LMFDB - Embedded newform 637.2.bt.a.309.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(36,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([12, 35]))

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

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

chi := DirichletCharacter("637.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bt (of order $42$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$64$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			309.21
Character	$\chi$	$=$	637.309
Dual form			637.2.bt.a.134.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.316510 - 1.02610i) q^{2} +(2.79159 + 0.420765i) q^{3} +(0.699773 - 0.477097i) q^{4} +(-1.92313 - 1.53365i) q^{5} +(-0.451820 - 2.99763i) q^{6} +(2.35639 - 1.20309i) q^{7} +(-2.39011 - 1.90605i) q^{8} +(4.74923 + 1.46494i) q^{9} +O(q^{10})$	\(q+(-0.316510 - 1.02610i) q^{2} +(2.79159 + 0.420765i) q^{3} +(0.699773 - 0.477097i) q^{4} +(-1.92313 - 1.53365i) q^{5} +(-0.451820 - 2.99763i) q^{6} +(2.35639 - 1.20309i) q^{7} +(-2.39011 - 1.90605i) q^{8} +(4.74923 + 1.46494i) q^{9} +(-0.964985 + 2.45874i) q^{10} +(-1.50949 - 4.89364i) q^{11} +(2.15423 - 1.03742i) q^{12} +(-2.43634 + 2.65786i) q^{13} +(-1.98031 - 2.03711i) q^{14} +(-4.72329 - 5.09050i) q^{15} +(-0.580461 + 1.47899i) q^{16} +(-0.304897 + 4.06856i) q^{17} -5.33686i q^{18} +(3.11790 + 1.80012i) q^{19} +(-2.07745 - 0.155684i) q^{20} +(7.08431 - 2.36704i) q^{21} +(-4.54360 + 3.09777i) q^{22} +(0.199750 + 2.66547i) q^{23} +(-5.87021 - 6.32658i) q^{24} +(0.233758 + 1.02416i) q^{25} +(3.49836 + 1.65870i) q^{26} +(5.01088 + 2.41311i) q^{27} +(1.07495 - 1.96612i) q^{28} +(-2.95413 - 2.01409i) q^{29} +(-3.72840 + 6.45777i) q^{30} +8.06174i q^{31} +(-4.39571 - 0.329413i) q^{32} +(-2.15480 - 14.2962i) q^{33} +(4.27126 - 0.974887i) q^{34} +(-6.37676 - 1.30018i) q^{35} +(4.02230 - 1.24072i) q^{36} +(1.18356 - 1.73596i) q^{37} +(0.860259 - 3.76904i) q^{38} +(-7.91962 + 6.39454i) q^{39} +(1.67329 + 7.33116i) q^{40} +(-0.234799 + 1.55779i) q^{41} +(-4.67107 - 6.52002i) q^{42} +(11.9060 - 1.79454i) q^{43} +(-3.39104 - 2.70426i) q^{44} +(-6.88669 - 10.1009i) q^{45} +(2.67182 - 1.04861i) q^{46} +(11.0864 + 2.53040i) q^{47} +(-2.24272 + 3.88450i) q^{48} +(4.10517 - 5.66988i) q^{49} +(0.976906 - 0.564017i) q^{50} +(-2.56306 + 11.2295i) q^{51} +(-0.436830 + 3.02227i) q^{52} +(8.35549 + 4.02379i) q^{53} +(0.890102 - 5.90544i) q^{54} +(-4.60216 + 11.7261i) q^{55} +(-7.92517 - 1.61589i) q^{56} +(7.94649 + 6.33712i) q^{57} +(-1.13165 + 3.66871i) q^{58} +(-0.956173 - 6.34380i) q^{59} +(-5.73390 - 1.30872i) q^{60} +(0.467153 - 6.23372i) q^{61} +(8.27216 - 2.55162i) q^{62} +(12.9535 - 2.26175i) q^{63} +(1.76037 + 7.71268i) q^{64} +(8.76163 - 1.37493i) q^{65} +(-13.9873 + 6.73593i) q^{66} +(-3.00632 + 1.73570i) q^{67} +(1.72774 + 2.99254i) q^{68} +(-0.563918 + 7.52496i) q^{69} +(0.684192 + 6.95472i) q^{70} +(4.84065 + 7.09993i) q^{71} +(-8.55892 - 12.5536i) q^{72} +(-5.88042 + 1.34217i) q^{73} +(-2.15588 - 0.665000i) q^{74} +(0.221626 + 2.95740i) q^{75} +(3.04066 - 0.227866i) q^{76} +(-9.44441 - 9.71529i) q^{77} +(9.06808 + 6.10239i) q^{78} -0.861308 q^{79} +(3.38455 - 1.95407i) q^{80} +(0.653676 + 0.445669i) q^{81} +(1.67276 - 0.252129i) q^{82} +(3.71364 - 0.847614i) q^{83} +(3.82810 - 5.03629i) q^{84} +(6.82609 - 7.35678i) q^{85} +(-5.60976 - 11.6488i) q^{86} +(-7.39926 - 6.86551i) q^{87} +(-5.71967 + 14.5735i) q^{88} +(-4.69225 - 5.05705i) q^{89} +(-8.18485 + 10.2635i) q^{90} +(-2.54335 + 9.19409i) q^{91} +(1.41147 + 1.76993i) q^{92} +(-3.39210 + 22.5051i) q^{93} +(-0.912515 - 12.1767i) q^{94} +(-3.23539 - 8.24363i) q^{95} +(-12.1324 - 2.76915i) q^{96} +(5.46068 + 3.15272i) q^{97} +(-7.11720 - 2.41774i) q^{98} -25.4523i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q - 15 q^{2} - 3 q^{3} - 69 q^{4} - 15 q^{6} - 21 q^{7} + 57 q^{9}+O(q^{10}) $ 768 * q - 15 * q^2 - 3 * q^3 - 69 * q^4 - 15 * q^6 - 21 * q^7 + 57 * q^9	$ 768 q - 15 q^{2} - 3 q^{3} - 69 q^{4} - 15 q^{6} - 21 q^{7} + 57 q^{9} - 13 q^{10} - 27 q^{11} - 16 q^{12} - 8 q^{13} - 20 q^{14} - 33 q^{15} + 47 q^{16} - 9 q^{17} - 30 q^{19} - 15 q^{20} - 13 q^{22} - 5 q^{23} - 21 q^{24} + 100 q^{25} + 50 q^{26} - 24 q^{27} + 105 q^{28} - 9 q^{29} - 14 q^{30} - 39 q^{32} + 9 q^{33} - 27 q^{35} - 49 q^{36} - 30 q^{37} - 56 q^{38} - 14 q^{39} - 132 q^{40} - 33 q^{41} - 53 q^{42} + 9 q^{43} - 120 q^{45} + 15 q^{46} - 88 q^{48} - 27 q^{49} - 378 q^{50} - 16 q^{51} + 50 q^{52} - 62 q^{53} + 6 q^{54} - 22 q^{55} - 107 q^{56} - 15 q^{58} - 63 q^{59} + 2 q^{61} - 15 q^{62} - 117 q^{63} + 228 q^{64} - 62 q^{65} - 116 q^{66} - 54 q^{67} - 168 q^{68} + 49 q^{69} + 15 q^{71} - 39 q^{72} - 19 q^{74} - 87 q^{75} + 9 q^{76} - 78 q^{77} + 16 q^{78} - 8 q^{79} + 60 q^{80} + 61 q^{81} + 136 q^{82} - 39 q^{84} - 165 q^{85} - 49 q^{87} - 47 q^{88} + 120 q^{89} + 468 q^{90} - 42 q^{91} - 236 q^{92} + 108 q^{93} - 6 q^{94} + 84 q^{95} + 180 q^{97} - 147 q^{98}+O(q^{100}) $ 768 * q - 15 * q^2 - 3 * q^3 - 69 * q^4 - 15 * q^6 - 21 * q^7 + 57 * q^9 - 13 * q^10 - 27 * q^11 - 16 * q^12 - 8 * q^13 - 20 * q^14 - 33 * q^15 + 47 * q^16 - 9 * q^17 - 30 * q^19 - 15 * q^20 - 13 * q^22 - 5 * q^23 - 21 * q^24 + 100 * q^25 + 50 * q^26 - 24 * q^27 + 105 * q^28 - 9 * q^29 - 14 * q^30 - 39 * q^32 + 9 * q^33 - 27 * q^35 - 49 * q^36 - 30 * q^37 - 56 * q^38 - 14 * q^39 - 132 * q^40 - 33 * q^41 - 53 * q^42 + 9 * q^43 - 120 * q^45 + 15 * q^46 - 88 * q^48 - 27 * q^49 - 378 * q^50 - 16 * q^51 + 50 * q^52 - 62 * q^53 + 6 * q^54 - 22 * q^55 - 107 * q^56 - 15 * q^58 - 63 * q^59 + 2 * q^61 - 15 * q^62 - 117 * q^63 + 228 * q^64 - 62 * q^65 - 116 * q^66 - 54 * q^67 - 168 * q^68 + 49 * q^69 + 15 * q^71 - 39 * q^72 - 19 * q^74 - 87 * q^75 + 9 * q^76 - 78 * q^77 + 16 * q^78 - 8 * q^79 + 60 * q^80 + 61 * q^81 + 136 * q^82 - 39 * q^84 - 165 * q^85 - 49 * q^87 - 47 * q^88 + 120 * q^89 + 468 * q^90 - 42 * q^91 - 236 * q^92 + 108 * q^93 - 6 * q^94 + 84 * q^95 + 180 * q^97 - 147 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{7}\right)$

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 $

$2$	−0.316510	−	1.02610i	−0.223807	−	0.725563i	−0.995933	−	0.0900943i	$-0.971283\pi$
$2$	−0.316510	−	1.02610i	−0.223807	−	0.725563i	0.772127	−	0.635469i	$-0.219193\pi$
$3$	2.79159	+	0.420765i	1.61173	+	0.242929i	0.892235	−	0.451572i	$-0.149136\pi$
$3$	2.79159	+	0.420765i	1.61173	+	0.242929i	0.719492	+	0.694500i	$0.244375\pi$
$4$	0.699773	−	0.477097i	0.349887	−	0.238549i
$5$	−1.92313	−	1.53365i	−0.860050	−	0.685867i	0.0906822	−	0.995880i	$-0.471095\pi$
$5$	−1.92313	−	1.53365i	−0.860050	−	0.685867i	−0.950732	+	0.310013i	$0.899667\pi$
$6$	−0.451820	−	2.99763i	−0.184455	−	1.22378i
$7$	2.35639	−	1.20309i	0.890633	−	0.454724i
$7$	2.35639	−	1.20309i	0.890633	−	0.454724i
$8$	−2.39011	−	1.90605i	−0.845031	−	0.673890i
$9$	4.74923	+	1.46494i	1.58308	+	0.488315i
$10$	−0.964985	+	2.45874i	−0.305155	+	0.777522i
$11$	−1.50949	−	4.89364i	−0.455127	−	1.47549i	−0.834897	−	0.550406i	$-0.814473\pi$
$11$	−1.50949	−	4.89364i	−0.455127	−	1.47549i	0.379770	−	0.925081i	$-0.376003\pi$
$12$	2.15423	−	1.03742i	0.621872	−	0.299478i
$13$	−2.43634	+	2.65786i	−0.675720	+	0.737158i
$13$	−2.43634	+	2.65786i	−0.675720	+	0.737158i
$14$	−1.98031	−	2.03711i	−0.529260	−	0.544440i
$15$	−4.72329	−	5.09050i	−1.21955	−	1.31436i
$16$	−0.580461	+	1.47899i	−0.145115	+	0.369748i
$17$	−0.304897	+	4.06856i	−0.0739483	+	0.986772i	0.829620	+	0.558328i	$0.188557\pi$
$17$	−0.304897	+	4.06856i	−0.0739483	+	0.986772i	−0.903569	+	0.428444i	$0.859062\pi$
$18$		−	5.33686i		−	1.25791i
$19$	3.11790	+	1.80012i	0.715296	+	0.412976i	0.813019	−	0.582237i	$-0.197822\pi$
$19$	3.11790	+	1.80012i	0.715296	+	0.412976i	−0.0977227	+	0.995214i	$0.531156\pi$
$20$	−2.07745	−	0.155684i	−0.464533	−	0.0348119i
$21$	7.08431	−	2.36704i	1.54592	−	0.516530i
$22$	−4.54360	+	3.09777i	−0.968698	+	0.660447i
$23$	0.199750	+	2.66547i	0.0416507	+	0.555789i	0.978526	+	0.206125i	$0.0660854\pi$
$23$	0.199750	+	2.66547i	0.0416507	+	0.555789i	−0.936875	+	0.349664i	$0.886296\pi$
$24$	−5.87021	−	6.32658i	−1.19825	−	1.29141i
$25$	0.233758	+	1.02416i	0.0467516	+	0.204832i
$26$	3.49836	+	1.65870i	0.686085	+	0.325297i
$27$	5.01088	+	2.41311i	0.964344	+	0.464404i
$28$	1.07495	−	1.96612i	0.203147	−	0.371561i
$29$	−2.95413	−	2.01409i	−0.548568	−	0.374007i	0.257091	−	0.966387i	$-0.417236\pi$
$29$	−2.95413	−	2.01409i	−0.548568	−	0.374007i	−0.805659	+	0.592380i	$0.798188\pi$
$30$	−3.72840	+	6.45777i	−0.680709	+	1.17902i
$31$			8.06174i			1.44793i	0.689836	+	0.723966i	$0.257683\pi$
$31$			8.06174i			1.44793i	−0.689836	+	0.723966i	$0.742317\pi$
$32$	−4.39571	−	0.329413i	−0.777060	−	0.0582326i
$33$	−2.15480	−	14.2962i	−0.375103	−	2.48865i
$34$	4.27126	−	0.974887i	0.732515	−	0.167192i
$35$	−6.37676	−	1.30018i	−1.07787	−	0.219771i
$36$	4.02230	−	1.24072i	0.670384	−	0.206786i
$37$	1.18356	−	1.73596i	0.194576	−	0.285390i	−0.716536	−	0.697550i	$-0.754273\pi$
$37$	1.18356	−	1.73596i	0.194576	−	0.285390i	0.911111	+	0.412160i	$0.135226\pi$
$38$	0.860259	−	3.76904i	0.139552	−	0.611419i
$39$	−7.91962	+	6.39454i	−1.26815	+	1.02395i
$40$	1.67329	+	7.33116i	0.264570	+	1.15916i
$41$	−0.234799	+	1.55779i	−0.0366694	+	0.243286i	−0.999655	−	0.0262673i	$-0.991638\pi$
$41$	−0.234799	+	1.55779i	−0.0366694	+	0.243286i	0.962986	+	0.269553i	$0.0868760\pi$
$42$	−4.67107	−	6.52002i	−0.720762	−	1.00606i
$43$	11.9060	−	1.79454i	1.81565	−	0.273665i	0.848746	−	0.528801i	$-0.177358\pi$
$43$	11.9060	−	1.79454i	1.81565	−	0.273665i	0.966905	+	0.255136i	$0.0821202\pi$
$44$	−3.39104	−	2.70426i	−0.511218	−	0.407683i
$45$	−6.88669	−	10.1009i	−1.02661	−	1.50576i
$46$	2.67182	−	1.04861i	0.393939	−	0.154609i
$47$	11.0864	+	2.53040i	1.61712	+	0.369097i	0.932887	−	0.360169i	$-0.117281\pi$
$47$	11.0864	+	2.53040i	1.61712	+	0.369097i	0.684231	+	0.729266i	$0.260138\pi$
$48$	−2.24272	+	3.88450i	−0.323708	+	0.560680i
