LMFDB - Embedded newform 216.2.v.b.11.28

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			11.28
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19259 + 0.760091i) q^{2} +(-1.08798 + 1.34770i) q^{3} +(0.844523 + 1.81295i) q^{4} +(2.35728 + 0.857979i) q^{5} +(-2.32189 + 0.780279i) q^{6} +(-2.09025 - 0.368567i) q^{7} +(-0.370840 + 2.80401i) q^{8} +(-0.632581 - 2.93255i) q^{9} +(2.15912 + 2.81496i) q^{10} +(-1.11223 - 3.05583i) q^{11} +(-3.36213 - 0.834298i) q^{12} +(2.68370 + 3.19831i) q^{13} +(-2.21266 - 2.02833i) q^{14} +(-3.72098 + 2.24343i) q^{15} +(-2.57356 + 3.06215i) q^{16} +(-0.433413 + 0.250231i) q^{17} +(1.47460 - 3.97814i) q^{18} +(2.69082 - 4.66064i) q^{19} +(0.435303 + 4.99821i) q^{20} +(2.77087 - 2.41603i) q^{21} +(0.996279 - 4.48974i) q^{22} +(0.499638 + 2.83359i) q^{23} +(-3.37549 - 3.55050i) 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} +(-6.14280 - 0.152798i) q^{30} +(1.22873 - 0.216658i) q^{31} +(-5.39671 + 1.69574i) q^{32} +(5.32843 + 1.82574i) q^{33} +(-0.707081 - 0.0310113i) q^{34} +(-4.61107 - 2.66221i) q^{35} +(4.78233 - 3.62344i) q^{36} +(8.56116 - 4.94279i) q^{37} +(6.75155 - 3.51294i) q^{38} +(-7.23018 + 0.137108i) q^{39} +(-3.27996 + 6.29166i) q^{40} +(-4.69827 - 5.59918i) q^{41} +(5.14091 - 0.775204i) q^{42} +(10.7825 - 3.92450i) q^{43} +(4.60076 - 4.59714i) q^{44} +(1.02490 - 7.45558i) q^{45} +(-1.55793 + 3.75907i) q^{46} +(0.561599 - 3.18499i) q^{47} +(-1.32686 - 6.79996i) q^{48} +(-2.34455 - 0.853348i) q^{49} +(0.549475 + 1.74391i) q^{50} +(0.134311 - 0.856358i) q^{51} +(-3.53192 + 7.56645i) q^{52} -11.9707 q^{53} +(3.75699 + 6.31546i) q^{54} -8.15772i q^{55} +(1.80861 - 5.72440i) q^{56} +(3.35356 + 8.69712i) q^{57} +(-0.163630 - 0.519325i) q^{58} +(-2.08516 + 5.72892i) q^{59} +(-7.20968 - 4.85131i) q^{60} +(4.59804 + 0.810759i) q^{61} +(1.63005 + 0.675563i) q^{62} +(0.241410 + 6.36290i) q^{63} +(-7.72495 - 2.07968i) q^{64} +(3.58215 + 9.84187i) q^{65} +(4.96688 + 6.22745i) q^{66} +(-9.39931 + 7.88696i) q^{67} +(-0.819683 - 0.574430i) q^{68} +(-4.36242 - 2.40954i) q^{69} +(-3.47558 - 6.67975i) q^{70} +(2.70354 + 4.68267i) q^{71} +(8.45748 - 0.686256i) q^{72} +(4.58071 - 7.93403i) q^{73} +(13.9669 + 0.612563i) q^{74} +(-2.19756 + 0.430603i) q^{75} +(10.7220 + 0.942305i) q^{76} +(1.19856 + 6.79738i) q^{77} +(-8.72682 - 5.33208i) 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} +(6.72020 + 2.98306i) q^{84} +(-1.23637 + 0.218005i) q^{85} +(15.8420 + 3.51536i) q^{86} +(0.654421 - 0.128231i) q^{87} +(8.98105 - 1.98549i) q^{88} +(-12.9048 - 7.45058i) q^{89} +(6.88920 - 8.11240i) q^{90} +(-4.43081 - 7.67438i) q^{91} +(-4.71520 + 3.29885i) q^{92} +(-1.04485 + 1.89168i) q^{93} +(3.09063 - 3.37150i) q^{94} +(10.3418 - 8.67776i) q^{95} +(3.58619 - 9.11807i) q^{96} +(-0.481380 + 0.175208i) q^{97} +(-2.14746 - 2.79976i) 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} - 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}+ \cdots - 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

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.19259	+	0.760091i	0.843286	+	0.537466i
$2$	1.19259	+	0.760091i	0.843286	+	0.537466i
$3$	−1.08798	+	1.34770i	−0.628148	+	0.778094i
$3$	−1.08798	+	1.34770i	−0.628148	+	0.778094i
$4$	0.844523	+	1.81295i	0.422261	+	0.906474i
$5$	2.35728	+	0.857979i	1.05421	+	0.383700i	0.810249	−	0.586086i	$-0.199332\pi$
$5$	2.35728	+	0.857979i	1.05421	+	0.383700i	0.243958	+	0.969786i	$0.421554\pi$
$6$	−2.32189	+	0.780279i	−0.947907	+	0.318547i
$7$	−2.09025	−	0.368567i	−0.790039	−	0.139305i	−0.235953	−	0.971764i	$-0.575821\pi$
$7$	−2.09025	−	0.368567i	−0.790039	−	0.139305i	−0.554086	+	0.832459i	$0.686932\pi$
$8$	−0.370840	+	2.80401i	−0.131112	+	0.991368i
$9$	−0.632581	−	2.93255i	−0.210860	−	0.977516i
$10$	2.15912	+	2.81496i	0.682772	+	0.890169i
$11$	−1.11223	−	3.05583i	−0.335351	−	0.921368i	−0.986694	−	0.162586i	$-0.948017\pi$
$11$	−1.11223	−	3.05583i	−0.335351	−	0.921368i	0.651344	−	0.758783i	$-0.274206\pi$
$12$	−3.36213	−	0.834298i	−0.970565	−	0.240841i
$13$	2.68370	+	3.19831i	0.744325	+	0.887051i	0.996749	−	0.0805651i	$-0.0256725\pi$
$13$	2.68370	+	3.19831i	0.744325	+	0.887051i	−0.252425	+	0.967617i	$0.581228\pi$
$14$	−2.21266	−	2.02833i	−0.591357	−	0.542093i
$15$	−3.72098	+	2.24343i	−0.960753	+	0.579252i
$16$	−2.57356	+	3.06215i	−0.643391	+	0.765538i
$17$	−0.433413	+	0.250231i	−0.105118	+	0.0606900i	−0.551637	−	0.834084i	$-0.685997\pi$
$17$	−0.433413	+	0.250231i	−0.105118	+	0.0606900i	0.446519	+	0.894774i	$0.352663\pi$
$18$	1.47460	−	3.97814i	0.347566	−	0.937656i
$19$	2.69082	−	4.66064i	0.617317	−	1.06922i	−0.372656	−	0.927969i	$-0.621553\pi$
$19$	2.69082	−	4.66064i	0.617317	−	1.06922i	0.989973	−	0.141255i	$-0.0451137\pi$
$20$	0.435303	+	4.99821i	0.0973367	+	1.11763i
$21$	2.77087	−	2.41603i	0.604654	−	0.527221i
$22$	0.996279	−	4.48974i	0.212407	−	0.957216i
$23$	0.499638	+	2.83359i	0.104182	+	0.590844i	0.991544	+	0.129771i	$0.0414243\pi$
$23$	0.499638	+	2.83359i	0.104182	+	0.590844i	−0.887362	+	0.461073i	$0.847465\pi$
$24$	−3.37549	−	3.55050i	−0.689019	−	0.724743i
$25$	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	$-0.289159\pi$
$29$	−0.294939	−	0.247483i	−0.0547687	−	0.0459564i	−0.669761	+	0.742577i	$0.733604\pi$
$30$	−6.14280	−	0.152798i	−1.12152	−	0.0278969i
$31$	1.22873	−	0.216658i	0.220686	−	0.0389130i	−0.0622115	−	0.998063i	$-0.519815\pi$
$31$	1.22873	−	0.216658i	0.220686	−	0.0389130i	0.282898	+	0.959150i	$0.408704\pi$
$32$	−5.39671	+	1.69574i	−0.954013	+	0.299767i
$33$	5.32843	+	1.82574i	0.927561	+	0.317821i
$34$	−0.707081	−	0.0310113i	−0.121263	−	0.00531840i
$35$	−4.61107	−	2.66221i	−0.779414	−	0.449995i
$36$	4.78233	−	3.62344i	0.797055	−	0.603907i
$37$	8.56116	−	4.94279i	1.40745	−	0.812589i	0.412305	−	0.911046i	$-0.364724\pi$
$37$	8.56116	−	4.94279i	1.40745	−	0.812589i	0.995141	+	0.0984564i	$0.0313905\pi$
$38$	6.75155	−	3.51294i	1.09525	−	0.569875i
$39$	−7.23018	+	0.137108i	−1.15776	+	0.0219548i
$40$	−3.27996	+	6.29166i	−0.518607	+	0.994799i
$41$	−4.69827	−	5.59918i	−0.733747	−	0.874445i	0.262142	−	0.965029i	$-0.415571\pi$
$41$	−4.69827	−	5.59918i	−0.733747	−	0.874445i	−0.995889	+	0.0905841i	$0.971127\pi$
$42$	5.14091	−	0.775204i	0.793259	−	0.119617i
$43$	10.7825	−	3.92450i	1.64431	−	0.598480i	0.656526	−	0.754303i	$-0.272025\pi$
$43$	10.7825	−	3.92450i	1.64431	−	0.598480i	0.987785	+	0.155823i	$0.0498029\pi$
$44$	4.60076	−	4.59714i	0.693591	−	0.693045i
$45$	1.02490	−	7.45558i	0.152783	−	1.11141i
$46$	−1.55793	+	3.75907i	−0.229704	+	0.554245i
$47$	0.561599	−	3.18499i	0.0819176	−	0.464578i	−0.916062	−	0.401037i	$-0.868650\pi$
$47$	0.561599	−	3.18499i	0.0819176	−	0.464578i	0.997979	−	0.0635404i	$-0.0202392\pi$
$48$	−1.32686	−	6.79996i	−0.191516	−	0.981490i
$49$	−2.34455	−	0.853348i	−0.334936	−	0.121907i
$50$	0.549475	+	1.74391i	0.0777075	+	0.246626i
$51$	0.134311	−	0.856358i	0.0188072	−	0.119914i
$52$	−3.53192	+	7.56645i	−0.489790	+	1.04928i
$53$	−11.9707			−1.64430			−0.822149	−	0.569273i	$-0.807225\pi$
$53$	−11.9707			−1.64430			−0.822149	+	0.569273i	$0.807225\pi$
$54$	3.75699	+	6.31546i	0.511261	+	0.859425i
$55$		−	8.15772i		−	1.09999i
$56$	1.80861	−	5.72440i	0.241686	−	0.764955i
$57$	3.35356	+	8.69712i	0.444190	+	1.15196i
$58$	−0.163630	−	0.519325i	−0.0214857	−	0.0681907i
$59$	−2.08516	+	5.72892i	−0.271464	+	0.745842i	0.726795	+	0.686855i	$0.241009\pi$
$59$	−2.08516	+	5.72892i	−0.271464	+	0.745842i	−0.998259	+	0.0589868i	$0.981213\pi$
$60$	−7.20968	−	4.85131i	−0.930765	−	0.626302i
$61$	4.59804	+	0.810759i	0.588719	+	0.103807i	0.460069	−	0.887883i	$-0.347825\pi$
$61$	4.59804	+	0.810759i	0.588719	+	0.103807i	0.128650	+	0.991690i	$0.458936\pi$
$62$	1.63005	+	0.675563i	0.207016	+	0.0857966i
$63$	0.241410	+	6.36290i	0.0304148	+	0.801650i
$64$	−7.72495	−	2.07968i	−0.965619	−	0.259960i
$65$	3.58215	+	9.84187i	0.444311	+	1.22073i
$66$	4.96688	+	6.22745i	0.611381	+	0.766546i
$67$	−9.39931	+	7.88696i	−1.14831	+	0.963545i	−0.999679	−	0.0253476i	$-0.991931\pi$
$67$	−9.39931	+	7.88696i	−1.14831	+	0.963545i	−0.148630	+	0.988893i	$0.547486\pi$
$68$	−0.819683	−	0.574430i	−0.0994012	−	0.0696598i
$69$	−4.36242	−	2.40954i	−0.525174	−	0.290075i
$70$	−3.47558	−	6.67975i	−0.415412	−	0.798382i
$71$	2.70354	+	4.68267i	0.320851	+	0.555731i	0.980664	−	0.195699i	$-0.0626977\pi$
$71$	2.70354	+	4.68267i	0.320851	+	0.555731i	−0.659813	+	0.751430i	$0.729364\pi$
$72$	8.45748	−	0.686256i	0.996724	−	0.0808761i
$73$	4.58071	−	7.93403i	0.536132	−	0.928608i	−0.462976	−	0.886371i	$-0.653218\pi$
$73$	4.58071	−	7.93403i	0.536132	−	0.928608i	0.999108	−	0.0422366i	$-0.0134483\pi$
$74$	13.9669	+	0.612563i	1.62362	+	0.0712090i
$75$	−2.19756	+	0.430603i	−0.253753	+	0.0497217i
$76$	10.7220	+	0.942305i	1.22989	+	0.108090i
$77$	1.19856	+	6.79738i	0.136589	+	0.774633i
$78$	−8.72682	−	5.33208i	−0.988118	−	0.603740i
