LMFDB - Embedded newform 624.4.bv.c.433.2

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			433.2
Root			$3.57071 + 2.06155i$ of defining polynomial
Character	$\chi$	$=$	624.433
Dual form			624.4.bv.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +3.05006i q^{5} +(5.78786 - 3.34162i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +3.05006i q^{5} +(5.78786 - 3.34162i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(27.9293 + 16.1250i) q^{11} +(-22.1364 + 41.3156i) q^{13} +(-7.92429 - 4.57509i) q^{15} +(-14.4293 - 24.9923i) q^{17} +(-87.6364 + 50.5969i) q^{19} +20.0497i q^{21} +(59.4950 - 103.048i) q^{23} +115.697 q^{25} +27.0000 q^{27} +(-80.0557 + 138.661i) q^{29} -38.0705i q^{31} +(-83.7879 + 48.3749i) q^{33} +(10.1921 + 17.6533i) q^{35} +(283.682 + 163.784i) q^{37} +(-74.1364 - 119.486i) q^{39} +(48.5707 + 28.0423i) q^{41} +(-63.9393 - 110.746i) q^{43} +(23.7729 - 13.7253i) q^{45} +517.983i q^{47} +(-149.167 + 258.365i) q^{49} +86.5757 q^{51} -695.546 q^{53} +(-49.1821 + 85.1860i) q^{55} -303.581i q^{57} +(-568.566 + 328.262i) q^{59} +(-350.652 - 607.347i) q^{61} +(-52.0907 - 30.0746i) q^{63} +(-126.015 - 67.5174i) q^{65} +(49.5150 + 28.5875i) q^{67} +(178.485 + 309.145i) q^{69} +(267.798 - 154.613i) q^{71} -389.711i q^{73} +(-173.546 + 300.590i) q^{75} +215.534 q^{77} -901.820 q^{79} +(-40.5000 + 70.1481i) q^{81} +687.095i q^{83} +(76.2279 - 44.0102i) q^{85} +(-240.167 - 415.982i) q^{87} +(-927.113 - 535.269i) q^{89} +(9.93858 + 313.100i) q^{91} +(98.9100 + 57.1057i) q^{93} +(-154.324 - 267.296i) q^{95} +(-1519.43 + 877.242i) q^{97} -290.250i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$			3.05006i			0.272806i	0.990653	+	0.136403i	$0.0435541\pi$
$5$			3.05006i			0.272806i	−0.990653	+	0.136403i	$0.956446\pi$
$6$		0			0
$7$	5.78786	−	3.34162i	0.312515	−	0.180431i	−0.335536	−	0.942027i	$-0.608918\pi$
$7$	5.78786	−	3.34162i	0.312515	−	0.180431i	0.648051	+	0.761597i	$0.275584\pi$
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	27.9293	+	16.1250i	0.765545	+	0.441988i	0.831283	−	0.555849i	$-0.187607\pi$
$11$	27.9293	+	16.1250i	0.765545	+	0.441988i	−0.0657380	+	0.997837i	$0.520940\pi$
$12$		0			0
$13$	−22.1364	+	41.3156i	−0.472272	+	0.881453i
$13$	−22.1364	+	41.3156i	−0.472272	+	0.881453i
$14$		0			0
$15$	−7.92429	−	4.57509i	−0.136403	−	0.0787522i
$16$		0			0
$17$	−14.4293	−	24.9923i	−0.205860	−	0.356560i	0.744547	−	0.667571i	$-0.232666\pi$
$17$	−14.4293	−	24.9923i	−0.205860	−	0.356560i	−0.950406	+	0.311011i	$0.899332\pi$
$18$		0			0
$19$	−87.6364	+	50.5969i	−1.05817	+	0.610933i	−0.924925	−	0.380150i	$-0.875872\pi$
$19$	−87.6364	+	50.5969i	−1.05817	+	0.610933i	−0.133242	+	0.991083i	$0.542539\pi$
$20$		0			0
$21$			20.0497i			0.208343i
$22$		0			0
$23$	59.4950	−	103.048i	0.539372	−	0.934220i	−0.459566	−	0.888144i	$-0.651995\pi$
$23$	59.4950	−	103.048i	0.539372	−	0.934220i	0.998938	−	0.0460765i	$-0.0146718\pi$
$24$		0			0
$25$	115.697			0.925577
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	−80.0557	+	138.661i	−0.512620	+	0.887883i	0.487273	+	0.873250i	$0.337992\pi$
$29$	−80.0557	+	138.661i	−0.512620	+	0.887883i	−0.999893	+	0.0146339i	$0.995342\pi$
$30$		0			0
$31$		−	38.0705i		−	0.220570i	−0.993900	−	0.110285i	$-0.964824\pi$
$31$		−	38.0705i		−	0.220570i	0.993900	−	0.110285i	$-0.0351763\pi$
$32$		0			0
$33$	−83.7879	+	48.3749i	−0.441988	+	0.255182i
$34$		0			0
$35$	10.1921	+	17.6533i	0.0492225	+	0.0852558i
$36$		0			0
$37$	283.682	+	163.784i	1.26046	+	0.727727i	0.973164	−	0.230114i	$-0.0739099\pi$
$37$	283.682	+	163.784i	1.26046	+	0.727727i	0.287297	+	0.957841i	$0.407243\pi$
$38$		0			0
$39$	−74.1364	−	119.486i	−0.304393	−	0.490590i
$40$		0			0
$41$	48.5707	+	28.0423i	0.185011	+	0.106816i	0.589645	−	0.807662i	$-0.299268\pi$
$41$	48.5707	+	28.0423i	0.185011	+	0.106816i	−0.404634	+	0.914479i	$0.632601\pi$
$42$		0			0
$43$	−63.9393	−	110.746i	−0.226759	−	0.392759i	0.730087	−	0.683355i	$-0.239480\pi$
$43$	−63.9393	−	110.746i	−0.226759	−	0.392759i	−0.956846	+	0.290596i	$0.906146\pi$
$44$		0			0
$45$	23.7729	−	13.7253i	0.0787522	−	0.0454676i
$46$		0			0
$47$			517.983i			1.60757i	0.594923	+	0.803783i	$0.297183\pi$
$47$			517.983i			1.60757i	−0.594923	+	0.803783i	$0.702817\pi$
$48$		0			0
$49$	−149.167	+	258.365i	−0.434890	+	0.753251i
$50$		0			0
$51$	86.5757			0.237706
$52$		0			0
$53$	−695.546			−1.80265			−0.901326	−	0.433141i	$-0.857405\pi$
$53$	−695.546			−1.80265			−0.901326	+	0.433141i	$0.857405\pi$
$54$		0			0
$55$	−49.1821	+	85.1860i	−0.120577	+	0.208845i
$56$		0			0
$57$		−	303.581i		−	0.705445i
$58$		0			0
$59$	−568.566	+	328.262i	−1.25459	+	0.724339i	−0.972018	−	0.234906i	$-0.924522\pi$
$59$	−568.566	+	328.262i	−1.25459	+	0.724339i	−0.282574	+	0.959245i	$0.591188\pi$
$60$		0			0
$61$	−350.652	−	607.347i	−0.736007	−	1.27480i	−0.954280	−	0.298913i	$-0.903376\pi$
$61$	−350.652	−	607.347i	−0.736007	−	1.27480i	0.218274	−	0.975888i	$-0.429957\pi$
$62$		0			0
$63$	−52.0907	−	30.0746i	−0.104172	−	0.0601435i
$64$		0			0
$65$	−126.015	−	67.5174i	−0.240465	−	0.128839i
$66$		0			0
$67$	49.5150	+	28.5875i	0.0902869	+	0.0521271i	0.544464	−	0.838784i	$-0.316733\pi$
$67$	49.5150	+	28.5875i	0.0902869	+	0.0521271i	−0.454177	+	0.890912i	$0.650067\pi$
$68$		0			0
$69$	178.485	+	309.145i	0.311407	+	0.539372i
$70$		0			0
$71$	267.798	−	154.613i	0.447630	−	0.258440i	−0.259199	−	0.965824i	$-0.583458\pi$
$71$	267.798	−	154.613i	0.447630	−	0.258440i	0.706829	+	0.707385i	$0.250125\pi$
$72$		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
$75$	−173.546	+	300.590i	−0.267191	+	0.462789i
$76$		0			0
$77$	215.534			0.318992
$78$		0			0
$79$	−901.820			−1.28434			−0.642169	−	0.766563i	$-0.721965\pi$
$79$	−901.820			−1.28434			−0.642169	+	0.766563i	$0.721965\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			687.095i			0.908657i	0.890834	+	0.454328i	$0.150121\pi$
$83$			687.095i			0.908657i	−0.890834	+	0.454328i	$0.849879\pi$
$84$		0			0
$85$	76.2279	−	44.0102i	0.0972714	−	0.0561597i
$86$		0			0
$87$	−240.167	−	415.982i	−0.295961	−	0.512620i
$88$		0			0
$89$	−927.113	−	535.269i	−1.10420	−	0.637510i	−0.166879	−	0.985977i	$-0.553369\pi$
$89$	−927.113	−	535.269i	−1.10420	−	0.637510i	−0.937321	+	0.348467i	$0.886702\pi$
$90$		0			0
$91$	9.93858	+	313.100i	0.0114489	+	0.360679i
$92$		0			0
