LMFDB - Embedded newform 252.4.x.a.209.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (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:	$14.8684813214$
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			209.21
Character	$\chi$	$=$	252.209
Dual form			252.4.x.a.41.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.66323 + 2.29222i) q^{3} +(5.16485 + 8.94579i) q^{5} +(-17.2289 - 6.79448i) q^{7} +(16.4915 + 21.3783i) q^{9} +O(q^{10})$	\(q+(4.66323 + 2.29222i) q^{3} +(5.16485 + 8.94579i) q^{5} +(-17.2289 - 6.79448i) q^{7} +(16.4915 + 21.3783i) q^{9} +(27.1307 + 15.6639i) q^{11} +(-39.0052 + 22.5196i) q^{13} +(3.57919 + 53.5552i) q^{15} +62.4900 q^{17} +132.928i q^{19} +(-64.7679 - 71.1767i) q^{21} +(-58.8009 + 33.9487i) q^{23} +(9.14862 - 15.8459i) q^{25} +(27.8997 + 137.494i) q^{27} +(-116.665 - 67.3568i) q^{29} +(-25.9914 + 15.0061i) q^{31} +(90.6116 + 135.234i) q^{33} +(-28.2028 - 189.219i) q^{35} +40.4778 q^{37} +(-233.510 + 15.6059i) q^{39} +(39.7514 + 68.8515i) q^{41} +(161.452 - 279.643i) q^{43} +(-106.070 + 257.945i) q^{45} +(-171.268 + 296.644i) q^{47} +(250.670 + 234.123i) q^{49} +(291.405 + 143.241i) q^{51} -64.9125i q^{53} +323.607i q^{55} +(-304.700 + 619.874i) q^{57} +(79.3800 + 137.490i) q^{59} +(493.640 + 285.003i) q^{61} +(-138.875 - 480.376i) q^{63} +(-402.912 - 232.621i) q^{65} +(150.833 + 261.251i) q^{67} +(-352.020 + 23.5261i) q^{69} -719.100i q^{71} -558.706i q^{73} +(78.9843 - 52.9223i) q^{75} +(-361.004 - 454.211i) q^{77} +(456.676 - 790.986i) q^{79} +(-185.064 + 705.119i) q^{81} +(-352.348 + 610.285i) q^{83} +(322.751 + 559.022i) q^{85} +(-389.641 - 581.524i) q^{87} +700.133 q^{89} +(825.026 - 122.969i) q^{91} +(-155.601 + 10.3991i) q^{93} +(-1189.15 + 686.554i) q^{95} +(-202.787 - 117.079i) q^{97} +(112.557 + 838.329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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
$3$	4.66323	+	2.29222i	0.897439	+	0.441138i
$3$	4.66323	+	2.29222i	0.897439	+	0.441138i
$4$		0			0
$5$	5.16485	+	8.94579i	0.461958	+	0.800135i	0.999059	−	0.0433831i	$-0.0138136\pi$
$5$	5.16485	+	8.94579i	0.461958	+	0.800135i	−0.537100	+	0.843518i	$0.680480\pi$
$6$		0			0
$7$	−17.2289	−	6.79448i	−0.930273	−	0.366867i
$7$	−17.2289	−	6.79448i	−0.930273	−	0.366867i
$8$		0			0
$9$	16.4915	+	21.3783i	0.610794	+	0.791789i
$10$		0			0
$11$	27.1307	+	15.6639i	0.743656	+	0.429350i	0.823397	−	0.567466i	$-0.192076\pi$
$11$	27.1307	+	15.6639i	0.743656	+	0.429350i	−0.0797412	+	0.996816i	$0.525409\pi$
$12$		0			0
$13$	−39.0052	+	22.5196i	−0.832161	+	0.480448i	−0.854592	−	0.519300i	$-0.826193\pi$
$13$	−39.0052	+	22.5196i	−0.832161	+	0.480448i	0.0224312	+	0.999748i	$0.492859\pi$
$14$		0			0
$15$	3.57919	+	53.5552i	0.0616095	+	0.921860i
$16$		0			0
$17$	62.4900			0.891532			0.445766	−	0.895150i	$-0.352931\pi$
$17$	62.4900			0.891532			0.445766	+	0.895150i	$0.352931\pi$
$18$		0			0
$19$			132.928i			1.60504i	0.596624	+	0.802521i	$0.296508\pi$
$19$			132.928i			1.60504i	−0.596624	+	0.802521i	$0.703492\pi$
$20$		0			0
$21$	−64.7679	−	71.1767i	−0.673025	−	0.739620i
$22$		0			0
$23$	−58.8009	+	33.9487i	−0.533080	+	0.307774i	−0.742270	−	0.670101i	$-0.766251\pi$
$23$	−58.8009	+	33.9487i	−0.533080	+	0.307774i	0.209190	+	0.977875i	$0.432917\pi$
$24$		0			0
$25$	9.14862	−	15.8459i	0.0731889	−	0.126767i
$26$		0			0
$27$	27.8997	+	137.494i	0.198863	+	0.980027i
$28$		0			0
$29$	−116.665	−	67.3568i	−0.747043	−	0.431305i	0.0775817	−	0.996986i	$-0.475280\pi$
$29$	−116.665	−	67.3568i	−0.747043	−	0.431305i	−0.824624	+	0.565681i	$0.808613\pi$
$30$		0			0
$31$	−25.9914	+	15.0061i	−0.150587	+	0.0869413i	−0.573400	−	0.819275i	$-0.694376\pi$
$31$	−25.9914	+	15.0061i	−0.150587	+	0.0869413i	0.422813	+	0.906217i	$0.361043\pi$
$32$		0			0
$33$	90.6116	+	135.234i	0.477983	+	0.713370i
$34$		0			0
$35$	−28.2028	−	189.219i	−0.136204	−	0.913822i
$36$		0			0
$37$	40.4778			0.179852			0.0899259	−	0.995948i	$-0.471337\pi$
$37$	40.4778			0.179852			0.0899259	+	0.995948i	$0.471337\pi$
$38$		0			0
$39$	−233.510	+	15.6059i	−0.958758	+	0.0640754i
$40$		0			0
$41$	39.7514	+	68.8515i	0.151418	+	0.262263i	0.931749	−	0.363103i	$-0.118283\pi$
$41$	39.7514	+	68.8515i	0.151418	+	0.262263i	−0.780331	+	0.625367i	$0.784949\pi$
$42$		0			0
$43$	161.452	−	279.643i	0.572586	−	0.991749i	−0.423713	−	0.905797i	$-0.639273\pi$
$43$	161.452	−	279.643i	0.572586	−	0.991749i	0.996299	−	0.0859521i	$-0.0273932\pi$
$44$		0			0
$45$	−106.070	+	257.945i	−0.351377	+	0.854492i
$46$		0			0
$47$	−171.268	+	296.644i	−0.531531	+	0.920638i	0.467792	+	0.883839i	$0.345050\pi$
$47$	−171.268	+	296.644i	−0.531531	+	0.920638i	−0.999323	+	0.0367994i	$0.988284\pi$
$48$		0			0
$49$	250.670	+	234.123i	0.730817	+	0.682574i
$50$		0			0
$51$	291.405	+	143.241i	0.800096	+	0.393289i
$52$		0			0
$53$		−	64.9125i		−	0.168234i	−0.996456	−	0.0841172i	$-0.973193\pi$
$53$		−	64.9125i		−	0.168234i	0.996456	−	0.0841172i	$-0.0268070\pi$
$54$		0			0
$55$			323.607i			0.793367i
$56$		0			0
$57$	−304.700	+	619.874i	−0.708045	+	1.44043i
$58$		0			0
$59$	79.3800	+	137.490i	0.175159	+	0.303385i	0.940216	−	0.340578i	$-0.110623\pi$
$59$	79.3800	+	137.490i	0.175159	+	0.303385i	−0.765057	+	0.643962i	$0.777289\pi$
$60$		0			0
$61$	493.640	+	285.003i	1.03613	+	0.598212i	0.918736	−	0.394873i	$-0.129212\pi$
$61$	493.640	+	285.003i	1.03613	+	0.598212i	0.117397	+	0.993085i	$0.462545\pi$
$62$		0			0
$63$	−138.875	−	480.376i	−0.277724	−	0.960661i
$64$		0			0
$65$	−402.912	−	232.621i	−0.768847	−	0.443894i
$66$		0			0
$67$	150.833	+	261.251i	0.275033	+	0.476372i	0.970144	−	0.242531i	$-0.0779778\pi$
$67$	150.833	+	261.251i	0.275033	+	0.476372i	−0.695110	+	0.718903i	$0.744644\pi$
$68$		0			0
$69$	−352.020	+	23.5261i	−0.614178	+	0.0410465i
$70$		0			0
$71$		−	719.100i		−	1.20199i	−0.799252	−	0.600996i	$-0.794771\pi$
$71$		−	719.100i		−	1.20199i	0.799252	−	0.600996i	$-0.205229\pi$
$72$		0			0
$73$		−	558.706i		−	0.895775i	−0.894090	−	0.447888i	$-0.852176\pi$
$73$		−	558.706i		−	0.895775i	0.894090	−	0.447888i	$-0.147824\pi$
$74$		0			0
$75$	78.9843	−	52.9223i	0.121604	−	0.0814792i
$76$		0			0
$77$	−361.004	−	454.211i	−0.534289	−	0.672236i
$78$		0			0
$79$	456.676	−	790.986i	0.650381	−	1.12649i	−0.332650	−	0.943050i	$-0.607943\pi$
$79$	456.676	−	790.986i	0.650381	−	1.12649i	0.983031	−	0.183442i	$-0.0587239\pi$
$80$		0			0
$81$	−185.064	+	705.119i	−0.253860	+	0.967241i
$82$		0			0
$83$	−352.348	+	610.285i	−0.465967	+	0.807078i	−0.999245	−	0.0388620i	$-0.987627\pi$
