LMFDB - Embedded newform 135.3.i.a.116.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(71,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("135.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.i (of order $6$, degree $2$, not 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.5
Root			$0.0476108i$ of defining polynomial
Character	$\chi$	$=$	135.116
Dual form			135.3.i.a.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0412321 + 0.0238054i) q^{2} +(-1.99887 - 3.46214i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.90756 - 3.30399i) q^{7} -0.380778i q^{8} +O(q^{10})$	\(q+(0.0412321 + 0.0238054i) q^{2} +(-1.99887 - 3.46214i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.90756 - 3.30399i) q^{7} -0.380778i q^{8} -0.106461 q^{10} +(-15.9969 - 9.23583i) q^{11} +(-8.96536 - 15.5285i) q^{13} +(0.157306 - 0.0908204i) q^{14} +(-7.98640 + 13.8329i) q^{16} -9.22729i q^{17} +26.4996 q^{19} +(7.74158 + 4.46960i) q^{20} +(-0.439725 - 0.761626i) q^{22} +(-6.69903 + 3.86769i) q^{23} +(2.50000 - 4.33013i) q^{25} -0.853695i q^{26} -15.2518 q^{28} +(20.1925 + 11.6582i) q^{29} +(-0.881074 - 1.52607i) q^{31} +(-1.97765 + 1.14180i) q^{32} +(0.219659 - 0.380461i) q^{34} +8.53087i q^{35} +10.0487 q^{37} +(1.09264 + 0.630834i) q^{38} +(0.425723 + 0.737374i) q^{40} +(26.7193 - 15.4264i) q^{41} +(-23.2697 + 40.3043i) q^{43} +73.8448i q^{44} -0.368287 q^{46} +(7.03414 + 4.06116i) q^{47} +(17.2224 + 29.8301i) q^{49} +(0.206161 - 0.119027i) q^{50} +(-35.8411 + 62.0786i) q^{52} -88.2024i q^{53} +41.3039 q^{55} +(-1.25809 - 0.726357i) q^{56} +(0.555054 + 0.961382i) q^{58} +(45.6650 - 26.3647i) q^{59} +(3.99753 - 6.92392i) q^{61} -0.0838972i q^{62} +63.7825 q^{64} +(34.7227 + 20.0471i) q^{65} +(-22.5974 - 39.1398i) q^{67} +(-31.9462 + 18.4441i) q^{68} +(-0.203081 + 0.351746i) q^{70} +30.9868i q^{71} -51.5777 q^{73} +(0.414330 + 0.239214i) q^{74} +(-52.9692 - 91.7454i) q^{76} +(-61.0302 + 35.2358i) q^{77} +(41.1464 - 71.2677i) q^{79} -35.7163i q^{80} +1.46892 q^{82} +(-124.398 - 71.8213i) q^{83} +(10.3164 + 17.8686i) q^{85} +(-1.91892 + 1.10789i) q^{86} +(-3.51680 + 6.09128i) q^{88} +76.3730i q^{89} -68.4078 q^{91} +(26.7809 + 15.4620i) q^{92} +(0.193355 + 0.334901i) q^{94} +(-51.3163 + 29.6275i) q^{95} +(76.8993 - 133.193i) q^{97} +1.63995i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 16 * q^4 + 2 * q^7	$ 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) $ 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.0412321	+	0.0238054i	0.0206161	+	0.0119027i	0.510273	−	0.860013i	$-0.329544\pi$
$2$	0.0412321	+	0.0238054i	0.0206161	+	0.0119027i	−0.489657	+	0.871915i	$0.662878\pi$
$3$		0			0
$3$		0			0
$4$	−1.99887	−	3.46214i	−0.499717	−	0.865535i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	1.90756	−	3.30399i	0.272509	−	0.471999i	−0.696995	−	0.717076i	$-0.745480\pi$
$7$	1.90756	−	3.30399i	0.272509	−	0.471999i	0.969504	+	0.245077i	$0.0788134\pi$
$8$		−	0.380778i		−	0.0475973i
$9$		0			0
$10$	−0.106461			−0.0106461
$11$	−15.9969	−	9.23583i	−1.45427	−	0.839621i	−0.455547	−	0.890212i	$-0.650556\pi$
$11$	−15.9969	−	9.23583i	−1.45427	−	0.839621i	−0.998719	+	0.0505906i	$0.983890\pi$
$12$		0			0
$13$	−8.96536	−	15.5285i	−0.689643	−	1.19450i	−0.971953	−	0.235173i	$-0.924434\pi$
$13$	−8.96536	−	15.5285i	−0.689643	−	1.19450i	0.282311	−	0.959323i	$-0.408899\pi$
$14$	0.157306	−	0.0908204i	0.0112361	−	0.00648717i
$15$		0			0
$16$	−7.98640	+	13.8329i	−0.499150	+	0.864553i
$17$		−	9.22729i		−	0.542782i	−0.962469	−	0.271391i	$-0.912516\pi$
$17$		−	9.22729i		−	0.542782i	0.962469	−	0.271391i	$-0.0874836\pi$
$18$		0			0
$19$	26.4996			1.39472			0.697358	−	0.716723i	$-0.254359\pi$
$19$	26.4996			1.39472			0.697358	+	0.716723i	$0.254359\pi$
$20$	7.74158	+	4.46960i	0.387079	+	0.223480i
$21$		0			0
$22$	−0.439725	−	0.761626i	−0.0199875	−	0.0346194i
$23$	−6.69903	+	3.86769i	−0.291262	+	0.168160i	−0.638511	−	0.769613i	$-0.720449\pi$
$23$	−6.69903	+	3.86769i	−0.291262	+	0.168160i	0.347249	+	0.937773i	$0.387116\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		−	0.853695i		−	0.0328344i
$27$		0			0
$28$	−15.2518			−0.544708
$29$	20.1925	+	11.6582i	0.696294	+	0.402006i	0.805966	−	0.591962i	$-0.201647\pi$
$29$	20.1925	+	11.6582i	0.696294	+	0.402006i	−0.109672	+	0.993968i	$0.534980\pi$
$30$		0			0
$31$	−0.881074	−	1.52607i	−0.0284218	−	0.0492279i	0.851465	−	0.524412i	$-0.175715\pi$
$31$	−0.881074	−	1.52607i	−0.0284218	−	0.0492279i	−0.879886	+	0.475184i	$0.842381\pi$
$32$	−1.97765	+	1.14180i	−0.0618015	+	0.0356811i
$33$		0			0
$34$	0.219659	−	0.380461i	0.00646056	−	0.0111900i
$35$			8.53087i			0.243739i
$36$		0			0
$37$	10.0487			0.271587			0.135794	−	0.990737i	$-0.456642\pi$
$37$	10.0487			0.271587			0.135794	+	0.990737i	$0.456642\pi$
$38$	1.09264	+	0.630834i	0.0287536	+	0.0166009i
$39$		0			0
$40$	0.425723	+	0.737374i	0.0106431	+	0.0184343i
$41$	26.7193	−	15.4264i	0.651689	−	0.376253i	−0.137414	−	0.990514i	$-0.543879\pi$
$41$	26.7193	−	15.4264i	0.651689	−	0.376253i	0.789103	+	0.614261i	$0.210546\pi$
$42$		0			0
$43$	−23.2697	+	40.3043i	−0.541156	+	0.937310i	0.457682	+	0.889116i	$0.348680\pi$
$43$	−23.2697	+	40.3043i	−0.541156	+	0.937310i	−0.998838	+	0.0481942i	$0.984653\pi$
$44$			73.8448i			1.67829i
$45$		0			0
$46$	−0.368287			−0.00800624
$47$	7.03414	+	4.06116i	0.149663	+	0.0864077i	0.572961	−	0.819583i	$-0.305795\pi$
$47$	7.03414	+	4.06116i	0.149663	+	0.0864077i	−0.423299	+	0.905990i	$0.639128\pi$
$48$		0			0
$49$	17.2224	+	29.8301i	0.351478	+	0.608778i
$50$	0.206161	−	0.119027i	0.00412321	−	0.00238054i
$51$		0			0
$52$	−35.8411	+	62.0786i	−0.689252	+	1.19382i
$53$		−	88.2024i		−	1.66420i	−0.554629	−	0.832098i	$-0.687140\pi$
$53$		−	88.2024i		−	1.66420i	0.554629	−	0.832098i	$-0.312860\pi$
$54$		0			0
$55$	41.3039			0.750980
$56$	−1.25809	−	0.726357i	−0.0224658	−	0.0129707i
$57$		0			0
$58$	0.555054	+	0.961382i	0.00956990	+	0.0165755i
$59$	45.6650	−	26.3647i	0.773984	−	0.446860i	−0.0603101	−	0.998180i	$-0.519209\pi$
$59$	45.6650	−	26.3647i	0.773984	−	0.446860i	0.834294	+	0.551320i	$0.185876\pi$
$60$		0			0
$61$	3.99753	−	6.92392i	0.0655332	−	0.113507i	−0.831397	−	0.555679i	$-0.812459\pi$
$61$	3.99753	−	6.92392i	0.0655332	−	0.113507i	0.896930	+	0.442172i	$0.145792\pi$
$62$		−	0.0838972i		−	0.00135318i
$63$		0			0
$64$	63.7825			0.996601
$65$	34.7227	+	20.0471i	0.534195	+	0.308418i
$66$		0			0
$67$	−22.5974	−	39.1398i	−0.337274	−	0.584176i	0.646645	−	0.762791i	$-0.276172\pi$
$67$	−22.5974	−	39.1398i	−0.337274	−	0.584176i	−0.983919	+	0.178615i	$0.942838\pi$
$68$	−31.9462	+	18.4441i	−0.469797	+	0.271237i
$69$		0			0
$70$	−0.203081	+	0.351746i	−0.00290115	+	0.00502494i
$71$			30.9868i			0.436434i	0.975900	+	0.218217i	$0.0700240\pi$
$71$			30.9868i			0.436434i	−0.975900	+	0.218217i	$0.929976\pi$
$72$		0			0
$73$	−51.5777			−0.706544			−0.353272	−	0.935521i	$-0.614931\pi$
$73$	−51.5777			−0.706544			−0.353272	+	0.935521i	$0.614931\pi$
$74$	0.414330	+	0.239214i	0.00559906	+	0.00323262i
$75$		0			0
$76$	−52.9692	−	91.7454i	−0.696963	−	1.20718i
$77$	−61.0302	+	35.2358i	−0.792600	+	0.457608i
$78$		0			0
$79$	41.1464	−	71.2677i	0.520841	−	0.902123i	−0.478865	−	0.877888i	$-0.658952\pi$