$93$	98.9100	+	57.1057i	0.110285	+	0.0636730i
$94$		0			0
$95$	−154.324	−	267.296i	−0.166666	−	0.288674i
$96$		0			0
$97$	−1519.43	+	877.242i	−1.59046	+	0.918251i	−0.597230	+	0.802070i	$0.703732\pi$
$97$	−1519.43	+	877.242i	−1.59046	+	0.918251i	−0.993228	+	0.116182i	$0.962935\pi$
$98$		0			0
$99$		−	290.250i		−	0.294658i
$100$		0			0
$101$	−320.420	+	554.984i	−0.315673	+	0.546762i	−0.979580	−	0.201053i	$-0.935564\pi$
$101$	−320.420	+	554.984i	−0.315673	+	0.546762i	0.663907	+	0.747815i	$0.268897\pi$
$102$		0			0
$103$	−693.153			−0.663091			−0.331546	−	0.943439i	$-0.607570\pi$
$103$	−693.153			−0.663091			−0.331546	+	0.943439i	$0.607570\pi$
$104$		0			0
$105$	−61.1528			−0.0568372
$106$		0			0
$107$	−202.838	+	351.325i	−0.183262	+	0.317420i	−0.942990	−	0.332822i	$-0.891999\pi$
$107$	−202.838	+	351.325i	−0.183262	+	0.317420i	0.759727	+	0.650242i	$0.225332\pi$
$108$		0			0
$109$			479.516i			0.421370i	0.977554	+	0.210685i	$0.0675694\pi$
$109$			479.516i			0.421370i	−0.977554	+	0.210685i	$0.932431\pi$
$110$		0			0
$111$	−851.046	+	491.352i	−0.727727	+	0.420154i
$112$		0			0
$113$	773.602	+	1339.92i	0.644021	+	1.11548i	0.984527	+	0.175235i	$0.0560684\pi$
$113$	773.602	+	1339.92i	0.644021	+	1.11548i	−0.340506	+	0.940242i	$0.610598\pi$
$114$		0			0
$115$	314.304	+	181.463i	0.254861	+	0.147144i
$116$		0			0
$117$	421.637	−	13.3838i	0.333166	−	0.0105755i
$118$		0			0
$119$	−167.029	−	96.4344i	−0.128668	−	0.0742868i
$120$		0			0
$121$	−145.470	−	251.961i	−0.109294	−	0.189302i
$122$		0			0
$123$	−145.712	+	84.1269i	−0.106816	+	0.0616705i
$124$		0			0
$125$			734.140i			0.525308i
$126$		0			0
$127$	1247.58	−	2160.87i	0.871690	−	1.50981i	0.0114416	−	0.999935i	$-0.496358\pi$
$127$	1247.58	−	2160.87i	0.871690	−	1.50981i	0.860248	−	0.509876i	$-0.170309\pi$
$128$		0			0
$129$	383.636			0.261839
$130$		0			0
$131$	−43.7571			−0.0291838			−0.0145919	−	0.999894i	$-0.504645\pi$
$131$	−43.7571			−0.0291838			−0.0145919	+	0.999894i	$0.504645\pi$
$132$		0			0
$133$	−338.151	+	585.695i	−0.220462	+	0.381851i
$134$		0			0
$135$			82.3516i			0.0525015i
$136$		0			0
$137$	−178.569	+	103.097i	−0.111359	+	0.0642932i	−0.554645	−	0.832087i	$-0.687146\pi$
$137$	−178.569	+	103.097i	−0.111359	+	0.0642932i	0.443286	+	0.896380i	$0.353813\pi$
$138$		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
$141$	−1345.76	−	776.974i	−0.803783	−	0.464064i
$142$		0			0
$143$	−1284.47	+	796.966i	−0.751137	+	0.466053i
$144$		0			0
$145$	−422.923	−	244.175i	−0.242220	−	0.139846i
$146$		0			0
$147$	−447.501	−	775.095i	−0.251084	−	0.434890i
$148$		0			0
$149$	−329.480	+	190.225i	−0.181155	+	0.104590i	−0.587835	−	0.808981i	$-0.700020\pi$
$149$	−329.480	+	190.225i	−0.181155	+	0.104590i	0.406680	+	0.913571i	$0.366686\pi$
$150$		0			0
$151$			1517.45i			0.817805i	0.912578	+	0.408902i	$0.134088\pi$
$151$			1517.45i			0.817805i	−0.912578	+	0.408902i	$0.865912\pi$
$152$		0			0
$153$	−129.864	+	224.930i	−0.0686199	+	0.118853i
$154$		0			0
$155$	116.117			0.0601726
$156$		0			0
$157$	1450.16			0.737166			0.368583	−	0.929595i	$-0.379843\pi$
$157$	1450.16			0.737166			0.368583	+	0.929595i	$0.379843\pi$
$158$		0			0
$159$	1043.32	−	1807.08i	0.520381	−	0.901326i
$160$		0			0
$161$		−	795.239i		−	0.389277i
$162$		0			0
$163$	−2028.54	+	1171.18i	−0.974772	+	0.562785i	−0.900688	−	0.434467i	$-0.856937\pi$
$163$	−2028.54	+	1171.18i	−0.974772	+	0.562785i	−0.0740844	+	0.997252i	$0.523603\pi$
$164$		0			0
$165$	−147.546	−	255.558i	−0.0696150	−	0.120577i
$166$		0			0
$167$	−34.7043	−	20.0365i	−0.0160808	−	0.00928428i	0.491938	−	0.870630i	$-0.336289\pi$
$167$	−34.7043	−	20.0365i	−0.0160808	−	0.00928428i	−0.508019	+	0.861346i	$0.669622\pi$
$168$		0			0
$169$	−1216.96	−	1829.16i	−0.553918	−	0.832571i
$170$		0			0
$171$	788.728	+	455.372i	0.352722	+	0.203644i
$172$		0			0
$173$	954.770	+	1653.71i	0.419594	+	0.726759i	0.995899	−	0.0904765i	$-0.0288390\pi$
$173$	954.770	+	1653.71i	0.419594	+	0.726759i	−0.576304	+	0.817235i	$0.695506\pi$
$174$		0			0
$175$	669.639	−	386.616i	0.289257	−	0.167002i
$176$		0			0
$177$		−	1969.57i		−	0.836395i
$178$		0			0
$179$	254.979	−	441.637i	0.106470	−	0.184411i	−0.807868	−	0.589363i	$-0.799379\pi$
$179$	254.979	−	441.637i	0.106470	−	0.184411i	0.914338	+	0.404953i	$0.132712\pi$
$180$		0			0
$181$	2136.88			0.877531			0.438766	−	0.898602i	$-0.355416\pi$
$181$	2136.88			0.877531			0.438766	+	0.898602i	$0.355416\pi$
$182$		0			0
$183$	2103.91			0.849867
$184$		0			0
$185$	−499.551	+	865.247i	−0.198528	+	0.343861i
$186$		0			0
$187$		−	930.688i		−	0.363950i
$188$		0			0
$189$	156.272	−	90.2238i	0.0601435	−	0.0347239i
$190$		0			0
$191$	2028.87	+	3514.11i	0.768607	+	1.33127i	0.938318	+	0.345773i	$0.112383\pi$
$191$	2028.87	+	3514.11i	0.768607	+	1.33127i	−0.169711	+	0.985494i	$0.554283\pi$
$192$		0			0
$193$	−756.381	−	436.697i	−0.282101	−	0.162871i	0.352273	−	0.935897i	$-0.385409\pi$
$193$	−756.381	−	436.697i	−0.282101	−	0.162871i	−0.634374	+	0.773026i	$0.718742\pi$
$194$		0			0
$195$	364.438	−	226.120i	0.133836	−	0.0830401i
$196$		0			0
$197$	3591.62	+	2073.62i	1.29895	+	0.749947i	0.980222	−	0.197901i	$-0.0634124\pi$
$197$	3591.62	+	2073.62i	1.29895	+	0.749947i	0.318724	+	0.947848i	$0.396746\pi$
$198$		0			0
$199$	1202.03	+	2081.98i	0.428189	+	0.741646i	0.996712	−	0.0810216i	$-0.0258183\pi$
$199$	1202.03	+	2081.98i	0.428189	+	0.741646i	−0.568523	+	0.822667i	$0.692485\pi$
$200$		0			0
$201$	−148.545	+	85.7625i	−0.0521271	+	0.0300956i
$202$		0			0
$203$			1070.06i			0.369969i
$204$		0			0
$205$	−85.5307	+	148.144i	−0.0291401	+	0.0504722i
$206$		0			0
$207$	−1070.91			−0.359582
$208$		0			0
$209$	−3263.50			−1.08010
$210$		0			0
$211$	1934.43	−	3350.53i	0.631144	−	1.09317i	−0.356174	−	0.934420i	$-0.615919\pi$
$211$	1934.43	−	3350.53i	0.631144	−	1.09317i	0.987318	−	0.158754i	$-0.0507478\pi$
$212$		0			0
$213$			927.679i			0.298420i
$214$		0			0
$215$	337.782	−	195.019i	0.107147	−	0.0618612i
$216$		0			0
$217$	−127.217	−	220.346i	−0.0397975	−	0.0689313i
$218$		0			0
$219$	1012.50	+	584.567i	0.312413	+	0.180372i
$220$		0			0
$221$	1351.98	−	42.9153i	0.411512	−	0.0130624i
$222$		0			0
$223$	−2436.61	−	1406.78i	−0.731692	−	0.422443i	0.0873487	−	0.996178i	$-0.472161\pi$
$223$	−2436.61	−	1406.78i	−0.731692	−	0.422443i	−0.819041	+	0.573735i	$0.805494\pi$
