LMFDB - Embedded newform 672.4.bl.b.31.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,4,Mod(31,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("672.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	672.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$39.6492835239$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.17
Character	$\chi$	$=$	672.31
Dual form			672.4.bl.b.607.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(7.11284 - 4.10660i) q^{5} +(-18.3102 - 2.78176i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(7.11284 - 4.10660i) q^{5} +(-18.3102 - 2.78176i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(40.8910 + 23.6084i) q^{11} +81.4016i q^{13} -24.6396i q^{15} +(-94.4919 - 54.5549i) q^{17} +(22.4730 + 38.9245i) q^{19} +(-34.6925 + 43.3985i) q^{21} +(-21.3244 + 12.3117i) q^{23} +(-28.7716 + 49.8339i) q^{25} -27.0000 q^{27} -184.406 q^{29} +(2.55767 - 4.43001i) q^{31} +(122.673 - 70.8252i) q^{33} +(-141.661 + 55.4063i) q^{35} +(197.154 + 341.481i) q^{37} +(211.488 + 122.102i) q^{39} +220.708i q^{41} -140.609i q^{43} +(-64.0156 - 36.9594i) q^{45} +(56.9367 + 98.6172i) q^{47} +(327.524 + 101.869i) q^{49} +(-283.476 + 163.665i) q^{51} +(-60.9847 + 105.629i) q^{53} +387.801 q^{55} +134.838 q^{57} +(51.9763 - 90.0257i) q^{59} +(-57.8213 + 33.3831i) q^{61} +(60.7140 + 155.231i) q^{63} +(334.284 + 578.997i) q^{65} +(635.240 + 366.756i) q^{67} +73.8700i q^{69} -259.891i q^{71} +(-956.279 - 552.108i) q^{73} +(86.3149 + 149.502i) q^{75} +(-683.047 - 546.022i) q^{77} +(-328.369 + 189.584i) q^{79} +(-40.5000 + 70.1481i) q^{81} +693.821 q^{83} -896.142 q^{85} +(-276.609 + 479.101i) q^{87} +(-557.497 + 321.871i) q^{89} +(226.440 - 1490.48i) q^{91} +(-7.67300 - 13.2900i) q^{93} +(319.695 + 184.576i) q^{95} +345.596i q^{97} -424.951i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9}+O(q^{10}) $ 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9	$ 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9} - 12 q^{11} + 28 q^{19} + 120 q^{21} + 684 q^{25} - 1296 q^{27} + 460 q^{31} - 36 q^{33} + 568 q^{35} + 252 q^{37} + 324 q^{39} + 280 q^{47} - 184 q^{49} - 392 q^{53} + 848 q^{55} + 168 q^{57} - 964 q^{59} - 600 q^{61} + 180 q^{63} + 280 q^{65} - 660 q^{67} + 324 q^{73} - 2052 q^{75} + 1568 q^{77} - 2652 q^{79} - 1944 q^{81} + 1336 q^{83} - 1056 q^{85} - 3004 q^{91} - 1380 q^{93} - 3984 q^{95}+O(q^{100}) $ 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9 - 12 * q^11 + 28 * q^19 + 120 * q^21 + 684 * q^25 - 1296 * q^27 + 460 * q^31 - 36 * q^33 + 568 * q^35 + 252 * q^37 + 324 * q^39 + 280 * q^47 - 184 * q^49 - 392 * q^53 + 848 * q^55 + 168 * q^57 - 964 * q^59 - 600 * q^61 + 180 * q^63 + 280 * q^65 - 660 * q^67 + 324 * q^73 - 2052 * q^75 + 1568 * q^77 - 2652 * q^79 - 1944 * q^81 + 1336 * q^83 - 1056 * q^85 - 3004 * q^91 - 1380 * q^93 - 3984 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		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
$5$	7.11284	−	4.10660i	0.636192	−	0.367306i	−0.146954	−	0.989143i	$-0.546947\pi$
$5$	7.11284	−	4.10660i	0.636192	−	0.367306i	0.783146	+	0.621838i	$0.213614\pi$
$6$		0			0
$7$	−18.3102	−	2.78176i	−0.988655	−	0.150201i
$7$	−18.3102	−	2.78176i	−0.988655	−	0.150201i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	40.8910	+	23.6084i	1.12083	+	0.647109i	0.941612	−	0.336701i	$-0.109311\pi$
$11$	40.8910	+	23.6084i	1.12083	+	0.647109i	0.179214	+	0.983810i	$0.442644\pi$
$12$		0			0
$13$			81.4016i			1.73667i	0.495976	+	0.868336i	$0.334810\pi$
$13$			81.4016i			1.73667i	−0.495976	+	0.868336i	$0.665190\pi$
$14$		0			0
$15$		−	24.6396i		−	0.424128i
$16$		0			0
$17$	−94.4919	−	54.5549i	−1.34810	−	0.778324i	−0.360118	−	0.932907i	$-0.617263\pi$
$17$	−94.4919	−	54.5549i	−1.34810	−	0.778324i	−0.987980	+	0.154582i	$0.950597\pi$
$18$		0			0
$19$	22.4730	+	38.9245i	0.271351	+	0.469994i	0.969208	−	0.246243i	$-0.0791962\pi$
$19$	22.4730	+	38.9245i	0.271351	+	0.469994i	−0.697857	+	0.716237i	$0.745863\pi$
$20$		0			0
$21$	−34.6925	+	43.3985i	−0.360501	+	0.450968i
$22$		0			0
$23$	−21.3244	+	12.3117i	−0.193324	+	0.111616i	−0.593538	−	0.804806i	$-0.702269\pi$
$23$	−21.3244	+	12.3117i	−0.193324	+	0.111616i	0.400214	+	0.916422i	$0.368936\pi$
$24$		0			0
$25$	−28.7716	+	49.8339i	−0.230173	+	0.398671i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−184.406			−1.18080			−0.590402	−	0.807109i	$-0.701031\pi$
$29$	−184.406			−1.18080			−0.590402	+	0.807109i	$0.701031\pi$
$30$		0			0
$31$	2.55767	−	4.43001i	0.0148184	−	0.0256662i	−0.858521	−	0.512778i	$-0.828616\pi$
$31$	2.55767	−	4.43001i	0.0148184	−	0.0256662i	0.873340	+	0.487112i	$0.161950\pi$
$32$		0			0
$33$	122.673	−	70.8252i	0.647109	−	0.373609i
$34$		0			0
$35$	−141.661	+	55.4063i	−0.684145	+	0.267582i
$36$		0			0
$37$	197.154	+	341.481i	0.875998	+	1.51727i	0.855696	+	0.517479i	$0.173129\pi$
$37$	197.154	+	341.481i	0.875998	+	1.51727i	0.0203019	+	0.999794i	$0.493537\pi$
$38$		0			0
$39$	211.488	+	122.102i	0.868336	+	0.501334i
$40$		0			0
$41$			220.708i			0.840701i	0.907362	+	0.420350i	$0.138093\pi$
$41$			220.708i			0.840701i	−0.907362	+	0.420350i	$0.861907\pi$
$42$		0			0
$43$		−	140.609i		−	0.498667i	−0.968418	−	0.249334i	$-0.919788\pi$
$43$		−	140.609i		−	0.498667i	0.968418	−	0.249334i	$-0.0802116\pi$
$44$		0			0
$45$	−64.0156	−	36.9594i	−0.212064	−	0.122435i
$46$		0			0
$47$	56.9367	+	98.6172i	0.176704	+	0.306060i	0.940750	−	0.339102i	$-0.110123\pi$
$47$	56.9367	+	98.6172i	0.176704	+	0.306060i	−0.764046	+	0.645162i	$0.776790\pi$
$48$		0			0
$49$	327.524	+	101.869i	0.954879	+	0.296994i
$50$		0			0
$51$	−283.476	+	163.665i	−0.778324	+	0.449366i
$52$		0			0
$53$	−60.9847	+	105.629i	−0.158055	+	0.273759i	−0.934167	−	0.356836i	$-0.883856\pi$
$53$	−60.9847	+	105.629i	−0.158055	+	0.273759i	0.776112	+	0.630594i	$0.217189\pi$
$54$		0			0
$55$	387.801			0.950748
$56$		0			0
$57$	134.838			0.313329
$58$		0			0
$59$	51.9763	−	90.0257i	0.114691	−	0.198650i	−0.802965	−	0.596026i	$-0.796746\pi$
$59$	51.9763	−	90.0257i	0.114691	−	0.198650i	0.917656	+	0.397376i	$0.130079\pi$
$60$		0			0
$61$	−57.8213	+	33.3831i	−0.121365	+	0.0700700i	−0.559453	−	0.828862i	$-0.688989\pi$
$61$	−57.8213	+	33.3831i	−0.121365	+	0.0700700i	0.438089	+	0.898932i	$0.355656\pi$
$62$		0			0
$63$	60.7140	+	155.231i	0.121417	+	0.310434i
$64$		0			0
$65$	334.284	+	578.997i	0.637890	+	1.10486i
$66$		0			0
$67$	635.240	+	366.756i	1.15831	+	0.668752i	0.950899	−	0.309501i	$-0.100162\pi$
$67$	635.240	+	366.756i	1.15831	+	0.668752i	0.207414	+	0.978253i	$0.433495\pi$