$79$	41.1464	−	71.2677i	0.520841	−	0.902123i	0.999706	−	0.0242348i	$-0.00771493\pi$
$80$		−	35.7163i		−	0.446453i
$81$		0			0
$82$	1.46892			0.0179137
$83$	−124.398	−	71.8213i	−1.49877	−	0.865317i	−0.498773	−	0.866733i	$-0.666216\pi$
$83$	−124.398	−	71.8213i	−1.49877	−	0.865317i	−0.999999	+	0.00141595i	$0.999549\pi$
$84$		0			0
$85$	10.3164	+	17.8686i	0.121370	+	0.210219i
$86$	−1.91892	+	1.10789i	−0.0223130	+	0.0128824i
$87$		0			0
$88$	−3.51680	+	6.09128i	−0.0399637	+	0.0692191i
$89$			76.3730i			0.858123i	0.903275	+	0.429062i	$0.141156\pi$
$89$			76.3730i			0.858123i	−0.903275	+	0.429062i	$0.858844\pi$
$90$		0			0
$91$	−68.4078			−0.751734
$92$	26.7809	+	15.4620i	0.291097	+	0.168065i
$93$		0			0
$94$	0.193355	+	0.334901i	0.00205697	+	0.00356277i
$95$	−51.3163	+	29.6275i	−0.540172	+	0.311868i
$96$		0			0
$97$	76.8993	−	133.193i	0.792776	−	1.37313i	−0.131465	−	0.991321i	$-0.541968\pi$
$97$	76.8993	−	133.193i	0.792776	−	1.37313i	0.924242	−	0.381808i	$-0.124698\pi$
$98$			1.63995i			0.0167341i
$99$		0			0
$100$	−19.9887			−0.199887
$101$	−35.6495	−	20.5823i	−0.352965	−	0.203785i	0.313025	−	0.949745i	$-0.398658\pi$
$101$	−35.6495	−	20.5823i	−0.352965	−	0.203785i	−0.665991	+	0.745960i	$0.731991\pi$
$102$		0			0
$103$	6.93496	+	12.0117i	0.0673297	+	0.116619i	0.897725	−	0.440556i	$-0.145219\pi$
$103$	6.93496	+	12.0117i	0.0673297	+	0.116619i	−0.830395	+	0.557175i	$0.811885\pi$
$104$	−5.91290	+	3.41381i	−0.0568548	+	0.0328251i
$105$		0			0
$106$	2.09969	−	3.63677i	0.0198084	−	0.0343092i
$107$		−	136.532i		−	1.27600i	−0.770037	−	0.637999i	$-0.779762\pi$
$107$		−	136.532i		−	1.27600i	0.770037	−	0.637999i	$-0.220238\pi$
$108$		0			0
$109$	−28.8309			−0.264504			−0.132252	−	0.991216i	$-0.542221\pi$
$109$	−28.8309			−0.264504			−0.132252	+	0.991216i	$0.542221\pi$
$110$	1.70305	+	0.983255i	0.0154823	+	0.00893868i
$111$		0			0
$112$	30.4691	+	52.7740i	0.272045	+	0.471196i
$113$	132.805	−	76.6750i	1.17527	−	0.678540i	0.220351	−	0.975421i	$-0.429280\pi$
$113$	132.805	−	76.6750i	1.17527	−	0.678540i	0.954915	+	0.296881i	$0.0959463\pi$
$114$		0			0
$115$	8.64841	−	14.9795i	0.0752036	−	0.130256i
$116$		−	93.2124i		−	0.803556i
$117$		0			0
$118$	2.51049			0.0212753
$119$	−30.4869	−	17.6016i	−0.256192	−	0.147913i
$120$		0			0
$121$	110.101	+	190.701i	0.909927	+	1.57604i
$122$	0.329653	−	0.190325i	0.00270207	−	0.00156004i
$123$		0			0
$124$	−3.52230	+	6.10080i	−0.0284056	+	0.0492000i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−151.612			−1.19379			−0.596897	−	0.802318i	$-0.703600\pi$
$127$	−151.612			−1.19379			−0.596897	+	0.802318i	$0.703600\pi$
$128$	10.5405	+	6.08555i	0.0823475	+	0.0475433i
$129$		0			0
$130$	0.954460	+	1.65317i	0.00734200	+	0.0127167i
$131$	−146.805	+	84.7581i	−1.12065	+	0.647009i	−0.941567	−	0.336825i	$-0.890647\pi$
$131$	−146.805	+	84.7581i	−1.12065	+	0.647009i	−0.179085	+	0.983834i	$0.557314\pi$
$132$		0			0
$133$	50.5496	−	87.5545i	0.380072	−	0.658304i
$134$		−	2.15176i		−	0.0160579i
$135$		0			0
$136$	−3.51355			−0.0258349
$137$	168.197	+	97.1086i	1.22772	+	0.708822i	0.966552	−	0.256472i	$-0.0825603\pi$
$137$	168.197	+	97.1086i	1.22772	+	0.708822i	0.261164	+	0.965294i	$0.415894\pi$
$138$		0			0
$139$	7.58876	+	13.1441i	0.0545954	+	0.0945621i	0.892031	−	0.451973i	$-0.149280\pi$
$139$	7.58876	+	13.1441i	0.0545954	+	0.0945621i	−0.837436	+	0.546535i	$0.815946\pi$
$140$	29.5350	−	17.0521i	0.210965	−	0.121800i
$141$		0			0
$142$	−0.737652	+	1.27765i	−0.00519473	+	0.00899754i
$143$			331.210i			2.31615i
$144$		0			0
$145$	−52.1369			−0.359565
$146$	−2.12666	−	1.22783i	−0.0145661	−	0.00840977i
$147$		0			0
$148$	−20.0861	−	34.7901i	−0.135717	−	0.235068i
$149$	147.843	−	85.3574i	0.992237	−	0.572869i	0.0862950	−	0.996270i	$-0.472497\pi$
$149$	147.843	−	85.3574i	0.992237	−	0.572869i	0.905942	+	0.423401i	$0.139164\pi$
$150$		0			0
$151$	−19.6078	+	33.9618i	−0.129853	+	0.224913i	−0.923620	−	0.383310i	$-0.874784\pi$
$151$	−19.6078	+	33.9618i	−0.129853	+	0.224913i	0.793766	+	0.608223i	$0.208117\pi$
$152$		−	10.0905i		−	0.0663847i
$153$		0			0
$154$	−3.35521			−0.0217871
$155$	3.41239	+	1.97014i	0.0220154	+	0.0127106i
$156$		0			0
$157$	63.5403	+	110.055i	0.404715	+	0.700988i	0.994288	−	0.106728i	$-0.0340373\pi$
$157$	63.5403	+	110.055i	0.404715	+	0.700988i	−0.589573	+	0.807715i	$0.700704\pi$
$158$	3.39311	−	1.95901i	0.0214754	−	0.0123988i
$159$		0			0
$160$	2.55313	−	4.42215i	0.0159571	−	0.0276385i
$161$			29.5114i			0.183300i
$162$		0			0
$163$	−47.4451			−0.291075			−0.145537	−	0.989353i	$-0.546491\pi$
$163$	−47.4451			−0.291075			−0.145537	+	0.989353i	$0.546491\pi$
$164$	−106.816	−	61.6705i	−0.651320	−	0.376040i
$165$		0			0
$166$	−3.41947	−	5.92269i	−0.0205992	−	0.0356788i
$167$	−141.295	+	81.5765i	−0.846076	+	0.488482i	−0.859325	−	0.511430i	$-0.829116\pi$
$167$	−141.295	+	81.5765i	−0.846076	+	0.488482i	0.0132492	+	0.999912i	$0.495783\pi$
$168$		0			0
$169$	−76.2552	+	132.078i	−0.451214	+	0.781526i
$170$			0.982346i			0.00577850i
$171$		0			0
$172$	186.052			1.08170
$173$	143.779	+	83.0106i	0.831090	+	0.479830i	0.854226	−	0.519902i	$-0.174032\pi$
$173$	143.779	+	83.0106i	0.831090	+	0.479830i	−0.0231359	+	0.999732i	$0.507365\pi$
$174$		0			0
$175$	−9.53780	−	16.5200i	−0.0545017	−	0.0943997i
$176$	255.516	−	147.522i	1.45179	−	0.838194i
$177$		0			0
$178$	−1.81809	+	3.14902i	−0.0102140	+	0.0176911i
$179$		−	14.1408i		−	0.0789987i	−0.999220	−	0.0394994i	$-0.987424\pi$
$179$		−	14.1408i		−	0.0789987i	0.999220	−	0.0394994i	$-0.0125763\pi$
$180$		0			0
$181$	148.548			0.820706			0.410353	−	0.911927i	$-0.365406\pi$
$181$	148.548			0.820706			0.410353	+	0.911927i	$0.365406\pi$
$182$	−2.82060	−	1.62847i	−0.0154978	−	0.00894766i
$183$		0			0
$184$	1.47273	+	2.55084i	0.00800397	+	0.0138633i
$185$	−19.4593	+	11.2348i	−0.105185	+	0.0607287i
$186$		0			0
$187$	−85.2217	+	147.608i	−0.455731	+	0.789349i
$188$		−	32.4709i		−	0.172717i
$189$		0			0
$190$	−2.82117			−0.0148483
$191$	234.051	+	135.130i	1.22540	+	0.707485i	0.966064	−	0.258303i	$-0.0831632\pi$
$191$	234.051	+	135.130i	1.22540	+	0.707485i	0.259335	+	0.965787i	$0.416497\pi$
$192$		0			0
$193$	68.3202	+	118.334i	0.353991	+	0.613130i	0.986945	−	0.161059i	$-0.0514910\pi$
$193$	68.3202	+	118.334i	0.353991	+	0.613130i	−0.632954	+	0.774190i	$0.718158\pi$
$194$	6.34144	−	3.66123i	0.0326879	−	0.0188723i
$195$		0			0
$196$	68.8507	−	119.253i	0.351279	−	0.608433i
$197$		−	267.533i		−	1.35803i	−0.734123	−	0.679017i	$-0.762406\pi$
$197$		−	267.533i		−	1.35803i	0.734123	−	0.679017i	$-0.237594\pi$
$198$		0			0
$199$	−391.107			−1.96536			−0.982680	−	0.185310i	$-0.940671\pi$
$199$	−391.107			−1.96536			−0.982680	+	0.185310i	$0.940671\pi$
$200$	−1.64882	−	0.951945i	−0.00824409	−	0.00475973i
$201$		0			0
$202$	−0.979937	−	1.69730i	−0.00485117	−	0.00840248i
$203$	77.0369	−	44.4773i	0.379492	−	0.219100i
$204$		0			0
$205$	−34.4944	+	59.7461i	−0.168265	+	0.291444i
$206$			0.660358i			0.00320562i
$207$		0			0
$208$	286.404			1.37694
$209$	−423.913	−	244.746i	−2.02829	−	1.17103i
$210$		0			0
$211$	−26.9862	−	46.7415i	−0.127897	−	0.221524i	0.794965	−	0.606656i	$-0.207489\pi$
$211$	−26.9862	−	46.7415i	−0.127897	−	0.221524i	−0.922862	+	0.385132i	$0.874156\pi$
