	18.6782	+	6.06892i	1.28586	+	0.417802i	0.870641	−	0.491919i	$-0.163704\pi$
$211$	18.6782	+	6.06892i	1.28586	+	0.417802i	0.415220	+	0.909721i	$0.363704\pi$
$212$	1.81373	+	0.639205i	0.124567	+	0.0439008i
$213$	0.596526	−	1.17075i	0.0408733	−	0.0802183i
$214$	−2.41527	+	9.54021i	−0.165104	+	0.652156i
$215$	−21.0369	+	5.86378i	−1.43471	+	0.399907i
$216$	2.46467	−	1.38759i	0.167699	−	0.0944139i
$217$	−2.39614	+	15.1286i	−0.162660	+	1.02700i
$218$	1.00186	+	0.877273i	0.0678544	+	0.0594164i
$219$	0.663910	−	0.482359i	0.0448629	−	0.0325948i
$220$	−7.70329	+	1.94370i	−0.519356	+	0.131044i
$221$	15.1064	+	10.9755i	1.01617	+	0.738289i
$222$	−1.43129	−	6.30338i	−0.0960622	−	0.423055i
$223$	3.00746	+	5.90248i	0.201395	+	0.395259i	0.969510	−	0.245052i	$-0.0788052\pi$
$223$	3.00746	+	5.90248i	0.201395	+	0.395259i	−0.768115	+	0.640312i	$0.778805\pi$
$224$	19.0984	−	6.56323i	1.27606	−	0.438525i
$225$	3.78214	+	3.27038i	0.252143	+	0.218026i
$226$	−8.27195	+	0.548422i	−0.550242	+	0.0364805i
$227$	5.71398	−	2.91142i	0.379250	−	0.193237i	−0.253965	−	0.967213i	$-0.581735\pi$
$227$	5.71398	−	2.91142i	0.379250	−	0.193237i	0.633215	+	0.773976i	$0.281735\pi$
$228$	−4.57187	−	15.3495i	−0.302780	−	1.01655i
$229$	−6.76671	+	9.31357i	−0.447157	+	0.615458i	−0.971784	−	0.235874i	$-0.924205\pi$
$229$	−6.76671	+	9.31357i	−0.447157	+	0.615458i	0.524627	+	0.851332i	$0.324205\pi$
$230$	22.2522	−	12.0158i	1.46727	−	0.792297i
$231$	3.72773	+	5.13077i	0.245266	+	0.337580i
$232$	5.99024	−	9.00897i	0.393279	−	0.591468i
$233$	−28.3176	−	4.48506i	−1.85515	−	0.293826i	−0.873830	−	0.486231i	$-0.838371\pi$
$233$	−28.3176	−	4.48506i	−1.85515	−	0.293826i	−0.981316	+	0.192404i	$0.938371\pi$
$234$	4.70533	−	1.88134i	0.307597	−	0.122987i
$235$	−0.566002	+	1.51992i	−0.0369219	+	0.0991484i
$236$	0.746522	+	0.137198i	0.0485944	+	0.00893085i
$237$	−5.72095	−	2.91497i	−0.371616	−	0.189348i
$238$	24.1801	+	10.3671i	1.56736	+	0.671996i
$239$	−0.161118	+	0.495869i	−0.0104218	+	0.0320751i	−0.956132	−	0.292935i	$-0.905368\pi$
$239$	−0.161118	+	0.495869i	−0.0104218	+	0.0320751i	0.945710	+	0.325011i	$0.105368\pi$
$240$	1.97360	+	8.72381i	0.127396	+	0.563120i
$241$	1.91390	+	5.89039i	0.123285	+	0.379433i	0.993585	−	0.113090i	$-0.0360748\pi$
$241$	1.91390	+	5.89039i	0.123285	+	0.379433i	−0.870299	+	0.492523i	$0.836075\pi$
$242$	−1.00674	+	11.0474i	−0.0647154	+	0.710155i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	14.0229	+	14.7326i	0.897725	+	0.943159i
$245$	6.31056	−	11.1881i	0.403167	−	0.714781i
$246$	4.64513	−	7.37437i	0.296163	−	0.470172i
$247$	−4.48884	−	28.3414i	−0.285618	−	1.80332i
$248$	−7.53459	−	9.51335i	−0.478447	−	0.604098i
$249$		−	0.703125i		−	0.0445587i
$250$	−13.3324	+	8.49977i	−0.843217	+	0.537573i
$251$		−	13.5063i		−	0.852513i	−0.904602	−	0.426257i	$-0.859832\pi$
$251$		−	13.5063i		−	0.852513i	0.904602	−	0.426257i	$-0.140168\pi$
$252$	5.87808	−	4.05292i	0.370284	−	0.255310i
$253$	2.22244	+	14.0319i	0.139723	+	0.882179i
$254$	2.72345	+	1.71551i	0.170885	+	0.107640i
$255$	−5.72453	+	10.1491i	−0.358484	+	0.635562i
$256$	−6.41971	+	14.6556i	−0.401232	+	0.915976i
$257$	19.3654	−	19.3654i	1.20798	−	1.20798i	0.236303	−	0.971679i	$-0.424064\pi$
$257$	19.3654	−	19.3654i	1.20798	−	1.20798i	0.971679	−	0.236303i	$-0.0759358\pi$
$258$	−13.7551	−	1.25348i	−0.856356	−	0.0780385i
$259$	−5.04219	−	15.5183i	−0.313307	−	0.964259i
$260$	1.44161	+	15.9599i	0.0894048	+	0.989789i
$261$	1.18199	−	3.63779i	0.0731632	−	0.225173i
$262$	7.56455	−	17.6436i	0.467340	−	1.09002i
$263$	−15.6398	−	7.96889i	−0.964393	−	0.491383i	−0.100434	−	0.994944i	$-0.532023\pi$
$263$	−15.6398	−	7.96889i	−0.964393	−	0.491383i	−0.863960	+	0.503561i	$0.832023\pi$
$264$	−4.99118	−	0.579327i	−0.307186	−	0.0356551i
$265$	−0.750323	+	2.01488i	−0.0460920	+	0.123773i
$266$	−15.0097	−	37.5401i	−0.920305	−	2.30173i
$267$	−5.11801	−	0.810612i	−0.313217	−	0.0496087i
$268$	−16.6657	+	21.7870i	−1.01802	+	1.33085i
$269$	9.74908	+	13.4185i	0.594412	+	0.818137i	0.995182	−	0.0980409i	$-0.0312576\pi$
$269$	9.74908	+	13.4185i	0.594412	+	0.818137i	−0.400771	+	0.916178i	$0.631258\pi$
$270$	1.50251	+	2.78253i	0.0914401	+	0.169339i
$271$	−0.441635	+	0.607859i	−0.0268274	+	0.0369248i	−0.822220	−	0.569170i	$-0.807265\pi$
$271$	−0.441635	+	0.607859i	−0.0268274	+	0.0369248i	0.795393	+	0.606095i	$0.207265\pi$
$272$	−19.0165	+	8.53534i	−1.15304	+	0.517531i
$273$	11.3978	−	5.80747i	0.689827	−	0.351484i
$274$	1.80772	+	27.2662i	0.109208	+	1.64721i
$275$	−2.02082	−	8.64954i	−0.121860	−	0.521587i
$276$	15.8542	−	2.11152i	0.954313	−	0.127099i
$277$	−8.06741	−	15.8332i	−0.484724	−	0.951324i	−0.995780	−	0.0917765i	$-0.970745\pi$
$277$	−8.06741	−	15.8332i	−0.484724	−	0.951324i	0.511056	−	0.859547i	$-0.329255\pi$
$278$	18.1928	−	4.13100i	1.09113	−	0.247761i
$279$	−3.47117	−	2.52195i	−0.207813	−	0.150985i
$280$	6.96001	+	21.4788i	0.415940	+	1.28360i
$281$	1.40422	−	1.02023i	0.0837687	−	0.0608616i	−0.545113	−	0.838363i	$-0.683513\pi$
$281$	1.40422	−	1.02023i	0.0837687	−	0.0608616i	0.628881	+	0.777501i	$0.283513\pi$
$282$	−0.675756	+	0.771722i	−0.0402407	+	0.0459554i
$283$	−0.331065	+	2.09026i	−0.0196798	+	0.124253i	−0.995572	−	0.0939981i	$-0.970035\pi$
$283$	−0.331065	+	2.09026i	−0.0196798	+	0.124253i	0.975893	+	0.218251i	$0.0700353\pi$
$284$	1.13492	+	2.37022i	0.0673449	+	0.140647i
$285$	17.2488	−	4.80790i	1.02173	−	0.284795i
$286$	−8.72706	−	2.20940i	−0.516042	−	0.130645i
$287$	9.98807	−	19.6027i	0.589577	−	1.15711i
$288$	−0.790656	+	5.60133i	−0.0465898	+	0.330061i
$289$	−9.65795	−	3.13806i	−0.568115	−	0.184592i
$290$	9.95260	+	6.87398i	0.584437	+	0.403654i
$291$	8.11875	−	2.63794i	0.475929	−	0.154639i
$292$	−0.0404952	+	1.64078i	−0.00236980	+	0.0960191i
$293$	4.91240	+	4.91240i	0.286985	+	0.286985i	0.835887	−	0.548902i	$-0.184954\pi$
$293$	4.91240	+	4.91240i	0.286985	+	0.286985i	−0.548902	+	0.835887i	$0.684954\pi$
$294$	6.24213	−	5.19947i	0.364048	−	0.303239i
$295$	−0.168096	+	0.831800i	−0.00978691	+	0.0484293i
$296$	11.7524	+	5.38579i	0.683093	+	0.313043i
$297$	−1.75462	+	0.277905i	−0.101814	+	0.0161257i
$298$	13.0950	−	7.80408i	0.758576	−	0.452078i
$299$	28.6558			1.65721
$300$	−9.79093	+	2.03411i	−0.565280	+	0.117440i
$301$	−34.8663			−2.00966
$302$	6.48073	−	3.86223i	0.372924	−	0.222247i
$303$	−6.85542	+	1.08579i	−0.393834	+	0.0623771i
$304$	29.9387	+	11.3892i	1.71711	+	0.653214i
$305$	−16.7456	+	15.3850i	−0.958853	+	0.880943i
$306$	−5.66246	+	4.71662i	−0.323701	+	0.269631i
$307$	−16.3027	−	16.3027i	−0.930442	−	0.930442i	0.0672912	−	0.997733i	$-0.478564\pi$
$307$	−16.3027	−	16.3027i	−0.930442	−	0.930442i	−0.997733	+	0.0672912i	$0.978564\pi$
$308$	−12.6801	−	0.312952i	−0.722516	−	0.0178321i
$309$	−14.3431	+	4.66035i	−0.815950	+	0.265118i
$310$	10.7832	−	8.23494i	0.612447	−	0.467713i
$311$	−16.3710	−	5.31926i	−0.928315	−	0.301628i	−0.194442	−	0.980914i	$-0.562289\pi$
$311$	−16.3710	−	5.31926i	−0.928315	−	0.301628i	−0.733873	+	0.679286i	$0.762289\pi$
$312$	−2.72903	+	9.76067i	−0.154501	+	0.552589i
