LMFDB - Embedded newform 261.2.x.a.2.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.14
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.202514 - 0.149462i) q^{2} +(0.356874 + 1.69489i) q^{3} +(-0.570837 - 1.85061i) q^{4} +(-1.37930 + 3.51439i) q^{5} +(0.181050 - 0.396578i) q^{6} +(2.32547 + 0.717312i) q^{7} +(-0.327254 + 0.935237i) q^{8} +(-2.74528 + 1.20972i) q^{9} +O(q^{10})$	\(q+(-0.202514 - 0.149462i) q^{2} +(0.356874 + 1.69489i) q^{3} +(-0.570837 - 1.85061i) q^{4} +(-1.37930 + 3.51439i) q^{5} +(0.181050 - 0.396578i) q^{6} +(2.32547 + 0.717312i) q^{7} +(-0.327254 + 0.935237i) q^{8} +(-2.74528 + 1.20972i) q^{9} +(0.804596 - 0.505561i) q^{10} +(-5.39244 - 1.02030i) q^{11} +(2.93286 - 1.62794i) q^{12} +(0.597397 - 0.0447687i) q^{13} +(-0.363730 - 0.492836i) q^{14} +(-6.44872 - 1.08356i) q^{15} +(-2.99421 + 2.04142i) q^{16} +(1.78047 + 1.78047i) q^{17} +(0.736767 + 0.165330i) q^{18} +(4.09425 + 6.51596i) q^{19} +(7.29111 + 0.546393i) q^{20} +(-0.385863 + 4.19740i) q^{21} +(0.939549 + 1.01259i) q^{22} +(-0.267615 + 1.77551i) q^{23} +(-1.70191 - 0.220896i) q^{24} +(-6.78321 - 6.29390i) q^{25} +(-0.127673 - 0.0802220i) q^{26} +(-3.03006 - 4.22122i) q^{27} -4.71300i q^{28} +(5.21590 + 1.33954i) q^{29} +(1.14401 + 1.18328i) q^{30} +(-1.90011 - 4.35511i) q^{31} +(2.89178 + 0.108203i) q^{32} +(-0.195122 - 9.50369i) q^{33} +(-0.0944576 - 0.626685i) q^{34} +(-5.72842 + 7.18322i) q^{35} +(3.80583 + 4.38989i) q^{36} +(3.30296 + 1.15576i) q^{37} +(0.144747 - 1.93151i) q^{38} +(0.289073 + 0.996543i) q^{39} +(-2.83541 - 2.44006i) q^{40} +(2.05392 + 0.550346i) q^{41} +(0.705495 - 0.792361i) q^{42} +(5.57509 + 2.43238i) q^{43} +(1.19002 + 10.5617i) q^{44} +(-0.464881 - 11.3166i) q^{45} +(0.319568 - 0.319568i) q^{46} +(1.14454 - 6.04905i) q^{47} +(-4.52853 - 4.34632i) q^{48} +(-0.890400 - 0.607065i) q^{49} +(0.432996 + 2.28844i) q^{50} +(-2.38230 + 3.65311i) q^{51} +(-0.423866 - 1.07999i) q^{52} +(7.40369 - 5.90425i) q^{53} +(-0.0172826 + 1.30774i) q^{54} +(11.0235 - 17.5438i) q^{55} +(-1.43188 + 1.94012i) q^{56} +(-9.58268 + 9.26467i) q^{57} +(-0.856084 - 1.05086i) q^{58} +(5.96836 - 3.44584i) q^{59} +(1.67594 + 12.5526i) q^{60} +(-6.04723 + 3.19605i) q^{61} +(-0.266124 + 1.16597i) q^{62} +(-7.25182 + 0.843949i) q^{63} +(5.09712 + 4.06481i) q^{64} +(-0.666652 + 2.16123i) q^{65} +(-1.38093 + 1.95380i) q^{66} +(-3.00506 + 4.40761i) q^{67} +(2.27860 - 4.31132i) q^{68} +(-3.10479 + 0.180057i) q^{69} +(2.23371 - 0.598520i) q^{70} +(1.40000 + 0.674204i) q^{71} +(-0.232974 - 2.96338i) q^{72} +(6.77451 - 0.763304i) q^{73} +(-0.496155 - 0.727726i) q^{74} +(8.24669 - 13.7429i) q^{75} +(9.72135 - 11.2964i) q^{76} +(-11.8081 - 6.24075i) q^{77} +(0.0904041 - 0.245020i) q^{78} +(1.21131 + 1.40757i) q^{79} +(-3.04444 - 13.3385i) q^{80} +(6.07314 - 6.64206i) q^{81} +(-0.333692 - 0.418437i) q^{82} +(0.480134 - 0.517461i) q^{83} +(7.98801 - 1.68195i) q^{84} +(-8.71308 + 3.80148i) q^{85} +(-0.765484 - 1.32586i) q^{86} +(-0.408943 + 9.31841i) q^{87} +(2.71892 - 4.70931i) q^{88} +(0.509712 - 4.52382i) q^{89} +(-1.59725 + 2.36124i) q^{90} +(1.42134 + 0.324412i) q^{91} +(3.43854 - 0.518277i) q^{92} +(6.70331 - 4.77470i) q^{93} +(-1.13589 + 1.05395i) q^{94} +(-28.5468 + 5.40135i) q^{95} +(0.848610 + 4.93985i) q^{96} +(0.477131 + 12.7516i) q^{97} +(0.0895855 + 0.256021i) q^{98} +(16.0381 - 3.72233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.202514	−	0.149462i	−0.143199	−	0.105686i	0.519865	−	0.854249i	$-0.325982\pi$
$2$	−0.202514	−	0.149462i	−0.143199	−	0.105686i	−0.663064	+	0.748563i	$0.730744\pi$
$3$	0.356874	+	1.69489i	0.206041	+	0.978543i
$3$	0.356874	+	1.69489i	0.206041	+	0.978543i
$4$	−0.570837	−	1.85061i	−0.285419	−	0.925305i
$5$	−1.37930	+	3.51439i	−0.616840	+	1.57168i	0.190559	+	0.981676i	$0.438970\pi$
$5$	−1.37930	+	3.51439i	−0.616840	+	1.57168i	−0.807399	+	0.590006i	$0.799125\pi$
$6$	0.181050	−	0.396578i	0.0739132	−	0.161902i
$7$	2.32547	+	0.717312i	0.878945	+	0.271119i	0.701206	−	0.712959i	$-0.252645\pi$
$7$	2.32547	+	0.717312i	0.878945	+	0.271119i	0.177739	+	0.984078i	$0.443122\pi$
$8$	−0.327254	+	0.935237i	−0.115702	+	0.330656i
$9$	−2.74528	+	1.20972i	−0.915094	+	0.403241i
$10$	0.804596	−	0.505561i	0.254435	−	0.159872i
$11$	−5.39244	−	1.02030i	−1.62588	−	0.307633i	−0.708521	−	0.705690i	$-0.750637\pi$
$11$	−5.39244	−	1.02030i	−1.62588	−	0.307633i	−0.917361	+	0.398056i	$0.869685\pi$
$12$	2.93286	−	1.62794i	0.846642	−	0.469946i
$13$	0.597397	−	0.0447687i	0.165688	−	0.0124166i	0.00837223	−	0.999965i	$-0.497335\pi$
$13$	0.597397	−	0.0447687i	0.165688	−	0.0124166i	0.157316	+	0.987548i	$0.449716\pi$
$14$	−0.363730	−	0.492836i	−0.0972108	−	0.131716i
$15$	−6.44872	−	1.08356i	−1.66505	−	0.279773i
$16$	−2.99421	+	2.04142i	−0.748553	+	0.510355i
$17$	1.78047	+	1.78047i	0.431829	+	0.431829i	0.889250	−	0.457421i	$-0.151227\pi$
$17$	1.78047	+	1.78047i	0.431829	+	0.431829i	−0.457421	+	0.889250i	$0.651227\pi$
$18$	0.736767	+	0.165330i	0.173658	+	0.0389687i
$19$	4.09425	+	6.51596i	0.939285	+	1.49486i	0.867496	+	0.497444i	$0.165728\pi$
$19$	4.09425	+	6.51596i	0.939285	+	1.49486i	0.0717892	+	0.997420i	$0.477129\pi$
$20$	7.29111	+	0.546393i	1.63034	+	0.122177i
$21$	−0.385863	+	4.19740i	−0.0842022	+	0.915947i
$22$	0.939549	+	1.01259i	0.200312	+	0.215885i
$23$	−0.267615	+	1.77551i	−0.0558016	+	0.370220i	0.943449	+	0.331517i	$0.107561\pi$
$23$	−0.267615	+	1.77551i	−0.0558016	+	0.370220i	−0.999251	+	0.0387023i	$0.987678\pi$
$24$	−1.70191	−	0.220896i	−0.347401	−	0.0450902i
$25$	−6.78321	−	6.29390i	−1.35664	−	1.25878i
$26$	−0.127673	−	0.0802220i	−0.0250386	−	0.0157328i
$27$	−3.03006	−	4.22122i	−0.583136	−	0.812375i
$28$		−	4.71300i		−	0.890674i
$29$	5.21590	+	1.33954i	0.968569	+	0.248746i
$29$	5.21590	+	1.33954i	0.968569	+	0.248746i
$30$	1.14401	+	1.18328i	0.208866	+	0.216036i
$31$	−1.90011	−	4.35511i	−0.341270	−	0.782200i	−0.999567	−	0.0294411i	$-0.990627\pi$
$31$	−1.90011	−	4.35511i	−0.341270	−	0.782200i	0.658296	−	0.752759i	$-0.271277\pi$
$32$	2.89178	+	0.108203i	0.511199	+	0.0191277i
$33$	−0.195122	−	9.50369i	−0.0339664	−	1.65438i
$34$	−0.0944576	−	0.626685i	−0.0161993	−	0.107476i
$35$	−5.72842	+	7.18322i	−0.968280	+	1.21419i
$36$	3.80583	+	4.38989i	0.634306	+	0.731648i
$37$	3.30296	+	1.15576i	0.543004	+	0.190005i	0.587822	−	0.808990i	$-0.299985\pi$
$37$	3.30296	+	1.15576i	0.543004	+	0.190005i	−0.0448188	+	0.998995i	$0.514271\pi$
$38$	0.144747	−	1.93151i	0.0234810	−	0.313332i
$39$	0.289073	+	0.996543i	0.0462888	+	0.159575i
$40$	−2.83541	−	2.44006i	−0.448317	−	0.385808i
$41$	2.05392	+	0.550346i	0.320768	+	0.0859496i	0.415610	−	0.909543i	$-0.363568\pi$
$41$	2.05392	+	0.550346i	0.320768	+	0.0859496i	−0.0948421	+	0.995492i	$0.530235\pi$
$42$	0.705495	−	0.792361i	0.108860	−	0.122264i
$43$	5.57509	+	2.43238i	0.850193	+	0.370935i	0.779378	−	0.626554i	$-0.215535\pi$
$43$	5.57509	+	2.43238i	0.850193	+	0.370935i	0.0708147	+	0.997489i	$0.477440\pi$
$44$	1.19002	+	10.5617i	0.179402	+	1.59224i
$45$	−0.464881	−	11.3166i	−0.0693003	−	1.68697i
$46$	0.319568	−	0.319568i	0.0471177	−	0.0471177i
$47$	1.14454	−	6.04905i	0.166949	−	0.882345i	−0.794480	−	0.607290i	$-0.792257\pi$
$47$	1.14454	−	6.04905i	0.166949	−	0.882345i	0.961429	−	0.275054i	$-0.0886959\pi$
$48$	−4.52853	−	4.34632i	−0.653637	−	0.627337i
$49$	−0.890400	−	0.607065i	−0.127200	−	0.0867235i
$50$	0.432996	+	2.28844i	0.0612349	+	0.323634i
$51$	−2.38230	+	3.65311i	−0.333588	+	0.511538i
$52$	−0.423866	−	1.07999i	−0.0587796	−	0.149768i
$53$	7.40369	−	5.90425i	1.01698	−	0.811011i	0.0348790	−	0.999392i	$-0.488895\pi$
$53$	7.40369	−	5.90425i	1.01698	−	0.811011i	0.982096	+	0.188381i	$0.0603240\pi$
$54$	−0.0172826	+	1.30774i	−0.00235186	+	0.177961i
$55$	11.0235	−	17.5438i	1.48641	−	2.36561i
$56$	−1.43188	+	1.94012i	−0.191342	+	0.259260i
$57$	−9.58268	+	9.26467i	−1.26926	+	1.22714i
$58$	−0.856084	−	1.05086i	−0.112409	−	0.137984i
$59$	5.96836	−	3.44584i	0.777015	−	0.448610i	−0.0583566	−	0.998296i	$-0.518586\pi$
$59$	5.96836	−	3.44584i	0.777015	−	0.448610i	0.835371	+	0.549686i	$0.185253\pi$
$60$	1.67594	+	12.5526i	0.216362	+	1.62053i
$61$	−6.04723	+	3.19605i	−0.774269	+	0.409213i	−0.807225	−	0.590244i	$-0.799032\pi$
$61$	−6.04723	+	3.19605i	−0.774269	+	0.409213i	0.0329564	+	0.999457i	$0.489508\pi$
$62$	−0.266124	+	1.16597i	−0.0337978	+	0.148078i
$63$	−7.25182	+	0.843949i	−0.913643	+	0.106328i
$64$	5.09712	+	4.06481i	0.637139	+	0.508102i
$65$	−0.666652	+	2.16123i	−0.0826880	+	0.268068i
$66$	−1.38093	+	1.95380i	−0.169981	+	0.240496i
$67$	−3.00506	+	4.40761i	−0.367126	+	0.538476i	−0.964704	−	0.263335i	$-0.915177\pi$
$67$	−3.00506	+	4.40761i	−0.367126	+	0.538476i	0.597578	+	0.801811i	$0.296130\pi$
$68$	2.27860	−	4.31132i	0.276321	−	0.522825i
$69$	−3.10479	+	0.180057i	−0.373773	+	0.0216763i
$70$	2.23371	−	0.598520i	0.266979	−	0.0715368i
$71$	1.40000	+	0.674204i	0.166149	+	0.0800133i	0.515110	−	0.857124i	$-0.327751\pi$
$71$	1.40000	+	0.674204i	0.166149	+	0.0800133i	−0.348961	+	0.937137i	$0.613465\pi$
$72$	−0.232974	−	2.96338i	−0.0274563	−	0.349237i
$73$	6.77451	−	0.763304i	0.792896	−	0.0893379i	0.293780	−	0.955873i	$-0.405087\pi$
$73$	6.77451	−	0.763304i	0.792896	−	0.0893379i	0.499116	+	0.866535i	$0.333658\pi$
$74$	−0.496155	−	0.727726i	−0.0576768	−	0.0845964i
$75$	8.24669	−	13.7429i	0.952246	−	1.58689i
$76$	9.72135	−	11.2964i	1.11511	−	1.29579i
$77$	−11.8081	−	6.24075i	−1.34566	−	0.711200i
$78$	0.0904041	−	0.245020i	0.0102362	−	0.0277430i