$224$		0			0
$225$	−520.637	−	901.770i	−0.154263	−	0.267191i
$226$		0			0
$227$	−3913.02	+	2259.19i	−1.14413	+	0.660561i	−0.947449	−	0.319907i	$-0.896348\pi$
$227$	−3913.02	+	2259.19i	−1.14413	+	0.660561i	−0.196677	+	0.980468i	$0.563015\pi$
$228$		0			0
$229$		−	1305.27i		−	0.376658i	−0.982106	−	0.188329i	$-0.939693\pi$
$229$		−	1305.27i		−	0.376658i	0.982106	−	0.188329i	$-0.0603070\pi$
$230$		0			0
$231$	−323.301	+	559.975i	−0.0920852	+	0.159496i
$232$		0			0
$233$	3360.55			0.944879			0.472440	−	0.881363i	$-0.343373\pi$
$233$	3360.55			0.944879			0.472440	+	0.881363i	$0.343373\pi$
$234$		0			0
$235$	−1579.88			−0.438553
$236$		0			0
$237$	1352.73	−	2343.00i	0.370756	−	0.642169i
$238$		0			0
$239$		−	4737.17i		−	1.28210i	−0.767499	−	0.641050i	$-0.778499\pi$
$239$		−	4737.17i		−	1.28210i	0.767499	−	0.641050i	$-0.221501\pi$
$240$		0			0
$241$	4144.17	−	2392.64i	1.10767	−	0.639516i	0.169448	−	0.985539i	$-0.445801\pi$
$241$	4144.17	−	2392.64i	1.10767	−	0.639516i	0.938226	+	0.346023i	$0.112468\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−788.029	−	454.969i	−0.205491	−	0.118640i
$246$		0			0
$247$	−150.484	−	4740.79i	−0.0387655	−	1.22125i
$248$		0			0
$249$	−1785.13	−	1030.64i	−0.454328	−	0.262307i
$250$		0			0
$251$	1636.93	+	2835.25i	0.411642	+	0.712985i	0.995069	−	0.0991805i	$-0.0316221\pi$
$251$	1636.93	+	2835.25i	0.411642	+	0.712985i	−0.583428	+	0.812165i	$0.698289\pi$
$252$		0			0
$253$	3323.31	−	1918.71i	0.825828	−	0.476792i
$254$		0			0
$255$			264.061i			0.0648476i
$256$		0			0
$257$	−3272.91	+	5668.84i	−0.794390	+	1.37592i	0.128835	+	0.991666i	$0.458876\pi$
$257$	−3272.91	+	5668.84i	−0.794390	+	1.37592i	−0.923226	+	0.384258i	$0.874457\pi$
$258$		0			0
$259$	2189.22			0.525217
$260$		0			0
$261$	1441.00			0.341746
$262$		0			0
$263$	44.1007	−	76.3847i	0.0103398	−	0.0179091i	−0.860809	−	0.508928i	$-0.830042\pi$
$263$	44.1007	−	76.3847i	0.0103398	−	0.0179091i	0.871149	+	0.491019i	$0.163375\pi$
$264$		0			0
$265$		−	2121.46i		−	0.491773i
$266$		0			0
$267$	2781.34	−	1605.81i	0.637510	−	0.368067i
$268$		0			0
$269$	2263.80	+	3921.01i	0.513109	+	0.888730i	0.999884	+	0.0152033i	$0.00483956\pi$
$269$	2263.80	+	3921.01i	0.513109	+	0.888730i	−0.486776	+	0.873527i	$0.661827\pi$
$270$		0			0
$271$	7206.91	+	4160.91i	1.61546	+	0.932684i	0.988075	+	0.153971i	$0.0492062\pi$
$271$	7206.91	+	4160.91i	1.61546	+	0.932684i	0.627380	+	0.778713i	$0.284127\pi$
$272$		0			0
$273$	−828.366	−	443.829i	−0.183645	−	0.0983948i
$274$		0			0
$275$	3231.34	+	1865.61i	0.708571	+	0.409094i
$276$		0			0
$277$	−1440.65	−	2495.29i	−0.312493	−	0.541254i	0.666408	−	0.745587i	$-0.267831\pi$
$277$	−1440.65	−	2495.29i	−0.312493	−	0.541254i	−0.978901	+	0.204333i	$0.934497\pi$
$278$		0			0
$279$	−296.730	+	171.317i	−0.0636730	+	0.0367616i
$280$		0			0
$281$		−	2817.99i		−	0.598247i	−0.954214	−	0.299123i	$-0.903306\pi$
$281$		−	2817.99i		−	0.598247i	0.954214	−	0.299123i	$-0.0966942\pi$
$282$		0			0
$283$	−132.301	+	229.152i	−0.0277896	+	0.0481330i	−0.879586	−	0.475740i	$-0.842180\pi$
$283$	−132.301	+	229.152i	−0.0277896	+	0.0481330i	0.851796	+	0.523873i	$0.175514\pi$
$284$		0			0
$285$	925.941			0.192449
$286$		0			0
$287$	374.827			0.0770918
$288$		0			0
$289$	2040.09	−	3533.54i	0.415244	−	0.719223i
$290$		0			0
$291$		−	5263.45i		−	1.06031i
$292$		0			0
$293$	3717.43	−	2146.26i	0.741211	−	0.427938i	−0.0812984	−	0.996690i	$-0.525907\pi$
$293$	3717.43	−	2146.26i	0.741211	−	0.427938i	0.822509	+	0.568751i	$0.192573\pi$
$294$		0			0
$295$	−1001.22	−	1734.16i	−0.197604	−	0.342260i
$296$		0			0
$297$	754.091	+	435.374i	0.147329	+	0.0850606i
$298$		0			0
$299$	2940.50	+	4739.19i	0.568740	+	0.916638i
$300$		0			0
$301$	−740.143	−	427.322i	−0.141731	−	0.0818286i
$302$		0			0
$303$	−961.260	−	1664.95i	−0.182254	−	0.315673i
$304$		0			0
$305$	1852.45	−	1069.51i	0.347773	−	0.200787i
$306$		0			0
$307$		−	7026.26i		−	1.30622i	−0.757263	−	0.653110i	$-0.773464\pi$
$307$		−	7026.26i		−	1.30622i	0.757263	−	0.653110i	$-0.226536\pi$
$308$		0			0
$309$	1039.73	−	1800.86i	0.191418	−	0.331546i
$310$		0			0
$311$	−1133.21			−0.206618			−0.103309	−	0.994649i	$-0.532943\pi$
$311$	−1133.21			−0.206618			−0.103309	+	0.994649i	$0.532943\pi$
$312$		0			0
$313$	−5285.95			−0.954566			−0.477283	−	0.878750i	$-0.658378\pi$
$313$	−5285.95			−0.954566			−0.477283	+	0.878750i	$0.658378\pi$
$314$		0			0
$315$	91.7293	−	158.880i	0.0164075	−	0.0284186i
$316$		0			0
$317$			4782.16i			0.847296i	0.905827	+	0.423648i	$0.139251\pi$
$317$			4782.16i			0.847296i	−0.905827	+	0.423648i	$0.860749\pi$
$318$		0			0
$319$	−4471.80	+	2581.79i	−0.784867	+	0.453143i
$320$		0			0
$321$	−608.514	−	1053.98i	−0.105807	−	0.183262i
$322$		0			0
$323$	2529.06	+	1460.15i	0.435668	+	0.251533i
$324$		0			0
$325$	−2561.12	+	4780.10i	−0.437124	+	0.815852i
$326$		0			0
$327$	−1245.82	−	719.274i	−0.210685	−	0.121639i
$328$		0			0
$329$	1730.90	+	2998.01i	0.290054	+	0.502388i
$330$		0			0
$331$	7508.43	−	4334.99i	1.24683	−	0.719857i	0.276353	−	0.961056i	$-0.410874\pi$
$331$	7508.43	−	4334.99i	1.24683	−	0.719857i	0.970476	+	0.241199i	$0.0775407\pi$
$332$		0			0
$333$		−	2948.11i		−	0.485152i
$334$		0			0
$335$	−87.1936	+	151.024i	−0.0142206	+	0.0246308i
$336$		0			0
$337$	−8526.59			−1.37826			−0.689129	−	0.724639i	$-0.742007\pi$
$337$	−8526.59			−1.37826			−0.689129	+	0.724639i	$0.742007\pi$
$338$		0			0
$339$	−4641.61			−0.743651
$340$		0			0
$341$	613.886	−	1063.28i	0.0974891	−	0.168856i
$342$		0			0
$343$			4286.19i			0.674731i
$344$		0			0
$345$	−942.911	+	544.390i	−0.147144	+	0.0849535i
$346$		0			0
$347$	−6290.74	−	10895.9i	−0.973213	−	1.68565i	−0.685711	−	0.727874i	$-0.740509\pi$
$347$	−6290.74	−	10895.9i	−0.973213	−	1.68565i	−0.287501	−	0.957780i	$-0.592825\pi$
$348$		0			0
$349$	7760.61	+	4480.59i	1.19030	+	0.687222i	0.958375	−	0.285511i	$-0.0921633\pi$
$349$	7760.61	+	4480.59i	1.19030	+	0.687222i	0.231928	+	0.972733i	$0.425497\pi$
$350$		0			0
$351$	−597.684	+	1115.52i	−0.0908889	+	0.169636i
$352$		0			0
$353$	−4640.16	−	2679.00i	−0.699634	−	0.403934i	0.107577	−	0.994197i	$-0.465691\pi$
$353$	−4640.16	−	2679.00i	−0.699634	−	0.403934i	−0.807211	+	0.590263i	$0.799024\pi$
$354$		0			0
$355$	471.579	+	816.799i	0.0705037	+	0.122116i
$356$		0			0
$357$	501.088	−	289.303i	0.0742868	−	0.0428895i
