LMFDB - Embedded newform 252.4.x.a.41.21

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			41.21
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.21

$q$-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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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	−0.537100	−	0.843518i	$-0.680480\pi$
$5$	5.16485	−	8.94579i	0.461958	−	0.800135i	0.999059	+	0.0433831i	$0.0138136\pi$
$6$		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	−0.0797412	−	0.996816i	$-0.525409\pi$
$11$	27.1307	−	15.6639i	0.743656	−	0.429350i	0.823397	+	0.567466i	$0.192076\pi$
$12$		0			0
$13$	−39.0052	−	22.5196i	−0.832161	−	0.480448i	0.0224312	−	0.999748i	$-0.492859\pi$
$13$	−39.0052	−	22.5196i	−0.832161	−	0.480448i	−0.854592	+	0.519300i	$0.826193\pi$
$14$		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	$-0.703492\pi$
$19$		−	132.928i		−	1.60504i	0.596624	−	0.802521i	$-0.296508\pi$
$20$		0			0
$21$	−64.7679	+	71.1767i	−0.673025	+	0.739620i
$22$		0			0
$23$	−58.8009	−	33.9487i	−0.533080	−	0.307774i	0.209190	−	0.977875i	$-0.432917\pi$
$23$	−58.8009	−	33.9487i	−0.533080	−	0.307774i	−0.742270	+	0.670101i	$0.766251\pi$
$24$		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	−0.824624	−	0.565681i	$-0.808613\pi$
$29$	−116.665	+	67.3568i	−0.747043	+	0.431305i	0.0775817	+	0.996986i	$0.475280\pi$
$30$		0			0
$31$	−25.9914	−	15.0061i	−0.150587	−	0.0869413i	0.422813	−	0.906217i	$-0.361043\pi$
$31$	−25.9914	−	15.0061i	−0.150587	−	0.0869413i	−0.573400	+	0.819275i	$0.694376\pi$
$32$		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	−0.780331	−	0.625367i	$-0.784949\pi$
$41$	39.7514	−	68.8515i	0.151418	−	0.262263i	0.931749	+	0.363103i	$0.118283\pi$
$42$		0			0
$43$	161.452	+	279.643i	0.572586	+	0.991749i	0.996299	+	0.0859521i	$0.0273932\pi$
$43$	161.452	+	279.643i	0.572586	+	0.991749i	−0.423713	+	0.905797i	$0.639273\pi$
$44$		0			0
$45$	−106.070	−	257.945i	−0.351377	−	0.854492i
$46$		0			0
$47$	−171.268	−	296.644i	−0.531531	−	0.920638i	−0.999323	−	0.0367994i	$-0.988284\pi$
$47$	−171.268	−	296.644i	−0.531531	−	0.920638i	0.467792	−	0.883839i	$-0.345050\pi$
$48$		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	$0.0268070\pi$
$53$			64.9125i			0.168234i	−0.996456	+	0.0841172i	$0.973193\pi$
$54$		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	−0.765057	−	0.643962i	$-0.777289\pi$
$59$	79.3800	−	137.490i	0.175159	−	0.303385i	0.940216	+	0.340578i	$0.110623\pi$
$60$		0			0
$61$	493.640	−	285.003i	1.03613	−	0.598212i	0.117397	−	0.993085i	$-0.462545\pi$
$61$	493.640	−	285.003i	1.03613	−	0.598212i	0.918736	+	0.394873i	$0.129212\pi$
$62$		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	−0.695110	−	0.718903i	$-0.744644\pi$
$67$	150.833	−	261.251i	0.275033	−	0.476372i	0.970144	+	0.242531i	$0.0779778\pi$
$68$		0			0
$69$	−352.020	−	23.5261i	−0.614178	−	0.0410465i
$70$		0			0
$71$			719.100i			1.20199i	0.799252	+	0.600996i	$0.205229\pi$
$71$			719.100i			1.20199i	−0.799252	+	0.600996i	$0.794771\pi$
$72$		0			0
$73$			558.706i			0.895775i	0.894090	+	0.447888i	$0.147824\pi$
$73$			558.706i			0.895775i	−0.894090	+	0.447888i	$0.852176\pi$
$74$		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	0.983031	+	0.183442i	$0.0587239\pi$
