LMFDB - Embedded newform 684.3.t.a.265.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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, 3]))

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

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (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			265.2
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.90955 - 0.731127i) q^{3} +(-3.02121 + 5.23289i) q^{5} +(6.41336 + 11.1083i) q^{7} +(7.93091 + 4.25449i) q^{9} +O(q^{10})$	\(q+(-2.90955 - 0.731127i) q^{3} +(-3.02121 + 5.23289i) q^{5} +(6.41336 + 11.1083i) q^{7} +(7.93091 + 4.25449i) q^{9} +(3.09158 + 5.35477i) q^{11} +(7.08784 + 4.09217i) q^{13} +(12.6163 - 13.0164i) q^{15} +3.93927 q^{17} +(-18.6784 + 3.48124i) q^{19} +(-10.5384 - 37.0090i) q^{21} +(9.89019 - 17.1303i) q^{23} +(-5.75543 - 9.96870i) q^{25} +(-19.9648 - 18.1771i) q^{27} +(6.99256 - 4.03715i) q^{29} +(47.4342 + 27.3862i) q^{31} +(-5.08007 - 17.8403i) q^{33} -77.5045 q^{35} +65.6424i q^{37} +(-17.6305 - 17.0885i) q^{39} +(-53.7711 - 31.0448i) q^{41} +(-2.18842 - 3.79045i) q^{43} +(-46.2242 + 28.6478i) q^{45} +(33.2326 + 57.5606i) q^{47} +(-57.7625 + 100.048i) q^{49} +(-11.4615 - 2.88011i) q^{51} -84.8469i q^{53} -37.3613 q^{55} +(56.8907 + 3.52742i) q^{57} +(28.9792 + 16.7311i) q^{59} +(-24.0816 - 41.7106i) q^{61} +(3.60372 + 115.384i) q^{63} +(-42.8277 + 24.7266i) q^{65} +(-86.2509 - 49.7970i) q^{67} +(-41.3004 + 42.6104i) q^{69} +130.931i q^{71} +71.9876 q^{73} +(9.45731 + 33.2123i) q^{75} +(-39.6548 + 68.6842i) q^{77} +(-31.6592 + 18.2784i) q^{79} +(44.7986 + 67.4840i) q^{81} +(10.0429 + 17.3949i) q^{83} +(-11.9014 + 20.6138i) q^{85} +(-23.2968 + 6.63384i) q^{87} -131.363i q^{89} +104.978i q^{91} +(-117.989 - 114.362i) q^{93} +(38.2143 - 108.259i) q^{95} +(-87.5043 + 50.5206i) q^{97} +(1.73718 + 55.6213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−2.90955	−	0.731127i	−0.969848	−	0.243709i
$3$	−2.90955	−	0.731127i	−0.969848	−	0.243709i
$4$		0			0
$5$	−3.02121	+	5.23289i	−0.604242	+	1.04658i	0.387929	+	0.921689i	$0.373191\pi$
$5$	−3.02121	+	5.23289i	−0.604242	+	1.04658i	−0.992171	+	0.124889i	$0.960143\pi$
$6$		0			0
$7$	6.41336	+	11.1083i	0.916195	+	1.58690i	0.805143	+	0.593081i	$0.202089\pi$
$7$	6.41336	+	11.1083i	0.916195	+	1.58690i	0.111052	+	0.993815i	$0.464578\pi$
$8$		0			0
$9$	7.93091	+	4.25449i	0.881212	+	0.472722i
$10$		0			0
$11$	3.09158	+	5.35477i	0.281053	+	0.486798i	0.971644	−	0.236447i	$-0.0759831\pi$
$11$	3.09158	+	5.35477i	0.281053	+	0.486798i	−0.690592	+	0.723245i	$0.742650\pi$
$12$		0			0
$13$	7.08784	+	4.09217i	0.545218	+	0.314782i	0.747191	−	0.664609i	$-0.231402\pi$
$13$	7.08784	+	4.09217i	0.545218	+	0.314782i	−0.201973	+	0.979391i	$0.564735\pi$
$14$		0			0
$15$	12.6163	−	13.0164i	0.841084	−	0.867763i
$16$		0			0
$17$	3.93927			0.231722			0.115861	−	0.993265i	$-0.463037\pi$
$17$	3.93927			0.231722			0.115861	+	0.993265i	$0.463037\pi$
$18$		0			0
$19$	−18.6784	+	3.48124i	−0.983071	+	0.183223i
$19$	−18.6784	+	3.48124i	−0.983071	+	0.183223i
$20$		0			0
$21$	−10.5384	−	37.0090i	−0.501829	−	1.76233i
$22$		0			0
$23$	9.89019	−	17.1303i	0.430008	−	0.744796i	−0.566865	−	0.823810i	$-0.691844\pi$
$23$	9.89019	−	17.1303i	0.430008	−	0.744796i	0.996873	+	0.0790145i	$0.0251773\pi$
$24$		0			0
$25$	−5.75543	−	9.96870i	−0.230217	−	0.398748i
$26$		0			0
$27$	−19.9648	−	18.1771i	−0.739435	−	0.673227i
$28$		0			0
$29$	6.99256	−	4.03715i	0.241123	−	0.139212i	−0.374570	−	0.927199i	$-0.622210\pi$
$29$	6.99256	−	4.03715i	0.241123	−	0.139212i	0.615693	+	0.787986i	$0.288876\pi$
$30$		0			0
$31$	47.4342	+	27.3862i	1.53014	+	0.883425i	0.999355	+	0.0359163i	$0.0114350\pi$
$31$	47.4342	+	27.3862i	1.53014	+	0.883425i	0.530782	+	0.847509i	$0.321898\pi$
$32$		0			0
$33$	−5.08007	−	17.8403i	−0.153942	−	0.540615i
$34$		0			0
$35$	−77.5045			−2.21441
$36$		0			0
$37$			65.6424i			1.77412i	0.461656	+	0.887059i	$0.347255\pi$
$37$			65.6424i			1.77412i	−0.461656	+	0.887059i	$0.652745\pi$
$38$		0			0
$39$	−17.6305	−	17.0885i	−0.452064	−	0.438165i
$40$		0			0
$41$	−53.7711	−	31.0448i	−1.31149	−	0.757189i	−0.329147	−	0.944279i	$-0.606761\pi$
$41$	−53.7711	−	31.0448i	−1.31149	−	0.757189i	−0.982343	+	0.187089i	$0.940095\pi$
$42$		0			0
$43$	−2.18842	−	3.79045i	−0.0508934	−	0.0881500i	0.839456	−	0.543427i	$-0.182874\pi$
$43$	−2.18842	−	3.79045i	−0.0508934	−	0.0881500i	−0.890350	+	0.455277i	$0.849540\pi$
$44$		0			0
$45$	−46.2242	+	28.6478i	−1.02721	+	0.636619i
$46$		0			0
$47$	33.2326	+	57.5606i	0.707077	+	1.22469i	0.965937	+	0.258779i	$0.0833200\pi$
$47$	33.2326	+	57.5606i	0.707077	+	1.22469i	−0.258860	+	0.965915i	$0.583347\pi$
$48$		0			0
$49$	−57.7625	+	100.048i	−1.17883	+	2.04179i
$50$		0			0
$51$	−11.4615	−	2.88011i	−0.224735	−	0.0564727i
$52$		0			0
$53$		−	84.8469i		−	1.60088i	−0.599410	−	0.800442i	$-0.704598\pi$
$53$		−	84.8469i		−	1.60088i	0.599410	−	0.800442i	$-0.295402\pi$
$54$		0			0
$55$	−37.3613			−0.679296
$56$		0			0
$57$	56.8907	+	3.52742i	0.998083	+	0.0618846i
$58$		0			0
$59$	28.9792	+	16.7311i	0.491172	+	0.283578i	0.725061	−	0.688685i	$-0.241812\pi$
$59$	28.9792	+	16.7311i	0.491172	+	0.283578i	−0.233888	+	0.972263i	$0.575145\pi$
$60$		0			0
$61$	−24.0816	−	41.7106i	−0.394781	−	0.683780i	0.598293	−	0.801278i	$-0.295846\pi$
$61$	−24.0816	−	41.7106i	−0.394781	−	0.683780i	−0.993073	+	0.117498i	$0.962513\pi$
$62$		0			0
$63$	3.60372	+	115.384i	0.0572019	+	1.83150i
$64$		0			0
$65$	−42.8277	+	24.7266i	−0.658888	+	0.380409i
$66$		0			0
$67$	−86.2509	−	49.7970i	−1.28733	−	0.743239i	−0.309151	−	0.951013i	$-0.600045\pi$
$67$	−86.2509	−	49.7970i	−1.28733	−	0.743239i	−0.978177	+	0.207774i	$0.933378\pi$
$68$		0			0
$69$	−41.3004	+	42.6104i	−0.598556	+	0.617542i
$70$		0			0
$71$			130.931i			1.84410i	0.387066	+	0.922052i	$0.373488\pi$
$71$			130.931i			1.84410i	−0.387066	+	0.922052i	$0.626512\pi$
$72$		0			0
$73$	71.9876			0.986131			0.493065	−	0.869992i	$-0.335876\pi$
$73$	71.9876			0.986131			0.493065	+	0.869992i	$0.335876\pi$
$74$		0			0
$75$	9.45731	+	33.2123i	0.126097	+	0.442831i
$76$		0			0
$77$	−39.6548	+	68.6842i	−0.514998	+	0.892003i
$78$		0			0
$79$	−31.6592	+	18.2784i	−0.400749	+	0.231372i	−0.686807	−	0.726840i	$-0.740988\pi$
$79$	−31.6592	+	18.2784i	−0.400749	+	0.231372i	0.286058	+	0.958212i	$0.407655\pi$
$80$		0			0
$81$	44.7986	+	67.4840i	0.553069	+	0.833136i
$82$		0			0
$83$	10.0429	+	17.3949i	0.120999	+	0.209577i	0.920162	−	0.391538i	$-0.128057\pi$
