LMFDB - Embedded newform 216.2.v.b.59.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.10
Character	$\chi$	$=$	216.59
Dual form			216.2.v.b.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.955634 + 1.04248i) q^{2} +(-1.08798 - 1.34770i) q^{3} +(-0.173527 - 1.99246i) q^{4} +(-2.35728 + 0.857979i) q^{5} +(2.44466 + 0.153705i) q^{6} +(2.09025 - 0.368567i) q^{7} +(2.24292 + 1.72316i) q^{8} +(-0.632581 + 2.93255i) q^{9} +O(q^{10})$	\(q+(-0.955634 + 1.04248i) q^{2} +(-1.08798 - 1.34770i) q^{3} +(-0.173527 - 1.99246i) q^{4} +(-2.35728 + 0.857979i) q^{5} +(2.44466 + 0.153705i) q^{6} +(2.09025 - 0.368567i) q^{7} +(2.24292 + 1.72316i) q^{8} +(-0.632581 + 2.93255i) q^{9} +(1.35827 - 3.27733i) q^{10} +(-1.11223 + 3.05583i) q^{11} +(-2.49644 + 2.40162i) q^{12} +(-2.68370 + 3.19831i) q^{13} +(-1.61329 + 2.53126i) q^{14} +(3.72098 + 2.24343i) q^{15} +(-3.93978 + 0.691490i) q^{16} +(-0.433413 - 0.250231i) q^{17} +(-2.45261 - 3.46190i) q^{18} +(2.69082 + 4.66064i) q^{19} +(2.11854 + 4.54790i) q^{20} +(-2.77087 - 2.41603i) q^{21} +(-2.12276 - 4.07974i) q^{22} +(-0.499638 + 2.83359i) q^{23} +(-0.117963 - 4.89756i) q^{24} +(0.990413 - 0.831055i) q^{25} +(-0.769536 - 5.85412i) q^{26} +(4.64043 - 2.33804i) q^{27} +(-1.09707 - 4.10077i) q^{28} +(0.294939 - 0.247483i) q^{29} +(-5.89463 + 1.73514i) q^{30} +(-1.22873 - 0.216658i) q^{31} +(3.04412 - 4.76795i) q^{32} +(5.32843 - 1.82574i) q^{33} +(0.675045 - 0.212695i) q^{34} +(-4.61107 + 2.66221i) q^{35} +(5.95275 + 0.751515i) q^{36} +(-8.56116 - 4.94279i) q^{37} +(-7.43006 - 1.64874i) q^{38} +(7.23018 + 0.137108i) q^{39} +(-6.76564 - 2.13759i) q^{40} +(-4.69827 + 5.59918i) q^{41} +(5.16660 - 0.579740i) q^{42} +(10.7825 + 3.92450i) q^{43} +(6.28162 + 1.68581i) q^{44} +(-1.02490 - 7.45558i) q^{45} +(-2.47649 - 3.22874i) q^{46} +(-0.561599 - 3.18499i) q^{47} +(5.21833 + 4.55730i) q^{48} +(-2.34455 + 0.853348i) q^{49} +(-0.0801145 + 1.82667i) q^{50} +(0.134311 + 0.856358i) q^{51} +(6.83819 + 4.79217i) q^{52} +11.9707 q^{53} +(-1.99719 + 7.07186i) q^{54} -8.15772i q^{55} +(5.32337 + 2.77517i) q^{56} +(3.35356 - 8.69712i) q^{57} +(-0.0238576 + 0.543970i) q^{58} +(-2.08516 - 5.72892i) q^{59} +(3.82425 - 7.80319i) q^{60} +(-4.59804 + 0.810759i) q^{61} +(1.40008 - 1.07388i) q^{62} +(-0.241410 + 6.36290i) q^{63} +(2.06142 + 7.72985i) q^{64} +(3.58215 - 9.84187i) q^{65} +(-3.18873 + 7.29952i) q^{66} +(-9.39931 - 7.88696i) q^{67} +(-0.423366 + 0.906979i) q^{68} +(4.36242 - 2.40954i) q^{69} +(1.63121 - 7.35104i) q^{70} +(-2.70354 + 4.68267i) q^{71} +(-6.47209 + 5.48745i) q^{72} +(4.58071 + 7.93403i) q^{73} +(13.3341 - 4.20134i) q^{74} +(-2.19756 - 0.430603i) q^{75} +(8.81920 - 6.17010i) q^{76} +(-1.19856 + 6.79738i) q^{77} +(-7.05234 + 7.40629i) q^{78} +(9.18302 + 10.9439i) q^{79} +(8.69387 - 5.01028i) q^{80} +(-8.19968 - 3.71015i) q^{81} +(-1.34720 - 10.2486i) q^{82} +(-8.89271 - 10.5979i) q^{83} +(-4.33301 + 5.94010i) q^{84} +(1.23637 + 0.218005i) q^{85} +(-14.3953 + 7.49012i) q^{86} +(-0.654421 - 0.128231i) q^{87} +(-7.76035 + 4.93745i) q^{88} +(-12.9048 + 7.45058i) q^{89} +(8.75171 + 6.05637i) q^{90} +(-4.43081 + 7.67438i) q^{91} +(5.73251 + 0.503805i) q^{92} +(1.04485 + 1.89168i) q^{93} +(3.85697 + 2.45823i) q^{94} +(-10.3418 - 8.67776i) q^{95} +(-9.73771 + 1.08490i) q^{96} +(-0.481380 - 0.175208i) q^{97} +(1.35094 - 3.25964i) q^{98} +(-8.25780 - 5.19474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.955634	+	1.04248i	−0.675735	+	0.737144i
$2$	−0.955634	+	1.04248i	−0.675735	+	0.737144i
$3$	−1.08798	−	1.34770i	−0.628148	−	0.778094i
$3$	−1.08798	−	1.34770i	−0.628148	−	0.778094i
$4$	−0.173527	−	1.99246i	−0.0867634	−	0.996229i
$5$	−2.35728	+	0.857979i	−1.05421	+	0.383700i	−0.810249	−	0.586086i	$-0.800668\pi$
$5$	−2.35728	+	0.857979i	−1.05421	+	0.383700i	−0.243958	+	0.969786i	$0.578446\pi$
$6$	2.44466	+	0.153705i	0.998029	+	0.0627499i
$7$	2.09025	−	0.368567i	0.790039	−	0.139305i	0.235953	−	0.971764i	$-0.424179\pi$
$7$	2.09025	−	0.368567i	0.790039	−	0.139305i	0.554086	+	0.832459i	$0.313068\pi$
$8$	2.24292	+	1.72316i	0.792994	+	0.609230i
$9$	−0.632581	+	2.93255i	−0.210860	+	0.977516i
$10$	1.35827	−	3.27733i	0.429523	−	1.03638i
$11$	−1.11223	+	3.05583i	−0.335351	+	0.921368i	0.651344	+	0.758783i	$0.274206\pi$
$11$	−1.11223	+	3.05583i	−0.335351	+	0.921368i	−0.986694	+	0.162586i	$0.948017\pi$
$12$	−2.49644	+	2.40162i	−0.720659	+	0.693289i
$13$	−2.68370	+	3.19831i	−0.744325	+	0.887051i	−0.996749	−	0.0805651i	$-0.974328\pi$
$13$	−2.68370	+	3.19831i	−0.744325	+	0.887051i	0.252425	+	0.967617i	$0.418772\pi$
$14$	−1.61329	+	2.53126i	−0.431170	+	0.676507i
$15$	3.72098	+	2.24343i	0.960753	+	0.579252i
$16$	−3.93978	+	0.691490i	−0.984944	+	0.172872i
$17$	−0.433413	−	0.250231i	−0.105118	−	0.0606900i	0.446519	−	0.894774i	$-0.352663\pi$
$17$	−0.433413	−	0.250231i	−0.105118	−	0.0606900i	−0.551637	+	0.834084i	$0.685997\pi$
$18$	−2.45261	−	3.46190i	−0.578085	−	0.815977i
$19$	2.69082	+	4.66064i	0.617317	+	1.06922i	0.989973	+	0.141255i	$0.0451137\pi$
$19$	2.69082	+	4.66064i	0.617317	+	1.06922i	−0.372656	+	0.927969i	$0.621553\pi$
$20$	2.11854	+	4.54790i	0.473720	+	1.01694i
$21$	−2.77087	−	2.41603i	−0.604654	−	0.527221i
$22$	−2.12276	−	4.07974i	−0.452573	−	0.869803i
$23$	−0.499638	+	2.83359i	−0.104182	+	0.590844i	0.887362	+	0.461073i	$0.152535\pi$
$23$	−0.499638	+	2.83359i	−0.104182	+	0.590844i	−0.991544	+	0.129771i	$0.958576\pi$
$24$	−0.117963	−	4.89756i	−0.0240792	−	0.999710i
$25$	0.990413	−	0.831055i	0.198083	−	0.166211i
$26$	−0.769536	−	5.85412i	−0.150918	−	1.14809i
$27$	4.64043	−	2.33804i	0.893051	−	0.449956i
$28$	−1.09707	−	4.10077i	−0.207326	−	0.774974i
$29$	0.294939	−	0.247483i	0.0547687	−	0.0459564i	−0.614992	−	0.788533i	$-0.710841\pi$
$29$	0.294939	−	0.247483i	0.0547687	−	0.0459564i	0.669761	+	0.742577i	$0.266396\pi$
$30$	−5.89463	+	1.73514i	−1.07621	+	0.316792i
$31$	−1.22873	−	0.216658i	−0.220686	−	0.0389130i	0.0622115	−	0.998063i	$-0.480185\pi$
$31$	−1.22873	−	0.216658i	−0.220686	−	0.0389130i	−0.282898	+	0.959150i	$0.591296\pi$
$32$	3.04412	−	4.76795i	0.538130	−	0.842862i
$33$	5.32843	−	1.82574i	0.927561	−	0.317821i
$34$	0.675045	−	0.212695i	0.115769	−	0.0364769i
$35$	−4.61107	+	2.66221i	−0.779414	+	0.449995i
$36$	5.95275	+	0.751515i	0.992125	+	0.125252i
$37$	−8.56116	−	4.94279i	−1.40745	−	0.812589i	−0.412305	−	0.911046i	$-0.635276\pi$
$37$	−8.56116	−	4.94279i	−1.40745	−	0.812589i	−0.995141	+	0.0984564i	$0.968609\pi$
$38$	−7.43006	−	1.64874i	−1.20532	−	0.267461i
$39$	7.23018	+	0.137108i	1.15776	+	0.0219548i
$40$	−6.76564	−	2.13759i	−1.06974	−	0.337983i
$41$	−4.69827	+	5.59918i	−0.733747	+	0.874445i	−0.995889	−	0.0905841i	$-0.971127\pi$
$41$	−4.69827	+	5.59918i	−0.733747	+	0.874445i	0.262142	+	0.965029i	$0.415571\pi$
$42$	5.16660	−	0.579740i	0.797224	−	0.0894559i
$43$	10.7825	+	3.92450i	1.64431	+	0.598480i	0.987785	−	0.155823i	$-0.0498029\pi$
$43$	10.7825	+	3.92450i	1.64431	+	0.598480i	0.656526	+	0.754303i	$0.272025\pi$
$44$	6.28162	+	1.68581i	0.946990	+	0.254145i
$45$	−1.02490	−	7.45558i	−0.152783	−	1.11141i
$46$	−2.47649	−	3.22874i	−0.365138	−	0.476052i
$47$	−0.561599	−	3.18499i	−0.0819176	−	0.464578i	−0.997979	−	0.0635404i	$-0.979761\pi$
$47$	−0.561599	−	3.18499i	−0.0819176	−	0.464578i	0.916062	−	0.401037i	$-0.131350\pi$
$48$	5.21833	+	4.55730i	0.753202	+	0.657790i
$49$	−2.34455	+	0.853348i	−0.334936	+	0.121907i
$50$	−0.0801145	+	1.82667i	−0.0113299	+	0.258330i
$51$	0.134311	+	0.856358i	0.0188072	+	0.119914i
$52$	6.83819	+	4.79217i	0.948286	+	0.664554i
$53$	11.9707			1.64430			0.822149	−	0.569273i	$-0.192775\pi$
$53$	11.9707			1.64430			0.822149	+	0.569273i	$0.192775\pi$
$54$	−1.99719	+	7.07186i	−0.271784	+	0.962358i
$55$		−	8.15772i		−	1.09999i
$56$	5.32337	+	2.77517i	0.711365	+	0.370848i
$57$	3.35356	−	8.69712i	0.444190	−	1.15196i
$58$	−0.0238576	+	0.543970i	−0.00313265	+	0.0714268i
$59$	−2.08516	−	5.72892i	−0.271464	−	0.745842i	−0.998259	−	0.0589868i	$-0.981213\pi$
$59$	−2.08516	−	5.72892i	−0.271464	−	0.745842i	0.726795	−	0.686855i	$-0.241009\pi$
$60$	3.82425	−	7.80319i	0.493709	−	1.00739i
$61$	−4.59804	+	0.810759i	−0.588719	+	0.103807i	−0.460069	−	0.887883i	$-0.652175\pi$
$61$	−4.59804	+	0.810759i	−0.588719	+	0.103807i	−0.128650	+	0.991690i	$0.541064\pi$
$62$	1.40008	−	1.07388i	0.177810	−	0.136383i
$63$	−0.241410	+	6.36290i	−0.0304148	+	0.801650i
$64$	2.06142	+	7.72985i	0.257678	+	0.966231i
$65$	3.58215	−	9.84187i	0.444311	−	1.22073i
$66$	−3.18873	+	7.29952i	−0.392506	+	0.898509i
$67$	−9.39931	−	7.88696i	−1.14831	−	0.963545i	−0.148630	−	0.988893i	$-0.547486\pi$
$67$	−9.39931	−	7.88696i	−1.14831	−	0.963545i	−0.999679	+	0.0253476i	$0.991931\pi$
$68$	−0.423366	+	0.906979i	−0.0513407	+	0.109987i
$69$	4.36242	−	2.40954i	0.525174	−	0.290075i
$70$	1.63121	−	7.35104i	0.194966	−	0.878618i
$71$	−2.70354	+	4.68267i	−0.320851	+	0.555731i	−0.980664	−	0.195699i	$-0.937302\pi$
$71$	−2.70354	+	4.68267i	−0.320851	+	0.555731i	0.659813	+	0.751430i	$0.270636\pi$
$72$	−6.47209	+	5.48745i	−0.762743	+	0.646702i
$73$	4.58071	+	7.93403i	0.536132	+	0.928608i	0.999108	+	0.0422366i	$0.0134483\pi$
$73$	4.58071	+	7.93403i	0.536132	+	0.928608i	−0.462976	+	0.886371i	$0.653218\pi$
$74$	13.3341	−	4.20134i	1.55006	−	0.488396i
$75$	−2.19756	−	0.430603i	−0.253753	−	0.0497217i
$76$	8.81920	−	6.17010i	1.01163	−	0.707758i