$79$	456.676	+	790.986i	0.650381	+	1.12649i	−0.332650	+	0.943050i	$0.607943\pi$
$80$		0			0
$81$	−185.064	−	705.119i	−0.253860	−	0.967241i
$82$		0			0
$83$	−352.348	−	610.285i	−0.465967	−	0.807078i	0.533278	−	0.845940i	$-0.320960\pi$
$83$	−352.348	−	610.285i	−0.465967	−	0.807078i	−0.999245	+	0.0388620i	$0.987627\pi$
$84$		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	−0.602364	−	0.798221i	$-0.705775\pi$
$97$	−202.787	+	117.079i	−0.212267	+	0.122552i	0.390098	+	0.920773i	$0.372441\pi$
$98$		0			0
$99$	112.557	−	838.329i	0.114266	−	0.851063i
$100$		0			0
$101$	938.098	+	1624.83i	0.924200	+	1.60076i	0.792843	+	0.609427i	$0.208600\pi$
$101$	938.098	+	1624.83i	0.924200	+	1.60076i	0.131358	+	0.991335i	$0.458066\pi$
$102$		0			0
$103$	−524.507	−	302.824i	−0.501759	−	0.289691i	0.227681	−	0.973736i	$-0.426886\pi$
$103$	−524.507	−	302.824i	−0.501759	−	0.289691i	−0.729440	+	0.684045i	$0.760219\pi$
$104$		0			0
$105$	302.214	+	947.017i	0.280887	+	0.880184i
$106$		0			0
$107$			1299.63i			1.17420i	0.809513	+	0.587102i	$0.199731\pi$
$107$			1299.63i			1.17420i	−0.809513	+	0.587102i	$0.800269\pi$
$108$		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	0.879742	−	0.475451i	$-0.157715\pi$
$113$	1090.53	+	629.616i	0.907860	+	0.524153i	0.0281181	+	0.999605i	$0.491049\pi$
$114$		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	−0.0792242	+	0.996857i	$0.525244\pi$
$131$	−1353.80	+	2344.85i	−0.902915	+	1.56390i	−0.823691	+	0.567039i	$0.808089\pi$
$132$		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	−0.739915	+	0.672700i	$0.765134\pi$
$137$	−2713.91	+	1566.88i	−1.69245	+	0.977135i	−0.952533	+	0.304435i	$0.901532\pi$
$138$		0			0
$139$	86.5871	+	49.9911i	0.0528361	+	0.0305049i	0.526185	−	0.850370i	$-0.323622\pi$
$139$	86.5871	+	49.9911i	0.0528361	+	0.0305049i	−0.473349	+	0.880875i	$0.656955\pi$
$140$		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	0.971842	−	0.235634i	$-0.0757167\pi$
$149$	2280.20	+	1316.47i	1.25370	+	0.723823i	0.281856	+	0.959457i	$0.409050\pi$
$150$		0			0
$151$	−944.432	−	1635.80i	−0.508985	−	0.881588i	−0.999946	−	0.0104066i	$-0.996687\pi$
$151$	−944.432	−	1635.80i	−0.508985	−	0.881588i	0.490961	−	0.871182i	$-0.336646\pi$
$152$		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	0.754935	−	0.655800i	$-0.227669\pi$
$157$	1110.41	+	641.097i	0.564462	+	0.325892i	−0.190472	+	0.981693i	$0.561002\pi$
$158$		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	−0.954357	−	0.298667i	$-0.903458\pi$
$167$	−471.603	+	816.841i	−0.218526	+	0.378497i	0.735832	+	0.677164i	$0.236791\pi$
$168$		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	0.738100	−	0.674692i	$-0.235723\pi$
$173$	−489.793	−	848.347i	−0.215250	−	0.372824i	−0.953350	+	0.301867i	$0.902390\pi$
$174$		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	$-0.714796\pi$
$179$		−	3739.96i		−	1.56166i	0.624742	−	0.780831i	$-0.285204\pi$
$180$		0			0
$181$		−	1540.52i		−	0.632631i	−0.948654	−	0.316316i	$-0.897554\pi$
$181$		−	1540.52i		−	0.632631i	0.948654	−	0.316316i	$-0.102446\pi$
$182$		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	−0.617986	−	0.786189i	$-0.712051\pi$
$191$	−649.672	+	375.088i	−0.246118	+	0.142097i	0.371867	+	0.928286i	$0.378718\pi$
$192$		0			0