$358$		0			0
$359$			2705.40i			0.397731i	0.980027	+	0.198866i	$0.0637257\pi$
$359$			2705.40i			0.397731i	−0.980027	+	0.198866i	$0.936274\pi$
$360$		0			0
$361$	1690.60	−	2928.20i	0.246478	−	0.426913i
$362$		0			0
$363$	872.820			0.126202
$364$		0			0
$365$	1188.64			0.170456
$366$		0			0
$367$	5236.88	−	9070.54i	0.744858	−	1.29013i	−0.205403	−	0.978678i	$-0.565850\pi$
$367$	5236.88	−	9070.54i	0.744858	−	1.29013i	0.950261	−	0.311455i	$-0.100816\pi$
$368$		0			0
$369$		−	504.762i		−	0.0712110i
$370$		0			0
$371$	−4025.72	+	2324.25i	−0.563356	+	0.325254i
$372$		0			0
$373$	6381.51	+	11053.1i	0.885850	+	1.53434i	0.844737	+	0.535182i	$0.179757\pi$
$373$	6381.51	+	11053.1i	0.885850	+	1.53434i	0.0411127	+	0.999155i	$0.486910\pi$
$374$		0			0
$375$	−1907.35	−	1101.21i	−0.262654	−	0.151643i
$376$		0			0
$377$	−3956.70	−	6377.00i	−0.540531	−	0.871173i
$378$		0			0
$379$	2007.47	+	1159.01i	0.272076	+	0.157083i	0.629831	−	0.776733i	$-0.283124\pi$
$379$	2007.47	+	1159.01i	0.272076	+	0.157083i	−0.357755	+	0.933816i	$0.616458\pi$
$380$		0			0
$381$	3742.73	+	6482.60i	0.503270	+	0.871690i
$382$		0			0
$383$	1717.63	−	991.672i	0.229156	−	0.132303i	−0.381027	−	0.924564i	$-0.624429\pi$
$383$	1717.63	−	991.672i	0.229156	−	0.132303i	0.610183	+	0.792261i	$0.291096\pi$
$384$		0			0
$385$			657.392i			0.0870229i
$386$		0			0
$387$	−575.454	+	996.715i	−0.0755864	+	0.130920i
$388$		0			0
$389$	3244.51			0.422887			0.211444	−	0.977390i	$-0.432184\pi$
$389$	3244.51			0.422887			0.211444	+	0.977390i	$0.432184\pi$
$390$		0			0
$391$	−3433.88			−0.444140
$392$		0			0
$393$	65.6357	−	113.684i	0.00842464	−	0.0145919i
$394$		0			0
$395$		−	2750.60i		−	0.350374i
$396$		0			0
$397$	3256.02	−	1879.86i	0.411624	−	0.237651i	−0.279863	−	0.960040i	$-0.590289\pi$
$397$	3256.02	−	1879.86i	0.411624	−	0.237651i	0.691487	+	0.722389i	$0.256956\pi$
$398$		0			0
$399$	−1014.45	−	1757.09i	−0.127284	−	0.220462i
$400$		0			0
$401$	1729.93	+	998.773i	0.215432	+	0.124380i	0.603833	−	0.797110i	$-0.293639\pi$
$401$	1729.93	+	998.773i	0.215432	+	0.124380i	−0.388401	+	0.921490i	$0.626973\pi$
$402$		0			0
$403$	1572.90	+	842.744i	0.194422	+	0.104169i
$404$		0			0
$405$	−213.956	−	123.527i	−0.0262507	−	0.0151559i
$406$		0			0
$407$	5282.03	+	9148.74i	0.643293	+	1.11422i
$408$		0			0
$409$	4499.20	−	2597.62i	0.543940	−	0.314044i	−0.202735	−	0.979234i	$-0.564983\pi$
$409$	4499.20	−	2597.62i	0.543940	−	0.314044i	0.746674	+	0.665190i	$0.231650\pi$
$410$		0			0
$411$		−	618.582i		−	0.0742394i
$412$		0			0
$413$	−2193.85	+	3799.86i	−0.261386	+	0.452734i
$414$		0			0
$415$	−2095.68			−0.247887
$416$		0			0
$417$	300.000			0.0352304
$418$		0			0
$419$	−3411.05	+	5908.12i	−0.397711	+	0.688855i	−0.993443	−	0.114328i	$-0.963529\pi$
$419$	−3411.05	+	5908.12i	−0.397711	+	0.688855i	0.595732	+	0.803183i	$0.296862\pi$
$420$		0			0
$421$		−	7537.70i		−	0.872601i	−0.899801	−	0.436300i	$-0.856288\pi$
$421$		−	7537.70i		−	0.872601i	0.899801	−	0.436300i	$-0.143712\pi$
$422$		0			0
$423$	4037.28	−	2330.92i	0.464064	−	0.267928i
$424$		0			0
$425$	−1669.43	−	2891.53i	−0.190539	−	0.330023i
$426$		0			0
$427$	−4059.05	−	2343.49i	−0.460026	−	0.265596i
$428$		0			0
$429$	−143.876	−	4532.59i	−0.0161920	−	0.510107i
$430$		0			0
$431$	11608.4	+	6702.10i	1.29735	+	0.749023i	0.979945	−	0.199268i	$-0.0638565\pi$
$431$	11608.4	+	6702.10i	1.29735	+	0.749023i	0.317401	+	0.948291i	$0.397190\pi$
$432$		0			0
$433$	−8857.97	−	15342.5i	−0.983110	−	1.70280i	−0.650050	−	0.759892i	$-0.725252\pi$
$433$	−8857.97	−	15342.5i	−0.983110	−	1.70280i	−0.333061	−	0.942905i	$-0.608081\pi$
$434$		0			0
$435$	1268.77	−	732.524i	0.139846	−	0.0807398i
$436$		0			0
$437$			12041.1i			1.31808i
$438$		0			0
$439$	−3581.73	+	6203.75i	−0.389401	+	0.674462i	−0.992369	−	0.123303i	$-0.960651\pi$
$439$	−3581.73	+	6203.75i	−0.389401	+	0.674462i	0.602968	+	0.797765i	$0.293985\pi$
$440$		0			0
$441$	2685.01			0.289926
$442$		0			0
$443$	10169.2			1.09064			0.545321	−	0.838227i	$-0.316408\pi$
$443$	10169.2			1.09064			0.545321	+	0.838227i	$0.316408\pi$
$444$		0			0
$445$	1632.60	−	2827.75i	0.173916	−	0.301232i
$446$		0			0
$447$		−	1141.35i		−	0.120770i
$448$		0			0
$449$	−14845.8	+	8571.24i	−1.56040	+	0.900895i	−0.563179	+	0.826335i	$0.690422\pi$
$449$	−14845.8	+	8571.24i	−1.56040	+	0.900895i	−0.997217	+	0.0745603i	$0.976245\pi$
$450$		0			0
$451$	904.364	+	1566.40i	0.0944231	+	0.163546i
$452$		0			0
$453$	−3942.46	−	2276.18i	−0.408902	−	0.236080i
$454$		0			0
$455$	−954.974	+	30.3133i	−0.0983954	+	0.00312331i
$456$		0			0
$457$	12203.3	+	7045.57i	1.24912	+	0.721177i	0.970933	−	0.239351i	$-0.0769346\pi$
$457$	12203.3	+	7045.57i	1.24912	+	0.721177i	0.278183	+	0.960528i	$0.410268\pi$
$458$		0			0
$459$	−389.591	−	674.791i	−0.0396177	−	0.0686199i
$460$		0			0
$461$	2530.72	−	1461.11i	0.255678	−	0.147616i	−0.366684	−	0.930346i	$-0.619507\pi$
$461$	2530.72	−	1461.11i	0.255678	−	0.147616i	0.622361	+	0.782730i	$0.286174\pi$
$462$		0			0
$463$			2072.61i			0.208040i	0.994575	+	0.104020i	$0.0331706\pi$
$463$			2072.61i			0.208040i	−0.994575	+	0.104020i	$0.966829\pi$
$464$		0			0
$465$	−174.176	+	301.681i	−0.0173703	+	0.0300863i
$466$		0			0
$467$	−2664.19			−0.263992			−0.131996	−	0.991250i	$-0.542139\pi$
$467$	−2664.19			−0.263992			−0.131996	+	0.991250i	$0.542139\pi$
$468$		0			0
$469$	382.114			0.0376213
$470$		0			0
$471$	−2175.23	+	3767.61i	−0.212801	+	0.368583i
$472$		0			0
$473$		−	4124.08i		−	0.400899i
$474$		0			0
$475$	−10139.3	+	5853.92i	−0.979415	+	0.565466i
$476$		0			0
$477$	3129.96	+	5421.24i	0.300442	+	0.520381i
$478$		0			0
$479$	−4521.26	−	2610.35i	−0.431277	−	0.248998i	0.268614	−	0.963248i	$-0.413434\pi$
$479$	−4521.26	−	2610.35i	−0.431277	−	0.248998i	−0.699890	+	0.714250i	$0.746768\pi$
$480$		0			0
$481$	−13046.5	+	8094.91i	−1.23674	+	0.767351i
$482$		0			0
$483$	2066.09	+	1192.86i	0.194639	+	0.112375i
$484$		0			0
$485$	−2675.64	−	4634.34i	−0.250504	−	0.433886i
$486$		0			0
$487$	−10586.8	+	6112.30i	−0.985081	+	0.568737i	−0.903800	−	0.427954i	$-0.859234\pi$
$487$	−10586.8	+	6112.30i	−0.985081	+	0.568737i	−0.0812808	+	0.996691i	$0.525901\pi$
$488$		0			0
$489$		−	7027.08i		−	0.649848i
$490$		0			0
$491$	−9826.61	+	17020.2i	−0.903195	+	1.56438i	−0.0798720	+	0.996805i	$0.525451\pi$
