LMFDB - Embedded newform 624.4.bv.c.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 17x^{2} + 289 $ x^4 - 17*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.1
Root			$-3.57071 - 2.06155i$ of defining polynomial
Character	$\chi$	$=$	624.433
Dual form			624.4.bv.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} -13.4424i q^{5} +(27.2121 - 15.7109i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} -13.4424i q^{5} +(27.2121 - 15.7109i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(35.0707 + 20.2481i) q^{11} +(42.1364 - 20.5310i) q^{13} +(34.9243 + 20.1635i) q^{15} +(-21.5707 - 37.3616i) q^{17} +(-23.3636 + 13.4890i) q^{19} +94.2656i q^{21} +(9.50500 - 16.4631i) q^{23} -55.6971 q^{25} +27.0000 q^{27} +(77.0557 - 133.464i) q^{29} +308.270i q^{31} +(-105.212 + 60.7443i) q^{33} +(-211.192 - 365.796i) q^{35} +(-37.6821 - 21.7558i) q^{37} +(-9.86357 + 140.270i) q^{39} +(41.4293 + 23.9192i) q^{41} +(-171.061 - 296.286i) q^{43} +(-104.773 + 60.4906i) q^{45} -133.468i q^{47} +(322.167 - 558.010i) q^{49} +129.424 q^{51} -438.454 q^{53} +(272.182 - 471.433i) q^{55} -80.9338i q^{57} +(-511.434 + 295.277i) q^{59} +(270.652 + 468.783i) q^{61} +(-244.909 - 141.398i) q^{63} +(-275.985 - 566.413i) q^{65} +(199.485 + 115.173i) q^{67} +(28.5150 + 49.3894i) q^{69} +(389.202 - 224.706i) q^{71} -389.711i q^{73} +(83.5457 - 144.705i) q^{75} +1272.47 q^{77} +897.820 q^{79} +(-40.5000 + 70.1481i) q^{81} -1300.24i q^{83} +(-502.228 + 289.961i) q^{85} +(231.167 + 400.393i) q^{87} +(801.113 + 462.523i) q^{89} +(824.061 - 1220.69i) q^{91} +(-800.910 - 462.406i) q^{93} +(181.324 + 314.062i) q^{95} +(1351.43 - 780.247i) q^{97} -364.466i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 66 * q^7 - 18 * q^9	$ 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9} + 126 q^{11} + 40 q^{13} + 54 q^{15} - 72 q^{17} - 222 q^{19} + 138 q^{23} + 120 q^{25} + 108 q^{27} - 6 q^{29} - 378 q^{33} - 402 q^{35} + 492 q^{37} - 168 q^{39} + 180 q^{41} - 470 q^{43} - 162 q^{45} + 346 q^{49} + 432 q^{51} - 2268 q^{53} + 446 q^{55} - 2160 q^{59} - 160 q^{61} - 594 q^{63} - 804 q^{65} + 498 q^{67} + 414 q^{69} + 1314 q^{71} - 180 q^{75} + 2976 q^{77} - 8 q^{79} - 162 q^{81} - 852 q^{85} - 18 q^{87} - 252 q^{89} + 1668 q^{91} - 1404 q^{93} + 54 q^{95} - 336 q^{97}+O(q^{100}) $ 4 * q - 6 * q^3 + 66 * q^7 - 18 * q^9 + 126 * q^11 + 40 * q^13 + 54 * q^15 - 72 * q^17 - 222 * q^19 + 138 * q^23 + 120 * q^25 + 108 * q^27 - 6 * q^29 - 378 * q^33 - 402 * q^35 + 492 * q^37 - 168 * q^39 + 180 * q^41 - 470 * q^43 - 162 * q^45 + 346 * q^49 + 432 * q^51 - 2268 * q^53 + 446 * q^55 - 2160 * q^59 - 160 * q^61 - 594 * q^63 - 804 * q^65 + 498 * q^67 + 414 * q^69 + 1314 * q^71 - 180 * q^75 + 2976 * q^77 - 8 * q^79 - 162 * q^81 - 852 * q^85 - 18 * q^87 - 252 * q^89 + 1668 * q^91 - 1404 * q^93 + 54 * q^95 - 336 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$		0			0
$5$		−	13.4424i		−	1.20232i	−0.799128	−	0.601161i	$-0.794705\pi$
$5$		−	13.4424i		−	1.20232i	0.799128	−	0.601161i	$-0.205295\pi$
$6$		0			0
$7$	27.2121	−	15.7109i	1.46932	−	0.848311i	0.469910	−	0.882715i	$-0.344287\pi$
$7$	27.2121	−	15.7109i	1.46932	−	0.848311i	0.999408	+	0.0344037i	$0.0109532\pi$
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	35.0707	+	20.2481i	0.961293	+	0.555003i	0.896571	−	0.442901i	$-0.146051\pi$
$11$	35.0707	+	20.2481i	0.961293	+	0.555003i	0.0647219	+	0.997903i	$0.479384\pi$
$12$		0			0
$13$	42.1364	−	20.5310i	0.898965	−	0.438021i
$13$	42.1364	−	20.5310i	0.898965	−	0.438021i
$14$		0			0
$15$	34.9243	+	20.1635i	0.601161	+	0.347080i
$16$		0			0
$17$	−21.5707	−	37.3616i	−0.307745	−	0.533030i	0.670124	−	0.742249i	$-0.266241\pi$
$17$	−21.5707	−	37.3616i	−0.307745	−	0.533030i	−0.977869	+	0.209219i	$0.932908\pi$
$18$		0			0
$19$	−23.3636	+	13.4890i	−0.282104	+	0.162873i	−0.634375	−	0.773025i	$-0.718743\pi$
$19$	−23.3636	+	13.4890i	−0.282104	+	0.162873i	0.352272	+	0.935898i	$0.385409\pi$
$20$		0			0
$21$			94.2656i			0.979545i
$22$		0			0
$23$	9.50500	−	16.4631i	0.0861709	−	0.149252i	−0.819719	−	0.572766i	$-0.805870\pi$
$23$	9.50500	−	16.4631i	0.0861709	−	0.149252i	0.905890	+	0.423514i	$0.139204\pi$
$24$		0			0
$25$	−55.6971			−0.445577
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	77.0557	−	133.464i	0.493410	−	0.854611i	−0.506561	−	0.862204i	$-0.669084\pi$
$29$	77.0557	−	133.464i	0.493410	−	0.854611i	0.999971	+	0.00759297i	$0.00241694\pi$
$30$		0			0
$31$			308.270i			1.78603i	0.450025	+	0.893016i	$0.351415\pi$
$31$			308.270i			1.78603i	−0.450025	+	0.893016i	$0.648585\pi$
$32$		0			0
$33$	−105.212	+	60.7443i	−0.555003	+	0.320431i
$34$		0			0
$35$	−211.192	−	365.796i	−1.01994	−	1.76659i
$36$		0			0
$37$	−37.6821	−	21.7558i	−0.167430	−	0.0966657i	0.413944	−	0.910303i	$-0.364151\pi$
$37$	−37.6821	−	21.7558i	−0.167430	−	0.0966657i	−0.581373	+	0.813637i	$0.697484\pi$
$38$		0			0
$39$	−9.86357	+	140.270i	−0.0404983	+	0.575928i
$40$		0			0
$41$	41.4293	+	23.9192i	0.157809	+	0.0911110i	0.576825	−	0.816868i	$-0.304292\pi$
$41$	41.4293	+	23.9192i	0.157809	+	0.0911110i	−0.419016	+	0.907979i	$0.637625\pi$
$42$		0			0
$43$	−171.061	−	296.286i	−0.606663	−	1.05077i	−0.991786	−	0.127906i	$-0.959174\pi$
$43$	−171.061	−	296.286i	−0.606663	−	1.05077i	0.385123	−	0.922865i	$-0.374159\pi$
$44$		0			0
$45$	−104.773	+	60.4906i	−0.347080	+	0.200387i
$46$		0			0
$47$		−	133.468i		−	0.414218i	−0.978318	−	0.207109i	$-0.933594\pi$
$47$		−	133.468i		−	0.414218i	0.978318	−	0.207109i	$-0.0664055\pi$
$48$		0			0
$49$	322.167	−	558.010i	0.939263	−	1.62685i
$50$		0			0
$51$	129.424			0.355353
$52$		0			0
$53$	−438.454			−1.13635			−0.568173	−	0.822909i	$-0.692350\pi$
$53$	−438.454			−1.13635			−0.568173	+	0.822909i	$0.692350\pi$
$54$		0			0
$55$	272.182	−	471.433i	0.667291	−	1.15578i
$56$		0			0
$57$		−	80.9338i		−	0.188069i
$58$		0			0
$59$	−511.434	+	295.277i	−1.12853	+	0.651555i	−0.943564	−	0.331190i	$-0.892550\pi$
$59$	−511.434	+	295.277i	−1.12853	+	0.651555i	−0.184963	+	0.982746i	$0.559216\pi$
$60$		0			0
$61$	270.652	+	468.783i	0.568089	+	0.983960i	0.996755	+	0.0804965i	$0.0256506\pi$
$61$	270.652	+	468.783i	0.568089	+	0.983960i	−0.428665	+	0.903463i	$0.641016\pi$
$62$		0			0
$63$	−244.909	−	141.398i	−0.489773	−	0.282770i
$64$		0			0
$65$	−275.985	−	566.413i	−0.526642	−	1.08084i
$66$		0			0
$67$	199.485	+	115.173i	0.363746	+	0.210009i	0.670723	−	0.741708i	$-0.265984\pi$
$67$	199.485	+	115.173i	0.363746	+	0.210009i	−0.306977	+	0.951717i	$0.599317\pi$
$68$		0			0
$69$	28.5150	+	49.3894i	0.0497508	+	0.0861709i
$70$		0			0