$193$	2026.03	−	3509.19i	0.755632	−	1.30879i	−0.189428	−	0.981895i	$-0.560663\pi$
$193$	2026.03	−	3509.19i	0.755632	−	1.30879i	0.945060	−	0.326898i	$-0.106003\pi$
$194$		0			0
$195$	−1345.65	+	2008.33i	−0.494175	+	0.737536i
$196$		0			0
$197$			807.631i			0.292088i	0.989278	+	0.146044i	$0.0466541\pi$
$197$			807.631i			0.292088i	−0.989278	+	0.146044i	$0.953346\pi$
$198$		0			0
$199$		−	4386.10i		−	1.56243i	−0.624265	−	0.781213i	$-0.714601\pi$
$199$		−	4386.10i		−	1.56243i	0.624265	−	0.781213i	$-0.285399\pi$
$200$		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	0.274095	+	0.961702i	$0.411622\pi$
$211$	−2132.63	+	3693.82i	−0.695811	+	1.20518i	−0.969907	+	0.243478i	$0.921712\pi$
$212$		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	−0.741870	−	0.670544i	$-0.766061\pi$
$223$	−1771.94	+	1023.03i	−0.532097	+	0.307206i	0.209773	+	0.977750i	$0.432727\pi$
$224$		0			0
$225$	489.632	+	65.7394i	0.145076	+	0.0194784i
$226$		0			0
$227$	−2797.06	−	4844.65i	−0.817830	−	1.41652i	−0.907278	−	0.420532i	$-0.861843\pi$
$227$	−2797.06	−	4844.65i	−0.817830	−	1.41652i	0.0894471	−	0.995992i	$-0.471490\pi$
$228$		0			0
$229$	−318.820	−	184.071i	−0.0920009	−	0.0531168i	0.453294	−	0.891361i	$-0.350249\pi$
$229$	−318.820	−	184.071i	−0.0920009	−	0.0531168i	−0.545295	+	0.838244i	$0.683582\pi$
$230$		0			0
$231$	−642.293	+	2945.59i	−0.182943	+	0.838986i
$232$		0			0
$233$			3900.42i			1.09667i	0.836258	+	0.548336i	$0.184739\pi$
$233$			3900.42i			1.09667i	−0.836258	+	0.548336i	$0.815261\pi$
$234$		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	0.150783	−	0.988567i	$-0.451820\pi$
$239$	−2327.57	−	1343.82i	−0.629949	−	0.363701i	−0.780732	+	0.624866i	$0.785154\pi$
$240$		0			0
$241$	2125.83	−	1227.35i	0.568203	−	0.328052i	−0.188228	−	0.982125i	$-0.560274\pi$
$241$	2125.83	−	1227.35i	0.568203	−	0.328052i	0.756431	+	0.654073i	$0.226941\pi$
$242$		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	−0.980118	−	0.198415i	$-0.936421\pi$
$257$	−1311.10	+	2270.89i	−0.318227	+	0.551185i	0.661892	+	0.749600i	$0.269754\pi$
$258$		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	0.450447	−	0.892803i	$-0.351265\pi$
$263$	6179.60	−	3567.79i	1.44886	−	0.836500i	0.998414	+	0.0563032i	$0.0179313\pi$
$264$		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	$-0.984069\pi$
$271$		−	446.364i		−	0.100054i	0.998748	−	0.0500271i	$-0.0159308\pi$
$272$		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	−0.953129	−	0.302565i	$-0.902157\pi$
$277$	−3405.06	−	5897.74i	−0.738593	−	1.27928i	0.214535	−	0.976716i	$-0.431176\pi$
$278$		0			0
$279$	−749.441	+	308.179i	−0.160817	+	0.0661297i
$280$		0			0
$281$	2970.96	−	1715.29i	0.630722	−	0.364147i	−0.150310	−	0.988639i	$-0.548027\pi$
$281$	2970.96	−	1715.29i	0.630722	−	0.364147i	0.781031	+	0.624492i	$0.214694\pi$
$282$		0			0
$283$	275.171	+	158.870i	0.0577993	+	0.0333705i	0.528621	−	0.848858i	$-0.322709\pi$
$283$	275.171	+	158.870i	0.0577993	+	0.0333705i	−0.470822	+	0.882228i	$0.656043\pi$
$284$		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	0.215262	+	0.976556i	$0.430939\pi$
$293$	−3701.79	+	6411.69i	−0.738091	+	1.27841i	−0.953354	+	0.301856i	$0.902394\pi$
$294$		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	$0.357141\pi$
