LMFDB - Embedded newform 930.2.bs.a.107.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			107.11
Character	$\chi$	$=$	930.107
Dual form			930.2.bs.a.113.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(-0.827104 + 1.52181i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.791841 + 2.09117i) q^{5} +(1.73144 + 0.0460690i) q^{6} +(2.74072 - 2.21939i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-1.63180 - 2.51739i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.827104 + 1.52181i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.791841 + 2.09117i) q^{5} +(1.73144 + 0.0460690i) q^{6} +(2.74072 - 2.21939i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-1.63180 - 2.51739i) q^{9} +(1.50376 - 1.65491i) q^{10} +(0.00529841 + 0.0119004i) q^{11} +(-0.745009 - 1.56364i) q^{12} +(5.99101 - 3.89061i) q^{13} +(-3.22175 - 1.43442i) q^{14} +(-3.83729 - 0.524584i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.0187295 + 0.00718959i) q^{17} +(-1.50219 + 2.59681i) q^{18} +(-1.03829 - 4.88478i) q^{19} +(-2.15722 - 0.588545i) q^{20} +(1.11063 + 6.00651i) q^{21} +(0.00819793 - 0.0101236i) q^{22} +(-5.87514 - 0.930531i) q^{23} +(-1.05498 + 1.37368i) q^{24} +(-3.74597 + 3.31175i) q^{25} +(-6.18642 - 3.57173i) q^{26} +(5.18065 - 0.401140i) q^{27} +(0.184570 + 3.52181i) q^{28} +(2.05147 - 6.31378i) q^{29} +(1.27469 + 3.65721i) q^{30} +(4.50087 + 3.27752i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0224925 - 0.00177973i) q^{33} +(0.0149090 + 0.0134241i) q^{34} +(6.81133 + 3.97390i) q^{35} +(2.99576 + 0.159531i) q^{36} +(0.609670 - 2.27532i) q^{37} +(-3.88099 + 3.14277i) q^{38} +(0.965567 + 12.3351i) q^{39} +(0.454961 + 2.18929i) q^{40} +(6.48759 - 5.84145i) q^{41} +(4.84763 - 3.71647i) q^{42} +(0.250941 - 0.386416i) q^{43} +(-0.0127420 - 0.00270839i) q^{44} +(3.97216 - 5.40573i) q^{45} +(1.83815 + 5.65724i) q^{46} +(5.21539 + 2.65737i) q^{47} +(1.70291 + 0.316358i) q^{48} +(1.13046 - 5.31841i) q^{49} +(4.65143 + 1.83419i) q^{50} +(0.00455009 - 0.0344493i) q^{51} +(-0.373860 + 7.13367i) q^{52} +(-7.37509 + 9.10747i) q^{53} +(-2.70938 - 4.43387i) q^{54} +(-0.0206903 + 0.0205031i) q^{55} +(3.05416 - 1.76332i) q^{56} +(8.29247 + 2.46014i) q^{57} +(-6.55697 + 1.03852i) q^{58} +(0.714563 - 0.793603i) q^{59} +(2.67990 - 2.79609i) q^{60} +11.7733 q^{61} +(0.876940 - 5.49827i) q^{62} +(-10.0594 - 3.27785i) q^{63} +(0.951057 + 0.309017i) q^{64} +(12.8798 + 9.44747i) q^{65} +(0.00862563 + 0.0208489i) q^{66} +(-8.73244 + 2.33985i) q^{67} +(0.00519243 - 0.0193784i) q^{68} +(6.27544 - 8.17119i) q^{69} +(0.448491 - 7.87305i) q^{70} +(8.22401 - 0.864379i) q^{71} +(-1.21790 - 2.74166i) q^{72} +(-0.331133 + 0.862631i) q^{73} +(-2.30411 + 0.489753i) q^{74} +(-1.94153 - 8.43981i) q^{75} +(4.56216 + 2.03120i) q^{76} +(0.0409331 + 0.0208565i) q^{77} +(10.5523 - 6.46035i) q^{78} +(-2.68882 + 6.03918i) q^{79} +(1.74413 - 1.39929i) q^{80} +(-3.67447 + 8.21573i) q^{81} +(-8.15007 - 3.12852i) q^{82} +(0.477022 - 9.10212i) q^{83} +(-5.51218 - 2.63202i) q^{84} +(-0.0298654 - 0.0334736i) q^{85} +(-0.458224 - 0.0481613i) q^{86} +(7.91158 + 8.34410i) q^{87} +(0.00337154 + 0.0125828i) q^{88} +(2.19022 + 1.59129i) q^{89} +(-6.61987 - 1.08507i) q^{90} +(7.78490 - 23.9594i) q^{91} +(4.20614 - 4.20614i) q^{92} +(-8.71045 + 4.13861i) q^{93} -5.85337i q^{94} +(9.39273 - 6.03921i) q^{95} +(-0.491230 - 1.66093i) q^{96} +(2.06059 + 13.0101i) q^{97} +(-5.25196 + 1.40726i) q^{98} +(0.0213120 - 0.0327572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	−0.827104	+	1.52181i	−0.477529	+	0.878616i
$3$	−0.827104	+	1.52181i	−0.477529	+	0.878616i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	0.791841	+	2.09117i	0.354122	+	0.935199i
$5$	0.791841	+	2.09117i	0.354122	+	0.935199i
$6$	1.73144	+	0.0460690i	0.706857	+	0.0188076i
$7$	2.74072	−	2.21939i	1.03589	−	0.838850i	0.0487705	−	0.998810i	$-0.484470\pi$
$7$	2.74072	−	2.21939i	1.03589	−	0.838850i	0.987124	+	0.159960i	$0.0511364\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	−1.63180	−	2.51739i	−0.543932	−	0.839129i
$10$	1.50376	−	1.65491i	0.475530	−	0.523327i
$11$	0.00529841	+	0.0119004i	0.00159753	+	0.00358811i	0.914342	−	0.404942i	$-0.132708\pi$
$11$	0.00529841	+	0.0119004i	0.00159753	+	0.00358811i	−0.912745	+	0.408530i	$0.866042\pi$
$12$	−0.745009	−	1.56364i	−0.215065	−	0.451383i
$13$	5.99101	−	3.89061i	1.66161	−	1.07906i	0.756381	−	0.654132i	$-0.226966\pi$
$13$	5.99101	−	3.89061i	1.66161	−	1.07906i	0.905227	−	0.424929i	$-0.139701\pi$
$14$	−3.22175	−	1.43442i	−0.861049	−	0.383364i
$15$	−3.83729	−	0.524584i	−0.990785	−	0.135447i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−0.0187295	+	0.00718959i	−0.00454257	+	0.00174373i	−0.360638	−	0.932706i	$-0.617441\pi$
$17$	−0.0187295	+	0.00718959i	−0.00454257	+	0.00174373i	0.356096	+	0.934450i	$0.384108\pi$
$18$	−1.50219	+	2.59681i	−0.354069	+	0.612074i
$19$	−1.03829	−	4.88478i	−0.238200	−	1.12064i	−0.920856	−	0.389904i	$-0.872508\pi$
$19$	−1.03829	−	4.88478i	−0.238200	−	1.12064i	0.682655	−	0.730741i	$-0.260825\pi$
$20$	−2.15722	−	0.588545i	−0.482370	−	0.131603i
$21$	1.11063	+	6.00651i	0.242358	+	1.31073i
$22$	0.00819793	−	0.0101236i	0.00174780	−	0.00215836i
$23$	−5.87514	−	0.930531i	−1.22505	−	0.194029i	−0.489807	−	0.871831i	$-0.662933\pi$
$23$	−5.87514	−	0.930531i	−1.22505	−	0.194029i	−0.735245	+	0.677802i	$0.762933\pi$
$24$	−1.05498	+	1.37368i	−0.215348	+	0.280402i
$25$	−3.74597	+	3.31175i	−0.749195	+	0.662349i
$26$	−6.18642	−	3.57173i	−1.21326	−	0.700474i
$27$	5.18065	−	0.401140i	0.997016	−	0.0771995i
$28$	0.184570	+	3.52181i	0.0348805	+	0.665560i
$29$	2.05147	−	6.31378i	0.380949	−	1.17244i	−0.558428	−	0.829553i	$-0.688595\pi$
$29$	2.05147	−	6.31378i	0.380949	−	1.17244i	0.939377	−	0.342887i	$-0.111405\pi$
$30$	1.27469	+	3.65721i	0.232725	+	0.667712i
$31$	4.50087	+	3.27752i	0.808381	+	0.588660i
$31$	4.50087	+	3.27752i	0.808381	+	0.588660i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.0224925	−	0.00177973i	−0.00391544	−	0.000309811i
$34$	0.0149090	+	0.0134241i	0.00255687	+	0.00230222i
$35$	6.81133	+	3.97390i	1.15133	+	0.671712i
$36$	2.99576	+	0.159531i	0.499293	+	0.0265885i
$37$	0.609670	−	2.27532i	0.100229	−	0.374060i	−0.897531	−	0.440951i	$-0.854641\pi$
$37$	0.609670	−	2.27532i	0.100229	−	0.374060i	0.997760	+	0.0668909i	$0.0213079\pi$
$38$	−3.88099	+	3.14277i	−0.629580	+	0.509824i
$39$	0.965567	+	12.3351i	0.154614	+	1.97520i
$40$	0.454961	+	2.18929i	0.0719357	+	0.346158i
$41$	6.48759	−	5.84145i	1.01319	−	0.912281i	0.0170330	−	0.999855i	$-0.494578\pi$
$41$	6.48759	−	5.84145i	1.01319	−	0.912281i	0.996158	+	0.0875736i	$0.0279113\pi$
$42$	4.84763	−	3.71647i	0.748005	−	0.573464i
$43$	0.250941	−	0.386416i	0.0382682	−	0.0589279i	−0.819019	−	0.573767i	$-0.805482\pi$
$43$	0.250941	−	0.386416i	0.0382682	−	0.0589279i	0.857287	+	0.514839i	$0.172148\pi$
$44$	−0.0127420	−	0.00270839i	−0.00192092	−	0.000408305i
$45$	3.97216	−	5.40573i	0.592134	−	0.805839i
$46$	1.83815	+	5.65724i	0.271020	+	0.834115i
$47$	5.21539	+	2.65737i	0.760743	+	0.387618i	0.790914	−	0.611927i	$-0.209605\pi$
$47$	5.21539	+	2.65737i	0.760743	+	0.387618i	−0.0301714	+	0.999545i	$0.509605\pi$
$48$	1.70291	+	0.316358i	0.245795	+	0.0456624i
$49$	1.13046	−	5.31841i	0.161495	−	0.759773i
$50$	4.65143	+	1.83419i	0.657811	+	0.259393i
$51$	0.00455009	−	0.0344493i	0.000637140	−	0.00482386i
$52$	−0.373860	+	7.13367i	−0.0518450	+	0.989262i
$53$	−7.37509	+	9.10747i	−1.01305	+	1.25101i	−0.0453280	+	0.998972i	$0.514433\pi$
$53$	−7.37509	+	9.10747i	−1.01305	+	1.25101i	−0.967718	+	0.252035i	$0.918900\pi$
$54$	−2.70938	−	4.43387i	−0.368700	−	0.603374i
$55$	−0.0206903	+	0.0205031i	−0.00278988	+	0.00276464i
$56$	3.05416	−	1.76332i	0.408130	−	0.235634i
$57$	8.29247	+	2.46014i	1.09836	+	0.325853i
$58$	−6.55697	+	1.03852i	−0.860972	+	0.136365i
$59$	0.714563	−	0.793603i	0.0930282	−	0.103318i	−0.694833	−	0.719171i	$-0.744522\pi$
$59$	0.714563	−	0.793603i	0.0930282	−	0.103318i	0.787861	+	0.615853i	$0.211188\pi$
$60$	2.67990	−	2.79609i	0.345974	−	0.360974i
$61$	11.7733			1.50741			0.753706	−	0.657211i	$-0.228264\pi$
$61$	11.7733			1.50741			0.753706	+	0.657211i	$0.228264\pi$
$62$	0.876940	−	5.49827i	0.111371	−	0.698281i
$63$	−10.0594	−	3.27785i	−1.26736	−	0.412971i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	12.8798	+	9.44747i	1.59755	+	1.17181i
$66$	0.00862563	+	0.0208489i	0.00106174	+	0.00256633i
$67$	−8.73244	+	2.33985i	−1.06684	+	0.285858i	−0.749193	−	0.662352i	$-0.769558\pi$
$67$	−8.73244	+	2.33985i	−1.06684	+	0.285858i	−0.317644	+	0.948210i	$0.602892\pi$
$68$	0.00519243	−	0.0193784i	0.000629675	−	0.00234998i
$69$	6.27544	−	8.17119i	0.755474	−	0.983695i
$70$	0.448491	−	7.87305i	0.0536049	−	0.941010i
$71$	8.22401	−	0.864379i	0.976011	−	0.102583i	0.396926	−	0.917850i	$-0.370077\pi$
$71$	8.22401	−	0.864379i	0.976011	−	0.102583i	0.579084	+	0.815268i	$0.303410\pi$
$72$	−1.21790	−	2.74166i	−0.143531	−	0.323108i
$73$	−0.331133	+	0.862631i	−0.0387562	+	0.100963i	−0.951593	−	0.307362i	$-0.900554\pi$
$73$	−0.331133	+	0.862631i	−0.0387562	+	0.100963i	0.912836	+	0.408325i	$0.133887\pi$
$74$	−2.30411	+	0.489753i	−0.267847	+	0.0569327i
$75$	−1.94153	−	8.43981i	−0.224189	−	0.974546i
$76$	4.56216	+	2.03120i	0.523316	+	0.232995i
$77$	0.0409331	+	0.0208565i	0.00466476	+	0.00237682i
$78$	10.5523	−	6.46035i	1.19481	−	0.731490i
$79$	−2.68882	+	6.03918i	−0.302515	+	0.679461i	−0.999284	−	0.0378353i	$-0.987954\pi$
$79$	−2.68882	+	6.03918i	−0.302515	+	0.679461i	0.696769	+	0.717296i	$0.254620\pi$
$80$	1.74413	−	1.39929i	0.194999	−	0.156446i