$71$	389.202	−	224.706i	0.650561	−	0.375601i	−0.138110	−	0.990417i	$-0.544103\pi$
$71$	389.202	−	224.706i	0.650561	−	0.375601i	0.788671	+	0.614816i	$0.210770\pi$
$72$		0			0
$73$		−	389.711i		−	0.624826i	−0.949946	−	0.312413i	$-0.898863\pi$
$73$		−	389.711i		−	0.624826i	0.949946	−	0.312413i	$-0.101137\pi$
$74$		0			0
$75$	83.5457	−	144.705i	0.128627	−	0.222789i
$76$		0			0
$77$	1272.47			1.88326
$78$		0			0
$79$	897.820			1.27864			0.639321	−	0.768940i	$-0.279216\pi$
$79$	897.820			1.27864			0.639321	+	0.768940i	$0.279216\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	1300.24i		−	1.71952i	−0.510700	−	0.859759i	$-0.670614\pi$
$83$		−	1300.24i		−	1.71952i	0.510700	−	0.859759i	$-0.329386\pi$
$84$		0			0
$85$	−502.228	+	289.961i	−0.640874	+	0.370009i
$86$		0			0
$87$	231.167	+	400.393i	0.284870	+	0.493410i
$88$		0			0
$89$	801.113	+	462.523i	0.954132	+	0.550869i	0.894362	−	0.447344i	$-0.147630\pi$
$89$	801.113	+	462.523i	0.954132	+	0.550869i	0.0597703	+	0.998212i	$0.480963\pi$
$90$		0			0
$91$	824.061	−	1220.69i	0.949287	−	1.40619i
$92$		0			0
$93$	−800.910	−	462.406i	−0.893016	−	0.515583i
$94$		0			0
$95$	181.324	+	314.062i	0.195825	+	0.339179i
$96$		0			0
$97$	1351.43	−	780.247i	1.41460	−	0.816722i	0.418787	−	0.908085i	$-0.362455\pi$
$97$	1351.43	−	780.247i	1.41460	−	0.816722i	0.995818	+	0.0913623i	$0.0291221\pi$
$98$		0			0
$99$		−	364.466i		−	0.370002i
$100$		0			0
$101$	479.420	−	830.380i	0.472318	−	0.818078i	−0.527181	−	0.849753i	$-0.676751\pi$
$101$	479.420	−	830.380i	0.472318	−	0.818078i	0.999498	+	0.0316752i	$0.0100842\pi$
$102$		0			0
$103$	635.153			0.607606			0.303803	−	0.952735i	$-0.401743\pi$
$103$	635.153			0.607606			0.303803	+	0.952735i	$0.401743\pi$
$104$		0			0
$105$	1267.15			1.17773
$106$		0			0
$107$	−724.162	+	1254.29i	−0.654275	+	1.13324i	0.327800	+	0.944747i	$0.393693\pi$
$107$	−724.162	+	1254.29i	−0.654275	+	1.13324i	−0.982075	+	0.188490i	$0.939641\pi$
$108$		0			0
$109$			331.084i			0.290937i	0.989363	+	0.145468i	$0.0464689\pi$
$109$			331.084i			0.290937i	−0.989363	+	0.145468i	$0.953531\pi$
$110$		0			0
$111$	113.046	−	65.2674i	0.0966657	−	0.0558100i
$112$		0			0
$113$	−347.602	−	602.065i	−0.289378	−	0.501217i	0.684284	−	0.729216i	$-0.260115\pi$
$113$	−347.602	−	602.065i	−0.289378	−	0.501217i	−0.973661	+	0.227999i	$0.926782\pi$
$114$		0			0
$115$	−221.304	−	127.770i	−0.179449	−	0.103605i
$116$		0			0
$117$	−349.637	−	236.032i	−0.276273	−	0.186505i
$118$		0			0
$119$	−1173.97	−	677.792i	−0.904351	−	0.522127i
$120$		0			0
$121$	154.470	+	267.550i	0.116056	+	0.201014i
$122$		0			0
$123$	−124.288	+	71.7576i	−0.0911110	+	0.0526030i
$124$		0			0
$125$		−	931.594i		−	0.666595i
$126$		0			0
$127$	−123.577	+	214.042i	−0.0863441	+	0.149552i	−0.905963	−	0.423357i	$-0.860852\pi$
$127$	−123.577	+	214.042i	−0.0863441	+	0.149552i	0.819619	+	0.572909i	$0.194185\pi$
$128$		0			0
$129$	1026.36			0.700514
$130$		0			0
$131$	−472.243			−0.314962			−0.157481	−	0.987522i	$-0.550337\pi$
$131$	−472.243			−0.314962			−0.157481	+	0.987522i	$0.550337\pi$
$132$		0			0
$133$	−423.849	+	734.127i	−0.276333	+	0.478623i
$134$		0			0
$135$		−	362.944i		−	0.231387i
$136$		0			0
$137$	−1585.43	+	915.349i	−0.988704	+	0.570829i	−0.904887	−	0.425652i	$-0.860045\pi$
$137$	−1585.43	+	915.349i	−0.988704	+	0.570829i	−0.0838175	+	0.996481i	$0.526711\pi$
$138$		0			0
$139$	−50.0000	−	86.6025i	−0.0305104	−	0.0528456i	0.850367	−	0.526190i	$-0.176380\pi$
$139$	−50.0000	−	86.6025i	−0.0305104	−	0.0528456i	−0.880877	+	0.473344i	$0.843047\pi$
$140$		0			0
$141$	346.759	+	200.202i	0.207109	+	0.119575i
$142$		0			0
$143$	1893.47	+	133.146i	1.10727	+	0.0778615i
$144$		0			0
$145$	−1794.08	−	1035.81i	−1.02752	−	0.593237i
$146$		0			0
$147$	966.501	+	1674.03i	0.542284	+	0.939263i
$148$		0			0
$149$	−129.520	+	74.7784i	−0.0712127	+	0.0411147i	−0.535184	−	0.844736i	$-0.679758\pi$
$149$	−129.520	+	74.7784i	−0.0712127	+	0.0411147i	0.463971	+	0.885850i	$0.346424\pi$
$150$		0			0
$151$			800.032i			0.431163i	0.976486	+	0.215582i	$0.0691647\pi$
$151$			800.032i			0.431163i	−0.976486	+	0.215582i	$0.930835\pi$
$152$		0			0
$153$	−194.136	+	336.254i	−0.102582	+	0.177677i
$154$		0			0
$155$	4143.88			2.14739
$156$		0			0
$157$	−2706.16			−1.37564			−0.687818	−	0.725884i	$-0.741431\pi$
$157$	−2706.16			−1.37564			−0.687818	+	0.725884i	$0.741431\pi$
$158$		0			0
$159$	657.681	−	1139.14i	0.328035	−	0.568173i
$160$		0			0
$161$		−	597.330i		−	0.292399i
$162$		0			0
$163$	−3185.46	+	1839.12i	−1.53070	+	0.883750i	−0.531371	+	0.847139i	$0.678323\pi$
$163$	−3185.46	+	1839.12i	−1.53070	+	0.883750i	−0.999330	+	0.0366108i	$0.988344\pi$
$164$		0			0
$165$	816.546	+	1414.30i	0.385261	+	0.667291i
$166$		0			0
$167$	−2791.30	−	1611.56i	−1.29339	−	0.746742i	−0.314140	−	0.949377i	$-0.601716\pi$
$167$	−2791.30	−	1611.56i	−1.29339	−	0.746742i	−0.979254	+	0.202635i	$0.935050\pi$
$168$		0			0
$169$	1353.96	−	1730.20i	0.616275	−	0.787531i
$170$		0			0
$171$	210.272	+	121.401i	0.0940346	+	0.0542909i
$172$		0			0
$173$	−1344.77	−	2329.21i	−0.590988	−	1.02362i	−0.994100	−	0.108471i	$-0.965405\pi$
$173$	−1344.77	−	2329.21i	−0.590988	−	1.02362i	0.403111	−	0.915151i	$-0.367929\pi$
$174$		0			0
$175$	−1515.64	+	875.054i	−0.654694	+	0.377988i
$176$		0			0
$177$		−	1771.66i		−	0.752351i
$178$		0			0
$179$	762.021	−	1319.86i	0.318191	−	0.551122i	−0.661920	−	0.749574i	$-0.730258\pi$
$179$	762.021	−	1319.86i	0.318191	−	0.551122i	0.980111	+	0.198452i	$0.0635915\pi$
$180$		0			0
$181$	−476.881			−0.195836			−0.0979180	−	0.995194i	$-0.531218\pi$
$181$	−476.881			−0.195836			−0.0979180	+	0.995194i	$0.531218\pi$
$182$		0			0
$183$	−1623.91			−0.655973
$184$		0			0
$185$	−292.449	+	506.537i	−0.116223	+	0.201305i
$186$		0			0
$187$		−	1747.06i		−	0.683197i
$188$		0			0
$189$	734.728	−	424.195i	0.282770	−	0.163258i
$190$		0			0
$191$	−684.871	−	1186.23i	−0.259453	−	0.449386i	0.706642	−	0.707571i	$-0.250209\pi$
$191$	−684.871	−	1186.23i	−0.259453	−	0.449386i	−0.966096	+	0.258185i	$0.916876\pi$
$192$		0			0
$193$	1857.38	+	1072.36i	0.692732	+	0.399949i	0.804635	−	0.593770i	$-0.202361\pi$
$193$	1857.38	+	1072.36i	0.692732	+	0.399949i	−0.111903	+	0.993719i	$0.535695\pi$
$194$		0			0
$195$	1885.56	+	132.590i	0.692451	+	0.0486920i
$196$		0			0
$197$	−207.620	−	119.869i	−0.0750879	−	0.0433520i	0.461986	−	0.886887i	$-0.347137\pi$
$197$	−207.620	−	119.869i	−0.0750879	−	0.0433520i	−0.537074	+	0.843535i	$0.680470\pi$
$198$		0			0
$199$	794.969	+	1376.93i	0.283185	+	0.490491i	0.972167	−	0.234287i	$-0.0752755\pi$
$199$	794.969	+	1376.93i	0.283185	+	0.490491i	−0.688982	+	0.724778i	$0.741942\pi$