$307$			9692.73i			1.80193i	−0.433888	+	0.900967i	$0.642859\pi$
$308$		0			0
$309$	−3140.03	−	209.854i	−0.578092	−	0.0386348i
$310$		0			0
$311$	−3957.20	+	6854.07i	−0.721518	+	1.24971i	0.238873	+	0.971051i	$0.423222\pi$
$311$	−3957.20	+	6854.07i	−0.721518	+	1.24971i	−0.960391	+	0.278655i	$0.910111\pi$
$312$		0			0
$313$	4644.88	−	2681.72i	0.838799	−	0.484281i	−0.0180566	−	0.999837i	$-0.505748\pi$
$313$	4644.88	−	2681.72i	0.838799	−	0.484281i	0.856856	+	0.515556i	$0.172415\pi$
$314$		0			0
$315$	3580.07	+	3723.42i	0.640362	+	0.666002i
$316$		0			0
$317$	3741.29	−	2160.03i	0.662876	−	0.382712i	−0.130496	−	0.991449i	$-0.541657\pi$
$317$	3741.29	−	2160.03i	0.662876	−	0.382712i	0.793372	+	0.608737i	$0.208324\pi$
$318$		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	0.895237	−	0.445590i	$-0.147006\pi$
$331$	371.714	+	643.828i	0.0617259	+	0.106912i	−0.833511	+	0.552503i	$0.813673\pi$
$332$		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	−0.139338	−	0.990245i	$-0.544497\pi$
$337$	4874.39	−	8442.69i	0.787908	−	1.36470i	0.927246	−	0.374452i	$-0.122169\pi$
$338$		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	0.253857	−	0.967242i	$-0.418301\pi$
$347$	−2953.16	−	1705.01i	−0.456870	−	0.263774i	−0.710727	+	0.703468i	$0.751634\pi$
$348$		0			0
$349$	−8157.38	+	4709.67i	−1.25116	+	0.722357i	−0.971340	−	0.237695i	$-0.923608\pi$
$349$	−8157.38	+	4709.67i	−1.25116	+	0.722357i	−0.279820	+	0.960053i	$0.590275\pi$
$350$		0			0
$351$	−4184.55	+	4734.69i	−0.636338	+	0.719997i
$352$		0			0
$353$	−1363.14	−	2361.03i	−0.205532	−	0.355992i	0.744770	−	0.667321i	$-0.232559\pi$
$353$	−1363.14	−	2361.03i	−0.205532	−	0.355992i	−0.950302	+	0.311329i	$0.899226\pi$
$354$		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	$-0.770574\pi$
$359$		−	8978.19i		−	1.31992i	0.751302	−	0.659959i	$-0.229426\pi$
$360$		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	−0.889643	−	0.456657i	$-0.849047\pi$
$367$	−6601.74	+	3811.52i	−0.938987	+	0.542124i	−0.0493444	+	0.998782i	$0.515713\pi$
$368$		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	−0.939904	−	0.341438i	$-0.889086\pi$
$373$	−1255.32	+	2174.28i	−0.174258	+	0.301823i	0.765646	+	0.643262i	$0.222419\pi$
$374$		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	0.0685562	+	0.997647i	$0.478161\pi$
$383$	−6219.05	+	10771.7i	−0.829710	+	1.43710i	−0.898266	+	0.439452i	$0.855173\pi$
$384$		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	−0.659377	−	0.751813i	$-0.729180\pi$
$389$	−2593.05	+	1497.10i	−0.337976	+	0.195131i	0.321400	+	0.946943i	$0.395846\pi$
$390$		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	$-0.930957\pi$
$397$		−	3404.67i		−	0.430417i	0.976568	−	0.215208i	$-0.0690430\pi$
$398$		0			0
$399$	9461.38	+	8609.48i	1.18712	+	1.08023i
$400$		0			0
$401$	2674.32	+	1544.02i	0.333040	+	0.192281i	0.657190	−	0.753725i	$-0.271745\pi$
$401$	2674.32	+	1544.02i	0.333040	+	0.192281i	−0.324150	+	0.946006i	$0.605078\pi$
$402$		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	0.930617	−	0.365995i	$-0.119271\pi$
$409$	8924.66	+	5152.66i	1.07896	+	0.622940i	0.148347	+	0.988935i	$0.452605\pi$
$410$		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	−0.309701	−	0.950834i	$-0.600229\pi$
$419$	5734.36	−	9932.20i	0.668596	−	1.15804i	0.978297	−	0.207208i	$-0.0664378\pi$