$79$	−9.18302	+	10.9439i	−1.03317	+	1.23128i	−0.0607247	+	0.998155i	$0.519341\pi$
$79$	−9.18302	+	10.9439i	−1.03317	+	1.23128i	−0.972446	+	0.233130i	$0.925103\pi$
$80$	−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	0.0104696	+	0.999945i	$0.496667\pi$
$83$	−8.89271	+	10.5979i	−0.976102	+	1.16327i	−0.986572	+	0.163328i	$0.947777\pi$
$84$	6.72020	+	2.98306i	0.733234	+	0.325479i
$85$	−1.23637	+	0.218005i	−0.134103	+	0.0236460i
$86$	15.8420	+	3.51536i	1.70829	+	0.379071i
$87$	0.654421	−	0.128231i	0.0701613	−	0.0137478i
$88$	8.98105	−	1.98549i	0.957383	−	0.211653i
$89$	−12.9048	−	7.45058i	−1.36790	−	0.789760i	−0.377244	−	0.926114i	$-0.623128\pi$
$89$	−12.9048	−	7.45058i	−1.36790	−	0.789760i	−0.990660	+	0.136355i	$0.956461\pi$
$90$	6.88920	−	8.11240i	0.726185	−	0.855122i
$91$	−4.43081	−	7.67438i	−0.464475	−	0.804494i
$92$	−4.71520	+	3.29885i	−0.491593	+	0.343929i
$93$	−1.04485	+	1.89168i	−0.108346	+	0.196158i
$94$	3.09063	−	3.37150i	0.318775	−	0.347744i
$95$	10.3418	−	8.67776i	1.06104	−	0.890319i
$96$	3.58619	−	9.11807i	0.366014	−	0.930609i
$97$	−0.481380	+	0.175208i	−0.0488767	+	0.0177897i	−0.366343	−	0.930480i	$-0.619390\pi$
$97$	−0.481380	+	0.175208i	−0.0488767	+	0.0177897i	0.317466	+	0.948270i	$0.397168\pi$
$98$	−2.14746	−	2.79976i	−0.216926	−	0.282819i
$99$	−8.25780	+	5.19474i	−0.829940	+	0.522091i
$100$	−0.670234	+	2.49741i	−0.0670234	+	0.249741i
$101$	2.28428	−	12.9548i	0.227295	−	1.28905i	−0.630955	−	0.775820i	$-0.717337\pi$
$101$	2.28428	−	12.9548i	0.227295	−	1.28905i	0.858249	−	0.513233i	$-0.171552\pi$
$102$	0.811087	−	0.919192i	0.0803096	−	0.0910136i
$103$	3.94067	−	10.8269i	0.388286	−	1.06681i	−0.579487	−	0.814982i	$-0.696747\pi$
$103$	3.94067	−	10.8269i	0.388286	−	1.06681i	0.967773	−	0.251826i	$-0.0810309\pi$
$104$	−9.96332	+	6.33906i	−0.976984	+	0.621596i
$105$	8.60463	−	3.31790i	0.839725	−	0.323794i
$106$	−14.2761	−	9.09880i	−1.38661	−	0.883754i
$107$		−	2.94545i		−	0.284747i	−0.989813	−	0.142374i	$-0.954527\pi$
$107$		−	2.94545i		−	0.284747i	0.989813	−	0.142374i	$-0.0454734\pi$
$108$	−0.319796	+	10.3874i	−0.0307724	+	0.999526i
$109$			19.9795i			1.91368i	0.290607	+	0.956842i	$0.406143\pi$
$109$			19.9795i			1.91368i	−0.290607	+	0.956842i	$0.593857\pi$
$110$	6.20061	−	9.72879i	0.591205	−	0.927603i
$111$	−2.65302	+	16.9155i	−0.251814	+	1.60555i
$112$	6.50799	−	5.45213i	0.614948	−	0.515177i
$113$	−1.58914	+	4.36612i	−0.149493	+	0.410730i	−0.991724	−	0.128387i	$-0.959020\pi$
$113$	−1.58914	+	4.36612i	−0.149493	+	0.410730i	0.842231	+	0.539117i	$0.181242\pi$
$114$	−2.61119	+	12.9211i	−0.244560	+	1.21017i
$115$	−1.25337	+	7.10824i	−0.116878	+	0.662847i
$116$	0.199591	−	0.743713i	0.0185316	−	0.0690520i
$117$	7.68154	−	9.89327i	0.710159	−	0.914633i
$118$	−6.84123	+	5.24732i	−0.629786	+	0.483055i
$119$	0.998168	−	0.363303i	0.0915019	−	0.0333040i
$120$	−4.91072	−	11.2656i	−0.448285	−	1.02841i
$121$	0.325434	−	0.273072i	0.0295849	−	0.0248247i
$122$	4.86731	+	4.46183i	0.440666	+	0.403955i
$123$	12.6577	−	0.240030i	1.14130	−	0.0216428i
$124$	1.43048	+	2.04465i	0.128461	+	0.183615i
$125$	−4.64976	−	8.05362i	−0.415887	−	0.720337i
$126$	−4.54848	+	7.77180i	−0.405211	+	0.692367i
$127$	−14.8968	−	8.60068i	−1.32188	−	0.763187i	−0.337850	−	0.941200i	$-0.609700\pi$
$127$	−14.8968	−	8.60068i	−1.32188	−	0.763187i	−0.984028	+	0.178013i	$0.943033\pi$
$128$	−7.63193	−	8.35187i	−0.674573	−	0.738208i
$129$	−6.44212	+	18.8013i	−0.567197	+	1.65536i
$130$	−3.20870	+	14.4600i	−0.281422	+	1.26823i
$131$	17.0826	−	3.01211i	1.49251	−	0.263170i	0.632945	−	0.774197i	$-0.281846\pi$
$131$	17.0826	−	3.01211i	1.49251	−	0.263170i	0.859565	+	0.511027i	$0.170735\pi$
$132$	1.19000	+	11.2021i	0.103576	+	0.975014i
$133$	−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	−0.697310	−	0.716770i	$-0.745620\pi$
$137$	1.51760	−	1.80861i	0.129657	−	0.154520i	0.826967	+	0.562250i	$0.190064\pi$
$138$	−3.37110	−	6.18942i	−0.286967	−	0.526879i
$139$	−0.553906	−	3.14136i	−0.0469817	−	0.266446i	0.952264	−	0.305275i	$-0.0987484\pi$
$139$	−0.553906	−	3.14136i	−0.0469817	−	0.266446i	−0.999246	+	0.0388287i	$0.987637\pi$
$140$	0.932283	−	10.6079i	0.0787923	−	0.896534i
$141$	3.68139	+	4.22208i	0.310029	+	0.355563i
$142$	−0.335052	+	7.63942i	−0.0281169	+	0.641086i
$143$	6.78860	−	11.7582i	0.567691	−	0.983270i
$144$	10.6079	+	5.61004i	0.883991	+	0.467503i
$145$	−0.482917	−	0.836437i	−0.0401041	−	0.0694623i
$146$	11.4935	−	5.98025i	0.951207	−	0.494929i
$147$	3.70089	−	2.23132i	0.305244	−	0.184036i
$148$	16.1911	+	11.3466i	1.33090	+	0.932689i
$149$	−15.4423	+	12.9576i	−1.26508	+	1.06153i	−0.269963	+	0.962871i	$0.587011\pi$
$149$	−15.4423	+	12.9576i	−1.26508	+	1.06153i	−0.995121	+	0.0986604i	$0.968544\pi$
$150$	−2.94808	−	1.15682i	−0.240710	−	0.0944539i
$151$	−0.290439	−	0.797974i	−0.0236356	−	0.0649382i	0.927314	−	0.374285i	$-0.122112\pi$
$151$	−0.290439	−	0.797974i	−0.0236356	−	0.0649382i	−0.950949	+	0.309347i	$0.899890\pi$
$152$	12.0706	+	9.27345i	0.979057	+	0.752176i
$153$	1.00798	+	1.11271i	0.0814907	+	0.0899576i
$154$	−3.73724	+	9.01748i	−0.301156	+	0.726649i
$155$	3.08235	+	0.543501i	0.247580	+	0.0436551i
$156$	−6.35462	−	12.9922i	−0.508777	−	1.04020i
$157$	−2.55481	+	7.01929i	−0.203896	+	0.560200i	−0.998924	−	0.0463727i	$-0.985234\pi$
$157$	−2.55481	+	7.01929i	−0.203896	+	0.560200i	0.795028	+	0.606573i	$0.207456\pi$
$158$	−19.2699	+	6.07160i	−1.53303	+	0.483031i
$159$	13.0239	−	16.1328i	1.03286	−	1.27942i
$160$	−14.1765	−	0.632942i	−1.12075	−	0.0500385i
$161$		−	6.10706i		−	0.481304i
$162$	−12.5989	−	1.80784i	−0.989861	−	0.142037i
$163$	5.27568			0.413223			0.206612	−	0.978423i	$-0.433756\pi$
$163$	5.27568			0.413223			0.206612	+	0.978423i	$0.433756\pi$
$164$	6.18323	−	13.2464i	0.482829	−	1.03437i
$165$	10.9941	+	8.87547i	0.855893	+	0.690955i
$166$	−18.6607	+	5.87966i	−1.44835	+	0.456350i
$167$	−3.66882	−	1.33534i	−0.283902	−	0.103332i	0.196144	−	0.980575i	$-0.437158\pi$
$167$	−3.66882	−	1.33534i	−0.283902	−	0.103332i	−0.480046	+	0.877243i	$0.659380\pi$
$168$	5.74702	+	8.66552i	0.443392	+	0.668560i
$169$	−0.769510	+	4.36411i	−0.0591931	+	0.335701i
$170$	−1.64018	−	0.679763i	−0.125796	−	0.0521355i
$171$	−15.3697	−	4.94273i	−1.17535	−	0.377980i
$172$	16.2210	+	16.2337i	1.23684	+	1.23781i
$173$	−1.17536	+	0.427796i	−0.0893610	+	0.0325248i	−0.386314	−	0.922367i	$-0.626252\pi$
$173$	−1.17536	+	0.427796i	−0.0893610	+	0.0325248i	0.296953	+	0.954892i	$0.404030\pi$
$174$	0.877920	+	0.344493i	0.0665549	+	0.0261160i
$175$	−1.76391	−	2.10214i	−0.133339	−	0.158907i
$176$	12.2198	+	4.45856i	0.921104	+	0.336076i
$177$	−5.45224	−	9.04313i	−0.409815	−	0.679724i
$178$	−9.72694	−	18.6943i	−0.729065	−	1.40119i
$179$	11.6215	−	6.70967i	0.868631	−	0.501504i	0.00173797	−	0.999998i	$-0.499447\pi$
$179$	11.6215	−	6.70967i	0.868631	−	0.501504i	0.866893	+	0.498494i	$0.166113\pi$
$180$	14.3821	−	4.43832i	1.07198	−	0.330813i
$181$	2.75929	+	1.59308i	0.205097	+	0.118413i	0.599031	−	0.800726i	$-0.295553\pi$
$181$	2.75929	+	1.59308i	0.205097	+	0.118413i	−0.393934	+	0.919139i	$0.628886\pi$
$182$	0.549113	−	12.5202i	0.0407030	−	0.928058i
$183$	−6.09526	+	5.31468i	−0.450574	+	0.392873i
$184$	−8.13071	+	0.350182i	−0.599404	+	0.0258158i
$185$	24.4219	−	4.30623i	1.79553	−	0.316600i
$186$	−2.68392	+	1.46181i	−0.196795	+	0.107185i
$187$	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	$-0.242492\pi$
$191$	2.34242	+	1.96552i	0.169491	+	0.142220i	−0.554096	+	0.832452i	$0.686936\pi$
$192$	11.2074	−	8.14825i	0.808825	−	0.588049i
$193$	1.45237	+	8.23682i	0.104544	+	0.592899i	0.991401	+	0.130856i	$0.0417725\pi$
$193$	1.45237	+	8.23682i	0.104544	+	0.592899i	−0.886857	+	0.462044i	$0.847116\pi$
$194$	−0.707261	−	0.156942i	−0.0507784	−	0.0112678i
$195$	−17.1612	−	5.88014i	−1.22894	−	0.421086i
$196$	−0.432953	−	4.97123i	−0.0309252	−	0.355088i
$197$	−3.22383	+	5.58384i	−0.229688	+	0.397832i	−0.957716	−	0.287716i	$-0.907104\pi$
$197$	−3.22383	+	5.58384i	−0.229688	+	0.397832i	0.728027	+	0.685548i	$0.240437\pi$
$198$	−13.7966	−	0.0815134i	−0.980483	−	0.00579290i
$199$	−6.35032	+	3.66636i	−0.450162	+	0.259901i	−0.707899	−	0.706314i	$-0.750357\pi$
$199$	−6.35032	+	3.66636i	−0.450162	+	0.259901i	0.257737	+	0.966215i	$0.417023\pi$
$200$	−2.69757	+	2.46894i	−0.190747	+	0.174580i
$201$	−0.402938	−	21.2483i	−0.0284210	−	1.49874i
$202$	12.5710	−	13.7135i	0.884496	−	0.964876i
$203$	0.525281	+	0.626005i	0.0368675	+	0.0439369i
$204$	1.66596	−	0.479715i	0.116641	−	0.0335868i
$205$	−6.27115	−	17.2299i	−0.437996	−	1.20338i
$206$	12.9290	−	9.91675i	0.900808	−	0.690933i
$207$	7.99358	−	3.25769i	0.555592	−	0.226425i
$208$	−16.7004	−	0.0131538i	−1.15796	−	0.000912050i
$209$	−17.2350	−	3.03899i	−1.19217	−	0.210211i
$210$	12.7837	+	2.58342i	0.882156	+	0.178273i
$211$	3.08764	+	1.12381i	0.212562	+	0.0773662i	0.446107	−	0.894980i	$-0.352810\pi$
$211$	3.08764	+	1.12381i	0.212562	+	0.0773662i	−0.233545	+	0.972346i	$0.575032\pi$