$79$	1.21131	+	1.40757i	0.136283	+	0.158364i	0.821966	−	0.569536i	$-0.192877\pi$
$79$	1.21131	+	1.40757i	0.136283	+	0.158364i	−0.685683	+	0.727900i	$0.740496\pi$
$80$	−3.04444	−	13.3385i	−0.340378	−	1.49129i
$81$	6.07314	−	6.64206i	0.674793	−	0.738007i
$82$	−0.333692	−	0.418437i	−0.0368501	−	0.0462086i
$83$	0.480134	−	0.517461i	0.0527016	−	0.0567988i	−0.706151	−	0.708061i	$-0.749570\pi$
$83$	0.480134	−	0.517461i	0.0527016	−	0.0567988i	0.758852	+	0.651263i	$0.225760\pi$
$84$	7.98801	−	1.68195i	0.871563	−	0.183516i
$85$	−8.71308	+	3.80148i	−0.945066	+	0.412328i
$86$	−0.765484	−	1.32586i	−0.0825443	−	0.142971i
$87$	−0.408943	+	9.31841i	−0.0438433	+	0.999038i
$88$	2.71892	−	4.70931i	0.289838	−	0.502014i
$89$	0.509712	−	4.52382i	0.0540293	−	0.479524i	−0.937339	−	0.348418i	$-0.886719\pi$
$89$	0.509712	−	4.52382i	0.0540293	−	0.479524i	0.991368	−	0.131105i	$-0.0418526\pi$
$90$	−1.59725	+	2.36124i	−0.168365	+	0.248897i
$91$	1.42134	+	0.324412i	0.148997	+	0.0340076i
$92$	3.43854	−	0.518277i	0.358493	−	0.0540341i
$93$	6.70331	−	4.77470i	0.695101	−	0.495114i
$94$	−1.13589	+	1.05395i	−0.117158	+	0.108707i
$95$	−28.5468	+	5.40135i	−2.92884	+	0.554166i
$96$	0.848610	+	4.93985i	0.0866109	+	0.504172i
$97$	0.477131	+	12.7516i	0.0484453	+	1.29473i	0.785486	+	0.618879i	$0.212413\pi$
$97$	0.477131	+	12.7516i	0.0484453	+	1.29473i	−0.737041	+	0.675848i	$0.763778\pi$
$98$	0.0895855	+	0.256021i	0.00904950	+	0.0258620i
$99$	16.0381	−	3.72233i	1.61188	−	0.374109i
$100$	−7.77544	+	16.1459i	−0.777544	+	1.61459i
$101$	−7.02138	+	16.0932i	−0.698653	+	1.60133i	0.0967927	+	0.995305i	$0.469142\pi$
$101$	−7.02138	+	16.0932i	−0.698653	+	1.60133i	−0.795446	+	0.606025i	$0.792763\pi$
$102$	1.02845	−	0.383743i	0.101832	−	0.0379962i
$103$	−0.872091	−	11.6372i	−0.0859297	−	1.14665i	−0.858877	−	0.512182i	$-0.828837\pi$
$103$	−0.872091	−	11.6372i	−0.0859297	−	1.14665i	0.772947	−	0.634470i	$-0.218782\pi$
$104$	−0.153631	+	0.573358i	−0.0150647	+	0.0562224i
$105$	−14.2191	−	7.14552i	−1.38764	−	0.697332i
$106$	−2.38181	+	0.0891212i	−0.231342	+	0.00865622i
$107$	−0.283930	−	0.589586i	−0.0274485	−	0.0569974i	0.886794	−	0.462165i	$-0.152927\pi$
$107$	−0.283930	−	0.589586i	−0.0274485	−	0.0569974i	−0.914242	+	0.405168i	$0.867213\pi$
$108$	−6.08216	+	8.01709i	−0.585256	+	0.771445i
$109$	1.35897	−	0.310177i	0.130166	−	0.0297096i	−0.156941	−	0.987608i	$-0.550163\pi$
$109$	1.35897	−	0.310177i	0.130166	−	0.0297096i	0.287108	+	0.957898i	$0.407306\pi$
$110$	−4.85456	+	1.90527i	−0.462864	+	0.181661i
$111$	−0.780134	+	6.01061i	−0.0740470	+	0.570502i
$112$	−8.42729	+	2.59947i	−0.796304	+	0.245627i
$113$	−0.279235	+	7.46271i	−0.0262682	+	0.702032i	0.922488	+	0.386025i	$0.126152\pi$
$113$	−0.279235	+	7.46271i	−0.0262682	+	0.702032i	−0.948757	+	0.316008i	$0.897657\pi$
$114$	3.32535	−	0.443977i	0.311447	−	0.0415823i
$115$	−5.87071	−	3.38946i	−0.547447	−	0.316069i
$116$	−0.498472	−	10.4173i	−0.0462819	−	0.967218i
$117$	−1.58586	+	0.845587i	−0.146613	+	0.0781745i
$118$	−1.72370	−	0.194214i	−0.158680	−	0.0178789i
$119$	2.86328	+	5.41760i	0.262477	+	0.496630i
$120$	3.12375	−	5.67649i	0.285158	−	0.518190i
$121$	17.7978	+	6.98511i	1.61798	+	0.635010i
$122$	1.70234	+	0.256586i	0.154123	+	0.0232302i
$123$	−0.199783	+	3.67757i	−0.0180138	+	0.331595i
$124$	−6.97494	+	6.00242i	−0.626368	+	0.539034i
$125$	14.4678	−	6.96733i	1.29404	−	0.623177i
$126$	1.59473	+	0.912962i	0.142070	+	0.0813331i
$127$	−15.8700	+	5.55317i	−1.40824	+	0.492764i	−0.924074	−	0.382213i	$-0.875162\pi$
$127$	−15.8700	+	5.55317i	−1.40824	+	0.492764i	−0.484164	+	0.874977i	$0.660876\pi$
$128$	−1.92264	−	7.17541i	−0.169939	−	0.634222i
$129$	−2.13301	+	10.3172i	−0.187801	+	0.908378i
$130$	0.458029	−	0.338041i	0.0401718	−	0.0296482i
$131$	11.5848	−	8.54995i	1.01217	−	0.747013i	0.0444387	−	0.999012i	$-0.485850\pi$
$131$	11.5848	−	8.54995i	1.01217	−	0.747013i	0.967727	+	0.252000i	$0.0810882\pi$
$132$	−17.4762	+	5.78616i	−1.52111	+	0.503620i
$133$	4.84707	+	18.0895i	0.420295	+	1.56856i
$134$	1.26734	−	0.443461i	0.109481	−	0.0383092i
$135$	19.0144	−	4.82651i	1.63650	−	0.415400i
$136$	−2.24783	+	1.08250i	−0.192750	+	0.0928236i
$137$	−9.29913	+	8.00255i	−0.794478	+	0.683704i	−0.952771	−	0.303688i	$-0.901782\pi$
$137$	−9.29913	+	8.00255i	−0.794478	+	0.683704i	0.158293	+	0.987392i	$0.449401\pi$
$138$	0.655677	+	0.427586i	0.0558149	+	0.0363985i
$139$	8.56769	+	1.29137i	0.726702	+	0.109533i	0.501967	−	0.864887i	$-0.332610\pi$
$139$	8.56769	+	1.29137i	0.726702	+	0.109533i	0.224736	+	0.974420i	$0.427848\pi$
$140$	16.5633	+	6.50063i	1.39986	+	0.549403i
$141$	10.6609	−	0.218881i	0.897811	−	0.0184331i
$142$	−0.182752	−	0.345783i	−0.0153362	−	0.0290175i
$143$	−3.26710	−	0.368114i	−0.273209	−	0.0307832i
$144$	5.75040	−	9.22644i	0.479200	−	0.768870i
$145$	−11.9019	+	16.4831i	−0.988401	+	1.36885i
$146$	−1.48602	−	0.857954i	−0.122984	−	0.0710047i
$147$	0.711145	−	1.72577i	0.0586542	−	0.142339i
$148$	0.253399	−	6.77224i	0.0208293	−	0.556675i
$149$	−6.24750	+	1.92710i	−0.511815	+	0.157874i	−0.539896	−	0.841732i	$-0.681536\pi$
$149$	−6.24750	+	1.92710i	−0.511815	+	0.157874i	0.0280813	+	0.999606i	$0.491060\pi$
$150$	−3.72412	+	1.55056i	−0.304073	+	0.126603i
$151$	9.34614	−	3.66809i	0.760578	−	0.298505i	0.0468259	−	0.998903i	$-0.485089\pi$
$151$	9.34614	−	3.66809i	0.760578	−	0.298505i	0.713752	+	0.700398i	$0.246994\pi$
$152$	−7.43383	+	1.69672i	−0.602963	+	0.137622i
$153$	−7.04179	−	2.73402i	−0.569295	−	0.221033i
$154$	1.45855	+	3.02870i	0.117533	+	0.244060i
$155$	17.9264	−	0.670757i	1.43988	−	0.0538765i
$156$	1.67920	−	1.10383i	0.134443	−	0.0883768i
$157$	−5.81877	+	21.7159i	−0.464388	+	1.73312i	0.194522	+	0.980898i	$0.437685\pi$
$157$	−5.81877	+	21.7159i	−0.464388	+	1.73312i	−0.658910	+	0.752222i	$0.728982\pi$
$158$	−0.0349292	−	0.466098i	−0.00277882	−	0.0370808i
$159$	12.6492	+	10.4413i	1.00315	+	0.828052i
$160$	−4.36889	+	10.0136i	−0.345391	+	0.791644i
$161$	−1.89593	+	3.93693i	−0.149420	+	0.310274i
$162$	−2.22264	+	0.437406i	−0.174627	+	0.0343659i
$163$	−3.81544	−	10.9039i	−0.298849	−	0.854060i	−0.991185	−	0.132485i	$-0.957704\pi$
$163$	−3.81544	−	10.9039i	−0.298849	−	0.854060i	0.692336	−	0.721575i	$-0.256581\pi$
$164$	−0.153978	−	4.11516i	−0.0120237	−	0.321340i
$165$	33.6688	+	12.4227i	2.62111	+	0.967104i
$166$	−0.174575	+	0.0330314i	−0.0135496	+	0.00256373i
$167$	10.9817	−	10.1895i	0.849788	−	0.788488i	−0.129368	−	0.991597i	$-0.541295\pi$
$167$	10.9817	−	10.1895i	0.849788	−	0.788488i	0.979156	+	0.203108i	$0.0651043\pi$
$168$	−3.79929	−	1.73449i	−0.293121	−	0.133819i
$169$	−12.4999	+	1.88406i	−0.961532	+	0.144928i
$170$	2.33270	+	0.532424i	0.178910	+	0.0408350i
$171$	−19.1224	−	12.9352i	−1.46232	−	0.989182i
$172$	1.31893	−	11.7058i	0.100567	−	0.892559i
$173$	−3.65479	+	6.33029i	−0.277869	+	0.481283i	−0.970855	−	0.239668i	$-0.922961\pi$
$173$	−3.65479	+	6.33029i	−0.277869	+	0.481283i	0.692986	+	0.720951i	$0.256295\pi$
$174$	1.47557	−	1.82599i	0.111863	−	0.138428i
$175$	−11.2595	−	19.5019i	−0.851135	−	1.47421i
$176$	18.2290	−	7.95322i	1.37406	−	0.599497i
$177$	7.97026	+	8.88597i	0.599081	+	0.667910i
$178$	−0.779364	+	0.839955i	−0.0584158	+	0.0629573i
$179$	−16.0046	−	20.0692i	−1.19624	−	1.50004i	−0.818871	−	0.573978i	$-0.805400\pi$
$179$	−16.0046	−	20.0692i	−1.19624	−	1.50004i	−0.377371	−	0.926062i	$-0.623172\pi$
$180$	−20.6771	+	7.32022i	−1.54118	+	0.545617i
$181$	−1.45620	−	6.38002i	−0.108238	−	0.474223i	−0.999774	−	0.0212719i	$-0.993228\pi$
$181$	−1.45620	−	6.38002i	−0.108238	−	0.474223i	0.891535	−	0.452951i	$-0.149629\pi$
$182$	−0.239354	−	0.278135i	−0.0177421	−	0.0206167i
$183$	−7.57505	−	9.10878i	−0.559964	−	0.673341i
$184$	−1.57295	−	0.831326i	−0.115959	−	0.0612862i
$185$	−8.61754	+	10.0138i	−0.633574	+	0.736226i
$186$	−2.07115	−	0.0349470i	−0.151864	−	0.00256244i
$187$	−7.78448	−	11.4177i	−0.569257	−	0.834947i
$188$	−11.8478	+	1.33492i	−0.864088	+	0.0973593i
$189$	−4.01839	−	11.9898i	−0.292295	−	0.872131i
$190$	6.58843	+	3.17282i	0.477975	+	0.230181i
$191$	−6.93884	+	1.85926i	−0.502077	+	0.134531i	−0.500964	−	0.865468i	$-0.667021\pi$
$191$	−6.93884	+	1.85926i	−0.502077	+	0.134531i	−0.00111314	+	0.999999i	$0.500354\pi$
$192$	−5.07037	+	10.0897i	−0.365922	+	0.728159i
$193$	2.59999	−	4.91942i	0.187151	−	0.354108i	−0.772630	−	0.634857i	$-0.781059\pi$
$193$	2.59999	−	4.91942i	0.187151	−	0.354108i	0.959781	+	0.280749i	$0.0905829\pi$
$194$	1.80926	−	2.65369i	0.129897	−	0.190524i
$195$	−3.90096	−	0.358611i	−0.279353	−	0.0256807i
$196$	−0.615166	+	1.99432i	−0.0439404	+	0.142451i
$197$	16.5837	+	13.2250i	1.18154	+	0.942244i	0.999160	−	0.0409845i	$-0.0130494\pi$
$197$	16.5837	+	13.2250i	1.18154	+	0.942244i	0.182377	+	0.983229i	$0.441621\pi$
$198$	−3.80428	−	1.64326i	−0.270359	−	0.116781i
$199$	−3.87548	+	16.9796i	−0.274725	+	1.20365i	0.629639	+	0.776888i	$0.283203\pi$
$199$	−3.87548	+	16.9796i	−0.274725	+	1.20365i	−0.904364	+	0.426762i	$0.859654\pi$
$200$	8.10612	−	4.28421i	0.573189	−	0.302939i
$201$	−8.54283	−	3.52027i	−0.602565	−	0.248301i
$202$	3.82725	−	2.20966i	0.269284	−	0.155471i
$203$	11.1686	+	6.85648i	0.783879	+	0.481231i
$204$	8.12038	+	2.32337i	0.568540	+	0.162668i
$205$	−4.76709	+	6.45918i	−0.332948	+	0.451129i
$206$	−1.56272	+	2.48705i	−0.108880	+	0.173281i
$207$	−1.41320	−	5.19802i	−0.0982240	−	0.361287i
$208$	−1.69734	+	1.35358i	−0.117689	+	0.0938542i
$209$	−15.4297	−	39.3143i	−1.06730	−	2.71943i
$210$	1.81158	+	3.57228i	0.125011	+	0.246511i
$211$	−2.06613	−	10.9197i	−0.142238	−	0.751747i	−0.978950	−	0.204103i	$-0.934572\pi$