$49$	4.10517	−	5.66988i	0.586453	−	0.809983i
$50$	0.976906	−	0.564017i	0.138155	−	0.0797641i
$51$	−2.56306	+	11.2295i	−0.358900	+	1.57244i
$52$	−0.436830	+	3.02227i	−0.0605774	+	0.419114i
$53$	8.35549	+	4.02379i	1.14771	+	0.552710i	0.908346	−	0.418219i	$-0.137345\pi$
$53$	8.35549	+	4.02379i	1.14771	+	0.552710i	0.239368	+	0.970929i	$0.423060\pi$
$54$	0.890102	−	5.90544i	0.121128	−	0.803629i
$55$	−4.60216	+	11.7261i	−0.620555	+	1.58115i
$56$	−7.92517	−	1.61589i	−1.05905	−	0.215933i
$57$	7.94649	+	6.33712i	1.05254	+	0.839371i
$58$	−1.13165	+	3.66871i	−0.148593	+	0.481725i
$59$	−0.956173	−	6.34380i	−0.124483	−	0.825892i	−0.960719	−	0.277522i	$-0.910487\pi$
$59$	−0.956173	−	6.34380i	−0.124483	−	0.825892i	0.836236	−	0.548370i	$-0.184751\pi$
$60$	−5.73390	−	1.30872i	−0.740243	−	0.168956i
$61$	0.467153	−	6.23372i	0.0598128	−	0.798146i	−0.883962	−	0.467558i	$-0.845134\pi$
$61$	0.467153	−	6.23372i	0.0598128	−	0.798146i	0.943775	−	0.330588i	$-0.107247\pi$
$62$	8.27216	−	2.55162i	1.05057	−	0.324057i
$63$	12.9535	−	2.26175i	1.63199	−	0.284953i
$64$	1.76037	+	7.71268i	0.220046	+	0.964085i
$65$	8.76163	−	1.37493i	1.08675	−	0.170538i
$66$	−13.9873	+	6.73593i	−1.72172	+	0.829136i
$67$	−3.00632	+	1.73570i	−0.367281	+	0.212050i	−0.672270	−	0.740306i	$-0.734681\pi$
$67$	−3.00632	+	1.73570i	−0.367281	+	0.212050i	0.304989	+	0.952356i	$0.401347\pi$
$68$	1.72774	+	2.99254i	0.209520	+	0.362898i
$69$	−0.563918	+	7.52496i	−0.0678877	+	0.905899i
$70$	0.684192	+	6.95472i	0.0817766	+	0.831248i
$71$	4.84065	+	7.09993i	0.574479	+	0.842606i	0.997996	−	0.0632820i	$-0.0201568\pi$
$71$	4.84065	+	7.09993i	0.574479	+	0.842606i	−0.423516	+	0.905888i	$0.639204\pi$
$72$	−8.55892	−	12.5536i	−1.00868	−	1.47946i
$73$	−5.88042	+	1.34217i	−0.688252	+	0.157089i	−0.552324	−	0.833630i	$-0.686259\pi$
$73$	−5.88042	+	1.34217i	−0.688252	+	0.157089i	−0.135928	+	0.990719i	$0.543402\pi$
$74$	−2.15588	−	0.665000i	−0.250616	−	0.0773047i
$75$	0.221626	+	2.95740i	0.0255912	+	0.341491i
$76$	3.04066	−	0.227866i	0.348788	−	0.0261380i
$77$	−9.44441	−	9.71529i	−1.07629	−	1.10716i
$78$	9.06808	+	6.10239i	1.02676	+	0.690960i
$79$	−0.861308			−0.0969047			−0.0484524	−	0.998825i	$-0.515429\pi$
$79$	−0.861308			−0.0969047			−0.0484524	+	0.998825i	$0.515429\pi$
$80$	3.38455	−	1.95407i	0.378404	−	0.218472i
$81$	0.653676	+	0.445669i	0.0726306	+	0.0495187i
$82$	1.67276	−	0.252129i	0.184726	−	0.0278430i
$83$	3.71364	−	0.847614i	0.407625	−	0.0930377i	−0.0137916	−	0.999905i	$-0.504390\pi$
$83$	3.71364	−	0.847614i	0.407625	−	0.0930377i	0.421417	+	0.906867i	$0.361533\pi$
$84$	3.82810	−	5.03629i	0.417680	−	0.549504i
$85$	6.82609	−	7.35678i	0.740394	−	0.797954i
$86$	−5.60976	−	11.6488i	−0.604916	−	1.25612i
$87$	−7.39926	−	6.86551i	−0.793284	−	0.736060i
$88$	−5.71967	+	14.5735i	−0.609718	+	1.55354i
$89$	−4.69225	−	5.05705i	−0.497378	−	0.536046i	0.433608	−	0.901102i	$-0.357240\pi$
$89$	−4.69225	−	5.05705i	−0.497378	−	0.536046i	−0.930986	+	0.365056i	$0.881050\pi$
$90$	−8.18485	+	10.2635i	−0.862759	+	1.08187i
$91$	−2.54335	+	9.19409i	−0.266616	+	0.963803i
$92$	1.41147	+	1.76993i	0.147156	+	0.184528i
$93$	−3.39210	+	22.5051i	−0.351744	+	2.33367i
$94$	−0.912515	−	12.1767i	−0.0941187	−	1.25593i
$95$	−3.23539	−	8.24363i	−0.331944	−	0.845779i
$96$	−12.1324	−	2.76915i	−1.23826	−	0.282625i
$97$	5.46068	+	3.15272i	0.554448	+	0.320111i	0.750914	−	0.660400i	$-0.229613\pi$
$97$	5.46068	+	3.15272i	0.554448	+	0.320111i	−0.196466	+	0.980511i	$0.562947\pi$
$98$	−7.11720	−	2.41774i	−0.718946	−	0.244229i
$99$		−	25.4523i		−	2.55805i
$100$	0.652202	+	0.605155i	0.0652202	+	0.0605155i
$101$	−12.6830	−	1.91166i	−1.26201	−	0.190217i	−0.516252	−	0.856437i	$-0.672673\pi$
$101$	−12.6830	−	1.91166i	−1.26201	−	0.190217i	−0.745756	+	0.666220i	$0.767911\pi$
$102$	12.3338	−	0.924292i	1.22123	−	0.0915185i
$103$	−6.73472	+	8.44508i	−0.663592	+	0.832118i	−0.993729	−	0.111815i	$-0.964334\pi$
$103$	−6.73472	+	8.44508i	−0.663592	+	0.832118i	0.330137	+	0.943933i	$0.392905\pi$
$104$	10.8891	−	1.70879i	1.06777	−	0.167560i
$105$	−17.2542	−	6.31269i	−1.68384	−	0.616056i
$106$	1.48422	−	9.84715i	0.144160	−	0.956439i
$107$	6.09655	−	5.65677i	0.589375	−	0.546861i	−0.328105	−	0.944641i	$-0.606410\pi$
$107$	6.09655	−	5.65677i	0.589375	−	0.546861i	0.917481	+	0.397781i	$0.130220\pi$
$108$	4.65777	−	0.702046i	0.448194	−	0.0675544i
$109$	−11.3656	−	2.59412i	−1.08863	−	0.248472i	−0.359702	−	0.933067i	$-0.617122\pi$
$109$	−11.3656	−	2.59412i	−1.08863	−	0.248472i	−0.728923	+	0.684596i	$0.759979\pi$
$110$	13.4888	+	1.01085i	1.28611	+	0.0963805i
$111$	4.03444	−	4.34809i	0.382932	−	0.412703i
$112$	0.411558	+	4.18343i	0.0388886	+	0.395297i
$113$	−4.23872	−	1.30747i	−0.398745	−	0.122997i	0.0888955	−	0.996041i	$-0.471666\pi$
$113$	−4.23872	−	1.30747i	−0.398745	−	0.122997i	−0.487641	+	0.873044i	$0.662142\pi$
$114$	3.98737	−	10.1597i	0.373452	−	0.951540i
$115$	3.70375	−	5.43240i	0.345376	−	0.506574i
$116$	−3.02813			−0.281155
$117$	−15.4644	+	9.05369i	−1.42968	+	0.837014i
$118$	−6.20674	+	2.98901i	−0.571376	+	0.275160i
$119$	4.17637	+	9.95395i	0.382848	+	0.912477i
$120$	1.58645	+	21.1697i	0.144822	+	1.93252i
$121$	−12.5805	+	8.57724i	−1.14368	+	0.779749i
$122$	−6.54428	+	1.49369i	−0.592491	+	0.135232i
$123$	−1.31093	+	4.24992i	−0.118202	+	0.383202i
$124$	3.84624	+	5.64139i	0.345402	+	0.506612i
$125$	−4.21513	+	8.75281i	−0.377013	+	0.782875i
$126$	−6.42070	−	12.5757i	−0.572001	−	1.12034i
$127$	−11.6174	−	7.92062i	−1.03088	−	0.702841i	−0.0751749	−	0.997170i	$-0.523952\pi$
$127$	−11.6174	−	7.92062i	−1.03088	−	0.702841i	−0.955704	+	0.294329i	$0.904904\pi$
$128$	−0.278137	+	0.160582i	−0.0245841	+	0.0141936i
$129$	33.9918			2.99281
$130$	−4.18396	−	8.55513i	−0.366957	−	0.750335i
$131$	11.0057	+	13.8007i	0.961569	+	1.20577i	0.978570	+	0.205914i	$0.0660168\pi$
$131$	11.0057	+	13.8007i	0.961569	+	1.20577i	−0.0170006	+	0.999855i	$0.505412\pi$
$132$	−8.32854	−	8.97603i	−0.724906	−	0.781263i
$133$	9.51271	+	0.490691i	0.824856	+	0.0425483i
$134$	2.73254	+	2.53542i	0.236055	+	0.219027i
$135$	−5.93572	−	12.3256i	−0.510865	−	1.06082i
$136$	8.48361	−	9.14316i	0.727464	−	0.784019i
$137$	0.795595	+	5.27843i	0.0679723	+	0.450966i	0.996765	+	0.0803676i	$0.0256094\pi$
$137$	0.795595	+	5.27843i	0.0679723	+	0.450966i	−0.928793	+	0.370599i	$0.879152\pi$
$138$	7.89986	−	1.80309i	0.672481	−	0.153489i
$139$	1.28076	+	3.26332i	0.108632	+	0.276791i	0.974845	−	0.222885i	$-0.0715475\pi$
$139$	1.28076	+	3.26332i	0.108632	+	0.276791i	−0.866212	+	0.499676i	$0.833452\pi$
$140$	−5.08260	+	2.13250i	−0.429558	+	0.180229i
$141$	29.8840	+	11.7286i	2.51669	+	0.987727i
$142$	5.75313	−	7.21419i	0.482792	−	0.605402i
$143$	16.6842	+	7.91058i	1.39521	+	0.661516i
$144$	−4.92338	+	6.17372i	−0.410282	+	0.514477i
$145$	2.59227	+	8.40394i	0.215276	+	0.697909i
$146$	3.23842	+	5.60910i	0.268013	+	0.464212i
$147$	13.8457	−	14.1007i	1.14197	−	1.16301i
$148$		−	1.77945i		−	0.146270i
$149$	−12.4180	+	13.3834i	−1.01732	+	1.09641i	−0.0220041	+	0.999758i	$0.507005\pi$
$149$	−12.4180	+	13.3834i	−1.01732	+	1.09641i	−0.995318	+	0.0966546i	$0.969186\pi$
$150$	2.96444	−	1.16346i	0.242046	−	0.0949960i
$151$	2.85055	−	5.91922i	0.231974	−	0.481700i	−0.752193	−	0.658943i	$-0.771004\pi$
$151$	2.85055	−	5.91922i	0.231974	−	0.481700i	0.984167	+	0.177244i	$0.0567180\pi$
$152$	−4.02101	−	10.2454i	−0.326147	−	0.831008i
$153$	−7.40824	+	18.8759i	−0.598921	+	1.52603i
$154$	−6.97961	+	12.7659i	−0.562433	+	1.02871i
$155$	12.3639	−	15.5038i	0.993089	−	1.24529i
$156$	−2.49112	+	8.25315i	−0.199449	+	0.660781i
$157$	−5.97464	−	7.49197i	−0.476829	−	0.597924i	0.484000	−	0.875068i	$-0.339184\pi$
$157$	−5.97464	−	7.49197i	−0.476829	−	0.597924i	−0.960828	+	0.277144i	$0.910612\pi$
$158$	0.272613	+	0.883789i	0.0216879	+	0.0703105i
$159$	21.6321	+	14.7485i	1.71553	+	1.16963i
$160$	7.94833	+	7.37497i	0.628371	+	0.583043i
$161$	3.67748	+	6.04058i	0.289826	+	0.476065i
$162$	0.250406	−	0.811796i	0.0196737	−	0.0637807i
$163$	−0.964695	−	6.40034i	−0.0755608	−	0.501313i	−0.994315	−	0.106482i	$-0.966041\pi$
$163$	−0.964695	−	6.40034i	−0.0755608	−	0.501313i	0.918754	−	0.394831i	$-0.129197\pi$
$164$	0.578911	+	1.20212i	0.0452053	+	0.0938699i
$165$	−17.7813	+	30.7981i	−1.38427	+	2.39763i
$166$	−2.04514	−	3.54229i	−0.158734	−	0.274935i
$167$	0.334445	−	0.490540i	0.0258801	−	0.0379591i	−0.813081	−	0.582151i	$-0.802211\pi$
$167$	0.334445	−	0.490540i	0.0258801	−	0.0379591i	0.838961	+	0.544192i	$0.183164\pi$
$168$	−21.4439	−	7.84555i	−1.65444	−	0.605297i
$169$	−1.12845	−	12.9509i	−0.0868039	−	0.996225i
$170$	−9.70932	−	4.67576i	−0.744671	−	0.358615i
$171$	12.1706	+	13.1168i	0.930707	+	1.00306i
$172$	7.47534	−	6.93610i	0.569989	−	0.528873i
$173$	−2.37184	+	1.61709i	−0.180328	+	0.122945i	−0.650120	−	0.759832i	$-0.725281\pi$
$173$	−2.37184	+	1.61709i	−0.180328	+	0.122945i	0.469792	+	0.882777i	$0.344329\pi$
$174$	−4.70277	+	9.76539i	−0.356516	+	0.740313i
$175$	1.78298	+	2.13210i	0.134781	+	0.161171i
$176$	8.11384	+	0.608048i	0.611604	+	0.0458334i
$177$		−	18.1116i		−	1.36135i
$178$	−3.70389	+	6.41533i	−0.277619	+	0.480849i
$179$	−6.49997	−	4.43161i	−0.485831	−	0.331234i	0.295509	−	0.955340i	$-0.404511\pi$
$179$	−6.49997	−	4.43161i	−0.485831	−	0.331234i	−0.781340	+	0.624106i	$0.785463\pi$
$180$	−9.63824	−	3.78273i	−0.718392	−	0.281948i
$181$	2.89692	+	12.6922i	0.215326	+	0.943407i	0.960881	+	0.276962i	$0.0893276\pi$
$181$	2.89692	+	12.6922i	0.215326	+	0.943407i	−0.745555	+	0.666445i	$0.767815\pi$
$182$	10.2391	−	0.300291i	0.758970	−	0.0222590i
$183$	3.92703	−	17.2054i	0.290294	−	1.27186i
$184$	4.60309	−	6.75150i	0.339345	−	0.497727i
$185$	−4.93848	+	1.52332i	−0.363084	+	0.111997i
$186$	24.1662	−	3.64246i	1.77195	−	0.267078i
$187$	20.3703	−	4.64939i	1.48962	−	0.339997i
$188$	8.96521	−	3.51859i	0.653855	−	0.256619i
$189$	14.7108	−	0.342276i	1.07005	−	0.0248969i