$83$	10.0429	+	17.3949i	0.120999	+	0.209577i	−0.799163	+	0.601115i	$0.794723\pi$
$84$		0			0
$85$	−11.9014	+	20.6138i	−0.140016	+	0.242515i
$86$		0			0
$87$	−23.2968	+	6.63384i	−0.267780	+	0.0762510i
$88$		0			0
$89$		−	131.363i		−	1.47598i	−0.674810	−	0.737992i	$-0.735774\pi$
$89$		−	131.363i		−	1.47598i	0.674810	−	0.737992i	$-0.264226\pi$
$90$		0			0
$91$			104.978i			1.15361i
$92$		0			0
$93$	−117.989	−	114.362i	−1.26870	−	1.22970i
$94$		0			0
$95$	38.2143	−	108.259i	0.402256	−	1.13957i
$96$		0			0
$97$	−87.5043	+	50.5206i	−0.902106	+	0.520831i	−0.877883	−	0.478876i	$-0.841045\pi$
$97$	−87.5043	+	50.5206i	−0.902106	+	0.520831i	−0.0242230	+	0.999707i	$0.507711\pi$
$98$		0			0
$99$	1.73718	+	55.6213i	0.0175473	+	0.561831i
$100$		0			0
$101$	−8.84210	−	15.3150i	−0.0875456	−	0.151633i	0.818928	−	0.573897i	$-0.194569\pi$
$101$	−8.84210	−	15.3150i	−0.0875456	−	0.151633i	−0.906473	+	0.422264i	$0.861236\pi$
$102$		0			0
$103$	34.8444	+	20.1174i	0.338296	+	0.195315i	0.659518	−	0.751689i	$-0.270760\pi$
$103$	34.8444	+	20.1174i	0.338296	+	0.195315i	−0.321223	+	0.947004i	$0.604094\pi$
$104$		0			0
$105$	225.503	+	56.6656i	2.14765	+	0.539673i
$106$		0			0
$107$		−	73.7576i		−	0.689324i	−0.938727	−	0.344662i	$-0.887994\pi$
$107$		−	73.7576i		−	0.689324i	0.938727	−	0.344662i	$-0.112006\pi$
$108$		0			0
$109$		−	45.1885i		−	0.414573i	−0.978280	−	0.207287i	$-0.933537\pi$
$109$		−	45.1885i		−	0.414573i	0.978280	−	0.207287i	$-0.0664633\pi$
$110$		0			0
$111$	47.9929	−	190.989i	0.432368	−	1.72063i
$112$		0			0
$113$	−138.251	−	79.8194i	−1.22346	−	0.706366i	−0.257808	−	0.966196i	$-0.583000\pi$
$113$	−138.251	−	79.8194i	−1.22346	−	0.706366i	−0.965654	+	0.259830i	$0.916333\pi$
$114$		0			0
$115$	59.7607	+	103.509i	0.519658	+	0.900074i
$116$		0			0
$117$	38.8029	+	62.6098i	0.331649	+	0.535126i
$118$		0			0
$119$	25.2640	+	43.7585i	0.212302	+	0.367718i
$120$		0			0
$121$	41.3843	−	71.6797i	0.342019	−	0.592394i
$122$		0			0
$123$	133.752	+	129.640i	1.08741	+	1.05398i
$124$		0			0
$125$	−81.5070			−0.652056
$126$		0			0
$127$		−	52.9056i		−	0.416579i	−0.978067	−	0.208290i	$-0.933210\pi$
$127$		−	52.9056i		−	0.416579i	0.978067	−	0.208290i	$-0.0667897\pi$
$128$		0			0
$129$	3.59600	+	12.6285i	0.0278760	+	0.0978953i
$130$		0			0
$131$	−77.4058	+	134.071i	−0.590884	+	1.02344i	0.403230	+	0.915099i	$0.367887\pi$
$131$	−77.4058	+	134.071i	−0.590884	+	1.02344i	−0.994114	+	0.108342i	$0.965446\pi$
$132$		0			0
$133$	−158.462	−	185.158i	−1.19144	−	1.39216i
$134$		0			0
$135$	155.437	−	49.5564i	1.15138	−	0.367085i
$136$		0			0
$137$	−94.1384	−	163.053i	−0.687142	−	1.19016i	−0.972759	−	0.231821i	$-0.925532\pi$
$137$	−94.1384	−	163.053i	−0.687142	−	1.19016i	0.285617	−	0.958344i	$-0.407802\pi$
$138$		0			0
$139$	−91.5760	+	158.614i	−0.658820	+	1.14111i	0.322101	+	0.946705i	$0.395611\pi$
$139$	−91.5760	+	158.614i	−0.658820	+	1.14111i	−0.980921	+	0.194405i	$0.937722\pi$
$140$		0			0
$141$	−54.6077	−	191.772i	−0.387289	−	1.36009i
$142$		0			0
$143$			50.6050i			0.353881i
$144$		0			0
$145$			48.7884i			0.336472i
$146$		0			0
$147$	241.210	−	248.861i	1.64088	−	1.69293i
$148$		0			0
$149$	94.9284	−	164.421i	0.637103	−	1.10350i	−0.348962	−	0.937137i	$-0.613466\pi$
$149$	94.9284	−	164.421i	0.637103	−	1.10350i	0.986065	−	0.166359i	$-0.0532009\pi$
$150$		0			0
$151$	73.4448	−	42.4034i	0.486389	−	0.280817i	−0.236686	−	0.971586i	$-0.576061\pi$
$151$	73.4448	−	42.4034i	0.486389	−	0.280817i	0.723075	+	0.690769i	$0.242728\pi$
$152$		0			0
$153$	31.2420	+	16.7596i	0.204196	+	0.109540i
$154$		0			0
$155$	−286.618	+	165.479i	−1.84915	+	1.06761i
$156$		0			0
$157$	−36.6048	+	63.4014i	−0.233152	+	0.403830i	−0.958734	−	0.284305i	$-0.908237\pi$
$157$	−36.6048	+	63.4014i	−0.233152	+	0.403830i	0.725582	+	0.688135i	$0.241570\pi$
$158$		0			0
$159$	−62.0338	+	246.866i	−0.390150	+	1.55262i
$160$		0			0
$161$	253.717			1.57588
$162$		0			0
$163$	69.7807			0.428103			0.214051	−	0.976822i	$-0.431334\pi$
$163$	69.7807			0.428103			0.214051	+	0.976822i	$0.431334\pi$
$164$		0			0
$165$	108.704	+	27.3158i	0.658814	+	0.165550i
$166$		0			0
$167$	−106.631	−	61.5635i	−0.638510	−	0.368644i	0.145531	−	0.989354i	$-0.453511\pi$
$167$	−106.631	−	61.5635i	−0.638510	−	0.368644i	−0.784040	+	0.620710i	$0.786844\pi$
$168$		0			0
$169$	−51.0084	−	88.3491i	−0.301825	−	0.522776i
$170$		0			0
$171$	−162.947	−	51.8575i	−0.952908	−	0.303261i
$172$		0			0
$173$	34.7548	−	20.0657i	0.200895	−	0.115987i	−0.396178	−	0.918174i	$-0.629664\pi$
$173$	34.7548	−	20.0657i	0.200895	−	0.115987i	0.597073	+	0.802187i	$0.296330\pi$
$174$		0			0
$175$	73.8234	−	127.866i	0.421848	−	0.730662i
$176$		0			0
$177$	−72.0836	−	69.8674i	−0.407252	−	0.394731i
$178$		0			0
$179$		−	13.9784i		−	0.0780914i	−0.999237	−	0.0390457i	$-0.987568\pi$
$179$		−	13.9784i		−	0.0780914i	0.999237	−	0.0390457i	$-0.0124318\pi$
$180$		0			0
$181$			114.847i			0.634516i	0.948339	+	0.317258i	$0.102762\pi$
$181$			114.847i			0.634516i	−0.948339	+	0.317258i	$0.897238\pi$
$182$		0			0
$183$	39.5708	+	138.966i	0.216234	+	0.759375i
$184$		0			0
$185$	−343.499	−	198.319i	−1.85675	−	1.07200i
$186$		0			0
$187$	12.1786	+	21.0939i	0.0651260	+	0.112802i
$188$		0			0
$189$	73.8754	−	338.351i	0.390875	−	1.79021i
$190$		0			0
$191$	−19.9028	−	34.4727i	−0.104203	−	0.180485i	0.809209	−	0.587521i	$-0.199896\pi$
$191$	−19.9028	−	34.4727i	−0.104203	−	0.180485i	−0.913412	+	0.407035i	$0.866563\pi$
$192$		0			0
$193$	286.888	+	165.635i	1.48647	+	0.858212i	0.999881	−	0.0154206i	$-0.00490874\pi$
$193$	286.888	+	165.635i	1.48647	+	0.858212i	0.486586	+	0.873633i	$0.338242\pi$
$194$		0			0
$195$	142.687	−	40.6306i	0.731731	−	0.208362i
$196$		0			0
$197$	76.0755			0.386170			0.193085	−	0.981182i	$-0.438151\pi$
$197$	76.0755			0.386170			0.193085	+	0.981182i	$0.438151\pi$
$198$		0			0
$199$	271.466			1.36415			0.682075	−	0.731283i	$-0.261078\pi$
$199$	271.466			1.36415			0.682075	+	0.731283i	$0.261078\pi$
$200$		0			0
$201$	214.543	+	207.947i	1.06738	+	1.03456i
$202$		0			0
$203$	89.6916	+	51.7835i	0.441831	+	0.255091i
$204$		0			0
$205$	324.908	−	187.586i	1.58492	−	0.915051i
$206$		0			0
$207$	151.319	−	93.7811i	0.731009	−	0.453049i
$208$		0			0
$209$	−76.3869	−	89.2558i	−0.365487	−	0.427061i
$210$		0			0
$211$	109.762	+	63.3709i	0.520198	+	0.300336i	0.737015	−	0.675876i	$-0.236234\pi$
$211$	109.762	+	63.3709i	0.520198	+	0.300336i	−0.216818	+	0.976212i	$0.569568\pi$
