LMFDB - Embedded newform 192.4.k.a.143.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,4,Mod(47,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("192.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	192.k (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.3283667211$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.19
Character	$\chi$	$=$	192.143
Dual form			192.4.k.a.47.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.66767 - 2.28317i) q^{3} +(-11.5146 + 11.5146i) q^{5} -0.829117 q^{7} +(16.5743 - 21.3142i) q^{9} +O(q^{10})$	\(q+(4.66767 - 2.28317i) q^{3} +(-11.5146 + 11.5146i) q^{5} -0.829117 q^{7} +(16.5743 - 21.3142i) q^{9} +(38.2302 + 38.2302i) q^{11} +(-20.0189 + 20.0189i) q^{13} +(-27.4566 + 80.0363i) q^{15} +77.9578i q^{17} +(37.6931 + 37.6931i) q^{19} +(-3.87005 + 1.89301i) q^{21} +159.603i q^{23} -140.173i q^{25} +(28.6995 - 137.329i) q^{27} +(26.6150 + 26.6150i) q^{29} -226.344i q^{31} +(265.732 + 91.1601i) q^{33} +(9.54698 - 9.54698i) q^{35} +(176.815 + 176.815i) q^{37} +(-47.7351 + 139.148i) q^{39} -301.571 q^{41} +(96.1344 - 96.1344i) q^{43} +(54.5779 + 436.271i) q^{45} +122.486 q^{47} -342.313 q^{49} +(177.991 + 363.881i) q^{51} +(138.452 - 138.452i) q^{53} -880.414 q^{55} +(261.999 + 89.8792i) q^{57} +(168.375 + 168.375i) q^{59} +(-178.364 + 178.364i) q^{61} +(-13.7420 + 17.6719i) q^{63} -461.021i q^{65} +(233.257 + 233.257i) q^{67} +(364.402 + 744.976i) q^{69} -668.427i q^{71} -1216.50i q^{73} +(-320.039 - 654.283i) q^{75} +(-31.6974 - 31.6974i) q^{77} +39.4578i q^{79} +(-179.586 - 706.534i) q^{81} +(293.710 - 293.710i) q^{83} +(-897.655 - 897.655i) q^{85} +(184.997 + 63.4635i) q^{87} -732.996 q^{89} +(16.5980 - 16.5980i) q^{91} +(-516.781 - 1056.50i) q^{93} -868.044 q^{95} +451.695 q^{97} +(1448.48 - 181.207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{3} + 8 q^{7}+O(q^{10}) $ 44 * q + 2 * q^3 + 8 * q^7	$ 44 q + 2 q^{3} + 8 q^{7} - 4 q^{13} - 20 q^{19} - 56 q^{21} + 134 q^{27} - 4 q^{33} - 4 q^{37} - 596 q^{39} + 436 q^{43} - 252 q^{45} + 972 q^{49} + 648 q^{51} - 280 q^{55} - 916 q^{61} + 1636 q^{67} + 52 q^{69} - 1454 q^{75} - 4 q^{81} + 736 q^{85} - 1284 q^{87} - 424 q^{91} - 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) $ 44 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 - 20 * q^19 - 56 * q^21 + 134 * q^27 - 4 * q^33 - 4 * q^37 - 596 * q^39 + 436 * q^43 - 252 * q^45 + 972 * q^49 + 648 * q^51 - 280 * q^55 - 916 * q^61 + 1636 * q^67 + 52 * q^69 - 1454 * q^75 - 4 * q^81 + 736 * q^85 - 1284 * q^87 - 424 * q^91 - 2084 * q^93 - 8 * q^97 - 1196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.66767	−	2.28317i	0.898293	−	0.439396i
$3$	4.66767	−	2.28317i	0.898293	−	0.439396i
$4$		0			0
$5$	−11.5146	+	11.5146i	−1.02990	+	1.02990i	−0.0303606	+	0.999539i	$0.509666\pi$
$5$	−11.5146	+	11.5146i	−1.02990	+	1.02990i	−0.999539	+	0.0303606i	$0.990334\pi$