$190$	−7.43476	+	5.92903i	−0.539375	+	0.430137i
$191$	6.04732	+	15.4083i	0.437569	+	1.11491i	0.964285	+	0.264866i	$0.0853276\pi$
$191$	6.04732	+	15.4083i	0.437569	+	1.11491i	−0.526717	+	0.850041i	$0.676577\pi$
$192$	1.66901	+	22.2714i	0.120450	+	1.60730i
$193$	−3.56085	+	23.6247i	−0.256315	+	1.70054i	0.376645	+	0.926358i	$0.377078\pi$
$193$	−3.56085	+	23.6247i	−0.256315	+	1.70054i	−0.632961	+	0.774184i	$0.718161\pi$
$194$	1.50665	−	6.60108i	0.108171	−	0.473930i
$195$	25.0374	−	0.151647i	1.79297	−	0.0108597i
$196$	0.167603	−	5.92620i	0.0119717	−	0.423300i
$197$	−7.96291	+	4.59739i	−0.567334	+	0.327550i	−0.756084	−	0.654475i	$-0.772890\pi$
$197$	−7.96291	+	4.59739i	−0.567334	+	0.327550i	0.188750	+	0.982025i	$0.439556\pi$
$198$	−26.1167	+	8.05592i	−1.85603	+	0.572509i
$199$	6.17975	+	15.7458i	0.438071	+	1.11619i	0.964057	+	0.265694i	$0.0856011\pi$
$199$	6.17975	+	15.7458i	0.438071	+	1.11619i	−0.525986	+	0.850493i	$0.676304\pi$
$200$	1.39339	−	2.89341i	0.0985278	−	0.204595i
$201$	−9.12275	+	3.58042i	−0.643469	+	0.252543i
$202$	2.05275	+	13.6191i	0.144431	+	0.958238i
$203$	−9.38420	−	1.19192i	−0.658642	−	0.0836563i
$204$	3.56400	+	9.08092i	0.249530	+	0.635792i
$205$	2.84064	−	2.63573i	0.198399	−	0.184088i
$206$	10.7971	+	4.23755i	0.752270	+	0.295244i
$207$	−2.95611	+	12.9516i	−0.205464	+	0.900196i
$208$	−2.51675	−	5.14611i	−0.174505	−	0.356819i
$209$	4.10271	−	17.9752i	0.283790	−	1.24337i
$210$	−1.01631	+	19.7026i	−0.0701324	+	1.35961i
$211$	1.26016	−	1.16925i	0.0867527	−	0.0804947i	−0.635605	−	0.772015i	$-0.719249\pi$
$211$	1.26016	−	1.16925i	0.0867527	−	0.0804947i	0.722357	+	0.691520i	$0.243059\pi$
$212$	7.76669	−	1.17064i	0.533418	−	0.0803999i
$213$	10.5257	+	21.8569i	0.721211	+	1.49761i
$214$	−7.73404	−	4.46525i	−0.528688	−	0.305238i
$215$	−25.6490	−	14.8085i	−1.74925	−	1.00993i
$216$	−7.37704	−	15.3186i	−0.501944	−	1.04230i
$217$	9.69897	+	18.9966i	0.658409	+	1.28958i
$218$	0.935494	+	12.4833i	0.0633597	+	0.845476i
$219$	−16.9805	+	1.27251i	−1.14744	+	0.0859884i
$220$	2.37403	+	10.4013i	0.160057	+	0.701256i
$221$	−10.0708	−	10.7228i	−0.677438	−	0.721293i
$222$	−5.73853	−	2.76353i	−0.385145	−	0.185476i
$223$	−18.9927	+	1.42330i	−1.27184	+	0.0953114i	−0.693484	−	0.720472i	$-0.743925\pi$
$223$	−18.9927	+	1.42330i	−1.27184	+	0.0953114i	−0.578358	+	0.815783i	$0.696306\pi$
$224$	−10.7543	+	4.51219i	−0.718554	+	0.301483i
$225$	−0.390167	+	5.20642i	−0.0260112	+	0.347095i
$226$			4.76319i			0.316842i
$227$	−7.06634	−	4.07975i	−0.469009	−	0.270783i	0.246816	−	0.969062i	$-0.420616\pi$
$227$	−7.06634	−	4.07975i	−0.469009	−	0.270783i	−0.715825	+	0.698280i	$0.753949\pi$
$228$	8.58416	+	0.643294i	0.568500	+	0.0426032i
$229$	14.8566	−	11.8477i	0.981751	−	0.782920i	0.00559329	−	0.999984i	$-0.498220\pi$
$229$	14.8566	−	11.8477i	0.981751	−	0.782920i	0.976157	+	0.217064i	$0.0696482\pi$
$230$	−6.74646	−	2.08101i	−0.444848	−	0.137218i
$231$	−22.2771	−	31.0950i	−1.46572	−	2.04590i
$232$	3.22173	+	10.4446i	0.211517	+	0.685721i
$233$	20.6791	−	9.95852i	1.35473	−	0.652404i	0.391276	−	0.920273i	$-0.372034\pi$
$233$	20.6791	−	9.95852i	1.35473	−	0.652404i	0.963455	+	0.267869i	$0.0863194\pi$
$234$	14.1846	+	13.0024i	0.927278	+	0.849995i
$235$	−17.4399	−	21.8689i	−1.13765	−	1.42657i
$236$	−3.69571	−	3.98303i	−0.240570	−	0.259273i
$237$	−2.40442	−	0.362408i	−0.156184	−	0.0235409i
$238$	8.89189	−	7.43591i	0.576376	−	0.481998i
$239$	−22.6511	+	18.0636i	−1.46518	+	1.16844i	−0.514813	+	0.857303i	$0.672139\pi$
$239$	−22.6511	+	18.0636i	−1.46518	+	1.16844i	−0.950365	+	0.311138i	$0.899290\pi$
$240$	10.2705	−	4.03087i	0.662957	−	0.260192i
$241$	−10.6301	−	15.5915i	−0.684745	−	1.00434i	−0.998496	−	0.0548313i	$-0.982538\pi$
$241$	−10.6301	−	15.5915i	−0.684745	−	1.00434i	0.313750	−	0.949505i	$-0.398414\pi$
$242$	12.7830	+	10.1941i	0.821720	+	0.655300i
$243$	−10.5937	−	9.82949i	−0.679584	−	0.630562i
$244$	−2.64719	−	4.58507i	−0.169469	−	0.293529i
$245$	−16.5904	+	4.60805i	−1.05992	+	0.294397i
$246$	4.77577			0.304492
$247$	−12.3808	+	3.90124i	−0.787769	+	0.248230i
$248$	15.3661	−	19.2684i	0.975746	−	1.22355i
$249$	10.7236	−	0.803624i	0.679582	−	0.0509276i
$250$	10.3154	+	1.55480i	0.652403	+	0.0983340i
$251$	25.8682	−	3.89900i	1.63278	−	0.246103i	0.732297	−	0.680985i	$-0.238448\pi$
$251$	25.8682	−	3.89900i	1.63278	−	0.246103i	0.900487	+	0.434882i	$0.143210\pi$
$252$	7.98544	−	7.76279i	0.503035	−	0.489010i
$253$	12.7423	−	5.00100i	0.801104	−	0.314410i
$254$	−4.45033	+	14.4276i	−0.279238	+	0.905268i
$255$	22.1511	−	17.6649i	1.38716	−	1.10622i
$256$	11.8512	+	10.9963i	0.740699	+	0.687268i
$257$	−18.8568	−	12.8564i	−1.17626	−	0.801957i	−0.192469	−	0.981303i	$-0.561650\pi$
$257$	−18.8568	−	12.8564i	−1.17626	−	0.801957i	−0.983786	+	0.179346i	$0.942602\pi$
$258$	−10.7588	−	34.8791i	−0.669811	−	2.17148i
$259$	0.700418	−	5.51452i	0.0435219	−	0.342656i
$260$	5.47518	−	5.14228i	0.339556	−	0.318911i
$261$	−11.0793	−	13.8930i	−0.685792	−	0.859955i
$262$	10.6775	−	15.6610i	0.659656	−	0.967538i
$263$	−3.31132	−	5.73538i	−0.204185	−	0.353659i	0.745688	−	0.666295i	$-0.232121\pi$
$263$	−3.31132	−	5.73538i	−0.204185	−	0.353659i	−0.949873	+	0.312637i	$0.898788\pi$
$264$	−22.0990	+	38.2766i	−1.36010	+	2.35576i
$265$	−9.89763	−	20.5526i	−0.608006	−	1.26254i
$266$	−2.50737	−	9.91631i	−0.153737	−	0.608008i
$267$	−10.9710	−	16.0915i	−0.671416	−	0.984787i
$268$	−1.27565	+	2.64891i	−0.0779225	+	0.161808i
$269$	−22.1152	−	6.82163i	−1.34839	−	0.415922i	−0.465308	−	0.885149i	$-0.654056\pi$
$269$	−22.1152	−	6.82163i	−1.34839	−	0.415922i	−0.883078	+	0.469227i	$0.844533\pi$
$270$	−10.7686	+	9.99184i	−0.655358	+	0.608084i
$271$	24.4709	−	1.83384i	1.48650	−	0.111398i	0.693428	−	0.720526i	$-0.256100\pi$
$271$	24.4709	−	1.83384i	1.48650	−	0.111398i	0.793072	+	0.609128i	$0.208480\pi$
$272$	−5.84039	−	2.81258i	−0.354125	−	0.170538i
$273$	−10.9686	+	24.5960i	−0.663847	+	1.48862i
$274$	5.16439	−	2.48704i	0.311992	−	0.150247i
$275$	4.65902	−	2.68989i	0.280949	−	0.162206i
$276$	3.19552	+	5.53481i	0.192348	+	0.333156i
$277$	−1.22219	+	16.3091i	−0.0734346	+	0.979916i	0.831820	+	0.555046i	$0.187299\pi$
$277$	−1.22219	+	16.3091i	−0.0734346	+	0.979916i	−0.905254	+	0.424870i	$0.860320\pi$
$278$	2.94312	−	2.34706i	0.176517	−	0.140767i
$279$	−11.8100	+	38.2871i	−0.707046	+	2.29219i
$280$	12.7629	+	15.2620i	0.762731	+	0.912077i
$281$	−22.3384	−	5.09859i	−1.33260	−	0.304156i	−0.503854	−	0.863789i	$-0.668085\pi$
$281$	−22.3384	−	5.09859i	−1.33260	−	0.304156i	−0.828741	+	0.559632i	$0.810942\pi$
$282$	2.57614	−	34.3762i	0.153407	−	2.04708i
$283$	10.7587	−	3.31861i	0.639536	−	0.197271i	0.0420059	−	0.999117i	$-0.486625\pi$
$283$	10.7587	−	3.31861i	0.639536	−	0.197271i	0.597530	+	0.801847i	$0.296149\pi$
$284$	6.77471	+	2.65888i	0.402005	+	0.157775i
$285$	−5.56325	−	24.3742i	−0.329539	−	1.44380i
$286$	2.83632	−	19.6235i	0.167715	−	1.16036i
$287$	1.32087	+	3.95325i	0.0779688	+	0.233353i
$288$	−20.3937	−	8.00393i	−1.20171	−	0.471636i
$289$	0.349874	+	0.0527350i	0.0205808	+	0.00310206i
$290$	7.80281	−	5.31987i	0.458197	−	0.312393i
$291$	13.9174	+	11.0988i	0.815855	+	0.650622i
$292$	−3.47462	+	3.74475i	−0.203337	+	0.219145i
$293$	12.8525	+	7.42041i	0.750853	+	0.433505i	0.826002	−	0.563667i	$-0.190610\pi$
$293$	12.8525	+	7.42041i	0.750853	+	0.433505i	−0.0751490	+	0.997172i	$0.523943\pi$
$294$	−18.8510	−	9.74403i	−1.09941	−	0.568283i
$295$	−7.89029	+	13.6664i	−0.459390	+	0.795687i
$296$	−6.13765	+	1.89321i	−0.356744	+	0.110041i
$297$	4.24504	−	28.1640i	0.246322	−	1.63424i
$298$	17.6632	+	8.50613i	1.02320	+	0.492747i
$299$	−7.57111	−	5.96310i	−0.437849	−	0.344855i
$300$	1.56606	+	1.96377i	0.0904163	+	0.113378i
$301$	25.8963	−	18.5526i	1.49264	−	1.06935i
$302$	−6.97595	−	1.05146i	−0.401421	−	0.0605044i
$303$	−34.6015	−	10.6731i	−1.98780	−	0.613156i
$304$	−4.47219	+	3.56645i	−0.256497	+	0.204550i
$305$	−10.4587	+	11.2718i	−0.598864	+	0.645422i
$306$	21.7134	+	1.62719i	1.24127	+	0.0930203i
$307$	−11.1741	−	2.55042i	−0.637740	−	0.145560i	−0.108588	−	0.994087i	$-0.534633\pi$
$307$	−11.1741	−	2.55042i	−0.637740	−	0.145560i	−0.529152	+	0.848527i	$0.677490\pi$
$308$	−11.2441	−	2.29260i	−0.640691	−	0.130633i
$309$	−22.3540	+	20.7415i	−1.27167	+	1.17994i
$310$	−19.8217	−	7.77946i	−1.12580	−	0.441844i
$311$	−2.08091	+	1.00211i	−0.117997	+	0.0568246i	−0.491951	−	0.870623i	$-0.663716\pi$
$311$	−2.08091	+	1.00211i	−0.117997	+	0.0568246i	0.373954	+	0.927447i	$0.378002\pi$
$312$	31.1170	−	0.188470i	1.76166	−	0.0106700i
$313$	−26.0804			−1.47415			−0.737076	−	0.675810i	$-0.763794\pi$
$313$	−26.0804			−1.47415			−0.737076	+	0.675810i	$0.763794\pi$
$314$	−5.79648	+	8.50187i	−0.327114	+	0.479788i
$315$	−28.3800	−	15.5164i	−1.59903	−	0.874253i
$316$	−0.602720	+	0.410928i	−0.0339057	+	0.0231165i
$317$	13.2964	−	27.6102i	0.746798	−	1.55074i	−0.0854533	−	0.996342i	$-0.527234\pi$
$317$	13.2964	−	27.6102i	0.746798	−	1.55074i	0.832251	−	0.554399i	$-0.187052\pi$
$318$	8.28667	−	26.8647i	0.464693	−	1.50650i
$319$	−5.39701	+	17.4967i	−0.302174	+	0.979625i
$320$	8.44309	−	17.5323i	0.471983	−	0.980084i
$321$	19.3992	−	13.2262i	1.08276	−	0.738214i
$322$	5.03429	−	5.68537i	0.280550	−	0.316833i
$323$	−8.27455	+	12.1365i	−0.460408	+	0.675295i
$324$	0.670052			0.0372251
$325$	−3.29159	−	1.87391i	−0.182585	−	0.103946i
$326$	−6.26205	+	3.01565i	−0.346823	+	0.167021i
$327$	−30.6366	−	12.0240i	−1.69421	−	0.664927i
$328$	3.53041	−	3.27575i	0.194935	−	0.180873i
$329$	29.1682	−	7.37527i	1.60809	−	0.406612i
$330$	37.2300	+	8.49749i	2.04944	+	0.467772i
$331$	11.0368	+	0.827091i	0.606636	+	0.0454611i	0.374507	−	0.927224i	$-0.377812\pi$
$331$	11.0368	+	0.827091i	0.606636	+	0.0454611i	0.232129	+	0.972685i	$0.425431\pi$
$332$	2.19431	−	2.36491i	0.120428	−	0.129791i
$333$	8.16407	−	6.51063i	0.447388	−	0.356780i
$334$	−0.609199	−	0.187913i	−0.0333339	−	0.0102821i
$335$	8.44350	+	1.27265i	0.461318	+	0.0695325i