$491$	−9826.61	+	17020.2i	−0.903195	+	1.56438i	−0.823323	+	0.567574i	$0.807882\pi$
$492$		0			0
$493$	4620.59			0.422111
$494$		0			0
$495$	885.279			0.0803845
$496$		0			0
$497$	1033.32	−	1789.76i	0.0932608	−	0.161532i
$498$		0			0
$499$		−	11713.6i		−	1.05084i	−0.850842	−	0.525422i	$-0.823907\pi$
$499$		−	11713.6i		−	1.05084i	0.850842	−	0.525422i	$-0.176093\pi$
$500$		0			0
$501$	104.113	−	60.1096i	0.00928428	−	0.00536028i
$502$		0			0
$503$	6501.67	+	11261.2i	0.576332	+	0.998236i	0.995896	+	0.0905104i	$0.0288498\pi$
$503$	6501.67	+	11261.2i	0.576332	+	0.998236i	−0.419563	+	0.907726i	$0.637817\pi$
$504$		0			0
$505$	−1692.73	−	977.300i	−0.149160	−	0.0861174i
$506$		0			0
$507$	6577.73	−	418.008i	0.576188	−	0.0366162i
$508$		0			0
$509$	−4614.99	−	2664.47i	−0.401878	−	0.232024i	0.285416	−	0.958404i	$-0.407868\pi$
$509$	−4614.99	−	2664.47i	−0.401878	−	0.232024i	−0.687294	+	0.726379i	$0.741202\pi$
$510$		0			0
$511$	−1302.27	−	2255.59i	−0.112738	−	0.195267i
$512$		0			0
$513$	−2366.18	+	1366.12i	−0.203644	+	0.117574i
$514$		0			0
$515$		−	2114.16i		−	0.180895i
$516$		0			0
$517$	−8352.47	+	14466.9i	−0.710524	+	1.23066i
$518$		0			0
$519$	−5728.62			−0.484506
$520$		0			0
$521$	−11700.3			−0.983876			−0.491938	−	0.870630i	$-0.663711\pi$
$521$	−11700.3			−0.983876			−0.491938	+	0.870630i	$0.663711\pi$
$522$		0			0
$523$	−2267.52	+	3927.46i	−0.189583	+	0.328367i	−0.945111	−	0.326749i	$-0.894047\pi$
$523$	−2267.52	+	3927.46i	−0.189583	+	0.328367i	0.755528	+	0.655116i	$0.227380\pi$
$524$		0			0
$525$			2319.70i			0.192838i
$526$		0			0
$527$	−951.467	+	549.330i	−0.0786462	+	0.0454064i
$528$		0			0
$529$	−995.810	−	1724.79i	−0.0818451	−	0.141760i
$530$		0			0
$531$	5117.09	+	2954.35i	0.418197	+	0.241446i
$532$		0			0
$533$	−2233.77	+	1385.97i	−0.181529	+	0.112632i
$534$		0			0
$535$	−1071.56	−	618.667i	−0.0865939	−	0.0499950i
$536$		0			0
$537$	764.938	+	1324.91i	0.0614702	+	0.106470i
$538$		0			0
$539$	−8332.26	+	4810.63i	−0.665855	+	0.384432i
$540$		0			0
$541$		−	5184.89i		−	0.412044i	−0.978547	−	0.206022i	$-0.933948\pi$
$541$		−	5184.89i		−	0.412044i	0.978547	−	0.206022i	$-0.0660519\pi$
$542$		0			0
$543$	−3205.32	+	5551.78i	−0.253321	+	0.438766i
$544$		0			0
$545$	−1462.55			−0.114952
$546$		0			0
$547$	−5609.12			−0.438443			−0.219222	−	0.975675i	$-0.570352\pi$
$547$	−5609.12			−0.438443			−0.219222	+	0.975675i	$0.570352\pi$
$548$		0			0
$549$	−3155.87	+	5466.13i	−0.245336	+	0.424934i
$550$		0			0
$551$		−	16202.3i		−	1.25271i
$552$		0			0
$553$	−5219.61	+	3013.54i	−0.401375	+	0.231734i
$554$		0			0
$555$	−1498.65	−	2595.74i	−0.114620	−	0.198528i
$556$		0			0
$557$	17450.9	+	10075.3i	1.32750	+	0.766432i	0.984912	−	0.173055i	$-0.0553637\pi$
$557$	17450.9	+	10075.3i	1.32750	+	0.766432i	0.342586	+	0.939486i	$0.388697\pi$
$558$		0			0
$559$	5990.93	−	190.167i	0.453290	−	0.0143886i
$560$		0			0
$561$	2418.00	+	1396.03i	0.181975	+	0.105063i
$562$		0			0
$563$	−8146.10	−	14109.5i	−0.609800	−	1.05620i	−0.991273	−	0.131824i	$-0.957917\pi$
$563$	−8146.10	−	14109.5i	−0.609800	−	1.05620i	0.381474	−	0.924380i	$-0.375417\pi$
$564$		0			0
$565$	−4086.83	+	2359.53i	−0.304308	+	0.175692i
$566$		0			0
$567$			541.343i			0.0400957i
$568$		0			0
$569$	5230.27	−	9059.09i	0.385350	−	0.667446i	−0.606468	−	0.795108i	$-0.707414\pi$
$569$	5230.27	−	9059.09i	0.385350	−	0.667446i	0.991818	+	0.127662i	$0.0407474\pi$
$570$		0			0
$571$	2225.96			0.163141			0.0815705	−	0.996668i	$-0.474006\pi$
$571$	2225.96			0.163141			0.0815705	+	0.996668i	$0.474006\pi$
$572$		0			0
$573$	−12173.2			−0.887511
$574$		0			0
$575$	6883.40	−	11922.4i	0.499231	−	0.864693i
$576$		0			0
$577$		−	4686.23i		−	0.338112i	−0.985606	−	0.169056i	$-0.945928\pi$
$577$		−	4686.23i		−	0.338112i	0.985606	−	0.169056i	$-0.0540718\pi$
$578$		0			0
$579$	2269.14	−	1310.09i	0.162871	−	0.0940337i
$580$		0			0
$581$	2296.01	+	3976.81i	0.163949	+	0.283969i
$582$		0			0
$583$	−19426.1	−	11215.7i	−1.38001	−	0.796750i
$584$		0			0
$585$	40.8214	+	1286.02i	0.00288505	+	0.0908894i
$586$		0			0
$587$	−10470.7	−	6045.28i	−0.736241	−	0.425069i	0.0844601	−	0.996427i	$-0.473083\pi$
$587$	−10470.7	−	6045.28i	−0.736241	−	0.425069i	−0.820701	+	0.571358i	$0.806417\pi$
$588$		0			0
$589$	1926.25	+	3336.36i	0.134753	+	0.233400i
$590$		0			0
$591$	−10774.9	+	6220.87i	−0.749947	+	0.432982i
$592$		0			0
$593$			6135.97i			0.424914i	0.977170	+	0.212457i	$0.0681466\pi$
$593$			6135.97i			0.424914i	−0.977170	+	0.212457i	$0.931853\pi$
$594$		0			0
$595$	294.131	−	509.449i	0.0202658	−	0.0351015i
$596$		0			0
$597$	−7212.18			−0.494431
$598$		0			0
$599$	6198.80			0.422831			0.211416	−	0.977396i	$-0.432193\pi$
$599$	6198.80			0.422831			0.211416	+	0.977396i	$0.432193\pi$
$600$		0			0
$601$	−9172.69	+	15887.6i	−0.622565	+	1.07831i	0.366441	+	0.930441i	$0.380576\pi$
$601$	−9172.69	+	15887.6i	−0.622565	+	1.07831i	−0.989006	+	0.147873i	$0.952757\pi$
$602$		0			0
$603$		−	514.575i		−	0.0347514i
$604$		0			0
$605$	768.497	−	443.692i	0.0516427	−	0.0298159i
$606$		0			0
$607$	5194.06	+	8996.38i	0.347315	+	0.601568i	0.985772	−	0.168090i	$-0.0537600\pi$
$607$	5194.06	+	8996.38i	0.347315	+	0.601568i	−0.638456	+	0.769658i	$0.720427\pi$
$608$		0			0
$609$	−2780.11	−	1605.10i	−0.184985	−	0.106801i
$610$		0			0
$611$	−21400.8	−	11466.3i	−1.41699	−	0.759209i
$612$		0			0
$613$	−696.701	−	402.240i	−0.0459045	−	0.0265030i	0.476872	−	0.878973i	$-0.341770\pi$
$613$	−696.701	−	402.240i	−0.0459045	−	0.0265030i	−0.522777	+	0.852470i	$0.675104\pi$
$614$		0			0
$615$	−256.592	−	444.431i	−0.0168241	−	0.0291401i
$616$		0			0
$617$	−13179.4	+	7609.13i	−0.859940	+	0.496486i	−0.863992	−	0.503505i	$-0.832043\pi$
$617$	−13179.4	+	7609.13i	−0.859940	+	0.496486i	0.00405239	+	0.999992i	$0.498710\pi$
$618$		0			0
$619$			11462.5i			0.744291i	0.928174	+	0.372145i	$0.121378\pi$
$619$			11462.5i			0.744291i	−0.928174	+	0.372145i	$0.878622\pi$
$620$		0			0
$621$	1606.36	−	2782.31i	0.103802	−	0.179791i
$622$		0			0
$623$	−7154.66			−0.460105
$624$		0			0
$625$	12223.0			0.782270
$626$		0			0
$627$	4895.25	−	8478.81i	0.311798	−	0.540050i
$628$		0			0
$629$		−	9453.14i		−	0.599239i
$630$		0			0
$631$	3869.99	−	2234.34i	0.244155	−	0.140963i	−0.372930	−	0.927860i	$-0.621647\pi$
$631$	3869.99	−	2234.34i	0.244155	−	0.140963i	0.617085	+	0.786896i	$0.288313\pi$
$632$		0			0