$211$	−2.06613	−	10.9197i	−0.142238	−	0.751747i	0.836711	−	0.547644i	$-0.184475\pi$
$212$	−15.1528	−	10.3310i	−1.04070	−	0.709534i
$213$	−0.643076	+	2.61345i	−0.0440628	+	0.179070i
$214$	−0.0306211	+	0.161836i	−0.00209321	+	0.0110629i
$215$	−16.2380	+	16.2380i	−1.10742	+	1.10742i
$216$	4.93944	−	1.45242i	0.336087	−	0.0988245i
$217$	−1.29468	−	11.4906i	−0.0878889	−	0.780036i
$218$	−0.321571	−	0.140300i	−0.0217796	−	0.00950233i
$219$	3.71136	+	11.2096i	0.250790	+	0.757476i
$220$	−38.7594	−	10.3855i	−2.61316	−	0.700194i
$221$	1.14336	+	0.983940i	0.0769107	+	0.0661870i
$222$	1.05635	−	1.10063i	0.0708974	−	0.0738696i
$223$	1.94203	−	25.9146i	0.130048	−	1.73537i	−0.426444	−	0.904514i	$-0.640234\pi$
$223$	1.94203	−	25.9146i	0.130048	−	1.73537i	0.556492	−	0.830853i	$-0.312147\pi$
$224$	6.64713	+	2.32593i	0.444130	+	0.155408i
$225$	26.2357	+	9.07272i	1.74905	+	0.604848i
$226$	1.17194	−	1.46957i	0.0779565	−	0.0977543i
$227$	−0.525150	−	3.48414i	−0.0348554	−	0.231251i	0.964620	−	0.263645i	$-0.0849248\pi$
$227$	−0.525150	−	3.48414i	−0.0348554	−	0.231251i	−0.999475	+	0.0323945i	$0.989687\pi$
$228$	22.6154	+	12.4452i	1.49774	+	0.824202i
$229$	20.1516	+	0.754020i	1.33166	+	0.0498270i	0.693710	−	0.720255i	$-0.255975\pi$
$229$	20.1516	+	0.754020i	1.33166	+	0.0498270i	0.637945	+	0.770082i	$0.279785\pi$
$230$	0.682307	+	1.56386i	0.0449900	+	0.103118i
$231$	6.36337	−	22.2405i	0.418679	−	1.46332i
$232$	−2.95971	+	4.43974i	−0.194314	+	0.291483i
$233$		−	2.86468i		−	0.187672i	−0.995588	−	0.0938359i	$-0.970087\pi$
$233$		−	2.86468i		−	0.187672i	0.995588	−	0.0938359i	$-0.0299129\pi$
$234$	0.447543	+	0.0657835i	0.0292568	+	0.00430040i
$235$	19.6800	+	12.3658i	1.28378	+	0.806655i
$236$	−9.78386	−	9.07809i	−0.636875	−	0.590934i
$237$	−1.95338	+	2.55536i	−0.126886	+	0.165988i
$238$	0.229871	−	1.52509i	0.0149003	−	0.0988571i
$239$	−11.2215	−	12.0939i	−0.725861	−	0.782292i	0.257045	−	0.966399i	$-0.417251\pi$
$239$	−11.2215	−	12.0939i	−0.725861	−	0.782292i	−0.982906	+	0.184108i	$0.941061\pi$
$240$	21.5208	−	9.92016i	1.38916	−	0.640344i
$241$	26.3979	+	1.97825i	1.70044	+	0.127430i	0.889270	−	0.457383i	$-0.151213\pi$
$241$	26.3979	+	1.97825i	1.70044	+	0.127430i	0.811168	+	0.584813i	$0.198832\pi$
$242$	−2.56029	−	4.07468i	−0.164582	−	0.261930i
$243$	13.4249	+	7.92291i	0.861207	+	0.508255i
$244$	9.36663	+	9.36663i	0.599637	+	0.599637i
$245$	3.36159	−	2.29189i	0.214764	−	0.146424i
$246$	0.590116	−	0.714899i	0.0376244	−	0.0455803i
$247$	2.73760	+	3.70932i	0.174189	+	0.236018i
$248$	4.69488	−	0.351832i	0.298125	−	0.0223414i
$249$	1.04839	+	0.629104i	0.0664388	+	0.0398678i
$250$	−3.97129	−	0.751409i	−0.251167	−	0.0475233i
$251$	−6.49910	+	4.08366i	−0.410220	+	0.257758i	−0.721296	−	0.692627i	$-0.756453\pi$
$251$	−6.49910	+	4.08366i	−0.410220	+	0.257758i	0.311077	+	0.950385i	$0.399310\pi$
$252$	5.70143	+	12.9385i	0.359156	+	0.815050i
$253$	3.25466	−	9.30128i	0.204619	−	0.584767i
$254$	4.04390	+	1.24738i	0.253737	+	0.0782674i
$255$	−9.55255	−	13.4110i	−0.598204	−	0.839832i
$256$	4.08056	−	10.3971i	0.255035	−	0.649818i
$257$	−6.62282	−	21.4707i	−0.413120	−	1.33930i	−0.888239	−	0.459381i	$-0.848071\pi$
$257$	−6.62282	−	21.4707i	−0.413120	−	1.33930i	0.475119	−	0.879922i	$-0.342405\pi$
$258$	1.97400	−	1.77057i	0.122896	−	0.110231i
$259$	6.85190	+	5.05693i	0.425756	+	0.314222i
$260$	4.38015			0.271645
$261$	−15.9396	+	2.63239i	−0.986636	+	0.162941i
$262$	−3.62398			−0.223890
$263$	9.84614	+	7.26678i	0.607139	+	0.448089i	0.853503	−	0.521088i	$-0.174474\pi$
$263$	9.84614	+	7.26678i	0.607139	+	0.448089i	−0.246364	+	0.969177i	$0.579236\pi$
$264$	8.95206	+	2.92763i	0.550961	+	0.180183i
$265$	10.5379	+	34.1631i	0.647340	+	2.09863i
$266$	1.72210	−	4.38784i	0.105589	−	0.269036i
$267$	7.84926	−	0.750530i	0.480367	−	0.0459317i
$268$	9.87217	+	3.04516i	0.603039	+	0.186013i
$269$	1.73400	−	4.95549i	0.105724	−	0.302141i	−0.878853	−	0.477092i	$-0.841691\pi$
$269$	1.73400	−	4.95549i	0.105724	−	0.302141i	0.984577	+	0.174951i	$0.0559766\pi$
$270$	−4.57206	−	1.86449i	−0.278247	−	0.113470i
$271$	−7.11955	+	4.47351i	−0.432482	+	0.271746i	−0.730631	−	0.682773i	$-0.760774\pi$
$271$	−7.11955	+	4.47351i	−0.432482	+	0.271746i	0.298149	+	0.954519i	$0.403631\pi$
$272$	−8.96582	−	1.69642i	−0.543633	−	0.102861i
$273$	−0.0426012	+	2.52479i	−0.00257834	+	0.152807i
$274$	3.07929	−	0.230761i	0.186026	−	0.0139408i
$275$	30.1563	+	40.8604i	1.81850	+	2.46397i
$276$	2.10555	+	5.64298i	0.126739	+	0.339667i
$277$	−8.65283	+	5.89940i	−0.519898	+	0.354460i	−0.794663	−	0.607051i	$-0.792352\pi$
$277$	−8.65283	+	5.89940i	−0.519898	+	0.354460i	0.274765	+	0.961511i	$0.411400\pi$
$278$	−1.54207	−	1.54207i	−0.0924871	−	0.0924871i
$279$	10.4848	+	9.65738i	0.627710	+	0.578172i
$280$	−4.84336	−	7.70817i	−0.289446	−	0.460651i
$281$	−2.44004	−	0.182856i	−0.145561	−	0.0109083i	0.00175050	−	0.999998i	$-0.499443\pi$
$281$	−2.44004	−	0.182856i	−0.145561	−	0.0109083i	−0.147311	+	0.989090i	$0.547062\pi$
$282$	−2.19170	−	1.54908i	−0.130514	−	0.0922463i
$283$	16.1289	+	17.3829i	0.958765	+	1.03330i	0.999417	+	0.0341300i	$0.0108660\pi$
$283$	16.1289	+	17.3829i	0.958765	+	1.03330i	−0.0406520	+	0.999173i	$0.512944\pi$
$284$	0.448517	−	2.97571i	0.0266146	−	0.176576i
$285$	−19.3423	−	46.4560i	−1.14574	−	2.75181i
$286$	0.606616	+	0.562857i	0.0358699	+	0.0332824i
$287$	4.38156	+	2.75312i	0.258635	+	0.162511i
$288$	−8.06964	+	3.20121i	−0.475508	+	0.188633i
$289$		−	10.6598i		−	0.627048i
$290$	4.87391	−	1.55917i	0.286206	−	0.0915576i
$291$	−21.4422	+	5.35940i	−1.25696	+	0.314173i
$292$	−5.27972	−	12.1012i	−0.308972	−	0.708172i
$293$	2.97216	+	0.111210i	0.173635	+	0.00649698i	0.124068	−	0.992274i	$-0.460406\pi$
$293$	2.97216	+	0.111210i	0.173635	+	0.00649698i	0.0495679	+	0.998771i	$0.484216\pi$
$294$	−0.401955	+	0.243204i	−0.0234425	+	0.0141840i
$295$	3.87787	+	25.7280i	0.225778	+	1.49794i
$296$	−2.16181	+	2.71083i	−0.125653	+	0.157564i
$297$	12.0325	+	25.8543i	0.698197	+	1.50022i
$298$	1.55324	+	0.543501i	0.0899765	+	0.0314841i
$299$	−0.0803851	+	1.07266i	−0.00464879	+	0.0620338i
$300$	−30.1403	−	7.41644i	−1.74015	−	0.428188i
$301$	11.2199	+	9.65551i	0.646705	+	0.556535i
$302$	−2.44097	−	0.654056i	−0.140462	−	0.0376367i
$303$	−29.7818	−	6.15720i	−1.71092	−	0.353722i
$304$	−25.5609	−	11.1521i	−1.46602	−	0.639616i
$305$	−2.89126	−	25.6606i	−0.165553	−	1.46932i
$306$	1.01743	+	1.60616i	0.0581625	+	0.0918181i
$307$	22.6896	−	22.6896i	1.29497	−	1.29497i	0.363289	−	0.931677i	$-0.381654\pi$
$307$	22.6896	−	22.6896i	1.29497	−	1.29497i	0.931677	−	0.363289i	$-0.118346\pi$
$308$	−4.80870	+	25.4146i	−0.274001	+	1.44813i
$309$	19.4126	−	5.63113i	1.10434	−	0.320344i
$310$	−3.73059	−	2.54348i	−0.211884	−	0.144460i
$311$	−0.296426	−	1.56665i	−0.0168088	−	0.0888367i	0.973158	−	0.230140i	$-0.0739184\pi$
$311$	−0.296426	−	1.56665i	−0.0168088	−	0.0888367i	−0.989966	+	0.141303i	$0.954871\pi$
$312$	−1.02660	−	0.0557701i	−0.0581200	−	0.00315736i
$313$	−6.91875	−	17.6287i	−0.391071	−	0.996432i	−0.981860	−	0.189607i	$-0.939279\pi$
$313$	−6.91875	−	17.6287i	−0.391071	−	0.996432i	0.590789	−	0.806826i	$-0.298816\pi$
$314$	4.42410	−	3.52810i	0.249666	−	0.199102i
$315$	7.03643	−	26.6498i	0.396458	−	1.50154i
$316$	1.91340	−	3.04516i	0.107637	−	0.171303i
$317$	0.106952	−	0.144915i	0.00600704	−	0.00813925i	−0.801584	−	0.597882i	$-0.796009\pi$
$317$	0.106952	−	0.144915i	0.00600704	−	0.00813925i	0.807591	+	0.589743i	$0.200771\pi$
$318$	−1.00106	−	4.00510i	−0.0561366	−	0.224595i
$319$	−26.7597	−	12.5452i	−1.49826	−	0.702396i
$320$	−21.3158	+	12.3067i	−1.19159	+	0.687963i
$321$	0.897954	−	0.691636i	0.0501189	−	0.0386034i
$322$	0.972375	−	0.513915i	0.0541883	−	0.0286394i
$323$	−4.31180	+	18.8912i	−0.239915	+	1.05114i
$324$	−15.7586	−	7.44747i	−0.875480	−	0.413749i
$325$	−4.33403	−	3.45628i	−0.240409	−	0.191720i
$326$	−0.857042	+	2.77846i	−0.0474672	+	0.153885i
$327$	1.01070	+	2.19261i	0.0558917	+	0.121252i
$328$	−1.18686	+	1.74080i	−0.0655332	+	0.0961196i
$329$	7.00066	−	13.2459i	0.385959	−	0.730269i
$330$	−4.96169	−	7.54798i	−0.273132	−	0.415503i
$331$	9.33870	−	2.50230i	0.513301	−	0.137539i	0.00713494	−	0.999975i	$-0.497729\pi$
$331$	9.33870	−	2.50230i	0.513301	−	0.137539i	0.506166	+	0.862436i	$0.331062\pi$
$332$	−1.23170	−	0.593154i	−0.0675982	−	0.0325536i
$333$	−10.4657	+	0.822792i	−0.573517	+	0.0450887i
$334$	−3.74690	+	0.422174i	−0.205021	+	0.0231003i
$335$	−11.3452	−	16.6403i	−0.619854	−	0.909159i
$336$	−7.41329	−	13.3556i	−0.404428	−	0.728608i
$337$	0.724932	−	0.842386i	0.0394896	−	0.0458877i	−0.737880	−	0.674932i	$-0.764173\pi$
$337$	0.724932	−	0.842386i	0.0394896	−	0.0458877i	0.777369	+	0.629045i	$0.216554\pi$
$338$	2.81301	+	1.48672i	0.153007	+	0.0808668i
$339$	−12.7481	+	2.18998i	−0.692381	+	0.118943i
$340$	12.0088	+	13.9545i	0.651269	+	0.756788i
$341$	5.80271	+	25.4233i	0.314234	+	1.37675i
$342$	1.93922	+	5.47764i	0.104861	+	0.296197i
$343$	−12.2564	−	15.3690i	−0.661781	−	0.829847i
$344$	−4.09932	+	4.41802i	−0.221021	+	0.238204i
$345$	3.64964	−	11.1598i	0.196490	−	0.600824i
$346$	1.68629	−	0.735720i	0.0906554	−	0.0395525i
$347$	1.03466	+	1.79208i	0.0555433	+	0.0962038i	0.892460	−	0.451126i	$-0.148978\pi$
$347$	1.03466	+	1.79208i	0.0555433	+	0.0962038i	−0.836917	+	0.547330i	$0.815644\pi$
$348$	17.4782	−	4.56250i	0.936928	−	0.244576i
$349$	0.839137	−	1.45343i	0.0449180	−	0.0778002i	−0.842692	−	0.538395i	$-0.819031\pi$
$349$	0.839137	−	1.45343i	0.0449180	−	0.0778002i	0.887610	+	0.460595i	$0.152364\pi$