$77$	−1.19856	+	6.79738i	−0.136589	+	0.774633i
$78$	−7.05234	+	7.40629i	−0.798520	+	0.838597i
$79$	9.18302	+	10.9439i	1.03317	+	1.23128i	0.972446	+	0.233130i	$0.0748967\pi$
$79$	9.18302	+	10.9439i	1.03317	+	1.23128i	0.0607247	+	0.998155i	$0.480659\pi$
$80$	8.69387	−	5.01028i	0.972004	−	0.560166i
$81$	−8.19968	−	3.71015i	−0.911076	−	0.412239i
$82$	−1.34720	−	10.2486i	−0.148774	−	1.13177i
$83$	−8.89271	−	10.5979i	−0.976102	−	1.16327i	−0.986572	−	0.163328i	$-0.947777\pi$
$83$	−8.89271	−	10.5979i	−0.976102	−	1.16327i	0.0104696	−	0.999945i	$-0.496667\pi$
$84$	−4.33301	+	5.94010i	−0.472771	+	0.648118i
$85$	1.23637	+	0.218005i	0.134103	+	0.0236460i
$86$	−14.3953	+	7.49012i	−1.55229	+	0.807680i
$87$	−0.654421	−	0.128231i	−0.0701613	−	0.0137478i
$88$	−7.76035	+	4.93745i	−0.827256	+	0.526334i
$89$	−12.9048	+	7.45058i	−1.36790	+	0.789760i	−0.990660	−	0.136355i	$-0.956461\pi$
$89$	−12.9048	+	7.45058i	−1.36790	+	0.789760i	−0.377244	+	0.926114i	$0.623128\pi$
$90$	8.75171	+	6.05637i	0.922511	+	0.638397i
$91$	−4.43081	+	7.67438i	−0.464475	+	0.804494i
$92$	5.73251	+	0.503805i	0.597656	+	0.0525253i
$93$	1.04485	+	1.89168i	0.108346	+	0.196158i
$94$	3.85697	+	2.45823i	0.397816	+	0.253547i
$95$	−10.3418	−	8.67776i	−1.06104	−	0.890319i
$96$	−9.73771	+	1.08490i	−0.993851	+	0.110727i
$97$	−0.481380	−	0.175208i	−0.0488767	−	0.0177897i	0.317466	−	0.948270i	$-0.397168\pi$
$97$	−0.481380	−	0.175208i	−0.0488767	−	0.0177897i	−0.366343	+	0.930480i	$0.619390\pi$
$98$	1.35094	−	3.25964i	0.136465	−	0.329273i
$99$	−8.25780	−	5.19474i	−0.829940	−	0.522091i
$100$	−1.82771	−	1.82915i	−0.182771	−	0.182915i
$101$	−2.28428	−	12.9548i	−0.227295	−	1.28905i	−0.858249	−	0.513233i	$-0.828448\pi$
$101$	−2.28428	−	12.9548i	−0.227295	−	1.28905i	0.630955	−	0.775820i	$-0.282663\pi$
$102$	−1.02109	−	0.678349i	−0.101103	−	0.0671665i
$103$	−3.94067	−	10.8269i	−0.388286	−	1.06681i	−0.967773	−	0.251826i	$-0.918969\pi$
$103$	−3.94067	−	10.8269i	−0.388286	−	1.06681i	0.579487	−	0.814982i	$-0.303253\pi$
$104$	−11.5305	+	2.54911i	−1.13066	+	0.249961i
$105$	8.60463	+	3.31790i	0.839725	+	0.323794i
$106$	−11.4396	+	12.4792i	−1.11111	+	1.21208i
$107$			2.94545i			0.284747i	0.989813	+	0.142374i	$0.0454734\pi$
$107$			2.94545i			0.284747i	−0.989813	+	0.142374i	$0.954527\pi$
$108$	−5.46368	−	8.84015i	−0.525743	−	0.850643i
$109$			19.9795i			1.91368i	0.290607	+	0.956842i	$0.406143\pi$
$109$			19.9795i			1.91368i	−0.290607	+	0.956842i	$0.593857\pi$
$110$	8.50426	+	7.79580i	0.810849	+	0.743300i
$111$	2.65302	+	16.9155i	0.251814	+	1.60555i
$112$	−7.98025	+	2.89746i	−0.754063	+	0.273784i
$113$	−1.58914	−	4.36612i	−0.149493	−	0.410730i	0.842231	−	0.539117i	$-0.181242\pi$
$113$	−1.58914	−	4.36612i	−0.149493	−	0.410730i	−0.991724	+	0.128387i	$0.959020\pi$
$114$	5.86179	+	11.8073i	0.549007	+	1.10585i
$115$	−1.25337	−	7.10824i	−0.116878	−	0.662847i
$116$	−0.544279	−	0.544708i	−0.0505350	−	0.0505748i
$117$	−7.68154	−	9.89327i	−0.710159	−	0.914633i
$118$	7.96493	+	3.30102i	0.733231	+	0.303883i
$119$	−0.998168	−	0.363303i	−0.0915019	−	0.0333040i
$120$	4.48008	+	11.4437i	0.408973	+	1.04466i
$121$	0.325434	+	0.273072i	0.0295849	+	0.0248247i
$122$	3.54885	−	5.56816i	0.321298	−	0.504117i
$123$	12.6577	+	0.240030i	1.14130	+	0.0216428i
$124$	−0.218465	+	2.48579i	−0.0196187	+	0.223230i
$125$	4.64976	−	8.05362i	0.415887	−	0.720337i
$126$	−6.40250	−	6.33227i	−0.570380	−	0.564124i
$127$	14.8968	−	8.60068i	1.32188	−	0.763187i	0.337850	−	0.941200i	$-0.390300\pi$
$127$	14.8968	−	8.60068i	1.32188	−	0.763187i	0.984028	+	0.178013i	$0.0569670\pi$
$128$	−10.0282	−	5.23792i	−0.886374	−	0.462971i
$129$	−6.44212	−	18.8013i	−0.567197	−	1.65536i
$130$	6.83672	+	13.1395i	0.599620	+	1.15241i
$131$	17.0826	+	3.01211i	1.49251	+	0.263170i	0.859565	−	0.511027i	$-0.170735\pi$
$131$	17.0826	+	3.01211i	1.49251	+	0.263170i	0.632945	+	0.774197i	$0.281846\pi$
$132$	−4.56235	−	10.2999i	−0.397101	−	0.896488i
$133$	7.34224	+	8.75015i	0.636653	+	0.758734i
$134$	17.2043	−	2.26154i	1.48622	−	0.195367i
$135$	−8.93279	+	9.49280i	−0.768813	+	0.817010i
$136$	−0.540924	−	1.30809i	−0.0463838	−	0.112168i
$137$	1.51760	+	1.80861i	0.129657	+	0.154520i	0.826967	−	0.562250i	$-0.190064\pi$
$137$	1.51760	+	1.80861i	0.129657	+	0.154520i	−0.697310	+	0.716770i	$0.745620\pi$
$138$	−1.65699	+	6.85038i	−0.141052	+	0.583143i
$139$	−0.553906	+	3.14136i	−0.0469817	+	0.266446i	−0.999246	−	0.0388287i	$-0.987637\pi$
$139$	−0.553906	+	3.14136i	−0.0469817	+	0.266446i	0.952264	+	0.305275i	$0.0987484\pi$
$140$	6.10448	+	8.72541i	0.515922	+	0.737432i
$141$	−3.68139	+	4.22208i	−0.310029	+	0.355563i
$142$	−2.29799	−	7.29331i	−0.192843	−	0.612041i
$143$	−6.78860	−	11.7582i	−0.567691	−	0.983270i
$144$	0.464400	−	11.9910i	0.0387000	−	0.999251i
$145$	−0.482917	+	0.836437i	−0.0401041	+	0.0694623i
$146$	−12.6485	−	2.80673i	−1.04680	−	0.232286i
$147$	3.70089	+	2.23132i	0.305244	+	0.184036i
$148$	−8.36271	+	17.9155i	−0.687410	+	1.47264i
$149$	15.4423	+	12.9576i	1.26508	+	1.06153i	0.995121	+	0.0986604i	$0.0314558\pi$
$149$	15.4423	+	12.9576i	1.26508	+	1.06153i	0.269963	+	0.962871i	$0.412989\pi$
$150$	2.54896	−	1.87942i	0.208122	−	0.153454i
$151$	0.290439	−	0.797974i	0.0236356	−	0.0649382i	−0.927314	−	0.374285i	$-0.877888\pi$
$151$	0.290439	−	0.797974i	0.0236356	−	0.0649382i	0.950949	+	0.309347i	$0.100110\pi$
$152$	−1.99573	+	15.0902i	−0.161875	+	1.22398i
$153$	1.00798	−	1.11271i	0.0814907	−	0.0899576i
$154$	−5.94074	−	7.74529i	−0.478719	−	0.624133i
$155$	3.08235	−	0.543501i	0.247580	−	0.0436551i
$156$	−0.981449	−	14.4296i	−0.0785788	−	1.15529i
$157$	2.55481	+	7.01929i	0.203896	+	0.560200i	0.998924	−	0.0463727i	$-0.0147662\pi$
$157$	2.55481	+	7.01929i	0.203896	+	0.560200i	−0.795028	+	0.606573i	$0.792544\pi$
$158$	−20.1844	−	0.885252i	−1.60578	−	0.0704268i
$159$	−13.0239	−	16.1328i	−1.03286	−	1.27942i
$160$	−3.08504	+	13.8512i	−0.243894	+	1.09503i
$161$			6.10706i			0.481304i
$162$	11.7036	−	5.00246i	0.919526	−	0.393030i
$163$	5.27568			0.413223			0.206612	−	0.978423i	$-0.433756\pi$
$163$	5.27568			0.413223			0.206612	+	0.978423i	$0.433756\pi$
$164$	11.9714	+	8.38950i	0.934810	+	0.655110i
$165$	−10.9941	+	8.87547i	−0.855893	+	0.690955i
$166$	19.5463	+	0.857266i	1.51709	+	0.0665368i
$167$	3.66882	−	1.33534i	0.283902	−	0.103332i	−0.196144	−	0.980575i	$-0.562842\pi$
$167$	3.66882	−	1.33534i	0.283902	−	0.103332i	0.480046	+	0.877243i	$0.340620\pi$
$168$	−2.05165	−	10.1936i	−0.158288	−	0.786456i
$169$	−0.769510	−	4.36411i	−0.0591931	−	0.335701i
$170$	−1.40878	+	1.08056i	−0.108049	+	0.0828748i
$171$	−15.3697	+	4.94273i	−1.17535	+	0.377980i
$172$	5.94835	−	22.1646i	0.453557	−	1.69004i
$173$	1.17536	+	0.427796i	0.0893610	+	0.0325248i	0.386314	−	0.922367i	$-0.373748\pi$
$173$	1.17536	+	0.427796i	0.0893610	+	0.0325248i	−0.296953	+	0.954892i	$0.595970\pi$
$174$	0.759065	−	0.559678i	0.0575445	−	0.0424291i
$175$	1.76391	−	2.10214i	0.133339	−	0.158907i
$176$	2.26887	−	12.8084i	0.171022	−	0.965469i
$177$	−5.45224	+	9.04313i	−0.409815	+	0.679724i
$178$	4.56517	−	20.5730i	0.342174	−	1.54201i
$179$	11.6215	+	6.70967i	0.868631	+	0.501504i	0.866893	−	0.498494i	$-0.166113\pi$
$179$	11.6215	+	6.70967i	0.868631	+	0.501504i	0.00173797	+	0.999998i	$0.499447\pi$
$180$	−14.6771	+	3.33581i	−1.09396	+	0.248636i
$181$	−2.75929	+	1.59308i	−0.205097	+	0.118413i	−0.599031	−	0.800726i	$-0.704447\pi$
$181$	−2.75929	+	1.59308i	−0.205097	+	0.118413i	0.393934	+	0.919139i	$0.371114\pi$
$182$	−3.76616	−	11.9529i	−0.279166	−	0.886010i
$183$	6.09526	+	5.31468i	0.450574	+	0.392873i
$184$	−6.00339	+	5.49457i	−0.442576	+	0.405065i
$185$	24.4219	+	4.30623i	1.79553	+	0.316600i
$186$	−2.97053	−	0.718519i	−0.217810	−	0.0526843i
$187$	1.24672	−	1.04612i	0.0911692	−	0.0765001i
$188$	−6.24850	+	1.67164i	−0.455719	+	0.121917i
$189$	8.83792	−	6.59739i	0.642864	−	0.479890i
$190$	18.9293	−	2.48830i	1.37328	−	0.180520i
$191$	−2.34242	+	1.96552i	−0.169491	+	0.142220i	−0.723588	−	0.690232i	$-0.757508\pi$
$191$	−2.34242	+	1.96552i	−0.169491	+	0.142220i	0.554096	+	0.832452i	$0.313064\pi$
$192$	8.17471	−	11.1881i	0.589959	−	0.807433i
$193$	1.45237	−	8.23682i	0.104544	−	0.592899i	−0.886857	−	0.462044i	$-0.847116\pi$
$193$	1.45237	−	8.23682i	0.104544	−	0.592899i	0.991401	−	0.130856i	$-0.0417725\pi$
$194$	0.642674	−	0.334394i	0.0461413	−	0.0240081i
$195$	−17.1612	+	5.88014i	−1.22894	+	0.421086i
$196$	2.10710	+	4.52334i	0.150507	+	0.323096i
$197$	3.22383	+	5.58384i	0.229688	+	0.397832i	0.957716	−	0.287716i	$-0.0928959\pi$
$197$	3.22383	+	5.58384i	0.229688	+	0.397832i	−0.728027	+	0.685548i	$0.759563\pi$
$198$	13.3068	−	3.64432i	0.945676	−	0.258991i
$199$	6.35032	+	3.66636i	0.450162	+	0.259901i	0.707899	−	0.706314i	$-0.249643\pi$
$199$	6.35032	+	3.66636i	0.450162	+	0.259901i	−0.257737	+	0.966215i	$0.582977\pi$
$200$	3.65346	−	0.157351i	0.258339	−	0.0111264i
$201$	−0.402938	+	21.2483i	−0.0284210	+	1.49874i
$202$	15.6881	+	9.99875i	1.10381	+	0.703509i
$203$	0.525281	−	0.626005i	0.0368675	−	0.0439369i
$204$	1.68295	−	0.416209i	0.117830	−	0.0291405i
$205$	6.27115	−	17.2299i	0.437996	−	1.20338i
$206$	15.0527	+	6.23850i	1.04877	+	0.434657i
$207$	−7.99358	−	3.25769i	−0.555592	−	0.226425i
$208$	8.36158	−	14.4564i	0.579771	−	1.00237i
$209$	−17.2350	+	3.03899i	−1.19217	+	0.210211i
$210$	−11.6817	+	5.79945i	−0.806115	+	0.400200i
$211$	3.08764	−	1.12381i	0.212562	−	0.0773662i	−0.233545	−	0.972346i	$-0.575032\pi$