$633$	5803.28	+	10051.6i	0.364391	+	0.631144i
$634$		0			0
$635$	6590.77	+	3805.18i	0.411885	+	0.237802i
$636$		0			0
$637$	−7372.48	−	11882.2i	−0.458569	−	0.739074i
$638$		0			0
$639$	−2410.18	−	1391.52i	−0.149210	−	0.0861465i
$640$		0			0
$641$	3071.18	+	5319.44i	0.189242	+	0.327777i	0.944998	−	0.327077i	$-0.106064\pi$
$641$	3071.18	+	5319.44i	0.189242	+	0.327777i	−0.755756	+	0.654854i	$0.772730\pi$
$642$		0			0
$643$	17959.8	−	10369.1i	1.10150	−	0.635951i	0.164886	−	0.986313i	$-0.447274\pi$
$643$	17959.8	−	10369.1i	1.10150	−	0.635951i	0.936615	+	0.350361i	$0.113941\pi$
$644$		0			0
$645$			1170.11i			0.0714312i
$646$		0			0
$647$	−426.379	+	738.509i	−0.0259083	+	0.0448745i	−0.878689	−	0.477395i	$-0.841581\pi$
$647$	−426.379	+	738.509i	−0.0259083	+	0.0448745i	0.852781	+	0.522269i	$0.174914\pi$
$648$		0			0
$649$	−21172.8			−1.28060
$650$		0			0
$651$	763.303			0.0459542
$652$		0			0
$653$	3672.88	−	6361.61i	0.220108	−	0.381239i	−0.734732	−	0.678357i	$-0.762692\pi$
$653$	3672.88	−	6361.61i	0.220108	−	0.381239i	0.954841	+	0.297118i	$0.0960256\pi$
$654$		0			0
$655$		−	133.462i		−	0.00796151i
$656$		0			0
$657$	−3037.50	+	1753.70i	−0.180372	+	0.104138i
$658$		0			0
$659$	6270.33	+	10860.5i	0.370648	+	0.641982i	0.989665	−	0.143396i	$-0.0458022\pi$
$659$	6270.33	+	10860.5i	0.370648	+	0.641982i	−0.619017	+	0.785378i	$0.712469\pi$
$660$		0			0
$661$	1942.45	+	1121.48i	0.114301	+	0.0659915i	0.556060	−	0.831142i	$-0.312312\pi$
$661$	1942.45	+	1121.48i	0.114301	+	0.0659915i	−0.441760	+	0.897133i	$0.645646\pi$
$662$		0			0
$663$	−1916.48	+	3576.93i	−0.112262	+	0.209527i
$664$		0			0
$665$	−1786.41	−	1031.38i	−0.104171	−	0.0601433i
$666$		0			0
$667$	9525.83	+	16499.2i	0.552986	+	0.957800i
$668$		0			0
$669$	7309.83	−	4220.33i	0.422443	−	0.243897i
$670$		0			0
$671$		−	22617.0i		−	1.30122i
$672$		0			0
$673$	−2388.23	+	4136.53i	−0.136790	+	0.236927i	−0.926280	−	0.376837i	$-0.877012\pi$
$673$	−2388.23	+	4136.53i	−0.136790	+	0.236927i	0.789490	+	0.613763i	$0.210345\pi$
$674$		0			0
$675$	3123.82			0.178127
$676$		0			0
$677$	−7933.57			−0.450387			−0.225193	−	0.974314i	$-0.572301\pi$
$677$	−7933.57			−0.450387			−0.225193	+	0.974314i	$0.572301\pi$
$678$		0			0
$679$	−5862.82	+	10154.7i	−0.331361	+	0.573935i
$680$		0			0
$681$		−	13555.1i		−	0.762750i
$682$		0			0
$683$	−20415.5	+	11786.9i	−1.14374	+	0.660340i	−0.947355	−	0.320186i	$-0.896255\pi$
$683$	−20415.5	+	11786.9i	−1.14374	+	0.660340i	−0.196388	+	0.980526i	$0.562921\pi$
$684$		0			0
$685$	−314.452	−	544.647i	−0.0175396	−	0.0303794i
$686$		0			0
$687$	3391.19	+	1957.90i	0.188329	+	0.108732i
$688$		0			0
$689$	15396.9	−	28736.9i	0.851343	−	1.58895i
$690$		0			0
$691$	10863.2	+	6271.89i	0.598056	+	0.345288i	0.768276	−	0.640118i	$-0.221115\pi$
$691$	10863.2	+	6271.89i	0.598056	+	0.345288i	−0.170221	+	0.985406i	$0.554448\pi$
$692$		0			0
$693$	−969.904	−	1679.92i	−0.0531654	−	0.0920852i
$694$		0			0
$695$	264.143	−	152.503i	0.0144166	−	0.00832340i
$696$		0			0
$697$		−	1618.52i		−	0.0879568i
$698$		0			0
$699$	−5040.82	+	8730.96i	−0.272763	+	0.472440i
$700$		0			0
$701$	581.786			0.0313463			0.0156731	−	0.999877i	$-0.495011\pi$
$701$	581.786			0.0313463			0.0156731	+	0.999877i	$0.495011\pi$
$702$		0			0
$703$	−33147.9			−1.77837
$704$		0			0
$705$	2369.82	−	4104.64i	0.126599	−	0.219276i
$706$		0			0
$707$			4282.89i			0.227828i
$708$		0			0
$709$	−17963.1	+	10371.0i	−0.951507	+	0.549353i	−0.893549	−	0.448966i	$-0.851792\pi$
$709$	−17963.1	+	10371.0i	−0.951507	+	0.549353i	−0.0579583	+	0.998319i	$0.518459\pi$
$710$		0			0
$711$	4058.19	+	7028.99i	0.214056	+	0.370756i
$712$		0			0
$713$	−3923.10	−	2265.00i	−0.206061	−	0.118969i
$714$		0			0
$715$	−2430.79	−	3917.70i	−0.127142	−	0.204914i
$716$		0			0
$717$	12307.5	+	7105.75i	0.641050	+	0.370110i
$718$		0			0
$719$	−12675.1	−	21953.9i	−0.657443	−	1.13872i	−0.981275	−	0.192610i	$-0.938305\pi$
$719$	−12675.1	−	21953.9i	−0.657443	−	1.13872i	0.323832	−	0.946114i	$-0.395029\pi$
$720$		0			0
$721$	−4011.87	+	2316.25i	−0.207226	+	0.119642i
$722$		0			0
$723$			14355.8i			0.738449i
$724$		0			0
$725$	−9262.22	+	16042.6i	−0.474469	+	0.821805i
$726$		0			0
$727$	33428.2			1.70534			0.852672	−	0.522447i	$-0.174981\pi$
$727$	33428.2			1.70534			0.852672	+	0.522447i	$0.174981\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−1845.20	+	3195.97i	−0.0933612	+	0.161706i
$732$		0			0
$733$			3842.67i			0.193632i	0.995302	+	0.0968160i	$0.0308658\pi$
$733$			3842.67i			0.193632i	−0.995302	+	0.0968160i	$0.969134\pi$
$734$		0			0
$735$	2364.09	−	1364.91i	0.118640	−	0.0684970i
$736$		0			0
$737$	921.946	+	1596.86i	0.0460791	+	0.0798114i
$738$		0			0
$739$	25140.4	+	14514.8i	1.25143	+	0.722511i	0.971393	−	0.237479i	$-0.0763211\pi$
$739$	25140.4	+	14514.8i	1.25143	+	0.722511i	0.280034	+	0.959990i	$0.409654\pi$
$740$		0			0
$741$	12542.7	+	6720.21i	0.621816	+	0.333162i
$742$		0			0
$743$	30308.0	+	17498.3i	1.49649	+	0.864000i	0.999992	−	0.00403656i	$-0.00128488\pi$
$743$	30308.0	+	17498.3i	1.49649	+	0.864000i	0.496500	+	0.868037i	$0.334618\pi$
$744$		0			0
$745$	−580.199	−	1004.93i	−0.0285327	−	0.0494200i
$746$		0			0
$747$	5355.38	−	3091.93i	0.262307	−	0.151443i
$748$		0			0
$749$			2711.23i			0.132265i
$750$		0			0
$751$	−5227.06	+	9053.52i	−0.253979	+	0.439904i	−0.964618	−	0.263653i	$-0.915073\pi$
$751$	−5227.06	+	9053.52i	−0.253979	+	0.439904i	0.710639	+	0.703557i	$0.248406\pi$
$752$		0			0
$753$	−9821.58			−0.475323
$754$		0			0
$755$	−4628.32			−0.223102
$756$		0			0
$757$	14065.2	−	24361.6i	0.675308	−	1.16967i	−0.301071	−	0.953602i	$-0.597344\pi$
$757$	14065.2	−	24361.6i	0.675308	−	1.16967i	0.976379	−	0.216065i	$-0.0693225\pi$
$758$		0			0
$759$			11512.3i			0.550552i
$760$		0			0
$761$	18261.9	−	10543.5i	0.869899	−	0.502236i	0.00258400	−	0.999997i	$-0.499177\pi$
$761$	18261.9	−	10543.5i	0.869899	−	0.502236i	0.867315	+	0.497761i	$0.165844\pi$
$762$		0			0
$763$	1602.36	+	2775.37i	0.0760280	+	0.131684i
$764$		0			0
$765$	−686.051	−	396.092i	−0.0324238	−	0.0187199i
$766$		0			0
$767$	−976.309	−	30757.2i	−0.0459615	−	1.44795i
$768$		0			0
$769$	16911.7	+	9763.96i	0.793044	+	0.457864i	0.841033	−	0.540984i	$-0.181948\pi$
$769$	16911.7	+	9763.96i	0.793044	+	0.457864i	−0.0479893	+	0.998848i	$0.515281\pi$
$770$		0			0