$336$	−0.611337	+	11.8516i	−0.0333512	+	0.646557i
$337$	−16.5265	−	20.7235i	−0.900253	−	1.12888i	−0.991114	−	0.133018i	$-0.957533\pi$
$337$	−16.5265	−	20.7235i	−0.900253	−	1.12888i	0.0908605	−	0.995864i	$-0.471038\pi$
$338$	−12.9318	+	5.25701i	−0.703397	+	0.285943i
$339$	−11.2827	−	5.43344i	−0.612789	−	0.295104i
$340$	1.26682	−	8.40478i	0.0687028	−	0.455813i
$341$	39.4512	−	12.1691i	2.13640	−	0.658994i
$342$	9.60700	−	16.6398i	0.519487	−	0.899778i
$343$	2.85204	−	18.2993i	0.153996	−	0.988071i
$344$	−31.8772	−	18.4043i	−1.71870	−	0.992292i
$345$	12.6251	−	13.6066i	0.679713	−	0.732557i
$346$	2.41001	+	1.92192i	0.129563	+	0.103323i
$347$	1.92383	−	1.31164i	0.103276	−	0.0704127i	−0.510581	−	0.859830i	$-0.670569\pi$
$347$	1.92383	−	1.31164i	0.103276	−	0.0704127i	0.613857	+	0.789417i	$0.289617\pi$
$348$	−8.45332	−	1.27413i	−0.453146	−	0.0683007i
$349$	−13.9881	−	5.48992i	−0.748766	−	0.293869i	−0.0398916	−	0.999204i	$-0.512701\pi$
$349$	−13.9881	−	5.48992i	−0.748766	−	0.293869i	−0.708874	+	0.705335i	$0.750796\pi$
$350$	1.62341	−	2.50435i	0.0867751	−	0.133863i
$351$	−18.6219	+	7.43905i	−0.993966	+	0.397067i
$352$	5.02324	+	22.0083i	0.267740	+	1.17304i
$353$	0.218578	+	0.0857857i	0.0116338	+	0.00456591i	0.371151	−	0.928573i	$-0.378963\pi$
$353$	0.218578	+	0.0857857i	0.0116338	+	0.00456591i	−0.359517	+	0.933139i	$0.617059\pi$
$354$	−18.5843	+	5.73251i	−0.987747	+	0.304680i
$355$	1.57957	−	21.0779i	0.0838350	−	1.11870i
$356$	−5.69621	−	1.30012i	−0.301899	−	0.0689064i
$357$	7.47046	+	29.5447i	0.395379	+	1.56367i
$358$	−2.48997	+	8.07228i	−0.131599	+	0.426633i
$359$	−23.9694	+	19.1150i	−1.26506	+	1.00885i	−0.266067	+	0.963954i	$0.585724\pi$
$359$	−23.9694	+	19.1150i	−1.26506	+	1.00885i	−0.998992	+	0.0448964i	$0.985704\pi$
$360$	−2.79290	+	37.2686i	−0.147199	+	1.96423i
$361$	−3.01912	−	5.22926i	−0.158901	−	0.275224i
$362$	12.1066	−	6.98976i	0.636309	−	0.367373i
$363$	−38.7286	+	18.6507i	−2.03273	+	0.978909i
$364$	2.60671	+	7.64721i	0.136629	+	0.400822i
$365$	13.3672	+	6.43732i	0.699673	+	0.336945i
$366$	−18.8975	+	1.41617i	−0.987786	+	0.0740244i
$367$	−15.0960	+	14.0070i	−0.788004	+	0.731161i	−0.967575	−	0.252584i	$-0.918720\pi$
$367$	−15.0960	+	14.0070i	−0.788004	+	0.731161i	0.179571	+	0.983745i	$0.442529\pi$
$368$	−4.05816	−	1.25178i	−0.211546	−	0.0652533i
$369$	−3.39719	+	7.05433i	−0.176851	+	0.367234i
$370$	3.12616	+	4.58524i	0.162521	+	0.238375i
$371$	24.5298	−	0.570734i	1.27352	−	0.0296310i
$372$	8.36343	+	17.3668i	0.433623	+	0.900428i
$373$	−3.03306	+	5.25341i	−0.157046	+	0.272011i	−0.933802	−	0.357790i	$-0.883530\pi$
$373$	−3.03306	+	5.25341i	−0.157046	+	0.272011i	0.776756	+	0.629801i	$0.216864\pi$
$374$	−11.2182	−	19.4304i	−0.580077	−	1.00472i
$375$	−15.4498	+	22.6607i	−0.797825	+	1.17019i
$376$	−21.6746	−	27.1791i	−1.11778	−	1.40166i
$377$	12.5504	−	2.94464i	0.646381	−	0.151657i
$378$	−5.00732	−	14.9864i	−0.257549	−	0.770818i
$379$	0.182453	+	0.591498i	0.00937197	+	0.0303832i	0.960138	−	0.279526i	$-0.0901774\pi$
$379$	0.182453	+	0.591498i	0.00937197	+	0.0303832i	−0.950766	+	0.309910i	$0.899701\pi$
$380$	−6.19705	−	4.22508i	−0.317902	−	0.216742i
$381$	−29.0984	−	26.9994i	−1.49076	−	1.38322i
$382$	13.8964	−	11.0820i	0.711004	−	0.567007i
$383$	0.113537	−	0.368078i	0.00580147	−	0.0188079i	−0.952626	−	0.304145i	$-0.901629\pi$
$383$	0.113537	−	0.368078i	0.00580147	−	0.0188079i	0.958427	+	0.285337i	$0.0921055\pi$
$384$	−0.844013	+	0.331251i	−0.0430709	+	0.0169041i
$385$	3.26302	+	33.1681i	0.166299	+	1.69040i
$386$	25.3683	−	3.82366i	1.29121	−	0.194619i
$387$	59.1733	+	8.91895i	3.00795	+	0.453375i
$388$	5.32539	−	0.399083i	0.270356	−	0.0202604i
$389$	−0.239247	+	0.300006i	−0.0121303	+	0.0152109i	−0.787860	−	0.615855i	$-0.788811\pi$
$389$	−0.239247	+	0.300006i	−0.0121303	+	0.0152109i	0.775729	+	0.631066i	$0.217382\pi$
$390$	−8.08020	−	25.6429i	−0.409157	−	1.29848i
$391$	−10.9055			−0.551517
$392$	−20.6189	+	5.72698i	−1.04141	+	0.289256i
$393$	24.9165	+	43.1566i	1.25687	+	2.17696i
$394$	7.23772	+	6.71563i	0.364631	+	0.338328i
$395$	1.65641	+	1.32094i	0.0833429	+	0.0664637i
$396$	−12.1432	−	17.8108i	−0.610220	−	0.895029i
$397$	34.3646	−	13.4871i	1.72471	−	0.676898i	0.724780	−	0.688980i	$-0.241941\pi$
$397$	34.3646	−	13.4871i	1.72471	−	0.676898i	0.999927	+	0.0120821i	$0.00384596\pi$
$398$	14.2008	−	11.3247i	0.711821	−	0.567658i
$399$	26.3491	+	5.37242i	1.31911	+	0.268958i
$400$	−1.65041	−	0.248760i	−0.0825206	−	0.0124380i
$401$	16.2178	+	17.4786i	0.809876	+	0.872839i	0.993923	−	0.110079i	$-0.0351103\pi$
$401$	16.2178	+	17.4786i	0.809876	+	0.872839i	−0.184047	+	0.982917i	$0.558920\pi$
$402$	6.56131	+	8.22763i	0.327249	+	0.410357i
$403$	−21.4270	−	19.6412i	−1.06735	−	0.978397i
$404$	−9.78728	+	4.71331i	−0.486936	+	0.234496i
$405$	−0.573606	−	1.85959i	−0.0285027	−	0.0924035i
$406$	1.74717	+	10.0064i	0.0867105	+	0.496609i
$407$	−10.2817	−	3.17149i	−0.509646	−	0.157205i
$408$	27.5299	−	21.9544i	1.36293	−	1.08690i
$409$	−28.1551	−	2.10994i	−1.39218	−	0.104330i	−0.642580	−	0.766219i	$-0.722136\pi$
$409$	−28.1551	−	2.10994i	−1.39218	−	0.104330i	−0.749602	+	0.661889i	$0.769755\pi$
$410$	−3.60362	−	2.08055i	−0.177970	−	0.102751i
$411$			15.0700i			0.743347i
$412$	−0.683656	+	9.12276i	−0.0336813	+	0.449446i
$413$	−9.88525	−	13.7981i	−0.486421	−	0.678961i
$414$	14.2253	−	1.06604i	0.699133	−	0.0523928i
$415$	−8.44176	−	4.06534i	−0.414389	−	0.199559i
$416$	11.5850	−	10.8806i	0.568002	−	0.533467i
$417$	2.20227	+	9.64876i	0.107845	+	0.472502i
$418$	−19.7429	+	1.47952i	−0.965655	+	0.0723659i
$419$	0.350554	+	4.67782i	0.0171257	+	0.228526i	0.999199	+	0.0400253i	$0.0127438\pi$
$419$	0.350554	+	4.67782i	0.0171257	+	0.228526i	−0.982073	+	0.188501i	$0.939637\pi$
$420$	−15.0858	+	3.81450i	−0.736113	+	0.186128i
$421$	−6.12966	−	12.7284i	−0.298741	−	0.620343i	0.696524	−	0.717533i	$-0.254729\pi$
$421$	−6.12966	−	12.7284i	−0.298741	−	0.620343i	−0.995266	+	0.0971901i	$0.969015\pi$
$422$	−1.59862	−	0.922966i	−0.0778198	−	0.0449293i
$423$	48.9450	+	28.2584i	2.37979	+	1.37397i
$424$	−12.3010	−	25.5433i	−0.597389	−	1.24049i
$425$	−4.23814	+	0.638797i	−0.205580	+	0.0309862i
$426$	19.0959	−	17.7184i	0.925198	−	0.858458i
$427$	−6.39890	−	15.2511i	−0.309664	−	0.738053i
$428$	1.56737	−	6.86710i	0.0757617	−	0.331934i
$429$	43.2471	+	29.1033i	2.08799	+	1.40512i
$430$	−7.07681	+	31.0055i	−0.341274	+	1.49522i
$431$	−22.8856	−	8.98194i	−1.10236	−	0.432645i	−0.256768	−	0.966473i	$-0.582658\pi$
$431$	−22.8856	−	8.98194i	−1.10236	−	0.432645i	−0.845593	+	0.533828i	$0.820753\pi$
$432$	−6.47759	+	6.01033i	−0.311653	+	0.289172i
$433$	5.84991	+	14.9053i	0.281129	+	0.716304i	0.999781	+	0.0209345i	$0.00666415\pi$
$433$	5.84991	+	14.9053i	0.281129	+	0.716304i	−0.718652	+	0.695370i	$0.755241\pi$
$434$	16.4226	−	15.9647i	0.788312	−	0.766332i
$435$	3.70049	+	24.5511i	0.177425	+	1.17714i
$436$	−9.19098	+	3.60719i	−0.440168	+	0.172753i
$437$	−4.17538	+	8.67026i	−0.199735	+	0.414755i
$438$	6.68022	+	17.0209i	0.319193	+	0.813292i
$439$	15.8879	−	4.90078i	0.758290	−	0.233901i	0.108584	−	0.994087i	$-0.465368\pi$
$439$	15.8879	−	4.90078i	0.758290	−	0.233901i	0.649706	+	0.760186i	$0.274892\pi$
$440$	33.3502	−	19.2547i	1.58991	−	0.917934i
$441$	27.8025	−	20.9137i	1.32393	−	0.995892i
$442$	−7.81515	+	13.7276i	−0.371729	+	0.652954i
$443$	1.95539	−	8.56713i	0.0929034	−	0.407036i	−0.906997	−	0.421137i	$-0.861631\pi$
$443$	1.95539	−	8.56713i	0.0929034	−	0.407036i	0.999901	+	0.0141002i	$0.00448839\pi$
$444$	0.748730	−	4.96750i	0.0355332	−	0.235747i
$445$	1.26810	+	16.9216i	0.0601137	+	0.802161i
$446$	7.47182	+	19.0379i	0.353801	+	0.901470i
$447$	−40.2973	+	32.1360i	−1.90600	+	1.51998i
$448$	13.4271	+	16.0562i	0.634372	+	0.758585i
$449$	7.05067	−	2.76718i	0.332741	−	0.130591i	−0.193088	−	0.981181i	$-0.561850\pi$
$449$	7.05067	−	2.76718i	0.332741	−	0.130591i	0.525829	+	0.850590i	$0.323755\pi$
$450$	5.46581	−	1.24753i	0.257661	−	0.0588093i
$451$	7.97768	−	1.20244i	0.375654	−	0.0566208i
$452$	−3.58994	+	1.10735i	−0.168856	+	0.0520853i
$453$	10.4482	−	15.3247i	0.490898	−	0.720015i
$454$	−1.94967	+	8.54206i	−0.0915025	+	0.400899i
$455$	18.9917	−	13.7808i	0.890343	−	0.646056i
$456$	−6.91413	−	30.2928i	−0.323784	−	1.41859i
$457$	−4.00700	−	1.57263i	−0.187439	−	0.0735646i	0.269765	−	0.962926i	$-0.413054\pi$
$457$	−4.00700	−	1.57263i	−0.187439	−	0.0735646i	−0.457204	+	0.889362i	$0.651149\pi$
$458$	−16.8592	−	11.4944i	−0.787780	−	0.537099i
$459$	−11.3457	+	19.6513i	−0.529572	+	0.917246i
$460$		−	5.56849i		−	0.259632i
$461$	24.9117	+	1.86688i	1.16025	+	0.0869491i	0.640910	−	0.767616i	$-0.278557\pi$
$461$	24.9117	+	1.86688i	1.16025	+	0.0869491i	0.519345	+	0.854565i	$0.326176\pi$
$462$	−24.8557	+	32.7004i	−1.15639	+	1.52136i
$463$	−5.53672	+	11.4971i	−0.257313	+	0.534316i	−0.989105	−	0.147212i	$-0.952970\pi$
$463$	−5.53672	+	11.4971i	−0.257313	+	0.534316i	0.731792	+	0.681528i	$0.238684\pi$
$464$	4.69357	−	3.20002i	0.217894	−	0.148557i
$465$	41.0383	−	38.0780i	1.90311	−	1.76582i
$466$	−16.7636	−	18.0669i	−0.776558	−	0.836931i
$467$	16.9019	+	8.13952i	0.782126	+	0.376652i	0.781945	−	0.623348i	$-0.214228\pi$
$467$	16.9019	+	8.13952i	0.782126	+	0.376652i	0.000181528		1.00000i	$0.499942\pi$
$468$	−6.50207	+	13.7135i	−0.300558	+	0.633909i
$469$	−4.99588	+	7.70686i	−0.230688	+	0.355870i
$470$	−16.9198	+	24.8168i	−0.780452	+	1.14471i
$471$	−13.5264	−	23.4284i	−0.623265	−	1.07953i
$472$	−9.80622	+	16.9849i	−0.451368	+	0.781792i
$473$	−26.7538	−	55.5549i	−1.23014	−	2.55442i
$474$	0.389156	+	2.58188i	0.0178745	+	0.118590i
$475$	−1.11478	+	3.61403i	−0.0511497	+	0.165823i
$476$	7.67152	+	4.97297i	0.351623	+	0.227936i
$477$	33.7875	+	31.3502i	1.54702	+	1.43543i
$478$	25.7044	+	17.5250i	1.17569	+	0.801574i
$479$	−6.16475	−	19.9856i	−0.281675	−	0.913167i	−0.980272	−	0.197652i	$-0.936668\pi$
$479$	−6.16475	−	19.9856i	−0.281675	−	0.913167i	0.698597	−	0.715515i	$-0.253808\pi$