$81$	−3.67447	+	8.21573i	−0.408275	+	0.912859i
$82$	−8.15007	−	3.12852i	−0.900025	−	0.345487i
$83$	0.477022	−	9.10212i	0.0523600	−	0.999087i	−0.838526	−	0.544861i	$-0.816582\pi$
$83$	0.477022	−	9.10212i	0.0523600	−	0.999087i	0.890886	−	0.454226i	$-0.150084\pi$
$84$	−5.51218	−	2.63202i	−0.601428	−	0.287177i
$85$	−0.0298654	−	0.0334736i	−0.00323936	−	0.00363072i
$86$	−0.458224	−	0.0481613i	−0.0494116	−	0.00519337i
$87$	7.91158	+	8.34410i	0.848211	+	0.894582i
$88$	0.00337154	+	0.0125828i	0.000359408	+	0.00134133i
$89$	2.19022	+	1.59129i	0.232163	+	0.168676i	0.697784	−	0.716308i	$-0.254169\pi$
$89$	2.19022	+	1.59129i	0.232163	+	0.168676i	−0.465622	+	0.884984i	$0.654169\pi$
$90$	−6.61987	−	1.08507i	−0.697795	−	0.114376i
$91$	7.78490	−	23.9594i	0.816079	−	2.51163i
$92$	4.20614	−	4.20614i	0.438520	−	0.438520i
$93$	−8.71045	+	4.13861i	−0.903231	+	0.429154i
$94$		−	5.85337i		−	0.603729i
$95$	9.39273	−	6.03921i	0.963674	−	0.619610i
$96$	−0.491230	−	1.66093i	−0.0501359	−	0.169518i
$97$	2.06059	+	13.0101i	0.209221	+	1.32097i	0.838972	+	0.544175i	$0.183157\pi$
$97$	2.06059	+	13.0101i	0.209221	+	1.32097i	−0.629750	+	0.776798i	$0.716843\pi$
$98$	−5.25196	+	1.40726i	−0.530528	+	0.142155i
$99$	0.0213120	−	0.0327572i	0.00214194	−	0.00329223i
$100$	−0.477431	−	4.97715i	−0.0477431	−	0.497715i
$101$	4.85270	+	6.67917i	0.482861	+	0.664602i	0.979052	−	0.203612i	$-0.0652681\pi$
$101$	4.85270	+	6.67917i	0.482861	+	0.664602i	−0.496190	+	0.868214i	$0.665268\pi$
$102$	−0.0327602	+	0.0115855i	−0.00324374	+	0.00114713i
$103$	2.22619	+	0.116670i	0.219353	+	0.0114958i	0.161696	−	0.986841i	$-0.448304\pi$
$103$	2.22619	+	0.116670i	0.219353	+	0.0114958i	0.0576572	+	0.998336i	$0.481637\pi$
$104$	6.52588	−	2.90551i	0.639915	−	0.284908i
$105$	−11.6812	+	7.07871i	−1.13997	+	0.690811i
$106$	11.4630	+	2.43654i	1.11339	+	0.236658i
$107$	−8.42936	+	3.23573i	−0.814897	+	0.312810i	−0.729885	−	0.683570i	$-0.760426\pi$
$107$	−8.42936	+	3.23573i	−0.814897	+	0.312810i	−0.0850123	+	0.996380i	$0.527093\pi$
$108$	−2.72058	+	4.42701i	−0.261788	+	0.425990i
$109$	−4.84256	+	1.57344i	−0.463833	+	0.150708i	−0.531605	−	0.846992i	$-0.678411\pi$
$109$	−4.84256	+	1.57344i	−0.463833	+	0.150708i	0.0677723	+	0.997701i	$0.478411\pi$
$110$	0.0276616	+	0.00912697i	0.00263743	+	0.000870222i
$111$	2.95834	+	2.80973i	0.280793	+	0.266687i
$112$	−2.95769	−	1.92075i	−0.279476	−	0.181494i
$113$	−6.78116	−	2.60304i	−0.637917	−	0.244874i	0.0178451	−	0.999841i	$-0.494319\pi$
$113$	−6.78116	−	2.60304i	−0.637917	−	0.244874i	−0.655763	+	0.754967i	$0.727653\pi$
$114$	−1.57270	−	8.50552i	−0.147297	−	0.796615i
$115$	−2.70628	−	13.0227i	−0.252362	−	1.21438i
$116$	3.90213	+	5.37082i	0.362304	+	0.498669i
$117$	−19.5703	−	8.73301i	−1.80927	−	0.807367i
$118$	−1.03151	−	0.276392i	−0.0949582	−	0.0254440i
$119$	−0.0353758	+	0.0612727i	−0.00324290	+	0.00561686i
$120$	−3.70799	−	1.11841i	−0.338491	−	0.102096i
$121$	7.36032	−	8.17447i	0.669120	−	0.743133i
$122$	−5.34495	−	10.4901i	−0.483909	−	0.949725i
$123$	3.52365	+	14.7043i	0.317717	+	1.32585i
$124$	−5.29712	+	1.71480i	−0.475695	+	0.153994i
$125$	−9.89164	−	5.21109i	−0.884735	−	0.466094i
$126$	1.64626	+	10.4511i	0.146661	+	0.931055i
$127$	−17.2958	+	0.906436i	−1.53476	+	0.0804332i	−0.800870	−	0.598839i	$-0.795629\pi$
$127$	−17.2958	+	0.906436i	−1.53476	+	0.0804332i	−0.733887	+	0.679272i	$0.762296\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	0.380496	+	0.701491i	0.0335008	+	0.0617628i
$130$	2.57043	−	15.7651i	0.225442	−	1.38269i
$131$	−7.35536	−	0.773079i	−0.642640	−	0.0675442i	−0.222398	−	0.974956i	$-0.571388\pi$
$131$	−7.35536	−	0.773079i	−0.642640	−	0.0675442i	−0.420243	+	0.907412i	$0.638055\pi$
$132$	0.0146606	−	0.0171507i	0.00127604	−	0.00149278i
$133$	−13.6869	−	11.0834i	−1.18680	−	0.961055i
$134$	6.04927	+	6.71839i	0.522577	+	0.580381i
$135$	4.94110	+	10.5160i	0.425262	+	0.905070i
$136$	−0.0196236	+	0.00417113i	−0.00168271	+	0.000357671i
$137$	13.6511	−	8.86513i	1.16629	−	0.757399i	0.191715	−	0.981451i	$-0.438595\pi$
$137$	13.6511	−	8.86513i	1.16629	−	0.757399i	0.974577	+	0.224052i	$0.0719285\pi$
$138$	−10.1296	−	1.88182i	−0.862287	−	0.160191i
$139$	−1.43019	+	0.464697i	−0.121307	+	0.0394151i	−0.369042	−	0.929413i	$-0.620314\pi$
$139$	−1.43019	+	0.464697i	−0.121307	+	0.0394151i	0.247734	+	0.968828i	$0.420314\pi$
$140$	−7.21855	+	3.17468i	−0.610079	+	0.268310i
$141$	−8.35769	+	5.73890i	−0.703844	+	0.483302i
$142$	−4.50379	−	6.93523i	−0.377950	−	0.581992i
$143$	0.0780427	+	0.0506815i	0.00652626	+	0.00423820i
$144$	−1.88992	+	2.32985i	−0.157494	+	0.194154i
$145$	14.8276	−	0.709538i	1.23137	−	0.0589239i
$146$	0.918941	−	0.0965846i	0.0760521	−	0.00799340i
$147$	7.15859	+	6.11923i	0.590430	+	0.504705i
$148$	1.48242	+	1.83063i	0.121854	+	0.150477i
$149$	10.8574	+	18.8056i	0.889474	+	1.54061i	0.840499	+	0.541814i	$0.182262\pi$
$149$	10.8574	+	18.8056i	0.889474	+	1.54061i	0.0489750	+	0.998800i	$0.484405\pi$
$150$	−6.63849	+	5.56151i	−0.542031	+	0.454096i
$151$	−15.1563	−	11.0117i	−1.23340	−	0.896119i	−0.236262	−	0.971689i	$-0.575922\pi$
$151$	−15.1563	−	11.0117i	−1.23340	−	0.896119i	−0.997140	+	0.0755703i	$0.975922\pi$
$152$	−0.261361	−	4.98706i	−0.0211992	−	0.404504i
$153$	0.0486618	+	0.0354175i	0.00393407	+	0.00286333i
$154$		−	0.0459403i		−	0.00370198i
$155$	−3.28987	+	12.0074i	−0.264249	+	0.964454i
$156$	−10.5469	−	6.46923i	−0.844424	−	0.517953i
$157$	10.9465	−	5.57754i	0.873629	−	0.445136i	0.0411242	−	0.999154i	$-0.486906\pi$
$157$	10.9465	−	5.57754i	0.873629	−	0.445136i	0.832505	+	0.554018i	$0.186906\pi$
$158$	6.60164	−	0.345978i	0.525199	−	0.0275245i
$159$	−7.75986	−	18.7563i	−0.615397	−	1.48747i
$160$	−2.03860	−	0.918763i	−0.161165	−	0.0726346i
$161$	−18.1673	+	10.4889i	−1.43179	+	0.826641i
$162$	8.98845	−	0.455883i	0.706199	−	0.0358175i
$163$	−2.78026	+	17.5539i	−0.217767	+	1.37493i	0.600287	+	0.799784i	$0.295053\pi$
$163$	−2.78026	+	17.5539i	−0.217767	+	1.37493i	−0.818054	+	0.575141i	$0.804947\pi$
$164$	0.912524	+	8.68209i	0.0712562	+	0.677957i
$165$	−0.0140888	−	0.0484449i	−0.00109681	−	0.00377143i
$166$	−8.32661	+	3.70725i	−0.646270	+	0.287738i
$167$	−10.6895	+	16.4604i	−0.827177	+	1.27374i	0.132090	+	0.991238i	$0.457831\pi$
$167$	−10.6895	+	16.4604i	−0.827177	+	1.27374i	−0.959267	+	0.282503i	$0.908835\pi$
$168$	0.157326	+	6.10630i	0.0121380	+	0.471111i
$169$	15.4678	−	34.7413i	1.18983	−	2.67240i
$170$	−0.0162665	+	0.0418070i	−0.00124759	+	0.00320645i
$171$	−10.6026	+	10.5847i	−0.810801	+	0.809436i
$172$	0.165117	+	0.430146i	0.0125901	+	0.0327983i
$173$	4.17192	+	6.42419i	0.317185	+	0.488422i	0.960920	−	0.276827i	$-0.0892827\pi$
$173$	4.17192	+	6.42419i	0.317185	+	0.488422i	−0.643735	+	0.765249i	$0.722616\pi$
$174$	3.84287	−	10.8374i	0.291327	−	0.821582i
$175$	−2.91660	+	17.3903i	−0.220474	+	1.31459i
$176$	0.00968068	−	0.00871652i	0.000729709	−	0.000657033i
$177$	0.616693	+	1.74382i	0.0463535	+	0.131074i
$178$	0.423508	−	2.67393i	0.0317433	−	0.200419i
$179$	1.28835	−	12.2578i	0.0962958	−	0.916194i	−0.834587	−	0.550876i	$-0.814294\pi$
$179$	1.28835	−	12.2578i	0.0962958	−	0.916194i	0.930883	−	0.365318i	$-0.119040\pi$
$180$	2.03856	+	6.39095i	0.151945	+	0.476354i
$181$	−11.7429	+	20.3393i	−0.872844	+	1.51181i	−0.0138025	+	0.999905i	$0.504394\pi$
$181$	−11.7429	+	20.3393i	−0.872844	+	1.51181i	−0.859042	+	0.511906i	$0.828940\pi$
$182$	−24.8823	+	3.94097i	−1.84440	+	0.292124i
$183$	−9.73772	+	17.9166i	−0.719833	+	1.32444i
$184$	−5.65724	−	1.83815i	−0.417057	−	0.135510i
$185$	5.24084	−	0.526769i	0.385314	−	0.0387288i
$186$	7.64199	+	5.88218i	0.560338	+	0.431302i
$187$	−0.000184796	0	0.000184796i	−1.35136e−5	0	1.35136e-5i
$188$	−5.21539	+	2.65737i	−0.380372	+	0.193809i
$189$	13.3084	−	12.5973i	0.968044	−	0.916318i
$190$	−9.64519	−	5.62724i	−0.699735	−	0.408243i
$191$	−3.69079	−	2.13088i	−0.267056	−	0.154185i	0.360493	−	0.932762i	$-0.382609\pi$
$191$	−3.69079	−	2.13088i	−0.267056	−	0.154185i	−0.627549	+	0.778577i	$0.715942\pi$
$192$	−1.25689	+	1.19174i	−0.0907080	+	0.0860061i
$193$	0.217852	+	0.269025i	0.0156813	+	0.0193648i	0.784926	−	0.619589i	$-0.212701\pi$
$193$	0.217852	+	0.269025i	0.0156813	+	0.0193648i	−0.769245	+	0.638954i	$0.779367\pi$
$194$	10.6566	−	7.74245i	0.765097	−	0.555875i
$195$	−25.0302	+	11.7866i	−1.79245	+	0.844057i
$196$	3.63822	+	4.04065i	0.259873	+	0.288618i
$197$	−0.112367	+	0.292727i	−0.00800583	+	0.0208559i	−0.937525	−	0.347918i	$-0.886889\pi$
$197$	−0.112367	+	0.292727i	−0.00800583	+	0.0208559i	0.929519	+	0.368774i	$0.120222\pi$
$198$	−0.0388624	−	0.00411770i	−0.00276183	−	0.000292632i
$199$	−1.20840	+	5.68508i	−0.0856613	+	0.403005i	−0.999998	−	0.00194979i	$-0.999379\pi$
$199$	−1.20840	+	5.68508i	−0.0856613	+	0.403005i	0.914337	+	0.404955i	$0.132713\pi$
$200$	−4.21793	+	2.68497i	−0.298252	+	0.189856i
$201$	3.66184	−	15.2244i	0.258286	−	1.07385i
$202$	3.74810	−	7.35606i	0.263715	−	0.517571i
$203$	−8.39024	−	21.8573i	−0.588879	−	1.53408i
$204$	0.0251956	+	0.0239299i	0.00176404	+	0.00167543i
$205$	17.3526	+	8.94114i	1.21196	+	0.624476i
$206$	−0.906716	−	2.03652i	−0.0631739	−	0.141891i
$207$	7.24453	+	16.3084i	0.503530	+	1.13351i
$208$	−5.55151	−	4.49553i	−0.384928	−	0.311709i
$209$	0.0526296	−	0.0382377i	0.00364047	−	0.00264495i
$210$	11.6103	+	7.19435i	0.801189	+	0.496458i
$211$	4.34767	+	7.53038i	0.299306	+	0.518413i	0.975977	−	0.217872i	$-0.0699116\pi$
$211$	4.34767	+	7.53038i	0.299306	+	0.518413i	−0.676671	+	0.736285i	$0.736578\pi$
$212$	−3.03313	−	11.3198i	−0.208316	−	0.777448i
$213$	−5.48670	+	13.2303i	−0.375942	+	0.906525i