$420$		0			0
$421$	−3002.26	−	5200.07i	−0.347557	−	0.601986i	0.638258	−	0.769822i	$-0.279655\pi$
$421$	−3002.26	−	5200.07i	−0.347557	−	0.601986i	−0.985815	+	0.167837i	$0.946322\pi$
$422$		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	$-0.846241\pi$
$431$		−	8312.17i		−	0.928963i	0.885583	−	0.464481i	$-0.153759\pi$
$432$		0			0
$433$		−	4419.65i		−	0.490519i	−0.969458	−	0.245259i	$-0.921127\pi$
$433$		−	4419.65i		−	0.490519i	0.969458	−	0.245259i	$-0.0788731\pi$
$434$		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	0.523918	−	0.851769i	$-0.324470\pi$
$439$	14013.5	−	8090.72i	1.52353	−	0.879610i	0.999612	−	0.0278416i	$-0.00886340\pi$
$440$		0			0
$441$	−871.235	−	9219.93i	−0.0940757	−	0.995565i
$442$		0			0
$443$	2983.47	−	1722.51i	0.319976	−	0.184738i	−0.331406	−	0.943488i	$-0.607523\pi$
$443$	2983.47	−	1722.51i	0.319976	−	0.184738i	0.651382	+	0.758750i	$0.274190\pi$
$444$		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	$0.0562634\pi$
$449$			3345.89i			0.351675i	−0.984419	+	0.175838i	$0.943737\pi$
$450$		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	0.973420	−	0.229025i	$-0.0735539\pi$
$457$	2817.23	+	4879.58i	0.288368	+	0.499469i	−0.685052	+	0.728494i	$0.740221\pi$
$458$		0			0
$459$	1743.45	−	8592.00i	0.177292	−	0.873726i
$460$		0			0
$461$	−8810.53	−	15260.3i	−0.890124	−	1.54174i	−0.839726	−	0.543011i	$-0.817284\pi$
$461$	−8810.53	−	15260.3i	−0.890124	−	1.54174i	−0.0503981	−	0.998729i	$-0.516049\pi$
$462$		0			0
$463$	1050.86	−	1820.15i	0.105481	−	0.182699i	−0.808454	−	0.588560i	$-0.799695\pi$
$463$	1050.86	−	1820.15i	0.105481	−	0.182699i	0.913935	+	0.405861i	$0.133028\pi$
$464$		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	0.803513	−	0.595287i	$-0.202961\pi$
$479$	−1192.77	−	2065.94i	−0.113777	−	0.197067i	−0.917290	+	0.398220i	$0.869628\pi$
$480$		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	−0.958899	−	0.283748i	$-0.908422\pi$
$491$	−18322.5	−	10578.5i	−1.68408	−	0.972305i	−0.725183	−	0.688556i	$-0.758245\pi$
$492$		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	−0.523933	−	0.851760i	$-0.675536\pi$
$499$	5302.31	−	9183.86i	0.475679	−	0.823900i	0.999612	+	0.0278593i	$0.00886904\pi$
$500$		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	0.450135	+	0.892961i	$0.351376\pi$
$509$	−6295.97	+	10904.9i	−0.548259	+	0.949613i	−0.998394	+	0.0566522i	$0.981957\pi$
$510$		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	$-0.952904\pi$
$523$		−	3526.37i		−	0.294833i	0.989075	−	0.147416i	$-0.0470957\pi$
$524$		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	0.990732	+	0.135833i	$0.0433710\pi$
$547$	7842.27	+	13583.2i	0.613001	+	1.06175i	−0.377731	+	0.925915i	$0.623296\pi$
$548$		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	$0.295234\pi$
$557$			21036.4i			1.60025i	−0.599833	+	0.800126i	$0.704766\pi$
$558$		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	−0.999594	−	0.0284899i	$-0.990930\pi$
$563$	−6347.02	+	10993.4i	−0.475124	+	0.822939i	0.524470	+	0.851429i	$0.324264\pi$
$564$		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	−0.951456	−	0.307783i	$-0.900413\pi$
$569$	−15753.0	+	9095.03i	−1.16064	+	0.670094i	−0.209180	+	0.977877i	$0.567079\pi$
$570$		0			0