$6$		0			0
$7$	−0.829117			−0.0447681			−0.0223841	−	0.999749i	$-0.507126\pi$
$7$	−0.829117			−0.0447681			−0.0223841	+	0.999749i	$0.507126\pi$
$8$		0			0
$9$	16.5743	−	21.3142i	0.613862	−	0.789413i
$10$		0			0
$11$	38.2302	+	38.2302i	1.04790	+	1.04790i	0.998794	+	0.0491019i	$0.0156359\pi$
$11$	38.2302	+	38.2302i	1.04790	+	1.04790i	0.0491019	+	0.998794i	$0.484364\pi$
$12$		0			0
$13$	−20.0189	+	20.0189i	−0.427096	+	0.427096i	−0.887638	−	0.460542i	$-0.847655\pi$
$13$	−20.0189	+	20.0189i	−0.427096	+	0.427096i	0.460542	+	0.887638i	$0.347655\pi$
$14$		0			0
$15$	−27.4566	+	80.0363i	−0.472618	+	1.37769i
$16$		0			0
$17$			77.9578i			1.11221i	0.831113	+	0.556104i	$0.187704\pi$
$17$			77.9578i			1.11221i	−0.831113	+	0.556104i	$0.812296\pi$
$18$		0			0
$19$	37.6931	+	37.6931i	0.455126	+	0.455126i	0.897052	−	0.441926i	$-0.145705\pi$
$19$	37.6931	+	37.6931i	0.455126	+	0.455126i	−0.441926	+	0.897052i	$0.645705\pi$
$20$		0			0
$21$	−3.87005	+	1.89301i	−0.0402149	+	0.0196709i
$22$		0			0
$23$			159.603i			1.44694i	0.690356	+	0.723470i	$0.257454\pi$
$23$			159.603i			1.44694i	−0.690356	+	0.723470i	$0.742546\pi$
$24$		0			0
$25$		−	140.173i		−	1.12139i
$26$		0			0
$27$	28.6995	−	137.329i	0.204563	−	0.978853i
$28$		0			0
$29$	26.6150	+	26.6150i	0.170424	+	0.170424i	0.787165	−	0.616742i	$-0.211548\pi$
$29$	26.6150	+	26.6150i	0.170424	+	0.170424i	−0.616742	+	0.787165i	$0.711548\pi$
$30$		0			0
$31$		−	226.344i		−	1.31137i	−0.755034	−	0.655686i	$-0.772379\pi$
$31$		−	226.344i		−	1.31137i	0.755034	−	0.655686i	$-0.227621\pi$
$32$		0			0
$33$	265.732	+	91.1601i	1.40176	+	0.480877i
$34$		0			0
$35$	9.54698	−	9.54698i	0.0461067	−	0.0461067i
$36$		0			0
$37$	176.815	+	176.815i	0.785626	+	0.785626i	0.980774	−	0.195148i	$-0.0625188\pi$
$37$	176.815	+	176.815i	0.785626	+	0.785626i	−0.195148	+	0.980774i	$0.562519\pi$
$38$		0			0
$39$	−47.7351	+	139.148i	−0.195993	+	0.571322i
$40$		0			0
$41$	−301.571			−1.14872			−0.574359	−	0.818604i	$-0.694749\pi$
$41$	−301.571			−1.14872			−0.574359	+	0.818604i	$0.694749\pi$
$42$		0			0
$43$	96.1344	−	96.1344i	0.340938	−	0.340938i	−0.515782	−	0.856720i	$-0.672498\pi$
$43$	96.1344	−	96.1344i	0.340938	−	0.340938i	0.856720	+	0.515782i	$0.172498\pi$
$44$		0			0
$45$	54.5779	+	436.271i	0.180800	+	1.44523i
$46$		0			0
$47$	122.486			0.380135			0.190068	−	0.981771i	$-0.439129\pi$
$47$	122.486			0.380135			0.190068	+	0.981771i	$0.439129\pi$
$48$		0			0
$49$	−342.313			−0.997996
$50$		0			0
$51$	177.991	+	363.881i	0.488700	+	0.999089i
$52$		0			0
$53$	138.452	−	138.452i	0.358828	−	0.358828i	−0.504553	−	0.863381i	$-0.668343\pi$
$53$	138.452	−	138.452i	0.358828	−	0.358828i	0.863381	+	0.504553i	$0.168343\pi$
$54$		0			0
$55$	−880.414			−2.15845
$56$		0			0
$57$	261.999	+	89.8792i	0.608817	+	0.208856i
$58$		0			0
$59$	168.375	+	168.375i	0.371535	+	0.371535i	0.868036	−	0.496501i	$-0.165382\pi$