$771$	−9818.72	−	17006.5i	−0.458641	−	0.794390i
$772$		0			0
$773$	25419.6	−	14676.0i	1.18277	−	0.682870i	0.226113	−	0.974101i	$-0.427398\pi$
$773$	25419.6	−	14676.0i	1.18277	−	0.682870i	0.956653	+	0.291231i	$0.0940648\pi$
$774$		0			0
$775$		−	4404.64i		−	0.204154i
$776$		0			0
$777$	−3283.82	+	5687.75i	−0.151617	+	0.262609i
$778$		0			0
$779$	−5675.42			−0.261031
$780$		0			0
$781$	9972.54			0.456908
$782$		0			0
$783$	−2161.50	+	3743.84i	−0.0986537	+	0.170873i
$784$		0			0
$785$			4423.06i			0.201103i
$786$		0			0
$787$	−3865.18	+	2231.56i	−0.175068	+	0.101076i	−0.584974	−	0.811052i	$-0.698895\pi$
$787$	−3865.18	+	2231.56i	−0.175068	+	0.101076i	0.409905	+	0.912128i	$0.365562\pi$
$788$		0			0
$789$	132.302	+	229.154i	0.00596968	+	0.0103398i
$790$		0			0
$791$	8955.00	+	5170.17i	0.402532	+	0.232402i
$792$		0			0
$793$	32855.1	−	1042.90i	1.47127	−	0.0467018i
$794$		0			0
$795$	5511.70	+	3182.18i	0.245887	+	0.141963i
$796$		0			0
$797$	−17392.7	−	30125.1i	−0.773002	−	1.33888i	−0.935911	−	0.352237i	$-0.885421\pi$
$797$	−17392.7	−	30125.1i	−0.773002	−	1.33888i	0.162909	−	0.986641i	$-0.447912\pi$
$798$		0			0
$799$	12945.6	−	7474.12i	0.573193	−	0.330933i
$800$		0			0
$801$			9634.84i			0.425007i
$802$		0			0
$803$	6284.09	−	10884.4i	0.276165	−	0.478332i
$804$		0			0
$805$	2425.53			0.106197
$806$		0			0
$807$	−13582.8			−0.592487
$808$		0			0
$809$	5309.98	−	9197.15i	0.230765	−	0.399697i	−0.727268	−	0.686353i	$-0.759210\pi$
$809$	5309.98	−	9197.15i	0.230765	−	0.399697i	0.958033	+	0.286656i	$0.0925438\pi$
$810$		0			0
$811$			5497.87i			0.238047i	0.992891	+	0.119024i	$0.0379764\pi$
$811$			5497.87i			0.238047i	−0.992891	+	0.119024i	$0.962024\pi$
$812$		0			0
$813$	−21620.7	+	12482.7i	−0.932684	+	0.538485i
$814$		0			0
$815$	−3572.17	−	6187.18i	−0.153531	−	0.265923i
$816$		0			0
$817$	11206.8	+	6470.26i	0.479898	+	0.277070i
$818$		0			0
$819$	2395.65	−	1486.42i	0.102211	−	0.0634182i
$820$		0			0
$821$	18451.0	+	10652.7i	0.784340	+	0.452839i	0.837966	−	0.545722i	$-0.183745\pi$
$821$	18451.0	+	10652.7i	0.784340	+	0.452839i	−0.0536261	+	0.998561i	$0.517078\pi$
$822$		0			0
$823$	−8671.28	−	15019.1i	−0.367268	−	0.636127i	0.621869	−	0.783121i	$-0.286374\pi$
$823$	−8671.28	−	15019.1i	−0.367268	−	0.636127i	−0.989137	+	0.146994i	$0.953040\pi$
$824$		0			0
$825$	−9694.02	+	5596.84i	−0.409094	+	0.236190i
$826$		0			0
$827$		−	5129.96i		−	0.215703i	−0.994167	−	0.107851i	$-0.965603\pi$
$827$		−	5129.96i		−	0.215703i	0.994167	−	0.107851i	$-0.0343971\pi$
$828$		0			0
$829$	−4235.90	+	7336.80i	−0.177466	+	0.307380i	−0.941012	−	0.338374i	$-0.890123\pi$
$829$	−4235.90	+	7336.80i	−0.177466	+	0.307380i	0.763546	+	0.645753i	$0.223457\pi$
$830$		0			0
$831$	8643.93			0.360836
$832$		0			0
$833$	8609.50			0.358105
$834$		0			0
$835$	61.1126	−	105.850i	0.00253280	−	0.00438694i
$836$		0			0
$837$		−	1027.90i		−	0.0424486i
$838$		0			0
$839$	16588.8	−	9577.52i	0.682607	−	0.394103i	−0.118230	−	0.992986i	$-0.537722\pi$
$839$	16588.8	−	9577.52i	0.682607	−	0.394103i	0.800837	+	0.598883i	$0.204389\pi$
$840$		0			0
$841$	−623.334	−	1079.65i	−0.0255580	−	0.0442678i
$842$		0			0
$843$	7321.36	+	4226.99i	0.299123	+	0.172699i
$844$		0			0
$845$	5579.04	−	3711.79i	0.227130	−	0.151112i
$846$		0			0
$847$	−1683.92	−	972.211i	−0.0683119	−	0.0394399i
$848$		0			0
$849$	−396.902	−	687.455i	−0.0160443	−	0.0277896i
$850$		0			0
$851$	33755.3	−	19488.7i	1.35972	−	0.785032i
$852$		0			0
$853$		−	18075.1i		−	0.725532i	−0.931880	−	0.362766i	$-0.881832\pi$
$853$		−	18075.1i		−	0.725532i	0.931880	−	0.362766i	$-0.118168\pi$
$854$		0			0
$855$	−1388.91	+	2405.67i	−0.0555553	+	0.0962246i
$856$		0			0
$857$	21054.6			0.839219			0.419609	−	0.907705i	$-0.362167\pi$
$857$	21054.6			0.839219			0.419609	+	0.907705i	$0.362167\pi$
$858$		0			0
$859$	−920.322			−0.0365553			−0.0182776	−	0.999833i	$-0.505818\pi$
$859$	−920.322			−0.0365553			−0.0182776	+	0.999833i	$0.505818\pi$
$860$		0			0
$861$	−562.241	+	973.830i	−0.0222545	+	0.0385459i
$862$		0			0
$863$		−	19427.5i		−	0.766304i	−0.923685	−	0.383152i	$-0.874839\pi$
$863$		−	19427.5i		−	0.766304i	0.923685	−	0.383152i	$-0.125161\pi$
$864$		0			0
$865$	−5043.91	+	2912.10i	−0.198264	+	0.114468i
$866$		0			0
$867$	6120.27	+	10600.6i	0.239741	+	0.415244i
$868$		0			0
$869$	−25187.2	−	14541.8i	−0.983218	−	0.567661i
$870$		0			0
$871$	−2277.19	+	1412.92i	−0.0885876	+	0.0549654i
$872$		0			0
$873$	13674.8	+	7895.17i	0.530153	+	0.306084i
$874$		0			0
$875$	2453.22	+	4249.10i	0.0947816	+	0.164167i
$876$		0			0
$877$	−12879.7	+	7436.09i	−0.495914	+	0.286316i	−0.727024	−	0.686612i	$-0.759097\pi$
$877$	−12879.7	+	7436.09i	−0.495914	+	0.286316i	0.231111	+	0.972927i	$0.425764\pi$
$878$		0			0
$879$			12877.6i			0.494141i
$880$		0			0
$881$	−6470.30	+	11206.9i	−0.247435	+	0.428570i	−0.962813	−	0.270167i	$-0.912921\pi$
$881$	−6470.30	+	11206.9i	−0.247435	+	0.428570i	0.715379	+	0.698737i	$0.246254\pi$
$882$		0			0
$883$	−25585.5			−0.975108			−0.487554	−	0.873093i	$-0.662111\pi$
$883$	−25585.5			−0.975108			−0.487554	+	0.873093i	$0.662111\pi$
$884$		0			0
$885$	6007.30			0.228173
$886$		0			0
$887$	1858.23	−	3218.55i	0.0703418	−	0.121836i	−0.828709	−	0.559679i	$-0.810924\pi$
$887$	1858.23	−	3218.55i	0.0703418	−	0.121836i	0.899051	+	0.437844i	$0.144258\pi$
$888$		0			0
$889$		−	16675.7i		−	0.629118i
$890$		0			0
$891$	−2262.27	+	1306.12i	−0.0850606	+	0.0491097i
$892$		0			0
$893$	−26208.3	−	45394.2i	−0.982115	−	1.70107i
$894$		0			0
$895$	1347.02	+	777.702i	0.0503082	+	0.0290455i
$896$		0			0
$897$	−16723.5	+	530.846i	−0.622500	+	0.0197597i
$898$		0			0
$899$	5278.87	+	3047.76i	0.195840	+	0.113068i
$900$		0			0
$901$	10036.2	+	17383.3i	0.371093	+	0.642753i
$902$		0			0
$903$	2220.43	−	1281.97i	0.0818286	−	0.0472438i
$904$		0			0
$905$			6517.61i			0.239395i
$906$		0			0
$907$	6480.21	−	11224.0i	0.237235	−	0.410902i	−0.722685	−	0.691177i	$-0.757092\pi$
$907$	6480.21	−	11224.0i	0.237235	−	0.410902i	0.959920	+	0.280275i	$0.0904257\pi$
$908$		0			0
$909$	5767.56			0.210449
$910$		0			0
$911$	36607.1			1.33134			0.665668	−	0.746248i	$-0.268147\pi$
$911$	36607.1			1.33134			0.665668	+	0.746248i	$0.268147\pi$
$912$		0			0
$913$	−11079.4	+	19190.1i	−0.401615	+	0.695618i
$914$		0			0
$915$			6417.06i			0.231849i
$916$		0			0