$313$	6.04074	−	11.8556i	0.341443	−	0.670119i	−0.654886	−	0.755728i	$-0.727283\pi$
$313$	6.04074	−	11.8556i	0.341443	−	0.670119i	0.996329	+	0.0856085i	$0.0272834\pi$
$314$	−5.25427	−	1.33021i	−0.296516	−	0.0750680i
$315$	4.41464	+	6.65082i	0.248737	+	0.374731i
$316$	11.5823	−	5.54586i	0.651553	−	0.311979i
$317$	1.57231	−	9.92720i	0.0883099	−	0.557567i	−0.903372	−	0.428857i	$-0.858916\pi$
$317$	1.57231	−	9.92720i	0.0883099	−	0.557567i	0.991682	−	0.128710i	$-0.0410836\pi$
$318$	−0.895818	+	1.02304i	−0.0502350	+	0.0573690i
$319$	−5.49733	+	3.99405i	−0.307792	+	0.223624i
$320$	−16.2563	−	7.46546i	−0.908754	−	0.417332i
$321$	−5.62977	−	4.09027i	−0.314223	−	0.228296i
$322$	39.3725	−	8.94022i	2.19414	−	0.498219i
$323$	18.9450	+	37.1816i	1.05413	+	2.06884i
$324$	0.264035	+	1.98249i	0.0146686	+	0.110139i
$325$	−17.8693	+	1.29666i	−0.991213	+	0.0719259i
$326$	1.22633	+	18.4970i	0.0679201	+	1.02445i
$327$	−0.838997	+	0.427490i	−0.0463966	+	0.0236403i
$328$	6.07000	+	16.3398i	0.335160	+	0.902215i
$329$	−1.52200	+	2.09485i	−0.0839106	+	0.115493i
$330$	0.746071	−	5.56801i	0.0410698	−	0.306509i
$331$	4.32087	+	5.94717i	0.237496	+	0.326886i	0.911083	−	0.412222i	$-0.135247\pi$
$331$	4.32087	+	5.94717i	0.237496	+	0.326886i	−0.673587	+	0.739108i	$0.735247\pi$
$332$	1.11694	+	0.854391i	0.0613000	+	0.0468908i
$333$	4.51435	+	0.715003i	0.247385	+	0.0391819i
$334$	−5.52665	−	13.8224i	−0.302405	−	0.756330i
$335$	−24.0260	−	19.0597i	−1.31268	−	1.04134i
$336$	−0.704436	+	14.2624i	−0.0384302	+	0.778077i
$337$	7.42745	+	3.78448i	0.404599	+	0.206154i	0.644434	−	0.764660i	$-0.277093\pi$
$337$	7.42745	+	3.78448i	0.404599	+	0.206154i	−0.239835	+	0.970814i	$0.577093\pi$
$338$	0.0892798	−	0.208236i	0.00485618	−	0.0113266i
$339$	1.81146	−	5.57509i	0.0983848	−	0.302797i
$340$	−9.16617	−	21.4262i	−0.497105	−	1.16200i
$341$	2.35540	+	7.24917i	0.127552	+	0.392564i
$342$	11.2783	+	1.02777i	0.609858	+	0.0555755i
$343$	−3.16929	+	3.16929i	−0.171126	+	0.171126i
$344$	18.7055	−	20.3273i	1.00853	−	1.09598i
$345$	2.04761	+	17.7645i	0.110240	+	0.956407i
$346$	22.2214	+	13.9973i	1.19463	+	0.752500i
$347$	0.533505	+	3.36842i	0.0286400	+	0.180826i	0.997861	−	0.0653646i	$-0.0208211\pi$
$347$	0.533505	+	3.36842i	0.0286400	+	0.180826i	−0.969221	+	0.246191i	$0.920821\pi$
$348$	4.34248	+	6.29803i	0.232781	+	0.337610i
$349$		−	5.41345i		−	0.289775i	−0.989448	−	0.144888i	$-0.953718\pi$
$349$		−	5.41345i		−	0.289775i	0.989448	−	0.144888i	$-0.0462820\pi$
$350$	−24.1476	+	7.35659i	−1.29074	+	0.393226i
$351$			3.58327i			0.191261i
$352$	6.98523	−	7.22470i	0.372314	−	0.385078i
$353$	−2.10117	−	13.2663i	−0.111834	−	0.706092i	−0.978352	−	0.206946i	$-0.933647\pi$
$353$	−2.10117	−	13.2663i	−0.111834	−	0.706092i	0.866518	−	0.499145i	$-0.166353\pi$
$354$	−0.286055	+	0.454127i	−0.0152037	+	0.0241366i
$355$	−2.67196	+	1.22192i	−0.141813	+	0.0648527i
$356$	7.50675	−	7.14514i	0.397857	−	0.378691i
$357$	−13.1544	+	13.1544i	−0.696205	+	0.696205i
$358$	−1.33691	+	14.6706i	−0.0706578	+	0.775364i
$359$	0.690853	+	2.12623i	0.0364618	+	0.112218i	0.967631	−	0.252370i	$-0.0812099\pi$
$359$	0.690853	+	2.12623i	0.0364618	+	0.112218i	−0.931169	+	0.364588i	$0.881210\pi$
$360$	−6.24590	−	0.994344i	−0.329188	−	0.0524065i
$361$	13.9452	−	42.9189i	0.733958	−	2.25889i
$362$	−18.8298	−	8.07313i	−0.989670	−	0.424314i
$363$	−6.98912	−	3.56113i	−0.366833	−	0.186911i
$364$	−4.62449	+	25.1627i	−0.242389	+	1.31888i
$365$	−1.83336	−	0.0776368i	−0.0959623	−	0.00406370i
$366$	−13.3543	+	5.33946i	−0.698038	+	0.279098i
$367$	30.7353	+	4.86799i	1.60437	+	0.254107i	0.893449	−	0.449165i	$-0.148278\pi$
$367$	30.7353	+	4.86799i	1.60437	+	0.254107i	0.710921	+	0.703272i	$0.248278\pi$
$368$	−15.9108	+	27.7508i	−0.829408	+	1.44661i
$369$	3.62236	+	4.98575i	0.188573	+	0.259548i
$370$	−6.25241	+	13.0313i	−0.325047	+	0.677463i
$371$	−2.01764	+	2.77705i	−0.104751	+	0.144177i
$372$	8.22415	−	2.44957i	0.426402	−	0.127004i
$373$	0.877412	−	0.447064i	0.0454307	−	0.0231481i	−0.431128	−	0.902291i	$-0.641884\pi$
$373$	0.877412	−	0.447064i	0.0454307	−	0.0231481i	0.476558	+	0.879143i	$0.341884\pi$
$374$	13.0632	−	0.866079i	0.675484	−	0.0447839i
$375$	−2.08070	−	10.9850i	−0.107447	−	0.567264i
$376$	−0.404775	−	2.01121i	−0.0208747	−	0.103720i
$377$	6.22238	+	12.2121i	0.320469	+	0.628956i
$378$	1.11793	+	4.92334i	0.0575002	+	0.253229i
$379$	−3.72897	−	2.70926i	−0.191544	−	0.139165i	0.487880	−	0.872911i	$-0.337770\pi$
$379$	−3.72897	−	2.70926i	−0.191544	−	0.139165i	−0.679424	+	0.733746i	$0.737770\pi$
$380$	−13.3221	+	33.2426i	−0.683411	+	1.70531i
$381$	−1.84130	+	1.33779i	−0.0943329	+	0.0685369i
$382$	−14.2781	−	12.5026i	−0.730532	−	0.639688i
$383$	−0.000646826		0.00408390i	−3.30513e−5		0.000208678i	−0.987705	−	0.156330i	$-0.950034\pi$
$383$	−0.000646826		0.00408390i	−3.30513e−5		0.000208678i	0.987672	+	0.156539i	$0.0500336\pi$
$384$	−7.93716	−	8.06235i	−0.405041	−	0.411430i
$385$	0.599987	−	14.1684i	0.0305782	−	0.722089i
$386$	−0.938475	+	3.70694i	−0.0477671	+	0.188678i
$387$	4.43396	−	8.70213i	0.225391	−	0.442354i
$388$	−5.67490	+	16.1024i	−0.288100	+	0.817474i
$389$	31.1826	+	10.1318i	1.58102	+	0.513705i	0.962320	−	0.271921i	$-0.0876589\pi$
$389$	31.1826	+	10.1318i	1.58102	+	0.513705i	0.618702	+	0.785626i	$0.287659\pi$
$390$	−10.8572	−	3.24323i	−0.549777	−	0.164227i
$391$	−39.6337	+	12.8778i	−2.00436	+	0.651256i
$392$	0.674525	+	16.2339i	0.0340687	+	0.819936i
$393$	9.59841	+	9.59841i	0.484176	+	0.484176i
$394$	0.543237	+	0.652173i	0.0273679	+	0.0328560i
$395$	5.97100	+	13.0568i	0.300434	+	0.656957i
$396$	1.69064	−	3.12497i	0.0849579	−	0.157036i
$397$	−29.0939	+	4.60802i	−1.46018	+	0.231270i	−0.835448	−	0.549570i	$-0.814792\pi$
$397$	−29.0939	+	4.60802i	−1.46018	+	0.231270i	−0.624732	+	0.780839i	$0.714792\pi$
$398$	−9.76163	−	16.3798i	−0.489306	−	0.821044i
$399$	28.5880			1.43119
$400$	8.66604	−	18.0250i	0.433302	−	0.901249i
$401$	9.63208			0.481003			0.240501	−	0.970649i	$-0.422688\pi$
$401$	9.63208			0.481003			0.240501	+	0.970649i	$0.422688\pi$
$402$	−9.92962	−	16.6617i	−0.495245	−	0.831008i
$403$	15.1851	−	2.40508i	0.756422	−	0.119806i
$404$	6.60544	−	12.2095i	0.328633	−	0.607444i
$405$	−2.22136	+	0.256044i	−0.110380	+	0.0127229i
$406$	12.3594	+	14.8379i	0.613389	+	0.736392i
$407$	−5.74149	−	5.74149i	−0.284595	−	0.284595i
$408$	−0.611886	−	14.7263i	−0.0302929	−	0.729063i
$409$	−12.9665	+	4.21307i	−0.641152	+	0.208323i	−0.611509	−	0.791238i	$-0.709437\pi$
$409$	−12.9665	+	4.21307i	−0.641152	+	0.208323i	−0.0296432	+	0.999561i	$0.509437\pi$
$410$	−18.3854	+	6.46306i	−0.907988	+	0.319188i
$411$	−18.3767	−	5.97096i	−0.906457	−	0.294526i
$412$	10.0256	−	28.4475i	0.493928	−	1.40151i
$413$	−0.615083	+	1.20717i	−0.0302663	+	0.0594009i
$414$	−2.77566	+	10.9637i	−0.136416	+	0.538838i
$415$	−0.977125	+	1.23173i	−0.0479652	+	0.0604631i
$416$	−12.1890	−	16.1957i	−0.597617	−	0.794059i
$417$	−2.06364	+	13.0293i	−0.101057	+	0.638048i
$418$	−15.1361	−	13.2538i	−0.740329	−	0.648267i