$83$	−352.348	+	610.285i	−0.465967	+	0.807078i	0.533278	+	0.845940i	$0.320960\pi$
$84$		0			0
$85$	322.751	+	559.022i	0.411851	+	0.713346i
$86$		0			0
$87$	−389.641	−	581.524i	−0.480160	−	0.716619i
$88$		0			0
$89$	700.133			0.833865			0.416932	−	0.908938i	$-0.363105\pi$
$89$	700.133			0.833865			0.416932	+	0.908938i	$0.363105\pi$
$90$		0			0
$91$	825.026	−	122.969i	0.950398	−	0.141656i
$92$		0			0
$93$	−155.601	+	10.3991i	−0.173496	+	0.0115950i
$94$		0			0
$95$	−1189.15	+	686.554i	−1.28425	+	0.741463i
$96$		0			0
$97$	−202.787	−	117.079i	−0.212267	−	0.122552i	0.390098	−	0.920773i	$-0.372441\pi$
$97$	−202.787	−	117.079i	−0.212267	−	0.122552i	−0.602364	+	0.798221i	$0.705775\pi$
$98$		0			0
$99$	112.557	+	838.329i	0.114266	+	0.851063i
$100$		0			0
$101$	938.098	−	1624.83i	0.924200	−	1.60076i	0.131358	−	0.991335i	$-0.458066\pi$
$101$	938.098	−	1624.83i	0.924200	−	1.60076i	0.792843	−	0.609427i	$-0.208600\pi$
$102$		0			0
$103$	−524.507	+	302.824i	−0.501759	+	0.289691i	−0.729440	−	0.684045i	$-0.760219\pi$
$103$	−524.507	+	302.824i	−0.501759	+	0.289691i	0.227681	+	0.973736i	$0.426886\pi$
$104$		0			0
$105$	302.214	−	947.017i	0.280887	−	0.880184i
$106$		0			0
$107$		−	1299.63i		−	1.17420i	−0.809513	−	0.587102i	$-0.800269\pi$
$107$		−	1299.63i		−	1.17420i	0.809513	−	0.587102i	$-0.199731\pi$
$108$		0			0
$109$	2079.24			1.82711			0.913554	−	0.406717i	$-0.133326\pi$
$109$	2079.24			1.82711			0.913554	+	0.406717i	$0.133326\pi$
$110$		0			0
$111$	188.758	+	92.7841i	0.161406	+	0.0793395i
$112$		0			0
$113$	1090.53	−	629.616i	0.907860	−	0.524153i	0.0281181	−	0.999605i	$-0.491049\pi$
$113$	1090.53	−	629.616i	0.907860	−	0.524153i	0.879742	+	0.475451i	$0.157715\pi$
$114$		0			0
$115$	−607.396	−	350.680i	−0.492522	−	0.284358i
$116$		0			0
$117$	−1124.68	−	462.483i	−0.888693	−	0.365441i
$118$		0			0
$119$	−1076.63	−	424.587i	−0.829368	−	0.327074i
$120$		0			0
$121$	−174.783	−	302.734i	−0.131317	−	0.227448i
$122$		0			0
$123$	27.5473	+	412.190i	0.0201940	+	0.302162i
$124$		0			0
$125$	1480.22			1.05916
$126$		0			0
$127$	−1015.62			−0.709623			−0.354811	−	0.934938i	$-0.615455\pi$
$127$	−1015.62			−0.709623			−0.354811	+	0.934938i	$0.615455\pi$
$128$		0			0
$129$	1393.89	−	933.957i	0.951359	−	0.637445i
$130$		0			0
$131$	−1353.80	−	2344.85i	−0.902915	−	1.56390i	−0.823691	−	0.567039i	$-0.808089\pi$
$131$	−1353.80	−	2344.85i	−0.902915	−	1.56390i	−0.0792242	−	0.996857i	$-0.525244\pi$
$132$		0			0
$133$	903.177	−	2290.21i	0.588837	−	1.49313i
$134$		0			0
$135$	−1085.89	+	959.721i	−0.692288	+	0.611849i
$136$		0			0
$137$	−2713.91	−	1566.88i	−1.69245	−	0.977135i	−0.952533	−	0.304435i	$-0.901532\pi$
$137$	−2713.91	−	1566.88i	−1.69245	−	0.977135i	−0.739915	−	0.672700i	$-0.765134\pi$
$138$		0			0
$139$	86.5871	−	49.9911i	0.0528361	−	0.0305049i	−0.473349	−	0.880875i	$-0.656955\pi$
$139$	86.5871	−	49.9911i	0.0528361	−	0.0305049i	0.526185	+	0.850370i	$0.323622\pi$
$140$		0			0
$141$	−1478.63	+	990.737i	−0.883145	+	0.591738i
$142$		0			0
$143$	−1410.98			−0.825121
$144$		0			0
$145$		−	1391.55i		−	0.796980i
$146$		0			0
$147$	632.272	+	1666.36i	0.354754	+	0.934960i
$148$		0			0
$149$	2280.20	−	1316.47i	1.25370	−	0.723823i	0.281856	−	0.959457i	$-0.409050\pi$
$149$	2280.20	−	1316.47i	1.25370	−	0.723823i	0.971842	+	0.235634i	$0.0757167\pi$
$150$		0			0
$151$	−944.432	+	1635.80i	−0.508985	+	0.881588i	0.490961	+	0.871182i	$0.336646\pi$
$151$	−944.432	+	1635.80i	−0.508985	+	0.881588i	−0.999946	+	0.0104066i	$0.996687\pi$
$152$		0			0
$153$	1030.55	+	1335.93i	0.544543	+	0.705905i
$154$		0			0
$155$	−268.483	−	155.009i	−0.139130	−	0.0803266i
$156$		0			0
$157$	1110.41	−	641.097i	0.564462	−	0.325892i	−0.190472	−	0.981693i	$-0.561002\pi$
$157$	1110.41	−	641.097i	0.564462	−	0.325892i	0.754935	+	0.655800i	$0.227669\pi$
$158$		0			0
$159$	148.794	−	302.702i	0.0742146	−	0.150980i
$160$		0			0
$161$	1243.74	−	185.378i	0.608822	−	0.0907442i
$162$		0			0
$163$	3558.63			1.71002			0.855011	−	0.518610i	$-0.173550\pi$
$163$	3558.63			1.71002			0.855011	+	0.518610i	$0.173550\pi$
$164$		0			0
$165$	−741.779	+	1509.06i	−0.349984	+	0.711999i
$166$		0			0
$167$	−471.603	−	816.841i	−0.218526	−	0.378497i	0.735832	−	0.677164i	$-0.236791\pi$
$167$	−471.603	−	816.841i	−0.218526	−	0.378497i	−0.954357	+	0.298667i	$0.903458\pi$
$168$		0			0
$169$	−84.2309	+	145.892i	−0.0383390	+	0.0664052i
$170$		0			0
$171$	−2841.78	+	2192.18i	−1.27085	+	0.980351i
$172$		0			0
$173$	−489.793	+	848.347i	−0.215250	+	0.372824i	−0.953350	−	0.301867i	$-0.902390\pi$
$173$	−489.793	+	848.347i	−0.215250	+	0.372824i	0.738100	+	0.674692i	$0.235723\pi$
$174$		0			0
$175$	−265.285	+	210.847i	−0.114592	+	0.0910773i
$176$		0			0
$177$	55.0095	+	823.105i	0.0233602	+	0.349539i
$178$		0			0
$179$			3739.96i			1.56166i	0.624742	+	0.780831i	$0.285204\pi$
$179$			3739.96i			1.56166i	−0.624742	+	0.780831i	$0.714796\pi$
$180$		0			0
$181$			1540.52i			0.632631i	0.948654	+	0.316316i	$0.102446\pi$
$181$			1540.52i			0.632631i	−0.948654	+	0.316316i	$0.897554\pi$
$182$		0			0
$183$	1648.67	+	2460.57i	0.665972	+	0.993936i
$184$		0			0
$185$	209.062	+	362.106i	0.0830840	+	0.143906i
$186$		0			0
$187$	1695.40	+	978.838i	0.662993	+	0.382779i
$188$		0			0
$189$	453.520	−	2558.43i	0.174543	−	0.984649i
$190$		0			0
$191$	−649.672	−	375.088i	−0.246118	−	0.142097i	0.371867	−	0.928286i	$-0.378718\pi$
$191$	−649.672	−	375.088i	−0.246118	−	0.142097i	−0.617986	+	0.786189i	$0.712051\pi$
$192$		0			0
$193$	2026.03	+	3509.19i	0.755632	+	1.30879i	0.945060	+	0.326898i	$0.106003\pi$
$193$	2026.03	+	3509.19i	0.755632	+	1.30879i	−0.189428	+	0.981895i	$0.560663\pi$
$194$		0			0
$195$	−1345.65	−	2008.33i	−0.494175	−	0.737536i
$196$		0			0
$197$		−	807.631i		−	0.292088i	−0.989278	−	0.146044i	$-0.953346\pi$
$197$		−	807.631i		−	0.292088i	0.989278	−	0.146044i	$-0.0466541\pi$
$198$		0			0
$199$			4386.10i			1.56243i	0.624265	+	0.781213i	$0.285399\pi$
$199$			4386.10i			1.56243i	−0.624265	+	0.781213i	$0.714601\pi$
$200$		0			0
$201$	104.526	+	1564.02i	0.0366801	+	0.548842i
$202$		0			0
$203$	1552.36	+	1953.17i	0.536722	+	0.675297i
$204$		0			0
$205$	−410.621	+	711.216i	−0.139897	+	0.242310i
$206$		0			0
$207$	−1695.48	−	697.201i	−0.569295	−	0.234100i
$208$		0			0
$209$	−2082.17	+	3606.43i	−0.689124	+	1.19360i
$210$		0			0
$211$	−2132.63	−	3693.82i	−0.695811	−	1.20518i	−0.969907	−	0.243478i	$-0.921712\pi$
$211$	−2132.63	−	3693.82i	−0.695811	−	1.20518i	0.274095	−	0.961702i	$-0.411622\pi$
$212$		0			0