$212$		0			0
$213$	95.7274	−	380.951i	0.449425	−	1.78850i
$214$		0			0
$215$	26.4467			0.123008
$216$		0			0
$217$			702.550i			3.23756i
$218$		0			0
$219$	−209.451	−	52.6320i	−0.956398	−	0.240329i
$220$		0			0
$221$	27.9209	+	16.1201i	0.126339	+	0.0729418i
$222$		0			0
$223$	36.8682	−	21.2859i	0.165328	−	0.0954524i	−0.415053	−	0.909797i	$-0.636237\pi$
$223$	36.8682	−	21.2859i	0.165328	−	0.0954524i	0.580381	+	0.814345i	$0.302904\pi$
$224$		0			0
$225$	−3.23402	−	103.547i	−0.0143734	−	0.460210i
$226$		0			0
$227$	−247.903	+	143.127i	−1.09208	+	0.630514i	−0.934130	−	0.356933i	$-0.883823\pi$
$227$	−247.903	+	143.127i	−1.09208	+	0.630514i	−0.157952	+	0.987447i	$0.550489\pi$
$228$		0			0
$229$	51.5721	−	89.3256i	0.225206	−	0.390068i	−0.731175	−	0.682190i	$-0.761028\pi$
$229$	51.5721	−	89.3256i	0.225206	−	0.390068i	0.956381	+	0.292122i	$0.0943612\pi$
$230$		0			0
$231$	165.594	−	170.847i	0.716859	−	0.739598i
$232$		0			0
$233$	367.035			1.57526			0.787630	−	0.616149i	$-0.211308\pi$
$233$	367.035			1.57526			0.787630	+	0.616149i	$0.211308\pi$
$234$		0			0
$235$	−401.611			−1.70898
$236$		0			0
$237$	105.478	−	30.0350i	0.445053	−	0.126730i
$238$		0			0
$239$	−81.1361	+	140.532i	−0.339481	+	0.587999i	−0.984335	−	0.176307i	$-0.943585\pi$
$239$	−81.1361	+	140.532i	−0.339481	+	0.587999i	0.644854	+	0.764306i	$0.276918\pi$
$240$		0			0
$241$	−44.8582	+	25.8989i	−0.186133	+	0.107464i	−0.590171	−	0.807278i	$-0.700940\pi$
$241$	−44.8582	+	25.8989i	−0.186133	+	0.107464i	0.404038	+	0.914742i	$0.367606\pi$
$242$		0			0
$243$	−81.0041	−	229.101i	−0.333350	−	0.942803i
$244$		0			0
$245$	−349.025	−	604.529i	−1.42459	−	2.46747i
$246$		0			0
$247$	−146.635	−	51.7605i	−0.593664	−	0.209556i
$248$		0			0
$249$	−16.5025	−	57.9538i	−0.0662751	−	0.232746i
$250$		0			0
$251$	266.417			1.06142			0.530710	−	0.847553i	$-0.321925\pi$
$251$	266.417			1.06142			0.530710	+	0.847553i	$0.321925\pi$
$252$		0			0
$253$	122.305			0.483420
$254$		0			0
$255$	49.6988	−	51.2753i	0.194897	−	0.201080i
$256$		0			0
$257$	−220.621	−	127.376i	−0.858449	−	0.495626i	0.00504349	−	0.999987i	$-0.498395\pi$
$257$	−220.621	−	127.376i	−0.858449	−	0.495626i	−0.863493	+	0.504361i	$0.831728\pi$
$258$		0			0
$259$	−729.173	+	420.988i	−2.81534	+	1.62544i
$260$		0			0
$261$	72.6334	−	2.26851i	0.278289	−	0.00869160i
$262$		0			0
$263$	37.3821	+	64.7477i	0.142137	+	0.246189i	0.928301	−	0.371829i	$-0.121269\pi$
$263$	37.3821	+	64.7477i	0.142137	+	0.246189i	−0.786164	+	0.618018i	$0.787936\pi$
$264$		0			0
$265$	443.995	+	256.340i	1.67545	+	0.967322i
$266$		0			0
$267$	−96.0427	+	382.205i	−0.359710	+	1.43148i
$268$		0			0
$269$			392.096i			1.45761i	0.684723	+	0.728804i	$0.259923\pi$
$269$			392.096i			1.45761i	−0.684723	+	0.728804i	$0.740077\pi$
$270$		0			0
$271$	407.914			1.50522			0.752609	−	0.658468i	$-0.228795\pi$
$271$	407.914			1.50522			0.752609	+	0.658468i	$0.228795\pi$
$272$		0			0
$273$	76.7524	−	305.439i	0.281144	−	1.11882i
$274$		0			0
$275$	35.5868	−	61.6381i	0.129406	−	0.224138i
$276$		0			0
$277$	−124.657	−	215.913i	−0.450026	−	0.779468i	0.548361	−	0.836242i	$-0.315252\pi$
$277$	−124.657	−	215.913i	−0.450026	−	0.779468i	−0.998387	+	0.0567740i	$0.981919\pi$
$278$		0			0
$279$	259.682	+	419.006i	0.930761	+	1.50181i
$280$		0			0
$281$	228.651	−	132.012i	0.813705	−	0.469793i	−0.0345362	−	0.999403i	$-0.510995\pi$
$281$	228.651	−	132.012i	0.813705	−	0.469793i	0.848241	+	0.529611i	$0.177662\pi$
$282$		0			0
$283$	111.895	−	193.807i	0.395388	−	0.684832i	−0.597763	−	0.801673i	$-0.703944\pi$
$283$	111.895	−	193.807i	0.395388	−	0.684832i	0.993151	+	0.116841i	$0.0372769\pi$
$284$		0			0
$285$	−190.338	+	287.046i	−0.667851	+	1.00718i
$286$		0			0
$287$		−	796.405i		−	2.77493i
$288$		0			0
$289$	−273.482			−0.946305
$290$		0			0
$291$	291.535	−	83.0153i	1.00184	−	0.285276i
$292$		0			0
$293$	149.394	+	86.2527i	0.509878	+	0.294378i	0.732783	−	0.680462i	$-0.238221\pi$
$293$	149.394	+	86.2527i	0.509878	+	0.294378i	−0.222906	+	0.974840i	$0.571554\pi$
$294$		0			0
$295$	−175.104	+	101.097i	−0.593574	+	0.342700i
$296$		0			0
$297$	35.6118	−	163.103i	0.119905	−	0.549168i
$298$		0			0
$299$	140.200	−	80.9446i	0.468897	−	0.270718i
$300$		0			0
$301$	28.0702	−	48.6191i	0.0932566	−	0.161525i
$302$		0			0
$303$	14.5293	+	51.0243i	0.0479515	+	0.168397i
$304$		0			0
$305$	291.023			0.954172
$306$		0			0
$307$			284.301i			0.926062i	0.886342	+	0.463031i	$0.153238\pi$
$307$			284.301i			0.926062i	−0.886342	+	0.463031i	$0.846762\pi$
$308$		0			0
$309$	−86.6731	−	84.0083i	−0.280495	−	0.271872i
$310$		0			0
$311$	−64.4237	+	111.585i	−0.207150	+	0.358795i	−0.950816	−	0.309757i	$-0.899752\pi$
$311$	−64.4237	+	111.585i	−0.207150	+	0.358795i	0.743665	+	0.668552i	$0.233086\pi$
$312$		0			0
$313$	205.933	+	356.686i	0.657932	+	1.13957i	0.981150	+	0.193247i	$0.0619020\pi$
$313$	205.933	+	356.686i	0.657932	+	1.13957i	−0.323218	+	0.946325i	$0.604765\pi$
$314$		0			0
$315$	−614.681	−	329.742i	−1.95137	−	1.04680i
$316$		0			0
$317$	−232.494	+	134.230i	−0.733419	+	0.423440i	−0.819672	−	0.572833i	$-0.805844\pi$
$317$	−232.494	+	134.230i	−0.733419	+	0.423440i	0.0862524	+	0.996273i	$0.472511\pi$
$318$		0			0
$319$	43.2361	+	24.9624i	0.135536	+	0.0782519i
$320$		0			0
$321$	−53.9262	+	214.601i	−0.167994	+	0.668539i
$322$		0			0
$323$	−73.5791	+	13.7135i	−0.227799	+	0.0424568i
$324$		0			0
$325$		−	94.2087i		−	0.289873i
$326$		0			0
$327$	−33.0385	+	131.478i	−0.101035	+	0.402073i
$328$		0			0
$329$	−426.266	+	738.314i	−1.29564	+	2.24412i
$330$		0			0
$331$	111.890	−	64.5996i	0.338035	−	0.195165i	−0.321368	−	0.946955i	$-0.604142\pi$
$331$	111.890	−	64.5996i	0.338035	−	0.195165i	0.659403	+	0.751790i	$0.270809\pi$
$332$		0			0
$333$	−279.275	+	520.603i	−0.838664	+	1.56337i
$334$		0			0
$335$	521.165	−	300.895i	1.55572	−	0.898193i
$336$		0			0
$337$	182.771	+	105.523i	0.542346	+	0.313124i	0.746029	−	0.665913i	$-0.231958\pi$
$337$	182.771	+	105.523i	0.542346	+	0.313124i	−0.203683	+	0.979037i	$0.565291\pi$
$338$		0			0
$339$	343.890	+	333.317i	1.01442	+	0.983237i
$340$		0			0
$341$			338.666i			0.993156i
$342$		0			0
$343$	−853.297			−2.48775
$344$		0			0
$345$	−98.1985	−	344.855i	−0.284633	−	0.999581i
$346$		0			0
$347$	116.820	−	202.337i	0.336656	−	0.583105i	−0.647146	−	0.762366i	$-0.724037\pi$
$347$	116.820	−	202.337i	0.336656	−	0.583105i	0.983801	+	0.179261i	$0.0573708\pi$
$348$		0			0