$211$	3.08764	−	1.12381i	0.212562	−	0.0773662i	0.446107	+	0.894980i	$0.352810\pi$
$212$	−2.07723	−	23.8511i	−0.142665	−	1.63810i
$213$	9.25224	−	1.45111i	0.633953	−	0.0994287i
$214$	−3.07057	−	2.81477i	−0.209900	−	0.192414i
$215$	−28.7844			−1.96308
$216$	14.4370	+	2.75217i	0.982310	+	0.187261i
$217$	−2.64820			−0.179772
$218$	−20.8282	−	19.0930i	−1.41066	−	1.29314i
$219$	5.70893	−	14.8055i	0.385774	−	1.00046i
$220$	−16.2539	+	1.41558i	−1.09584	+	0.0954386i
$221$	1.96347	−	0.714644i	0.132077	−	0.0480721i
$222$	−20.1694	−	13.3993i	−1.35368	−	0.899305i
$223$	−13.8982	+	2.45063i	−0.930693	+	0.164106i	−0.618386	−	0.785875i	$-0.712213\pi$
$223$	−13.8982	+	2.45063i	−0.930693	+	0.164106i	−0.312307	+	0.949981i	$0.601102\pi$
$224$	4.60566	−	11.0882i	0.307729	−	0.740859i
$225$	1.81059	+	3.43014i	0.120706	+	0.228676i
$226$	6.07022	+	2.51577i	0.403785	+	0.167346i
$227$	1.45117	−	3.98706i	0.0963177	−	0.264631i	−0.882172	−	0.470928i	$-0.843919\pi$
$227$	1.45117	−	3.98706i	0.0963177	−	0.264631i	0.978489	+	0.206297i	$0.0661414\pi$
$228$	−17.9106	−	5.17265i	−1.18616	−	0.342567i
$229$	2.88614	−	3.43957i	0.190722	−	0.227293i	−0.662207	−	0.749321i	$-0.730380\pi$
$229$	2.88614	−	3.43957i	0.190722	−	0.227293i	0.852928	+	0.522028i	$0.174824\pi$
$230$	8.60796	+	5.48626i	0.567592	+	0.361753i
$231$	10.4648	−	5.78014i	0.688536	−	0.380306i
$232$	1.08798	−	0.0468582i	0.0714293	−	0.00307639i
$233$	13.0676	+	7.54460i	0.856089	+	0.494263i	0.862701	−	0.505715i	$-0.168771\pi$
$233$	13.0676	+	7.54460i	0.856089	+	0.494263i	−0.00661180	+	0.999978i	$0.502105\pi$
$234$	17.6543	+	1.44650i	1.15410	+	0.0945606i
$235$	4.05650	+	7.02606i	0.264617	+	0.458330i
$236$	−11.0528	+	5.14871i	−0.719476	+	0.335152i
$237$	4.75809	−	24.2827i	0.309071	−	1.57733i
$238$	1.33262	−	0.693384i	0.0863809	−	0.0449454i
$239$	2.20515	−	12.5060i	0.142639	−	0.808946i	−0.826593	−	0.562799i	$-0.809724\pi$
$239$	2.20515	−	12.5060i	0.142639	−	0.808946i	0.969233	−	0.246147i	$-0.0791646\pi$
$240$	−16.2111	−	6.26560i	−1.04642	−	0.404443i
$241$	7.55053	−	6.33565i	0.486373	−	0.408115i	−0.366352	−	0.930477i	$-0.619393\pi$
$241$	7.55053	−	6.33565i	0.486373	−	0.408115i	0.852724	+	0.522361i	$0.174949\pi$
$242$	−0.595667	+	0.0783018i	−0.0382909	+	0.00503343i
$243$	3.92097	+	15.0873i	0.251530	+	0.967849i
$244$	2.41329	+	9.02072i	0.154495	+	0.577492i
$245$	4.79461	−	4.02316i	0.306316	−	0.257030i
$246$	−12.3463	+	12.9660i	−0.787172	+	0.826679i
$247$	−22.1275	−	3.90168i	−1.40794	−	0.248258i
$248$	−2.38261	−	2.60325i	−0.151296	−	0.165307i
$249$	−4.60767	+	23.5151i	−0.291999	+	1.49021i
$250$	3.95226	+	12.5436i	0.249963	+	0.793326i
$251$	−11.6620	+	6.73304i	−0.736097	+	0.424986i	−0.820649	−	0.571433i	$-0.806388\pi$
$251$	−11.6620	+	6.73304i	−0.736097	+	0.424986i	0.0845514	+	0.996419i	$0.473054\pi$
$252$	12.7197	−	0.623136i	0.801266	−	0.0392539i
$253$	−8.10327	−	4.67842i	−0.509448	−	0.294130i
$254$	−5.26987	+	23.7487i	−0.330661	+	1.49013i
$255$	−1.05134	−	1.90344i	−0.0658377	−	0.119198i
$256$	15.0437	−	5.44863i	0.940230	−	0.340539i
$257$	9.56428	−	11.3983i	0.596603	−	0.711004i	−0.380258	−	0.924881i	$-0.624165\pi$
$257$	9.56428	−	11.3983i	0.596603	−	0.711004i	0.976861	+	0.213877i	$0.0686091\pi$
$258$	25.7563	+	11.2514i	1.60352	+	0.700481i
$259$	−19.7167	−	7.17629i	−1.22514	−	0.445913i
$260$	−20.2311	−	5.42945i	−1.25468	−	0.336720i
$261$	0.539183	+	1.02147i	0.0333746	+	0.0632277i
$262$	−19.4647	+	14.9297i	−1.20254	+	0.922362i
$263$	3.85332	+	21.8533i	0.237606	+	1.34753i	0.837056	+	0.547118i	$0.184275\pi$
$263$	3.85332	+	21.8533i	0.237606	+	1.34753i	−0.599450	+	0.800412i	$0.704614\pi$
$264$	15.0973	+	5.08675i	0.929176	+	0.313068i
$265$	−28.2182	+	10.2706i	−1.73343	+	0.630917i
$266$	−16.1383	−	0.707799i	−0.989505	−	0.0433980i
$267$	24.0813	+	9.28564i	1.47375	+	0.568272i
$268$	−14.0834	+	20.0963i	−0.860281	+	1.22758i
$269$	6.95017			0.423760			0.211880	−	0.977296i	$-0.432041\pi$
$269$	6.95017			0.423760			0.211880	+	0.977296i	$0.432041\pi$
$270$	−1.35957	−	18.3839i	−0.0827406	−	1.11881i
$271$		−	18.3855i		−	1.11684i	−0.829559	−	0.558419i	$-0.811408\pi$
$271$		−	18.3855i		−	1.11684i	0.829559	−	0.558419i	$-0.188592\pi$
$272$	1.88058	+	0.686154i	0.114027	+	0.0416042i
$273$	15.1634	−	2.37822i	0.917731	−	0.143936i
$274$	−3.33571	−	0.146298i	−0.201517	−	0.00883820i
$275$	1.43800	+	3.95086i	0.0867144	+	0.238246i
$276$	−5.55790	−	8.27383i	−0.334547	−	0.498026i
$277$	−11.8225	+	2.08462i	−0.710343	+	0.125253i	−0.517133	−	0.855905i	$-0.673001\pi$
$277$	−11.8225	+	2.08462i	−0.710343	+	0.125253i	−0.193210	+	0.981157i	$0.561890\pi$
$278$	−2.74547	−	3.57942i	−0.164662	−	0.214680i
$279$	1.41263	−	3.46626i	0.0845721	−	0.207519i
$280$	−14.9297	−	1.97451i	−0.892220	−	0.117999i
$281$	3.95786	−	10.8741i	0.236106	−	0.648696i	−0.763888	−	0.645348i	$-0.776712\pi$
$281$	3.95786	−	10.8741i	0.236106	−	0.648696i	0.999994	−	0.00334740i	$-0.00106551\pi$
$282$	−0.883371	−	7.87254i	−0.0526040	−	0.468803i
$283$	2.63822	+	2.21373i	0.156826	+	0.131593i	0.717824	−	0.696224i	$-0.245138\pi$
$283$	2.63822	+	2.21373i	0.156826	+	0.131593i	−0.560998	+	0.827817i	$0.689583\pi$
$284$	9.79916	+	4.57412i	0.581473	+	0.271424i
$285$	−0.443339	+	23.3788i	−0.0262611	+	1.38484i
$286$	18.7451	+	4.15956i	1.10842	+	0.245960i
$287$	−7.75688	+	13.4353i	−0.457874	+	0.793061i
$288$	12.0566	+	11.9431i	0.710441	+	0.703757i
$289$	−8.37477	−	14.5055i	−0.492633	−	0.853266i
$290$	−0.410476	−	1.30276i	−0.0241040	−	0.0765007i
$291$	0.287606	+	0.839378i	0.0168598	+	0.0492052i
$292$	15.0133	−	10.5036i	0.878589	−	0.614679i
$293$	−4.70231	+	26.6681i	−0.274712	+	1.55797i	0.465164	+	0.885224i	$0.345995\pi$
$293$	−4.70231	+	26.6681i	−0.274712	+	1.55797i	−0.739876	+	0.672743i	$0.765116\pi$
$294$	−5.86281	+	1.72578i	−0.341926	+	0.100649i
$295$	9.83059	+	11.7156i	0.572359	+	0.682111i
$296$	−10.6848	−	25.8386i	−0.621042	−	1.50184i
$297$	1.98342	+	16.7808i	0.115090	+	0.973722i
$298$	−28.2653	+	3.71553i	−1.63736	+	0.215235i
$299$	−7.72182	−	9.20251i	−0.446564	−	0.532195i
$300$	−0.476621	+	4.45328i	−0.0275178	+	0.257110i
$301$	23.9845	+	4.22911i	1.38244	+	0.243762i
$302$	0.554318	+	1.06535i	0.0318974	+	0.0613039i
$303$	−14.9739	+	17.1732i	−0.860229	+	0.986572i
$304$	−13.8240	−	16.5012i	−0.792862	−	0.946409i
$305$	10.1433	−	5.85621i	0.580801	−	0.335326i
$306$	0.196717	+	2.11415i	0.0112456	+	0.120858i
$307$	3.55520	−	6.15780i	0.202906	−	0.351444i	−0.746557	−	0.665321i	$-0.768295\pi$
$307$	3.55520	−	6.15780i	0.202906	−	0.351444i	0.949464	+	0.313877i	$0.101628\pi$
$308$	13.7515	+	1.20856i	0.783563	+	0.0688639i
$309$	−10.3040	+	17.0903i	−0.586175	+	0.972236i
$310$	−2.37901	+	3.73267i	−0.135119	+	0.212002i
$311$	3.90024	+	3.27269i	0.221162	+	0.185577i	0.746636	−	0.665232i	$-0.231668\pi$
$311$	3.90024	+	3.27269i	0.221162	+	0.185577i	−0.525474	+	0.850810i	$0.676112\pi$
$312$	15.9805	+	12.7663i	0.904717	+	0.722749i
$313$	22.0859	+	8.03860i	1.24837	+	0.454369i	0.879850	−	0.475252i	$-0.157643\pi$
$313$	22.0859	+	8.03860i	1.24837	+	0.454369i	0.368518	+	0.929621i	$0.379865\pi$
$314$	−9.75892	−	4.04453i	−0.550728	−	0.228246i
$315$	−4.89017	−	15.2063i	−0.275530	−	0.856776i
$316$	20.2118	−	20.1958i	1.13700	−	1.13610i
$317$	1.74582	+	9.90105i	0.0980551	+	0.556098i	0.993768	+	0.111466i	$0.0355546\pi$
$317$	1.74582	+	9.90105i	0.0980551	+	0.556098i	−0.895713	+	0.444632i	$0.853334\pi$
$318$	29.2642	+	1.83995i	1.64106	+	0.103179i
$319$	0.428226	+	1.17654i	0.0239761	+	0.0658737i
$320$	−11.4914	−	16.4527i	−0.642388	−	0.919737i
$321$	3.96958	−	3.20460i	0.221560	−	0.178863i
$322$	−6.36648	−	5.83611i	−0.354790	−	0.325234i
$323$		−	2.69331i		−	0.149860i
$324$	−5.96945	+	16.9813i	−0.331636	+	0.943407i
$325$			5.39795i			0.299424i
$326$	−5.04162	+	5.49979i	−0.279229	+	0.304605i
$327$	26.9263	−	21.7373i	1.48903	−	1.20208i
$328$	−20.1862	+	4.46266i	−1.11459	+	0.246409i
$329$	−2.34776	−	6.45042i	−0.129436	−	0.355623i
$330$	1.25388	−	19.9429i	0.0690241	−	1.09782i
$331$	−0.758072	−	4.29924i	−0.0416674	−	0.236308i	0.956861	−	0.290548i	$-0.0938375\pi$
$331$	−0.758072	−	4.29924i	−0.0416674	−	0.236308i	−0.998528	+	0.0542401i	$0.982726\pi$
$332$	−19.5728	+	19.5574i	−1.07420	+	1.07335i
$333$	19.9106	−	21.9793i	1.09109	−	1.20446i
$334$	−2.11398	+	5.10076i	−0.115672	+	0.279101i
$335$	28.9236	+	10.5273i	1.58027	+	0.575170i
$336$	12.5873	+	7.60258i	0.686693	+	0.414755i
$337$	−15.2139	−	12.7660i	−0.828757	−	0.695409i	0.126249	−	0.991999i	$-0.459706\pi$
$337$	−15.2139	−	12.7660i	−0.828757	−	0.695409i	−0.955005	+	0.296589i	$0.904151\pi$
$338$	5.28486	+	3.36829i	0.287459	+	0.183211i
$339$	−4.15525	+	6.89195i	−0.225682	+	0.374319i
$340$	0.219823	−	2.50124i	0.0119216	−	0.135649i
$341$	2.02871	−	3.51382i	0.109861	−	0.190284i
$342$	9.53513	−	20.7461i	0.515601	−	1.12182i
$343$	−17.4531	+	10.0766i	−0.942380	+	0.544083i
$344$	17.4217	+	27.3823i	0.939316	+	1.47635i
$345$	−8.21611	+	9.42283i	−0.442341	+	0.507308i
$346$	−1.56918	+	0.816473i	−0.0843598	+	0.0438938i
$347$	13.3624	+	2.35616i	0.717334	+	0.126485i	0.520389	−	0.853929i	$-0.325787\pi$
$347$	13.3624	+	2.35616i	0.717334	+	0.126485i	0.196945	+	0.980415i	$0.436898\pi$
$348$	−0.141935	+	1.32616i	−0.00760850	+	0.0710895i
$349$	−20.5757	−	24.5212i	−1.10139	−	1.31259i	−0.945794	−	0.324767i	$-0.894714\pi$
$349$	−20.5757	−	24.5212i	−1.10139	−	1.31259i	−0.155598	−	0.987820i	$-0.549730\pi$