$200$		0			0
$201$	−598.455	+	345.518i	−0.210009	+	0.121249i
$202$		0			0
$203$		−	4842.47i		−	1.67426i
$204$		0			0
$205$	321.531	−	556.908i	0.109545	−	0.189737i
$206$		0			0
$207$	−171.090			−0.0574472
$208$		0			0
$209$	−1092.50			−0.361579
$210$		0			0
$211$	−936.427	+	1621.94i	−0.305527	+	0.529189i	−0.977379	−	0.211497i	$-0.932166\pi$
$211$	−936.427	+	1621.94i	−0.305527	+	0.529189i	0.671851	+	0.740686i	$0.265499\pi$
$212$		0			0
$213$			1348.24i			0.433707i
$214$		0			0
$215$	−3982.78	+	2299.46i	−1.26337	+	0.729404i
$216$		0			0
$217$	4843.22	+	8388.70i	1.51511	+	2.62425i
$218$		0			0
$219$	1012.50	+	584.567i	0.312413	+	0.180372i
$220$		0			0
$221$	−1675.98	−	1131.42i	−0.510130	−	0.344377i
$222$		0			0
$223$	48.6085	+	28.0642i	0.0145967	+	0.00842742i	0.507281	−	0.861781i	$-0.330651\pi$
$223$	48.6085	+	28.0642i	0.0145967	+	0.00842742i	−0.492684	+	0.870208i	$0.663984\pi$
$224$		0			0
$225$	250.637	+	434.116i	0.0742629	+	0.128627i
$226$		0			0
$227$	−577.976	+	333.695i	−0.168994	+	0.0975687i	−0.582111	−	0.813109i	$-0.697773\pi$
$227$	−577.976	+	333.695i	−0.168994	+	0.0975687i	0.413117	+	0.910678i	$0.364440\pi$
$228$		0			0
$229$			723.299i			0.208720i	0.994540	+	0.104360i	$0.0332795\pi$
$229$			723.299i			0.208720i	−0.994540	+	0.104360i	$0.966721\pi$
$230$		0			0
$231$	−1908.70	+	3305.96i	−0.543650	+	0.941629i
$232$		0			0
$233$	275.451			0.0774482			0.0387241	−	0.999250i	$-0.487671\pi$
$233$	275.451			0.0774482			0.0387241	+	0.999250i	$0.487671\pi$
$234$		0			0
$235$	−1794.12			−0.498024
$236$		0			0
$237$	−1346.73	+	2332.60i	−0.369112	+	0.639321i
$238$		0			0
$239$		−	1529.39i		−	0.413925i	−0.978349	−	0.206963i	$-0.933642\pi$
$239$		−	1529.39i		−	0.413925i	0.978349	−	0.206963i	$-0.0663579\pi$
$240$		0			0
$241$	844.830	−	487.763i	0.225810	−	0.130372i	−0.382827	−	0.923820i	$-0.625050\pi$
$241$	844.830	−	487.763i	0.225810	−	0.130372i	0.608638	+	0.793448i	$0.291716\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−7500.97	−	4330.69i	−1.95600	−	1.12930i
$246$		0			0
$247$	−707.516	+	1048.05i	−0.182260	+	0.269984i
$248$		0			0
$249$	3378.13	+	1950.36i	0.859759	+	0.496382i
$250$		0			0
$251$	937.070	+	1623.05i	0.235647	+	0.408152i	0.959460	−	0.281843i	$-0.0909458\pi$
$251$	937.070	+	1623.05i	0.235647	+	0.408152i	−0.723814	+	0.689995i	$0.757613\pi$
$252$		0			0
$253$	666.694	−	384.916i	0.165671	−	0.0956501i
$254$		0			0
$255$		−	1739.77i		−	0.427249i
$256$		0			0
$257$	−909.094	+	1574.60i	−0.220653	+	0.382181i	−0.955006	−	0.296586i	$-0.904152\pi$
$257$	−909.094	+	1574.60i	−0.220653	+	0.382181i	0.734354	+	0.678767i	$0.237485\pi$
$258$		0			0
$259$	−1367.22			−0.328010
$260$		0			0
$261$	−1387.00			−0.328940
$262$		0			0
$263$	336.899	−	583.527i	0.0789890	−	0.136813i	−0.823825	−	0.566844i	$-0.808164\pi$
$263$	336.899	−	583.527i	0.0789890	−	0.136813i	0.902814	+	0.430031i	$0.141497\pi$
$264$		0			0
$265$			5893.86i			1.36625i
$266$		0			0
$267$	−2403.34	+	1387.57i	−0.550869	+	0.318044i
$268$		0			0
$269$	1678.20	+	2906.73i	0.380378	+	0.658834i	0.991116	−	0.132998i	$-0.0424605\pi$
$269$	1678.20	+	2906.73i	0.380378	+	0.658834i	−0.610738	+	0.791833i	$0.709127\pi$
$270$		0			0
$271$	7721.09	+	4457.77i	1.73071	+	0.999227i	0.885013	+	0.465567i	$0.154150\pi$
$271$	7721.09	+	4457.77i	1.73071	+	0.999227i	0.845699	+	0.533660i	$0.179184\pi$
$272$		0			0
$273$	1935.37	+	3972.02i	0.429061	+	0.880577i
$274$		0			0
$275$	−1953.34	−	1127.76i	−0.428330	−	0.247296i
$276$		0			0
$277$	2008.65	+	3479.09i	0.435698	+	0.754651i	0.997352	−	0.0727208i	$-0.0231682\pi$
$277$	2008.65	+	3479.09i	0.435698	+	0.754651i	−0.561654	+	0.827372i	$0.689835\pi$
$278$		0			0
$279$	2402.73	−	1387.22i	0.515583	−	0.297672i
$280$		0			0
$281$			1841.12i			0.390860i	0.980718	+	0.195430i	$0.0626103\pi$
$281$			1841.12i			0.390860i	−0.980718	+	0.195430i	$0.937390\pi$
$282$		0			0
$283$	−2424.70	+	4199.70i	−0.509305	+	0.882143i	0.490637	+	0.871364i	$0.336764\pi$
$283$	−2424.70	+	4199.70i	−0.509305	+	0.882143i	−0.999942	+	0.0107784i	$0.996569\pi$
$284$		0			0
$285$	−1087.94			−0.226120
$286$		0			0
$287$	1503.17			0.309162
$288$		0			0
$289$	1525.91	−	2642.95i	0.310586	−	0.537951i
$290$		0			0
$291$			4681.48i			0.943070i
$292$		0			0
$293$	−1224.43	+	706.927i	−0.244137	+	0.140953i	−0.617077	−	0.786903i	$-0.711683\pi$
$293$	−1224.43	+	706.927i	−0.244137	+	0.140953i	0.372940	+	0.927856i	$0.378350\pi$
$294$		0			0
$295$	3969.22	+	6874.89i	0.783379	+	1.35685i
$296$		0			0
$297$	946.909	+	546.698i	0.185001	+	0.106810i
$298$		0			0
$299$	62.5022	−	888.845i	0.0120889	−	0.171917i
$300$		0			0
$301$	−9309.86	−	5375.05i	−1.78276	−	1.02928i
$302$		0			0
$303$	1438.26	+	2491.14i	0.272693	+	0.472318i
$304$		0			0
$305$	6301.55	−	3638.20i	1.18304	−	0.683026i
$306$		0			0
$307$			4625.64i			0.859932i	0.902845	+	0.429966i	$0.141474\pi$
$307$			4625.64i			0.859932i	−0.902845	+	0.429966i	$0.858526\pi$
$308$		0			0
$309$	−952.729	+	1650.18i	−0.175401	+	0.303803i
$310$		0			0
$311$	−6060.79			−1.10507			−0.552534	−	0.833490i	$-0.686339\pi$
$311$	−6060.79			−1.10507			−0.552534	+	0.833490i	$0.686339\pi$
$312$		0			0
$313$	969.946			0.175158			0.0875792	−	0.996158i	$-0.472087\pi$
$313$	969.946			0.175158			0.0875792	+	0.996158i	$0.472087\pi$
$314$		0			0
$315$	−1900.73	+	3292.16i	−0.339981	+	0.588864i
$316$		0			0
$317$		−	8741.63i		−	1.54883i	−0.632679	−	0.774414i	$-0.718045\pi$
$317$		−	8741.63i		−	1.54883i	0.632679	−	0.774414i	$-0.281955\pi$
$318$		0			0
$319$	5404.80	−	3120.46i	0.948623	−	0.547687i
$320$		0			0
$321$	−2172.49	−	3762.86i	−0.377746	−	0.654275i
$322$		0			0
$323$	1007.94	+	581.933i	0.173632	+	0.100247i
$324$		0			0
$325$	−2346.88	+	1143.52i	−0.400558	+	0.195172i
$326$		0			0
$327$	−860.181	−	496.626i	−0.145468	−	0.0839862i
$328$		0			0
$329$	−2096.90	−	3631.94i	−0.351386	−	0.608618i
$330$		0			0
$331$	6051.57	−	3493.88i	1.00491	−	0.580184i	0.0952114	−	0.995457i	$-0.469647\pi$
$331$	6051.57	−	3493.88i	1.00491	−	0.580184i	0.909697	+	0.415273i	$0.136314\pi$
$332$		0			0
$333$			391.604i			0.0644438i
$334$		0			0
$335$	1548.19	−	2681.55i	0.252498	−	0.437339i
$336$		0			0
$337$	4156.59			0.671881			0.335940	−	0.941883i	$-0.390946\pi$
$337$	4156.59			0.671881			0.335940	+	0.941883i	$0.390946\pi$
$338$		0			0
$339$	2085.61			0.334144
$340$		0			0
$341$	−6241.89	+	10811.3i	−0.991252	+	1.71690i
$342$		0			0
$343$		−	9468.49i		−	1.49053i
$344$		0			0
$345$	663.911	−	383.309i	0.103605	−	0.0598164i
$346$		0			0
$347$	−156.256	−	270.644i	−0.0241737	−	0.0418701i	0.853685	−	0.520789i	$-0.174362\pi$