$419$	−14.8180	+	10.7659i	−0.723908	+	0.525950i	−0.887631	−	0.460556i	$-0.847650\pi$
$419$	−14.8180	+	10.7659i	−0.723908	+	0.525950i	0.163722	+	0.986507i	$0.447650\pi$
$420$	−15.9295	−	1.06883i	−0.777278	−	0.0521534i
$421$	−6.14229	−	4.46264i	−0.299357	−	0.217496i	0.427959	−	0.903798i	$-0.359233\pi$
$421$	−6.14229	−	4.46264i	−0.299357	−	0.217496i	−0.727316	+	0.686302i	$0.759233\pi$
$422$	−6.15010	−	27.0849i	−0.299382	−	1.31847i
$423$	−0.329292	−	0.646272i	−0.0160107	−	0.0314228i
$424$	−0.536591	−	2.66617i	−0.0260592	−	0.129481i
$425$	24.1323	−	9.82380i	1.17059	−	0.476524i
$426$	−1.85415	+	0.122928i	−0.0898339	+	0.00595589i
$427$	−32.3483	+	16.4823i	−1.56544	+	0.797632i
$428$	13.3385	−	3.97287i	0.644739	−	0.192036i
$429$	3.74164	−	5.14992i	0.180648	−	0.248640i
$430$	22.3541	+	21.3112i	1.07801	+	1.02772i
$431$	3.20041	+	4.40499i	0.154158	+	0.212181i	0.879110	−	0.476619i	$-0.158138\pi$
$431$	3.20041	+	4.40499i	0.154158	+	0.212181i	−0.724951	+	0.688800i	$0.758138\pi$
$432$	−3.47010	−	1.98957i	−0.166955	−	0.0957231i
$433$	11.0230	+	1.74587i	0.529732	+	0.0839013i	0.415571	−	0.909561i	$-0.363582\pi$
$433$	11.0230	+	1.74587i	0.529732	+	0.0839013i	0.114161	+	0.993462i	$0.463582\pi$
$434$	20.1136	−	8.04207i	0.965485	−	0.386032i
$435$	−7.12598	+	4.73004i	−0.341665	+	0.226788i
$436$	0.340410	−	1.85224i	0.0163027	−	0.0887060i
$437$	57.0607	+	29.0739i	2.72958	+	1.39079i
$438$	−1.06665	−	0.457320i	−0.0509667	−	0.0218516i
$439$	9.42835	−	29.0175i	0.449991	−	1.38493i	−0.426926	−	0.904287i	$-0.640404\pi$
$439$	9.42835	−	29.0175i	0.449991	−	1.38493i	0.876917	−	0.480642i	$-0.159596\pi$
$440$	7.93840	+	7.95104i	0.378449	+	0.379051i
$441$	1.77515	+	5.46335i	0.0845309	+	0.260159i
$442$	2.39650	−	26.2980i	0.113990	−	1.25087i
$443$	23.1555	−	23.1555i	1.10015	−	1.10015i	0.105759	−	0.994392i	$-0.466273\pi$
$443$	23.1555	−	23.1555i	1.10015	−	1.10015i	0.994392	−	0.105759i	$-0.0337273\pi$
$444$	−6.62136	+	6.30239i	−0.314236	+	0.299098i
$445$	7.83917	+	8.53246i	0.371612	+	0.404477i
$446$	4.99319	−	7.92694i	0.236434	−	0.375351i
$447$	1.68624	+	10.6465i	0.0797566	+	0.503563i
$448$	−21.8003	−	18.4497i	−1.02997	−	0.871669i
$449$		−	30.2498i		−	1.42757i	−0.700362	−	0.713787i	$-0.746978\pi$
$449$		−	30.2498i		−	1.42757i	0.700362	−	0.713787i	$-0.253022\pi$
$450$	1.23476	−	6.96243i	0.0582069	−	0.328212i
$451$		−	10.9481i		−	0.515524i
$452$	6.65507	+	9.65205i	0.313028	+	0.453994i
$453$	0.834521	+	5.26896i	0.0392092	+	0.247557i
$454$	−7.67377	−	4.83372i	−0.360148	−	0.226858i
$455$	−28.0371	−	5.66593i	−1.31440	−	0.265623i
$456$	−15.3372	+	16.6670i	−0.718232	+	0.780505i
$457$	4.51323	−	4.51323i	0.211120	−	0.211120i	−0.593623	−	0.804743i	$-0.702303\pi$
$457$	4.51323	−	4.51323i	0.211120	−	0.211120i	0.804743	+	0.593623i	$0.202303\pi$
$458$	16.2135	+	1.47752i	0.757609	+	0.0690398i
$459$	−1.61030	−	4.95600i	−0.0751624	−	0.231326i
$460$	−30.7076	−	18.3335i	−1.43175	−	0.854805i
$461$	−5.35766	+	16.4892i	−0.249531	+	0.767977i	0.745327	+	0.666699i	$0.232293\pi$
$461$	−5.35766	+	16.4892i	−0.249531	+	0.767977i	−0.994858	+	0.101278i	$0.967707\pi$
$462$	3.53423	−	8.24323i	0.164427	−	0.383510i
$463$	−3.65507	−	1.86235i	−0.169866	−	0.0865509i	0.366990	−	0.930225i	$-0.380388\pi$
$463$	−3.65507	−	1.86235i	−0.169866	−	0.0865509i	−0.536856	+	0.843674i	$0.680388\pi$
$464$	−15.2813	−	0.754764i	−0.709419	−	0.0350390i
$465$	2.57603	+	9.24177i	0.119460	+	0.428577i
$466$	15.0531	+	37.6485i	0.697319	+	1.74403i
$467$	−11.9491	−	1.89255i	−0.552938	−	0.0875768i	−0.126288	−	0.991994i	$-0.540306\pi$
$467$	−11.9491	−	1.89255i	−0.552938	−	0.0875768i	−0.426650	+	0.904417i	$0.640306\pi$
$468$	−5.69215	−	4.35415i	−0.263120	−	0.201271i
$469$	−28.7792	−	39.6112i	−1.32890	−	1.82908i
$470$	2.25624	−	0.412805i	0.104072	−	0.0190413i
$471$	2.25272	−	3.10060i	0.103800	−	0.142868i
$472$	−0.373802	−	1.00624i	−0.0172056	−	0.0463157i
$473$	−15.4593	+	7.87690i	−0.710819	+	0.362180i
$474$	0.600699	+	9.06046i	0.0275910	+	0.416161i
$475$	−36.8978	−	15.5481i	−1.69299	−	0.713395i
$476$	−4.91188	−	36.8806i	−0.225136	−	1.69042i
$477$	−0.436527	−	0.856733i	−0.0199872	−	0.0392271i
$478$	0.719050	−	0.163273i	0.0328886	−	0.00746793i
$479$	11.7109	+	8.50844i	0.535083	+	0.388761i	0.822256	−	0.569118i	$-0.192715\pi$
$479$	11.7109	+	8.50844i	0.535083	+	0.388761i	−0.287173	+	0.957879i	$0.592715\pi$
$480$	9.16916	−	8.71358i	0.418513	−	0.397719i
$481$	−13.2499	+	9.62661i	−0.604143	+	0.438936i
$482$	5.77023	−	6.58968i	0.262827	−	0.300152i
$483$	−4.46609	+	28.1978i	−0.203214	+	1.28304i
$484$	14.1497	−	6.77521i	0.643168	−	0.307964i
$485$	−17.8882	−	6.66141i	−0.812264	−	0.302479i
$486$	−1.37096	−	0.347082i	−0.0621881	−	0.0157440i
$487$	7.38610	−	14.4960i	0.334696	−	0.656878i	−0.660915	−	0.750460i	$-0.729832\pi$
$487$	7.38610	−	14.4960i	0.334696	−	0.656878i	0.995612	+	0.0935824i	$0.0298318\pi$
$488$	7.74530	−	27.7019i	0.350613	−	1.25401i
$489$	−12.4665	−	4.05061i	−0.563755	−	0.183175i
$490$	−18.1605	+	0.433766i	−0.820409	+	0.0195955i
$491$	−5.37125	+	1.74523i	−0.242401	+	0.0787609i	−0.427698	−	0.903922i	$-0.640675\pi$
$491$	−5.37125	+	1.74523i	−0.242401	+	0.0787609i	0.185297	+	0.982683i	$0.440675\pi$
$492$	−12.3217	−	0.304107i	−0.555506	−	0.0137102i
$493$	−14.0942	−	14.0942i	−0.634771	−	0.634771i
$494$	−31.1804	+	25.9722i	−1.40287	+	1.16854i
$495$	3.45993	+	1.95155i	0.155512	+	0.0877155i
$496$	−6.10222	+	16.0409i	−0.273998	+	0.720258i
$497$	−4.63302	+	0.733798i	−0.207819	+	0.0329153i
$498$	−0.854184	+	0.509057i	−0.0382769	+	0.0228114i
$499$	42.0345			1.88172			0.940861	−	0.338792i	$-0.110018\pi$
$499$	42.0345			1.88172			0.940861	+	0.338792i	$0.110018\pi$
$500$	19.9784	+	10.0430i	0.893463	+	0.449137i
$501$	10.5262			0.470278
$502$	−16.4081	+	9.77848i	−0.732327	+	0.436435i
$503$	−13.5346	+	2.14367i	−0.603479	+	0.0955817i	−0.450695	−	0.892678i	$-0.648824\pi$
$503$	−13.5346	+	2.14367i	−0.603479	+	0.0955817i	−0.152784	+	0.988260i	$0.548824\pi$
$504$	−9.17933	−	4.20664i	−0.408880	−	0.187379i
$505$	13.5182	+	7.62482i	0.601550	+	0.339300i
$506$	15.4375	−	12.8589i	0.686281	−	0.571648i
$507$	0.113284	+	0.113284i	0.00503112	+	0.00503112i
$508$	0.112311	−	4.55057i	0.00498297	−	0.201899i
$509$	15.7867	−	5.12941i	0.699733	−	0.227357i	0.0625186	−	0.998044i	$-0.480087\pi$
$509$	15.7867	−	5.12941i	0.699733	−	0.227357i	0.637214	+	0.770687i	$0.280087\pi$
$510$	16.4741	−	0.393484i	0.729484	−	0.0174238i
$511$	−2.78624	−	0.905305i	−0.123256	−	0.0400484i
$512$	22.4521	−	2.81163i	0.992250	−	0.124258i
$513$	−3.63554	+	7.13516i	−0.160513	+	0.315025i
$514$	−37.5463	−	9.50549i	−1.65610	−	0.419269i
$515$	31.6025	+	11.7685i	1.39257	+	0.518581i
$516$	8.43580	+	17.6178i	0.371366	+	0.775579i
$517$	−0.201572	+	1.27268i	−0.00886514	+	0.0559723i
$518$	−15.2017	+	17.3606i	−0.667925	+	0.762779i
$519$	−15.0237	+	10.9154i	−0.659469	+	0.479132i
$520$	18.3450	−	13.3061i	0.804481	−	0.583513i
$521$	−24.1796	−	17.5675i	−1.05933	−	0.769648i	−0.0853650	−	0.996350i	$-0.527206\pi$
$521$	−24.1796	−	17.5675i	−1.05933	−	0.769648i	−0.973964	+	0.226702i	$0.927206\pi$
