LMFDB - Embedded newform 405.3.h.k.134.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(134,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.134"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			134.5
Character	$\chi$	$=$	405.134
Dual form			405.3.h.k.269.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14196 - 1.97794i) q^{2} +(-0.608153 + 1.05335i) q^{4} +(-4.77039 - 1.49780i) q^{5} +(2.98475 - 1.72325i) q^{7} -6.35774 q^{8} +(2.48505 + 11.1459i) q^{10} +(3.89854 - 2.25082i) q^{11} +(-10.2564 - 5.92153i) q^{13} +(-6.81695 - 3.93577i) q^{14} +(9.69291 + 16.7886i) q^{16} -23.3048 q^{17} +11.0739 q^{19} +(4.47884 - 4.11401i) q^{20} +(-8.90397 - 5.14071i) q^{22} +(-14.9182 + 25.8391i) q^{23} +(20.5132 + 14.2902i) q^{25} +27.0487i q^{26} +4.19199i q^{28} +(30.8581 - 17.8160i) q^{29} +(-15.1515 + 26.2432i) q^{31} +(9.42238 - 16.3200i) q^{32} +(26.6132 + 46.0954i) q^{34} +(-16.8195 + 3.75000i) q^{35} +5.11748i q^{37} +(-12.6460 - 21.9035i) q^{38} +(30.3289 + 9.52263i) q^{40} +(-19.6134 - 11.3238i) q^{41} +(-58.8579 + 33.9816i) q^{43} +5.47538i q^{44} +68.1442 q^{46} +(23.1234 + 40.0508i) q^{47} +(-18.5608 + 32.1483i) q^{49} +(4.83975 - 56.8926i) q^{50} +(12.4749 - 7.20240i) q^{52} +68.0017 q^{53} +(-21.9688 + 4.89807i) q^{55} +(-18.9763 + 10.9560i) q^{56} +(-70.4776 - 40.6903i) q^{58} +(-29.9499 - 17.2916i) q^{59} +(-8.68165 - 15.0371i) q^{61} +69.2099 q^{62} +34.5033 q^{64} +(40.0577 + 43.6100i) q^{65} +(85.1195 + 49.1438i) q^{67} +(14.1729 - 24.5482i) q^{68} +(26.6245 + 28.9856i) q^{70} +134.669i q^{71} -134.962i q^{73} +(10.1221 - 5.84397i) q^{74} +(-6.73463 + 11.6647i) q^{76} +(7.75746 - 13.4363i) q^{77} +(-24.6869 - 42.7589i) q^{79} +(-21.0930 - 94.6062i) q^{80} +51.7254i q^{82} +(-14.3418 - 24.8408i) q^{83} +(111.173 + 34.9059i) q^{85} +(134.427 + 77.6114i) q^{86} +(-24.7859 + 14.3102i) q^{88} -65.9204i q^{89} -40.8171 q^{91} +(-18.1451 - 31.4283i) q^{92} +(52.8120 - 91.4730i) q^{94} +(-52.8268 - 16.5865i) q^{95} +(-62.1331 + 35.8725i) q^{97} +84.7830 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) $ 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.14196	−	1.97794i	−0.570981	−	0.988968i	−0.996466	−	0.0840022i	$-0.973230\pi$
$2$	−1.14196	−	1.97794i	−0.570981	−	0.988968i	0.425485	−	0.904966i	$-0.360104\pi$
$3$		0			0
$3$		0			0
$4$	−0.608153	+	1.05335i	−0.152038	+	0.263338i
$5$	−4.77039	−	1.49780i	−0.954077	−	0.299560i
$5$	−4.77039	−	1.49780i	−0.954077	−	0.299560i
$6$		0			0
$7$	2.98475	−	1.72325i	0.426393	−	0.246178i	−0.271416	−	0.962462i	$-0.587492\pi$
$7$	2.98475	−	1.72325i	0.426393	−	0.246178i	0.697809	+	0.716284i	$0.254158\pi$
$8$	−6.35774			−0.794718
$9$		0			0
$10$	2.48505	+	11.1459i	0.248505	+	1.11459i
$11$	3.89854	−	2.25082i	0.354413	−	0.204620i	−0.312214	−	0.950012i	$-0.601071\pi$
$11$	3.89854	−	2.25082i	0.354413	−	0.204620i	0.666627	+	0.745391i	$0.267737\pi$
$12$		0			0
$13$	−10.2564	−	5.92153i	−0.788954	−	0.455503i	0.0506403	−	0.998717i	$-0.483874\pi$
$13$	−10.2564	−	5.92153i	−0.788954	−	0.455503i	−0.839594	+	0.543214i	$0.817207\pi$
$14$	−6.81695	−	3.93577i	−0.486925	−	0.281126i
$15$		0			0
$16$	9.69291	+	16.7886i	0.605807	+	1.04929i
$17$	−23.3048			−1.37087			−0.685436	−	0.728133i	$-0.740388\pi$
$17$	−23.3048			−1.37087			−0.685436	+	0.728133i	$0.740388\pi$
$18$		0			0
$19$	11.0739			0.582837			0.291419	−	0.956596i	$-0.405873\pi$
$19$	11.0739			0.582837			0.291419	+	0.956596i	$0.405873\pi$
$20$	4.47884	−	4.11401i	0.223942	−	0.205700i
$21$		0			0
$22$	−8.90397	−	5.14071i	−0.404726	−	0.233669i
$23$	−14.9182	+	25.8391i	−0.648619	+	1.12344i	0.334834	+	0.942277i	$0.391320\pi$
$23$	−14.9182	+	25.8391i	−0.648619	+	1.12344i	−0.983453	+	0.181164i	$0.942014\pi$
$24$		0			0
$25$	20.5132	+	14.2902i	0.820528	+	0.571607i
$26$			27.0487i			1.04033i
$27$		0			0
$28$			4.19199i			0.149714i
$29$	30.8581	−	17.8160i	1.06407	−	0.614343i	0.137518	−	0.990499i	$-0.456088\pi$
$29$	30.8581	−	17.8160i	1.06407	−	0.614343i	0.926556	+	0.376156i	$0.122754\pi$
$30$		0			0
$31$	−15.1515	+	26.2432i	−0.488759	+	0.846556i	−0.999916	−	0.0129312i	$-0.995884\pi$
$31$	−15.1515	+	26.2432i	−0.488759	+	0.846556i	0.511157	+	0.859487i	$0.329217\pi$
$32$	9.42238	−	16.3200i	0.294449	−	0.510001i
$33$		0			0
$34$	26.6132	+	46.0954i	0.782741	+	1.35575i
$35$	−16.8195	+	3.75000i	−0.480557	+	0.107143i
$36$		0			0
$37$			5.11748i			0.138310i	0.997606	+	0.0691552i	$0.0220304\pi$
$37$			5.11748i			0.138310i	−0.997606	+	0.0691552i	$0.977970\pi$
$38$	−12.6460	−	21.9035i	−0.332789	−	0.576407i
$39$		0			0
$40$	30.3289	+	9.52263i	0.758223	+	0.238066i
$41$	−19.6134	−	11.3238i	−0.478376	−	0.276190i	0.241364	−	0.970435i	$-0.422405\pi$
$41$	−19.6134	−	11.3238i	−0.478376	−	0.276190i	−0.719739	+	0.694244i	$0.755739\pi$
$42$		0			0
$43$	−58.8579	+	33.9816i	−1.36879	+	0.790270i	−0.990773	−	0.135529i	$-0.956727\pi$
$43$	−58.8579	+	33.9816i	−1.36879	+	0.790270i	−0.378015	+	0.925799i	$0.623393\pi$
$44$			5.47538i			0.124441i
$45$		0			0
$46$	68.1442			1.48140
$47$	23.1234	+	40.0508i	0.491986	+	0.852145i	0.999957	−	0.00922888i	$-0.00293769\pi$
$47$	23.1234	+	40.0508i	0.491986	+	0.852145i	−0.507971	+	0.861374i	$0.669604\pi$
$48$		0			0
$49$	−18.5608	+	32.1483i	−0.378792	+	0.656088i
$50$	4.83975	−	56.8926i	0.0967950	−	1.13785i
$51$		0			0
$52$	12.4749	−	7.20240i	0.239902	−	0.138508i
$53$	68.0017			1.28305			0.641525	−	0.767102i	$-0.278302\pi$
$53$	68.0017			1.28305			0.641525	+	0.767102i	$0.278302\pi$
$54$		0			0
$55$	−21.9688	+	4.89807i	−0.399434	+	0.0890558i
$56$	−18.9763	+	10.9560i	−0.338862	+	0.195642i
$57$		0			0
$58$	−70.4776	−	40.6903i	−1.21513	−	0.701557i
$59$	−29.9499	−	17.2916i	−0.507626	−	0.293078i	0.224231	−	0.974536i	$-0.428013\pi$
$59$	−29.9499	−	17.2916i	−0.507626	−	0.293078i	−0.731857	+	0.681458i	$0.761346\pi$
$60$		0			0
$61$	−8.68165	−	15.0371i	−0.142322	−	0.246509i	0.786049	−	0.618165i	$-0.212124\pi$
$61$	−8.68165	−	15.0371i	−0.142322	−	0.246509i	−0.928371	+	0.371656i	$0.878790\pi$
$62$	69.2099			1.11629
$63$		0			0
$64$	34.5033			0.539114
$65$	40.0577	+	43.6100i	0.616273	+	0.670924i
$66$		0			0
$67$	85.1195	+	49.1438i	1.27044	+	0.733489i	0.975071	−	0.221894i	$-0.0712240\pi$
$67$	85.1195	+	49.1438i	1.27044	+	0.733489i	0.295369	+	0.955383i	$0.404557\pi$
$68$	14.1729	−	24.5482i	0.208425	−	0.361002i
$69$		0			0
$70$	26.6245	+	28.9856i	0.380350	+	0.414079i
$71$			134.669i			1.89674i	0.317164	+	0.948371i	$0.397269\pi$
$71$			134.669i			1.89674i	−0.317164	+	0.948371i	$0.602731\pi$
$72$		0			0
$73$		−	134.962i		−	1.84879i	−0.381436	−	0.924395i	$-0.624570\pi$
$73$		−	134.962i		−	1.84879i	0.381436	−	0.924395i	$-0.375430\pi$
$74$	10.1221	−	5.84397i	0.136784	−	0.0789726i
$75$		0			0
$76$	−6.73463	+	11.6647i	−0.0886135	+	0.153483i
$77$	7.75746	−	13.4363i	0.100746	−	0.174498i
$78$		0			0
$79$	−24.6869	−	42.7589i	−0.312492	−	0.541252i	0.666409	−	0.745586i	$-0.267831\pi$
$79$	−24.6869	−	42.7589i	−0.312492	−	0.541252i	−0.978901	+	0.204334i	$0.934497\pi$
$80$	−21.0930	−	94.6062i	−0.263662	−	1.18258i
$81$		0			0
$82$			51.7254i			0.630798i