$213$	1648.34	−	3353.33i	0.530244	−	1.07871i
$214$		0			0
$215$	3335.50			1.05804
$216$		0			0
$217$	549.762	−	81.9413i	0.171983	−	0.0256338i
$218$		0			0
$219$	1280.68	−	2605.38i	0.395161	−	0.803904i
$220$		0			0
$221$	−2437.43	+	1407.25i	−0.741898	+	0.428335i
$222$		0			0
$223$	−1771.94	−	1023.03i	−0.532097	−	0.307206i	0.209773	−	0.977750i	$-0.432727\pi$
$223$	−1771.94	−	1023.03i	−0.532097	−	0.307206i	−0.741870	+	0.670544i	$0.766061\pi$
$224$		0			0
$225$	489.632	−	65.7394i	0.145076	−	0.0194784i
$226$		0			0
$227$	−2797.06	+	4844.65i	−0.817830	+	1.41652i	0.0894471	+	0.995992i	$0.471490\pi$
$227$	−2797.06	+	4844.65i	−0.817830	+	1.41652i	−0.907278	+	0.420532i	$0.861843\pi$
$228$		0			0
$229$	−318.820	+	184.071i	−0.0920009	+	0.0531168i	−0.545295	−	0.838244i	$-0.683582\pi$
$229$	−318.820	+	184.071i	−0.0920009	+	0.0531168i	0.453294	+	0.891361i	$0.350249\pi$
$230$		0			0
$231$	−642.293	−	2945.59i	−0.182943	−	0.838986i
$232$		0			0
$233$		−	3900.42i		−	1.09667i	−0.836258	−	0.548336i	$-0.815261\pi$
$233$		−	3900.42i		−	1.09667i	0.836258	−	0.548336i	$-0.184739\pi$
$234$		0			0
$235$	−3538.29			−0.982180
$236$		0			0
$237$	3942.70	−	2641.75i	1.08062	−	0.724051i
$238$		0			0
$239$	−2327.57	+	1343.82i	−0.629949	+	0.363701i	−0.780732	−	0.624866i	$-0.785154\pi$
$239$	−2327.57	+	1343.82i	−0.629949	+	0.363701i	0.150783	+	0.988567i	$0.451820\pi$
$240$		0			0
$241$	2125.83	+	1227.35i	0.568203	+	0.328052i	0.756431	−	0.654073i	$-0.226941\pi$
$241$	2125.83	+	1227.35i	0.568203	+	0.328052i	−0.188228	+	0.982125i	$0.560274\pi$
$242$		0			0
$243$	−2479.28	+	2863.92i	−0.654511	+	0.756053i
$244$		0			0
$245$	−799.738	+	3451.65i	−0.208544	+	0.900073i
$246$		0			0
$247$	−2993.49	−	5184.88i	−0.771139	−	1.33565i
$248$		0			0
$249$	−3041.99	+	2038.24i	−0.774210	+	0.518748i
$250$		0			0
$251$	3096.36			0.778648			0.389324	−	0.921101i	$-0.372709\pi$
$251$	3096.36			0.778648			0.389324	+	0.921101i	$0.372709\pi$
$252$		0			0
$253$	−2127.08			−0.528571
$254$		0			0
$255$	223.663	+	3346.67i	0.0549268	+	0.821868i
$256$		0			0
$257$	−1311.10	−	2270.89i	−0.318227	−	0.551185i	0.661892	−	0.749600i	$-0.269754\pi$
$257$	−1311.10	−	2270.89i	−0.318227	−	0.551185i	−0.980118	+	0.198415i	$0.936421\pi$
$258$		0			0
$259$	−697.389	−	275.026i	−0.167311	−	0.0659817i
$260$		0			0
$261$	−484.008	−	3604.92i	−0.114787	−	0.854939i
$262$		0			0
$263$	6179.60	+	3567.79i	1.44886	+	0.836500i	0.998414	−	0.0563032i	$-0.0179313\pi$
$263$	6179.60	+	3567.79i	1.44886	+	0.836500i	0.450447	+	0.892803i	$0.351265\pi$
$264$		0			0
$265$	580.693	−	335.263i	0.134610	−	0.0777173i
$266$		0			0
$267$	3264.88	+	1604.86i	0.748343	+	0.367849i
$268$		0			0
$269$	3846.62			0.871869			0.435934	−	0.899978i	$-0.356418\pi$
$269$	3846.62			0.871869			0.435934	+	0.899978i	$0.356418\pi$
$270$		0			0
$271$			446.364i			0.100054i	0.998748	+	0.0500271i	$0.0159308\pi$
$271$			446.364i			0.100054i	−0.998748	+	0.0500271i	$0.984069\pi$
$272$		0			0
$273$	4129.16	+	1317.71i	0.915414	+	0.292129i
$274$		0			0
$275$	496.417	−	286.606i	0.108855	−	0.0628473i
$276$		0			0
$277$	−3405.06	+	5897.74i	−0.738593	+	1.27928i	0.214535	+	0.976716i	$0.431176\pi$
$277$	−3405.06	+	5897.74i	−0.738593	+	1.27928i	−0.953129	+	0.302565i	$0.902157\pi$
$278$		0			0
$279$	−749.441	−	308.179i	−0.160817	−	0.0661297i
$280$		0			0
$281$	2970.96	+	1715.29i	0.630722	+	0.364147i	0.781031	−	0.624492i	$-0.214694\pi$
$281$	2970.96	+	1715.29i	0.630722	+	0.364147i	−0.150310	+	0.988639i	$0.548027\pi$
$282$		0			0
$283$	275.171	−	158.870i	0.0577993	−	0.0333705i	−0.470822	−	0.882228i	$-0.656043\pi$
$283$	275.171	−	158.870i	0.0577993	−	0.0333705i	0.528621	+	0.848858i	$0.322709\pi$
$284$		0			0
$285$	−7119.00	+	475.774i	−1.47962	+	0.0988857i
$286$		0			0
$287$	−217.064	−	1456.33i	−0.0446441	−	0.299527i
$288$		0			0
$289$	−1008.00			−0.205171
$290$		0			0
$291$	−677.270	−	1010.80i	−0.136434	−	0.203622i
$292$		0			0
$293$	−3701.79	−	6411.69i	−0.738091	−	1.27841i	−0.953354	−	0.301856i	$-0.902394\pi$
$293$	−3701.79	−	6411.69i	−0.738091	−	1.27841i	0.215262	−	0.976556i	$-0.430939\pi$
$294$		0			0
$295$	−819.972	+	1420.23i	−0.161833	+	0.280302i
$296$		0			0
$297$	−1396.76	+	4167.33i	−0.272889	+	0.814185i
$298$		0			0
$299$	1529.03	−	2648.35i	0.295739	−	0.512235i
$300$		0			0
$301$	−4681.67	+	3720.96i	−0.896502	+	0.712534i
$302$		0			0
$303$	8099.04	−	5426.65i	1.53557	−	1.02889i
$304$		0			0
$305$			5887.99i			1.10540i
$306$		0			0
$307$		−	9692.73i		−	1.80193i	−0.433888	−	0.900967i	$-0.642859\pi$
$307$		−	9692.73i		−	1.80193i	0.433888	−	0.900967i	$-0.357141\pi$
$308$		0			0
$309$	−3140.03	+	209.854i	−0.578092	+	0.0386348i
$310$		0			0
$311$	−3957.20	−	6854.07i	−0.721518	−	1.24971i	−0.960391	−	0.278655i	$-0.910111\pi$
$311$	−3957.20	−	6854.07i	−0.721518	−	1.24971i	0.238873	−	0.971051i	$-0.423222\pi$
$312$		0			0
$313$	4644.88	+	2681.72i	0.838799	+	0.484281i	0.856856	−	0.515556i	$-0.172415\pi$
$313$	4644.88	+	2681.72i	0.838799	+	0.484281i	−0.0180566	+	0.999837i	$0.505748\pi$
$314$		0			0
$315$	3580.07	−	3723.42i	0.640362	−	0.666002i
$316$		0			0
$317$	3741.29	+	2160.03i	0.662876	+	0.382712i	0.793372	−	0.608737i	$-0.208324\pi$
$317$	3741.29	+	2160.03i	0.662876	+	0.382712i	−0.130496	+	0.991449i	$0.541657\pi$
$318$		0			0
$319$	−2110.14	−	3654.88i	−0.370362	−	0.641485i
$320$		0			0
$321$	2979.04	−	6060.47i	0.517986	−	1.05378i
$322$		0			0
$323$			8306.67i			1.43095i
$324$		0			0
$325$			824.095i			0.140654i
$326$		0			0
$327$	9695.97	+	4766.07i	1.63972	+	0.806007i
$328$		0			0
$329$	4966.29	−	3947.18i	0.832221	−	0.661444i
$330$		0			0
$331$	371.714	−	643.828i	0.0617259	−	0.106912i	−0.833511	−	0.552503i	$-0.813673\pi$
$331$	371.714	−	643.828i	0.0617259	−	0.106912i	0.895237	+	0.445590i	$0.147006\pi$
$332$		0			0
$333$	667.538	+	865.348i	0.109852	+	0.142405i
$334$		0			0
$335$	−1558.06	+	2698.65i	−0.254108	+	0.440128i
$336$		0			0
$337$	4874.39	+	8442.69i	0.787908	+	1.36470i	0.927246	+	0.374452i	$0.122169\pi$
$337$	4874.39	+	8442.69i	0.787908	+	1.36470i	−0.139338	+	0.990245i	$0.544497\pi$
$338$		0			0
$339$	6528.60	−	436.317i	1.04597	−	0.0699041i
$340$		0			0
$341$	−940.219			−0.149313
$342$		0			0
$343$	−2728.03	−	5736.85i	−0.429445	−	0.903093i
$344$		0			0
$345$	−2028.59	−	3027.59i	−0.316567	−	0.472464i
$346$		0			0
$347$	−2953.16	+	1705.01i	−0.456870	+	0.263774i	−0.710727	−	0.703468i	$-0.751634\pi$
$347$	−2953.16	+	1705.01i	−0.456870	+	0.263774i	0.253857	+	0.967242i	$0.418301\pi$
$348$		0			0
$349$	−8157.38	−	4709.67i	−1.25116	−	0.722357i	−0.279820	−	0.960053i	$-0.590275\pi$