$214$	6.70990	+	6.04163i	0.458680	+	0.412997i
$215$	1.00677	+	0.218781i	0.0686609	+	0.0149207i
$216$	5.17962	+	0.414230i	0.352428	+	0.0281848i
$217$	19.6097	−	1.00643i	1.33119	−	0.0683208i
$218$	3.60042	+	3.60042i	0.243851	+	0.243851i
$219$	−1.03888	−	1.21741i	−0.0702008	−	0.0822647i
$220$	−0.00442592	−	0.0287902i	−0.000298395	−	0.00194104i
$221$	−0.0842369	+	0.115942i	−0.00566638	+	0.00779911i
$222$	1.16043	−	3.91149i	0.0778828	−	0.262522i
$223$	23.5958	+	6.32248i	1.58009	+	0.423385i	0.938955	−	0.344040i	$-0.111796\pi$
$223$	23.5958	+	6.32248i	1.58009	+	0.423385i	0.641139	+	0.767425i	$0.278462\pi$
$224$	−0.368635	+	3.50733i	−0.0246304	+	0.234343i
$225$	14.4496	+	4.02597i	0.963308	+	0.268398i
$226$	0.759253	+	7.22381i	0.0505048	+	0.480521i
$227$	8.66425	+	0.454074i	0.575067	+	0.0301380i	0.337653	−	0.941271i	$-0.390367\pi$
$227$	8.66425	+	0.454074i	0.575067	+	0.0301380i	0.237414	+	0.971409i	$0.423700\pi$
$228$	−6.86448	+	5.26271i	−0.454612	+	0.348532i
$229$	−1.71640	−	8.07503i	−0.113423	−	0.533613i	−0.997768	−	0.0667789i	$-0.978728\pi$
$229$	−1.71640	−	8.07503i	−0.113423	−	0.533613i	0.884345	−	0.466834i	$-0.154606\pi$
$230$	−10.3747	+	8.32352i	−0.684089	+	0.548836i
$231$	−0.0655955	+	0.0450419i	−0.00431587	+	0.00296354i
$232$	3.01391	−	5.91513i	0.197873	−	0.388347i
$233$	4.15409	−	8.15286i	0.272143	−	0.534112i	−0.713972	−	0.700175i	$-0.753105\pi$
$233$	4.15409	−	8.15286i	0.272143	−	0.534112i	0.986115	+	0.166063i	$0.0531055\pi$
$234$	1.10355	+	21.4020i	0.0721416	+	1.39909i
$235$	−1.42726	+	13.0105i	−0.0931040	+	0.848710i
$236$	0.222028	+	1.04456i	0.0144528	+	0.0679952i
$237$	−6.96654	−	9.08689i	−0.452525	−	0.590257i
$238$	0.0706547	+	0.00370286i	0.00457986	+	0.000240020i
$239$	0.410478	+	3.90544i	0.0265516	+	0.252622i	0.999744	+	0.0226289i	$0.00720363\pi$
$239$	0.410478	+	3.90544i	0.0265516	+	0.252622i	−0.973192	+	0.229993i	$0.926130\pi$
$240$	0.686879	+	3.81159i	0.0443378	+	0.246037i
$241$	2.64050	−	25.1227i	0.170090	−	1.61830i	−0.493187	−	0.869923i	$-0.664168\pi$
$241$	2.64050	−	25.1227i	0.170090	−	1.61830i	0.663277	−	0.748374i	$-0.269165\pi$
$242$	−10.6250	−	2.84697i	−0.683002	−	0.183010i
$243$	−9.46359	−	12.3871i	−0.607090	−	0.794633i
$244$	−6.92015	+	9.52477i	−0.443017	+	0.609761i
$245$	12.0168	−	1.84735i	0.767728	−	0.118023i
$246$	11.5020	−	9.81523i	0.733339	−	0.625796i
$247$	−25.2252	−	25.2252i	−1.60504	−	1.60504i
$248$	3.93274	+	3.94126i	0.249729	+	0.250270i
$249$	13.4571	+	8.25434i	0.852811	+	0.523097i
$250$	−0.152403	+	11.1793i	−0.00963879	+	0.707041i
$251$	−13.9412	−	12.5527i	−0.879963	−	0.792322i	0.0992697	−	0.995061i	$-0.468349\pi$
$251$	−13.9412	−	12.5527i	−0.879963	−	0.792322i	−0.979233	+	0.202738i	$0.935016\pi$
$252$	8.56458	−	6.21152i	0.539518	−	0.391289i
$253$	−0.0200552	−	0.0748470i	−0.00126086	−	0.00470559i
$254$	8.65978	+	14.9992i	0.543363	+	0.941132i
$255$	0.0756422	−	0.0177633i	0.00473690	−	0.00111238i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	6.46660	+	5.23655i	0.403375	+	0.326647i	0.809446	−	0.587195i	$-0.199768\pi$
$257$	6.46660	+	5.23655i	0.403375	+	0.326647i	−0.406070	+	0.913842i	$0.633101\pi$
$258$	0.452291	−	0.657495i	0.0281584	−	0.0409338i
$259$	−3.37889	−	7.58910i	−0.209954	−	0.471564i
$260$	−15.2137	+	4.86693i	−0.943517	+	0.301834i
$261$	−19.2418	+	5.13846i	−1.19104	+	0.318063i
$262$	2.65044	+	6.90464i	0.163745	+	0.426570i
$263$	3.10239	−	6.08878i	0.191301	−	0.375450i	−0.775356	−	0.631525i	$-0.782429\pi$
$263$	3.10239	−	6.08878i	0.191301	−	0.375450i	0.966657	+	0.256075i	$0.0824293\pi$
$264$	−0.0219372	−	0.00527642i	−0.00135014	−	0.000324741i
$265$	−24.8852	−	8.21088i	−1.52868	−	0.504390i
$266$	−3.66169	+	17.2269i	−0.224512	+	1.05625i
$267$	−4.23317	+	2.01693i	−0.259066	+	0.123434i
$268$	3.23982	−	8.44002i	0.197904	−	0.515556i
$269$	−2.90554	−	3.22693i	−0.177154	−	0.196749i	0.648028	−	0.761617i	$-0.275594\pi$
$269$	−2.90554	−	3.22693i	−0.177154	−	0.196749i	−0.825182	+	0.564867i	$0.808927\pi$
$270$	7.12658	−	9.17670i	0.433710	−	0.558476i
$271$	0.933161	−	0.677981i	0.0566855	−	0.0411844i	−0.559082	−	0.829113i	$-0.688846\pi$
$271$	0.933161	−	0.677981i	0.0566855	−	0.0411844i	0.615767	+	0.787928i	$0.288846\pi$
$272$	0.0126254	+	0.0155911i	0.000765530	+	0.000945351i
$273$	30.0228	+	31.6641i	1.81706	+	1.91640i
$274$	−14.0964	−	8.13853i	−0.851592	−	0.491667i
$275$	−0.0592589	−	0.0270317i	−0.00357345	−	0.00163007i
$276$	2.92202	+	9.87984i	0.175885	+	0.594697i
$277$	−20.7241	+	10.5595i	−1.24519	+	0.634458i	−0.947363	−	0.320161i	$-0.896263\pi$
$277$	−20.7241	+	10.5595i	−1.24519	+	0.634458i	−0.297830	+	0.954619i	$0.596263\pi$
$278$	1.06334	+	1.06334i	0.0637750	+	0.0637750i
$279$	0.906278	−	16.6787i	0.0542575	−	0.998527i
$280$	6.10582	+	4.99050i	0.364892	+	0.298240i
$281$	27.7730	+	9.02401i	1.65680	+	0.538327i	0.980198	−	0.198021i	$-0.0634514\pi$
$281$	27.7730	+	9.02401i	1.65680	+	0.538327i	0.676603	+	0.736348i	$0.263451\pi$
$282$	8.90770	+	4.84135i	0.530446	+	0.288298i
$283$	−17.4943	+	2.77083i	−1.03993	+	0.164709i	−0.652967	−	0.757386i	$-0.726476\pi$
$283$	−17.4943	+	2.77083i	−1.03993	+	0.164709i	−0.386963	+	0.922095i	$0.626476\pi$
$284$	−4.13466	+	7.16144i	−0.245347	+	0.424953i
$285$	1.42175	+	19.2890i	0.0842172	+	1.14258i
$286$	0.00972693	−	0.0925455i	0.000575165	−	0.00547233i
$287$	4.81619	−	30.4083i	0.284291	−	1.79494i
$288$	2.93392	+	0.626206i	0.172883	+	0.0368996i
$289$	−12.6332	+	11.3750i	−0.743127	+	0.669115i
$290$	−7.36381	−	12.8894i	−0.432418	−	0.756891i
$291$	−21.5031	−	7.62486i	−1.26054	−	0.446977i
$292$	−0.503248	−	0.774934i	−0.0294504	−	0.0453496i
$293$	−2.66387	−	6.93961i	−0.155625	−	0.405416i	0.833495	−	0.552526i	$-0.186336\pi$
$293$	−2.66387	−	6.93961i	−0.155625	−	0.405416i	−0.989120	+	0.147110i	$0.953003\pi$
$294$	2.20234	−	9.15642i	0.128443	−	0.534013i
$295$	2.22538	+	0.865865i	0.129567	+	0.0504126i
$296$	0.958102	−	2.15193i	0.0556885	−	0.125079i
$297$	0.0322229	+	0.0595265i	0.00186976	+	0.00345408i
$298$	11.8267	−	18.2116i	0.685105	−	1.05497i
$299$	−38.8184	+	17.2830i	−2.24492	+	0.999504i
$300$	7.96916	+	3.39007i	0.460099	+	0.195726i
$301$	−0.169848	−	1.61599i	−0.00978987	−	0.0931444i
$302$	−2.93068	+	18.5036i	−0.168642	+	1.06476i
$303$	−14.1781	+	1.86051i	−0.814510	+	0.106883i
$304$	−4.32485	+	2.49695i	−0.248047	+	0.143210i
$305$	9.32256	+	24.6199i	0.533808	+	1.40973i
$306$	0.00946524	−	0.0594371i	0.000541092	−	0.00339780i
$307$	−13.7262	+	0.719360i	−0.783396	+	0.0410560i	−0.439840	−	0.898076i	$-0.644965\pi$
$307$	−13.7262	+	0.719360i	−0.783396	+	0.0410560i	−0.343556	+	0.939132i	$0.611631\pi$
$308$	−0.0409331	+	0.0208565i	−0.00233238	+	0.00118841i
$309$	−2.01884	+	3.29134i	−0.114848	+	0.187238i
$310$	12.1922	−	2.51993i	0.692471	−	0.143122i
$311$		−	17.1130i		−	0.970390i	−0.874406	−	0.485195i	$-0.838749\pi$
$311$		−	17.1130i		−	0.970390i	0.874406	−	0.485195i	$-0.161251\pi$
$312$	−0.975956	+	12.3343i	−0.0552526	+	0.698291i
$313$	0.0116887	+	0.223033i	0.000660684	+	0.0126066i	0.998940	−	0.0460316i	$-0.0146575\pi$
$313$	0.0116887	+	0.223033i	0.000660684	+	0.0126066i	−0.998279	+	0.0586382i	$0.981324\pi$
$314$	−9.93925	−	7.22129i	−0.560904	−	0.407521i
$315$	−1.11087	−	23.6314i	−0.0625904	−	1.33148i
$316$	−3.30535	−	5.72504i	−0.185941	−	0.322059i
$317$	−4.90480	−	6.05693i	−0.275481	−	0.340191i	0.620562	−	0.784157i	$-0.286904\pi$
$317$	−4.90480	−	6.05693i	−0.275481	−	0.340191i	−0.896044	+	0.443966i	$0.853571\pi$
$318$	−13.1891	+	15.4293i	−0.739607	+	0.865230i
$319$	0.0860062	−	0.00903962i	0.00481543	−	0.000506122i
$320$	0.106879	+	2.23351i	0.00597472	+	0.124857i
$321$	2.04780	−	15.5041i	0.114297	−	0.865357i
$322$	17.5935	+	11.4253i	0.980446	+	0.636709i
$323$	0.0545662	+	0.0840246i	0.00303615	+	0.00467525i
$324$	−4.48686	−	7.80180i	−0.249270	−	0.433433i
$325$	−9.55747	+	34.4148i	−0.530153	+	1.90899i
$326$	16.9028	−	5.49206i	0.936161	−	0.304177i
$327$	1.61082	−	8.67084i	0.0890787	−	0.479498i
$328$	7.32152	−	4.75465i	0.404263	−	0.262532i
$329$	20.1917	−	4.29187i	1.11320	−	0.236619i
$330$	−0.0367685	+	0.0345467i	−0.00202404	+	0.00190173i
$331$	−4.80234	−	5.33353i	−0.263960	−	0.293158i	0.596566	−	0.802564i	$-0.296532\pi$
$331$	−4.80234	−	5.33353i	−0.263960	−	0.293158i	−0.860526	+	0.509407i	$0.829865\pi$
$332$	7.08338	+	5.73601i	0.388751	+	0.314804i
$333$	−6.72272	+	2.17808i	−0.368403	+	0.119358i
$334$	19.5192	+	2.05155i	1.06804	+	0.112256i
$335$	−11.8077	−	16.4082i	−0.645125	−	0.896477i
$336$	5.36933	−	2.91238i	0.292921	−	0.158883i
$337$	−0.215729	−	1.36206i	−0.0117515	−	0.0741962i	0.981116	−	0.193422i	$-0.0619587\pi$
$337$	−0.215729	−	1.36206i	−0.0117515	−	0.0741962i	−0.992867	+	0.119226i	$0.961959\pi$
$338$	−37.9769	+	1.99029i	−2.06567	+	0.108257i
$339$	9.57005	−	8.16663i	0.519774	−	0.443550i
$340$	0.0446352	−	0.00448638i	0.00242068	−	0.000243308i
$341$	−0.0151564	+	0.0709279i	−0.000820767	+	0.00384096i
$342$	14.2446	+	4.64160i	0.770257	+	0.250989i
$343$	2.50210	+	4.91064i	0.135101	+	0.265150i
$344$	0.308301	−	0.342403i	0.0166225	−	0.0184611i
$345$	22.0565	+	6.65273i	1.18748	+	0.358171i
$346$	3.82998	−	6.63372i	0.205901	−	0.356631i
$347$	−19.2407	−	5.15554i	−1.03290	−	0.276764i	−0.297729	−	0.954650i	$-0.596229\pi$
$347$	−19.2407	−	5.15554i	−1.03290	−	0.276764i	−0.735166	+	0.677887i	$0.762896\pi$
$348$	−11.4008	+	1.49606i	−0.611149	+	0.0801974i
$349$	−4.88101	−	6.71814i	−0.261275	−	0.359614i	0.658145	−	0.752891i	$-0.271341\pi$
$349$	−4.88101	−	6.71814i	−0.261275	−	0.359614i	−0.919420	+	0.393277i	$0.871341\pi$
$350$	16.8190	−	5.29634i	0.899014	−	0.283101i