$59$	168.375	+	168.375i	0.371535	+	0.371535i	−0.496501	+	0.868036i	$0.665382\pi$
$60$		0			0
$61$	−178.364	+	178.364i	−0.374379	+	0.374379i	−0.869069	−	0.494690i	$-0.835282\pi$
$61$	−178.364	+	178.364i	−0.374379	+	0.374379i	0.494690	+	0.869069i	$0.335282\pi$
$62$		0			0
$63$	−13.7420	+	17.6719i	−0.0274815	+	0.0353406i
$64$		0			0
$65$		−	461.021i		−	0.879732i
$66$		0			0
$67$	233.257	+	233.257i	0.425326	+	0.425326i	0.887033	−	0.461707i	$-0.152763\pi$
$67$	233.257	+	233.257i	0.425326	+	0.425326i	−0.461707	+	0.887033i	$0.652763\pi$
$68$		0			0
$69$	364.402	+	744.976i	0.635780	+	1.29978i
$70$		0			0
$71$		−	668.427i		−	1.11729i	−0.829406	−	0.558646i	$-0.811321\pi$
$71$		−	668.427i		−	1.11729i	0.829406	−	0.558646i	$-0.188679\pi$
$72$		0			0
$73$		−	1216.50i		−	1.95041i	−0.221297	−	0.975207i	$-0.571029\pi$
$73$		−	1216.50i		−	1.95041i	0.221297	−	0.975207i	$-0.428971\pi$
$74$		0			0
$75$	−320.039	−	654.283i	−0.492733	−	1.00733i
$76$		0			0
$77$	−31.6974	−	31.6974i	−0.0469123	−	0.0469123i
$78$		0			0
$79$			39.4578i			0.0561943i	0.999605	+	0.0280971i	$0.00894478\pi$
$79$			39.4578i			0.0561943i	−0.999605	+	0.0280971i	$0.991055\pi$
$80$		0			0
$81$	−179.586	−	706.534i	−0.246346	−	0.969182i
$82$		0			0
$83$	293.710	−	293.710i	0.388419	−	0.388419i	−0.485704	−	0.874123i	$-0.661437\pi$
$83$	293.710	−	293.710i	0.388419	−	0.388419i	0.874123	+	0.485704i	$0.161437\pi$
$84$		0			0
$85$	−897.655	−	897.655i	−1.14546	−	1.14546i
$86$		0			0
$87$	184.997	+	63.4635i	0.227974	+	0.0782069i
$88$		0			0
$89$	−732.996			−0.873004			−0.436502	−	0.899703i	$-0.643783\pi$
$89$	−732.996			−0.873004			−0.436502	+	0.899703i	$0.643783\pi$
$90$		0			0
$91$	16.5980	−	16.5980i	0.0191203	−	0.0191203i
$92$		0			0
$93$	−516.781	−	1056.50i	−0.576212	−	1.17800i
$94$		0			0
$95$	−868.044			−0.937467
$96$		0			0
$97$	451.695			0.472811			0.236406	−	0.971654i	$-0.424031\pi$
$97$	451.695			0.472811			0.236406	+	0.971654i	$0.424031\pi$
$98$		0			0
$99$	1448.48	−	181.207i	1.47049	−	0.183959i
$100$		0			0
$101$	991.920	−	991.920i	0.977225	−	0.977225i	−0.0225216	−	0.999746i	$-0.507169\pi$
$101$	991.920	−	991.920i	0.977225	−	0.977225i	0.999746	+	0.0225216i	$0.00716945\pi$
$102$		0			0
$103$	−173.550			−0.166023			−0.0830114	−	0.996549i	$-0.526454\pi$
$103$	−173.550			−0.166023			−0.0830114	+	0.996549i	$0.526454\pi$
$104$		0			0
$105$	22.7648	−	66.3595i	0.0211582	−	0.0616764i
$106$		0			0
$107$	−216.201	−	216.201i	−0.195336	−	0.195336i	0.602661	−	0.797997i	$-0.294107\pi$
$107$	−216.201	−	216.201i	−0.195336	−	0.195336i	−0.797997	+	0.602661i	$0.794107\pi$
$108$		0			0
$109$	−883.171	+	883.171i	−0.776078	+	0.776078i	−0.979161	−	0.203084i	$-0.934904\pi$
$109$	−883.171	+	883.171i	−0.776078	+	0.776078i	0.203084	+	0.979161i	$0.434904\pi$
$110$		0			0
$111$	1229.01	+	421.615i	1.05092	+	0.360522i
$112$		0			0
$113$			1915.77i			1.59487i	0.603403	+	0.797437i	$0.293811\pi$