$349$	−8157.38	−	4709.67i	−1.25116	−	0.722357i	−0.971340	+	0.237695i	$0.923608\pi$
$350$		0			0
$351$	−4184.55	−	4734.69i	−0.636338	−	0.719997i
$352$		0			0
$353$	−1363.14	+	2361.03i	−0.205532	+	0.355992i	−0.950302	−	0.311329i	$-0.899226\pi$
$353$	−1363.14	+	2361.03i	−0.205532	+	0.355992i	0.744770	+	0.667321i	$0.232559\pi$
$354$		0			0
$355$	6432.91	−	3714.04i	0.961756	−	0.555270i
$356$		0			0
$357$	−4047.35	−	4447.83i	−0.600023	−	0.659395i
$358$		0			0
$359$			8978.19i			1.31992i	0.751302	+	0.659959i	$0.229426\pi$
$359$			8978.19i			1.31992i	−0.751302	+	0.659959i	$0.770574\pi$
$360$		0			0
$361$	−10810.9			−1.57616
$362$		0			0
$363$	−121.123	−	1812.36i	−0.0175133	−	0.262050i
$364$		0			0
$365$	4998.06	−	2885.63i	0.716742	−	0.413811i
$366$		0			0
$367$	−6601.74	−	3811.52i	−0.938987	−	0.542124i	−0.0493444	−	0.998782i	$-0.515713\pi$
$367$	−6601.74	−	3811.52i	−0.938987	−	0.542124i	−0.889643	+	0.456657i	$0.849047\pi$
$368$		0			0
$369$	−816.370	+	1985.28i	−0.115172	+	0.280080i
$370$		0			0
$371$	−441.047	+	1118.37i	−0.0617197	+	0.156504i
$372$		0			0
$373$	−1255.32	−	2174.28i	−0.174258	−	0.301823i	0.765646	−	0.643262i	$-0.222419\pi$
$373$	−1255.32	−	2174.28i	−0.174258	−	0.301823i	−0.939904	+	0.341438i	$0.889086\pi$
$374$		0			0
$375$	6902.60	+	3392.99i	0.950530	+	0.467235i
$376$		0			0
$377$	6067.41			0.828879
$378$		0			0
$379$	−7234.68			−0.980529			−0.490265	−	0.871574i	$-0.663100\pi$
$379$	−7234.68			−0.980529			−0.490265	+	0.871574i	$0.663100\pi$
$380$		0			0
$381$	−4736.09	−	2328.04i	−0.636844	−	0.313042i
$382$		0			0
$383$	−6219.05	−	10771.7i	−0.829710	−	1.43710i	−0.898266	−	0.439452i	$-0.855173\pi$
$383$	−6219.05	−	10771.7i	−0.829710	−	1.43710i	0.0685562	−	0.997647i	$-0.478161\pi$
$384$		0			0
$385$	2198.74	−	5575.40i	0.291060	−	0.738048i
$386$		0			0
$387$	8640.88	−	1160.15i	1.13499	−	0.152387i
$388$		0			0
$389$	−2593.05	−	1497.10i	−0.337976	−	0.195131i	0.321400	−	0.946943i	$-0.395846\pi$
$389$	−2593.05	−	1497.10i	−0.337976	−	0.195131i	−0.659377	+	0.751813i	$0.729180\pi$
$390$		0			0
$391$	−3674.47	+	2121.46i	−0.475258	+	0.274390i
$392$		0			0
$393$	−938.168	−	14037.8i	−0.120418	−	1.80181i
$394$		0			0
$395$	9434.66			1.20180
$396$		0			0
$397$			3404.67i			0.430417i	0.976568	+	0.215208i	$0.0690430\pi$
$397$			3404.67i			0.430417i	−0.976568	+	0.215208i	$0.930957\pi$
$398$		0			0
$399$	9461.38	−	8609.48i	1.18712	−	1.08023i
$400$		0			0
$401$	2674.32	−	1544.02i	0.333040	−	0.192281i	−0.324150	−	0.946006i	$-0.605078\pi$
$401$	2674.32	−	1544.02i	0.333040	−	0.192281i	0.657190	+	0.753725i	$0.271745\pi$
$402$		0			0
$403$	675.866	−	1170.63i	0.0835416	−	0.144698i
$404$		0			0
$405$	−7263.67	+	1986.29i	−0.891196	+	0.243703i
$406$		0			0
$407$	1098.19	+	634.041i	0.133748	+	0.0772193i
$408$		0			0
$409$	8924.66	−	5152.66i	1.07896	−	0.622940i	0.148347	−	0.988935i	$-0.452605\pi$
$409$	8924.66	−	5152.66i	1.07896	−	0.622940i	0.930617	+	0.365995i	$0.119271\pi$
$410$		0			0
$411$	−9063.98	−	13527.6i	−1.08782	−	1.62352i
$412$		0			0
$413$	−433.456	−	2908.15i	−0.0516440	−	0.346491i
$414$		0			0
$415$	−7279.31			−0.861029
$416$		0			0
$417$	518.366	−	34.6433i	0.0608741	−	0.00406832i
$418$		0			0
$419$	5734.36	+	9932.20i	0.668596	+	1.15804i	0.978297	+	0.207208i	$0.0664378\pi$
$419$	5734.36	+	9932.20i	0.668596	+	1.15804i	−0.309701	+	0.950834i	$0.600229\pi$
$420$		0			0
$421$	−3002.26	+	5200.07i	−0.347557	+	0.601986i	−0.985815	−	0.167837i	$-0.946322\pi$
$421$	−3002.26	+	5200.07i	−0.347557	+	0.601986i	0.638258	+	0.769822i	$0.279655\pi$
$422$		0			0
$423$	−9166.20	+	1230.68i	−1.05361	+	0.141460i
$424$		0			0
$425$	571.697	−	990.208i	0.0652503	−	0.113017i
$426$		0			0
$427$	−6568.43	−	8264.32i	−0.744422	−	0.936624i
$428$		0			0
$429$	−6579.74	−	3234.29i	−0.740496	−	0.363992i
$430$		0			0
$431$			8312.17i			0.928963i	0.885583	+	0.464481i	$0.153759\pi$
$431$			8312.17i			0.928963i	−0.885583	+	0.464481i	$0.846241\pi$
$432$		0			0
$433$			4419.65i			0.490519i	0.969458	+	0.245259i	$0.0788731\pi$
$433$			4419.65i			0.490519i	−0.969458	+	0.245259i	$0.921127\pi$
$434$		0			0
$435$	3189.74	−	6489.13i	0.351578	−	0.715241i
$436$		0			0
$437$	−4512.74	−	7816.30i	−0.493990	−	0.855616i
$438$		0			0
$439$	14013.5	+	8090.72i	1.52353	+	0.879610i	0.999612	+	0.0278416i	$0.00886340\pi$
$439$	14013.5	+	8090.72i	1.52353	+	0.879610i	0.523918	+	0.851769i	$0.324470\pi$
$440$		0			0
$441$	−871.235	+	9219.93i	−0.0940757	+	0.995565i
$442$		0			0
$443$	2983.47	+	1722.51i	0.319976	+	0.184738i	0.651382	−	0.758750i	$-0.274190\pi$
$443$	2983.47	+	1722.51i	0.319976	+	0.184738i	−0.331406	+	0.943488i	$0.607523\pi$
$444$		0			0
$445$	3616.08	+	6263.24i	0.385211	+	0.667205i
$446$		0			0
$447$	13650.7	−	912.300i	1.44442	−	0.0965332i
$448$		0			0
$449$		−	3345.89i		−	0.351675i	−0.984419	−	0.175838i	$-0.943737\pi$
$449$		−	3345.89i		−	0.351675i	0.984419	−	0.175838i	$-0.0562634\pi$
$450$		0			0
$451$			2490.65i			0.260045i
$452$		0			0
$453$	−8153.73	+	5463.29i	−0.845686	+	0.566639i
$454$		0			0
$455$	5361.19	+	6745.39i	0.552388	+	0.695008i
$456$		0			0
$457$	2817.23	−	4879.58i	0.288368	−	0.499469i	−0.685052	−	0.728494i	$-0.740221\pi$
$457$	2817.23	−	4879.58i	0.288368	−	0.499469i	0.973420	+	0.229025i	$0.0735539\pi$
$458$		0			0
$459$	1743.45	+	8592.00i	0.177292	+	0.873726i
$460$		0			0
$461$	−8810.53	+	15260.3i	−0.890124	+	1.54174i	−0.0503981	+	0.998729i	$0.516049\pi$
$461$	−8810.53	+	15260.3i	−0.890124	+	1.54174i	−0.839726	+	0.543011i	$0.817284\pi$
$462$		0			0
$463$	1050.86	+	1820.15i	0.105481	+	0.182699i	0.913935	−	0.405861i	$-0.133028\pi$
$463$	1050.86	+	1820.15i	0.105481	+	0.182699i	−0.808454	+	0.588560i	$0.799695\pi$
$464$		0			0
$465$	−896.685	−	1338.27i	−0.0894253	−	0.133464i
$466$		0			0
$467$	−4439.19			−0.439874			−0.219937	−	0.975514i	$-0.570585\pi$
$467$	−4439.19			−0.439874			−0.219937	+	0.975514i	$0.570585\pi$
$468$		0			0
$469$	−823.629	−	5525.91i	−0.0810910	−	0.544057i
$470$		0			0
$471$	6647.65	−	444.273i	0.650334	−	0.0434629i
$472$		0			0
$473$	8760.62	−	5057.94i	0.851614	−	0.491680i
$474$		0			0
$475$	2106.36	+	1216.11i	0.203466	+	0.117471i
$476$		0			0
$477$	1387.72	−	1070.50i	0.133206	−	0.102757i
$478$		0			0
$479$	−1192.77	+	2065.94i	−0.113777	+	0.197067i	−0.917290	−	0.398220i	$-0.869628\pi$
$479$	−1192.77	+	2065.94i	−0.113777	+	0.197067i	0.803513	+	0.595287i	$0.202961\pi$
$480$		0			0
$481$	−1578.85	+	911.547i	−0.149666	+	0.0864095i
$482$		0			0
$483$	6224.77	+	1986.47i	0.586412	+	0.187137i
