LMFDB - Embedded newform 684.3.bl.a.373.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(373,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("684.373");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.bl (of order $6$, degree $2$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.15
Character	$\chi$	$=$	684.373
Dual form			684.3.bl.a.673.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43106 + 2.63668i) q^{3} +5.52048 q^{5} +(0.838417 + 1.45218i) q^{7} +(-4.90416 - 7.54647i) q^{9} +O(q^{10})$	\(q+(-1.43106 + 2.63668i) q^{3} +5.52048 q^{5} +(0.838417 + 1.45218i) q^{7} +(-4.90416 - 7.54647i) q^{9} +(0.764365 + 1.32392i) q^{11} +(-17.9605 + 10.3695i) q^{13} +(-7.90012 + 14.5557i) q^{15} +(9.66839 + 16.7462i) q^{17} +(-16.1509 - 10.0074i) q^{19} +(-5.02876 + 0.132486i) q^{21} +(-7.35650 - 12.7418i) q^{23} +5.47574 q^{25} +(26.9158 - 2.13128i) q^{27} +40.8226i q^{29} +(23.1199 + 13.3483i) q^{31} +(-4.58460 + 0.120784i) q^{33} +(4.62847 + 8.01674i) q^{35} +59.7594i q^{37} +(-1.63857 - 62.1953i) q^{39} +36.9438i q^{41} +(2.38108 - 4.12414i) q^{43} +(-27.0733 - 41.6602i) q^{45} -54.0607 q^{47} +(23.0941 - 40.0002i) q^{49} +(-57.9902 + 1.52779i) q^{51} +(-17.5032 - 10.1055i) q^{53} +(4.21966 + 7.30867i) q^{55} +(49.4992 - 28.2635i) q^{57} -98.9167i q^{59} -87.2069 q^{61} +(6.84711 - 13.4488i) q^{63} +(-99.1504 + 57.2445i) q^{65} +(-74.7887 + 43.1793i) q^{67} +(44.1237 - 1.16247i) q^{69} +(-76.0630 + 43.9150i) q^{71} +(30.5689 + 52.9469i) q^{73} +(-7.83609 + 14.4378i) q^{75} +(-1.28171 + 2.21999i) q^{77} +(-31.1924 - 18.0089i) q^{79} +(-32.8984 + 74.0182i) q^{81} +(4.38181 + 7.58953i) q^{83} +(53.3742 + 92.4469i) q^{85} +(-107.636 - 58.4194i) q^{87} +(63.7489 + 36.8055i) q^{89} +(-30.1167 - 17.3879i) q^{91} +(-68.2810 + 41.8577i) q^{93} +(-89.1607 - 55.2459i) q^{95} +(-41.8517 - 24.1631i) q^{97} +(6.24234 - 12.2610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.43106	+	2.63668i	−0.477018	+	0.878893i
$3$	−1.43106	+	2.63668i	−0.477018	+	0.878893i
$4$		0			0
$5$	5.52048			1.10410			0.552048	−	0.833812i	$-0.313846\pi$
$5$	5.52048			1.10410			0.552048	+	0.833812i	$0.313846\pi$
$6$		0			0
$7$	0.838417	+	1.45218i	0.119774	+	0.207454i	0.919678	−	0.392673i	$-0.128450\pi$
$7$	0.838417	+	1.45218i	0.119774	+	0.207454i	−0.799904	+	0.600128i	$0.795116\pi$
$8$		0			0
$9$	−4.90416	−	7.54647i	−0.544907	−	0.838497i
$10$		0			0
$11$	0.764365	+	1.32392i	0.0694877	+	0.120356i	0.898676	−	0.438613i	$-0.144530\pi$
$11$	0.764365	+	1.32392i	0.0694877	+	0.120356i	−0.829188	+	0.558970i	$0.811197\pi$
$12$		0			0
$13$	−17.9605	+	10.3695i	−1.38157	+	0.797652i	−0.992346	−	0.123490i	$-0.960591\pi$
$13$	−17.9605	+	10.3695i	−1.38157	+	0.797652i	−0.389227	+	0.921142i	$0.627258\pi$
$14$		0			0
$15$	−7.90012	+	14.5557i	−0.526675	+	0.970383i
$16$		0			0
$17$	9.66839	+	16.7462i	0.568729	+	0.985068i	0.996692	+	0.0812714i	$0.0258980\pi$
$17$	9.66839	+	16.7462i	0.568729	+	0.985068i	−0.427963	+	0.903796i	$0.640769\pi$
$18$		0			0
$19$	−16.1509	−	10.0074i	−0.850047	−	0.526707i
$19$	−16.1509	−	10.0074i	−0.850047	−	0.526707i
$20$		0			0
$21$	−5.02876	+	0.132486i	−0.239465	+	0.00630885i
$22$		0			0
$23$	−7.35650	−	12.7418i	−0.319848	−	0.553993i	0.660608	−	0.750731i	$-0.270299\pi$
$23$	−7.35650	−	12.7418i	−0.319848	−	0.553993i	−0.980456	+	0.196738i	$0.936965\pi$
$24$		0			0
$25$	5.47574			0.219030
$26$		0			0
$27$	26.9158	−	2.13128i	0.996880	−	0.0789365i
$28$		0			0
$29$			40.8226i			1.40768i	0.710360	+	0.703838i	$0.248532\pi$
$29$			40.8226i			1.40768i	−0.710360	+	0.703838i	$0.751468\pi$
$30$		0			0
$31$	23.1199	+	13.3483i	0.745803	+	0.430590i	0.824176	−	0.566334i	$-0.191639\pi$
$31$	23.1199	+	13.3483i	0.745803	+	0.430590i	−0.0783722	+	0.996924i	$0.524972\pi$
$32$		0			0
$33$	−4.58460	+	0.120784i	−0.138927	+	0.00366013i
$34$		0			0
$35$	4.62847	+	8.01674i	0.132242	+	0.229050i
$36$		0			0
$37$			59.7594i			1.61512i	0.589787	+	0.807559i	$0.299212\pi$
$37$			59.7594i			1.61512i	−0.589787	+	0.807559i	$0.700788\pi$
$38$		0			0
$39$	−1.63857	−	62.1953i	−0.0420147	−	1.59475i
$40$		0			0
$41$			36.9438i			0.901067i	0.892759	+	0.450534i	$0.148766\pi$
$41$			36.9438i			0.901067i	−0.892759	+	0.450534i	$0.851234\pi$
$42$		0			0
$43$	2.38108	−	4.12414i	0.0553738	−	0.0959103i	−0.837010	−	0.547188i	$-0.815698\pi$
$43$	2.38108	−	4.12414i	0.0553738	−	0.0959103i	0.892384	+	0.451278i	$0.149032\pi$
$44$		0			0
$45$	−27.0733	−	41.6602i	−0.601630	−	0.925781i
$46$		0			0
$47$	−54.0607			−1.15023			−0.575114	−	0.818073i	$-0.695042\pi$
$47$	−54.0607			−1.15023			−0.575114	+	0.818073i	$0.695042\pi$
$48$		0			0
$49$	23.0941	−	40.0002i	0.471308	−	0.816330i
$50$		0			0
$51$	−57.9902	+	1.52779i	−1.13706	+	0.0299567i
$52$		0			0
$53$	−17.5032	−	10.1055i	−0.330250	−	0.190670i	0.325702	−	0.945472i	$-0.394399\pi$
$53$	−17.5032	−	10.1055i	−0.330250	−	0.190670i	−0.655952	+	0.754803i	$0.727733\pi$
$54$		0			0
$55$	4.21966	+	7.30867i	0.0767211	+	0.132885i
$56$		0			0
$57$	49.4992	−	28.2635i	0.868407	−	0.495852i
$58$		0			0
$59$		−	98.9167i		−	1.67655i	−0.545245	−	0.838277i	$-0.683563\pi$
$59$		−	98.9167i		−	1.67655i	0.545245	−	0.838277i	$-0.316437\pi$
$60$		0			0
$61$	−87.2069			−1.42962			−0.714811	−	0.699318i	$-0.753487\pi$
$61$	−87.2069			−1.42962			−0.714811	+	0.699318i	$0.753487\pi$
$62$		0			0
$63$	6.84711	−	13.4488i	0.108684	−	0.213473i
$64$		0			0
$65$	−99.1504	+	57.2445i	−1.52539	+	0.880685i
$66$		0			0
$67$	−74.7887	+	43.1793i	−1.11625	+	0.644467i	−0.940441	−	0.339958i	$-0.889587\pi$
$67$	−74.7887	+	43.1793i	−1.11625	+	0.644467i	−0.175808	+	0.984424i	$0.556254\pi$
$68$		0			0
$69$	44.1237	−	1.16247i	0.639474	−	0.0168474i
$70$		0			0
$71$	−76.0630	+	43.9150i	−1.07131	+	0.618521i	−0.928539	−	0.371234i	$-0.878935\pi$
$71$	−76.0630	+	43.9150i	−1.07131	+	0.618521i	−0.142771	+	0.989756i	$0.545601\pi$
$72$		0			0
$73$	30.5689	+	52.9469i	0.418752	+	0.725300i	0.995814	−	0.0914003i	$-0.0291343\pi$
$73$	30.5689	+	52.9469i	0.418752	+	0.725300i	−0.577062	+	0.816700i	$0.695801\pi$
$74$		0			0
$75$	−7.83609	+	14.4378i	−0.104481	+	0.192504i
$76$		0			0
$77$	−1.28171	+	2.21999i	−0.0166456	+	0.0288311i
$78$		0			0
$79$	−31.1924	−	18.0089i	−0.394840	−	0.227961i	0.289415	−	0.957204i	$-0.406539\pi$
$79$	−31.1924	−	18.0089i	−0.394840	−	0.227961i	−0.684255	+	0.729243i	$0.739873\pi$
$80$		0			0
$81$	−32.8984	+	74.0182i	−0.406153	+	0.913805i
$82$		0			0
$83$	4.38181	+	7.58953i	0.0527930	+	0.0914401i	0.891214	−	0.453583i	$-0.149854\pi$