$212$	−10.1095	−	21.7022i	−0.694323	−	1.49051i
$213$	−9.25224	−	1.45111i	−0.633953	−	0.0994287i
$214$	2.23881	−	3.51270i	0.153042	−	0.240123i
$215$	28.7844			1.96308
$216$	−8.27674	+	12.1448i	−0.563161	+	0.826347i
$217$	−2.64820			−0.179772
$218$	−15.1862	+	23.8272i	−1.02854	+	1.61378i
$219$	5.70893	+	14.8055i	0.385774	+	1.00046i
$220$	14.7895	−	6.88938i	0.997110	−	0.464482i
$221$	−1.96347	−	0.714644i	−0.132077	−	0.0480721i
$222$	−16.0213	+	18.1567i	−1.07528	+	1.21860i
$223$	13.8982	+	2.45063i	0.930693	+	0.164106i	0.618386	−	0.785875i	$-0.287787\pi$
$223$	13.8982	+	2.45063i	0.930693	+	0.164106i	0.312307	+	0.949981i	$0.398898\pi$
$224$	11.9055	−	1.55546i	0.795467	−	0.103929i
$225$	1.81059	−	3.43014i	0.120706	−	0.228676i
$226$	−5.21383	+	3.99908i	−0.346819	+	0.266015i
$227$	1.45117	+	3.98706i	0.0963177	+	0.264631i	0.978489	−	0.206297i	$-0.0661414\pi$
$227$	1.45117	+	3.98706i	0.0963177	+	0.264631i	−0.882172	+	0.470928i	$0.843919\pi$
$228$	−12.9353	+	13.4248i	−0.856659	+	0.889076i
$229$	−2.88614	−	3.43957i	−0.190722	−	0.227293i	0.662207	−	0.749321i	$-0.269620\pi$
$229$	−2.88614	−	3.43957i	−0.190722	−	0.227293i	−0.852928	+	0.522028i	$0.825176\pi$
$230$	−6.89767	+	7.52451i	−0.454819	+	0.496152i
$231$	−10.4648	−	5.78014i	−0.688536	−	0.380306i
$232$	0.803320	−	0.735234i	0.0527405	−	0.0482705i
$233$	13.0676	−	7.54460i	0.856089	−	0.494263i	−0.00661180	−	0.999978i	$-0.502105\pi$
$233$	13.0676	−	7.54460i	0.856089	−	0.494263i	0.862701	+	0.505715i	$0.168771\pi$
$234$	16.6807	−	5.95990i	1.09045	−	0.389611i
$235$	4.05650	−	7.02606i	0.264617	−	0.458330i
$236$	−12.1472	+	1.05792i	−0.790715	+	0.0688648i
$237$	−4.75809	−	24.2827i	−0.309071	−	1.57733i
$238$	1.46654	+	0.325428i	0.0950620	+	0.0210944i
$239$	−2.20515	−	12.5060i	−0.142639	−	0.808946i	−0.969233	−	0.246147i	$-0.920835\pi$
$239$	−2.20515	−	12.5060i	−0.142639	−	0.808946i	0.826593	−	0.562799i	$-0.190276\pi$
$240$	2.70644	−	17.1678i	0.174700	−	1.10818i
$241$	7.55053	+	6.33565i	0.486373	+	0.408115i	0.852724	−	0.522361i	$-0.174949\pi$
$241$	7.55053	+	6.33565i	0.486373	+	0.408115i	−0.366352	+	0.930477i	$0.619393\pi$
$242$	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
$246$	15.2778	+	9.33471i	0.974076	+	0.595160i
$247$	22.1275	−	3.90168i	1.40794	−	0.248258i
$248$	0.151850	+	3.52572i	0.00964246	+	0.223883i
$249$	−4.60767	−	23.5151i	−0.291999	−	1.49021i
$250$	0.576248	−	13.1389i	0.0364451	−	0.830975i
$251$	−11.6620	−	6.73304i	−0.736097	−	0.424986i	0.0845514	−	0.996419i	$-0.473054\pi$
$251$	−11.6620	−	6.73304i	−0.736097	−	0.424986i	−0.820649	+	0.571433i	$0.806388\pi$
$252$	−11.3317	+	5.81128i	−0.713832	+	0.366076i
$253$	8.10327	−	4.67842i	0.509448	−	0.294130i
$254$	−11.2284	−	21.5800i	−0.704534	−	1.35405i
$255$	1.05134	−	1.90344i	0.0658377	−	0.119198i
$256$	−2.75355	−	15.7613i	−0.172097	−	0.985080i
$257$	9.56428	+	11.3983i	0.596603	+	0.711004i	0.976861	−	0.213877i	$-0.0686091\pi$
$257$	9.56428	+	11.3983i	0.596603	+	0.711004i	−0.380258	+	0.924881i	$0.624165\pi$
$258$	−21.9735	+	17.5256i	−1.36801	+	1.09109i
$259$	−19.7167	+	7.17629i	−1.22514	+	0.445913i
$260$	−14.8176	+	14.8059i	−0.918948	+	0.918225i
$261$	−0.539183	+	1.02147i	−0.0333746	+	0.0632277i
$262$	22.6619	+	9.39209i	1.40006	+	0.580245i
$263$	−3.85332	+	21.8533i	−0.237606	+	1.34753i	0.599450	+	0.800412i	$0.295386\pi$
$263$	−3.85332	+	21.8533i	−0.237606	+	1.34753i	−0.837056	+	0.547118i	$0.815725\pi$
$264$	−7.09541	+	14.2639i	−0.436692	+	0.877884i
$265$	−28.2182	−	10.2706i	−1.73343	−	0.630917i
$266$	−15.4072	+	4.85453i	−0.944674	+	0.297650i
$267$	24.0813	−	9.28564i	1.47375	−	0.568272i
$268$	−22.2366	−	10.3797i	−1.35832	−	0.634044i
$269$	−6.95017			−0.423760			−0.211880	−	0.977296i	$-0.567959\pi$
$269$	−6.95017			−0.423760			−0.211880	+	0.977296i	$0.567959\pi$
$270$	3.43773	+	18.1107i	0.209214	+	1.10218i
$271$		−	18.3855i		−	1.11684i	−0.829559	−	0.558419i	$-0.811408\pi$
$271$		−	18.3855i		−	1.11684i	0.829559	−	0.558419i	$-0.188592\pi$
$272$	0.349170	−	1.97116i	0.0211716	−	0.119519i
$273$	15.1634	+	2.37822i	0.917731	+	0.143936i
$274$	3.18458	−	1.00340i	0.192387	−	0.0606178i
$275$	1.43800	−	3.95086i	0.0867144	−	0.238246i
$276$	0.684206	−	9.94376i	0.0411844	−	0.598544i
$277$	11.8225	+	2.08462i	0.710343	+	0.125253i	0.517133	−	0.855905i	$-0.326999\pi$
$277$	11.8225	+	2.08462i	0.710343	+	0.125253i	0.193210	+	0.981157i	$0.438110\pi$
$278$	1.72714	−	4.16736i	0.103587	−	0.249941i
$279$	−1.41263	−	3.46626i	−0.0845721	−	0.207519i
$280$	9.17482	−	11.9423i	0.548301	−	0.713686i
$281$	3.95786	+	10.8741i	0.236106	+	0.648696i	0.999994	+	0.00334740i	$0.00106551\pi$
$281$	3.95786	+	10.8741i	0.236106	+	0.648696i	−0.763888	+	0.645348i	$0.776712\pi$
$282$	1.18121	+	7.83338i	0.0703398	+	0.466471i
$283$	2.63822	−	2.21373i	0.156826	−	0.131593i	−0.560998	−	0.827817i	$-0.689583\pi$
$283$	2.63822	−	2.21373i	0.156826	−	0.131593i	0.717824	+	0.696224i	$0.245138\pi$
$284$	−6.20624	+	8.85600i	−0.368272	+	0.525507i
$285$	0.443339	+	23.3788i	0.0262611	+	1.38484i
$286$	17.0333	−	8.86271i	1.00720	−	0.524063i
$287$	7.75688	+	13.4353i	0.457874	+	0.793061i
$288$	8.38668	+	14.7534i	0.494190	+	0.869354i
$289$	−8.37477	+	14.5055i	−0.492633	+	0.853266i
$290$	0.0598483	−	1.36458i	0.00351441	−	0.0801312i
$291$	0.287606	−	0.839378i	0.0168598	−	0.0492052i
$292$	18.2525	+	1.60413i	1.06815	+	0.0938746i
$293$	4.70231	+	26.6681i	0.274712	+	1.55797i	0.739876	+	0.672743i	$0.234884\pi$
$293$	4.70231	+	26.6681i	0.274712	+	1.55797i	−0.465164	+	0.885224i	$0.654005\pi$
$294$	6.10964	+	0.151973i	0.356321	+	0.00886324i
$295$	−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
$300$	−2.63655	−	3.62042i	−0.152222	−	0.209025i
$301$	−23.9845	+	4.22911i	−1.38244	+	0.243762i
$302$	0.260160	−	1.17241i	0.0149705	−	0.0674647i
$303$	14.9739	+	17.1732i	0.860229	+	0.986572i
$304$	7.34659	+	20.2342i	0.421356	+	1.16051i
$305$	10.1433	+	5.85621i	0.580801	+	0.335326i
$306$	0.356344	+	2.09317i	0.0203708	+	0.119658i
$307$	3.55520	+	6.15780i	0.202906	+	0.351444i	0.949464	−	0.313877i	$-0.101628\pi$
$307$	3.55520	+	6.15780i	0.202906	+	0.351444i	−0.746557	+	0.665321i	$0.768295\pi$
$308$	−11.3111	+	7.91347i	−0.644509	+	0.450912i
$309$	10.3040	+	17.0903i	0.586175	+	0.972236i
$310$	3.26285	+	2.99104i	0.185318	+	0.169880i
$311$	−3.90024	+	3.27269i	−0.221162	+	0.185577i	−0.746636	−	0.665232i	$-0.768332\pi$
$311$	−3.90024	+	3.27269i	−0.221162	+	0.185577i	0.525474	+	0.850810i	$0.323888\pi$
$312$	2.29679	−	20.3243i	0.130030	−	1.15064i
$313$	22.0859	−	8.03860i	1.24837	−	0.454369i	0.368518	−	0.929621i	$-0.379865\pi$
$313$	22.0859	−	8.03860i	1.24837	−	0.454369i	0.879850	+	0.475252i	$0.157643\pi$
$314$	−8.38213	+	6.42921i	−0.473031	+	0.362821i
$315$	−4.89017	+	15.2063i	−0.275530	+	0.856776i
$316$	−27.5960	−	7.40597i	−1.55240	−	0.416618i
$317$	−1.74582	+	9.90105i	−0.0980551	+	0.556098i	0.895713	+	0.444632i	$0.146666\pi$
$317$	−1.74582	+	9.90105i	−0.0980551	+	0.556098i	−0.993768	+	0.111466i	$0.964445\pi$
$318$	27.7946	−	9.34046i	1.55864	−	0.523787i
$319$	−0.428226	+	1.17654i	−0.0239761	+	0.0658737i
$320$	−16.4256	−	11.5302i	−0.918216	−	0.644560i
$321$	3.96958	+	3.20460i	0.221560	+	0.178863i
$322$	4.64192	−	7.28319i	0.258684	−	0.405876i
$323$			2.69331i			0.149860i
$324$	−13.6511	−	11.7323i	−0.758396	−	0.651794i
$325$			5.39795i			0.299424i
$326$	6.29170	+	4.01000i	0.348465	+	0.222093i
$327$	−26.9263	−	21.7373i	−1.48903	−	1.20208i
$328$	17.4425	−	11.0976i	0.963100	−	0.612763i
$329$	−2.34776	+	6.45042i	−0.129436	+	0.355623i
$330$	6.36530	+	18.9413i	0.350398	+	1.04269i
$331$	−0.758072	+	4.29924i	−0.0416674	+	0.236308i	−0.998528	−	0.0542401i	$-0.982726\pi$
$331$	−0.758072	+	4.29924i	−0.0416674	+	0.236308i	0.956861	+	0.290548i	$0.0938375\pi$
$332$	−26.7236	−	7.17184i	−1.46665	−	0.393606i
$333$	−19.9106	−	21.9793i	−1.09109	−	1.20446i
$334$	−3.36040	−	4.38114i	−0.183873	−	0.239726i
$335$	−28.9236	+	10.5273i	−1.58027	+	0.575170i
$336$	0.267226	+	14.7026i	0.0145784	+	0.802095i
$337$	−15.2139	+	12.7660i	−0.828757	+	0.695409i	−0.955005	−	0.296589i	$-0.904151\pi$
$337$	−15.2139	+	12.7660i	−0.828757	+	0.695409i	0.126249	+	0.991999i	$0.459706\pi$
$338$	−4.23483	+	4.61968i	−0.230344	+	0.251277i
$339$	−4.15525	−	6.89195i	−0.225682	−	0.374319i
$340$	−1.43937	−	2.05736i	−0.0780610	−	0.111576i
$341$	−2.02871	−	3.51382i	−0.109861	−	0.190284i
$342$	−14.5728	−	17.5770i	−0.788006	−	0.950457i
$343$	17.4531	+	10.0766i	0.942380	+	0.544083i
$344$	7.00576	+	31.6895i	0.377725	+	1.70858i
$345$	−8.21611	−	9.42283i	−0.442341	−	0.507308i
$346$	−1.72688	−	0.383197i	−0.0928378	−	0.0206008i
$347$	13.3624	−	2.35616i	0.717334	−	0.126485i	0.196945	−	0.980415i	$-0.436898\pi$
$347$	13.3624	−	2.35616i	0.717334	−	0.126485i	0.520389	+	0.853929i	$0.325787\pi$
$348$	0.785149	+	1.07814i	0.0420884	+	0.0577942i
$349$	20.5757	−	24.5212i	1.10139	−	1.31259i	0.155598	−	0.987820i	$-0.450270\pi$