$571$	−10146.0	+	17573.3i	−0.743599	+	1.28795i	0.207247	+	0.978289i	$0.433550\pi$
$571$	−10146.0	+	17573.3i	−0.743599	+	1.28795i	−0.950846	+	0.309663i	$0.899784\pi$
$572$		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	$-0.852938\pi$
$577$		−	12356.1i		−	0.891494i	0.895159	−	0.445747i	$-0.147062\pi$
$578$		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	0.811179	−	0.584798i	$-0.198826\pi$
$587$	−1434.42	−	2484.50i	−0.100860	−	0.174695i	−0.912039	+	0.410103i	$0.865493\pi$
$588$		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	0.989926	−	0.141584i	$-0.0452195\pi$
$599$	19971.2	+	11530.4i	1.36227	+	0.786509i	0.372348	+	0.928093i	$0.378553\pi$
$600$		0			0
$601$	−10827.8	+	6251.41i	−0.734897	+	0.424293i	−0.820211	−	0.572061i	$-0.806144\pi$
$601$	−10827.8	+	6251.41i	−0.734897	+	0.424293i	0.0853138	+	0.996354i	$0.472811\pi$
$602$		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	0.705260	−	0.708949i	$-0.250830\pi$
$607$	6638.81	+	3832.92i	0.443923	+	0.256299i	−0.261338	+	0.965247i	$0.584164\pi$
$608$		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	−0.0396720	−	0.999213i	$-0.512631\pi$
$617$	−14174.2	−	8183.50i	−0.924852	−	0.533963i	−0.885180	+	0.465249i	$0.845965\pi$
$618$		0			0
$619$	6056.80	−	3496.90i	0.393285	−	0.227063i	−0.290298	−	0.956936i	$-0.593754\pi$
$619$	6056.80	−	3496.90i	0.393285	−	0.227063i	0.683583	+	0.729873i	$0.260421\pi$
$620$		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	−0.576855	−	0.816846i	$-0.695720\pi$
$641$	−2562.09	+	1479.23i	−0.157873	+	0.0911481i	0.418982	+	0.907994i	$0.362387\pi$
$642$		0			0
$643$	−11590.6	−	6691.85i	−0.710870	−	0.410421i	0.100513	−	0.994936i	$-0.467952\pi$
$643$	−11590.6	−	6691.85i	−0.710870	−	0.410421i	−0.811383	+	0.584515i	$0.801285\pi$
$644$		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	0.0365814	−	0.999331i	$-0.488353\pi$
$653$	−13525.8	−	7809.11i	−0.810574	−	0.467985i	−0.847155	+	0.531346i	$0.821687\pi$
$654$		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	−0.662778	−	0.748816i	$-0.730623\pi$
$659$	−5847.81	+	3376.24i	−0.345673	+	0.199574i	0.317105	+	0.948390i	$0.397289\pi$
$660$		0			0
$661$	−8658.65	−	4999.07i	−0.509504	−	0.294162i	0.223126	−	0.974790i	$-0.428374\pi$
$661$	−8658.65	−	4999.07i	−0.509504	−	0.294162i	−0.732630	+	0.680627i	$0.761707\pi$
$662$		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	0.865116	−	0.501572i	$-0.167245\pi$
$673$	−31.7088	−	54.9213i	−0.00181617	−	0.00314570i	−0.866932	+	0.498426i	$0.833911\pi$
$674$		0			0
$675$	2433.96	−	815.786i	0.138790	−	0.0465180i
$676$		0			0
$677$	8874.33	+	15370.8i	0.503793	+	0.872596i	0.999990	+	0.00438565i	$0.00139600\pi$
$677$	8874.33	+	15370.8i	0.503793	+	0.872596i	−0.496197	+	0.868210i	$0.665271\pi$
$678$		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	$0.0752069\pi$
$683$			8356.42i			0.468155i	−0.972218	+	0.234077i	$0.924793\pi$
$684$		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	0.396174	−	0.918175i	$-0.370338\pi$
$691$	25237.8	−	14571.1i	1.38942	−	0.802185i	0.993250	+	0.115991i	$0.0370042\pi$
$692$		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	$0.304846\pi$
$701$			30359.4i			1.63574i	−0.575400	+	0.817872i	$0.695154\pi$