$83$	4.38181	+	7.58953i	0.0527930	+	0.0914401i	−0.838421	+	0.545023i	$0.816521\pi$
$84$		0			0
$85$	53.3742	+	92.4469i	0.627932	+	1.08761i
$86$		0			0
$87$	−107.636	−	58.4194i	−1.23720	−	0.671488i
$88$		0			0
$89$	63.7489	+	36.8055i	0.716280	+	0.413544i	0.813382	−	0.581730i	$-0.197624\pi$
$89$	63.7489	+	36.8055i	0.716280	+	0.413544i	−0.0971020	+	0.995274i	$0.530957\pi$
$90$		0			0
$91$	−30.1167	−	17.3879i	−0.330953	−	0.191076i
$92$		0			0
$93$	−68.2810	+	41.8577i	−0.734204	+	0.450082i
$94$		0			0
$95$	−89.1607	−	55.2459i	−0.938534	−	0.581535i
$96$		0			0
$97$	−41.8517	−	24.1631i	−0.431461	−	0.249104i	0.268508	−	0.963277i	$-0.413469\pi$
$97$	−41.8517	−	24.1631i	−0.431461	−	0.249104i	−0.699969	+	0.714173i	$0.746803\pi$
$98$		0			0
$99$	6.24234	−	12.2610i	0.0630540	−	0.123848i
$100$		0			0
$101$	−28.1075			−0.278292			−0.139146	−	0.990272i	$-0.544436\pi$
$101$	−28.1075			−0.278292			−0.139146	+	0.990272i	$0.544436\pi$
$102$		0			0
$103$	76.8268	+	44.3560i	0.745891	+	0.430641i	0.824207	−	0.566288i	$-0.191621\pi$
$103$	76.8268	+	44.3560i	0.745891	+	0.430641i	−0.0783160	+	0.996929i	$0.524954\pi$
$104$		0			0
$105$	−27.7612	+	0.731386i	−0.264392	+	0.00696558i
$106$		0			0
$107$		−	12.6565i		−	0.118285i	−0.998250	−	0.0591424i	$-0.981163\pi$
$107$		−	12.6565i		−	0.118285i	0.998250	−	0.0591424i	$-0.0188366\pi$
$108$		0			0
$109$	100.232	−	57.8690i	0.919560	−	0.530908i	0.0360650	−	0.999349i	$-0.488518\pi$
$109$	100.232	−	57.8690i	0.919560	−	0.530908i	0.883495	+	0.468442i	$0.155184\pi$
$110$		0			0
$111$	−157.566	−	85.5190i	−1.41952	−	0.770441i
$112$		0			0
$113$	100.398	+	57.9648i	0.888477	+	0.512963i	0.873444	−	0.486924i	$-0.161881\pi$
$113$	100.398	+	57.9648i	0.888477	+	0.512963i	0.0150332	+	0.999887i	$0.495215\pi$
$114$		0			0
$115$	−40.6115	−	70.3411i	−0.353143	−	0.611662i
$116$		0			0
$117$	166.334	+	84.6845i	1.42166	+	0.723799i
$118$		0			0
$119$	−16.2123	+	28.0805i	−0.136238	+	0.235971i
$120$		0			0
$121$	59.3315	−	102.765i	0.490343	−	0.849299i
$122$		0			0
$123$	−97.4089	−	52.8686i	−0.791942	−	0.429826i
$124$		0			0
$125$	−107.783			−0.862267
$126$		0			0
$127$	93.8993	+	54.2128i	0.739364	+	0.426872i	0.821838	−	0.569721i	$-0.192949\pi$
$127$	93.8993	+	54.2128i	0.739364	+	0.426872i	−0.0824738	+	0.996593i	$0.526282\pi$
$128$		0			0
$129$	7.46659	+	12.1800i	0.0578806	+	0.0944187i
$130$		0			0
$131$	−161.825			−1.23531			−0.617653	−	0.786451i	$-0.711916\pi$
$131$	−161.825			−1.23531			−0.617653	+	0.786451i	$0.711916\pi$
$132$		0			0
$133$	0.991416	−	31.8444i	0.00745426	−	0.239432i
$134$		0			0
$135$	148.588	−	11.7657i	1.10065	−	0.0871535i
$136$		0			0
$137$	−140.521			−1.02570			−0.512851	−	0.858478i	$-0.671411\pi$
$137$	−140.521			−1.02570			−0.512851	+	0.858478i	$0.671411\pi$
$138$		0			0
$139$	97.7068	+	169.233i	0.702926	+	1.21750i	0.967435	+	0.253121i	$0.0814570\pi$
$139$	97.7068	+	169.233i	0.702926	+	1.21750i	−0.264508	+	0.964383i	$0.585210\pi$
$140$		0			0
$141$	77.3639	−	142.541i	0.548680	−	1.01093i
$142$		0			0
$143$	−27.4567	−	15.8521i	−0.192005	−	0.110854i
$144$		0			0
$145$			225.361i			1.55421i
$146$		0			0
$147$	72.4187	+	118.134i	0.492644	+	0.803634i
$148$		0			0
$149$	−62.0000			−0.416107			−0.208054	−	0.978117i	$-0.566713\pi$
$149$	−62.0000			−0.416107			−0.208054	+	0.978117i	$0.566713\pi$
$150$		0			0
$151$	198.836	−	114.798i	1.31680	−	0.760252i	0.333584	−	0.942720i	$-0.391742\pi$
$151$	198.836	−	114.798i	1.31680	−	0.760252i	0.983212	+	0.182468i	$0.0584086\pi$
$152$		0			0
$153$	78.9590	−	155.088i	0.516072	−	1.01365i
$154$		0			0
$155$	127.633	+	73.6890i	0.823439	+	0.475413i
$156$		0			0
$157$	151.432			0.964538			0.482269	−	0.876023i	$-0.339813\pi$
$157$	151.432			0.964538			0.482269	+	0.876023i	$0.339813\pi$
$158$		0			0
$159$	51.6931	−	31.6889i	0.325114	−	0.199301i
$160$		0			0
$161$	12.3356	−	21.3659i	0.0766188	−	0.132708i
$162$		0			0
$163$	224.865			1.37954			0.689770	−	0.724029i	$-0.257712\pi$
$163$	224.865			1.37954			0.689770	+	0.724029i	$0.257712\pi$
$164$		0			0
$165$	−25.3092	+	0.666787i	−0.153389	+	0.00404113i
$166$		0			0
$167$	89.5358	−	51.6935i	0.536143	−	0.309542i	−0.207372	−	0.978262i	$-0.566491\pi$
$167$	89.5358	−	51.6935i	0.536143	−	0.309542i	0.743514	+	0.668720i	$0.233158\pi$
$168$		0			0
$169$	130.552	−	226.123i	0.772496	−	1.33800i
$170$		0			0
$171$	3.68580	+	170.960i	0.0215544	+	0.999768i
$172$		0			0
$173$	−205.008	−	118.361i	−1.18502	−	0.684170i	−0.227848	−	0.973697i	$-0.573169\pi$
$173$	−205.008	−	118.361i	−1.18502	−	0.684170i	−0.957170	+	0.289527i	$0.906502\pi$
$174$		0			0
$175$	4.59095	+	7.95177i	0.0262340	+	0.0454387i
$176$		0			0
$177$	260.812	+	141.555i	1.47351	+	0.799747i
$178$		0			0
$179$		−	165.052i		−	0.922081i	−0.887379	−	0.461040i	$-0.847476\pi$
$179$		−	165.052i		−	0.922081i	0.887379	−	0.461040i	$-0.152524\pi$
$180$		0			0
$181$	9.86440	+	5.69521i	0.0544994	+	0.0314653i	0.527002	−	0.849864i	$-0.323316\pi$
$181$	9.86440	+	5.69521i	0.0544994	+	0.0314653i	−0.472503	+	0.881329i	$0.656649\pi$
$182$		0			0
$183$	124.798	−	229.937i	0.681956	−	1.25648i
$184$		0			0
$185$			329.901i			1.78325i
$186$		0			0
$187$	−14.7804	+	25.6003i	−0.0790393	+	0.136900i
$188$		0			0
$189$	25.6616	+	37.2996i	0.135776	+	0.197353i
$190$		0			0
$191$	139.076	+	240.886i	0.728146	+	1.26119i	0.957666	+	0.287882i	$0.0929510\pi$
$191$	139.076	+	240.886i	0.728146	+	1.26119i	−0.229520	+	0.973304i	$0.573716\pi$
$192$		0			0
$193$			292.808i			1.51714i	0.651592	+	0.758570i	$0.274102\pi$
$193$			292.808i			1.51714i	−0.651592	+	0.758570i	$0.725898\pi$
$194$		0			0
$195$	−9.04572	−	343.348i	−0.0463883	−	1.76076i
$196$		0			0
$197$	200.140			1.01594			0.507971	−	0.861374i	$-0.330396\pi$
$197$	200.140			1.01594			0.507971	+	0.861374i	$0.330396\pi$
$198$		0			0
$199$	−3.26766	+	5.65976i	−0.0164204	+	0.0284410i	−0.874119	−	0.485712i	$-0.838560\pi$
$199$	−3.26766	+	5.65976i	−0.0164204	+	0.0284410i	0.857698	+	0.514153i	$0.171894\pi$
$200$		0			0
$201$	−6.82315	−	258.986i	−0.0339460	−	1.28849i
$202$		0			0
$203$	−59.2818	+	34.2264i	−0.292029	+	0.168603i
$204$		0			0
$205$			203.947i			0.994866i
$206$		0			0
$207$	−60.0784	+	118.004i	−0.290234	+	0.570066i
$208$		0			0
$209$	0.903850	−	29.0318i	0.00432464	−	0.138908i
$210$		0			0
$211$		−	213.884i		−	1.01367i	−0.862043	−	0.506835i	$-0.830815\pi$
$211$		−	213.884i		−	1.01367i	0.862043	−	0.506835i	$-0.169185\pi$
$212$		0			0
$213$	−6.93941	−	263.399i	−0.0325794	−	1.23661i