$349$	20.5757	−	24.5212i	1.10139	−	1.31259i	0.945794	−	0.324767i	$-0.105286\pi$
$350$	−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	−0.832671	−	0.553768i	$-0.813190\pi$
$353$	−2.68155	+	3.19575i	−0.142725	+	0.170093i	0.689947	+	0.723860i	$0.257634\pi$
$354$	0.371346	−	14.9289i	0.0197368	−	0.793463i
$355$	2.35537	+	13.3579i	0.125010	+	0.708966i
$356$	2.60913	−	29.6879i	0.138284	−	1.57345i
$357$	−0.596368	+	1.74050i	−0.0315631	+	0.0921169i
$358$	18.9596	+	0.831534i	1.00205	+	0.0439479i
$359$	−5.32400	+	9.22145i	−0.280990	+	0.486689i	−0.971629	−	0.236511i	$-0.923996\pi$
$359$	−5.32400	+	9.22145i	−0.280990	+	0.486689i	0.690639	+	0.723200i	$0.257330\pi$
$360$	20.5254	+	5.63865i	1.08179	+	0.297183i
$361$	−4.98105	−	8.62742i	−0.262160	−	0.454075i
$362$	2.07981	+	3.99720i	0.109312	+	0.210088i
$363$	0.0139510	+	0.735684i	0.000732237	+	0.0386134i
$364$	10.1713	−	14.5140i	0.533123	−	0.760741i
$365$	17.6052	−	14.7726i	0.921501	−	0.773231i
$366$	−11.3088	+	1.70526i	−0.591118	+	0.0891355i
$367$	−1.17353	−	3.22425i	−0.0612578	−	0.168304i	0.905288	−	0.424798i	$-0.139655\pi$
$367$	−1.17353	−	3.22425i	−0.0612578	−	0.168304i	−0.966546	+	0.256494i	$0.917433\pi$
$368$	−9.96274	−	5.76246i	−0.519343	−	0.300389i
$369$	−13.4478	+	17.3198i	−0.700066	+	0.901635i
$370$	32.3983	+	13.4273i	1.68431	+	0.698051i
$371$	25.0217	+	4.41199i	1.29906	+	0.229059i
$372$	−4.31191	−	0.296692i	−0.223562	−	0.0153828i
$373$	−4.78365	+	13.1430i	−0.247688	+	0.680517i	0.752082	+	0.659069i	$0.229050\pi$
$373$	−4.78365	+	13.1430i	−0.247688	+	0.680517i	−0.999770	+	0.0214474i	$0.993173\pi$
$374$	0.691673	+	2.19521i	0.0357655	+	0.113512i
$375$	15.9127	+	2.49574i	0.821729	+	0.128879i
$376$	8.72247	+	2.75585i	0.449827	+	0.142122i
$377$		−	1.60747i		−	0.0827891i
$378$	−5.52536	−	14.5856i	−0.284194	−	0.750201i
$379$	−3.34127			−0.171629			−0.0858147	−	0.996311i	$-0.527349\pi$
$379$	−3.34127			−0.171629			−0.0858147	+	0.996311i	$0.527349\pi$
$380$	24.4662	+	11.4205i	1.25509	+	0.585859i
$381$	27.7986	−	10.7190i	1.42417	−	0.549151i
$382$	1.29956	+	4.12450i	0.0664912	+	0.211028i
$383$	−11.8647	−	4.31841i	−0.606260	−	0.220660i	0.0206063	−	0.999788i	$-0.493440\pi$
$383$	−11.8647	−	4.31841i	−0.606260	−	0.220660i	−0.626866	+	0.779127i	$0.715663\pi$
$384$	19.5592	−	1.19883i	0.998127	−	0.0611776i
$385$	−3.00667	+	17.0517i	−0.153234	+	0.869033i
$386$	−4.52866	+	10.9271i	−0.230502	+	0.556172i
$387$	−18.3296	−	29.1376i	−0.931744	−	1.48115i
$388$	−0.724179	−	0.724750i	−0.0367646	−	0.0367936i
$389$	33.8930	−	12.3361i	1.71845	−	0.625463i	0.720743	−	0.693203i	$-0.243801\pi$
$389$	33.8930	−	12.3361i	1.71845	−	0.625463i	0.997703	+	0.0677397i	$0.0215787\pi$
$390$	−15.9967	−	20.0566i	−0.810027	−	1.01561i
$391$	−0.925603	−	1.10309i	−0.0468097	−	0.0557857i
$392$	3.26225	−	6.25770i	0.164769	−	0.316061i
$393$	−14.5261	+	26.2993i	−0.732746	+	1.32662i
$394$	−8.08892	+	4.20880i	−0.407514	+	0.212036i
$395$	−31.0366	+	17.9190i	−1.56162	+	0.901601i
$396$	−16.3917	−	10.5839i	−0.823713	−	0.531861i
$397$	15.9084	+	9.18470i	0.798418	+	0.460967i	0.842918	−	0.538042i	$-0.180836\pi$
$397$	15.9084	+	9.18470i	0.798418	+	0.460967i	−0.0444994	+	0.999009i	$0.514169\pi$
$398$	−10.3601	−	0.454374i	−0.519303	−	0.0227757i
$399$	−3.80431	−	19.4151i	−0.190454	−	0.971973i
$400$	−5.09371	+	0.894022i	−0.254685	+	0.0447011i
$401$	6.51556	−	1.14887i	0.325372	−	0.0573718i	−0.00857653	−	0.999963i	$-0.502730\pi$
$401$	6.51556	−	1.14887i	0.325372	−	0.0573718i	0.333948	+	0.942591i	$0.391619\pi$
$402$	15.6701	−	25.6467i	0.781555	−	1.27914i
$403$	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
$408$	2.35143	+	0.694180i	0.116413	+	0.0343670i
$409$	0.528720	+	2.99852i	0.0261435	+	0.148267i	0.995085	−	0.0990218i	$-0.0315714\pi$
$409$	0.528720	+	2.99852i	0.0261435	+	0.148267i	−0.968942	+	0.247289i	$0.920460\pi$
$410$	5.61737	−	25.3147i	0.277422	−	1.25021i
$411$	0.786330	+	4.01300i	0.0387868	+	0.197947i
$412$	22.9566	−	1.99933i	1.13099	−	0.0985001i
$413$	6.46998	−	11.2063i	0.318367	−	0.551428i
$414$	12.0092	+	2.19078i	0.590219	+	0.107671i
$415$	−30.0554	+	17.3525i	−1.47536	+	0.851801i
$416$	−19.9066	−	12.7095i	−0.976003	−	0.623135i
$417$	4.83624	+	2.67125i	0.236832	+	0.130812i
$418$	−18.2443	−	16.7244i	−0.892356	−	0.818017i
$419$	−17.1887	−	20.4847i	−0.839723	−	1.00074i	−0.999907	−	0.0136562i	$-0.995653\pi$
$419$	−17.1887	−	20.4847i	−0.839723	−	1.00074i	0.160183	−	0.987087i	$-0.448791\pi$
$420$	13.2820	+	12.7977i	0.648094	+	0.624464i
$421$	−10.4312	−	28.6596i	−0.508387	−	1.39678i	−0.882900	−	0.469560i	$-0.844412\pi$
$421$	−10.4312	−	28.6596i	−0.508387	−	1.39678i	0.374513	−	0.927222i	$-0.377810\pi$
$422$	2.82808	+	3.68713i	0.137669	+	0.179487i
$423$	−9.69538	+	0.367845i	−0.471406	+	0.0178852i
$424$	4.43921	−	33.5659i	0.215587	−	1.63010i
$425$	−0.637214	−	0.112358i	−0.0309094	−	0.00545016i
$426$	−9.93111	−	8.76312i	−0.481164	−	0.424575i
$427$	−9.31223	−	3.38938i	−0.450651	−	0.164023i
$428$	5.33995	−	2.48750i	0.258116	−	0.120238i
$429$	8.46062	+	21.9417i	0.408482	+	1.05936i
$430$	34.3279	+	21.8788i	1.65544	+	1.05509i
$431$	−9.80169			−0.472131			−0.236065	−	0.971737i	$-0.575858\pi$
$431$	−9.80169			−0.472131			−0.236065	+	0.971737i	$0.575858\pi$
$432$	−19.1019	+	8.19261i	−0.919039	+	0.394167i
$433$	−17.0457			−0.819163			−0.409582	−	0.912273i	$-0.634325\pi$
$433$	−17.0457			−0.819163			−0.409582	+	0.912273i	$0.634325\pi$
$434$	−3.15821	−	2.01288i	−0.151599	−	0.0966212i
$435$	1.65267	+	0.259204i	0.0792395	+	0.0124279i
$436$	−36.2217	+	16.8731i	−1.73471	+	0.808075i
$437$	14.5508	+	5.29605i	0.696058	+	0.253345i
$438$	−4.44515	+	21.9962i	−0.212397	+	1.05102i
$439$	−1.11745	−	0.197037i	−0.0533332	−	0.00940408i	0.146918	−	0.989149i	$-0.453065\pi$
$439$	−1.11745	−	0.197037i	−0.0533332	−	0.00940408i	−0.200251	+	0.979745i	$0.564176\pi$
$440$	22.8743	+	3.02521i	1.09049	+	0.144221i
$441$	−1.01936	+	7.41533i	−0.0485411	+	0.353111i
$442$	−1.79841	−	2.34469i	−0.0855416	−	0.111525i
$443$	−4.36044	−	11.9802i	−0.207171	−	0.569198i	0.791973	−	0.610556i	$-0.209054\pi$
$443$	−4.36044	−	11.9802i	−0.207171	−	0.569198i	−0.999144	+	0.0413580i	$0.986832\pi$
$444$	−32.9075	+	9.47576i	−1.56172	+	0.449700i
$445$	−24.0277	−	28.6351i	−1.13902	−	1.35743i
$446$	14.7121	+	13.4865i	0.696638	+	0.638604i
$447$	−0.661994	−	34.9093i	−0.0313113	−	1.65115i
$448$	15.3806	+	7.19421i	0.726664	+	0.339895i
$449$	−9.50475	+	5.48757i	−0.448557	+	0.258974i	−0.707221	−	0.706993i	$-0.750051\pi$
$449$	−9.50475	+	5.48757i	−0.448557	+	0.258974i	0.258664	+	0.965967i	$0.416718\pi$
$450$	4.76651	−	2.71452i	0.224695	−	0.127964i
$451$	−11.8846	+	20.5847i	−0.559624	+	0.969297i
$452$	−9.25761	+	0.806262i	−0.435441	+	0.0379234i
$453$	1.39142	+	0.476759i	0.0653746	+	0.0224001i
$454$	−1.29988	+	5.85794i	−0.0610066	+	0.274927i
$455$	−3.86019	−	21.8922i	−0.180968	−	1.02632i
$456$	−25.6305	+	6.17819i	−1.20026	+	0.289320i
$457$	−1.04379	−	0.875846i	−0.0488265	−	0.0409703i	0.618048	−	0.786140i	$-0.287924\pi$
$457$	−1.04379	−	0.875846i	−0.0488265	−	0.0409703i	−0.666874	+	0.745170i	$0.732368\pi$
$458$	−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	$-0.157278\pi$
$461$	12.1576	+	10.2015i	0.566237	+	0.475129i	−0.314158	+	0.949371i	$0.601722\pi$
$462$	−8.08678	−	14.8475i	−0.376231	−	0.690770i
$463$	−3.06325	+	0.540133i	−0.142361	+	0.0251021i	−0.244375	−	0.969681i	$-0.578583\pi$
$463$	−3.06325	+	0.540133i	−0.142361	+	0.0251021i	0.102013	+	0.994783i	$0.467472\pi$
$464$	1.51687	−	0.266234i	0.0704191	−	0.0123596i
$465$	−4.08602	+	3.56275i	−0.189485	+	0.165219i
$466$	21.3189	+	0.935007i	0.987577	+	0.0433134i
$467$	26.1173	+	15.0788i	1.20857	+	0.697766i	0.962446	−	0.271474i	$-0.0875111\pi$
$467$	26.1173	+	15.0788i	1.20857	+	0.697766i	0.246120	+	0.969239i	$0.420844\pi$
$468$	24.4232	+	5.57115i	1.12896	+	0.257526i
$469$	22.5538	−	13.0214i	1.04144	−	0.601273i
$470$	10.1782	−	5.29587i	0.469484	−	0.244280i
$471$	−6.68028	−	11.0800i	−0.307811	−	0.510539i
$472$	−15.2907	−	7.97131i	−0.703811	−	0.366909i
$473$	−23.9852	−	28.5845i	−1.10284	−	1.31432i
$474$	12.7827	−	32.5758i	0.587127	−	1.49626i
$475$	6.53827	−	2.37974i	0.299997	−	0.109190i
$476$	1.50163	+	1.50281i	0.0688269	+	0.0688811i
$477$	7.57241	+	35.1046i	0.346717	+	1.60733i
$478$	6.87588	−	16.5906i	0.314495	−	0.758836i
$479$	−4.70699	+	26.6947i	−0.215068	+	1.21971i	0.665721	+	0.746201i	$0.268124\pi$
$479$	−4.70699	+	26.6947i	−0.215068	+	1.21971i	−0.880789	+	0.473510i	$0.842987\pi$
$480$	16.2768	−	18.4170i	0.742930	−	0.840615i
$481$	38.7842	+	14.1163i	1.76841	+	0.643647i
$482$	4.18899	+	13.2949i	0.190803	+	0.605566i
$483$	8.23047	+	6.64438i	0.374499	+	0.302330i
$484$	0.769901	+	0.359380i	0.0349955	+	0.0163355i
$485$	−1.28507			−0.0583521
$486$	16.1438	−	15.0126i	0.732298	−	0.680985i
$487$		−	12.4692i		−	0.565032i	−0.959263	−	0.282516i	$-0.908831\pi$
$487$		−	12.4692i		−	0.565032i	0.959263	−	0.282516i	$-0.0911691\pi$
$488$	−3.97852	+	12.5923i	−0.180099	+	0.570027i