$350$	0.505791	+	3.84772i	0.0270357	+	0.205669i
$351$	−4.97575	+	21.1161i	−0.265586	+	1.12710i
$352$	11.1843	+	14.6054i	0.596124	+	0.778470i
$353$	−2.68155	−	3.19575i	−0.142725	−	0.170093i	0.689947	−	0.723860i	$-0.257634\pi$
$353$	−2.68155	−	3.19575i	−0.142725	−	0.170093i	−0.832671	+	0.553768i	$0.813190\pi$
$354$	−4.21694	−	14.3258i	−0.224128	−	0.761406i
$355$	2.35537	−	13.3579i	0.125010	−	0.708966i
$356$	17.0843	+	24.4194i	0.905465	+	1.29422i
$357$	0.596368	+	1.74050i	0.0315631	+	0.0921169i
$358$	−18.1006	+	5.70318i	−0.956646	+	0.301422i
$359$	5.32400	+	9.22145i	0.280990	+	0.486689i	0.971629	−	0.236511i	$-0.0760038\pi$
$359$	5.32400	+	9.22145i	0.280990	+	0.486689i	−0.690639	+	0.723200i	$0.742670\pi$
$360$	10.5484	−	18.4884i	0.555950	−	0.974422i
$361$	−4.98105	+	8.62742i	−0.262160	+	0.454075i
$362$	0.976122	−	4.39890i	0.0513039	−	0.231201i
$363$	0.0139510	−	0.735684i	0.000732237	−	0.0386134i
$364$	16.0598	+	7.49649i	0.841760	+	0.392923i
$365$	−17.6052	−	14.7726i	−0.921501	−	0.773231i
$366$	−11.3653	+	1.27529i	−0.594073	+	0.0666604i
$367$	1.17353	−	3.22425i	0.0612578	−	0.168304i	−0.905288	−	0.424798i	$-0.860345\pi$
$367$	1.17353	−	3.22425i	0.0612578	−	0.168304i	0.966546	+	0.256494i	$0.0825673\pi$
$368$	0.00906503	−	11.5092i	0.000472547	−	0.599959i
$369$	−13.4478	−	17.3198i	−0.700066	−	0.901635i
$370$	−27.8275	+	21.3441i	−1.44668	+	1.10963i
$371$	25.0217	−	4.41199i	1.29906	−	0.229059i
$372$	3.58778	−	2.41007i	0.186018	−	0.124957i
$373$	4.78365	+	13.1430i	0.247688	+	0.680517i	0.999770	+	0.0214474i	$0.00682744\pi$
$373$	4.78365	+	13.1430i	0.247688	+	0.680517i	−0.752082	+	0.659069i	$0.770950\pi$
$374$	−0.100847	+	2.29939i	−0.00521469	+	0.118899i
$375$	−15.9127	+	2.49574i	−0.821729	+	0.128879i
$376$	4.22862	−	8.11141i	0.218075	−	0.418314i
$377$			1.60747i			0.0827891i
$378$	−1.56818	+	15.5180i	−0.0806583	+	0.798162i
$379$	−3.34127			−0.171629			−0.0858147	−	0.996311i	$-0.527349\pi$
$379$	−3.34127			−0.171629			−0.0858147	+	0.996311i	$0.527349\pi$
$380$	−15.4955	+	22.1113i	−0.794902	+	1.13429i
$381$	−27.7986	−	10.7190i	−1.42417	−	0.549151i
$382$	0.189478	−	4.32024i	0.00969454	−	0.221043i
$383$	11.8647	−	4.31841i	0.606260	−	0.220660i	−0.0206063	−	0.999788i	$-0.506560\pi$
$383$	11.8647	−	4.31841i	0.606260	−	0.220660i	0.626866	+	0.779127i	$0.284337\pi$
$384$	3.85136	+	19.2137i	0.196539	+	0.980496i
$385$	−3.00667	−	17.0517i	−0.153234	−	0.869033i
$386$	7.19878	+	9.38546i	0.366408	+	0.477707i
$387$	−18.3296	+	29.1376i	−0.931744	+	1.48115i
$388$	−0.265562	+	0.989532i	−0.0134819	+	0.0502359i
$389$	−33.8930	−	12.3361i	−1.71845	−	0.625463i	−0.720743	−	0.693203i	$-0.756199\pi$
$389$	−33.8930	−	12.3361i	−1.71845	−	0.625463i	−0.997703	+	0.0677397i	$0.978421\pi$
$390$	10.2699	−	23.5094i	0.520036	−	1.19045i
$391$	0.925603	−	1.10309i	0.0468097	−	0.0557857i
$392$	−6.72911	−	2.12605i	−0.339872	−	0.107382i
$393$	−14.5261	−	26.2993i	−0.732746	−	1.32662i
$394$	−8.90184	−	1.97533i	−0.448468	−	0.0995157i
$395$	−31.0366	−	17.9190i	−1.56162	−	0.901601i
$396$	−8.91734	+	17.3547i	−0.448113	+	0.872109i
$397$	−15.9084	+	9.18470i	−0.798418	+	0.460967i	−0.842918	−	0.538042i	$-0.819164\pi$
$397$	−15.9084	+	9.18470i	−0.798418	+	0.460967i	0.0444994	+	0.999009i	$0.485831\pi$
$398$	−9.89068	+	3.11638i	−0.495775	+	0.156210i
$399$	3.80431	−	19.4151i	0.190454	−	0.971973i
$400$	−3.32734	+	3.95903i	−0.166367	+	0.197952i
$401$	6.51556	+	1.14887i	0.325372	+	0.0573718i	0.333948	−	0.942591i	$-0.391619\pi$
$401$	6.51556	+	1.14887i	0.325372	+	0.0573718i	−0.00857653	+	0.999963i	$0.502730\pi$
$402$	−21.7659	−	20.7257i	−1.08558	−	1.03370i
$403$	3.99048	−	3.34841i	0.198780	−	0.166796i
$404$	−25.4155	+	6.79935i	−1.26447	+	0.338280i
$405$	22.5122	+	1.71069i	1.11864	+	0.0850051i
$406$	0.150621	+	1.14583i	0.00747521	+	0.0568664i
$407$	24.6263	−	20.6640i	1.22068	−	1.02427i
$408$	−1.17440	+	2.15218i	−0.0581412	+	0.106549i
$409$	0.528720	−	2.99852i	0.0261435	−	0.148267i	−0.968942	−	0.247289i	$-0.920460\pi$
$409$	0.528720	−	2.99852i	0.0261435	−	0.148267i	0.995085	+	0.0990218i	$0.0315714\pi$
$410$	11.9688	+	23.0030i	0.591099	+	1.13604i
$411$	0.786330	−	4.01300i	0.0387868	−	0.197947i
$412$	−20.8884	+	9.73039i	−1.02910	+	0.479382i
$413$	−6.46998	−	11.2063i	−0.318367	−	0.551428i
$414$	11.0350	−	5.21998i	0.542341	−	0.256548i
$415$	30.0554	+	17.3525i	1.47536	+	0.851801i
$416$	7.07986	+	22.5318i	0.347119	+	1.10471i
$417$	4.83624	−	2.67125i	0.236832	−	0.130812i
$418$	13.3022	−	20.8712i	0.650633	−	1.02085i
$419$	−17.1887	+	20.4847i	−0.839723	+	1.00074i	0.160183	+	0.987087i	$0.448791\pi$
$419$	−17.1887	+	20.4847i	−0.839723	+	1.00074i	−0.999907	+	0.0136562i	$0.995653\pi$
$420$	5.11764	−	17.7201i	0.249715	−	0.864652i
$421$	10.4312	−	28.6596i	0.508387	−	1.39678i	−0.374513	−	0.927222i	$-0.622190\pi$
$421$	10.4312	−	28.6596i	0.508387	−	1.39678i	0.882900	−	0.469560i	$-0.155588\pi$
$422$	−1.77911	+	4.29275i	−0.0866056	+	0.208968i
$423$	9.69538	+	0.367845i	0.471406	+	0.0178852i
$424$	26.8493	+	20.6274i	1.30392	+	1.00176i
$425$	−0.637214	+	0.112358i	−0.0309094	+	0.00545016i
$426$	−7.32900	+	11.0320i	−0.355091	+	0.534502i
$427$	−9.31223	+	3.38938i	−0.450651	+	0.164023i
$428$	5.86868	−	0.511114i	0.283673	−	0.0247056i
$429$	−8.46062	+	21.9417i	−0.408482	+	1.05936i
$430$	27.5074	−	30.0072i	1.32652	−	1.44707i
$431$	9.80169			0.472131			0.236065	−	0.971737i	$-0.424142\pi$
$431$	9.80169			0.472131			0.236065	+	0.971737i	$0.424142\pi$
$432$	−16.6655	+	12.4202i	−0.801820	+	0.597565i
$433$	−17.0457			−0.819163			−0.409582	−	0.912273i	$-0.634325\pi$
$433$	−17.0457			−0.819163			−0.409582	+	0.912273i	$0.634325\pi$
$434$	2.53071	−	2.76070i	0.121478	−	0.132518i
$435$	1.65267	−	0.259204i	0.0792395	−	0.0124279i
$436$	39.8082	−	3.46697i	1.90647	−	0.166038i
$437$	−14.5508	+	5.29605i	−0.696058	+	0.253345i
$438$	9.97879	+	20.1001i	0.476805	+	0.960420i
$439$	1.11745	−	0.197037i	0.0533332	−	0.00940408i	−0.146918	−	0.989149i	$-0.546935\pi$
$439$	1.11745	−	0.197037i	0.0533332	−	0.00940408i	0.200251	+	0.979745i	$0.435824\pi$
$440$	14.0571	−	18.2972i	0.670145	−	0.872283i
$441$	−1.01936	−	7.41533i	−0.0485411	−	0.353111i
$442$	−1.13136	+	2.72981i	−0.0538131	+	0.129844i
$443$	−4.36044	+	11.9802i	−0.207171	+	0.569198i	−0.999144	−	0.0413580i	$-0.986832\pi$
$443$	−4.36044	+	11.9802i	−0.207171	+	0.569198i	0.791973	+	0.610556i	$0.209054\pi$
$444$	33.2431	−	8.22133i	1.57765	−	0.390167i
$445$	24.0277	−	28.6351i	1.13902	−	1.35743i
$446$	10.7269	−	16.8305i	0.507932	−	0.796947i
$447$	0.661994	−	34.9093i	0.0313113	−	1.65115i
$448$	7.15785	+	15.3975i	0.338177	+	0.727465i
$449$	−9.50475	−	5.48757i	−0.448557	−	0.258974i	0.258664	−	0.965967i	$-0.416718\pi$
$449$	−9.50475	−	5.48757i	−0.448557	−	0.258974i	−0.707221	+	0.706993i	$0.750051\pi$
$450$	−5.30612	−	1.39046i	−0.250133	−	0.0655467i
$451$	−11.8846	−	20.5847i	−0.559624	−	0.969297i
$452$	−8.42355	+	3.92393i	−0.396210	+	0.184566i
$453$	−1.39142	+	0.476759i	−0.0653746	+	0.0224001i
$454$	2.76964	+	5.32299i	0.129986	+	0.249820i
$455$	3.86019	−	21.8922i	0.180968	−	1.02632i
$456$	22.5083	−	13.7282i	1.05405	−	0.642884i
$457$	−1.04379	+	0.875846i	−0.0488265	+	0.0409703i	−0.666874	−	0.745170i	$-0.732368\pi$
$457$	−1.04379	+	0.875846i	−0.0488265	+	0.0409703i	0.618048	+	0.786140i	$0.287924\pi$
$458$	0.827586	+	6.29572i	0.0386705	+	0.294180i
$459$	−2.59627	−	0.147843i	−0.121184	−	0.00690073i
$460$	−13.9454	+	3.73077i	−0.650207	+	0.173948i
$461$	−12.1576	+	10.2015i	−0.566237	+	0.475129i	−0.880395	−	0.474242i	$-0.842722\pi$
$461$	−12.1576	+	10.2015i	−0.566237	+	0.475129i	0.314158	+	0.949371i	$0.398278\pi$
$462$	−3.97487	+	16.4331i	−0.184928	+	0.764536i
$463$	3.06325	+	0.540133i	0.142361	+	0.0251021i	0.244375	−	0.969681i	$-0.421417\pi$
$463$	3.06325	+	0.540133i	0.142361	+	0.0251021i	−0.102013	+	0.994783i	$0.532528\pi$
$464$	−0.990860	+	1.17897i	−0.0459995	+	0.0547325i
$465$	−4.08602	−	3.56275i	−0.189485	−	0.165219i
$466$	−20.3530	+	6.41286i	−0.942833	+	0.297070i
$467$	26.1173	−	15.0788i	1.20857	−	0.697766i	0.246120	−	0.969239i	$-0.420844\pi$
$467$	26.1173	−	15.0788i	1.20857	−	0.697766i	0.962446	+	0.271474i	$0.0875111\pi$
$468$	−18.3790	+	17.0219i	−0.849568	+	0.786837i
$469$	−22.5538	−	13.0214i	−1.04144	−	0.601273i
$470$	−11.2010	−	2.48553i	−0.516666	−	0.114649i
$471$	6.68028	−	11.0800i	0.307811	−	0.510539i
$472$	5.19501	−	16.4426i	0.239120	−	0.756832i
$473$	−23.9852	+	28.5845i	−1.10284	+	1.31432i
$474$	20.7672	+	28.1656i	0.953871	+	1.29369i
$475$	6.53827	+	2.37974i	0.299997	+	0.109190i
$476$	−0.550658	+	2.05185i	−0.0252394	+	0.0940464i
$477$	−7.57241	+	35.1046i	−0.346717	+	1.60733i
$478$	10.9299	+	14.2500i	0.499924	+	0.651779i
$479$	4.70699	+	26.6947i	0.215068	+	1.21971i	0.880789	+	0.473510i	$0.157013\pi$
$479$	4.70699	+	26.6947i	0.215068	+	1.21971i	−0.665721	+	0.746201i	$0.731876\pi$
$480$	22.0237	−	10.9122i	1.00524	−	0.498069i
$481$	38.7842	−	14.1163i	1.76841	−	0.643647i
$482$	−0.610763	+	13.9258i	−0.0278195	+	0.634305i
$483$	8.23047	−	6.64438i	0.374499	−	0.302330i
$484$	0.487612	−	0.695799i	0.0221642	−	0.0316272i
$485$	1.28507			0.0583521
$486$	−19.4752	−	10.3304i	−0.883413	−	0.468596i
$487$		−	12.4692i		−	0.565032i	−0.959263	−	0.282516i	$-0.908831\pi$
$487$		−	12.4692i		−	0.565032i	0.959263	−	0.282516i	$-0.0911691\pi$
$488$	−11.7101	−	6.10471i	−0.530093	−	0.276347i
$489$	−5.73986	−	7.11002i	−0.259565	−	0.321526i