$214$		0			0
$215$	13.1447	−	22.7673i	0.0611381	−	0.105894i
$216$		0			0
$217$			44.7657i			0.206294i
$218$		0			0
$219$	−183.350	+	4.83047i	−0.837214	+	0.0220569i
$220$		0			0
$221$	−347.297	−	200.512i	−1.57148	−	0.907295i
$222$		0			0
$223$	300.535	+	173.514i	1.34769	+	0.778090i	0.987922	−	0.154952i	$-0.0495223\pi$
$223$	300.535	+	173.514i	1.34769	+	0.778090i	0.359769	+	0.933042i	$0.382856\pi$
$224$		0			0
$225$	−26.8539	−	41.3225i	−0.119351	−	0.183656i
$226$		0			0
$227$	−324.621	+	187.420i	−1.43005	+	0.825640i	−0.997124	−	0.0757900i	$-0.975852\pi$
$227$	−324.621	+	187.420i	−1.43005	+	0.825640i	−0.432926	+	0.901430i	$0.642519\pi$
$228$		0			0
$229$	−15.6607	+	27.1251i	−0.0683872	+	0.118450i	−0.898191	−	0.439604i	$-0.855119\pi$
$229$	−15.6607	+	27.1251i	−0.0683872	+	0.118450i	0.829804	+	0.558054i	$0.188452\pi$
$230$		0			0
$231$	−4.01920	−	6.55640i	−0.0173992	−	0.0283827i
$232$		0			0
$233$	30.2550	+	52.4032i	0.129850	+	0.224907i	0.923618	−	0.383314i	$-0.125217\pi$
$233$	30.2550	+	52.4032i	0.129850	+	0.224907i	−0.793768	+	0.608220i	$0.791884\pi$
$234$		0			0
$235$	−298.441			−1.26996
$236$		0			0
$237$	92.1218	−	56.4725i	0.388699	−	0.238281i
$238$		0			0
$239$	96.9628	−	167.944i	0.405702	−	0.702696i	−0.588701	−	0.808351i	$-0.700360\pi$
$239$	96.9628	−	167.944i	0.405702	−	0.702696i	0.994403	+	0.105655i	$0.0336938\pi$
$240$		0			0
$241$			195.379i			0.810700i	0.914162	+	0.405350i	$0.132850\pi$
$241$			195.379i			0.810700i	−0.914162	+	0.405350i	$0.867150\pi$
$242$		0			0
$243$	−148.083	−	192.667i	−0.609394	−	0.792867i
$244$		0			0
$245$	127.491	−	220.820i	0.520370	−	0.901308i
$246$		0			0
$247$	393.849	+	12.2618i	1.59453	+	0.0496427i
$248$		0			0
$249$	−26.2818	+	0.692410i	−0.105549	+	0.00278076i
$250$		0			0
$251$	−3.93929	+	6.82305i	−0.0156944	+	0.0271835i	−0.873766	−	0.486347i	$-0.838329\pi$
$251$	−3.93929	+	6.82305i	−0.0156944	+	0.0271835i	0.858072	+	0.513530i	$0.171663\pi$
$252$		0			0
$253$	11.2461	−	19.4788i	0.0444510	−	0.0769914i
$254$		0			0
$255$	−320.134	+	8.43414i	−1.25543	+	0.0330751i
$256$		0			0
$257$	437.956	−	252.854i	1.70411	−	0.983867i	0.762602	−	0.646867i	$-0.223921\pi$
$257$	437.956	−	252.854i	1.70411	−	0.983867i	0.941505	−	0.336999i	$-0.109412\pi$
$258$		0			0
$259$	−86.7814	+	50.1033i	−0.335063	+	0.193449i
$260$		0			0
$261$	308.067	−	200.201i	1.18033	−	0.767053i
$262$		0			0
$263$	−132.636	+	229.733i	−0.504321	+	0.873509i	0.495667	+	0.868513i	$0.334924\pi$
$263$	−132.636	+	229.733i	−0.504321	+	0.873509i	−0.999988	+	0.00499640i	$0.998410\pi$
$264$		0			0
$265$	−96.6264	−	55.7873i	−0.364628	−	0.210518i
$266$		0			0
$267$	−188.272	+	115.415i	−0.705140	+	0.432265i
$268$		0			0
$269$	55.3986	−	31.9844i	0.205943	−	0.118901i	−0.393482	−	0.919332i	$-0.628730\pi$
$269$	55.3986	−	31.9844i	0.205943	−	0.118901i	0.599424	+	0.800431i	$0.295396\pi$
$270$		0			0
$271$	−261.759	−	453.380i	−0.965901	−	1.67299i	−0.707175	−	0.707038i	$-0.750031\pi$
$271$	−261.759	−	453.380i	−0.965901	−	1.67299i	−0.258726	−	0.965951i	$-0.583303\pi$
$272$		0			0
$273$	88.9449	−	54.5251i	0.325806	−	0.199725i
$274$		0			0
$275$	4.18546	+	7.24943i	0.0152199	+	0.0263616i
$276$		0			0
$277$	−38.1732	−	66.1179i	−0.137809	−	0.238693i	0.788858	−	0.614576i	$-0.210673\pi$
$277$	−38.1732	−	66.1179i	−0.137809	−	0.238693i	−0.926667	+	0.375883i	$0.877339\pi$
$278$		0			0
$279$	−12.6513	−	239.936i	−0.0453452	−	0.859985i
$280$		0			0
$281$			458.998i			1.63344i	0.577031	+	0.816722i	$0.304211\pi$
$281$			458.998i			1.63344i	−0.577031	+	0.816722i	$0.695789\pi$
$282$		0			0
$283$	126.719			0.447770			0.223885	−	0.974616i	$-0.428126\pi$
$283$	126.719			0.447770			0.223885	+	0.974616i	$0.428126\pi$
$284$		0			0
$285$	273.260	−	156.028i	0.958806	−	0.547468i
$286$		0			0
$287$	−53.6490	+	30.9743i	−0.186930	+	0.107924i
$288$		0			0
$289$	−42.4557	+	73.5354i	−0.146906	+	0.254448i
$290$		0			0
$291$	123.602	−	75.7708i	0.424751	−	0.260381i
$292$		0			0
$293$	142.675	+	82.3734i	0.486945	+	0.281138i	0.723306	−	0.690527i	$-0.242621\pi$
$293$	142.675	+	82.3734i	0.486945	+	0.281138i	−0.236361	+	0.971665i	$0.575955\pi$
$294$		0			0
$295$		−	546.068i		−	1.85108i
$296$		0			0
$297$	23.3951	+	34.0052i	0.0787714	+	0.114496i
$298$		0			0
$299$	264.252	+	152.566i	0.883787	+	0.510255i
$300$		0			0
$301$	7.98534			0.0265294
$302$		0			0
$303$	40.2234	−	74.1105i	0.132750	−	0.244589i
$304$		0			0
$305$	−481.424			−1.57844
$306$		0			0
$307$	−143.939	+	83.1031i	−0.468856	+	0.270694i	−0.715761	−	0.698346i	$-0.753920\pi$
$307$	−143.939	+	83.1031i	−0.468856	+	0.270694i	0.246905	+	0.969040i	$0.420587\pi$
$308$		0			0
$309$	−226.896	+	139.092i	−0.734291	+	0.450135i
$310$		0			0
$311$	129.031	−	223.488i	0.414891	−	0.718612i	−0.580526	−	0.814241i	$-0.697153\pi$
$311$	129.031	−	223.488i	0.414891	−	0.718612i	0.995417	+	0.0956298i	$0.0304865\pi$
$312$		0			0
$313$	268.054			0.856404			0.428202	−	0.903683i	$-0.359147\pi$
$313$	268.054			0.856404			0.428202	+	0.903683i	$0.359147\pi$
$314$		0			0
$315$	37.7993	−	74.2440i	0.119998	−	0.235695i
$316$		0			0
$317$			534.558i			1.68630i	0.537675	+	0.843152i	$0.319303\pi$
$317$			534.558i			1.68630i	−0.537675	+	0.843152i	$0.680697\pi$
$318$		0			0
$319$	−54.0458	+	31.2034i	−0.169423	+	0.0978162i
$320$		0			0
$321$	33.3711	+	18.1121i	0.103960	+	0.0564241i
$322$		0			0
$323$	11.4327	−	367.221i	0.0353955	−	1.13691i
$324$		0			0
$325$	−98.3468	+	56.7805i	−0.302606	+	0.174709i
$326$		0			0
$327$	9.14440	+	347.093i	0.0279645	+	1.06145i
$328$		0			0
$329$	−45.3254	−	78.5060i	−0.137767	−	0.238620i
$330$		0			0
$331$	−255.142	+	147.306i	−0.770821	+	0.445034i	−0.833168	−	0.553021i	$-0.813475\pi$
$331$	−255.142	+	147.306i	−0.770821	+	0.445034i	0.0623461	+	0.998055i	$0.480142\pi$
$332$		0			0
$333$	450.972	−	293.070i	1.35427	−	0.880089i
$334$		0			0
$335$	−412.870	+	238.370i	−1.23245	+	0.711554i
$336$		0			0
$337$		−	234.469i		−	0.695754i	−0.937540	−	0.347877i	$-0.886903\pi$
$337$		−	234.469i		−	0.695754i	0.937540	−	0.347877i	$-0.113097\pi$
$338$		0			0
$339$	−296.510	+	181.766i	−0.874660	+	0.536184i
$340$		0			0
$341$			40.8118i			0.119683i
$342$		0			0
$343$	159.615			0.465349
$344$		0			0
$345$	243.584	−	6.41738i	0.706041	−	0.0186011i
$346$		0			0
$347$	588.236			1.69520			0.847602	−	0.530633i	$-0.178046\pi$
$347$	588.236			1.69520			0.847602	+	0.530633i	$0.178046\pi$
$348$		0			0
$349$	230.931	+	399.985i	0.661695	+	1.14609i	0.980170	+	0.198158i	$0.0634958\pi$