$489$	−5.73986	+	7.11002i	−0.259565	+	0.321526i
$490$	−2.66002	−	8.44230i	−0.120167	−	0.381384i
$491$	−7.94617	+	21.8319i	−0.358606	+	0.985261i	0.620908	+	0.783883i	$0.286764\pi$
$491$	−7.94617	+	21.8319i	−0.358606	+	0.985261i	−0.979514	+	0.201377i	$0.935458\pi$
$492$	11.1248	+	22.7450i	0.501546	+	1.02542i
$493$	0.189758	+	0.0334595i	0.00854628	+	0.00150694i
$494$	29.3546	+	12.1659i	1.32073	+	0.547368i
$495$	−23.9229	+	5.16042i	−1.07526	+	0.231944i
$496$	−2.49877	+	4.32014i	−0.112198	+	0.193980i
$497$	−3.92519	−	10.7844i	−0.176069	−	0.483745i
$498$	12.3786	−	31.5460i	0.554696	−	1.41361i
$499$	2.97245	−	2.49418i	0.133065	−	0.111655i	−0.573826	−	0.818977i	$-0.694542\pi$
$499$	2.97245	−	2.49418i	0.133065	−	0.111655i	0.706891	+	0.707322i	$0.250097\pi$
$500$	10.6740	−	15.2312i	0.477354	−	0.681161i
$501$	5.79125	−	3.49163i	0.258734	−	0.155994i
$502$	−8.79018	−	16.8939i	−0.392325	−	0.754011i
$503$	4.27407	+	7.40291i	0.190571	+	0.330079i	0.945440	−	0.325797i	$-0.105633\pi$
$503$	4.27407	+	7.40291i	0.190571	+	0.330079i	−0.754868	+	0.655876i	$0.772299\pi$
$504$	−17.9312	−	1.68271i	−0.798718	−	0.0749536i
$505$	16.4997	−	28.5782i	0.734225	−	1.27172i
$506$	13.2199	+	0.579800i	0.587695	+	0.0257753i
$507$	−5.04428	−	5.78515i	−0.224025	−	0.256927i
$508$	3.01189	−	34.2706i	0.133631	−	1.52051i
$509$	0.382218	+	2.16767i	0.0169415	+	0.0960802i	0.992106	−	0.125401i	$-0.0400219\pi$
$509$	0.382218	+	2.16767i	0.0169415	+	0.0960802i	−0.975165	+	0.221482i	$0.928911\pi$
$510$	2.70061	−	1.47090i	0.119585	−	0.0651324i
$511$	−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
$516$	−39.5263	+	4.19890i	−1.74005	+	0.184846i
$517$	−10.3574	+	1.82629i	−0.455519	+	0.0803202i
$518$	−28.9685	−	6.42815i	−1.27280	−	0.282437i
$519$	0.702234	−	2.04947i	0.0308246	−	0.0899616i
$520$	−28.9251	+	6.39462i	−1.26845	+	0.280423i
$521$	0.771434	+	0.445388i	0.0337971	+	0.0195128i	0.516803	−	0.856104i	$-0.327122\pi$
$521$	0.771434	+	0.445388i	0.0337971	+	0.0195128i	−0.483006	+	0.875617i	$0.660455\pi$
$522$	−1.41944	+	0.808368i	−0.0621270	+	0.0353813i
$523$	−3.36736	−	5.83244i	−0.147244	−	0.255035i	0.782964	−	0.622067i	$-0.213707\pi$
$523$	−3.36736	−	5.83244i	−0.147244	−	0.255035i	−0.930208	+	0.367033i	$0.880374\pi$
$524$	19.8874	+	28.4260i	0.868785	+	1.24179i
$525$	4.75216	−	0.0901165i	0.207401	−	0.00393301i
$526$	−21.2059	+	23.1330i	−0.924621	+	1.00865i
$527$	−0.478333	+	0.401369i	−0.0208365	+	0.0174839i
$528$	−19.3038	+	11.6178i	−0.840088	+	0.505600i
$529$	13.8333	−	5.03492i	0.601449	−	0.218910i
$530$	−25.8460	−	33.6970i	−1.12268	−	1.46370i
$531$	18.1194	+	2.49082i	0.786313	+	0.108092i
$532$	−22.0643	−	5.92141i	−0.956607	−	0.256726i
$533$	5.29916	−	30.0530i	0.229532	−	1.30174i
$534$	35.7770	+	7.23008i	1.54822	+	0.312876i
$535$	2.52713	−	6.94324i	0.109258	−	0.300183i
$536$	−18.6295	−	29.2806i	−0.804671	−	1.26473i
$537$	−3.60139	+	22.9623i	−0.155411	+	0.990895i
$538$	−8.28868	−	5.28277i	−0.357350	−	0.227756i
$539$			8.11368i			0.349481i
$540$	−9.66601	+	24.2116i	−0.415959	+	1.04190i
$541$			29.9430i			1.28735i	0.765299	+	0.643675i	$0.222591\pi$
$541$			29.9430i			1.28735i	−0.765299	+	0.643675i	$0.777409\pi$
$542$	13.9746	−	21.9263i	0.600262	−	0.941813i
$543$	−5.14905	+	1.98545i	−0.220967	+	0.0852038i
$544$	1.91468	−	2.08538i	0.0820912	−	0.0894099i
$545$	−17.1420	+	47.0971i	−0.734281	+	2.01742i
$546$	16.2760	+	14.3618i	0.696548	+	0.614628i
$547$	0.156388	−	0.886918i	0.00668665	−	0.0379219i	−0.981282	−	0.192577i	$-0.938316\pi$
$547$	0.156388	−	0.886918i	0.00668665	−	0.0379219i	0.987969	+	0.154655i	$0.0494266\pi$
$548$	4.56056	+	1.22392i	0.194817	+	0.0522834i
$549$	−0.531043	−	13.9969i	−0.0226644	−	0.597371i
$550$	4.71795	−	3.61873i	0.201174	−	0.154303i
$551$	−1.94706	+	0.708670i	−0.0829473	+	0.0301904i
$552$	8.37414	−	11.3387i	0.356427	−	0.482608i
$553$	23.2283	−	19.4909i	0.987770	−	0.828837i
$554$	12.5148	+	11.4722i	0.531703	+	0.487409i
$555$	−20.7671	+	37.5984i	−0.881514	+	1.59596i
$556$	5.22733	−	3.65715i	0.221688	−	0.155098i
$557$	2.99133	+	5.18113i	0.126747	+	0.219531i	0.922414	−	0.386202i	$-0.126213\pi$
$557$	2.99133	+	5.18113i	0.126747	+	0.219531i	−0.795668	+	0.605733i	$0.792880\pi$
$558$	0.949987	−	5.20754i	0.0402161	−	0.220453i
$559$	41.4887	+	23.9535i	1.75478	+	1.01313i
$560$	20.0190	−	7.26846i	0.845956	−	0.307148i
$561$	−2.76627	+	0.542038i	−0.116792	+	0.0228849i
$562$	−3.54524	+	15.9767i	−0.149547	+	0.673935i
$563$	33.0591	−	5.82922i	1.39328	−	0.245672i	0.573899	−	0.818926i	$-0.305430\pi$
$563$	33.0591	−	5.82922i	1.39328	−	0.245672i	0.819378	+	0.573254i	$0.194319\pi$
$564$	−4.54540	+	10.2398i	−0.191396	+	0.431174i
$565$	−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	−0.378670	−	0.925532i	$-0.623618\pi$
$569$	14.2778	−	17.0156i	0.598557	−	0.713332i	0.977226	+	0.212200i	$0.0680628\pi$
$570$	−17.2413	+	28.2182i	−0.722159	+	1.18193i
$571$	−5.16056	−	29.2670i	−0.215963	−	1.22479i	−0.879228	−	0.476401i	$-0.841941\pi$
$571$	−5.16056	−	29.2670i	−0.215963	−	1.22479i	0.663265	−	0.748384i	$-0.269170\pi$
$572$	27.0501	+	2.37732i	1.13102	+	0.0994006i
$573$	−5.19744	+	1.01841i	−0.217126	+	0.0425449i
$574$	−0.961315	+	21.9187i	−0.0401245	+	0.914869i
$575$	−1.86002	+	3.22165i	−0.0775683	+	0.134352i
$576$	−1.21211	+	23.9694i	−0.0505044	+	0.998724i
$577$	4.32870	+	7.49753i	0.180206	+	0.312126i	0.941951	−	0.335751i	$-0.108990\pi$
$577$	4.32870	+	7.49753i	0.180206	+	0.312126i	−0.761744	+	0.647878i	$0.775657\pi$
$578$	−21.0132	+	10.9335i	−0.874032	+	0.454774i
$579$	−12.6809	−	7.00417i	−0.527001	−	0.291083i
$580$	1.10858	−	1.58189i	0.0460314	−	0.0656846i
$581$	22.4940	−	18.8747i	0.933209	−	0.783056i
$582$	0.980999	−	0.782424i	0.0406637	−	0.0324325i
$583$	13.3142	+	36.5804i	0.551416	+	1.51500i
$584$	20.5484	+	15.7866i	0.850298	+	0.653255i
$585$	26.5958	−	16.7306i	1.09960	−	0.691725i
$586$	−14.6623	+	35.3782i	−0.605694	+	1.46146i
$587$	−35.9900	−	6.34601i	−1.48547	−	0.261928i	−0.628707	−	0.777642i	$-0.716415\pi$
$587$	−35.9900	−	6.34601i	−1.48547	−	0.261928i	−0.856760	+	0.515715i	$0.827527\pi$
$588$	7.17076	+	4.82512i	0.295717	+	0.198985i
$589$	2.29653	−	6.30966i	0.0946268	−	0.259985i
$590$	−20.6288	+	6.49976i	−0.849273	+	0.267591i
$591$	−4.01785	−	10.4199i	−0.165272	−	0.428617i
$592$	−6.89712	+	38.9362i	−0.283470	+	1.60027i
$593$		−	10.8958i		−	0.447436i	−0.974654	−	0.223718i	$-0.928181\pi$
$593$		−	10.8958i		−	0.447436i	0.974654	−	0.223718i	$-0.0718194\pi$
$594$	15.1204	−	18.5050i	0.620396	−	0.759269i
$595$	2.66467			0.109241
$596$	−36.5329	−	17.0531i	−1.49645	−	0.698522i
$597$	1.96790	−	12.5473i	0.0805409	−	0.513525i
$598$	−16.2037	+	5.10549i	−0.662618	+	0.208779i
$599$	−30.9493	−	11.2646i	−1.26455	−	0.460260i	−0.379259	−	0.925291i	$-0.623821\pi$
$599$	−30.9493	−	11.2646i	−1.26455	−	0.460260i	−0.885295	+	0.465031i	$0.846043\pi$
$600$	−0.392469	−	6.32168i	−0.0160225	−	0.258082i
$601$	−0.286907	+	1.62713i	−0.0117032	+	0.0663720i	−0.990100	−	0.140364i	$-0.955173\pi$
$601$	−0.286907	+	1.62713i	−0.0117032	+	0.0663720i	0.978397	+	0.206736i	$0.0662840\pi$
$602$	−31.8181	−	13.1868i	−1.29681	−	0.537454i
$603$	29.0747	+	22.5748i	1.18401	+	0.919317i
$604$	1.20140	−	1.20046i	0.0488844	−	0.0488459i
$605$	1.00143	−	0.364490i	0.0407139	−	0.0148186i
$606$	4.80452	+	31.8620i	0.195170	+	1.29431i
$607$	15.4385	+	18.3989i	0.626628	+	0.746787i	0.982195	−	0.187864i	$-0.0601565\pi$
$607$	15.4385	+	18.3989i	0.626628	+	0.746787i	−0.355567	+	0.934651i	$0.615712\pi$
$608$	−6.61837	+	29.7150i	−0.268410	+	1.20510i
$609$	−1.41516	+	0.0268361i	−0.0573453	+	0.00108745i
$610$	7.64545	+	14.6938i	0.309555	+	0.594936i
$611$	11.6937	−	6.75138i	0.473078	−	0.273132i
$612$	−1.16603	+	2.76713i	−0.0471338	+	0.111855i
$613$	−33.2300	−	19.1854i	−1.34215	−	0.774889i	−0.355025	−	0.934857i	$-0.615528\pi$
$613$	−33.2300	−	19.1854i	−1.34215	−	0.774889i	−0.987122	+	0.159968i	$0.948861\pi$
$614$	−0.440599	+	10.0460i	−0.0177811	+	0.405423i
$615$	30.0436	+	10.2942i	1.21147	+	0.415102i
$616$	−19.5044	+	0.840037i	−0.785855	+	0.0338461i
$617$	−3.23994	+	0.571288i	−0.130435	+	0.0229992i	−0.238484	−	0.971146i	$-0.576651\pi$
$617$	−3.23994	+	0.571288i	−0.130435	+	0.0229992i	0.108050	+	0.994146i	$0.465539\pi$
$618$	−0.701795	+	28.2137i	−0.0282303	+	1.13492i
$619$	−13.4224	−	11.2627i	−0.539493	−	0.452688i	0.331872	−	0.943325i	$-0.392320\pi$
$619$	−13.4224	−	11.2627i	−0.539493	−	0.452688i	−0.871364	+	0.490636i	$0.836764\pi$
$620$	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
$624$	18.1875	−	22.4928i	0.728082	−	0.900431i
$625$	−5.17348	−	29.3403i	−0.206939	−	1.17361i
$626$	32.4494	+	7.20056i	1.29694	+	0.287792i
$627$	22.8470	−	19.9211i	0.912421	−	0.795574i
$628$	−14.8832	+	1.29621i	−0.593904	+	0.0517242i
$629$	−2.47368	+	4.28454i	−0.0986321	+	0.170836i
$630$	−17.3901	+	14.4178i	−0.692838	+	0.574419i
$631$	−41.4323	+	23.9209i	−1.64939	+	0.952277i	−0.672078	+	0.740480i	$0.734598\pi$