$480$	19.0854	+	23.9323i	0.871124	+	1.09235i
$481$	1.73039	+	7.37513i	0.0788988	+	0.336277i
$482$	−12.6339	+	15.8424i	−0.575459	+	0.721603i
$483$	7.72436	+	18.4102i	0.351471	+	0.837693i
$484$	−4.71132	+	12.0042i	−0.214151	+	0.545647i
$485$	−5.66644	−	14.4378i	−0.257300	−	0.655589i
$486$	−6.73305	+	13.9813i	−0.305417	+	0.634205i
$487$	36.8425	−	14.4596i	1.66949	−	0.655228i	0.673059	−	0.739588i	$-0.264980\pi$
$487$	36.8425	−	14.4596i	1.66949	−	0.655228i	0.996435	+	0.0843599i	$0.0268846\pi$
$488$	−12.9983	+	14.0088i	−0.588406	+	0.634150i
$489$		−	18.2730i		−	0.826336i
$490$	9.97934	+	15.5649i	0.450821	+	0.703151i
$491$	−7.54077	−	13.0610i	−0.340310	−	0.589435i	0.644180	−	0.764874i	$-0.277199\pi$
$491$	−7.54077	−	13.0610i	−0.340310	−	0.589435i	−0.984490	+	0.175439i	$0.943865\pi$
$492$	1.11027	+	3.59942i	0.0500550	+	0.162274i
$493$	9.09516	−	11.4050i	0.409625	−	0.513654i
$494$	7.92170	+	11.4691i	0.356414	+	0.516021i
$495$	−39.0348	+	48.9481i	−1.75449	+	2.20006i
$496$	−11.9232	−	4.67953i	−0.535369	−	0.210117i
$497$	19.9483	+	10.9065i	0.894803	+	0.489224i
$498$	−4.21873	−	10.7492i	−0.189046	−	0.481681i
$499$	1.94561	−	0.444072i	0.0870973	−	0.0198794i	−0.178750	−	0.983894i	$-0.557205\pi$
$499$	1.94561	−	0.444072i	0.0870973	−	0.0198794i	0.265847	+	0.964015i	$0.414348\pi$
$500$	1.22631	+	8.13601i	0.0548421	+	0.363853i
$501$	1.14004	−	1.22867i	0.0509330	−	0.0548927i
$502$	−12.1883	−	25.3093i	−0.543991	−	1.12961i
$503$	−3.62312	−	3.36176i	−0.161547	−	0.149894i	0.595258	−	0.803535i	$-0.297050\pi$
$503$	−3.62312	−	3.36176i	−0.161547	−	0.149894i	−0.756804	+	0.653641i	$0.773241\pi$
$504$	−35.2713	−	19.2842i	−1.57111	−	0.858985i
$505$	21.4593	+	23.1276i	0.954926	+	1.02917i
$506$	−9.16461	−	11.4921i	−0.407416	−	0.510884i
$507$	2.29912	−	36.6285i	0.102108	−	1.62673i
$508$	−11.9085			−0.528353
$509$	−14.8270	+	8.56038i	−0.657195	+	0.379432i	−0.791208	−	0.611548i	$-0.790547\pi$
$509$	−14.8270	+	8.56038i	−0.657195	+	0.379432i	0.134012	+	0.990980i	$0.457214\pi$
$510$	−25.1371	−	17.1382i	−1.11309	−	0.758891i
$511$	−12.2418	+	10.2373i	−0.541547	+	0.452873i
$512$	7.25359	−	15.0622i	0.320566	−	0.665663i
$513$	11.2795	+	16.5441i	0.498004	+	0.730438i
$514$	−7.22354	+	23.4182i	−0.318617	+	1.03293i
$515$	25.9035	−	5.91231i	1.14144	−	0.260527i
$516$	23.7866	−	16.2174i	1.04715	−	0.713932i
$517$	−4.35193	−	58.0724i	−0.191397	−	2.55402i
$518$	−5.88015	+	1.02670i	−0.258359	+	0.0451108i
$519$	−7.30163	+	3.51628i	−0.320506	+	0.154348i
$520$	−23.5619	−	13.4139i	−1.03326	−	0.588236i
$521$	23.4485			1.02730			0.513649	−	0.858001i	$-0.328293\pi$
$521$	23.4485			1.02730			0.513649	+	0.858001i	$0.328293\pi$
$522$	−10.7489	+	15.7658i	−0.470467	+	0.690049i
$523$	−3.48750	+	8.88600i	−0.152498	+	0.388558i	−0.986623	−	0.163017i	$-0.947877\pi$
$523$	−3.48750	+	8.88600i	−0.152498	+	0.388558i	0.834126	+	0.551574i	$0.185973\pi$
$524$	14.2857	+	4.40656i	0.624075	+	0.192502i
$525$	4.08024	+	6.70216i	0.178076	+	0.292506i
$526$	−4.83701	+	5.21306i	−0.210904	+	0.227300i
$527$	−32.7997	−	2.45800i	−1.42878	−	0.107072i
$528$	22.3947	+	5.11144i	0.974604	+	0.222447i
$529$	15.6783	−	2.36312i	0.681664	−	0.102744i
$530$	−17.9564	+	16.6611i	−0.779975	+	0.723711i
$531$	4.75221	−	31.5289i	0.206229	−	1.36824i
$532$	6.89084	−	4.19511i	0.298756	−	0.181881i
$533$	−3.56834	−	4.41937i	−0.154562	−	0.191424i
$534$	−13.0391	+	16.3505i	−0.564257	+	0.707556i
$535$	−20.3999	+	1.52876i	−0.881966	+	0.0660942i
$536$	10.4938	+	1.58168i	0.453262	+	0.0683182i
$537$	−16.2806	−	15.1062i	−0.702560	−	0.651881i
$538$			24.8515i			1.07142i
$539$	−33.9430	−	11.5306i	−1.46203	−	0.496658i
$540$	−10.0342	−	5.79324i	−0.431803	−	0.249301i
$541$	−42.5041	−	9.70128i	−1.82739	−	0.417090i	−0.836079	−	0.548609i	$-0.815158\pi$
$541$	−42.5041	−	9.70128i	−1.82739	−	0.417090i	−0.991314	+	0.131518i	$0.958015\pi$
$542$	−9.62699	−	24.5292i	−0.413514	−	1.05362i
$543$	2.74657	+	36.6505i	0.117867	+	1.57282i
$544$	2.68048	−	17.7838i	0.114925	−	0.762474i
$545$	17.8790	+	22.4196i	0.765854	+	0.960350i
$546$	28.7097	+	3.46995i	1.22866	+	0.148500i
$547$	−3.37479	+	4.23186i	−0.144296	+	0.180941i	−0.848727	−	0.528831i	$-0.822631\pi$
$547$	−3.37479	+	4.23186i	−0.144296	+	0.180941i	0.704432	+	0.709772i	$0.251202\pi$
$548$	3.07506	+	3.31413i	0.131360	+	0.141572i
$549$	11.3507	−	28.9210i	0.484434	−	1.23432i
$550$	−4.23472	−	3.92925i	−0.180569	−	0.167544i
$551$	−5.58508	−	11.5975i	−0.237932	−	0.494071i
$552$	15.6908	−	16.9106i	0.667843	−	0.719764i
$553$	−2.02958	+	1.03623i	−0.0863065	+	0.0440648i
$554$	17.1216	−	3.90789i	0.727426	−	0.166030i
$555$	−14.4272	+	2.17455i	−0.612400	+	0.0923045i
$556$	2.45316	+	1.67254i	0.104037	+	0.0709313i
$557$	−16.1553	+	9.32730i	−0.684524	+	0.395210i	−0.801557	−	0.597918i	$-0.795995\pi$
$557$	−16.1553	+	9.32730i	−0.684524	+	0.395210i	0.117033	+	0.993128i	$0.462662\pi$
$558$	43.0244			1.82137
$559$	−24.2375	+	36.0167i	−1.02514	+	1.52334i
$560$	5.62441	−	8.67646i	0.237675	−	0.366647i
$561$	58.8219	−	4.40809i	2.48346	−	0.186110i
$562$	1.83866	+	24.5352i	0.0775591	+	1.03495i
$563$	−6.18594	−	1.90811i	−0.260706	−	0.0804172i	0.161647	−	0.986849i	$-0.448320\pi$
$563$	−6.18594	−	1.90811i	−0.260706	−	0.0804172i	−0.422353	+	0.906431i	$0.638796\pi$
$564$	26.5077	−	6.05021i	1.11618	−	0.254760i
$565$	6.14642	+	9.01514i	0.258582	+	0.379270i
$566$	−6.81045	−	9.98909i	−0.286264	−	0.419873i
$567$	2.07649	+	0.263742i	0.0872045	+	0.0110761i
$568$	1.96313	−	26.1961i	0.0823710	−	1.09916i
$569$	13.3024	+	23.0405i	0.557666	+	0.965907i	0.997691	+	0.0679208i	$0.0216365\pi$
$569$	13.3024	+	23.0405i	0.557666	+	0.965907i	−0.440024	+	0.897986i	$0.645030\pi$
$570$	−23.2496	+	13.4231i	−0.973817	+	0.562234i
$571$	1.04120	−	0.501418i	0.0435731	−	0.0209837i	−0.411970	−	0.911197i	$-0.635159\pi$
$571$	1.04120	−	0.501418i	0.0435731	−	0.0209837i	0.455543	+	0.890214i	$0.349445\pi$
$572$	15.4493	−	2.42439i	0.645967	−	0.101369i
$573$	10.3984	+	45.5582i	0.434398	+	1.90322i
$574$	3.63836	−	2.60659i	0.151862	−	0.108797i
$575$	−2.68318	+	0.827652i	−0.111896	+	0.0345155i
$576$	−2.93824	+	39.2081i	−0.122427	+	1.63367i
$577$	−27.5080	−	6.27851i	−1.14517	−	0.261378i	−0.392486	−	0.919758i	$-0.628385\pi$
$577$	−27.5080	−	6.27851i	−1.14517	−	0.261378i	−0.752686	+	0.658380i	$0.771242\pi$
$578$	−0.0566272	−	0.375697i	−0.00235538	−	0.0156269i
$579$	−19.8809	+	64.4522i	−0.826221	+	2.67854i
$580$	5.82350	+	4.64409i	0.241808	+	0.192835i
$581$	7.73104	−	6.46514i	0.320738	−	0.268219i
$582$	6.98346	−	17.7936i	0.289474	−	0.737567i
$583$	7.07847	−	46.9626i	0.293160	−	1.94499i
$584$	16.6131	+	8.00044i	0.687454	+	0.331061i
$585$	43.6252	+	6.30545i	1.80368	+	0.260698i
$586$	3.54614	−	15.5366i	0.146490	−	0.641813i
$587$	26.7865	−	15.4652i	1.10560	−	0.638318i	0.167913	−	0.985802i	$-0.446297\pi$
$587$	26.7865	−	15.4652i	1.10560	−	0.638318i	0.937686	+	0.347484i	$0.112964\pi$
$588$	2.96142	−	16.4730i	0.122127	−	0.679335i
$589$	−14.5121	+	25.1357i	−0.597962	+	1.03570i
$590$	16.5204	+	3.77068i	0.680136	+	0.155237i
$591$	−24.1636	+	9.48352i	−0.993958	+	0.390100i
$592$	1.88046	+	2.75813i	0.0772864	+	0.113358i
$593$	14.0584	+	11.2112i	0.577309	+	0.460388i	0.868094	−	0.496400i	$-0.165345\pi$
$593$	14.0584	+	11.2112i	0.577309	+	0.460388i	−0.290785	+	0.956788i	$0.593916\pi$
$594$	−30.2427	+	4.55835i	−1.24087	+	0.187031i
$595$	7.23412	−	25.5478i	0.296570	−	1.04736i
$596$	−2.30459	+	15.2900i	−0.0943997	+	0.626301i
$597$	10.6261	+	46.5560i	0.434897	+	1.90541i
$598$	−3.72241	+	9.65611i	−0.152221	+	0.394868i
$599$	7.51541	−	32.9272i	0.307071	−	1.34537i	−0.552142	−	0.833750i	$-0.686189\pi$
$599$	7.51541	−	32.9272i	0.307071	−	1.34537i	0.859213	−	0.511617i	$-0.170953\pi$
$600$	5.10723	−	7.49093i	0.208502	−	0.305816i
$601$	25.5779	−	7.88974i	1.04335	−	0.321829i	0.274717	−	0.961525i	$-0.411416\pi$
$601$	25.5779	−	7.88974i	1.04335	−	0.321829i	0.768628	+	0.639696i	$0.220940\pi$
$602$	−27.2333	−	20.7001i	−1.10995	−	0.843673i
$603$	−16.8204	+	3.83915i	−0.684981	+	0.156342i
$604$	−0.829308	−	5.50210i	−0.0337441	−	0.223877i
$605$	37.3484	+	2.79887i	1.51843	+	0.113790i
$606$			38.8828i			1.57950i
$607$	13.5050	−	23.3914i	0.548153	−	0.949428i	−0.450249	−	0.892903i	$-0.648665\pi$
$607$	13.5050	−	23.3914i	0.548153	−	0.949428i	0.998401	−	0.0565250i	$-0.0180021\pi$
$608$	−13.1124	−	8.93990i	−0.531779	−	0.362561i
$609$	−25.6954	−	7.27590i	−1.04123	−	0.294834i
$610$	14.8763	+	7.16405i	0.602324	+	0.290064i
$611$	−33.7357	+	23.3012i	−1.36480	+	0.942665i
$612$	3.82155	+	16.7433i	0.154477	+	0.676808i
$613$	−8.51865	−	9.18092i	−0.344065	−	0.370814i	0.537185	−	0.843465i	$-0.319488\pi$
$613$	−8.51865	−	9.18092i	−0.344065	−	0.370814i	−0.881250	+	0.472651i	$0.843297\pi$
$614$	0.919734	+	12.2730i	0.0371174	+	0.495298i
$615$	9.03895	−	6.16265i	0.364486	−	0.248502i
$616$	4.05535	+	41.2221i	0.163395	+	1.66088i
$617$	48.7650	+	3.65443i	1.96321	+	0.147122i	0.994770	−	0.102140i	$-0.0325689\pi$
$617$	48.7650	+	3.65443i	1.96321	+	0.147122i	0.968436	+	0.249262i	$0.0801879\pi$
$618$	28.3581	+	16.3726i	1.14073	+	0.658601i
$619$			8.05039i			0.323573i	0.986826	+	0.161786i	$0.0517255\pi$
$619$			8.05039i			0.323573i	−0.986826	+	0.161786i	$0.948274\pi$
$620$	1.25508	−	16.7479i	0.0504053	−	0.672612i
$621$	−5.43116	+	13.8384i	−0.217945	+	0.555315i
$622$	1.68690	+	1.81804i	0.0676384	+	0.0728969i
$623$	−17.1408	−	6.27120i	−0.686733	−	0.251250i
$624$	−4.86043	−	15.4248i	−0.194573	−	0.617487i
$625$	26.2623	−	12.6473i	1.05049	−	0.505890i
$626$	8.25472	+	26.7611i	0.329925	+	1.06959i
$627$	19.0164	−	48.4530i	0.759442	−	1.93503i
$628$	−7.75529	−	2.39219i	−0.309470	−	0.0954588i
$629$	6.70200	+	5.34467i	0.267226	+	0.213106i
$630$	−6.93888	+	34.0319i	−0.276452	+	1.35586i
$631$	−2.31506	−	15.3594i	−0.0921611	−	0.611449i	−0.986463	−	0.163985i	$-0.947565\pi$
$631$	−2.31506	−	15.3594i	−0.0921611	−	0.611449i	0.894302	−	0.447464i	$-0.147673\pi$
$632$	2.05862	+	1.64169i	0.0818874	+	0.0653031i