$522$	−5.27508	+	1.19780i	−0.230884	+	0.0524263i
$523$	19.4370	+	38.1472i	0.849919	+	1.66806i	0.738467	+	0.674289i	$0.235550\pi$
$523$	19.4370	+	38.1472i	0.849919	+	1.66806i	0.111452	+	0.993770i	$0.464450\pi$
$524$	−26.9108	+	3.58406i	−1.17560	+	0.156571i
$525$	1.50905	−	17.7858i	0.0658604	−	0.776237i
$526$	1.64218	+	24.7693i	0.0716024	+	1.07999i
$527$	−19.9216	+	10.1505i	−0.867797	+	0.442165i
$528$	2.90978	+	6.48291i	0.126632	+	0.282132i
$529$	−24.0721	+	33.1324i	−1.04661	+	1.44054i
$530$	2.99099	−	0.547236i	0.129920	−	0.0237704i
$531$	−0.223072	−	0.307032i	−0.00968049	−	0.0133240i
$532$	−34.7383	+	45.4131i	−1.50610	+	1.96891i
$533$	−21.8108	−	3.45450i	−0.944732	−	0.149631i
$534$	2.72063	+	6.80443i	0.117733	+	0.294457i
$535$	4.17797	+	14.9889i	0.180630	+	0.648027i
$536$	38.5335	+	4.47259i	1.66439	+	0.193186i
$537$	−9.28130	−	4.72906i	−0.400518	−	0.204074i
$538$	9.24302	−	21.5584i	0.398495	−	0.929449i
$539$	3.15354	−	9.70560i	0.135833	−	0.418050i
$540$	2.29252	−	3.83984i	0.0986542	−	0.165240i
$541$	0.176397	+	0.542895i	0.00758391	+	0.0233409i	0.954777	−	0.297323i	$-0.0960939\pi$
$541$	0.176397	+	0.542895i	0.00758391	+	0.0233409i	−0.947193	+	0.320664i	$0.896094\pi$
$542$	1.05819	+	0.0964315i	0.0454532	+	0.00414209i
$543$	10.2437	−	10.2437i	0.439600	−	0.439600i
$544$	24.1369	+	16.9225i	1.03486	+	0.725546i
$545$	2.06382	+	0.417071i	0.0884045	+	0.0178654i
$546$	−15.3071	−	9.64195i	−0.655082	−	0.412637i
$547$	6.11765	+	38.6253i	0.261572	+	1.65150i	0.672695	+	0.739920i	$0.265137\pi$
$547$	6.11765	+	38.6253i	0.261572	+	1.65150i	−0.411123	+	0.911580i	$0.634863\pi$
$548$	31.8153	−	21.9366i	1.35908	−	0.937084i
$549$		−	10.1697i		−	0.434033i
$550$	−9.04475	+	8.71717i	−0.385670	+	0.371701i
$551$			30.6304i			1.30490i
$552$	−14.0435	−	17.7316i	−0.597731	−	0.754709i
$553$	3.58576	+	22.6396i	0.152482	+	0.962734i
$554$	−13.3940	+	21.2637i	−0.569059	+	0.903408i
$555$	−6.91457	−	7.52608i	−0.293507	−	0.319464i
$556$	−18.1899	−	19.1105i	−0.771425	−	0.810467i
$557$	3.14101	−	3.14101i	0.133089	−	0.133089i	−0.637424	−	0.770513i	$-0.720000\pi$
$557$	3.14101	−	3.14101i	0.133089	−	0.133089i	0.770513	+	0.637424i	$0.220000\pi$
$558$	−0.550670	+	6.04278i	−0.0233117	+	0.255811i
$559$	10.8145	+	33.2836i	0.457404	+	1.40775i
$560$	21.0543	−	24.0058i	0.889707	−	1.01443i
$561$	−2.86069	+	8.80430i	−0.120778	+	0.371718i
$562$	−2.25605	−	0.967268i	−0.0951659	−	0.0408017i
$563$	13.8062	+	7.03460i	0.581861	+	0.296473i	0.720038	−	0.693935i	$-0.244124\pi$
$563$	13.8062	+	7.03460i	0.581861	+	0.296473i	−0.138177	+	0.990408i	$0.544124\pi$
$564$	1.42676	+	0.262215i	0.0600775	+	0.0110412i
$565$	−10.9209	+	7.24902i	−0.459447	+	0.304969i
$566$	2.77902	−	1.11114i	0.116811	−	0.0467048i
$567$	−3.52599	−	0.558462i	−0.148078	−	0.0234532i
$568$	2.05777	−	3.09476i	0.0863420	−	0.129853i
$569$	24.2879	+	33.4294i	1.01820	+	1.40143i	0.913458	+	0.406932i	$0.133402\pi$
$569$	24.2879	+	33.4294i	1.01820	+	1.40143i	0.104742	+	0.994499i	$0.466598\pi$
$570$	−18.3288	−	17.4737i	−0.767711	−	0.731892i
$571$	21.3423	−	29.3752i	0.893147	−	1.22931i	−0.0794554	−	0.996838i	$-0.525318\pi$
$571$	21.3423	−	29.3752i	0.893147	−	1.22931i	0.972603	−	0.232473i	$-0.0746819\pi$
$572$	3.63424	+	12.2016i	0.151955	+	0.510173i
$573$	11.9571	−	6.09244i	0.499514	−	0.254515i
$574$	−31.0454	+	2.05828i	−1.29581	+	0.0859108i
$575$	21.1001	−	33.9652i	0.879935	−	1.41645i
$576$	7.37714	−	3.09479i	0.307381	−	0.128950i
$577$	−11.7252	−	23.0120i	−0.488127	−	0.958004i	−0.995362	−	0.0961960i	$-0.969332\pi$
$577$	−11.7252	−	23.0120i	−0.488127	−	0.958004i	0.507235	−	0.861808i	$-0.330668\pi$
$578$	3.18004	+	14.0048i	0.132272	+	0.582523i
$579$	−2.18750	−	1.58931i	−0.0909094	−	0.0660495i
$580$	1.14519	−	17.0675i	0.0475513	−	0.708690i
$581$	−2.03073	+	1.47541i	−0.0842488	+	0.0612103i
$582$	−9.08258	−	7.95313i	−0.376485	−	0.329668i
$583$	−0.267215	+	1.68713i	−0.0110669	+	0.0698737i
$584$	2.02260	−	1.13871i	0.0836957	−	0.0471202i
$585$	4.97962	−	6.27713i	0.205882	−	0.259527i
$586$	2.41124	−	9.52432i	0.0996076	−	0.393446i
$587$	−14.1378	+	27.7471i	−0.583531	+	1.14524i	0.390873	+	0.920444i	$0.372173\pi$
$587$	−14.1378	+	27.7471i	−0.583531	+	1.14524i	−0.974405	+	0.224800i	$0.927827\pi$
$588$	−10.8358	−	3.81881i	−0.446860	−	0.157485i
$589$	32.6774	+	10.6175i	1.34645	+	0.437487i
$590$	1.13220	−	0.398007i	0.0466121	−	0.0163857i
$591$	−0.570807	+	0.185466i	−0.0234799	+	0.00762907i
$592$	−1.96574	−	18.1765i	−0.0807914	−	0.747050i
$593$	−15.4757	−	15.4757i	−0.635512	−	0.635512i	0.313933	−	0.949445i	$-0.398353\pi$
$593$	−15.4757	−	15.4757i	−0.635512	−	0.635512i	−0.949445	+	0.313933i	$0.898353\pi$
$594$	1.60794	+	1.93038i	0.0659747	+	0.0792046i
$595$	41.3243	−	4.76322i	1.69413	−	0.195273i
$596$	−18.9614	−	10.2583i	−0.776690	−	0.420196i
$597$	13.3171	−	2.10922i	0.545032	−	0.0863245i
$598$	−20.7466	−	34.8122i	−0.848390	−	1.42358i
$599$	31.3256			1.27993			0.639964	−	0.768405i	$-0.278949\pi$
$599$	31.3256			1.27993			0.639964	+	0.768405i	$0.278949\pi$
$600$	9.55967	+	10.4217i	0.390272	+	0.425466i
$601$	28.3857			1.15788			0.578938	−	0.815371i	$-0.303467\pi$
$601$	28.3857			1.15788			0.578938	+	0.815371i	$0.303467\pi$
$602$	25.2429	+	42.3570i	1.02883	+	1.72634i
$603$	13.5463	−	2.14552i	0.551646	−	0.0873722i
$604$	−9.38399	−	5.07683i	−0.381829	−	0.206573i
$605$	7.29460	+	15.9510i	0.296567	+	0.648502i
$606$	6.28233	+	7.54213i	0.255202	+	0.306378i
$607$	28.9484	+	28.9484i	1.17498	+	1.17498i	0.981007	+	0.193971i	$0.0621367\pi$
$607$	28.9484	+	28.9484i	1.17498	+	1.17498i	0.193971	+	0.981007i	$0.437863\pi$
$608$	−7.83938	−	44.6165i	−0.317929	−	1.80944i
$609$	−12.9867	+	4.21963i	−0.526247	+	0.170988i
$610$	30.8140	+	9.20465i	1.24762	+	0.372686i
$611$	2.47184	+	0.803149i	0.0999998	+	0.0324919i
$612$	9.82951	+	3.46418i	0.397335	+	0.140031i
$613$	12.3671	−	24.2717i	0.499501	−	0.980325i	−0.494315	−	0.869283i	$-0.664581\pi$
$613$	12.3671	−	24.2717i	0.499501	−	0.980325i	0.993816	−	0.111042i	$-0.0354189\pi$
$614$	−8.00214	+	31.6081i	−0.322940	+	1.27560i
$615$	0.583028	−	13.7679i	0.0235100	−	0.555177i
$616$	8.80011	+	15.6309i	0.354566	+	0.629786i
$617$	6.15144	−	38.8387i	0.247648	−	1.56359i	−0.479772	−	0.877393i	$-0.659281\pi$
$617$	6.15144	−	38.8387i	0.247648	−	1.56359i	0.727420	−	0.686193i	$-0.240719\pi$
$618$	16.0459	+	14.0505i	0.645459	+	0.565194i
$619$	−16.7641	+	12.1798i	−0.673805	+	0.489548i	−0.871297	−	0.490757i	$-0.836720\pi$
$619$	−16.7641	+	12.1798i	−0.673805	+	0.489548i	0.197492	+	0.980305i	$0.436720\pi$
$620$	−17.8111	−	7.13788i	−0.715311	−	0.286664i
$621$	−6.46980	−	4.70059i	−0.259624	−	0.188628i
$622$	5.39042	+	23.7393i	0.216136	+	0.951858i
$623$	8.39825	+	16.4825i	0.336469	+	0.660358i
$624$	13.8335	−	3.75131i	0.553781	−	0.150173i
$625$	−11.6208	+	22.1350i	−0.464832	+	0.885399i
$626$	−18.7761	+	1.24484i	−0.750445	+	0.0497537i
$627$	12.6756	−	6.45852i	0.506213	−	0.257928i
$628$	2.18806	+	7.34616i	0.0873131	+	0.293144i
$629$	13.9997	−	19.2689i	0.558205	−	0.768303i
$630$	4.88352	−	10.1782i	0.194564	−	0.405510i