$113$			1915.77i			1.59487i	−0.603403	+	0.797437i	$0.706189\pi$
$114$		0			0
$115$	−1837.77	−	1837.77i	−1.49020	−	1.49020i
$116$		0			0
$117$	94.8871	+	758.485i	0.0749771	+	0.599333i
$118$		0			0
$119$		−	64.6361i		−	0.0497915i
$120$		0			0
$121$			1592.10i			1.19617i
$122$		0			0
$123$	−1407.63	+	688.537i	−1.03189	+	0.504742i
$124$		0			0
$125$	174.715	+	174.715i	0.125016	+	0.125016i
$126$		0			0
$127$		−	42.9875i		−	0.0300357i	−0.999887	−	0.0150178i	$-0.995219\pi$
$127$		−	42.9875i		−	0.0300357i	0.999887	−	0.0150178i	$-0.00478050\pi$
$128$		0			0
$129$	229.232	−	668.214i	0.156456	−	0.456070i
$130$		0			0
$131$	−556.534	+	556.534i	−0.371180	+	0.371180i	−0.867907	−	0.496727i	$-0.834535\pi$
$131$	−556.534	+	556.534i	−0.371180	+	0.371180i	0.496727	+	0.867907i	$0.334535\pi$
$132$		0			0
$133$	−31.2520	−	31.2520i	−0.0203751	−	0.0203751i
$134$		0			0
$135$	1250.83	+	1911.76i	0.797441	+	1.21880i
$136$		0			0
$137$	1557.02			0.970988			0.485494	−	0.874240i	$-0.338640\pi$
$137$	1557.02			0.970988			0.485494	+	0.874240i	$0.338640\pi$
$138$		0			0
$139$	682.898	−	682.898i	0.416710	−	0.416710i	−0.467358	−	0.884068i	$-0.654794\pi$
$139$	682.898	−	682.898i	0.416710	−	0.416710i	0.884068	+	0.467358i	$0.154794\pi$
$140$		0			0
$141$	571.722	−	279.655i	0.341473	−	0.167030i
$142$		0			0
$143$	−1530.66			−0.895104
$144$		0			0
$145$	−612.924			−0.351038
$146$		0			0
$147$	−1597.80	+	781.557i	−0.896493	+	0.438515i
$148$		0			0
$149$	143.722	−	143.722i	0.0790215	−	0.0790215i	−0.666491	−	0.745513i	$-0.732205\pi$
$149$	143.722	−	143.722i	0.0790215	−	0.0790215i	0.745513	+	0.666491i	$0.232205\pi$
$150$		0			0
$151$	1427.53			0.769340			0.384670	−	0.923054i	$-0.374315\pi$
$151$	1427.53			0.769340			0.384670	+	0.923054i	$0.374315\pi$
$152$		0			0
$153$	1661.60	+	1292.09i	0.877992	+	0.682742i
$154$		0			0
$155$	2606.26	+	2606.26i	1.35058	+	1.35058i
$156$		0			0
$157$	2228.30	−	2228.30i	1.13273	−	1.13273i	0.143003	−	0.989722i	$-0.454324\pi$
$157$	2228.30	−	2228.30i	1.13273	−	1.13273i	0.989722	−	0.143003i	$-0.0456760\pi$
$158$		0			0
$159$	330.140	−	962.360i	0.164665	−	0.480000i
$160$		0			0
$161$		−	132.330i		−	0.0647768i
$162$		0			0
$163$	418.032	+	418.032i	0.200876	+	0.200876i	0.800375	−	0.599499i	$-0.204634\pi$
$163$	418.032	+	418.032i	0.200876	+	0.200876i	−0.599499	+	0.800375i	$0.704634\pi$
$164$		0			0
$165$	−4109.48	+	2010.13i	−1.93893	+	0.948416i
$166$		0			0
$167$		−	3870.40i		−	1.79342i	−0.442623	−	0.896708i	$-0.645952\pi$
$167$		−	3870.40i		−	1.79342i	0.442623	−	0.896708i	$-0.354048\pi$
$168$		0			0
$169$			1395.49i			0.635178i
$170$		0			0
$171$	1428.13	−	178.660i	0.638667	−	0.0798977i
$172$		0			0
$173$	1289.55	+	1289.55i	0.566721	+	0.566721i	0.931208	−	0.364487i	$-0.118756\pi$
$173$	1289.55	+	1289.55i	0.566721	+	0.566721i	−0.364487	+	0.931208i	$0.618756\pi$
$174$		0			0
$175$			116.220i			0.0502024i
$176$		0			0