$212$	−305.369	+	176.305i	−1.44042	+	0.831626i
$213$		0			0
$214$	3.25019	−	5.62949i	0.0151878	−	0.0263061i
$215$		−	104.065i		−	0.484025i
$216$		0			0
$217$	−6.72281			−0.0309807
$218$	−1.18876	−	0.686332i	−0.00545303	−	0.00314831i
$219$		0			0
$220$	−82.5610	−	143.000i	−0.375277	−	0.649999i
$221$	−143.286	+	82.7259i	−0.648351	+	0.374326i
$222$		0			0
$223$	96.4834	−	167.114i	0.432661	−	0.749391i	−0.564441	−	0.825474i	$-0.690908\pi$
$223$	96.4834	−	167.114i	0.432661	−	0.749391i	0.997101	+	0.0760830i	$0.0242414\pi$
$224$			8.71217i			0.0388936i
$225$		0			0
$226$	7.30111			0.0323058
$227$	186.250	+	107.532i	0.820485	+	0.473707i	0.850584	−	0.525840i	$-0.176249\pi$
$227$	186.250	+	107.532i	0.820485	+	0.473707i	−0.0300987	+	0.999547i	$0.509582\pi$
$228$		0			0
$229$	−87.7329	−	151.958i	−0.383113	−	0.663571i	0.608392	−	0.793636i	$-0.291815\pi$
$229$	−87.7329	−	151.958i	−0.383113	−	0.663571i	−0.991505	+	0.130065i	$0.958481\pi$
$230$	0.713185	−	0.411757i	0.00310080	−	0.00179025i
$231$		0			0
$232$	4.43917	−	7.68887i	0.0191344	−	0.0331417i
$233$			198.965i			0.853927i	0.904269	+	0.426963i	$0.140417\pi$
$233$			198.965i			0.853927i	−0.904269	+	0.426963i	$0.859583\pi$
$234$		0			0
$235$	−18.1621			−0.0772854
$236$	−182.557	−	105.399i	−0.773545	−	0.446607i
$237$		0			0
$238$	−0.838026	−	1.45150i	−0.00352112	−	0.00609876i
$239$	−21.1746	+	12.2252i	−0.0885968	+	0.0511514i	−0.543644	−	0.839316i	$-0.682956\pi$
$239$	−21.1746	+	12.2252i	−0.0885968	+	0.0511514i	0.455047	+	0.890467i	$0.349622\pi$
$240$		0			0
$241$	33.9880	−	58.8690i	0.141029	−	0.244270i	−0.786855	−	0.617138i	$-0.788292\pi$
$241$	33.9880	−	58.8690i	0.141029	−	0.244270i	0.927884	+	0.372868i	$0.121626\pi$
$242$			10.4840i			0.0433223i
$243$		0			0
$244$	−31.9621			−0.130992
$245$	−66.7022	−	38.5105i	−0.272254	−	0.157186i
$246$		0			0
$247$	−237.579	−	411.498i	−0.961856	−	1.66598i
$248$	−0.581092	+	0.335494i	−0.00234311	+	0.00135280i
$249$		0			0
$250$	−0.266152	+	0.460989i	−0.00106461	+	0.00184396i
$251$			275.461i			1.09745i	0.836002	+	0.548726i	$0.184887\pi$
$251$			275.461i			1.09745i	−0.836002	+	0.548726i	$0.815113\pi$
$252$		0			0
$253$	142.885			0.564764
$254$	−6.25128	−	3.60918i	−0.0246113	−	0.0142094i
$255$		0			0
$256$	−127.275	−	220.447i	−0.497169	−	0.861122i
$257$	170.830	−	98.6286i	0.664707	−	0.383769i	−0.129361	−	0.991598i	$-0.541293\pi$
$257$	170.830	−	98.6286i	0.664707	−	0.383769i	0.794068	+	0.607829i	$0.207959\pi$
$258$		0			0
$259$	19.1685	−	33.2009i	0.0740098	−	0.128189i
$260$		−	160.286i		−	0.616486i
$261$		0			0
$262$	−8.07080			−0.0308046
$263$	−324.945	−	187.607i	−1.23553	−	0.713335i	−0.267355	−	0.963598i	$-0.586150\pi$
$263$	−324.945	−	187.607i	−1.23553	−	0.713335i	−0.968178	+	0.250263i	$0.919483\pi$
$264$		0			0
$265$	98.6132	+	170.803i	0.372125	+	0.644540i
$266$	4.16854	−	2.40671i	0.0156712	−	0.00904777i
$267$		0			0
$268$	−90.3382	+	156.470i	−0.337083	+	0.583845i
$269$		−	178.378i		−	0.663115i	−0.943435	−	0.331558i	$-0.892426\pi$
$269$		−	178.378i		−	0.663115i	0.943435	−	0.331558i	$-0.107574\pi$
$270$		0			0
$271$	161.479			0.595863			0.297931	−	0.954587i	$-0.403703\pi$
$271$	161.479			0.595863			0.297931	+	0.954587i	$0.403703\pi$
$272$	127.640	+	73.6929i	0.469264	+	0.270930i
$273$		0			0
$274$	4.62341	+	8.00799i	0.0168738	+	0.0292262i
$275$	−79.9847	+	46.1792i	−0.290853	+	0.167924i
$276$		0			0
$277$	77.1999	−	133.714i	0.278700	−	0.482723i	−0.692362	−	0.721550i	$-0.743430\pi$
$277$	77.1999	−	133.714i	0.278700	−	0.482723i	0.971062	+	0.238828i	$0.0767631\pi$
$278$			0.722614i			0.00259933i
$279$		0			0
$280$	3.24837			0.0116013
$281$	95.5379	+	55.1588i	0.339992	+	0.196295i	0.660269	−	0.751029i	$-0.270442\pi$
$281$	95.5379	+	55.1588i	0.339992	+	0.196295i	−0.320276	+	0.947324i	$0.603776\pi$
$282$		0			0
$283$	39.6434	+	68.6644i	0.140083	+	0.242630i	0.927528	−	0.373755i	$-0.121930\pi$
$283$	39.6434	+	68.6644i	0.140083	+	0.242630i	−0.787445	+	0.616385i	$0.788597\pi$
$284$	107.281	−	61.9384i	0.377748	−	0.218093i
$285$		0			0
$286$	−7.88458	+	13.6565i	−0.0275685	+	0.0477500i
$287$		−	117.707i		−	0.410129i
$288$		0			0
$289$	203.857			0.705388
$290$	−2.14971	−	1.24114i	−0.00741281	−	0.00427979i
$291$		0			0
$292$	103.097	+	178.569i	0.353072	+	0.611538i
$293$	38.4382	−	22.1923i	0.131188	−	0.0757416i	−0.432970	−	0.901409i	$-0.642534\pi$
$293$	38.4382	−	22.1923i	0.131188	−	0.0757416i	0.564158	+	0.825667i	$0.309201\pi$
$294$		0			0
$295$	−58.9533	+	102.110i	−0.199842	+	0.346136i
$296$		−	3.82634i		−	0.0129268i
$297$		0			0
$298$	8.12786			0.0272747
$299$	120.118	+	69.3504i	0.401734	+	0.231941i
$300$		0			0
$301$	88.7768	+	153.766i	0.294939	+	0.510850i
$302$	−1.61695	+	0.933545i	−0.00535413	+	0.00309121i
$303$		0			0
$304$	−211.637	+	366.565i	−0.696173	+	1.20581i
$305$			17.8775i			0.0586147i
$306$		0			0
$307$	173.121			0.563911			0.281956	−	0.959427i	$-0.409017\pi$
$307$	173.121			0.563911			0.281956	+	0.959427i	$0.409017\pi$
$308$	243.982	+	140.863i	0.792151	+	0.457349i
$309$		0			0
$310$	0.0938000	+	0.162466i	0.000302581	+	0.000524085i
$311$	−33.6152	+	19.4077i	−0.108087	+	0.0624042i	−0.553069	−	0.833135i	$-0.686543\pi$
$311$	−33.6152	+	19.4077i	−0.108087	+	0.0624042i	0.444982	+	0.895540i	$0.353210\pi$
$312$		0			0
$313$	−81.8501	+	141.769i	−0.261502	+	0.452935i	−0.966641	−	0.256134i	$-0.917551\pi$
$313$	−81.8501	+	141.769i	−0.261502	+	0.452935i	0.705139	+	0.709069i	$0.250884\pi$
$314$			6.05041i			0.0192688i
$315$		0			0
$316$	−328.985			−1.04109
$317$	−134.696	−	77.7668i	−0.424909	−	0.245321i	0.272267	−	0.962222i	$-0.412227\pi$
$317$	−134.696	−	77.7668i	−0.424909	−	0.245321i	−0.697175	+	0.716901i	$0.745560\pi$
$318$		0			0
$319$	−215.346	−	372.990i	−0.675065	−	1.16925i
$320$	−123.514	+	71.3110i	−0.385982	+	0.222847i
$321$		0			0
$322$	−0.702529	+	1.21682i	−0.00218177	+	0.00377893i
$323$		−	244.520i		−	0.757027i
$324$		0			0
$325$	−89.6536			−0.275857
$326$	−1.95626	−	1.12945i	−0.00600081	−	0.00346457i
$327$		0			0
$328$	−5.87402	−	10.1741i	−0.0179086	−	0.0310186i
$329$	26.8361	−	15.4938i	0.0815686	−	0.0470937i
$330$		0			0
$331$	−257.164	+	445.421i	−0.776930	+	1.34568i	0.156774	+	0.987635i	$0.449891\pi$
$331$	−257.164	+	445.421i	−0.776930	+	1.34568i	−0.933704	+	0.358047i	$0.883443\pi$
$332$			574.245i			1.72965i
$333$		0			0
$334$	−7.76784			−0.0232570
$335$	87.5192	+	50.5292i	0.261251	+	0.150834i
$336$		0			0
$337$	107.327	+	185.895i	0.318477	+	0.551618i	0.980170	−	0.198156i	$-0.0634954\pi$
$337$	107.327	+	185.895i	0.318477	+	0.551618i	−0.661694	+	0.749774i	$0.730162\pi$
$338$	−6.28833	+	3.63057i	−0.0186045	+	0.0107413i
$339$		0			0
$340$	41.2423	−	71.4338i	0.121301	−	0.210099i
$341$			32.5498i			0.0954540i
$342$		0			0
$343$	318.352			0.928140
$344$	15.3470	+	8.86060i	0.0446134	+	0.0257576i
$345$		0			0
$346$	3.95220	+	6.84541i	0.0114225	+	0.0197844i
$347$	192.941	−	111.395i	0.556027	−	0.321023i	−0.195522	−	0.980699i	$-0.562640\pi$
$347$	192.941	−	111.395i	0.556027	−	0.321023i	0.751549	+	0.659677i	$0.229307\pi$
$348$		0			0
$349$	97.8973	−	169.563i	0.280508	−	0.485854i	−0.691002	−	0.722853i	$-0.742830\pi$
$349$	97.8973	−	169.563i	0.280508	−	0.485854i	0.971510	+	0.236999i	$0.0761637\pi$