$631$	−3.00791	−	4.14003i	−0.119743	−	0.164812i	0.744938	−	0.667134i	$-0.232479\pi$
$631$	−3.00791	−	4.14003i	−0.119743	−	0.164812i	−0.864681	+	0.502322i	$0.832479\pi$
$632$	−15.1228	−	10.0554i	−0.601553	−	0.399984i
$633$	19.3976	+	3.07228i	0.770987	+	0.122112i
$634$	−13.1983	+	5.27710i	−0.524171	+	0.209580i
$635$	5.08468	+	0.215320i	0.201780	+	0.00854472i
$636$	1.89139	+	0.347606i	0.0749985	+	0.0137835i
$637$	−18.3405	−	9.34497i	−0.726679	−	0.370261i
$638$	8.83215	+	3.78672i	0.349668	+	0.149918i
$639$	0.406036	−	1.24965i	0.0160625	−	0.0494354i
$640$	2.70008	+	25.1537i	0.106730	+	0.994288i
$641$	−5.97115	−	18.3773i	−0.235846	−	0.725860i	−0.997008	−	0.0772982i	$-0.975371\pi$
$641$	−5.97115	−	18.3773i	−0.235846	−	0.725860i	0.761162	−	0.648562i	$-0.224629\pi$
$642$	−0.893114	+	9.80059i	−0.0352484	+	0.386798i
$643$	32.4834	−	32.4834i	1.28102	−	1.28102i	0.340934	−	0.940087i	$-0.389257\pi$
$643$	32.4834	−	32.4834i	1.28102	−	1.28102i	0.940087	−	0.340934i	$-0.110743\pi$
$644$	−39.3663	−	41.3586i	−1.55125	−	1.62976i
$645$	−19.8606	+	9.08249i	−0.782011	+	0.357623i
$646$	31.4537	−	49.9343i	1.23753	−	1.96464i
$647$	7.74473	+	48.8983i	0.304477	+	1.92239i	0.379466	+	0.925206i	$0.376108\pi$
$647$	7.74473	+	48.8983i	0.304477	+	1.92239i	−0.0749889	+	0.997184i	$0.523892\pi$
$648$	2.21725	−	1.75607i	0.0871020	−	0.0689849i
$649$			0.674201i			0.0264647i
$650$	14.5125	+	20.7696i	0.569227	+	0.814652i
$651$			15.3172i			0.600328i
$652$	21.5830	−	14.8815i	0.845256	−	0.582803i
$653$	4.30130	+	27.1573i	0.168323	+	1.06275i	0.916730	+	0.399508i	$0.130819\pi$
$653$	4.30130	+	27.1573i	0.168323	+	1.06275i	−0.748407	+	0.663240i	$0.769181\pi$
$654$	1.12676	+	0.709748i	0.0440598	+	0.0277533i
$655$	−3.47559	−	30.1532i	−0.135803	−	1.17818i
$656$	15.4556	−	19.2040i	0.603440	−	0.749788i
$657$	0.580278	−	0.580278i	0.0226388	−	0.0226388i
$658$	3.64683	+	0.332330i	0.142168	+	0.0129556i
$659$	−9.63281	−	29.6468i	−0.375241	−	1.15487i	−0.943316	−	0.331897i	$-0.892312\pi$
$659$	−9.63281	−	29.6468i	−0.375241	−	1.15487i	0.568075	−	0.822977i	$-0.307688\pi$
$660$	−7.30438	+	3.12483i	−0.284323	+	0.121634i
$661$	−4.52162	+	13.9161i	−0.175871	+	0.541275i	−0.999672	−	0.0256039i	$-0.991849\pi$
$661$	−4.52162	+	13.9161i	−0.175871	+	0.541275i	0.823801	+	0.566879i	$0.191849\pi$
$662$	4.09658	−	9.55486i	0.159218	−	0.371360i
$663$	16.6374	+	8.47716i	0.646142	+	0.329226i
$664$	0.229294	−	1.97548i	0.00889833	−	0.0766633i
$665$	−50.0802	−	39.7284i	−1.94203	−	1.54060i
$666$	−2.39974	−	6.00187i	−0.0929880	−	0.232568i
$667$	−30.2123	−	4.78516i	−1.16983	−	0.185282i
$668$	−12.7908	+	16.7213i	−0.494891	+	0.646968i
$669$	3.89379	+	5.35934i	0.150543	+	0.207204i
$670$	−5.75991	+	42.9868i	−0.222525	+	1.66073i
$671$	−10.6192	+	14.6160i	−0.409949	+	0.564246i
$672$	17.8365	−	9.47007i	0.688059	−	0.365316i
$673$	−16.1307	+	8.21898i	−0.621791	+	0.316818i	−0.736353	−	0.676598i	$-0.763454\pi$
$673$	−16.1307	+	8.21898i	−0.621791	+	0.316818i	0.114562	+	0.993416i	$0.463454\pi$
$674$	−0.779880	−	11.7631i	−0.0300399	−	0.453097i
$675$	4.24718	+	2.63846i	0.163474	+	0.101554i
$676$	−0.317611	+	0.0423005i	−0.0122158	+	0.00162694i
$677$	5.17897	+	10.1643i	0.199044	+	0.390646i	0.968856	−	0.247625i	$-0.0796500\pi$
$677$	5.17897	+	10.1643i	0.199044	+	0.390646i	−0.769812	+	0.638271i	$0.779650\pi$
$678$	−8.08432	+	1.83569i	−0.310476	+	0.0704992i
$679$	−24.6548	−	17.9128i	−0.946165	−	0.687429i
$680$	−19.3931	+	26.6478i	−0.743693	+	1.02190i
$681$	5.18818	−	3.76943i	0.198812	−	0.144445i
$682$	7.10129	−	8.10977i	0.271922	−	0.310539i
$683$	4.41481	−	27.8740i	0.168928	−	1.06657i	−0.746882	−	0.664957i	$-0.768450\pi$
$683$	4.41481	−	27.8740i	0.168928	−	1.06657i	0.915810	−	0.401612i	$-0.131550\pi$
$684$	−6.91678	−	14.4454i	−0.264470	−	0.552332i
$685$	23.8944	+	35.9978i	0.912957	+	1.37540i
$686$	6.14473	+	1.55564i	0.234607	+	0.0593947i
$687$	−5.22643	+	10.2575i	−0.199401	+	0.391346i
$688$	−38.2371	−	8.00738i	−1.45778	−	0.305278i
$689$	3.27680	+	1.06470i	0.124836	+	0.0405617i
$690$	20.0985	−	15.3489i	0.765138	−	0.584321i
$691$	−18.6645	+	6.06447i	−0.710032	+	0.230703i	−0.641696	−	0.766959i	$-0.721769\pi$
$691$	−18.6645	+	6.06447i	−0.710032	+	0.230703i	−0.0683357	+	0.997662i	$0.521769\pi$
$692$	0.916374	−	37.1294i	0.0348353	−	1.41145i
$693$	4.48446	+	4.48446i	0.170351	+	0.170351i
$694$	3.70583	−	3.08683i	0.140672	−	0.117174i
$695$	21.7217	−	19.9568i	0.823953	−	0.757004i
$696$	4.50718	−	9.83514i	0.170844	−	0.372800i
$697$	31.7189	−	5.02378i	1.20144	−	0.190289i
$698$	−6.57647	+	3.91929i	−0.248923	+	0.148347i
$699$	−28.6706			−1.08442
$700$	26.4197	+	24.0093i	0.998572	+	0.907468i
$701$	−17.2805			−0.652676			−0.326338	−	0.945253i	$-0.605815\pi$
$701$	−17.2805			−0.652676			−0.326338	+	0.945253i	$0.605815\pi$
$702$	4.35309	−	2.59425i	0.164297	−	0.0979138i
$703$	−36.1508	+	5.72573i	−1.36345	+	0.215950i
$704$	−13.8341	−	3.25531i	−0.521393	−	0.122689i
$705$	−0.321266	+	1.58975i	−0.0120996	+	0.0598733i
$706$	−14.5952	+	12.1572i	−0.549296	+	0.457544i
$707$	17.5211	+	17.5211i	0.658948	+	0.658948i
$708$	0.758793	+	0.0187274i	0.0285172	+	0.000703820i
$709$	40.5291	−	13.1687i	1.52210	−	0.494561i	0.575730	−	0.817640i	$-0.304718\pi$
$709$	40.5291	−	13.1687i	1.52210	−	0.494561i	0.946372	+	0.323078i	$0.104718\pi$
$710$	3.41891	+	2.36135i	0.128310	+	0.0886198i
$711$	−6.10652	−	1.98413i	−0.229012	−	0.0744107i
$712$	−14.1150	−	3.94648i	−0.528983	−	0.147901i
$713$	−15.5775	+	30.5726i	−0.583382	+	1.14495i
$714$	25.5042	+	6.45682i	0.954470	+	0.241640i
$715$	−13.7113	+	3.82187i	−0.512775	+	0.142930i
$716$	18.7903	−	8.99724i	0.702227	−	0.336243i
$717$	−0.0815630	+	0.514969i	−0.00304603	+	0.0192319i
$718$	2.08285	−	2.37865i	0.0777314	−	0.0887703i
$719$	31.8154	−	23.1153i	1.18652	−	0.862054i	0.193624	−	0.981076i	$-0.437976\pi$
$719$	31.8154	−	23.1153i	1.18652	−	0.862054i	0.992892	+	0.119022i	$0.0379759\pi$
$720$	3.31401	+	8.30767i	0.123506	+	0.309608i
$721$	43.5568	+	31.6458i	1.62214	+	1.17855i
$722$	−62.2358	+	14.1317i	−2.31618	+	0.525929i
$723$	2.81180	+	5.51847i	0.104572	+	0.205234i
$724$	3.82503	+	28.7200i	0.142156	+	1.06737i
$725$	19.0565	+	1.61686i	0.707741	+	0.0600488i
$726$	0.733855	+	11.0689i	0.0272359	+	0.410805i
$727$	18.3617	−	9.35574i	0.680997	−	0.346985i	−0.0790342	−	0.996872i	$-0.525184\pi$
$727$	18.3617	−	9.35574i	0.680997	−	0.346985i	0.760031	+	0.649887i	$0.225184\pi$
$728$	33.9167	−	12.5996i	1.25704	−	0.466971i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	1.23302	+	2.28344i	0.0456361	+	0.0845141i
$731$	−29.9150	−	41.1744i	−1.10644	−	1.52289i
$732$	16.1550	+	12.3576i	0.597104	+	0.456749i
$733$	−47.2049	−	7.47652i	−1.74355	−	0.276151i	−0.798244	−	0.602334i	$-0.794238\pi$
$733$	−47.2049	−	7.47652i	−1.74355	−	0.276151i	−0.945307	+	0.326182i	$0.894238\pi$
$734$	−16.3383	−	40.8629i	−0.603057	−	1.50828i
$735$	4.48266	−	12.0375i	0.165345	−	0.444011i
$736$	45.2321	−	0.762277i	1.66728	−	0.0280979i
$737$	−21.7092	−	11.0614i	−0.799669	−	0.407452i
$738$	3.43433	−	8.01023i	0.126420	−	0.294861i