$351$	29.4766	−	22.5591i	1.57335	−	1.20412i
$352$	−0.0121614	−	0.00466833i	−0.000648206	−	0.000248823i
$353$	25.3904	+	16.4887i	1.35139	+	0.877605i	0.998317	−	0.0579894i	$-0.0184689\pi$
$353$	25.3904	+	16.4887i	1.35139	+	0.877605i	0.353076	+	0.935595i	$0.385136\pi$
$354$	1.27378	−	1.34116i	0.0677008	−	0.0712816i
$355$	8.31967	+	16.5134i	0.441562	+	0.876438i
$356$	−2.57476	+	0.836589i	−0.136462	+	0.0443391i
$357$	−0.0639858	−	0.104514i	−0.00338649	−	0.00553147i
$358$	−11.5067	+	4.41701i	−0.608149	+	0.233446i
$359$	13.2339	+	2.81296i	0.698460	+	0.148462i	0.543439	−	0.839449i	$-0.317122\pi$
$359$	13.2339	+	2.81296i	0.698460	+	0.148462i	0.155021	+	0.987911i	$0.450455\pi$
$360$	4.76890	−	4.71780i	0.251343	−	0.248650i
$361$	−5.42563	+	2.41565i	−0.285560	+	0.127139i
$362$	23.4536	+	1.22915i	1.23270	+	0.0646029i
$363$	6.35221	+	17.9621i	0.333405	+	0.942767i
$364$	14.8078	+	20.3811i	0.776137	+	1.06826i
$365$	−2.06611	−	0.00938829i	−0.108145	−	0.000491406i
$366$	20.3847	+	0.542382i	1.06552	+	0.0283508i
$367$	−27.0409	+	7.24558i	−1.41152	+	0.378216i	−0.882468	−	0.470373i	$-0.844120\pi$
$367$	−27.0409	+	7.24558i	−1.41152	+	0.378216i	−0.529053	+	0.848589i	$0.677453\pi$
$368$	0.930531	+	5.87514i	0.0485073	+	0.306263i
$369$	−25.2916	−	6.79971i	−1.31663	−	0.353979i
$370$	−2.84864	−	4.43047i	−0.148094	−	0.230329i
$371$			41.3292i			2.14571i
$372$	1.77167	−	9.47951i	0.0918566	−	0.491490i
$373$	7.27196	−	7.27196i	0.376528	−	0.376528i	−0.493320	−	0.869848i	$-0.664217\pi$
$373$	7.27196	−	7.27196i	0.376528	−	0.376528i	0.869848	+	0.493320i	$0.164217\pi$
$374$	−8.07587e−5	0	0.000248550i	−4.17593e−6	0	1.28522e-5i
$375$	16.1117	−	10.7431i	0.832004	−	0.554769i
$376$	4.73548	+	3.44053i	0.244214	+	0.177432i
$377$	−12.2741	−	45.8074i	−0.632146	−	2.35920i
$378$	−17.2662	−	6.13883i	−0.888075	−	0.315747i
$379$	−4.51539	−	0.474586i	−0.231940	−	0.0243779i	−0.0121546	−	0.999926i	$-0.503869\pi$
$379$	−4.51539	−	0.474586i	−0.231940	−	0.0243779i	−0.219785	+	0.975548i	$0.570536\pi$
$380$	−0.635085	+	11.1486i	−0.0325792	+	0.571913i
$381$	12.9260	−	27.0706i	0.662221	−	1.38687i
$382$	−0.223043	+	4.25592i	−0.0114119	+	0.217752i
$383$	2.12551	+	0.815906i	0.108608	+	0.0416909i	0.412065	−	0.911154i	$-0.364808\pi$
$383$	2.12551	+	0.815906i	0.108608	+	0.0416909i	−0.303457	+	0.952845i	$0.598141\pi$
$384$	1.63246	+	0.578858i	0.0833061	+	0.0295397i
$385$	−0.0112019	+	0.102113i	−0.000570900	+	0.00520417i
$386$	0.140800	−	0.316242i	0.00716654	−	0.0160963i
$387$	−1.38224	−	0.00116422i	−0.0702634	−	5.91807e-5i
$388$	−11.7366	−	5.98007i	−0.595833	−	0.303592i
$389$	−11.7235	−	5.21965i	−0.594407	−	0.264647i	0.0874070	−	0.996173i	$-0.472142\pi$
$389$	−11.7235	−	5.21965i	−0.594407	−	0.264647i	−0.681814	+	0.731526i	$0.738809\pi$
$390$	21.8654	+	16.9511i	1.10720	+	0.858351i
$391$	0.116729	−	0.0248114i	0.00590322	−	0.00125477i
$392$	1.94853	−	5.07609i	0.0984155	−	0.256381i
$393$	7.26012	−	10.5540i	0.366225	−	0.532380i
$394$	0.311835	−	0.0327752i	0.0157100	−	0.00165119i
$395$	−14.7581	−	0.840697i	−0.742559	−	0.0423001i
$396$	0.0139743	+	0.0364960i	0.000702233	+	0.00183399i
$397$	−1.18067	+	4.40631i	−0.0592560	+	0.221146i	−0.989204	−	0.146544i	$-0.953185\pi$
$397$	−1.18067	+	4.40631i	−0.0592560	+	0.221146i	0.929948	+	0.367691i	$0.119852\pi$
$398$	5.61405	−	1.50428i	0.281407	−	0.0754027i
$399$	28.1873	−	11.6617i	1.41113	−	0.583814i
$400$	4.30723	+	2.53925i	0.215361	+	0.126962i
$401$	−13.0081	−	4.22660i	−0.649596	−	0.211066i	−0.0343598	−	0.999410i	$-0.510939\pi$
$401$	−13.0081	−	4.22660i	−0.649596	−	0.211066i	−0.615236	+	0.788343i	$0.710939\pi$
$402$	−15.2275	+	3.64901i	−0.759477	+	0.181996i
$403$	39.7163	+	2.12454i	1.97841	+	0.105831i
$404$	−8.25590			−0.410746
$405$	−20.0901	−	1.17839i	−0.998284	−	0.0585548i
$406$	−15.6659	+	17.3988i	−0.777487	+	0.863487i
$407$	0.0303075	−	0.00480024i	0.00150229	−	0.000237939i
$408$	0.00988312	−	0.0333133i	0.000489288	−	0.00164926i
$409$	7.16754	−	4.13818i	0.354412	−	0.204620i	−0.312215	−	0.950012i	$-0.601071\pi$
$409$	7.16754	−	4.13818i	0.354412	−	0.204620i	0.666627	+	0.745392i	$0.267737\pi$
$410$	0.0886999	−	19.5205i	0.00438058	−	0.964047i
$411$	2.20014	+	28.1067i	0.108525	+	1.38640i
$412$	−1.40291	+	1.73245i	−0.0691164	+	0.0853517i
$413$	0.197102	−	3.76094i	0.00969877	−	0.185064i
$414$	11.2420	−	13.8588i	0.552513	−	0.681123i
$415$	19.4118	−	6.20990i	0.952888	−	0.304832i
$416$	−1.48521	+	6.98736i	−0.0728184	+	0.342583i
$417$	0.475737	−	2.56083i	0.0232969	−	0.125404i
$418$	−0.0579634	−	0.0295338i	−0.00283508	−	0.00144455i
$419$	−10.1475	−	31.2309i	−0.495739	−	1.52573i	−0.815802	−	0.578332i	$-0.803704\pi$
$419$	−10.1475	−	31.2309i	−0.495739	−	1.52573i	0.320062	−	0.947397i	$-0.396296\pi$
$420$	1.13924	−	13.6110i	0.0555891	−	0.664151i
$421$	0.904542	+	0.192266i	0.0440847	+	0.00937049i	0.229901	−	0.973214i	$-0.426160\pi$
$421$	0.904542	+	0.192266i	0.0440847	+	0.00937049i	−0.185817	+	0.982584i	$0.559493\pi$
$422$	4.73582	−	7.29252i	0.230536	−	0.354994i
$423$	−1.82082	−	17.4655i	−0.0885314	−	0.849200i
$424$	−8.70901	+	7.84163i	−0.422947	+	0.380823i
$425$	0.0463502	−	0.0889594i	0.00224831	−	0.00431517i
$426$	14.2792	−	1.11775i	0.691829	−	0.0541550i
$427$	32.2672	−	26.1295i	1.56152	−	1.26449i
$428$	2.33689	−	8.72141i	0.112958	−	0.421565i
$429$	−0.141677	+	0.0768471i	−0.00684023	+	0.00371021i
$430$	−0.262127	−	0.996360i	−0.0126409	−	0.0480488i
$431$	−17.0639	−	15.3644i	−0.821938	−	0.740076i	0.146533	−	0.989206i	$-0.453189\pi$
$431$	−17.0639	−	15.3644i	−0.821938	−	0.740076i	−0.968470	+	0.249130i	$0.919855\pi$
$432$	−1.98241	−	4.80313i	−0.0953790	−	0.231091i
$433$	−10.2767	+	10.2767i	−0.493865	+	0.493865i	−0.909522	−	0.415656i	$-0.863552\pi$
$433$	−10.2767	+	10.2767i	−0.493865	+	0.493865i	0.415656	+	0.909522i	$0.363552\pi$
$434$	−9.79936	−	17.0155i	−0.470384	−	0.816769i
$435$	−11.1842	+	23.1517i	−0.536242	+	1.11004i
$436$	1.57344	−	4.84256i	0.0753542	−	0.231916i
$437$	1.55467	+	29.6649i	0.0743701	+	1.41907i
$438$	−0.613077	+	1.47834i	−0.0292939	+	0.0706377i
$439$	26.2416	+	15.1506i	1.25245	+	0.723100i	0.971595	−	0.236652i	$-0.0760501\pi$
$439$	26.2416	+	15.1506i	1.25245	+	0.723100i	0.280851	+	0.959751i	$0.409383\pi$
$440$	−0.0236430	+	0.0170140i	−0.00112713	+	0.000811111i
$441$	−15.2332	+	5.83276i	−0.725390	+	0.277750i
$442$	0.141548	+	0.0224190i	0.00673275	+	0.00106636i
$443$	3.43083	−	4.23672i	0.163003	−	0.201293i	−0.689099	−	0.724667i	$-0.741994\pi$
$443$	3.43083	−	4.23672i	0.163003	−	0.201293i	0.852103	+	0.523374i	$0.175327\pi$
$444$	−4.01198	+	0.741830i	−0.190400	+	0.0352057i
$445$	−1.59334	+	5.84016i	−0.0755317	+	0.276850i
$446$	−5.07891	−	23.8944i	−0.240493	−	1.13143i
$447$	−37.5987	+	0.968712i	−1.77836	+	0.0458185i
$448$	3.29241	−	1.26384i	0.155552	−	0.0597107i
$449$	−6.27725	−	19.3194i	−0.296242	−	0.911738i	−0.982802	−	0.184665i	$-0.940880\pi$
$449$	−6.27725	−	19.3194i	−0.296242	−	0.911738i	0.686560	−	0.727073i	$-0.259120\pi$
$450$	−2.97283	−	14.7025i	−0.140140	−	0.693081i
$451$	0.103890	+	0.0462547i	0.00489197	+	0.00217805i
$452$	6.09177	−	3.95604i	0.286533	−	0.186077i
$453$	29.2935	−	13.9572i	1.37633	−	0.655764i
$454$	−3.52890	−	7.92605i	−0.165620	−	0.371988i
$455$	56.2677	−	2.69254i	2.63787	−	0.126228i
$456$	7.80552	+	3.72708i	0.365527	+	0.174536i
$457$	−6.48705	−	1.02745i	−0.303451	−	0.0480620i	0.00285204	−	0.999996i	$-0.499092\pi$
$457$	−6.48705	−	1.02745i	−0.303451	−	0.0480620i	−0.306303	+	0.951934i	$0.599092\pi$
$458$	−6.41568	+	5.19531i	−0.299785	+	0.242761i
$459$	−0.0941469	+	0.0447599i	−0.00439440	+	0.00208921i
$460$	12.1263	+	5.46515i	0.565393	+	0.254814i
$461$	−0.337177	+	0.464085i	−0.0157039	+	0.0216146i	−0.816797	−	0.576926i	$-0.804252\pi$
$461$	−0.337177	+	0.464085i	−0.0157039	+	0.0216146i	0.801093	+	0.598540i	$0.204252\pi$
$462$	0.0699123	+	0.0379974i	0.00325262	+	0.00176780i
$463$	−1.59755	−	3.13537i	−0.0742444	−	0.145713i	0.850901	−	0.525327i	$-0.176057\pi$
$463$	−1.59755	−	3.13537i	−0.0742444	−	0.145713i	−0.925145	+	0.379614i	$0.876057\pi$
$464$	−6.63870			−0.308194
$465$	−15.5518	−	14.9379i	−0.721199	−	0.692728i
$466$	−9.15017			−0.423873
$467$	−14.8515	−	29.1477i	−0.687246	−	1.34880i	−0.925929	−	0.377698i	$-0.876716\pi$
$467$	−14.8515	−	29.1477i	−0.687246	−	1.34880i	0.238683	−	0.971098i	$-0.423284\pi$
$468$	18.5683	−	10.6996i	0.858319	−	0.494587i
$469$	−18.7401	+	25.7936i	−0.865338	+	1.19104i
$470$	12.2404	−	4.63494i	0.564607	−	0.213794i
$471$	−0.565985	+	21.2717i	−0.0260792	+	0.980150i
$472$	0.829913	−	0.672050i	0.0381998	−	0.0309336i
$473$	0.00592811		0.000938920i	0.000272575		4.31716e-5i
$474$	−4.93374	+	10.3326i	−0.226614	+	0.474592i
$475$	20.0666	+	14.8597i	0.920717	+	0.681809i
$476$	−0.0287773	−	0.0646349i	−0.00131900	−	0.00296253i
$477$	34.9617	+	3.70440i	1.60079	+	0.169613i
$478$	3.29342	−	2.13877i	0.150637	−	0.0978251i
$479$	33.5202	+	14.9241i	1.53158	+	0.681902i	0.987570	−	0.157179i	$-0.0502401\pi$
$479$	33.5202	+	14.9241i	1.53158	+	0.681902i	0.544006	+	0.839081i	$0.316907\pi$
$480$	3.08431	−	2.34244i	0.140779	−	0.106917i
$481$	−5.19983	−	16.0034i	−0.237092	−	0.729694i
$482$	−23.5833	+	9.05277i	−1.07419	+	0.412342i
$483$	−0.935833	−	36.3226i	−0.0425819	−	1.65273i
$484$	2.28699	+	10.7595i	0.103954	+	0.489066i
$485$	−25.5746	+	14.6110i	−1.16128	+	0.663449i
$486$	−6.74062	+	14.0557i	−0.305761	+	0.637582i
$487$	−5.11760	+	6.31971i	−0.231901	+	0.286374i	−0.879792	−	0.475360i	$-0.842318\pi$
$487$	−5.11760	+	6.31971i	−0.231901	+	0.286374i	0.647891	+	0.761733i	$0.275651\pi$
$488$	11.6283	+	1.84174i	0.526389	+	0.0833719i
$489$	−24.4141	−	18.7499i	−1.10404	−	0.847900i