$631$	−41.4323	+	23.9209i	−1.64939	+	0.952277i	−0.977314	+	0.211797i	$0.932069\pi$
$632$	−27.2814	−	29.8077i	−1.08519	−	1.18569i
$633$	−4.87386	+	2.93852i	−0.193719	+	0.116796i
$634$	−9.60774	+	10.4809i	−0.381572	+	0.416248i
$635$	−27.7367	−	33.0554i	−1.10070	−	1.31176i
$636$	40.2470	+	9.98710i	1.59590	+	0.396014i
$637$	−3.56281	−	9.78874i	−0.141164	−	0.387844i
$638$	−1.40498	+	1.07764i	−0.0556235	+	0.0426640i
$639$	12.0220	−	10.8904i	0.475581	−	0.430819i
$640$	−10.8248	−	26.2357i	−0.427890	−	1.03706i
$641$	14.9095	+	2.62895i	0.588891	+	0.103837i	0.460150	−	0.887841i	$-0.347796\pi$
$641$	14.9095	+	2.62895i	0.588891	+	0.103837i	0.128740	+	0.991678i	$0.458907\pi$
$642$	2.29827	+	6.83900i	0.0907055	+	0.269914i
$643$	−6.97052	−	2.53706i	−0.274890	−	0.100052i	0.200897	−	0.979612i	$-0.435614\pi$
$643$	−6.97052	−	2.53706i	−0.274890	−	0.100052i	−0.475787	+	0.879561i	$0.657837\pi$
$644$	11.0718	−	5.15755i	0.436289	−	0.203236i
$645$	−31.3170	+	38.7927i	−1.23311	+	1.52746i
$646$	−2.04716	+	3.21200i	−0.0805445	+	0.126375i
$647$	−6.00521			−0.236089			−0.118045	−	0.993008i	$-0.537663\pi$
$647$	−6.00521			−0.236089			−0.118045	+	0.993008i	$0.537663\pi$
$648$	−7.36252	−	24.3679i	−0.289227	−	0.957260i
$649$	19.8258			0.778231
$650$	−4.10293	+	6.43752i	−0.160930	+	0.252500i
$651$	2.88120	−	3.56898i	0.112923	−	0.139879i
$652$	4.45543	+	9.56453i	0.174488	+	0.374576i
$653$	−37.1742	−	13.5303i	−1.45474	−	0.529482i	−0.510829	−	0.859683i	$-0.670661\pi$
$653$	−37.1742	−	13.5303i	−1.45474	−	0.529482i	−0.943911	+	0.330201i	$0.892884\pi$
$654$	−15.5895	−	46.3901i	−0.609599	−	1.81400i
$655$	42.8527	+	7.55608i	1.67439	+	0.295241i
$656$	29.2368	+	0.0230279i	1.14151	+	0.000899088i
$657$	−26.1646	−	8.41425i	−1.02078	−	0.328271i
$658$	−7.70282	+	5.90817i	−0.300287	+	0.230324i
$659$	−6.31505	−	17.3504i	−0.245999	−	0.675877i	−0.999823	−	0.0188010i	$-0.994015\pi$
$659$	−6.31505	−	17.3504i	−0.245999	−	0.675877i	0.753824	−	0.657076i	$-0.228207\pi$
$660$	−6.80597	+	27.4274i	−0.264922	+	1.06761i
$661$	12.6354	+	15.0583i	0.491460	+	0.585699i	0.953588	−	0.301114i	$-0.0973584\pi$
$661$	12.6354	+	15.0583i	0.491460	+	0.585699i	−0.462128	+	0.886813i	$0.652914\pi$
$662$	−4.17188	+	4.55101i	−0.162145	+	0.176880i
$663$	3.09935	−	1.86864i	0.120369	−	0.0725720i
$664$	−26.4189	−	28.8654i	−1.02525	−	1.12020i
$665$	−24.8152	+	14.3270i	−0.962291	+	0.555579i
$666$	−7.03882	−	41.3461i	−0.272749	−	1.60213i
$667$	0.553902	−	0.959387i	0.0214472	−	0.0371476i
$668$	−0.677496	−	7.77910i	−0.0262131	−	0.300982i
$669$	−18.4237	+	16.0643i	−0.712303	+	0.621083i
$670$	−42.4957	−	9.42984i	−1.64175	−	0.364307i
$671$	−2.63655	−	14.9526i	−0.101783	−	0.577239i
$672$	−10.8567	+	17.7373i	−0.418805	+	0.684230i
$673$	−37.6088	−	31.5575i	−1.44971	−	1.21645i	−0.932790	−	0.360420i	$-0.882633\pi$
$673$	−37.6088	−	31.5575i	−1.44971	−	1.21645i	−0.516921	−	0.856033i	$-0.672922\pi$
$674$	−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	$-0.182992\pi$
$677$	11.6959	+	9.81403i	0.449510	+	0.377184i	−0.389744	+	0.920923i	$0.627436\pi$
$678$	0.283010	−	11.3776i	0.0108689	−	0.436954i
$679$	1.07078	−	0.188807i	0.0410927	−	0.00724576i
$680$	−0.152794	−	3.54764i	−0.00585936	−	0.136046i
$681$	−6.95221	−	2.38212i	−0.266409	−	0.0912830i
$682$	0.251419	−	5.73253i	0.00962732	−	0.219510i
$683$	3.01291	+	1.73950i	0.115286	+	0.0665602i	0.556534	−	0.830825i	$-0.312131\pi$
$683$	3.01291	+	1.73950i	0.115286	+	0.0665602i	−0.441248	+	0.897385i	$0.645464\pi$
$684$	−4.01915	−	32.0388i	−0.153676	−	1.22503i
$685$	5.12916	−	2.96132i	0.195975	−	0.113146i
$686$	13.1552	+	25.2831i	0.502269	+	0.965314i
$687$	7.77558	−	0.147450i	0.296657	−	0.00562559i
$688$	−15.7320	+	43.1175i	−0.599775	+	1.64384i
$689$	−32.1257	−	38.2859i	−1.22389	−	1.45858i
$690$	−2.63621	−	17.4825i	−0.100359	−	0.665548i
$691$	29.8872	−	10.8781i	1.13696	−	0.413821i	0.296148	−	0.955142i	$-0.404298\pi$
$691$	29.8872	−	10.8781i	1.13696	−	0.413821i	0.840816	+	0.541321i	$0.182076\pi$
$692$	−1.76819	−	1.76958i	−0.0672165	−	0.0672695i
$693$	19.1755	−	7.81473i	0.728416	−	0.296857i
$694$	17.7268	+	7.34675i	0.672899	+	0.278879i
$695$	1.38951	−	7.88029i	0.0527071	−	0.298917i
$696$	0.116875	+	1.88256i	0.00443013	+	0.0713581i
$697$	3.43738	+	1.25110i	0.130200	+	0.0473890i
$698$	43.1766	−	13.6042i	1.63426	−	0.514926i
$699$	−4.04953	+	25.8196i	−0.153167	+	0.976588i
$700$	2.32142	−	4.97318i	0.0877414	−	0.187969i
$701$	36.8471			1.39170			0.695848	−	0.718189i	$-0.255029\pi$
$701$	36.8471			1.39170			0.695848	+	0.718189i	$0.255029\pi$
$702$	−10.1162	+	28.9648i	−0.381810	+	1.09321i
$703$		−	53.2007i		−	2.00650i
$704$	2.23679	+	25.9193i	0.0843021	+	0.976869i
$705$	5.05560	+	13.1112i	0.190405	+	0.493795i
$706$	−5.62704	+	1.77298i	−0.211776	+	0.0667270i
$707$	−9.54944	+	26.2369i	−0.359144	+	0.986739i
$708$	11.7902	−	17.5218i	0.443103	−	0.658508i
$709$	−30.3426	−	5.35021i	−1.13954	−	0.200932i	−0.428135	−	0.903715i	$-0.640829\pi$
$709$	−30.3426	−	5.35021i	−1.13954	−	0.200932i	−0.711404	+	0.702783i	$0.751940\pi$
$710$	−7.34428	+	17.7208i	−0.275626	+	0.665049i
$711$	37.9025	+	20.0068i	1.42146	+	0.750312i
$712$	25.6771	−	33.4222i	0.962290	−	1.25255i
$713$	1.22784	+	3.37347i	0.0459830	+	0.126337i
$714$	−2.03416	+	1.62240i	−0.0761264	+	0.0607168i
$715$	26.0909	−	21.8929i	0.975745	−	0.818747i
$716$	21.9789	+	15.4027i	0.821390	+	0.575626i
$717$	19.2535	+	10.6345i	0.719035	+	0.397151i
$718$	−13.3585	+	6.95064i	−0.498534	+	0.259396i
$719$	−17.6740	−	30.6122i	−0.659128	−	1.14164i	−0.980842	−	0.194807i	$-0.937592\pi$
$719$	−17.6740	−	30.6122i	−0.659128	−	1.14164i	0.321713	−	0.946837i	$-0.395741\pi$
$720$	20.1925	+	22.3258i	0.752529	+	0.832033i
$721$	−12.2274	+	21.1785i	−0.455373	+	0.788730i
$722$	0.617304	−	14.0750i	0.0229737	−	0.523817i
$723$	−16.7534	+	3.28275i	−0.623066	+	0.122087i
$724$	−0.557883	+	6.34784i	−0.0207336	+	0.235916i
$725$	−0.0864391	−	0.490220i	−0.00321027	−	0.0182063i
$726$	−0.542550	+	0.887971i	−0.0201359	+	0.0329557i
$727$	15.6576	−	18.6601i	0.580710	−	0.692063i	−0.393082	−	0.919503i	$-0.628591\pi$
$727$	15.6576	−	18.6601i	0.580710	−	0.692063i	0.973792	+	0.227440i	$0.0730356\pi$
$728$	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
$732$	−14.7828	−	6.56202i	−0.546389	−	0.242539i
$733$	−15.9357	+	2.80990i	−0.588600	+	0.103786i	−0.460013	−	0.887912i	$-0.652155\pi$
$733$	−15.9357	+	2.80990i	−0.588600	+	0.103786i	−0.128587	+	0.991698i	$0.541044\pi$
$734$	1.05119	−	4.73718i	0.0388000	−	0.174853i
$735$	10.6385	−	2.08456i	0.392406	−	0.0768901i
$736$	−7.50143	−	14.4448i	−0.276506	−	0.532443i
$737$	34.5554	+	19.9506i	1.27287	+	0.734890i
$738$	−29.2024	+	10.4338i	−1.07495	+	0.384074i
$739$	−4.57312	−	7.92087i	−0.168225	−	0.291374i	0.769571	−	0.638561i	$-0.220470\pi$
$739$	−4.57312	−	7.92087i	−0.168225	−	0.291374i	−0.937796	+	0.347187i	$0.887137\pi$
$740$	28.4318	+	40.6389i	1.04517	+	1.49391i
$741$	−18.8161	+	34.0662i	−0.691227	+	1.25145i
$742$	26.4870	+	24.2804i	0.972367	+	0.891363i
$743$	11.2333	−	9.42584i	0.412109	−	0.345800i	−0.413043	−	0.910712i	$-0.635534\pi$
$743$	11.2333	−	9.42584i	0.412109	−	0.345800i	0.825152	+	0.564911i	$0.191090\pi$
$744$	−4.91681	−	3.63128i	−0.180259	−	0.133129i
$745$	−47.5192	+	17.2956i	−1.74097	+	0.633661i
$746$	−15.6948	+	12.0381i	−0.574626	+	0.440746i
$747$	36.7043	+	19.3743i	1.34294	+	0.708868i
$748$	−0.843683	+	3.14371i	−0.0308481	+	0.114946i
$749$	−1.08560	+	6.15672i	−0.0396668	+	0.224962i
$750$	17.0803	+	15.0715i	0.623684	+	0.550333i
$751$	−1.10642	+	3.03986i	−0.0403737	+	0.110926i	−0.958241	−	0.285961i	$-0.907687\pi$
$751$	−1.10642	+	3.03986i	−0.0403737	+	0.110926i	0.917868	+	0.396887i	$0.129909\pi$
$752$	8.30760	+	9.91646i	0.302947	+	0.361616i
$753$	21.7622	−	8.39137i	0.793057	−	0.305799i
$754$	1.22183	−	1.91705i	0.0444963	−	0.0698149i
$755$		−	2.13024i		−	0.0775273i
$756$	4.49690	−	21.5943i	0.163551	−	0.785379i
$757$			20.3830i			0.740831i	0.928866	+	0.370415i	$0.120785\pi$
$757$			20.3830i			0.740831i	−0.928866	+	0.370415i	$0.879215\pi$
$758$	−3.98475	−	2.53967i	−0.144733	−	0.0922449i
$759$	−2.51112	+	16.0108i	−0.0911480	+	0.581155i
$760$	20.4974	+	32.2164i	0.743519	+	1.16861i
$761$	8.81961	−	24.2317i	0.319711	−	0.878398i	−0.670883	−	0.741563i	$-0.734085\pi$
$761$	8.81961	−	24.2317i	0.319711	−	0.878398i	0.990594	−	0.136835i	$-0.0436930\pi$
$762$	41.2997	+	8.34615i	1.49613	+	0.302349i
$763$	7.36377	−	41.7620i	0.266586	−	1.51189i
$764$	−1.58516	+	5.90661i	−0.0573492	+	0.213694i
$765$	1.42141	+	3.48781i	0.0513913	+	0.126102i
$766$	−10.8673	−	14.1684i	−0.392653	−	0.511923i
$767$	−23.9188	+	8.70573i	−0.863657	+	0.314346i
$768$	24.2373	+	13.4371i	0.874587	+	0.484869i
$769$	4.58553	−	3.84772i	0.165359	−	0.138752i	−0.556353	−	0.830946i	$-0.687800\pi$
$769$	4.58553	−	3.84772i	0.165359	−	0.138752i	0.721712	+	0.692193i	$0.243355\pi$
$770$	−16.5465	+	18.0502i	−0.596296	+	0.650485i
