LMFDB - Embedded newform 135.3.i.a.71.6

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			71.6
Root			$-1.39204i$ of defining polynomial
Character	$\chi$	$=$	135.71
Dual form			135.3.i.a.116.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20554 - 0.696021i) q^{2} +(-1.03111 + 1.78593i) q^{4} +(1.93649 + 1.11803i) q^{5} +(4.41004 + 7.63842i) q^{7} +8.43886i q^{8} +O(q^{10})$	\(q+(1.20554 - 0.696021i) q^{2} +(-1.03111 + 1.78593i) q^{4} +(1.93649 + 1.11803i) q^{5} +(4.41004 + 7.63842i) q^{7} +8.43886i q^{8} +3.11270 q^{10} +(0.805373 - 0.464982i) q^{11} +(12.2405 - 21.2011i) q^{13} +(10.6330 + 6.13897i) q^{14} +(1.74919 + 3.02969i) q^{16} +18.3007i q^{17} -5.58727 q^{19} +(-3.99347 + 2.30563i) q^{20} +(0.647275 - 1.12111i) q^{22} +(-20.6131 - 11.9010i) q^{23} +(2.50000 + 4.33013i) q^{25} -34.0785i q^{26} -18.1889 q^{28} +(23.7620 - 13.7190i) q^{29} +(4.66760 - 8.08452i) q^{31} +(-25.0156 - 14.4428i) q^{32} +(12.7377 + 22.0623i) q^{34} +19.7223i q^{35} -24.7588 q^{37} +(-6.73570 + 3.88886i) q^{38} +(-9.43494 + 16.3418i) q^{40} +(6.45555 + 3.72712i) q^{41} +(-17.7288 - 30.7071i) q^{43} +1.91779i q^{44} -33.1333 q^{46} +(0.298523 - 0.172352i) q^{47} +(-14.3970 + 24.9363i) q^{49} +(6.02772 + 3.48011i) q^{50} +(25.2425 + 43.7214i) q^{52} -81.8155i q^{53} +2.07946 q^{55} +(-64.4596 + 37.2158i) q^{56} +(19.0975 - 33.0778i) q^{58} +(65.9707 + 38.0882i) q^{59} +(-29.6213 - 51.3056i) q^{61} -12.9950i q^{62} -54.2035 q^{64} +(47.4072 - 27.3705i) q^{65} +(40.9845 - 70.9873i) q^{67} +(-32.6838 - 18.8700i) q^{68} +(13.7271 + 23.7761i) q^{70} +37.5733i q^{71} +3.49191 q^{73} +(-29.8478 + 17.2326i) q^{74} +(5.76108 - 9.97849i) q^{76} +(7.10346 + 4.10119i) q^{77} +(62.0348 + 107.447i) q^{79} +7.82263i q^{80} +10.3766 q^{82} +(-48.4851 + 27.9929i) q^{83} +(-20.4608 + 35.4392i) q^{85} +(-42.7456 - 24.6792i) q^{86} +(3.92392 + 6.79643i) q^{88} +6.78556i q^{89} +215.924 q^{91} +(42.5086 - 24.5424i) q^{92} +(0.239921 - 0.415556i) q^{94} +(-10.8197 - 6.24676i) q^{95} +(-58.5960 - 101.491i) q^{97} +40.0824i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	1.20554	−	0.696021i	0.602772	−	0.348011i	−0.167359	−	0.985896i	$-0.553524\pi$
$2$	1.20554	−	0.696021i	0.602772	−	0.348011i	0.770131	+	0.637885i	$0.220191\pi$
$3$		0			0
$3$		0			0
$4$	−1.03111	+	1.78593i	−0.257777	+	0.446483i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		0			0
$7$	4.41004	+	7.63842i	0.630006	+	1.09120i	0.987550	+	0.157306i	$0.0502810\pi$
$7$	4.41004	+	7.63842i	0.630006	+	1.09120i	−0.357544	+	0.933896i	$0.616386\pi$
$8$			8.43886i			1.05486i
$9$		0			0
$10$	3.11270			0.311270
$11$	0.805373	−	0.464982i	0.0732157	−	0.0422711i	−0.462945	−	0.886387i	$-0.653207\pi$
$11$	0.805373	−	0.464982i	0.0732157	−	0.0422711i	0.536161	+	0.844116i	$0.319874\pi$
$12$		0			0
$13$	12.2405	−	21.2011i	0.941576	−	1.63086i	0.179109	−	0.983829i	$-0.442679\pi$
$13$	12.2405	−	21.2011i	0.941576	−	1.63086i	0.762467	−	0.647027i	$-0.223988\pi$
$14$	10.6330	+	6.13897i	0.759500	+	0.438498i
$15$		0			0
$16$	1.74919	+	3.02969i	0.109325	+	0.189356i
$17$			18.3007i			1.07651i	0.842781	+	0.538256i	$0.180917\pi$
$17$			18.3007i			1.07651i	−0.842781	+	0.538256i	$0.819083\pi$
$18$		0			0
$19$	−5.58727			−0.294067			−0.147033	−	0.989132i	$-0.546972\pi$
$19$	−5.58727			−0.294067			−0.147033	+	0.989132i	$0.546972\pi$
$20$	−3.99347	+	2.30563i	−0.199673	+	0.115281i
$21$		0			0
$22$	0.647275	−	1.12111i	0.0294216	−	0.0509597i
$23$	−20.6131	−	11.9010i	−0.896221	−	0.517433i	−0.0202485	−	0.999795i	$-0.506446\pi$
$23$	−20.6131	−	11.9010i	−0.896221	−	0.517433i	−0.875972	+	0.482362i	$0.839779\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$		−	34.0785i		−	1.31071i
$27$		0			0
$28$	−18.1889			−0.649605
$29$	23.7620	−	13.7190i	0.819381	−	0.473070i	−0.0308220	−	0.999525i	$-0.509813\pi$
$29$	23.7620	−	13.7190i	0.819381	−	0.473070i	0.850203	+	0.526455i	$0.176479\pi$
$30$		0			0
$31$	4.66760	−	8.08452i	0.150568	−	0.260791i	−0.780869	−	0.624695i	$-0.785223\pi$
$31$	4.66760	−	8.08452i	0.150568	−	0.260791i	0.931436	+	0.363904i	$0.118556\pi$
$32$	−25.0156	−	14.4428i	−0.781738	−	0.451337i
$33$		0			0
$34$	12.7377	+	22.0623i	0.374638	+	0.648891i
$35$			19.7223i			0.563495i
$36$		0			0
$37$	−24.7588			−0.669156			−0.334578	−	0.942368i	$-0.608594\pi$
$37$	−24.7588			−0.669156			−0.334578	+	0.942368i	$0.608594\pi$
$38$	−6.73570	+	3.88886i	−0.177255	+	0.102338i
$39$		0			0
$40$	−9.43494	+	16.3418i	−0.235873	+	0.408545i
$41$	6.45555	+	3.72712i	0.157453	+	0.0909053i	0.576656	−	0.816987i	$-0.304357\pi$
$41$	6.45555	+	3.72712i	0.157453	+	0.0909053i	−0.419203	+	0.907892i	$0.637691\pi$
$42$		0			0
$43$	−17.7288	−	30.7071i	−0.412297	−	0.714119i	0.582844	−	0.812584i	$-0.301940\pi$
$43$	−17.7288	−	30.7071i	−0.412297	−	0.714119i	−0.995140	+	0.0984653i	$0.968607\pi$
$44$			1.91779i			0.0435861i
$45$		0			0
$46$	−33.1333			−0.720289
$47$	0.298523	−	0.172352i	0.00635154	−	0.00366707i	−0.496821	−	0.867853i	$-0.665499\pi$
$47$	0.298523	−	0.172352i	0.00635154	−	0.00366707i	0.503172	+	0.864186i	$0.332166\pi$
$48$		0			0
$49$	−14.3970	+	24.9363i	−0.293816	+	0.508904i
$50$	6.02772	+	3.48011i	0.120554	+	0.0696021i
$51$		0			0
$52$	25.2425	+	43.7214i	0.485433	+	0.840795i
$53$		−	81.8155i		−	1.54369i	−0.635812	−	0.771844i	$-0.719335\pi$
$53$		−	81.8155i		−	1.54369i	0.635812	−	0.771844i	$-0.280665\pi$
$54$		0			0
$55$	2.07946			0.0378084
$56$	−64.4596	+	37.2158i	−1.15106	+	0.664567i
$57$		0			0
$58$	19.0975	−	33.0778i	0.329267	−	0.570307i
$59$	65.9707	+	38.0882i	1.11815	+	0.645562i	0.940927	−	0.338609i	$-0.109956\pi$
$59$	65.9707	+	38.0882i	1.11815	+	0.645562i	0.177220	+	0.984171i	$0.443290\pi$
$60$		0			0
$61$	−29.6213	−	51.3056i	−0.485595	−	0.841075i	0.514268	−	0.857629i	$-0.328064\pi$
$61$	−29.6213	−	51.3056i	−0.485595	−	0.841075i	−0.999863	+	0.0165547i	$0.994730\pi$
$62$		−	12.9950i		−	0.209597i
$63$		0			0
$64$	−54.2035			−0.846929
$65$	47.4072	−	27.3705i	0.729341	−	0.421085i
$66$		0			0
$67$	40.9845	−	70.9873i	0.611710	−	1.05951i	−0.379243	−	0.925297i	$-0.623815\pi$
$67$	40.9845	−	70.9873i	0.611710	−	1.05951i	0.990952	−	0.134215i	$-0.0428512\pi$
$68$	−32.6838	−	18.8700i	−0.480645	−	0.277500i
$69$		0			0
$70$	13.7271	+	23.7761i	0.196102	+	0.339659i
$71$			37.5733i			0.529201i	0.964358	+	0.264600i	$0.0852401\pi$
$71$			37.5733i			0.529201i	−0.964358	+	0.264600i	$0.914760\pi$
$72$		0			0
$73$	3.49191			0.0478343			0.0239172	−	0.999714i	$-0.492386\pi$
$73$	3.49191			0.0478343			0.0239172	+	0.999714i	$0.492386\pi$
$74$	−29.8478	+	17.2326i	−0.403348	+	0.232873i
$75$		0			0
$76$	5.76108	−	9.97849i	0.0758037	−	0.131296i
$77$	7.10346	+	4.10119i	0.0922527	+	0.0532621i
$78$		0			0
$79$	62.0348	+	107.447i	0.785251	+	1.36009i	0.928849	+	0.370459i	$0.120799\pi$
$79$	62.0348	+	107.447i	0.785251	+	1.36009i	−0.143598	+	0.989636i	$0.545867\pi$
$80$			7.82263i			0.0977829i
$81$		0			0
$82$	10.3766			0.126544
$83$	−48.4851	+	27.9929i	−0.584158	+	0.337264i	−0.762784	−	0.646653i	$-0.776168\pi$
$83$	−48.4851	+	27.9929i	−0.584158	+	0.337264i	0.178626	+	0.983917i	$0.442835\pi$
$84$		0			0