$83$	−14.3418	−	24.8408i	−0.172793	−	0.299286i	0.766602	−	0.642122i	$-0.221946\pi$
$83$	−14.3418	−	24.8408i	−0.172793	−	0.299286i	−0.939395	+	0.342836i	$0.888613\pi$
$84$		0			0
$85$	111.173	+	34.9059i	1.30792	+	0.410658i
$86$	134.427	+	77.6114i	1.56310	+	0.902459i
$87$		0			0
$88$	−24.7859	+	14.3102i	−0.281658	+	0.162616i
$89$		−	65.9204i		−	0.740679i	−0.928897	−	0.370339i	$-0.879241\pi$
$89$		−	65.9204i		−	0.740679i	0.928897	−	0.370339i	$-0.120759\pi$
$90$		0			0
$91$	−40.8171			−0.448540
$92$	−18.1451	−	31.4283i	−0.197230	−	0.341612i
$93$		0			0
$94$	52.8120	−	91.4730i	0.561829	−	0.973117i
$95$	−52.8268	−	16.5865i	−0.556072	−	0.174595i
$96$		0			0
$97$	−62.1331	+	35.8725i	−0.640547	+	0.369820i	−0.784825	−	0.619717i	$-0.787247\pi$
$97$	−62.1331	+	35.8725i	−0.640547	+	0.369820i	0.144278	+	0.989537i	$0.453914\pi$
$98$	84.7830			0.865133
$99$		0			0
$100$	−27.5277	+	12.9170i	−0.275277	+	0.129170i
$101$	−43.7945	+	25.2848i	−0.433609	+	0.250344i	−0.700883	−	0.713276i	$-0.747211\pi$
$101$	−43.7945	+	25.2848i	−0.433609	+	0.250344i	0.267274	+	0.963621i	$0.413877\pi$
$102$		0			0
$103$	−167.504	−	96.7084i	−1.62625	−	0.938917i	−0.985198	−	0.171421i	$-0.945164\pi$
$103$	−167.504	−	96.7084i	−1.62625	−	0.938917i	−0.641054	−	0.767496i	$-0.721502\pi$
$104$	65.2076	+	37.6476i	0.626996	+	0.361996i
$105$		0			0
$106$	−77.6553	−	134.503i	−0.732597	−	1.26890i
$107$	−129.069			−1.20626			−0.603128	−	0.797644i	$-0.706079\pi$
$107$	−129.069			−1.20626			−0.603128	+	0.797644i	$0.706079\pi$
$108$		0			0
$109$	−189.029			−1.73421			−0.867107	−	0.498122i	$-0.834023\pi$
$109$	−189.029			−1.73421			−0.867107	+	0.498122i	$0.834023\pi$
$110$	34.7756	+	37.8596i	0.316142	+	0.344178i
$111$		0			0
$112$	57.8619	+	33.4066i	0.516624	+	0.298273i
$113$	−70.1155	+	121.444i	−0.620491	+	1.07472i	0.368903	+	0.929468i	$0.379734\pi$
$113$	−70.1155	+	121.444i	−0.620491	+	1.07472i	−0.989394	+	0.145255i	$0.953600\pi$
$114$		0			0
$115$	109.868	−	100.918i	0.955371	−	0.877550i
$116$			43.3393i			0.373615i
$117$		0			0
$118$			78.9854i			0.669368i
$119$	−69.5591	+	40.1600i	−0.584530	+	0.337479i
$120$		0			0
$121$	−50.3676	+	87.2392i	−0.416261	+	0.720985i
$122$	−19.8282	+	34.3435i	−0.162526	+	0.281504i
$123$		0			0
$124$	−18.4289	−	31.9198i	−0.148620	−	0.257418i
$125$	−76.4521	−	98.8943i	−0.611617	−	0.791154i
$126$		0			0
$127$		−	12.6839i		−	0.0998729i	−0.998752	−	0.0499364i	$-0.984098\pi$
$127$		−	12.6839i		−	0.0998729i	0.998752	−	0.0499364i	$-0.0159019\pi$
$128$	−77.0910	−	133.525i	−0.602273	−	1.04317i
$129$		0			0
$130$	40.5135	−	129.033i	0.311642	−	0.992559i
$131$	99.0310	+	57.1756i	0.755962	+	0.436455i	0.827844	−	0.560958i	$-0.189567\pi$
$131$	99.0310	+	57.1756i	0.755962	+	0.436455i	−0.0718823	+	0.997413i	$0.522901\pi$
$132$		0			0
$133$	33.0529	−	19.0831i	0.248518	−	0.143482i
$134$		−	224.481i		−	1.67523i
$135$		0			0
$136$	148.166			1.08946
$137$	−9.61235	−	16.6491i	−0.0701631	−	0.121526i	0.828810	−	0.559531i	$-0.189019\pi$
$137$	−9.61235	−	16.6491i	−0.0701631	−	0.121526i	−0.898973	+	0.438005i	$0.855685\pi$
$138$		0			0
$139$	28.0615	−	48.6040i	0.201881	−	0.349669i	−0.747253	−	0.664539i	$-0.768628\pi$
$139$	28.0615	−	48.6040i	0.201881	−	0.349669i	0.949135	+	0.314871i	$0.101961\pi$
$140$	6.27877	−	19.9974i	0.0448483	−	0.142839i
$141$		0			0
$142$	266.366	−	153.786i	1.87582	−	1.08300i
$143$	−53.3134			−0.372821
$144$		0			0
$145$	−173.890	+	38.7697i	−1.19924	+	0.267377i
$146$	−266.946	+	154.121i	−1.82839	+	1.05562i
$147$		0			0
$148$	−5.39051	−	3.11221i	−0.0364224	−	0.0210285i
$149$	−153.921	−	88.8666i	−1.03303	−	0.596420i	−0.115179	−	0.993345i	$-0.536744\pi$
$149$	−153.921	−	88.8666i	−1.03303	−	0.596420i	−0.917851	+	0.396925i	$0.870077\pi$
$150$		0			0
$151$	−141.104	−	244.400i	−0.934465	−	1.61854i	−0.775586	−	0.631242i	$-0.782545\pi$
$151$	−141.104	−	244.400i	−0.934465	−	1.61854i	−0.158879	−	0.987298i	$-0.550788\pi$
$152$	−70.4050			−0.463191
$153$		0			0
$154$	−35.4349			−0.230097
$155$	111.586	−	102.496i	0.719909	−	0.661268i
$156$		0			0
$157$	−161.719	−	93.3683i	−1.03005	−	0.594702i	−0.113055	−	0.993589i	$-0.536063\pi$
$157$	−161.719	−	93.3683i	−1.03005	−	0.594702i	−0.917000	+	0.398886i	$0.869397\pi$
$158$	−56.3830	+	97.6582i	−0.356854	+	0.618090i
$159$		0			0
$160$	−69.3926	+	63.7401i	−0.433704	+	0.398376i
$161$			102.831i			0.638704i
$162$		0			0
$163$			33.6033i			0.206155i	0.994673	+	0.103078i	$0.0328690\pi$
$163$			33.6033i			0.206155i	−0.994673	+	0.103078i	$0.967131\pi$
$164$	23.8559	−	13.7732i	0.145463	−	0.0839830i
$165$		0			0
$166$	−32.7556	+	56.7344i	−0.197323	+	0.341774i
$167$	25.0253	−	43.3450i	0.149852	−	0.259551i	−0.781321	−	0.624130i	$-0.785454\pi$
$167$	25.0253	−	43.3450i	0.149852	−	0.259551i	0.931173	+	0.364579i	$0.118787\pi$
$168$		0			0
$169$	−14.3708	−	24.8910i	−0.0850346	−	0.147284i
$170$	−57.9136	−	259.754i	−0.340668	−	1.52797i
$171$		0			0
$172$		−	82.6641i		−	0.480605i
$173$	−37.7803	−	65.4373i	−0.218383	−	0.378251i	0.735931	−	0.677057i	$-0.236745\pi$
$173$	−37.7803	−	65.4373i	−0.218383	−	0.378251i	−0.954314	+	0.298806i	$0.903412\pi$
$174$		0			0
$175$	85.8523	+	7.30330i	0.490585	+	0.0417332i
$176$	75.5765	+	43.6341i	0.429412	+	0.247921i
$177$		0			0
$178$	−130.386	+	75.2786i	−0.732507	+	0.422913i
$179$			116.454i			0.650583i	0.945614	+	0.325291i	$0.105462\pi$
$179$			116.454i			0.650583i	−0.945614	+	0.325291i	$0.894538\pi$
$180$		0			0
$181$	−45.4016			−0.250838			−0.125419	−	0.992104i	$-0.540027\pi$
$181$	−45.4016			−0.250838			−0.125419	+	0.992104i	$0.540027\pi$
$182$	46.6116	+	80.7336i	0.256107	+	0.443591i
$183$		0			0
$184$	94.8463	−	164.279i	0.515469	−	0.892819i
$185$	7.66496	−	24.4124i	0.0414322	−	0.131959i
$186$		0			0
$187$	−90.8548	+	52.4550i	−0.485855	+	0.280508i
$188$	−56.2502			−0.299203
$189$		0			0
$190$	27.5192	+	123.429i	0.144838	+	0.649627i
$191$	129.563	−	74.8030i	0.678338	−	0.391639i	−0.120890	−	0.992666i	$-0.538575\pi$
$191$	129.563	−	74.8030i	0.678338	−	0.391639i	0.799229	+	0.601027i	$0.205242\pi$
$192$		0			0
$193$	122.804	+	70.9011i	0.636292	+	0.367363i	0.783185	−	0.621789i	$-0.213594\pi$
$193$	122.804	+	70.9011i	0.636292	+	0.367363i	−0.146893	+	0.989152i	$0.546927\pi$
$194$	141.907	+	81.9301i	0.731480	+	0.422320i
$195$		0			0
$196$	−22.5757	−	39.1022i	−0.115182	−	0.199501i
$197$	121.128			0.614864			0.307432	−	0.951570i	$-0.400530\pi$
$197$	121.128			0.614864			0.307432	+	0.951570i	$0.400530\pi$
$198$		0			0
$199$	−25.7205			−0.129249			−0.0646243	−	0.997910i	$-0.520585\pi$
$199$	−25.7205			−0.129249			−0.0646243	+	0.997910i	$0.520585\pi$
$200$	−130.418	−	90.8532i	−0.652088	−	0.454266i
$201$		0			0
$202$	100.023	+	57.7485i	0.495165	+	0.285884i
$203$	61.4026	−	106.352i	0.302476	−	0.523904i
$204$		0			0
$205$	76.6027	+	83.3959i	0.373672	+	0.406809i
$206$			441.749i			2.14441i
$207$		0			0
$208$		−	229.588i		−	1.10379i
$209$	43.1721	−	24.9254i	0.206565	−	0.119260i
$210$		0			0
$211$	−38.4483	+	66.5944i	−0.182219	+	0.315613i	−0.942636	−	0.333822i	$-0.891661\pi$
$211$	−38.4483	+	66.5944i	−0.182219	+	0.315613i	0.760417	+	0.649436i	$0.224995\pi$