$177$	1170.35	+	401.491i	0.496999	+	0.170496i
$178$		0			0
$179$	−1767.33	+	1767.33i	−0.737970	+	0.737970i	−0.972185	−	0.234215i	$-0.924748\pi$
$179$	−1767.33	+	1767.33i	−0.737970	+	0.737970i	0.234215	+	0.972185i	$0.424748\pi$
$180$		0			0
$181$	417.552	+	417.552i	0.171472	+	0.171472i	0.787626	−	0.616154i	$-0.211310\pi$
$181$	417.552	+	417.552i	0.171472	+	0.171472i	−0.616154	+	0.787626i	$0.711310\pi$
$182$		0			0
$183$	−425.308	+	1239.78i	−0.171802	+	0.500803i
$184$		0			0
$185$	−4071.91			−1.61823
$186$		0			0
$187$	−2980.34	+	2980.34i	−1.16548	+	1.16548i
$188$		0			0
$189$	−23.7952	+	113.862i	−0.00915792	+	0.0438214i
$190$		0			0
$191$	1181.47			0.447580			0.223790	−	0.974637i	$-0.428157\pi$
$191$	1181.47			0.447580			0.223790	+	0.974637i	$0.428157\pi$
$192$		0			0
$193$	−1794.87			−0.669417			−0.334709	−	0.942322i	$-0.608638\pi$
$193$	−1794.87			−0.669417			−0.334709	+	0.942322i	$0.608638\pi$
$194$		0			0
$195$	−1052.59	−	2151.89i	−0.386551	−	0.790257i
$196$		0			0
$197$	31.7151	−	31.7151i	0.0114701	−	0.0114701i	−0.701348	−	0.712819i	$-0.747418\pi$
$197$	31.7151	−	31.7151i	0.0114701	−	0.0114701i	0.712819	+	0.701348i	$0.247418\pi$
$198$		0			0
$199$	4332.32			1.54327			0.771634	−	0.636067i	$-0.219440\pi$
$199$	4332.32			1.54327			0.771634	+	0.636067i	$0.219440\pi$
$200$		0			0
$201$	1621.33	+	556.200i	0.568954	+	0.195181i
$202$		0			0
$203$	−22.0670	−	22.0670i	−0.00762955	−	0.00762955i
$204$		0			0
$205$	3472.47	−	3472.47i	1.18306	−	1.18306i
$206$		0			0
$207$	3401.81	+	2645.31i	1.14223	+	0.888222i
$208$		0			0
$209$			2882.03i			0.953848i
$210$		0			0
$211$	2291.21	+	2291.21i	0.747553	+	0.747553i	0.974019	−	0.226466i	$-0.0727173\pi$
$211$	2291.21	+	2291.21i	0.747553	+	0.747553i	−0.226466	+	0.974019i	$0.572717\pi$
$212$		0			0
$213$	−1526.13	−	3120.00i	−0.490934	−	1.00366i
$214$		0			0
$215$			2213.90i			0.702265i
$216$		0			0
$217$			187.666i			0.0587077i
$218$		0			0
$219$	−2777.47	−	5678.20i	−0.857004	−	1.75204i
$220$		0			0
$221$	−1560.63	−	1560.63i	−0.475020	−	0.475020i
$222$		0			0
$223$		−	1012.13i		−	0.303933i	−0.988386	−	0.151966i	$-0.951439\pi$
$223$		−	1012.13i		−	0.303933i	0.988386	−	0.151966i	$-0.0485605\pi$
$224$		0			0
$225$	−2987.68	−	2323.27i	−0.885237	−	0.688377i
$226$		0			0
$227$	218.272	−	218.272i	0.0638202	−	0.0638202i	−0.674476	−	0.738297i	$-0.735631\pi$
$227$	218.272	−	218.272i	0.0638202	−	0.0638202i	0.738297	+	0.674476i	$0.235631\pi$
$228$		0			0
$229$	−563.164	−	563.164i	−0.162510	−	0.162510i	0.621167	−	0.783678i	$-0.286659\pi$
$229$	−563.164	−	563.164i	−0.162510	−	0.162510i	−0.783678	+	0.621167i	$0.786659\pi$
$230$		0			0
$231$	−220.323	−	75.5824i	−0.0627541	−	0.0215279i
$232$		0			0
$233$	646.432			0.181756			0.0908781	−	0.995862i	$-0.471033\pi$
$233$	646.432			0.181756			0.0908781	+	0.995862i	$0.471033\pi$
$234$		0			0
$235$	−1410.38	+	1410.38i	−0.391501	+	0.391501i