$85$	−20.4608	+	35.4392i	−0.240715	+	0.416931i
$86$	−42.7456	−	24.6792i	−0.497042	−	0.286967i
$87$		0			0
$88$	3.92392	+	6.79643i	0.0445900	+	0.0772322i
$89$			6.78556i			0.0762423i	0.999273	+	0.0381211i	$0.0121373\pi$
$89$			6.78556i			0.0762423i	−0.999273	+	0.0381211i	$0.987863\pi$
$90$		0			0
$91$	215.924			2.37279
$92$	42.5086	−	24.5424i	0.462051	−	0.266765i
$93$		0			0
$94$	0.239921	−	0.415556i	0.00255236	−	0.00442081i
$95$	−10.8197	−	6.24676i	−0.113892	−	0.0657553i
$96$		0			0
$97$	−58.5960	−	101.491i	−0.604082	−	1.04630i	−0.992196	−	0.124690i	$-0.960206\pi$
$97$	−58.5960	−	101.491i	−0.604082	−	1.04630i	0.388113	−	0.921612i	$-0.373127\pi$
$98$			40.0824i			0.409004i
$99$		0			0
$100$	−10.3111			−0.103111
$101$	93.7854	−	54.1470i	0.928568	−	0.536109i	0.0422099	−	0.999109i	$-0.486560\pi$
$101$	93.7854	−	54.1470i	0.928568	−	0.536109i	0.886359	+	0.463000i	$0.153227\pi$
$102$		0			0
$103$	−35.3243	+	61.1834i	−0.342954	+	0.594014i	−0.984980	−	0.172669i	$-0.944761\pi$
$103$	−35.3243	+	61.1834i	−0.342954	+	0.594014i	0.642026	+	0.766683i	$0.278094\pi$
$104$	178.914	+	103.296i	1.72032	+	0.993229i
$105$		0			0
$106$	−56.9453	−	98.6322i	−0.537220	−	0.930492i
$107$			100.895i			0.942946i	0.881880	+	0.471473i	$0.156278\pi$
$107$			100.895i			0.942946i	−0.881880	+	0.471473i	$0.843722\pi$
$108$		0			0
$109$	97.8997			0.898163			0.449081	−	0.893491i	$-0.351751\pi$
$109$	97.8997			0.898163			0.449081	+	0.893491i	$0.351751\pi$
$110$	2.50689	−	1.44735i	0.0227899	−	0.0131577i
$111$		0			0
$112$	−15.4280	+	26.7221i	−0.137750	+	0.238591i
$113$	10.6876	+	6.17047i	0.0945802	+	0.0546059i	0.546544	−	0.837430i	$-0.315943\pi$
$113$	10.6876	+	6.17047i	0.0945802	+	0.0546059i	−0.451964	+	0.892036i	$0.649276\pi$
$114$		0			0
$115$	−26.6114	−	46.0922i	−0.231403	−	0.400802i
$116$			56.5832i			0.487786i
$117$		0			0
$118$	106.041			0.898650
$119$	−139.788	+	80.7069i	−1.17469	+	0.678209i
$120$		0			0
$121$	−60.0676	+	104.040i	−0.496426	+	0.859836i
$122$	−71.4195	−	41.2341i	−0.585406	−	0.337984i
$123$		0			0
$124$	9.62561	+	16.6720i	0.0776259	+	0.134452i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−86.8931			−0.684198			−0.342099	−	0.939664i	$-0.611138\pi$
$127$	−86.8931			−0.684198			−0.342099	+	0.939664i	$0.611138\pi$
$128$	34.7178	−	20.0443i	0.271233	−	0.156596i
$129$		0			0
$130$	38.1010	−	65.9928i	0.293084	−	0.507637i
$131$	−17.5042	−	10.1060i	−0.133620	−	0.0771453i	0.431700	−	0.902017i	$-0.357914\pi$
$131$	−17.5042	−	10.1060i	−0.133620	−	0.0771453i	−0.565320	+	0.824872i	$0.691247\pi$
$132$		0			0
$133$	−24.6401	−	42.6779i	−0.185264	−	0.320887i
$134$		−	114.104i		−	0.851526i
$135$		0			0
$136$	−154.437			−1.13557
$137$	127.414	−	73.5624i	0.930028	−	0.536952i	0.0432078	−	0.999066i	$-0.486242\pi$
$137$	127.414	−	73.5624i	0.930028	−	0.536952i	0.886821	+	0.462114i	$0.152909\pi$
$138$		0			0
$139$	−61.3294	+	106.226i	−0.441219	+	0.764213i	−0.997780	−	0.0665934i	$-0.978787\pi$
$139$	−61.3294	+	106.226i	−0.441219	+	0.764213i	0.556562	+	0.830806i	$0.312120\pi$
$140$	−35.2227	−	20.3359i	−0.251591	−	0.145256i
$141$		0			0
$142$	26.1518	+	45.2962i	0.184168	+	0.318988i
$143$		−	22.7664i		−	0.159206i
$144$		0			0
$145$	61.3533			0.423126
$146$	4.20965	−	2.43044i	0.0288332	−	0.0166469i
$147$		0			0
$148$	25.5290	−	44.2175i	0.172493	−	0.298767i
$149$	−188.144	−	108.625i	−1.26271	−	0.729028i	−0.289115	−	0.957294i	$-0.593361\pi$
$149$	−188.144	−	108.625i	−1.26271	−	0.729028i	−0.973599	+	0.228266i	$0.926694\pi$
$150$		0			0
$151$	81.1971	+	140.637i	0.537729	+	0.931374i	0.999026	+	0.0441282i	$0.0140510\pi$
$151$	81.1971	+	140.637i	0.537729	+	0.931374i	−0.461297	+	0.887246i	$0.652616\pi$
$152$		−	47.1502i		−	0.310199i
$153$		0			0
$154$	11.4180			0.0741432
$155$	18.0775	−	10.4371i	0.116629	−	0.0673360i
$156$		0			0
$157$	−57.4586	+	99.5212i	−0.365978	+	0.633893i	−0.988933	−	0.148365i	$-0.952599\pi$
$157$	−57.4586	+	99.5212i	−0.365978	+	0.633893i	0.622954	+	0.782258i	$0.285932\pi$
$158$	149.571	+	86.3551i	0.946655	+	0.546551i
$159$		0			0
$160$	−32.2950	−	55.9366i	−0.201844	−	0.349604i
$161$		−	209.935i		−	1.30394i
$162$		0			0
$163$	−138.760			−0.851286			−0.425643	−	0.904891i	$-0.639952\pi$
$163$	−138.760			−0.851286			−0.425643	+	0.904891i	$0.639952\pi$
$164$	−13.3128	+	7.68613i	−0.0811754	+	0.0468666i
$165$		0			0
$166$	−38.9673	+	67.4933i	−0.234743	+	0.406586i
$167$	−258.339	−	149.152i	−1.54694	−	0.893126i	−0.998373	−	0.0570195i	$-0.981840\pi$
$167$	−258.339	−	149.152i	−1.54694	−	0.893126i	−0.548567	−	0.836107i	$-0.684826\pi$
$168$		0			0
$169$	−215.159	−	372.666i	−1.27313	−	2.20512i
$170$			56.9646i			0.335086i
$171$		0			0
$172$	73.1211			0.425123
$173$	−235.252	+	135.823i	−1.35984	+	0.785102i	−0.989602	−	0.143836i	$-0.954056\pi$
$173$	−235.252	+	135.823i	−1.35984	+	0.785102i	−0.370235	+	0.928938i	$0.620723\pi$
$174$		0			0
$175$	−22.0502	+	38.1921i	−0.126001	+	0.218241i
$176$	2.81751	+	1.62669i	0.0160086	+	0.00924255i
$177$		0			0
$178$	4.72289	+	8.18029i	0.0265331	+	0.0459567i
$179$		−	67.8828i		−	0.379234i	−0.981858	−	0.189617i	$-0.939275\pi$
$179$		−	67.8828i		−	0.379234i	0.981858	−	0.189617i	$-0.0607246\pi$
$180$		0			0
$181$	−0.394050			−0.00217707			−0.00108854	−	0.999999i	$-0.500346\pi$
$181$	−0.394050			−0.00217707			−0.00108854	+	0.999999i	$0.500346\pi$
$182$	260.306	−	150.288i	1.43025	−	0.825757i
$183$		0			0
$184$	100.431	−	173.951i	0.545819	−	0.945386i
$185$	−47.9451	−	27.6811i	−0.259163	−	0.149628i
$186$		0			0
$187$	8.50951	+	14.7389i	0.0455054	+	0.0788176i
$188$			0.710855i			0.00378114i
$189$		0			0
$190$	−17.3915			−0.0915342
$191$	−28.9892	+	16.7369i	−0.151776	+	0.0876278i	−0.573965	−	0.818880i	$-0.694595\pi$
$191$	−28.9892	+	16.7369i	−0.151776	+	0.0876278i	0.422189	+	0.906508i	$0.361262\pi$
$192$		0			0
$193$	−26.4249	+	45.7692i	−0.136916	+	0.237146i	−0.926328	−	0.376718i	$-0.877052\pi$
$193$	−26.4249	+	45.7692i	−0.136916	+	0.237146i	0.789412	+	0.613864i	$0.210386\pi$
$194$	−141.280	−	81.5681i	−0.728248	−	0.420454i
$195$		0			0
$196$	−29.6897	−	51.4240i	−0.151478	−	0.262367i
$197$			371.096i			1.88374i	0.335984	+	0.941868i	$0.390931\pi$
$197$			371.096i			1.88374i	−0.335984	+	0.941868i	$0.609069\pi$
$198$		0			0
$199$	−102.813			−0.516650			−0.258325	−	0.966058i	$-0.583170\pi$
$199$	−102.813			−0.516650			−0.258325	+	0.966058i	$0.583170\pi$
$200$	−36.5414	+	21.0972i	−0.182707	+	0.105486i
$201$		0			0
$202$	75.3750	−	130.553i	0.373143	−	0.646303i
$203$	209.583	+	121.003i	1.03243	+	0.596074i
$204$		0			0
$205$	8.33409	+	14.4351i	0.0406541	+	0.0704149i
$206$			98.3457i			0.477407i
$207$		0			0
$208$	85.6439			0.411749
$209$	−4.49984	+	2.59798i	−0.0215303	+	0.0124305i
$210$		0			0
$211$	−15.3065	+	26.5116i	−0.0725425	+	0.125647i	−0.900015	−	0.435859i	$-0.856445\pi$
$211$	−15.3065	+	26.5116i	−0.0725425	+	0.125647i	0.827472	+	0.561506i	$0.189778\pi$
$212$	146.117	+	84.3607i	0.689231	+	0.397928i
$213$		0			0
$214$	70.2253	+	121.634i	0.328155	+	0.568382i
$215$		−	79.2854i		−	0.368769i
$216$		0			0
$217$	82.3373			0.379434
$218$	118.022	−	68.1403i	0.541387	−	0.312570i
$219$		0			0
$220$	−2.14415	+	3.71378i	−0.00974616	+	0.0168808i