$347$	−156.256	−	270.644i	−0.0241737	−	0.0418701i	−0.877859	+	0.478919i	$0.841029\pi$
$348$		0			0
$349$	3861.39	+	2229.37i	0.592251	+	0.341936i	0.765987	−	0.642856i	$-0.222251\pi$
$349$	3861.39	+	2229.37i	0.592251	+	0.341936i	−0.173736	+	0.984792i	$0.555584\pi$
$350$		0			0
$351$	1137.68	−	554.337i	0.173006	−	0.0842972i
$352$		0			0
$353$	−1947.84	−	1124.59i	−0.293692	−	0.169563i	0.345914	−	0.938266i	$-0.387569\pi$
$353$	−1947.84	−	1124.59i	−0.293692	−	0.169563i	−0.639605	+	0.768703i	$0.720902\pi$
$354$		0			0
$355$	−3020.58	−	5231.80i	−0.451594	−	0.782183i
$356$		0			0
$357$	3521.91	−	2033.38i	0.522127	−	0.301450i
$358$		0			0
$359$			7842.79i			1.15300i	0.817098	+	0.576499i	$0.195582\pi$
$359$			7842.79i			1.15300i	−0.817098	+	0.576499i	$0.804418\pi$
$360$		0			0
$361$	−3065.60	+	5309.77i	−0.446945	+	0.774131i
$362$		0			0
$363$	−926.820			−0.134009
$364$		0			0
$365$	−5238.64			−0.751241
$366$		0			0
$367$	3330.12	−	5767.94i	0.473653	−	0.820392i	−0.525892	−	0.850552i	$-0.676268\pi$
$367$	3330.12	−	5767.94i	0.473653	−	0.820392i	0.999545	+	0.0301597i	$0.00960160\pi$
$368$		0			0
$369$		−	430.546i		−	0.0607407i
$370$		0			0
$371$	−11931.3	+	6888.53i	−1.66965	+	0.963975i
$372$		0			0
$373$	18.4936	+	32.0319i	0.00256720	+	0.00444651i	0.867306	−	0.497775i	$-0.165850\pi$
$373$	18.4936	+	32.0319i	0.00256720	+	0.00444651i	−0.864739	+	0.502222i	$0.832516\pi$
$374$		0			0
$375$	2420.35	+	1397.39i	0.333297	+	0.192429i
$376$		0			0
$377$	506.696	−	7205.74i	0.0692207	−	0.984389i
$378$		0			0
$379$	−10461.5	−	6039.93i	−1.41786	−	0.818603i	−0.421751	−	0.906712i	$-0.638584\pi$
$379$	−10461.5	−	6039.93i	−1.41786	−	0.818603i	−0.996111	+	0.0881092i	$0.971918\pi$
$380$		0			0
$381$	−370.731	−	642.126i	−0.0498508	−	0.0863441i
$382$		0			0
$383$	−9151.63	+	5283.69i	−1.22096	+	0.704919i	−0.965122	−	0.261801i	$-0.915684\pi$
$383$	−9151.63	+	5283.69i	−1.22096	+	0.704919i	−0.255835	+	0.966721i	$0.582350\pi$
$384$		0			0
$385$		−	17104.9i		−	2.26428i
$386$		0			0
$387$	−1539.55	+	2666.57i	−0.202221	+	0.350257i
$388$		0			0
$389$	9757.49			1.27179			0.635893	−	0.771778i	$-0.280632\pi$
$389$	9757.49			1.27179			0.635893	+	0.771778i	$0.280632\pi$
$390$		0			0
$391$	−820.119			−0.106075
$392$		0			0
$393$	708.364	−	1226.92i	0.0909218	−	0.157481i
$394$		0			0
$395$		−	12068.8i		−	1.53734i
$396$		0			0
$397$	−12298.0	+	7100.26i	−1.55471	+	0.897612i	−0.556962	+	0.830538i	$0.688033\pi$
$397$	−12298.0	+	7100.26i	−1.55471	+	0.897612i	−0.997748	+	0.0670737i	$0.978634\pi$
$398$		0			0
$399$	−1271.55	−	2202.38i	−0.159541	−	0.276333i
$400$		0			0
$401$	10978.1	+	6338.19i	1.36713	+	0.789313i	0.990561	−	0.137076i	$-0.0437705\pi$
$401$	10978.1	+	6338.19i	1.36713	+	0.789313i	0.376569	+	0.926389i	$0.377104\pi$
$402$		0			0
$403$	6329.10	+	12989.4i	0.782319	+	1.60558i
$404$		0			0
$405$	942.956	+	544.416i	0.115693	+	0.0667956i
$406$		0			0
$407$	−881.026	−	1525.98i	−0.107299	−	0.185848i
$408$		0			0
$409$	−1328.20	+	766.838i	−0.160576	+	0.0927083i	−0.578134	−	0.815942i	$-0.696219\pi$
$409$	−1328.20	+	766.838i	−0.160576	+	0.0927083i	0.417559	+	0.908650i	$0.362886\pi$
$410$		0			0
$411$		−	5492.09i		−	0.659136i
$412$		0			0
$413$	−9278.15	+	16070.2i	−1.10544	+	1.91468i
$414$		0			0
$415$	−17478.3			−2.06741
$416$		0			0
$417$	300.000			0.0352304
$418$		0			0
$419$	−1082.95	+	1875.72i	−0.126266	+	0.218699i	−0.922227	−	0.386649i	$-0.873633\pi$
$419$	−1082.95	+	1875.72i	−0.126266	+	0.218699i	0.795961	+	0.605348i	$0.206966\pi$
$420$		0			0
$421$		−	734.575i		−	0.0850380i	−0.999096	−	0.0425190i	$-0.986462\pi$
$421$		−	734.575i		−	0.0850380i	0.999096	−	0.0425190i	$-0.0135383\pi$
$422$		0			0
$423$	−1040.28	+	600.605i	−0.119575	+	0.0690364i
$424$		0			0
$425$	1201.43	+	2080.93i	0.137124	+	0.237506i
$426$		0			0
$427$	14730.0	+	8504.40i	1.66941	+	0.963833i
$428$		0			0
$429$	−3186.12	+	4719.66i	−0.358572	+	0.531159i
$430$		0			0
$431$	11872.6	+	6854.66i	1.32688	+	0.766073i	0.984815	−	0.173605i	$-0.0555416\pi$
$431$	11872.6	+	6854.66i	1.32688	+	0.766073i	0.342061	+	0.939678i	$0.388875\pi$
$432$		0			0
$433$	5024.97	+	8703.50i	0.557701	+	0.965967i	0.997688	+	0.0679624i	$0.0216498\pi$
$433$	5024.97	+	8703.50i	0.557701	+	0.965967i	−0.439987	+	0.898004i	$0.645017\pi$
$434$		0			0
$435$	5382.23	−	3107.43i	0.593237	−	0.342506i
$436$		0			0
$437$			512.850i			0.0561395i
$438$		0			0
$439$	4066.73	−	7043.79i	0.442129	−	0.765790i	−0.555718	−	0.831371i	$-0.687557\pi$
$439$	4066.73	−	7043.79i	0.442129	−	0.765790i	0.997847	+	0.0655807i	$0.0208900\pi$
$440$		0			0
$441$	−5799.01			−0.626175
$442$		0			0
$443$	2370.78			0.254264			0.127132	−	0.991886i	$-0.459423\pi$
$443$	2370.78			0.254264			0.127132	+	0.991886i	$0.459423\pi$
$444$		0			0
$445$	6217.40	−	10768.9i	0.662321	−	1.14717i
$446$		0			0
$447$		−	448.670i		−	0.0474751i
$448$		0			0
$449$	11191.8	−	6461.60i	1.17634	−	0.679158i	0.221172	−	0.975235i	$-0.429012\pi$
$449$	11191.8	−	6461.60i	1.17634	−	0.679158i	0.955164	+	0.296077i	$0.0956785\pi$
$450$		0			0
$451$	968.636	+	1677.73i	0.101134	+	0.175169i
$452$		0			0
$453$	−2078.54	−	1200.05i	−0.215582	−	0.124466i
$454$		0			0
$455$	−16409.0	−	11077.3i	−1.69070	−	1.14135i
$456$		0			0
$457$	7275.71	+	4200.63i	0.744734	+	0.429972i	0.823788	−	0.566898i	$-0.191857\pi$
$457$	7275.71	+	4200.63i	0.744734	+	0.429972i	−0.0790543	+	0.996870i	$0.525190\pi$
$458$		0			0
$459$	−582.409	−	1008.76i	−0.0592256	−	0.102582i
$460$		0			0
$461$	−15265.7	+	8813.67i	−1.54229	+	0.890441i	−0.543596	+	0.839347i	$0.682937\pi$
$461$	−15265.7	+	8813.67i	−1.54229	+	0.890441i	−0.998694	+	0.0510940i	$0.983729\pi$
$462$		0			0
$463$			5461.81i			0.548233i	0.961697	+	0.274116i	$0.0883853\pi$
$463$			5461.81i			0.548233i	−0.961697	+	0.274116i	$0.911615\pi$
$464$		0			0
$465$	−6215.82	+	10766.1i	−0.619897	+	1.07369i
$466$		0			0
$467$	8262.19			0.818691			0.409345	−	0.912379i	$-0.365757\pi$
$467$	8262.19			0.818691			0.409345	+	0.912379i	$0.365757\pi$
$468$		0			0
$469$	7237.89			0.712611
$470$		0			0
$471$	4059.23	−	7030.80i	0.397112	−	0.687818i
$472$		0			0
$473$		−	13854.6i		−	1.34680i
$474$		0			0
$475$	1301.28	−	751.297i	0.125699	−	0.0725723i
$476$		0			0
$477$	1973.04	+	3417.41i	0.189391	+	0.328035i
$478$		0			0
$479$	−1364.74	−	787.935i	−0.130181	−	0.0751601i	0.433495	−	0.901156i	$-0.357280\pi$
$479$	−1364.74	−	787.935i	−0.130181	−	0.0751601i	−0.563676	+	0.825996i	$0.690613\pi$
$480$		0			0
$481$	−2034.46	−	143.060i	−0.192855	−	0.0135613i
$482$		0			0
$483$	1551.91	+	895.995i	0.146199	+	0.0844082i
$484$		0			0
$485$	−10488.4	−	18166.4i	−0.981963	−	1.70081i
$486$		0			0