$484$		0			0
$485$		−	2418.78i		−	0.226456i
$486$		0			0
$487$	−1032.17			−0.0960409			−0.0480205	−	0.998846i	$-0.515291\pi$
$487$	−1032.17			−0.0960409			−0.0480205	+	0.998846i	$0.515291\pi$
$488$		0			0
$489$	16594.7	+	8157.17i	1.53464	+	0.754356i
$490$		0			0
$491$	−18322.5	+	10578.5i	−1.68408	+	0.972305i	−0.725183	+	0.688556i	$0.758245\pi$
$491$	−18322.5	+	10578.5i	−1.68408	+	0.972305i	−0.958899	+	0.283748i	$0.908422\pi$
$492$		0			0
$493$	−7290.42	−	4209.13i	−0.666012	−	0.384522i
$494$		0			0
$495$	−6918.17	+	5336.75i	−0.628179	+	0.484584i
$496$		0			0
$497$	−4885.91	+	12389.3i	−0.440972	+	1.11818i
$498$		0			0
$499$	5302.31	+	9183.86i	0.475679	+	0.823900i	0.999612	−	0.0278593i	$-0.00886904\pi$
$499$	5302.31	+	9183.86i	0.475679	+	0.823900i	−0.523933	+	0.851760i	$0.675536\pi$
$500$		0			0
$501$	−326.816	−	4890.14i	−0.0291438	−	0.436078i
$502$		0			0
$503$	−4721.95			−0.418572			−0.209286	−	0.977855i	$-0.567114\pi$
$503$	−4721.95			−0.418572			−0.209286	+	0.977855i	$0.567114\pi$
$504$		0			0
$505$	19380.5			1.70777
$506$		0			0
$507$	−727.205	+	487.253i	−0.0637008	+	0.0426818i
$508$		0			0
$509$	−6295.97	−	10904.9i	−0.548259	−	0.949613i	−0.998394	−	0.0566522i	$-0.981957\pi$
$509$	−6295.97	−	10904.9i	−0.548259	−	0.949613i	0.450135	−	0.892961i	$-0.351376\pi$
$510$		0			0
$511$	−3796.12	+	9625.89i	−0.328631	+	0.833316i
$512$		0			0
$513$	−18276.8	+	3708.65i	−1.57298	+	0.319183i
$514$		0			0
$515$	−5418.00	−	3128.08i	−0.463583	−	0.267650i
$516$		0			0
$517$	−9293.22	+	5365.44i	−0.790552	+	0.456425i
$518$		0			0
$519$	−4228.62	+	2833.32i	−0.357641	+	0.239632i
$520$		0			0
$521$	11584.6			0.974145			0.487072	−	0.873362i	$-0.338065\pi$
$521$	11584.6			0.974145			0.487072	+	0.873362i	$0.338065\pi$
$522$		0			0
$523$			3526.37i			0.294833i	0.989075	+	0.147416i	$0.0470957\pi$
$523$			3526.37i			0.294833i	−0.989075	+	0.147416i	$0.952904\pi$
$524$		0			0
$525$	−1720.39	+	375.136i	−0.143017	+	0.0311853i
$526$		0			0
$527$	−1624.20	+	937.733i	−0.134253	+	0.0775110i
$528$		0			0
$529$	−3778.47	+	6544.50i	−0.310550	+	0.537889i
$530$		0			0
$531$	−1630.22	+	3964.42i	−0.133230	+	0.323995i
$532$		0			0
$533$	−3101.02	−	1790.38i	−0.252008	−	0.145497i
$534$		0			0
$535$	11626.2	−	6712.39i	0.939523	−	0.542434i
$536$		0			0
$537$	−8572.81	+	17440.3i	−0.688909	+	1.40150i
$538$		0			0
$539$	3133.58	+	10278.4i	0.250413	+	0.821376i
$540$		0			0
$541$	7849.84			0.623828			0.311914	−	0.950110i	$-0.399030\pi$
$541$	7849.84			0.623828			0.311914	+	0.950110i	$0.399030\pi$
$542$		0			0
$543$	−3531.22	+	7183.82i	−0.279078	+	0.567748i
$544$		0			0
$545$	10739.0	+	18600.4i	0.844048	+	1.46193i
$546$		0			0
$547$	7842.27	−	13583.2i	0.613001	−	1.06175i	−0.377731	−	0.925915i	$-0.623296\pi$
$547$	7842.27	−	13583.2i	0.613001	−	1.06175i	0.990732	−	0.135833i	$-0.0433710\pi$
$548$		0			0
$549$	2047.95	+	15253.3i	0.159207	+	1.18578i
$550$		0			0
$551$	8953.62	−	15508.1i	0.692263	−	1.19903i
$552$		0			0
$553$	−13242.4	+	10524.9i	−1.01831	+	0.809342i
$554$		0			0
$555$	144.878	+	2167.80i	0.0110806	+	0.165798i
$556$		0			0
$557$		−	21036.4i		−	1.60025i	−0.599833	−	0.800126i	$-0.704766\pi$
$557$		−	21036.4i		−	1.60025i	0.599833	−	0.800126i	$-0.295234\pi$
$558$		0			0
$559$			14543.4i			1.10039i
$560$		0			0
$561$	5662.32	+	8450.77i	0.426137	+	0.635992i
$562$		0			0
$563$	−6347.02	−	10993.4i	−0.475124	−	0.822939i	0.524470	−	0.851429i	$-0.324264\pi$
$563$	−6347.02	−	10993.4i	−0.475124	−	0.822939i	−0.999594	+	0.0284899i	$0.990930\pi$
$564$		0			0
$565$	11264.8	+	6503.75i	0.838787	+	0.484274i
$566$		0			0
$567$	7979.36	−	10891.0i	0.591008	−	0.806665i
$568$		0			0
$569$	−15753.0	−	9095.03i	−1.16064	−	0.670094i	−0.209180	−	0.977877i	$-0.567079\pi$
$569$	−15753.0	−	9095.03i	−1.16064	−	0.670094i	−0.951456	+	0.307783i	$0.900413\pi$
$570$		0			0
$571$	−10146.0	−	17573.3i	−0.743599	−	1.28795i	−0.950846	−	0.309663i	$-0.899784\pi$
$571$	−10146.0	−	17573.3i	−0.743599	−	1.28795i	0.207247	−	0.978289i	$-0.433550\pi$
$572$		0			0
$573$	−2169.79	−	3238.32i	−0.158192	−	0.236095i
$574$		0			0
$575$			1242.34i			0.0901026i
$576$		0			0
$577$			12356.1i			0.891494i	0.895159	+	0.445747i	$0.147062\pi$
$577$			12356.1i			0.891494i	−0.895159	+	0.445747i	$0.852938\pi$
$578$		0			0
$579$	1404.02	+	21008.3i	0.100775	+	1.50790i
$580$		0			0
$581$	10217.1	−	8120.52i	0.729567	−	0.579855i
$582$		0			0
$583$	1016.78	−	1761.12i	0.0722314	−	0.125108i
$584$		0			0
$585$	−1671.55	−	12449.8i	−0.118137	−	0.879893i
$586$		0			0
$587$	−1434.42	+	2484.50i	−0.100860	+	0.174695i	−0.912039	−	0.410103i	$-0.865493\pi$
$587$	−1434.42	+	2484.50i	−0.100860	+	0.174695i	0.811179	+	0.584798i	$0.198826\pi$
$588$		0			0
$589$	−1994.74	−	3454.99i	−0.139544	−	0.241698i
$590$		0			0
$591$	1851.27	−	3766.17i	0.128851	−	0.262131i
$592$		0			0
$593$	3259.99			0.225754			0.112877	−	0.993609i	$-0.463993\pi$
$593$	3259.99			0.225754			0.112877	+	0.993609i	$0.463993\pi$
$594$		0			0
$595$	−1762.39	−	11824.3i	−0.121430	−	0.814702i
$596$		0			0
$597$	−10053.9	+	20453.4i	−0.689245	+	1.40218i
$598$		0			0
$599$	19971.2	−	11530.4i	1.36227	−	0.786509i	0.372348	−	0.928093i	$-0.378553\pi$
$599$	19971.2	−	11530.4i	1.36227	−	0.786509i	0.989926	+	0.141584i	$0.0452195\pi$
$600$		0			0
$601$	−10827.8	−	6251.41i	−0.734897	−	0.424293i	0.0853138	−	0.996354i	$-0.472811\pi$
$601$	−10827.8	−	6251.41i	−0.734897	−	0.424293i	−0.820211	+	0.572061i	$0.806144\pi$
$602$		0			0
$603$	−3097.65	+	7532.97i	−0.209197	+	0.508734i
$604$		0			0
$605$	1805.46	−	3127.15i	0.121326	−	0.210143i
$606$		0			0
$607$	6638.81	−	3832.92i	0.443923	−	0.256299i	−0.261338	−	0.965247i	$-0.584164\pi$
$607$	6638.81	−	3832.92i	0.443923	−	0.256299i	0.705260	+	0.708949i	$0.250830\pi$
$608$		0			0
$609$	2761.94	+	12666.4i	0.183776	+	0.842807i
$610$		0			0
$611$		−	15427.5i		−	1.02149i
$612$		0			0
$613$	20585.4			1.35634			0.678170	−	0.734905i	$-0.262773\pi$
$613$	20585.4			1.35634			0.678170	+	0.734905i	$0.262773\pi$
$614$		0			0
$615$	−3545.08	+	2375.33i	−0.232441	+	0.155744i
$616$		0			0
$617$	−14174.2	+	8183.50i	−0.924852	+	0.533963i	−0.885180	−	0.465249i	$-0.845965\pi$
$617$	−14174.2	+	8183.50i	−0.924852	+	0.533963i	−0.0396720	+	0.999213i	$0.512631\pi$
$618$		0			0
$619$	6056.80	+	3496.90i	0.393285	+	0.227063i	0.683583	−	0.729873i	$-0.260421\pi$
$619$	6056.80	+	3496.90i	0.393285	+	0.227063i	−0.290298	+	0.956936i	$0.593754\pi$
$620$		0			0
$621$	−6308.28	−	7137.62i	−0.407637	−	0.461228i
$622$		0			0
$623$	−12062.5	−	4757.04i	−0.775722	−	0.305918i