$221$	387.996	+	224.009i	1.75564	+	1.01362i
$222$		0			0
$223$	160.484	+	277.966i	0.719659	+	1.24649i	0.961135	+	0.276078i	$0.0890350\pi$
$223$	160.484	+	277.966i	0.719659	+	1.24649i	−0.241477	+	0.970407i	$0.577632\pi$
$224$		−	254.773i		−	1.13738i
$225$		0			0
$226$	17.1791			0.0760137
$227$	−200.515	+	115.767i	−0.883325	+	0.509988i	−0.871753	−	0.489945i	$-0.837017\pi$
$227$	−200.515	+	115.767i	−0.883325	+	0.509988i	−0.0115717	+	0.999933i	$0.503683\pi$
$228$		0			0
$229$	118.247	−	204.809i	0.516361	−	0.894363i	−0.483459	−	0.875367i	$-0.660620\pi$
$229$	118.247	−	204.809i	0.516361	−	0.894363i	0.999820	−	0.0189957i	$-0.00604689\pi$
$230$	−64.1623	−	37.0441i	−0.278967	−	0.161062i
$231$		0			0
$232$	115.773	+	200.525i	0.499021	+	0.864331i
$233$		−	148.884i		−	0.638987i	−0.947588	−	0.319493i	$-0.896487\pi$
$233$		−	148.884i		−	0.638987i	0.947588	−	0.319493i	$-0.103513\pi$
$234$		0			0
$235$	0.770782			0.00327992
$236$	−136.046	+	78.5461i	−0.576466	+	0.332823i
$237$		0			0
$238$	−112.347	+	194.591i	−0.472048	+	0.817611i
$239$	228.982	+	132.203i	0.958083	+	0.553149i	0.895582	−	0.444896i	$-0.146759\pi$
$239$	228.982	+	132.203i	0.958083	+	0.553149i	0.0625002	+	0.998045i	$0.480093\pi$
$240$		0			0
$241$	104.234	+	180.539i	0.432507	+	0.749124i	0.997088	−	0.0762533i	$-0.0242958\pi$
$241$	104.234	+	180.539i	0.432507	+	0.749124i	−0.564582	+	0.825377i	$0.690962\pi$
$242$			167.233i			0.691046i
$243$		0			0
$244$	122.171			0.500701
$245$	−55.7592	+	32.1926i	−0.227589	+	0.131398i
$246$		0			0
$247$	−68.3909	+	118.456i	−0.276886	+	0.479581i
$248$	68.2242	+	39.3893i	0.275098	+	0.158828i
$249$		0			0
$250$	7.78175	+	13.4784i	0.0311270	+	0.0539136i
$251$			236.856i			0.943651i	0.881692	+	0.471826i	$0.156405\pi$
$251$			236.856i			0.943651i	−0.881692	+	0.471826i	$0.843595\pi$
$252$		0			0
$253$	−22.1350			−0.0874899
$254$	−104.754	+	60.4795i	−0.412415	+	0.238108i
$255$		0			0
$256$	136.310	−	236.095i	0.532459	−	0.922246i
$257$	−255.746	−	147.655i	−0.995121	−	0.574533i	−0.0883198	−	0.996092i	$-0.528150\pi$
$257$	−255.746	−	147.655i	−0.995121	−	0.574533i	−0.906801	+	0.421559i	$0.861483\pi$
$258$		0			0
$259$	−109.187	−	189.118i	−0.421572	−	0.730185i
$260$			112.888i			0.434185i
$261$		0			0
$262$	−28.1361			−0.107390
$263$	365.389	−	210.957i	1.38931	−	0.802119i	0.396074	−	0.918219i	$-0.370372\pi$
$263$	365.389	−	210.957i	1.38931	−	0.802119i	0.993238	+	0.116099i	$0.0370391\pi$
$264$		0			0
$265$	91.4725	−	158.435i	0.345179	−	0.597868i
$266$	−59.4095	−	34.3001i	−0.223344	−	0.128948i
$267$		0			0
$268$	84.5190	+	146.391i	0.315370	+	0.546236i
$269$		−	316.354i		−	1.17604i	−0.808848	−	0.588018i	$-0.799908\pi$
$269$		−	316.354i		−	1.17604i	0.808848	−	0.588018i	$-0.200092\pi$
$270$		0			0
$271$	−10.8891			−0.0401814			−0.0200907	−	0.999798i	$-0.506395\pi$
$271$	−10.8891			−0.0401814			−0.0200907	+	0.999798i	$0.506395\pi$
$272$	−55.4455	+	32.0115i	−0.203844	+	0.117689i
$273$		0			0
$274$	102.402	−	177.366i	0.373730	−	0.647319i
$275$	4.02687	+	2.32491i	0.0146431	+	0.00845423i
$276$		0			0
$277$	−38.7124	−	67.0519i	−0.139756	−	0.242065i	0.787648	−	0.616125i	$-0.211299\pi$
$277$	−38.7124	−	67.0519i	−0.139756	−	0.242065i	−0.927404	+	0.374061i	$0.877965\pi$
$278$			170.746i			0.614195i
$279$		0			0
$280$	−166.434			−0.594407
$281$	140.912	−	81.3557i	0.501467	−	0.289522i	−0.227852	−	0.973696i	$-0.573170\pi$
$281$	140.912	−	81.3557i	0.501467	−	0.289522i	0.729319	+	0.684174i	$0.239837\pi$
$282$		0			0
$283$	−10.3582	+	17.9410i	−0.0366015	+	0.0633956i	−0.883746	−	0.467967i	$-0.844987\pi$
$283$	−10.3582	+	17.9410i	−0.0366015	+	0.0633956i	0.847144	+	0.531363i	$0.178320\pi$
$284$	−67.1033	−	38.7421i	−0.236279	−	0.136416i
$285$		0			0
$286$	−15.8459	−	27.4459i	−0.0554053	−	0.0959648i
$287$			65.7470i			0.229084i
$288$		0			0
$289$	−45.9158			−0.158878
$290$	73.9642	−	42.7032i	0.255049	−	0.147253i
$291$		0			0
$292$	−3.60054	+	6.23631i	−0.0123306	+	0.0213572i
$293$	116.350	+	67.1748i	0.397100	+	0.229266i	0.685232	−	0.728325i	$-0.259701\pi$
$293$	116.350	+	67.1748i	0.397100	+	0.229266i	−0.288132	+	0.957591i	$0.593034\pi$
$294$		0			0
$295$	85.1678	+	147.515i	0.288704	+	0.500051i
$296$		−	208.936i		−	0.705864i
$297$		0			0
$298$	−302.422			−1.01484
$299$	−504.628	+	291.347i	−1.68772	+	0.974405i
$300$		0			0
$301$	156.369	−	270.839i	0.519499	−	0.899799i
$302$	195.773	+	113.030i	0.648256	+	0.374271i
$303$		0			0
$304$	−9.77322	−	16.9277i	−0.0321487	−	0.0556832i
$305$		−	132.470i		−	0.434329i
$306$		0			0
$307$	96.2672			0.313574			0.156787	−	0.987632i	$-0.449886\pi$
$307$	96.2672			0.313574			0.156787	+	0.987632i	$0.449886\pi$
$308$	−14.6489	+	8.45754i	−0.0475613	+	0.0274595i
$309$		0			0
$310$	14.5288	−	25.1647i	0.0468673	−	0.0811765i
$311$	−327.909	−	189.319i	−1.05437	−	0.608742i	−0.130501	−	0.991448i	$-0.541659\pi$
$311$	−327.909	−	189.319i	−1.05437	−	0.608742i	−0.923870	+	0.382707i	$0.874992\pi$
$312$		0			0
$313$	−113.733	−	196.991i	−0.363364	−	0.629365i	0.625148	−	0.780506i	$-0.285039\pi$
$313$	−113.733	−	196.991i	−0.363364	−	0.629365i	−0.988512	+	0.151141i	$0.951705\pi$
$314$			159.970i			0.509457i
$315$		0			0
$316$	−255.859			−0.809679
$317$	196.306	−	113.337i	0.619260	−	0.357530i	−0.157321	−	0.987548i	$-0.550286\pi$
$317$	196.306	−	113.337i	0.619260	−	0.357530i	0.776581	+	0.630017i	$0.216952\pi$
$318$		0			0
$319$	12.7582	−	22.0979i	0.0399944	−	0.0692723i
$320$	−104.965	−	60.6013i	−0.328014	−	0.189379i
$321$		0			0
$322$	−146.119	−	253.086i	−0.453787	−	0.785981i
$323$		−	102.251i		−	0.316566i
$324$		0			0
$325$	122.405			0.376630
$326$	−167.281	+	96.5797i	−0.513132	+	0.296257i
$327$		0			0
$328$	−31.4526	+	54.4776i	−0.0958922	+	0.166090i
$329$	2.63300	+	1.52016i	0.00800303	+	0.00462055i
$330$		0			0
$331$	142.567	+	246.934i	0.430717	+	0.746024i	0.996935	−	0.0782317i	$-0.0249274\pi$
$331$	142.567	+	246.934i	0.430717	+	0.746024i	−0.566218	+	0.824255i	$0.691594\pi$
$332$		−	115.455i		−	0.347755i
$333$		0			0
$334$	−415.252			−1.24327
$335$	158.732	−	91.6442i	0.473828	−	0.273565i
$336$		0			0
$337$	−64.7530	+	112.155i	−0.192145	+	0.332805i	−0.945961	−	0.324281i	$-0.894878\pi$
$337$	−64.7530	+	112.155i	−0.192145	+	0.332805i	0.753816	+	0.657086i	$0.228211\pi$
$338$	−518.767	−	299.510i	−1.53481	−	0.886125i
$339$		0			0
$340$	−42.1946	−	73.0833i	−0.124102	−	0.214951i
$341$		−	8.68141i		−	0.0254587i
$342$		0			0
$343$	178.219			0.519590
$344$	259.133	−	149.611i	0.753294	−	0.434915i
$345$		0			0
$346$	−189.071	+	327.480i	−0.546448	+	0.946475i
$347$	84.1318	+	48.5735i	0.242455	+	0.139981i	0.616304	−	0.787508i	$-0.288629\pi$
$347$	84.1318	+	48.5735i	0.242455	+	0.139981i	−0.373850	+	0.927489i	$0.621962\pi$
$348$		0			0
$349$	115.403	+	199.884i	0.330668	+	0.572734i	0.982643	−	0.185507i	$-0.0593926\pi$
$349$	115.403	+	199.884i	0.330668	+	0.572734i	−0.651975	+	0.758241i	$0.726059\pi$
$350$			61.3897i			0.175399i
$351$		0			0
$352$	−26.8625			−0.0763141
$353$	−363.619	+	209.935i	−1.03008	+	0.594718i	−0.917008	−	0.398869i	$-0.869403\pi$
$353$	−363.619	+	209.935i	−1.03008	+	0.594718i	−0.113074	+	0.993587i	$0.536070\pi$