$350$	−0.634606	+	5.63229i	−0.0339211	+	0.301058i
$351$	−1.99913	−	2.38609i	−0.106706	−	0.127360i
$352$	−15.4833	−	3.53397i	−0.825265	−	0.188361i
$353$	16.7114	−	2.51884i	0.889458	−	0.134064i	0.311611	−	0.950210i	$-0.399131\pi$
$353$	16.7114	−	2.51884i	0.889458	−	0.134064i	0.577847	+	0.816145i	$0.303893\pi$
$354$	−0.285973	−	2.99079i	−0.0151993	−	0.158959i
$355$	−4.30043	+	3.99022i	−0.228243	+	0.211779i
$356$	−8.66278	+	1.63909i	−0.459126	+	0.0868714i
$357$	−8.16038	+	6.78634i	−0.431893	+	0.359171i
$358$	0.241581	+	6.45638i	0.0127679	+	0.341230i
$359$	2.52260	+	7.20917i	0.133138	+	0.380485i	0.991081	−	0.133258i	$-0.0425440\pi$
$359$	2.52260	+	7.20917i	0.133138	+	0.380485i	−0.857944	+	0.513744i	$0.828258\pi$
$360$	10.7358	+	3.26861i	0.565826	+	0.172271i
$361$	−17.4511	+	36.2375i	−0.918478	+	1.90724i
$362$	−0.658671	+	1.50969i	−0.0346190	+	0.0793476i
$363$	−5.48740	+	32.6580i	−0.288014	+	1.71410i
$364$	−0.210995	−	2.81553i	−0.0110591	−	0.147574i
$365$	−6.66150	+	24.8611i	−0.348679	+	1.30129i
$366$	0.172636	+	2.97684i	0.00902385	+	0.155602i
$367$	−26.6068	+	0.995555i	−1.38886	+	0.0519676i	−0.721319	−	0.692603i	$-0.756464\pi$
$367$	−26.6068	+	0.995555i	−1.38886	+	0.0519676i	−0.667543	+	0.744571i	$0.732654\pi$
$368$	−2.82327	−	5.86257i	−0.147173	−	0.305608i
$369$	−6.30435	+	0.973819i	−0.328192	+	0.0506950i
$370$	3.24185	−	0.739932i	0.168536	−	0.0384672i
$371$	21.4522	−	8.41938i	1.11374	−	0.437113i
$372$	−12.6626	−	9.67963i	−0.656526	−	0.501865i
$373$	−13.8603	+	4.27533i	−0.717659	+	0.221368i	−0.632014	−	0.774957i	$-0.717771\pi$
$373$	−13.8603	+	4.27533i	−0.717659	+	0.221368i	−0.0856452	+	0.996326i	$0.527295\pi$
$374$	−0.130053	+	3.47574i	−0.00672488	+	0.179726i
$375$	16.9720	+	22.0348i	0.876432	+	1.13787i
$376$	5.28274	+	3.04999i	0.272437	+	0.157291i
$377$	3.17593	+	0.566726i	0.163569	+	0.0291879i
$378$	−0.978247	+	3.02871i	−0.0503156	+	0.155780i
$379$	27.1395	+	3.05789i	1.39406	+	0.157073i	0.776832	−	0.629708i	$-0.216825\pi$
$379$	27.1395	+	3.05789i	1.39406	+	0.157073i	0.617232	+	0.786781i	$0.288254\pi$
$380$	26.2914	+	49.7457i	1.34872	+	2.55190i
$381$	−15.0756	−	24.9161i	−0.772346	−	1.27649i
$382$	1.68310	+	0.660569i	0.0861150	+	0.0337977i
$383$	6.71245	+	1.01174i	0.342990	+	0.0516975i	0.318279	−	0.947997i	$-0.396895\pi$
$383$	6.71245	+	1.01174i	0.342990	+	0.0516975i	0.0247115	+	0.999695i	$0.492133\pi$
$384$	11.4754	−	5.81938i	0.585600	−	0.296969i
$385$	38.2193	−	32.8903i	1.94783	−	1.67625i
$386$	−1.26180	+	0.607652i	−0.0642241	+	0.0309287i
$387$	−18.2477	+	0.0667272i	−0.927582	+	0.00339194i
$388$	23.3258	−	8.16206i	1.18419	−	0.414366i
$389$	5.85478	+	21.8504i	0.296849	+	1.10786i	0.939738	+	0.341897i	$0.111069\pi$
$389$	5.85478	+	21.8504i	0.296849	+	1.10786i	−0.642888	+	0.765960i	$0.722264\pi$
$390$	0.736400	+	0.655670i	0.0372891	+	0.0332011i
$391$	−3.63773	+	2.68477i	−0.183968	+	0.135775i
$392$	0.859136	−	0.634071i	0.0433929	−	0.0320254i
$393$	18.6255	+	16.5836i	0.939532	+	0.836533i
$394$	−1.38178	−	5.15689i	−0.0696133	−	0.259800i
$395$	−6.61750	+	2.31556i	−0.332963	+	0.116509i
$396$	−16.0437	−	27.5553i	−0.806226	−	1.38471i
$397$	1.70335	−	0.820291i	0.0854888	−	0.0411692i	−0.390651	−	0.920539i	$-0.627750\pi$
$397$	1.70335	−	0.820291i	0.0854888	−	0.0411692i	0.476140	+	0.879370i	$0.342036\pi$
$398$	3.32265	−	2.85937i	0.166549	−	0.143327i
$399$	−28.9299	+	14.6709i	−1.44831	+	0.734465i
$400$	33.1589	+	4.99789i	1.65794	+	0.249895i
$401$	−15.1552	−	5.94797i	−0.756814	−	0.297028i	−0.0446140	−	0.999004i	$-0.514206\pi$
$401$	−15.1552	−	5.94797i	−0.756814	−	0.297028i	−0.712200	+	0.701977i	$0.752301\pi$
$402$	1.20390	+	1.98974i	0.0600449	+	0.0992390i
$403$	−1.33009	−	2.51666i	−0.0662567	−	0.125364i
$404$	33.7902	+	3.80724i	1.68113	+	0.189417i
$405$	14.9661	+	30.5047i	0.743672	+	1.51579i
$406$	−1.23701	−	3.05781i	−0.0613915	−	0.151757i
$407$	−16.6318	−	9.60238i	−0.824408	−	0.475972i
$408$	−2.63691	−	3.42351i	−0.130546	−	0.169489i
$409$	0.156647	−	4.18648i	0.00774569	−	0.207008i	−0.990053	−	0.140694i	$-0.955067\pi$
$409$	0.156647	−	4.18648i	0.00774569	−	0.207008i	0.997799	−	0.0663139i	$-0.0211239\pi$
$410$	1.93081	−	0.595576i	0.0953558	−	0.0294134i
$411$	−16.8820	−	12.9051i	−0.832729	−	0.636560i
$412$	−21.0382	+	8.25687i	−1.03648	+	0.406787i
$413$	16.3510	−	3.73201i	0.804579	−	0.183640i
$414$	−0.490715	+	1.26389i	−0.0241173	+	0.0621169i
$415$	1.15631	+	2.40111i	0.0567612	+	0.117866i
$416$	1.73238	−	0.0648212i	0.0849371	−	0.00317812i
$417$	0.868860	+	14.9821i	0.0425483	+	0.733678i
$418$	−2.75127	+	10.2679i	−0.134569	+	0.502218i
$419$	−0.952469	−	12.7098i	−0.0465311	−	0.620915i	−0.970911	−	0.239441i	$-0.923036\pi$
$419$	−0.952469	−	12.7098i	−0.0465311	−	0.620915i	0.924380	−	0.381474i	$-0.124583\pi$
$420$	−5.10680	+	30.3929i	−0.249186	+	1.48302i
$421$	6.11862	−	14.0240i	0.298203	−	0.683489i	−0.701367	−	0.712800i	$-0.747427\pi$
$421$	6.11862	−	14.0240i	0.298203	−	0.683489i	0.999570	+	0.0293113i	$0.00933142\pi$
$422$	−1.21367	+	2.52021i	−0.0590806	+	0.122682i
$423$	4.17558	+	17.9909i	0.203024	+	0.874749i
$424$	3.09899	+	8.85639i	0.150500	+	0.430104i
$425$	−0.871206	−	23.2835i	−0.0422597	−	1.12941i
$426$	0.520844	−	0.433145i	0.0252350	−	0.0209859i
$427$	−16.3552	+	3.09457i	−0.791485	+	0.149757i
$428$	−0.929015	+	0.862000i	−0.0449056	+	0.0416664i
$429$	−0.542033	−	5.66874i	−0.0261696	−	0.273689i
$430$	5.71541	−	0.861459i	0.275621	−	0.0415432i
$431$	18.1306	+	4.13818i	0.873319	+	0.199329i	0.635613	−	0.772008i	$-0.280747\pi$
$431$	18.1306	+	4.13818i	0.873319	+	0.199329i	0.237706	+	0.971337i	$0.423605\pi$
$432$	17.6899	+	6.45361i	0.851108	+	0.310499i
$433$	−0.0940766	+	0.834953i	−0.00452103	+	0.0401253i	−0.995770	−	0.0918790i	$-0.970713\pi$
$433$	−0.0940766	+	0.834953i	−0.00452103	+	0.0401253i	0.991249	+	0.132004i	$0.0421413\pi$
$434$	−1.45523	+	2.52052i	−0.0698531	+	0.120989i
$435$	−32.1845	−	14.2900i	−1.54313	−	0.685154i
$436$	−1.34977	−	2.33787i	−0.0646422	−	0.111964i
$437$	−12.6648	+	5.52561i	−0.605841	+	0.264326i
$438$	0.923812	−	2.82482i	0.0441414	−	0.134975i
$439$	10.2872	−	11.0870i	0.490983	−	0.529154i	−0.438149	−	0.898903i	$-0.644366\pi$
$439$	10.2872	−	11.0870i	0.490983	−	0.529154i	0.929132	+	0.369748i	$0.120556\pi$
$440$	12.8002	+	16.0509i	0.610223	+	0.765196i
$441$	3.17878	+	0.589426i	0.151370	+	0.0280679i
$442$	−0.0844845	−	0.370151i	−0.00401852	−	0.0176063i
$443$	−9.57251	−	11.1235i	−0.454804	−	0.528491i	0.483017	−	0.875611i	$-0.339541\pi$
$443$	−9.57251	−	11.1235i	−0.454804	−	0.528491i	−0.937821	+	0.347119i	$0.887160\pi$
$444$	11.5686	−	1.98736i	0.549022	−	0.0943157i
$445$	15.1954	+	8.03101i	0.720331	+	0.380706i
$446$	−4.26654	+	4.95781i	−0.202026	+	0.234759i
$447$	−5.49578	−	9.90107i	−0.259942	−	0.468304i
$448$	8.93744	+	13.1088i	0.422255	+	0.619334i
$449$	4.88033	−	0.549881i	0.230317	−	0.0259505i	0.00394836	−	0.999992i	$-0.498743\pi$
$449$	4.88033	−	0.549881i	0.230317	−	0.0259505i	0.226369	+	0.974042i	$0.427315\pi$
$450$	−3.95707	−	5.75860i	−0.186538	−	0.271463i
$451$	−10.5141	−	5.06333i	−0.495090	−	0.238423i
$452$	13.9700	−	3.74324i	0.657091	−	0.176067i
$453$	9.55240	+	14.5316i	0.448811	+	0.682754i
$454$	−0.414398	+	0.784079i	−0.0194486	+	0.0367986i
$455$	−3.10056	+	4.54768i	−0.145356	+	0.213199i
$456$	−5.52869	−	11.9940i	−0.258905	−	0.561669i
$457$	5.09567	−	16.5197i	0.238365	−	0.772761i	−0.754791	−	0.655966i	$-0.772262\pi$
$457$	5.09567	−	16.5197i	0.238365	−	0.772761i	0.993156	−	0.116795i	$-0.0372622\pi$
$458$	−3.96829	−	3.16460i	−0.185426	−	0.147872i
$459$	2.12083	−	12.9107i	0.0989918	−	0.602621i
$460$	−2.92134	+	12.7992i	−0.136208	+	0.596767i
$461$	−32.2428	+	17.0408i	−1.50170	+	0.793670i	−0.997551	−	0.0699487i	$-0.977716\pi$
$461$	−32.2428	+	17.0408i	−1.50170	+	0.793670i	−0.504146	+	0.863618i	$0.668193\pi$
$462$	−4.61279	+	3.55294i	−0.214606	+	0.165298i
$463$	−3.99107	+	2.30425i	−0.185481	+	0.107087i	−0.589865	−	0.807502i	$-0.700819\pi$
$463$	−3.99107	+	2.30425i	−0.185481	+	0.107087i	0.404384	+	0.914589i	$0.367486\pi$
$464$	−18.3521	+	6.63699i	−0.851974	+	0.308114i
$465$	7.53431	+	30.1438i	0.349395	+	1.39788i
$466$	−0.428162	+	0.580139i	−0.0198342	+	0.0268744i
$467$	−0.0547478	+	0.0871306i	−0.00253342	+	0.00403192i	−0.847989	−	0.530015i	$-0.822186\pi$
$467$	−0.0547478	+	0.0871306i	−0.00253342	+	0.00403192i	0.845455	+	0.534047i	$0.179329\pi$
$468$	2.47012	+	2.45212i	0.114181	+	0.113349i
$469$	−10.1498	+	8.09420i	−0.468675	+	0.373756i
$470$	−2.13727	−	5.44568i	−0.0985849	−	0.251190i
$471$	−38.8826	−	2.11229i	−1.79162	−	0.0973293i
$472$	1.26951	+	6.70950i	0.0584337	+	0.308830i
$473$	−27.5815	−	18.8048i	−1.26820	−	0.864644i
$474$	0.777518	−	0.225539i	0.0357126	−	0.0103594i
$475$	13.2386	−	69.9679i	0.607431	−	3.21035i
$476$	8.39138	−	8.39138i	0.384618	−	0.384618i
$477$	−13.1827	+	25.1652i	−0.603595	+	1.15224i
$478$	0.464933	+	4.12639i	0.0212655	+	0.188737i
$479$	7.41764	+	3.23628i	0.338921	+	0.147870i	0.562458	−	0.826826i	$-0.309856\pi$
$479$	7.41764	+	3.23628i	0.338921	+	0.147870i	−0.223538	+	0.974695i	$0.571761\pi$
$480$	−18.5310	−	3.83117i	−0.845823	−	0.174868i
$481$	2.02492	+	0.542576i	0.0923284	+	0.0247393i
$482$	−5.05028	−	4.34611i	−0.230034	−	0.197960i
$483$	−7.34926	−	1.80839i	−0.334403	−	0.0822846i
$484$	2.76708	−	36.9241i	0.125776	−	1.67837i
$485$	−45.4721	−	15.9114i	−2.06478	−	0.722499i
$486$	−1.53455	−	3.61102i	−0.0696088	−	0.163799i
$487$	0.618612	−	0.775715i	0.0280320	−	0.0351510i	−0.767618	−	0.640908i	$-0.778558\pi$