$490$	−7.10153	−	9.86841i	−0.320814	−	0.445809i
$491$	8.40056	+	4.85006i	0.379112	+	0.218880i	0.677432	−	0.735586i	$-0.263093\pi$
$491$	8.40056	+	4.85006i	0.379112	+	0.218880i	−0.298320	+	0.954466i	$0.596426\pi$
$492$	−13.9672	−	5.79230i	−0.629691	−	0.261137i
$493$	0.00697041	+	0.133003i	0.000313931	+	0.00599017i
$494$	−11.0238	+	33.9278i	−0.495984	+	1.52648i
$495$	0.0853767	+	0.0186286i	0.00383740	+	0.000837291i
$496$	1.72626	−	5.29339i	0.0775115	−	0.237680i
$497$	20.6213	−	20.6213i	0.924992	−	0.924992i
$498$	1.24526	−	15.7378i	0.0558014	−	0.705227i
$499$	1.12870	+	1.01628i	0.0505275	+	0.0454952i	0.694008	−	0.719968i	$-0.255843\pi$
$499$	1.12870	+	1.01628i	0.0505275	+	0.0454952i	−0.643480	+	0.765463i	$0.722510\pi$
$500$	10.0300	−	4.93950i	0.448556	−	0.220901i
$501$	−16.2082	−	29.8818i	−0.724128	−	1.33502i
$502$	−4.85539	+	18.1206i	−0.216707	+	0.808760i
$503$	−11.3173	+	9.16461i	−0.504616	+	0.408630i	−0.847539	−	0.530734i	$-0.821916\pi$
$503$	−11.3173	+	9.16461i	−0.504616	+	0.408630i	0.342923	+	0.939364i	$0.388583\pi$
$504$	−9.42274	−	4.81113i	−0.419722	−	0.214305i
$505$	−10.1247	+	15.4366i	−0.450543	+	0.686922i
$506$	−0.0575843	+	0.0518491i	−0.00255993	+	0.00230498i
$507$	40.0760	+	52.2737i	1.77984	+	2.32155i
$508$	9.43291	−	14.5254i	0.418518	−	0.644461i
$509$	34.1789	+	7.26494i	1.51495	+	0.322013i	0.889021	−	0.457866i	$-0.151386\pi$
$509$	34.1789	+	7.26494i	1.51495	+	0.322013i	0.625930	+	0.779879i	$0.284720\pi$
$510$	−0.0501681	−	0.0593333i	−0.00222148	−	0.00262732i
$511$	1.00697	+	3.09914i	0.0445458	+	0.137098i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−7.33850	−	24.8898i	−0.324003	−	1.09891i
$514$	1.73002	−	8.13912i	0.0763081	−	0.359001i
$515$	1.51881	+	4.74773i	0.0669269	+	0.209210i
$516$	−0.791168	−	0.104498i	−0.0348292	−	0.00460028i
$517$	−0.00399060	+	0.0761452i	−0.000175507	+	0.00334886i
$518$	−5.22796	+	6.45599i	−0.229703	+	0.283660i
$519$	−13.2270	+	1.03538i	−0.580600	+	0.0454482i
$520$	11.2434	+	11.3460i	0.493054	+	0.497555i
$521$	9.32896	−	5.38608i	0.408709	−	0.235968i	−0.281526	−	0.959554i	$-0.590841\pi$
$521$	9.32896	−	5.38608i	0.408709	−	0.235968i	0.690235	+	0.723585i	$0.257507\pi$
$522$	13.3140	+	14.8118i	0.582738	+	0.648294i
$523$	−27.1346	+	4.29769i	−1.18651	+	0.187925i	−0.718327	−	0.695706i	$-0.755092\pi$
$523$	−27.1346	+	4.29769i	−1.18651	+	0.187925i	−0.468184	+	0.883631i	$0.655092\pi$
$524$	4.94880	−	5.49620i	0.216190	−	0.240103i
$525$	−24.0524	−	18.8221i	−1.04973	−	0.821465i
$526$	−6.83360			−0.297959
$527$	−0.107863	−	0.0290270i	−0.00469859	−	0.00126443i
$528$	0.00525794	+	0.0219416i	0.000228822	+	0.000954886i
$529$	11.7771	+	3.82661i	0.512047	+	0.166374i
$530$	3.98168	+	25.9005i	0.172953	+	1.12505i
$531$	−3.16383	−	0.503833i	−0.137298	−	0.0218645i
$532$	17.0116	−	4.55825i	0.737548	−	0.197625i
$533$	16.1404	−	60.2369i	0.699119	−	2.60915i
$534$	3.71892	+	2.85611i	0.160933	+	0.123596i
$535$	−13.4412	−	15.0650i	−0.581112	−	0.651318i
$536$	−8.99096	+	0.944988i	−0.388350	+	0.0408173i
$537$	17.5885	+	12.0991i	0.758999	+	0.522116i
$538$	−1.55613	+	4.05385i	−0.0670894	+	0.174774i
$539$	0.0692810	−	0.0147261i	0.00298414	−	0.000634299i
$540$	−11.4119	−	2.18369i	−0.491090	−	0.0939712i
$541$	23.9380	+	10.6579i	1.02917	+	0.458218i	0.850658	−	0.525719i	$-0.176204\pi$
$541$	23.9380	+	10.6579i	1.02917	+	0.458218i	0.178516	+	0.983937i	$0.442870\pi$
$542$	−1.02773	−	0.523656i	−0.0441449	−	0.0224929i
$543$	−21.2399	−	34.6932i	−0.911493	−	1.48883i
$544$	0.00815996	−	0.0183276i	0.000349855	−	0.000785788i
$545$	−7.12487	−	8.88068i	−0.305196	−	0.380407i
$546$	14.5829	−	41.1257i	0.624088	−	1.76002i
$547$	20.0599	+	7.70026i	0.857698	+	0.329239i	0.747169	−	0.664634i	$-0.231412\pi$
$547$	20.0599	+	7.70026i	0.857698	+	0.329239i	0.110528	+	0.993873i	$0.464746\pi$
$548$	−0.851876	+	16.2548i	−0.0363903	+	0.694369i
$549$	−19.2116	−	29.6379i	−0.819931	−	1.26491i
$550$	0.00281757	+	0.0650722i	0.000120141	+	0.00277469i
$551$	−32.9714	−	3.46544i	−1.40463	−	0.147633i
$552$	7.47644	−	7.08889i	0.318218	−	0.301723i
$553$	6.03401	+	22.5192i	0.256592	+	0.957615i
$554$	18.8171	+	13.6714i	0.799463	+	0.580844i
$555$	−3.53308	+	8.41124i	−0.149971	+	0.357037i
$556$	0.464697	−	1.43019i	0.0197076	−	0.0606536i
$557$	−10.3532	+	10.3532i	−0.438677	+	0.438677i	−0.891567	−	0.452890i	$-0.850393\pi$
$557$	−10.3532	+	10.3532i	−0.438677	+	0.438677i	0.452890	+	0.891567i	$0.350393\pi$
$558$	−15.2723	+	6.76447i	−0.646526	+	0.286363i
$559$		−	3.29134i		−	0.139209i
$560$	1.67459	−	7.70596i	0.0707642	−	0.325636i
$561$	0.000434069	0	0.000128378i	1.83264e−5	0	5.42014e-6i
$562$	−4.56825	−	28.8428i	−0.192700	−	1.21666i
$563$	−13.7585	+	3.68659i	−0.579853	+	0.155371i	−0.536812	−	0.843702i	$-0.680371\pi$
$563$	−13.7585	+	3.68659i	−0.579853	+	0.155371i	−0.0430416	+	0.999073i	$0.513705\pi$
$564$	0.269659	−	10.1347i	0.0113547	−	0.426750i
$565$	0.0738015	−	16.2417i	0.00310485	−	0.683295i
$566$	10.4111	+	14.3296i	0.437611	+	0.602319i
$567$	8.16321	+	30.6721i	0.342823	+	1.28811i
$568$	8.25798	+	0.432782i	0.346497	+	0.0181591i
$569$	3.82464	−	1.70284i	0.160337	−	0.0713868i	−0.324999	−	0.945714i	$-0.605364\pi$
$569$	3.82464	−	1.70284i	0.160337	−	0.0713868i	0.485336	+	0.874328i	$0.338697\pi$
$570$	16.5412	−	10.0238i	0.692833	−	0.419851i
$571$	−0.960416	−	0.204143i	−0.0401921	−	0.00854310i	0.187772	−	0.982213i	$-0.439873\pi$
$571$	−0.960416	−	0.204143i	−0.0401921	−	0.00854310i	−0.227964	+	0.973670i	$0.573207\pi$
$572$	−0.0868746	+	0.0333480i	−0.00363241	+	0.00139435i
$573$	6.29546	−	3.85422i	0.262997	−	0.161012i
$574$	−29.2805	+	9.51380i	−1.22214	+	0.397098i
$575$	25.0898	−	15.9712i	1.04632	−	0.666047i
$576$	−0.774016	−	2.89843i	−0.0322507	−	0.120768i
$577$	16.6784	+	10.8311i	0.694330	+	0.450903i	0.842951	−	0.537991i	$-0.180817\pi$
$577$	16.6784	+	10.8311i	0.694330	+	0.450903i	−0.148620	+	0.988894i	$0.547483\pi$
$578$	15.8705	+	6.09211i	0.660125	+	0.253398i
$579$	−0.589591	+	0.109017i	−0.0245026	+	0.00453061i
$580$	−8.14143	+	12.4129i	−0.338055	+	0.515416i
$581$	−18.8938	−	26.0050i	−0.783846	−	1.07887i
$582$	2.96843	+	22.6211i	0.123045	+	0.937673i
$583$	−0.147459	−	0.0395115i	−0.00610713	−	0.00163640i
$584$	−0.462001	+	0.800210i	−0.0191178	+	0.0331129i
$585$	2.76564	−	47.8399i	0.114345	−	1.97794i
$586$	−4.97387	+	5.52404i	−0.205468	+	0.228196i
$587$	0.812680	+	1.59497i	0.0335429	+	0.0658316i	0.907170	−	0.420765i	$-0.138238\pi$
$587$	0.812680	+	1.59497i	0.0335429	+	0.0658316i	−0.873627	+	0.486596i	$0.838238\pi$
$588$	−9.15827	+	2.19463i	−0.377681	+	0.0905049i
$589$	11.3367	−	25.3888i	0.467122	−	1.04613i
$590$	−0.238809	−	2.37592i	−0.00983162	−	0.0978151i
$591$	−0.352534	−	0.413117i	−0.0145013	−	0.0169934i
$592$	−2.35235	+	0.123282i	−0.0966812	+	0.00506685i
$593$	3.56355	+	22.4994i	0.146337	+	0.923939i	0.946159	+	0.323701i	$0.104927\pi$
$593$	3.56355	+	22.4994i	0.146337	+	0.923939i	−0.799822	+	0.600237i	$0.795073\pi$
$594$	0.0384096	−	0.0557353i	0.00157596	−	0.00228685i
$595$	−0.156144	−	0.0254586i	−0.00640127	−	0.00104370i
$596$	−21.5959	−	2.26982i	−0.884601	−	0.0929753i
$597$	−7.65213	−	6.54111i	−0.313181	−	0.267710i
$598$	33.0225	+	26.7411i	1.35039	+	1.09352i
$599$	9.97386	+	11.0771i	0.407521	+	0.452598i	0.911611	−	0.411053i	$-0.134839\pi$
$599$	9.97386	+	11.0771i	0.407521	+	0.452598i	−0.504091	+	0.863651i	$0.668172\pi$
$600$	−0.597350	−	8.63963i	−0.0243867	−	0.352711i
$601$	−43.6149	+	9.27062i	−1.77909	+	0.378157i	−0.976011	−	0.217720i	$-0.930138\pi$
$601$	−43.6149	+	9.27062i	−1.77909	+	0.378157i	−0.803076	+	0.595877i	$0.796805\pi$
$602$	−1.36275	+	0.884982i	−0.0555416	+	0.0360692i
$603$	20.1399	+	18.1648i	0.820159	+	0.739727i
$604$	17.8173	−	5.78919i	0.724976	−	0.235559i
$605$	22.9224	+	8.91880i	0.931928	+	0.362601i
$606$	8.09444	+	11.7881i	0.328814	+	0.478860i
$607$	0.912171	+	1.40462i	0.0370239	+	0.0570117i	0.856698	−	0.515818i	$-0.172512\pi$
$607$	0.912171	+	1.40462i	0.0370239	+	0.0570117i	−0.819674	+	0.572830i	$0.805845\pi$
$608$	4.18824	+	2.71988i	0.169856	+	0.110306i
$609$	40.2022	+	5.30995i	1.62908	+	0.215170i
$610$	17.7041	−	19.4837i	0.716819	−	0.788870i
$611$	41.5843	−	4.37068i	1.68232	−	0.176819i
$612$	−0.0572560	+	0.0185503i	−0.00231444	+	0.000749852i
$613$	−2.79116	−	3.44680i	−0.112734	−	0.139215i	0.717655	−	0.696398i	$-0.245215\pi$
$613$	−2.79116	−	3.44680i	−0.112734	−	0.139215i	−0.830389	+	0.557184i	$0.811882\pi$
$614$	6.87252	+	11.9036i	0.277352	+	0.480388i
$615$	−27.9591	+	19.0121i	−1.12742	+	0.766640i
$616$	0.0371665	+	0.0270030i	0.00149748	+	0.00108798i
$617$	1.18633	+	22.6365i	0.0477599	+	0.911312i	0.912496	+	0.409086i	$0.134152\pi$
$617$	1.18633	+	22.6365i	0.0477599	+	0.911312i	−0.864736	+	0.502227i	$0.832514\pi$
$618$	3.84914	+	0.304565i	0.154835	+	0.0122514i
$619$			22.0790i			0.887429i	0.896168	+	0.443714i	$0.146340\pi$
$619$			22.0790i			0.887429i	−0.896168	+	0.443714i	$0.853660\pi$
$620$	−7.78042	−	9.71931i	−0.312469	−	0.390337i
$621$	−30.8103	−	2.46399i	−1.23637	−	0.0988767i
$622$	−15.2478	+	7.76915i	−0.611381	+	0.311514i
$623$	9.53445	−	0.499680i	0.381990	−	0.0200192i
$624$	11.4330	−	4.73007i	0.457686	−	0.189354i
$625$	3.06466	−	24.8114i	0.122586	−	0.992458i
$626$	0.193418	−	0.111670i	0.00773053	−	0.00446322i
$627$	0.0146602	+	0.111719i	0.000585471	+	0.00446162i
$628$	−1.92189	+	12.1343i	−0.0766917	+	0.484213i
$629$	0.00493978	+	0.0469989i	0.000196962	+	0.00187397i
$630$	−20.5514	+	11.7182i	−0.818786	+	0.466864i
$631$	34.1593	−	15.2087i	1.35986	−	0.605449i	0.408282	−	0.912856i	$-0.366128\pi$