$354$		0			0
$355$	−42.0082	+	72.7603i	−0.118333	+	0.204959i
$356$	−12.1186	−	6.99665i	−0.0340409	−	0.0196535i
$357$		0			0
$358$	−47.2479	−	81.8357i	−0.131977	−	0.228591i
$359$			171.798i			0.478545i	0.970952	+	0.239273i	$0.0769090\pi$
$359$			171.798i			0.478545i	−0.970952	+	0.239273i	$0.923091\pi$
$360$		0			0
$361$	−329.782			−0.913525
$362$	−0.475045	+	0.274267i	−0.00131228	+	0.000757644i
$363$		0			0
$364$	−222.641	+	385.626i	−0.611652	+	1.05941i
$365$	6.76205	+	3.90407i	0.0185262	+	0.0106961i
$366$		0			0
$367$	22.3738	+	38.7526i	0.0609641	+	0.105593i	0.894897	−	0.446274i	$-0.147249\pi$
$367$	22.3738	+	38.7526i	0.0609641	+	0.105593i	−0.833933	+	0.551866i	$0.813916\pi$
$368$		−	83.2683i		−	0.226273i
$369$		0			0
$370$	−77.0666			−0.208288
$371$	624.941	−	360.810i	1.68448	−	0.972533i
$372$		0			0
$373$	154.578	−	267.737i	0.414419	−	0.717794i	−0.580949	−	0.813940i	$-0.697318\pi$
$373$	154.578	−	267.737i	0.414419	−	0.717794i	0.995367	+	0.0961461i	$0.0306516\pi$
$374$	20.5172	+	11.8456i	0.0548587	+	0.0316727i
$375$		0			0
$376$	1.45446	+	2.51919i	0.00386823	+	0.00669998i
$377$		−	671.710i		−	1.78172i
$378$		0			0
$379$	65.7442			0.173468			0.0867338	−	0.996232i	$-0.472357\pi$
$379$	65.7442			0.173468			0.0867338	+	0.996232i	$0.472357\pi$
$380$	22.3126	−	12.8822i	0.0587173	−	0.0339005i
$381$		0			0
$382$	−23.2985	+	40.3542i	−0.0609908	+	0.105639i
$383$	90.0606	+	51.9965i	0.235145	+	0.135761i	0.612943	−	0.790127i	$-0.289985\pi$
$383$	90.0606	+	51.9965i	0.235145	+	0.135761i	−0.377798	+	0.925888i	$0.623319\pi$
$384$		0			0
$385$	9.17053	+	15.8838i	0.0238196	+	0.0412567i
$386$			73.5691i			0.190593i
$387$		0			0
$388$	241.675			0.622875
$389$	481.264	−	277.858i	1.23718	−	0.714287i	0.268665	−	0.963234i	$-0.413418\pi$
$389$	481.264	−	277.858i	1.23718	−	0.714287i	0.968517	+	0.248946i	$0.0800843\pi$
$390$		0			0
$391$	217.796	−	377.234i	0.557023	−	0.964792i
$392$	−210.434	−	121.494i	−0.536821	−	0.309934i
$393$		0			0
$394$	258.291	+	447.372i	0.655560	+	1.13546i
$395$			277.428i			0.702350i
$396$		0			0
$397$	−406.903			−1.02494			−0.512472	−	0.858704i	$-0.671270\pi$
$397$	−406.903			−1.02494			−0.512472	+	0.858704i	$0.671270\pi$
$398$	−123.946	+	71.5602i	−0.311422	+	0.179800i
$399$		0			0
$400$	−8.74597	+	15.1485i	−0.0218649	+	0.0378711i
$401$	−44.8956	−	25.9205i	−0.111959	−	0.0646396i	0.442975	−	0.896534i	$-0.353923\pi$
$401$	−44.8956	−	25.9205i	−0.111959	−	0.0646396i	−0.554934	+	0.831894i	$0.687256\pi$
$402$		0			0
$403$	−114.267	−	197.917i	−0.283542	−	0.491109i
$404$			223.326i			0.552787i
$405$		0			0
$406$	336.883			0.829760
$407$	−19.9400	+	11.5124i	−0.0489927	+	0.0282860i
$408$		0			0
$409$	−235.985	+	408.739i	−0.576981	+	0.999361i	0.418842	+	0.908059i	$0.362436\pi$
$409$	−235.985	+	408.739i	−0.576981	+	0.999361i	−0.995823	+	0.0913019i	$0.970897\pi$
$410$	20.0942	+	11.6014i	0.0490103	+	0.0282961i
$411$		0			0
$412$	−72.8463	−	126.174i	−0.176811	−	0.306246i
$413$			671.882i			1.62683i
$414$		0			0
$415$	−125.188			−0.301658
$416$	−612.407	+	353.573i	−1.47213	+	0.849935i
$417$		0			0
$418$	−3.61650	+	6.26396i	−0.00865192	+	0.0149856i
$419$	262.279	+	151.427i	0.625964	+	0.361400i	0.779187	−	0.626791i	$-0.215632\pi$
$419$	262.279	+	151.427i	0.625964	+	0.361400i	−0.153223	+	0.988192i	$0.548965\pi$
$420$		0			0
$421$	−75.2249	−	130.293i	−0.178682	−	0.309485i	0.762748	−	0.646696i	$-0.223850\pi$
$421$	−75.2249	−	130.293i	−0.178682	−	0.309485i	−0.941429	+	0.337211i	$0.890517\pi$
$422$			42.6145i			0.100982i
$423$		0			0
$424$	690.430			1.62837
$425$	−79.2444	+	45.7518i	−0.186457	+	0.107651i
$426$		0			0
$427$	261.262	−	452.519i	0.611855	−	1.05976i
$428$	−180.192	−	104.034i	−0.421010	−	0.243070i
$429$		0			0
$430$	−55.1843	−	95.5821i	−0.128336	−	0.222284i
$431$		−	117.043i		−	0.271561i	−0.990739	−	0.135780i	$-0.956646\pi$
$431$		−	117.043i		−	0.271561i	0.990739	−	0.135780i	$-0.0433541\pi$
$432$		0			0
$433$	102.502			0.236725			0.118363	−	0.992970i	$-0.462235\pi$
$433$	102.502			0.236725			0.118363	+	0.992970i	$0.462235\pi$
$434$	99.2612	−	57.3085i	0.228713	−	0.132047i
$435$		0			0
$436$	−100.945	+	174.842i	−0.231526	+	0.401015i
$437$	115.171	+	66.4939i	0.263549	+	0.152160i
$438$		0			0
$439$	−8.02840	−	13.9056i	−0.0182879	−	0.0316756i	0.856737	−	0.515754i	$-0.172488\pi$
$439$	−8.02840	−	13.9056i	−0.0182879	−	0.0316756i	−0.875025	+	0.484079i	$0.839155\pi$
$440$			17.5483i			0.0398825i
$441$		0			0
$442$	623.661			1.41100
$443$	−279.019	+	161.092i	−0.629840	+	0.363639i	−0.780690	−	0.624918i	$-0.785132\pi$
$443$	−279.019	+	161.092i	−0.629840	+	0.363639i	0.150850	+	0.988557i	$0.451799\pi$
$444$		0			0
$445$	−7.58649	+	13.1402i	−0.0170483	+	0.0295285i
$446$	386.941	+	223.400i	0.867580	+	0.500898i
$447$		0			0
$448$	−239.040	−	414.029i	−0.533571	−	0.924171i
$449$			550.718i			1.22654i	0.789872	+	0.613271i	$0.210147\pi$
$449$			550.718i			1.22654i	−0.789872	+	0.613271i	$0.789853\pi$
$450$		0			0
$451$	6.93217			0.0153707
$452$	−22.0401	+	12.7248i	−0.0487612	+	0.0281523i
$453$		0			0
$454$	−161.153	+	279.125i	−0.354962	+	0.614813i
$455$	418.135	+	241.411i	0.918979	+	0.530573i
$456$		0			0
$457$	−297.150	−	514.680i	−0.650220	−	1.12621i	−0.983069	−	0.183234i	$-0.941343\pi$
$457$	−297.150	−	514.680i	−0.650220	−	1.12621i	0.332849	−	0.942980i	$-0.391990\pi$
$458$		−	329.208i		−	0.718796i
$459$		0			0
$460$	109.757			0.238602
$461$	−80.7434	+	46.6172i	−0.175148	+	0.101122i	−0.585011	−	0.811025i	$-0.698910\pi$
$461$	−80.7434	+	46.6172i	−0.175148	+	0.101122i	0.409863	+	0.912147i	$0.365577\pi$
$462$		0			0
$463$	425.678	−	737.296i	0.919391	−	1.59243i	0.119048	−	0.992889i	$-0.462016\pi$
$463$	425.678	−	737.296i	0.919391	−	1.59243i	0.800343	−	0.599543i	$-0.204651\pi$
$464$	83.1288	+	47.9945i	0.179157	+	0.103436i
$465$		0			0
$466$	−103.626	−	179.486i	−0.222374	−	0.385163i
$467$			8.00225i			0.0171354i	0.999963	+	0.00856772i	$0.00272722\pi$
$467$			8.00225i			0.0171354i	−0.999963	+	0.00856772i	$0.997273\pi$
$468$		0			0
$469$	722.974			1.54152
$470$	0.929212	−	0.536481i	0.00197705	−	0.00114145i
$471$		0			0
$472$	−321.421	+	556.718i	−0.680977	+	1.17949i
$473$	−28.5565	−	16.4871i	−0.0603732	−	0.0348565i
$474$		0			0
$475$	−13.9682	−	24.1936i	−0.0294067	−	0.0509339i
$476$		−	332.870i		−	0.699308i
$477$		0			0
$478$	368.063			0.770007
$479$	−102.836	+	59.3723i	−0.214688	+	0.123950i	−0.603488	−	0.797372i	$-0.706223\pi$
$479$	−102.836	+	59.3723i	−0.214688	+	0.123950i	0.388800	+	0.921322i	$0.372890\pi$
$480$		0			0
$481$	−303.059	+	524.914i	−0.630061	+	1.09130i
$482$	251.318	+	145.098i	0.521406	+	0.301034i
$483$		0			0
$484$	−123.872	−	214.553i	−0.255935	−	0.443292i
$485$		−	262.049i		−	0.540308i
$486$		0			0
$487$	109.899			0.225665			0.112832	−	0.993614i	$-0.464008\pi$
$487$	109.899			0.225665			0.112832	+	0.993614i	$0.464008\pi$
$488$	432.961	−	249.970i	0.887214	−	0.512233i
$489$		0			0
$490$	−44.8135	+	77.6192i	−0.0914560	+	0.158406i
$491$	−652.657	−	376.812i	−1.32924	−	0.767437i	−0.344058	−	0.938948i	$-0.611802\pi$
$491$	−652.657	−	376.812i	−1.32924	−	0.767437i	−0.985182	+	0.171511i	$0.945135\pi$