$771$	−25.7672	+	0.488630i	−0.927983	+	0.0175976i
$772$	−13.7064	+	9.58926i	−0.493303	+	0.345125i
$773$	−21.7483	−	37.6692i	−0.782233	−	1.35487i	−0.930638	−	0.365941i	$-0.880747\pi$
$773$	−21.7483	−	37.6692i	−0.782233	−	1.35487i	0.148405	−	0.988927i	$-0.452586\pi$
$774$	0.287619	−	48.6812i	0.0103382	−	1.74981i
$775$	1.39701	+	0.806561i	0.0501819	+	0.0289725i
$776$	−0.312770	−	1.41477i	−0.0112278	−	0.0507872i
$777$	11.7800	−	34.3799i	0.422605	−	1.23337i
$778$	49.7969	+	11.0500i	1.78531	+	0.396162i
$779$	−38.7380	+	6.83055i	−1.38793	+	0.244730i
$780$	−3.83261	−	36.0783i	−0.137230	−	1.29181i
$781$	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
$786$	−37.3135	+	20.3229i	−1.33093	+	0.724895i
$787$	8.60165	+	48.7824i	0.306616	+	1.73890i	0.615801	+	0.787902i	$0.288833\pi$
$787$	8.60165	+	48.7824i	0.306616	+	1.73890i	−0.309185	+	0.951002i	$0.600056\pi$
$788$	−12.8458	−	1.12896i	−0.457613	−	0.0402176i
$789$	−25.2593	−	28.9691i	−0.899253	−	1.03133i
$790$	−50.6338	−	2.22071i	−1.80147	−	0.0790093i
$791$	4.93090	−	8.54057i	0.175323	−	0.303668i
$792$	−11.5038	−	25.0814i	−0.408769	−	0.891228i
$793$	9.74671	+	16.8818i	0.346116	+	0.599490i
$794$	11.9909	+	23.0454i	0.425541	+	0.817849i
$795$	44.5426	−	26.8554i	1.57976	−	0.952462i
$796$	−12.0099	−	8.41648i	−0.425680	−	0.298314i
$797$	−17.6198	+	14.7848i	−0.624127	+	0.523705i	−0.899098	−	0.437748i	$-0.855776\pi$
$797$	−17.6198	+	14.7848i	−0.624127	+	0.523705i	0.274971	+	0.961453i	$0.411332\pi$
$798$	10.2203	−	26.0459i	0.361795	−	0.922013i
$799$	0.553578	+	1.52094i	0.0195842	+	0.0538071i
$800$	−6.75422	−	2.80548i	−0.238798	−	0.0991888i
$801$	−13.6859	+	42.5570i	−0.483566	+	1.50368i
$802$	8.64362	+	3.58230i	0.305217	+	0.126495i
$803$	−29.3399	−	5.17341i	−1.03538	−	0.182566i
$804$	38.1818	−	18.6752i	1.34657	−	0.658623i
$805$	5.23973	−	14.3960i	0.184676	−	0.507394i
$806$	2.21390	+	7.02640i	0.0779811	+	0.247495i
$807$	7.56168	−	9.36674i	0.266184	−	0.329725i
$808$	35.4783	+	11.2093i	1.24812	+	0.394343i
$809$			37.2955i			1.31124i	0.755090	+	0.655621i	$0.227593\pi$
$809$			37.2955i			1.31124i	−0.755090	+	0.655621i	$0.772407\pi$
$810$	−28.1480	−	15.0712i	−0.989019	−	0.529546i
$811$	34.1131			1.19787			0.598937	−	0.800796i	$-0.295590\pi$
$811$	34.1131			1.19787			0.598937	+	0.800796i	$0.295590\pi$
$812$	−0.691303	+	1.48098i	−0.0242600	+	0.0519723i
$813$	24.7781	+	20.0031i	0.869005	+	0.701539i
$814$	−13.6625	−	43.3618i	−0.478872	−	1.51983i
$815$	12.4362	+	4.52642i	0.435623	+	0.158554i
$816$	2.27664	+	2.61517i	0.0796984	+	0.0915492i
$817$	10.7230	−	60.8133i	0.375151	−	2.12759i
$818$	−1.64861	+	3.97787i	−0.0576422	+	0.139083i
$819$	−19.7027	+	17.8482i	−0.688467	+	0.623667i
$820$	25.9407	−	25.9203i	0.905888	−	0.905175i
$821$	−4.63164	+	1.68578i	−0.161645	+	0.0588340i	−0.421575	−	0.906793i	$-0.638523\pi$
$821$	−4.63164	+	1.68578i	−0.161645	+	0.0588340i	0.259930	+	0.965627i	$0.416300\pi$
$822$	−2.11248	+	5.38353i	−0.0736813	+	0.187772i
$823$	15.0760	+	17.9669i	0.525518	+	0.626287i	0.961876	−	0.273485i	$-0.0881765\pi$
$823$	15.0760	+	17.9669i	0.525518	+	0.626287i	−0.436359	+	0.899773i	$0.643732\pi$
$824$	28.8974	+	15.0647i	1.00669	+	0.524805i
$825$	3.76005	+	6.23646i	0.130908	+	0.217126i
$826$	16.2339	−	8.44675i	0.564848	−	0.293900i
$827$	−12.0532	+	6.95894i	−0.419132	+	0.241986i	−0.694706	−	0.719294i	$-0.744466\pi$
$827$	−12.0532	+	6.95894i	−0.419132	+	0.241986i	0.275574	+	0.961280i	$0.411132\pi$
$828$	12.6568	+	11.7408i	0.439854	+	0.408019i
$829$	−44.9965	−	25.9788i	−1.56279	−	0.902279i	−0.996973	−	0.0777511i	$-0.975226\pi$
$829$	−44.9965	−	25.9788i	−1.56279	−	0.902279i	−0.565821	−	0.824528i	$-0.691441\pi$
$830$	−49.0331	−	2.15051i	−1.70197	−	0.0746452i
$831$	−15.6721	+	13.6651i	−0.543659	+	0.474036i
$832$	−14.0800	−	30.2880i	−0.488136	−	1.05005i
$833$	1.22969	−	0.216828i	0.0426064	−	0.00751265i
$834$	3.73724	+	6.86168i	0.129410	+	0.237601i
$835$	−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	$-0.273670\pi$
$839$	0.572631	+	0.480495i	0.0197694	+	0.0165885i	−0.632849	+	0.774275i	$0.718115\pi$
$840$	6.11249	+	25.3579i	0.210901	+	0.874930i
$841$	−5.01006	−	28.4134i	−0.172761	−	0.979774i
$842$	9.34375	−	42.1077i	0.322007	−	1.45113i
$843$	−18.9611	−	6.49688i	−0.653056	−	0.223764i
$844$	0.570174	+	6.54682i	0.0196262	+	0.225351i
$845$	−5.55826	+	9.62719i	−0.191210	+	0.331186i
$846$	−11.8422	−	6.93069i	−0.407142	−	0.238282i
$847$	−0.780883	+	0.450843i	−0.0268315	+	0.0154912i
$848$	30.8073	−	36.6560i	1.05793	−	1.25877i
$849$	0.113098	+	5.96403i	0.00388150	+	0.204685i
$850$	−0.674530	−	0.618337i	−0.0231362	−	0.0212088i
$851$	18.2833	+	21.7892i	0.626744	+	0.746925i
$852$	−5.18293	−	17.9993i	−0.177564	−	0.616647i
$853$	10.5662	+	29.0305i	0.361781	+	0.993986i	0.978399	+	0.206723i	$0.0662800\pi$
$853$	10.5662	+	29.0305i	0.361781	+	0.993986i	−0.616618	+	0.787262i	$0.711498\pi$
$854$	−8.52940	−	11.1203i	−0.291870	−	0.380528i
$855$	−31.9899	−	24.8383i	−1.09403	−	0.849452i
$856$	8.25907	+	1.09229i	0.282289	+	0.0373337i
$857$	39.9870	+	7.05078i	1.36593	+	0.240850i	0.808070	−	0.589086i	$-0.200512\pi$
$857$	39.9870	+	7.05078i	1.36593	+	0.240850i	0.557859	+	0.829936i	$0.311623\pi$
$858$	−6.58770	+	32.5982i	−0.224900	+	1.11289i
$859$	32.4767	+	11.8206i	1.10809	+	0.403312i	0.830293	−	0.557327i	$-0.188173\pi$
$859$	32.4767	+	11.8206i	1.10809	+	0.403312i	0.277798	+	0.960639i	$0.410395\pi$
$860$	24.3091	+	52.1847i	0.828933	+	1.77948i
$861$	−26.5461	−	4.16347i	−0.904689	−	0.141891i
$862$	−11.6894	−	7.45018i	−0.398141	−	0.253754i
$863$	42.3075			1.44017			0.720083	−	0.693888i	$-0.244104\pi$
$863$	42.3075			1.44017			0.720083	+	0.693888i	$0.244104\pi$
$864$	−29.0077	−	4.74877i	−0.986863	−	0.161557i
$865$	−3.13769			−0.106685
$866$	−20.3284	−	12.9563i	−0.690789	−	0.440272i
$867$	−10.4375	−	27.0684i	−0.354475	−	0.919293i
$868$	−2.23647	−	4.80106i	−0.0759107	−	0.162959i
$869$	43.6564	+	15.8896i	1.48094	+	0.539018i
$870$	1.77393	+	1.56530i	0.0601420	+	0.0530688i
$871$	−50.4499	−	8.89567i	−1.70943	−	0.301418i
$872$	−56.0226	−	7.40919i	−1.89717	−	0.250907i
$873$	0.818317	+	1.30084i	0.0276958	+	0.0440266i
$874$	13.3276	+	17.3759i	0.450812	+	0.587749i
$875$	6.75085	+	18.5478i	0.228220	+	0.627030i
$876$	−22.0203	+	22.8536i	−0.743997	+	0.772151i
$877$	9.16086	+	10.9175i	0.309340	+	0.368657i	0.898207	−	0.439573i	$-0.144870\pi$
$877$	9.16086	+	10.9175i	0.309340	+	0.368657i	−0.588867	+	0.808230i	$0.700426\pi$
$878$	−1.18289	−	1.08435i	−0.0399207	−	0.0365951i
$879$	−41.0566	−	22.6772i	−1.38480	−	0.764883i
$880$	24.9802	+	20.9944i	0.842082	+	0.707722i
$881$	16.6372	−	9.60547i	0.560520	−	0.323616i	−0.192834	−	0.981231i	$-0.561768\pi$
$881$	16.6372	−	9.60547i	0.560520	−	0.323616i	0.753354	+	0.657615i	$0.228435\pi$
$882$	−6.85200	+	8.06861i	−0.230719	+	0.271684i
$883$	−7.04315	+	12.1991i	−0.237021	+	0.410532i	−0.959858	−	0.280486i	$-0.909504\pi$
$883$	−7.04315	+	12.1991i	−0.237021	+	0.410532i	0.722837	+	0.691018i	$0.242838\pi$
$884$	−0.362581	−	4.16320i	−0.0121949	−	0.140024i
$885$	−5.09362	−	25.9951i	−0.171220	−	0.873816i
$886$	3.90586	−	17.6018i	0.131220	−	0.591343i
$887$	6.56011	+	37.2043i	0.220267	+	1.24920i	0.871529	+	0.490344i	$0.163129\pi$
$887$	6.56011	+	37.2043i	0.220267	+	1.24920i	−0.651262	+	0.758853i	$0.725760\pi$
$888$	−46.4475	−	13.7121i	−1.55868	−	0.460147i
$889$	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
$894$	25.7448	−	42.1355i	0.861034	−	1.40922i
$895$	33.1519	−	5.84557i	1.10814	−	0.195396i
$896$	12.8744	+	20.2704i	0.430103	+	0.677185i
$897$	−4.00098	−	20.4189i	−0.133589	−	0.681766i
$898$	−15.5063	−	0.680078i	−0.517452	−	0.0226945i
$899$	−0.416019	−	0.240189i	−0.0138750	−	0.00801074i
$900$	7.74776	+	0.385678i	0.258259	+	0.0128559i
$901$	5.18824	−	2.99543i	0.172845	−	0.0997924i
$902$	−29.8197	+	15.5157i	−0.992886	+	0.516615i
$903$	20.3952	−	36.9250i	0.678709	−	1.22879i
$904$	−11.6533	−	6.07509i	−0.387584	−	0.202055i
$905$	5.13759	+	6.12274i	0.170779	+	0.203527i
$906$	1.29701	+	1.62618i	0.0430902	+	0.0540263i
$907$	−35.9262	+	13.0761i	−1.19291	+	0.434184i	−0.860745	−	0.509037i	$-0.830002\pi$
$907$	−35.9262	+	13.0761i	−1.19291	+	0.434184i	−0.332166	+	0.943221i	$0.607779\pi$
$908$	−6.00279	+	5.99807i	−0.199210	+	0.199053i
$909$	−39.4356	+	1.49619i	−1.30800	+	0.0496257i
$910$	12.0365	−	29.0424i	0.399005	−	0.962747i
$911$	8.92255	−	50.6023i	0.295617	−	1.67653i	−0.369065	−	0.929404i	$-0.620322\pi$
$911$	8.92255	−	50.6023i	0.295617	−	1.67653i	0.664682	−	0.747126i	$-0.268567\pi$
$912$	−35.2625	−	12.1135i	−1.16766	−	0.401117i
$913$	42.2763	+	15.3873i	1.39914	+	0.509245i
$914$	−0.579089	−	1.83790i	−0.0191546	−	0.0607923i
$915$	−18.9281	+	7.29858i	−0.625744	+	0.241284i
$916$	3.79835	−	8.13723i	0.125501	−	0.268862i
$917$	−36.8169			−1.21580
$918$	−3.20865	−	1.79709i	−0.105901	−	0.0593128i
$919$		−	7.02685i		−	0.231794i	−0.993261	−	0.115897i	$-0.963026\pi$
$919$		−	7.02685i		−	0.231794i	0.993261	−	0.115897i	$-0.0369743\pi$