$349$	230.931	+	399.985i	0.661695	+	1.14609i	−0.318475	+	0.947931i	$0.603171\pi$
$350$		0			0
$351$	−461.319	+	317.381i	−1.31430	+	0.904219i
$352$		0			0
$353$	−225.135	−	389.946i	−0.637777	−	1.10466i	−0.985919	−	0.167221i	$-0.946521\pi$
$353$	−225.135	−	389.946i	−0.637777	−	1.10466i	0.348142	−	0.937442i	$-0.386813\pi$
$354$		0			0
$355$	−419.905	+	242.432i	−1.18283	+	0.682907i
$356$		0			0
$357$	−50.8386	−	82.9314i	−0.142405	−	0.232301i
$358$		0			0
$359$	91.4010	+	158.311i	0.254599	+	0.440978i	0.964786	−	0.263034i	$-0.0847232\pi$
$359$	91.4010	+	158.311i	0.254599	+	0.440978i	−0.710188	+	0.704012i	$0.751390\pi$
$360$		0			0
$361$	160.703	+	323.258i	0.445160	+	0.895451i
$362$		0			0
$363$	186.052	+	303.501i	0.512540	+	0.836090i
$364$		0			0
$365$	168.755	+	292.292i	0.462343	+	0.800801i
$366$		0			0
$367$	80.8772			0.220374			0.110187	−	0.993911i	$-0.464855\pi$
$367$	80.8772			0.220374			0.110187	+	0.993911i	$0.464855\pi$
$368$		0			0
$369$	278.795	−	181.178i	0.755542	−	0.490998i
$370$		0			0
$371$		−	33.8905i		−	0.0913491i
$372$		0			0
$373$	129.659	+	74.8584i	0.347610	+	0.200693i	0.663632	−	0.748059i	$-0.269014\pi$
$373$	129.659	+	74.8584i	0.347610	+	0.200693i	−0.316022	+	0.948752i	$0.602347\pi$
$374$		0			0
$375$	154.244	−	284.190i	0.411317	−	0.757841i
$376$		0			0
$377$	−423.309	−	733.193i	−1.12284	−	1.94481i
$378$		0			0
$379$			454.252i			1.19855i	0.800542	+	0.599277i	$0.204545\pi$
$379$			454.252i			1.19855i	−0.800542	+	0.599277i	$0.795455\pi$
$380$		0			0
$381$	−277.317	+	170.001i	−0.727866	+	0.446196i
$382$		0			0
$383$			98.3469i			0.256781i	0.991724	+	0.128390i	$0.0409810\pi$
$383$			98.3469i			0.256781i	−0.991724	+	0.128390i	$0.959019\pi$
$384$		0			0
$385$	−7.07567	+	12.2554i	−0.0183784	+	0.0318323i
$386$		0			0
$387$	−42.7999	+	2.25675i	−0.110594	+	0.00583139i
$388$		0			0
$389$	336.895			0.866054			0.433027	−	0.901381i	$-0.357445\pi$
$389$	336.895			0.866054			0.433027	+	0.901381i	$0.357445\pi$
$390$		0			0
$391$	142.251	−	246.386i	0.363814	−	0.630144i
$392$		0			0
$393$	231.580	−	426.681i	0.589263	−	1.08570i
$394$		0			0
$395$	−172.197	−	99.4180i	−0.435942	−	0.251691i
$396$		0			0
$397$	−140.690	−	243.683i	−0.354384	−	0.613811i	0.632628	−	0.774455i	$-0.281976\pi$
$397$	−140.690	−	243.683i	−0.354384	−	0.613811i	−0.987012	+	0.160645i	$0.948643\pi$
$398$		0			0
$399$	82.5448	+	48.1852i	0.206879	+	0.120765i
$400$		0			0
$401$		−	260.401i		−	0.649378i	−0.945821	−	0.324689i	$-0.894740\pi$
$401$		−	260.401i		−	0.649378i	0.945821	−	0.324689i	$-0.105260\pi$
$402$		0			0
$403$	−553.659			−1.37384
$404$		0			0
$405$	−181.615	+	408.616i	−0.448433	+	1.00893i
$406$		0			0
$407$	−79.1165	+	45.6779i	−0.194389	+	0.112231i
$408$		0			0
$409$	−160.526	+	92.6800i	−0.392485	+	0.226601i	−0.683236	−	0.730197i	$-0.739428\pi$
$409$	−160.526	+	92.6800i	−0.392485	+	0.226601i	0.290751	+	0.956799i	$0.406095\pi$
$410$		0			0
$411$	201.094	−	370.509i	0.489279	−	0.901483i
$412$		0			0
$413$	143.645	−	82.9334i	0.347809	−	0.200807i
$414$		0			0
$415$	24.1897	+	41.8979i	0.0582885	+	0.100959i
$416$		0			0
$417$	−586.037	+	15.4395i	−1.40537	+	0.0370253i
$418$		0			0
$419$	42.6325	−	73.8416i	0.101748	−	0.176233i	−0.810657	−	0.585522i	$-0.800890\pi$
$419$	42.6325	−	73.8416i	0.101748	−	0.176233i	0.912405	+	0.409289i	$0.134223\pi$
$420$		0			0
$421$	526.755	+	304.122i	1.25120	+	0.722381i	0.971348	−	0.237662i	$-0.0763812\pi$
$421$	526.755	+	304.122i	1.25120	+	0.722381i	0.279852	+	0.960043i	$0.409715\pi$
$422$		0			0
$423$	265.123	+	407.968i	0.626767	+	0.964463i
$424$		0			0
$425$	52.9416	+	91.6976i	0.124569	+	0.215759i
$426$		0			0
$427$	−73.1158	−	126.640i	−0.171231	−	0.296581i
$428$		0			0
$429$	81.0890	−	49.7092i	0.189019	−	0.115872i
$430$		0			0
$431$	79.3761	+	45.8278i	0.184167	+	0.106329i	0.589249	−	0.807951i	$-0.299424\pi$
$431$	79.3761	+	45.8278i	0.184167	+	0.106329i	−0.405082	+	0.914280i	$0.632757\pi$
$432$		0			0
$433$	547.653	+	316.188i	1.26479	+	0.730225i	0.973997	−	0.226561i	$-0.0727484\pi$
$433$	547.653	+	316.188i	1.26479	+	0.730225i	0.290791	+	0.956787i	$0.406082\pi$
$434$		0			0
$435$	−594.204	−	322.504i	−1.36599	−	0.741388i
$436$		0			0
$437$	−8.69896	+	279.412i	−0.0199061	+	0.639386i
$438$		0			0
$439$	−348.320	−	201.103i	−0.793440	−	0.458093i	0.0477324	−	0.998860i	$-0.484801\pi$
$439$	−348.320	−	201.103i	−0.793440	−	0.458093i	−0.841172	+	0.540768i	$0.818134\pi$
$440$		0			0
$441$	−415.117	+	21.8883i	−0.941309	+	0.0496333i
$442$		0			0
$443$	−118.638			−0.267807			−0.133903	−	0.990994i	$-0.542751\pi$
$443$	−118.638			−0.267807			−0.133903	+	0.990994i	$0.542751\pi$
$444$		0			0
$445$	351.925	+	203.184i	0.790842	+	0.456593i
$446$		0			0
$447$	88.7254	−	163.474i	0.198491	−	0.365714i
$448$		0			0
$449$			217.699i			0.484853i	0.970170	+	0.242426i	$0.0779433\pi$
$449$			217.699i			0.484853i	−0.970170	+	0.242426i	$0.922057\pi$
$450$		0			0
$451$	−48.9105	+	28.2385i	−0.108449	+	0.0626131i
$452$		0			0
$453$	18.1403	+	688.550i	0.0400448	+	1.51998i
$454$		0			0
$455$	−166.259	−	95.9895i	−0.365404	−	0.210966i
$456$		0			0
$457$	−28.8170	−	49.9125i	−0.0630568	−	0.109218i	0.832774	−	0.553614i	$-0.186752\pi$
$457$	−28.8170	−	49.9125i	−0.0630568	−	0.109218i	−0.895830	+	0.444396i	$0.853418\pi$
$458$		0			0
$459$	295.923	+	430.129i	0.644712	+	0.937100i
$460$		0			0
$461$	−232.941	+	403.466i	−0.505295	+	0.875197i	0.494686	+	0.869072i	$0.335283\pi$
$461$	−232.941	+	403.466i	−0.505295	+	0.875197i	−0.999981	+	0.00612534i	$0.998050\pi$
$462$		0			0
$463$	−46.1604	+	79.9521i	−0.0996984	+	0.172683i	−0.911560	−	0.411168i	$-0.865121\pi$
$463$	−46.1604	+	79.9521i	−0.0996984	+	0.172683i	0.811861	+	0.583850i	$0.198454\pi$
$464$		0			0
$465$	−376.944	+	231.074i	−0.810633	+	0.496934i
$466$		0			0
$467$	−601.527			−1.28807			−0.644033	−	0.764998i	$-0.722740\pi$
$467$	−601.527			−1.28807			−0.644033	+	0.764998i	$0.722740\pi$
$468$		0			0
$469$	−125.408	−	72.4045i	−0.267395	−	0.154381i
$470$		0			0
$471$	−216.708	+	399.279i	−0.460102	+	0.847726i
$472$		0			0
$473$	7.28004			0.0153912
$474$		0			0
$475$	−88.4381	−	54.7981i	−0.186185	−	0.115364i
$476$		0			0
$477$	9.57785	+	181.647i	0.0200793	+	0.380811i
$478$		0			0
$479$	−372.868			−0.778430			−0.389215	−	0.921147i	$-0.627254\pi$
$479$	−372.868			−0.778430			−0.389215	+	0.921147i	$0.627254\pi$
$480$		0			0
$481$	−619.673	−	1073.31i	−1.28830	−	2.23140i
$482$		0			0
$483$	38.6822	+	63.1010i	0.0800873	+	0.130644i
$484$		0			0