$490$	−0.387836	+	8.84295i	−0.0175206	+	0.399484i
$491$	−7.94617	−	21.8319i	−0.358606	−	0.985261i	−0.979514	−	0.201377i	$-0.935458\pi$
$491$	−7.94617	−	21.8319i	−0.358606	−	0.985261i	0.620908	−	0.783883i	$-0.286764\pi$
$492$	−1.71819	−	25.2615i	−0.0774621	−	1.13888i
$493$	−0.189758	+	0.0334595i	−0.00854628	+	0.00150694i
$494$	25.2132	−	19.3389i	1.13440	−	0.870099i
$495$	23.9229	+	5.16042i	1.07526	+	0.231944i
$496$	4.99074	+	0.00393087i	0.224091	+	0.000176501i
$497$	−3.92519	+	10.7844i	−0.176069	+	0.483745i
$498$	−20.1107	−	27.2752i	−0.901183	−	1.22223i
$499$	2.97245	+	2.49418i	0.133065	+	0.111655i	0.706891	−	0.707322i	$-0.250097\pi$
$499$	2.97245	+	2.49418i	0.133065	+	0.111655i	−0.573826	+	0.818977i	$0.694542\pi$
$500$	−16.8534	−	7.86693i	−0.753705	−	0.351820i
$501$	−5.79125	−	3.49163i	−0.258734	−	0.155994i
$502$	4.12552	−	18.5917i	0.184131	−	0.829788i
$503$	−4.27407	+	7.40291i	−0.190571	+	0.330079i	−0.945440	−	0.325797i	$-0.894367\pi$
$503$	−4.27407	+	7.40291i	−0.190571	+	0.330079i	0.754868	+	0.655876i	$0.227701\pi$
$504$	−11.5058	+	13.8555i	−0.512508	+	0.617174i
$505$	16.4997	+	28.5782i	0.734225	+	1.27172i
$506$	12.6209	−	3.97663i	0.561068	−	0.176783i
$507$	−5.04428	+	5.78515i	−0.224025	+	0.256927i
$508$	−19.7215	−	28.1888i	−0.874999	−	1.25068i
$509$	−0.382218	+	2.16767i	−0.0169415	+	0.0960802i	−0.992106	−	0.125401i	$-0.959978\pi$
$509$	−0.382218	+	2.16767i	−0.0169415	+	0.0960802i	0.975165	+	0.221482i	$0.0710893\pi$
$510$	2.98900	+	0.722985i	0.132355	+	0.0320143i
$511$	12.4990	+	14.8958i	0.552925	+	0.658951i
$512$	−8.69617	+	20.8896i	−0.384320	+	0.923200i
$513$	23.3833	+	15.3361i	1.03240	+	0.677106i
$514$	2.74250	+	20.8631i	0.120967	+	0.920233i
$515$	18.5785	+	22.1410i	0.818668	+	0.975651i
$516$	−36.3429	+	16.0982i	−1.59991	+	0.708683i
$517$	10.3574	+	1.82629i	0.455519	+	0.0803202i
$518$	26.3231	−	13.6963i	1.15657	−	0.601783i
$519$	−0.702234	−	2.04947i	−0.0308246	−	0.0899616i
$520$	24.9936	−	15.9019i	1.09604	−	0.697346i
$521$	0.771434	−	0.445388i	0.0337971	−	0.0195128i	−0.483006	−	0.875617i	$-0.660455\pi$
$521$	0.771434	−	0.445388i	0.0337971	−	0.0195128i	0.516803	+	0.856104i	$0.327122\pi$
$522$	−1.58013	−	0.414069i	−0.0691603	−	0.0181233i
$523$	−3.36736	+	5.83244i	−0.147244	+	0.255035i	−0.930208	−	0.367033i	$-0.880374\pi$
$523$	−3.36736	+	5.83244i	−0.147244	+	0.255035i	0.782964	+	0.622067i	$0.213707\pi$
$524$	3.03723	−	34.5589i	0.132682	−	1.50971i
$525$	−4.75216	−	0.0901165i	−0.207401	−	0.00393301i
$526$	−26.4639	−	16.8667i	−1.15388	−	0.735424i
$527$	0.478333	+	0.401369i	0.0208365	+	0.0174839i
$528$	−19.7303	+	10.8776i	−0.858653	+	0.473386i
$529$	13.8333	+	5.03492i	0.601449	+	0.218910i
$530$	16.2594	−	39.2318i	0.706263	−	1.70412i
$531$	18.1194	−	2.49082i	0.786313	−	0.108092i
$532$	16.1602	−	16.1475i	0.700634	−	0.700083i
$533$	−5.29916	−	30.0530i	−0.229532	−	1.30174i
$534$	−32.6930	+	16.2306i	−1.41477	+	0.702367i
$535$	−2.52713	−	6.94324i	−0.109258	−	0.300183i
$536$	−7.49143	−	33.8864i	−0.323581	−	1.46367i
$537$	−3.60139	−	22.9623i	−0.155411	−	0.990895i
$538$	−6.64182	+	7.24541i	−0.286349	+	0.312372i
$539$		−	8.11368i		−	0.349481i
$540$	20.4641	+	16.1510i	0.880634	+	0.695027i
$541$			29.9430i			1.28735i	0.765299	+	0.643675i	$0.222591\pi$
$541$			29.9430i			1.28735i	−0.765299	+	0.643675i	$0.777409\pi$
$542$	19.1665	+	17.5698i	0.823270	+	0.754687i
$543$	5.14905	+	1.98545i	0.220967	+	0.0852038i
$544$	−2.51245	+	1.30476i	−0.107720	+	0.0559410i
$545$	−17.1420	−	47.0971i	−0.734281	−	2.01742i
$546$	−12.0114	+	18.0802i	−0.514041	+	0.773763i
$547$	0.156388	+	0.886918i	0.00668665	+	0.0379219i	0.987969	−	0.154655i	$-0.0494266\pi$
$547$	0.156388	+	0.886918i	0.00668665	+	0.0379219i	−0.981282	+	0.192577i	$0.938316\pi$
$548$	3.34023	−	3.33760i	0.142687	−	0.142575i
$549$	0.531043	−	13.9969i	0.0226644	−	0.597371i
$550$	−5.49289	−	2.27650i	−0.234218	−	0.0970702i
$551$	1.94706	+	0.708670i	0.0829473	+	0.0301904i
$552$	13.9366	+	2.11275i	0.593182	+	0.0899246i
$553$	23.2283	+	19.4909i	0.987770	+	0.828837i
$554$	9.12478	−	14.3168i	0.387675	−	0.608263i
$555$	−20.7671	−	37.5984i	−0.881514	−	1.59596i
$556$	6.35514	+	0.558525i	0.269518	+	0.0236867i
$557$	−2.99133	+	5.18113i	−0.126747	+	0.219531i	−0.922414	−	0.386202i	$-0.873787\pi$
$557$	−2.99133	+	5.18113i	−0.126747	+	0.219531i	0.795668	+	0.605733i	$0.207120\pi$
$558$	2.26354	+	4.78511i	0.0958234	+	0.202570i
$559$	−41.4887	+	23.9535i	−1.75478	+	1.01313i
$560$	16.3257	−	13.6770i	0.689887	−	0.577959i
$561$	−2.76627	−	0.542038i	−0.116792	−	0.0228849i
$562$	7.55378	+	14.5177i	0.318637	+	0.612391i
$563$	33.0591	+	5.82922i	1.39328	+	0.245672i	0.819378	−	0.573254i	$-0.194319\pi$
$563$	33.0591	+	5.82922i	1.39328	+	0.245672i	0.573899	+	0.818926i	$0.305430\pi$
$564$	9.05114	+	6.60237i	0.381122	+	0.278010i
$565$	7.49208	+	8.92871i	0.315194	+	0.375634i
$566$	−4.82894	+	0.634775i	−0.202976	+	0.0266816i
$567$	−18.5068	−	4.73300i	−0.777213	−	0.198767i
$568$	−14.1328	+	5.84424i	−0.593001	+	0.245219i
$569$	14.2778	+	17.0156i	0.598557	+	0.713332i	0.977226	−	0.212200i	$-0.0680628\pi$
$569$	14.2778	+	17.0156i	0.598557	+	0.713332i	−0.378670	+	0.925532i	$0.623618\pi$
$570$	−23.9483	−	22.8038i	−1.00308	−	0.955145i
$571$	−5.16056	+	29.2670i	−0.215963	+	1.22479i	0.663265	+	0.748384i	$0.269170\pi$
$571$	−5.16056	+	29.2670i	−0.215963	+	1.22479i	−0.879228	+	0.476401i	$0.841941\pi$
$572$	−22.2497	+	15.5664i	−0.930308	+	0.650862i
$573$	5.19744	+	1.01841i	0.217126	+	0.0425449i
$574$	−6.59329	−	20.9256i	−0.275199	−	0.873419i
$575$	1.86002	+	3.22165i	0.0775683	+	0.134352i
$576$	−23.9722	+	1.15547i	−0.998840	+	0.0481444i
$577$	4.32870	−	7.49753i	0.180206	−	0.312126i	−0.761744	−	0.647878i	$-0.775657\pi$
$577$	4.32870	−	7.49753i	0.180206	−	0.312126i	0.941951	+	0.335751i	$0.108990\pi$
$578$	23.1249	+	5.13145i	0.961870	+	0.213440i
$579$	−12.6809	+	7.00417i	−0.527001	+	0.291083i
$580$	1.75036	+	0.817048i	0.0726799	+	0.0339261i
$581$	−22.4940	−	18.8747i	−0.933209	−	0.783056i
$582$	−1.14988	−	0.502315i	−0.0476641	−	0.0208216i
$583$	−13.3142	+	36.5804i	−0.551416	+	1.51500i
$584$	−3.39743	+	25.6887i	−0.140586	+	1.06301i
$585$	26.5958	+	16.7306i	1.09960	+	0.691725i
$586$	−23.3073	−	30.3870i	−0.962814	−	1.25528i
$587$	−35.9900	+	6.34601i	−1.48547	+	0.261928i	−0.856760	−	0.515715i	$-0.827527\pi$
$587$	−35.9900	+	6.34601i	−1.48547	+	0.261928i	−0.628707	+	0.777642i	$0.716415\pi$
$588$	3.80361	−	7.76107i	0.156858	−	0.320061i
$589$	−2.29653	−	6.30966i	−0.0946268	−	0.259985i
$590$	−21.6078	−	0.947678i	−0.889577	−	0.0390153i
$591$	4.01785	−	10.4199i	0.165272	−	0.428617i
$592$	37.1470	+	13.5535i	1.52673	+	0.557047i
$593$			10.8958i			0.447436i	0.974654	+	0.223718i	$0.0718194\pi$
$593$			10.8958i			0.447436i	−0.974654	+	0.223718i	$0.928181\pi$
$594$	−19.3891	−	13.9686i	−0.795544	−	0.573140i
$595$	2.66467			0.109241
$596$	23.1379	−	33.0167i	0.947765	−	1.35242i
$597$	−1.96790	−	12.5473i	−0.0805409	−	0.513525i
$598$	16.9727	+	0.744391i	0.694064	+	0.0304404i
$599$	30.9493	−	11.2646i	1.26455	−	0.460260i	0.379259	−	0.925291i	$-0.376179\pi$
$599$	30.9493	−	11.2646i	1.26455	−	0.460260i	0.885295	+	0.465031i	$0.153957\pi$
$600$	−4.18697	−	4.75257i	−0.170932	−	0.194023i
$601$	−0.286907	−	1.62713i	−0.0117032	−	0.0663720i	0.978397	−	0.206736i	$-0.0662840\pi$
$601$	−0.286907	−	1.62713i	−0.0117032	−	0.0663720i	−0.990100	+	0.140364i	$0.955173\pi$
$602$	−27.3291	+	20.9618i	−1.11385	+	0.854341i
$603$	29.0747	−	22.5748i	1.18401	−	0.919317i
$604$	−1.64033	−	0.440217i	−0.0667440	−	0.0179122i
$605$	−1.00143	−	0.364490i	−0.0407139	−	0.0148186i
$606$	−3.59308	−	32.0213i	−0.145959	−	1.30077i
$607$	−15.4385	+	18.3989i	−0.626628	+	0.746787i	−0.982195	−	0.187864i	$-0.939843\pi$
$607$	−15.4385	+	18.3989i	−0.626628	+	0.746787i	0.355567	+	0.934651i	$0.384288\pi$
$608$	30.4129	+	1.35786i	1.23341	+	0.0550683i
$609$	−1.41516	−	0.0268361i	−0.0573453	−	0.00108745i
$610$	−3.58826	+	16.1705i	−0.145284	+	0.654726i
$611$	11.6937	+	6.75138i	0.473078	+	0.273132i
$612$	−2.39195	−	1.81528i	−0.0966887	−	0.0733783i
$613$	33.2300	−	19.1854i	1.34215	−	0.774889i	0.355025	−	0.934857i	$-0.384472\pi$
$613$	33.2300	−	19.1854i	1.34215	−	0.774889i	0.987122	+	0.159968i	$0.0511390\pi$
$614$	3.02190	+	9.59083i	0.121954	+	0.387054i
$615$	−30.0436	+	10.2942i	−1.21147	+	0.415102i
$616$	−14.4013	+	13.1807i	−0.580244	+	0.531065i
$617$	−3.23994	−	0.571288i	−0.130435	−	0.0229992i	0.108050	−	0.994146i	$-0.465539\pi$
$617$	−3.23994	−	0.571288i	−0.130435	−	0.0229992i	−0.238484	+	0.971146i	$0.576651\pi$
$618$	−7.96946	−	27.0738i	−0.320579	−	1.08907i
$619$	−13.4224	+	11.2627i	−0.539493	+	0.452688i	−0.871364	−	0.490636i	$-0.836764\pi$
$619$	−13.4224	+	11.2627i	−0.539493	+	0.452688i	0.331872	+	0.943325i	$0.392320\pi$
$620$	−1.61777	−	6.04714i	−0.0649713	−	0.242859i
$621$	4.30651	+	14.3172i	0.172814	+	0.574531i
$622$	−7.13891	+	0.938426i	−0.286244	+	0.0376274i
$623$	−24.2281	+	20.3298i	−0.970680	+	0.814497i
$624$	−28.5801	+	4.45942i	−1.14412	+	0.178520i
$625$	−5.17348	+	29.3403i	−0.206939	+	1.17361i
$626$	−29.4861	+	15.3421i	−1.17850	+	0.613194i
$627$	22.8470	+	19.9211i	0.912421	+	0.795574i
$628$	13.5423	−	6.30839i	0.540397	−	0.251732i
$629$	2.47368	+	4.28454i	0.0986321	+	0.170836i
$630$	20.5254	+	9.43372i	0.817753	+	0.375848i
$631$	41.4323	+	23.9209i	1.64939	+	0.952277i	0.977314	+	0.211797i	$0.0679314\pi$