$631$	34.1593	−	15.2087i	1.35986	−	0.605449i	0.951578	+	0.307407i	$0.0994613\pi$
$632$	−3.60045	+	5.54420i	−0.143218	+	0.220537i
$633$	−15.0558	+	0.387904i	−0.598413	+	0.0154178i
$634$	−3.17003	+	7.12000i	−0.125898	+	0.282771i
$635$	−15.5911	−	35.4507i	−0.618712	−	1.40682i
$636$	19.7353	+	4.74681i	0.782555	+	0.188223i
$637$	−13.9192	−	36.2608i	−0.551500	−	1.43671i
$638$	−0.0471004	−	0.0725282i	−0.00186472	−	0.00287142i
$639$	−15.5959	−	19.2925i	−0.616964	−	0.763201i
$640$	1.94155	−	1.10922i	0.0767466	−	0.0438459i
$641$	−28.1545	+	25.3504i	−1.11203	+	1.00128i	−0.112063	+	0.993701i	$0.535746\pi$
$641$	−28.1545	+	25.3504i	−1.11203	+	1.00128i	−0.999971	+	0.00757913i	$0.997587\pi$
$642$	−14.7440	+	5.21413i	−0.581899	+	0.205785i
$643$	−1.23018	+	7.76704i	−0.0485135	+	0.306302i	−0.999999	−	0.00139129i	$-0.999557\pi$
$643$	−1.23018	+	7.76704i	−0.0485135	+	0.306302i	0.951486	+	0.307694i	$0.0995571\pi$
$644$	2.19278	−	20.8629i	0.0864076	−	0.822113i
$645$	−1.16564	+	1.35115i	−0.0458972	+	0.0532015i
$646$	0.0500939	−	0.0867652i	0.00197092	−	0.00341373i
$647$	−7.40922	+	1.17350i	−0.291286	+	0.0461352i	−0.300368	−	0.953824i	$-0.597109\pi$
$647$	−7.40922	+	1.17350i	−0.291286	+	0.0461352i	0.00908120	+	0.999959i	$0.497109\pi$
$648$	−4.91446	+	7.53977i	−0.193058	+	0.296190i
$649$	0.0132303	+	0.00429877i	0.000519333	+	0.000168742i
$650$	35.0028	−	7.10824i	1.37292	−	0.278808i
$651$	−14.6877	+	30.6746i	−0.575656	+	1.20223i
$652$	−12.5672	−	12.5672i	−0.492169	−	0.492169i
$653$	−2.06709	+	1.05324i	−0.0808915	+	0.0412163i	−0.493968	−	0.869480i	$-0.664454\pi$
$653$	−2.06709	+	1.05324i	−0.0808915	+	0.0412163i	0.413077	+	0.910696i	$0.364454\pi$
$654$	−8.45707	+	2.50122i	−0.330698	+	0.0978056i
$655$	−4.20764	−	15.9934i	−0.164406	−	0.624916i
$656$	−7.56032	−	4.36496i	−0.295181	−	0.170423i
$657$	2.71192	−	0.574049i	0.105802	−	0.0223958i
$658$	−12.9909	−	16.0424i	−0.506438	−	0.625399i
$659$	−29.9613	+	21.7682i	−1.16713	+	0.847967i	−0.990662	−	0.136339i	$-0.956466\pi$
$659$	−29.9613	+	21.7682i	−1.16713	+	0.847967i	−0.176465	+	0.984307i	$0.556466\pi$
$660$	0.0474739	+	0.0170771i	0.00184792	+	0.000664726i
$661$	8.16527	+	9.06845i	0.317592	+	0.352722i	0.880711	−	0.473654i	$-0.157065\pi$
$661$	8.16527	+	9.06845i	0.317592	+	0.352722i	−0.563119	+	0.826376i	$0.690399\pi$
$662$	−2.57200	+	6.70029i	−0.0999636	+	0.260414i
$663$	−0.106769	−	0.224089i	−0.00414656	−	0.00870288i
$664$	1.89503	−	8.91544i	0.0735416	−	0.345986i
$665$	12.3395	−	37.3979i	0.478504	−	1.45023i
$666$	4.99274	+	5.00115i	0.193465	+	0.193791i
$667$	−17.9279	+	35.1854i	−0.694169	+	1.36238i
$668$	−7.03359	−	18.3231i	−0.272138	−	0.708943i
$669$	−29.1378	+	30.6790i	−1.12653	+	1.18612i
$670$	−9.25923	+	17.9699i	−0.357715	+	0.694239i
$671$	0.0623796	+	0.140107i	0.00240814	+	0.00540877i
$672$	−5.03258	−	3.46192i	−0.194136	−	0.133546i
$673$	15.4022	+	12.4725i	0.593711	+	0.480778i	0.878454	−	0.477826i	$-0.158575\pi$
$673$	15.4022	+	12.4725i	0.593711	+	0.480778i	−0.284743	+	0.958604i	$0.591908\pi$
$674$	−1.11567	+	0.810579i	−0.0429739	+	0.0312223i
$675$	−18.0781	+	18.6597i	−0.695826	+	0.718210i
$676$	19.0145	+	32.9341i	0.731328	+	1.26670i
$677$	−3.00186	−	11.2031i	−0.115371	−	0.430569i	0.883944	−	0.467593i	$-0.154879\pi$
$677$	−3.00186	−	11.2031i	−0.115371	−	0.430569i	−0.999314	+	0.0370241i	$0.988212\pi$
$678$	−11.6212	−	4.81941i	−0.446311	−	0.185088i
$679$	34.5219	+	31.0837i	1.32483	+	1.19288i
$680$	−0.0242613	−	0.0377334i	−0.000930380	−	0.00144701i
$681$	−7.85725	+	12.8098i	−0.301091	+	0.490871i
$682$	0.0700781	−	0.0186961i	0.00268343	−	0.000715912i
$683$	23.1459	+	23.1459i	0.885653	+	0.885653i	0.994102	−	0.108449i	$-0.0345884\pi$
$683$	23.1459	+	23.1459i	0.885653	+	0.885653i	−0.108449	+	0.994102i	$0.534588\pi$
$684$	−2.33119	−	14.7992i	−0.0891354	−	0.565863i
$685$	29.3480	+	21.5270i	1.12133	+	0.822504i
$686$	3.23949	−	4.45877i	0.123684	−	0.170237i
$687$	13.7083	+	4.06686i	0.523004	+	0.155160i
$688$	−0.445049	−	0.119250i	−0.0169673	−	0.00454638i
$689$	−8.75061	+	83.2565i	−0.333372	+	3.17182i
$690$	−4.08581	−	22.6728i	−0.155544	−	0.863137i
$691$	4.42797	+	42.1293i	0.168448	+	1.60267i	0.673234	+	0.739429i	$0.264904\pi$
$691$	4.42797	+	42.1293i	0.168448	+	1.60267i	−0.504787	+	0.863244i	$0.668429\pi$
$692$	−7.64947	−	0.400892i	−0.290789	−	0.0152396i
$693$	−0.0142908	−	0.137078i	−0.000542861	−	0.00520717i
$694$	4.14149	+	19.4842i	0.157209	+	0.739609i
$695$	−2.10424	−	2.62280i	−0.0798186	−	0.0994887i
$696$	6.50887	+	9.47902i	0.246718	+	0.359301i
$697$	−0.0795118	+	0.156051i	−0.00301172	+	0.00591084i
$698$	−3.76997	+	7.39899i	−0.142696	+	0.280056i
$699$	8.97122	+	13.0650i	0.339323	+	0.494163i
$700$	−12.3547	−	12.5814i	−0.466966	−	0.475531i
$701$	6.54114	+	30.7737i	0.247056	+	1.16230i	0.910315	+	0.413916i	$0.135839\pi$
$701$	6.54114	+	30.7737i	0.247056	+	1.16230i	−0.663260	+	0.748389i	$0.730828\pi$
$702$	−33.4824	−	16.0222i	−1.26371	−	0.604721i
$703$	−11.7474	−	0.615657i	−0.443063	−	0.0232200i
$704$	0.00136165	+	0.0129553i	5.13193e−5	+	0.000488270i
$705$	−18.6190	−	12.9330i	−0.701231	−	0.487086i
$706$	3.16455	−	30.1087i	0.119100	−	1.13316i
$707$	28.1235	+	7.53568i	1.05769	+	0.283408i
$708$	−1.77326	−	0.526077i	−0.0666433	−	0.0197712i
$709$	14.4242	−	19.8531i	0.541710	−	0.745601i	−0.447148	−	0.894460i	$-0.647560\pi$
$709$	14.4242	−	19.8531i	0.541710	−	0.745601i	0.988858	+	0.148860i	$0.0475602\pi$
$710$	10.9364	−	14.9098i	0.410438	−	0.559554i
$711$	19.5906	−	3.08593i	0.734703	−	0.115731i
$712$	1.91432	+	1.91432i	0.0717422	+	0.0717422i
$713$	−23.3934	−	23.4441i	−0.876091	−	0.877988i
$714$	−0.0640738	+	0.104460i	−0.00239790	+	0.00390933i
$715$	−0.0441862	+	0.203332i	−0.00165247	+	0.00760419i
$716$	9.15953	+	8.24727i	0.342308	+	0.308215i
$717$	−6.28283	−	2.60554i	−0.234637	−	0.0973055i
$718$	−3.50171	−	13.0686i	−0.130683	−	0.487715i
$719$	10.4447	+	18.0908i	0.389523	+	0.674674i	0.992385	−	0.123171i	$-0.0393064\pi$
$719$	10.4447	+	18.0908i	0.389523	+	0.674674i	−0.602862	+	0.797845i	$0.705973\pi$
$720$	−6.36862	−	2.10728i	−0.237345	−	0.0785338i
$721$	6.36030	−	4.62103i	0.236870	−	0.172096i
$722$	4.61554	+	3.73759i	0.171773	+	0.139099i
$723$	36.0480	+	24.7974i	1.34064	+	0.922227i
$724$	−9.55255	−	21.4554i	−0.355018	−	0.797383i
$725$	13.2249	+	30.4452i	0.491160	+	1.13071i
$726$	13.1205	−	13.8145i	0.486949	−	0.512704i
$727$	6.02235	+	15.6888i	0.223357	+	0.581864i	0.998770	−	0.0495906i	$-0.0157916\pi$
$727$	6.02235	+	15.6888i	0.223357	+	0.581864i	−0.775413	+	0.631454i	$0.782458\pi$
$728$	11.4371	−	22.4466i	0.423888	−	0.831928i
$729$	26.6782	−	4.15633i	0.988080	−	0.153938i
$730$	0.929630	+	1.84518i	0.0344071	+	0.0682932i
$731$	−0.00192184	+	0.00904155i	−7.10818e−5	+	0.000334414i
$732$	−8.77119	−	18.4091i	−0.324192	−	0.680421i
$733$	−7.66536	+	19.9689i	−0.283126	+	0.737570i	0.716091	+	0.698007i	$0.245930\pi$
$733$	−7.66536	+	19.9689i	−0.283126	+	0.737570i	−0.999217	+	0.0395623i	$0.987404\pi$
$734$	18.7321	+	20.8042i	0.691416	+	0.767895i
$735$	−7.12787	+	19.8153i	−0.262916	+	0.730897i
$736$	4.81234	−	3.49637i	0.177385	−	0.128878i
$737$	−0.0741133	−	0.0915223i	−0.00273000	−	0.00337127i
$738$	5.42357	+	25.6220i	0.199644	+	0.943159i
$739$	21.6830	+	12.5187i	0.797624	+	0.460508i	0.842640	−	0.538478i	$-0.181001\pi$
$739$	21.6830	+	12.5187i	0.797624	+	0.460508i	−0.0450159	+	0.998986i	$0.514334\pi$
$740$	−2.65432	+	4.54955i	−0.0975748	+	0.167245i
$741$	59.2517	−	17.5240i	2.17667	−	0.643761i
$742$	36.8246	−	18.7631i	1.35187	−	0.688814i
$743$	11.1720	+	11.1720i	0.409863	+	0.409863i	0.881691	−	0.471828i	$-0.156406\pi$
$743$	11.1720	+	11.1720i	0.409863	+	0.409863i	−0.471828	+	0.881691i	$0.656406\pi$
$744$	−9.25063	+	2.72504i	−0.339145	+	0.0999049i
$745$	−30.7283	+	37.5957i	−1.12580	+	1.37740i
$746$	−9.78077	−	3.17796i	−0.358099	−	0.116354i
$747$	−23.6920	+	13.6520i	−0.866844	+	0.499499i
$748$	0.000258123	0	4.08827e-5i	9.43792e−6	0	1.49482e-6i
$749$	−15.9212	+	27.5763i	−0.581746	+	1.00761i
$750$	−16.8867	−	9.47837i	−0.616615	−	0.346101i
$751$	5.60546	−	53.3324i	0.204546	−	1.94613i	−0.103204	−	0.994660i	$-0.532909\pi$
$751$	5.60546	−	53.3324i	0.204546	−	1.94613i	0.307750	−	0.951467i	$-0.400424\pi$
$752$	0.915669	−	5.78131i	0.0333910	−	0.210823i
$753$	30.6337	−	10.8335i	1.11636	−	0.394793i
$754$	−35.2424	+	31.7324i	−1.28345	+	1.15563i
$755$	11.0259	−	40.4139i	0.401275	−	1.47081i
$756$	2.36894	+	18.1712i	0.0861573	+	0.660881i
$757$	−11.5658	−	17.8098i	−0.420366	−	0.647307i	0.563520	−	0.826102i	$-0.309447\pi$
$757$	−11.5658	−	17.8098i	−0.420366	−	0.647307i	−0.983886	+	0.178795i	$0.942780\pi$
$758$	1.62708	+	4.23870i	0.0590983	+	0.153956i
$759$	0.130490	+	0.0313861i	0.00473650	+	0.00113924i
$760$	10.2218	−	4.49551i	0.370785	−	0.163069i
$761$	−18.3819	+	41.2865i	−0.666344	+	1.49663i	0.190839	+	0.981621i	$0.438879\pi$
$761$	−18.3819	+	41.2865i	−0.666344	+	1.49663i	−0.857183	+	0.515012i	$0.827787\pi$
$762$	−29.9884	+	0.772637i	−1.08637	+	0.0279897i
$763$	−9.78000	+	15.0599i	−0.354060	+	0.545204i
$764$	3.89331	−	1.73341i	0.140855	−	0.0627127i
$765$	−0.0355316	+	0.129805i	−0.00128465	+	0.00469311i
$766$	−0.237983	−	2.26426i	−0.00859867	−	0.0818109i
$767$	1.19336	−	7.53457i	0.0430897	−	0.272058i
$768$	−0.225355	−	1.71733i	−0.00813179	−	0.0619687i
$769$	−16.6722	+	9.62569i	−0.601214	+	0.347111i	−0.769519	−	0.638624i	$-0.779504\pi$
$769$	−16.6722	+	9.62569i	−0.601214	+	0.347111i	0.168305	+	0.985735i	$0.446171\pi$
$770$	0.0960690	−	0.0363774i	0.00346209	−	0.00131095i
$771$	−13.3176	+	5.50975i	−0.479621	+	0.198429i
$772$	−0.345696	+	0.0181172i	−0.0124419	+	0.000652051i