$485$	−231.042	−	133.392i	−0.476374	−	0.275035i
$486$		0			0
$487$		−	733.353i		−	1.50586i	−0.658102	−	0.752929i	$-0.728640\pi$
$487$		−	733.353i		−	1.50586i	0.658102	−	0.752929i	$-0.271360\pi$
$488$		0			0
$489$	−321.794	+	592.897i	−0.658066	+	1.21247i
$490$		0			0
$491$	−45.9359			−0.0935559			−0.0467779	−	0.998905i	$-0.514895\pi$
$491$	−45.9359			−0.0935559			−0.0467779	+	0.998905i	$0.514895\pi$
$492$		0			0
$493$	−683.622	+	394.689i	−1.38666	+	0.800587i
$494$		0			0
$495$	34.4608	−	67.6864i	0.0696177	−	0.136740i
$496$		0			0
$497$	−127.545	−	73.6382i	−0.256630	−	0.148165i
$498$		0			0
$499$	345.818			0.693023			0.346511	−	0.938046i	$-0.387366\pi$
$499$	345.818			0.693023			0.346511	+	0.938046i	$0.387366\pi$
$500$		0			0
$501$	8.16856	+	310.054i	0.0163045	+	0.618870i
$502$		0			0
$503$	−293.370	+	508.133i	−0.583242	+	1.01020i	0.411851	+	0.911251i	$0.364883\pi$
$503$	−293.370	+	508.133i	−0.583242	+	1.01020i	−0.995092	+	0.0989526i	$0.968451\pi$
$504$		0			0
$505$	−155.167			−0.307261
$506$		0			0
$507$	409.386	+	667.817i	0.807467	+	1.31719i
$508$		0			0
$509$	104.974	−	60.6066i	0.206235	−	0.119070i	−0.393325	−	0.919399i	$-0.628675\pi$
$509$	104.974	−	60.6066i	0.206235	−	0.119070i	0.599561	+	0.800329i	$0.295342\pi$
$510$		0			0
$511$	−51.2590	+	88.7832i	−0.100311	+	0.173744i
$512$		0			0
$513$	−456.042	−	234.935i	−0.888971	−	0.457964i
$514$		0			0
$515$	424.121	+	244.866i	0.823536	+	0.475469i
$516$		0			0
$517$	−41.3221	−	71.5720i	−0.0799267	−	0.138437i
$518$		0			0
$519$	605.459	−	371.159i	1.16659	−	0.715142i
$520$		0			0
$521$		−	462.527i		−	0.887768i	−0.896084	−	0.443884i	$-0.853600\pi$
$521$		−	462.527i		−	0.887768i	0.896084	−	0.443884i	$-0.146400\pi$
$522$		0			0
$523$	−720.329	−	415.882i	−1.37730	−	0.795185i	−0.385467	−	0.922721i	$-0.625960\pi$
$523$	−720.329	−	415.882i	−1.37730	−	0.795185i	−0.991834	+	0.127536i	$0.959293\pi$
$524$		0			0
$525$	−27.5362	+	0.725458i	−0.0524499	+	0.00138183i
$526$		0			0
$527$			516.226i			0.979556i
$528$		0			0
$529$	156.264	−	270.657i	0.295395	−	0.511638i
$530$		0			0
$531$	−746.472	+	485.103i	−1.40579	+	0.913566i
$532$		0			0
$533$	−383.087	−	663.527i	−0.718738	−	1.24489i
$534$		0			0
$535$		−	69.8699i		−	0.130598i
$536$		0			0
$537$	435.191	+	236.199i	0.810411	+	0.439850i
$538$		0			0
$539$	70.6093			0.131001
$540$		0			0
$541$	−208.868	+	361.769i	−0.386077	+	0.668705i	−0.991918	−	0.126881i	$-0.959503\pi$
$541$	−208.868	+	361.769i	−0.386077	+	0.668705i	0.605841	+	0.795586i	$0.292837\pi$
$542$		0			0
$543$	−29.1330	+	17.8591i	−0.0536519	+	0.0328897i
$544$		0			0
$545$	553.329	−	319.465i	1.01528	−	0.586174i
$546$		0			0
$547$		−	514.242i		−	0.940114i	−0.882636	−	0.470057i	$-0.844233\pi$
$547$		−	514.242i		−	0.940114i	0.882636	−	0.470057i	$-0.155767\pi$
$548$		0			0
$549$	427.677	+	658.104i	0.779010	+	1.19873i
$550$		0			0
$551$	408.530	−	659.322i	0.741433	−	1.19659i
$552$		0			0
$553$		−	60.3959i		−	0.109215i
$554$		0			0
$555$	−869.842	−	472.106i	−1.56728	−	0.850642i
$556$		0			0
$557$	−331.389	+	573.982i	−0.594953	+	1.03049i	0.398600	+	0.917125i	$0.369496\pi$
$557$	−331.389	+	573.982i	−0.594953	+	1.03049i	−0.993553	+	0.113364i	$0.963837\pi$
$558$		0			0
$559$			98.7620i			0.176676i
$560$		0			0
$561$	−46.3484	−	75.6066i	−0.0826174	−	0.134771i
$562$		0			0
$563$	700.676	+	404.536i	1.24454	+	0.718536i	0.970015	−	0.243044i	$-0.0781460\pi$
$563$	700.676	+	404.536i	1.24454	+	0.718536i	0.274525	+	0.961580i	$0.411479\pi$
$564$		0			0
$565$	554.245	+	319.994i	0.980965	+	0.566360i
$566$		0			0
$567$	−135.070	+	14.2837i	−0.238219	+	0.0251917i
$568$		0			0
$569$	−173.823	+	100.357i	−0.305488	+	0.176374i	−0.644906	−	0.764262i	$-0.723103\pi$
$569$	−173.823	+	100.357i	−0.305488	+	0.176374i	0.339418	+	0.940636i	$0.389770\pi$
$570$		0			0
$571$	174.282	−	301.865i	0.305222	−	0.528660i	−0.672089	−	0.740471i	$-0.734603\pi$
$571$	174.282	−	301.865i	0.305222	−	0.528660i	0.977311	+	0.211811i	$0.0679360\pi$
$572$		0			0
$573$	−834.166	+	21.9766i	−1.45579	+	0.0383536i
$574$		0			0
$575$	−40.2823	−	69.7710i	−0.0700562	−	0.121341i
$576$		0			0
$577$	−102.187			−0.177101			−0.0885503	−	0.996072i	$-0.528223\pi$
$577$	−102.187			−0.177101			−0.0885503	+	0.996072i	$0.528223\pi$
$578$		0			0
$579$	−772.041	−	419.024i	−1.33340	−	0.723704i
$580$		0			0
$581$	−7.34758	+	12.7264i	−0.0126464	+	0.0219043i
$582$		0			0
$583$		−	30.8972i		−	0.0529968i
$584$		0			0
$585$	918.243	+	467.499i	1.56965	+	0.799144i
$586$		0			0
$587$	284.222	−	492.288i	0.484195	−	0.838650i	−0.515640	−	0.856805i	$-0.672446\pi$
$587$	284.222	−	492.288i	0.484195	−	0.838650i	0.999835	+	0.0181550i	$0.00577925\pi$
$588$		0			0
$589$	−239.825	−	446.958i	−0.407173	−	0.758841i
$590$		0			0
$591$	−286.412	+	527.706i	−0.484623	+	0.892904i
$592$		0			0
$593$	551.047	−	954.441i	0.929252	−	1.60951i	0.144677	−	0.989479i	$-0.453786\pi$
$593$	551.047	−	954.441i	0.929252	−	1.60951i	0.784576	−	0.620033i	$-0.212881\pi$
$594$		0			0
$595$	−89.4997	+	155.018i	−0.150420	+	0.260534i
$596$		0			0
$597$	−10.2468	−	16.7152i	−0.0171638	−	0.0279987i
$598$		0			0
$599$	504.389	−	291.209i	0.842051	−	0.486159i	−0.0159097	−	0.999873i	$-0.505064\pi$
$599$	504.389	−	291.209i	0.842051	−	0.486159i	0.857961	+	0.513715i	$0.171731\pi$
$600$		0			0
$601$	−462.788	+	267.191i	−0.770031	+	0.444577i	−0.832886	−	0.553445i	$-0.813313\pi$
$601$	−462.788	+	267.191i	−0.770031	+	0.444577i	0.0628549	+	0.998023i	$0.479979\pi$
$602$		0			0
$603$	692.627	+	352.633i	1.14863	+	0.584797i
$604$		0			0
$605$	327.539	−	567.313i	0.541386	−	0.937708i
$606$		0			0
$607$	−549.907	−	317.489i	−0.905942	−	0.523046i	−0.0268186	−	0.999640i	$-0.508538\pi$
$607$	−549.907	−	317.489i	−0.905942	−	0.523046i	−0.879123	+	0.476595i	$0.841871\pi$
$608$		0			0
$609$	−5.40842	−	205.287i	−0.00888082	−	0.337089i
$610$		0			0
$611$	970.955	−	560.581i	1.58913	−	0.917482i
$612$		0			0
$613$	−73.8570	−	127.924i	−0.120484	−	0.208685i	0.799474	−	0.600700i	$-0.205111\pi$
$613$	−73.8570	−	127.924i	−0.120484	−	0.208685i	−0.919959	+	0.392015i	$0.871778\pi$
$614$		0			0
$615$	−537.744	−	291.860i	−0.874381	−	0.474569i
$616$		0			0
$617$	−212.890	−	368.736i	−0.345040	−	0.597627i	0.640321	−	0.768108i	$-0.278801\pi$
$617$	−212.890	−	368.736i	−0.345040	−	0.597627i	−0.985361	+	0.170480i	$0.945468\pi$
$618$		0			0
$619$	−294.086	−	509.373i	−0.475099	−	0.822896i	0.524494	−	0.851414i	$-0.324255\pi$
$619$	−294.086	−	509.373i	−0.475099	−	0.822896i	−0.999593	+	0.0285181i	$0.990921\pi$