$487$	0.618612	−	0.775715i	0.0280320	−	0.0351510i	0.795650	+	0.605757i	$0.207130\pi$
$488$	−1.01009	−	6.70152i	−0.0457247	−	0.303363i
$489$	17.1193	−	10.3581i	0.774160	−	0.468408i
$490$	−1.02332	−	0.0382899i	−0.0462289	−	0.00172976i
$491$	16.3465	+	37.4666i	0.737708	+	1.69084i	0.722898	+	0.690954i	$0.242809\pi$
$491$	16.3465	+	37.4666i	0.737708	+	1.69084i	0.0148096	+	0.999890i	$0.495286\pi$
$492$	6.91978	−	1.72957i	0.311968	−	0.0779751i
$493$	6.90177	+	11.6718i	0.310840	+	0.525671i
$494$		−	1.16036i		−	0.0522070i
$495$	−9.03949	+	61.4981i	−0.406295	+	2.76414i
$496$	14.5799	+	9.16119i	0.654659	+	0.411349i
$497$	2.77204	+	2.57208i	0.124343	+	0.115373i
$498$	−0.118286	−	0.284097i	−0.00530051	−	0.0127307i
$499$	3.62956	−	24.0805i	0.162481	−	1.07799i	−0.747776	−	0.663951i	$-0.768878\pi$
$499$	3.62956	−	24.0805i	0.162481	−	1.07799i	0.910258	−	0.414042i	$-0.135883\pi$
$500$	−21.1526	−	22.7971i	−0.945972	−	1.01952i
$501$	21.1892	+	14.9763i	0.946662	+	0.669093i
$502$	1.92651	+	0.144372i	0.0859845	+	0.00644365i
$503$	−3.17760	−	5.05713i	−0.141682	−	0.225486i	0.768343	−	0.640038i	$-0.221081\pi$
$503$	−3.17760	−	5.05713i	−0.141682	−	0.225486i	−0.910026	+	0.414552i	$0.863938\pi$
$504$	1.58389	−	7.05835i	0.0705521	−	0.314404i
$505$	−46.8731	−	46.8731i	−2.08582	−	2.08582i
$506$	−2.04931	+	1.39719i	−0.0911028	+	0.0621128i
$507$	−7.65417	−	20.5136i	−0.339934	−	0.911040i
$508$	19.3360	+	26.1993i	0.857894	+	1.16241i
$509$	20.8953	−	1.56589i	0.926168	−	0.0694067i	0.396900	−	0.917862i	$-0.370086\pi$
$509$	20.8953	−	1.56589i	0.926168	−	0.0694067i	0.529267	+	0.848455i	$0.322467\pi$
$510$	−0.0699170	+	4.14367i	−0.00309598	+	0.183485i
$511$	16.3014	+	3.08440i	0.721133	+	0.136446i
$512$	−14.9602	+	9.40010i	−0.661153	+	0.415430i
$513$	15.0995	−	37.0265i	0.666658	−	1.63476i
$514$	−1.86784	+	5.33798i	−0.0823869	+	0.235448i
$515$	42.1007	+	12.9863i	1.85518	+	0.572246i
$516$	20.3107	−	1.94207i	0.894128	−	0.0854947i
$517$	−12.3437	+	31.4514i	−0.542877	+	1.38323i
$518$	−0.631786	−	2.04820i	−0.0277591	−	0.0899928i
$519$	−12.0334	−	3.93534i	−0.528209	−	0.172742i
$520$	−1.80310	−	1.33075i	−0.0790712	−	0.0583572i
$521$	3.96403			0.173668			0.0868338	−	0.996223i	$-0.472325\pi$
$521$	3.96403			0.173668			0.0868338	+	0.996223i	$0.472325\pi$
$522$	3.62144	+	1.84927i	0.158506	+	0.0809404i
$523$	−32.2747			−1.41127			−0.705637	−	0.708574i	$-0.749339\pi$
$523$	−32.2747			−1.41127			−0.705637	+	0.708574i	$0.749339\pi$
$524$	−22.4356	−	16.5583i	−0.980105	−	0.723351i
$525$	29.0354	−	26.0432i	1.26721	−	1.13662i
$526$	−0.907874	−	2.94325i	−0.0395852	−	0.128332i
$527$	4.37105	−	11.1373i	0.190406	−	0.485147i
$528$	19.9853	+	28.0578i	0.869747	+	1.22106i
$529$	18.8974	+	5.82906i	0.821624	+	0.253437i
$530$	2.97202	−	8.49355i	0.129096	−	0.368936i
$531$	−12.2163	+	16.6799i	−0.530143	+	0.723844i
$532$	30.7097	−	19.2962i	1.33144	−	0.836597i
$533$	1.25164	+	0.236824i	0.0542147	+	0.0102580i
$534$	−1.70176	−	1.02118i	−0.0736425	−	0.0441906i
$535$	2.46366	−	0.184626i	0.106513	−	0.00798206i
$536$	−3.13875	−	4.25285i	−0.135573	−	0.183695i
$537$	28.3033	−	34.2882i	1.22138	−	1.47964i
$538$	−1.09182	+	0.744389i	−0.0470716	+	0.0320929i
$539$	4.18204	+	4.18204i	0.180133	+	0.180133i
$540$	−19.7861	−	32.4330i	−0.851458	−	1.39569i
$541$	−0.350159	−	0.557275i	−0.0150545	−	0.0239591i	0.839112	−	0.543958i	$-0.183075\pi$
$541$	−0.350159	−	0.557275i	−0.0150545	−	0.0239591i	−0.854167	+	0.519999i	$0.825932\pi$
$542$	2.11043	+	0.158155i	0.0906508	+	0.00679334i
$543$	10.2937	−	4.74495i	0.441746	−	0.203625i
$544$	4.95609	+	5.34139i	0.212491	+	0.229010i
$545$	−0.784345	+	5.20379i	−0.0335976	+	0.222906i
$546$	0.385988	−	0.504938i	0.0165187	−	0.0216093i
$547$	−8.90811	−	8.26552i	−0.380883	−	0.353408i	0.466377	−	0.884586i	$-0.345559\pi$
$547$	−8.90811	−	8.26552i	−0.380883	−	0.353408i	−0.847260	+	0.531178i	$0.821750\pi$
$548$	20.1179	+	12.6409i	0.859393	+	0.539993i
$549$	12.7350	−	16.0895i	0.543517	−	0.686685i
$550$		−	12.7821i		−	0.545028i
$551$	12.6268	+	39.4710i	0.537921	+	1.68152i
$552$	0.847659	−	2.96264i	0.0360788	−	0.126098i
$553$	1.80720	+	4.14215i	0.0768500	+	0.176142i
$554$	2.63406	+	0.0985595i	0.111910	+	0.00418739i
$555$	−20.0476	−	11.0321i	−0.850972	−	0.468286i
$556$	−2.50093	−	16.5926i	−0.106063	−	0.703684i
$557$	−15.0241	+	18.8396i	−0.636592	+	0.798261i	−0.990572	−	0.136992i	$-0.956257\pi$
$557$	−15.0241	+	18.8396i	−0.636592	+	0.798261i	0.353980	+	0.935253i	$0.384828\pi$
$558$	−0.679910	−	3.52284i	−0.0287829	−	0.149134i
$559$	3.43943	+	1.20351i	0.145472	+	0.0509030i
$560$	2.48816	−	33.2022i	0.105144	−	1.40305i
$561$	16.5737	−	17.2685i	0.699741	−	0.729077i
$562$	0.466813	+	0.401725i	0.0196913	+	0.0169457i
$563$	18.6353	+	4.99331i	0.785383	+	0.210443i	0.629157	−	0.777278i	$-0.283400\pi$
$563$	18.6353	+	4.99331i	0.785383	+	0.210443i	0.156227	+	0.987721i	$0.450067\pi$
$564$	−6.49071	−	19.6042i	−0.273308	−	0.825487i
$565$	−25.8417	−	11.2746i	−1.08717	−	0.474327i
$566$	−0.668257	−	5.93094i	−0.0280889	−	0.249296i
$567$	18.8873	−	11.0896i	0.793194	−	0.465718i
$568$	−1.08870	+	1.08870i	−0.0456807	+	0.0456807i
$569$	2.84807	−	15.0524i	0.119397	−	0.631029i	−0.870832	−	0.491580i	$-0.836419\pi$
$569$	2.84807	−	15.0524i	0.119397	−	0.631029i	0.990229	−	0.139449i	$-0.0445330\pi$
$570$	−3.02633	+	12.2989i	−0.126759	+	0.515146i
$571$	34.9474	+	23.8267i	1.46250	+	0.997117i	0.993489	+	0.113926i	$0.0363428\pi$
$571$	34.9474	+	23.8267i	1.46250	+	0.997117i	0.469013	+	0.883191i	$0.344610\pi$
$572$	1.18375	+	6.25626i	0.0494950	+	0.261588i
$573$	−5.62752	−	11.0970i	−0.235093	−	0.463585i
$574$	−0.475841	−	1.21242i	−0.0198612	−	0.0506055i
$575$	12.9902	−	10.3593i	0.541728	−	0.432013i
$576$	−18.9103	−	4.99296i	−0.787930	−	0.208040i
$577$	−17.4444	+	27.7626i	−0.726220	+	1.15577i	0.255751	+	0.966743i	$0.417677\pi$
$577$	−17.4444	+	27.7626i	−0.726220	+	1.15577i	−0.981971	+	0.189030i	$0.939466\pi$
$578$	−1.59324	+	2.15877i	−0.0662701	+	0.0897928i
$579$	9.26573	+	2.65107i	0.385071	+	0.110175i
$580$	37.2978	+	12.6167i	1.54871	+	0.523878i
$581$	1.48772	−	0.858935i	0.0617210	−	0.0356346i
$582$	5.14338	+	2.11945i	0.213200	+	0.0878540i
$583$	−45.9481	+	24.2843i	−1.90298	+	1.00575i
$584$	−1.50311	+	6.58556i	−0.0621992	+	0.272513i
$585$	−0.784345	−	6.73966i	−0.0324287	−	0.278650i
$586$	−0.585283	−	0.466747i	−0.0241778	−	0.0192812i
$587$	6.63577	−	21.5127i	0.273888	−	0.887922i	−0.709235	−	0.704973i	$-0.750959\pi$
$587$	6.63577	−	21.5127i	0.273888	−	0.887922i	0.983122	−	0.182950i	$-0.0585645\pi$
$588$	−3.59968	−	0.330915i	−0.148448	−	0.0136467i
$589$	20.5982	−	30.2120i	0.848733	−	1.24486i
$590$	3.06004	−	5.78987i	0.125980	−	0.238365i
$591$	−16.4966	+	32.8271i	−0.678581	+	1.35033i
$592$	−12.2492	+	3.28215i	−0.503437	+	0.134896i
$593$	−4.71334	−	2.26982i	−0.193554	−	0.0932105i	0.334597	−	0.942361i	$-0.391400\pi$
$593$	−4.71334	−	2.26982i	−0.193554	−	0.0932105i	−0.528150	+	0.849151i	$0.677114\pi$
$594$	1.42749	−	7.03426i	0.0585705	−	0.288619i
$595$	−22.9889	+	2.59022i	−0.942451	+	0.106189i
$596$	7.13261	+	10.4616i	0.292163	+	0.428524i
$597$	−30.1615	−	0.508921i	−1.23443	−	0.0208287i
$598$	0.176602	−	0.205215i	0.00722180	−	0.00839188i
$599$	11.3830	+	6.01607i	0.465095	+	0.245810i	0.683363	−	0.730079i	$-0.260517\pi$
$599$	11.3830	+	6.01607i	0.465095	+	0.245810i	−0.218268	+	0.975889i	$0.570041\pi$
$600$	10.1541	+	12.2100i	0.414540	+	0.498472i
$601$	21.1908	+	24.6242i	0.864393	+	1.00444i	0.999907	+	0.0136671i	$0.00435052\pi$
$601$	21.1908	+	24.6242i	0.864393	+	1.00444i	−0.135514	+	0.990775i	$0.543269\pi$
$602$	−0.829056	−	3.63233i	−0.0337898	−	0.148043i
$603$	2.91774	−	15.7354i	0.118820	−	0.640796i
$604$	−12.1233	−	15.2022i	−0.493291	−	0.618568i
$605$	−49.0968	+	52.9138i	−1.99607	+	2.15125i
$606$	5.11098	+	5.69818i	0.207619	+	0.231473i
$607$	−18.9184	+	8.25400i	−0.767873	+	0.335019i	−0.747054	−	0.664764i	$-0.768532\pi$
$607$	−18.9184	+	8.25400i	−0.767873	+	0.335019i	−0.0208191	+	0.999783i	$0.506627\pi$
$608$	11.1346	+	19.2857i	0.451569	+	0.782140i
$609$	−7.63519	+	21.3763i	−0.309394	+	0.866213i
$610$	−3.24978	+	5.62878i	−0.131580	+	0.227902i
$611$	0.412937	−	3.66492i	0.0167057	−	0.148267i
$612$	−1.03989	+	14.5923i	−0.0420352	+	0.589858i
$613$	−18.9778	−	4.33157i	−0.766507	−	0.174950i	−0.178647	−	0.983913i	$-0.557172\pi$
$613$	−18.9778	−	4.33157i	−0.766507	−	0.174950i	−0.587860	+	0.808963i	$0.700029\pi$
$614$	−7.98622	+	1.20373i	−0.322297	+	0.0485785i
$615$	−12.6488	−	5.77457i	−0.510050	−	0.232853i
$616$	9.70082	−	9.00104i	0.390857	−	0.362662i
$617$	19.5601	−	3.70097i	0.787459	−	0.148995i	0.223397	−	0.974728i	$-0.428285\pi$
$617$	19.5601	−	3.70097i	0.787459	−	0.148995i	0.564062	+	0.825732i	$0.309238\pi$
$618$	−4.77297	−	1.76107i	−0.191997	−	0.0708405i
$619$	−0.106709	−	2.85185i	−0.00428899	−	0.114626i	−0.999800	−	0.0199832i	$-0.993639\pi$
$619$	−0.106709	−	2.85185i	−0.00428899	−	0.114626i	0.995511	−	0.0946424i	$-0.0301708\pi$
$620$	−11.4743	−	32.7918i	−0.460821	−	1.31695i
$621$	8.30571	−	4.25025i	0.333297	−	0.170557i
$622$	−0.174125	+	0.361574i	−0.00698177	+	0.0144978i
$623$	4.43031	−	10.1544i	0.177497	−	0.406826i
$624$	−2.89991	−	2.39374i	−0.116089	−	0.0958263i
$625$	1.07299	+	14.3180i	0.0429195	+	0.572720i
$626$	−1.23368	+	4.60415i	−0.0493077	+	0.184019i
$627$	61.1268	−	40.1819i	2.44117	−	1.60471i
$628$	43.5093	−	1.62800i	1.73621	−	0.0649644i
$629$	3.82305	+	7.93864i	0.152435	+	0.316534i
$630$	−5.40811	+	4.34527i	−0.215464	+	0.173120i
$631$	−3.28442	+	0.749647i	−0.130751	+	0.0298430i	−0.287395	−	0.957812i	$-0.592789\pi$