$624$		0			0
$625$	6501.53	+	11261.0i	0.416098	+	0.720703i
$626$		0			0
$627$	−17976.4	+	12044.8i	−1.14499	+	0.767183i
$628$		0			0
$629$	2529.46			0.160344
$630$		0			0
$631$	8776.78			0.553721			0.276861	−	0.960910i	$-0.410706\pi$
$631$	8776.78			0.553721			0.276861	+	0.960910i	$0.410706\pi$
$632$		0			0
$633$	−1477.89	−	22113.6i	−0.0927974	−	1.38852i
$634$		0			0
$635$	−5245.55	−	9085.56i	−0.327816	−	0.567794i
$636$		0			0
$637$	−15049.8	−	3487.00i	−0.936098	−	0.216891i
$638$		0			0
$639$	15373.1	−	11859.0i	0.951724	−	0.734170i
$640$		0			0
$641$	−2562.09	−	1479.23i	−0.157873	−	0.0911481i	0.418982	−	0.907994i	$-0.362387\pi$
$641$	−2562.09	−	1479.23i	−0.157873	−	0.0911481i	−0.576855	+	0.816846i	$0.695720\pi$
$642$		0			0
$643$	−11590.6	+	6691.85i	−0.710870	+	0.410421i	−0.811383	−	0.584515i	$-0.801285\pi$
$643$	−11590.6	+	6691.85i	−0.710870	+	0.410421i	0.100513	+	0.994936i	$0.467952\pi$
$644$		0			0
$645$	15554.2	+	7645.71i	0.949530	+	0.466744i
$646$		0			0
$647$	−20353.0			−1.23672			−0.618362	−	0.785893i	$-0.712203\pi$
$647$	−20353.0			−1.23672			−0.618362	+	0.785893i	$0.712203\pi$
$648$		0			0
$649$			4973.61i			0.300818i
$650$		0			0
$651$	2751.49	+	878.064i	0.165652	+	0.0528634i
$652$		0			0
$653$	−13525.8	+	7809.11i	−0.810574	+	0.467985i	−0.847155	−	0.531346i	$-0.821687\pi$
$653$	−13525.8	+	7809.11i	−0.810574	+	0.467985i	0.0365814	+	0.999331i	$0.488353\pi$
$654$		0			0
$655$	13984.3	−	24221.6i	0.834219	−	1.44491i
$656$		0			0
$657$	11944.2	−	9213.87i	0.709265	−	0.547135i
$658$		0			0
$659$	−5847.81	−	3376.24i	−0.345673	−	0.199574i	0.317105	−	0.948390i	$-0.397289\pi$
$659$	−5847.81	−	3376.24i	−0.345673	−	0.199574i	−0.662778	+	0.748816i	$0.730623\pi$
$660$		0			0
$661$	−8658.65	+	4999.07i	−0.509504	+	0.294162i	−0.732630	−	0.680627i	$-0.761707\pi$
$661$	−8658.65	+	4999.07i	−0.509504	+	0.294162i	0.223126	+	0.974790i	$0.428374\pi$
$662$		0			0
$663$	−14592.0	+	975.210i	−0.854763	+	0.0571252i
$664$		0			0
$665$	25152.5	−	3748.94i	1.46672	−	0.218613i
$666$		0			0
$667$	9146.72			0.530978
$668$		0			0
$669$	−5917.94	−	8832.28i	−0.342004	−	0.510427i
$670$		0			0
$671$	8928.53	+	15464.7i	0.513684	+	0.889727i
$672$		0			0
$673$	−31.7088	+	54.9213i	−0.00181617	+	0.00314570i	−0.866932	−	0.498426i	$-0.833911\pi$
$673$	−31.7088	+	54.9213i	−0.00181617	+	0.00314570i	0.865116	+	0.501572i	$0.167245\pi$
$674$		0			0
$675$	2433.96	+	815.786i	0.138790	+	0.0465180i
$676$		0			0
$677$	8874.33	−	15370.8i	0.503793	−	0.872596i	−0.496197	−	0.868210i	$-0.665271\pi$
$677$	8874.33	−	15370.8i	0.503793	−	0.872596i	0.999990	−	0.00438565i	$-0.00139600\pi$
$678$		0			0
$679$	2698.30	+	3394.97i	0.152506	+	0.191881i
$680$		0			0
$681$	−24148.4	+	16180.3i	−1.35884	+	0.910468i
$682$		0			0
$683$		−	8356.42i		−	0.468155i	−0.972218	−	0.234077i	$-0.924793\pi$
$683$		−	8356.42i		−	0.468155i	0.972218	−	0.234077i	$-0.0752069\pi$
$684$		0			0
$685$		−	32370.8i		−	1.80558i
$686$		0			0
$687$	−1908.66	+	127.559i	−0.105997	+	0.00708396i
$688$		0			0
$689$	1461.81	+	2531.92i	0.0808279	+	0.139998i
$690$		0			0
$691$	25237.8	+	14571.1i	1.38942	+	0.802185i	0.993250	−	0.115991i	$-0.0370042\pi$
$691$	25237.8	+	14571.1i	1.38942	+	0.802185i	0.396174	+	0.918175i	$0.370338\pi$
$692$		0			0
$693$	3756.78	−	15208.3i	0.205928	−	0.833642i
$694$		0			0
$695$	894.419	+	516.393i	0.0488162	+	0.0281840i
$696$		0			0
$697$	2484.07	+	4302.53i	0.134994	+	0.233816i
$698$		0			0
$699$	8940.61	−	18188.5i	0.483784	−	0.984197i
$700$		0			0
$701$		−	30359.4i		−	1.63574i	−0.575400	−	0.817872i	$-0.695154\pi$
$701$		−	30359.4i		−	1.63574i	0.575400	−	0.817872i	$-0.304846\pi$
$702$		0			0
$703$			5380.64i			0.288670i
$704$		0			0
$705$	−16499.8	−	8110.53i	−0.881447	−	0.433277i
$706$		0			0
$707$	−27202.3	+	21620.2i	−1.44703	+	1.15009i
$708$		0			0
$709$	−6063.83	+	10502.9i	−0.321202	+	0.556338i	−0.980736	−	0.195337i	$-0.937420\pi$
$709$	−6063.83	+	10502.9i	−0.321202	+	0.556338i	0.659535	+	0.751674i	$0.270753\pi$
$710$		0			0
$711$	24441.2	−	3281.55i	1.28919	−	0.173091i
$712$		0			0
$713$	1018.88	−	1764.75i	0.0535166	−	0.0926934i
$714$		0			0
$715$	−7287.52	−	12622.4i	−0.381172	−	0.660209i
$716$		0			0
$717$	−13934.3	+	931.254i	−0.725783	+	0.0485053i
$718$		0			0
$719$	9928.20			0.514964			0.257482	−	0.966283i	$-0.417107\pi$
$719$	9928.20			0.514964			0.257482	+	0.966283i	$0.417107\pi$
$720$		0			0
$721$	11094.2	−	1653.58i	0.573051	−	0.0854125i
$722$		0			0
$723$	7099.90	+	10596.3i	0.365212	+	0.545063i
$724$		0			0
$725$	−2134.66	+	1232.44i	−0.109351	+	0.0631335i
$726$		0			0
$727$	−26251.7	−	15156.4i	−1.33923	−	0.773204i	−0.352536	−	0.935798i	$-0.614681\pi$
$727$	−26251.7	−	15156.4i	−1.33923	−	0.773204i	−0.986693	+	0.162594i	$0.948014\pi$
$728$		0			0
$729$	−18126.2	+	7672.07i	−0.920907	+	0.389782i
$730$		0			0
$731$	10089.1	−	17474.9i	0.510479	−	0.884176i
$732$		0			0
$733$	16344.8	−	9436.67i	0.823613	−	0.475513i	−0.0280476	−	0.999607i	$-0.508929\pi$
$733$	16344.8	−	9436.67i	0.823613	−	0.475513i	0.851661	+	0.524093i	$0.175596\pi$
$734$		0			0
$735$	−11641.3	+	14262.7i	−0.584212	+	0.715764i
$736$		0			0
$737$			9450.57i			0.472342i
$738$		0			0
$739$	24825.4			1.23575			0.617873	−	0.786278i	$-0.287995\pi$
$739$	24825.4			1.23575			0.617873	+	0.786278i	$0.287995\pi$
$740$		0			0
$741$	−2074.46	−	31040.1i	−0.102844	−	1.53885i
$742$		0			0
$743$	22599.1	−	13047.6i	1.11586	−	0.644241i	0.175517	−	0.984476i	$-0.443840\pi$
$743$	22599.1	−	13047.6i	1.11586	−	0.644241i	0.940340	+	0.340236i	$0.110507\pi$
$744$		0			0
$745$	23553.7	+	13598.8i	1.15831	+	0.668752i
$746$		0			0
$747$	−18857.6	+	2531.88i	−0.923646	+	0.124011i
$748$		0			0
$749$	−8830.30	+	22391.2i	−0.430777	+	1.09233i
$750$		0			0
$751$	13211.2	+	22882.5i	0.641922	+	1.11184i	0.985003	+	0.172536i	$0.0551962\pi$
$751$	13211.2	+	22882.5i	0.641922	+	1.11184i	−0.343081	+	0.939306i	$0.611470\pi$
$752$		0			0
$753$	14439.1	+	7097.54i	0.698789	+	0.343491i
$754$		0			0
$755$	−19511.4			−0.940520
$756$		0			0
$757$	28263.9			1.35703			0.678513	−	0.734588i	$-0.262625\pi$
$757$	28263.9			1.35703			0.678513	+	0.734588i	$0.262625\pi$
$758$		0			0
$759$	−9919.07	−	4875.74i	−0.474360	−	0.233173i
$760$		0			0
$761$	−19195.4	−	33247.5i	−0.914369	−	1.58373i	−0.807823	−	0.589425i	$-0.799354\pi$
$761$	−19195.4	−	33247.5i	−0.914369	−	1.58373i	−0.106545	−	0.994308i	$-0.533979\pi$
$762$		0			0
$763$	−35823.0	−	14127.3i	−1.69971	−	0.670307i
$764$		0			0
$765$	−6628.30	+	16119.0i	−0.313264	+	0.761807i
$766$		0			0