$349$	138.421	+	239.752i	0.396621	+	0.686968i	0.993307	−	0.115507i	$-0.0368493\pi$
$349$	138.421	+	239.752i	0.396621	+	0.686968i	−0.596685	+	0.802475i	$0.703516\pi$
$350$		0			0
$351$	−67.1231	−	210.536i	−0.191234	−	0.599817i
$352$		0			0
$353$	−185.483	−	321.267i	−0.525449	−	0.910104i	−0.999561	−	0.0296395i	$-0.990564\pi$
$353$	−185.483	−	321.267i	−0.525449	−	0.910104i	0.474112	−	0.880465i	$-0.342769\pi$
$354$		0			0
$355$	−685.150	−	395.571i	−1.93000	−	1.11429i
$356$		0			0
$357$	−41.5137	−	145.788i	−0.116285	−	0.408371i
$358$		0			0
$359$	361.002			1.00558			0.502788	−	0.864409i	$-0.332307\pi$
$359$	361.002			1.00558			0.502788	+	0.864409i	$0.332307\pi$
$360$		0			0
$361$	336.762	−	130.048i	0.932859	−	0.360243i
$362$		0			0
$363$	−172.816	+	178.298i	−0.476078	+	0.491179i
$364$		0			0
$365$	−217.490	+	376.703i	−0.595862	+	1.03206i
$366$		0			0
$367$	84.8641	+	146.989i	0.231237	+	0.400515i	0.958172	−	0.286191i	$-0.0923893\pi$
$367$	84.8641	+	146.989i	0.231237	+	0.400515i	−0.726935	+	0.686706i	$0.759056\pi$
$368$		0			0
$369$	−294.374	−	474.982i	−0.797761	−	1.28721i
$370$		0			0
$371$	942.502	−	544.154i	2.54044	−	1.46672i
$372$		0			0
$373$	−554.119	−	319.921i	−1.48557	−	0.857697i	−0.485710	−	0.874120i	$-0.661439\pi$
$373$	−554.119	−	319.921i	−1.48557	−	0.857697i	−0.999865	+	0.0164233i	$0.994772\pi$
$374$		0			0
$375$	237.148	+	59.5920i	0.632396	+	0.158912i
$376$		0			0
$377$	66.0828			0.175286
$378$		0			0
$379$		−	310.051i		−	0.818076i	−0.912517	−	0.409038i	$-0.865864\pi$
$379$		−	310.051i		−	0.818076i	0.912517	−	0.409038i	$-0.134136\pi$
$380$		0			0
$381$	−38.6807	+	153.931i	−0.101524	+	0.404019i
$382$		0			0
$383$	−343.504	−	198.322i	−0.896877	−	0.517812i	−0.0206914	−	0.999786i	$-0.506587\pi$
$383$	−343.504	−	198.322i	−0.896877	−	0.517812i	−0.876186	+	0.481974i	$0.839920\pi$
$384$		0			0
$385$	−239.611	−	415.019i	−0.622367	−	1.07797i
$386$		0			0
$387$	−1.22969	−	39.3723i	−0.00317749	−	0.101737i
$388$		0			0
$389$	−115.269	−	199.652i	−0.296322	−	0.513244i	0.678970	−	0.734166i	$-0.262427\pi$
$389$	−115.269	−	199.652i	−0.296322	−	0.513244i	−0.975291	+	0.220922i	$0.929093\pi$
$390$		0			0
$391$	38.9601	−	67.4809i	0.0996423	−	0.172585i
$392$		0			0
$393$	323.238	−	333.491i	0.822489	−	0.848579i
$394$		0			0
$395$		−	220.892i		−	0.559220i
$396$		0			0
$397$	−388.596			−0.978832			−0.489416	−	0.872051i	$-0.662790\pi$
$397$	−388.596			−0.978832			−0.489416	+	0.872051i	$0.662790\pi$
$398$		0			0
$399$	325.677	+	654.580i	0.816234	+	1.64055i
$400$		0			0
$401$	213.713	+	123.387i	0.532951	+	0.307699i	0.742217	−	0.670159i	$-0.233774\pi$
$401$	213.713	+	123.387i	0.532951	+	0.307699i	−0.209266	+	0.977859i	$0.567108\pi$
$402$		0			0
$403$	224.137	+	388.218i	0.556172	+	0.963319i
$404$		0			0
$405$	−488.482	+	30.5427i	−1.20613	+	0.0754140i
$406$		0			0
$407$	−351.500	+	202.939i	−0.863636	+	0.498621i
$408$		0			0
$409$	−58.3572	−	33.6926i	−0.142683	−	0.0823779i	0.426959	−	0.904271i	$-0.359585\pi$
$409$	−58.3572	−	33.6926i	−0.142683	−	0.0823779i	−0.569642	+	0.821893i	$0.692918\pi$
$410$		0			0
$411$	154.688	+	543.236i	0.376370	+	1.32174i
$412$		0			0
$413$			429.211i			1.03925i
$414$		0			0
$415$	−121.367			−0.292451
$416$		0			0
$417$	382.412	−	394.542i	0.917055	−	0.946144i
$418$		0			0
$419$	−161.678	+	280.034i	−0.385866	+	0.668340i	−0.991889	−	0.127107i	$-0.959431\pi$
$419$	−161.678	+	280.034i	−0.385866	+	0.668340i	0.606023	+	0.795447i	$0.292764\pi$
$420$		0			0
$421$	259.833	−	150.014i	0.617180	−	0.356329i	−0.158591	−	0.987344i	$-0.550695\pi$
$421$	259.833	−	150.014i	0.617180	−	0.356329i	0.775770	+	0.631016i	$0.217362\pi$
$422$		0			0
$423$	18.6737	+	597.896i	0.0441458	+	1.41347i
$424$		0			0
$425$	−22.6722	−	39.2694i	−0.0533464	−	0.0923986i
$426$		0			0
$427$	308.888	−	535.010i	0.723392	−	1.25295i
$428$		0			0
$429$	36.9987	−	147.238i	0.0862440	−	0.343211i
$430$		0			0
$431$			125.454i			0.291076i	0.989353	+	0.145538i	$0.0464914\pi$
$431$			125.454i			0.291076i	−0.989353	+	0.145538i	$0.953509\pi$
$432$		0			0
$433$		−	43.1270i		−	0.0996004i	−0.998759	−	0.0498002i	$-0.984142\pi$
$433$		−	43.1270i		−	0.0996004i	0.998759	−	0.0498002i	$-0.0158585\pi$
$434$		0			0
$435$	35.6705	−	141.952i	0.0820011	−	0.326326i
$436$		0			0
$437$	−125.098	+	354.396i	−0.286265	+	0.810975i
$438$		0			0
$439$	317.996	−	183.595i	0.724365	−	0.418212i	−0.0919924	−	0.995760i	$-0.529324\pi$
$439$	317.996	−	183.595i	0.724365	−	0.418212i	0.816357	+	0.577548i	$0.195990\pi$
$440$		0			0
$441$	−883.760	+	547.717i	−2.00399	+	1.24199i
$442$		0			0
$443$	−235.982	−	408.733i	−0.532691	−	0.922647i	−0.999271	−	0.0381687i	$-0.987848\pi$
$443$	−235.982	−	408.733i	−0.532691	−	0.922647i	0.466581	−	0.884479i	$-0.345486\pi$
$444$		0			0
$445$	687.406	+	396.874i	1.54473	+	0.891851i
$446$		0			0
$447$	−396.411	+	408.985i	−0.886825	+	0.914955i
$448$		0			0
$449$			371.273i			0.826890i	0.910529	+	0.413445i	$0.135675\pi$
$449$			371.273i			0.826890i	−0.910529	+	0.413445i	$0.864325\pi$
$450$		0			0
$451$		−	383.909i		−	0.851240i
$452$		0			0
$453$	−244.693	+	69.6771i	−0.540162	+	0.153813i
$454$		0			0
$455$	−549.339	−	317.161i	−1.20734	−	0.697058i
$456$		0			0
$457$	−17.0295	−	29.4960i	−0.0372637	−	0.0645426i	0.846792	−	0.531924i	$-0.178531\pi$
$457$	−17.0295	−	29.4960i	−0.0372637	−	0.0645426i	−0.884056	+	0.467381i	$0.845197\pi$
$458$		0			0
$459$	−78.6466	−	71.6047i	−0.171343	−	0.156001i
$460$		0			0
$461$	−53.3364	−	92.3813i	−0.115697	−	0.200393i	0.802361	−	0.596839i	$-0.203577\pi$
$461$	−53.3364	−	92.3813i	−0.115697	−	0.200393i	−0.918058	+	0.396446i	$0.870244\pi$
$462$		0			0
$463$	−184.241	+	319.114i	−0.397928	+	0.689231i	−0.993470	−	0.114093i	$-0.963604\pi$
$463$	−184.241	+	319.114i	−0.397928	+	0.689231i	0.595542	+	0.803324i	$0.296937\pi$
$464$		0			0
$465$	954.913	−	271.914i	2.05358	−	0.584762i
$466$		0			0
$467$	768.129			1.64482			0.822408	−	0.568899i	$-0.192630\pi$
$467$	768.129			1.64482			0.822408	+	0.568899i	$0.192630\pi$
$468$		0			0
$469$		−	1277.47i		−	2.72381i
$470$		0			0
$471$	152.858	−	157.706i	0.324539	−	0.334833i
$472$		0			0
$473$	13.5313	−	23.4370i	0.0286075	−	0.0495496i
$474$		0			0
$475$	142.205	+	166.163i	0.299380	+	0.349817i
$476$		0			0
$477$	360.981	−	672.913i	0.756773	−	1.41072i
$478$		0			0
$479$	307.515	+	532.631i	0.641993	+	1.11197i	0.984987	+	0.172627i	$0.0552257\pi$
$479$	307.515	+	532.631i	0.641993	+	1.11197i	−0.342994	+	0.939338i	$0.611441\pi$