$68$		0			0
$69$			73.8700i			0.128883i
$70$		0			0
$71$		−	259.891i		−	0.434413i	−0.976126	−	0.217207i	$-0.930305\pi$
$71$		−	259.891i		−	0.434413i	0.976126	−	0.217207i	$-0.0696946\pi$
$72$		0			0
$73$	−956.279	−	552.108i	−1.53321	−	0.885197i	−0.999211	−	0.0397089i	$-0.987357\pi$
$73$	−956.279	−	552.108i	−1.53321	−	0.885197i	−0.533995	−	0.845488i	$-0.679310\pi$
$74$		0			0
$75$	86.3149	+	149.502i	0.132890	+	0.230173i
$76$		0			0
$77$	−683.047	−	546.022i	−1.01091	−	0.808117i
$78$		0			0
$79$	−328.369	+	189.584i	−0.467650	+	0.269998i	−0.715256	−	0.698863i	$-0.753690\pi$
$79$	−328.369	+	189.584i	−0.467650	+	0.269998i	0.247605	+	0.968861i	$0.420356\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	693.821			0.917552			0.458776	−	0.888552i	$-0.348288\pi$
$83$	693.821			0.917552			0.458776	+	0.888552i	$0.348288\pi$
$84$		0			0
$85$	−896.142			−1.14353
$86$		0			0
$87$	−276.609	+	479.101i	−0.340869	+	0.590402i
$88$		0			0
$89$	−557.497	+	321.871i	−0.663984	+	0.383351i	−0.793793	−	0.608188i	$-0.791897\pi$
$89$	−557.497	+	321.871i	−0.663984	+	0.383351i	0.129809	+	0.991539i	$0.458563\pi$
$90$		0			0
$91$	226.440	−	1490.48i	0.260850	−	1.71697i
$92$		0			0
$93$	−7.67300	−	13.2900i	−0.00855541	−	0.0148184i
$94$		0			0
$95$	319.695	+	184.576i	0.345263	+	0.199338i
$96$		0			0
$97$			345.596i			0.361752i	0.983506	+	0.180876i	$0.0578933\pi$
$97$			345.596i			0.361752i	−0.983506	+	0.180876i	$0.942107\pi$
$98$		0			0
$99$		−	424.951i		−	0.431406i
$100$		0			0
$101$	901.580	+	520.528i	0.888224	+	0.512816i	0.873361	−	0.487073i	$-0.161936\pi$
$101$	901.580	+	520.528i	0.888224	+	0.512816i	0.0148626	+	0.999890i	$0.495269\pi$
$102$		0			0
$103$	766.154	+	1327.02i	0.732927	+	1.26947i	0.955627	+	0.294579i	$0.0951794\pi$
$103$	766.154	+	1327.02i	0.732927	+	1.26947i	−0.222701	+	0.974887i	$0.571487\pi$
$104$		0			0
$105$	−68.5415	+	451.155i	−0.0637044	+	0.419317i
$106$		0			0
$107$	1818.71	−	1050.03i	1.64319	−	0.948697i	0.663502	−	0.748174i	$-0.269069\pi$
$107$	1818.71	−	1050.03i	1.64319	−	0.948697i	0.979689	−	0.200522i	$-0.0642639\pi$
$108$		0			0
$109$	−1059.81	+	1835.64i	−0.931294	+	1.61305i	−0.150182	+	0.988658i	$0.547986\pi$
$109$	−1059.81	+	1835.64i	−0.931294	+	1.61305i	−0.781113	+	0.624390i	$0.785348\pi$
$110$		0			0
$111$	1182.92			1.01152
$112$		0			0
$113$	269.039			0.223974			0.111987	−	0.993710i	$-0.464279\pi$
$113$	269.039			0.223974			0.111987	+	0.993710i	$0.464279\pi$
$114$		0			0
$115$	−101.118	+	175.142i	−0.0819942	+	0.142018i
$116$		0			0
$117$	634.463	−	366.307i	0.501334	−	0.289445i
$118$		0			0
$119$	1578.40	+	1261.76i	1.21590	+	0.971980i
$120$		0			0
$121$	449.214	+	778.061i	0.337501	+	0.584568i
$122$		0			0
$123$	573.415	+	331.061i	0.420350	+	0.242689i
$124$		0			0
$125$			1499.27i			1.07279i
$126$		0			0
$127$			1326.96i			0.927156i	0.886056	+	0.463578i	$0.153435\pi$
$127$			1326.96i			0.927156i	−0.886056	+	0.463578i	$0.846565\pi$
$128$		0			0
$129$	−365.313	−	210.914i	−0.249334	−	0.143953i
$130$		0			0
$131$	767.720	+	1329.73i	0.512031	+	0.886863i	0.999903	+	0.0139481i	$0.00443996\pi$
$131$	767.720	+	1329.73i	0.512031	+	0.886863i	−0.487872	+	0.872915i	$0.662227\pi$
$132$		0			0
$133$	−303.206	−	775.227i	−0.197679	−	0.505419i
$134$		0			0
$135$	−192.047	+	110.878i	−0.122435	+	0.0706880i
$136$		0			0
$137$	880.026	−	1524.25i	0.548800	−	0.950550i	−0.449557	−	0.893252i	$-0.648418\pi$
$137$	880.026	−	1524.25i	0.548800	−	0.950550i	0.998357	−	0.0572984i	$-0.0182486\pi$
$138$		0			0
$139$	−2717.18			−1.65805			−0.829023	−	0.559214i	$-0.811103\pi$
$139$	−2717.18			−1.65805			−0.829023	+	0.559214i	$0.811103\pi$
$140$		0			0
$141$	341.620			0.204040
$142$		0			0
$143$	−1921.76	+	3328.59i	−1.12382	+	1.94651i
$144$		0			0
$145$	−1311.65	+	757.282i	−0.751219	+	0.433716i
$146$		0			0
$147$	755.949	−	698.128i	0.424147	−	0.391705i
$148$		0			0
$149$	−857.940	−	1486.00i	−0.471713	−	0.817030i	0.527764	−	0.849391i	$-0.323031\pi$
$149$	−857.940	−	1486.00i	−0.471713	−	0.817030i	−0.999476	+	0.0323610i	$0.989697\pi$
$150$		0			0
$151$	−876.950	−	506.307i	−0.472617	−	0.272866i	0.244717	−	0.969594i	$-0.421305\pi$
$151$	−876.950	−	506.307i	−0.472617	−	0.272866i	−0.717335	+	0.696729i	$0.754638\pi$
$152$		0			0
$153$			981.989i			0.518883i
$154$		0			0
$155$		−	42.0133i		−	0.0217715i
$156$		0			0
$157$	2204.53	+	1272.79i	1.12064	+	0.647003i	0.941565	−	0.336832i	$-0.109355\pi$
$157$	2204.53	+	1272.79i	1.12064	+	0.647003i	0.179078	+	0.983835i	$0.442689\pi$
$158$		0			0
$159$	182.954	+	316.886i	0.0912529	+	0.158055i
$160$		0			0
$161$	424.702	−	166.109i	0.207896	−	0.0813120i
$162$		0			0
$163$	1609.94	−	929.496i	0.773619	−	0.446649i	−0.0605453	−	0.998165i	$-0.519284\pi$
$163$	1609.94	−	929.496i	0.773619	−	0.446649i	0.834164	+	0.551516i	$0.185951\pi$
$164$		0			0
$165$	581.702	−	1007.54i	0.274457	−	0.475374i
$166$		0			0
$167$	1181.19			0.547326			0.273663	−	0.961826i	$-0.411765\pi$
$167$	1181.19			0.547326			0.273663	+	0.961826i	$0.411765\pi$
$168$		0			0
$169$	−4429.22			−2.01603
$170$		0			0
$171$	202.257	−	350.320i	0.0904504	−	0.156665i
$172$		0			0
$173$	−3762.06	+	2172.03i	−1.65332	+	0.954544i	−0.677625	+	0.735407i	$0.736991\pi$
$173$	−3762.06	+	2172.03i	−1.65332	+	0.954544i	−0.975694	+	0.219137i	$0.929676\pi$
$174$		0			0
$175$	665.439	−	832.431i	0.287443	−	0.359576i
$176$		0			0
$177$	−155.929	−	270.077i	−0.0662166	−	0.114691i
$178$		0			0
$179$	−3960.64	−	2286.68i	−1.65381	−	0.954829i	−0.975484	−	0.220069i	$-0.929372\pi$
$179$	−3960.64	−	2286.68i	−1.65381	−	0.954829i	−0.678327	−	0.734760i	$-0.737295\pi$
$180$		0			0
$181$		−	478.812i		−	0.196629i	−0.995155	−	0.0983144i	$-0.968655\pi$
$181$		−	478.812i		−	0.196629i	0.995155	−	0.0983144i	$-0.0313451\pi$
$182$		0			0
$183$			200.299i			0.0809099i
$184$		0			0
$185$	2804.65	+	1619.27i	1.11461	+	0.643518i
$186$		0			0
$187$	−2575.91	−	4461.61i	−1.00732	−	1.74473i
$188$		0			0
$189$	494.374	+	75.1075i	0.190267	+	0.0289062i
$190$		0			0
$191$	−1459.86	+	842.853i	−0.553048	+	0.319302i	−0.750350	−	0.661040i	$-0.770115\pi$
$191$	−1459.86	+	842.853i	−0.553048	+	0.319302i	0.197303	+	0.980343i	$0.436782\pi$
$192$		0			0
$193$	60.0489	−	104.008i	0.0223959	−	0.0387909i	−0.854610	−	0.519270i	$-0.826204\pi$
$193$	60.0489	−	104.008i	0.0223959	−	0.0387909i	0.877006	+	0.480479i	$0.159537\pi$
$194$		0			0
$195$	2005.70			0.736571
$196$		0			0
$197$	2577.93			0.932334			0.466167	−	0.884697i	$-0.345635\pi$
$197$	2577.93			0.932334			0.466167	+	0.884697i	$0.345635\pi$
$198$		0			0
$199$	1386.88	−	2402.15i	0.494038	−	0.855698i	−0.505939	−	0.862569i	$-0.668854\pi$