$212$	−41.3554	+	71.6297i	−0.195073	+	0.337876i
$213$		0			0
$214$	147.392	+	255.291i	0.688749	+	1.19295i
$215$	331.673	−	73.9482i	1.54266	−	0.343945i
$216$		0			0
$217$			104.439i			0.481288i
$218$	215.864	+	373.888i	0.990203	+	1.71508i
$219$		0			0
$220$	8.20103	−	26.1197i	0.0372774	−	0.118726i
$221$	239.023	+	138.000i	1.08155	+	0.624435i
$222$		0			0
$223$	168.362	−	97.2036i	0.754984	−	0.435890i	−0.0725076	−	0.997368i	$-0.523100\pi$
$223$	168.362	−	97.2036i	0.754984	−	0.435890i	0.827492	+	0.561477i	$0.189767\pi$
$224$		−	64.9484i		−	0.289948i
$225$		0			0
$226$	320.277			1.41715
$227$	76.1824	+	131.952i	0.335605	+	0.581285i	0.983601	−	0.180359i	$-0.0577259\pi$
$227$	76.1824	+	131.952i	0.335605	+	0.581285i	−0.647996	+	0.761644i	$0.724393\pi$
$228$		0			0
$229$	−133.207	+	230.722i	−0.581691	+	1.00752i	0.413588	+	0.910464i	$0.364276\pi$
$229$	−133.207	+	230.722i	−0.581691	+	1.00752i	−0.995279	+	0.0970548i	$0.969058\pi$
$230$	−325.074	−	102.066i	−1.41337	−	0.443767i
$231$		0			0
$232$	−196.188	+	113.269i	−0.845639	+	0.488230i
$233$	107.497			0.461361			0.230681	−	0.973029i	$-0.425905\pi$
$233$	107.497			0.461361			0.230681	+	0.973029i	$0.425905\pi$
$234$		0			0
$235$	−50.3193	−	225.692i	−0.214124	−	0.960392i
$236$	36.4283	−	21.0319i	0.154357	−	0.0891181i
$237$		0			0
$238$	158.868	+	91.7223i	0.667511	+	0.385388i
$239$	−269.946	−	155.853i	−1.12948	−	0.652106i	−0.185677	−	0.982611i	$-0.559448\pi$
$239$	−269.946	−	155.853i	−1.12948	−	0.652106i	−0.943804	+	0.330504i	$0.892781\pi$
$240$		0			0
$241$	80.1604	+	138.842i	0.332616	+	0.576108i	0.983024	−	0.183477i	$-0.0587354\pi$
$241$	80.1604	+	138.842i	0.332616	+	0.576108i	−0.650408	+	0.759585i	$0.725402\pi$
$242$	230.071			0.950708
$243$		0			0
$244$	21.1191			0.0865537
$245$	136.694	−	125.559i	0.557935	−	0.512488i
$246$		0			0
$247$	−113.578	−	65.5745i	−0.459831	−	0.265484i
$248$	96.3296	−	166.848i	0.388426	−	0.672773i
$249$		0			0
$250$	−108.301	+	264.151i	−0.433205	+	1.05660i
$251$			357.272i			1.42339i	0.702487	+	0.711697i	$0.252073\pi$
$251$			357.272i			1.42339i	−0.702487	+	0.711697i	$0.747927\pi$
$252$		0			0
$253$			134.313i			0.530883i
$254$	−25.0879	+	14.4845i	−0.0987711	+	0.0570255i
$255$		0			0
$256$	−107.063	+	185.439i	−0.418216	+	0.724371i
$257$	227.924	−	394.776i	0.886865	−	1.53609i	0.0433031	−	0.999062i	$-0.486212\pi$
$257$	227.924	−	394.776i	0.886865	−	1.53609i	0.843562	−	0.537033i	$-0.180455\pi$
$258$		0			0
$259$	8.81869	+	15.2744i	0.0340490	+	0.0589746i
$260$	−70.2980	+	15.6733i	−0.270377	+	0.0602819i
$261$		0			0
$262$		−	261.169i		−	0.996829i
$263$	30.4177	+	52.6851i	0.115657	+	0.200323i	0.918042	−	0.396483i	$-0.129769\pi$
$263$	30.4177	+	52.6851i	0.115657	+	0.200323i	−0.802385	+	0.596806i	$0.796436\pi$
$264$		0			0
$265$	−324.394	−	101.853i	−1.22413	−	0.384350i
$266$	−75.4902	−	43.5843i	−0.283798	−	0.163851i
$267$		0			0
$268$	−103.531	+	59.7738i	−0.386311	+	0.223037i
$269$		−	213.484i		−	0.793620i	−0.917901	−	0.396810i	$-0.870117\pi$
$269$		−	213.484i		−	0.793620i	0.917901	−	0.396810i	$-0.129883\pi$
$270$		0			0
$271$	259.475			0.957474			0.478737	−	0.877958i	$-0.341095\pi$
$271$	259.475			0.957474			0.478737	+	0.877958i	$0.341095\pi$
$272$	−225.891	−	391.255i	−0.830483	−	1.43844i
$273$		0			0
$274$	−21.9539	+	38.0252i	−0.0801236	+	0.138778i
$275$	112.136	+	9.53923i	0.407768	+	0.0346881i
$276$		0			0
$277$	−220.134	+	127.095i	−0.794709	+	0.458825i	−0.841618	−	0.540074i	$-0.818396\pi$
$277$	−220.134	+	127.095i	−0.794709	+	0.458825i	0.0469089	+	0.998899i	$0.485063\pi$
$278$	−128.181			−0.461081
$279$		0			0
$280$	106.934	−	23.8415i	0.381908	−	0.0851483i
$281$	−216.919	+	125.238i	−0.771953	+	0.445687i	−0.833571	−	0.552413i	$-0.813707\pi$
$281$	−216.919	+	125.238i	−0.771953	+	0.445687i	0.0616182	+	0.998100i	$0.480374\pi$
$282$		0			0
$283$	299.891	+	173.142i	1.05969	+	0.611810i	0.925345	−	0.379126i	$-0.123775\pi$
$283$	299.891	+	173.142i	1.05969	+	0.611810i	0.134340	+	0.990935i	$0.457108\pi$
$284$	−141.853	−	81.8991i	−0.499484	−	0.288377i
$285$		0			0
$286$	60.8818	+	105.450i	0.212873	+	0.368708i
$287$	−78.0549			−0.271968
$288$		0			0
$289$	254.114			0.879287
$290$	275.260	+	299.670i	0.949172	+	1.03334i
$291$		0			0
$292$	142.162	+	82.0774i	0.486857	+	0.281087i
$293$	156.518	−	271.098i	0.534192	−	0.925248i	−0.465010	−	0.885305i	$-0.653949\pi$
$293$	156.518	−	271.098i	0.534192	−	0.925248i	0.999202	−	0.0399422i	$-0.0127174\pi$
$294$		0			0
$295$	116.973	+	127.347i	0.396520	+	0.431683i
$296$		−	32.5356i		−	0.109918i
$297$		0			0
$298$			405.929i			1.36218i
$299$	306.015	−	176.678i	1.02346	−	0.590895i
$300$		0			0
$301$	−117.118	+	202.854i	−0.389095	+	0.673932i
$302$	−322.271	+	558.190i	−1.06712	+	1.84831i
$303$		0			0
$304$	107.338	+	185.916i	0.353087	+	0.611564i
$305$	18.8923	+	84.7360i	0.0619421	+	0.277823i
$306$		0			0
$307$			267.727i			0.872074i	0.899929	+	0.436037i	$0.143618\pi$
$307$			267.727i			0.872074i	−0.899929	+	0.436037i	$0.856382\pi$
$308$	9.43545	+	16.3427i	0.0306346	+	0.0530606i
$309$		0			0
$310$	−330.158	−	103.663i	−1.06503	−	0.334395i
$311$	−305.814	−	176.562i	−0.983325	−	0.567723i	−0.0800530	−	0.996791i	$-0.525509\pi$
$311$	−305.814	−	176.562i	−0.983325	−	0.567723i	−0.903272	+	0.429067i	$0.858842\pi$
$312$		0			0
$313$	330.055	−	190.557i	1.05449	−	0.608809i	0.130586	−	0.991437i	$-0.458314\pi$
$313$	330.055	−	190.557i	1.05449	−	0.608809i	0.923903	+	0.382628i	$0.124981\pi$
$314$			426.492i			1.35825i
$315$		0			0
$316$	60.0536			0.190043
$317$	−0.541332	−	0.937615i	−0.00170767	−	0.00295778i	0.865170	−	0.501478i	$-0.167210\pi$
$317$	−0.541332	−	0.937615i	−0.00170767	−	0.00295778i	−0.866878	+	0.498520i	$0.833877\pi$
$318$		0			0
$319$	80.2012	−	138.913i	0.251414	−	0.435463i
$320$	−164.594	−	51.6790i	−0.514357	−	0.161497i
$321$		0			0
$322$	203.394	−	117.429i	0.631657	−	0.364688i
$323$	−258.075			−0.798994
$324$		0			0
$325$	−125.772	−	268.035i	−0.386990	−	0.824724i
$326$	66.4652	−	38.3737i	0.203881	−	0.117711i
$327$		0			0
$328$	124.697	+	71.9938i	0.380174	+	0.219493i
$329$	138.035	+	79.6946i	0.419559	+	0.242233i
$330$		0			0
$331$	67.4397	+	116.809i	0.203745	+	0.352898i	0.949732	−	0.313063i	$-0.101355\pi$
$331$	67.4397	+	116.809i	0.203745	+	0.352898i	−0.745987	+	0.665961i	$0.768022\pi$
$332$	34.8881			0.105085
$333$		0			0
$334$	−114.312			−0.342250
$335$	−332.445	−	361.927i	−0.992374	−	1.08038i
$336$		0			0
$337$	−297.583	−	171.810i	−0.883036	−	0.509821i	−0.0113779	−	0.999935i	$-0.503622\pi$
$337$	−297.583	−	171.810i	−0.883036	−	0.509821i	−0.871658	+	0.490114i	$0.836955\pi$
$338$	−32.8219	+	56.8492i	−0.0971063	+	0.168193i
$339$		0			0
$340$	−104.378	+	95.8761i	−0.306995	+	0.281989i
$341$			136.414i			0.400041i
$342$		0			0
$343$			296.818i			0.865359i
$344$	374.204	−	216.046i	1.08780	−	0.628042i
$345$		0			0
$346$	−86.2872	+	149.454i	−0.249385	+	0.431948i
$347$	−99.7471	+	172.767i	−0.287456	+	0.497888i	−0.973202	−	0.229953i	$-0.926143\pi$
$347$	−99.7471	+	172.767i	−0.287456	+	0.497888i	0.685746	+	0.727841i	$0.259476\pi$
$348$		0			0
$349$	103.789	+	179.767i	0.297389	+	0.515093i	0.975538	−	0.219832i	$-0.0705508\pi$