$480$		0			0
$481$	−268.619	+	465.262i	−0.558460	+	0.967282i
$482$		0			0
$483$	−738.202	−	185.500i	−1.52837	−	0.384057i
$484$		0			0
$485$		−	610.534i		−	1.25883i
$486$		0			0
$487$			187.493i			0.384996i	0.981297	+	0.192498i	$0.0616589\pi$
$487$			187.493i			0.384996i	−0.981297	+	0.192498i	$0.938341\pi$
$488$		0			0
$489$	−203.030	−	51.0186i	−0.415195	−	0.104332i
$490$		0			0
$491$	−198.081	+	343.087i	−0.403424	+	0.698751i	−0.994137	−	0.108131i	$-0.965513\pi$
$491$	−198.081	+	343.087i	−0.403424	+	0.698751i	0.590713	+	0.806882i	$0.298847\pi$
$492$		0			0
$493$	27.5456	−	15.9034i	0.0558734	−	0.0322585i
$494$		0			0
$495$	−296.309	−	158.953i	−0.598603	−	0.321118i
$496$		0			0
$497$	−1454.42	+	839.710i	−2.92640	+	1.68956i
$498$		0			0
$499$	159.385	−	276.063i	0.319409	−	0.553233i	−0.660956	−	0.750425i	$-0.729849\pi$
$499$	159.385	−	276.063i	0.319409	−	0.553233i	0.980365	+	0.197192i	$0.0631823\pi$
$500$		0			0
$501$	265.237	+	257.083i	0.529416	+	0.513139i
$502$		0			0
$503$	−439.081			−0.872925			−0.436462	−	0.899723i	$-0.643769\pi$
$503$	−439.081			−0.872925			−0.436462	+	0.899723i	$0.643769\pi$
$504$		0			0
$505$	106.855			0.211595
$506$		0			0
$507$	83.8167	+	294.349i	0.165319	+	0.580570i
$508$		0			0
$509$	310.266	+	179.132i	0.609561	+	0.351930i	0.772793	−	0.634658i	$-0.218859\pi$
$509$	310.266	+	179.132i	0.609561	+	0.351930i	−0.163233	+	0.986588i	$0.552192\pi$
$510$		0			0
$511$	461.682	+	799.657i	0.903488	+	1.56489i
$512$		0			0
$513$	436.188	+	270.017i	0.850269	+	0.526349i
$514$		0			0
$515$	−210.545	+	121.558i	−0.408825	+	0.236035i
$516$		0			0
$517$	−205.483	+	355.906i	−0.397452	+	0.688407i
$518$		0			0
$519$	−115.791	+	32.9719i	−0.223105	+	0.0635297i
$520$		0			0
$521$			602.430i			1.15630i	0.815932	+	0.578148i	$0.196224\pi$
$521$			602.430i			1.15630i	−0.815932	+	0.578148i	$0.803776\pi$
$522$		0			0
$523$			17.5172i			0.0334937i	0.999860	+	0.0167469i	$0.00533094\pi$
$523$			17.5172i			0.0334937i	−0.999860	+	0.0167469i	$0.994669\pi$
$524$		0			0
$525$	−308.279	+	318.057i	−0.587197	+	0.605823i
$526$		0			0
$527$	186.856	+	107.882i	0.354566	+	0.204709i
$528$		0			0
$529$	68.8684	+	119.284i	0.130186	+	0.225489i
$530$		0			0
$531$	158.649	+	255.985i	0.298773	+	0.482080i
$532$		0			0
$533$	−254.081	−	440.081i	−0.476699	−	0.825667i
$534$		0			0
$535$	385.966	+	222.837i	0.721431	+	0.416518i
$536$		0			0
$537$	−10.2200	+	40.6707i	−0.0190316	+	0.0757368i
$538$		0			0
$539$	−714.309			−1.32525
$540$		0			0
$541$	−445.648			−0.823749			−0.411874	−	0.911241i	$-0.635126\pi$
$541$	−445.648			−0.823749			−0.411874	+	0.911241i	$0.635126\pi$
$542$		0			0
$543$	83.9681	−	334.154i	0.154637	−	0.615385i
$544$		0			0
$545$	236.467	+	136.524i	0.433884	+	0.250503i
$546$		0			0
$547$	−653.688	+	377.407i	−1.19504	+	0.689958i	−0.959446	−	0.281893i	$-0.909038\pi$
$547$	−653.688	+	377.407i	−1.19504	+	0.689958i	−0.235596	+	0.971851i	$0.575704\pi$
$548$		0			0
$549$	−13.5316	−	433.258i	−0.0246478	−	0.789176i
$550$		0			0
$551$	−116.555	+	99.7502i	−0.211534	+	0.181035i
$552$		0			0
$553$	−406.083	−	234.452i	−0.734328	−	0.423965i
$554$		0			0
$555$	854.430	+	828.161i	1.53951	+	1.49218i
$556$		0			0
$557$	−64.7060			−0.116169			−0.0580844	−	0.998312i	$-0.518499\pi$
$557$	−64.7060			−0.116169			−0.0580844	+	0.998312i	$0.518499\pi$
$558$		0			0
$559$		−	35.8215i		−	0.0640813i
$560$		0			0
$561$	−20.0118	−	70.2777i	−0.0356716	−	0.125272i
$562$		0			0
$563$	548.657	+	316.767i	0.974523	+	0.562641i	0.900612	−	0.434624i	$-0.143119\pi$
$563$	548.657	+	316.767i	0.974523	+	0.562641i	0.0739110	+	0.997265i	$0.476452\pi$
$564$		0			0
$565$	835.372	−	482.302i	1.47853	−	0.853633i
$566$		0			0
$567$	−462.321	+	930.434i	−0.815381	+	1.64098i
$568$		0			0
$569$	−478.854	+	276.466i	−0.841571	+	0.485881i	−0.857798	−	0.513987i	$-0.828168\pi$
$569$	−478.854	+	276.466i	−0.841571	+	0.485881i	0.0162269	+	0.999868i	$0.494835\pi$
$570$		0			0
$571$	56.0921	−	97.1543i	0.0982348	−	0.170148i	−0.812719	−	0.582655i	$-0.802014\pi$
$571$	56.0921	−	97.1543i	0.0982348	−	0.170148i	0.910954	+	0.412508i	$0.135347\pi$
$572$		0			0
$573$	32.7042	+	114.851i	0.0570755	+	0.200439i
$574$		0			0
$575$	−227.689			−0.395981
$576$		0			0
$577$	440.514			0.763456			0.381728	−	0.924275i	$-0.375329\pi$
$577$	440.514			0.763456			0.381728	+	0.924275i	$0.375329\pi$
$578$		0			0
$579$	−713.614	−	691.674i	−1.23249	−	1.19460i
$580$		0			0
$581$	−128.818	+	223.119i	−0.221718	+	0.384026i
$582$		0			0
$583$	454.336	−	262.311i	0.779307	−	0.449933i
$584$		0			0
$585$	−444.862	+	13.8941i	−0.760447	+	0.0237505i
$586$		0			0
$587$	294.343	+	509.817i	0.501436	+	0.868512i	0.999999	+	0.00165864i	$0.000527962\pi$
$587$	294.343	+	509.817i	0.501436	+	0.868512i	−0.498563	+	0.866854i	$0.666139\pi$
$588$		0			0
$589$	−981.331	−	346.399i	−1.66610	−	0.588113i
$590$		0			0
$591$	−221.345	−	55.6209i	−0.374527	−	0.0941132i
$592$		0			0
$593$	−1123.15			−1.89401			−0.947003	−	0.321226i	$-0.895905\pi$
$593$	−1123.15			−1.89401			−0.947003	+	0.321226i	$0.895905\pi$
$594$		0			0
$595$	−305.311			−0.513128
$596$		0			0
$597$	−789.842	−	198.476i	−1.32302	−	0.332455i
$598$		0			0
$599$	747.708	+	431.689i	1.24826	+	0.720683i	0.970762	−	0.240043i	$-0.0771616\pi$
$599$	747.708	+	431.689i	1.24826	+	0.720683i	0.277498	+	0.960726i	$0.410495\pi$
$600$		0			0
$601$	416.728	−	240.598i	0.693390	−	0.400329i	−0.111490	−	0.993766i	$-0.535562\pi$
$601$	416.728	−	240.598i	0.693390	−	0.400329i	0.804881	+	0.593436i	$0.202229\pi$
$602$		0			0
$603$	−472.187	−	761.890i	−0.783063	−	1.26350i
$604$		0			0
$605$	250.061	+	433.119i	0.413324	+	0.715899i
$606$		0			0
$607$	82.1691	+	47.4403i	0.135369	+	0.0781554i	0.566155	−	0.824299i	$-0.308430\pi$
$607$	82.1691	+	47.4403i	0.135369	+	0.0781554i	−0.430786	+	0.902454i	$0.641764\pi$
$608$		0			0
$609$	−223.101	−	216.242i	−0.366341	−	0.355078i
$610$		0			0
$611$			543.974i			0.890301i
$612$		0			0
$613$	48.6639			0.0793864			0.0396932	−	0.999212i	$-0.487362\pi$
$613$	48.6639			0.0793864			0.0396932	+	0.999212i	$0.487362\pi$
$614$		0			0
$615$	−1082.48	+	308.240i	−1.76013	+	0.501203i
$616$		0			0
$617$	362.940	−	628.630i	0.588233	−	1.01885i	−0.406231	−	0.913771i	$-0.633157\pi$
$617$	362.940	−	628.630i	0.588233	−	1.01885i	0.994464	−	0.105079i	$-0.0335096\pi$
$618$		0			0
$619$	−340.988	−	590.609i	−0.550869	−	0.954134i	−0.998212	−	0.0597711i	$-0.980963\pi$
$619$	−340.988	−	590.609i	−0.550869	−	0.954134i	0.447343	−	0.894363i	$-0.352370\pi$