$492$		0			0
$493$	251.068	+	434.862i	0.509265	+	0.882073i
$494$			190.406i			0.385437i
$495$		0			0
$496$	32.6581			0.0658430
$497$	−287.000	+	165.700i	−0.577466	+	0.333400i
$498$		0			0
$499$	−276.591	+	479.069i	−0.554290	+	0.960058i	0.443669	+	0.896191i	$0.353677\pi$
$499$	−276.591	+	479.069i	−0.554290	+	0.960058i	−0.997958	+	0.0638671i	$0.979657\pi$
$500$	−19.9673	−	11.5281i	−0.0399347	−	0.0230563i
$501$		0			0
$502$	164.857	+	285.541i	0.328401	+	0.568807i
$503$		−	546.276i		−	1.08604i	−0.839721	−	0.543018i	$-0.817282\pi$
$503$		−	546.276i		−	1.08604i	0.839721	−	0.543018i	$-0.182718\pi$
$504$		0			0
$505$	242.153			0.479511
$506$	−26.6847	+	15.4064i	−0.0527365	+	0.0304474i
$507$		0			0
$508$	89.5963	−	155.185i	0.176371	−	0.305483i
$509$	361.100	+	208.481i	0.709430	+	0.409590i	0.810850	−	0.585254i	$-0.199005\pi$
$509$	361.100	+	208.481i	0.709430	+	0.409590i	−0.101420	+	0.994844i	$0.532339\pi$
$510$		0			0
$511$	15.3995	+	26.6726i	0.0301359	+	0.0521970i
$512$		−	219.142i		−	0.428013i
$513$		0			0
$514$	−411.084			−0.799775
$515$	−136.810	+	78.9874i	−0.265651	+	0.153374i
$516$		0			0
$517$	0.160281	−	0.277616i	0.000310022	−	0.000536974i
$518$	−263.260	−	151.993i	−0.508224	−	0.293423i
$519$		0			0
$520$	230.976	+	400.063i	0.444185	+	0.769352i
$521$			201.720i			0.387178i	0.981083	+	0.193589i	$0.0620129\pi$
$521$			201.720i			0.387178i	−0.981083	+	0.193589i	$0.937987\pi$
$522$		0			0
$523$	−796.751			−1.52342			−0.761712	−	0.647915i	$-0.775641\pi$
$523$	−796.751			−1.52342			−0.761712	+	0.647915i	$0.775641\pi$
$524$	36.0974	−	20.8408i	0.0688882	−	0.0397726i
$525$		0			0
$526$	293.662	−	508.637i	0.558292	−	0.966990i
$527$	147.952	+	85.4204i	0.280745	+	0.162088i
$528$		0			0
$529$	18.7659	+	32.5034i	0.0354742	+	0.0614432i
$530$		−	254.667i		−	0.480504i
$531$		0			0
$532$	101.627			0.191027
$533$	158.038	−	91.2434i	0.296507	−	0.171188i
$534$		0			0
$535$	−112.804	+	195.383i	−0.210849	+	0.365202i
$536$	599.052	+	345.863i	1.11763	+	0.645267i
$537$		0			0
$538$	−220.189	−	381.378i	−0.409273	−	0.708882i
$539$			26.7773i			0.0496797i
$540$		0			0
$541$	332.884			0.615312			0.307656	−	0.951498i	$-0.400455\pi$
$541$	332.884			0.615312			0.307656	+	0.951498i	$0.400455\pi$
$542$	−13.1273	+	7.57908i	−0.0242202	+	0.0139835i
$543$		0			0
$544$	264.313	−	457.804i	0.485870	−	0.841551i
$545$	189.582	+	109.455i	0.347857	+	0.200835i
$546$		0			0
$547$	140.609	+	243.541i	0.257054	+	0.445231i	0.965451	−	0.260583i	$-0.0839148\pi$
$547$	140.609	+	243.541i	0.257054	+	0.445231i	−0.708397	+	0.705814i	$0.750581\pi$
$548$			303.404i			0.553656i
$549$		0			0
$550$	6.47275			0.0117686
$551$	−132.765	+	76.6519i	−0.240953	+	0.139114i
$552$		0			0
$553$	−547.153	+	947.696i	−0.989426	+	1.71374i
$554$	−93.3391	−	53.8894i	−0.168482	−	0.0972732i
$555$		0			0
$556$	−126.475	−	219.060i	−0.227472	−	0.393993i
$557$			565.965i			1.01609i	0.861329	+	0.508047i	$0.169632\pi$
$557$			565.965i			1.01609i	−0.861329	+	0.508047i	$0.830368\pi$
$558$		0			0
$559$	−868.034			−1.55283
$560$	−59.7525	+	34.4981i	−0.106701	+	0.0616038i
$561$		0			0
$562$	113.251	−	196.156i	0.201514	−	0.349032i
$563$	−654.894	−	378.103i	−1.16322	−	0.671586i	−0.211147	−	0.977454i	$-0.567720\pi$
$563$	−654.894	−	378.103i	−1.16322	−	0.671586i	−0.952074	+	0.305868i	$0.901053\pi$
$564$		0			0
$565$	13.7976	+	23.8981i	0.0244205	+	0.0422975i
$566$			28.8382i			0.0509508i
$567$		0			0
$568$	−317.076			−0.558232
$569$	496.884	−	286.876i	0.873258	−	0.504176i	0.00482865	−	0.999988i	$-0.498463\pi$
$569$	496.884	−	286.876i	0.873258	−	0.504176i	0.868430	+	0.495812i	$0.165130\pi$
$570$		0			0
$571$	357.832	−	619.784i	0.626677	−	1.08544i	−0.361537	−	0.932358i	$-0.617748\pi$
$571$	357.832	−	619.784i	0.626677	−	1.08544i	0.988214	−	0.153078i	$-0.0489187\pi$
$572$	40.6593	+	23.4747i	0.0710827	+	0.0410396i
$573$		0			0
$574$	45.7613	+	79.2609i	0.0797235	+	0.138085i
$575$		−	119.010i		−	0.206973i
$576$		0			0
$577$	−66.8708			−0.115894			−0.0579469	−	0.998320i	$-0.518455\pi$
$577$	−66.8708			−0.115894			−0.0579469	+	0.998320i	$0.518455\pi$
$578$	−55.3535	+	31.9584i	−0.0957674	+	0.0552913i
$579$		0			0
$580$	−63.2620	+	109.573i	−0.109072	+	0.188919i
$581$	−427.643	−	246.900i	−0.736046	−	0.424956i
$582$		0			0
$583$	−38.0428	−	65.8920i	−0.0652534	−	0.113022i
$584$			29.4677i			0.0504584i
$585$		0			0
$586$	187.020			0.319147
$587$	−167.810	+	96.8852i	−0.285877	+	0.165051i	−0.636081	−	0.771622i	$-0.719446\pi$
$587$	−167.810	+	96.8852i	−0.285877	+	0.165051i	0.350204	+	0.936674i	$0.386112\pi$
$588$		0			0
$589$	−26.0791	+	45.1704i	−0.0442770	+	0.0766900i
$590$	205.347	+	118.557i	0.348046	+	0.200944i
$591$		0			0
$592$	−43.3079	−	75.0114i	−0.0731552	−	0.126708i
$593$		−	341.602i		−	0.576057i	−0.957622	−	0.288028i	$-0.907000\pi$
$593$		−	341.602i		−	0.576057i	0.957622	−	0.288028i	$-0.0929997\pi$
$594$		0			0
$595$	−360.932			−0.606609
$596$	387.995	−	224.009i	0.650998	−	0.375854i
$597$		0			0
$598$	−405.567	+	702.463i	−0.678206	+	1.17469i
$599$	−782.385	−	451.710i	−1.30615	−	0.754107i	−0.324700	−	0.945817i	$-0.605263\pi$
$599$	−782.385	−	451.710i	−1.30615	−	0.754107i	−0.981452	+	0.191710i	$0.938597\pi$
$600$		0			0
$601$	−391.926	−	678.836i	−0.652123	−	1.12951i	−0.982607	−	0.185699i	$-0.940545\pi$
$601$	−391.926	−	678.836i	−0.652123	−	1.12951i	0.330484	−	0.943812i	$-0.392788\pi$
$602$		−	435.345i		−	0.723165i
$603$		0			0
$604$	−334.892			−0.554457
$605$	−232.641	+	134.315i	−0.384530	+	0.222009i
$606$		0			0
$607$	−32.1813	+	55.7397i	−0.0530170	+	0.0918281i	−0.891316	−	0.453383i	$-0.850217\pi$
$607$	−32.1813	+	55.7397i	−0.0530170	+	0.0918281i	0.838299	+	0.545211i	$0.183550\pi$
$608$	139.769	+	80.6957i	0.229883	+	0.132723i
$609$		0			0
$610$	−92.2022	−	159.699i	−0.151151	−	0.261801i
$611$		−	8.43869i		−	0.0138113i
$612$		0			0
$613$	671.468			1.09538			0.547690	−	0.836681i	$-0.315507\pi$
$613$	671.468			1.09538			0.547690	+	0.836681i	$0.315507\pi$
$614$	116.054	−	67.0040i	0.189014	−	0.109127i
$615$		0			0
$616$	−34.6093	+	59.9451i	−0.0561840	+	0.0973135i
$617$	−174.533	−	100.767i	−0.282874	−	0.163317i	0.351850	−	0.936056i	$-0.385553\pi$
$617$	−174.533	−	100.767i	−0.282874	−	0.163317i	−0.634724	+	0.772739i	$0.718886\pi$
$618$		0			0
$619$	120.671	+	209.008i	0.194945	+	0.337655i	0.946882	−	0.321580i	$-0.104214\pi$
$619$	120.671	+	209.008i	0.194945	+	0.337655i	−0.751938	+	0.659234i	$0.770881\pi$
$620$			43.0470i			0.0694307i
$621$		0			0
$622$	−527.079			−0.847394
$623$	−51.8310	+	29.9246i	−0.0831958	+	0.0480331i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−274.220	−	158.321i	−0.438051	−	0.252909i
$627$		0			0
$628$	−118.492	−	205.234i	−0.188682	−	0.326806i
$629$		−	453.103i		−	0.720354i
$630$		0			0
$631$	−443.396			−0.702687			−0.351344	−	0.936247i	$-0.614275\pi$
$631$	−443.396			−0.702687			−0.351344	+	0.936247i	$0.614275\pi$
$632$	−906.735	+	523.504i	−1.43471	+	0.828328i
$633$		0			0
$634$	157.770	−	273.266i	0.248849	−	0.431018i
$635$	−168.268	−	97.1495i	−0.264989	−	0.152991i
$636$		0			0
$637$	352.452	+	610.464i	0.553299	+	0.958342i