$349$	103.789	+	179.767i	0.297389	+	0.515093i	−0.678149	+	0.734925i	$0.737218\pi$
$350$	−83.5946	−	178.150i	−0.238842	−	0.509001i
$351$		0			0
$352$		−	84.8325i		−	0.241001i
$353$	39.9141	+	69.1332i	0.113071	+	0.195845i	0.917007	−	0.398871i	$-0.130598\pi$
$353$	39.9141	+	69.1332i	0.113071	+	0.195845i	−0.803936	+	0.594716i	$0.797265\pi$
$354$		0			0
$355$	201.707	−	642.422i	0.568188	−	1.80964i
$356$	69.4374	+	40.0897i	0.195049	+	0.112611i
$357$		0			0
$358$	230.339	−	132.986i	0.643405	−	0.371470i
$359$		−	234.273i		−	0.652571i	−0.945271	−	0.326285i	$-0.894203\pi$
$359$		−	234.273i		−	0.652571i	0.945271	−	0.326285i	$-0.105797\pi$
$360$		0			0
$361$	−238.369			−0.660301
$362$	51.8469	+	89.8014i	0.143223	+	0.248070i
$363$		0			0
$364$	24.8230	−	42.9948i	0.0681952	−	0.118118i
$365$	−202.146	+	643.820i	−0.553823	+	1.76389i
$366$		0			0
$367$	−189.916	+	109.648i	−0.517481	+	0.298768i	−0.735904	−	0.677086i	$-0.763242\pi$
$367$	−189.916	+	109.648i	−0.517481	+	0.298768i	0.218422	+	0.975854i	$0.429909\pi$
$368$	−578.405			−1.57175
$369$		0			0
$370$	−57.0392	+	12.7172i	−0.154160	+	0.0343708i
$371$	202.968	−	117.184i	0.547084	−	0.315859i
$372$		0			0
$373$	139.806	+	80.7171i	0.374815	+	0.216400i	0.675560	−	0.737305i	$-0.263902\pi$
$373$	139.806	+	80.7171i	0.374815	+	0.216400i	−0.300745	+	0.953705i	$0.597235\pi$
$374$	207.505	+	119.803i	0.554827	+	0.320330i
$375$		0			0
$376$	−147.012	−	254.633i	−0.390990	−	0.677215i
$377$	−421.991			−1.11934
$378$		0			0
$379$	227.627			0.600598			0.300299	−	0.953845i	$-0.402914\pi$
$379$	227.627			0.600598			0.300299	+	0.953845i	$0.402914\pi$
$380$	49.5982	−	45.5581i	0.130522	−	0.119890i
$381$		0			0
$382$	−295.911	−	170.844i	−0.774636	−	0.447237i
$383$	90.0556	−	155.981i	0.235132	−	0.407261i	−0.724179	−	0.689612i	$-0.757781\pi$
$383$	90.0556	−	155.981i	0.235132	−	0.407261i	0.959311	+	0.282351i	$0.0911144\pi$
$384$		0			0
$385$	−57.1310	+	52.4773i	−0.148392	+	0.136305i
$386$		−	323.866i		−	0.839030i
$387$		0			0
$388$		−	87.2640i		−	0.224907i
$389$	−630.749	+	364.163i	−1.62146	+	0.936153i	−0.634935	+	0.772566i	$0.718973\pi$
$389$	−630.749	+	364.163i	−1.62146	+	0.936153i	−0.986529	+	0.163587i	$0.947694\pi$
$390$		0			0
$391$	347.667	−	602.176i	0.889173	−	1.54009i
$392$	118.005	−	204.391i	0.301033	−	0.521405i
$393$		0			0
$394$	−138.324	−	239.584i	−0.351076	−	0.608081i
$395$	53.7217	+	240.953i	0.136004	+	0.610007i
$396$		0			0
$397$			417.565i			1.05180i	0.850546	+	0.525901i	$0.176272\pi$
$397$			417.565i			1.05180i	−0.850546	+	0.525901i	$0.823728\pi$
$398$	29.3718	+	50.8734i	0.0737984	+	0.127823i
$399$		0			0
$400$	−41.0796	+	482.901i	−0.102699	+	1.20725i
$401$	399.514	+	230.659i	0.996294	+	0.575211i	0.907150	−	0.420808i	$-0.138253\pi$
$401$	399.514	+	230.659i	0.996294	+	0.575211i	0.0891442	+	0.996019i	$0.471587\pi$
$402$		0			0
$403$	310.801	−	179.441i	0.771217	−	0.445263i
$404$		−	61.5081i		−	0.152248i
$405$		0			0
$406$	−280.478			−0.690832
$407$	11.5186	+	19.9507i	0.0283011	+	0.0490190i
$408$		0			0
$409$	−266.014	+	460.749i	−0.650400	+	1.12653i	0.332626	+	0.943059i	$0.392065\pi$
$409$	−266.014	+	460.749i	−0.650400	+	1.12653i	−0.983026	+	0.183467i	$0.941268\pi$
$410$	77.4743	−	246.750i	0.188962	−	0.601830i
$411$		0			0
$412$	203.736	−	117.627i	0.494505	−	0.285503i
$413$	−119.191			−0.288598
$414$		0			0
$415$	31.2096	+	139.981i	0.0752038	+	0.337304i
$416$	−193.279	+	111.590i	−0.464614	+	0.268245i
$417$		0			0
$418$	−98.6017	−	56.9277i	−0.235889	−	0.136191i
$419$	−406.390	−	234.629i	−0.969903	−	0.559974i	−0.0706967	−	0.997498i	$-0.522522\pi$
$419$	−406.390	−	234.629i	−0.969903	−	0.559974i	−0.899207	+	0.437524i	$0.855856\pi$
$420$		0			0
$421$	110.269	+	190.992i	0.261922	+	0.453662i	0.966753	−	0.255713i	$-0.0823103\pi$
$421$	110.269	+	190.992i	0.261922	+	0.453662i	−0.704831	+	0.709376i	$0.748977\pi$
$422$	175.626			0.416175
$423$		0			0
$424$	−432.337			−1.01966
$425$	−478.056	−	333.030i	−1.12484	−	0.783599i
$426$		0			0
$427$	−51.8252	−	29.9213i	−0.121370	−	0.0700733i
$428$	78.4940	−	135.956i	0.183397	−	0.317653i
$429$		0			0
$430$	−525.022	−	571.581i	−1.22098	−	1.32926i
$431$		−	487.110i		−	1.13018i	−0.825028	−	0.565092i	$-0.808840\pi$
$431$		−	487.110i		−	1.13018i	0.825028	−	0.565092i	$-0.191160\pi$
$432$		0			0
$433$		−	462.822i		−	1.06887i	−0.845208	−	0.534437i	$-0.820524\pi$
$433$		−	462.822i		−	1.06887i	0.845208	−	0.534437i	$-0.179476\pi$
$434$	206.575	−	119.266i	0.475978	−	0.274806i
$435$		0			0
$436$	114.959	−	199.114i	0.263667	−	0.456685i
$437$	−165.203	+	286.140i	−0.378039	+	0.654783i
$438$		0			0
$439$	−400.695	−	694.024i	−0.912744	−	1.58092i	−0.810171	−	0.586194i	$-0.800626\pi$
$439$	−400.695	−	694.024i	−0.912744	−	1.58092i	−0.102573	−	0.994725i	$-0.532708\pi$
$440$	139.672	−	31.1407i	0.317437	−	0.0707743i
$441$		0			0
$442$		−	630.364i		−	1.42616i
$443$	−37.1602	−	64.3634i	−0.0838832	−	0.145290i	0.821032	−	0.570883i	$-0.193399\pi$
$443$	−37.1602	−	64.3634i	−0.0838832	−	0.145290i	−0.904915	+	0.425593i	$0.860066\pi$
$444$		0			0
$445$	−98.7355	+	314.466i	−0.221878	+	0.706665i
$446$	−384.525	−	222.006i	−0.862163	−	0.497770i
$447$		0			0
$448$	102.984	−	59.4578i	0.229875	−	0.132718i
$449$		−	358.472i		−	0.798379i	−0.916868	−	0.399190i	$-0.869291\pi$
$449$		−	358.472i		−	0.798379i	0.916868	−	0.399190i	$-0.130709\pi$
$450$		0			0
$451$	−101.952			−0.226057
$452$	−85.2819	−	147.713i	−0.188677	−	0.326798i
$453$		0			0
$454$	173.995	−	301.368i	0.383248	−	0.663805i
$455$	194.713	+	61.1358i	0.427941	+	0.134364i
$456$		0			0
$457$	−100.270	+	57.8908i	−0.219409	+	0.126676i	−0.605676	−	0.795711i	$-0.707097\pi$
$457$	−100.270	+	57.8908i	−0.219409	+	0.126676i	0.386268	+	0.922387i	$0.373764\pi$
$458$	608.471			1.32854
$459$		0			0
$460$	39.4861	+	177.103i	0.0858393	+	0.385007i
$461$	−172.918	+	99.8343i	−0.375093	+	0.216560i	−0.675681	−	0.737194i	$-0.736150\pi$
$461$	−172.918	+	99.8343i	−0.375093	+	0.216560i	0.300588	+	0.953754i	$0.402817\pi$
$462$		0			0
$463$	517.092	+	298.543i	1.11683	+	0.644802i	0.940590	−	0.339546i	$-0.110273\pi$
$463$	517.092	+	298.543i	1.11683	+	0.644802i	0.176240	+	0.984347i	$0.443607\pi$
$464$	598.211	+	345.377i	1.28925	+	0.744347i
$465$		0			0
$466$	−122.758	−	212.623i	−0.263429	−	0.456272i
$467$	605.150			1.29582			0.647912	−	0.761715i	$-0.275643\pi$
$467$	605.150			1.29582			0.647912	+	0.761715i	$0.275643\pi$
$468$		0			0
$469$	338.748			0.722276
$470$	−388.942	+	357.260i	−0.827536	+	0.760128i
$471$		0			0
$472$	190.414	+	109.936i	0.403419	+	0.232914i
$473$	−152.973	+	264.958i	−0.323411	+	0.560164i
$474$		0			0
$475$	227.161	+	158.248i	0.478234	+	0.333154i
$476$		−	97.6936i		−	0.205239i
$477$		0			0
$478$			711.915i			1.48936i
$479$	−468.023	+	270.213i	−0.977083	+	0.564119i	−0.901388	−	0.433012i	$-0.857451\pi$
$479$	−468.023	+	270.213i	−0.977083	+	0.564119i	−0.0756945	+	0.997131i	$0.524117\pi$
$480$		0			0
$481$	30.3034	−	52.4869i	0.0630007	−	0.109120i
$482$	183.080	−	317.104i	0.379835	−	0.657893i
$483$		0			0
$484$	−61.2624	−	106.110i	−0.126575	−	0.219235i