$487$	−10908.2	+	6297.84i	−1.01498	+	0.586001i	−0.912647	−	0.408749i	$-0.865965\pi$
$487$	−10908.2	+	6297.84i	−1.01498	+	0.586001i	−0.102337	+	0.994750i	$0.532632\pi$
$488$		0			0
$489$		−	11034.7i		−	1.02047i
$490$		0			0
$491$	535.606	−	927.697i	0.0492293	−	0.0852676i	−0.840361	−	0.542028i	$-0.817657\pi$
$491$	535.606	−	927.697i	0.0492293	−	0.0852676i	0.889590	+	0.456760i	$0.150990\pi$
$492$		0			0
$493$	−6648.59			−0.607378
$494$		0			0
$495$	−4899.28			−0.444861
$496$		0			0
$497$	7060.68	−	12229.5i	0.637253	−	1.10376i
$498$		0			0
$499$		−	1422.30i		−	0.127597i	−0.997963	−	0.0637985i	$-0.979678\pi$
$499$		−	1422.30i		−	0.127597i	0.997963	−	0.0637985i	$-0.0203215\pi$
$500$		0			0
$501$	8373.89	−	4834.67i	0.746742	−	0.431132i
$502$		0			0
$503$	−4674.67	−	8096.76i	−0.414380	−	0.717727i	0.580983	−	0.813916i	$-0.302668\pi$
$503$	−4674.67	−	8096.76i	−0.414380	−	0.717727i	−0.995363	+	0.0961884i	$0.969335\pi$
$504$		0			0
$505$	−11162.3	−	6444.54i	−0.983593	−	0.567878i
$506$		0			0
$507$	2464.27	+	6112.99i	0.215862	+	0.535478i
$508$		0			0
$509$	11896.0	+	6868.15i	1.03591	+	0.598086i	0.918673	−	0.395018i	$-0.129262\pi$
$509$	11896.0	+	6868.15i	1.03591	+	0.598086i	0.117241	+	0.993103i	$0.462595\pi$
$510$		0			0
$511$	−6122.73	−	10604.9i	−0.530046	−	0.918067i
$512$		0			0
$513$	−630.816	+	364.202i	−0.0542909	+	0.0313449i
$514$		0			0
$515$		−	8537.96i		−	0.730538i
$516$		0			0
$517$	2702.47	−	4680.81i	0.229892	−	0.398185i
$518$		0			0
$519$	8068.62			0.682414
$520$		0			0
$521$	11052.3			0.929386			0.464693	−	0.885472i	$-0.346165\pi$
$521$	11052.3			0.929386			0.464693	+	0.885472i	$0.346165\pi$
$522$		0			0
$523$	3238.52	−	5609.28i	0.270766	−	0.468980i	−0.698292	−	0.715813i	$-0.746056\pi$
$523$	3238.52	−	5609.28i	0.270766	−	0.468980i	0.969058	+	0.246832i	$0.0793897\pi$
$524$		0			0
$525$		−	5250.33i		−	0.436463i
$526$		0			0
$527$	11517.5	−	6649.61i	0.952009	−	0.549643i
$528$		0			0
$529$	5902.81	+	10224.0i	0.485149	+	0.840303i
$530$		0			0
$531$	4602.91	+	2657.49i	0.376176	+	0.217185i
$532$		0			0
$533$	2236.77	+	157.286i	0.181773	+	0.0127820i
$534$		0			0
$535$	16860.6	+	9734.45i	1.36252	+	0.786649i
$536$		0			0
$537$	2286.06	+	3959.58i	0.183707	+	0.318191i
$538$		0			0
$539$	22597.3	−	13046.5i	1.80581	−	1.04259i
$540$		0			0
$541$			18341.5i			1.45761i	0.684723	+	0.728803i	$0.259923\pi$
$541$			18341.5i			1.45761i	−0.684723	+	0.728803i	$0.740077\pi$
$542$		0			0
$543$	715.322	−	1238.97i	0.0565330	−	0.0979180i
$544$		0			0
$545$	4450.55			0.349799
$546$		0			0
$547$	18943.1			1.48071			0.740356	−	0.672215i	$-0.234657\pi$
$547$	18943.1			1.48071			0.740356	+	0.672215i	$0.234657\pi$
$548$		0			0
$549$	2435.87	−	4219.05i	0.189363	−	0.327987i
$550$		0			0
$551$			4157.61i			0.321452i
$552$		0			0
$553$	24431.6	−	14105.6i	1.87873	−	1.08469i
$554$		0			0
$555$	−877.348	−	1519.61i	−0.0671015	−	0.116223i
$556$		0			0
$557$	−359.861	−	207.766i	−0.0273749	−	0.0158049i	0.486250	−	0.873820i	$-0.338364\pi$
$557$	−359.861	−	207.766i	−0.0273749	−	0.0158049i	−0.513625	+	0.858015i	$0.671698\pi$
$558$		0			0
$559$	−13290.9	−	8972.38i	−1.00563	−	0.678875i
$560$		0			0
$561$	4539.00	+	2620.59i	0.341599	+	0.197222i
$562$		0			0
$563$	−9145.90	−	15841.2i	−0.684643	−	1.18584i	−0.973549	−	0.228478i	$-0.926625\pi$
$563$	−9145.90	−	15841.2i	−0.684643	−	1.18584i	0.288907	−	0.957357i	$-0.406708\pi$
$564$		0			0
$565$	−8093.17	+	4672.59i	−0.602623	+	0.347925i
$566$		0			0
$567$			2545.17i			0.188514i
$568$		0			0
$569$	2173.73	−	3765.02i	0.160154	−	0.277395i	−0.774770	−	0.632244i	$-0.782134\pi$
$569$	2173.73	−	3765.02i	0.160154	−	0.277395i	0.934924	+	0.354848i	$0.115468\pi$
$570$		0			0
$571$	−16756.0			−1.22805			−0.614024	−	0.789288i	$-0.710450\pi$
$571$	−16756.0			−1.22805			−0.614024	+	0.789288i	$0.710450\pi$
$572$		0			0
$573$	4109.23			0.299591
$574$		0			0
$575$	−529.401	+	916.950i	−0.0383958	+	0.0665034i
$576$		0			0
$577$		−	19974.7i		−	1.44117i	−0.693364	−	0.720587i	$-0.743872\pi$
$577$		−	19974.7i		−	1.44117i	0.693364	−	0.720587i	$-0.256128\pi$
$578$		0			0
$579$	−5572.14	+	3217.08i	−0.399949	+	0.230911i
$580$		0			0
$581$	−20428.0	−	35382.4i	−1.45869	−	2.52652i
$582$		0			0
$583$	−15376.9	−	8877.86i	−1.09236	−	0.630675i
$584$		0			0
$585$	−3172.82	+	4699.95i	−0.224239	+	0.332169i
$586$		0			0
$587$	13638.7	+	7874.33i	0.958996	+	0.553677i	0.895864	−	0.444329i	$-0.146558\pi$
$587$	13638.7	+	7874.33i	0.958996	+	0.553677i	0.0631321	+	0.998005i	$0.479891\pi$
$588$		0			0
$589$	−4158.25	−	7202.30i	−0.290896	−	0.503846i
$590$		0			0
$591$	622.860	−	359.608i	0.0433520	−	0.0250293i
$592$		0			0
$593$			13318.4i			0.922297i	0.887323	+	0.461148i	$0.152562\pi$
$593$			13318.4i			0.922297i	−0.887323	+	0.461148i	$0.847438\pi$
$594$		0			0
$595$	−9111.13	+	15780.9i	−0.627765	+	1.08732i
$596$		0			0
$597$	−4769.82			−0.326994
$598$		0			0
$599$	−2970.80			−0.202644			−0.101322	−	0.994854i	$-0.532307\pi$
$599$	−2970.80			−0.202644			−0.101322	+	0.994854i	$0.532307\pi$
$600$		0			0
$601$	−5316.31	+	9208.13i	−0.360827	+	0.624971i	−0.988097	−	0.153831i	$-0.950839\pi$
$601$	−5316.31	+	9208.13i	−0.360827	+	0.624971i	0.627270	+	0.778802i	$0.284172\pi$
$602$		0			0
$603$		−	2073.11i		−	0.140006i
$604$		0			0
$605$	3596.50	−	2076.44i	0.241684	−	0.139536i
$606$		0			0
$607$	5793.94	+	10035.4i	0.387428	+	0.671045i	0.992103	−	0.125428i	$-0.0400303\pi$
$607$	5793.94	+	10035.4i	0.387428	+	0.671045i	−0.604675	+	0.796472i	$0.706697\pi$
$608$		0			0
$609$	12581.1	+	7263.71i	0.837130	+	0.483317i
$610$		0			0
$611$	−2740.22	−	5623.85i	−0.181436	−	0.372368i
$612$		0			0
$613$	18006.7	+	10396.2i	1.18643	+	0.684988i	0.957494	−	0.288453i	$-0.0931409\pi$
$613$	18006.7	+	10396.2i	1.18643	+	0.684988i	0.228939	+	0.973441i	$0.426474\pi$
$614$		0			0
$615$	964.592	+	1670.72i	0.0632457	+	0.109545i
$616$		0			0
$617$	1353.40	−	781.388i	0.0883079	−	0.0509846i	−0.455196	−	0.890391i	$-0.650431\pi$
$617$	1353.40	−	781.388i	0.0883079	−	0.0509846i	0.543504	+	0.839407i	$0.317097\pi$
$618$		0			0
$619$		−	758.406i		−	0.0492454i	−0.999697	−	0.0246227i	$-0.992162\pi$
$619$		−	758.406i		−	0.0492454i	0.999697	−	0.0246227i	$-0.00783844\pi$
$620$		0			0
$621$	256.635	−	444.505i	0.0165836	−	0.0287236i
$622$		0			0
$623$	29066.7			1.86923
$624$		0			0
$625$	−19485.0			−1.24704
$626$		0			0
$627$	1638.75	−	2838.41i	0.104379	−	0.180789i
$628$		0			0
$629$			1877.15i			0.118994i
$630$		0			0
$631$	12354.0	−	7132.59i	0.779406	−	0.449990i	−0.0568136	−	0.998385i	$-0.518094\pi$
$631$	12354.0	−	7132.59i	0.779406	−	0.449990i	0.836220	+	0.548394i	$0.184761\pi$
$632$		0			0
$633$	−2809.28	−	4865.82i	−0.176396	−	0.305527i