$633$	4.00982	−	2.73385i	0.159376	−	0.108661i
$634$	−32.5392	−	4.90450i	−1.29230	−	0.194783i
$635$	10.1944	+	33.0494i	0.404552	+	1.31153i
$636$	22.1740			0.879256
$637$	5.06815	+	24.7248i	0.200807	+	0.979631i
$638$	19.6615			0.778408
$639$	12.5884	+	40.8105i	0.497988	+	1.61444i
$640$	0.781170	+	0.117742i	0.0308785	+	0.00465418i
$641$	−13.0391	+	8.88994i	−0.515015	+	0.351131i	−0.792770	−	0.609521i	$-0.791362\pi$
$641$	−13.0391	+	8.88994i	−0.515015	+	0.351131i	0.277755	+	0.960652i	$0.410410\pi$
$642$	−19.7115	−	15.7194i	−0.777949	−	0.620394i
$643$	−4.21845	−	27.9876i	−0.166359	−	1.10372i	−0.903689	−	0.428189i	$-0.859152\pi$
$643$	−4.21845	−	27.9876i	−0.166359	−	1.10372i	0.737330	−	0.675533i	$-0.236086\pi$
$644$	5.45535	+	2.47252i	0.214971	+	0.0974311i
$645$	−65.3708	−	52.1314i	−2.57397	−	2.05267i
$646$	15.0723	+	4.64919i	0.593012	+	0.182920i
$647$	16.2029	−	41.2844i	0.637003	−	1.62306i	−0.137512	−	0.990500i	$-0.543910\pi$
$647$	16.2029	−	41.2844i	0.637003	−	1.62306i	0.774514	−	0.632556i	$-0.217994\pi$
$648$	−0.712890	−	2.31113i	−0.0280050	−	0.0907899i
$649$	−29.6009	+	14.2550i	−1.16194	+	0.559559i
$650$	−0.881001	+	3.97062i	−0.0345557	+	0.155741i
$651$	19.0825	+	57.1119i	0.747900	+	2.23839i
$652$	−3.72865	−	4.01853i	−0.146025	−	0.157378i
$653$	−2.48893	+	6.34169i	−0.0973994	+	0.248170i	−0.971266	−	0.237996i	$-0.923510\pi$
$653$	−2.48893	+	6.34169i	−0.0973994	+	0.248170i	0.873867	+	0.486165i	$0.161605\pi$
$654$	−2.64102	+	35.2419i	−0.103272	+	1.37807i
$655$		−	43.4193i		−	1.69653i
$656$	−2.16766	−	1.25150i	−0.0846330	−	0.0488629i
$657$	−29.8937	−	2.24022i	−1.16626	−	0.0873994i
$658$	−16.7998	−	27.5952i	−0.654925	−	1.07577i
$659$	−35.8852	+	24.4661i	−1.39789	+	0.953064i	−0.398533	+	0.917154i	$0.630480\pi$
$659$	−35.8852	+	24.4661i	−1.39789	+	0.953064i	−0.999355	+	0.0359097i	$0.988567\pi$
$660$	2.25082	+	30.0351i	0.0876131	+	1.16912i
$661$	17.0529	+	18.3786i	0.663280	+	0.714846i	0.971651	−	0.236420i	$-0.0759742\pi$
$661$	17.0529	+	18.3786i	0.663280	+	0.714846i	−0.308371	+	0.951266i	$0.599784\pi$
$662$	−2.64457	−	11.5866i	−0.102784	−	0.450327i
$663$	−23.6019	−	34.1711i	−0.916623	−	1.32710i
$664$	−10.4916	−	5.05249i	−0.407153	−	0.196074i
$665$	−17.5416	−	15.5328i	−0.680235	−	0.602336i
$666$	−9.26457	−	6.31648i	−0.358995	−	0.244759i
$667$	4.77841	−	8.27646i	0.185021	−	0.320466i
$668$		−	0.502829i		−	0.0194551i
$669$	−53.6186	−	4.01816i	−2.07302	−	0.155351i
$670$	−1.36658	−	9.06669i	−0.0527957	−	0.350277i
$671$	−31.2107	+	7.12364i	−1.20488	+	0.275005i
$672$	−31.9203	+	8.07115i	−1.23135	+	0.311352i
$673$	0.118847	−	0.0366595i	0.00458123	−	0.00141312i	−0.292464	−	0.956277i	$-0.594475\pi$
$673$	0.118847	−	0.0366595i	0.00458123	−	0.00141312i	0.297045	+	0.954863i	$0.403999\pi$
$674$	−16.0336	+	23.5170i	−0.617592	+	0.905841i
$675$	−1.30008	+	5.69603i	−0.0500402	+	0.219240i
$676$	−6.96851	−	8.52433i	−0.268020	−	0.327859i
$677$	−5.19332	−	22.7534i	−0.199596	−	0.874485i	−0.971178	−	0.238356i	$-0.923392\pi$
$677$	−5.19332	−	22.7534i	−0.199596	−	0.874485i	0.771582	−	0.636129i	$-0.219466\pi$
$678$	−2.00418	+	13.2969i	−0.0769701	+	0.510663i
$679$	16.6605	+	0.859394i	0.639371	+	0.0329805i
$680$	−30.3375	+	4.57264i	−1.16339	+	0.175353i
$681$	−18.0097	−	14.3623i	−0.690134	−	0.550364i
$682$	−24.9734	−	36.6293i	−0.956283	−	1.40261i
$683$	−6.98158	+	2.74007i	−0.267143	+	0.104846i	−0.495132	−	0.868818i	$-0.664880\pi$
$683$	−6.98158	+	2.74007i	−0.267143	+	0.104846i	0.227989	+	0.973664i	$0.426785\pi$
$684$	14.7746	+	3.37221i	0.564921	+	0.128940i
$685$	6.56520	−	11.3713i	0.250844	−	0.434474i
$686$	−19.6797	+	2.86544i	−0.751373	+	0.109403i
$687$	46.4586	−	26.8229i	1.77251	−	1.02336i
$688$	−4.25687	+	18.6505i	−0.162292	+	0.711046i
$689$	−31.0515	+	12.4044i	−1.18297	+	0.472570i
$690$	−17.9578	−	8.64800i	−0.683640	−	0.329224i
$691$	−1.45936	+	9.68223i	−0.0555167	+	0.368329i	0.943771	+	0.330599i	$0.107251\pi$
$691$	−1.45936	+	9.68223i	−0.0555167	+	0.368329i	−0.999288	+	0.0377302i	$0.987987\pi$
$692$	−0.888240	+	2.26320i	−0.0337658	+	0.0860339i
$693$	−30.6213	−	59.9757i	−1.16321	−	2.27829i
$694$	−1.95479	−	1.55889i	−0.0742028	−	0.0591748i
$695$	2.54171	−	8.24002i	0.0964125	−	0.312562i
$696$	4.59904	+	30.5127i	0.174326	+	1.15658i
$697$	−6.26637	−	1.43026i	−0.237356	−	0.0541749i
$698$	−1.20584	+	16.0908i	−0.0456417	+	0.609046i
$699$	61.9178	−	19.0991i	2.34195	−	0.722395i
$700$	2.26490	+	0.641328i	0.0856051	+	0.0242399i
$701$	−0.972828	−	4.26224i	−0.0367432	−	0.160983i	0.953228	−	0.302253i	$-0.0977386\pi$
$701$	−0.972828	−	4.26224i	−0.0367432	−	0.160983i	−0.989971	+	0.141270i	$0.954881\pi$
$702$	13.5273	+	16.7535i	0.510553	+	0.632319i
$703$	6.81516	−	3.28201i	0.257039	−	0.123783i
$704$	35.0858	−	20.2568i	1.32235	−	0.763456i
$705$	−39.4833	−	68.3871i	−1.48703	−	2.57561i
$706$	0.0188425	−	0.251436i	0.000709147	−	0.00946290i
$707$	−32.1861	+	10.7541i	−1.21048	+	0.404451i
$708$	−8.64100	−	12.6740i	−0.324749	−	0.476319i
$709$	15.7842	+	23.1511i	0.592787	+	0.869459i	0.999018	−	0.0443117i	$-0.0141095\pi$
$709$	15.7842	+	23.1511i	0.592787	+	0.869459i	−0.406231	+	0.913771i	$0.633157\pi$
$710$	−22.1280	+	5.05058i	−0.830450	+	0.189545i
$711$	−4.09055	−	1.26177i	−0.153408	−	0.0473200i
$712$	1.57602	+	21.0305i	0.0590639	+	0.788153i
$713$	−21.4884	+	1.61033i	−0.804745	+	0.0603073i
$714$	27.9513	−	17.0166i	1.04605	−	0.636831i
$715$	−19.9539	−	40.8008i	−0.746235	−	1.52586i
$716$	−6.66281			−0.249001
$717$	−70.8332	+	40.8956i	−2.64531	+	1.52727i
$718$	27.2005	+	18.5450i	1.01511	+	0.692092i
$719$	0.790617	−	0.119166i	0.0294850	−	0.00444415i	−0.134283	−	0.990943i	$-0.542873\pi$
$719$	0.790617	−	0.119166i	0.0294850	−	0.00444415i	0.163768	+	0.986499i	$0.447635\pi$
$720$	18.9366	−	4.32216i	0.705726	−	0.161077i
$721$	−5.70951	+	28.0024i	−0.212633	+	1.04286i
$722$	−4.41017	+	4.75303i	−0.164130	+	0.176890i
$723$	−23.1146	−	47.9979i	−0.859640	−	1.78506i
$724$	8.08262	+	7.49957i	0.300388	+	0.278719i
$725$	1.37220	−	3.49631i	0.0509623	−	0.129850i
$726$	31.3955	+	33.8363i	1.16520	+	1.25578i
$727$	−30.6873	+	38.4807i	−1.13813	+	1.42717i	−0.249601	+	0.968349i	$0.580300\pi$
$727$	−30.6873	+	38.4807i	−1.13813	+	1.42717i	−0.888529	+	0.458821i	$0.848272\pi$
$728$	23.6033	−	17.1271i	0.874795	−	0.634774i
$729$	−26.9171	−	33.7530i	−0.996931	−	1.25011i
$730$	2.37447	−	15.7536i	0.0878833	−	0.583067i
$731$	3.67111	+	48.9875i	0.135781	+	1.81187i
$732$	−5.46064	−	13.9135i	−0.201831	−	0.514257i
$733$	41.7119	+	9.52048i	1.54067	+	0.351647i	0.906721	−	0.421731i	$-0.138577\pi$
$733$	41.7119	+	9.52048i	1.54067	+	0.351647i	0.633945	+	0.773378i	$0.281435\pi$
$734$	19.1507	+	11.0566i	0.706864	+	0.408108i
$735$	−48.2525	+	5.88315i	−1.77982	+	0.217003i
$736$		−	11.7825i		−	0.434307i
$737$	13.0319	+	12.0918i	0.480036	+	0.445408i
$738$	8.31370	+	1.25309i	0.306032	+	0.0461268i
$739$	−9.25086	+	0.693256i	−0.340298	+	0.0255018i	−0.243783	−	0.969830i	$-0.578389\pi$
$739$	−9.25086	+	0.693256i	−0.340298	+	0.0255018i	−0.0965149	+	0.995332i	$0.530770\pi$
$740$	−2.72905	+	3.42211i	−0.100322	+	0.125799i
$741$	−36.2036	+	5.68127i	−1.32997	+	0.208707i
$742$	−8.34956	−	24.9894i	−0.306522	−	0.917389i
$743$	−0.914371	+	6.06646i	−0.0335450	+	0.222557i	−0.999322	−	0.0368171i	$-0.988278\pi$
$743$	−0.914371	+	6.06646i	−0.0335450	+	0.222557i	0.965777	+	0.259374i	$0.0835162\pi$
$744$	51.0033	−	47.3241i	1.86987	−	1.73499i
$745$	44.4069	−	6.69326i	1.62694	−	0.245222i
$746$	6.35052	+	1.44947i	0.232509	+	0.0530687i
$747$	18.8786	+	1.41476i	0.690733	+	0.0517633i
$748$	12.0364	−	12.9721i	0.440094	−	0.474308i
$749$	7.56028	−	20.6642i	0.276247	−	0.755055i
$750$	28.1422	+	8.68072i	1.02761	+	0.316975i
$751$	1.02478	−	2.61110i	0.0373948	−	0.0952804i	−0.910956	−	0.412502i	$-0.864655\pi$
$751$	1.02478	−	2.61110i	0.0373948	−	0.0952804i	0.948351	+	0.317222i	$0.102750\pi$
$752$	−10.1777	+	14.9279i	−0.371141	+	0.544364i
$753$	73.8540			2.69139
$754$	−6.99384	−	11.9460i	−0.254701	−	0.435048i
$755$	−14.5600	+	7.01171i	−0.529891	+	0.255182i
$756$	10.1309	−	7.25799i	0.368458	−	0.263970i
$757$	−1.59566	−	21.2925i	−0.0579951	−	0.773891i	−0.948067	−	0.318071i	$-0.896965\pi$
$757$	−1.59566	−	21.2925i	−0.0579951	−	0.773891i	0.890072	−	0.455820i	$-0.150654\pi$
$758$	0.549188	−	0.374430i	0.0199474	−	0.0135999i
$759$	37.6757	−	8.59922i	1.36754	−	0.312132i
$760$	−7.97983	+	25.8700i	−0.289459	+	0.938402i
$761$	9.00517	+	13.2082i	0.326437	+	0.478795i	0.954015	−	0.299758i	$-0.0969061\pi$
$761$	9.00517	+	13.2082i	0.326437	+	0.478795i	−0.627578	+	0.778554i	$0.715954\pi$
$762$	−18.4941	+	38.4035i	−0.669972	+	1.39121i
$763$	−29.9027	+	7.56100i	−1.08255	+	0.273727i
$764$	11.5830	+	7.89717i	0.419059	+	0.285709i
$765$	43.1959	−	24.9392i	1.56175	−	0.901678i
$766$	−0.413621			−0.0149447
$767$	19.1905	+	12.9143i	0.692929	+	0.466308i
$768$	28.4568	+	35.6837i	1.02685	+	1.28763i
$769$	2.96775	+	3.19848i	0.107020	+	0.115340i	0.784290	−	0.620395i	$-0.213028\pi$
$769$	2.96775	+	3.19848i	0.107020	+	0.115340i	−0.677270	+	0.735735i	$0.736837\pi$
$770$	33.0011	−	13.8462i	1.18928	−	0.498984i
$771$	−47.2310	−	43.8240i	−1.70098	−	1.57828i
$772$	8.77948	+	18.2308i	0.315981	+	0.656140i
$773$	−15.1266	+	16.3026i	−0.544066	+	0.586364i	−0.943903	−	0.330222i	$-0.892876\pi$
$773$	−15.1266	+	16.3026i	−0.544066	+	0.586364i	0.399837	+	0.916586i	$0.369067\pi$
$774$	−9.57723	−	63.5408i	−0.344246	−	2.28393i
$775$	−8.25653	+	1.88450i	−0.296583	+	0.0676932i
$776$	−7.04237	−	17.9437i	−0.252806	−	0.644140i
$777$	4.27560	−	15.0996i	0.153386	−	0.541695i
$778$	0.383561	+	0.150537i	0.0137513	+	0.00539700i
$779$	−3.53629	+	4.43437i	−0.126701	+	0.158878i
$780$	17.4482	−	12.0514i	0.624744	−	0.431509i
$781$	27.4376	−	34.4056i	0.981793	−	1.23113i
$782$	3.45172	+	11.1902i	0.123433	+	0.400161i
$783$	−9.94255	−	17.2210i	−0.355318	−	0.615428i
$784$	6.00281	+	9.36265i	0.214386	+	0.334381i
$785$			23.5710i			0.841286i
$786$	36.3967	−	39.2264i	1.29823	−	1.39916i