$773$	−39.5826	+	20.1683i	−1.42369	+	0.725404i	−0.984890	−	0.173182i	$-0.944595\pi$
$773$	−39.5826	+	20.1683i	−1.42369	+	0.725404i	−0.438796	+	0.898587i	$0.644595\pi$
$774$	0.626488	+	1.23212i	0.0225187	+	0.0442875i
$775$	−27.7145	+	2.62824i	−0.995533	+	0.0944092i
$776$			13.1722i			0.472856i
$777$	14.3438	+	1.13496i	0.514583	+	0.0407166i
$778$	0.671628	+	12.8154i	0.0240790	+	0.459455i
$779$	−35.2702	−	25.6253i	−1.26369	−	0.918121i
$780$	5.17682	−	27.1779i	0.185360	−	0.973123i
$781$	0.0538607	+	0.0932894i	0.00192729	+	0.00333816i
$782$	−0.0751009	−	0.0927418i	−0.00268560	−	0.00331644i
$783$	8.09524	−	33.5324i	0.289300	−	1.19835i
$784$	−5.40744	+	0.568345i	−0.193123	+	0.0202980i
$785$	20.3315	+	18.4745i	0.725662	+	0.659385i
$786$	−12.6997	−	1.67739i	−0.452984	−	0.0598306i
$787$	−6.07958	−	3.94813i	−0.216714	−	0.140736i	0.431717	−	0.902009i	$-0.357908\pi$
$787$	−6.07958	−	3.94813i	−0.216714	−	0.140736i	−0.648431	+	0.761273i	$0.724574\pi$
$788$	−0.170773	−	0.262967i	−0.00608354	−	0.00936783i
$789$	6.69995	+	9.75729i	0.238525	+	0.347369i
$790$	5.95095	+	13.5312i	0.211725	+	0.481418i
$791$	−24.3624	+	7.91582i	−0.866227	+	0.281454i
$792$	0.0261740	−	0.0290200i	0.000930053	−	0.00103118i
$793$	70.5338	−	45.8052i	2.50473	−	1.62659i
$794$	4.46206	−	0.948441i	0.158353	−	0.0336589i
$795$	33.0780	−	31.0792i	1.17316	−	1.10226i
$796$	−3.88905	−	4.31923i	−0.137844	−	0.153091i
$797$	−33.6223	−	27.2268i	−1.19096	−	0.964421i	−0.191108	−	0.981569i	$-0.561208\pi$
$797$	−33.6223	−	27.2268i	−1.19096	−	0.964421i	−0.999853	+	0.0171476i	$0.994541\pi$
$798$	−23.1874	−	19.8208i	−0.820825	−	0.701649i
$799$	−0.116787	−	0.0122748i	−0.00413163	−	0.000434252i
$800$	0.307045	−	4.99056i	0.0108557	−	0.176443i
$801$	0.431892	−	8.11028i	0.0152602	−	0.286563i
$802$	2.13964	+	13.5092i	0.0755534	+	0.477026i
$803$	−0.0120202		0.000629949i	−0.000424182		2.22304e-5i
$804$	10.1644	+	11.9112i	0.358472	+	0.420074i
$805$	−36.3197	−	29.6854i	−1.28010	−	1.04627i
$806$	−16.1379	−	36.3520i	−0.568432	−	1.28045i
$807$	7.31395	−	1.75267i	0.257463	−	0.0616968i
$808$	3.74810	+	7.35606i	0.131858	+	0.258785i
$809$	−19.5190	+	21.6780i	−0.686250	+	0.762158i	−0.981124	−	0.193378i	$-0.938056\pi$
$809$	−19.5190	+	21.6780i	−0.686250	+	0.762158i	0.294874	+	0.955536i	$0.404722\pi$
$810$	8.07075	+	18.4354i	0.283577	+	0.647753i
$811$	−15.3038	+	26.5070i	−0.537390	+	0.930787i	0.461653	+	0.887060i	$0.347256\pi$
$811$	−15.3038	+	26.5070i	−0.537390	+	0.930787i	−0.999044	+	0.0437266i	$0.986077\pi$
$812$	22.6146	+	6.05956i	0.793617	+	0.212649i
$813$	0.259936	+	1.98085i	0.00911634	+	0.0694715i
$814$	−0.0180364	−	0.0248250i	−0.000632175	−	0.000870114i
$815$	−38.9096	+	8.08589i	−1.36295	+	0.283236i
$816$	−0.0341692	+	0.00631801i	−0.00119616	+	0.000221175i
$817$	−2.14811	−	0.824581i	−0.0751527	−	0.0288484i
$818$	−6.94114	−	4.50763i	−0.242691	−	0.157606i
$819$	−73.0186	+	19.4994i	−2.55148	+	0.681363i
$820$	−17.4331	+	8.78308i	−0.608792	+	0.306718i
$821$	−0.811994	+	0.263833i	−0.0283388	+	0.00920783i	−0.323152	−	0.946347i	$-0.604743\pi$
$821$	−0.811994	+	0.263833i	−0.0283388	+	0.00920783i	0.294813	+	0.955555i	$0.404743\pi$
$822$	24.0444	−	14.7205i	0.838646	−	0.513437i
$823$	−28.1505	+	10.8060i	−0.981265	+	0.376672i	−0.795521	−	0.605926i	$-0.792803\pi$
$823$	−28.1505	+	10.8060i	−0.981265	+	0.376672i	−0.185744	+	0.982598i	$0.559469\pi$
$824$	2.18053	+	0.463486i	0.0759624	+	0.0161463i
$825$	0.0901503	−	0.0678226i	0.00313863	−	0.00236128i
$826$	−3.44050	+	1.53181i	−0.119710	+	0.0532985i
$827$	15.9575	+	0.836299i	0.554898	+	0.0290810i	0.327724	−	0.944773i	$-0.393718\pi$
$827$	15.9575	+	0.836299i	0.554898	+	0.0290810i	0.227173	+	0.973854i	$0.427052\pi$
$828$	−17.4520	−	3.72491i	−0.606500	−	0.129450i
$829$	−5.57863	−	7.67832i	−0.193754	−	0.266679i	0.701076	−	0.713086i	$-0.252703\pi$
$829$	−5.57863	−	7.67832i	−0.193754	−	0.266679i	−0.894830	+	0.446407i	$0.852703\pi$
$830$	−14.3458	−	14.4768i	−0.497951	−	0.502497i
$831$	1.07153	−	40.2720i	0.0371710	−	1.39702i
$832$	6.90005	−	1.84886i	0.239216	−	0.0640978i
$833$	0.0170642	+	0.107739i	0.000591238	+	0.00373293i
$834$	−2.49770	+	0.738707i	−0.0864881	+	0.0255793i
$835$	−42.8857	−	9.31952i	−1.48412	−	0.322515i
$836$			0.0650538i			0.00224993i
$837$	24.6322	+	15.1742i	0.851412	+	0.524497i
$838$	−23.2200	+	23.2200i	−0.802123	+	0.802123i
$839$	−10.0359	+	30.8874i	−0.346478	+	1.06635i	0.614309	+	0.789066i	$0.289435\pi$
$839$	−10.0359	+	30.8874i	−0.346478	+	1.06635i	−0.960788	+	0.277286i	$0.910565\pi$
$840$	−12.6447	+	5.16422i	−0.436285	+	0.178182i
$841$	−12.1938	−	8.85933i	−0.420477	−	0.305494i
$842$	−0.239343	−	0.893240i	−0.00824830	−	0.0307831i
$843$	−36.7040	+	34.8014i	−1.26415	+	1.19863i
$844$	−8.64770	−	0.908910i	−0.297666	−	0.0312860i
$845$	84.8979	+	4.83623i	2.92058	+	0.166371i
$846$	−14.7352	+	9.55151i	−0.506607	+	0.328388i
$847$	2.03024	−	38.7393i	0.0697600	−	1.33110i
$848$	10.9407	+	4.19976i	0.375707	+	0.144220i
$849$	10.2530	−	28.9148i	0.351881	−	0.992353i
$850$	−0.100306		0.000911588i	−0.00344047		3.12672e-5i
$851$	−5.69915	+	12.8005i	−0.195364	+	0.438796i
$852$	−7.47854	−	12.2154i	−0.256210	−	0.418493i
$853$	−40.2583	−	20.5126i	−1.37842	−	0.702339i	−0.401481	−	0.915868i	$-0.631504\pi$
$853$	−40.2583	−	20.5126i	−1.37842	−	0.702339i	−0.976937	+	0.213529i	$0.931504\pi$
$854$	−37.9305	−	16.8878i	−1.29796	−	0.577887i
$855$	−30.5301	−	13.7904i	−1.04411	−	0.471621i
$856$	−8.83176	+	1.87725i	−0.301863	+	0.0641630i
$857$	−15.0439	+	39.1908i	−0.513891	+	1.33873i	0.393840	+	0.919179i	$0.371147\pi$
$857$	−15.0439	+	39.1908i	−0.513891	+	1.33873i	−0.907731	+	0.419553i	$0.862187\pi$
$858$	0.132791	+	0.0913473i	0.00453342	+	0.00311854i
$859$	43.4759	−	4.56950i	1.48338	−	0.155909i	0.672053	−	0.740503i	$-0.265413\pi$
$859$	43.4759	−	4.56950i	1.48338	−	0.155909i	0.811326	+	0.584594i	$0.198746\pi$
$860$	−0.768760	+	0.685895i	−0.0262145	+	0.0233888i
$861$	42.2920	+	32.4801i	1.44131	+	1.10692i
$862$	−5.94292	+	22.1793i	−0.202417	+	0.755430i
$863$	54.4214	−	14.5822i	1.85253	−	0.496383i	0.852858	−	0.522143i	$-0.174867\pi$
$863$	54.4214	−	14.5822i	1.85253	−	0.496383i	0.999668	+	0.0257601i	$0.00820059\pi$
$864$	−3.37962	+	3.94692i	−0.114977	+	0.134277i
$865$	−10.1306	+	13.8111i	−0.344450	+	0.469592i
$866$	13.8221	+	4.49107i	0.469694	+	0.152613i
$867$	−6.86155	−	28.6335i	−0.233030	−	0.972445i
$868$	−10.7121	+	16.4562i	−0.363592	+	0.558558i
$869$	−0.0861152			−0.00292126
$870$	25.7058	−	0.545428i	0.871508	−	0.0184917i
$871$	−43.2127	+	47.9926i	−1.46421	+	1.62617i
$872$	−5.02908	+	0.796527i	−0.170306	+	0.0269738i
$873$	29.3889	−	26.4171i	0.994664	−	0.894083i
$874$	25.7258	−	14.8528i	0.870189	−	0.502404i
$875$	−38.6756	+	7.67128i	−1.30748	+	0.259337i
$876$	1.59554	−	0.124896i	0.0539083	−	0.00421983i
$877$	28.9664	−	35.7705i	0.978126	−	1.20788i	−2.73676e−5	−	1.00000i	$-0.500009\pi$
$877$	28.9664	−	35.7705i	0.978126	−	1.20788i	0.978153	−	0.207885i	$-0.0666580\pi$
$878$	1.58584	−	30.2597i	0.0535197	−	1.02122i
$879$	12.7640	+	1.68589i	0.430520	+	0.0568635i
$880$	0.0258933	+	0.0133418i	0.000872862	+	0.000449753i
$881$	−8.36247	+	39.3423i	−0.281739	+	1.32548i	0.578541	+	0.815654i	$0.303622\pi$
$881$	−8.36247	+	39.3423i	−0.281739	+	1.32548i	−0.860279	+	0.509823i	$0.829711\pi$
$882$	12.1127	+	10.9249i	0.407857	+	0.367859i
$883$	−52.3056	−	26.6511i	−1.76022	−	0.896879i	−0.950888	−	0.309534i	$-0.899827\pi$
$883$	−52.3056	−	26.6511i	−1.76022	−	0.896879i	−0.809337	−	0.587345i	$-0.800173\pi$
$884$	−0.0442859	−	0.136298i	−0.00148950	−	0.00458420i
$885$	−3.15830	+	2.67044i	−0.106165	+	0.0897658i
$886$	−5.33251	−	1.13346i	−0.179149	−	0.0380793i
$887$	−3.25753	+	5.01616i	−0.109377	+	0.168426i	−0.889120	−	0.457673i	$-0.848683\pi$
$887$	−3.25753	+	5.01616i	−0.109377	+	0.168426i	0.779743	+	0.626099i	$0.215350\pi$
$888$	2.48238	+	3.23792i	0.0833031	+	0.108657i
$889$	−45.3913	+	40.8705i	−1.52237	+	1.37075i
$890$	5.92698	−	1.23170i	0.198673	−	0.0412866i
$891$	−0.117240		0.000197495i	−0.00392767		6.61632e-6i
$892$	−18.9843	+	15.3732i	−0.635640	+	0.514732i
$893$	7.56559	−	28.2352i	0.253173	−	0.944853i
$894$	17.9326	+	33.0609i	0.599755	+	1.10572i
$895$	26.6534	−	7.01210i	0.890924	−	0.234389i
$896$	−2.62081	−	2.35979i	−0.0875551	−	0.0788349i
$897$	5.80535	−	73.3690i	0.193835	−	2.44972i
$898$	−14.3639	+	14.3639i	−0.479329	+	0.479329i
$899$	29.9270	−	21.6938i	0.998121	−	0.723528i
$900$	−11.7504	+	9.32359i	−0.391678	+	0.310786i
$901$	0.0726528	−	0.223602i	0.00242042	−	0.00744928i
$902$	−0.00595172	−	0.113566i	−0.000198170	−	0.00378132i
$903$	2.59971	+	1.07812i	0.0865131	+	0.0358776i
$904$	−6.29046	−	3.63180i	−0.209218	−	0.120792i
$905$	−51.8315	−	8.45090i	−1.72294	−	0.280918i
$906$	−25.7349	−	19.7643i	−0.854985	−	0.656625i
$907$	5.14318	+	0.814599i	0.170776	+	0.0270483i	0.241237	−	0.970466i	$-0.422447\pi$
$907$	5.14318	+	0.814599i	0.170776	+	0.0270483i	−0.0704606	+	0.997515i	$0.522447\pi$
$908$	−5.46007	+	6.74263i	−0.181199	+	0.223762i
$909$	8.89542	−	23.1152i	0.295043	−	0.766682i
$910$	−27.9441	−	48.9125i	−0.926336	−	1.62143i
$911$	−1.94856	−	9.16726i	−0.0645587	−	0.303725i	0.934008	−	0.357253i	$-0.116287\pi$
$911$	−1.94856	−	9.16726i	−0.0645587	−	0.303725i	−0.998566	+	0.0535282i	$0.982953\pi$
$912$	−0.222781	−	8.64683i	−0.00737702	−	0.286325i
$913$	0.110847	−	0.0425500i	0.00366849	−	0.00140820i
$914$	2.02960	+	6.24645i	0.0671330	+	0.206614i
$915$	−45.1775	−	6.17607i	−1.49352	−	0.204175i
$916$	7.54171	+	3.35779i	0.249185	+	0.110944i
$917$	−21.8747	+	14.2056i	−0.722367	+	0.469111i
$918$	0.0826232	+	0.0635650i	0.00272697	+	0.00209796i