$634$		0			0
$635$	2877.23	+	1661.17i	0.179810	+	0.103813i
$636$		0			0
$637$	2118.48	−	30127.0i	0.131770	−	1.87390i
$638$		0			0
$639$	−3502.82	−	2022.35i	−0.216854	−	0.125200i
$640$		0			0
$641$	1992.82	+	3451.67i	0.122795	+	0.212688i	0.920869	−	0.389872i	$-0.127481\pi$
$641$	1992.82	+	3451.67i	0.122795	+	0.212688i	−0.798074	+	0.602560i	$0.794147\pi$
$642$		0			0
$643$	−7063.78	+	4078.28i	−0.433232	+	0.250127i	−0.700723	−	0.713434i	$-0.747139\pi$
$643$	−7063.78	+	4078.28i	−0.433232	+	0.250127i	0.267490	+	0.963561i	$0.413806\pi$
$644$		0			0
$645$		−	13796.8i		−	0.842243i
$646$		0			0
$647$	−5639.62	+	9768.11i	−0.342684	+	0.593546i	−0.984930	−	0.172953i	$-0.944669\pi$
$647$	−5639.62	+	9768.11i	−0.342684	+	0.593546i	0.642246	+	0.766498i	$0.278003\pi$
$648$		0			0
$649$	−23915.2			−1.44646
$650$		0			0
$651$	−29059.3			−1.74950
$652$		0			0
$653$	−3282.88	+	5686.11i	−0.196736	+	0.340757i	−0.947468	−	0.319850i	$-0.896368\pi$
$653$	−3282.88	+	5686.11i	−0.196736	+	0.340757i	0.750732	+	0.660607i	$0.229701\pi$
$654$		0			0
$655$			6348.06i			0.378686i
$656$		0			0
$657$	−3037.50	+	1753.70i	−0.180372	+	0.104138i
$658$		0			0
$659$	2399.67	+	4156.36i	0.141848	+	0.245688i	0.928193	−	0.372100i	$-0.121362\pi$
$659$	2399.67	+	4156.36i	0.141848	+	0.245688i	−0.786344	+	0.617788i	$0.788029\pi$
$660$		0			0
$661$	−13504.5	−	7796.80i	−0.794648	−	0.458790i	0.0469482	−	0.998897i	$-0.485050\pi$
$661$	−13504.5	−	7796.80i	−0.794648	−	0.458790i	−0.841596	+	0.540107i	$0.818384\pi$
$662$		0			0
$663$	5453.48	−	2657.21i	0.319450	−	0.155652i
$664$		0			0
$665$	9868.41	+	5697.53i	0.575459	+	0.332242i
$666$		0			0
$667$	−1464.83	−	2537.16i	−0.0850351	−	0.147285i
$668$		0			0
$669$	−145.826	+	84.1925i	−0.00842742	+	0.00486557i
$670$		0			0
$671$			21920.8i			1.26116i
$672$		0			0
$673$	−1102.77	+	1910.06i	−0.0631630	+	0.109402i	−0.895878	−	0.444301i	$-0.853452\pi$
$673$	−1102.77	+	1910.06i	−0.0631630	+	0.109402i	0.832715	+	0.553702i	$0.186785\pi$
$674$		0			0
$675$	−1503.82			−0.0857514
$676$		0			0
$677$	−15046.4			−0.854182			−0.427091	−	0.904209i	$-0.640462\pi$
$677$	−15046.4			−0.854182			−0.427091	+	0.904209i	$0.640462\pi$
$678$		0			0
$679$	24516.8	−	42464.4i	1.38567	−	2.40005i
$680$		0			0
$681$		−	2002.17i		−	0.112663i
$682$		0			0
$683$	−26528.5	+	15316.3i	−1.48622	+	0.858068i	−0.999877	−	0.0157020i	$-0.995002\pi$
$683$	−26528.5	+	15316.3i	−1.48622	+	0.858068i	−0.486340	+	0.873770i	$0.661668\pi$
$684$		0			0
$685$	12304.5	+	21311.9i	0.686320	+	1.18874i
$686$		0			0
$687$	−1879.19	−	1084.95i	−0.104360	−	0.0602524i
$688$		0			0
$689$	−18474.9	+	9001.90i	−1.02153	+	0.497743i
$690$		0			0
$691$	−1884.22	−	1087.86i	−0.103733	−	0.0598901i	0.447236	−	0.894416i	$-0.352408\pi$
$691$	−1884.22	−	1087.86i	−0.103733	−	0.0598901i	−0.550969	+	0.834526i	$0.685742\pi$
$692$		0			0
$693$	−5726.10	−	9917.89i	−0.313876	−	0.543650i
$694$		0			0
$695$	−1164.14	+	672.118i	−0.0635373	+	0.0366833i
$696$		0			0
$697$		−	2063.82i		−	0.112156i
$698$		0			0
$699$	−413.177	+	715.644i	−0.0223574	+	0.0387241i
$700$		0			0
$701$	32718.2			1.76284			0.881419	−	0.472335i	$-0.156589\pi$
$701$	32718.2			1.76284			0.881419	+	0.472335i	$0.156589\pi$
$702$		0			0
$703$	1173.85			0.0629768
$704$		0			0
$705$	2691.18	−	4661.26i	0.143767	−	0.249012i
$706$		0			0
$707$		−	30128.6i		−	1.60269i
$708$		0			0
$709$	−21840.9	+	12609.8i	−1.15691	+	0.667945i	−0.950563	−	0.310533i	$-0.899492\pi$
$709$	−21840.9	+	12609.8i	−1.15691	+	0.667945i	−0.206352	+	0.978478i	$0.566159\pi$
$710$		0			0
$711$	−4040.19	−	6997.81i	−0.213107	−	0.369112i
$712$		0			0
$713$	5075.10	+	2930.11i	0.266569	+	0.153904i
$714$		0			0
$715$	1789.79	−	25452.7i	0.0936146	−	1.33130i
$716$		0			0
$717$	3973.48	+	2294.09i	0.206963	+	0.119490i
$718$		0			0
$719$	17733.1	+	30714.6i	0.919796	+	1.59313i	0.799724	+	0.600368i	$0.204979\pi$
$719$	17733.1	+	30714.6i	0.919796	+	1.59313i	0.120071	+	0.992765i	$0.461688\pi$
$720$		0			0
$721$	17283.9	−	9978.85i	0.892767	−	0.515439i
$722$		0			0
$723$			2926.58i			0.150540i
$724$		0			0
$725$	−4291.78	+	7433.59i	−0.219852	+	0.380795i
$726$		0			0
$727$	−14262.2			−0.727588			−0.363794	−	0.931479i	$-0.618519\pi$
$727$	−14262.2			−0.727588			−0.363794	+	0.931479i	$0.618519\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−7379.80	+	12782.2i	−0.373395	+	0.646739i
$732$		0			0
$733$		−	16022.5i		−	0.807371i	−0.914898	−	0.403685i	$-0.867729\pi$
$733$		−	16022.5i		−	0.807371i	0.914898	−	0.403685i	$-0.132271\pi$
$734$		0			0
$735$	22502.9	−	12992.1i	1.12930	−	0.651999i
$736$		0			0
$737$	4664.05	+	8078.38i	0.233111	+	0.403760i
$738$		0			0
$739$	3287.61	+	1898.11i	0.163649	+	0.0944830i	0.579588	−	0.814910i	$-0.303214\pi$
$739$	3287.61	+	1898.11i	0.163649	+	0.0944830i	−0.415939	+	0.909393i	$0.636547\pi$
$740$		0			0
$741$	−1661.65	−	3410.26i	−0.0823782	−	0.169068i
$742$		0			0
$743$	26266.0	+	15164.7i	1.29691	+	0.748772i	0.979869	−	0.199639i	$-0.0639771\pi$
$743$	26266.0	+	15164.7i	1.29691	+	0.748772i	0.317042	+	0.948412i	$0.397310\pi$
$744$		0			0
$745$	1005.20	+	1741.05i	0.0494331	+	0.0856206i
$746$		0			0
$747$	−10134.4	+	5851.09i	−0.496382	+	0.286586i
$748$		0			0
$749$			45509.1i			2.22011i
$750$		0			0
$751$	−10775.9	+	18664.5i	−0.523595	+	0.906893i	0.476028	+	0.879430i	$0.342076\pi$
$751$	−10775.9	+	18664.5i	−0.523595	+	0.906893i	−0.999623	+	0.0274629i	$0.991257\pi$
$752$		0			0
$753$	−5622.42			−0.272101
$754$		0			0
$755$	10754.3			0.518397
$756$		0			0
$757$	10208.8	−	17682.2i	0.490153	−	0.848970i	−0.509783	−	0.860303i	$-0.670274\pi$
$757$	10208.8	−	17682.2i	0.490153	−	0.848970i	0.999936	+	0.0113335i	$0.00360764\pi$
$758$		0			0
$759$			2309.50i			0.110447i
$760$		0			0
$761$	−27171.9	+	15687.7i	−1.29432	+	0.747278i	−0.979417	−	0.201845i	$-0.935306\pi$
$761$	−27171.9	+	15687.7i	−1.29432	+	0.747278i	−0.314906	+	0.949123i	$0.601973\pi$
$762$		0			0
$763$	5201.64	+	9009.50i	0.246805	+	0.427478i
$764$		0			0
$765$	4520.05	+	2609.65i	0.213625	+	0.123336i
$766$		0			0
$767$	−15487.7	+	22942.2i	−0.729111	+	1.08004i
$768$		0			0
$769$	10784.3	+	6226.33i	0.505712	+	0.291973i	0.731069	−	0.682303i	$-0.239022\pi$
$769$	10784.3	+	6226.33i	0.505712	+	0.291973i	−0.225357	+	0.974276i	$0.572355\pi$
$770$		0			0
$771$	−2727.28	−	4723.79i	−0.127394	−	0.220653i
$772$		0			0
$773$	32432.4	−	18724.9i	1.50907	−	0.871264i	0.509129	−	0.860690i	$-0.329967\pi$
$773$	32432.4	−	18724.9i	1.50907	−	0.871264i	0.999944	−	0.0105740i	$-0.00336588\pi$
$774$		0			0
$775$		−	17169.8i		−	0.795815i
$776$		0			0
$777$	2050.82	−	3552.13i	0.0946884	−	0.164005i