$631$	−3.28442	+	0.749647i	−0.130751	+	0.0298430i	0.156645	+	0.987655i	$0.449932\pi$
$632$	−1.71282	+	0.672231i	−0.0681322	+	0.0267399i
$633$	17.7704	−	7.39883i	0.706310	−	0.294077i
$634$	−0.0433187	+	0.0133621i	−0.00172041	+	0.000530675i
$635$	2.37349	−	63.4330i	0.0941892	−	2.51726i
$636$	12.1022	−	29.3691i	0.479883	−	1.16456i
$637$	−0.559100	−	0.322796i	−0.0221523	−	0.0127897i
$638$	3.54419	+	6.54015i	0.140316	+	0.258927i
$639$	−4.65899	−	0.157269i	−0.184307	−	0.00622146i
$640$	27.8691	+	3.14009i	1.10162	+	0.124123i
$641$	−5.81340	−	10.9995i	−0.229615	−	0.434454i	0.742206	−	0.670172i	$-0.233780\pi$
$641$	−5.81340	−	10.9995i	−0.229615	−	0.434454i	−0.971821	+	0.235718i	$0.924256\pi$
$642$	−0.285222	+	0.00585595i	−0.0112568	+	0.000231116i
$643$	−11.5264	−	4.52378i	−0.454557	−	0.178400i	0.127006	−	0.991902i	$-0.459463\pi$
$643$	−11.5264	−	4.52378i	−0.454557	−	0.178400i	−0.581563	+	0.813502i	$0.697559\pi$
$644$	8.36799	+	1.26127i	0.329745	+	0.0497010i
$645$	−33.3166	−	21.7267i	−1.31184	−	0.855488i
$646$	3.69672	−	3.18129i	0.145446	−	0.125166i
$647$	10.3555	−	4.98695i	0.407117	−	0.196057i	−0.219106	−	0.975701i	$-0.570314\pi$
$647$	10.3555	−	4.98695i	0.407117	−	0.196057i	0.626223	+	0.779644i	$0.284600\pi$
$648$	4.22444	+	7.85347i	0.165952	+	0.308513i
$649$	−35.6998	+	12.4919i	−1.40134	+	0.490350i
$650$	0.361121	+	1.34772i	0.0141643	+	0.0528619i
$651$	19.0133	−	6.29506i	0.745190	−	0.246723i
$652$	−18.0009	+	13.2853i	−0.704969	+	0.520291i
$653$	−6.45828	+	4.76643i	−0.252732	+	0.186525i	−0.712817	−	0.701350i	$-0.752581\pi$
$653$	−6.45828	+	4.76643i	−0.252732	+	0.186525i	0.460085	+	0.887875i	$0.347819\pi$
$654$	0.123032	−	0.595097i	0.00481094	−	0.0232701i
$655$	14.0690	+	52.5063i	0.549722	+	2.05159i
$656$	−7.27336	+	2.54506i	−0.283977	+	0.0993679i
$657$	−17.6745	+	10.2908i	−0.689550	+	0.401481i
$658$	−3.39749	+	1.63615i	−0.132448	+	0.0637836i
$659$	23.6948	−	20.3910i	0.923018	−	0.794321i	−0.0559291	−	0.998435i	$-0.517812\pi$
$659$	23.6948	−	20.3910i	0.923018	−	0.794321i	0.978947	+	0.204113i	$0.0654311\pi$
$660$	3.77010	−	69.3991i	0.146751	−	2.70136i
$661$	−39.0469	−	5.88537i	−1.51875	−	0.228914i	−0.663911	−	0.747812i	$-0.731104\pi$
$661$	−39.0469	−	5.88537i	−1.51875	−	0.228914i	−0.854836	+	0.518898i	$0.826343\pi$
$662$	−2.26522	−	0.889033i	−0.0880402	−	0.0345532i
$663$	−1.25963	+	2.28901i	−0.0489200	+	0.0888977i
$664$	0.326823	+	0.618380i	0.0126832	+	0.0239978i
$665$	−70.2592	−	7.91631i	−2.72453	−	0.306981i
$666$	2.24243	+	1.39760i	0.0868924	+	0.0541560i
$667$	−3.77422	+	8.90241i	−0.146138	+	0.344703i
$668$	−25.1256	−	14.5063i	−0.972137	−	0.561264i
$669$	44.6153	−	5.95672i	1.72493	−	0.230300i
$670$	−0.189541	+	5.06559i	−0.00732260	+	0.195701i
$671$	35.8703	−	11.0645i	1.38476	−	0.427141i
$672$	−1.57000	+	12.0962i	−0.0605641	+	0.466621i
$673$	−12.8392	+	5.03901i	−0.494915	+	0.194240i	−0.599653	−	0.800260i	$-0.704695\pi$
$673$	−12.8392	+	5.03901i	−0.494915	+	0.194240i	0.104738	+	0.994500i	$0.466600\pi$
$674$	−0.272714	+	0.0622452i	−0.0105046	+	0.00239760i
$675$	−6.01439	+	47.7043i	−0.231494	+	1.83614i
$676$	10.6221	+	22.0570i	0.408542	+	0.848345i
$677$	41.6490	−	1.55839i	1.60070	−	0.0598939i	0.777960	−	0.628313i	$-0.216254\pi$
$677$	41.6490	−	1.55839i	1.60070	−	0.0598939i	0.822739	+	0.568419i	$0.192445\pi$
$678$	2.90899	+	1.46186i	0.111719	+	0.0561423i
$679$	−8.03732	+	29.9957i	−0.308444	+	1.15113i
$680$	−0.703896	−	9.39284i	−0.0269932	−	0.360199i
$681$	5.71781	−	2.13347i	0.219107	−	0.0817548i
$682$	2.62470	−	6.01588i	0.100505	−	0.230360i
$683$	17.7087	−	36.7724i	0.677603	−	1.40706i	−0.224042	−	0.974579i	$-0.571925\pi$
$683$	17.7087	−	36.7724i	0.677603	−	1.40706i	0.901645	−	0.432477i	$-0.142360\pi$
$684$	−13.0223	+	42.7720i	−0.497920	+	1.63543i
$685$	−15.2978	−	43.7186i	−0.584499	−	1.67040i
$686$	0.185003	+	4.94430i	0.00706344	+	0.188774i
$687$	5.91361	+	34.4238i	0.225618	+	1.31335i
$688$	−21.6585	+	4.09801i	−0.825723	+	0.156235i
$689$	4.15861	−	3.85863i	0.158431	−	0.147002i
$690$	−2.40707	+	1.71454i	−0.0916357	+	0.0652712i
$691$	−0.488412	+	0.0736162i	−0.0185801	+	0.00280049i	−0.158326	−	0.987387i	$-0.550610\pi$
$691$	−0.488412	+	0.0736162i	−0.0185801	+	0.00280049i	0.139746	+	0.990187i	$0.455372\pi$
$692$	13.8012	+	3.15003i	0.524642	+	0.119746i
$693$	39.9661	+	2.84812i	1.51819	+	0.108191i
$694$	0.0583154	−	0.517563i	0.00221362	−	0.0196464i
$695$	−16.3558	+	28.3290i	−0.620410	+	1.07458i
$696$	−8.58110	−	3.43194i	−0.325266	−	0.130087i
$697$	2.67708	+	4.63683i	0.101401	+	0.175632i
$698$	−0.387170	+	0.168920i	−0.0146546	+	0.00639373i
$699$	4.85532	−	1.02233i	0.183645	−	0.0386682i
$700$	−29.6632	+	31.9693i	−1.12116	+	1.20833i
$701$	−5.21340	−	6.53739i	−0.196907	−	0.246914i	0.673569	−	0.739124i	$-0.264760\pi$
$701$	−5.21340	−	6.53739i	−0.196907	−	0.246914i	−0.870476	+	0.492210i	$0.836189\pi$
$702$	0.0482212	+	0.782012i	0.00181999	+	0.0295151i
$703$	5.99229	+	26.2539i	0.226003	+	0.990186i
$704$	−23.3385	−	27.1199i	−0.879604	−	1.02212i
$705$	−13.9353	+	37.7685i	−0.524834	+	1.42244i
$706$	−3.76077	−	1.98762i	−0.141538	−	0.0748052i
$707$	−27.8718	+	32.3876i	−1.04823	+	1.21806i
$708$	11.8947	−	19.8223i	0.447031	−	0.744967i
$709$	12.0505	+	17.6748i	0.452564	+	0.663790i	0.982930	−	0.183979i	$-0.0588978\pi$
$709$	12.0505	+	17.6748i	0.452564	+	0.663790i	−0.530366	+	0.847769i	$0.677945\pi$
$710$	1.46728	−	0.165323i	0.0550662	−	0.00620447i
$711$	−5.02816	−	2.39882i	−0.188571	−	0.0899629i
$712$	4.06404	+	1.95714i	0.152306	+	0.0733468i
$713$	8.24104	−	2.20818i	0.308629	−	0.0826970i
$714$	2.66690	−	0.154662i	0.0998060	−	0.00578806i
$715$	5.80000	−	10.9741i	0.216908	−	0.410409i
$716$	−28.0041	+	41.0745i	−1.04656	+	1.53503i
$717$	16.4932	−	23.3352i	0.615949	−	0.871471i
$718$	0.566637	−	1.83699i	0.0211467	−	0.0685560i
$719$	−28.5051	−	22.7321i	−1.06306	−	0.847763i	−0.0742958	−	0.997236i	$-0.523671\pi$
$719$	−28.5051	−	22.7321i	−1.06306	−	0.847763i	−0.988766	+	0.149473i	$0.952242\pi$
$720$	24.4938	+	32.9351i	0.912829	+	1.22742i
$721$	6.31952	−	27.6876i	0.235351	−	1.03114i
$722$	8.95024	−	4.73034i	0.333093	−	0.176045i
$723$	6.06782	+	45.4474i	0.225665	+	1.69021i
$724$	−10.9757	+	6.33680i	−0.407907	+	0.235505i
$725$	−26.9496	−	41.9147i	−1.00088	−	1.55667i
$726$	5.99242	−	5.79355i	0.222400	−	0.215019i
$727$	29.8683	−	40.4701i	1.10775	−	1.50095i	0.263766	−	0.964587i	$-0.415035\pi$
$727$	29.8683	−	40.4701i	1.10775	−	1.50095i	0.843986	−	0.536364i	$-0.180203\pi$
$728$	−0.768541	+	1.22313i	−0.0284840	+	0.0453321i
$729$	−8.63743	+	25.5811i	−0.319905	+	0.947450i
$730$	5.06484	−	4.03908i	0.187458	−	0.149493i
$731$	5.59550	+	14.2571i	0.206957	+	0.527318i
$732$	−12.5327	+	19.2181i	−0.463221	+	0.710321i
$733$	−4.18440	−	22.1151i	−0.154554	−	0.816840i	−0.970938	−	0.239330i	$-0.923072\pi$
$733$	−4.18440	−	22.1151i	−0.154554	−	0.816840i	0.816384	−	0.577510i	$-0.195975\pi$
$734$	5.53705	+	3.77510i	0.204376	+	0.139341i
$735$	5.08416	+	4.87959i	0.187532	+	0.179986i
$736$	−0.965999	+	5.10543i	−0.0356072	+	0.188189i
$737$	20.7017	−	20.7017i	0.762557	−	0.762557i
$738$	1.42227	+	0.745051i	0.0523545	+	0.0274257i
$739$	−0.886859	−	7.87109i	−0.0326236	−	0.289543i	−0.999422	−	0.0340015i	$-0.989175\pi$
$739$	−0.886859	−	7.87109i	−0.0326236	−	0.289543i	0.966798	−	0.255541i	$-0.0822537\pi$
$740$	23.4508	+	10.2315i	0.862068	+	0.376116i
$741$	−5.30989	+	5.96368i	−0.195064	+	0.219081i
$742$	−5.60277	−	1.50126i	−0.205684	−	0.0551129i
$743$	−16.9845	−	14.6164i	−0.623102	−	0.536223i	0.283088	−	0.959094i	$-0.408641\pi$
$743$	−16.9845	−	14.6164i	−0.623102	−	0.536223i	−0.906190	+	0.422871i	$0.861022\pi$
$744$	2.27180	+	7.83172i	0.0832881	+	0.287125i
$745$	1.84458	−	24.6142i	0.0675801	−	0.901793i
$746$	3.44591	+	1.20578i	0.126164	+	0.0441466i
$747$	−0.692118	+	2.00141i	−0.0253233	+	0.0732276i
$748$	−16.6861	+	20.9237i	−0.610104	+	0.765046i
$749$	−0.237352	−	1.57473i	−0.00867267	−	0.0575394i
$750$	−0.143699	−	6.99905i	−0.00524714	−	0.255569i
$751$	8.13506	+	0.304392i	0.296852	+	0.0111074i	0.185403	−	0.982663i	$-0.440641\pi$
$751$	8.13506	+	0.304392i	0.296852	+	0.0111074i	0.111450	+	0.993770i	$0.464451\pi$
$752$	8.92165	+	20.4486i	0.325339	+	0.745685i
$753$	−9.24069	−	9.55789i	−0.336750	−	0.348309i
$754$	−0.558467	−	0.589452i	−0.0203382	−	0.0214666i
$755$			37.9054i			1.37952i
$756$	−19.8946	+	14.2807i	−0.723561	+	0.519384i
$757$	−4.33143	−	2.72162i	−0.157429	−	0.0989190i	0.451014	−	0.892517i	$-0.351063\pi$
$757$	−4.33143	−	2.72162i	−0.157429	−	0.0989190i	−0.608442	+	0.793598i	$0.708205\pi$
$758$	−5.03910	−	4.67561i	−0.183029	−	0.169826i
$759$	16.9261	+	2.19689i	0.614380	+	0.0797421i
$760$	4.29050	−	28.4656i	0.155633	−	1.03256i
$761$	17.5399	+	18.9035i	0.635822	+	0.685253i	0.965963	−	0.258678i	$-0.0832870\pi$
$761$	17.5399	+	18.9035i	0.635822	+	0.685253i	−0.330142	+	0.943931i	$0.607097\pi$
$762$	−0.671000	+	7.29911i	−0.0243078	+	0.264419i
$763$	3.38275	+	0.253502i	0.122464	+	0.00917738i
$764$	7.40171	+	11.7797i	0.267784	+	0.426176i
$765$	19.3211	−	20.9765i	0.698557	−	0.758408i
$766$	−1.20815	−	1.20815i	−0.0436523	−	0.0436523i
$767$	3.41121	−	2.32573i	0.123172	−	0.0839771i
$768$	19.0781	+	3.20563i	0.688423	+	0.115673i
$769$	−3.05465	−	4.13890i	−0.110153	−	0.149252i	0.746053	−	0.665887i	$-0.231947\pi$
$769$	−3.05465	−	4.13890i	−0.110153	−	0.149252i	−0.856206	+	0.516634i	$0.827185\pi$
$770$	−12.6558	+	0.948422i	−0.456084	+	0.0341787i
$771$	34.0268	−	18.8873i	1.22545	−	0.680208i
$772$	−10.5881	−	2.00338i	−0.381074	−	0.0721031i