$350$		−	0.908204i		−	0.00259487i
$351$		0			0
$352$	42.1817			0.119834
$353$	431.523	+	249.140i	1.22244	+	0.705778i	0.965438	−	0.260632i	$-0.0839308\pi$
$353$	431.523	+	249.140i	1.22244	+	0.705778i	0.257006	+	0.966410i	$0.417264\pi$
$354$		0			0
$355$	−34.6443	−	60.0056i	−0.0975895	−	0.169030i
$356$	264.414	−	152.659i	0.742735	−	0.428818i
$357$		0			0
$358$	0.336627	−	0.583054i	0.000940297	−	0.00162864i
$359$			406.420i			1.13209i	0.824374	+	0.566045i	$0.191527\pi$
$359$			406.420i			1.13209i	−0.824374	+	0.566045i	$0.808473\pi$
$360$		0			0
$361$	341.230			0.945235
$362$	6.12494	+	3.53624i	0.0169197	+	0.00976861i
$363$		0			0
$364$	136.738	+	236.837i	0.375654	+	0.650652i
$365$	99.8797	−	57.6656i	0.273643	−	0.157988i
$366$		0			0
$367$	−99.6916	+	172.671i	−0.271639	+	0.470493i	−0.969282	−	0.245953i	$-0.920899\pi$
$367$	−99.6916	+	172.671i	−0.271639	+	0.470493i	0.697642	+	0.716446i	$0.254232\pi$
$368$		−	123.556i		−	0.335749i
$369$		0			0
$370$	−1.06980			−0.00289134
$371$	−291.420	−	168.251i	−0.785498	−	0.453508i
$372$		0			0
$373$	−208.368	−	360.903i	−0.558627	−	0.967570i	−0.997611	−	0.0690751i	$-0.977995\pi$
$373$	−208.368	−	360.903i	−0.558627	−	0.967570i	0.438985	−	0.898494i	$-0.355338\pi$
$374$	−7.02775	+	4.05747i	−0.0187908	+	0.0108489i
$375$		0			0
$376$	1.54640	−	2.67845i	0.00411277	−	0.00712353i
$377$		−	418.078i		−	1.10896i
$378$		0			0
$379$	464.459			1.22548			0.612742	−	0.790283i	$-0.290066\pi$
$379$	464.459			1.22548			0.612742	+	0.790283i	$0.290066\pi$
$380$	205.149	+	118.443i	0.539865	+	0.311691i
$381$		0			0
$382$	6.43362	+	11.1434i	0.0168419	+	0.0291711i
$383$	−307.970	+	177.806i	−0.804099	+	0.464247i	−0.844902	−	0.534921i	$-0.820342\pi$
$383$	−307.970	+	177.806i	−0.804099	+	0.464247i	0.0408036	+	0.999167i	$0.487008\pi$
$384$		0			0
$385$	78.7897	−	136.468i	0.204648	−	0.354462i
$386$			6.50556i			0.0168538i
$387$		0			0
$388$	−614.846			−1.58465
$389$	126.875	+	73.2514i	0.326157	+	0.188307i	0.654134	−	0.756379i	$-0.273033\pi$
$389$	126.875	+	73.2514i	0.326157	+	0.188307i	−0.327977	+	0.944686i	$0.606367\pi$
$390$		0			0
$391$	35.6883	+	61.8139i	0.0912743	+	0.158092i
$392$	11.3587	−	6.55793i	0.0289762	−	0.0167294i
$393$		0			0
$394$	6.36871	−	11.0309i	0.0161642	−	0.0279973i
$395$			184.012i			0.465854i
$396$		0			0
$397$	−514.307			−1.29548			−0.647742	−	0.761860i	$-0.724286\pi$
$397$	−514.307			−1.29548			−0.647742	+	0.761860i	$0.724286\pi$
$398$	−16.1262	−	9.31044i	−0.0405180	−	0.0233931i
$399$		0			0
$400$	39.9320	+	69.1643i	0.0998300	+	0.172911i
$401$	−81.9711	+	47.3260i	−0.204417	+	0.118020i	−0.598714	−	0.800963i	$-0.704321\pi$
$401$	−81.9711	+	47.3260i	−0.204417	+	0.118020i	0.394297	+	0.918983i	$0.370988\pi$
$402$		0			0
$403$	−15.7983	+	27.3634i	−0.0392017	+	0.0678994i
$404$			164.565i			0.407338i
$405$		0			0
$406$	4.23519			0.0104315
$407$	−160.749	−	92.8083i	−0.394960	−	0.228030i
$408$		0			0
$409$	329.284	+	570.337i	0.805096	+	1.39447i	0.916226	+	0.400662i	$0.131220\pi$
$409$	329.284	+	570.337i	0.805096	+	1.39447i	−0.111130	+	0.993806i	$0.535447\pi$
$410$	−2.84456	+	1.64231i	−0.00693794	+	0.00400562i
$411$		0			0
$412$	27.7241	−	48.0196i	0.0672916	−	0.116552i
$413$		−	201.169i		−	0.487092i
$414$		0			0
$415$	321.195			0.773963
$416$	35.4606	+	20.4732i	0.0852419	+	0.0492144i
$417$		0			0
$418$	−11.6525	−	20.1828i	−0.0278769	−	0.0482842i
$419$	265.981	−	153.564i	0.634799	−	0.366502i	−0.147809	−	0.989016i	$-0.547222\pi$
$419$	265.981	−	153.564i	0.634799	−	0.366502i	0.782608	+	0.622514i	$0.213889\pi$
$420$		0			0
$421$	325.896	−	564.469i	0.774101	−	1.34078i	−0.161198	−	0.986922i	$-0.551536\pi$
$421$	325.896	−	564.469i	0.774101	−	1.34078i	0.935298	−	0.353860i	$-0.115131\pi$
$422$		−	2.56967i		−	0.00608927i
$423$		0			0
$424$	−33.5855			−0.0792112
$425$	−39.9553	−	23.0682i	−0.0940126	−	0.0542782i
$426$		0			0
$427$	−15.2510	−	26.4156i	−0.0357167	−	0.0618632i
$428$	−472.692	+	272.909i	−1.10442	+	0.637637i
$429$		0			0
$430$	2.47732	−	4.29084i	0.00576120	−	0.00997869i
$431$		−	702.181i		−	1.62919i	−0.580030	−	0.814595i	$-0.696959\pi$
$431$		−	702.181i		−	1.62919i	0.580030	−	0.814595i	$-0.303041\pi$
$432$		0			0
$433$	−762.480			−1.76092			−0.880462	−	0.474116i	$-0.842768\pi$
$433$	−762.480			−1.76092			−0.880462	+	0.474116i	$0.842768\pi$
$434$	−0.277196	−	0.160039i	−0.000638700	−	0.000368753i
$435$		0			0
$436$	57.6292	+	99.8167i	0.132177	+	0.228937i
$437$	−177.522	+	102.492i	−0.406228	+	0.234536i
$438$		0			0
$439$	225.279	−	390.195i	0.513165	−	0.888827i	−0.486719	−	0.873559i	$-0.661806\pi$
$439$	225.279	−	390.195i	0.513165	−	0.888827i	0.999883	−	0.0152687i	$-0.00486036\pi$
$440$		−	15.7276i		−	0.0357446i
$441$		0			0
$442$	−7.87729			−0.0178219
$443$	−629.134	−	363.231i	−1.42017	−	0.819934i	−0.423855	−	0.905730i	$-0.639323\pi$
$443$	−629.134	−	363.231i	−1.42017	−	0.819934i	−0.996313	+	0.0857960i	$0.972657\pi$
$444$		0			0
$445$	−85.3876	−	147.896i	−0.191882	−	0.332350i
$446$	7.95643	−	4.59365i	0.0178395	−	0.0102997i
$447$		0			0
$448$	121.669	−	210.737i	0.271582	−	0.470395i
$449$			112.578i			0.250731i	0.992111	+	0.125365i	$0.0400103\pi$
$449$			112.578i			0.250731i	−0.992111	+	0.125365i	$0.959990\pi$
$450$		0			0
$451$	−569.901			−1.26364
$452$	−530.919	−	306.526i	−1.17460	−	0.678155i
$453$		0			0
$454$	5.11966	+	8.86751i	0.0112768	+	0.0195320i
$455$	132.471	−	76.4823i	0.291145	−	0.168093i
$456$		0			0
$457$	−12.0837	+	20.9296i	−0.0264414	+	0.0457979i	−0.878943	−	0.476926i	$-0.841751\pi$
$457$	−12.0837	+	20.9296i	−0.0264414	+	0.0457979i	0.852502	+	0.522724i	$0.175084\pi$
$458$		−	8.35406i		−	0.0182403i
$459$		0			0
$460$	−69.1481			−0.150322
$461$	−245.257	−	141.599i	−0.532011	−	0.307157i	0.209824	−	0.977739i	$-0.432711\pi$
$461$	−245.257	−	141.599i	−0.532011	−	0.307157i	−0.741835	+	0.670583i	$0.766044\pi$
$462$		0			0
$463$	−37.5359	−	65.0140i	−0.0810710	−	0.140419i	0.822639	−	0.568564i	$-0.192501\pi$
$463$	−37.5359	−	65.0140i	−0.0810710	−	0.140419i	−0.903710	+	0.428145i	$0.859167\pi$
$464$	−322.531	+	186.214i	−0.695111	+	0.401322i
$465$		0			0
$466$	−4.73644	+	8.20375i	−0.0101640	+	0.0176046i
$467$			92.4237i			0.197909i	0.995092	+	0.0989547i	$0.0315499\pi$
$467$			92.4237i			0.197909i	−0.995092	+	0.0989547i	$0.968450\pi$
$468$		0			0
$469$	−172.423			−0.367640
$470$	−0.748861	−	0.432355i	−0.00159332	−	0.000919904i
$471$		0			0
$472$	−10.0391	−	17.3883i	−0.0212693	−	0.0368395i
$473$	744.488	−	429.831i	1.57397	−	0.908733i
$474$		0			0
$475$	66.2490	−	114.747i	0.139472	−	0.241572i
$476$			140.733i			0.295658i
$477$		0			0
$478$	−1.16410			−0.00243536
$479$	427.600	+	246.875i	0.892693	+	0.515396i	0.874822	−	0.484444i	$-0.160978\pi$
$479$	427.600	+	246.875i	0.892693	+	0.515396i	0.0178704	+	0.999840i	$0.494311\pi$
$480$		0			0
$481$	−90.0904	−	156.041i	−0.187298	−	0.324410i
$482$	2.80280	−	1.61820i	0.00581493	−	0.00335725i
$483$		0			0
$484$	440.155	−	762.371i	0.909412	−	1.57515i
$485$			343.904i			0.709081i
$486$		0			0
$487$	523.545			1.07504			0.537521	−	0.843251i	$-0.319361\pi$
$487$	523.545			1.07504			0.537521	+	0.843251i	$0.319361\pi$
$488$	−2.63648	−	1.52217i	−0.00540262	−	0.00311920i
$489$		0			0