$767$	−6192.46	−	3575.22i	−0.291521	−	0.168310i
$768$		0			0
$769$	26820.3	−	15484.7i	1.25769	−	0.726129i	0.285067	−	0.958508i	$-0.407984\pi$
$769$	26820.3	−	15484.7i	1.25769	−	0.726129i	0.972625	+	0.232378i	$0.0746507\pi$
$770$		0			0
$771$	−908.579	−	13595.0i	−0.0424405	−	0.635037i
$772$		0			0
$773$	−28691.6			−1.33501			−0.667507	−	0.744604i	$-0.732638\pi$
$773$	−28691.6			−1.33501			−0.667507	+	0.744604i	$0.732638\pi$
$774$		0			0
$775$			549.142i			0.0254526i
$776$		0			0
$777$	−2621.67	−	2881.08i	−0.121045	−	0.133022i
$778$		0			0
$779$	−9152.30	+	5284.08i	−0.420944	+	0.243032i
$780$		0			0
$781$	11263.9	−	19509.7i	0.516075	−	0.893868i
$782$		0			0
$783$	6006.24	−	17920.0i	0.274132	−	0.817893i
$784$		0			0
$785$	11470.2	+	6622.34i	0.521516	+	0.301097i
$786$		0			0
$787$	19658.2	−	11349.7i	0.890392	−	0.514068i	0.0163216	−	0.999867i	$-0.494804\pi$
$787$	19658.2	−	11349.7i	0.890392	−	0.514068i	0.874071	+	0.485798i	$0.161471\pi$
$788$		0			0
$789$	20638.7	+	30802.4i	0.931252	+	1.38986i
$790$		0			0
$791$	−23066.5	+	3438.03i	−1.03685	+	0.154542i
$792$		0			0
$793$	−25672.7			−1.14964
$794$		0			0
$795$	3476.41	−	232.334i	0.155089	−	0.0103648i
$796$		0			0
$797$	−4945.60	−	8566.03i	−0.219802	−	0.380708i	0.734945	−	0.678126i	$-0.237208\pi$
$797$	−4945.60	−	8566.03i	−0.219802	−	0.380708i	−0.954747	+	0.297418i	$0.903874\pi$
$798$		0			0
$799$	−10702.5	+	18537.3i	−0.473877	+	0.820778i
$800$		0			0
$801$	11546.2	+	14967.7i	0.509320	+	0.660245i
$802$		0			0
$803$	8751.53	−	15158.1i	0.384601	−	0.666149i
$804$		0			0
$805$	8082.08	+	10168.8i	0.353858	+	0.445220i
$806$		0			0
$807$	17937.7	+	8817.31i	0.782449	+	0.384614i
$808$		0			0
$809$		−	15328.4i		−	0.666155i	−0.942900	−	0.333077i	$-0.891913\pi$
$809$		−	15328.4i		−	0.666155i	0.942900	−	0.333077i	$-0.108087\pi$
$810$		0			0
$811$		−	4463.96i		−	0.193281i	−0.995319	−	0.0966406i	$-0.969190\pi$
$811$		−	4463.96i		−	0.193281i	0.995319	−	0.0966406i	$-0.0308097\pi$
$812$		0			0
$813$	−1023.16	+	2081.50i	−0.0441377	+	0.0897925i
$814$		0			0
$815$	18379.8	+	31834.8i	0.789959	+	1.36825i
$816$		0			0
$817$	37172.4	+	21461.5i	1.59180	+	0.919025i
$818$		0			0
$819$	16234.7	+	15609.7i	0.692659	+	0.665992i
$820$		0			0
$821$	13660.6	+	7886.94i	0.580704	+	0.335269i	0.761413	−	0.648267i	$-0.224506\pi$
$821$	13660.6	+	7886.94i	0.580704	+	0.335269i	−0.180709	+	0.983537i	$0.557839\pi$
$822$		0			0
$823$	−960.810	−	1664.17i	−0.0406947	−	0.0704853i	0.844961	−	0.534828i	$-0.179624\pi$
$823$	−960.810	−	1664.17i	−0.0406947	−	0.0704853i	−0.885655	+	0.464343i	$0.846290\pi$
$824$		0			0
$825$	2971.87	−	198.615i	0.125415	−	0.00838168i
$826$		0			0
$827$		−	28140.7i		−	1.18325i	−0.806214	−	0.591624i	$-0.798487\pi$
$827$		−	28140.7i		−	1.18325i	0.806214	−	0.591624i	$-0.201513\pi$
$828$		0			0
$829$			13305.9i			0.557460i	0.960370	+	0.278730i	$0.0899134\pi$
$829$			13305.9i			0.557460i	−0.960370	+	0.278730i	$0.910087\pi$
$830$		0			0
$831$	−29397.5	+	19697.4i	−1.22718	+	0.822256i
$832$		0			0
$833$	15664.4	+	14630.3i	0.651547	+	0.608536i
$834$		0			0
$835$	4871.52	−	8437.73i	0.201899	−	0.349700i
$836$		0			0
$837$	−2788.40	−	3154.99i	−0.115151	−	0.130290i
$838$		0			0
$839$	8913.20	−	15438.1i	0.366767	−	0.635260i	−0.622291	−	0.782786i	$-0.713798\pi$
$839$	8913.20	−	15438.1i	0.366767	−	0.635260i	0.989058	+	0.147526i	$0.0471311\pi$
$840$		0			0
$841$	−3120.61	−	5405.06i	−0.127952	−	0.221619i
$842$		0			0
$843$	9922.47	+	14808.9i	0.405395	+	0.605035i
$844$		0			0
$845$	−1740.16			−0.0708442
$846$		0			0
$847$	954.409	+	6403.33i	0.0387177	+	0.259765i
$848$		0			0
$849$	1647.35	−	110.095i	0.0665924	−	0.00445048i
$850$		0			0
$851$	−2380.14	+	1374.17i	−0.0958754	+	0.0553537i
$852$		0			0
$853$	−35437.7	−	20459.9i	−1.42247	−	0.821261i	−0.425956	−	0.904744i	$-0.640062\pi$
$853$	−35437.7	−	20459.9i	−1.42247	−	0.821261i	−0.996509	+	0.0834834i	$0.973395\pi$
$854$		0			0
$855$	−34288.1	−	14099.7i	−1.37150	−	0.563975i
$856$		0			0
$857$	14081.4	−	24389.8i	0.561275	−	0.972157i	−0.436110	−	0.899893i	$-0.643644\pi$
$857$	14081.4	−	24389.8i	0.561275	−	0.972157i	0.997386	−	0.0722641i	$-0.0230225\pi$
$858$		0			0
$859$	−3110.46	+	1795.83i	−0.123548	+	0.0713304i	−0.560500	−	0.828154i	$-0.689391\pi$
$859$	−3110.46	+	1795.83i	−0.123548	+	0.0713304i	0.436952	+	0.899485i	$0.356058\pi$
$860$		0			0
$861$	2326.00	−	7288.74i	0.0920673	−	0.288501i
$862$		0			0
$863$			18091.2i			0.713593i	0.934182	+	0.356796i	$0.116131\pi$
$863$			18091.2i			0.713593i	−0.934182	+	0.356796i	$0.883869\pi$
$864$		0			0
$865$	−10118.8			−0.397747
$866$		0			0
$867$	−4700.55	−	2310.57i	−0.184128	−	0.0905085i
$868$		0			0
$869$	24779.9	−	14306.7i	0.967319	−	0.558482i
$870$		0			0
$871$	−11766.6	−	6793.43i	−0.457744	−	0.264279i
$872$		0			0
$873$	−841.296	−	6266.03i	−0.0326158	−	0.242925i
$874$		0			0
$875$	−25502.5	−	10057.3i	−0.985306	−	0.388570i
$876$		0			0
$877$	−23215.3	−	40210.1i	−0.893871	−	1.54823i	−0.835195	−	0.549954i	$-0.814645\pi$
$877$	−23215.3	−	40210.1i	−0.893871	−	1.54823i	−0.0586762	−	0.998277i	$-0.518688\pi$
$878$		0			0
$879$	−2565.30	−	38384.5i	−0.0984362	−	1.47290i
$880$		0			0
$881$	5007.33			0.191488			0.0957441	−	0.995406i	$-0.469477\pi$
$881$	5007.33			0.191488			0.0957441	+	0.995406i	$0.469477\pi$
$882$		0			0
$883$	−49999.0			−1.90555			−0.952775	−	0.303677i	$-0.901786\pi$
$883$	−49999.0			−1.90555			−0.952775	+	0.303677i	$0.901786\pi$
$884$		0			0
$885$	−7079.20	+	4743.32i	−0.268887	+	0.180164i
$886$		0			0
$887$	1730.41	+	2997.16i	0.0655034	+	0.113455i	0.896917	−	0.442199i	$-0.145801\pi$
$887$	1730.41	+	2997.16i	0.0655034	+	0.113455i	−0.831414	+	0.555654i	$0.812468\pi$
$888$		0			0
$889$	17498.1	+	6900.64i	0.660143	+	0.260337i
$890$		0			0
$891$	−16065.8	+	16231.5i	−0.604069	+	0.610299i
$892$		0			0
$893$	−39432.3	−	22766.3i	−1.47766	−	0.853129i
$894$		0			0
$895$	−33456.9	+	19316.3i	−1.24954	+	0.721423i
$896$		0			0
$897$	13200.8	−	8845.01i	0.491374	−	0.329238i
$898$		0			0
$899$	4043.06			0.149993
$900$		0			0
$901$		−	4056.38i		−	0.149986i
$902$		0			0
$903$	−30361.0	+	6620.29i	−1.11888	+	0.243975i
$904$		0			0
$905$	−13781.2	+	7956.58i	−0.506191	+	0.292249i
$906$		0			0
$907$	14546.9	−	25196.0i	0.532550	−	0.922404i	−0.466727	−	0.884401i	$-0.654567\pi$
$907$	14546.9	−	25196.0i	0.532550	−	0.922404i	0.999278	−	0.0380031i	$-0.0120997\pi$
$908$		0			0
$909$	50206.8	−	6740.91i	1.83196	−	0.245965i
$910$		0			0
$911$	28776.2	+	16613.9i	1.04654	+	0.604220i	0.921679	−	0.387954i	$-0.126818\pi$