$620$		0			0
$621$	−508.835	+	162.227i	−0.819380	+	0.261235i
$622$		0			0
$623$	1459.21	−	842.476i	2.34223	−	1.35229i
$624$		0			0
$625$	390.136	−	675.735i	0.624217	−	1.08118i
$626$		0			0
$627$	156.994	+	315.542i	0.250389	+	0.503257i
$628$		0			0
$629$			258.583i			0.411102i
$630$		0			0
$631$	−169.095			−0.267979			−0.133989	−	0.990983i	$-0.542779\pi$
$631$	−169.095			−0.267979			−0.133989	+	0.990983i	$0.542779\pi$
$632$		0			0
$633$	−273.024	−	264.630i	−0.431318	−	0.418057i
$634$		0			0
$635$	276.849	+	159.839i	0.435983	+	0.251715i
$636$		0			0
$637$	−818.822	+	472.747i	−1.28543	+	0.742146i
$638$		0			0
$639$	−557.047	+	1038.40i	−0.871748	+	1.62505i
$640$		0			0
$641$	−423.832	+	244.700i	−0.661205	+	0.381747i	−0.792736	−	0.609565i	$-0.791344\pi$
$641$	−423.832	+	244.700i	−0.661205	+	0.381747i	0.131531	+	0.991312i	$0.458011\pi$
$642$		0			0
$643$	−345.744	+	598.846i	−0.537704	+	0.931331i	0.461323	+	0.887232i	$0.347375\pi$
$643$	−345.744	+	598.846i	−0.537704	+	0.931331i	−0.999027	+	0.0440985i	$0.985958\pi$
$644$		0			0
$645$	−76.9478	−	19.3359i	−0.119299	−	0.0299781i
$646$		0			0
$647$	104.090			0.160880			0.0804402	−	0.996759i	$-0.474367\pi$
$647$	104.090			0.160880			0.0804402	+	0.996759i	$0.474367\pi$
$648$		0			0
$649$			206.902i			0.318802i
$650$		0			0
$651$	513.653	−	2044.10i	0.789022	−	3.13994i
$652$		0			0
$653$	−453.246	+	785.044i	−0.694097	+	1.20221i	0.276387	+	0.961047i	$0.410863\pi$
$653$	−453.246	+	785.044i	−0.694097	+	1.20221i	−0.970484	+	0.241165i	$0.922470\pi$
$654$		0			0
$655$	−467.718	−	810.112i	−0.714074	−	1.23681i
$656$		0			0
$657$	570.927	+	306.271i	0.868990	+	0.466165i
$658$		0			0
$659$	995.824	−	574.939i	1.51111	−	0.872442i	0.511198	−	0.859463i	$-0.329202\pi$
$659$	995.824	−	574.939i	1.51111	−	0.872442i	0.999916	−	0.0129787i	$-0.00413137\pi$
$660$		0			0
$661$	699.447	+	403.826i	1.05817	+	0.610932i	0.924924	−	0.380152i	$-0.124128\pi$
$661$	699.447	+	403.826i	1.05817	+	0.610932i	0.133241	+	0.991084i	$0.457462\pi$
$662$		0			0
$663$	−69.4513	−	67.3160i	−0.104753	−	0.101532i
$664$		0			0
$665$	1447.66	−	269.812i	2.17693	−	0.405732i
$666$		0			0
$667$		−	159.713i		−	0.239450i
$668$		0			0
$669$	−122.833	+	34.9769i	−0.183606	+	0.0522824i
$670$		0			0
$671$	148.900	−	257.903i	0.221908	−	0.384356i
$672$		0			0
$673$	31.6772	−	18.2888i	0.0470687	−	0.0271751i	−0.476281	−	0.879293i	$-0.658015\pi$
$673$	31.6772	−	18.2888i	0.0470687	−	0.0271751i	0.523350	+	0.852118i	$0.324682\pi$
$674$		0			0
$675$	−66.2967	+	303.640i	−0.0982173	+	0.449837i
$676$		0			0
$677$	916.242	−	528.993i	1.35339	−	0.781378i	0.364664	−	0.931139i	$-0.381184\pi$
$677$	916.242	−	528.993i	1.35339	−	0.781378i	0.988722	+	0.149762i	$0.0478507\pi$
$678$		0			0
$679$	−1122.39	−	648.014i	−1.65301	−	0.954365i
$680$		0			0
$681$	825.928	−	235.185i	1.21282	−	0.345353i
$682$		0			0
$683$			123.765i			0.181208i	0.995887	+	0.0906038i	$0.0288797\pi$
$683$			123.765i			0.181208i	−0.995887	+	0.0906038i	$0.971120\pi$
$684$		0			0
$685$	1137.65			1.66080
$686$		0			0
$687$	−215.360	+	222.191i	−0.313479	+	0.323422i
$688$		0			0
$689$	347.208	−	601.381i	0.503930	−	0.872832i
$690$		0			0
$691$	−258.140	−	447.111i	−0.373574	−	0.647049i	0.616538	−	0.787325i	$-0.288534\pi$
$691$	−258.140	−	447.111i	−0.373574	−	0.647049i	−0.990112	+	0.140276i	$0.955201\pi$
$692$		0			0
$693$	−606.715	+	376.017i	−0.875491	+	0.542593i
$694$		0			0
$695$	−553.341	−	958.415i	−0.796174	−	1.37901i
$696$		0			0
$697$	−211.819	−	122.294i	−0.303901	−	0.175457i
$698$		0			0
$699$	−1067.91	−	268.349i	−1.52776	−	0.383905i
$700$		0			0
$701$	1003.30			1.43124			0.715622	−	0.698488i	$-0.246143\pi$
$701$	1003.30			1.43124			0.715622	+	0.698488i	$0.246143\pi$
$702$		0			0
$703$	−228.517	−	1226.09i	−0.325060	−	1.74408i
$704$		0			0
$705$	1168.51	+	293.629i	1.65745	+	0.416495i
$706$		0			0
$707$	113.415	−	196.441i	0.160418	−	0.277851i
$708$		0			0
$709$	−321.483	−	556.824i	−0.453431	−	0.785366i	0.545165	−	0.838329i	$-0.316467\pi$
$709$	−321.483	−	556.824i	−0.453431	−	0.785366i	−0.998596	+	0.0529628i	$0.983134\pi$
$710$		0			0
$711$	−328.851	+	10.2708i	−0.462519	+	0.0144456i
$712$		0			0
$713$	938.267	−	541.709i	1.31594	−	0.759760i
$714$		0			0
$715$	−264.811	−	152.888i	−0.370364	−	0.213830i
$716$		0			0
$717$	338.816	−	349.563i	0.472546	−	0.487535i
$718$		0			0
$719$	−47.3407			−0.0658424			−0.0329212	−	0.999458i	$-0.510481\pi$
$719$	−47.3407			−0.0658424			−0.0329212	+	0.999458i	$0.510481\pi$
$720$		0			0
$721$			516.082i			0.715786i
$722$		0			0
$723$	149.452	−	42.5569i	0.206711	−	0.0588616i
$724$		0			0
$725$	−80.4904	−	46.4711i	−0.111021	−	0.0640981i
$726$		0			0
$727$	−128.014	−	221.727i	−0.176085	−	0.304989i	0.764451	−	0.644682i	$-0.223010\pi$
$727$	−128.014	−	221.727i	−0.176085	−	0.304989i	−0.940536	+	0.339693i	$0.889677\pi$
$728$		0			0
$729$	68.1831	+	725.804i	0.0935296	+	0.995616i
$730$		0			0
$731$	−8.62077	−	14.9316i	−0.0117931	−	0.0204263i
$732$		0			0
$733$	−4.73153	+	8.19524i	−0.00645501	+	0.0111804i	−0.869235	−	0.494399i	$-0.835388\pi$
$733$	−4.73153	+	8.19524i	−0.00645501	+	0.0111804i	0.862780	+	0.505580i	$0.168721\pi$
$734$		0			0
$735$	573.517	+	2014.09i	0.780295	+	2.74025i
$736$		0			0
$737$		−	615.806i		−	0.835557i
$738$		0			0
$739$	1440.53			1.94930			0.974650	−	0.223734i	$-0.0718247\pi$
$739$	1440.53			1.94930			0.974650	+	0.223734i	$0.0718247\pi$
$740$		0			0
$741$	388.798	+	257.808i	0.524693	+	0.347919i
$742$		0			0
$743$	525.044	+	303.134i	0.706654	+	0.407987i	0.809821	−	0.586677i	$-0.199564\pi$
$743$	525.044	+	303.134i	0.706654	+	0.407987i	−0.103167	+	0.994664i	$0.532897\pi$
$744$		0			0
$745$	573.598	+	993.500i	0.769930	+	1.33356i
$746$		0			0
$747$	5.64320	+	180.685i	0.00755449	+	0.241880i
$748$		0			0
$749$	819.320	−	473.034i	1.09388	−	0.631555i
$750$		0			0
$751$	−283.958	−	163.943i	−0.378106	−	0.218300i	0.298888	−	0.954288i	$-0.403384\pi$
$751$	−283.958	−	163.943i	−0.378106	−	0.218300i	−0.676994	+	0.735988i	$0.736718\pi$
$752$		0			0
$753$	−775.151	−	194.784i	−1.02942	−	0.258678i
$754$		0			0
$755$			512.438i			0.678726i
$756$		0			0
$757$	853.795			1.12787			0.563933	−	0.825820i	$-0.309287\pi$
$757$	853.795			1.12787			0.563933	+	0.825820i	$0.309287\pi$
$758$		0			0
$759$	−355.853	−	89.4206i	−0.468844	−	0.117814i
$760$		0			0
$761$	−423.235	+	733.064i	−0.556156	+	0.963290i	0.441657	+	0.897184i	$0.354391\pi$