$917$	−253.260	+	146.220i	−0.00912038	+	0.00526565i
$918$		0			0
$919$	10178.1	+	17629.0i	0.365338	+	0.632784i	0.988830	−	0.149045i	$-0.0476200\pi$
$919$	10178.1	+	17629.0i	0.365338	+	0.632784i	−0.623492	+	0.781830i	$0.714287\pi$
$920$		0			0
$921$	18254.8	+	10539.4i	0.653110	+	0.377073i
$922$		0			0
$923$	459.847	+	14486.8i	0.0163988	+	0.516619i
$924$		0			0
$925$	32821.2	+	18949.3i	1.16665	+	0.673568i
$926$		0			0
$927$	3119.19	+	5402.59i	0.110515	+	0.191418i
$928$		0			0
$929$	39031.5	−	22534.8i	1.37845	−	0.795849i	0.386478	−	0.922298i	$-0.373691\pi$
$929$	39031.5	−	22534.8i	1.37845	−	0.795849i	0.991973	+	0.126449i	$0.0403580\pi$
$930$		0			0
$931$		−	30189.6i		−	1.06275i
$932$		0			0
$933$	1699.81	−	2944.16i	0.0596456	−	0.103309i
$934$		0			0
$935$	2838.65			0.0992876
$936$		0			0
$937$	−6771.10			−0.236075			−0.118037	−	0.993009i	$-0.537660\pi$
$937$	−6771.10			−0.236075			−0.118037	+	0.993009i	$0.537660\pi$
$938$		0			0
$939$	7928.92	−	13733.3i	0.275560	−	0.477283i
$940$		0			0
$941$		−	36690.7i		−	1.27108i	−0.772070	−	0.635538i	$-0.780778\pi$
$941$		−	36690.7i		−	1.27108i	0.772070	−	0.635538i	$-0.219222\pi$
$942$		0			0
$943$	5779.43	−	3336.76i	0.199580	−	0.115228i
$944$		0			0
$945$	275.188	+	476.639i	0.00947287	+	0.0164075i
$946$		0			0
$947$	−44047.1	−	25430.6i	−1.51145	−	0.872634i	−0.999911	−	0.0133718i	$-0.995744\pi$
$947$	−44047.1	−	25430.6i	−1.51145	−	0.872634i	−0.511536	−	0.859262i	$-0.670923\pi$
$948$		0			0
$949$	16101.2	+	8626.82i	0.550754	+	0.295088i
$950$		0			0
$951$	−12424.4	−	7173.24i	−0.423648	−	0.244593i
$952$		0			0
$953$	5927.79	+	10267.2i	0.201490	+	0.348991i	0.949009	−	0.315250i	$-0.102088\pi$
$953$	5927.79	+	10267.2i	0.201490	+	0.348991i	−0.747519	+	0.664241i	$0.768755\pi$
$954$		0			0
$955$	−10718.2	+	6188.18i	−0.363177	+	0.209680i
$956$		0			0
$957$		−	15490.8i		−	0.523245i
$958$		0			0
$959$	−689.022	+	1193.42i	−0.0232009	+	0.0401852i
$960$		0			0
$961$	28341.6			0.951349
$962$		0			0
$963$	3651.08			0.122175
$964$		0			0
$965$	1331.95	−	2307.01i	0.0444322	−	0.0769588i
$966$		0			0
$967$			40661.7i			1.35221i	0.736803	+	0.676107i	$0.236334\pi$
$967$			40661.7i			1.35221i	−0.736803	+	0.676107i	$0.763666\pi$
$968$		0			0
$969$	−7587.19	+	4380.46i	−0.251533	+	0.145223i
$970$		0			0
$971$	28659.1	+	49639.1i	0.947184	+	1.64057i	0.751318	+	0.659940i	$0.229418\pi$
$971$	28659.1	+	49639.1i	0.947184	+	1.64057i	0.195866	+	0.980631i	$0.437248\pi$
$972$		0			0
$973$	−578.786	−	334.162i	−0.0190699	−	0.0110100i
$974$		0			0
$975$	−8577.37	−	13824.1i	−0.281739	−	0.454079i
$976$		0			0
$977$	−2621.23	−	1513.37i	−0.0858347	−	0.0495567i	0.456468	−	0.889740i	$-0.349114\pi$
$977$	−2621.23	−	1513.37i	−0.0858347	−	0.0495567i	−0.542303	+	0.840183i	$0.682448\pi$
$978$		0			0
$979$	−17262.4	−	29899.4i	−0.563543	−	0.976085i
$980$		0			0
$981$	3737.46	−	2157.82i	0.121639	−	0.0702283i
$982$		0			0
$983$		−	33942.5i		−	1.10132i	−0.834730	−	0.550659i	$-0.814376\pi$
$983$		−	33942.5i		−	1.10132i	0.834730	−	0.550659i	$-0.185624\pi$
$984$		0			0
$985$	−6324.67	+	10954.7i	−0.204590	+	0.354360i
$986$		0			0
$987$	−10385.4			−0.334925
$988$		0			0
$989$	−15216.3			−0.489231
$990$		0			0
$991$	10818.7	−	18738.6i	0.346790	−	0.600658i	−0.638887	−	0.769300i	$-0.720605\pi$
$991$	10818.7	−	18738.6i	0.346790	−	0.600658i	0.985677	+	0.168642i	$0.0539383\pi$
$992$		0			0
$993$			26009.9i			0.831219i
$994$		0			0
$995$	−6350.16	+	3666.26i	−0.202325	+	0.116812i
$996$		0			0
$997$	−9812.31	−	16995.4i	−0.311694	−	0.539870i	0.667035	−	0.745026i	$-0.267563\pi$
$997$	−9812.31	−	16995.4i	−0.311694	−	0.539870i	−0.978729	+	0.205156i	$0.934230\pi$
$998$		0			0
$999$	7659.42	+	4422.17i	0.242576	+	0.140051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bv.c.433.2		4
4.3	odd	2		39.4.j.b.4.2	✓	4
12.11	even	2		117.4.q.d.82.1		4
13.10	even	6	inner	624.4.bv.c.49.1		4
52.7	even	12		507.4.a.k.1.4		4
52.19	even	12		507.4.a.k.1.1		4
52.23	odd	6		39.4.j.b.10.2	yes	4
52.35	odd	6		507.4.b.e.337.1		4
52.43	odd	6		507.4.b.e.337.4		4
156.23	even	6		117.4.q.d.10.1		4
156.59	odd	12		1521.4.a.z.1.1		4
156.71	odd	12		1521.4.a.z.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.b.4.2	✓	4	4.3	odd	2
39.4.j.b.10.2	yes	4	52.23	odd	6
117.4.q.d.10.1		4	156.23	even	6
117.4.q.d.82.1		4	12.11	even	2
507.4.a.k.1.1		4	52.19	even	12
507.4.a.k.1.4		4	52.7	even	12
507.4.b.e.337.1		4	52.35	odd	6
507.4.b.e.337.4		4	52.43	odd	6
624.4.bv.c.49.1		4	13.10	even	6	inner
624.4.bv.c.433.2		4	1.1	even	1	trivial
1521.4.a.z.1.1		4	156.59	odd	12
1521.4.a.z.1.4		4	156.71	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)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +3.05006i q^{5} +(5.78786 - 3.34162i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +3.05006i q^{5} +(5.78786 - 3.34162i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(27.9293 + 16.1250i) q^{11} +(-22.1364 + 41.3156i) q^{13} +(-7.92429 - 4.57509i) q^{15} +(-14.4293 - 24.9923i) q^{17} +(-87.6364 + 50.5969i) q^{19} +20.0497i q^{21} +(59.4950 - 103.048i) q^{23} +115.697 q^{25} +27.0000 q^{27} +(-80.0557 + 138.661i) q^{29} -38.0705i q^{31} +(-83.7879 + 48.3749i) q^{33} +(10.1921 + 17.6533i) q^{35} +(283.682 + 163.784i) q^{37} +(-74.1364 - 119.486i) q^{39} +(48.5707 + 28.0423i) q^{41} +(-63.9393 - 110.746i) q^{43} +(23.7729 - 13.7253i) q^{45} +517.983i q^{47} +(-149.167 + 258.365i) q^{49} +86.5757 q^{51} -695.546 q^{53} +(-49.1821 + 85.1860i) q^{55} -303.581i q^{57} +(-568.566 + 328.262i) q^{59} +(-350.652 - 607.347i) q^{61} +(-52.0907 - 30.0746i) q^{63} +(-126.015 - 67.5174i) q^{65} +(49.5150 + 28.5875i) q^{67} +(178.485 + 309.145i) q^{69} +(267.798 - 154.613i) q^{71} -389.711i q^{73} +(-173.546 + 300.590i) q^{75} +215.534 q^{77} -901.820 q^{79} +(-40.5000 + 70.1481i) q^{81} +687.095i q^{83} +(76.2279 - 44.0102i) q^{85} +(-240.167 - 415.982i) q^{87} +(-927.113 - 535.269i) q^{89} +(9.93858 + 313.100i) q^{91} +(98.9100 + 57.1057i) q^{93} +(-154.324 - 267.296i) q^{95} +(-1519.43 + 877.242i) q^{97} -290.250i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 66 q^{7} - 18 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

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Representations

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Database

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