$485$	350.129	−	78.0630i	0.721915	−	0.160955i
$486$		0			0
$487$		−	565.424i		−	1.16104i	−0.814248	−	0.580518i	$-0.802850\pi$
$487$		−	565.424i		−	1.16104i	0.814248	−	0.580518i	$-0.197150\pi$
$488$	55.1957	+	95.6018i	0.113106	+	0.195905i
$489$		0			0
$490$	−404.448	−	126.988i	−0.825404	−	0.259159i
$491$	231.247	+	133.510i	0.470971	+	0.271915i	0.716646	−	0.697437i	$-0.245676\pi$
$491$	231.247	+	133.510i	0.470971	+	0.271915i	−0.245675	+	0.969352i	$0.579010\pi$
$492$		0			0
$493$	−719.143	+	415.197i	−1.45871	+	0.842186i
$494$			299.534i			0.606345i
$495$		0			0
$496$	−587.450			−1.18438
$497$	232.067	+	401.953i	0.466937	+	0.808758i
$498$		0			0
$499$	310.161	−	537.214i	0.621564	−	1.07658i	−0.367630	−	0.929972i	$-0.619831\pi$
$499$	310.161	−	537.214i	0.621564	−	1.07658i	0.989195	−	0.146609i	$-0.0468358\pi$
$500$	150.665	−	20.3881i	0.301330	−	0.0407762i
$501$		0			0
$502$	706.660	−	407.991i	1.40769	−	0.812730i
$503$	433.671			0.862168			0.431084	−	0.902312i	$-0.358131\pi$
$503$	433.671			0.862168			0.431084	+	0.902312i	$0.358131\pi$
$504$		0			0
$505$	246.788	−	55.0228i	0.488690	−	0.108956i
$506$	265.663	−	153.381i	0.525026	−	0.303124i
$507$		0			0
$508$	13.3606	+	7.71373i	0.0263003	+	0.0151845i
$509$	225.376	+	130.121i	0.442781	+	0.255640i	0.704777	−	0.709429i	$-0.251047\pi$
$509$	225.376	+	130.121i	0.442781	+	0.255640i	−0.261995	+	0.965069i	$0.584381\pi$
$510$		0			0
$511$	−232.573	−	402.827i	−0.455132	−	0.788312i
$512$	−127.679			−0.249373
$513$		0			0
$514$	−1041.12			−2.02553
$515$	654.209	+	712.224i	1.27031	+	1.38296i
$516$		0			0
$517$	180.295	+	104.093i	0.348733	+	0.201341i
$518$	20.1412	−	34.8856i	0.0388827	−	0.0673467i
$519$		0			0
$520$	−254.677	−	277.261i	−0.489763	−	0.533195i
$521$		−	658.284i		−	1.26350i	−0.775172	−	0.631750i	$-0.782337\pi$
$521$		−	658.284i		−	1.26350i	0.775172	−	0.631750i	$-0.217663\pi$
$522$		0			0
$523$		−	401.215i		−	0.767142i	−0.923511	−	0.383571i	$-0.874694\pi$
$523$		−	401.215i		−	0.767142i	0.923511	−	0.383571i	$-0.125306\pi$
$524$	−120.452	+	69.5430i	−0.229870	+	0.132716i
$525$		0			0
$526$	69.4718	−	120.329i	0.132076	−	0.228762i
$527$	353.104	−	611.594i	0.670026	−	1.16052i
$528$		0			0
$529$	−180.608	−	312.822i	−0.341413	−	0.591345i
$530$	168.987	+	757.943i	0.318844	+	1.43008i
$531$		0			0
$532$			46.4217i			0.0872589i
$533$	134.109	+	232.283i	0.251611	+	0.435803i
$534$		0			0
$535$	615.711	+	193.320i	1.15086	+	0.361346i
$536$	−541.168	−	312.443i	−1.00964	−	0.582917i
$537$		0			0
$538$	−422.257	+	243.790i	−0.784864	+	0.453142i
$539$			167.109i			0.310035i
$540$		0			0
$541$	131.652			0.243350			0.121675	−	0.992570i	$-0.461173\pi$
$541$	131.652			0.243350			0.121675	+	0.992570i	$0.461173\pi$
$542$	−296.311	−	513.226i	−0.546699	−	0.946911i
$543$		0			0
$544$	−219.587	+	380.335i	−0.403652	+	0.699146i
$545$	901.743	+	283.128i	1.65457	+	0.519501i
$546$		0			0
$547$	−857.154	+	494.878i	−1.56701	+	0.904713i	−0.570494	+	0.821301i	$0.693248\pi$
$547$	−857.154	+	494.878i	−1.56701	+	0.904713i	−0.996515	+	0.0834119i	$0.973418\pi$
$548$	23.3831			0.0426699
$549$		0			0
$550$	−109.187	−	232.692i	−0.198522	−	0.423076i
$551$	341.720	−	197.292i	0.620182	−	0.358062i
$552$		0			0
$553$	−147.369	−	85.0833i	−0.266489	−	0.153858i
$554$	502.770	+	290.274i	0.907527	+	0.523961i
$555$		0			0
$556$	34.1314	+	59.1173i	0.0613874	+	0.106326i
$557$	−299.018			−0.536836			−0.268418	−	0.963302i	$-0.586501\pi$
$557$	−299.018			−0.536836			−0.268418	+	0.963302i	$0.586501\pi$
$558$		0			0
$559$	804.894			1.43988
$560$	−225.987	−	246.028i	−0.403549	−	0.439336i
$561$		0			0
$562$	495.426	+	286.034i	0.881540	+	0.508957i
$563$	−379.185	+	656.768i	−0.673508	+	1.16655i	0.303394	+	0.952865i	$0.401880\pi$
$563$	−379.185	+	656.768i	−0.673508	+	1.16655i	−0.976903	+	0.213685i	$0.931453\pi$
$564$		0			0
$565$	516.377	−	474.314i	0.913941	−	0.839494i
$566$		−	790.887i		−	1.39733i
$567$		0			0
$568$		−	856.189i		−	1.50737i
$569$	−503.382	+	290.628i	−0.884679	+	0.510770i	−0.872198	−	0.489152i	$-0.837306\pi$
$569$	−503.382	+	290.628i	−0.884679	+	0.510770i	−0.0124807	+	0.999922i	$0.503973\pi$
$570$		0			0
$571$	335.239	−	580.651i	0.587109	−	1.01690i	−0.407500	−	0.913205i	$-0.633599\pi$
$571$	335.239	−	580.651i	0.587109	−	1.01690i	0.994609	−	0.103697i	$-0.0330673\pi$
$572$	32.4227	−	56.1577i	0.0566830	−	0.0981778i
$573$		0			0
$574$	89.1357	+	154.388i	0.155289	+	0.268968i
$575$	−675.266	+	316.859i	−1.17438	+	0.551060i
$576$		0			0
$577$			135.394i			0.234652i	0.993093	+	0.117326i	$0.0374322\pi$
$577$			135.394i			0.234652i	−0.993093	+	0.117326i	$0.962568\pi$
$578$	−290.189	−	502.621i	−0.502056	−	0.869587i
$579$		0			0
$580$	64.9136	−	206.745i	0.111920	−	0.356457i
$581$	−85.6137	−	49.4291i	−0.147356	−	0.0850758i
$582$		0			0
$583$	265.107	−	153.060i	0.454730	−	0.262538i
$584$			858.052i			1.46927i
$585$		0			0
$586$	−714.951			−1.22005
$587$	179.702	+	311.253i	0.306136	+	0.530243i	0.977514	−	0.210872i	$-0.0676304\pi$
$587$	179.702	+	311.253i	0.306136	+	0.530243i	−0.671377	+	0.741116i	$0.734297\pi$
$588$		0			0
$589$	−167.787	+	290.615i	−0.284867	+	0.493404i
$590$	118.304	−	376.791i	0.200516	−	0.638628i
$591$		0			0
$592$	−85.9154	+	49.6033i	−0.145127	+	0.0837894i
$593$	540.430			0.911349			0.455675	−	0.890146i	$-0.349398\pi$
$593$	540.430			0.911349			0.455675	+	0.890146i	$0.349398\pi$
$594$		0			0
$595$	391.975	−	87.3930i	0.658782	−	0.146879i
$596$	187.216	−	108.089i	0.314120	−	0.181357i
$597$		0			0
$598$	−698.914	−	403.518i	−1.16875	−	0.674780i
$599$	−499.301	−	288.271i	−0.833557	−	0.481254i	0.0215119	−	0.999769i	$-0.493152\pi$
$599$	−499.301	−	288.271i	−0.833557	−	0.481254i	−0.855069	+	0.518514i	$0.826485\pi$
$600$		0			0
$601$	513.210	+	888.906i	0.853927	+	1.47905i	0.877637	+	0.479326i	$0.159119\pi$
$601$	513.210	+	888.906i	0.853927	+	1.47905i	−0.0237095	+	0.999719i	$0.507548\pi$
$602$	534.975			0.888663
$603$		0			0
$604$	343.252			0.568298
$605$	370.940	−	340.724i	0.613123	−	0.563181i
$606$		0			0
$607$	−143.178	−	82.6636i	−0.235877	−	0.136184i	0.377403	−	0.926049i	$-0.376817\pi$
$607$	−143.178	−	82.6636i	−0.235877	−	0.136184i	−0.613280	+	0.789865i	$0.710150\pi$
$608$	104.343	−	180.727i	0.171616	−	0.297248i
$609$		0			0
$610$	146.028	−	134.133i	0.239390	−	0.219890i
$611$		−	547.703i		−	0.896404i
$612$		0			0
$613$			251.007i			0.409473i	0.978817	+	0.204737i	$0.0656338\pi$
$613$			251.007i			0.409473i	−0.978817	+	0.204737i	$0.934366\pi$
$614$	529.546	−	305.734i	0.862453	−	0.497938i
$615$		0			0
$616$	−49.3199	+	85.4246i	−0.0800648	+	0.138676i
$617$	−458.546	+	794.224i	−0.743186	+	1.28724i	0.207852	+	0.978160i	$0.433353\pi$
$617$	−458.546	+	794.224i	−0.743186	+	1.28724i	−0.951038	+	0.309075i	$0.899981\pi$
$618$		0			0
$619$	138.795	+	240.399i	0.224224	+	0.388367i	0.956086	−	0.293085i	$-0.0946820\pi$
$619$	138.795	+	240.399i	0.224224	+	0.388367i	−0.731862	+	0.681452i	$0.761349\pi$
$620$	40.1036	+	179.873i	0.0646832	+	0.290117i
$621$		0			0
$622$			806.508i			1.29664i
$623$	−113.597	−	196.756i	−0.182339	−	0.315820i
$624$		0			0