$236$		0			0
$237$	90.0888	+	184.176i	0.0246915	+	0.0504790i
$238$		0			0
$239$	−996.350			−0.269659			−0.134830	−	0.990869i	$-0.543049\pi$
$239$	−996.350			−0.269659			−0.134830	+	0.990869i	$0.543049\pi$
$240$		0			0
$241$	4528.91			1.21051			0.605255	−	0.796032i	$-0.293071\pi$
$241$	4528.91			1.21051			0.605255	+	0.796032i	$0.293071\pi$
$242$		0			0
$243$	−2451.39	−	2887.84i	−0.647146	−	0.762366i
$244$		0			0
$245$	3941.60	−	3941.60i	1.02784	−	1.02784i
$246$		0			0
$247$	−1509.15			−0.388765
$248$		0			0
$249$	700.351	−	2041.53i	0.178245	−	0.519585i
$250$		0			0
$251$	3612.53	+	3612.53i	0.908449	+	0.908449i	0.996147	−	0.0876984i	$-0.0279512\pi$
$251$	3612.53	+	3612.53i	0.908449	+	0.908449i	−0.0876984	+	0.996147i	$0.527951\pi$
$252$		0			0
$253$	−6101.68	+	6101.68i	−1.51624	+	1.51624i
$254$		0			0
$255$	−6239.45	−	2140.46i	−1.53227	−	0.525650i
$256$		0			0
$257$		−	1679.73i		−	0.407699i	−0.979002	−	0.203850i	$-0.934655\pi$
$257$		−	1679.73i		−	0.407699i	0.979002	−	0.203850i	$-0.0653453\pi$
$258$		0			0
$259$	−146.600	−	146.600i	−0.0351710	−	0.0351710i
$260$		0			0
$261$	1008.40	−	126.152i	0.239151	−	0.0299180i
$262$		0			0
$263$		−	1574.43i		−	0.369139i	−0.982819	−	0.184569i	$-0.940911\pi$
$263$		−	1574.43i		−	0.369139i	0.982819	−	0.184569i	$-0.0590890\pi$
$264$		0			0
$265$			3188.45i			0.739114i
$266$		0			0
$267$	−3421.38	+	1673.55i	−0.784214	+	0.383595i
$268$		0			0
$269$	−1316.04	−	1316.04i	−0.298290	−	0.298290i	0.542054	−	0.840344i	$-0.317647\pi$
$269$	−1316.04	−	1316.04i	−0.298290	−	0.298290i	−0.840344	+	0.542054i	$0.817647\pi$
$270$		0			0
$271$			4047.05i			0.907162i	0.891215	+	0.453581i	$0.149854\pi$
$271$			4047.05i			0.907162i	−0.891215	+	0.453581i	$0.850146\pi$
$272$		0			0
$273$	39.5780	−	115.370i	0.00877425	−	0.0255770i
$274$		0			0
$275$	5358.86	−	5358.86i	1.17510	−	1.17510i
$276$		0			0
$277$	4498.76	+	4498.76i	0.975829	+	0.975829i	0.999715	−	0.0238859i	$-0.00760383\pi$
$277$	4498.76	+	4498.76i	0.975829	+	0.975829i	−0.0238859	+	0.999715i	$0.507604\pi$
$278$		0			0
$279$	−4824.33	−	3751.49i	−1.03521	−	0.805002i
$280$		0			0
$281$	−2856.76			−0.606476			−0.303238	−	0.952915i	$-0.598068\pi$
$281$	−2856.76			−0.606476			−0.303238	+	0.952915i	$0.598068\pi$
$282$		0			0
$283$	5461.16	−	5461.16i	1.14711	−	1.14711i	0.159992	−	0.987118i	$-0.448853\pi$
$283$	5461.16	−	5461.16i	1.14711	−	1.14711i	0.987118	−	0.159992i	$-0.0511469\pi$
$284$		0			0
$285$	−4051.74	+	1981.89i	−0.842121	+	0.411919i
$286$		0			0
$287$	250.038			0.0514260
$288$		0			0
$289$	−1164.41			−0.237006
$290$		0			0
$291$	2108.36	−	1031.30i	0.424723	−	0.207751i
$292$		0			0
$293$	−4624.96	+	4624.96i	−0.922162	+	0.922162i	−0.997182	−	0.0750205i	$-0.976098\pi$
$293$	−4624.96	+	4624.96i	−0.922162	+	0.922162i	0.0750205	+	0.997182i	$0.476098\pi$
$294$		0			0
$295$	−3877.55			−0.765288
$296$		0			0
$297$	6347.32	−	4152.95i	1.24010	−	0.811375i