$787$	−9.67754	+	3.79815i	−0.344967	+	0.135390i	−0.531498	−	0.847059i	$-0.678371\pi$
$787$	−9.67754	+	3.79815i	−0.344967	+	0.135390i	0.186531	+	0.982449i	$0.440275\pi$
$788$	−3.37883	+	7.01621i	−0.120366	+	0.249942i
$789$	−6.83062	−	17.4041i	−0.243176	−	0.619603i
$790$	0.831149	−	2.11773i	0.0295709	−	0.0753455i
$791$	−11.5611	+	2.01863i	−0.411065	+	0.0717741i
$792$	−48.5133	+	60.8338i	−1.72385	+	2.16163i
$793$	15.4302	+	16.4291i	0.547943	+	0.583415i
$794$	−24.7159	−	30.9927i	−0.877133	−	1.09989i
$795$	−18.9823	−	61.5392i	−0.673234	−	2.18257i
$796$	11.8367	+	8.07011i	0.419540	+	0.286038i
$797$	28.7667	+	26.6916i	1.01897	+	0.945465i	0.998523	−	0.0543262i	$-0.0173011\pi$
$797$	28.7667	+	26.6916i	1.01897	+	0.945465i	0.0204455	+	0.999791i	$0.493492\pi$
$798$	−2.82712	−	28.7373i	−0.100079	−	1.01729i
$799$	−13.6753	+	44.3342i	−0.483797	+	1.56843i
$800$	−0.690162	−	4.57892i	−0.0244009	−	0.161889i
$801$	−14.8763	−	30.8910i	−0.525628	−	1.09148i
$802$	12.8017	−	22.1732i	0.452044	−	0.782963i
$803$	15.4445	+	26.7507i	0.545025	+	0.944011i
$804$	−4.67565	+	6.85792i	−0.164897	+	0.241860i
$805$	2.19184	−	17.2568i	0.0772523	−	0.608222i
$806$	−13.3720	+	28.2029i	−0.471008	+	0.993405i
$807$	−58.8663	−	28.3485i	−2.07219	−	0.997914i
$808$	26.6701	+	28.7435i	0.938250	+	1.01119i
$809$	3.98345	−	3.69610i	0.140051	−	0.129948i	−0.607037	−	0.794674i	$-0.707642\pi$
$809$	3.98345	−	3.69610i	0.140051	−	0.129948i	0.747088	+	0.664726i	$0.231452\pi$
$810$	−1.72657	+	1.17716i	−0.0606655	+	0.0413610i
$811$	−6.27139	+	13.0227i	−0.220218	+	0.457288i	−0.981583	−	0.191036i	$-0.938815\pi$
$811$	−6.27139	+	13.0227i	−0.220218	+	0.457288i	0.761365	+	0.648324i	$0.224530\pi$
$812$	−7.13547	+	3.64310i	−0.250406	+	0.127848i
$813$	69.0843	+	5.17716i	2.42289	+	0.181571i
$814$			11.5539i			0.404964i
$815$	−7.96061	+	13.7882i	−0.278848	+	0.482979i
$816$	−15.1205	−	10.3090i	−0.529325	−	0.360888i
$817$	40.3522	+	15.8371i	1.41175	+	0.554069i
$818$	6.74638	+	29.5578i	0.235882	+	1.03347i
$819$	−25.5478	+	39.9390i	−0.892712	+	1.39558i
$820$	0.730306	−	3.19968i	0.0255034	−	0.111738i
$821$	−19.9994	+	29.3337i	−0.697984	+	1.02375i	0.299586	+	0.954069i	$0.403152\pi$
$821$	−19.9994	+	29.3337i	−0.697984	+	1.02375i	−0.997569	+	0.0696843i	$0.977801\pi$
$822$	15.4633	−	4.76980i	0.539345	−	0.166366i
$823$	25.7961	−	3.88813i	0.899194	−	0.135532i	0.316851	−	0.948475i	$-0.397374\pi$
$823$	25.7961	−	3.88813i	0.899194	−	0.135532i	0.582343	+	0.812943i	$0.302136\pi$
$824$	32.1934	−	7.34794i	1.12151	−	0.255978i
$825$	14.1379	−	5.54872i	0.492218	−	0.193181i
$826$	−11.0295	+	14.5105i	−0.383765	+	0.504885i
$827$	38.0123	−	30.3138i	1.32182	−	1.05411i	0.327816	−	0.944742i	$-0.393688\pi$
$827$	38.0123	−	30.3138i	1.32182	−	1.05411i	0.994001	−	0.109372i	$-0.0348839\pi$
$828$	4.11055	+	10.4735i	0.142851	+	0.363980i
$829$	3.95772	+	52.8121i	0.137457	+	1.83424i	0.460273	+	0.887777i	$0.347752\pi$
$829$	3.95772	+	52.8121i	0.137457	+	1.83424i	−0.322816	+	0.946462i	$0.604629\pi$
$830$	−1.49954	+	9.94881i	−0.0520499	+	0.345328i
$831$	−10.2741	+	45.0140i	−0.356406	+	1.56152i
$832$	−24.7881	−	14.1119i	−0.859372	−	0.489243i
$833$	21.8166	+	18.4309i	0.755901	+	0.638592i
$834$	9.20356	−	5.31368i	0.318693	−	0.183998i
$835$	−1.39550	+	0.430453i	−0.0482931	+	0.0148964i
$836$	−5.70493	−	14.5359i	−0.197309	−	0.502735i
$837$	−19.4539	+	40.3964i	−0.672425	+	1.39630i
$838$	4.68896	−	1.84028i	0.161977	−	0.0635714i
$839$	1.85544	+	12.3101i	0.0640571	+	0.424991i	0.997757	+	0.0669352i	$0.0213221\pi$
$839$	1.85544	+	12.3101i	0.0640571	+	0.424991i	−0.933700	+	0.358056i	$0.883440\pi$
$840$	29.2072	+	47.9754i	1.00774	+	1.65531i
$841$	−5.92458	−	15.0956i	−0.204296	−	0.520538i
$842$	−11.1205	+	10.3183i	−0.383238	+	0.355593i
$843$	−60.2143	−	23.6324i	−2.07389	−	0.813943i
$844$	0.323975	−	1.41943i	0.0111517	−	0.0488588i
$845$	−17.6920	+	26.6370i	−0.608623	+	0.916340i
$846$	13.5044	−	59.1666i	0.464290	−	2.03419i
$847$	−19.3254	+	35.3468i	−0.664030	+	1.21453i
$848$	−10.8012	+	10.0220i	−0.370914	+	0.344158i
$849$	31.4301	−	4.73733i	1.07868	−	0.162585i
$850$	1.99688	+	4.14657i	0.0684926	+	0.142226i
$851$	4.86357	+	2.80798i	0.166721	+	0.0962564i
$852$	17.7935	+	10.2731i	0.609594	+	0.351950i
$853$	−13.3336	−	27.6876i	−0.456535	−	0.948005i	−0.994470	−	0.105019i	$-0.966510\pi$
$853$	−13.3336	−	27.6876i	−0.456535	−	0.948005i	0.537935	−	0.842986i	$-0.319205\pi$
$854$	−13.6239	+	11.3930i	−0.466199	+	0.389862i
$855$	−3.28914	−	43.8906i	−0.112486	−	1.50103i
$856$	−25.3535	+	1.89998i	−0.866564	+	0.0649400i
$857$	1.89530	+	8.30385i	0.0647422	+	0.283654i	0.996928	−	0.0783267i	$-0.0249577\pi$
$857$	1.89530	+	8.30385i	0.0647422	+	0.283654i	−0.932186	+	0.361981i	$0.882101\pi$
$858$	16.1747	−	53.5874i	0.552196	−	1.82944i
$859$	36.4180	+	17.5380i	1.24257	+	0.598389i	0.935509	−	0.353302i	$-0.114941\pi$
$859$	36.4180	+	17.5380i	1.24257	+	0.598389i	0.307058	+	0.951691i	$0.400655\pi$
$860$	−25.0136	+	1.87451i	−0.852956	+	0.0639202i
$861$	2.02396	+	11.5916i	0.0689763	+	0.395042i
$862$	−1.97285	+	26.3258i	−0.0671955	+	0.896661i
$863$		−	29.3731i		−	0.999871i	−0.866063	−	0.499936i	$-0.833357\pi$
$863$		−	29.3731i		−	0.999871i	0.866063	−	0.499936i	$-0.166643\pi$
$864$	−21.2315	−	12.2580i	−0.722310	−	0.417026i
$865$	7.04141	+	0.527681i	0.239415	+	0.0179417i
$866$	13.4428	−	10.7203i	0.456805	−	0.364290i
$867$	0.954516	+	0.294429i	0.0324171	+	0.00999934i
$868$	15.8503	+	8.66598i	0.537995	+	0.294143i
$869$	1.30013	+	4.21493i	0.0441040	+	0.142982i
$870$	24.0207	−	11.5678i	0.814377	−	0.392184i
$871$	2.71118	−	12.2192i	0.0918650	−	0.414030i
$872$	22.2205	+	27.8636i	0.752479	+	0.943579i
$873$	21.3155	+	22.9726i	0.721419	+	0.777505i
$874$	10.2181	+	1.54013i	0.345633	+	0.0520958i
$875$	0.597874	+	25.6962i	0.0202118	+	0.868691i
$876$	−11.2754	+	8.99182i	−0.380960	+	0.303805i
$877$	52.7867	−	20.7172i	1.78248	−	0.699571i	0.785769	−	0.618520i	$-0.212267\pi$
$877$	52.7867	−	20.7172i	1.78248	−	0.699571i	0.996710	−	0.0810515i	$-0.0258278\pi$
$878$	−10.0574	−	14.7515i	−0.339420	−	0.497838i
$879$	32.7568	+	26.1227i	1.10486	+	0.881096i
$880$	−14.6714	−	13.6131i	−0.494574	−	0.458898i
$881$	−8.88382	−	15.3872i	−0.299303	−	0.518409i	0.676673	−	0.736283i	$-0.263421\pi$
$881$	−8.88382	−	15.3872i	−0.299303	−	0.518409i	−0.975977	+	0.217875i	$0.930088\pi$
$882$	−30.2594	−	21.9087i	−1.01889	−	0.737705i
$883$	8.97713			0.302105			0.151052	−	0.988526i	$-0.451734\pi$
$883$	8.97713			0.302105			0.151052	+	0.988526i	$0.451734\pi$
$884$	−12.1631	−	2.69875i	−0.409090	−	0.0907689i
$885$	−27.7768	+	34.8310i	−0.933707	+	1.17083i
$886$	−9.40964	+	0.705155i	−0.316123	+	0.0236901i
$887$	1.44467	+	0.217750i	0.0485074	+	0.00731132i	0.173251	−	0.984878i	$-0.444573\pi$
$887$	1.44467	+	0.217750i	0.0485074	+	0.00731132i	−0.124744	+	0.992189i	$0.539811\pi$
$888$	−17.9304	+	2.70258i	−0.601706	+	0.0906925i
$889$	−36.9044	−	4.68735i	−1.23773	−	0.157209i
$890$	16.9619	−	6.65706i	0.568565	−	0.223145i
$891$	1.19422	−	3.87158i	0.0400080	−	0.129703i
$892$	−12.6115	+	10.0573i	−0.422264	+	0.336744i
$893$	30.0113	+	27.8464i	1.00429	+	0.931845i
$894$	45.7293	+	31.1777i	1.52942	+	1.04274i
$895$	5.70378	+	18.4912i	0.190656	+	0.618093i
$896$	−0.462206	+	0.713018i	−0.0154412	+	0.0238203i
$897$	−18.6264	−	19.8322i	−0.621918	−	0.662178i
$898$	−5.07102	−	6.35885i	−0.169222	−	0.212198i
$899$	16.2371	−	23.8154i	0.541537	−	0.794289i
$900$	2.21094	+	3.82946i	0.0736980	+	0.127649i
$901$	−18.9186	+	32.7680i	−0.630270	+	1.09166i
$902$	−3.75884	−	7.80532i	−0.125156	−	0.259889i
$903$	80.0981	−	40.8951i	2.66550	−	1.36090i
$904$	7.63890	+	11.2042i	0.254066	+	0.372646i
$905$	13.8942	−	28.8517i	0.461860	−	0.959062i
$906$	−19.0316	−	5.87047i	−0.632282	−	0.195033i
$907$	4.14161	−	3.84285i	0.137520	−	0.127600i	−0.608414	−	0.793620i	$-0.708194\pi$
$907$	4.14161	−	3.84285i	0.137520	−	0.127600i	0.745934	+	0.666020i	$0.232004\pi$
$908$	−6.89127	+	0.516430i	−0.228695	+	0.0171383i
$909$	−57.4341	−	27.6588i	−1.90497	−	0.917385i
$910$	−20.1516	−	15.1256i	−0.668019	−	0.501409i
$911$	−10.6975	+	5.15165i	−0.354424	+	0.170682i	−0.602620	−	0.798028i	$-0.705877\pi$
$911$	−10.6975	+	5.15165i	−0.354424	+	0.170682i	0.248196	+	0.968710i	$0.420162\pi$
$912$	−13.9852	+	8.07434i	−0.463095	+	0.267368i
$913$	−9.75361	−	16.8937i	−0.322797	−	0.559101i
$914$	−0.345422	+	4.60934i	−0.0114256	+	0.152463i
$915$	−33.9392	+	27.0656i	−1.12200	+	0.894762i
$916$	4.74372	−	15.3788i	0.156737	−	0.508128i
$917$	42.5370	+	19.2790i	1.40470	+	0.636650i
$918$	23.7553	+	5.42199i	0.784041	+	0.178952i
$919$	2.75604	−	36.7768i	0.0909135	−	1.21316i	−0.746047	−	0.665893i	$-0.768051\pi$
$919$	2.75604	−	36.7768i	0.0909135	−	1.21316i	0.836961	−	0.547263i	$-0.184330\pi$
$920$	−19.2068	+	5.92450i	−0.633228	+	0.195325i
$921$	−30.1204	−	11.8214i	−0.992502	−	0.389528i
$922$	−5.96921	−	26.1528i	−0.196586	−	0.861298i
$923$	−30.6641	−	4.43210i	−1.00932	−	0.145884i
$924$	−30.4242	−	11.1311i	−1.00088	−	0.366187i
$925$	2.05457	+	0.806359i	0.0675538	+	0.0265129i
$926$	13.5496	+	2.04228i	0.445269	+	0.0671134i
$927$	−44.3563	+	30.2416i	−1.45685	+	0.993265i
$928$	12.3220	+	9.82649i	0.404490	+	0.322570i
$929$	2.18349	−	2.35324i	0.0716380	−	0.0772074i	−0.696216	−	0.717833i	$-0.745134\pi$
$929$	2.18349	−	2.35324i	0.0716380	−	0.0772074i	0.767854	+	0.640625i	$0.221325\pi$
$930$	−52.0609	−	30.0574i	−1.70714	−	0.985620i
$931$	23.0060	−	10.2883i	0.753992	−	0.337187i
$932$	9.71948	−	16.8346i	0.318372	−	0.551437i
$933$	−6.23070	+	1.92192i	−0.203984	+	0.0629207i
$934$	3.00235	−	19.9193i	0.0982399	−	0.651779i
$935$	−46.3053	−	22.2994i	−1.51434	−	0.729270i
$936$	54.2183	+	7.83655i	1.77218	+	0.256146i
$937$	−17.6008	−	22.0707i	−0.574992	−	0.721018i	0.406257	−	0.913759i	$-0.366834\pi$
$937$	−17.6008	−	22.0707i	−0.574992	−	0.721018i	−0.981250	+	0.192741i	$0.938262\pi$
$938$	9.48926	+	2.68698i	0.309835	+	0.0877329i
$939$	−72.8059	−	10.9737i	−2.37593	−	0.358114i