$490$	−1.83352	−	3.17574i	−0.00374187	−	0.00648111i
$491$	−0.616240	+	0.355787i	−0.00125507	+	0.000724616i	−0.500627	−	0.865663i	$-0.666897\pi$
$491$	−0.616240	+	0.355787i	−0.00125507	+	0.000724616i	0.499372	+	0.866387i	$0.333564\pi$
$492$		0			0
$493$	107.573	−	186.322i	0.218201	−	0.377936i
$494$		−	22.6226i		−	0.0457947i
$495$		0			0
$496$	28.1465			0.0567469
$497$	102.380	+	59.1091i	0.205996	+	0.118932i
$498$		0			0
$499$	35.0102	+	60.6394i	0.0701607	+	0.121522i	0.898972	−	0.438007i	$-0.144315\pi$
$499$	35.0102	+	60.6394i	0.0701607	+	0.121522i	−0.828811	+	0.559529i	$0.810982\pi$
$500$	38.7079	−	22.3480i	0.0774158	−	0.0446960i
$501$		0			0
$502$	−6.55745	+	11.3578i	−0.0130626	+	0.0226252i
$503$		−	51.5098i		−	0.102405i	−0.998688	−	0.0512026i	$-0.983695\pi$
$503$		−	51.5098i		−	0.102405i	0.998688	−	0.0512026i	$-0.0163054\pi$
$504$		0			0
$505$	92.0467			0.182271
$506$	5.89146	+	3.40144i	0.0116432	+	0.00672221i
$507$		0			0
$508$	303.052	+	524.901i	0.596559	+	1.03327i
$509$	−749.606	+	432.785i	−1.47270	+	0.850266i	−0.999529	−	0.0307028i	$-0.990225\pi$
$509$	−749.606	+	432.785i	−1.47270	+	0.850266i	−0.473175	+	0.880969i	$0.656892\pi$
$510$		0			0
$511$	−98.3875	+	170.412i	−0.192539	+	0.333488i
$512$		−	60.8037i		−	0.118757i
$513$		0			0
$514$	9.39156			0.0182715
$515$	−26.8590	−	15.5070i	−0.0521534	−	0.0301108i
$516$		0			0
$517$	−75.0164	−	129.932i	−0.145099	−	0.251320i
$518$	1.58072	−	0.912629i	0.00305158	−	0.00176183i
$519$		0			0
$520$	7.63351	−	13.2216i	0.0146798	−	0.0254262i
$521$			243.099i			0.466600i	0.972405	+	0.233300i	$0.0749524\pi$
$521$			243.099i			0.466600i	−0.972405	+	0.233300i	$0.925048\pi$
$522$		0			0
$523$	−67.4741			−0.129014			−0.0645068	−	0.997917i	$-0.520547\pi$
$523$	−67.4741			−0.129014			−0.0645068	+	0.997917i	$0.520547\pi$
$524$	586.889	+	338.840i	1.12002	+	0.646642i
$525$		0			0
$526$	−8.93212	−	15.4709i	−0.0169812	−	0.0294123i
$527$	−14.0815	+	8.12993i	−0.0267200	+	0.0154268i
$528$		0			0
$529$	−234.582	+	406.308i	−0.443444	+	0.768068i
$530$			9.39010i			0.0177172i
$531$		0			0
$532$	−404.168			−0.759714
$533$	−479.095	−	276.606i	−0.898865	−	0.518960i
$534$		0			0
$535$	152.647	+	264.393i	0.285322	+	0.494192i
$536$	−14.9036	+	8.60458i	−0.0278052	+	0.0160533i
$537$		0			0
$538$	4.24636	−	7.35490i	0.00789285	−	0.0136708i
$539$		−	636.254i		−	1.18043i
$540$		0			0
$541$	−507.417			−0.937923			−0.468962	−	0.883218i	$-0.655372\pi$
$541$	−507.417			−0.937923			−0.468962	+	0.883218i	$0.655372\pi$
$542$	6.65812	+	3.84407i	0.0122843	+	0.00709237i
$543$		0			0
$544$	10.5357	+	18.2483i	0.0193671	+	0.0335447i
$545$	55.8309	−	32.2340i	0.102442	−	0.0591449i
$546$		0			0
$547$	141.848	−	245.687i	0.259319	−	0.449154i	−0.706741	−	0.707473i	$-0.749835\pi$
$547$	141.848	−	245.687i	0.259319	−	0.449154i	0.966060	+	0.258319i	$0.0831685\pi$
$548$		−	776.429i		−	1.41684i
$549$		0			0
$550$	−4.39725			−0.00799500
$551$	535.094	+	308.937i	0.971133	+	0.560684i
$552$		0			0
$553$	−156.979	−	271.895i	−0.283867	−	0.491673i
$554$	6.36623	−	3.67555i	0.0114914	−	0.00663456i
$555$		0			0
$556$	30.3379	−	52.5467i	0.0545645	−	0.0945085i
$557$			897.852i			1.61194i	0.591955	+	0.805971i	$0.298356\pi$
$557$			897.852i			1.61194i	−0.591955	+	0.805971i	$0.701644\pi$
$558$		0			0
$559$	834.485			1.49282
$560$	−118.006	−	68.1309i	−0.210725	−	0.121662i
$561$		0			0
$562$	2.62615	+	4.54863i	0.00467287	+	0.00809365i
$563$	−287.552	+	166.018i	−0.510749	+	0.294881i	−0.733142	−	0.680076i	$-0.761947\pi$
$563$	−287.552	+	166.018i	−0.510749	+	0.294881i	0.222392	+	0.974957i	$0.428613\pi$
$564$		0			0
$565$	−171.451	+	296.961i	−0.303452	+	0.525595i
$566$			3.77490i			0.00666944i
$567$		0			0
$568$	11.7991			0.0207730
$569$	680.149	+	392.684i	1.19534	+	0.690130i	0.959513	−	0.281665i	$-0.0908865\pi$
$569$	680.149	+	392.684i	1.19534	+	0.690130i	0.235828	+	0.971795i	$0.424220\pi$
$570$		0			0
$571$	19.6421	+	34.0210i	0.0343994	+	0.0595815i	0.882713	−	0.469913i	$-0.155715\pi$
$571$	19.6421	+	34.0210i	0.0343994	+	0.0595815i	−0.848313	+	0.529495i	$0.822382\pi$
$572$	1146.70	−	662.045i	2.00471	−	1.15742i
$573$		0			0
$574$	2.80206	−	4.85331i	0.00488163	−	0.00845524i
$575$			38.6769i			0.0672641i
$576$		0			0
$577$	−99.4757			−0.172402			−0.0862008	−	0.996278i	$-0.527473\pi$
$577$	−99.4757			−0.172402			−0.0862008	+	0.996278i	$0.527473\pi$
$578$	8.40546	+	4.85290i	0.0145423	+	0.00839601i
$579$		0			0
$580$	104.215	+	180.505i	0.179680	+	0.311216i
$581$	−474.594	+	274.007i	−0.816857	+	0.471612i
$582$		0			0
$583$	−814.622	+	1410.97i	−1.39729	+	2.42018i
$584$			19.6397i			0.0336295i
$585$		0			0
$586$	2.11318			0.00360611
$587$	281.091	+	162.288i	0.478860	+	0.276470i	0.719941	−	0.694035i	$-0.244169\pi$
$587$	281.091	+	162.288i	0.478860	+	0.276470i	−0.241082	+	0.970505i	$0.577502\pi$
$588$		0			0
$589$	−23.3481	−	40.4402i	−0.0396403	−	0.0686590i
$590$	−4.86154	+	2.80681i	−0.00823990	+	0.00475731i
$591$		0			0
$592$	−80.2532	+	139.003i	−0.135563	+	0.234802i
$593$			382.584i			0.645168i	0.946541	+	0.322584i	$0.104551\pi$
$593$			382.584i			0.645168i	−0.946541	+	0.322584i	$0.895449\pi$
$594$		0			0
$595$	78.7168			0.132297
$596$	−591.038	−	341.236i	−0.991675	−	0.572544i
$597$		0			0
$598$	3.30182	+	5.71893i	0.00552144	+	0.00956342i
$599$	505.642	−	291.933i	0.844144	−	0.487367i	−0.0145266	−	0.999894i	$-0.504624\pi$
$599$	505.642	−	291.933i	0.844144	−	0.487367i	0.858671	+	0.512528i	$0.171291\pi$
$600$		0			0
$601$	−279.891	+	484.785i	−0.465708	+	0.806630i	−0.999233	−	0.0391542i	$-0.987534\pi$
$601$	−279.891	+	484.785i	−0.465708	+	0.806630i	0.533525	+	0.845784i	$0.320867\pi$
$602$			8.45346i			0.0140423i
$603$		0			0
$604$	156.774			0.259559
$605$	−426.420	−	246.194i	−0.704827	−	0.406932i
$606$		0			0
$607$	105.354	+	182.479i	0.173566	+	0.300625i	0.939664	−	0.342099i	$-0.111138\pi$
$607$	105.354	+	182.479i	0.173566	+	0.300625i	−0.766098	+	0.642723i	$0.777804\pi$
$608$	−52.4069	+	30.2571i	−0.0861956	+	0.0497650i
$609$		0			0
$610$	−0.425580	+	0.737126i	−0.000697672	+	0.00120840i
$611$		−	145.639i		−	0.238362i
$612$		0			0
$613$	615.587			1.00422			0.502110	−	0.864804i	$-0.332557\pi$
$613$	615.587			1.00422			0.502110	+	0.864804i	$0.332557\pi$
$614$	7.13814	+	4.12121i	0.0116256	+	0.00671206i
$615$		0			0
$616$	13.4170	+	23.2390i	0.0217809	+	0.0377256i
$617$	−25.9899	+	15.0053i	−0.0421231	+	0.0243198i	−0.520914	−	0.853609i	$-0.674409\pi$
$617$	−25.9899	+	15.0053i	−0.0421231	+	0.0243198i	0.478791	+	0.877929i	$0.341075\pi$
$618$		0			0
$619$	−220.475	+	381.874i	−0.356180	+	0.616921i	−0.987319	−	0.158748i	$-0.949254\pi$
$619$	−220.475	+	381.874i	−0.356180	+	0.616921i	0.631139	+	0.775669i	$0.282588\pi$
$620$		−	15.7522i		−	0.0254068i
$621$		0			0
$622$	−1.84803			−0.00297111
$623$	252.336	+	145.686i	0.405033	+	0.233846i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−6.74971	+	3.89695i	−0.0107823	+	0.00622516i
$627$		0			0
$628$	254.017	−	439.971i	0.404486	−	0.700590i
$629$		−	92.7225i		−	0.147413i
$630$		0			0
$631$	425.272			0.673965			0.336983	−	0.941511i	$-0.390594\pi$
$631$	425.272			0.673965			0.336983	+	0.941511i	$0.390594\pi$
$632$	−27.1372	−	15.6677i	−0.0429386	−	0.0247906i
$633$		0			0
$634$	−3.70254	−	6.41298i	−0.00583996	−	0.0101151i