$199$	1386.88	−	2402.15i	0.494038	−	0.855698i	0.999976	+	0.00687102i	$0.00218713\pi$
$200$		0			0
$201$	1905.72	−	1100.27i	0.668752	−	0.386104i
$202$		0			0
$203$	3376.50	+	512.973i	1.16741	+	0.177358i
$204$		0			0
$205$	906.358	+	1569.86i	0.308794	+	0.534847i
$206$		0			0
$207$	191.920	+	110.805i	0.0644413	+	0.0372052i
$208$		0			0
$209$			2122.21i			0.702375i
$210$		0			0
$211$		−	2599.69i		−	0.848200i	−0.905615	−	0.424100i	$-0.860590\pi$
$211$		−	2599.69i		−	0.848200i	0.905615	−	0.424100i	$-0.139410\pi$
$212$		0			0
$213$	−675.216	−	389.836i	−0.217207	−	0.125404i
$214$		0			0
$215$	−577.426	−	1000.13i	−0.183163	−	0.317248i
$216$		0			0
$217$	−59.1545	+	73.9994i	−0.0185054	+	0.0231493i
$218$		0			0
$219$	−2868.84	+	1656.32i	−0.885197	+	0.511069i
$220$		0			0
$221$	4440.86	−	7691.79i	1.35169	−	2.34120i
$222$		0			0
$223$	−1922.13			−0.577198			−0.288599	−	0.957450i	$-0.593189\pi$
$223$	−1922.13			−0.577198			−0.288599	+	0.957450i	$0.593189\pi$
$224$		0			0
$225$	517.889			0.153449
$226$		0			0
$227$	685.559	−	1187.42i	0.200450	−	0.347190i	−0.748224	−	0.663447i	$-0.769093\pi$
$227$	685.559	−	1187.42i	0.200450	−	0.347190i	0.948673	+	0.316257i	$0.102426\pi$
$228$		0			0
$229$	−2574.44	+	1486.36i	−0.742900	+	0.428913i	−0.823123	−	0.567864i	$-0.807770\pi$
$229$	−2574.44	+	1486.36i	−0.742900	+	0.428913i	0.0802229	+	0.996777i	$0.474437\pi$
$230$		0			0
$231$	−2443.18	+	955.574i	−0.695884	+	0.272174i
$232$		0			0
$233$	−63.5321	−	110.041i	−0.0178632	−	0.0309400i	0.856956	−	0.515390i	$-0.172353\pi$
$233$	−63.5321	−	110.041i	−0.0178632	−	0.0309400i	−0.874819	+	0.484450i	$0.839020\pi$
$234$		0			0
$235$	809.963	+	467.633i	0.224835	+	0.129808i
$236$		0			0
$237$			1137.50i			0.311767i
$238$		0			0
$239$			6394.34i			1.73061i	0.501246	+	0.865305i	$0.332875\pi$
$239$			6394.34i			1.73061i	−0.501246	+	0.865305i	$0.667125\pi$
$240$		0			0
$241$	−5791.82	−	3343.91i	−1.54807	−	0.893776i	−0.998289	−	0.0584649i	$-0.981379\pi$
$241$	−5791.82	−	3343.91i	−1.54807	−	0.893776i	−0.549777	−	0.835312i	$-0.685287\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$		0			0
$245$	2747.96	−	620.432i	0.716574	−	0.161787i
$246$		0			0
$247$	−3168.51	+	1829.34i	−0.816225	+	0.471248i
$248$		0			0
$249$	1040.73	−	1802.60i	0.264874	−	0.458776i
$250$		0			0
$251$	−5459.52			−1.37292			−0.686458	−	0.727169i	$-0.740836\pi$
$251$	−5459.52			−1.37292			−0.686458	+	0.727169i	$0.740836\pi$
$252$		0			0
$253$	−1162.64			−0.288910
$254$		0			0
$255$	−1344.21	+	2328.24i	−0.330109	+	0.571766i
$256$		0			0
$257$	3473.96	−	2005.69i	0.843190	−	0.486816i	−0.0151575	−	0.999885i	$-0.504825\pi$
$257$	3473.96	−	2005.69i	0.843190	−	0.486816i	0.858347	+	0.513069i	$0.171492\pi$
$258$		0			0
$259$	−2660.00	−	6801.00i	−0.638164	−	1.63164i
$260$		0			0
$261$	829.827	+	1437.30i	0.196801	+	0.340869i
$262$		0			0
$263$	4992.70	+	2882.54i	1.17058	+	0.675836i	0.953817	−	0.300388i	$-0.0971161\pi$
$263$	4992.70	+	2882.54i	1.17058	+	0.675836i	0.216765	+	0.976224i	$0.430449\pi$
$264$		0			0
$265$			1001.76i			0.232217i
$266$		0			0
$267$			1931.23i			0.442656i
$268$		0			0
$269$	−2355.68	−	1360.05i	−0.533933	−	0.308266i	0.208683	−	0.977983i	$-0.433082\pi$
$269$	−2355.68	−	1360.05i	−0.533933	−	0.308266i	−0.742617	+	0.669717i	$0.766416\pi$
$270$		0			0
$271$	−1282.56	−	2221.46i	−0.287491	−	0.497949i	0.685719	−	0.727866i	$-0.259488\pi$
$271$	−1282.56	−	2221.46i	−0.287491	−	0.497949i	−0.973210	+	0.229917i	$0.926154\pi$
$272$		0			0
$273$	−3532.71	−	2824.02i	−0.783184	−	0.626072i
$274$		0			0
$275$	−2353.00	+	1358.50i	−0.515968	+	0.297894i
$276$		0			0
$277$	1506.83	−	2609.90i	0.326847	−	0.566115i	−0.655038	−	0.755596i	$-0.727347\pi$
$277$	1506.83	−	2609.90i	0.326847	−	0.566115i	0.981884	+	0.189481i	$0.0606806\pi$
$278$		0			0
$279$	−46.0380			−0.00987894
$280$		0			0
$281$	2758.53			0.585623			0.292811	−	0.956170i	$-0.405409\pi$
$281$	2758.53			0.585623			0.292811	+	0.956170i	$0.405409\pi$
$282$		0			0
$283$	−288.776	+	500.175i	−0.0606571	+	0.105061i	−0.894759	−	0.446549i	$-0.852653\pi$
$283$	−288.776	+	500.175i	−0.0606571	+	0.105061i	0.834102	+	0.551610i	$0.185986\pi$
$284$		0			0
$285$	959.084	−	553.727i	0.199338	−	0.115088i
$286$		0			0
$287$	613.955	−	4041.19i	0.126274	−	0.831163i
$288$		0			0
$289$	3495.98	+	6055.22i	0.711578	+	1.23249i
$290$		0			0
$291$	897.885	+	518.394i	0.180876	+	0.104429i
$292$		0			0
$293$		−	3660.64i		−	0.729886i	−0.931030	−	0.364943i	$-0.881088\pi$
$293$		−	3660.64i		−	0.729886i	0.931030	−	0.364943i	$-0.118912\pi$
$294$		0			0
$295$		−	853.785i		−	0.168506i
$296$		0			0
$297$	−1104.06	−	637.427i	−0.215703	−	0.124536i
$298$		0			0
$299$	−1002.19	−	1735.84i	−0.193840	−	0.335740i
$300$		0			0
$301$	−391.141	+	2574.58i	−0.0749003	+	0.493010i
$302$		0			0
$303$	2704.74	−	1561.58i	0.512816	−	0.296075i
$304$		0			0
$305$	−274.183	+	474.898i	−0.0514743	+	0.0891560i
$306$		0			0
$307$	2883.84			0.536121			0.268061	−	0.963402i	$-0.413617\pi$
$307$	2883.84			0.536121			0.268061	+	0.963402i	$0.413617\pi$
$308$		0			0
$309$	4596.93			0.846311
$310$		0			0
$311$	1528.53	−	2647.49i	0.278697	−	0.482718i	−0.692364	−	0.721548i	$-0.743431\pi$
$311$	1528.53	−	2647.49i	0.278697	−	0.482718i	0.971061	+	0.238831i	$0.0767640\pi$
$312$		0			0
$313$	367.070	−	211.928i	0.0662876	−	0.0382712i	−0.466490	−	0.884527i	$-0.654482\pi$
$313$	367.070	−	211.928i	0.0662876	−	0.0382712i	0.532777	+	0.846255i	$0.321148\pi$
$314$		0			0
$315$	1069.32	+	854.809i	0.191268	+	0.152898i
$316$		0			0
$317$	−2544.92	−	4407.94i	−0.450906	−	0.780992i	0.547537	−	0.836782i	$-0.315566\pi$
$317$	−2544.92	−	4407.94i	−0.450906	−	0.780992i	−0.998443	+	0.0557900i	$0.982232\pi$
$318$		0			0
$319$	−7540.54	−	4353.53i	−1.32348	−	0.764110i
$320$		0			0
$321$		−	6300.20i		−	1.09546i
$322$		0			0
$323$		−	4904.06i		−	0.844797i
$324$		0			0
$325$	−4056.56	−	2342.06i	−0.692361	−	0.399735i
$326$		0			0
$327$	3179.42	+	5506.92i	0.537683	+	0.931294i
$328$		0			0
$329$	−768.190	−	1964.08i	−0.128729	−	0.329128i
$330$		0			0
$331$	−3465.52	+	2000.82i	−0.575474	+	0.332250i	−0.759333	−	0.650703i	$-0.774475\pi$
$331$	−3465.52	+	2000.82i	−0.575474	+	0.332250i	0.183859	+	0.982953i	$0.441141\pi$
$332$		0			0
$333$	1774.39	−	3073.33i	0.291999	−	0.505758i
$334$		0			0
$335$	6024.49			0.982546
$336$		0			0
$337$	6215.04			1.00461			0.502307	−	0.864689i	$-0.332485\pi$
$337$	6215.04			1.00461			0.502307	+	0.864689i	$0.332485\pi$
$338$		0			0
$339$	403.558	−	698.983i	0.0646557	−	0.111987i
$340$		0			0