$778$		0			0
$779$	−1290.58			−0.0593580
$780$		0			0
$781$	18199.5			0.833839
$782$		0			0
$783$	2080.50	−	3603.54i	0.0949568	−	0.164470i
$784$		0			0
$785$			36377.1i			1.65396i
$786$		0			0
$787$	22915.2	−	13230.1i	1.03791	−	0.599240i	0.118672	−	0.992934i	$-0.462136\pi$
$787$	22915.2	−	13230.1i	1.03791	−	0.599240i	0.919242	+	0.393694i	$0.128803\pi$
$788$		0			0
$789$	1010.70	+	1750.58i	0.0456043	+	0.0789890i
$790$		0			0
$791$	−18918.0	−	10922.3i	−0.850375	−	0.490964i
$792$		0			0
$793$	21028.9	+	14196.1i	0.941687	+	0.635710i
$794$		0			0
$795$	−15312.7	−	8840.79i	−0.683127	−	0.394403i
$796$		0			0
$797$	2374.74	+	4113.17i	0.105543	+	0.182805i	0.913960	−	0.405805i	$-0.133009\pi$
$797$	2374.74	+	4113.17i	0.105543	+	0.182805i	−0.808417	+	0.588610i	$0.799675\pi$
$798$		0			0
$799$	−4986.56	+	2878.99i	−0.220791	+	0.127474i
$800$		0			0
$801$		−	8325.41i		−	0.367246i
$802$		0			0
$803$	7890.91	−	13667.5i	0.346780	−	0.600640i
$804$		0			0
$805$	−8029.53			−0.351557
$806$		0			0
$807$	−10069.2			−0.439223
$808$		0			0
$809$	2232.02	−	3865.98i	0.0970009	−	0.168010i	−0.813441	−	0.581647i	$-0.802408\pi$
$809$	2232.02	−	3865.98i	0.0970009	−	0.168010i	0.910442	+	0.413637i	$0.135742\pi$
$810$		0			0
$811$		−	20774.6i		−	0.899499i	−0.893155	−	0.449749i	$-0.851513\pi$
$811$		−	20774.6i		−	0.899499i	0.893155	−	0.449749i	$-0.148487\pi$
$812$		0			0
$813$	−23163.3	+	13373.3i	−0.999227	+	0.576904i
$814$		0			0
$815$	24722.2	+	42820.1i	1.06255	+	1.84039i
$816$		0			0
$817$	7993.18	+	4614.86i	0.342284	+	0.197618i
$818$		0			0
$819$	−13222.7	−	929.796i	−0.564148	−	0.0396700i
$820$		0			0
$821$	30977.0	+	17884.6i	1.31682	+	0.760264i	0.983215	−	0.182450i	$-0.0584029\pi$
$821$	30977.0	+	17884.6i	1.31682	+	0.760264i	0.333601	+	0.942714i	$0.391736\pi$
$822$		0			0
$823$	−1472.72	−	2550.83i	−0.0623764	−	0.108039i	0.833151	−	0.553046i	$-0.186535\pi$
$823$	−1472.72	−	2550.83i	−0.0623764	−	0.108039i	−0.895527	+	0.445007i	$0.853201\pi$
$824$		0			0
$825$	5860.02	−	3383.28i	0.247296	−	0.142777i
$826$		0			0
$827$		−	17878.6i		−	0.751753i	−0.926670	−	0.375877i	$-0.877342\pi$
$827$		−	17878.6i		−	0.751753i	0.926670	−	0.375877i	$-0.122658\pi$
$828$		0			0
$829$	6711.90	−	11625.4i	0.281199	−	0.487051i	−0.690481	−	0.723350i	$-0.742601\pi$
$829$	6711.90	−	11625.4i	0.281199	−	0.487051i	0.971680	+	0.236299i	$0.0759345\pi$
$830$		0			0
$831$	−12051.9			−0.503101
$832$		0			0
$833$	−27797.5			−1.15621
$834$		0			0
$835$	−21663.1	+	37521.6i	−0.897824	+	1.55508i
$836$		0			0
$837$			8323.30i			0.343722i
$838$		0			0
$839$	−27316.8	+	15771.3i	−1.12405	+	0.648971i	−0.942432	−	0.334398i	$-0.891467\pi$
$839$	−27316.8	+	15771.3i	−1.12405	+	0.648971i	−0.181619	+	0.983369i	$0.558134\pi$
$840$		0			0
$841$	319.334	+	553.103i	0.0130934	+	0.0226784i
$842$		0			0
$843$	−4783.36	−	2761.67i	−0.195430	−	0.112832i
$844$		0			0
$845$	−23258.0	−	18200.4i	−0.946865	−	0.740961i
$846$		0			0
$847$	8406.92	+	4853.74i	0.341045	+	0.196902i
$848$		0			0
$849$	−7274.10	−	12599.1i	−0.294048	−	0.509305i
$850$		0			0
$851$	−716.338	+	413.578i	−0.0288552	+	0.0166595i
$852$		0			0
$853$		−	21810.6i		−	0.875476i	−0.899103	−	0.437738i	$-0.855780\pi$
$853$		−	21810.6i		−	0.875476i	0.899103	−	0.437738i	$-0.144220\pi$
$854$		0			0
$855$	1631.91	−	2826.55i	0.0652751	−	0.113060i
$856$		0			0
$857$	−33234.6			−1.32470			−0.662352	−	0.749193i	$-0.730442\pi$
$857$	−33234.6			−1.32470			−0.662352	+	0.749193i	$0.730442\pi$
$858$		0			0
$859$	−42697.7			−1.69596			−0.847978	−	0.530032i	$-0.822180\pi$
$859$	−42697.7			−1.69596			−0.847978	+	0.530032i	$0.822180\pi$
$860$		0			0
$861$	−2254.76	+	3905.36i	−0.0892474	+	0.154581i
$862$		0			0
$863$			27419.2i			1.08153i	0.841174	+	0.540765i	$0.181865\pi$
$863$			27419.2i			1.08153i	−0.841174	+	0.540765i	$0.818135\pi$
$864$		0			0
$865$	−31310.1	+	18076.9i	−1.23072	+	0.710558i
$866$		0			0
$867$	4577.73	+	7928.85i	0.179317	+	0.310586i
$868$		0			0
$869$	31487.2	+	18179.1i	1.22915	+	0.709649i
$870$		0			0
$871$	10770.2	+	757.343i	0.418983	+	0.0294622i
$872$		0			0
$873$	−12162.8	−	7022.22i	−0.471535	−	0.272241i
$874$		0			0
$875$	−14636.2	−	25350.7i	−0.565479	−	0.979439i
$876$		0			0
$877$	−36896.3	+	21302.1i	−1.42064	+	0.820206i	−0.996353	−	0.0853227i	$-0.972808\pi$
$877$	−36896.3	+	21302.1i	−1.42064	+	0.820206i	−0.424285	+	0.905529i	$0.639475\pi$
$878$		0			0
$879$		−	4241.56i		−	0.162758i
$880$		0			0
$881$	−2349.70	+	4069.80i	−0.0898562	+	0.155636i	−0.907450	−	0.420160i	$-0.861974\pi$
$881$	−2349.70	+	4069.80i	−0.0898562	+	0.155636i	0.817594	+	0.575795i	$0.195307\pi$
$882$		0			0
$883$	22233.5			0.847358			0.423679	−	0.905812i	$-0.360738\pi$
$883$	22233.5			0.847358			0.423679	+	0.905812i	$0.360738\pi$
$884$		0			0
$885$	−23815.3			−0.904568
$886$		0			0
$887$	−4426.23	+	7666.45i	−0.167552	+	0.290208i	−0.937558	−	0.347828i	$-0.886919\pi$
$887$	−4426.23	+	7666.45i	−0.167552	+	0.290208i	0.770007	+	0.638036i	$0.220253\pi$
$888$		0			0
$889$			7766.05i			0.292986i
$890$		0			0
$891$	−2840.73	+	1640.09i	−0.106810	+	0.0616669i
$892$		0			0
$893$	1800.34	+	3118.28i	0.0674649	+	0.116853i
$894$		0			0
$895$	−17742.0	−	10243.4i	−0.662626	−	0.382567i
$896$		0			0
$897$	2215.53	+	1495.65i	0.0824688	+	0.0556727i
$898$		0			0
$899$	41143.1	+	23754.0i	1.52636	+	0.881246i
$900$		0			0
$901$	9457.77	+	16381.3i	0.349705	+	0.605707i
$902$		0			0
$903$	27929.6	−	16125.1i	1.02928	−	0.594254i
$904$		0			0
$905$			6410.41i			0.235458i
$906$		0			0
$907$	−18586.2	+	32192.3i	−0.680424	+	1.17853i	0.294427	+	0.955674i	$0.404871\pi$
$907$	−18586.2	+	32192.3i	−0.680424	+	1.17853i	−0.974851	+	0.222856i	$0.928462\pi$
$908$		0			0
$909$	−8629.56			−0.314878
$910$		0			0
$911$	−38035.1			−1.38327			−0.691635	−	0.722247i	$-0.743109\pi$
$911$	−38035.1			−1.38327			−0.691635	+	0.722247i	$0.743109\pi$
$912$		0			0
$913$	26327.4	−	45600.4i	0.954337	−	1.65296i
$914$		0			0
$915$			21829.2i			0.788691i
$916$		0			0
$917$	−12850.7	+	7419.38i	−0.462780	+	0.267186i
$918$		0			0
$919$	−4176.14	−	7233.28i	−0.149900	−	0.259634i	0.781290	−	0.624168i	$-0.214562\pi$
$919$	−4176.14	−	7233.28i	−0.149900	−	0.259634i	−0.931190	+	0.364533i	$0.881228\pi$
$920$		0			0
$921$	−12017.8	−	6938.46i	−0.429966	−	0.248241i
$922$		0			0
$923$	11786.2	−	17459.0i	0.420310	−	0.622611i
$924$		0			0
$925$	2098.79	+	1211.74i	0.0746029	+	0.0430720i
$926$		0			0
$927$	−2858.19	−	4950.53i	−0.101268	−	0.175401i
$928$		0			0
$929$	−17521.5	+	10116.0i	−0.618796	+	0.357262i	−0.776400	−	0.630240i	$-0.782956\pi$
$929$	−17521.5	+	10116.0i	−0.618796	+	0.357262i	0.157604	+	0.987502i	$0.449623\pi$