$702$		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	0.659535	−	0.751674i	$-0.270753\pi$
$709$	−6063.83	−	10502.9i	−0.321202	−	0.556338i	−0.980736	+	0.195337i	$0.937420\pi$
$710$		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	−0.986693	−	0.162594i	$-0.948014\pi$
$727$	−26251.7	+	15156.4i	−1.33923	+	0.773204i	−0.352536	+	0.935798i	$0.614681\pi$
$728$		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	0.851661	−	0.524093i	$-0.175596\pi$
$733$	16344.8	+	9436.67i	0.823613	+	0.475513i	−0.0280476	+	0.999607i	$0.508929\pi$
$734$		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	0.940340	−	0.340236i	$-0.110507\pi$
$743$	22599.1	+	13047.6i	1.11586	+	0.644241i	0.175517	+	0.984476i	$0.443840\pi$
$744$		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	−0.343081	−	0.939306i	$-0.611470\pi$
$751$	13211.2	−	22882.5i	0.641922	−	1.11184i	0.985003	−	0.172536i	$-0.0551962\pi$
$752$		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	−0.106545	+	0.994308i	$0.533979\pi$
$761$	−19195.4	+	33247.5i	−0.914369	+	1.58373i	−0.807823	+	0.589425i	$0.799354\pi$
$762$		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	0.972625	−	0.232378i	$-0.0746507\pi$
$769$	26820.3	+	15484.7i	1.25769	+	0.726129i	0.285067	+	0.958508i	$0.407984\pi$
$770$		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	0.874071	−	0.485798i	$-0.161471\pi$
$787$	19658.2	+	11349.7i	0.890392	+	0.514068i	0.0163216	+	0.999867i	$0.494804\pi$
$788$		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	−0.954747	−	0.297418i	$-0.903874\pi$
$797$	−4945.60	+	8566.03i	−0.219802	+	0.380708i	0.734945	+	0.678126i	$0.237208\pi$
$798$		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	$0.108087\pi$
$809$			15328.4i			0.666155i	−0.942900	+	0.333077i	$0.891913\pi$
$810$		0			0
$811$			4463.96i			0.193281i	0.995319	+	0.0966406i	$0.0308097\pi$
$811$			4463.96i			0.193281i	−0.995319	+	0.0966406i	$0.969190\pi$
$812$		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	−0.180709	−	0.983537i	$-0.557839\pi$
$821$	13660.6	−	7886.94i	0.580704	−	0.335269i	0.761413	+	0.648267i	$0.224506\pi$
$822$		0			0
$823$	−960.810	+	1664.17i	−0.0406947	+	0.0704853i	−0.885655	−	0.464343i	$-0.846290\pi$
$823$	−960.810	+	1664.17i	−0.0406947	+	0.0704853i	0.844961	+	0.534828i	$0.179624\pi$
$824$		0			0
$825$	2971.87	+	198.615i	0.125415	+	0.00838168i
$826$		0			0
$827$			28140.7i			1.18325i	0.806214	+	0.591624i	$0.201513\pi$
$827$			28140.7i			1.18325i	−0.806214	+	0.591624i	$0.798487\pi$
$828$		0			0
$829$		−	13305.9i		−	0.557460i	−0.960370	−	0.278730i	$-0.910087\pi$
$829$		−	13305.9i		−	0.557460i	0.960370	−	0.278730i	$-0.0899134\pi$
$830$		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	0.989058	−	0.147526i	$-0.0471311\pi$
$839$	8913.20	+	15438.1i	0.366767	+	0.635260i	−0.622291	+	0.782786i	$0.713798\pi$
$840$		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	−0.996509	−	0.0834834i	$-0.973395\pi$
$853$	−35437.7	+	20459.9i	−1.42247	+	0.821261i	−0.425956	+	0.904744i	$0.640062\pi$
$854$		0			0
$855$	−34288.1	+	14099.7i	−1.37150	+	0.563975i
$856$		0			0
$857$	14081.4	+	24389.8i	0.561275	+	0.972157i	0.997386	+	0.0722641i	$0.0230225\pi$
$857$	14081.4	+	24389.8i	0.561275	+	0.972157i	−0.436110	+	0.899893i	$0.643644\pi$
$858$		0			0
$859$	−3110.46	−	1795.83i	−0.123548	−	0.0713304i	0.436952	−	0.899485i	$-0.356058\pi$