$635$	293.595	−	169.507i	0.462354	−	0.266940i
$636$		0			0
$637$	308.810	−	534.875i	0.484789	−	0.839679i
$638$		−	20.5055i		−	0.0321403i
$639$		0			0
$640$	−27.2154			−0.0425241
$641$	897.923	+	518.416i	1.40082	+	0.808762i	0.994476	−	0.104960i	$-0.0334715\pi$
$641$	897.923	+	518.416i	1.40082	+	0.808762i	0.406340	+	0.913722i	$0.366805\pi$
$642$		0			0
$643$	370.728	+	642.120i	0.576560	+	0.998631i	0.995870	+	0.0907879i	$0.0289385\pi$
$643$	370.728	+	642.120i	0.576560	+	0.998631i	−0.419310	+	0.907843i	$0.637728\pi$
$644$	102.172	−	58.9893i	0.158653	−	0.0915983i
$645$		0			0
$646$	5.82089	−	10.0821i	0.00901066	−	0.0156069i
$647$			404.846i			0.625727i	0.949798	+	0.312864i	$0.101288\pi$
$647$			404.846i			0.625727i	−0.949798	+	0.312864i	$0.898712\pi$
$648$		0			0
$649$	−974.001			−1.50077
$650$	−3.69661	−	2.13424i	−0.00568709	−	0.00328344i
$651$		0			0
$652$	94.8365	+	164.262i	0.145455	+	0.251935i
$653$	352.954	−	203.778i	0.540512	−	0.312065i	−0.204774	−	0.978809i	$-0.565646\pi$
$653$	352.954	−	203.778i	0.540512	−	0.312065i	0.745286	+	0.666744i	$0.232313\pi$
$654$		0			0
$655$	189.525	−	328.267i	0.289351	−	0.501171i
$656$			492.805i			0.751227i
$657$		0			0
$658$	1.47534			0.00224217
$659$	−186.215	−	107.511i	−0.282572	−	0.163143i	0.352015	−	0.935994i	$-0.385497\pi$
$659$	−186.215	−	107.511i	−0.282572	−	0.163143i	−0.634587	+	0.772851i	$0.718830\pi$
$660$		0			0
$661$	−72.2822	−	125.196i	−0.109353	−	0.189405i	0.806155	−	0.591704i	$-0.201545\pi$
$661$	−72.2822	−	125.196i	−0.109353	−	0.189405i	−0.915508	+	0.402299i	$0.868211\pi$
$662$	−21.2068	+	12.2438i	−0.0320345	+	0.0184951i
$663$		0			0
$664$	−27.3480	+	47.3681i	−0.0411867	+	0.0713375i
$665$			226.065i			0.339947i
$666$		0			0
$667$	−180.360			−0.270405
$668$	564.858	+	326.121i	0.845596	+	0.488205i
$669$		0			0
$670$	2.40574	+	4.16686i	0.00359065	+	0.00621919i
$671$	−127.896	+	73.8410i	−0.190605	+	0.110046i
$672$		0			0
$673$	491.156	−	850.708i	0.729801	−	1.26405i	−0.227166	−	0.973856i	$-0.572946\pi$
$673$	491.156	−	850.708i	0.729801	−	1.26405i	0.956967	−	0.290197i	$-0.0937208\pi$
$674$			10.2198i			0.0151629i
$675$		0			0
$676$	609.696			0.901917
$677$	−920.873	−	531.666i	−1.36023	−	0.785327i	−0.370572	−	0.928804i	$-0.620838\pi$
$677$	−920.873	−	531.666i	−1.36023	−	0.785327i	−0.989654	+	0.143477i	$0.954172\pi$
$678$		0			0
$679$	−293.380	−	508.149i	−0.432077	−	0.748379i
$680$	6.80396	−	3.92827i	0.0100058	−	0.00577687i
$681$		0			0
$682$	−0.774861	+	1.34210i	−0.00113616	+	0.00196789i
$683$			561.814i			0.822568i	0.911507	+	0.411284i	$0.134920\pi$
$683$			561.814i			0.822568i	−0.911507	+	0.411284i	$0.865080\pi$
$684$		0			0
$685$	−434.283			−0.633990
$686$	13.1263	+	7.57849i	0.0191346	+	0.0110474i
$687$		0			0
$688$	−371.683	−	643.773i	−0.540237	−	0.935717i
$689$	−1369.65	+	790.766i	−1.98788	+	1.14770i
$690$		0			0
$691$	152.934	−	264.890i	0.221323	−	0.383343i	−0.733887	−	0.679272i	$-0.762296\pi$
$691$	152.934	−	264.890i	0.221323	−	0.383343i	0.955210	+	0.295929i	$0.0956291\pi$
$692$		−	663.708i		−	0.959116i
$693$		0			0
$694$	10.6072			0.0152841
$695$	−29.3912	−	16.9690i	−0.0422894	−	0.0244158i
$696$		0			0
$697$	−142.344	−	246.546i	−0.204223	−	0.353725i
$698$	8.07303	−	4.66096i	0.0115659	−	0.00667760i
$699$		0			0
$700$	−38.1296	+	66.0424i	−0.0544708	+	0.0943462i
$701$		−	1190.38i		−	1.69811i	−0.528303	−	0.849056i	$-0.677172\pi$
$701$		−	1190.38i		−	1.69811i	0.528303	−	0.849056i	$-0.322828\pi$
$702$		0			0
$703$	266.287			0.378787
$704$	−1020.32	−	589.084i	−1.44932	−	0.836768i
$705$		0			0
$706$	11.8617	+	20.5451i	0.0168013	+	0.0291007i
$707$	−136.007	+	78.5238i	−0.192372	+	0.111066i
$708$		0			0
$709$	−334.731	+	579.771i	−0.472117	+	0.817731i	−0.999491	−	0.0319025i	$-0.989843\pi$
$709$	−334.731	+	579.771i	−0.472117	+	0.817731i	0.527374	+	0.849633i	$0.323177\pi$
$710$		−	3.29888i		−	0.00464631i
$711$		0			0
$712$	29.0812			0.0408443
$713$	11.8047	+	6.81544i	0.0165564	+	0.00955882i
$714$		0			0
$715$	−370.304	−	641.386i	−0.517908	−	0.897043i
$716$	−48.9573	+	28.2655i	−0.0683761	+	0.0394770i
$717$		0			0
$718$	−9.67499	+	16.7576i	−0.0134749	+	0.0233392i
$719$		−	528.816i		−	0.735488i	−0.929927	−	0.367744i	$-0.880130\pi$
$719$		−	528.816i		−	0.735488i	0.929927	−	0.367744i	$-0.119870\pi$
$720$		0			0
$721$	52.9154			0.0733917
$722$	14.0696	+	8.12311i	0.0194870	+	0.0112508i
$723$		0			0
$724$	−296.927	−	514.293i	−0.410120	−	0.710349i
$725$	100.963	−	58.2908i	0.139259	−	0.0804011i
$726$		0			0
$727$	−619.102	+	1072.32i	−0.851585	+	1.47499i	0.0281921	+	0.999603i	$0.491025\pi$
$727$	−619.102	+	1072.32i	−0.851585	+	1.47499i	−0.879777	+	0.475386i	$0.842308\pi$
$728$			26.0482i			0.0357805i
$729$		0			0
$730$	5.49101			0.00752193
$731$	371.900	+	214.717i	0.508755	+	0.293730i
$732$		0			0
$733$	−218.105	−	377.769i	−0.297552	−	0.515374i	0.678024	−	0.735040i	$-0.262837\pi$
$733$	−218.105	−	377.769i	−0.297552	−	0.515374i	−0.975575	+	0.219666i	$0.929503\pi$
$734$	−8.22099	+	4.74639i	−0.0112003	+	0.00646648i
$735$		0			0
$736$	8.83221	−	15.2978i	0.0120003	−	0.0207851i
$737$			834.822i			1.13273i
$738$		0			0
$739$	158.537			0.214529			0.107265	−	0.994231i	$-0.465791\pi$
$739$	158.537			0.214529			0.107265	+	0.994231i	$0.465791\pi$
$740$	77.7930	+	44.9138i	0.105126	+	0.0606943i
$741$		0			0
$742$	−8.01057	−	13.8747i	−0.0107959	−	0.0186991i
$743$	−219.765	+	126.881i	−0.295780	+	0.170769i	−0.640546	−	0.767920i	$-0.721292\pi$
$743$	−219.765	+	126.881i	−0.295780	+	0.170769i	0.344765	+	0.938689i	$0.387958\pi$
$744$		0			0
$745$	−190.865	+	330.588i	−0.256195	+	0.443742i
$746$		−	19.8411i		−	0.0265966i
$747$		0			0
$748$	681.387			0.910946
$749$	−451.100	−	260.442i	−0.602269	−	0.347720i
$750$		0			0
$751$	−534.666	−	926.069i	−0.711939	−	1.23311i	−0.964128	−	0.265437i	$-0.914484\pi$
$751$	−534.666	−	926.069i	−0.711939	−	1.23311i	0.252189	−	0.967678i	$-0.418849\pi$
$752$	−112.355	+	64.8681i	−0.149408	+	0.0862608i
$753$		0			0
$754$	9.95251	−	17.2383i	0.0131996	−	0.0228624i
$755$		−	87.6890i		−	0.116144i
$756$		0			0
$757$	1021.32			1.34917			0.674586	−	0.738196i	$-0.264322\pi$
$757$	1021.32			1.34917			0.674586	+	0.738196i	$0.264322\pi$
$758$	19.1506	+	11.0566i	0.0252647	+	0.0145866i
$759$		0			0
$760$	11.2815	+	19.5401i	0.0148441	+	0.0257107i
$761$	365.306	−	210.910i	0.480034	−	0.277148i	−0.240397	−	0.970675i	$-0.577277\pi$
$761$	365.306	−	210.910i	0.480034	−	0.277148i	0.720431	+	0.693527i	$0.243944\pi$
$762$		0			0
$763$	−54.9967	+	95.2572i	−0.0720796	+	0.124846i
$764$		−	1080.42i		−	1.41417i
$765$		0			0
$766$	−16.9310			−0.0221031
$767$	−818.807	−	472.738i	−1.06754	−	0.616347i
$768$		0			0
$769$	144.717	+	250.657i	0.188189	+	0.325952i	0.944646	−	0.328090i	$-0.106405\pi$
$769$	144.717	+	250.657i	0.188189	+	0.325952i	−0.756458	+	0.654042i	$0.773072\pi$
$770$	6.49733	−	3.75124i	0.00843809	−	0.00487173i
$771$		0			0
$772$	273.126	−	473.068i	0.353790	−	0.612783i
$773$			626.617i			0.810630i	0.914177	+	0.405315i	$0.132838\pi$
$773$			626.617i			0.810630i	−0.914177	+	0.405315i	$0.867162\pi$
$774$		0			0
$775$	−8.81074			−0.0113687
$776$	−50.7172	−	29.2816i	−0.0653572	−	0.0377340i
$777$		0			0
$778$	3.48755	+	6.04062i	0.00448272	+	0.00776429i