$298$		0			0
$299$	−3195.09	−	3195.09i	−0.617982	−	0.617982i
$300$		0			0
$301$	−79.7067	+	79.7067i	−0.0152632	+	0.0152632i
$302$		0			0
$303$	2365.23	−	6894.67i	0.448446	−	1.30722i
$304$		0			0
$305$		−	4107.58i		−	0.771146i
$306$		0			0
$307$	−1372.35	−	1372.35i	−0.255128	−	0.255128i	0.567941	−	0.823069i	$-0.307740\pi$
$307$	−1372.35	−	1372.35i	−0.255128	−	0.255128i	−0.823069	+	0.567941i	$0.807740\pi$
$308$		0			0
$309$	−810.073	+	396.243i	−0.149137	+	0.0729498i
$310$		0			0
$311$		−	3244.39i		−	0.591551i	−0.955258	−	0.295775i	$-0.904422\pi$
$311$		−	3244.39i		−	0.591551i	0.955258	−	0.295775i	$-0.0955780\pi$
$312$		0			0
$313$		−	6287.66i		−	1.13546i	−0.823214	−	0.567731i	$-0.807822\pi$
$313$		−	6287.66i		−	1.13546i	0.823214	−	0.567731i	$-0.192178\pi$
$314$		0			0
$315$	−45.2515	−	361.720i	−0.00809407	−	0.0647004i
$316$		0			0
$317$	−4723.19	−	4723.19i	−0.836848	−	0.836848i	0.151595	−	0.988443i	$-0.451559\pi$
$317$	−4723.19	−	4723.19i	−0.836848	−	0.836848i	−0.988443	+	0.151595i	$0.951559\pi$
$318$		0			0
$319$			2035.00i			0.357172i
$320$		0			0
$321$	−1502.78	−	515.532i	−0.261299	−	0.0896392i
$322$		0			0
$323$	−2938.47	+	2938.47i	−0.506194	+	0.506194i
$324$		0			0
$325$	2806.12	+	2806.12i	0.478940	+	0.478940i
$326$		0			0
$327$	−2105.92	+	6138.78i	−0.356140	+	1.03815i
$328$		0			0
$329$	−101.555			−0.0170179
$330$		0			0
$331$	6112.31	−	6112.31i	1.01499	−	1.01499i	0.0151076	−	0.999886i	$-0.495191\pi$
$331$	6112.31	−	6112.31i	1.01499	−	1.01499i	0.999886	−	0.0151076i	$-0.00480907\pi$
$332$		0			0
$333$	6699.23	−	838.079i	1.10245	−	0.137917i
$334$		0			0
$335$	−5371.72			−0.876086
$336$		0			0
$337$	5377.59			0.869246			0.434623	−	0.900613i	$-0.356882\pi$
$337$	5377.59			0.869246			0.434623	+	0.900613i	$0.356882\pi$
$338$		0			0
$339$	4374.03	+	8942.19i	0.700781	+	1.43266i
$340$		0			0
$341$	8653.18	−	8653.18i	1.37418	−	1.37418i
$342$		0			0
$343$	568.205			0.0894465
$344$		0			0
$345$	−12774.1	−	4382.17i	−1.99343	−	0.683850i
$346$		0			0
$347$	−3586.40	−	3586.40i	−0.554835	−	0.554835i	0.372997	−	0.927832i	$-0.378330\pi$
$347$	−3586.40	−	3586.40i	−0.554835	−	0.554835i	−0.927832	+	0.372997i	$0.878330\pi$
$348$		0			0
$349$	−3892.45	+	3892.45i	−0.597015	+	0.597015i	−0.939517	−	0.342502i	$-0.888726\pi$
$349$	−3892.45	+	3892.45i	−0.597015	+	0.597015i	0.342502	+	0.939517i	$0.388726\pi$
$350$		0			0
$351$	2174.65	+	3323.72i	0.330696	+	0.505433i
$352$		0			0
$353$		−	2306.40i		−	0.347754i	−0.984767	−	0.173877i	$-0.944370\pi$
$353$		−	2306.40i		−	0.347754i	0.984767	−	0.173877i	$-0.0556296\pi$
$354$		0			0
$355$	7696.69	+	7696.69i	1.15070	+	1.15070i
$356$		0			0
$357$	−147.575	−	301.700i	−0.0218782	−	0.0447274i
$358$		0			0
$359$			3997.53i			0.587693i	0.955853	+	0.293846i	$0.0949354\pi$
$359$			3997.53i			0.587693i	−0.955853	+	0.293846i	$0.905065\pi$
$360$		0			0
$361$		−	4017.46i		−	0.585721i
$362$		0			0