$341$	209.171	−	120.765i	0.0332177	−	0.0191783i
$342$		0			0
$343$	−5713.63	−	2776.33i	−0.899438	−	0.437048i
$344$		0			0
$345$	303.355	+	525.426i	0.0473394	+	0.0819942i
$346$		0			0
$347$	−1959.90	−	1131.55i	−0.303207	−	0.175057i	0.340676	−	0.940181i	$-0.389344\pi$
$347$	−1959.90	−	1131.55i	−0.303207	−	0.175057i	−0.643883	+	0.765124i	$0.722677\pi$
$348$		0			0
$349$		−	3056.05i		−	0.468730i	−0.972149	−	0.234365i	$-0.924699\pi$
$349$		−	3056.05i		−	0.468730i	0.972149	−	0.234365i	$-0.0753011\pi$
$350$		0			0
$351$		−	2197.84i		−	0.334223i
$352$		0			0
$353$	2799.56	+	1616.33i	0.422113	+	0.243707i	0.695981	−	0.718060i	$-0.254970\pi$
$353$	2799.56	+	1616.33i	0.422113	+	0.243707i	−0.273868	+	0.961767i	$0.588303\pi$
$354$		0			0
$355$	−1067.27	−	1848.56i	−0.159563	−	0.276370i
$356$		0			0
$357$	5645.76	−	2208.17i	0.836990	−	0.327363i
$358$		0			0
$359$	−7704.11	+	4447.97i	−1.13261	+	0.653913i	−0.944590	−	0.328252i	$-0.893541\pi$
$359$	−7704.11	+	4447.97i	−1.13261	+	0.653913i	−0.188021	+	0.982165i	$0.560207\pi$
$360$		0			0
$361$	2419.42	−	4190.57i	0.352737	−	0.610959i
$362$		0			0
$363$	2695.28			0.389712
$364$		0			0
$365$	−9069.16			−1.30055
$366$		0			0
$367$	−4855.36	+	8409.73i	−0.690593	+	1.19614i	0.281051	+	0.959693i	$0.409317\pi$
$367$	−4855.36	+	8409.73i	−0.690593	+	1.19614i	−0.971644	+	0.236449i	$0.924016\pi$
$368$		0			0
$369$	1720.24	−	993.184i	0.242689	−	0.140117i
$370$		0			0
$371$	1410.47	−	1764.43i	0.197380	−	0.246913i
$372$		0			0
$373$	−589.352	−	1020.79i	−0.0818109	−	0.141701i	0.822217	−	0.569174i	$-0.192737\pi$
$373$	−589.352	−	1020.79i	−0.0818109	−	0.141701i	−0.904028	+	0.427474i	$0.859404\pi$
$374$		0			0
$375$	3895.21	+	2248.90i	0.536393	+	0.309687i
$376$		0			0
$377$		−	15010.9i		−	2.05067i
$378$		0			0
$379$		−	12717.5i		−	1.72362i	−0.507228	−	0.861812i	$-0.669330\pi$
$379$		−	12717.5i		−	1.72362i	0.507228	−	0.861812i	$-0.330670\pi$
$380$		0			0
$381$	3447.55	+	1990.44i	0.463578	+	0.267647i
$382$		0			0
$383$	−7240.04	−	12540.1i	−0.965924	−	1.67303i	−0.707112	−	0.707101i	$-0.750002\pi$
$383$	−7240.04	−	12540.1i	−0.965924	−	1.67303i	−0.258811	−	0.965928i	$-0.583331\pi$
$384$		0			0
$385$	−7100.70	−	1078.77i	−0.939962	−	0.142803i
$386$		0			0
$387$	−1095.94	+	632.741i	−0.143953	+	0.0831112i
$388$		0			0
$389$	−118.125	+	204.599i	−0.0153964	+	0.0266673i	−0.873621	−	0.486607i	$-0.838234\pi$
$389$	−118.125	+	204.599i	−0.0153964	+	0.0266673i	0.858225	+	0.513274i	$0.171568\pi$
$390$		0			0
$391$	2686.65			0.347493
$392$		0			0
$393$	4606.32			0.591242
$394$		0			0
$395$	−1557.09	+	2696.96i	−0.198344	+	0.343541i
$396$		0			0
$397$	−10069.8	+	5813.82i	−1.27302	+	0.734980i	−0.975556	−	0.219752i	$-0.929475\pi$
$397$	−10069.8	+	5813.82i	−1.27302	+	0.734980i	−0.297468	+	0.954732i	$0.596142\pi$
$398$		0			0
$399$	−2468.91	−	375.088i	−0.309775	−	0.0470623i
$400$		0			0
$401$	6163.99	+	10676.3i	0.767618	+	1.32955i	0.938851	+	0.344323i	$0.111891\pi$
$401$	6163.99	+	10676.3i	0.767618	+	1.32955i	−0.171234	+	0.985230i	$0.554775\pi$
$402$		0			0
$403$	360.610	+	208.198i	0.0445738	+	0.0257347i
$404$		0			0
$405$			665.270i			0.0816235i
$406$		0			0
$407$			18618.0i			2.26747i
$408$		0			0
$409$	−7142.52	−	4123.74i	−0.863509	−	0.498547i	0.00167708	−	0.999999i	$-0.499466\pi$
$409$	−7142.52	−	4123.74i	−0.863509	−	0.498547i	−0.865186	+	0.501452i	$0.832800\pi$
$410$		0			0
$411$	−2640.08	−	4572.75i	−0.316850	−	0.548800i
$412$		0			0
$413$	−1202.12	+	1503.80i	−0.143227	+	0.179170i
$414$		0			0
$415$	4935.04	−	2849.25i	0.583739	−	0.337022i
$416$		0			0
$417$	−4075.77	+	7059.45i	−0.478637	+	0.829023i
$418$		0			0
$419$	11595.5			1.35197			0.675986	−	0.736914i	$-0.263718\pi$
$419$	11595.5			1.35197			0.675986	+	0.736914i	$0.263718\pi$
$420$		0			0
$421$	12667.9			1.46649			0.733246	−	0.679963i	$-0.238004\pi$
$421$	12667.9			1.46649			0.733246	+	0.679963i	$0.238004\pi$
$422$		0			0
$423$	512.430	−	887.555i	0.0589012	−	0.102020i
$424$		0			0
$425$	5437.37	−	3139.27i	0.620591	−	0.358299i
$426$		0			0
$427$	1151.58	−	450.405i	0.130513	−	0.0510460i
$428$		0			0
$429$	5765.28	+	9985.77i	0.648836	+	1.12382i
$430$		0			0
$431$	1601.91	+	924.863i	0.179028	+	0.103362i	0.586836	−	0.809706i	$-0.300373\pi$
$431$	1601.91	+	924.863i	0.179028	+	0.103362i	−0.407808	+	0.913068i	$0.633707\pi$
$432$		0			0
$433$		−	1481.53i		−	0.164429i	−0.996615	−	0.0822147i	$-0.973801\pi$
$433$		−	1481.53i		−	0.164429i	0.996615	−	0.0822147i	$-0.0261993\pi$
$434$		0			0
$435$			4543.69i			0.500813i
$436$		0			0
$437$	−958.450	−	553.361i	−0.104917	−	0.0605741i
$438$		0			0
$439$	−6660.84	−	11536.9i	−0.724156	−	1.25428i	−0.959320	−	0.282319i	$-0.908896\pi$
$439$	−6660.84	−	11536.9i	−0.724156	−	1.25428i	0.235164	−	0.971956i	$-0.424437\pi$
$440$		0			0
$441$	−679.867	−	3011.20i	−0.0734118	−	0.325149i
$442$		0			0
$443$	−3682.77	+	2126.25i	−0.394974	+	0.228039i	−0.684313	−	0.729188i	$-0.739898\pi$
$443$	−3682.77	+	2126.25i	−0.394974	+	0.228039i	0.289339	+	0.957227i	$0.406565\pi$
$444$		0			0
$445$	−2643.59	+	4578.84i	−0.281614	+	0.487770i
$446$		0			0
$447$	−5147.64			−0.544687
$448$		0			0
$449$	11588.4			1.21802			0.609010	−	0.793163i	$-0.291567\pi$
$449$	11588.4			1.21802			0.609010	+	0.793163i	$0.291567\pi$
$450$		0			0
$451$	−5210.55	+	9024.94i	−0.544025	+	0.942279i
$452$		0			0
$453$	−2630.85	+	1518.92i	−0.272866	+	0.157539i
$454$		0			0
$455$	−4510.16	−	11531.4i	−0.464702	−	1.18813i
$456$		0			0
$457$	−1519.63	−	2632.08i	−0.155548	−	0.269417i	0.777710	−	0.628623i	$-0.216381\pi$
$457$	−1519.63	−	2632.08i	−0.155548	−	0.269417i	−0.933258	+	0.359206i	$0.883048\pi$
$458$		0			0
$459$	2551.28	+	1472.98i	0.259441	+	0.149789i
$460$		0			0
$461$			7884.53i			0.796571i	0.917261	+	0.398286i	$0.130395\pi$
$461$			7884.53i			0.796571i	−0.917261	+	0.398286i	$0.869605\pi$
$462$		0			0
$463$		−	6854.97i		−	0.688073i	−0.938956	−	0.344036i	$-0.888206\pi$
$463$		−	6854.97i		−	0.688073i	0.938956	−	0.344036i	$-0.111794\pi$
$464$		0			0
$465$	−109.154	−	63.0200i	−0.0108858	−	0.00628490i
$466$		0			0
$467$	2688.66	+	4656.90i	0.266417	+	0.461447i	0.967934	−	0.251205i	$-0.0808270\pi$
$467$	2688.66	+	4656.90i	0.266417	+	0.461447i	−0.701517	+	0.712653i	$0.747494\pi$
$468$		0			0
$469$	−10611.1	−	8482.45i	−1.04473	−	0.835145i
$470$		0			0
$471$	6613.60	−	3818.36i	0.647003	−	0.373548i
$472$		0			0
$473$	3319.56	−	5749.64i	0.322692	−	0.558920i
$474$		0			0
$475$	−2586.34			−0.249831
$476$		0			0
$477$	1097.72			0.105370
$478$		0			0
$479$	2570.92	−	4452.96i	0.245237	−	0.424762i	−0.716962	−	0.697113i	$-0.754468\pi$