$930$		0			0
$931$			17382.8i			0.611921i
$932$		0			0
$933$	9091.19	−	15746.4i	0.319006	−	0.552534i
$934$		0			0
$935$	−23484.7			−0.821423
$936$		0			0
$937$	−27766.9			−0.968095			−0.484048	−	0.875042i	$-0.660834\pi$
$937$	−27766.9			−0.968095			−0.484048	+	0.875042i	$0.660834\pi$
$938$		0			0
$939$	−1454.92	+	2519.99i	−0.0505639	+	0.0875792i
$940$		0			0
$941$			400.765i			0.0138837i	0.999976	+	0.00694185i	$0.00220968\pi$
$941$			400.765i			0.0138837i	−0.999976	+	0.00694185i	$0.997790\pi$
$942$		0			0
$943$	787.571	−	454.704i	0.0271971	−	0.0157022i
$944$		0			0
$945$	−5702.19	−	9876.48i	−0.196288	−	0.339981i
$946$		0			0
$947$	18883.1	+	10902.2i	0.647961	+	0.374101i	0.787675	−	0.616091i	$-0.211285\pi$
$947$	18883.1	+	10902.2i	0.647961	+	0.374101i	−0.139713	+	0.990192i	$0.544618\pi$
$948$		0			0
$949$	−8001.16	−	16421.0i	−0.273687	−	0.561696i
$950$		0			0
$951$	22711.4	+	13112.4i	0.774414	+	0.447108i
$952$		0			0
$953$	15240.2	+	26396.8i	0.518026	+	0.897248i	0.999781	+	0.0209414i	$0.00666633\pi$
$953$	15240.2	+	26396.8i	0.518026	+	0.897248i	−0.481755	+	0.876306i	$0.660000\pi$
$954$		0			0
$955$	−15945.8	+	9206.29i	−0.540307	+	0.311946i
$956$		0			0
$957$			18722.8i			0.632415i
$958$		0			0
$959$	−28762.0	+	49817.2i	−0.968480	+	1.67746i
$960$		0			0
$961$	−65239.6			−2.18991
$962$		0			0
$963$	13034.9			0.436183
$964$		0			0
$965$	14415.0	−	24967.6i	0.480867	−	0.832886i
$966$		0			0
$967$			23864.1i			0.793608i	0.917903	+	0.396804i	$0.129881\pi$
$967$			23864.1i			0.793608i	−0.917903	+	0.396804i	$0.870119\pi$
$968$		0			0
$969$	−3023.81	+	1745.80i	−0.100247	+	0.0578774i
$970$		0			0
$971$	−7005.15	−	12133.3i	−0.231520	−	0.401004i	0.726736	−	0.686917i	$-0.241037\pi$
$971$	−7005.15	−	12133.3i	−0.231520	−	0.401004i	−0.958256	+	0.285913i	$0.907703\pi$
$972$		0			0
$973$	−2721.21	−	1571.09i	−0.0896589	−	0.0517646i
$974$		0			0
$975$	549.373	−	7812.65i	0.0180451	−	0.256620i
$976$		0			0
$977$	−22038.8	−	12724.1i	−0.721681	−	0.416663i	0.0936898	−	0.995601i	$-0.470134\pi$
$977$	−22038.8	−	12724.1i	−0.721681	−	0.416663i	−0.815371	+	0.578938i	$0.803467\pi$
$978$		0			0
$979$	18730.4	+	32442.0i	0.611467	+	1.05909i
$980$		0			0
$981$	2580.54	−	1489.88i	0.0839862	−	0.0484894i
$982$		0			0
$983$		−	52479.9i		−	1.70280i	−0.524519	−	0.851399i	$-0.675755\pi$
$983$		−	52479.9i		−	1.70280i	0.524519	−	0.851399i	$-0.324245\pi$
$984$		0			0
$985$	−1611.33	+	2790.90i	−0.0521230	+	0.0902798i
$986$		0			0
$987$	12581.4			0.405746
$988$		0			0
$989$	−6503.73			−0.209107
$990$		0			0
$991$	19024.3	−	32951.0i	0.609814	−	1.05623i	−0.381457	−	0.924386i	$-0.624578\pi$
$991$	19024.3	−	32951.0i	0.609814	−	1.05623i	0.991271	−	0.131842i	$-0.0420890\pi$
$992$		0			0
$993$			20963.3i			0.669939i
$994$		0			0
$995$	18509.2	−	10686.3i	0.589728	−	0.340480i
$996$		0			0
$997$	15618.3	+	27051.7i	0.496125	+	0.859314i	0.999990	−	0.00446833i	$-0.00142232\pi$
$997$	15618.3	+	27051.7i	0.496125	+	0.859314i	−0.503865	+	0.863783i	$0.668089\pi$
$998$		0			0
$999$	−1017.42	−	587.406i	−0.0322219	−	0.0186033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bv.c.433.1		4
4.3	odd	2		39.4.j.b.4.1	✓	4
12.11	even	2		117.4.q.d.82.2		4
13.10	even	6	inner	624.4.bv.c.49.2		4
52.7	even	12		507.4.a.k.1.2		4
52.19	even	12		507.4.a.k.1.3		4
52.23	odd	6		39.4.j.b.10.1	yes	4
52.35	odd	6		507.4.b.e.337.3		4
52.43	odd	6		507.4.b.e.337.2		4
156.23	even	6		117.4.q.d.10.2		4
156.59	odd	12		1521.4.a.z.1.3		4
156.71	odd	12		1521.4.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.b.4.1	✓	4	4.3	odd	2
39.4.j.b.10.1	yes	4	52.23	odd	6
117.4.q.d.10.2		4	156.23	even	6
117.4.q.d.82.2		4	12.11	even	2
507.4.a.k.1.2		4	52.7	even	12
507.4.a.k.1.3		4	52.19	even	12
507.4.b.e.337.2		4	52.43	odd	6
507.4.b.e.337.3		4	52.35	odd	6
624.4.bv.c.49.2		4	13.10	even	6	inner
624.4.bv.c.433.1		4	1.1	even	1	trivial
1521.4.a.z.1.2		4	156.71	odd	12
1521.4.a.z.1.3		4	156.59	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} -13.4424i q^{5} +(27.2121 - 15.7109i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} -13.4424i q^{5} +(27.2121 - 15.7109i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(35.0707 + 20.2481i) q^{11} +(42.1364 - 20.5310i) q^{13} +(34.9243 + 20.1635i) q^{15} +(-21.5707 - 37.3616i) q^{17} +(-23.3636 + 13.4890i) q^{19} +94.2656i q^{21} +(9.50500 - 16.4631i) q^{23} -55.6971 q^{25} +27.0000 q^{27} +(77.0557 - 133.464i) q^{29} +308.270i q^{31} +(-105.212 + 60.7443i) q^{33} +(-211.192 - 365.796i) q^{35} +(-37.6821 - 21.7558i) q^{37} +(-9.86357 + 140.270i) q^{39} +(41.4293 + 23.9192i) q^{41} +(-171.061 - 296.286i) q^{43} +(-104.773 + 60.4906i) q^{45} -133.468i q^{47} +(322.167 - 558.010i) q^{49} +129.424 q^{51} -438.454 q^{53} +(272.182 - 471.433i) q^{55} -80.9338i q^{57} +(-511.434 + 295.277i) q^{59} +(270.652 + 468.783i) q^{61} +(-244.909 - 141.398i) q^{63} +(-275.985 - 566.413i) q^{65} +(199.485 + 115.173i) q^{67} +(28.5150 + 49.3894i) q^{69} +(389.202 - 224.706i) q^{71} -389.711i q^{73} +(83.5457 - 144.705i) q^{75} +1272.47 q^{77} +897.820 q^{79} +(-40.5000 + 70.1481i) q^{81} -1300.24i q^{83} +(-502.228 + 289.961i) q^{85} +(231.167 + 400.393i) q^{87} +(801.113 + 462.523i) q^{89} +(824.061 - 1220.69i) q^{91} +(-800.910 - 462.406i) q^{93} +(181.324 + 314.062i) q^{95} +(1351.43 - 780.247i) q^{97} -364.466i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 66 * q^7 - 18 * q^9	\( 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9} + 126 q^{11} + 40 q^{13} + 54 q^{15} - 72 q^{17} - 222 q^{19} + 138 q^{23} + 120 q^{25} + 108 q^{27} - 6 q^{29} - 378 q^{33} - 402 q^{35} + 492 q^{37} - 168 q^{39} + 180 q^{41} - 470 q^{43} - 162 q^{45} + 346 q^{49} + 432 q^{51} - 2268 q^{53} + 446 q^{55} - 2160 q^{59} - 160 q^{61} - 594 q^{63} - 804 q^{65} + 498 q^{67} + 414 q^{69} + 1314 q^{71} - 180 q^{75} + 2976 q^{77} - 8 q^{79} - 162 q^{81} - 852 q^{85} - 18 q^{87} - 252 q^{89} + 1668 q^{91} - 1404 q^{93} + 54 q^{95} - 336 q^{97}+O(q^{100}) \) 4 * q - 6 * q^3 + 66 * q^7 - 18 * q^9 + 126 * q^11 + 40 * q^13 + 54 * q^15 - 72 * q^17 - 222 * q^19 + 138 * q^23 + 120 * q^25 + 108 * q^27 - 6 * q^29 - 378 * q^33 - 402 * q^35 + 492 * q^37 - 168 * q^39 + 180 * q^41 - 470 * q^43 - 162 * q^45 + 346 * q^49 + 432 * q^51 - 2268 * q^53 + 446 * q^55 - 2160 * q^59 - 160 * q^61 - 594 * q^63 - 804 * q^65 + 498 * q^67 + 414 * q^69 + 1314 * q^71 - 180 * q^75 + 2976 * q^77 - 8 * q^79 - 162 * q^81 - 852 * q^85 - 18 * q^87 - 252 * q^89 + 1668 * q^91 - 1404 * q^93 + 54 * q^95 - 336 * q^97

Introduction

L-functions

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