$620$		0			0
$621$	−225.162	−	327.277i	−0.362580	−	0.527017i
$622$		0			0
$623$			123.433i			0.198127i
$624$		0			0
$625$	−731.910			−1.17106
$626$		0			0
$627$	75.2541	+	43.9293i	0.120022	+	0.0700626i
$628$		0			0
$629$	−1000.74	+	577.777i	−1.59100	+	0.918565i
$630$		0			0
$631$	249.213	−	431.649i	0.394949	−	0.684071i	−0.598146	−	0.801387i	$-0.704096\pi$
$631$	249.213	−	431.649i	0.394949	−	0.684071i	0.993095	+	0.117316i	$0.0374290\pi$
$632$		0			0
$633$	563.944	+	306.080i	0.890907	+	0.483539i
$634$		0			0
$635$	518.369	+	299.281i	0.816330	+	0.471308i
$636$		0			0
$637$			957.895i			1.50376i
$638$		0			0
$639$	704.429	+	358.641i	1.10239	+	0.561254i
$640$		0			0
$641$	−418.804	−	241.797i	−0.653361	−	0.377218i	0.136382	−	0.990656i	$-0.456453\pi$
$641$	−418.804	−	241.797i	−0.653361	−	0.377218i	−0.789743	+	0.613438i	$0.789786\pi$
$642$		0			0
$643$	919.540			1.43008			0.715039	−	0.699085i	$-0.246409\pi$
$643$	919.540			1.43008			0.715039	+	0.699085i	$0.246409\pi$
$644$		0			0
$645$	41.2192	+	67.2395i	0.0639058	+	0.104247i
$646$		0			0
$647$	917.882			1.41867			0.709337	−	0.704869i	$-0.248994\pi$
$647$	917.882			1.41867			0.709337	+	0.704869i	$0.248994\pi$
$648$		0			0
$649$	130.958	−	75.6084i	0.201784	−	0.116500i
$650$		0			0
$651$	−118.033	−	64.0622i	−0.181310	−	0.0984059i
$652$		0			0
$653$	−188.112	+	325.820i	−0.288074	+	0.498958i	−0.973350	−	0.229325i	$-0.926348\pi$
$653$	−188.112	+	325.820i	−0.288074	+	0.498958i	0.685276	+	0.728283i	$0.259681\pi$
$654$		0			0
$655$	−893.352			−1.36390
$656$		0			0
$657$	249.647	−	490.347i	0.379981	−	0.746343i
$658$		0			0
$659$			862.027i			1.30808i	0.756458	+	0.654042i	$0.226928\pi$
$659$			862.027i			1.30808i	−0.756458	+	0.654042i	$0.773072\pi$
$660$		0			0
$661$	−1005.25	+	580.382i	−1.52080	+	0.878037i	−0.521106	+	0.853492i	$0.674480\pi$
$661$	−1005.25	+	580.382i	−1.52080	+	0.878037i	−0.999699	+	0.0245451i	$0.992186\pi$
$662$		0			0
$663$	1025.69	−	628.768i	1.54704	−	0.948368i
$664$		0			0
$665$	5.47310	−	175.797i	0.00823022	−	0.264356i
$666$		0			0
$667$	520.155	−	300.312i	0.779843	−	0.450243i
$668$		0			0
$669$	−887.583	+	544.106i	−1.32673	+	0.813313i
$670$		0			0
$671$	−66.6579	−	115.455i	−0.0993411	−	0.172064i
$672$		0			0
$673$	793.000	−	457.839i	1.17831	−	0.680296i	0.222685	−	0.974891i	$-0.428518\pi$
$673$	793.000	−	457.839i	1.17831	−	0.680296i	0.955622	+	0.294595i	$0.0951847\pi$
$674$		0			0
$675$	147.384	−	11.6704i	0.218346	−	0.0172894i
$676$		0			0
$677$	499.660	−	288.479i	0.738051	−	0.426114i	−0.0833095	−	0.996524i	$-0.526549\pi$
$677$	499.660	−	288.479i	0.738051	−	0.426114i	0.821360	+	0.570410i	$0.193216\pi$
$678$		0			0
$679$		−	81.0350i		−	0.119345i
$680$		0			0
$681$	−29.6160	−	1124.13i	−0.0434889	−	1.65071i
$682$		0			0
$683$			110.380i			0.161611i	0.996730	+	0.0808054i	$0.0257492\pi$
$683$			110.380i			0.161611i	−0.996730	+	0.0808054i	$0.974251\pi$
$684$		0			0
$685$	−775.745			−1.13247
$686$		0			0
$687$	−49.1088	−	80.1096i	−0.0714830	−	0.116608i
$688$		0			0
$689$	419.155			0.608353
$690$		0			0
$691$	316.990	+	549.043i	0.458741	+	0.794564i	0.998895	−	0.0470031i	$-0.0149671\pi$
$691$	316.990	+	549.043i	0.458741	+	0.794564i	−0.540153	+	0.841567i	$0.681634\pi$
$692$		0			0
$693$	23.0388	−	1.21479i	0.0332451	−	0.00175294i
$694$		0			0
$695$	539.389	+	934.249i	0.776099	+	1.34424i
$696$		0			0
$697$	−618.666	+	357.187i	−0.887612	+	0.512463i
$698$		0			0
$699$	−181.467	+	4.78087i	−0.259610	+	0.00683958i
$700$		0			0
$701$	−314.952	−	545.513i	−0.449290	−	0.778192i	0.549050	−	0.835789i	$-0.314990\pi$
$701$	−314.952	−	545.513i	−0.449290	−	0.778192i	−0.998340	+	0.0575969i	$0.981656\pi$
$702$		0			0
$703$	598.038	−	965.167i	0.850694	−	1.37293i
$704$		0			0
$705$	427.086	−	786.895i	0.605796	−	1.11616i
$706$		0			0
$707$	−23.5658	−	40.8172i	−0.0333321	−	0.0577329i
$708$		0			0
$709$	634.859			0.895429			0.447714	−	0.894177i	$-0.352238\pi$
$709$	634.859			0.895429			0.447714	+	0.894177i	$0.352238\pi$
$710$		0			0
$711$	17.0686	+	323.711i	0.0240065	+	0.455290i
$712$		0			0
$713$		−	392.787i		−	0.550893i
$714$		0			0
$715$	−151.574	−	87.5113i	−0.211992	−	0.122393i
$716$		0			0
$717$	304.057	+	495.998i	0.424068	+	0.691768i
$718$		0			0
$719$	−426.697	−	739.061i	−0.593459	−	1.02790i	−0.993762	−	0.111518i	$-0.964429\pi$
$719$	−426.697	−	739.061i	−0.593459	−	1.02790i	0.400304	−	0.916383i	$-0.368905\pi$
$720$		0			0
$721$			148.755i			0.206318i
$722$		0			0
$723$	−515.151	−	279.598i	−0.712519	−	0.386719i
$724$		0			0
$725$			223.534i			0.308323i
$726$		0			0
$727$	−320.492	+	555.108i	−0.440842	+	0.763560i	−0.997752	−	0.0670123i	$-0.978653\pi$
$727$	−320.492	+	555.108i	−0.440842	+	0.763560i	0.556910	+	0.830573i	$0.311987\pi$
$728$		0			0
$729$	719.915	−	114.730i	0.987538	−	0.157380i
$730$		0			0
$731$	92.0847			0.125971
$732$		0			0
$733$	−460.500	+	797.610i	−0.628241	+	1.08814i	0.359664	+	0.933082i	$0.382891\pi$
$733$	−460.500	+	797.610i	−0.628241	+	1.08814i	−0.987905	+	0.155063i	$0.950442\pi$
$734$		0			0
$735$	399.786	+	652.158i	0.543927	+	0.887290i
$736$		0			0
$737$	−114.332	−	66.0094i	−0.155131	−	0.0895650i
$738$		0			0
$739$	−21.6756	−	37.5432i	−0.0293310	−	0.0508027i	0.850987	−	0.525186i	$-0.176004\pi$
$739$	−21.6756	−	37.5432i	−0.0293310	−	0.0508027i	−0.880318	+	0.474384i	$0.842671\pi$
$740$		0			0
$741$	−595.950	+	1020.91i	−0.804251	+	1.37774i
$742$		0			0
$743$			971.585i			1.30765i	0.756645	+	0.653826i	$0.226837\pi$
$743$			971.585i			1.30765i	−0.756645	+	0.653826i	$0.773163\pi$
$744$		0			0
$745$	−342.270			−0.459423
$746$		0			0
$747$	35.7850	−	70.2875i	0.0479050	−	0.0940930i
$748$		0			0
$749$	18.3795	−	10.6114i	0.0245387	−	0.0141674i
$750$		0			0
$751$	−815.627	+	470.903i	−1.08605	+	0.627034i	−0.932523	−	0.361110i	$-0.882398\pi$
$751$	−815.627	+	470.903i	−1.08605	+	0.627034i	−0.153532	+	0.988144i	$0.549065\pi$
$752$		0			0
$753$	−12.3529	−	20.1508i	−0.0164049	−	0.0267607i
$754$		0			0
$755$	1097.67	−	633.741i	1.45387	−	0.839392i
$756$		0			0
$757$	147.926	+	256.215i	0.195411	+	0.338461i	0.947035	−	0.321130i	$-0.104063\pi$
$757$	147.926	+	256.215i	0.195411	+	0.338461i	−0.751624	+	0.659591i	$0.770729\pi$
$758$		0			0
$759$	35.2656	+	57.5276i	0.0464633	+	0.0757940i
$760$		0			0
$761$	−47.8819	+	82.9339i	−0.0629198	+	0.108980i	−0.895769	−	0.444519i	$-0.853375\pi$
$761$	−47.8819	+	82.9339i	−0.0629198	+	0.108980i	0.832850	+	0.553499i	$0.186708\pi$
$762$		0			0