$479$	2570.92	−	4452.96i	0.245237	−	0.424762i	0.962198	+	0.272351i	$0.0878010\pi$
$480$		0			0
$481$	−27797.1	+	16048.6i	−2.63501	+	1.52132i
$482$		0			0
$483$	205.489	−	1352.57i	0.0193583	−	0.127421i
$484$		0			0
$485$	1419.23	+	2458.17i	0.132874	+	0.230144i
$486$		0			0
$487$	6760.47	+	3903.16i	0.629047	+	0.363181i	0.780383	−	0.625302i	$-0.215024\pi$
$487$	6760.47	+	3903.16i	0.629047	+	0.363181i	−0.151336	+	0.988482i	$0.548357\pi$
$488$		0			0
$489$		−	5576.98i		−	0.515746i
$490$		0			0
$491$			15179.4i			1.39519i	0.716493	+	0.697595i	$0.245746\pi$
$491$			15179.4i			1.39519i	−0.716493	+	0.697595i	$0.754254\pi$
$492$		0			0
$493$	17424.9	+	10060.3i	1.59184	+	0.919049i
$494$		0			0
$495$	−1745.11	−	3022.61i	−0.158458	−	0.274457i
$496$		0			0
$497$	−722.954	+	4758.64i	−0.0652493	+	0.429485i
$498$		0			0
$499$	−17185.6	+	9922.10i	−1.54175	+	0.890129i	−0.543019	+	0.839720i	$0.682719\pi$
$499$	−17185.6	+	9922.10i	−1.54175	+	0.890129i	−0.998729	+	0.0504084i	$0.983948\pi$
$500$		0			0
$501$	1771.79	−	3068.83i	0.158000	−	0.273663i
$502$		0			0
$503$	3894.11			0.345189			0.172594	−	0.984993i	$-0.444785\pi$
$503$	3894.11			0.345189			0.172594	+	0.984993i	$0.444785\pi$
$504$		0			0
$505$	8550.40			0.753441
$506$		0			0
$507$	−6643.83	+	11507.4i	−0.581978	+	1.00801i
$508$		0			0
$509$	−14465.8	+	8351.85i	−1.25970	+	0.727287i	−0.973016	−	0.230739i	$-0.925886\pi$
$509$	−14465.8	+	8351.85i	−1.25970	+	0.727287i	−0.286682	+	0.958026i	$0.592552\pi$
$510$		0			0
$511$	15973.8	+	12769.3i	1.38286	+	1.10544i
$512$		0			0
$513$	−606.772	−	1050.96i	−0.0522215	−	0.0904504i
$514$		0			0
$515$	10899.1	+	6292.58i	0.932564	+	0.538416i
$516$		0			0
$517$			5376.74i			0.457386i
$518$		0			0
$519$			13032.2i			1.10221i
$520$		0			0
$521$	12739.7	+	7355.29i	1.07128	+	0.618505i	0.928531	−	0.371254i	$-0.121072\pi$
$521$	12739.7	+	7355.29i	1.07128	+	0.618505i	0.142750	+	0.989759i	$0.454405\pi$
$522$		0			0
$523$	−3021.64	−	5233.63i	−0.252633	−	0.437573i	0.711617	−	0.702568i	$-0.247963\pi$
$523$	−3021.64	−	5233.63i	−0.252633	−	0.437573i	−0.964250	+	0.264995i	$0.914630\pi$
$524$		0			0
$525$	−1164.56	−	2977.51i	−0.0968107	−	0.247522i
$526$		0			0
$527$	−483.358	+	279.067i	−0.0399533	+	0.0230671i
$528$		0			0
$529$	−5780.35	+	10011.9i	−0.475084	+	0.822869i
$530$		0			0
$531$	−935.574			−0.0764604
$532$		0			0
$533$	−17965.9			−1.46002
$534$		0			0
$535$	8624.14	−	14937.4i	0.696924	−	1.20711i
$536$		0			0
$537$	−11881.9	+	6860.03i	−0.954829	+	0.551271i
$538$		0			0
$539$	10987.8	+	11897.8i	0.878066	+	0.950790i
$540$		0			0
$541$	−101.020	−	174.972i	−0.00802808	−	0.0139050i	0.861983	−	0.506936i	$-0.169222\pi$
$541$	−101.020	−	174.972i	−0.00802808	−	0.0139050i	−0.870012	+	0.493031i	$0.835889\pi$
$542$		0			0
$543$	−1243.99	−	718.218i	−0.0983144	−	0.0567619i
$544$		0			0
$545$			17408.8i			1.36828i
$546$		0			0
$547$			14260.6i			1.11470i	0.830279	+	0.557348i	$0.188181\pi$
$547$			14260.6i			1.11470i	−0.830279	+	0.557348i	$0.811819\pi$
$548$		0			0
$549$	520.392	+	300.448i	0.0404550	+	0.0233567i
$550$		0			0
$551$	−4144.16	−	7177.90i	−0.320413	−	0.554971i
$552$		0			0
$553$	6539.86	−	2557.87i	0.502899	−	0.196694i
$554$		0			0
$555$	8413.96	−	4857.80i	0.643518	−	0.371535i
$556$		0			0
$557$	9396.60	−	16275.4i	0.714805	−	1.23808i	−0.248229	−	0.968701i	$-0.579849\pi$
$557$	9396.60	−	16275.4i	0.714805	−	1.23808i	0.963035	−	0.269378i	$-0.0868180\pi$
$558$		0			0
$559$	11445.8			0.866022
$560$		0			0
$561$	−15455.5			−1.16316
$562$		0			0
$563$	3498.08	−	6058.86i	0.261859	−	0.453553i	−0.704877	−	0.709330i	$-0.748998\pi$
$563$	3498.08	−	6058.86i	0.261859	−	0.453553i	0.966736	+	0.255777i	$0.0823311\pi$
$564$		0			0
$565$	1913.63	−	1104.84i	0.142490	−	0.0822669i
$566$		0			0
$567$	936.696	−	1171.76i	0.0693784	−	0.0867889i
$568$		0			0
$569$	9179.23	+	15898.9i	0.676298	+	1.17138i	0.976088	+	0.217377i	$0.0697501\pi$
$569$	9179.23	+	15898.9i	0.676298	+	1.17138i	−0.299790	+	0.954005i	$0.596917\pi$
$570$		0			0
$571$	18813.8	+	10862.2i	1.37887	+	0.796090i	0.992023	−	0.126055i	$-0.0402317\pi$
$571$	18813.8	+	10862.2i	1.37887	+	0.796090i	0.386844	+	0.922145i	$0.373565\pi$
$572$		0			0
$573$			5057.12i			0.368698i
$574$		0			0
$575$		−	1416.91i		−	0.102764i
$576$		0			0
$577$	−13148.6	−	7591.34i	−0.948671	−	0.547715i	−0.0560028	−	0.998431i	$-0.517836\pi$
$577$	−13148.6	−	7591.34i	−0.948671	−	0.547715i	−0.892668	+	0.450715i	$0.851169\pi$
$578$		0			0
$579$	−180.147	−	312.023i	−0.0129303	−	0.0223959i
$580$		0			0
$581$	−12704.0	−	1930.04i	−0.907143	−	0.137817i
$582$		0			0
$583$	−4987.45	+	2879.50i	−0.354303	+	0.204557i
$584$		0			0
$585$	3008.56	−	5210.97i	0.212630	−	0.368286i
$586$		0			0
$587$	−3428.94			−0.241103			−0.120551	−	0.992707i	$-0.538466\pi$
$587$	−3428.94			−0.241103			−0.120551	+	0.992707i	$0.538466\pi$
$588$		0			0
$589$	229.914			0.0160840
$590$		0			0
$591$	3866.89	−	6697.65i	0.269142	−	0.466167i
$592$		0			0
$593$	−13768.6	+	7949.31i	−0.953472	+	0.550487i	−0.894158	−	0.447752i	$-0.852225\pi$
$593$	−13768.6	+	7949.31i	−0.953472	+	0.550487i	−0.0593141	+	0.998239i	$0.518891\pi$
$594$		0			0
$595$	16408.5	+	2492.85i	1.13056	+	0.171760i
$596$		0			0
$597$	−4160.65	−	7206.45i	−0.285233	−	0.494038i
$598$		0			0
$599$	−1577.37	−	910.697i	−0.107596	−	0.0621203i	0.445237	−	0.895413i	$-0.353120\pi$
$599$	−1577.37	−	910.697i	−0.107596	−	0.0621203i	−0.552832	+	0.833293i	$0.686453\pi$
$600$		0			0
$601$			9901.30i			0.672018i	0.941859	+	0.336009i	$0.109077\pi$
$601$			9901.30i			0.672018i	−0.941859	+	0.336009i	$0.890923\pi$
$602$		0			0
$603$		−	6601.61i		−	0.445835i
$604$		0			0
$605$	6390.37	+	3689.48i	0.429431	+	0.247932i
$606$		0			0
$607$	−8454.27	−	14643.2i	−0.565319	−	0.979161i	−0.997020	−	0.0771439i	$-0.975420\pi$
$607$	−8454.27	−	14643.2i	−0.565319	−	0.979161i	0.431701	−	0.902017i	$-0.357913\pi$
$608$		0			0
$609$	6397.50	−	8002.95i	0.425681	−	0.532506i
$610$		0			0
$611$	−8027.60	+	4634.74i	−0.531525	+	0.306876i
$612$		0			0
$613$	740.944	−	1283.35i	0.0488196	−	0.0845581i	−0.840583	−	0.541683i	$-0.817787\pi$
$613$	740.944	−	1283.35i	0.0488196	−	0.0845581i	0.889403	+	0.457125i	$0.151121\pi$
$614$		0			0
$615$	5438.15			0.356565
$616$		0			0
$617$	3569.43			0.232901			0.116450	−	0.993197i	$-0.462848\pi$
$617$	3569.43			0.232901			0.116450	+	0.993197i	$0.462848\pi$
$618$		0			0
$619$	3046.20	−	5276.18i	0.197799	−	0.342597i	−0.750016	−	0.661420i	$-0.769954\pi$
$619$	3046.20	−	5276.18i	0.197799	−	0.342597i	0.947814	+	0.318823i	$0.103287\pi$
$620$		0			0