$779$	708.050	−	408.793i	0.908922	−	0.524766i
$780$		0			0
$781$	286.189	−	495.693i	0.366439	−	0.634691i
$782$			3.39829i			0.00434564i
$783$		0			0
$784$	−550.181			−0.701761
$785$	−246.091	−	142.080i	−0.313491	−	0.180994i
$786$		0			0
$787$	63.6489	+	110.243i	0.0808753	+	0.140080i	0.903626	−	0.428322i	$-0.140895\pi$
$787$	63.6489	+	110.243i	0.0808753	+	0.140080i	−0.822751	+	0.568402i	$0.807562\pi$
$788$	−926.235	+	534.762i	−1.17542	+	0.678632i
$789$		0			0
$790$	−4.38049	+	7.58723i	−0.00554492	+	0.00960409i
$791$		−	585.049i		−	0.739632i
$792$		0			0
$793$	−143.357			−0.180778
$794$	−21.2060	−	12.2433i	−0.0267078	−	0.0154197i
$795$		0			0
$796$	781.770	+	1354.07i	0.982123	+	1.70109i
$797$	510.690	−	294.847i	0.640765	−	0.369946i	−0.144144	−	0.989557i	$-0.546043\pi$
$797$	510.690	−	294.847i	0.640765	−	0.369946i	0.784909	+	0.619611i	$0.212710\pi$
$798$		0			0
$799$	37.4735	−	64.9060i	0.0469005	−	0.0812341i
$800$			11.4180i			0.0142724i
$801$		0			0
$802$	−4.50646			−0.00561902
$803$	825.085	+	476.363i	1.02750	+	0.593229i
$804$		0			0
$805$	−32.9947	−	57.1485i	−0.0409872	−	0.0709920i
$806$	−1.30279	+	0.752169i	−0.00161637	+	0.000933212i
$807$		0			0
$808$	−7.83727	+	13.5746i	−0.00969960	+	0.0168002i
$809$		−	988.576i		−	1.22197i	−0.791641	−	0.610986i	$-0.790773\pi$
$809$		−	988.576i		−	1.22197i	0.791641	−	0.610986i	$-0.209227\pi$
$810$		0			0
$811$	1127.66			1.39046			0.695231	−	0.718786i	$-0.255302\pi$
$811$	1127.66			1.39046			0.695231	+	0.718786i	$0.255302\pi$
$812$	−307.973	−	177.808i	−0.379277	−	0.218976i
$813$		0			0
$814$	−4.41868	−	7.65337i	−0.00542835	−	0.00940218i
$815$	91.8771	−	53.0453i	0.112733	−	0.0650862i
$816$		0			0
$817$	−616.639	+	1068.05i	−0.754760	+	1.30728i
$818$			31.3550i			0.0383312i
$819$		0			0
$820$	275.799			0.336340
$821$	−581.152	−	335.528i	−0.707859	−	0.408683i	0.102409	−	0.994742i	$-0.467345\pi$
$821$	−581.152	−	335.528i	−0.707859	−	0.408683i	−0.810268	+	0.586060i	$0.800678\pi$
$822$		0			0
$823$	−249.129	−	431.505i	−0.302709	−	0.524307i	0.674040	−	0.738695i	$-0.264558\pi$
$823$	−249.129	−	431.505i	−0.302709	−	0.524307i	−0.976749	+	0.214388i	$0.931224\pi$
$824$	4.57380	−	2.64068i	0.00555072	−	0.00320471i
$825$		0			0
$826$	4.78891	−	8.29463i	0.00579771	−	0.0100419i
$827$			738.770i			0.893313i	0.894705	+	0.446657i	$0.147385\pi$
$827$			738.770i			0.893313i	−0.894705	+	0.446657i	$0.852615\pi$
$828$		0			0
$829$	−1357.40			−1.63740			−0.818699	−	0.574223i	$-0.805304\pi$
$829$	−1357.40			−1.63740			−0.818699	+	0.574223i	$0.805304\pi$
$830$	13.2435	+	7.64616i	0.0159561	+	0.00921224i
$831$		0			0
$832$	−571.833	−	990.443i	−0.687299	−	1.19044i
$833$	275.251	−	158.916i	0.330434	−	0.190776i
$834$		0			0
$835$	182.411	−	315.944i	0.218456	−	0.378376i
$836$			1956.86i			2.34074i
$837$		0			0
$838$	14.6226			0.0174494
$839$	640.357	+	369.710i	0.763238	+	0.440656i	0.830457	−	0.557083i	$-0.188079\pi$
$839$	640.357	+	369.710i	0.763238	+	0.440656i	−0.0672192	+	0.997738i	$0.521413\pi$
$840$		0			0
$841$	−148.675	−	257.512i	−0.176783	−	0.306197i
$842$	26.8748	−	15.5162i	0.0319178	−	0.0184278i
$843$		0			0
$844$	−107.884	+	186.860i	−0.127824	+	0.221398i
$845$		−	341.024i		−	0.403578i
$846$		0			0
$847$	840.099			0.991852
$848$	1220.09	+	704.420i	1.43879	+	0.830683i
$849$		0			0
$850$	−1.09830	−	1.90230i	−0.00129211	−	0.00223801i
$851$	−67.3167	+	38.8653i	−0.0791031	+	0.0456702i
$852$		0			0
$853$	478.762	−	829.239i	0.561268	−	0.972145i	−0.436118	−	0.899889i	$-0.643647\pi$
$853$	478.762	−	829.239i	0.561268	−	0.972145i	0.997386	−	0.0722553i	$-0.0230196\pi$
$854$		−	1.45223i		−	0.00170050i
$855$		0			0
$856$	−51.9883			−0.0607340
$857$	342.505	+	197.745i	0.399656	+	0.230742i	0.686336	−	0.727285i	$-0.259218\pi$
$857$	342.505	+	197.745i	0.399656	+	0.230742i	−0.286680	+	0.958027i	$0.592551\pi$
$858$		0			0
$859$	−162.379	−	281.249i	−0.189033	−	0.327414i	0.755895	−	0.654692i	$-0.227202\pi$
$859$	−162.379	−	281.249i	−0.189033	−	0.327414i	−0.944928	+	0.327278i	$0.893869\pi$
$860$	−360.289	+	208.013i	−0.418940	+	0.241875i
$861$		0			0
$862$	16.7157	−	28.9524i	0.0193917	−	0.0335875i
$863$			78.5594i			0.0910306i	0.998964	+	0.0455153i	$0.0144930\pi$
$863$			78.5594i			0.0910306i	−0.998964	+	0.0455153i	$0.985507\pi$
$864$		0			0
$865$	−371.235			−0.429173
$866$	−31.4387	−	18.1511i	−0.0363033	−	0.0209597i
$867$		0			0
$868$	13.4380	+	23.2753i	0.0154816	+	0.0268149i
$869$	−1316.43	+	760.043i	−1.51488	+	0.874618i
$870$		0			0
$871$	−405.187	+	701.804i	−0.465197	+	0.805745i
$872$			10.9782i			0.0125897i
$873$		0			0
$874$	−9.75946			−0.0111664
$875$	36.9397	+	21.3272i	0.0422168	+	0.0243739i
$876$		0			0
$877$	244.560	+	423.590i	0.278859	+	0.482999i	0.971102	−	0.238667i	$-0.0767103\pi$
$877$	244.560	+	423.590i	0.278859	+	0.482999i	−0.692242	+	0.721665i	$0.743377\pi$
$878$	18.5775	−	10.7257i	0.0211589	−	0.0122161i
$879$		0			0
$880$	−329.870	+	571.351i	−0.374852	+	0.649262i
$881$			137.312i			0.155859i	0.996959	+	0.0779297i	$0.0248310\pi$
$881$			137.312i			0.155859i	−0.996959	+	0.0779297i	$0.975169\pi$
$882$		0			0
$883$	698.385			0.790923			0.395462	−	0.918483i	$-0.370585\pi$
$883$	698.385			0.790923			0.395462	+	0.918483i	$0.370585\pi$
$884$	572.817	+	330.716i	0.647983	+	0.374113i
$885$		0			0
$886$	−17.2937	−	29.9536i	−0.0195188	−	0.0338076i
$887$	944.807	−	545.485i	1.06517	−	0.614977i	0.138314	−	0.990388i	$-0.455832\pi$
$887$	944.807	−	545.485i	1.06517	−	0.614977i	0.926858	+	0.375411i	$0.122499\pi$
$888$		0			0
$889$	−289.209	+	500.924i	−0.325319	+	0.563469i
$890$		−	8.13073i		−	0.00913566i
$891$		0			0
$892$	−771.430			−0.864831
$893$	186.402	+	107.619i	0.208737	+	0.120514i
$894$		0			0
$895$	15.8099	+	27.3835i	0.0176647	+	0.0305961i
$896$	40.2132	−	23.2171i	0.0448808	−	0.0259119i
$897$		0			0
$898$	−2.67996	+	4.64183i	−0.00298437	+	0.00516908i
$899$		−	41.0868i		−	0.0457028i
$900$		0			0
$901$	−813.869			−0.903295
$902$	−23.4983	−	13.5667i	−0.0260513	−	0.0150407i
$903$		0			0
$904$	−29.1962	−	50.5693i	−0.0322967	−	0.0559394i
$905$	−287.662	+	166.081i	−0.317858	+	0.183515i
$906$		0			0
$907$	618.592	−	1071.43i	0.682020	−	1.18129i	−0.292343	−	0.956313i	$-0.594435\pi$
$907$	618.592	−	1071.43i	0.682020	−	1.18129i	0.974363	−	0.224980i	$-0.0722316\pi$
$908$		−	859.765i		−	0.946878i
$909$		0			0
$910$	7.28276			0.00800303
$911$	−491.664	−	283.862i	−0.539697	−	0.311594i	0.205259	−	0.978708i	$-0.434196\pi$
$911$	−491.664	−	283.862i	−0.539697	−	0.311594i	−0.744956	+	0.667113i	$0.767530\pi$
$912$		0			0
$913$	1326.66	+	2297.84i	1.45308	+	2.51680i
$914$	−0.996476	+	0.575316i	−0.00109024	+	0.000629448i
$915$		0			0
$916$	−350.733	+	607.487i	−0.382896	+	0.663195i
$917$			646.725i			0.705262i
$918$		0			0
$919$	508.271			0.553070			0.276535	−	0.961004i	$-0.410814\pi$
$919$	508.271			0.553070			0.276535	+	0.961004i	$0.410814\pi$
$920$	−5.70386	−	3.29313i	−0.00619985	−	0.00357948i
$921$		0			0
$922$	−6.74165	−	11.6769i	−0.00731198	−	0.0126647i
$923$	481.177	−	277.807i	0.521318	−	0.300983i
$924$		0			0
$925$	25.1218	−	43.5123i	0.0271587	−	0.0470403i
$926$		−	3.57422i		−	0.00385985i
$927$		0			0
$928$	−53.2449			−0.0573760
$929$	−754.122	−	435.393i	−0.811757	−	0.468668i	0.0358085	−	0.999359i	$-0.488599\pi$