$859$	−3110.46	−	1795.83i	−0.123548	−	0.0713304i	−0.560500	+	0.828154i	$0.689391\pi$
$860$		0			0
$861$	2326.00	+	7288.74i	0.0920673	+	0.288501i
$862$		0			0
$863$		−	18091.2i		−	0.713593i	−0.934182	−	0.356796i	$-0.883869\pi$
$863$		−	18091.2i		−	0.713593i	0.934182	−	0.356796i	$-0.116131\pi$
$864$		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	−0.0586762	+	0.998277i	$0.518688\pi$
$877$	−23215.3	+	40210.1i	−0.893871	+	1.54823i	−0.835195	+	0.549954i	$0.814645\pi$
$878$		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	−0.831414	−	0.555654i	$-0.812468\pi$
$887$	1730.41	−	2997.16i	0.0655034	−	0.113455i	0.896917	+	0.442199i	$0.145801\pi$
$888$		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	0.999278	+	0.0380031i	$0.0120997\pi$
$907$	14546.9	+	25196.0i	0.532550	+	0.922404i	−0.466727	+	0.884401i	$0.654567\pi$
$908$		0			0
$909$	50206.8	+	6740.91i	1.83196	+	0.245965i
$910$		0			0
$911$	28776.2	−	16613.9i	1.04654	−	0.604220i	0.124861	−	0.992174i	$-0.460151\pi$
$911$	28776.2	−	16613.9i	1.04654	−	0.604220i	0.921679	+	0.387954i	$0.126818\pi$
$912$		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	0.977042	+	0.213045i	$0.0683381\pi$
$929$	19057.0	+	33007.6i	0.673024	+	1.16571i	−0.304019	+	0.952666i	$0.598329\pi$
$930$		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	$-0.871979\pi$
$937$		−	22454.2i		−	0.782869i	0.920206	−	0.391435i	$-0.128021\pi$
$938$		0			0
$939$	15513.1	−	23152.6i	0.539137	−	0.804639i
$940$		0			0
$941$	6159.92	−	10669.3i	0.213398	−	0.369616i	−0.739378	−	0.673291i	$-0.764880\pi$
$941$	6159.92	−	10669.3i	0.213398	−	0.369616i	0.952776	+	0.303675i	$0.0982135\pi$
$942$		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	−0.252223	−	0.967669i	$-0.581162\pi$
$947$	13396.5	−	7734.46i	0.459691	−	0.265403i	0.711914	+	0.702266i	$0.247828\pi$
$948$		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	$-0.971465\pi$
$953$		−	5267.67i		−	0.179052i	0.995984	−	0.0895260i	$-0.0285352\pi$
$954$		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	−0.743484	−	0.668754i	$-0.766828\pi$
$967$	6237.09	−	10803.0i	0.207416	−	0.359255i	0.950900	+	0.309499i	$0.100161\pi$
$968$		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	0.737938	−	0.674868i	$-0.235800\pi$
$977$	15954.7	+	9211.48i	0.522454	+	0.301639i	−0.215484	+	0.976507i	$0.569133\pi$
$978$		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	0.787922	−	0.615775i	$-0.211157\pi$
$983$	−4293.70	−	7436.90i	−0.139316	−	0.241302i	−0.927238	+	0.374473i	$0.877824\pi$
$984$		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	−0.432124	−	0.901814i	$-0.642236\pi$
$997$	4180.85	−	2413.82i	0.132807	−	0.0766764i	0.564932	+	0.825138i	$0.308903\pi$
$998$		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.41.21	yes	48
3.2	odd	2		756.4.x.a.125.7		48
7.6	odd	2	inner	252.4.x.a.41.4	✓	48
9.2	odd	6	inner	252.4.x.a.209.4	yes	48
9.4	even	3		2268.4.f.a.1133.14		48
9.5	odd	6		2268.4.f.a.1133.35		48
9.7	even	3		756.4.x.a.629.18		48
21.20	even	2		756.4.x.a.125.18		48
63.13	odd	6		2268.4.f.a.1133.36		48
63.20	even	6	inner	252.4.x.a.209.21	yes	48
63.34	odd	6		756.4.x.a.629.7		48
63.41	even	6		2268.4.f.a.1133.13		48

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