$621$	575.760	−	332.415i	0.0372052	−	0.0214804i
$622$		0			0
$623$	11103.2	−	4342.69i	0.714031	−	0.279271i
$624$		0			0
$625$	2560.43	+	4434.80i	0.163868	+	0.283827i
$626$		0			0
$627$	5513.67	+	3183.32i	0.351188	+	0.202758i
$628$		0			0
$629$		−	43022.9i		−	2.72724i
$630$		0			0
$631$		−	12560.5i		−	0.792431i	−0.918158	−	0.396215i	$-0.870323\pi$
$631$		−	12560.5i		−	0.792431i	0.918158	−	0.396215i	$-0.129677\pi$
$632$		0			0
$633$	−6754.20	−	3899.54i	−0.424100	−	0.244854i
$634$		0			0
$635$	5449.30	+	9438.47i	0.340550	+	0.589849i
$636$		0			0
$637$	−8292.29	+	26660.9i	−0.515781	+	1.65831i
$638$		0			0
$639$	−2025.65	+	1169.51i	−0.125404	+	0.0724022i
$640$		0			0
$641$	−5147.70	+	8916.07i	−0.317195	+	0.549397i	−0.979902	−	0.199482i	$-0.936074\pi$
$641$	−5147.70	+	8916.07i	−0.317195	+	0.549397i	0.662707	+	0.748879i	$0.269408\pi$
$642$		0			0
$643$	−7660.53			−0.469832			−0.234916	−	0.972016i	$-0.575481\pi$
$643$	−7660.53			−0.469832			−0.234916	+	0.972016i	$0.575481\pi$
$644$		0			0
$645$	−3464.56			−0.211499
$646$		0			0
$647$	12532.7	−	21707.2i	0.761530	−	1.31901i	−0.180531	−	0.983569i	$-0.557782\pi$
$647$	12532.7	−	21707.2i	0.761530	−	1.31901i	0.942062	−	0.335440i	$-0.108885\pi$
$648$		0			0
$649$	4250.72	−	2454.16i	0.257096	−	0.148435i
$650$		0			0
$651$	103.524	+	264.687i	0.00623262	+	0.0159353i
$652$		0			0
$653$	3393.47	+	5877.67i	0.203364	+	0.352237i	0.949610	−	0.313433i	$-0.101479\pi$
$653$	3393.47	+	5877.67i	0.203364	+	0.352237i	−0.746246	+	0.665670i	$0.768146\pi$
$654$		0			0
$655$	10921.3	+	6305.44i	0.651500	+	0.376144i
$656$		0			0
$657$			9937.95i			0.590131i
$658$		0			0
$659$			11856.9i			0.700877i	0.936586	+	0.350438i	$0.113967\pi$
$659$			11856.9i			0.700877i	−0.936586	+	0.350438i	$0.886033\pi$
$660$		0			0
$661$	24659.1	+	14236.9i	1.45103	+	0.837750i	0.998540	−	0.0540209i	$-0.0172038\pi$
$661$	24659.1	+	14236.9i	1.45103	+	0.837750i	0.452486	+	0.891771i	$0.350537\pi$
$662$		0			0
$663$	−13322.6	−	23075.4i	−0.780401	−	1.35169i
$664$		0			0
$665$	−5340.21	−	4268.92i	−0.311405	−	0.248935i
$666$		0			0
$667$	3932.36	−	2270.35i	0.228278	−	0.131796i
$668$		0			0
$669$	−2883.19	+	4993.83i	−0.166623	+	0.288599i
$670$		0			0
$671$	−3152.49			−0.181372
$672$		0			0
$673$	6474.43			0.370834			0.185417	−	0.982660i	$-0.440636\pi$
$673$	6474.43			0.370834			0.185417	+	0.982660i	$0.440636\pi$
$674$		0			0
$675$	776.834	−	1345.52i	0.0442968	−	0.0767243i
$676$		0			0
$677$	999.203	−	576.890i	0.0567245	−	0.0327499i	−0.471370	−	0.881936i	$-0.656240\pi$
$677$	999.203	−	576.890i	0.0567245	−	0.0327499i	0.528094	+	0.849186i	$0.322907\pi$
$678$		0			0
$679$	961.366	−	6327.92i	0.0543355	−	0.357648i
$680$		0			0
$681$	−2056.68	−	3562.27i	−0.115730	−	0.200450i
$682$		0			0
$683$	17174.4	+	9915.66i	0.962169	+	0.555508i	0.896840	−	0.442355i	$-0.145857\pi$
$683$	17174.4	+	9915.66i	0.962169	+	0.555508i	0.0653288	+	0.997864i	$0.479190\pi$
$684$		0			0
$685$		−	14455.7i		−	0.806310i
$686$		0			0
$687$			8918.14i			0.495267i
$688$		0			0
$689$	−8598.34	−	4964.25i	−0.475429	−	0.274489i
$690$		0			0
$691$	9852.12	+	17064.4i	0.542391	+	0.939449i	0.998766	+	0.0496613i	$0.0158142\pi$
$691$	9852.12	+	17064.4i	0.542391	+	0.939449i	−0.456375	+	0.889787i	$0.650852\pi$
$692$		0			0
$693$	−1182.11	+	7780.92i	−0.0647976	+	0.426512i
$694$		0			0
$695$	−19326.9	+	11158.4i	−1.05484	+	0.609010i
$696$		0			0
$697$	12040.7	−	20855.1i	0.654338	−	1.13335i
$698$		0			0
$699$	−381.192			−0.0206266
$700$		0			0
$701$	−14049.5			−0.756976			−0.378488	−	0.925606i	$-0.623556\pi$
$701$	−14049.5			−0.756976			−0.378488	+	0.925606i	$0.623556\pi$
$702$		0			0
$703$	−8861.30	+	15348.2i	−0.475406	+	0.823427i
$704$		0			0
$705$	2429.89	−	1402.90i	0.129808	−	0.0749450i
$706$		0			0
$707$	−15060.1	−	12038.9i	−0.801122	−	0.640411i
$708$		0			0
$709$	7451.93	+	12907.1i	0.394729	+	0.683691i	0.993067	−	0.117553i	$-0.0375051\pi$
$709$	7451.93	+	12907.1i	0.394729	+	0.683691i	−0.598337	+	0.801244i	$0.704172\pi$
$710$		0			0
$711$	2955.32	+	1706.25i	0.155883	+	0.0899994i
$712$		0			0
$713$			125.957i			0.00661587i
$714$		0			0
$715$			31567.6i			1.65114i
$716$		0			0
$717$	16613.0	+	9591.52i	0.865305	+	0.499584i
$718$		0			0
$719$	15722.5	+	27232.1i	0.815507	+	1.41250i	0.908963	+	0.416876i	$0.136875\pi$
$719$	15722.5	+	27232.1i	0.815507	+	1.41250i	−0.0934560	+	0.995623i	$0.529791\pi$
$720$		0			0
$721$	−10337.0	−	26429.2i	−0.533937	−	1.36515i
$722$		0			0
$723$	−17375.5	+	10031.7i	−0.893776	+	0.516022i
$724$		0			0
$725$	5305.66	−	9189.67i	0.271789	−	0.470753i
$726$		0			0
$727$	25428.5			1.29724			0.648618	−	0.761114i	$-0.275347\pi$
$727$	25428.5			1.29724			0.648618	+	0.761114i	$0.275347\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−7670.93	+	13286.4i	−0.388125	+	0.672252i
$732$		0			0
$733$	−4287.96	+	2475.66i	−0.216070	+	0.124748i	−0.604129	−	0.796886i	$-0.706479\pi$
$733$	−4287.96	+	2475.66i	−0.216070	+	0.124748i	0.388059	+	0.921634i	$0.373146\pi$
$734$		0			0
$735$	2510.01	−	8070.06i	0.125963	−	0.404991i
$736$		0			0
$737$	17317.1	+	29994.0i	0.865512	+	1.49911i
$738$		0			0
$739$	17783.4	+	10267.3i	0.885215	+	0.511079i	0.872374	−	0.488838i	$-0.162579\pi$
$739$	17783.4	+	10267.3i	0.885215	+	0.511079i	0.0128407	+	0.999918i	$0.495913\pi$
$740$		0			0
$741$			10976.0i			0.544150i
$742$		0			0
$743$		−	19070.6i		−	0.941634i	−0.882231	−	0.470817i	$-0.843959\pi$
$743$		−	19070.6i		−	0.941634i	0.882231	−	0.470817i	$-0.156041\pi$
$744$		0			0
$745$	−12204.8	−	7046.44i	−0.600200	−	0.346526i
$746$		0			0
$747$	−3122.20	−	5407.80i	−0.152925	−	0.264874i
$748$		0			0
$749$	−36221.8	+	14167.1i	−1.76705	+	0.691126i
$750$		0			0
$751$	−26097.3	+	15067.3i	−1.26805	+	0.732107i	−0.974618	−	0.223874i	$-0.928130\pi$
$751$	−26097.3	+	15067.3i	−1.26805	+	0.732107i	−0.293428	+	0.955981i	$0.594796\pi$
$752$		0			0
$753$	−8189.29	+	14184.3i	−0.396327	+	0.686458i
$754$		0			0
$755$	−8316.81			−0.400900
$756$		0			0
$757$	34967.7			1.67889			0.839446	−	0.543443i	$-0.182880\pi$
$757$	34967.7			1.67889			0.839446	+	0.543443i	$0.182880\pi$
$758$		0			0
$759$	−1743.95	+	3020.62i	−0.0834012	+	0.144455i
$760$		0			0
$761$	−3501.17	+	2021.40i	−0.166777	+	0.0962887i	−0.581065	−	0.813857i	$-0.697364\pi$
$761$	−3501.17	+	2021.40i	−0.166777	+	0.0962887i	0.414288	+	0.910146i	$0.364031\pi$
$762$		0			0
$763$	24511.5	−	30662.7i	1.16301	−	1.45487i
$764$		0			0
$765$	4032.64	+	6984.73i	0.190589	+	0.330109i
$766$		0			0
$767$	7328.23	+	4230.96i	0.344990	+	0.199180i
$768$		0			0
$769$		−	17771.8i		−	0.833378i	−0.909049	−	0.416689i	$-0.863190\pi$