$920$	−19.4668	−	6.15050i	−0.641801	−	0.202776i
$921$	−12.1669	−	1.90824i	−0.400912	−	0.0628787i
$922$	6.74497	+	21.4070i	0.222134	+	0.705003i
$923$	−7.72113	+	21.2136i	−0.254144	+	0.698256i
$924$	1.64131	−	23.8537i	0.0539952	−	0.784728i
$925$	12.5868	+	2.21939i	0.413852	+	0.0729732i
$926$	−4.06373	−	1.68419i	−0.133543	−	0.0553460i
$927$	−34.2432	−	4.70732i	−1.12470	−	0.154609i
$928$	2.01136	+	0.835455i	0.0660262	+	0.0274252i
$929$	−19.0465	−	52.3299i	−0.624896	−	1.71689i	−0.694674	−	0.719325i	$-0.744451\pi$
$929$	−19.0465	−	52.3299i	−0.624896	−	1.71689i	0.0697781	−	0.997563i	$-0.477771\pi$
$930$	−7.58095	+	1.14314i	−0.248589	+	0.0374851i
$931$	−10.2859	+	8.63091i	−0.337107	+	0.282867i
$932$	24.7139	+	17.3193i	0.809530	+	0.567314i
$933$	−0.167199	−	8.81698i	−0.00547384	−	0.288655i
$934$	19.6859	+	37.8344i	0.644141	+	1.23798i
$935$	2.04132	+	3.53566i	0.0667582	+	0.115629i
$936$	24.8922	+	25.2079i	0.813627	+	0.823948i
$937$	−24.5562	+	42.5326i	−0.802216	+	1.38948i	0.115939	+	0.993256i	$0.463012\pi$
$937$	−24.5562	+	42.5326i	−0.802216	+	1.38948i	−0.918155	+	0.396222i	$0.870321\pi$
$938$	36.7948	+	1.61375i	1.20139	+	0.0526909i
$939$	−13.1955	+	38.5110i	−0.430618	+	1.25676i
$940$	16.1637	+	1.42055i	0.527201	+	0.0463334i
$941$	3.33638	+	18.9215i	0.108763	+	0.616825i	0.989650	+	0.143499i	$0.0458355\pi$
$941$	3.33638	+	18.9215i	0.108763	+	0.616825i	−0.880888	+	0.473326i	$0.843053\pi$
$942$	0.454987	−	18.2915i	0.0148243	−	0.595968i
$943$	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	0.142299	−	0.989824i	$-0.454551\pi$
$947$	33.6161	−	40.0620i	1.09237	−	1.30184i	0.950076	−	0.312018i	$-0.101005\pi$
$948$	40.0050	−	29.1335i	1.29930	−	0.946211i
$949$	37.6687	−	6.64201i	1.22278	−	0.215609i
$950$	9.60627	+	2.13164i	0.311669	+	0.0691596i
$951$	−11.4442	−	13.1250i	−0.371104	−	0.425608i
$952$	0.648546	+	2.93360i	0.0210195	+	0.0950786i
$953$	−27.4810	−	15.8662i	−0.890198	−	0.513956i	−0.0161907	−	0.999869i	$-0.505154\pi$
$953$	−27.4810	−	15.8662i	−0.890198	−	0.513956i	−0.874007	+	0.485913i	$0.838487\pi$
$954$	−17.6519	+	47.6209i	−0.571502	+	1.54178i
$955$	3.83535	+	6.64303i	0.124109	+	0.214963i
$956$	20.8104	−	14.5594i	0.673058	−	0.470885i
$957$	−1.11972	−	1.85718i	−0.0361954	−	0.0600340i
$958$	−25.9039	+	28.2579i	−0.836916	+	0.912973i
$959$	−3.83876	+	3.22110i	−0.123960	+	0.104015i
$960$	33.4100	−	9.59197i	1.07830	−	0.309579i
$961$	−27.6676	+	10.0702i	−0.892504	+	0.324845i
$962$	35.5238	+	46.3144i	1.14533	+	1.49324i
$963$	−8.63767	+	1.86323i	−0.278345	+	0.0600419i
$964$	−5.10961	+	19.0393i	−0.164569	+	0.613216i
$965$	−3.64337	+	20.6626i	−0.117284	+	0.665152i
$966$	4.76521	+	14.1799i	0.153318	+	0.456231i
$967$	0.0970671	−	0.266690i	0.00312147	−	0.00857616i	−0.938122	−	0.346305i	$-0.887436\pi$
$967$	0.0970671	−	0.266690i	0.00312147	−	0.00857616i	0.941244	+	0.337729i	$0.109659\pi$
$968$	0.645012	+	1.01379i	0.0207315	+	0.0325843i
$969$	−3.62977	−	2.93028i	−0.116605	−	0.0941341i
$970$	−1.53256	−	0.976771i	−0.0492075	−	0.0313622i
$971$		−	37.7792i		−	1.21239i	−0.795315	−	0.606196i	$-0.792695\pi$
$971$		−	37.7792i		−	1.21239i	0.795315	−	0.606196i	$-0.207305\pi$
$972$	30.6638	−	5.63304i	0.983542	−	0.180680i
$973$			6.77037i			0.217048i
$974$	9.47771	−	14.8706i	0.303685	−	0.476484i
$975$	−7.27481	−	5.87288i	−0.232980	−	0.188083i
$976$	−14.3160	+	11.9934i	−0.458245	+	0.383898i
$977$	−6.98432	+	19.1893i	−0.223448	+	0.613919i	−0.999867	−	0.0162980i	$-0.994812\pi$
$977$	−6.98432	+	19.1893i	−0.223448	+	0.613919i	0.776419	+	0.630217i	$0.217034\pi$
$978$	−12.2495	+	4.11650i	−0.391697	+	0.131631i
$979$	−8.41461	+	47.7216i	−0.268932	+	1.52519i
$980$	3.24462	−	12.0900i	0.103645	−	0.386202i
$981$	58.5907	−	12.6386i	1.87066	−	0.403520i
$982$	−26.0707	+	19.9966i	−0.831951	+	0.638118i
$983$	32.8266	−	11.9479i	1.04700	−	0.381079i	0.239473	−	0.970903i	$-0.423025\pi$
$983$	32.8266	−	11.9479i	1.04700	−	0.381079i	0.807532	+	0.589824i	$0.200803\pi$
$984$	−4.02092	+	35.5812i	−0.128182	+	1.13429i
$985$	−12.3903	+	10.3967i	−0.394787	+	0.331266i
$986$	0.200871	+	0.184137i	0.00639702	+	0.00586411i
$987$	−6.13890	−	10.1820i	−0.195403	−	0.324098i
$988$	25.7607	+	36.8210i	0.819558	+	1.17143i
$989$	16.5078	+	28.5923i	0.524916	+	0.909181i
$990$	−32.4525	−	12.0294i	−1.03141	−	0.382318i
$991$	7.41357	+	4.28023i	0.235500	+	0.135966i	0.613107	−	0.790000i	$-0.289920\pi$
$991$	7.41357	+	4.28023i	0.235500	+	0.135966i	−0.377607	+	0.925966i	$0.623253\pi$
$992$	−6.26371	+	3.25284i	−0.198873	+	0.103278i
$993$	−4.96931	−	5.69916i	−0.157696	−	0.180857i
$994$	3.51598	−	15.8448i	0.111520	−	0.502567i
$995$	−18.1151	+	3.19419i	−0.574288	+	0.101263i
$996$	38.7403	−	28.2125i	1.22753	−	0.893947i
$997$	7.41930	−	8.84198i	0.234972	−	0.280028i	−0.635654	−	0.771974i	$-0.719270\pi$
$997$	7.41930	−	8.84198i	0.234972	−	0.280028i	0.870626	+	0.491946i	$0.163714\pi$
$998$	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.11.28	yes	192
3.2	odd	2		648.2.v.b.35.5		192
4.3	odd	2		864.2.bh.b.335.24		192
8.3	odd	2	inner	216.2.v.b.11.10	✓	192
8.5	even	2		864.2.bh.b.335.23		192
24.11	even	2		648.2.v.b.35.23		192
27.5	odd	18	inner	216.2.v.b.59.10	yes	192
27.22	even	9		648.2.v.b.611.23		192
108.59	even	18		864.2.bh.b.815.23		192
216.5	odd	18		864.2.bh.b.815.24		192
216.59	even	18	inner	216.2.v.b.59.28	yes	192
216.211	odd	18		648.2.v.b.611.5		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.10	✓	192	8.3	odd	2	inner
216.2.v.b.11.28	yes	192	1.1	even	1	trivial
216.2.v.b.59.10	yes	192	27.5	odd	18	inner
216.2.v.b.59.28	yes	192	216.59	even	18	inner
648.2.v.b.35.5		192	3.2	odd	2
648.2.v.b.35.23		192	24.11	even	2
648.2.v.b.611.5		192	216.211	odd	18
648.2.v.b.611.23		192	27.22	even	9
864.2.bh.b.335.23		192	8.5	even	2
864.2.bh.b.335.24		192	4.3	odd	2
864.2.bh.b.815.23		192	108.59	even	18
864.2.bh.b.815.24		192	216.5	odd	18

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 $\F_{q}$
Belyi maps

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+(1.19259 + 0.760091i) q^{2} +(-1.08798 + 1.34770i) q^{3} +(0.844523 + 1.81295i) q^{4} +(2.35728 + 0.857979i) q^{5} +(-2.32189 + 0.780279i) q^{6} +(-2.09025 - 0.368567i) q^{7} +(-0.370840 + 2.80401i) q^{8} +(-0.632581 - 2.93255i) q^{9} +(2.15912 + 2.81496i) q^{10} +(-1.11223 - 3.05583i) q^{11} +(-3.36213 - 0.834298i) q^{12} +(2.68370 + 3.19831i) q^{13} +(-2.21266 - 2.02833i) q^{14} +(-3.72098 + 2.24343i) q^{15} +(-2.57356 + 3.06215i) q^{16} +(-0.433413 + 0.250231i) q^{17} +(1.47460 - 3.97814i) q^{18} +(2.69082 - 4.66064i) q^{19} +(0.435303 + 4.99821i) q^{20} +(2.77087 - 2.41603i) q^{21} +(0.996279 - 4.48974i) q^{22} +(0.499638 + 2.83359i) q^{23} +(-3.37549 - 3.55050i) 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} +(-6.14280 - 0.152798i) q^{30} +(1.22873 - 0.216658i) q^{31} +(-5.39671 + 1.69574i) q^{32} +(5.32843 + 1.82574i) q^{33} +(-0.707081 - 0.0310113i) q^{34} +(-4.61107 - 2.66221i) q^{35} +(4.78233 - 3.62344i) q^{36} +(8.56116 - 4.94279i) q^{37} +(6.75155 - 3.51294i) q^{38} +(-7.23018 + 0.137108i) q^{39} +(-3.27996 + 6.29166i) q^{40} +(-4.69827 - 5.59918i) q^{41} +(5.14091 - 0.775204i) q^{42} +(10.7825 - 3.92450i) q^{43} +(4.60076 - 4.59714i) q^{44} +(1.02490 - 7.45558i) q^{45} +(-1.55793 + 3.75907i) q^{46} +(0.561599 - 3.18499i) q^{47} +(-1.32686 - 6.79996i) q^{48} +(-2.34455 - 0.853348i) q^{49} +(0.549475 + 1.74391i) q^{50} +(0.134311 - 0.856358i) q^{51} +(-3.53192 + 7.56645i) q^{52} -11.9707 q^{53} +(3.75699 + 6.31546i) q^{54} -8.15772i q^{55} +(1.80861 - 5.72440i) q^{56} +(3.35356 + 8.69712i) q^{57} +(-0.163630 - 0.519325i) q^{58} +(-2.08516 + 5.72892i) q^{59} +(-7.20968 - 4.85131i) q^{60} +(4.59804 + 0.810759i) q^{61} +(1.63005 + 0.675563i) q^{62} +(0.241410 + 6.36290i) q^{63} +(-7.72495 - 2.07968i) q^{64} +(3.58215 + 9.84187i) q^{65} +(4.96688 + 6.22745i) q^{66} +(-9.39931 + 7.88696i) q^{67} +(-0.819683 - 0.574430i) q^{68} +(-4.36242 - 2.40954i) q^{69} +(-3.47558 - 6.67975i) q^{70} +(2.70354 + 4.68267i) q^{71} +(8.45748 - 0.686256i) q^{72} +(4.58071 - 7.93403i) q^{73} +(13.9669 + 0.612563i) q^{74} +(-2.19756 + 0.430603i) q^{75} +(10.7220 + 0.942305i) q^{76} +(1.19856 + 6.79738i) q^{77} +(-8.72682 - 5.33208i) 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} +(6.72020 + 2.98306i) q^{84} +(-1.23637 + 0.218005i) q^{85} +(15.8420 + 3.51536i) q^{86} +(0.654421 - 0.128231i) q^{87} +(8.98105 - 1.98549i) q^{88} +(-12.9048 - 7.45058i) q^{89} +(6.88920 - 8.11240i) q^{90} +(-4.43081 - 7.67438i) q^{91} +(-4.71520 + 3.29885i) q^{92} +(-1.04485 + 1.89168i) q^{93} +(3.09063 - 3.37150i) q^{94} +(10.3418 - 8.67776i) q^{95} +(3.58619 - 9.11807i) q^{96} +(-0.481380 + 0.175208i) q^{97} +(-2.14746 - 2.79976i) q^{98} +(-8.25780 + 5.19474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) \) 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

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