$625$	216.582	+	586.274i	0.346532	+	0.938038i
$626$	−753.820	−	435.218i	−1.20419	−	0.695237i
$627$		0			0
$628$	196.699	−	113.564i	0.313216	−	0.180835i
$629$		−	119.262i		−	0.189606i
$630$		0			0
$631$	322.116			0.510485			0.255243	−	0.966877i	$-0.417845\pi$
$631$	322.116			0.510485			0.255243	+	0.966877i	$0.417845\pi$
$632$	156.953	+	271.850i	0.248343	+	0.430143i
$633$		0			0
$634$	−1.23636	+	2.14144i	−0.00195010	+	0.00337767i
$635$	−18.9979	+	60.5069i	−0.0299179	+	0.0952865i
$636$		0			0
$637$	380.735	−	219.817i	0.597700	−	0.345082i
$638$	−366.347			−0.574211
$639$		0			0
$640$	167.759	+	752.435i	0.262124	+	1.17568i
$641$	−239.860	+	138.483i	−0.374196	+	0.216042i	−0.675290	−	0.737552i	$-0.735982\pi$
$641$	−239.860	+	138.483i	−0.374196	+	0.216042i	0.301094	+	0.953594i	$0.402648\pi$
$642$		0			0
$643$	−743.356	−	429.177i	−1.15607	−	0.667460i	−0.205714	−	0.978612i	$-0.565952\pi$
$643$	−743.356	−	429.177i	−1.15607	−	0.667460i	−0.950360	+	0.311152i	$0.899285\pi$
$644$	−108.318	−	62.5372i	−0.168195	−	0.0971074i
$645$		0			0
$646$	294.712	+	510.456i	0.456210	+	0.790180i
$647$	−1065.93			−1.64749			−0.823746	−	0.566960i	$-0.808120\pi$
$647$	−1065.93			−1.64749			−0.823746	+	0.566960i	$0.808120\pi$
$648$		0			0
$649$	−155.681			−0.239879
$650$	−386.530	+	554.854i	−0.594661	+	0.853622i
$651$		0			0
$652$	−35.3961	−	20.4360i	−0.0542886	−	0.0313435i
$653$	−178.126	+	308.523i	−0.272781	+	0.472470i	−0.969573	−	0.244803i	$-0.921277\pi$
$653$	−178.126	+	308.523i	−0.272781	+	0.472470i	0.696792	+	0.717273i	$0.254610\pi$
$654$		0			0
$655$	−386.779	−	421.078i	−0.590502	−	0.642867i
$656$		−	439.043i		−	0.669272i
$657$		0			0
$658$		−	364.033i		−	0.553241i
$659$	−33.6473	+	19.4263i	−0.0510581	+	0.0294784i	−0.525312	−	0.850910i	$-0.676051\pi$
$659$	−33.6473	+	19.4263i	−0.0510581	+	0.0294784i	0.474254	+	0.880388i	$0.342718\pi$
$660$		0			0
$661$	−100.918	+	174.795i	−0.152674	+	0.264440i	−0.932210	−	0.361918i	$-0.882122\pi$
$661$	−100.918	+	174.795i	−0.152674	+	0.264440i	0.779535	+	0.626358i	$0.215455\pi$
$662$	154.027	−	266.783i	0.232670	−	0.402995i
$663$		0			0
$664$	91.1817	+	157.931i	0.137322	+	0.237848i
$665$	−186.258	+	41.5271i	−0.280087	+	0.0624468i
$666$		0			0
$667$			1063.13i			1.59390i
$668$	30.4384	+	52.7208i	0.0455665	+	0.0789234i
$669$		0			0
$670$	−336.228	+	1070.86i	−0.501832	+	1.59830i
$671$	−67.6916	−	39.0818i	−0.100882	−	0.0582441i
$672$		0			0
$673$	−389.128	+	224.663i	−0.578200	+	0.333824i	−0.760418	−	0.649434i	$-0.775006\pi$
$673$	−389.128	+	224.663i	−0.578200	+	0.333824i	0.182218	+	0.983258i	$0.441672\pi$
$674$			784.801i			1.16439i
$675$		0			0
$676$	34.9587			0.0517141
$677$	−351.405	−	608.651i	−0.519062	−	0.899042i	−0.999755	−	0.0221524i	$-0.992948\pi$
$677$	−351.405	−	608.651i	−0.519062	−	0.899042i	0.480693	−	0.876889i	$-0.340385\pi$
$678$		0			0
$679$	−123.635	+	214.141i	−0.182083	+	0.315378i
$680$	−706.809	−	221.923i	−1.03943	−	0.326357i
$681$		0			0
$682$	269.818	−	155.779i	0.395627	−	0.228416i
$683$	−705.068			−1.03231			−0.516155	−	0.856495i	$-0.672637\pi$
$683$	−705.068			−1.03231			−0.516155	+	0.856495i	$0.672637\pi$
$684$		0			0
$685$	20.9177	+	93.8199i	0.0305367	+	0.136963i
$686$	587.087	−	338.955i	0.855812	−	0.494103i
$687$		0			0
$688$	−1141.01	−	658.762i	−1.65844	−	0.957503i
$689$	−697.452	−	402.674i	−1.01227	−	0.584433i
$690$		0			0
$691$	442.125	+	765.783i	0.639833	+	1.10822i	0.985469	+	0.169855i	$0.0543300\pi$
$691$	442.125	+	765.783i	0.639833	+	1.10822i	−0.345636	+	0.938369i	$0.612337\pi$
$692$	91.9047			0.132810
$693$		0			0
$694$	455.630			0.656527
$695$	−206.663	+	189.829i	−0.297357	+	0.273136i
$696$		0			0
$697$	457.087	+	263.899i	0.655791	+	0.378621i
$698$	237.046	−	410.575i	0.339607	−	0.588216i
$699$		0			0
$700$	−59.9043	+	85.9912i	−0.0855776	+	0.122845i
$701$		−	267.537i		−	0.381651i	−0.981624	−	0.190826i	$-0.938884\pi$
$701$		−	267.537i		−	0.381651i	0.981624	−	0.190826i	$-0.0611165\pi$
$702$		0			0
$703$			56.6705i			0.0806124i
$704$	134.513	−	77.6609i	0.191069	−	0.110314i
$705$		0			0
$706$	91.1607	−	157.895i	0.129123	−	0.223647i
$707$	−87.1439	+	150.938i	−0.123259	+	0.213490i
$708$		0			0
$709$	266.623	+	461.805i	0.376056	+	0.651348i	0.990484	−	0.137625i	$-0.0439468\pi$
$709$	266.623	+	461.805i	0.376056	+	0.651348i	−0.614429	+	0.788972i	$0.710613\pi$
$710$	−1501.01	+	334.658i	−2.11410	+	0.471349i
$711$		0			0
$712$			419.105i			0.588631i
$713$	−452.069	−	783.006i	−0.634037	−	1.09818i
$714$		0			0
$715$	254.325	+	79.8527i	0.355700	+	0.111682i
$716$	−122.667	−	70.8220i	−0.171323	−	0.0989134i
$717$		0			0
$718$	−463.377	+	267.531i	−0.645372	+	0.372606i
$719$		−	101.956i		−	0.141803i	−0.997483	−	0.0709015i	$-0.977412\pi$
$719$		−	101.956i		−	0.141803i	0.997483	−	0.0709015i	$-0.0225876\pi$
$720$		0			0
$721$	−666.611			−0.924564
$722$	272.208	+	471.478i	0.377019	+	0.653016i
$723$		0			0
$724$	27.6111	−	47.8239i	0.0381369	−	0.0660551i
$725$	887.592	+	75.5059i	1.22426	+	0.104146i
$726$		0			0
$727$	636.475	−	367.469i	0.875482	−	0.505460i	0.00631598	−	0.999980i	$-0.497990\pi$
$727$	636.475	−	367.469i	0.875482	−	0.505460i	0.869166	+	0.494520i	$0.164656\pi$
$728$	259.505			0.356462
$729$		0			0
$730$	1504.28	−	335.386i	2.06065	−	0.459433i
$731$	1371.67	−	791.935i	1.87643	−	1.08336i
$732$		0			0
$733$	−1146.80	−	662.106i	−1.56453	−	0.903282i	−0.996789	−	0.0800754i	$-0.974484\pi$
$733$	−1146.80	−	662.106i	−1.56453	−	0.903282i	−0.567742	−	0.823207i	$-0.692183\pi$
$734$	433.753	+	250.427i	0.590944	+	0.341182i
$735$		0			0
$736$	281.131	+	486.933i	0.381971	+	0.661593i
$737$	442.456			0.600347
$738$		0			0
$739$	978.711			1.32437			0.662186	−	0.749340i	$-0.269629\pi$
$739$	978.711			1.32437			0.662186	+	0.749340i	$0.269629\pi$
$740$	21.0534	+	22.9204i	0.0284505	+	0.0309735i
$741$		0			0
$742$	−463.564	−	267.639i	−0.624749	−	0.360699i
$743$	−464.088	+	803.824i	−0.624614	+	1.08186i	0.364002	+	0.931398i	$0.381410\pi$
$743$	−464.088	+	803.824i	−0.624614	+	1.08186i	−0.988615	+	0.150464i	$0.951923\pi$
$744$		0			0
$745$	601.161	+	654.472i	0.806927	+	0.878486i
$746$		−	368.704i		−	0.494241i
$747$		0			0
$748$		−	127.603i		−	0.170592i
$749$	−385.240	+	222.419i	−0.514340	+	0.296954i
$750$		0			0
$751$	268.998	−	465.919i	0.358187	−	0.620398i	−0.629471	−	0.777024i	$-0.716728\pi$
$751$	268.998	−	465.919i	0.358187	−	0.620398i	0.987658	+	0.156626i	$0.0500618\pi$
$752$	−448.265	+	776.418i	−0.596097	+	1.03247i
$753$		0			0
$754$	481.898	+	834.672i	0.639122	+	1.10699i
$755$	307.060	+	1377.23i	0.406702	+	1.82414i
$756$		0			0
$757$		−	981.098i		−	1.29603i	−0.761626	−	0.648017i	$-0.775599\pi$
$757$		−	981.098i		−	1.29603i	0.761626	−	0.648017i	$-0.224401\pi$
$758$	−259.941	−	450.231i	−0.342930	−	0.593972i
$759$		0			0
$760$	335.859	+	105.453i	0.441920	+	0.138753i
$761$	−495.891	−	286.303i	−0.651630	−	0.376219i	0.137450	−	0.990509i	$-0.456109\pi$
$761$	−495.891	−	286.303i	−0.651630	−	0.376219i	−0.789080	+	0.614290i	$0.789443\pi$
$762$		0			0
$763$	−564.206	+	325.745i	−0.739457	+	0.426926i
$764$			181.967i			0.238176i
$765$		0			0
$766$	−411.360			−0.537024