$769$		−	17771.8i		−	0.833378i	0.909049	−	0.416689i	$-0.136810\pi$
$770$		0			0
$771$		−	12034.2i		−	0.562126i
$772$		0			0
$773$	4512.24	+	2605.14i	0.209953	+	0.121217i	0.601290	−	0.799031i	$-0.294654\pi$
$773$	4512.24	+	2605.14i	0.209953	+	0.121217i	−0.391336	+	0.920248i	$0.627987\pi$
$774$		0			0
$775$	147.177	+	254.917i	0.00682160	+	0.0118154i
$776$		0			0
$777$	−21659.5	−	3290.61i	−1.00004	−	0.151931i
$778$		0			0
$779$	−8590.92	+	4959.97i	−0.395124	+	0.228125i
$780$		0			0
$781$	6135.61	−	10627.2i	0.281113	−	0.486902i
$782$		0			0
$783$	4978.96			0.227246
$784$		0			0
$785$	20907.3			0.950592
$786$		0			0
$787$	959.889	−	1662.58i	0.0434769	−	0.0753042i	−0.843468	−	0.537179i	$-0.819490\pi$
$787$	959.889	−	1662.58i	0.0434769	−	0.0753042i	0.886945	+	0.461875i	$0.152823\pi$
$788$		0			0
$789$	14978.1	−	8647.61i	0.675836	−	0.390194i
$790$		0			0
$791$	−4926.14	−	748.401i	−0.221433	−	0.0336411i
$792$		0			0
$793$	−2717.44	−	4706.74i	−0.121689	−	0.210771i
$794$		0			0
$795$	2602.65	+	1502.64i	0.116109	+	0.0670354i
$796$		0			0
$797$			6915.49i			0.307352i	0.988121	+	0.153676i	$0.0491112\pi$
$797$			6915.49i			0.307352i	−0.988121	+	0.153676i	$0.950889\pi$
$798$		0			0
$799$		−	12424.7i		−	0.550131i
$800$		0			0
$801$	5017.47	+	2896.84i	0.221328	+	0.127784i
$802$		0			0
$803$	−26068.8	−	45152.5i	−1.14564	−	1.98430i
$804$		0			0
$805$	2338.69	−	2925.59i	0.102395	−	0.128091i
$806$		0			0
$807$	−7067.03	+	4080.15i	−0.308266	+	0.177978i
$808$		0			0
$809$	6054.09	−	10486.0i	0.263103	−	0.455708i	−0.703962	−	0.710238i	$-0.748587\pi$
$809$	6054.09	−	10486.0i	0.263103	−	0.455708i	0.967065	+	0.254530i	$0.0819208\pi$
$810$		0			0
$811$	−37167.6			−1.60928			−0.804642	−	0.593760i	$-0.797643\pi$
$811$	−37167.6			−1.60928			−0.804642	+	0.593760i	$0.797643\pi$
$812$		0			0
$813$	−7695.37			−0.331966
$814$		0			0
$815$	7634.15	−	13222.7i	0.328113	−	0.568309i
$816$		0			0
$817$	5473.14	−	3159.92i	0.234371	−	0.135314i
$818$		0			0
$819$	−12636.1	+	4942.22i	−0.539122	+	0.210861i
$820$		0			0
$821$	2040.21	+	3533.75i	0.0867283	+	0.150218i	0.906126	−	0.423007i	$-0.139025\pi$
$821$	2040.21	+	3533.75i	0.0867283	+	0.150218i	−0.819398	+	0.573225i	$0.805692\pi$
$822$		0			0
$823$	18704.5	+	10799.0i	0.792221	+	0.457389i	0.840744	−	0.541433i	$-0.182118\pi$
$823$	18704.5	+	10799.0i	0.792221	+	0.457389i	−0.0485231	+	0.998822i	$0.515451\pi$
$824$		0			0
$825$			8151.03i			0.343979i
$826$		0			0
$827$		−	23867.6i		−	1.00358i	−0.864991	−	0.501788i	$-0.832676\pi$
$827$		−	23867.6i		−	1.00358i	0.864991	−	0.501788i	$-0.167324\pi$
$828$		0			0
$829$	−14730.1	−	8504.44i	−0.617127	−	0.356298i	0.158623	−	0.987339i	$-0.449295\pi$
$829$	−14730.1	−	8504.44i	−0.617127	−	0.356298i	−0.775750	+	0.631041i	$0.782628\pi$
$830$		0			0
$831$	−4520.49	−	7829.71i	−0.188705	−	0.326847i
$832$		0			0
$833$	−25390.9	−	27493.8i	−1.05611	−	1.14358i
$834$		0			0
$835$	8401.65	−	4850.69i	0.348205	−	0.201036i
$836$		0			0
$837$	−69.0570	+	119.610i	−0.00285180	+	0.00493947i
$838$		0			0
$839$	−2200.67			−0.0905551			−0.0452775	−	0.998974i	$-0.514417\pi$
$839$	−2200.67			−0.0905551			−0.0452775	+	0.998974i	$0.514417\pi$
$840$		0			0
$841$	9616.58			0.394300
$842$		0			0
$843$	4137.79	−	7166.86i	0.169055	−	0.292811i
$844$		0			0
$845$	−31504.3	+	18189.0i	−1.28258	+	0.740499i
$846$		0			0
$847$	−6060.79	−	15496.0i	−0.245869	−	0.628630i
$848$		0			0
$849$	866.328	+	1500.52i	0.0350204	+	0.0606571i
$850$		0			0
$851$	−8408.40	−	4854.59i	−0.338703	−	0.195550i
$852$		0			0
$853$		−	35822.1i		−	1.43789i	−0.695065	−	0.718947i	$-0.744624\pi$
$853$		−	35822.1i		−	1.43789i	0.695065	−	0.718947i	$-0.255376\pi$
$854$		0			0
$855$		−	3322.36i		−	0.132892i
$856$		0			0
$857$	14010.3	+	8088.82i	0.558438	+	0.322414i	0.752518	−	0.658571i	$-0.228839\pi$
$857$	14010.3	+	8088.82i	0.558438	+	0.322414i	−0.194080	+	0.980986i	$0.562172\pi$
$858$		0			0
$859$	16698.0	+	28921.7i	0.663245	+	1.14877i	0.979758	+	0.200185i	$0.0641544\pi$
$859$	16698.0	+	28921.7i	0.663245	+	1.14877i	−0.316513	+	0.948588i	$0.602512\pi$
$860$		0			0
$861$	−9578.38	−	7656.89i	−0.379129	−	0.303073i
$862$		0			0
$863$	13338.4	−	7700.94i	0.526124	−	0.303758i	−0.213312	−	0.976984i	$-0.568425\pi$
$863$	13338.4	−	7700.94i	0.526124	−	0.303758i	0.739437	+	0.673226i	$0.235092\pi$
$864$		0			0
$865$	−17839.3	+	30898.6i	−0.701219	+	1.21455i
$866$		0			0
$867$	20975.9			0.821660
$868$		0			0
$869$	−17903.1			−0.698873
$870$		0			0
$871$	−29854.5	+	51709.6i	−1.16140	+	2.01161i
$872$		0			0
$873$	2693.66	−	1555.18i	0.104429	−	0.0602921i
$874$		0			0
$875$	4170.60	−	27451.8i	0.161134	−	1.06062i
$876$		0			0
$877$	11494.2	+	19908.5i	0.442567	+	0.766548i	0.997879	−	0.0650939i	$-0.0207347\pi$
$877$	11494.2	+	19908.5i	0.442567	+	0.766548i	−0.555313	+	0.831642i	$0.687401\pi$
$878$		0			0
$879$	−9510.61	−	5490.95i	−0.364943	−	0.210700i
$880$		0			0
$881$			44097.1i			1.68635i	0.537643	+	0.843173i	$0.319315\pi$
$881$			44097.1i			1.68635i	−0.537643	+	0.843173i	$0.680685\pi$
$882$		0			0
$883$			21367.6i			0.814355i	0.913349	+	0.407178i	$0.133487\pi$
$883$			21367.6i			0.814355i	−0.913349	+	0.407178i	$0.866513\pi$
$884$		0			0
$885$	−2218.20	−	1280.68i	−0.0842530	−	0.0486435i
$886$		0			0
$887$	−17222.8	−	29830.7i	−0.651956	−	1.12922i	−0.982648	−	0.185482i	$-0.940616\pi$
$887$	−17222.8	−	29830.7i	−0.651956	−	1.12922i	0.330692	−	0.943739i	$-0.392718\pi$
$888$		0			0
$889$	3691.29	−	24296.9i	0.139260	−	0.916638i
$890$		0			0
$891$	−3312.17	+	1912.28i	−0.124536	+	0.0719010i
$892$		0			0
$893$	−2559.08	+	4432.46i	−0.0958974	+	0.166099i
$894$		0			0
$895$	−37561.9			−1.40286
$896$		0			0
$897$	−6013.14			−0.223827
$898$		0			0
$899$	−471.649	+	816.921i	−0.0174976	+	0.0303068i
$900$		0			0
$901$	11525.1	−	6654.03i	0.426146	−	0.246036i
$902$		0			0
$903$	6102.23	+	4878.08i	0.224883	+	0.179770i
$904$		0			0
$905$	−1966.29	−	3405.72i	−0.0722229	−	0.125094i
$906$		0			0
$907$	−5854.66	−	3380.19i	−0.214334	−	0.123746i	0.388990	−	0.921242i	$-0.372824\pi$
$907$	−5854.66	−	3380.19i	−0.214334	−	0.123746i	−0.603324	+	0.797496i	$0.706157\pi$
$908$		0			0
$909$		−	9369.50i		−	0.341877i
$910$		0			0
$911$		−	17345.6i		−	0.630830i	−0.948954	−	0.315415i	$-0.897856\pi$
$911$		−	17345.6i		−	0.630830i	0.948954	−	0.315415i	$-0.102144\pi$
$912$		0			0
$913$	28371.0	+	16380.0i	1.02842	+	0.593756i
$914$		0			0
$915$	822.548	+	1424.69i	0.0297187	+	0.0514743i
$916$		0			0
$917$	−10358.1	−	26483.2i	−0.373014	−	0.953710i
$918$		0			0
$919$	−27620.4	+	15946.7i	−0.991418	+	0.572396i	−0.905698	−	0.423923i	$-0.860653\pi$