$763$	168.072	+	97.0366i	0.220278	+	0.127178i
$764$		0			0
$765$	435.892	−	856.161i	0.569793	−	1.11916i
$766$		0			0
$767$	1025.71	+	1776.59i	1.33731	+	2.31628i
$768$		0			0
$769$	283.214	+	490.542i	0.368289	+	0.637896i	0.989298	−	0.145908i	$-0.0466103\pi$
$769$	283.214	+	490.542i	0.368289	+	0.637896i	−0.621009	+	0.783803i	$0.713277\pi$
$770$		0			0
$771$	39.9557	+	1516.60i	0.0518232	+	1.96705i
$772$		0			0
$773$	−667.545	−	385.407i	−0.863577	−	0.498587i	0.00163121	−	0.999999i	$-0.499481\pi$
$773$	−667.545	−	385.407i	−0.863577	−	0.498587i	−0.865209	+	0.501412i	$0.832814\pi$
$774$		0			0
$775$	126.599	+	73.0917i	0.163353	+	0.0943119i
$776$		0			0
$777$	−7.91727	−	300.515i	−0.0101895	−	0.386764i
$778$		0			0
$779$	369.712	−	596.675i	0.474598	−	0.765950i
$780$		0			0
$781$	−116.280	−	67.1342i	−0.148886	−	0.0859592i
$782$		0			0
$783$	87.0046	+	1098.77i	0.111117	+	1.40328i
$784$		0			0
$785$	835.980			1.06494
$786$		0			0
$787$	536.750	+	309.893i	0.682020	+	0.393764i	0.800616	−	0.599178i	$-0.204506\pi$
$787$	536.750	+	309.893i	0.682020	+	0.393764i	−0.118596	+	0.992943i	$0.537839\pi$
$788$		0			0
$789$	−415.922	−	678.480i	−0.527151	−	0.859924i
$790$		0			0
$791$			194.395i			0.245758i
$792$		0			0
$793$	1566.28	−	904.290i	1.97513	−	1.14034i
$794$		0			0
$795$	285.371	−	174.938i	0.358957	−	0.220048i
$796$		0			0
$797$	323.319	+	186.669i	0.405670	+	0.234214i	0.688928	−	0.724830i	$-0.258082\pi$
$797$	323.319	+	186.669i	0.405670	+	0.234214i	−0.283257	+	0.959044i	$0.591415\pi$
$798$		0			0
$799$	−522.681	−	905.309i	−0.654168	−	1.13305i
$800$		0			0
$801$	−34.8837	−	661.579i	−0.0435502	−	0.825942i
$802$		0			0
$803$	−46.7316	+	80.9415i	−0.0581962	+	0.100799i
$804$		0			0
$805$	68.0987	−	117.950i	0.0845946	−	0.146522i
$806$		0			0
$807$	5.05414	+	191.840i	0.00626288	+	0.237720i
$808$		0			0
$809$	−398.989			−0.493188			−0.246594	−	0.969119i	$-0.579311\pi$
$809$	−398.989			−0.493188			−0.246594	+	0.969119i	$0.579311\pi$
$810$		0			0
$811$	−492.099	−	284.113i	−0.606780	−	0.350325i	0.164924	−	0.986306i	$-0.447262\pi$
$811$	−492.099	−	284.113i	−0.606780	−	0.350325i	−0.771704	+	0.635982i	$0.780595\pi$
$812$		0			0
$813$	1570.01	−	41.3629i	1.93113	−	0.0508769i
$814$		0			0
$815$	1241.36			1.52315
$816$		0			0
$817$	−79.7286	+	42.7801i	−0.0975870	+	0.0523625i
$818$		0			0
$819$	16.4800	+	312.548i	0.0201221	+	0.381621i
$820$		0			0
$821$	319.131			0.388710			0.194355	−	0.980931i	$-0.437739\pi$
$821$	319.131			0.388710			0.194355	+	0.980931i	$0.437739\pi$
$822$		0			0
$823$	−413.122	−	715.548i	−0.501971	−	0.869438i	−0.999997	−	0.00227688i	$-0.999275\pi$
$823$	−413.122	−	715.548i	−0.501971	−	0.869438i	0.498027	−	0.867162i	$-0.334058\pi$
$824$		0			0
$825$	−25.1041	+	0.661383i	−0.0304292	+	0.000801676i
$826$		0			0
$827$	−640.947	−	370.051i	−0.775026	−	0.447462i	0.0596384	−	0.998220i	$-0.481005\pi$
$827$	−640.947	−	370.051i	−0.775026	−	0.447462i	−0.834665	+	0.550758i	$0.814339\pi$
$828$		0			0
$829$		−	1430.53i		−	1.72561i	−0.505539	−	0.862804i	$-0.668706\pi$
$829$		−	1430.53i		−	1.72561i	0.505539	−	0.862804i	$-0.331294\pi$
$830$		0			0
$831$	228.960	−	6.03209i	0.275523	−	0.00725883i
$832$		0			0
$833$	893.132			1.07219
$834$		0			0
$835$	494.281	−	285.373i	0.591953	−	0.341764i
$836$		0			0
$837$	650.739	+	310.004i	0.777465	+	0.370375i
$838$		0			0
$839$	235.161	+	135.771i	0.280288	+	0.161824i	0.633554	−	0.773699i	$-0.281596\pi$
$839$	235.161	+	135.771i	0.280288	+	0.161824i	−0.353266	+	0.935523i	$0.614929\pi$
$840$		0			0
$841$	−825.487			−0.981554
$842$		0			0
$843$	−1210.23	−	656.852i	−1.43562	−	0.779183i
$844$		0			0
$845$	720.710	−	1248.31i	0.852911	−	1.47728i
$846$		0			0
$847$	198.978			0.234921
$848$		0			0
$849$	−181.342	+	334.117i	−0.213594	+	0.393542i
$850$		0			0
$851$	761.444	−	439.620i	0.894764	−	0.516592i
$852$		0			0
$853$	28.6469	−	49.6180i	0.0335838	−	0.0581688i	−0.848745	−	0.528802i	$-0.822641\pi$
$853$	28.6469	−	49.6180i	0.0335838	−	0.0581688i	0.882329	+	0.470634i	$0.155975\pi$
$854$		0			0
$855$	20.3474	+	943.783i	0.0237981	+	1.10384i
$856$		0			0
$857$	−475.737	−	274.667i	−0.555119	−	0.320498i	0.196065	−	0.980591i	$-0.437184\pi$
$857$	−475.737	−	274.667i	−0.555119	−	0.320498i	−0.751184	+	0.660093i	$0.770517\pi$
$858$		0			0
$859$	124.904	+	216.339i	0.145406	+	0.251850i	0.929524	−	0.368761i	$-0.120218\pi$
$859$	124.904	+	216.339i	0.145406	+	0.251850i	−0.784119	+	0.620611i	$0.786885\pi$
$860$		0			0
$861$	−4.89453	−	185.781i	−0.00568470	−	0.215774i
$862$		0			0
$863$		−	33.3471i		−	0.0386409i	−0.999813	−	0.0193204i	$-0.993850\pi$
$863$		−	33.3471i		−	0.0386409i	0.999813	−	0.0193204i	$-0.00615027\pi$
$864$		0			0
$865$	−1131.74	−	653.412i	−1.30837	−	0.755390i
$866$		0			0
$867$	−133.133	−	217.175i	−0.153556	−	0.250491i
$868$		0			0
$869$		−	55.0615i		−	0.0633619i
$870$		0			0
$871$	895.493	−	1551.04i	1.02812	−	1.78076i
$872$		0			0
$873$	22.9014	+	434.332i	0.0262330	+	0.497517i
$874$		0			0
$875$	−90.3674	−	156.521i	−0.103277	−	0.178881i
$876$		0			0
$877$			895.620i			1.02123i	0.859809	+	0.510616i	$0.170583\pi$
$877$			895.620i			1.02123i	−0.859809	+	0.510616i	$0.829417\pi$
$878$		0			0
$879$	−421.368	+	258.307i	−0.479372	+	0.293865i
$880$		0			0
$881$	−449.443			−0.510151			−0.255075	−	0.966921i	$-0.582100\pi$
$881$	−449.443			−0.510151			−0.255075	+	0.966921i	$0.582100\pi$
$882$		0			0
$883$	−432.651	+	749.374i	−0.489979	+	0.848669i	−0.999933	−	0.0115329i	$-0.996329\pi$
$883$	−432.651	+	749.374i	−0.489979	+	0.848669i	0.509954	+	0.860201i	$0.329662\pi$
$884$		0			0
$885$	1439.81	+	781.454i	1.62690	+	0.882998i
$886$		0			0
$887$	806.404	−	465.577i	0.909136	−	0.524890i	0.0289829	−	0.999580i	$-0.490773\pi$
$887$	806.404	−	465.577i	0.909136	−	0.524890i	0.880153	+	0.474690i	$0.157440\pi$
$888$		0			0
$889$			181.812i			0.204513i
$890$		0			0
$891$	−123.140	+	13.0221i	−0.138205	+	0.0146151i
$892$		0			0
$893$	873.129	+	541.009i	0.977748	+	0.605833i
$894$		0			0
$895$		−	911.170i		−	1.01807i
$896$		0			0
$897$	−780.428	+	478.418i	−0.870042	+	0.533353i
$898$		0			0
$899$	−544.912	+	943.815i	−0.606131	+	1.04985i
$900$		0			0
$901$		−	390.816i		−	0.433758i
$902$		0			0
$903$	−11.4275	+	21.0548i	−0.0126550	+	0.0233165i
$904$		0			0
$905$	54.4563	+	31.4403i	0.0601727	+	0.0347407i
$906$		0			0
$907$	217.224	+	125.414i	0.239497	+	0.138274i	0.614946	−	0.788569i	$-0.289178\pi$
$907$	217.224	+	125.414i	0.239497	+	0.138274i	−0.375448	+	0.926843i	$0.622511\pi$
$908$		0			0