$773$	−2.34322	+	1.47234i	−0.0842797	+	0.0529565i	−0.573513	−	0.819197i	$-0.694420\pi$
$773$	−2.34322	+	1.47234i	−0.0842797	+	0.0529565i	0.489233	+	0.872153i	$0.337277\pi$
$774$	3.70539	+	2.71383i	0.133188	+	0.0975466i
$775$	−14.5217	+	41.5007i	−0.521636	+	1.49075i
$776$	−12.0819	−	3.72677i	−0.433715	−	0.133783i
$777$	−6.12566	+	13.4179i	−0.219757	+	0.481364i
$778$	2.08013	−	5.30008i	0.0745762	−	0.190017i
$779$	4.82323	+	15.6365i	0.172810	+	0.560236i
$780$	1.56316	+	7.42385i	0.0559702	+	0.265817i
$781$	−6.86152	−	5.06403i	−0.245524	−	0.181205i
$782$	1.13796			0.0406935
$783$	−10.1500	−	26.0764i	−0.362733	−	0.931893i
$784$	3.90532			0.139476
$785$	−68.2924	−	50.4021i	−2.43746	−	1.79893i
$786$	−1.29330	−	6.14223i	−0.0461306	−	0.219086i
$787$	−15.6772	−	50.8242i	−0.558832	−	1.81169i	−0.583662	−	0.811997i	$-0.698381\pi$
$787$	−15.6772	−	50.8242i	−0.558832	−	1.81169i	0.0248304	−	0.999692i	$-0.492095\pi$
$788$	15.0078	−	38.2392i	0.534630	−	1.36222i
$789$	−8.80254	+	19.2814i	−0.313379	+	0.686437i
$790$	1.68623	+	0.520132i	0.0599933	+	0.0185055i
$791$	−6.00244	+	17.1540i	−0.213422	+	0.609926i
$792$	−1.76725	+	16.2175i	−0.0627963	+	0.576265i
$793$	−3.46951	+	2.18004i	−0.123206	+	0.0774154i
$794$	−0.467555	−	0.0884663i	−0.0165929	−	0.00313955i
$795$	−54.1419	+	30.0525i	−1.92022	+	1.06585i
$796$	33.6348	−	2.52058i	1.19215	−	0.0893396i
$797$	9.88903	+	13.3992i	0.350287	+	0.474623i	0.943949	−	0.330093i	$-0.107080\pi$
$797$	9.88903	+	13.3992i	0.350287	+	0.474623i	−0.593661	+	0.804715i	$0.702318\pi$
$798$	8.05147	+	1.35286i	0.285019	+	0.0478906i
$799$	12.8080	−	8.73235i	0.453115	−	0.308928i
$800$	−18.9345	−	18.9345i	−0.669437	−	0.669437i
$801$	4.07326	+	13.0358i	0.143922	+	0.460596i
$802$	2.18014	+	3.46968i	0.0769835	+	0.122519i
$803$	−37.3099	−	2.79599i	−1.31664	−	0.0986684i
$804$	−1.63808	+	17.8189i	−0.0577706	+	0.628426i
$805$	−11.2209	−	12.0932i	−0.395483	−	0.426230i
$806$	−0.106783	+	0.708458i	−0.00376127	+	0.0249544i
$807$	9.01781	+	1.17045i	0.317442	+	0.0412017i
$808$	−12.7532	−	11.8332i	−0.448654	−	0.416290i
$809$	26.6286	+	16.7319i	0.936211	+	0.588261i	0.911440	−	0.411433i	$-0.134971\pi$
$809$	26.6286	+	16.7319i	0.936211	+	0.588261i	0.0247711	+	0.999693i	$0.492114\pi$
$810$	1.52846	−	8.41451i	0.0537045	−	0.295656i
$811$			1.55471i			0.0545933i	0.999627	+	0.0272966i	$0.00868987\pi$
$811$			1.55471i			0.0545933i	−0.999627	+	0.0272966i	$0.991310\pi$
$812$	6.31324	−	24.5826i	0.221551	−	0.862679i
$813$	−10.1229	−	10.4704i	−0.355025	−	0.367211i
$814$	1.93298	+	4.43045i	0.0677510	+	0.155287i
$815$	43.5832	+	1.63077i	1.52665	+	0.0571233i
$816$	−0.324423	−	15.8015i	−0.0113571	−	0.553162i
$817$	6.97647	+	46.2858i	0.244076	+	1.61934i
$818$	−0.657444	+	0.824409i	−0.0229870	+	0.0288248i
$819$	−4.29443	+	0.828827i	−0.150059	+	0.0289616i
$820$	14.6747	+	5.13488i	0.512461	+	0.179318i
$821$	−0.0962963	+	1.28498i	−0.00336076	+	0.0448463i	−0.998632	−	0.0522881i	$-0.983349\pi$
$821$	−0.0962963	+	1.28498i	−0.00336076	+	0.0448463i	0.995271	+	0.0971343i	$0.0309676\pi$
$822$	1.49003	+	5.13669i	0.0519708	+	0.179163i
$823$	−21.4977	−	18.5003i	−0.749362	−	0.644879i	0.192339	−	0.981329i	$-0.438393\pi$
$823$	−21.4977	−	18.5003i	−0.749362	−	0.644879i	−0.941701	+	0.336450i	$0.890774\pi$
$824$	11.1690	+	2.99272i	0.389090	+	0.104256i
$825$	−58.4917	+	65.6936i	−2.03642	+	2.28716i
$826$	−3.86910	−	1.68807i	−0.134623	−	0.0587355i
$827$	1.87566	+	16.6470i	0.0652232	+	0.578872i	0.983238	+	0.182326i	$0.0583626\pi$
$827$	1.87566	+	16.6470i	0.0652232	+	0.578872i	−0.918015	+	0.396546i	$0.870209\pi$
$828$	−8.81279	+	5.58250i	−0.306266	+	0.194005i
$829$	−11.1000	+	11.1000i	−0.385520	+	0.385520i	−0.873086	−	0.487566i	$-0.837885\pi$
$829$	−11.1000	+	11.1000i	−0.385520	+	0.385520i	0.487566	+	0.873086i	$0.337885\pi$
$830$	0.124705	−	0.659084i	0.00432859	−	0.0228771i
$831$	−13.0868	−	12.5602i	−0.453975	−	0.435709i
$832$	3.22698	+	2.20011i	0.111875	+	0.0762753i
$833$	−0.504472	−	2.66620i	−0.0174789	−	0.0923783i
$834$	2.06331	−	3.16396i	0.0714465	−	0.109559i
$835$	20.6629	+	52.6483i	0.715070	+	1.82197i
$836$	−63.9476	+	50.9965i	−2.21167	+	1.76375i
$837$	−12.6264	+	21.2170i	−0.436432	+	0.733369i
$838$	−1.70675	+	2.71628i	−0.0589587	+	0.0938322i
$839$	−17.6305	+	23.8885i	−0.608673	+	0.824722i	−0.995231	−	0.0975425i	$-0.968902\pi$
$839$	−17.6305	+	23.8885i	−0.608673	+	0.824722i	0.386559	+	0.922265i	$0.373664\pi$
$840$	11.3360	−	10.9598i	0.391129	−	0.378149i
$841$	25.4113	+	13.9738i	0.876251	+	0.481855i
$842$	−3.33517	+	1.92556i	−0.114938	+	0.0663592i
$843$	−0.560868	−	4.20085i	−0.0193173	−	0.144685i
$844$	−19.0288	+	10.0570i	−0.654997	+	0.346176i
$845$	10.6198	−	46.5283i	0.365331	−	1.60062i
$846$	1.84335	−	4.26751i	0.0633757	−	0.146720i
$847$	36.3777	+	29.0102i	1.24995	+	0.996803i
$848$	−10.1152	+	32.7926i	−0.347357	+	1.12610i
$849$	−23.7060	+	33.5402i	−0.813587	+	1.15110i
$850$	−3.30357	+	4.84544i	−0.113311	+	0.166197i
$851$	−2.93598	+	5.55515i	−0.100644	+	0.190428i
$852$	5.20356	−	0.301771i	0.178271	−	0.0103385i
$853$	16.5156	−	4.42534i	0.565483	−	0.151521i	0.0352587	−	0.999378i	$-0.488774\pi$
$853$	16.5156	−	4.42534i	0.565483	−	0.151521i	0.530224	+	0.847858i	$0.322108\pi$
$854$	3.77469	+	1.81779i	0.129167	+	0.0622036i
$855$	71.8349	−	49.3619i	2.45670	−	1.68814i
$856$	0.644320	−	0.0725974i	0.0220224	−	0.00248133i
$857$	−29.0069	−	42.5452i	−0.990855	−	1.45332i	−0.888667	−	0.458553i	$-0.848368\pi$
$857$	−29.0069	−	42.5452i	−0.990855	−	1.45332i	−0.102188	−	0.994765i	$-0.532584\pi$
$858$	−0.737493	+	1.22901i	−0.0251776	+	0.0419578i
$859$	−34.1155	+	39.6429i	−1.16400	+	1.35260i	−0.239744	+	0.970836i	$0.577064\pi$
$859$	−34.1155	+	39.6429i	−1.16400	+	1.35260i	−0.924261	+	0.381762i	$0.875317\pi$
$860$	39.3195	+	20.7810i	1.34078	+	0.708626i
$861$	−3.10255	+	8.40876i	−0.105735	+	0.286570i
$862$	−3.05320	−	3.54788i	−0.103992	−	0.120841i
$863$	−3.42770	−	15.0177i	−0.116680	−	0.511209i	−0.999165	−	0.0408674i	$-0.986988\pi$
$863$	−3.42770	−	15.0177i	−0.116680	−	0.511209i	0.882484	−	0.470342i	$-0.155869\pi$
$864$	−8.30553	−	12.5347i	−0.282560	−	0.426439i
$865$	−17.2061	−	21.5757i	−0.585023	−	0.733596i
$866$	0.143846	−	0.155029i	0.00488808	−	0.00526810i
$867$	18.0672	−	3.80422i	0.613594	−	0.129198i
$868$	−20.5256	+	8.95524i	−0.696685	+	0.303961i
$869$	−5.09577	−	8.82614i	−0.172862	−	0.299406i
$870$	4.38199	+	7.70430i	0.148563	+	0.261200i
$871$	−1.59789	+	2.76763i	−0.0541424	+	0.0937774i
$872$	−0.154640	+	1.37247i	−0.00523678	+	0.0464777i
$873$	−16.7357	−	34.4295i	−0.566419	−	1.16526i
$874$	3.39068	+	0.773901i	0.114692	+	0.0261776i
$875$	38.6422	−	5.82438i	1.30635	−	0.196900i
$876$	18.6260	−	13.2671i	0.629316	−	0.448255i
$877$	−26.7728	+	24.8415i	−0.904052	+	0.838837i	−0.987491	−	0.157676i	$-0.949600\pi$
$877$	−26.7728	+	24.8415i	−0.904052	+	0.838837i	0.0834394	+	0.996513i	$0.473409\pi$
$878$	−3.74040	+	0.707722i	−0.126232	+	0.0238845i
$879$	0.872198	+	5.07716i	0.0294185	+	0.171248i
$880$	2.80756	+	75.0336i	0.0946428	+	2.52938i
$881$	−11.3902	−	32.5512i	−0.383745	−	1.09668i	−0.960143	−	0.279510i	$-0.909828\pi$
$881$	−11.3902	−	32.5512i	−0.383745	−	1.09668i	0.576398	−	0.817169i	$-0.304458\pi$
$882$	−0.555651	−	0.594475i	−0.0187097	−	0.0200170i
$883$	21.1701	−	43.9603i	0.712432	−	1.47938i	−0.158180	−	0.987410i	$-0.550563\pi$
$883$	21.1701	−	43.9603i	0.712432	−	1.47938i	0.870612	−	0.491970i	$-0.163723\pi$
$884$	1.16822	−	2.67758i	0.0392914	−	0.0900568i
$885$	−42.2221	+	15.7542i	−1.41928	+	0.529571i
$886$	0.276032	+	3.68339i	0.00927347	+	0.123746i
$887$	7.70756	−	28.7650i	0.258795	−	0.965835i	−0.707145	−	0.707068i	$-0.750017\pi$
$887$	7.70756	−	28.7650i	0.258795	−	0.965835i	0.965940	−	0.258767i	$-0.0833160\pi$
$888$	−5.36604	−	2.69660i	−0.180073	−	0.0904921i
$889$	−40.8887	+	1.52995i	−1.37136	+	0.0513127i
$890$	−1.87695	−	3.89753i	−0.0629156	−	0.130646i
$891$	−39.5260	+	29.6205i	−1.32417	+	0.992323i
$892$	−49.0663	+	11.1991i	−1.64286	+	0.374972i
$893$	44.1014	−	17.3085i	1.47580	−	0.579208i
$894$	−0.366862	+	2.82652i	−0.0122697	+	0.0945329i
$895$	92.6060	−	28.5652i	3.09548	−	0.954828i
$896$	0.675957	−	18.0653i	0.0225821	−	0.603520i
$897$	−1.84673	+	0.246563i	−0.0616606	+	0.00823249i
$898$	−1.07052	−	0.618066i	−0.0357238	−	0.0206251i
$899$	−4.07698	−	25.2611i	−0.135975	−	0.842504i
$900$	1.81374	−	53.7310i	0.0604582	−	1.79103i
$901$	23.6944	+	2.66972i	0.789376	+	0.0889414i
$902$	1.37248	+	2.59686i	0.0456986	+	0.0864660i
$903$	−12.3609	+	22.4623i	−0.411345	+	0.747498i
$904$	−6.88802	−	2.70335i	−0.229092	−	0.0899120i
$905$	24.4304	+	3.68229i	0.812093	+	0.122403i
$906$	0.237431	−	4.37058i	0.00788812	−	0.145203i
$907$	−3.49338	+	3.00630i	−0.115996	+	0.0998224i	−0.708373	−	0.705838i	$-0.750570\pi$
$907$	−3.49338	+	3.00630i	−0.115996	+	0.0998224i	0.592377	+	0.805661i	$0.298190\pi$
$908$	−6.14801	+	2.96073i	−0.204029	+	0.0982552i
$909$	−0.192616	−	52.6742i	−0.00638868	−	1.74709i
$910$	1.30761	−	0.457554i	0.0433470	−	0.0151678i
$911$	8.91446	+	33.2692i	0.295349	+	1.10226i	0.940939	+	0.338575i	$0.109945\pi$
$911$	8.91446	+	33.2692i	0.295349	+	1.10226i	−0.645590	+	0.763684i	$0.723389\pi$
$912$	9.77952	−	47.3027i	0.323832	−	1.56635i
$913$	−3.11706	+	2.30050i	−0.103160	+	0.0761353i
$914$	−3.50102	+	2.58387i	−0.115804	+	0.0854669i
$915$	42.4600	−	14.0580i	1.40369	−	0.464742i
$916$	−10.1079	−	37.7232i	−0.333974	−	1.24641i
$917$	33.0730	−	11.5727i	1.09217	−	0.382166i
$918$	−2.35917	+	2.29762i	−0.0778641	+	0.0758329i