$940$	−22.6375	−	6.98276i	−0.738355	−	0.227752i
$941$	−42.0679	+	33.5480i	−1.37137	+	1.09363i	−0.386136	+	0.922442i	$0.626190\pi$
$941$	−42.0679	+	33.5480i	−1.37137	+	1.09363i	−0.985238	+	0.171192i	$0.945238\pi$
$942$	−19.7587	+	21.2948i	−0.643773	+	0.693823i
$943$	−4.19914	−	0.314682i	−0.136743	−	0.0102475i
$944$	9.93743	+	2.26815i	0.323436	+	0.0738221i
$945$	−28.8157	−	21.9029i	−0.937374	−	0.712501i
$946$	−48.5371	+	45.0358i	−1.57808	+	1.46424i
$947$	45.6134	+	17.9019i	1.48224	+	0.581735i	0.962184	−	0.272400i	$-0.0878173\pi$
$947$	45.6134	+	17.9019i	1.48224	+	0.581735i	0.520052	+	0.854135i	$0.325913\pi$
$948$	−1.85545	+	0.893539i	−0.0602623	+	0.0290208i
$949$	10.7594	−	18.8993i	0.349266	−	0.613498i
$950$	4.06120			0.131763
$951$	48.7354	−	71.4817i	1.58035	−	2.31795i
$952$	8.99072	−	31.7514i	0.291391	−	1.02907i
$953$	−7.02467	+	4.78934i	−0.227551	+	0.155142i	−0.671729	−	0.740797i	$-0.734448\pi$
$953$	−7.02467	+	4.78934i	−0.227551	+	0.155142i	0.444178	+	0.895939i	$0.353496\pi$
$954$	21.4744	−	44.5921i	0.695260	−	1.44372i
$955$	12.0011	−	38.9066i	0.388347	−	1.25899i
$956$	−7.23251	+	23.4472i	−0.233916	+	0.758338i
$957$	−22.4282	+	46.5727i	−0.725002	+	1.50548i
$958$	−18.5561	+	12.6513i	−0.599520	+	0.408746i
$959$	8.22513	+	11.4809i	0.265603	+	0.370737i
$960$	30.9466	−	45.3904i	0.998799	−	1.46497i
$961$	−33.9917			−1.09651
$962$	7.01994	−	4.10985i	0.226332	−	0.132507i
$963$	37.2408	−	17.9342i	1.20007	−	0.577922i
$964$	−14.8773	−	5.83892i	−0.479166	−	0.188059i
$965$	43.0799	−	39.9723i	1.38679	−	1.28675i
$966$	16.4459	−	13.7530i	0.529138	−	0.442495i
$967$	55.3461	+	12.6324i	1.77981	+	0.406230i	0.980789	−	0.195073i	$-0.0624944\pi$
$967$	55.3461	+	12.6324i	1.77981	+	0.406230i	0.799021	+	0.601303i	$0.205352\pi$
$968$	46.4174	+	3.47850i	1.49191	+	0.111803i
$969$	−28.2058	+	30.3986i	−0.906101	+	0.976545i
$970$	−13.0212	+	10.3841i	−0.418086	+	0.333412i
$971$	−24.3659	−	7.51587i	−0.781938	−	0.241196i	−0.122014	−	0.992528i	$-0.538935\pi$
$971$	−24.3659	−	7.51587i	−0.781938	−	0.241196i	−0.659924	+	0.751333i	$0.729411\pi$
$972$	−12.1028	−	1.82420i	−0.388197	−	0.0585113i
$973$	6.94402	+	6.14880i	0.222615	+	0.197121i
$974$	−26.4981	−	33.2275i	−0.849053	−	1.06468i
$975$	−8.40032	−	6.61619i	−0.269025	−	0.211888i
$976$	8.94844	+	4.30934i	0.286433	+	0.137939i
$977$	5.24724	−	34.8132i	0.167874	−	1.11377i	−0.733170	−	0.680045i	$-0.761960\pi$
$977$	5.24724	−	34.8132i	0.167874	−	1.11377i	0.901044	−	0.433727i	$-0.142802\pi$
$978$	−18.7500	+	5.78361i	−0.599558	+	0.184939i
$979$	−17.6644	+	30.5957i	−0.564558	+	0.977843i
$980$	−9.41101	+	11.1398i	−0.300624	+	0.355848i
$981$	−50.1775	−	28.9700i	−1.60205	−	0.924941i
$982$	−11.0152	+	11.8715i	−0.351508	+	0.378836i
$983$	−21.0538	−	16.7898i	−0.671511	−	0.535512i	0.227313	−	0.973822i	$-0.427006\pi$
$983$	−21.0538	−	16.7898i	−0.671511	−	0.535512i	−0.898824	+	0.438310i	$0.855577\pi$
$984$	11.2338	−	7.65907i	0.358120	−	0.244162i
$985$	22.3645	+	3.37090i	0.712591	+	0.107406i
$986$	−14.5814	−	5.72276i	−0.464365	−	0.182250i
$987$	84.5290	−	8.31581i	2.69059	−	0.264695i
$988$	−6.80246	+	8.63681i	−0.216415	+	0.274774i
$989$	7.16153	+	31.3767i	0.227723	+	0.997721i
$990$	62.5807	+	24.5611i	1.98894	+	0.780603i
$991$	−0.501602	+	0.154724i	−0.0159339	+	0.00491496i	−0.302712	−	0.953082i	$-0.597892\pi$
$991$	−0.501602	+	0.154724i	−0.0159339	+	0.00491496i	0.286778	+	0.957997i	$0.407416\pi$
$992$	2.65565	−	35.4371i	0.0843168	−	1.12513i
$993$	30.4622	+	6.95279i	0.966687	+	0.220640i
$994$	4.87734	−	23.9210i	0.154700	−	0.758727i
$995$	12.2639	−	39.7587i	0.388793	−	1.26044i
$996$	7.12069	−	5.67856i	0.225628	−	0.179932i
$997$	1.87952	−	25.0804i	0.0595249	−	0.794305i	−0.884943	−	0.465700i	$-0.845803\pi$
$997$	1.87952	−	25.0804i	0.0595249	−	0.794305i	0.944468	−	0.328605i	$-0.106578\pi$
$998$	−1.07147	−	1.85583i	−0.0339167	−	0.0587454i
$999$	10.1197	−	5.84263i	0.320174	−	0.184853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bt.a.309.21	yes	768
13.4	even	6	inner	637.2.bt.a.407.44	yes	768
49.36	even	7	inner	637.2.bt.a.36.44	✓	768
637.134	even	42	inner	637.2.bt.a.134.21	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bt.a.36.44	✓	768	49.36	even	7	inner
637.2.bt.a.134.21	yes	768	637.134	even	42	inner
637.2.bt.a.309.21	yes	768	1.1	even	1	trivial
637.2.bt.a.407.44	yes	768	13.4	even	6	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bt (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.316510 - 1.02610i) q^{2} +(2.79159 + 0.420765i) q^{3} +(0.699773 - 0.477097i) q^{4} +(-1.92313 - 1.53365i) q^{5} +(-0.451820 - 2.99763i) q^{6} +(2.35639 - 1.20309i) q^{7} +(-2.39011 - 1.90605i) q^{8} +(4.74923 + 1.46494i) q^{9} +O(q^{10})\)	\(q+(-0.316510 - 1.02610i) q^{2} +(2.79159 + 0.420765i) q^{3} +(0.699773 - 0.477097i) q^{4} +(-1.92313 - 1.53365i) q^{5} +(-0.451820 - 2.99763i) q^{6} +(2.35639 - 1.20309i) q^{7} +(-2.39011 - 1.90605i) q^{8} +(4.74923 + 1.46494i) q^{9} +(-0.964985 + 2.45874i) q^{10} +(-1.50949 - 4.89364i) q^{11} +(2.15423 - 1.03742i) q^{12} +(-2.43634 + 2.65786i) q^{13} +(-1.98031 - 2.03711i) q^{14} +(-4.72329 - 5.09050i) q^{15} +(-0.580461 + 1.47899i) q^{16} +(-0.304897 + 4.06856i) q^{17} -5.33686i q^{18} +(3.11790 + 1.80012i) q^{19} +(-2.07745 - 0.155684i) q^{20} +(7.08431 - 2.36704i) q^{21} +(-4.54360 + 3.09777i) q^{22} +(0.199750 + 2.66547i) q^{23} +(-5.87021 - 6.32658i) q^{24} +(0.233758 + 1.02416i) q^{25} +(3.49836 + 1.65870i) q^{26} +(5.01088 + 2.41311i) q^{27} +(1.07495 - 1.96612i) q^{28} +(-2.95413 - 2.01409i) q^{29} +(-3.72840 + 6.45777i) q^{30} +8.06174i q^{31} +(-4.39571 - 0.329413i) q^{32} +(-2.15480 - 14.2962i) q^{33} +(4.27126 - 0.974887i) q^{34} +(-6.37676 - 1.30018i) q^{35} +(4.02230 - 1.24072i) q^{36} +(1.18356 - 1.73596i) q^{37} +(0.860259 - 3.76904i) q^{38} +(-7.91962 + 6.39454i) q^{39} +(1.67329 + 7.33116i) q^{40} +(-0.234799 + 1.55779i) q^{41} +(-4.67107 - 6.52002i) q^{42} +(11.9060 - 1.79454i) q^{43} +(-3.39104 - 2.70426i) q^{44} +(-6.88669 - 10.1009i) q^{45} +(2.67182 - 1.04861i) q^{46} +(11.0864 + 2.53040i) q^{47} +(-2.24272 + 3.88450i) q^{48} +(4.10517 - 5.66988i) q^{49} +(0.976906 - 0.564017i) q^{50} +(-2.56306 + 11.2295i) q^{51} +(-0.436830 + 3.02227i) q^{52} +(8.35549 + 4.02379i) q^{53} +(0.890102 - 5.90544i) q^{54} +(-4.60216 + 11.7261i) q^{55} +(-7.92517 - 1.61589i) q^{56} +(7.94649 + 6.33712i) q^{57} +(-1.13165 + 3.66871i) q^{58} +(-0.956173 - 6.34380i) q^{59} +(-5.73390 - 1.30872i) q^{60} +(0.467153 - 6.23372i) q^{61} +(8.27216 - 2.55162i) q^{62} +(12.9535 - 2.26175i) q^{63} +(1.76037 + 7.71268i) q^{64} +(8.76163 - 1.37493i) q^{65} +(-13.9873 + 6.73593i) q^{66} +(-3.00632 + 1.73570i) q^{67} +(1.72774 + 2.99254i) q^{68} +(-0.563918 + 7.52496i) q^{69} +(0.684192 + 6.95472i) q^{70} +(4.84065 + 7.09993i) q^{71} +(-8.55892 - 12.5536i) q^{72} +(-5.88042 + 1.34217i) q^{73} +(-2.15588 - 0.665000i) q^{74} +(0.221626 + 2.95740i) q^{75} +(3.04066 - 0.227866i) q^{76} +(-9.44441 - 9.71529i) q^{77} +(9.06808 + 6.10239i) q^{78} -0.861308 q^{79} +(3.38455 - 1.95407i) q^{80} +(0.653676 + 0.445669i) q^{81} +(1.67276 - 0.252129i) q^{82} +(3.71364 - 0.847614i) q^{83} +(3.82810 - 5.03629i) q^{84} +(6.82609 - 7.35678i) q^{85} +(-5.60976 - 11.6488i) q^{86} +(-7.39926 - 6.86551i) q^{87} +(-5.71967 + 14.5735i) q^{88} +(-4.69225 - 5.05705i) q^{89} +(-8.18485 + 10.2635i) q^{90} +(-2.54335 + 9.19409i) q^{91} +(1.41147 + 1.76993i) q^{92} +(-3.39210 + 22.5051i) q^{93} +(-0.912515 - 12.1767i) q^{94} +(-3.23539 - 8.24363i) q^{95} +(-12.1324 - 2.76915i) q^{96} +(5.46068 + 3.15272i) q^{97} +(-7.11720 - 2.41774i) q^{98} -25.4523i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q - 15 q^{2} - 3 q^{3} - 69 q^{4} - 15 q^{6} - 21 q^{7} + 57 q^{9}+O(q^{10}) \) 768 * q - 15 * q^2 - 3 * q^3 - 69 * q^4 - 15 * q^6 - 21 * q^7 + 57 * q^9	\( 768 q - 15 q^{2} - 3 q^{3} - 69 q^{4} - 15 q^{6} - 21 q^{7} + 57 q^{9} - 13 q^{10} - 27 q^{11} - 16 q^{12} - 8 q^{13} - 20 q^{14} - 33 q^{15} + 47 q^{16} - 9 q^{17} - 30 q^{19} - 15 q^{20} - 13 q^{22} - 5 q^{23} - 21 q^{24} + 100 q^{25} + 50 q^{26} - 24 q^{27} + 105 q^{28} - 9 q^{29} - 14 q^{30} - 39 q^{32} + 9 q^{33} - 27 q^{35} - 49 q^{36} - 30 q^{37} - 56 q^{38} - 14 q^{39} - 132 q^{40} - 33 q^{41} - 53 q^{42} + 9 q^{43} - 120 q^{45} + 15 q^{46} - 88 q^{48} - 27 q^{49} - 378 q^{50} - 16 q^{51} + 50 q^{52} - 62 q^{53} + 6 q^{54} - 22 q^{55} - 107 q^{56} - 15 q^{58} - 63 q^{59} + 2 q^{61} - 15 q^{62} - 117 q^{63} + 228 q^{64} - 62 q^{65} - 116 q^{66} - 54 q^{67} - 168 q^{68} + 49 q^{69} + 15 q^{71} - 39 q^{72} - 19 q^{74} - 87 q^{75} + 9 q^{76} - 78 q^{77} + 16 q^{78} - 8 q^{79} + 60 q^{80} + 61 q^{81} + 136 q^{82} - 39 q^{84} - 165 q^{85} - 49 q^{87} - 47 q^{88} + 120 q^{89} + 468 q^{90} - 42 q^{91} - 236 q^{92} + 108 q^{93} - 6 q^{94} + 84 q^{95} + 180 q^{97} - 147 q^{98}+O(q^{100}) \) 768 * q - 15 * q^2 - 3 * q^3 - 69 * q^4 - 15 * q^6 - 21 * q^7 + 57 * q^9 - 13 * q^10 - 27 * q^11 - 16 * q^12 - 8 * q^13 - 20 * q^14 - 33 * q^15 + 47 * q^16 - 9 * q^17 - 30 * q^19 - 15 * q^20 - 13 * q^22 - 5 * q^23 - 21 * q^24 + 100 * q^25 + 50 * q^26 - 24 * q^27 + 105 * q^28 - 9 * q^29 - 14 * q^30 - 39 * q^32 + 9 * q^33 - 27 * q^35 - 49 * q^36 - 30 * q^37 - 56 * q^38 - 14 * q^39 - 132 * q^40 - 33 * q^41 - 53 * q^42 + 9 * q^43 - 120 * q^45 + 15 * q^46 - 88 * q^48 - 27 * q^49 - 378 * q^50 - 16 * q^51 + 50 * q^52 - 62 * q^53 + 6 * q^54 - 22 * q^55 - 107 * q^56 - 15 * q^58 - 63 * q^59 + 2 * q^61 - 15 * q^62 - 117 * q^63 + 228 * q^64 - 62 * q^65 - 116 * q^66 - 54 * q^67 - 168 * q^68 + 49 * q^69 + 15 * q^71 - 39 * q^72 - 19 * q^74 - 87 * q^75 + 9 * q^76 - 78 * q^77 + 16 * q^78 - 8 * q^79 + 60 * q^80 + 61 * q^81 + 136 * q^82 - 39 * q^84 - 165 * q^85 - 49 * q^87 - 47 * q^88 + 120 * q^89 + 468 * q^90 - 42 * q^91 - 236 * q^92 + 108 * q^93 - 6 * q^94 + 84 * q^95 + 180 * q^97 - 147 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more