$638$		−	35.5199i		−	0.0556739i
$639$		0			0
$640$	89.6410			0.140064
$641$	−250.091	+	144.390i	−0.390157	+	0.225258i	−0.682228	−	0.731139i	$-0.738989\pi$
$641$	−250.091	+	144.390i	−0.390157	+	0.225258i	0.292071	+	0.956397i	$0.405656\pi$
$642$		0			0
$643$	592.700	−	1026.59i	0.921772	−	1.59656i	0.125100	−	0.992144i	$-0.460075\pi$
$643$	592.700	−	1026.59i	0.921772	−	1.59656i	0.796672	−	0.604412i	$-0.206592\pi$
$644$	374.930	+	216.466i	0.582189	+	0.336127i
$645$		0			0
$646$	−71.1689	−	123.268i	−0.110168	−	0.190817i
$647$		−	52.8484i		−	0.0816823i	−0.999166	−	0.0408411i	$-0.986996\pi$
$647$		−	52.8484i		−	0.0816823i	0.999166	−	0.0408411i	$-0.0130038\pi$
$648$		0			0
$649$	70.8413			0.109155
$650$	147.564	−	85.1964i	0.227022	−	0.131071i
$651$		0			0
$652$	143.076	−	247.815i	0.219442	−	0.380085i
$653$	491.257	+	283.627i	0.752308	+	0.434345i	0.826527	−	0.562897i	$-0.190313\pi$
$653$	491.257	+	283.627i	0.752308	+	0.434345i	−0.0742194	+	0.997242i	$0.523647\pi$
$654$		0			0
$655$	−22.5978	−	39.1405i	−0.0345004	−	0.0597565i
$656$			26.0778i			0.0397527i
$657$		0			0
$658$	4.23226			0.00643200
$659$	1063.51	−	614.020i	1.61383	−	0.931746i	0.625360	−	0.780337i	$-0.284952\pi$
$659$	1063.51	−	614.020i	1.61383	−	0.931746i	0.988471	−	0.151409i	$-0.0483810\pi$
$660$		0			0
$661$	−588.296	+	1018.96i	−0.890009	+	1.54154i	−0.0501453	+	0.998742i	$0.515968\pi$
$661$	−588.296	+	1018.96i	−0.890009	+	1.54154i	−0.839863	+	0.542798i	$0.817365\pi$
$662$	343.742	+	198.460i	0.519248	+	0.299788i
$663$		0			0
$664$	−236.228	−	409.159i	−0.355765	−	0.616203i
$665$		−	110.194i		−	0.165705i
$666$		0			0
$667$	−653.078			−0.979128
$668$	532.751	−	307.584i	0.797532	−	0.460455i
$669$		0			0
$670$	127.573	−	220.962i	0.190407	−	0.329794i
$671$	−47.7124	−	27.5467i	−0.0711063	−	0.0410533i
$672$		0			0
$673$	230.657	+	399.509i	0.342729	+	0.593624i	0.984939	−	0.172905i	$-0.0553153\pi$
$673$	230.657	+	399.509i	0.342729	+	0.593624i	−0.642209	+	0.766529i	$0.721982\pi$
$674$			180.278i			0.267474i
$675$		0			0
$676$	887.409			1.31273
$677$	−493.586	+	284.972i	−0.729078	+	0.420933i	−0.818085	−	0.575098i	$-0.804964\pi$
$677$	−493.586	+	284.972i	−0.729078	+	0.420933i	0.0890070	+	0.996031i	$0.471631\pi$
$678$		0			0
$679$	516.822	−	895.162i	0.761151	−	1.31835i
$680$	−299.066	−	172.666i	−0.439803	−	0.253921i
$681$		0			0
$682$	−6.04244	−	10.4658i	−0.00885989	−	0.0153458i
$683$		−	836.526i		−	1.22478i	−0.790555	−	0.612391i	$-0.790208\pi$
$683$		−	836.526i		−	1.22478i	0.790555	−	0.612391i	$-0.209792\pi$
$684$		0			0
$685$	328.981			0.480265
$686$	214.851	−	124.044i	0.313194	−	0.180823i
$687$		0			0
$688$	62.0221	−	107.425i	0.0901484	−	0.156142i
$689$	−1734.58	−	1001.46i	−2.51753	−	1.45350i
$690$		0			0
$691$	358.397	+	620.762i	0.518664	+	0.898353i	0.999765	+	0.0216875i	$0.00690389\pi$
$691$	358.397	+	620.762i	0.518664	+	0.898353i	−0.481100	+	0.876665i	$0.659763\pi$
$692$		−	560.192i		−	0.809526i
$693$		0			0
$694$	135.233			0.194860
$695$	−237.528	+	137.137i	−0.341766	+	0.197319i
$696$		0			0
$697$	−68.2089	+	118.141i	−0.0978606	+	0.169500i
$698$	278.247	+	160.646i	0.398635	+	0.230152i
$699$		0			0
$700$	−45.4723	−	78.7604i	−0.0649605	−	0.112515i
$701$			1133.20i			1.61654i	0.588809	+	0.808272i	$0.299597\pi$
$701$			1133.20i			1.61654i	−0.588809	+	0.808272i	$0.700403\pi$
$702$		0			0
$703$	138.334			0.196777
$704$	−43.6540	+	25.2037i	−0.0620085	+	0.0358007i
$705$		0			0
$706$	−292.239	+	506.173i	−0.413936	+	0.716959i
$707$	827.195	+	477.581i	1.17001	+	0.675504i
$708$		0			0
$709$	376.605	+	652.299i	0.531178	+	0.920027i	0.999338	+	0.0363836i	$0.0115838\pi$
$709$	376.605	+	652.299i	0.531178	+	0.920027i	−0.468160	+	0.883644i	$0.655083\pi$
$710$			116.954i			0.164724i
$711$		0			0
$712$	−57.2624			−0.0804248
$713$	−192.427	+	111.098i	−0.269884	+	0.155818i
$714$		0			0
$715$	25.4536	−	44.0870i	0.0355995	−	0.0616602i
$716$	121.234	+	69.9946i	0.169321	+	0.0977578i
$717$		0			0
$718$	119.575	+	207.110i	0.166539	+	0.288454i
$719$			1275.56i			1.77407i	0.461700	+	0.887036i	$0.347240\pi$
$719$			1275.56i			1.77407i	−0.461700	+	0.887036i	$0.652760\pi$
$720$		0			0
$721$	−623.126			−0.864253
$722$	−397.567	+	229.536i	−0.550647	+	0.317916i
$723$		0			0
$724$	0.406308	−	0.703747i	0.000561199	−	0.000972026i
$725$	118.810	+	68.5951i	0.163876	+	0.0946140i
$726$		0			0
$727$	358.445	+	620.845i	0.493047	+	0.853983i	0.999968	−	0.00801006i	$-0.00254971\pi$
$727$	358.445	+	620.845i	0.493047	+	0.853983i	−0.506921	+	0.861993i	$0.669216\pi$
$728$			1822.16i			2.50296i
$729$		0			0
$730$	10.8693			0.0148894
$731$	561.962	−	324.449i	0.768758	−	0.443842i
$732$		0			0
$733$	−250.532	+	433.935i	−0.341790	+	0.591998i	−0.984765	−	0.173889i	$-0.944367\pi$
$733$	−250.532	+	433.935i	−0.341790	+	0.591998i	0.642975	+	0.765887i	$0.277700\pi$
$734$	53.9452	+	31.1453i	0.0734949	+	0.0424323i
$735$		0			0
$736$	343.766	+	595.420i	0.467073	+	0.808995i
$737$		−	76.2284i		−	0.103431i
$738$		0			0
$739$	−332.861			−0.450420			−0.225210	−	0.974310i	$-0.572307\pi$
$739$	−332.861			−0.450420			−0.225210	+	0.974310i	$0.572307\pi$
$740$	98.8733	−	57.0845i	0.133613	−	0.0771413i
$741$		0			0
$742$	502.263	−	869.944i	0.676904	−	1.17243i
$743$	1098.68	+	634.324i	1.47871	+	0.853733i	0.999710	−	0.0240816i	$-0.00766614\pi$
$743$	1098.68	+	634.324i	1.47871	+	0.853733i	0.479000	+	0.877815i	$0.340999\pi$
$744$		0			0
$745$	−242.893	−	420.704i	−0.326031	−	0.564703i
$746$		−	430.359i		−	0.576888i
$747$		0			0
$748$	−35.0969			−0.0469210
$749$	−770.680	+	444.953i	−1.02895	+	0.594062i
$750$		0			0
$751$	32.8278	−	56.8594i	0.0437121	−	0.0757116i	−0.843342	−	0.537378i	$-0.819415\pi$
$751$	32.8278	−	56.8594i	0.0437121	−	0.0757116i	0.887054	+	0.461666i	$0.152748\pi$
$752$	1.04435	+	0.602954i	0.00138876	+	0.000801801i
$753$		0			0
$754$	−467.524	−	809.776i	−0.620059	−	1.07397i
$755$			363.124i			0.480960i
$756$		0			0
$757$	1027.67			1.35756			0.678781	−	0.734340i	$-0.262508\pi$
$757$	1027.67			1.35756			0.678781	+	0.734340i	$0.262508\pi$
$758$	79.2575	−	45.7593i	0.104561	−	0.0603685i
$759$		0			0
$760$	52.7155	−	91.3060i	0.0693626	−	0.120139i
$761$	442.319	+	255.373i	0.581234	+	0.335576i	0.761624	−	0.648020i	$-0.224402\pi$
$761$	442.319	+	255.373i	0.581234	+	0.335576i	−0.180389	+	0.983595i	$0.557736\pi$
$762$		0			0
$763$	431.742	+	747.799i	0.565848	+	0.980078i
$764$		−	69.0303i		−	0.0903538i
$765$		0			0
$766$	144.763			0.188985
$767$	1615.03	−	932.435i	2.10564	−	1.21569i
$768$		0			0
$769$	739.257	−	1280.43i	0.961323	−	1.66506i	0.242137	−	0.970242i	$-0.422152\pi$
$769$	739.257	−	1280.43i	0.961323	−	1.66506i	0.719186	−	0.694818i	$-0.244515\pi$
$770$	22.1110	+	12.7658i	0.0287155	+	0.0165789i
$771$		0			0
$772$	−54.4938	−	94.3861i	−0.0705878	−	0.122262i
$773$			1408.06i			1.82156i	0.412896	+	0.910778i	$0.364517\pi$
$773$			1408.06i			1.82156i	−0.412896	+	0.910778i	$0.635483\pi$
$774$		0			0
$775$	46.6760			0.0602271
$776$	856.471	−	494.484i	1.10370	−	0.637221i
$777$		0			0
$778$	386.790	−	669.940i	0.497159	−	0.861105i
$779$	−36.0689	−	20.8244i	−0.0463016	−	0.0267322i
$780$		0			0
$781$	17.4709	+	30.2605i	0.0223699	+	0.0387458i