$631$	41.4323	+	23.9209i	1.64939	+	0.952277i	0.672078	+	0.740480i	$0.265402\pi$
$632$	1.73871	+	40.3702i	0.0691621	+	1.60584i
$633$	−4.87386	−	2.93852i	−0.193719	−	0.116796i
$634$	−11.9900	−	7.64180i	−0.476184	−	0.303494i
$635$	−27.7367	+	33.0554i	−1.10070	+	1.31176i
$636$	−29.8840	+	28.7490i	−1.18498	+	1.13997i
$637$	3.56281	−	9.78874i	0.141164	−	0.387844i
$638$	−1.63575	−	0.677926i	−0.0647599	−	0.0268394i
$639$	−12.0220	−	10.8904i	−0.475581	−	0.430819i
$640$	28.1332	+	3.74327i	1.11206	+	0.147966i
$641$	14.9095	−	2.62895i	0.588891	−	0.103837i	0.128740	−	0.991678i	$-0.458907\pi$
$641$	14.9095	−	2.62895i	0.588891	−	0.103837i	0.460150	+	0.887841i	$0.347796\pi$
$642$	−0.452731	+	7.20063i	−0.0178679	+	0.284186i
$643$	−6.97052	+	2.53706i	−0.274890	+	0.100052i	−0.475787	−	0.879561i	$-0.657837\pi$
$643$	−6.97052	+	2.53706i	−0.274890	+	0.100052i	0.200897	+	0.979612i	$0.435614\pi$
$644$	12.1681	−	1.05974i	0.479489	−	0.0417595i
$645$	31.3170	+	38.7927i	1.23311	+	1.52746i
$646$	2.80772	+	2.57382i	0.110468	+	0.101266i
$647$	6.00521			0.236089			0.118045	−	0.993008i	$-0.462337\pi$
$647$	6.00521			0.236089			0.118045	+	0.993008i	$0.462337\pi$
$648$	−11.9981	−	22.4510i	−0.471329	−	0.881957i
$649$	19.8258			0.778231
$650$	−5.62725	−	5.15846i	−0.220719	−	0.202332i
$651$	2.88120	+	3.56898i	0.112923	+	0.139879i
$652$	−0.915472	−	10.5116i	−0.0358526	−	0.411665i
$653$	37.1742	−	13.5303i	1.45474	−	0.529482i	0.510829	−	0.859683i	$-0.329339\pi$
$653$	37.1742	−	13.5303i	1.45474	−	0.529482i	0.943911	+	0.330201i	$0.107116\pi$
$654$	−3.07095	+	48.8430i	−0.120083	+	1.90991i
$655$	−42.8527	+	7.55608i	−1.67439	+	0.295241i
$656$	14.6384	−	25.3083i	0.571532	−	0.988124i
$657$	−26.1646	+	8.41425i	−1.02078	+	0.328271i
$658$	8.96804	+	3.71675i	0.349610	+	0.144894i
$659$	−6.31505	+	17.3504i	−0.245999	+	0.675877i	0.753824	+	0.657076i	$0.228207\pi$
$659$	−6.31505	+	17.3504i	−0.245999	+	0.675877i	−0.999823	+	0.0188010i	$0.994015\pi$
$660$	19.5918	+	20.3652i	0.762609	+	0.792716i
$661$	−12.6354	+	15.0583i	−0.491460	+	0.585699i	−0.953588	−	0.301114i	$-0.902642\pi$
$661$	−12.6354	+	15.0583i	−0.491460	+	0.585699i	0.462128	+	0.886813i	$0.347086\pi$
$662$	5.20631	+	3.31822i	0.202349	+	0.128966i
$663$	−3.09935	−	1.86864i	−0.120369	−	0.0725720i
$664$	−1.68374	−	39.0939i	−0.0653418	−	1.51714i
$665$	−24.8152	−	14.3270i	−0.962291	−	0.555579i
$666$	3.88573	+	41.7606i	0.150569	+	1.61819i
$667$	0.553902	+	0.959387i	0.0214472	+	0.0371476i
$668$	−3.29725	−	7.07825i	−0.127574	−	0.273866i
$669$	18.4237	+	16.0643i	0.712303	+	0.621083i
$670$	−38.6150	+	20.0920i	−1.49183	+	0.776222i
$671$	2.63655	−	14.9526i	0.101783	−	0.577239i
$672$	−19.9544	+	5.85670i	−0.769757	+	0.225927i
$673$	−37.6088	+	31.5575i	−1.44971	+	1.21645i	−0.516921	+	0.856033i	$0.672922\pi$
$673$	−37.6088	+	31.5575i	−1.44971	+	1.21645i	−0.932790	+	0.360420i	$0.882633\pi$
$674$	27.8473	−	3.66059i	1.07264	−	0.141000i
$675$	2.65290	−	6.17207i	0.102110	−	0.237563i
$676$	−8.56177	+	2.29051i	−0.329299	+	0.0880964i
$677$	−11.6959	+	9.81403i	−0.449510	+	0.377184i	−0.839254	−	0.543739i	$-0.817008\pi$
$677$	−11.6959	+	9.81403i	−0.449510	+	0.377184i	0.389744	+	0.920923i	$0.372564\pi$
$678$	−3.21381	−	10.9179i	−0.123426	−	0.419301i
$679$	−1.07078	−	0.188807i	−0.0410927	−	0.00724576i
$680$	2.39742	+	2.61943i	0.0919370	+	0.100451i
$681$	−6.95221	+	2.38212i	−0.266409	+	0.0912830i
$682$	1.72439	+	5.47281i	0.0660301	+	0.209565i
$683$	3.01291	−	1.73950i	0.115286	−	0.0665602i	−0.441248	−	0.897385i	$-0.645464\pi$
$683$	3.01291	−	1.73950i	0.115286	−	0.0665602i	0.556534	+	0.830825i	$0.312131\pi$
$684$	12.5152	+	29.7658i	0.478533	+	1.13812i
$685$	−5.12916	−	2.96132i	−0.195975	−	0.113146i
$686$	6.17418	−	27.8240i	0.235731	−	1.06233i
$687$	−7.77558	−	0.147450i	−0.296657	−	0.00562559i
$688$	−45.1943	−	8.00568i	−1.72302	−	0.305214i
$689$	−32.1257	+	38.2859i	−1.22389	+	1.45858i
$690$	−1.97150	−	17.5699i	−0.0750539	−	0.668875i
$691$	29.8872	+	10.8781i	1.13696	+	0.413821i	0.840816	−	0.541321i	$-0.182076\pi$
$691$	29.8872	+	10.8781i	1.13696	+	0.413821i	0.296148	+	0.955142i	$0.404298\pi$
$692$	0.648409	−	2.41609i	0.0246488	−	0.0918460i
$693$	−19.1755	−	7.81473i	−0.728416	−	0.296857i
$694$	−15.2259	+	11.6784i	−0.577966	+	0.443308i
$695$	−1.38951	−	7.88029i	−0.0527071	−	0.298917i
$696$	−1.24685	−	1.41528i	−0.0472619	−	0.0536462i
$697$	3.43738	−	1.25110i	0.130200	−	0.0473890i
$698$	45.2256	+	1.98352i	1.71182	+	0.0750772i
$699$	−4.04953	−	25.8196i	−0.153167	−	0.976588i
$700$	−4.49452	−	3.14974i	−0.169877	−	0.119049i
$701$	−36.8471			−1.39170			−0.695848	−	0.718189i	$-0.744971\pi$
$701$	−36.8471			−1.39170			−0.695848	+	0.718189i	$0.744971\pi$
$702$	−17.2581	−	25.3664i	−0.651366	−	0.957393i
$703$		−	53.2007i		−	2.00650i
$704$	−25.9139	−	2.29803i	−0.976667	−	0.0866101i
$705$	5.05560	−	13.1112i	0.190405	−	0.493795i
$706$	5.89408	+	0.258504i	0.221827	+	0.00972893i
$707$	−9.54944	−	26.2369i	−0.359144	−	0.986739i
$708$	18.9642	+	9.29413i	0.712717	+	0.349295i
$709$	30.3426	−	5.35021i	1.13954	−	0.200932i	0.428135	−	0.903715i	$-0.359171\pi$
$709$	30.3426	−	5.35021i	1.13954	−	0.200932i	0.711404	+	0.702783i	$0.248060\pi$
$710$	11.6745	+	15.2207i	0.438137	+	0.571224i
$711$	−37.9025	+	20.0068i	−1.42146	+	0.750312i
$712$	−41.7830	−	5.52595i	−1.56588	−	0.207094i
$713$	1.22784	−	3.37347i	0.0459830	−	0.126337i
$714$	−2.38434	−	1.04158i	−0.0892318	−	0.0389801i
$715$	26.0909	+	21.8929i	0.975745	+	0.818747i
$716$	11.3521	−	24.3196i	0.424248	−	0.908868i
$717$	−19.2535	+	10.6345i	−0.719035	+	0.397151i
$718$	−14.7010	−	3.26216i	−0.548635	−	0.121743i
$719$	17.6740	−	30.6122i	0.659128	−	1.14164i	−0.321713	−	0.946837i	$-0.604259\pi$
$719$	17.6740	−	30.6122i	0.659128	−	1.14164i	0.980842	−	0.194807i	$-0.0624080\pi$
$720$	9.19332	+	28.6646i	0.342615	+	1.06827i
$721$	−12.2274	−	21.1785i	−0.455373	−	0.788730i
$722$	−4.23385	−	13.4373i	−0.157568	−	0.500084i
$723$	−16.7534	−	3.28275i	−0.623066	−	0.122087i
$724$	3.65295	+	5.22133i	0.135761	+	0.194049i
$725$	0.0864391	−	0.490220i	0.00321027	−	0.0182063i
$726$	0.753604	+	0.717589i	0.0279689	+	0.0266322i
$727$	−15.6576	−	18.6601i	−0.580710	−	0.692063i	0.393082	−	0.919503i	$-0.371409\pi$
$727$	−15.6576	−	18.6601i	−0.580710	−	0.692063i	−0.973792	+	0.227440i	$0.926964\pi$
$728$	−23.1622	+	9.57806i	−0.858447	+	0.354987i
$729$	16.0672	−	21.6990i	0.595080	−	0.803667i
$730$	32.2243	−	4.23595i	1.19267	−	0.156780i
$731$	−3.69123	−	4.39904i	−0.136525	−	0.162704i
$732$	9.53159	−	13.0668i	0.352298	−	0.482962i
$733$	15.9357	+	2.80990i	0.588600	+	0.103786i	0.460013	−	0.887912i	$-0.347845\pi$
$733$	15.9357	+	2.80990i	0.588600	+	0.103786i	0.128587	+	0.991698i	$0.458956\pi$
$734$	2.23975	+	4.30458i	0.0826706	+	0.158885i
$735$	−10.6385	−	2.08456i	−0.392406	−	0.0768901i
$736$	11.9895	+	11.0080i	0.441937	+	0.405762i
$737$	34.5554	−	19.9506i	1.27287	−	0.734890i
$738$	30.9068	+	2.53234i	1.13769	+	0.0932167i
$739$	−4.57312	+	7.92087i	−0.168225	+	0.291374i	−0.937796	−	0.347187i	$-0.887137\pi$
$739$	−4.57312	+	7.92087i	−0.168225	+	0.291374i	0.769571	+	0.638561i	$0.220470\pi$
$740$	4.34214	−	49.4068i	0.159620	−	1.81623i
$741$	18.8161	+	34.0662i	0.691227	+	1.25145i
$742$	−19.3121	+	30.3008i	−0.708971	+	1.11238i
$743$	−11.2333	−	9.42584i	−0.412109	−	0.345800i	0.413043	−	0.910712i	$-0.364466\pi$
$743$	−11.2333	−	9.42584i	−0.412109	−	0.345800i	−0.825152	+	0.564911i	$0.808910\pi$
$744$	−0.916152	+	6.04334i	−0.0335877	+	0.221559i
$745$	−47.5192	−	17.2956i	−1.74097	−	0.633661i
$746$	−18.2727	−	7.57301i	−0.669011	−	0.277268i
$747$	36.7043	−	19.3743i	1.34294	−	0.708868i
$748$	−2.30070	−	2.30251i	−0.0841218	−	0.0841880i
$749$	1.08560	+	6.15672i	0.0396668	+	0.224962i
$750$	12.6050	−	18.9737i	0.460269	−	0.692821i
$751$	1.10642	+	3.03986i	0.0403737	+	0.110926i	0.958241	−	0.285961i	$-0.0923128\pi$
$751$	1.10642	+	3.03986i	0.0403737	+	0.110926i	−0.917868	+	0.396887i	$0.870091\pi$
$752$	4.41496	+	12.1598i	0.160997	+	0.443422i
$753$	21.7622	+	8.39137i	0.793057	+	0.305799i
$754$	−1.67576	−	1.53616i	−0.0610275	−	0.0559436i
$755$			2.13024i			0.0775273i
$756$	−14.6786	−	16.4644i	−0.533857	−	0.598803i
$757$			20.3830i			0.740831i	0.928866	+	0.370415i	$0.120785\pi$
$757$			20.3830i			0.740831i	−0.928866	+	0.370415i	$0.879215\pi$
$758$	3.19303	−	3.48320i	0.115976	−	0.126516i
$759$	2.51112	+	16.0108i	0.0911480	+	0.581155i
$760$	−8.24258	−	37.2841i	−0.298990	−	1.35244i
$761$	8.81961	+	24.2317i	0.319711	+	0.878398i	0.990594	+	0.136835i	$0.0436930\pi$
$761$	8.81961	+	24.2317i	0.319711	+	0.878398i	−0.670883	+	0.741563i	$0.734085\pi$
$762$	37.7396	−	18.7360i	1.36716	−	0.678735i
$763$	7.36377	+	41.7620i	0.266586	+	1.51189i
$764$	4.32269	+	4.32610i	0.156389	+	0.156513i
$765$	−1.42141	+	3.48781i	−0.0513913	+	0.126102i
$766$	−6.83649	+	16.4956i	−0.247012	+	0.596009i
$767$	23.9188	+	8.70573i	0.863657	+	0.314346i
$768$	−23.7104	−	14.3463i	−0.855575	−	0.517678i
$769$	4.58553	+	3.84772i	0.165359	+	0.138752i	0.721712	−	0.692193i	$-0.243355\pi$
$769$	4.58553	+	3.84772i	0.165359	+	0.138752i	−0.556353	+	0.830946i	$0.687800\pi$
$770$	20.6493	+	13.1608i	0.744149	+	0.474281i
$771$	−25.7672	−	0.488630i	−0.927983	−	0.0175976i
$772$	−16.6635	−	1.46448i	−0.599734	−	0.0527079i
$773$	21.7483	−	37.6692i	0.782233	−	1.35487i	−0.148405	−	0.988927i	$-0.547414\pi$
$773$	21.7483	−	37.6692i	0.782233	−	1.35487i	0.930638	−	0.365941i	$-0.119253\pi$