$911$	28776.2	+	16613.9i	1.04654	+	0.604220i	0.124861	+	0.992174i	$0.460151\pi$
$912$		0			0
$913$	−19118.9	+	11038.3i	−0.693038	+	0.400126i
$914$		0			0
$915$	−13496.6	+	27457.1i	−0.487632	+	0.992025i
$916$		0			0
$917$	7392.44	+	49597.5i	0.266216	+	1.78610i
$918$		0			0
$919$	−11642.5			−0.417902			−0.208951	−	0.977926i	$-0.567005\pi$
$919$	−11642.5			−0.417902			−0.208951	+	0.977926i	$0.567005\pi$
$920$		0			0
$921$	22217.9	−	45199.5i	0.794901	−	1.61713i
$922$		0			0
$923$	16193.9	+	28048.6i	0.577495	+	1.00025i
$924$		0			0
$925$	370.316	−	641.407i	0.0131632	−	0.0227993i
$926$		0			0
$927$	−15123.7	−	6219.06i	−0.535845	−	0.220346i
$928$		0			0
$929$	19057.0	−	33007.6i	0.673024	−	1.16571i	−0.304019	−	0.952666i	$-0.598329\pi$
$929$	19057.0	−	33007.6i	0.673024	−	1.16571i	0.977042	−	0.213045i	$-0.0683381\pi$
$930$		0			0
$931$	−31121.5	+	33321.1i	−1.09556	+	1.17299i
$932$		0			0
$933$	−2742.29	−	41032.9i	−0.0962258	−	1.43982i
$934$		0			0
$935$			20222.2i			0.707312i
$936$		0			0
$937$			22454.2i			0.782869i	0.920206	+	0.391435i	$0.128021\pi$
$937$			22454.2i			0.782869i	−0.920206	+	0.391435i	$0.871979\pi$
$938$		0			0
$939$	15513.1	+	23152.6i	0.539137	+	0.804639i
$940$		0			0
$941$	6159.92	+	10669.3i	0.213398	+	0.369616i	0.952776	−	0.303675i	$-0.0982135\pi$
$941$	6159.92	+	10669.3i	0.213398	+	0.369616i	−0.739378	+	0.673291i	$0.764880\pi$
$942$		0			0
$943$	−4674.84	−	2699.02i	−0.161436	−	0.0932049i
$944$		0			0
$945$	25229.6	−	9156.85i	0.868485	−	0.315209i
$946$		0			0
$947$	13396.5	+	7734.46i	0.459691	+	0.265403i	0.711914	−	0.702266i	$-0.247828\pi$
$947$	13396.5	+	7734.46i	0.459691	+	0.265403i	−0.252223	+	0.967669i	$0.581162\pi$
$948$		0			0
$949$	12581.9	+	21792.4i	0.430374	+	0.745429i
$950$		0			0
$951$	12495.2	+	18648.6i	0.426062	+	0.635880i
$952$		0			0
$953$			5267.67i			0.179052i	0.995984	+	0.0895260i	$0.0285352\pi$
$953$			5267.67i			0.179052i	−0.995984	+	0.0895260i	$0.971465\pi$
$954$		0			0
$955$		−	7749.10i		−	0.262571i
$956$		0			0
$957$	−1462.31	−	21880.4i	−0.0493936	−	0.739075i
$958$		0			0
$959$	36111.6	+	45435.2i	1.21596	+	1.52991i
$960$		0			0
$961$	−14445.1	+	25019.7i	−0.484882	+	0.839841i
$962$		0			0
$963$	27783.9	−	21432.8i	0.929723	−	0.717198i
$964$		0			0
$965$	−20928.3	+	36248.9i	−0.698141	+	1.20922i
$966$		0			0
$967$	6237.09	+	10803.0i	0.207416	+	0.359255i	0.950900	−	0.309499i	$-0.100161\pi$
$967$	6237.09	+	10803.0i	0.207416	+	0.359255i	−0.743484	+	0.668754i	$0.766828\pi$
$968$		0			0
$969$	−19040.7	+	38735.9i	−0.631245	+	1.28419i
$970$		0			0
$971$	−57914.6			−1.91407			−0.957037	−	0.289964i	$-0.906357\pi$
$971$	−57914.6			−1.91407			−0.957037	+	0.289964i	$0.906357\pi$
$972$		0			0
$973$	−1831.46	+	272.977i	−0.0603433	+	0.00899409i
$974$		0			0
$975$	−1889.01	+	3842.94i	−0.0620478	+	0.126228i
$976$		0			0
$977$	15954.7	−	9211.48i	0.522454	−	0.301639i	−0.215484	−	0.976507i	$-0.569133\pi$
$977$	15954.7	−	9211.48i	0.522454	−	0.301639i	0.737938	+	0.674868i	$0.235800\pi$
$978$		0			0
$979$	18995.1	+	10966.8i	0.620108	+	0.358020i
$980$		0			0
$981$	34289.6	+	44450.6i	1.11599	+	1.44668i
$982$		0			0
$983$	−4293.70	+	7436.90i	−0.139316	+	0.241302i	−0.927238	−	0.374473i	$-0.877824\pi$
$983$	−4293.70	+	7436.90i	−0.139316	+	0.241302i	0.787922	+	0.615775i	$0.211157\pi$
$984$		0			0
$985$	7224.90	−	4171.30i	0.233710	−	0.134933i
$986$		0			0
$987$	32206.8	−	7022.77i	1.03866	−	0.226481i
$988$		0			0
$989$			21924.4i			0.704909i
$990$		0			0
$991$	−17639.5			−0.565426			−0.282713	−	0.959205i	$-0.591234\pi$
$991$	−17639.5			−0.565426			−0.282713	+	0.959205i	$0.591234\pi$
$992$		0			0
$993$	3209.19	−	2150.27i	0.102558	−	0.0687177i
$994$		0			0
$995$	−39237.1	+	22653.6i	−1.25015	+	0.721776i
$996$		0			0
$997$	4180.85	+	2413.82i	0.132807	+	0.0766764i	0.564932	−	0.825138i	$-0.308903\pi$
$997$	4180.85	+	2413.82i	0.132807	+	0.0766764i	−0.432124	+	0.901814i	$0.642236\pi$
$998$		0			0
$999$	1129.32	+	5565.46i	0.0357658	+	0.176260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.209.21	yes	48
3.2	odd	2		756.4.x.a.629.7		48
7.6	odd	2	inner	252.4.x.a.209.4	yes	48
9.2	odd	6		2268.4.f.a.1133.36		48
9.4	even	3		756.4.x.a.125.18		48
9.5	odd	6	inner	252.4.x.a.41.4	✓	48
9.7	even	3		2268.4.f.a.1133.13		48
21.20	even	2		756.4.x.a.629.18		48
63.13	odd	6		756.4.x.a.125.7		48
63.20	even	6		2268.4.f.a.1133.14		48
63.34	odd	6		2268.4.f.a.1133.35		48
63.41	even	6	inner	252.4.x.a.41.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.4	✓	48	9.5	odd	6	inner
252.4.x.a.41.21	yes	48	63.41	even	6	inner
252.4.x.a.209.4	yes	48	7.6	odd	2	inner
252.4.x.a.209.21	yes	48	1.1	even	1	trivial
756.4.x.a.125.7		48	63.13	odd	6
756.4.x.a.125.18		48	9.4	even	3
756.4.x.a.629.7		48	3.2	odd	2
756.4.x.a.629.18		48	21.20	even	2
2268.4.f.a.1133.13		48	9.7	even	3
2268.4.f.a.1133.14		48	63.20	even	6
2268.4.f.a.1133.35		48	63.34	odd	6
2268.4.f.a.1133.36		48	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.66323 + 2.29222i) q^{3} +(5.16485 + 8.94579i) q^{5} +(-17.2289 - 6.79448i) q^{7} +(16.4915 + 21.3783i) q^{9} +O(q^{10})\)	\(q+(4.66323 + 2.29222i) q^{3} +(5.16485 + 8.94579i) q^{5} +(-17.2289 - 6.79448i) q^{7} +(16.4915 + 21.3783i) q^{9} +(27.1307 + 15.6639i) q^{11} +(-39.0052 + 22.5196i) q^{13} +(3.57919 + 53.5552i) q^{15} +62.4900 q^{17} +132.928i q^{19} +(-64.7679 - 71.1767i) q^{21} +(-58.8009 + 33.9487i) q^{23} +(9.14862 - 15.8459i) q^{25} +(27.8997 + 137.494i) q^{27} +(-116.665 - 67.3568i) q^{29} +(-25.9914 + 15.0061i) q^{31} +(90.6116 + 135.234i) q^{33} +(-28.2028 - 189.219i) q^{35} +40.4778 q^{37} +(-233.510 + 15.6059i) q^{39} +(39.7514 + 68.8515i) q^{41} +(161.452 - 279.643i) q^{43} +(-106.070 + 257.945i) q^{45} +(-171.268 + 296.644i) q^{47} +(250.670 + 234.123i) q^{49} +(291.405 + 143.241i) q^{51} -64.9125i q^{53} +323.607i q^{55} +(-304.700 + 619.874i) q^{57} +(79.3800 + 137.490i) q^{59} +(493.640 + 285.003i) q^{61} +(-138.875 - 480.376i) q^{63} +(-402.912 - 232.621i) q^{65} +(150.833 + 261.251i) q^{67} +(-352.020 + 23.5261i) q^{69} -719.100i q^{71} -558.706i q^{73} +(78.9843 - 52.9223i) q^{75} +(-361.004 - 454.211i) q^{77} +(456.676 - 790.986i) q^{79} +(-185.064 + 705.119i) q^{81} +(-352.348 + 610.285i) q^{83} +(322.751 + 559.022i) q^{85} +(-389.641 - 581.524i) q^{87} +700.133 q^{89} +(825.026 - 122.969i) q^{91} +(-155.601 + 10.3991i) q^{93} +(-1189.15 + 686.554i) q^{95} +(-202.787 - 117.079i) q^{97} +(112.557 + 838.329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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