$782$		−	606.363i		−	0.775400i
$783$		0			0
$784$	−100.732			−0.128485
$785$	−222.536	+	128.481i	−0.283486	+	0.163670i
$786$		0			0
$787$	116.476	−	201.743i	0.148000	−	0.256344i	−0.782488	−	0.622666i	$-0.786050\pi$
$787$	116.476	−	201.743i	0.148000	−	0.256344i	0.930488	+	0.366322i	$0.119383\pi$
$788$	−662.752	−	382.640i	−0.841056	−	0.485584i
$789$		0			0
$790$	193.096	+	334.452i	0.244425	+	0.423357i
$791$			108.848i			0.137608i
$792$		0			0
$793$	−1450.31			−1.82890
$794$	−490.539	+	283.213i	−0.617807	+	0.356691i
$795$		0			0
$796$	106.012	−	183.618i	0.133181	−	0.230675i
$797$	1112.23	+	642.147i	1.39552	+	0.805705i	0.993919	−	0.110110i	$-0.0351202\pi$
$797$	1112.23	+	642.147i	1.39552	+	0.805705i	0.401602	+	0.915814i	$0.368454\pi$
$798$		0			0
$799$	3.15417	+	5.46317i	0.00394764	+	0.00683751i
$800$		−	144.428i		−	0.180535i
$801$		0			0
$802$	−72.1648			−0.0899810
$803$	2.81229	−	1.62367i	0.00350223	−	0.00202201i
$804$		0			0
$805$	234.715	−	406.538i	0.291571	−	0.505016i
$806$	−275.509	−	159.065i	−0.341822	−	0.197351i
$807$		0			0
$808$	456.939	+	791.442i	0.565519	+	0.979508i
$809$		−	755.370i		−	0.933708i	−0.884334	−	0.466854i	$-0.845387\pi$
$809$		−	755.370i		−	0.933708i	0.884334	−	0.466854i	$-0.154613\pi$
$810$		0			0
$811$	−205.503			−0.253394			−0.126697	−	0.991941i	$-0.540438\pi$
$811$	−205.503			−0.253394			−0.126697	+	0.991941i	$0.540438\pi$
$812$	−432.206	+	249.534i	−0.532274	+	0.307308i
$813$		0			0
$814$	−16.0257	+	27.7574i	−0.0196876	+	0.0341000i
$815$	−268.707	−	155.138i	−0.329702	−	0.190353i
$816$		0			0
$817$	99.0554	+	171.569i	0.121243	+	0.209999i
$818$			657.003i			0.803183i
$819$		0			0
$820$	−34.3734			−0.0419188
$821$	−533.936	+	308.268i	−0.650348	+	0.375479i	−0.788590	−	0.614920i	$-0.789188\pi$
$821$	−533.936	+	308.268i	−0.650348	+	0.375479i	0.138241	+	0.990399i	$0.455855\pi$
$822$		0			0
$823$	−411.665	+	713.025i	−0.500201	+	0.866373i	0.499799	+	0.866141i	$0.333407\pi$
$823$	−411.665	+	713.025i	−0.500201	+	0.866373i	−1.00000		0.000231631i	$0.999926\pi$
$824$	−516.319	−	298.097i	−0.626600	−	0.361768i
$825$		0			0
$826$	467.644	+	809.984i	0.566155	+	0.980610i
$827$		−	1571.93i		−	1.90077i	−0.311084	−	0.950383i	$-0.600692\pi$
$827$		−	1571.93i		−	1.90077i	0.311084	−	0.950383i	$-0.399308\pi$
$828$		0			0
$829$	981.235			1.18364			0.591819	−	0.806071i	$-0.298410\pi$
$829$	981.235			1.18364			0.591819	+	0.806071i	$0.298410\pi$
$830$	−150.920	+	87.1335i	−0.181831	+	0.104980i
$831$		0			0
$832$	−663.477	+	1149.18i	−0.797448	+	1.38122i
$833$	−456.351	−	263.475i	−0.547841	−	0.316296i
$834$		0			0
$835$	−333.514	−	577.664i	−0.399418	−	0.691813i
$836$		−	10.7152i		−	0.0128172i
$837$		0			0
$838$	421.585			0.503085
$839$	−425.520	+	245.674i	−0.507175	+	0.292818i	−0.731672	−	0.681657i	$-0.761260\pi$
$839$	−425.520	+	245.674i	−0.507175	+	0.292818i	0.224497	+	0.974475i	$0.427926\pi$
$840$		0			0
$841$	−44.0768	+	76.3432i	−0.0524100	+	0.0907767i
$842$	−181.374	−	104.716i	−0.215408	−	0.124366i
$843$		0			0
$844$	−31.5653	−	54.6726i	−0.0373996	−	0.0647780i
$845$		−	962.219i		−	1.13872i
$846$		0			0
$847$	−1059.60			−1.25101
$848$	247.876	−	143.111i	0.292306	−	0.168763i
$849$		0			0
$850$	−63.6884	+	110.312i	−0.0749275	+	0.129778i
$851$	510.354	+	294.653i	0.599711	+	0.346243i
$852$		0			0
$853$	−358.141	−	620.318i	−0.419860	−	0.727219i	0.576065	−	0.817404i	$-0.304587\pi$
$853$	−358.141	−	620.318i	−0.419860	−	0.727219i	−0.995925	+	0.0901850i	$0.971254\pi$
$854$		−	727.376i		−	0.851729i
$855$		0			0
$856$	−851.442			−0.994675
$857$	−356.924	+	206.070i	−0.416481	+	0.240455i	−0.693570	−	0.720389i	$-0.743963\pi$
$857$	−356.924	+	206.070i	−0.416481	+	0.240455i	0.277090	+	0.960844i	$0.410630\pi$
$858$		0			0
$859$	−663.548	+	1149.30i	−0.772466	+	1.33795i	0.163742	+	0.986503i	$0.447643\pi$
$859$	−663.548	+	1149.30i	−0.772466	+	1.33795i	−0.936208	+	0.351446i	$0.885690\pi$
$860$	141.598	+	81.7519i	0.164649	+	0.0950604i
$861$		0			0
$862$	−81.4642	−	141.100i	−0.0945060	−	0.163689i
$863$		−	1365.68i		−	1.58248i	−0.611506	−	0.791240i	$-0.709436\pi$
$863$		−	1365.68i		−	1.58248i	0.611506	−	0.791240i	$-0.290564\pi$
$864$		0			0
$865$	−607.417			−0.702217
$866$	123.571	−	71.3437i	0.142692	−	0.0823830i
$867$		0			0
$868$	−84.8987	+	147.049i	−0.0978096	+	0.169411i
$869$	99.9224	+	57.6902i	0.114985	+	0.0663869i
$870$		0			0
$871$	−1003.34	−	1737.84i	−1.15194	−	1.99522i
$872$			826.163i			0.947434i
$873$		0			0
$874$	185.125			0.211813
$875$	−85.4001	+	49.3058i	−0.0976001	+	0.0563495i
$876$		0			0
$877$	444.069	−	769.150i	0.506350	−	0.877024i	−0.493623	−	0.869676i	$-0.664328\pi$
$877$	444.069	−	769.150i	0.506350	−	0.877024i	0.999973	−	0.00734817i	$-0.00233902\pi$
$878$	−19.3572	−	11.1759i	−0.0220469	−	0.0127288i
$879$		0			0
$880$	3.63739	+	6.30014i	0.00413339	+	0.00715925i
$881$			326.117i			0.370166i	0.982723	+	0.185083i	$0.0592554\pi$
$881$			326.117i			0.370166i	−0.982723	+	0.185083i	$0.940745\pi$
$882$		0			0
$883$	1431.31			1.62096			0.810481	−	0.585765i	$-0.199206\pi$
$883$	1431.31			1.62096			0.810481	+	0.585765i	$0.199206\pi$
$884$	−800.132	+	461.956i	−0.905126	+	0.522575i
$885$		0			0
$886$	−224.247	+	388.407i	−0.253100	+	0.438382i
$887$	−1189.90	−	686.990i	−1.34149	−	0.774510i	−0.354464	−	0.935069i	$-0.615337\pi$
$887$	−1189.90	−	686.990i	−1.34149	−	0.774510i	−0.987026	+	0.160560i	$0.948670\pi$
$888$		0			0
$889$	−383.202	−	663.726i	−0.431049	−	0.746599i
$890$			21.1214i			0.0237319i
$891$		0			0
$892$	−661.905			−0.742046
$893$	−1.66793	+	0.962978i	−0.00186778	+	0.00107836i
$894$		0			0
$895$	75.8953	−	131.455i	0.0847992	−	0.146877i
$896$	306.214	+	176.793i	0.341757	+	0.197313i
$897$		0			0
$898$	383.311	+	663.914i	0.426850	+	0.739325i
$899$		−	256.140i		−	0.284916i
$900$		0			0
$901$	1497.28			1.66180
$902$	8.35704	−	4.82494i	0.00926501	−	0.00534916i
$903$		0			0
$904$	−52.0717	+	90.1909i	−0.0576015	+	0.0997687i
$905$	−0.763074	−	0.440561i	−0.000843176	−	0.000486808i
$906$		0			0
$907$	−528.280	−	915.008i	−0.582448	−	1.00883i	−0.995188	−	0.0979805i	$-0.968762\pi$
$907$	−528.280	−	915.008i	−0.582448	−	1.00883i	0.412741	−	0.910849i	$-0.364572\pi$
$908$		−	477.475i		−	0.525853i
$909$		0			0
$910$	672.108			0.738580
$911$	−1010.84	+	583.611i	−1.10960	+	0.640627i	−0.938725	−	0.344666i	$-0.887992\pi$
$911$	−1010.84	+	583.611i	−1.10960	+	0.640627i	−0.170873	+	0.985293i	$0.554659\pi$
$912$		0			0
$913$	−26.0324	+	45.0894i	−0.0285130	+	0.0493860i
$914$	−716.456	−	413.646i	−0.783869	−	0.452567i
$915$		0			0
$916$	243.850	+	422.361i	0.266212	+	0.461093i
$917$		−	178.272i		−	0.194408i
$918$		0			0
$919$	−728.791			−0.793027			−0.396513	−	0.918029i	$-0.629780\pi$
$919$	−728.791			−0.793027			−0.396513	+	0.918029i	$0.629780\pi$
$920$	388.966	−	224.570i	0.422789	−	0.244097i
$921$		0			0
$922$	−64.8932	+	112.398i	−0.0703831	+	0.121907i
$923$	796.596	+	459.915i	0.863051	+	0.498283i
$924$		0			0
$925$	−61.8969	−	107.209i	−0.0669156	−	0.115901i
$926$		−	1185.12i		−	1.27983i
$927$		0			0
$928$	−792.563			−0.854055
$929$	1218.79	−	703.671i	1.31194	−	0.757450i	0.329524	−	0.944147i	$-0.393112\pi$