$929$	−754.122	−	435.393i	−0.811757	−	0.468668i	−0.847566	+	0.530690i	$0.821933\pi$
$930$		0			0
$931$	456.388	+	790.487i	0.490213	+	0.849073i
$932$	688.844	−	397.704i	0.739103	−	0.426722i
$933$		0			0
$934$	−2.20018	+	3.81082i	−0.00235565	+	0.00408011i
$935$		−	381.123i		−	0.407618i
$936$		0			0
$937$	−612.508			−0.653691			−0.326845	−	0.945078i	$-0.605986\pi$
$937$	−612.508			−0.653691			−0.326845	+	0.945078i	$0.605986\pi$
$938$	−7.10938	−	4.10460i	−0.00757929	−	0.00437591i
$939$		0			0
$940$	36.3035	+	62.8796i	0.0386208	+	0.0668932i
$941$	1081.74	−	624.541i	1.14956	−	0.663700i	0.200781	−	0.979636i	$-0.435652\pi$
$941$	1081.74	−	624.541i	1.14956	−	0.663700i	0.948780	+	0.315936i	$0.102319\pi$
$942$		0			0
$943$	−119.329	+	206.683i	−0.126542	+	0.219176i
$944$			842.237i			0.892200i
$945$		0			0
$946$	40.9291			0.0432655
$947$	1186.77	+	685.182i	1.25319	+	0.723529i	0.971741	−	0.236048i	$-0.0758523\pi$
$947$	1186.77	+	685.182i	1.25319	+	0.723529i	0.281447	+	0.959577i	$0.409186\pi$
$948$		0			0
$949$	462.412	+	800.921i	0.487263	+	0.843964i
$950$	5.46318	−	3.15417i	0.00575071	−	0.00332018i
$951$		0			0
$952$	−6.70231	+	11.6087i	−0.00704024	+	0.0121941i
$953$		−	208.486i		−	0.218768i	−0.994000	−	0.109384i	$-0.965112\pi$
$953$		−	208.486i		−	0.218768i	0.994000	−	0.109384i	$-0.0348878\pi$
$954$		0			0
$955$	−604.318			−0.632793
$956$	84.6506	+	48.8730i	0.0885466	+	0.0511224i
$957$		0			0
$958$	11.7539	+	20.3584i	0.0122692	+	0.0212509i
$959$	641.692	−	370.481i	0.669126	−	0.386320i
$960$		0			0
$961$	478.947	−	829.561i	0.498384	−	0.863227i
$962$		−	8.57854i		−	0.00891741i
$963$		0			0
$964$	−271.750			−0.281899
$965$	−264.603	−	152.769i	−0.274200	−	0.158310i
$966$		0			0
$967$	762.477	+	1320.65i	0.788498	+	1.36572i	0.926887	+	0.375340i	$0.122474\pi$
$967$	762.477	+	1320.65i	0.788498	+	1.36572i	−0.138390	+	0.990378i	$0.544193\pi$
$968$	72.6147	−	41.9241i	0.0750152	−	0.0433101i
$969$		0			0
$970$	−8.18677	+	14.1799i	−0.00843997	+	0.0146185i
$971$			1060.61i			1.09229i	0.837691	+	0.546145i	$0.183905\pi$
$971$			1060.61i			1.09229i	−0.837691	+	0.546145i	$0.816095\pi$
$972$		0			0
$973$	57.9041			0.0595109
$974$	21.5869	+	12.4632i	0.0221631	+	0.0127959i
$975$		0			0
$976$	63.8517	+	110.594i	0.0654218	+	0.113314i
$977$	−879.807	+	507.957i	−0.900518	+	0.519915i	−0.877368	−	0.479817i	$-0.840703\pi$
$977$	−879.807	+	507.957i	−0.900518	+	0.519915i	−0.0231501	+	0.999732i	$0.507370\pi$
$978$		0			0
$979$	705.368	−	1221.73i	0.720498	−	1.24794i
$980$			307.910i			0.314193i
$981$		0			0
$982$	−0.0338785			−3.44995e−5
$983$	−1135.53	−	655.597i	−1.15517	−	0.666935i	−0.205025	−	0.978757i	$-0.565728\pi$
$983$	−1135.53	−	655.597i	−1.15517	−	0.666935i	−0.950141	+	0.311821i	$0.899061\pi$
$984$		0			0
$985$	299.110	+	518.075i	0.303665	+	0.525964i
$986$	8.87095	−	5.12165i	0.00899691	−	0.00519437i
$987$		0			0
$988$	−949.775	+	1645.06i	−0.961311	+	1.66504i
$989$		−	360.000i		−	0.364004i
$990$		0			0
$991$	−1092.89			−1.10282			−0.551408	−	0.834236i	$-0.685909\pi$
$991$	−1092.89			−1.10282			−0.551408	+	0.834236i	$0.685909\pi$
$992$	3.48491	+	2.01201i	0.00351301	+	0.00202824i
$993$		0			0
$994$	2.81423	+	4.87439i	0.00283122	+	0.00490381i
$995$	757.375	−	437.271i	0.761181	−	0.439468i
$996$		0			0
$997$	896.194	−	1552.25i	0.898891	−	1.55692i	0.0699773	−	0.997549i	$-0.477707\pi$
$997$	896.194	−	1552.25i	0.898891	−	1.55692i	0.828914	−	0.559376i	$-0.188959\pi$
$998$			3.33372i			0.00334040i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.i.a.116.5		16
3.2	odd	2		45.3.i.a.11.4	✓	16
4.3	odd	2		2160.3.bs.c.1601.2		16
5.2	odd	4		675.3.i.c.224.8		32
5.3	odd	4		675.3.i.c.224.9		32
5.4	even	2		675.3.j.b.251.4		16
9.2	odd	6		405.3.c.a.161.9		16
9.4	even	3		45.3.i.a.41.4	yes	16
9.5	odd	6	inner	135.3.i.a.71.5		16
9.7	even	3		405.3.c.a.161.8		16
12.11	even	2		720.3.bs.c.641.6		16
15.2	even	4		225.3.i.b.74.9		32
15.8	even	4		225.3.i.b.74.8		32
15.14	odd	2		225.3.j.b.101.5		16
36.23	even	6		2160.3.bs.c.881.2		16
36.31	odd	6		720.3.bs.c.401.6		16
45.4	even	6		225.3.j.b.176.5		16
45.13	odd	12		225.3.i.b.149.9		32
45.14	odd	6		675.3.j.b.476.4		16
45.22	odd	12		225.3.i.b.149.8		32
45.23	even	12		675.3.i.c.449.8		32
45.32	even	12		675.3.i.c.449.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.4	✓	16	3.2	odd	2
45.3.i.a.41.4	yes	16	9.4	even	3
135.3.i.a.71.5		16	9.5	odd	6	inner
135.3.i.a.116.5		16	1.1	even	1	trivial
225.3.i.b.74.8		32	15.8	even	4
225.3.i.b.74.9		32	15.2	even	4
225.3.i.b.149.8		32	45.22	odd	12
225.3.i.b.149.9		32	45.13	odd	12
225.3.j.b.101.5		16	15.14	odd	2
225.3.j.b.176.5		16	45.4	even	6
405.3.c.a.161.8		16	9.7	even	3
405.3.c.a.161.9		16	9.2	odd	6
675.3.i.c.224.8		32	5.2	odd	4
675.3.i.c.224.9		32	5.3	odd	4
675.3.i.c.449.8		32	45.23	even	12
675.3.i.c.449.9		32	45.32	even	12
675.3.j.b.251.4		16	5.4	even	2
675.3.j.b.476.4		16	45.14	odd	6
720.3.bs.c.401.6		16	36.31	odd	6
720.3.bs.c.641.6		16	12.11	even	2
2160.3.bs.c.881.2		16	36.23	even	6
2160.3.bs.c.1601.2		16	4.3	odd	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0412321 + 0.0238054i) q^{2} +(-1.99887 - 3.46214i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.90756 - 3.30399i) q^{7} -0.380778i q^{8} +O(q^{10})\)	\(q+(0.0412321 + 0.0238054i) q^{2} +(-1.99887 - 3.46214i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.90756 - 3.30399i) q^{7} -0.380778i q^{8} -0.106461 q^{10} +(-15.9969 - 9.23583i) q^{11} +(-8.96536 - 15.5285i) q^{13} +(0.157306 - 0.0908204i) q^{14} +(-7.98640 + 13.8329i) q^{16} -9.22729i q^{17} +26.4996 q^{19} +(7.74158 + 4.46960i) q^{20} +(-0.439725 - 0.761626i) q^{22} +(-6.69903 + 3.86769i) q^{23} +(2.50000 - 4.33013i) q^{25} -0.853695i q^{26} -15.2518 q^{28} +(20.1925 + 11.6582i) q^{29} +(-0.881074 - 1.52607i) q^{31} +(-1.97765 + 1.14180i) q^{32} +(0.219659 - 0.380461i) q^{34} +8.53087i q^{35} +10.0487 q^{37} +(1.09264 + 0.630834i) q^{38} +(0.425723 + 0.737374i) q^{40} +(26.7193 - 15.4264i) q^{41} +(-23.2697 + 40.3043i) q^{43} +73.8448i q^{44} -0.368287 q^{46} +(7.03414 + 4.06116i) q^{47} +(17.2224 + 29.8301i) q^{49} +(0.206161 - 0.119027i) q^{50} +(-35.8411 + 62.0786i) q^{52} -88.2024i q^{53} +41.3039 q^{55} +(-1.25809 - 0.726357i) q^{56} +(0.555054 + 0.961382i) q^{58} +(45.6650 - 26.3647i) q^{59} +(3.99753 - 6.92392i) q^{61} -0.0838972i q^{62} +63.7825 q^{64} +(34.7227 + 20.0471i) q^{65} +(-22.5974 - 39.1398i) q^{67} +(-31.9462 + 18.4441i) q^{68} +(-0.203081 + 0.351746i) q^{70} +30.9868i q^{71} -51.5777 q^{73} +(0.414330 + 0.239214i) q^{74} +(-52.9692 - 91.7454i) q^{76} +(-61.0302 + 35.2358i) q^{77} +(41.1464 - 71.2677i) q^{79} -35.7163i q^{80} +1.46892 q^{82} +(-124.398 - 71.8213i) q^{83} +(10.3164 + 17.8686i) q^{85} +(-1.91892 + 1.10789i) q^{86} +(-3.51680 + 6.09128i) q^{88} +76.3730i q^{89} -68.4078 q^{91} +(26.7809 + 15.4620i) q^{92} +(0.193355 + 0.334901i) q^{94} +(-51.3163 + 29.6275i) q^{95} +(76.8993 - 133.193i) q^{97} +1.63995i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 16 * q^4 + 2 * q^7	\( 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) \) 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

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