$767$	204.786	+	354.699i	0.266996	+	0.462450i
$768$		0			0
$769$	−466.186	+	807.457i	−0.606223	+	1.05001i	0.385634	+	0.922652i	$0.373983\pi$
$769$	−466.186	+	807.457i	−0.606223	+	1.05001i	−0.991857	+	0.127358i	$0.959350\pi$
$770$	169.038	+	53.0744i	0.219530	+	0.0689277i
$771$		0			0
$772$	−149.368	+	86.2375i	−0.193482	+	0.111707i
$773$	280.315			0.362632			0.181316	−	0.983425i	$-0.441964\pi$
$773$	280.315			0.362632			0.181316	+	0.983425i	$0.441964\pi$
$774$		0			0
$775$	−685.827	+	321.815i	−0.884938	+	0.415245i
$776$	395.026	−	228.068i	0.509054	−	0.293903i
$777$		0			0
$778$	1440.58	+	831.721i	1.85165	+	1.06905i
$779$	−217.197	−	125.399i	−0.278815	−	0.160974i
$780$		0			0
$781$	303.116	+	525.011i	0.388112	+	0.672230i
$782$	−1588.09			−2.03080
$783$		0			0
$784$	−719.634			−0.917901
$785$	631.613	+	687.625i	0.804603	+	0.875955i
$786$		0			0
$787$	612.463	+	353.606i	0.778225	+	0.449308i	0.835801	−	0.549033i	$-0.185004\pi$
$787$	612.463	+	353.606i	0.778225	+	0.449308i	−0.0575759	+	0.998341i	$0.518337\pi$
$788$	−73.6645	+	127.591i	−0.0934829	+	0.161917i
$789$		0			0
$790$	415.241	−	381.417i	0.525621	−	0.482806i
$791$			483.306i			0.611006i
$792$		0			0
$793$			205.635i			0.259313i
$794$	825.918	−	476.844i	1.04020	−	0.600559i
$795$		0			0
$796$	15.6420	−	27.0927i	0.0196507	−	0.0340361i
$797$	673.041	−	1165.74i	0.844468	−	1.46266i	−0.0416138	−	0.999134i	$-0.513250\pi$
$797$	673.041	−	1165.74i	0.844468	−	1.46266i	0.886082	−	0.463528i	$-0.153417\pi$
$798$		0			0
$799$	−538.885	−	933.377i	−0.674450	−	1.16818i
$800$	426.499	−	200.129i	0.533124	−	0.250161i
$801$		0			0
$802$		−	1053.62i		−	1.31374i
$803$	−303.775	−	526.154i	−0.378300	−	0.655235i
$804$		0			0
$805$	154.021	−	490.545i	0.191330	−	0.609373i
$806$	−709.845	−	409.829i	−0.880701	−	0.508473i
$807$		0			0
$808$	278.434	−	160.754i	0.344597	−	0.198953i
$809$			63.7611i			0.0788147i	0.999223	+	0.0394073i	$0.0125470\pi$
$809$			63.7611i			0.0788147i	−0.999223	+	0.0394073i	$0.987453\pi$
$810$		0			0
$811$	869.786			1.07249			0.536243	−	0.844064i	$-0.319843\pi$
$811$	869.786			1.07249			0.536243	+	0.844064i	$0.319843\pi$
$812$	74.6844	+	129.357i	0.0919759	+	0.159307i
$813$		0			0
$814$	26.3075	−	45.5659i	0.0323188	−	0.0559778i
$815$	50.3311	−	160.301i	0.0617559	−	0.196688i
$816$		0			0
$817$	−651.787	+	376.309i	−0.797781	+	0.460599i
$818$	1215.11			1.48546
$819$		0			0
$820$	−134.431	+	29.9722i	−0.163941	+	0.0365515i
$821$	−500.175	+	288.776i	−0.609227	+	0.351737i	−0.772663	−	0.634817i	$-0.781076\pi$
$821$	−500.175	+	288.776i	−0.609227	+	0.351737i	0.163436	+	0.986554i	$0.447742\pi$
$822$		0			0
$823$	−301.155	−	173.872i	−0.365923	−	0.211266i	0.305753	−	0.952111i	$-0.401092\pi$
$823$	−301.155	−	173.872i	−0.365923	−	0.211266i	−0.671676	+	0.740845i	$0.734425\pi$
$824$	1064.95	+	614.847i	1.29241	+	0.746174i
$825$		0			0
$826$	136.111	+	235.752i	0.164784	+	0.285414i
$827$	19.0847			0.0230770			0.0115385	−	0.999933i	$-0.496327\pi$
$827$	19.0847			0.0230770			0.0115385	+	0.999933i	$0.496327\pi$
$828$		0			0
$829$	−39.6514			−0.0478303			−0.0239152	−	0.999714i	$-0.507613\pi$
$829$	−39.6514			−0.0478303			−0.0239152	+	0.999714i	$0.507613\pi$
$830$	241.234	−	221.584i	0.290643	−	0.266968i
$831$		0			0
$832$	−353.880	−	204.313i	−0.425336	−	0.245568i
$833$	432.557	−	749.210i	0.519276	−	0.899412i
$834$		0			0
$835$	−184.302	+	169.290i	−0.220721	+	0.202742i
$836$			60.6339i			0.0725286i
$837$		0			0
$838$			1071.75i			1.27894i
$839$	−326.716	+	188.630i	−0.389411	+	0.224827i	−0.681905	−	0.731441i	$-0.738848\pi$
$839$	−326.716	+	188.630i	−0.389411	+	0.224827i	0.292494	+	0.956267i	$0.405515\pi$
$840$		0			0
$841$	214.317	−	371.207i	0.254835	−	0.441388i
$842$	251.846	−	436.211i	0.299105	−	0.518065i
$843$		0			0
$844$	−46.7649	−	80.9991i	−0.0554086	−	0.0959705i
$845$	31.2727	+	140.265i	0.0370091	+	0.165994i
$846$		0			0
$847$			347.183i			0.409898i
$848$	659.134	+	1141.65i	0.777281	+	1.34629i
$849$		0			0
$850$	−112.789	+	1325.87i	−0.132694	+	1.55985i
$851$	−132.231	−	76.3438i	−0.155384	−	0.0897107i
$852$		0			0
$853$	−142.059	+	82.0178i	−0.166540	+	0.0961521i	−0.580954	−	0.813937i	$-0.697320\pi$
$853$	−142.059	+	82.0178i	−0.166540	+	0.0961521i	0.414413	+	0.910089i	$0.363987\pi$
$854$			136.676i			0.160042i
$855$		0			0
$856$	820.590			0.958634
$857$	157.693	+	273.132i	0.184006	+	0.318707i	0.943241	−	0.332109i	$-0.107760\pi$
$857$	157.693	+	273.132i	0.184006	+	0.318707i	−0.759235	+	0.650816i	$0.774427\pi$
$858$		0			0
$859$	46.8200	−	81.0946i	0.0545052	−	0.0944058i	−0.837485	−	0.546460i	$-0.815975\pi$
$859$	46.8200	−	81.0946i	0.0545052	−	0.0944058i	0.891991	+	0.452054i	$0.149309\pi$
$860$	−123.814	+	394.340i	−0.143970	+	0.458535i
$861$		0			0
$862$	−963.472	+	556.261i	−1.11772	+	0.645314i
$863$	1055.96			1.22360			0.611799	−	0.791013i	$-0.290446\pi$
$863$	1055.96			1.22360			0.611799	+	0.791013i	$0.290446\pi$
$864$		0			0
$865$	82.2145	+	368.749i	0.0950457	+	0.426299i
$866$	−915.433	+	528.525i	−1.05708	+	0.610306i
$867$		0			0
$868$	−110.012	−	63.5152i	−0.126741	−	0.0731742i
$869$	−192.486	−	111.132i	−0.221503	−	0.127885i
$870$		0			0
$871$	−582.013	−	1008.08i	−0.668212	−	1.15738i
$872$	1201.80			1.37821
$873$		0			0
$874$	754.623			0.863413
$875$	−398.610	−	163.429i	−0.455554	−	0.186776i
$876$		0			0
$877$	182.957	+	105.630i	0.208617	+	0.120445i	0.600668	−	0.799498i	$-0.294901\pi$
$877$	182.957	+	105.630i	0.208617	+	0.120445i	−0.392052	+	0.919943i	$0.628235\pi$
$878$	−915.156	+	1585.10i	−1.04232	+	1.80535i
$879$		0			0
$880$	−295.174	−	321.350i	−0.335425	−	0.365170i
$881$		−	824.884i		−	0.936304i	−0.883648	−	0.468152i	$-0.844920\pi$
$881$		−	824.884i		−	0.936304i	0.883648	−	0.468152i	$-0.155080\pi$
$882$		0			0
$883$		−	1155.63i		−	1.30875i	−0.756171	−	0.654375i	$-0.772932\pi$
$883$		−	1155.63i		−	1.30875i	0.756171	−	0.654375i	$-0.227068\pi$
$884$	−290.726	+	167.851i	−0.328875	+	0.189876i
$885$		0			0
$886$	−84.8711	+	147.001i	−0.0957914	+	0.165916i
$887$	628.207	−	1088.09i	0.708238	−	1.22670i	−0.257272	−	0.966339i	$-0.582824\pi$
$887$	628.207	−	1088.09i	0.708238	−	1.22670i	0.965510	−	0.260366i	$-0.0838431\pi$
$888$		0			0
$889$	−21.8574	−	37.8582i	−0.0245865	−	0.0425851i
$890$	734.745	−	163.815i	0.825557	−	0.184062i
$891$		0			0
$892$			236.459i			0.265088i
$893$	256.066	+	443.519i	0.286748	+	0.496662i
$894$		0			0
$895$	174.425	−	555.532i	0.194888	−	0.620706i
$896$	−460.195	−	265.694i	−0.513611	−	0.296533i
$897$		0			0
$898$	−709.035	+	409.362i	−0.789572	+	0.455859i
$899$			1079.76i			1.20106i
$900$		0			0
$901$	−1584.77			−1.75890
$902$	116.425	+	201.654i	0.129074	+	0.223563i
$903$		0			0
$904$	445.777	−	772.108i	0.493116	−	0.854101i
$905$	216.583	+	68.0025i	0.239318	+	0.0751409i
$906$		0			0
$907$	999.793	−	577.230i	1.10231	−	0.636417i	0.165481	−	0.986213i	$-0.447082\pi$
$907$	999.793	−	577.230i	1.10231	−	0.636417i	0.936826	+	0.349796i	$0.113749\pi$
$908$	−185.322			−0.204099
$909$		0			0
$910$	−101.432	−	454.945i	−0.111464	−	0.499940i
$911$	−302.953	+	174.910i	−0.332550	+	0.191998i	−0.656973	−	0.753914i	$-0.728163\pi$