$929$	1218.79	−	703.671i	1.31194	−	0.757450i	0.982418	+	0.186697i	$0.0597783\pi$
$930$		0			0
$931$	80.4397	−	139.326i	0.0864014	−	0.149652i
$932$	265.897	+	153.516i	0.285297	+	0.164716i
$933$		0			0
$934$	5.56974	+	9.64707i	0.00596332	+	0.0103288i
$935$			38.0557i			0.0407012i
$936$		0			0
$937$	190.016			0.202792			0.101396	−	0.994846i	$-0.467669\pi$
$937$	190.016			0.202792			0.101396	+	0.994846i	$0.467669\pi$
$938$	871.578	−	503.206i	0.929187	−	0.536466i
$939$		0			0
$940$	−0.794760	+	1.37657i	−0.000845490	+	0.00146443i
$941$	−846.712	−	488.849i	−0.899800	−	0.519500i	−0.0226649	−	0.999743i	$-0.507215\pi$
$941$	−846.712	−	488.849i	−0.899800	−	0.519500i	−0.877135	+	0.480243i	$0.840548\pi$
$942$		0			0
$943$	−88.7125	−	153.655i	−0.0940748	−	0.162942i
$944$			266.494i			0.282303i
$945$		0			0
$946$	−45.9016			−0.0485217
$947$	−333.805	+	192.723i	−0.352487	+	0.203509i	−0.665780	−	0.746148i	$-0.731901\pi$
$947$	−333.805	+	192.723i	−0.352487	+	0.203509i	0.313293	+	0.949657i	$0.398568\pi$
$948$		0			0
$949$	42.7426	−	74.0324i	0.0450396	−	0.0780109i
$950$	−33.6785	−	19.4443i	−0.0354511	−	0.0204677i
$951$		0			0
$952$	−681.075	−	1179.66i	−0.715415	−	1.23913i
$953$			704.718i			0.739473i	0.929137	+	0.369736i	$0.120552\pi$
$953$			704.718i			0.739473i	−0.929137	+	0.369736i	$0.879448\pi$
$954$		0			0
$955$	−74.8498			−0.0783767
$956$	−472.210	+	272.631i	−0.493944	+	0.285179i
$957$		0			0
$958$	−82.6487	+	143.152i	−0.0862721	+	0.149428i
$959$	1123.80	+	648.827i	1.17185	+	0.676566i
$960$		0			0
$961$	436.927	+	756.780i	0.454659	+	0.787492i
$962$			843.743i			0.877071i
$963$		0			0
$964$	−429.907			−0.445962
$965$	−102.343	+	59.0878i	−0.106055	+	0.0612309i
$966$		0			0
$967$	−4.82389	+	8.35523i	−0.00498851	+	0.00864036i	−0.868509	−	0.495674i	$-0.834921\pi$
$967$	−4.82389	+	8.35523i	−0.00498851	+	0.00864036i	0.863520	+	0.504314i	$0.168255\pi$
$968$	−877.980	−	506.902i	−0.907005	−	0.523659i
$969$		0			0
$970$	−182.392	−	315.912i	−0.188033	−	0.325682i
$971$		−	382.240i		−	0.393656i	−0.980438	−	0.196828i	$-0.936936\pi$
$971$		−	382.240i		−	0.393656i	0.980438	−	0.196828i	$-0.0630640\pi$
$972$		0			0
$973$	−1081.86			−1.11188
$974$	132.488	−	76.4919i	0.136024	−	0.0785337i
$975$		0			0
$976$	103.627	−	179.487i	0.106175	−	0.183900i
$977$	120.284	+	69.4460i	0.123116	+	0.0710809i	0.560293	−	0.828294i	$-0.310688\pi$
$977$	120.284	+	69.4460i	0.123116	+	0.0710809i	−0.437177	+	0.899375i	$0.644022\pi$
$978$		0			0
$979$	3.15517	+	5.46491i	0.00322285	+	0.00558213i
$980$		−	132.776i		−	0.135486i
$981$		0			0
$982$	−1049.08			−1.06831
$983$	−224.640	+	129.696i	−0.228525	+	0.131939i	−0.609892	−	0.792485i	$-0.708787\pi$
$983$	−224.640	+	129.696i	−0.228525	+	0.131939i	0.381366	+	0.924424i	$0.375454\pi$
$984$		0			0
$985$	−414.898	+	718.624i	−0.421216	+	0.729567i
$986$	605.347	+	349.497i	0.613942	+	0.354459i
$987$		0			0
$988$	−141.037	−	244.283i	−0.142750	−	0.247250i
$989$			843.957i			0.853344i
$990$		0			0
$991$	−265.646			−0.268058			−0.134029	−	0.990977i	$-0.542792\pi$
$991$	−265.646			−0.268058			−0.134029	+	0.990977i	$0.542792\pi$
$992$	−233.526	+	134.826i	−0.235409	+	0.135914i
$993$		0			0
$994$	−230.661	+	399.517i	−0.232053	+	0.401928i
$995$	−199.097	−	114.949i	−0.200098	−	0.115526i
$996$		0			0
$997$	522.352	+	904.740i	0.523924	+	0.907463i	0.999612	+	0.0278489i	$0.00886573\pi$
$997$	522.352	+	904.740i	0.523924	+	0.907463i	−0.475688	+	0.879614i	$0.657801\pi$
$998$			770.052i			0.771595i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.i.a.71.6		16
3.2	odd	2		45.3.i.a.41.3	yes	16
4.3	odd	2		2160.3.bs.c.881.5		16
5.2	odd	4		675.3.i.c.449.11		32
5.3	odd	4		675.3.i.c.449.6		32
5.4	even	2		675.3.j.b.476.3		16
9.2	odd	6	inner	135.3.i.a.116.6		16
9.4	even	3		405.3.c.a.161.11		16
9.5	odd	6		405.3.c.a.161.6		16
9.7	even	3		45.3.i.a.11.3	✓	16
12.11	even	2		720.3.bs.c.401.3		16
15.2	even	4		225.3.i.b.149.6		32
15.8	even	4		225.3.i.b.149.11		32
15.14	odd	2		225.3.j.b.176.6		16
36.7	odd	6		720.3.bs.c.641.3		16
36.11	even	6		2160.3.bs.c.1601.5		16
45.2	even	12		675.3.i.c.224.6		32
45.7	odd	12		225.3.i.b.74.11		32
45.29	odd	6		675.3.j.b.251.3		16
45.34	even	6		225.3.j.b.101.6		16
45.38	even	12		675.3.i.c.224.11		32
45.43	odd	12		225.3.i.b.74.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.3	✓	16	9.7	even	3
45.3.i.a.41.3	yes	16	3.2	odd	2
135.3.i.a.71.6		16	1.1	even	1	trivial
135.3.i.a.116.6		16	9.2	odd	6	inner
225.3.i.b.74.6		32	45.43	odd	12
225.3.i.b.74.11		32	45.7	odd	12
225.3.i.b.149.6		32	15.2	even	4
225.3.i.b.149.11		32	15.8	even	4
225.3.j.b.101.6		16	45.34	even	6
225.3.j.b.176.6		16	15.14	odd	2
405.3.c.a.161.6		16	9.5	odd	6
405.3.c.a.161.11		16	9.4	even	3
675.3.i.c.224.6		32	45.2	even	12
675.3.i.c.224.11		32	45.38	even	12
675.3.i.c.449.6		32	5.3	odd	4
675.3.i.c.449.11		32	5.2	odd	4
675.3.j.b.251.3		16	45.29	odd	6
675.3.j.b.476.3		16	5.4	even	2
720.3.bs.c.401.3		16	12.11	even	2
720.3.bs.c.641.3		16	36.7	odd	6
2160.3.bs.c.881.5		16	4.3	odd	2
2160.3.bs.c.1601.5		16	36.11	even	6

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)

\(f(q)\)	\(=\)	\(q+(1.20554 - 0.696021i) q^{2} +(-1.03111 + 1.78593i) q^{4} +(1.93649 + 1.11803i) q^{5} +(4.41004 + 7.63842i) q^{7} +8.43886i q^{8} +O(q^{10})\)	\(q+(1.20554 - 0.696021i) q^{2} +(-1.03111 + 1.78593i) q^{4} +(1.93649 + 1.11803i) q^{5} +(4.41004 + 7.63842i) q^{7} +8.43886i q^{8} +3.11270 q^{10} +(0.805373 - 0.464982i) q^{11} +(12.2405 - 21.2011i) q^{13} +(10.6330 + 6.13897i) q^{14} +(1.74919 + 3.02969i) q^{16} +18.3007i q^{17} -5.58727 q^{19} +(-3.99347 + 2.30563i) q^{20} +(0.647275 - 1.12111i) q^{22} +(-20.6131 - 11.9010i) q^{23} +(2.50000 + 4.33013i) q^{25} -34.0785i q^{26} -18.1889 q^{28} +(23.7620 - 13.7190i) q^{29} +(4.66760 - 8.08452i) q^{31} +(-25.0156 - 14.4428i) q^{32} +(12.7377 + 22.0623i) q^{34} +19.7223i q^{35} -24.7588 q^{37} +(-6.73570 + 3.88886i) q^{38} +(-9.43494 + 16.3418i) q^{40} +(6.45555 + 3.72712i) q^{41} +(-17.7288 - 30.7071i) q^{43} +1.91779i q^{44} -33.1333 q^{46} +(0.298523 - 0.172352i) q^{47} +(-14.3970 + 24.9363i) q^{49} +(6.02772 + 3.48011i) q^{50} +(25.2425 + 43.7214i) q^{52} -81.8155i q^{53} +2.07946 q^{55} +(-64.4596 + 37.2158i) q^{56} +(19.0975 - 33.0778i) q^{58} +(65.9707 + 38.0882i) q^{59} +(-29.6213 - 51.3056i) q^{61} -12.9950i q^{62} -54.2035 q^{64} +(47.4072 - 27.3705i) q^{65} +(40.9845 - 70.9873i) q^{67} +(-32.6838 - 18.8700i) q^{68} +(13.7271 + 23.7761i) q^{70} +37.5733i q^{71} +3.49191 q^{73} +(-29.8478 + 17.2326i) q^{74} +(5.76108 - 9.97849i) q^{76} +(7.10346 + 4.10119i) q^{77} +(62.0348 + 107.447i) q^{79} +7.82263i q^{80} +10.3766 q^{82} +(-48.4851 + 27.9929i) q^{83} +(-20.4608 + 35.4392i) q^{85} +(-42.7456 - 24.6792i) q^{86} +(3.92392 + 6.79643i) q^{88} +6.78556i q^{89} +215.924 q^{91} +(42.5086 - 24.5424i) q^{92} +(0.239921 - 0.415556i) q^{94} +(-10.8197 - 6.24676i) q^{95} +(-58.5960 - 101.491i) q^{97} +40.0824i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) \) 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

Introduction

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