$919$	−27620.4	+	15946.7i	−0.991418	+	0.572396i	−0.0857205	+	0.996319i	$0.527319\pi$
$920$		0			0
$921$	4325.76	−	7492.43i	0.154765	−	0.268061i
$922$		0			0
$923$	21155.5			0.754434
$924$		0			0
$925$	−22689.8			−0.806524
$926$		0			0
$927$	6895.39	−	11943.2i	0.244309	−	0.423155i
$928$		0			0
$929$	34785.7	−	20083.6i	1.22851	−	0.709279i	0.261790	−	0.965125i	$-0.415687\pi$
$929$	34785.7	−	20083.6i	1.22851	−	0.709279i	0.966718	+	0.255846i	$0.0823540\pi$
$930$		0			0
$931$	3395.26	+	15038.0i	0.119522	+	0.529377i
$932$		0			0
$933$	−4585.58	−	7942.46i	−0.160906	−	0.278697i
$934$		0			0
$935$	−36644.1	−	21156.5i	−1.28170	−	0.739990i
$936$		0			0
$937$		−	53552.4i		−	1.86711i	−0.358437	−	0.933554i	$-0.616690\pi$
$937$		−	53552.4i		−	1.86711i	0.358437	−	0.933554i	$-0.383310\pi$
$938$		0			0
$939$		−	1271.57i		−	0.0441917i
$940$		0			0
$941$	−12878.3	−	7435.29i	−0.446143	−	0.257581i	0.260057	−	0.965593i	$-0.416259\pi$
$941$	−12878.3	−	7435.29i	−0.446143	−	0.257581i	−0.706200	+	0.708013i	$0.749592\pi$
$942$		0			0
$943$	−2717.28	−	4706.46i	−0.0938354	−	0.162528i
$944$		0			0
$945$	3824.84	−	1495.97i	0.131664	−	0.0514962i
$946$		0			0
$947$	−27577.0	+	15921.6i	−0.946284	+	0.546338i	−0.891925	−	0.452184i	$-0.850645\pi$
$947$	−27577.0	+	15921.6i	−0.946284	+	0.546338i	−0.0543597	+	0.998521i	$0.517312\pi$
$948$		0			0
$949$	44942.5	−	77842.6i	1.53730	−	2.66268i
$950$		0			0
$951$	−15269.5			−0.520661
$952$		0			0
$953$	27066.7			0.920016			0.460008	−	0.887915i	$-0.347846\pi$
$953$	27066.7			0.920016			0.460008	+	0.887915i	$0.347846\pi$
$954$		0			0
$955$	−6922.53	+	11990.2i	−0.234563	+	0.406275i
$956$		0			0
$957$	−22621.6	+	13060.6i	−0.764110	+	0.441159i
$958$		0			0
$959$	−20353.5	+	25461.2i	−0.685348	+	0.857336i
$960$		0			0
$961$	14882.4	+	25777.1i	0.499561	+	0.865265i
$962$		0			0
$963$	−16368.4	−	9450.30i	−0.547730	−	0.316232i
$964$		0			0
$965$		−	986.388i		−	0.0329046i
$966$		0			0
$967$			13564.1i			0.451077i	0.974234	+	0.225538i	$0.0724141\pi$
$967$			13564.1i			0.451077i	−0.974234	+	0.225538i	$0.927586\pi$
$968$		0			0
$969$	−12741.1	−	7356.09i	−0.422398	−	0.243872i
$970$		0			0
$971$	−26845.6	−	46497.9i	−0.887245	−	1.53675i	−0.843118	−	0.537728i	$-0.819283\pi$
$971$	−26845.6	−	46497.9i	−0.887245	−	1.53675i	−0.0441269	−	0.999026i	$-0.514051\pi$
$972$		0			0
$973$	49752.0	+	7558.55i	1.63924	+	0.249040i
$974$		0			0
$975$	−12169.7	+	7026.17i	−0.399735	+	0.230787i
$976$		0			0
$977$	−10299.0	+	17838.3i	−0.337250	+	0.584134i	−0.983914	−	0.178640i	$-0.942830\pi$
$977$	−10299.0	+	17838.3i	−0.337250	+	0.584134i	0.646664	+	0.762775i	$0.276163\pi$
$978$		0			0
$979$	−30395.5			−0.992281
$980$		0			0
$981$	19076.5			0.620863
$982$		0			0
$983$	−12478.0	+	21612.5i	−0.404868	+	0.701251i	−0.994306	−	0.106562i	$-0.966016\pi$
$983$	−12478.0	+	21612.5i	−0.404868	+	0.701251i	0.589438	+	0.807813i	$0.299349\pi$
$984$		0			0
$985$	18336.4	−	10586.5i	0.593144	−	0.342452i
$986$		0			0
$987$	−6255.12	−	950.305i	−0.201725	−	0.0306470i
$988$		0			0
$989$	1731.13	+	2998.41i	0.0556591	+	0.0964044i
$990$		0			0
$991$	50408.0	+	29103.1i	1.61580	+	0.932885i	0.987989	+	0.154522i	$0.0493838\pi$
$991$	50408.0	+	29103.1i	1.61580	+	0.932885i	0.627815	+	0.778363i	$0.283950\pi$
$992$		0			0
$993$			12004.9i			0.383649i
$994$		0			0
$995$		−	22781.5i		−	0.725852i
$996$		0			0
$997$	15421.5	+	8903.61i	0.489874	+	0.282829i	0.724522	−	0.689252i	$-0.242061\pi$
$997$	15421.5	+	8903.61i	0.489874	+	0.282829i	−0.234648	+	0.972080i	$0.575394\pi$
$998$		0			0
$999$	−5323.16	−	9219.98i	−0.168586	−	0.291999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.4.bl.b.31.17	yes	48
4.3	odd	2		672.4.bl.a.31.17	✓	48
7.5	odd	6		672.4.bl.a.607.17	yes	48
28.19	even	6	inner	672.4.bl.b.607.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.4.bl.a.31.17	✓	48	4.3	odd	2
672.4.bl.a.607.17	yes	48	7.5	odd	6
672.4.bl.b.31.17	yes	48	1.1	even	1	trivial
672.4.bl.b.607.17	yes	48	28.19	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(7.11284 - 4.10660i) q^{5} +(-18.3102 - 2.78176i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(7.11284 - 4.10660i) q^{5} +(-18.3102 - 2.78176i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(40.8910 + 23.6084i) q^{11} +81.4016i q^{13} -24.6396i q^{15} +(-94.4919 - 54.5549i) q^{17} +(22.4730 + 38.9245i) q^{19} +(-34.6925 + 43.3985i) q^{21} +(-21.3244 + 12.3117i) q^{23} +(-28.7716 + 49.8339i) q^{25} -27.0000 q^{27} -184.406 q^{29} +(2.55767 - 4.43001i) q^{31} +(122.673 - 70.8252i) q^{33} +(-141.661 + 55.4063i) q^{35} +(197.154 + 341.481i) q^{37} +(211.488 + 122.102i) q^{39} +220.708i q^{41} -140.609i q^{43} +(-64.0156 - 36.9594i) q^{45} +(56.9367 + 98.6172i) q^{47} +(327.524 + 101.869i) q^{49} +(-283.476 + 163.665i) q^{51} +(-60.9847 + 105.629i) q^{53} +387.801 q^{55} +134.838 q^{57} +(51.9763 - 90.0257i) q^{59} +(-57.8213 + 33.3831i) q^{61} +(60.7140 + 155.231i) q^{63} +(334.284 + 578.997i) q^{65} +(635.240 + 366.756i) q^{67} +73.8700i q^{69} -259.891i q^{71} +(-956.279 - 552.108i) q^{73} +(86.3149 + 149.502i) q^{75} +(-683.047 - 546.022i) q^{77} +(-328.369 + 189.584i) q^{79} +(-40.5000 + 70.1481i) q^{81} +693.821 q^{83} -896.142 q^{85} +(-276.609 + 479.101i) q^{87} +(-557.497 + 321.871i) q^{89} +(226.440 - 1490.48i) q^{91} +(-7.67300 - 13.2900i) q^{93} +(319.695 + 184.576i) q^{95} +345.596i q^{97} -424.951i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9}+O(q^{10}) \) 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9	\( 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9} - 12 q^{11} + 28 q^{19} + 120 q^{21} + 684 q^{25} - 1296 q^{27} + 460 q^{31} - 36 q^{33} + 568 q^{35} + 252 q^{37} + 324 q^{39} + 280 q^{47} - 184 q^{49} - 392 q^{53} + 848 q^{55} + 168 q^{57} - 964 q^{59} - 600 q^{61} + 180 q^{63} + 280 q^{65} - 660 q^{67} + 324 q^{73} - 2052 q^{75} + 1568 q^{77} - 2652 q^{79} - 1944 q^{81} + 1336 q^{83} - 1056 q^{85} - 3004 q^{91} - 1380 q^{93} - 3984 q^{95}+O(q^{100}) \) 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9 - 12 * q^11 + 28 * q^19 + 120 * q^21 + 684 * q^25 - 1296 * q^27 + 460 * q^31 - 36 * q^33 + 568 * q^35 + 252 * q^37 + 324 * q^39 + 280 * q^47 - 184 * q^49 - 392 * q^53 + 848 * q^55 + 168 * q^57 - 964 * q^59 - 600 * q^61 + 180 * q^63 + 280 * q^65 - 660 * q^67 + 324 * q^73 - 2052 * q^75 + 1568 * q^77 - 2652 * q^79 - 1944 * q^81 + 1336 * q^83 - 1056 * q^85 - 3004 * q^91 - 1380 * q^93 - 3984 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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