$761$	−423.235	+	733.064i	−0.556156	+	0.963290i	−0.997813	+	0.0661060i	$0.978942\pi$
$762$		0			0
$763$	501.966	−	289.810i	0.657885	−	0.379830i
$764$		0			0
$765$	−182.090	+	112.852i	−0.238026	+	0.147518i
$766$		0			0
$767$	136.933	+	237.175i	0.178531	+	0.309224i
$768$		0			0
$769$	655.072	−	1134.62i	0.851850	−	1.47545i	−0.0276873	−	0.999617i	$-0.508814\pi$
$769$	655.072	−	1134.62i	0.851850	−	1.47545i	0.879537	−	0.475830i	$-0.157852\pi$
$770$		0			0
$771$	548.780	+	531.908i	0.711777	+	0.689894i
$772$		0			0
$773$			1016.80i			1.31539i	0.753283	+	0.657696i	$0.228469\pi$
$773$			1016.80i			1.31539i	−0.753283	+	0.657696i	$0.771531\pi$
$774$		0			0
$775$		−	630.477i		−	0.813519i
$776$		0			0
$777$	2429.36	−	691.766i	3.12659	−	0.890304i
$778$		0			0
$779$	1112.43	+	392.675i	1.42802	+	0.504076i
$780$		0			0
$781$	−701.108	+	404.785i	−0.897705	+	0.518290i
$782$		0			0
$783$	−212.989	−	46.5039i	−0.272016	−	0.0593919i
$784$		0			0
$785$	−221.182	−	383.098i	−0.281760	−	0.488023i
$786$		0			0
$787$	324.429	+	187.309i	0.412236	+	0.238004i	0.691750	−	0.722137i	$-0.256840\pi$
$787$	324.429	+	187.309i	0.412236	+	0.238004i	−0.279514	+	0.960142i	$0.590173\pi$
$788$		0			0
$789$	−61.4262	−	215.718i	−0.0778532	−	0.273406i
$790$		0			0
$791$		−	2047.64i		−	2.58868i
$792$		0			0
$793$		−	394.184i		−	0.497079i
$794$		0			0
$795$	−1104.40	−	1070.45i	−1.38919	−	1.34648i
$796$		0			0
$797$	−315.037	−	181.887i	−0.395279	−	0.228214i	0.289166	−	0.957279i	$-0.406622\pi$
$797$	−315.037	−	181.887i	−0.395279	−	0.228214i	−0.684445	+	0.729065i	$0.739955\pi$
$798$		0			0
$799$	130.912	+	226.747i	0.163845	+	0.283788i
$800$		0			0
$801$	558.881	−	1041.82i	0.697729	−	1.30065i
$802$		0			0
$803$	222.555	+	385.477i	0.277155	+	0.480046i
$804$		0			0
$805$	−766.534	+	1327.68i	−0.952216	+	1.64929i
$806$		0			0
$807$	286.672	−	1140.82i	0.355232	−	1.41366i
$808$		0			0
$809$	1288.68			1.59293			0.796464	−	0.604686i	$-0.206701\pi$
$809$	1288.68			1.59293			0.796464	+	0.604686i	$0.206701\pi$
$810$		0			0
$811$		−	520.516i		−	0.641820i	−0.947110	−	0.320910i	$-0.896011\pi$
$811$		−	520.516i		−	0.641820i	0.947110	−	0.320910i	$-0.103989\pi$
$812$		0			0
$813$	−1186.84	−	298.237i	−1.45983	−	0.366835i
$814$		0			0
$815$	−210.822	+	365.155i	−0.258678	+	0.448043i
$816$		0			0
$817$	54.0715	+	63.1810i	0.0661830	+	0.0773329i
$818$		0			0
$819$	−446.629	+	832.572i	−0.545335	+	1.01657i
$820$		0			0
$821$	375.364	+	650.149i	0.457203	+	0.791899i	0.998812	−	0.0487316i	$-0.0155179\pi$
$821$	375.364	+	650.149i	0.457203	+	0.791899i	−0.541609	+	0.840631i	$0.682185\pi$
$822$		0			0
$823$	203.915	−	353.191i	0.247770	−	0.429150i	−0.715137	−	0.698985i	$-0.753636\pi$
$823$	203.915	−	353.191i	0.247770	−	0.429150i	0.962907	+	0.269834i	$0.0869689\pi$
$824$		0			0
$825$	−148.607	+	153.320i	−0.180129	+	0.185843i
$826$		0			0
$827$			734.634i			0.888312i	0.895950	+	0.444156i	$0.146496\pi$
$827$			734.634i			0.888312i	−0.895950	+	0.444156i	$0.853504\pi$
$828$		0			0
$829$			677.769i			0.817575i	0.912630	+	0.408787i	$0.134048\pi$
$829$			677.769i			0.817575i	−0.912630	+	0.408787i	$0.865952\pi$
$830$		0			0
$831$	204.836	+	719.347i	0.246494	+	0.865641i
$832$		0			0
$833$	−227.542	+	394.114i	−0.273160	+	0.473126i
$834$		0			0
$835$	644.310	−	371.993i	0.771629	−	0.445500i
$836$		0			0
$837$	−449.211	−	1408.98i	−0.536691	−	1.68337i
$838$		0			0
$839$	457.517	−	264.148i	0.545313	−	0.314836i	−0.201917	−	0.979403i	$-0.564717\pi$
$839$	457.517	−	264.148i	0.545313	−	0.314836i	0.747229	+	0.664566i	$0.231384\pi$
$840$		0			0
$841$	−387.903	+	671.867i	−0.461240	+	0.798891i
$842$		0			0
$843$	−761.788	+	216.921i	−0.903663	+	0.257320i
$844$		0			0
$845$	616.428			0.729501
$846$		0			0
$847$	1061.65			1.25342
$848$		0			0
$849$	−467.261	+	482.082i	−0.550366	+	0.567823i
$850$		0			0
$851$	1124.47	+	649.215i	1.32136	+	0.762885i
$852$		0			0
$853$	−691.679	−	1198.02i	−0.810878	−	1.40448i	−0.912250	−	0.409633i	$-0.865657\pi$
$853$	−691.679	−	1198.02i	−0.810878	−	1.40448i	0.101373	−	0.994849i	$-0.467677\pi$
$854$		0			0
$855$	763.663	−	696.012i	0.893173	−	0.814050i
$856$		0			0
$857$	347.810	−	200.808i	0.405845	−	0.234315i	−0.283158	−	0.959073i	$-0.591382\pi$
$857$	347.810	−	200.808i	0.405845	−	0.234315i	0.689003	+	0.724758i	$0.258049\pi$
$858$		0			0
$859$	−9.85751	+	17.0737i	−0.0114756	+	0.0198763i	−0.871706	−	0.490029i	$-0.836986\pi$
$859$	−9.85751	+	17.0737i	−0.0114756	+	0.0198763i	0.860231	+	0.509905i	$0.170320\pi$
$860$		0			0
$861$	−582.273	+	2317.18i	−0.676276	+	2.69126i
$862$		0			0
$863$		−	190.074i		−	0.220248i	−0.993918	−	0.110124i	$-0.964875\pi$
$863$		−	190.074i		−	0.220248i	0.993918	−	0.110124i	$-0.0351248\pi$
$864$		0			0
$865$			242.491i			0.280336i
$866$		0			0
$867$	795.709	+	199.950i	0.917772	+	0.230623i
$868$		0			0
$869$	−195.754	−	113.018i	−0.225263	−	0.130056i
$870$		0			0
$871$	−407.555	−	705.906i	−0.467916	−	0.810455i
$872$		0			0
$873$	−908.928	+	28.3879i	−1.04115	+	0.0325177i
$874$		0			0
$875$	−522.734	−	905.402i	−0.597411	−	1.03475i
$876$		0			0
$877$	3.98342	+	2.29983i	0.00454210	+	0.00262238i	0.502269	−	0.864711i	$-0.332499\pi$
$877$	3.98342	+	2.29983i	0.00454210	+	0.00262238i	−0.497727	+	0.867334i	$0.665832\pi$
$878$		0			0
$879$	−371.607	−	360.182i	−0.422761	−	0.409764i
$880$		0			0
$881$	974.532			1.10617			0.553083	−	0.833126i	$-0.313451\pi$
$881$	974.532			1.10617			0.553083	+	0.833126i	$0.313451\pi$
$882$		0			0
$883$	−378.186			−0.428297			−0.214149	−	0.976801i	$-0.568698\pi$
$883$	−378.186			−0.428297			−0.214149	+	0.976801i	$0.568698\pi$
$884$		0			0
$885$	583.389	−	166.121i	0.659196	−	0.187708i
$886$		0			0
$887$	−1093.87	−	631.547i	−1.23323	−	0.712004i	−0.265526	−	0.964104i	$-0.585546\pi$
$887$	−1093.87	−	631.547i	−1.23323	−	0.712004i	−0.967701	+	0.252100i	$0.918879\pi$
$888$		0			0
$889$	587.690	−	339.303i	0.661068	−	0.381668i
$890$		0			0
$891$	−222.863	+	448.518i	−0.250127	+	0.503387i
$892$		0			0
$893$	−821.113	−	959.447i	−0.919500	−	1.07441i
$894$		0			0
$895$	73.1473	+	42.2316i	0.0817288	+	0.0471861i
$896$		0			0
$897$	−467.099	+	133.008i	−0.520735	+	0.148281i
$898$		0			0
$899$	442.249			0.491934
$900$		0			0
$901$		−	334.235i		−	0.370960i
$902$		0			0
$903$	−117.218	+	120.936i	−0.129810	+	0.133927i
$904$		0			0
$905$	−600.984	−	346.978i	−0.664071	−	0.383401i
$906$		0			0
$907$	116.720	−	67.3882i	0.128688	−	0.0742979i	−0.434274	−	0.900781i	$-0.642995\pi$