$919$	22.3056	−	10.7418i	0.735793	−	0.354339i	−0.0281667	−	0.999603i	$-0.508967\pi$
$919$	22.3056	−	10.7418i	0.735793	−	0.354339i	0.763960	+	0.645264i	$0.223253\pi$
$920$	5.09116	−	4.38130i	0.167851	−	0.144447i
$921$	46.5537	+	30.3590i	1.53400	+	1.00036i
$922$	9.07658	+	1.36807i	0.298921	+	0.0450551i
$923$	0.866538	+	0.340091i	0.0285225	+	0.0111942i
$924$	−44.7909	+	0.919612i	−1.47351	+	0.0302530i
$925$	−15.1305	−	28.6282i	−0.497487	−	0.941291i
$926$	1.15265	+	0.129872i	0.0378783	+	0.00426786i
$927$	16.4720	+	30.8925i	0.541011	+	1.01464i
$928$	14.9383	+	4.43802i	0.490374	+	0.145685i
$929$	34.9819	+	20.1968i	1.14772	+	0.662636i	0.948330	−	0.317285i	$-0.102771\pi$
$929$	34.9819	+	20.1968i	1.14772	+	0.662636i	0.199389	+	0.979920i	$0.436104\pi$
$930$	2.97955	−	7.23064i	0.0977033	−	0.237102i
$931$	0.310088	−	8.28729i	0.0101627	−	0.271605i
$932$	−5.30141	+	1.63527i	−0.173654	+	0.0535650i
$933$	2.54951	−	1.06151i	0.0834672	−	0.0347522i
$934$	0.0241099	−	0.00946245i	0.000788901	−	0.000309621i
$935$	50.8634	−	11.6092i	1.66341	−	0.379663i
$936$	−0.271845	−	1.75988i	−0.00888552	−	0.0575235i
$937$	6.28219	+	13.0451i	0.205230	+	0.426165i	0.978024	−	0.208492i	$-0.0668557\pi$
$937$	6.28219	+	13.0451i	0.205230	+	0.426165i	−0.772794	+	0.634657i	$0.781141\pi$
$938$	3.26526	−	0.122177i	0.106614	−	0.00398923i
$939$	27.4095	−	18.0177i	0.894475	−	0.587986i
$940$	11.6501	−	43.4789i	0.379986	−	1.41813i
$941$	−2.34778	−	31.3290i	−0.0765355	−	1.02130i	−0.894804	−	0.446459i	$-0.852685\pi$
$941$	−2.34778	−	31.3290i	−0.0765355	−	1.02130i	0.818268	−	0.574836i	$-0.194934\pi$
$942$	7.55857	+	6.23925i	0.246272	+	0.203286i
$943$	−1.52681	+	3.49948i	−0.0497196	+	0.113959i
$944$	−10.8362	+	22.5015i	−0.352687	+	0.732361i
$945$	47.6794	+	2.41535i	1.55101	+	0.0785712i
$946$	2.77505	+	7.93064i	0.0902246	+	0.257847i
$947$	0.898102	+	24.0023i	0.0291844	+	0.779969i	0.934654	+	0.355558i	$0.115709\pi$
$947$	0.898102	+	24.0023i	0.0291844	+	0.779969i	−0.905470	+	0.424411i	$0.860481\pi$
$948$	5.84404	+	2.15626i	0.189805	+	0.0700319i
$949$	4.01290	−	0.759281i	0.130264	−	0.0246473i
$950$	−13.1386	+	12.1908i	−0.426272	+	0.395522i
$951$	0.283783	+	0.129556i	0.00920231	+	0.00420113i
$952$	−6.00376	+	0.904921i	−0.194583	+	0.0293287i
$953$	34.2071	+	7.80756i	1.10808	+	0.252912i	0.737136	−	0.675744i	$-0.236178\pi$
$953$	34.2071	+	7.80756i	1.10808	+	0.252912i	0.370942	+	0.928656i	$0.379035\pi$
$954$	6.43094	−	3.12600i	0.208209	−	0.101208i
$955$	3.03656	−	26.9502i	0.0982609	−	0.872089i
$956$	−15.9755	+	27.6703i	−0.516684	+	0.894923i
$957$	11.7128	−	49.8317i	0.378622	−	1.61083i
$958$	−1.01847	−	1.76405i	−0.0329054	−	0.0569939i
$959$	−27.3652	+	11.9393i	−0.883667	+	0.385540i
$960$	−28.4654	−	31.7359i	−0.918718	−	1.02427i
$961$	5.72884	−	6.17422i	0.184801	−	0.199168i
$962$	−0.328981	−	0.412529i	−0.0106068	−	0.0133005i
$963$	1.49270	+	1.27510i	0.0481016	+	0.0410896i
$964$	−11.4079	−	49.9814i	−0.367425	−	1.60979i
$965$	13.7026	+	15.9227i	0.441102	+	0.512570i
$966$	1.21804	+	1.46466i	0.0391899	+	0.0471247i
$967$	14.4802	+	7.65299i	0.465650	+	0.246103i	0.683600	−	0.729857i	$-0.260413\pi$
$967$	14.4802	+	7.65299i	0.465650	+	0.246103i	−0.217950	+	0.975960i	$0.569937\pi$
$968$	−12.3571	+	14.3592i	−0.397173	+	0.461523i
$969$	−33.5572	−	0.566218i	−1.07801	−	0.0181895i
$970$	6.83060	+	10.0187i	0.219317	+	0.321679i
$971$	−50.4807	+	5.68781i	−1.62000	+	0.182530i	−0.874860	−	0.484375i	$-0.839047\pi$
$971$	−50.4807	+	5.68781i	−1.62000	+	0.182530i	−0.745142	+	0.666905i	$0.767618\pi$
$972$	6.99877	−	29.3669i	0.224486	−	0.941944i
$973$	18.9976	+	9.14876i	0.609035	+	0.293296i
$974$	−0.241218	+	0.0646341i	−0.00772912	+	0.00207101i
$975$	4.31129	−	8.57915i	0.138072	−	0.274753i
$976$	11.5822	−	21.9146i	0.370737	−	0.701469i
$977$	−13.9823	+	20.5083i	−0.447334	+	0.656118i	−0.981986	−	0.188954i	$-0.939490\pi$
$977$	−13.9823	+	20.5083i	−0.447334	+	0.656118i	0.534652	+	0.845072i	$0.320443\pi$
$978$	−5.01504	−	0.461028i	−0.160363	−	0.0147420i
$979$	−7.36426	+	23.8743i	−0.235363	+	0.763027i
$980$	−6.16031	−	4.91269i	−0.196784	−	0.156930i
$981$	−3.35554	+	2.49551i	−0.107134	+	0.0796753i
$982$	2.28944	−	10.0307i	0.0730591	−	0.320093i
$983$	−1.01290	+	0.535331i	−0.0323063	+	0.0170744i	−0.483344	−	0.875431i	$-0.660578\pi$
$983$	−1.01290	+	0.535331i	−0.0323063	+	0.0170744i	0.451037	+	0.892505i	$0.351054\pi$
$984$	−3.37402	−	1.39034i	−0.107560	−	0.0443225i
$985$	−69.3516	+	40.0402i	−2.20973	+	1.27579i
$986$	0.346787	−	3.39526i	0.0110439	−	0.108127i
$987$	24.9486	+	7.13820i	0.794124	+	0.227211i
$988$	5.30177	−	7.18365i	0.168672	−	0.228542i
$989$	−5.81070	+	9.24768i	−0.184770	+	0.294059i
$990$	11.0223	−	11.1032i	0.350311	−	0.352882i
$991$	−43.3590	+	34.5777i	−1.37734	+	1.09840i	−0.393509	+	0.919321i	$0.628739\pi$
$991$	−43.3590	+	34.5777i	−1.37734	+	1.09840i	−0.983835	+	0.179075i	$0.942690\pi$
$992$	−5.02348	−	12.7996i	−0.159495	−	0.406388i
$993$	7.57385	+	14.9350i	0.240349	+	0.473949i
$994$	−0.176949	−	0.935198i	−0.00561248	−	0.0296627i
$995$	−54.3274	−	37.0398i	−1.72229	−	1.17424i
$996$	0.565768	−	2.29927i	0.0179270	−	0.0728551i
$997$	−1.93840	+	10.2447i	−0.0613898	+	0.324453i	−0.999777	−	0.0211337i	$-0.993272\pi$
$997$	−1.93840	+	10.2447i	−0.0613898	+	0.324453i	0.938387	+	0.345587i	$0.112320\pi$
$998$	−4.33417	+	4.33417i	−0.137196	+	0.137196i
$999$	−5.12948	−	17.4446i	−0.162290	−	0.551921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.14	✓	672
3.2	odd	2		783.2.be.a.89.15		672
9.4	even	3		783.2.be.a.611.15		672
9.5	odd	6	inner	261.2.x.a.176.14	yes	672
29.15	odd	28	inner	261.2.x.a.218.14	yes	672
87.44	even	28		783.2.be.a.305.15		672
261.131	even	84	inner	261.2.x.a.131.14	yes	672
261.247	odd	84		783.2.be.a.44.15		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.14	✓	672	1.1	even	1	trivial
261.2.x.a.131.14	yes	672	261.131	even	84	inner
261.2.x.a.176.14	yes	672	9.5	odd	6	inner
261.2.x.a.218.14	yes	672	29.15	odd	28	inner
783.2.be.a.44.15		672	261.247	odd	84
783.2.be.a.89.15		672	3.2	odd	2
783.2.be.a.305.15		672	87.44	even	28
783.2.be.a.611.15		672	9.4	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.202514 - 0.149462i) q^{2} +(0.356874 + 1.69489i) q^{3} +(-0.570837 - 1.85061i) q^{4} +(-1.37930 + 3.51439i) q^{5} +(0.181050 - 0.396578i) q^{6} +(2.32547 + 0.717312i) q^{7} +(-0.327254 + 0.935237i) q^{8} +(-2.74528 + 1.20972i) q^{9} +O(q^{10})\)	\(q+(-0.202514 - 0.149462i) q^{2} +(0.356874 + 1.69489i) q^{3} +(-0.570837 - 1.85061i) q^{4} +(-1.37930 + 3.51439i) q^{5} +(0.181050 - 0.396578i) q^{6} +(2.32547 + 0.717312i) q^{7} +(-0.327254 + 0.935237i) q^{8} +(-2.74528 + 1.20972i) q^{9} +(0.804596 - 0.505561i) q^{10} +(-5.39244 - 1.02030i) q^{11} +(2.93286 - 1.62794i) q^{12} +(0.597397 - 0.0447687i) q^{13} +(-0.363730 - 0.492836i) q^{14} +(-6.44872 - 1.08356i) q^{15} +(-2.99421 + 2.04142i) q^{16} +(1.78047 + 1.78047i) q^{17} +(0.736767 + 0.165330i) q^{18} +(4.09425 + 6.51596i) q^{19} +(7.29111 + 0.546393i) q^{20} +(-0.385863 + 4.19740i) q^{21} +(0.939549 + 1.01259i) q^{22} +(-0.267615 + 1.77551i) q^{23} +(-1.70191 - 0.220896i) q^{24} +(-6.78321 - 6.29390i) q^{25} +(-0.127673 - 0.0802220i) q^{26} +(-3.03006 - 4.22122i) q^{27} -4.71300i q^{28} +(5.21590 + 1.33954i) q^{29} +(1.14401 + 1.18328i) q^{30} +(-1.90011 - 4.35511i) q^{31} +(2.89178 + 0.108203i) q^{32} +(-0.195122 - 9.50369i) q^{33} +(-0.0944576 - 0.626685i) q^{34} +(-5.72842 + 7.18322i) q^{35} +(3.80583 + 4.38989i) q^{36} +(3.30296 + 1.15576i) q^{37} +(0.144747 - 1.93151i) q^{38} +(0.289073 + 0.996543i) q^{39} +(-2.83541 - 2.44006i) q^{40} +(2.05392 + 0.550346i) q^{41} +(0.705495 - 0.792361i) q^{42} +(5.57509 + 2.43238i) q^{43} +(1.19002 + 10.5617i) q^{44} +(-0.464881 - 11.3166i) q^{45} +(0.319568 - 0.319568i) q^{46} +(1.14454 - 6.04905i) q^{47} +(-4.52853 - 4.34632i) q^{48} +(-0.890400 - 0.607065i) q^{49} +(0.432996 + 2.28844i) q^{50} +(-2.38230 + 3.65311i) q^{51} +(-0.423866 - 1.07999i) q^{52} +(7.40369 - 5.90425i) q^{53} +(-0.0172826 + 1.30774i) q^{54} +(11.0235 - 17.5438i) q^{55} +(-1.43188 + 1.94012i) q^{56} +(-9.58268 + 9.26467i) q^{57} +(-0.856084 - 1.05086i) q^{58} +(5.96836 - 3.44584i) q^{59} +(1.67594 + 12.5526i) q^{60} +(-6.04723 + 3.19605i) q^{61} +(-0.266124 + 1.16597i) q^{62} +(-7.25182 + 0.843949i) q^{63} +(5.09712 + 4.06481i) q^{64} +(-0.666652 + 2.16123i) q^{65} +(-1.38093 + 1.95380i) q^{66} +(-3.00506 + 4.40761i) q^{67} +(2.27860 - 4.31132i) q^{68} +(-3.10479 + 0.180057i) q^{69} +(2.23371 - 0.598520i) q^{70} +(1.40000 + 0.674204i) q^{71} +(-0.232974 - 2.96338i) q^{72} +(6.77451 - 0.763304i) q^{73} +(-0.496155 - 0.727726i) q^{74} +(8.24669 - 13.7429i) q^{75} +(9.72135 - 11.2964i) q^{76} +(-11.8081 - 6.24075i) q^{77} +(0.0904041 - 0.245020i) q^{78} +(1.21131 + 1.40757i) q^{79} +(-3.04444 - 13.3385i) q^{80} +(6.07314 - 6.64206i) q^{81} +(-0.333692 - 0.418437i) q^{82} +(0.480134 - 0.517461i) q^{83} +(7.98801 - 1.68195i) q^{84} +(-8.71308 + 3.80148i) q^{85} +(-0.765484 - 1.32586i) q^{86} +(-0.408943 + 9.31841i) q^{87} +(2.71892 - 4.70931i) q^{88} +(0.509712 - 4.52382i) q^{89} +(-1.59725 + 2.36124i) q^{90} +(1.42134 + 0.324412i) q^{91} +(3.43854 - 0.518277i) q^{92} +(6.70331 - 4.77470i) q^{93} +(-1.13589 + 1.05395i) q^{94} +(-28.5468 + 5.40135i) q^{95} +(0.848610 + 4.93985i) q^{96} +(0.477131 + 12.7516i) q^{97} +(0.0895855 + 0.256021i) q^{98} +(16.0381 - 3.72233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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Database

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