$919$	5.69534	+	12.7919i	0.187872	+	0.421967i	0.982784	−	0.184757i	$-0.0591498\pi$
$919$	5.69534	+	12.7919i	0.187872	+	0.421967i	−0.794912	+	0.606724i	$0.792483\pi$
$920$	−0.635756	−	13.2858i	−0.0209603	−	0.438019i
$921$	10.2583	−	21.4836i	0.338021	−	0.707909i
$922$	0.566578	+	0.0897371i	0.0186592	+	0.00295533i
$923$	45.9072	−	37.1749i	1.51105	−	1.22363i
$924$	0.00211642	−	0.0795428i	6.96252e−5	−	0.00261677i
$925$	5.25147	+	10.5424i	0.172667	+	0.346631i
$926$	−2.06836	+	2.84685i	−0.0679705	+	0.0935534i
$927$	−3.33899	−	5.79457i	−0.109667	−	0.190319i
$928$	3.01391	+	5.91513i	0.0989364	+	0.194174i
$929$	−38.2940			−1.25638			−0.628192	−	0.778058i	$-0.716205\pi$
$929$	−38.2940			−1.25638			−0.628192	+	0.778058i	$0.716205\pi$
$930$	−6.24938	+	20.6384i	−0.204925	+	0.676761i
$931$	−27.1530			−0.889904
$932$	4.15409	+	8.15286i	0.136072	+	0.267056i
$933$	26.0427	+	14.1542i	0.852600	+	0.463389i
$934$	−19.2284	+	26.4656i	−0.629172	+	0.865980i
$935$	0.000240110	0	0.000532768i	7.85245e−6	0	1.74234e-5i
$936$	−17.9632	−	11.6870i	−0.587145	−	0.382000i
$937$	39.4934	−	31.9811i	1.29019	−	1.04478i	0.294162	−	0.955756i	$-0.404959\pi$
$937$	39.4934	−	31.9811i	1.29019	−	1.04478i	0.996030	−	0.0890213i	$-0.0283739\pi$
$938$	31.4901	+	4.98754i	1.02819	+	0.162849i
$939$	−0.349082	−	0.166684i	−0.0113919	−	0.00543952i
$940$	−9.68678	−	8.80205i	−0.315948	−	0.287091i
$941$	−23.5492	−	52.8923i	−0.767681	−	1.72424i	−0.686023	−	0.727580i	$-0.740645\pi$
$941$	−23.5492	−	52.8923i	−0.767681	−	1.72424i	−0.0816586	−	0.996660i	$-0.526022\pi$
$942$	19.2102	−	9.15287i	0.625902	−	0.298217i
$943$	−43.5511	+	28.2824i	−1.41822	+	0.921003i
$944$	−0.975573	−	0.434353i	−0.0317522	−	0.0141370i
$945$	36.8812	+	17.8551i	1.19975	+	0.580825i
$946$	−0.00185472	−	0.00570824i	−6.03021e−5	−	0.000185591i
$947$	−36.5136	+	14.0162i	−1.18653	+	0.455467i	−0.869970	−	0.493105i	$-0.835862\pi$
$947$	−36.5136	+	14.0162i	−1.18653	+	0.455467i	−0.316562	+	0.948572i	$0.602529\pi$
$948$	11.4463	−	0.294908i	0.371758	−	0.00957816i
$949$	1.37234	+	6.45634i	0.0445479	+	0.209582i
$950$	4.13006	−	24.6256i	0.133997	−	0.798960i
$951$	13.2743	−	2.45446i	0.430447	−	0.0795912i
$952$	−0.0445255	+	0.0549844i	−0.00144308	+	0.00178205i
$953$	−11.8990	−	1.88462i	−0.385447	−	0.0610488i	−0.0392960	−	0.999228i	$-0.512512\pi$
$953$	−11.8990	−	1.88462i	−0.385447	−	0.0610488i	−0.346151	+	0.938179i	$0.612512\pi$
$954$	−12.5716	−	32.8328i	−0.407022	−	1.06300i
$955$	1.53351	−	9.40539i	0.0496232	−	0.304351i
$956$	−3.40084	−	1.96348i	−0.109991	−	0.0635033i
$957$	−0.0573796	+	0.138362i	−0.00185482	+	0.00447260i
$958$	−1.92033	−	36.6421i	−0.0620431	−	1.18385i
$959$	17.7386	−	54.5939i	0.572811	−	1.76293i
$960$	−3.48738	−	1.68470i	−0.112555	−	0.0543734i
$961$	9.51571	+	29.5034i	0.306958	+	0.951723i
$962$	−11.8985	+	11.8985i	−0.383623	+	0.383623i
$963$	21.9006	+	15.9399i	0.705737	+	0.513656i
$964$	18.7727	+	16.9030i	0.604627	+	0.544408i
$965$	−0.390072	+	0.668591i	−0.0125569	+	0.0215227i
$966$	−31.9388	+	17.3239i	−1.02761	+	0.557389i
$967$	−6.90425	+	25.7670i	−0.222026	+	0.828611i	0.761549	+	0.648108i	$0.224439\pi$
$967$	−6.90425	+	25.7670i	−0.222026	+	0.828611i	−0.983574	+	0.180503i	$0.942227\pi$
$968$	8.54847	−	6.92242i	0.274758	−	0.222495i
$969$	−0.173001	+	0.0135422i	−0.00555760	+	0.000435038i
$970$	24.6291	+	16.1539i	0.790792	+	0.518670i
$971$	38.2656	−	34.4545i	1.22800	−	1.10570i	0.237047	−	0.971498i	$-0.423821\pi$
$971$	38.2656	−	34.4545i	1.22800	−	1.10570i	0.990954	−	0.134199i	$-0.0428461\pi$
$972$	15.5839	−	0.375244i	0.499855	−	0.0120360i
$973$	−2.88841	+	4.44776i	−0.0925981	+	0.142589i
$974$	7.95425	+	1.69073i	0.254871	+	0.0541744i
$975$	−44.4677	−	43.0093i	−1.42411	−	1.37740i
$976$	−3.63814	−	11.1970i	−0.116454	−	0.358409i
$977$	8.06888	+	4.11130i	0.258146	+	0.131532i	0.578275	−	0.815842i	$-0.303726\pi$
$977$	8.06888	+	4.11130i	0.258146	+	0.131532i	−0.320129	+	0.947374i	$0.603726\pi$
$978$	−5.62254	+	30.2654i	−0.179789	+	0.967780i
$979$	−0.00733231	+	0.0344958i	−0.000234342	+	0.00110249i
$980$	−5.56879	+	10.8077i	−0.177888	+	0.345238i
$981$	11.8630	+	9.62305i	0.378757	+	0.307240i
$982$	0.507666	−	9.68683i	0.0162003	−	0.309119i
$983$	18.4152	−	22.7409i	0.587354	−	0.725321i	−0.393661	−	0.919256i	$-0.628792\pi$
$983$	18.4152	−	22.7409i	0.587354	−	0.725321i	0.981014	+	0.193935i	$0.0621249\pi$
$984$	1.18000	+	15.0745i	0.0376172	+	0.480559i
$985$	−0.701118	−	0.00318584i	−0.0223395	−	0.000101509i
$986$	0.115342	−	0.0665929i	0.00367325	−	0.00212075i
$987$	−10.1692	+	34.2777i	−0.323690	+	1.09107i
$988$	35.2346	−	5.58061i	1.12096	−	0.177543i
$989$	−1.83389	+	2.03674i	−0.0583143	+	0.0647645i
$990$	−0.0221620	−	0.0845283i	−0.000704355	−	0.00268649i
$991$	2.45863			0.0781009			0.0390504	−	0.999237i	$-0.487567\pi$
$991$	2.45863			0.0781009			0.0390504	+	0.999237i	$0.487567\pi$
$992$	−5.50016	+	0.865040i	−0.174630	+	0.0274650i
$993$	12.0886	−	2.89684i	0.383622	−	0.0919285i
$994$	−27.7356	−	9.01184i	−0.879720	−	0.285838i
$995$	−12.8453	+	1.97471i	−0.407224	+	0.0626025i
$996$	−14.5878	+	6.03527i	−0.462232	+	0.191235i
$997$	39.3196	−	10.5356i	1.24526	−	0.333667i	0.424758	−	0.905307i	$-0.360359\pi$
$997$	39.3196	−	10.5356i	1.24526	−	0.333667i	0.820505	+	0.571639i	$0.193692\pi$
$998$	0.393098	−	1.46706i	0.0124433	−	0.0464390i
$999$	2.24576	−	12.0322i	0.0710527	−	0.380681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.107.11	✓	1024
3.2	odd	2	inner	930.2.bs.a.107.54	yes	1024
5.3	odd	4	inner	930.2.bs.a.293.5	yes	1024
15.8	even	4	inner	930.2.bs.a.293.38	yes	1024
31.20	even	15	inner	930.2.bs.a.857.38	yes	1024
93.20	odd	30	inner	930.2.bs.a.857.5	yes	1024
155.113	odd	60	inner	930.2.bs.a.113.54	yes	1024
465.113	even	60	inner	930.2.bs.a.113.11	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.11	✓	1024	1.1	even	1	trivial
930.2.bs.a.107.54	yes	1024	3.2	odd	2	inner
930.2.bs.a.113.11	yes	1024	465.113	even	60	inner
930.2.bs.a.113.54	yes	1024	155.113	odd	60	inner
930.2.bs.a.293.5	yes	1024	5.3	odd	4	inner
930.2.bs.a.293.38	yes	1024	15.8	even	4	inner
930.2.bs.a.857.5	yes	1024	93.20	odd	30	inner
930.2.bs.a.857.38	yes	1024	31.20	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.827104 + 1.52181i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.791841 + 2.09117i) q^{5} +(1.73144 + 0.0460690i) q^{6} +(2.74072 - 2.21939i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-1.63180 - 2.51739i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-0.827104 + 1.52181i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.791841 + 2.09117i) q^{5} +(1.73144 + 0.0460690i) q^{6} +(2.74072 - 2.21939i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-1.63180 - 2.51739i) q^{9} +(1.50376 - 1.65491i) q^{10} +(0.00529841 + 0.0119004i) q^{11} +(-0.745009 - 1.56364i) q^{12} +(5.99101 - 3.89061i) q^{13} +(-3.22175 - 1.43442i) q^{14} +(-3.83729 - 0.524584i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-0.0187295 + 0.00718959i) q^{17} +(-1.50219 + 2.59681i) q^{18} +(-1.03829 - 4.88478i) q^{19} +(-2.15722 - 0.588545i) q^{20} +(1.11063 + 6.00651i) q^{21} +(0.00819793 - 0.0101236i) q^{22} +(-5.87514 - 0.930531i) q^{23} +(-1.05498 + 1.37368i) q^{24} +(-3.74597 + 3.31175i) q^{25} +(-6.18642 - 3.57173i) q^{26} +(5.18065 - 0.401140i) q^{27} +(0.184570 + 3.52181i) q^{28} +(2.05147 - 6.31378i) q^{29} +(1.27469 + 3.65721i) q^{30} +(4.50087 + 3.27752i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0224925 - 0.00177973i) q^{33} +(0.0149090 + 0.0134241i) q^{34} +(6.81133 + 3.97390i) q^{35} +(2.99576 + 0.159531i) q^{36} +(0.609670 - 2.27532i) q^{37} +(-3.88099 + 3.14277i) q^{38} +(0.965567 + 12.3351i) q^{39} +(0.454961 + 2.18929i) q^{40} +(6.48759 - 5.84145i) q^{41} +(4.84763 - 3.71647i) q^{42} +(0.250941 - 0.386416i) q^{43} +(-0.0127420 - 0.00270839i) q^{44} +(3.97216 - 5.40573i) q^{45} +(1.83815 + 5.65724i) q^{46} +(5.21539 + 2.65737i) q^{47} +(1.70291 + 0.316358i) q^{48} +(1.13046 - 5.31841i) q^{49} +(4.65143 + 1.83419i) q^{50} +(0.00455009 - 0.0344493i) q^{51} +(-0.373860 + 7.13367i) q^{52} +(-7.37509 + 9.10747i) q^{53} +(-2.70938 - 4.43387i) q^{54} +(-0.0206903 + 0.0205031i) q^{55} +(3.05416 - 1.76332i) q^{56} +(8.29247 + 2.46014i) q^{57} +(-6.55697 + 1.03852i) q^{58} +(0.714563 - 0.793603i) q^{59} +(2.67990 - 2.79609i) q^{60} +11.7733 q^{61} +(0.876940 - 5.49827i) q^{62} +(-10.0594 - 3.27785i) q^{63} +(0.951057 + 0.309017i) q^{64} +(12.8798 + 9.44747i) q^{65} +(0.00862563 + 0.0208489i) q^{66} +(-8.73244 + 2.33985i) q^{67} +(0.00519243 - 0.0193784i) q^{68} +(6.27544 - 8.17119i) q^{69} +(0.448491 - 7.87305i) q^{70} +(8.22401 - 0.864379i) q^{71} +(-1.21790 - 2.74166i) q^{72} +(-0.331133 + 0.862631i) q^{73} +(-2.30411 + 0.489753i) q^{74} +(-1.94153 - 8.43981i) q^{75} +(4.56216 + 2.03120i) q^{76} +(0.0409331 + 0.0208565i) q^{77} +(10.5523 - 6.46035i) q^{78} +(-2.68882 + 6.03918i) q^{79} +(1.74413 - 1.39929i) q^{80} +(-3.67447 + 8.21573i) q^{81} +(-8.15007 - 3.12852i) q^{82} +(0.477022 - 9.10212i) q^{83} +(-5.51218 - 2.63202i) q^{84} +(-0.0298654 - 0.0334736i) q^{85} +(-0.458224 - 0.0481613i) q^{86} +(7.91158 + 8.34410i) q^{87} +(0.00337154 + 0.0125828i) q^{88} +(2.19022 + 1.59129i) q^{89} +(-6.61987 - 1.08507i) q^{90} +(7.78490 - 23.9594i) q^{91} +(4.20614 - 4.20614i) q^{92} +(-8.71045 + 4.13861i) q^{93} -5.85337i q^{94} +(9.39273 - 6.03921i) q^{95} +(-0.491230 - 1.66093i) q^{96} +(2.06059 + 13.0101i) q^{97} +(-5.25196 + 1.40726i) q^{98} +(0.0213120 - 0.0327572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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