$739$	1.15571	−	3.55691i	0.0425135	−	0.130843i	−0.927547	−	0.373707i	$-0.878087\pi$
$739$	1.15571	−	3.55691i	0.0425135	−	0.130843i	0.970060	+	0.242864i	$0.0780867\pi$
$740$	20.3576	−	1.83884i	0.748360	−	0.0675971i
$741$	−8.86715	−	27.2903i	−0.325743	−	1.00253i
$742$	4.83443	+	0.440555i	0.177477	+	0.0161733i
$743$	−2.21502	+	2.21502i	−0.0812612	+	0.0812612i	−0.746569	−	0.665308i	$-0.768300\pi$
$743$	−2.21502	+	2.21502i	−0.0812612	+	0.0812612i	0.665308	+	0.746569i	$0.268300\pi$
$744$	−8.93005	−	8.21756i	−0.327391	−	0.301270i
$745$	11.8414	−	20.9938i	0.433836	−	0.769154i
$746$	−1.17835	−	0.742244i	−0.0431424	−	0.0271755i
$747$	−0.109993	−	0.694468i	−0.00402443	−	0.0254093i
$748$	−10.5098	−	15.2427i	−0.384277	−	0.557329i
$749$			24.8425i			0.907723i
$750$	−11.8386	+	10.4808i	−0.432286	+	0.382704i
$751$			6.92884i			0.252837i	0.991977	+	0.126419i	$0.0403482\pi$
$751$			6.92884i			0.252837i	−0.991977	+	0.126419i	$0.959652\pi$
$752$	−2.15024	+	1.94784i	−0.0784113	+	0.0710302i
$753$	−2.11286	−	13.3401i	−0.0769968	−	0.486139i
$754$	10.3308	−	16.4007i	0.376226	−	0.597277i
$755$	5.86031	−	10.3898i	0.213278	−	0.378125i
$756$	5.17169	−	4.92256i	0.188093	−	0.179032i
$757$	−22.6524	+	22.6524i	−0.823315	+	0.823315i	−0.986582	−	0.163267i	$-0.947797\pi$
$757$	−22.6524	+	22.6524i	−0.823315	+	0.823315i	0.163267	+	0.986582i	$0.447797\pi$
$758$	−0.591569	+	6.49159i	−0.0214868	+	0.235785i
$759$	4.39015	+	13.5115i	0.159352	+	0.490436i
$760$	50.0296	−	7.88314i	1.81476	−	0.285952i
$761$	0.235070	−	0.723470i	0.00852126	−	0.0262258i	−0.946705	−	0.322100i	$-0.895611\pi$
$761$	0.235070	−	0.723470i	0.00852126	−	0.0262258i	0.955227	+	0.295875i	$0.0956111\pi$
$762$	2.95828	+	1.26834i	0.107167	+	0.0459473i
$763$	2.99517	+	1.52612i	0.108433	+	0.0552491i
$764$	−4.85140	+	26.3974i	−0.175518	+	0.955025i
$765$	−4.06638	+	10.9197i	−0.147020	+	0.394802i
$766$	0.00542958	−	0.00217092i	0.000196179	−	7.84385e-5i
$767$	1.34315	+	0.212734i	0.0484984	+	0.00768139i
$768$	−4.04803	+	15.4795i	−0.146071	+	0.558567i
$769$	−30.0152	−	41.3124i	−1.08238	−	1.48976i	−0.856878	−	0.515520i	$-0.827599\pi$
$769$	−30.0152	−	41.3124i	−1.08238	−	1.48976i	−0.225499	−	0.974243i	$-0.572401\pi$
$770$	−17.6467	+	9.52892i	−0.635944	+	0.343399i
$771$	16.0976	−	22.1564i	0.579741	−	0.797944i
$772$	5.18278	−	1.54370i	0.186532	−	0.0555588i
$773$	17.0506	−	8.68774i	0.613269	−	0.312476i	−0.119625	−	0.992819i	$-0.538169\pi$
$773$	17.0506	−	8.68774i	0.613269	−	0.312476i	0.732894	+	0.680343i	$0.238169\pi$
$774$	−13.7819	+	0.913722i	−0.495378	+	0.0328431i
$775$	8.33052	−	19.7695i	0.299241	−	0.710142i
$776$	23.6704	−	4.76389i	0.849718	−	0.171014i
$777$	−7.40771	−	14.5384i	−0.265750	−	0.521564i
$778$	−10.2674	−	45.2173i	−0.368103	−	1.62112i
$779$	−39.9258	−	29.0078i	−1.43049	−	1.03931i
$780$	3.92053	+	15.5379i	0.140378	+	0.556345i
$781$	−1.88844	+	1.37203i	−0.0675738	+	0.0490952i
$782$	44.3389	+	38.8252i	1.58555	+	1.38839i
$783$	0.598361	−	3.77790i	0.0213837	−	0.135011i
$784$	19.2332	−	12.5726i	0.686901	−	0.449023i
$785$	−8.25515	+	2.30102i	−0.294639	+	0.0821269i
$786$	4.71136	−	18.6097i	0.168049	−	0.663786i
$787$	−9.10516	+	17.8699i	−0.324564	+	0.636993i	−0.994419	−	0.105499i	$-0.966356\pi$
$787$	−9.10516	+	17.8699i	−0.324564	+	0.636993i	0.669856	+	0.742491i	$0.266356\pi$
$788$	0.398987	−	1.13211i	0.0142133	−	0.0403299i
$789$	−16.6939	−	5.42417i	−0.594318	−	0.193106i
$790$	11.5389	−	16.7068i	0.410536	−	0.594401i
$791$	−19.9028	+	6.46680i	−0.707661	+	0.229933i
$792$	−5.02035	+	0.208598i	−0.178390	+	0.00741219i
$793$	25.7675	+	25.7675i	0.915031	+	0.915031i
$794$	26.6617	+	32.0082i	0.946189	+	1.13593i
$795$	−0.425888	+	2.10745i	−0.0151047	+	0.0747436i
$796$	−12.8315	+	23.7176i	−0.454799	+	0.840650i
$797$	−29.4775	+	4.66878i	−1.04415	+	0.165377i	−0.654868	−	0.755743i	$-0.727276\pi$
$797$	−29.4775	+	4.66878i	−1.04415	+	0.165377i	−0.389279	+	0.921120i	$0.627276\pi$
$798$	−20.6975	−	34.7299i	−0.732683	−	1.22942i
$799$	−3.77972			−0.133717
$800$	−28.1716	+	2.52208i	−0.996017	+	0.0891690i
$801$	−5.18180			−0.183090
$802$	−6.97354	−	11.7014i	−0.246244	−	0.413192i
$803$	−1.43991	+	0.228059i	−0.0508133	+	0.00804803i
$804$	−13.0523	+	24.1258i	−0.460319	+	0.850852i
$805$	47.0098	−	43.1901i	1.65688	−	1.52225i
$806$	−13.9157	−	16.7062i	−0.490158	−	0.588450i
$807$	11.7282	+	11.7282i	0.412851	+	0.412851i
$808$	−19.6148	+	0.815004i	−0.690047	+	0.0286717i
$809$	−36.0573	+	11.7157i	−1.26771	+	0.411903i	−0.864235	−	0.503088i	$-0.832197\pi$
$809$	−36.0573	+	11.7157i	−1.26771	+	0.411903i	−0.403473	+	0.914991i	$0.632197\pi$
$810$	1.91930	+	2.51322i	0.0674373	+	0.0883057i
$811$	−24.7577	−	8.04427i	−0.869361	−	0.282473i	−0.159828	−	0.987145i	$-0.551094\pi$
$811$	−24.7577	−	8.04427i	−0.869361	−	0.282473i	−0.709533	+	0.704672i	$0.751094\pi$
$812$	9.07754	−	25.7573i	0.318559	−	0.903902i
$813$	−0.341108	+	0.669462i	−0.0119632	+	0.0234791i
$814$	−2.81820	+	11.1318i	−0.0987778	+	0.390169i
$815$	16.2096	+	24.4204i	0.567797	+	0.855408i
$816$	−17.4472	+	11.4051i	−0.610773	+	0.399258i
$817$	−12.2349	+	77.2480i	−0.428044	+	2.70257i
$818$	14.5058	+	12.7020i	0.507185	+	0.444115i
$819$	10.3490	−	7.51898i	0.361623	−	0.262735i
$820$	21.1624	+	17.6561i	0.739024	+	0.616577i
$821$	36.7692	+	26.7144i	1.28325	+	0.932338i	0.999646	−	0.0266020i	$-0.00846867\pi$
$821$	36.7692	+	26.7144i	1.28325	+	0.932338i	0.283608	+	0.958940i	$0.408469\pi$
$822$	6.05083	+	26.6477i	0.211047	+	0.929445i
$823$	11.6738	+	22.9111i	0.406923	+	0.798632i	0.999979	−	0.00652958i	$-0.00207844\pi$
$823$	11.6738	+	22.9111i	0.406923	+	0.798632i	−0.593055	+	0.805162i	$0.702078\pi$
$824$	−41.8176	+	8.41619i	−1.45679	+	0.293192i
$825$	−3.34903	−	8.22693i	−0.116598	−	0.286425i
$826$	1.91183	−	0.126752i	0.0665212	−	0.00441028i
$827$	−30.8433	+	15.7154i	−1.07253	+	0.546480i	−0.898820	−	0.438318i	$-0.855574\pi$
$827$	−30.8433	+	15.7154i	−1.07253	+	0.546480i	−0.173707	+	0.984797i	$0.555574\pi$
$828$	15.3287	−	4.56567i	0.532710	−	0.158668i
$829$	−1.77914	+	2.44877i	−0.0617919	+	0.0850493i	−0.838795	−	0.544448i	$-0.816739\pi$
$829$	−1.77914	+	2.44877i	−0.0617919	+	0.0850493i	0.777003	+	0.629497i	$0.216739\pi$
$830$	2.20378	+	0.295290i	0.0764944	+	0.0102497i
$831$	−10.4449	−	14.3762i	−0.362331	−	0.498706i
$832$	−10.8504	+	26.5333i	−0.376170	+	0.919876i
$833$	29.5663	+	4.68284i	1.02441	+	0.162251i
$834$	17.3226	−	6.92612i	0.599832	−	0.239832i
$835$	−18.4398	−	14.6282i	−0.638134	−	0.506230i
$836$	−5.14291	+	27.9836i	−0.177871	+	0.967832i
$837$	−3.82295	−	1.94789i	−0.132141	−	0.0673290i
$838$	23.8070	+	10.2071i	0.822400	+	0.352598i
$839$	−1.63366	+	5.02788i	−0.0564001	+	0.173582i	−0.975288	−	0.220937i	$-0.929089\pi$
$839$	−1.63366	+	5.02788i	−0.0564001	+	0.173582i	0.918888	+	0.394518i	$0.129089\pi$
$840$	10.2343	+	20.1256i	0.353118	+	0.694398i
$841$	4.44040	+	13.6661i	0.153117	+	0.471246i
$842$	−0.974421	+	10.6928i	−0.0335808	+	0.368499i
$843$	1.22733	−	1.22733i	0.0422716	−	0.0422716i
$844$	−28.4512	+	27.0806i	−0.979330	+	0.932154i