$774$	−12.8589	−	46.9530i	−0.462205	−	1.68769i
$775$	−1.39701	+	0.806561i	−0.0501819	+	0.0289725i
$776$	−0.777787	−	1.22247i	−0.0279209	−	0.0438842i
$777$	11.7800	+	34.3799i	0.422605	+	1.23337i
$778$	45.2494	−	23.5440i	1.62227	−	0.844095i
$779$	−38.7380	−	6.83055i	−1.38793	−	0.244730i
$780$	14.6939	+	33.1726i	0.526125	+	1.18777i
$781$	−11.3025	−	13.4698i	−0.404435	−	0.481987i
$782$	0.265411	+	2.01907i	0.00949109	+	0.0722019i
$783$	0.790017	−	1.83800i	0.0282329	−	0.0656849i
$784$	8.64694	−	4.98323i	0.308819	−	0.177973i
$785$	−12.0448	−	14.3544i	−0.429897	−	0.512332i
$786$	41.2981	+	9.98928i	1.47305	+	0.356306i
$787$	8.60165	−	48.7824i	0.306616	−	1.73890i	−0.309185	−	0.951002i	$-0.600056\pi$
$787$	8.60165	−	48.7824i	0.306616	−	1.73890i	0.615801	−	0.787902i	$-0.288833\pi$
$788$	10.5661	−	7.39229i	0.376403	−	0.263340i
$789$	25.2593	−	28.9691i	0.899253	−	1.03133i
$790$	48.3398	−	15.2310i	1.71985	−	0.541895i
$791$	−4.93090	−	8.54057i	−0.175323	−	0.303668i
$792$	−9.57025	−	25.8809i	−0.340064	−	0.919639i
$793$	9.74671	−	16.8818i	0.346116	−	0.599490i
$794$	5.62772	−	25.3614i	0.199720	−	0.900041i
$795$	44.5426	+	26.8554i	1.57976	+	0.952462i
$796$	6.20311	−	13.2890i	0.219863	−	0.471014i
$797$	17.6198	+	14.7848i	0.624127	+	0.523705i	0.899098	−	0.437748i	$-0.144224\pi$
$797$	17.6198	+	14.7848i	0.624127	+	0.523705i	−0.274971	+	0.961453i	$0.588668\pi$
$798$	16.6044	+	22.5197i	0.587788	+	0.797189i
$799$	−0.553578	+	1.52094i	−0.0195842	+	0.0538071i
$800$	−0.947490	−	7.25207i	−0.0334988	−	0.256399i
$801$	−13.6859	−	42.5570i	−0.483566	−	1.50368i
$802$	−7.42417	+	5.69444i	−0.262156	+	0.201078i
$803$	−29.3399	+	5.17341i	−1.03538	+	0.182566i
$804$	42.4063	−	2.88432i	1.49555	−	0.101722i
$805$	−5.23973	−	14.3960i	−0.184676	−	0.507394i
$806$	−0.322790	+	7.35986i	−0.0113698	+	0.259240i
$807$	−7.56168	−	9.36674i	−0.266184	−	0.329725i
$808$	17.1998	−	32.9929i	0.605086	−	1.16069i
$809$		−	37.2955i		−	1.31124i	−0.755090	−	0.655621i	$-0.772407\pi$
$809$		−	37.2955i		−	1.31124i	0.755090	−	0.655621i	$-0.227593\pi$
$810$	−23.2968	+	21.8337i	−0.818565	+	0.767157i
$811$	34.1131			1.19787			0.598937	−	0.800796i	$-0.295590\pi$
$811$	34.1131			1.19787			0.598937	+	0.800796i	$0.295590\pi$
$812$	−1.33844	−	0.937971i	−0.0469700	−	0.0329163i
$813$	−24.7781	+	20.0031i	−0.869005	+	0.701539i
$814$	−1.99202	+	45.4196i	−0.0698204	+	1.59196i
$815$	−12.4362	+	4.52642i	−0.435623	+	0.158554i
$816$	−1.12132	−	3.28098i	−0.0392539	−	0.114857i
$817$	10.7230	+	60.8133i	0.375151	+	2.12759i
$818$	2.62063	+	3.41667i	0.0916283	+	0.119461i
$819$	−19.7027	−	17.8482i	−0.688467	−	0.623667i
$820$	−35.4180	−	9.50517i	−1.23685	−	0.331935i
$821$	4.63164	+	1.68578i	0.161645	+	0.0588340i	0.421575	−	0.906793i	$-0.361477\pi$
$821$	4.63164	+	1.68578i	0.161645	+	0.0588340i	−0.259930	+	0.965627i	$0.583700\pi$
$822$	3.43203	+	4.65470i	0.119706	+	0.162351i
$823$	−15.0760	+	17.9669i	−0.525518	+	0.626287i	−0.961876	−	0.273485i	$-0.911823\pi$
$823$	−15.0760	+	17.9669i	−0.525518	+	0.626287i	0.436359	+	0.899773i	$0.356268\pi$
$824$	9.81790	−	31.0744i	0.342023	−	1.08253i
$825$	3.76005	−	6.23646i	0.130908	−	0.217126i
$826$	17.8653	+	3.96434i	0.621614	+	0.137937i
$827$	−12.0532	−	6.95894i	−0.419132	−	0.241986i	0.275574	−	0.961280i	$-0.411132\pi$
$827$	−12.0532	−	6.95894i	−0.419132	−	0.241986i	−0.694706	+	0.719294i	$0.744466\pi$
$828$	−5.10371	+	16.4922i	−0.177366	+	0.573143i
$829$	44.9965	−	25.9788i	1.56279	−	0.902279i	0.565821	−	0.824528i	$-0.308559\pi$
$829$	44.9965	−	25.9788i	1.56279	−	0.902279i	0.996973	−	0.0777511i	$-0.0247739\pi$
$830$	−46.8116	+	14.7495i	−1.62485	+	0.511963i
$831$	15.6721	+	13.6651i	0.543659	+	0.474036i
$832$	−30.2547	−	14.1515i	−1.04889	−	0.490616i
$833$	1.22969	+	0.216828i	0.0426064	+	0.00751265i
$834$	−1.83696	+	7.59442i	−0.0636086	+	0.262973i
$835$	−7.50273	+	6.29554i	−0.259643	+	0.217866i
$836$	9.04578	+	33.8126i	0.312855	+	1.16943i
$837$	−6.20839	+	1.86743i	−0.214593	+	0.0645479i
$838$	−4.92877	−	37.4948i	−0.170261	−	1.29524i
$839$	−0.572631	+	0.480495i	−0.0197694	+	0.0165885i	−0.652619	−	0.757686i	$-0.726330\pi$
$839$	−0.572631	+	0.480495i	−0.0197694	+	0.0165885i	0.632849	+	0.774275i	$0.281885\pi$
$840$	13.5822	+	22.2690i	0.468632	+	0.768352i
$841$	−5.01006	+	28.4134i	−0.172761	+	0.979774i
$842$	19.9086	+	38.2624i	0.686095	+	1.31861i
$843$	−18.9611	+	6.49688i	−0.653056	+	0.223764i
$844$	−2.77493	−	5.95698i	−0.0955171	−	0.205048i
$845$	5.55826	+	9.62719i	0.191210	+	0.331186i
$846$	−9.64871	+	9.75571i	−0.331729	+	0.335408i
$847$	0.780883	+	0.450843i	0.0268315	+	0.0154912i
$848$	−47.1618	+	8.27759i	−1.61954	+	0.284254i
$849$	0.113098	−	5.96403i	0.00388150	−	0.204685i
$850$	0.491812	−	0.771655i	0.0168690	−	0.0264676i
$851$	18.2833	−	21.7892i	0.626744	−	0.746925i
$852$	−4.49679	−	18.1829i	−0.154058	−	0.622935i
$853$	−10.5662	+	29.0305i	−0.361781	+	0.993986i	0.616618	+	0.787262i	$0.288502\pi$
$853$	−10.5662	+	29.0305i	−0.361781	+	0.993986i	−0.978399	+	0.206723i	$0.933720\pi$
$854$	5.36573	−	12.9468i	0.183612	−	0.443031i
$855$	31.9899	−	24.8383i	1.09403	−	0.849452i
$856$	−5.07549	+	6.60642i	−0.173477	+	0.225803i
$857$	39.9870	−	7.05078i	1.36593	−	0.240850i	0.557859	−	0.829936i	$-0.311623\pi$
$857$	39.9870	−	7.05078i	1.36593	−	0.240850i	0.808070	+	0.589086i	$0.200512\pi$
$858$	−14.7885	−	29.7883i	−0.504873	−	1.01696i
$859$	32.4767	−	11.8206i	1.10809	−	0.403312i	0.277798	−	0.960639i	$-0.410395\pi$
$859$	32.4767	−	11.8206i	1.10809	−	0.403312i	0.830293	+	0.557327i	$0.188173\pi$
$860$	4.99487	+	57.3518i	0.170324	+	1.95568i
$861$	26.5461	−	4.16347i	0.904689	−	0.141891i
$862$	−9.36683	+	10.2181i	−0.319035	+	0.348028i
$863$	−42.3075			−1.44017			−0.720083	−	0.693888i	$-0.755896\pi$
$863$	−42.3075			−1.44017			−0.720083	+	0.693888i	$0.755896\pi$
$864$	2.97838	−	29.2426i	0.101327	−	0.994853i
$865$	−3.13769			−0.106685
$866$	16.2894	−	17.7698i	0.553538	−	0.603842i
$867$	−10.4375	+	27.0684i	−0.354475	+	0.919293i
$868$	0.459534	+	5.27644i	0.0155976	+	0.179094i
$869$	−43.6564	+	15.8896i	−1.48094	+	0.539018i
$870$	−1.30913	+	1.97058i	−0.0443838	+	0.0668089i
$871$	50.4499	−	8.89567i	1.70943	−	0.301418i
$872$	−34.4279	+	44.8124i	−1.16587	+	1.51754i
$873$	0.818317	−	1.30084i	0.0276958	−	0.0440266i
$874$	8.38420	−	20.2300i	0.283600	−	0.684289i
$875$	6.75085	−	18.5478i	0.228220	−	0.627030i
$876$	−30.4900	−	8.80565i	−1.03016	−	0.297515i
$877$	−9.16086	+	10.9175i	−0.309340	+	0.368657i	−0.898207	−	0.439573i	$-0.855130\pi$
$877$	−9.16086	+	10.9175i	−0.309340	+	0.368657i	0.588867	+	0.808230i	$0.299574\pi$
$878$	−0.862470	+	1.35322i	−0.0291069	+	0.0456689i
$879$	41.0566	−	22.6772i	1.38480	−	0.764883i
$880$	5.64098	+	32.1396i	0.190157	+	1.08343i
$881$	16.6372	+	9.60547i	0.560520	+	0.323616i	0.753354	−	0.657615i	$-0.228435\pi$
$881$	16.6372	+	9.60547i	0.560520	+	0.323616i	−0.192834	+	0.981231i	$0.561768\pi$
$882$	8.70447	+	6.02367i	0.293095	+	0.202828i
$883$	−7.04315	−	12.1991i	−0.237021	−	0.410532i	0.722837	−	0.691018i	$-0.242838\pi$
$883$	−7.04315	−	12.1991i	−0.237021	−	0.410532i	−0.959858	+	0.280486i	$0.909504\pi$
$884$	−1.76461	−	3.78812i	−0.0593503	−	0.127408i
$885$	5.09362	−	25.9951i	0.171220	−	0.873816i
$886$	−8.32215	−	15.9944i	−0.279588	−	0.537342i
$887$	−6.56011	+	37.2043i	−0.220267	+	1.24920i	0.651262	+	0.758853i	$0.274240\pi$
$887$	−6.56011	+	37.2043i	−0.220267	+	1.24920i	−0.871529	+	0.490344i	$0.836871\pi$
$888$	−23.1977	+	42.5119i	−0.778464	+	1.42660i
$889$	27.9681	−	23.4680i	0.938020	−	0.787092i
$890$	6.88982	+	52.4131i	0.230947	+	1.75689i
$891$	20.4575	−	20.9303i	0.685354	−	0.701192i
$892$	7.29449	+	27.2663i	0.244237	+	0.912945i
$893$	13.3329	−	11.1876i	0.446169	−	0.374380i
$894$	35.7596	+	34.0506i	1.19598	+	1.13882i
$895$	−33.1519	−	5.84557i	−1.10814	−	0.195396i
$896$	−22.8919	−	7.25249i	−0.764764	−	0.242289i
$897$	−4.00098	+	20.4189i	−0.133589	+	0.681766i
$898$	14.8037	−	4.66440i	0.494007	−	0.155653i
$899$	−0.416019	+	0.240189i	−0.0138750	+	0.00801074i
$900$	6.52023	−	4.20275i	0.217341	−	0.140092i
$901$	−5.18824	−	2.99543i	−0.172845	−	0.0997924i
$902$	32.8165	+	7.28202i	1.09267	+	0.242465i
$903$	−20.3952	−	36.9250i	−0.678709	−	1.22879i
$904$	3.95922	−	12.5312i	0.131682	−	0.416782i
$905$	5.13759	−	6.12274i	0.170779	−	0.203527i
$906$	0.832677	−	1.90613i	0.0276639	−	0.0633271i
$907$	−35.9262	−	13.0761i	−1.19291	−	0.434184i	−0.332166	−	0.943221i	$-0.607779\pi$
$907$	−35.9262	−	13.0761i	−1.19291	−	0.434184i	−0.860745	+	0.509037i	$0.830002\pi$
$908$	−8.19587	−	2.19954i	−0.271990	−	0.0729942i
$909$	39.4356	+	1.49619i	1.30800	+	0.0496257i
$910$	19.1332	+	24.9451i	0.634261	+	0.826922i
$911$	−8.92255	−	50.6023i	−0.295617	−	1.67653i	−0.664682	−	0.747126i	$-0.731433\pi$
$911$	−8.92255	−	50.6023i	−0.295617	−	1.67653i	0.369065	−	0.929404i	$-0.379678\pi$
$912$	−7.19833	+	36.5837i	−0.238360	+	1.21141i
$913$	42.2763	−	15.3873i	1.39914	−	0.509245i
$914$	0.0844324	−	1.92512i	0.00279277	−	0.0636773i
$915$	−18.9281	−	7.29858i	−0.625744	−	0.241284i
$916$	−7.35403	−	5.15366i	−0.242984	−	0.170282i
$917$	36.8169			1.21580
$918$	2.63521	−	2.56528i	0.0869749	−	0.0846668i
$919$		−	7.02685i		−	0.231794i	−0.993261	−	0.115897i	$-0.963026\pi$
$919$		−	7.02685i		−	0.231794i	0.993261	−	0.115897i	$-0.0369743\pi$
$920$	9.43743	−	18.1030i	0.311143	−	0.596839i
$921$	−12.1669	+	1.90824i	−0.400912	+	0.0628787i