$909$	137.844	+	212.112i	0.151643	+	0.233347i
$910$		0			0
$911$	−680.835	+	393.080i	−0.747349	+	0.431482i	−0.824735	−	0.565519i	$-0.808676\pi$
$911$	−680.835	+	393.080i	−0.747349	+	0.431482i	0.0773862	+	0.997001i	$0.475343\pi$
$912$		0			0
$913$	−6.69861	+	11.6023i	−0.00733692	+	0.0127079i
$914$		0			0
$915$	688.945	−	1269.36i	0.752945	−	1.38728i
$916$		0			0
$917$	−135.677	−	234.999i	−0.147957	−	0.256269i
$918$		0			0
$919$	668.462			0.727380			0.363690	−	0.931520i	$-0.381517\pi$
$919$	668.462			0.727380			0.363690	+	0.931520i	$0.381517\pi$
$920$		0			0
$921$	−13.1319	−	498.446i	−0.0142583	−	0.541201i
$922$		0			0
$923$	910.751	−	1577.47i	0.986729	−	1.70907i
$924$		0			0
$925$			327.227i			0.353759i
$926$		0			0
$927$	−42.0400	−	797.300i	−0.0453505	−	0.860086i
$928$		0			0
$929$	786.563	−	1362.37i	0.846677	−	1.46649i	−0.0374806	−	0.999297i	$-0.511933\pi$
$929$	786.563	−	1362.37i	0.846677	−	1.46649i	0.884157	−	0.467190i	$-0.154733\pi$
$930$		0			0
$931$	−773.290	+	414.926i	−0.830601	+	0.445678i
$932$		0			0
$933$	404.616	+	660.037i	0.433672	+	0.707436i
$934$		0			0
$935$	−81.5947	+	141.326i	−0.0872671	+	0.151151i
$936$		0			0
$937$	−351.661	+	609.095i	−0.375305	+	0.650048i	−0.990373	−	0.138427i	$-0.955795\pi$
$937$	−351.661	+	609.095i	−0.375305	+	0.650048i	0.615067	+	0.788475i	$0.289129\pi$
$938$		0			0
$939$	−383.601	+	706.774i	−0.408520	+	0.752688i
$940$		0			0
$941$	−1043.02	+	602.186i	−1.10841	+	0.639943i	−0.938418	−	0.345502i	$-0.887709\pi$
$941$	−1043.02	+	602.186i	−1.10841	+	0.639943i	−0.169996	+	0.985445i	$0.554375\pi$
$942$		0			0
$943$	470.731	−	271.777i	0.499185	−	0.288205i
$944$		0			0
$945$	141.665	+	205.912i	0.149910	+	0.217896i
$946$		0			0
$947$	402.675	−	697.454i	0.425211	−	0.736487i	−0.571229	−	0.820791i	$-0.693533\pi$
$947$	402.675	−	697.454i	0.425211	−	0.736487i	0.996440	+	0.0843034i	$0.0268665\pi$
$948$		0			0
$949$	−1098.06	−	633.967i	−1.15707	−	0.668037i
$950$		0			0
$951$	−1409.46	−	764.983i	−1.48208	−	0.804398i
$952$		0			0
$953$	−19.1016	+	11.0283i	−0.0200437	+	0.0115722i	−0.509988	−	0.860181i	$-0.670350\pi$
$953$	−19.1016	+	11.0283i	−0.0200437	+	0.0115722i	0.489945	+	0.871754i	$0.337017\pi$
$954$		0			0
$955$	767.766	+	1329.81i	0.803943	+	1.39247i
$956$		0			0
$957$	−4.93073	−	187.155i	−0.00515228	−	0.195565i
$958$		0			0
$959$	−117.815	−	204.062i	−0.122852	−	0.212786i
$960$		0			0
$961$	−124.147	−	215.028i	−0.129185	−	0.223755i
$962$		0			0
$963$	−95.5117	+	62.0694i	−0.0991814	+	0.0644542i
$964$		0			0
$965$			1616.44i			1.67507i
$966$		0			0
$967$	1102.89			1.14052			0.570261	−	0.821463i	$-0.306842\pi$
$967$	1102.89			1.14052			0.570261	+	0.821463i	$0.306842\pi$
$968$		0			0
$969$	951.883	+	555.658i	0.982336	+	0.573435i
$970$		0			0
$971$	−1145.08	+	661.109i	−1.17927	+	0.680854i	−0.955847	−	0.293866i	$-0.905058\pi$
$971$	−1145.08	+	661.109i	−1.17927	+	0.680854i	−0.223427	+	0.974721i	$0.571725\pi$
$972$		0			0
$973$	−163.838	+	283.776i	−0.168384	+	0.291650i
$974$		0			0
$975$	−8.97241	−	340.565i	−0.00920247	−	0.349298i
$976$		0			0
$977$	−1364.73	−	787.927i	−1.39686	−	0.806476i	−0.402795	−	0.915290i	$-0.631961\pi$
$977$	−1364.73	−	787.927i	−1.39686	−	0.806476i	−0.994062	+	0.108814i	$0.965295\pi$
$978$		0			0
$979$			112.531i			0.114945i
$980$		0			0
$981$	−928.260	−	472.599i	−0.946239	−	0.481752i
$982$		0			0
$983$	−181.250	−	104.645i	−0.184384	−	0.106454i	0.404967	−	0.914331i	$-0.367283\pi$
$983$	−181.250	−	104.645i	−0.184384	−	0.106454i	−0.589351	+	0.807877i	$0.700616\pi$
$984$		0			0
$985$	1104.87			1.12170
$986$		0			0
$987$	271.858	−	7.16228i	0.275439	−	0.00725662i
$988$		0			0
$989$	−70.0655			−0.0708448
$990$		0			0
$991$	117.245	−	67.6913i	0.118310	−	0.0683061i	−0.439677	−	0.898156i	$-0.644907\pi$
$991$	117.245	−	67.6913i	0.118310	−	0.0683061i	0.557987	+	0.829850i	$0.311574\pi$
$992$		0			0
$993$	−23.2772	−	883.531i	−0.0234413	−	0.889759i
$994$		0			0
$995$	−18.0391	+	31.2446i	−0.0181297	+	0.0314016i
$996$		0			0
$997$	−1087.30			−1.09057			−0.545285	−	0.838251i	$-0.683579\pi$
$997$	−1087.30			−1.09057			−0.545285	+	0.838251i	$0.683579\pi$
$998$		0			0
$999$	127.364	+	1608.47i	0.127492	+	1.61008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.bl.a.373.15	yes	80
3.2	odd	2		2052.3.bl.a.145.9		80
9.2	odd	6		2052.3.s.a.829.32		80
9.7	even	3		684.3.s.a.601.1	yes	80
19.8	odd	6		684.3.s.a.445.1	✓	80
57.8	even	6		2052.3.s.a.901.32		80
171.65	even	6		2052.3.bl.a.1585.9		80
171.160	odd	6	inner	684.3.bl.a.673.15	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.1	✓	80	19.8	odd	6
684.3.s.a.601.1	yes	80	9.7	even	3
684.3.bl.a.373.15	yes	80	1.1	even	1	trivial
684.3.bl.a.673.15	yes	80	171.160	odd	6	inner
2052.3.s.a.829.32		80	9.2	odd	6
2052.3.s.a.901.32		80	57.8	even	6
2052.3.bl.a.145.9		80	3.2	odd	2
2052.3.bl.a.1585.9		80	171.65	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43106 + 2.63668i) q^{3} +5.52048 q^{5} +(0.838417 + 1.45218i) q^{7} +(-4.90416 - 7.54647i) q^{9} +O(q^{10})\)	\(q+(-1.43106 + 2.63668i) q^{3} +5.52048 q^{5} +(0.838417 + 1.45218i) q^{7} +(-4.90416 - 7.54647i) q^{9} +(0.764365 + 1.32392i) q^{11} +(-17.9605 + 10.3695i) q^{13} +(-7.90012 + 14.5557i) q^{15} +(9.66839 + 16.7462i) q^{17} +(-16.1509 - 10.0074i) q^{19} +(-5.02876 + 0.132486i) q^{21} +(-7.35650 - 12.7418i) q^{23} +5.47574 q^{25} +(26.9158 - 2.13128i) q^{27} +40.8226i q^{29} +(23.1199 + 13.3483i) q^{31} +(-4.58460 + 0.120784i) q^{33} +(4.62847 + 8.01674i) q^{35} +59.7594i q^{37} +(-1.63857 - 62.1953i) q^{39} +36.9438i q^{41} +(2.38108 - 4.12414i) q^{43} +(-27.0733 - 41.6602i) q^{45} -54.0607 q^{47} +(23.0941 - 40.0002i) q^{49} +(-57.9902 + 1.52779i) q^{51} +(-17.5032 - 10.1055i) q^{53} +(4.21966 + 7.30867i) q^{55} +(49.4992 - 28.2635i) q^{57} -98.9167i q^{59} -87.2069 q^{61} +(6.84711 - 13.4488i) q^{63} +(-99.1504 + 57.2445i) q^{65} +(-74.7887 + 43.1793i) q^{67} +(44.1237 - 1.16247i) q^{69} +(-76.0630 + 43.9150i) q^{71} +(30.5689 + 52.9469i) q^{73} +(-7.83609 + 14.4378i) q^{75} +(-1.28171 + 2.21999i) q^{77} +(-31.1924 - 18.0089i) q^{79} +(-32.8984 + 74.0182i) q^{81} +(4.38181 + 7.58953i) q^{83} +(53.3742 + 92.4469i) q^{85} +(-107.636 - 58.4194i) q^{87} +(63.7489 + 36.8055i) q^{89} +(-30.1167 - 17.3879i) q^{91} +(-68.2810 + 41.8577i) q^{93} +(-89.1607 - 55.2459i) q^{95} +(-41.8517 - 24.1631i) q^{97} +(6.24234 - 12.2610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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