$907$	116.720	−	67.3882i	0.128688	−	0.0742979i	0.562962	+	0.826483i	$0.309662\pi$
$908$		0			0
$909$	−4.96845	−	159.080i	−0.00546584	−	0.175006i
$910$		0			0
$911$	−29.6728	+	17.1316i	−0.0325717	+	0.0188053i	−0.516197	−	0.856470i	$-0.672653\pi$
$911$	−29.6728	+	17.1316i	−0.0325717	+	0.0188053i	0.483626	+	0.875275i	$0.339320\pi$
$912$		0			0
$913$	−62.0971	+	107.555i	−0.0680143	+	0.117804i
$914$		0			0
$915$	−846.743	−	212.774i	−0.925403	−	0.232540i
$916$		0			0
$917$	−1985.73			−2.16546
$918$		0			0
$919$	573.135			0.623651			0.311826	−	0.950139i	$-0.399060\pi$
$919$	573.135			0.623651			0.311826	+	0.950139i	$0.399060\pi$
$920$		0			0
$921$	207.860	−	827.187i	0.225690	−	0.898140i
$922$		0			0
$923$	−535.793	+	928.021i	−0.580491	+	1.00544i
$924$		0			0
$925$	654.369	−	377.800i	0.707426	−	0.408433i
$926$		0			0
$927$	190.758	+	307.795i	0.205780	+	0.332034i
$928$		0			0
$929$	−468.918	−	812.190i	−0.504756	−	0.874262i	−0.999985	−	0.00550012i	$-0.998249\pi$
$929$	−468.918	−	812.190i	−0.504756	−	0.874262i	0.495229	−	0.868762i	$-0.335084\pi$
$930$		0			0
$931$	730.618	−	2069.81i	0.784767	−	2.22321i
$932$		0			0
$933$	269.027	−	277.560i	0.288346	−	0.297492i
$934$		0			0
$935$	−147.176			−0.157408
$936$		0			0
$937$	−849.086			−0.906175			−0.453088	−	0.891466i	$-0.649678\pi$
$937$	−849.086			−0.906175			−0.453088	+	0.891466i	$0.649678\pi$
$938$		0			0
$939$	−338.388	−	1188.36i	−0.360371	−	1.26556i
$940$		0			0
$941$	349.824	+	201.971i	0.371757	+	0.214634i	0.674226	−	0.738525i	$-0.264477\pi$
$941$	349.824	+	201.971i	0.371757	+	0.214634i	−0.302469	+	0.953159i	$0.597811\pi$
$942$		0			0
$943$	−1063.61	+	614.077i	−1.12790	+	0.651195i
$944$		0			0
$945$	1547.36	+	1408.81i	1.63742	+	1.49080i
$946$		0			0
$947$	−836.995	−	1449.72i	−0.883838	−	1.53085i	−0.847040	−	0.531530i	$-0.821617\pi$
$947$	−836.995	−	1449.72i	−0.883838	−	1.53085i	−0.0367986	−	0.999323i	$-0.511716\pi$
$948$		0			0
$949$	510.236	+	294.585i	0.537657	+	0.310416i
$950$		0			0
$951$	774.591	−	220.567i	0.814502	−	0.231932i
$952$		0			0
$953$			1249.36i			1.31098i	0.755204	+	0.655490i	$0.227538\pi$
$953$			1249.36i			1.31098i	−0.755204	+	0.655490i	$0.772462\pi$
$954$		0			0
$955$	240.523			0.251856
$956$		0			0
$957$	−107.547	−	104.240i	−0.112379	−	0.108924i
$958$		0			0
$959$	1207.49	−	2091.43i	1.25911	−	2.18085i
$960$		0			0
$961$	1019.50	+	1765.83i	1.06088	+	1.83750i
$962$		0			0
$963$	313.801	−	584.965i	0.325858	−	0.607440i
$964$		0			0
$965$	−1733.50	+	1000.84i	−1.79637	+	1.03714i
$966$		0			0
$967$	100.069	−	173.325i	0.103484	−	0.179240i	−0.809634	−	0.586936i	$-0.800334\pi$
$967$	100.069	−	173.325i	0.103484	−	0.179240i	0.913118	+	0.407695i	$0.133667\pi$
$968$		0			0
$969$	224.108	+	13.8955i	0.231278	+	0.0143400i
$970$		0			0
$971$			374.453i			0.385637i	0.981234	+	0.192818i	$0.0617628\pi$
$971$			374.453i			0.385637i	−0.981234	+	0.192818i	$0.938237\pi$
$972$		0			0
$973$	−2349.24			−2.41443
$974$		0			0
$975$	−68.8786	+	274.105i	−0.0706447	+	0.281133i
$976$		0			0
$977$	513.670	+	296.567i	0.525762	+	0.303549i	0.739289	−	0.673388i	$-0.235162\pi$
$977$	513.670	+	296.567i	0.525762	+	0.303549i	−0.213527	+	0.976937i	$0.568495\pi$
$978$		0			0
$979$	703.416	−	406.118i	0.718505	−	0.414829i
$980$		0			0
$981$	192.254	−	358.386i	0.195978	−	0.365327i
$982$		0			0
$983$	−1563.71	+	902.807i	−1.59075	+	0.918420i	−0.597572	+	0.801816i	$0.703868\pi$
$983$	−1563.71	+	902.807i	−1.59075	+	0.918420i	−0.993178	+	0.116604i	$0.962799\pi$
$984$		0			0
$985$	−229.840	+	398.095i	−0.233340	+	0.404157i
$986$		0			0
$987$	1780.04	−	1836.50i	1.80349	−	1.86069i
$988$		0			0
$989$	−86.5754			−0.0875383
$990$		0			0
$991$		−	771.466i		−	0.778472i	−0.921138	−	0.389236i	$-0.872739\pi$
$991$		−	771.466i		−	0.778472i	0.921138	−	0.389236i	$-0.127261\pi$
$992$		0			0
$993$	−372.779	+	106.150i	−0.375407	+	0.106898i
$994$		0			0
$995$	−820.155	+	1420.55i	−0.824277	+	1.42769i
$996$		0			0
$997$	134.829	+	233.531i	0.135235	+	0.234234i	0.925687	−	0.378290i	$-0.123488\pi$
$997$	134.829	+	233.531i	0.135235	+	0.234234i	−0.790452	+	0.612524i	$0.790154\pi$
$998$		0			0
$999$	1193.19	−	1310.53i	1.19438	−	1.31185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.2	✓	80
3.2	odd	2		2052.3.t.a.37.36		80
9.2	odd	6		2052.3.t.a.721.35		80
9.7	even	3	inner	684.3.t.a.493.39	yes	80
19.18	odd	2	inner	684.3.t.a.265.39	yes	80
57.56	even	2		2052.3.t.a.37.35		80
171.56	even	6		2052.3.t.a.721.36		80
171.151	odd	6	inner	684.3.t.a.493.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.2	✓	80	1.1	even	1	trivial
684.3.t.a.265.39	yes	80	19.18	odd	2	inner
684.3.t.a.493.2	yes	80	171.151	odd	6	inner
684.3.t.a.493.39	yes	80	9.7	even	3	inner
2052.3.t.a.37.35		80	57.56	even	2
2052.3.t.a.37.36		80	3.2	odd	2
2052.3.t.a.721.35		80	9.2	odd	6
2052.3.t.a.721.36		80	171.56	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.90955 - 0.731127i) q^{3} +(-3.02121 + 5.23289i) q^{5} +(6.41336 + 11.1083i) q^{7} +(7.93091 + 4.25449i) q^{9} +O(q^{10})\)	\(q+(-2.90955 - 0.731127i) q^{3} +(-3.02121 + 5.23289i) q^{5} +(6.41336 + 11.1083i) q^{7} +(7.93091 + 4.25449i) q^{9} +(3.09158 + 5.35477i) q^{11} +(7.08784 + 4.09217i) q^{13} +(12.6163 - 13.0164i) q^{15} +3.93927 q^{17} +(-18.6784 + 3.48124i) q^{19} +(-10.5384 - 37.0090i) q^{21} +(9.89019 - 17.1303i) q^{23} +(-5.75543 - 9.96870i) q^{25} +(-19.9648 - 18.1771i) q^{27} +(6.99256 - 4.03715i) q^{29} +(47.4342 + 27.3862i) q^{31} +(-5.08007 - 17.8403i) q^{33} -77.5045 q^{35} +65.6424i q^{37} +(-17.6305 - 17.0885i) q^{39} +(-53.7711 - 31.0448i) q^{41} +(-2.18842 - 3.79045i) q^{43} +(-46.2242 + 28.6478i) q^{45} +(33.2326 + 57.5606i) q^{47} +(-57.7625 + 100.048i) q^{49} +(-11.4615 - 2.88011i) q^{51} -84.8469i q^{53} -37.3613 q^{55} +(56.8907 + 3.52742i) q^{57} +(28.9792 + 16.7311i) q^{59} +(-24.0816 - 41.7106i) q^{61} +(3.60372 + 115.384i) q^{63} +(-42.8277 + 24.7266i) q^{65} +(-86.2509 - 49.7970i) q^{67} +(-41.3004 + 42.6104i) q^{69} +130.931i q^{71} +71.9876 q^{73} +(9.45731 + 33.2123i) q^{75} +(-39.6548 + 68.6842i) q^{77} +(-31.6592 + 18.2784i) q^{79} +(44.7986 + 67.4840i) q^{81} +(10.0429 + 17.3949i) q^{83} +(-11.9014 + 20.6138i) q^{85} +(-23.2968 + 6.63384i) q^{87} -131.363i q^{89} +104.978i q^{91} +(-117.989 - 114.362i) q^{93} +(38.2143 - 108.259i) q^{95} +(-87.5043 + 50.5206i) q^{97} +(1.73718 + 55.6213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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