$911$	−302.953	+	174.910i	−0.332550	+	0.191998i	0.324423	+	0.945912i	$0.394830\pi$
$912$		0			0
$913$	−111.824	−	64.5619i	−0.122480	−	0.0707140i
$914$	229.009	+	132.218i	0.250556	+	0.144659i
$915$		0			0
$916$	−162.021	−	280.628i	−0.176879	−	0.306363i
$917$	394.111			0.429783
$918$		0			0
$919$	−375.011			−0.408064			−0.204032	−	0.978964i	$-0.565405\pi$
$919$	−375.011			−0.408064			−0.204032	+	0.978964i	$0.565405\pi$
$920$	−698.510	+	641.612i	−0.759250	+	0.697404i
$921$		0			0
$922$	394.932	+	228.014i	0.428342	+	0.247303i
$923$	797.445	−	1381.22i	0.863971	−	1.49644i
$924$		0			0
$925$	−73.1297	+	104.976i	−0.0790591	+	0.113487i
$926$		−	1363.70i		−	1.47268i
$927$		0			0
$928$		−	671.475i		−	0.723572i
$929$	920.884	−	531.672i	0.991263	−	0.572306i	0.0856117	−	0.996329i	$-0.472716\pi$
$929$	920.884	−	531.672i	0.991263	−	0.572306i	0.905652	+	0.424022i	$0.139382\pi$
$930$		0			0
$931$	−205.541	+	356.007i	−0.220774	+	0.382392i
$932$	−65.3748	+	113.232i	−0.0701446	+	0.121494i
$933$		0			0
$934$	−691.058	−	1196.95i	−0.739890	−	1.28153i
$935$	511.980	−	114.149i	0.547572	−	0.122084i
$936$		0			0
$937$		−	1021.59i		−	1.09028i	−0.838344	−	0.545141i	$-0.816476\pi$
$937$		−	1021.59i		−	1.09028i	0.838344	−	0.545141i	$-0.183524\pi$
$938$	−386.837	−	670.021i	−0.412406	−	0.714308i
$939$		0			0
$940$	268.335	+	84.2515i	0.285463	+	0.0896292i
$941$	378.485	+	218.519i	0.402216	+	0.232220i	0.687440	−	0.726241i	$-0.258735\pi$
$941$	378.485	+	218.519i	0.402216	+	0.232220i	−0.285224	+	0.958461i	$0.592068\pi$
$942$		0			0
$943$	585.195	−	337.862i	0.620567	−	0.358285i
$944$		−	670.424i		−	0.710195i
$945$		0			0
$946$	698.759			0.738646
$947$	−829.222	−	1436.26i	−0.875631	−	1.51664i	−0.856089	−	0.516828i	$-0.827113\pi$
$947$	−829.222	−	1436.26i	−0.875631	−	1.51664i	−0.0195416	−	0.999809i	$-0.506221\pi$
$948$		0			0
$949$	−799.180	+	1384.22i	−0.842129	+	1.45861i
$950$	53.5949	−	630.023i	0.0564157	−	0.663182i
$951$		0			0
$952$	442.239	−	255.327i	0.464537	−	0.268200i
$953$	−413.980			−0.434397			−0.217198	−	0.976127i	$-0.569692\pi$
$953$	−413.980			−0.434397			−0.217198	+	0.976127i	$0.569692\pi$
$954$		0			0
$955$	−730.104	+	162.781i	−0.764507	+	0.170451i
$956$	328.337	−	189.565i	0.343449	−	0.198290i
$957$		0			0
$958$	1068.93	+	617.146i	1.11579	+	0.644202i
$959$	−57.3810	−	33.1289i	−0.0598342	−	0.0345453i
$960$		0			0
$961$	21.3614	+	36.9991i	0.0222283	+	0.0385006i
$962$	−138.421			−0.143889
$963$		0			0
$964$	−194.999			−0.202281
$965$	−479.629	−	522.162i	−0.497025	−	0.541101i
$966$		0			0
$967$	−88.8900	−	51.3207i	−0.0919235	−	0.0530720i	0.453334	−	0.891341i	$-0.350235\pi$
$967$	−88.8900	−	51.3207i	−0.0919235	−	0.0530720i	−0.545257	+	0.838269i	$0.683568\pi$
$968$	320.224	−	554.644i	0.330810	−	0.572980i
$969$		0			0
$970$	−554.237	−	603.387i	−0.571379	−	0.622048i
$971$			997.502i			1.02729i	0.858002	+	0.513647i	$0.171706\pi$
$971$			997.502i			1.02729i	−0.858002	+	0.513647i	$0.828294\pi$
$972$		0			0
$973$		−	193.428i		−	0.198795i
$974$	−1118.37	+	645.693i	−1.14823	+	0.662929i
$975$		0			0
$976$	168.301	−	291.506i	0.172440	−	0.298674i
$977$	−630.932	+	1092.81i	−0.645785	+	1.11853i	0.338335	+	0.941026i	$0.390136\pi$
$977$	−630.932	+	1092.81i	−0.645785	+	1.11853i	−0.984120	+	0.177506i	$0.943197\pi$
$978$		0			0
$979$	−148.375	−	256.993i	−0.151558	−	0.262506i
$980$	49.1274	+	220.346i	0.0501300	+	0.224843i
$981$		0			0
$982$		−	609.855i		−	0.621033i
$983$	518.098	+	897.372i	0.527058	+	0.912891i	0.999503	+	0.0315308i	$0.0100382\pi$
$983$	518.098	+	897.372i	0.527058	+	0.912891i	−0.472445	+	0.881360i	$0.656628\pi$
$984$		0			0
$985$	−577.829	−	181.426i	−0.586628	−	0.184189i
$986$	1642.47	+	948.279i	1.66579	+	0.961744i
$987$		0			0
$988$	138.146	−	79.7587i	0.139824	−	0.0807274i
$989$		−	2027.78i		−	2.05034i
$990$		0			0
$991$	−1503.88			−1.51754			−0.758770	−	0.651358i	$-0.774200\pi$
$991$	−1503.88			−1.51754			−0.758770	+	0.651358i	$0.774200\pi$
$992$	285.527	+	494.548i	0.287830	+	0.498536i
$993$		0			0
$994$	530.024	−	918.029i	0.533224	−	0.923571i
$995$	122.697	+	38.5241i	0.123313	+	0.0387177i
$996$		0			0
$997$	289.976	−	167.418i	0.290849	−	0.167922i	−0.347476	−	0.937689i	$-0.612961\pi$
$997$	289.976	−	167.418i	0.290849	−	0.167922i	0.638325	+	0.769767i	$0.279628\pi$
$998$	−1416.77			−1.41961
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.k.134.5		48
3.2	odd	2	inner	405.3.h.k.134.20		48
5.4	even	2	inner	405.3.h.k.134.19		48
9.2	odd	6	inner	405.3.h.k.269.19		48
9.4	even	3		405.3.d.b.404.20	yes	24
9.5	odd	6		405.3.d.b.404.5	✓	24
9.7	even	3	inner	405.3.h.k.269.6		48
15.14	odd	2	inner	405.3.h.k.134.6		48
45.4	even	6		405.3.d.b.404.6	yes	24
45.14	odd	6		405.3.d.b.404.19	yes	24
45.29	odd	6	inner	405.3.h.k.269.5		48
45.34	even	6	inner	405.3.h.k.269.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.d.b.404.5	✓	24	9.5	odd	6
405.3.d.b.404.6	yes	24	45.4	even	6
405.3.d.b.404.19	yes	24	45.14	odd	6
405.3.d.b.404.20	yes	24	9.4	even	3
405.3.h.k.134.5		48	1.1	even	1	trivial
405.3.h.k.134.6		48	15.14	odd	2	inner
405.3.h.k.134.19		48	5.4	even	2	inner
405.3.h.k.134.20		48	3.2	odd	2	inner
405.3.h.k.269.5		48	45.29	odd	6	inner
405.3.h.k.269.6		48	9.7	even	3	inner
405.3.h.k.269.19		48	9.2	odd	6	inner
405.3.h.k.269.20		48	45.34	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.14196 - 1.97794i) q^{2} +(-0.608153 + 1.05335i) q^{4} +(-4.77039 - 1.49780i) q^{5} +(2.98475 - 1.72325i) q^{7} -6.35774 q^{8} +(2.48505 + 11.1459i) q^{10} +(3.89854 - 2.25082i) q^{11} +(-10.2564 - 5.92153i) q^{13} +(-6.81695 - 3.93577i) q^{14} +(9.69291 + 16.7886i) q^{16} -23.3048 q^{17} +11.0739 q^{19} +(4.47884 - 4.11401i) q^{20} +(-8.90397 - 5.14071i) q^{22} +(-14.9182 + 25.8391i) q^{23} +(20.5132 + 14.2902i) q^{25} +27.0487i q^{26} +4.19199i q^{28} +(30.8581 - 17.8160i) q^{29} +(-15.1515 + 26.2432i) q^{31} +(9.42238 - 16.3200i) q^{32} +(26.6132 + 46.0954i) q^{34} +(-16.8195 + 3.75000i) q^{35} +5.11748i q^{37} +(-12.6460 - 21.9035i) q^{38} +(30.3289 + 9.52263i) q^{40} +(-19.6134 - 11.3238i) q^{41} +(-58.8579 + 33.9816i) q^{43} +5.47538i q^{44} +68.1442 q^{46} +(23.1234 + 40.0508i) q^{47} +(-18.5608 + 32.1483i) q^{49} +(4.83975 - 56.8926i) q^{50} +(12.4749 - 7.20240i) q^{52} +68.0017 q^{53} +(-21.9688 + 4.89807i) q^{55} +(-18.9763 + 10.9560i) q^{56} +(-70.4776 - 40.6903i) q^{58} +(-29.9499 - 17.2916i) q^{59} +(-8.68165 - 15.0371i) q^{61} +69.2099 q^{62} +34.5033 q^{64} +(40.0577 + 43.6100i) q^{65} +(85.1195 + 49.1438i) q^{67} +(14.1729 - 24.5482i) q^{68} +(26.6245 + 28.9856i) q^{70} +134.669i q^{71} -134.962i q^{73} +(10.1221 - 5.84397i) q^{74} +(-6.73463 + 11.6647i) q^{76} +(7.75746 - 13.4363i) q^{77} +(-24.6869 - 42.7589i) q^{79} +(-21.0930 - 94.6062i) q^{80} +51.7254i q^{82} +(-14.3418 - 24.8408i) q^{83} +(111.173 + 34.9059i) q^{85} +(134.427 + 77.6114i) q^{86} +(-24.7859 + 14.3102i) q^{88} -65.9204i q^{89} -40.8171 q^{91} +(-18.1451 - 31.4283i) q^{92} +(52.8120 - 91.4730i) q^{94} +(-52.8268 - 16.5865i) q^{95} +(-62.1331 + 35.8725i) q^{97} +84.7830 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more