$922$	0.983430	−	22.4229i	0.0323875	−	0.738460i
$923$	−7.72113	−	21.2136i	−0.254144	−	0.698256i
$924$	−13.3326	−	19.8477i	−0.438611	−	0.652942i
$925$	−12.5868	+	2.21939i	−0.413852	+	0.0729732i
$926$	−3.49042	+	2.67720i	−0.114702	+	0.0879783i
$927$	34.2432	−	4.70732i	1.12470	−	0.154609i
$928$	−0.282156	−	2.15962i	−0.00926224	−	0.0708930i
$929$	−19.0465	+	52.3299i	−0.624896	+	1.71689i	0.0697781	+	0.997563i	$0.477771\pi$
$929$	−19.0465	+	52.3299i	−0.624896	+	1.71689i	−0.694674	+	0.719325i	$0.744451\pi$
$930$	7.61884	−	0.854904i	0.249832	−	0.0280334i
$931$	−10.2859	−	8.63091i	−0.337107	−	0.282867i
$932$	12.7647	−	27.3459i	0.418122	−	0.895744i
$933$	0.167199	−	8.81698i	0.00547384	−	0.288655i
$934$	−9.23922	+	41.6366i	−0.302317	+	1.36239i
$935$	−2.04132	+	3.53566i	−0.0667582	+	0.115629i
$936$	−0.181403	−	35.4264i	−0.00592934	−	1.15795i
$937$	−24.5562	−	42.5326i	−0.802216	−	1.38948i	−0.918155	−	0.396222i	$-0.870321\pi$
$937$	−24.5562	−	42.5326i	−0.802216	−	1.38948i	0.115939	−	0.993256i	$-0.463012\pi$
$938$	35.1277	−	11.0681i	1.14696	−	0.361387i
$939$	−13.1955	−	38.5110i	−0.430618	−	1.25676i
$940$	13.2952	−	9.30161i	0.433642	−	0.303385i
$941$	−3.33638	+	18.9215i	−0.108763	+	0.616825i	0.880888	+	0.473326i	$0.156947\pi$
$941$	−3.33638	+	18.9215i	−0.108763	+	0.616825i	−0.989650	+	0.143499i	$0.954165\pi$
$942$	5.16675	+	17.5525i	0.168342	+	0.571890i
$943$	−13.5184	−	16.1105i	−0.440218	−	0.524631i
$944$	12.1765	+	21.1288i	0.396313	+	0.687684i
$945$	−15.1730	+	23.1346i	−0.493578	+	0.752570i
$946$	−6.87763	−	52.3204i	−0.223611	−	1.70108i
$947$	33.6161	+	40.0620i	1.09237	+	1.30184i	0.950076	+	0.312018i	$0.101005\pi$
$947$	33.6161	+	40.0620i	1.09237	+	1.30184i	0.142299	+	0.989824i	$0.454551\pi$
$948$	−49.2080	−	5.26659i	−1.59820	−	0.171051i
$949$	−37.6687	−	6.64201i	−1.22278	−	0.215609i
$950$	−8.72902	+	4.54186i	−0.283207	+	0.147357i
$951$	11.4442	−	13.1250i	0.371104	−	0.425608i
$952$	−1.61278	−	2.53487i	−0.0522706	−	0.0821555i
$953$	−27.4810	+	15.8662i	−0.890198	+	0.513956i	−0.874007	−	0.485913i	$-0.838487\pi$
$953$	−27.4810	+	15.8662i	−0.890198	+	0.513956i	−0.0161907	+	0.999869i	$0.505154\pi$
$954$	−29.3593	−	41.4412i	−0.950543	−	1.34171i
$955$	3.83535	−	6.64303i	0.124109	−	0.214963i
$956$	−25.3003	−	2.22353i	−0.818272	−	0.0719142i
$957$	1.11972	−	1.85718i	0.0361954	−	0.0600340i
$958$	−32.3268	−	20.6034i	−1.04443	−	0.665666i
$959$	3.83876	+	3.22110i	0.123960	+	0.104015i
$960$	−9.67088	+	33.3873i	−0.312126	+	1.07757i
$961$	−27.6676	−	10.0702i	−0.892504	−	0.324845i
$962$	−22.3475	+	53.9217i	−0.720513	+	1.73851i
$963$	−8.63767	−	1.86323i	−0.278345	−	0.0600419i
$964$	−13.9337	−	13.9447i	−0.448775	−	0.449129i
$965$	3.64337	+	20.6626i	0.117284	+	0.665152i
$966$	−0.938686	+	14.9297i	−0.0302017	+	0.480355i
$967$	−0.0970671	−	0.266690i	−0.00312147	−	0.00857616i	0.938122	−	0.346305i	$-0.112564\pi$
$967$	−0.0970671	−	0.266690i	−0.00312147	−	0.00857616i	−0.941244	+	0.337729i	$0.890341\pi$
$968$	0.259377	+	1.17325i	0.00833670	+	0.0377098i
$969$	−3.62977	+	2.93028i	−0.116605	+	0.0941341i
$970$	−1.22806	+	1.33966i	−0.0394306	+	0.0430139i
$971$			37.7792i			1.21239i	0.795315	+	0.606196i	$0.207305\pi$
$971$			37.7792i			1.21239i	−0.795315	+	0.606196i	$0.792695\pi$
$972$	29.3804	−	10.4304i	0.942376	−	0.334556i
$973$			6.77037i			0.217048i
$974$	12.9989	+	11.9160i	0.416510	+	0.381812i
$975$	7.27481	−	5.87288i	0.232980	−	0.188083i
$976$	17.5546	−	6.37371i	0.561910	−	0.204018i
$977$	−6.98432	−	19.1893i	−0.223448	−	0.613919i	0.776419	−	0.630217i	$-0.217034\pi$
$977$	−6.98432	−	19.1893i	−0.223448	−	0.613919i	−0.999867	+	0.0162980i	$0.994812\pi$
$978$	12.8973	+	0.810899i	0.412409	+	0.0259297i
$979$	−8.41461	−	47.7216i	−0.268932	−	1.52519i
$980$	−8.84796	−	8.85494i	−0.282638	−	0.282861i
$981$	−58.5907	−	12.6386i	−1.87066	−	0.403520i
$982$	30.3530	+	12.5796i	0.968602	+	0.401431i
$983$	−32.8266	−	11.9479i	−1.04700	−	0.381079i	−0.239473	−	0.970903i	$-0.576975\pi$
$983$	−32.8266	−	11.9479i	−1.04700	−	0.381079i	−0.807532	+	0.589824i	$0.799197\pi$
$984$	27.9765	+	22.3496i	0.891860	+	0.712478i
$985$	−12.3903	−	10.3967i	−0.394787	−	0.331266i
$986$	0.146459	−	0.229794i	0.00466419	−	0.00731813i
$987$	−6.13890	+	10.1820i	−0.195403	+	0.324098i
$988$	−3.93421	+	44.7652i	−0.125164	+	1.42417i
$989$	−16.5078	+	28.5923i	−0.524916	+	0.909181i
$990$	−28.2412	+	20.0077i	−0.897564	+	0.635886i
$991$	−7.41357	+	4.28023i	−0.235500	+	0.135966i	−0.613107	−	0.790000i	$-0.710080\pi$
$991$	−7.41357	+	4.28023i	−0.235500	+	0.135966i	0.377607	+	0.925966i	$0.376747\pi$
$992$	−4.77342	+	5.19899i	−0.151556	+	0.165068i
$993$	−4.96931	+	5.69916i	−0.157696	+	0.180857i
$994$	−7.49144	−	14.3979i	−0.237614	−	0.456672i
$995$	−18.1151	−	3.19419i	−0.574288	−	0.101263i
$996$	47.6523	+	5.10009i	1.50992	+	0.161603i
$997$	−7.41930	−	8.84198i	−0.234972	−	0.280028i	0.635654	−	0.771974i	$-0.280730\pi$
$997$	−7.41930	−	8.84198i	−0.234972	−	0.280028i	−0.870626	+	0.491946i	$0.836286\pi$
$998$	−5.44070	+	0.715192i	−0.172222	+	0.0226390i
$999$	−51.2839	−	2.92033i	−1.62255	−	0.0923952i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.59.10	yes	192
3.2	odd	2		648.2.v.b.611.23		192
4.3	odd	2		864.2.bh.b.815.23		192
8.3	odd	2	inner	216.2.v.b.59.28	yes	192
8.5	even	2		864.2.bh.b.815.24		192
24.11	even	2		648.2.v.b.611.5		192
27.11	odd	18	inner	216.2.v.b.11.28	yes	192
27.16	even	9		648.2.v.b.35.5		192
108.11	even	18		864.2.bh.b.335.24		192
216.11	even	18	inner	216.2.v.b.11.10	✓	192
216.43	odd	18		648.2.v.b.35.23		192
216.173	odd	18		864.2.bh.b.335.23		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.10	✓	192	216.11	even	18	inner
216.2.v.b.11.28	yes	192	27.11	odd	18	inner
216.2.v.b.59.10	yes	192	1.1	even	1	trivial
216.2.v.b.59.28	yes	192	8.3	odd	2	inner
648.2.v.b.35.5		192	27.16	even	9
648.2.v.b.35.23		192	216.43	odd	18
648.2.v.b.611.5		192	24.11	even	2
648.2.v.b.611.23		192	3.2	odd	2
864.2.bh.b.335.23		192	216.173	odd	18
864.2.bh.b.335.24		192	108.11	even	18
864.2.bh.b.815.23		192	4.3	odd	2
864.2.bh.b.815.24		192	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.955634 + 1.04248i) q^{2} +(-1.08798 - 1.34770i) q^{3} +(-0.173527 - 1.99246i) q^{4} +(-2.35728 + 0.857979i) q^{5} +(2.44466 + 0.153705i) q^{6} +(2.09025 - 0.368567i) q^{7} +(2.24292 + 1.72316i) q^{8} +(-0.632581 + 2.93255i) q^{9} +O(q^{10})\)	\(q+(-0.955634 + 1.04248i) q^{2} +(-1.08798 - 1.34770i) q^{3} +(-0.173527 - 1.99246i) q^{4} +(-2.35728 + 0.857979i) q^{5} +(2.44466 + 0.153705i) q^{6} +(2.09025 - 0.368567i) q^{7} +(2.24292 + 1.72316i) q^{8} +(-0.632581 + 2.93255i) q^{9} +(1.35827 - 3.27733i) q^{10} +(-1.11223 + 3.05583i) q^{11} +(-2.49644 + 2.40162i) q^{12} +(-2.68370 + 3.19831i) q^{13} +(-1.61329 + 2.53126i) q^{14} +(3.72098 + 2.24343i) q^{15} +(-3.93978 + 0.691490i) q^{16} +(-0.433413 - 0.250231i) q^{17} +(-2.45261 - 3.46190i) q^{18} +(2.69082 + 4.66064i) q^{19} +(2.11854 + 4.54790i) q^{20} +(-2.77087 - 2.41603i) q^{21} +(-2.12276 - 4.07974i) q^{22} +(-0.499638 + 2.83359i) q^{23} +(-0.117963 - 4.89756i) q^{24} +(0.990413 - 0.831055i) q^{25} +(-0.769536 - 5.85412i) q^{26} +(4.64043 - 2.33804i) q^{27} +(-1.09707 - 4.10077i) q^{28} +(0.294939 - 0.247483i) q^{29} +(-5.89463 + 1.73514i) q^{30} +(-1.22873 - 0.216658i) q^{31} +(3.04412 - 4.76795i) q^{32} +(5.32843 - 1.82574i) q^{33} +(0.675045 - 0.212695i) q^{34} +(-4.61107 + 2.66221i) q^{35} +(5.95275 + 0.751515i) q^{36} +(-8.56116 - 4.94279i) q^{37} +(-7.43006 - 1.64874i) q^{38} +(7.23018 + 0.137108i) q^{39} +(-6.76564 - 2.13759i) q^{40} +(-4.69827 + 5.59918i) q^{41} +(5.16660 - 0.579740i) q^{42} +(10.7825 + 3.92450i) q^{43} +(6.28162 + 1.68581i) q^{44} +(-1.02490 - 7.45558i) q^{45} +(-2.47649 - 3.22874i) q^{46} +(-0.561599 - 3.18499i) q^{47} +(5.21833 + 4.55730i) q^{48} +(-2.34455 + 0.853348i) q^{49} +(-0.0801145 + 1.82667i) q^{50} +(0.134311 + 0.856358i) q^{51} +(6.83819 + 4.79217i) q^{52} +11.9707 q^{53} +(-1.99719 + 7.07186i) q^{54} -8.15772i q^{55} +(5.32337 + 2.77517i) q^{56} +(3.35356 - 8.69712i) q^{57} +(-0.0238576 + 0.543970i) q^{58} +(-2.08516 - 5.72892i) q^{59} +(3.82425 - 7.80319i) q^{60} +(-4.59804 + 0.810759i) q^{61} +(1.40008 - 1.07388i) q^{62} +(-0.241410 + 6.36290i) q^{63} +(2.06142 + 7.72985i) q^{64} +(3.58215 - 9.84187i) q^{65} +(-3.18873 + 7.29952i) q^{66} +(-9.39931 - 7.88696i) q^{67} +(-0.423366 + 0.906979i) q^{68} +(4.36242 - 2.40954i) q^{69} +(1.63121 - 7.35104i) q^{70} +(-2.70354 + 4.68267i) q^{71} +(-6.47209 + 5.48745i) q^{72} +(4.58071 + 7.93403i) q^{73} +(13.3341 - 4.20134i) q^{74} +(-2.19756 - 0.430603i) q^{75} +(8.81920 - 6.17010i) q^{76} +(-1.19856 + 6.79738i) q^{77} +(-7.05234 + 7.40629i) q^{78} +(9.18302 + 10.9439i) q^{79} +(8.69387 - 5.01028i) q^{80} +(-8.19968 - 3.71015i) q^{81} +(-1.34720 - 10.2486i) q^{82} +(-8.89271 - 10.5979i) q^{83} +(-4.33301 + 5.94010i) q^{84} +(1.23637 + 0.218005i) q^{85} +(-14.3953 + 7.49012i) q^{86} +(-0.654421 - 0.128231i) q^{87} +(-7.76035 + 4.93745i) q^{88} +(-12.9048 + 7.45058i) q^{89} +(8.75171 + 6.05637i) q^{90} +(-4.43081 + 7.67438i) q^{91} +(5.73251 + 0.503805i) q^{92} +(1.04485 + 1.89168i) q^{93} +(3.85697 + 2.45823i) q^{94} +(-10.3418 - 8.67776i) q^{95} +(-9.73771 + 1.08490i) q^{96} +(-0.481380 - 0.175208i) q^{97} +(1.35094 - 3.25964i) q^{98} +(-8.25780 - 5.19474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more