$845$	−0.0410203	−	0.355880i	−0.00141114	−	0.0122426i
$846$	−0.546712	+	0.867933i	−0.0187964	+	0.0298401i
$847$	4.38062	+	27.6581i	0.150520	+	0.950344i
$848$	−2.85048	+	2.58215i	−0.0978858	+	0.0886716i
$849$			2.11632i			0.0726319i
$850$	−29.4059	−	22.2045i	−1.00861	−	0.761609i
$851$		−	36.5518i		−	1.25298i
$852$	1.49173	+	2.16350i	0.0511058	+	0.0741202i
$853$	−6.49369	−	40.9996i	−0.222340	−	1.40380i	−0.806056	−	0.591840i	$-0.798402\pi$
$853$	−6.49369	−	40.9996i	−0.222340	−	1.40380i	0.583716	−	0.811958i	$-0.301598\pi$
$854$	43.4432	+	27.3649i	1.48659	+	0.936409i
$855$	16.2843	−	7.44702i	0.556913	−	0.254683i
$856$	−14.4833	−	13.3278i	−0.495030	−	0.455534i
$857$	0.991705	−	0.991705i	0.0338760	−	0.0338760i	−0.689966	−	0.723842i	$-0.742374\pi$
$857$	0.991705	−	0.991705i	0.0338760	−	0.0338760i	0.723842	+	0.689966i	$0.242374\pi$
$858$	−8.96524	−	0.816990i	−0.306068	−	0.0278916i
$859$	−9.70831	−	29.8791i	−0.331243	−	1.01946i	−0.968543	−	0.248846i	$-0.919949\pi$
$859$	−9.70831	−	29.8791i	−0.331243	−	1.01946i	0.637300	−	0.770616i	$-0.280051\pi$
$860$	9.70546	−	42.5858i	0.330953	−	1.45216i
$861$	6.79856	−	20.9238i	0.231694	−	0.713082i
$862$	3.03429	−	7.07717i	0.103348	−	0.241049i
$863$	−38.7182	−	19.7279i	−1.31798	−	0.671546i	−0.353436	−	0.935459i	$-0.614987\pi$
$863$	−38.7182	−	19.7279i	−1.31798	−	0.671546i	−0.964546	+	0.263913i	$0.914987\pi$
$864$	0.0953190	+	5.65605i	0.00324282	+	0.192423i
$865$	41.4874	+	1.75686i	1.41061	+	0.0597350i
$866$	−5.85961	−	14.6552i	−0.199118	−	0.498004i
$867$	−10.0299	−	1.58859i	−0.340635	−	0.0539513i
$868$	−24.3319	−	18.6125i	−0.825880	−	0.631748i
$869$	6.70456	+	9.22803i	0.227436	+	0.313039i
$870$	10.9054	+	5.23242i	0.369727	+	0.177396i
$871$	−28.8866	+	39.7590i	−0.978786	+	1.34718i
$872$	−2.49662	+	0.927459i	−0.0845463	+	0.0314077i
$873$	7.60613	−	3.87551i	0.257428	−	0.131166i
$874$	−5.99136	−	90.3688i	−0.202661	−	3.05677i
$875$	−27.3603	+	29.0599i	−0.924946	+	0.982404i
$876$	0.216677	+	1.62691i	0.00732084	+	0.0549682i
$877$	−4.00172	−	7.85382i	−0.135129	−	0.265205i	0.813520	−	0.581537i	$-0.197548\pi$
$877$	−4.00172	−	7.85382i	−0.135129	−	0.265205i	−0.948648	+	0.316332i	$0.897548\pi$
$878$	−42.0776	+	9.55448i	−1.42005	+	0.322448i
$879$	5.62039	+	4.08345i	0.189571	+	0.137731i
$880$	3.91190	−	15.4004i	0.131870	−	0.519147i
$881$	3.68981	−	2.68080i	0.124313	−	0.0903185i	−0.523892	−	0.851785i	$-0.675520\pi$
$881$	3.68981	−	2.68080i	0.124313	−	0.0903185i	0.648204	+	0.761466i	$0.275520\pi$
$882$	5.35190	−	6.11194i	0.180208	−	0.205800i
$883$	−0.499287	+	3.15237i	−0.0168023	+	0.106086i	−0.994664	−	0.103166i	$-0.967103\pi$
$883$	−0.499287	+	3.15237i	−0.0168023	+	0.106086i	0.977862	+	0.209252i	$0.0671028\pi$
$884$	−33.6829	+	16.1282i	−1.13288	+	0.542449i
$885$	−0.0359040	+	0.847855i	−0.00120690	+	0.0285003i
$886$	−44.8946	−	11.3658i	−1.50826	−	0.381843i
$887$	8.83178	−	17.3333i	0.296542	−	0.581997i	−0.693877	−	0.720094i	$-0.744099\pi$
$887$	8.83178	−	17.3333i	0.296542	−	0.581997i	0.990419	+	0.138097i	$0.0440987\pi$
$888$	12.4502	+	3.48101i	0.417801	+	0.116815i
$889$	7.72744	+	2.51080i	0.259170	+	0.0842095i
$890$	4.69007	−	15.7008i	0.157212	−	0.526291i
$891$	−1.68955	+	0.548967i	−0.0566019	+	0.0183911i
$892$	−13.2450	−	0.326894i	−0.443475	−	0.0109452i
$893$	4.10716	+	4.10716i	0.137441	+	0.137441i
$894$	11.7130	−	9.75651i	0.391741	−	0.326307i
$895$	9.68697	+	21.1824i	0.323800	+	0.708051i
$896$	−6.63022	+	39.8414i	−0.221500	+	1.33101i
$897$	28.3030	−	4.48275i	0.945009	−	0.149675i
$898$	−36.7486	+	21.9006i	−1.22632	+	0.730832i
$899$	−16.4115			−0.547355
$900$	−9.35219	+	3.54071i	−0.311740	+	0.118024i
$901$	−5.01059			−0.166927
$902$	−13.3001	+	7.92630i	−0.442846	+	0.263917i
$903$	−34.4371	+	5.45430i	−1.14599	+	0.181508i
$904$	6.90748	−	15.0728i	0.229739	−	0.501315i
$905$	−32.1804	+	3.70926i	−1.06971	+	0.123300i
$906$	5.79676	−	4.82849i	0.192584	−	0.160416i
$907$	−8.53222	−	8.53222i	−0.283308	−	0.283308i	0.551119	−	0.834427i	$-0.314201\pi$
$907$	−8.53222	−	8.53222i	−0.283308	−	0.283308i	−0.834427	+	0.551119i	$0.814201\pi$
$908$	−0.316454	+	12.8220i	−0.0105019	+	0.425512i
$909$	−6.60116	+	2.14485i	−0.218947	+	0.0711401i
$910$	13.4155	+	38.1627i	0.444718	+	1.26508i
$911$	11.9166	+	3.87193i	0.394814	+	0.128283i	0.499694	−	0.866202i	$-0.333446\pi$
$911$	11.9166	+	3.87193i	0.394814	+	0.128283i	−0.104880	+	0.994485i	$0.533446\pi$
$912$	31.3518	+	6.56550i	1.03816	+	0.217406i
$913$	−0.567078	+	1.11295i	−0.0187676	+	0.0368334i
$914$	−8.75039	−	2.21531i	−0.289437	−	0.0732759i
$915$	−14.1327	+	17.8152i	−0.467214	+	0.588952i
$916$	−9.94352	−	20.7666i	−0.328543	−	0.686147i
$917$	7.58068	−	47.8625i	0.250336	−	1.58056i
$918$	−4.85490	+	5.54436i	−0.160236	+	0.182991i
$919$	14.7236	−	10.6973i	0.485687	−	0.352873i	−0.317836	−	0.948146i	$-0.602956\pi$
$919$	14.7236	−	10.6973i	0.485687	−	0.352873i	0.803523	+	0.595273i	$0.202956\pi$
$920$	−0.0402097	+	50.5782i	−0.00132568	+	1.66751i
$921$	−18.6523	−	13.5517i	−0.614613	−	0.446542i
$922$	23.9106	−	5.42933i	0.787454	−	0.178805i
$923$	2.13751	+	4.19510i	0.0703570	+	0.138083i
$924$	−12.5730	+	1.67451i	−0.413620	+	0.0550872i
$925$	1.65396	+	22.7932i	0.0543817	+	0.749436i
$926$	0.383782	+	5.78866i	0.0126118	+	0.190227i
$927$	−13.4375	+	6.84673i	−0.441344	+	0.224876i
$928$	10.1467	+	19.1108i	0.333080	+	0.627344i
$929$	1.07713	−	1.48254i	0.0353393	−	0.0486404i	−0.790982	−	0.611840i	$-0.790430\pi$
$929$	1.07713	−	1.48254i	0.0353393	−	0.0486404i	0.826321	+	0.563199i	$0.190430\pi$
$930$	9.36225	−	9.82043i	0.307000	−	0.322024i
$931$	−27.0392	−	37.2162i	−0.886174	−	1.21971i
$932$	34.8386	−	45.5442i	1.14118	−	1.49185i
$933$	−17.0016	−	2.69278i	−0.556606	−	0.0881578i
$934$	6.35190	+	15.8864i	0.207840	+	0.519820i
$935$	17.2466	−	11.4478i	0.564023	−	0.374383i
$936$	−1.16853	+	10.0674i	−0.0381945	+	0.329064i
$937$	19.6122	+	9.99291i	0.640702	+	0.326454i	0.743983	−	0.668198i	$-0.232934\pi$
$937$	19.6122	+	9.99291i	0.640702	+	0.326454i	−0.103281	+	0.994652i	$0.532934\pi$
$938$	−27.2854	+	63.6404i	−0.890899	+	2.07793i
$939$	4.11174	−	12.6546i	0.134182	−	0.412968i
$940$	−2.13499	−	2.44210i	−0.0696356	−	0.0796525i
$941$	−11.6466	−	35.8445i	−0.379668	−	1.16850i	−0.940275	−	0.340415i	$-0.889432\pi$
$941$	−11.6466	−	35.8445i	−0.379668	−	1.16850i	0.560608	−	0.828082i	$-0.310568\pi$
$942$	−5.39768	−	0.491883i	−0.175866	−	0.0160264i
$943$	34.8491	−	34.8491i	1.13484	−	1.13484i
$944$	−0.951785	+	1.18261i	−0.0309780	+	0.0384908i
$945$	5.40071	+	5.87834i	0.175685	+	0.191222i
$946$	20.7616	+	13.0778i	0.675017	+	0.425194i
$947$	−4.28065	−	27.0269i	−0.139102	−	0.878258i	−0.954251	−	0.299006i	$-0.903345\pi$
$947$	−4.28065	−	27.0269i	−0.139102	−	0.878258i	0.815149	−	0.579252i	$-0.196655\pi$
$948$	10.5721	−	7.28945i	0.343366	−	0.236750i
$949$			2.94056i			0.0954547i
$950$	7.82528	+	56.0816i	0.253886	+	1.81953i
$951$		−	10.0509i		−	0.325924i
$952$	−41.2479	+	32.6684i	−1.33685	+	1.05879i
$953$	−8.22502	−	51.9308i	−0.266435	−	1.68220i	−0.650979	−	0.759096i	$-0.725641\pi$
$953$	−8.22502	−	51.9308i	−0.266435	−	1.68220i	0.384544	−	0.923107i	$-0.374359\pi$
$954$	−0.724751	+	1.15058i	−0.0234647	+	0.0372513i
$955$	−29.4129	−	5.94395i	−0.951779	−	0.192342i
$956$	−0.718937	−	0.755322i	−0.0232521	−	0.0244289i
$957$	−4.80485	+	4.80485i	−0.155319	+	0.155319i
$958$	1.85783	−	20.3869i	0.0600237	−	0.658670i
$959$	21.3160	+	65.6039i	0.688329	+	2.11846i
$960$	−17.2240	−	4.83050i	−0.555902	−	0.155904i
$961$	3.89076	−	11.9745i	0.125508	−	0.386275i
$962$	21.2876	+	9.12691i	0.686340	+	0.294263i
$963$	−6.20032	−	3.15922i	−0.199802	−	0.101804i
$964$	−12.1830	−	2.23903i	−0.392388	−	0.0721144i
$965$	1.62339	+	5.82408i	0.0522588	+	0.187484i
$966$	37.4892	−	14.9894i	1.20619	−	0.482275i
$967$	−45.3669	−	7.18541i	−1.45890	−	0.231067i	−0.623981	−	0.781440i	$-0.714486\pi$
$967$	−45.3669	−	7.18541i	−1.45890	−	0.231067i	−0.834919	+	0.550372i	$0.814486\pi$
$968$	−18.4751	−	12.2844i	−0.593811	−	0.394837i
$969$	24.5282	+	33.7602i	0.787960	+	1.08453i
$970$	4.85839	+	26.5542i	0.155994	+	0.852603i
$971$	−3.78538	+	5.21013i	−0.121479	+	0.167201i	−0.865425	−	0.501038i	$-0.832952\pi$
$971$	−3.78538	+	5.21013i	−0.121479	+	0.167201i	0.743947	+	0.668239i	$0.232952\pi$
$972$	0.570915	+	1.91678i	0.0183121	+	0.0614808i
$973$	41.9608	−	21.3801i	1.34520	−	0.685415i
$974$	−22.9578	+	1.52208i	−0.735616	+	0.0487706i
$975$	−17.4465	+	4.07608i	−0.558735	+	0.130539i
$976$	−39.2609	+	10.6466i	−1.25671	+	0.340790i
$977$	22.5496	+	44.2561i	0.721426	+	1.41588i	0.901745	+	0.432269i	$0.142287\pi$
$977$	22.5496	+	44.2561i	0.721426	+	1.41588i	−0.180319	+	0.983608i	$0.557713\pi$
$978$	4.10480	+	18.0774i	0.131257	+	0.578052i
$979$	7.44736	+	5.41082i	0.238019	+	0.172931i
$980$	13.6750	+	21.7481i	0.436833	+	0.694717i
$981$	−0.761793	+	0.553475i	−0.0243222	+	0.0176711i
$982$	6.00891	+	5.26168i	0.191752	+	0.167907i
$983$	−3.83856	+	24.2357i	−0.122431	+	0.773000i	0.847710	+	0.530460i	$0.177981\pi$
$983$	−3.83856	+	24.2357i	−0.122431	+	0.773000i	−0.970141	+	0.242540i	$0.922019\pi$
$984$	8.55137	+	15.1891i	0.272608	+	0.484210i
$985$	1.25767	+	0.468345i	0.0400728	+	0.0149227i
$986$	−6.91811	+	27.3263i	−0.220318	+	0.870246i
$987$	−1.17555	+	2.30716i	−0.0374183	+	0.0734376i
$988$	54.1264	+	19.0756i	1.72199	+	0.606875i
$989$	−74.2822	−	24.1357i	−2.36204	−	0.767472i
$990$	−0.134143	−	5.61617i	−0.00426333	−	0.178493i
$991$	25.5462	−	8.30045i	0.811501	−	0.263673i	0.126267	−	0.991996i	$-0.459700\pi$
$991$	25.5462	−	8.30045i	0.811501	−	0.263673i	0.685233	+	0.728324i	$0.259700\pi$
$992$	23.9051	−	4.20027i	0.758987	−	0.133359i
$993$	5.19801	+	5.19801i	0.164954	+	0.164954i
$994$	4.24571	+	5.09711i	0.134666	+	0.161671i
$995$	−26.2599	−	14.8117i	−0.832494	−	0.469562i
$996$	1.23684	+	0.669145i	0.0391909	+	0.0212027i
$997$	−41.1715	+	6.52093i	−1.30391	+	0.206520i	−0.769470	−	0.638683i	$-0.779479\pi$
$997$	−41.1715	+	6.52093i	−1.30391	+	0.206520i	−0.534445	+	0.845203i	$0.679479\pi$
$998$	−30.4326	−	51.0652i	−0.963328	−	1.61644i
$999$	4.57063			0.144608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.9	yes	240
3.2	odd	2		900.2.bj.f.703.22		240
4.3	odd	2	inner	300.2.w.a.103.12	yes	240
12.11	even	2		900.2.bj.f.703.19		240
25.17	odd	20	inner	300.2.w.a.67.12	yes	240
75.17	even	20		900.2.bj.f.667.19		240
100.67	even	20	inner	300.2.w.a.67.9	✓	240
300.167	odd	20		900.2.bj.f.667.22		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.9	✓	240	100.67	even	20	inner
300.2.w.a.67.12	yes	240	25.17	odd	20	inner
300.2.w.a.103.9	yes	240	1.1	even	1	trivial
300.2.w.a.103.12	yes	240	4.3	odd	2	inner
900.2.bj.f.667.19		240	75.17	even	20
900.2.bj.f.667.22		240	300.167	odd	20
900.2.bj.f.703.19		240	12.11	even	2
900.2.bj.f.703.22		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.723992 - 1.21484i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-0.951672 + 1.75907i) q^{4} +(-1.94762 - 1.09854i) q^{5} +(-0.905121 - 1.08663i) q^{6} +(-2.52433 - 2.52433i) q^{7} +(2.82599 - 0.117421i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.723992 - 1.21484i) q^{2} +(0.987688 - 0.156434i) q^{3} +(-0.951672 + 1.75907i) q^{4} +(-1.94762 - 1.09854i) q^{5} +(-0.905121 - 1.08663i) q^{6} +(-2.52433 - 2.52433i) q^{7} +(2.82599 - 0.117421i) q^{8} +(0.951057 - 0.309017i) q^{9} +(0.0755097 + 3.16138i) q^{10} +(-1.68955 - 0.548967i) q^{11} +(-0.664777 + 1.88629i) q^{12} +(-1.62677 + 3.19271i) q^{13} +(-1.23906 + 4.89425i) q^{14} +(-2.09549 - 0.780339i) q^{15} +(-2.18864 - 3.34811i) q^{16} +(0.815187 - 5.14689i) q^{17} +(-1.06396 - 0.931656i) q^{18} +(-6.47859 + 4.70697i) q^{19} +(3.78590 - 2.38054i) q^{20} +(-2.88815 - 2.09836i) q^{21} +(0.556310 + 2.44998i) q^{22} +(-3.63061 - 7.12548i) q^{23} +(2.77283 - 0.558057i) q^{24} +(2.58643 + 4.27907i) q^{25} +(5.05640 - 0.335234i) q^{26} +(0.891007 - 0.453990i) q^{27} +(6.84281 - 2.03813i) q^{28} +(2.24828 - 3.09449i) q^{29} +(0.569128 + 3.11064i) q^{30} +(-2.52195 - 3.47117i) q^{31} +(-2.48286 + 5.08285i) q^{32} +(-1.75462 - 0.277905i) q^{33} +(-6.84283 + 2.73598i) q^{34} +(2.14336 + 7.68951i) q^{35} +(-0.361512 + 1.96706i) q^{36} +(4.07246 + 2.07502i) q^{37} +(10.4087 + 4.46264i) q^{38} +(-1.10729 + 3.40789i) q^{39} +(-5.63294 - 2.87577i) q^{40} +(1.90439 + 5.86111i) q^{41} +(-0.458179 + 5.02783i) q^{42} +(6.90605 - 6.90605i) q^{43} +(2.57356 - 2.44959i) q^{44} +(-2.19176 - 0.442926i) q^{45} +(-6.02779 + 9.56940i) q^{46} +(-0.113466 - 0.716398i) q^{47} +(-2.68545 - 2.96451i) q^{48} +5.74450i q^{49} +(3.32583 - 6.24010i) q^{50} -5.21104i q^{51} +(-4.06805 - 5.90001i) q^{52} +(-0.150417 - 0.949696i) q^{53} +(-1.19661 - 0.753745i) q^{54} +(2.68753 + 2.92521i) q^{55} +(-7.43014 - 6.83732i) q^{56} +(-5.66249 + 5.66249i) q^{57} +(-5.38704 - 0.490913i) q^{58} +(-0.117276 - 0.360938i) q^{59} +(3.36689 - 2.94348i) q^{60} +(3.14261 - 9.67197i) q^{61} +(-2.39104 + 5.57686i) q^{62} +(-3.18084 - 1.62072i) q^{63} +(7.97242 - 0.663661i) q^{64} +(6.67564 - 4.43111i) q^{65} +(0.932722 + 2.33279i) q^{66} +(13.5463 + 2.14552i) q^{67} +(8.27793 + 6.33212i) q^{68} +(-4.70059 - 6.46980i) q^{69} +(7.78975 - 8.17097i) q^{70} +(0.772327 - 1.06302i) q^{71} +(2.65139 - 0.984953i) q^{72} +(0.731193 - 0.372562i) q^{73} +(-0.427607 - 6.44968i) q^{74} +(3.22398 + 3.82178i) q^{75} +(-2.11439 - 15.8758i) q^{76} +(2.87920 + 5.65075i) q^{77} +(4.94171 - 1.12210i) q^{78} +(-5.19452 - 3.77404i) q^{79} +(0.584601 + 8.92515i) q^{80} +(0.809017 - 0.587785i) q^{81} +(5.74154 - 6.55692i) q^{82} +(0.109993 - 0.694468i) q^{83} +(6.43973 - 3.08349i) q^{84} +(-7.24173 + 9.12865i) q^{85} +(-13.3897 - 3.38982i) q^{86} +(1.73651 - 3.40809i) q^{87} +(-4.83910 - 1.35299i) q^{88} +(-4.92819 - 1.60126i) q^{89} +(1.04873 + 2.98331i) q^{90} +(12.1660 - 3.95296i) q^{91} +(15.9894 + 0.394626i) q^{92} +(-3.03391 - 3.03391i) q^{93} +(-0.788160 + 0.656510i) q^{94} +(17.7886 - 2.05039i) q^{95} +(-1.65716 + 5.40868i) q^{96} +(8.43146 - 1.33541i) q^{97} +(6.97865 - 4.15897i) q^{98} -1.77649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

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