$363$	3635.04	+	7431.41i	0.525593	+	1.07451i
$364$		0			0
$365$	14007.5	+	14007.5i	2.00873	+	2.00873i
$366$		0			0
$367$		−	4404.23i		−	0.626428i	−0.949683	−	0.313214i	$-0.898594\pi$
$367$		−	4404.23i		−	0.626428i	0.949683	−	0.313214i	$-0.101406\pi$
$368$		0			0
$369$	−4998.32	+	6427.73i	−0.705155	+	0.906813i
$370$		0			0
$371$	−114.793	+	114.793i	−0.0160641	+	0.0160641i
$372$		0			0
$373$	−6347.59	−	6347.59i	−0.881141	−	0.881141i	0.112509	−	0.993651i	$-0.464111\pi$
$373$	−6347.59	−	6347.59i	−0.881141	−	0.881141i	−0.993651	+	0.112509i	$0.964111\pi$
$374$		0			0
$375$	1214.42	+	416.608i	0.167232	+	0.0573694i
$376$		0			0
$377$	−1065.61			−0.145574
$378$		0			0
$379$	−7494.33	+	7494.33i	−1.01572	+	1.01572i	−0.0158460	+	0.999874i	$0.505044\pi$
$379$	−7494.33	+	7494.33i	−1.01572	+	1.01572i	−0.999874	+	0.0158460i	$0.994956\pi$
$380$		0			0
$381$	−98.1478	−	200.652i	−0.0131975	−	0.0269808i
$382$		0			0
$383$	14197.9			1.89420			0.947100	−	0.320940i	$-0.103999\pi$
$383$	14197.9			1.89420			0.947100	+	0.320940i	$0.103999\pi$
$384$		0			0
$385$	729.967			0.0966300
$386$		0			0
$387$	−455.665	−	3642.38i	−0.0598521	−	0.478431i
$388$		0			0
$389$	−9377.75	+	9377.75i	−1.22229	+	1.22229i	−0.255475	+	0.966816i	$0.582232\pi$
$389$	−9377.75	+	9377.75i	−1.22229	+	1.22229i	−0.966816	+	0.255475i	$0.917768\pi$
$390$		0			0
$391$	−12442.3			−1.60930
$392$		0			0
$393$	−1327.06	+	3868.38i	−0.170334	+	0.496524i
$394$		0			0
$395$	−454.342	−	454.342i	−0.0578745	−	0.0578745i
$396$		0			0
$397$	303.909	−	303.909i	0.0384201	−	0.0384201i	−0.687636	−	0.726056i	$-0.741351\pi$
$397$	303.909	−	303.909i	0.0384201	−	0.0384201i	0.726056	+	0.687636i	$0.241351\pi$
$398$		0			0
$399$	−217.228	−	74.5204i	−0.0272556	−	0.00935009i
$400$		0			0
$401$			13634.6i			1.69795i	0.528432	+	0.848976i	$0.322780\pi$
$401$			13634.6i			1.69795i	−0.528432	+	0.848976i	$0.677220\pi$
$402$		0			0
$403$	4531.16	+	4531.16i	0.560082	+	0.560082i
$404$		0			0
$405$	10203.3	+	6067.60i	1.25187	+	0.744448i
$406$		0			0
$407$			13519.3i			1.64651i
$408$		0			0
$409$			3759.45i			0.454506i	0.973836	+	0.227253i	$0.0729744\pi$
$409$			3759.45i			0.454506i	−0.973836	+	0.227253i	$0.927026\pi$
$410$		0			0
$411$	7267.66	−	3554.94i	0.872232	−	0.426648i
$412$		0			0
$413$	−139.603	−	139.603i	−0.0166329	−	0.0166329i
$414$		0			0
$415$			6763.91i			0.800066i
$416$		0			0
$417$	1628.37	−	4746.71i	0.191227	−	0.557428i
$418$		0			0
$419$	−4010.59	+	4010.59i	−0.467614	+	0.467614i	−0.901141	−	0.433527i	$-0.857269\pi$
$419$	−4010.59	+	4010.59i	−0.467614	+	0.467614i	0.433527	+	0.901141i	$0.357269\pi$
$420$		0			0
$421$	909.573	+	909.573i	0.105297	+	0.105297i	0.757792	−	0.652496i	$-0.226278\pi$
$421$	909.573	+	909.573i	0.105297	+	0.105297i	−0.652496	+	0.757792i	$0.726278\pi$
$422$		0			0
$423$	2030.11	−	2610.68i	0.233351	−	0.300084i
$424$		0			0
$425$	10927.6			1.24721
$426$		0			0
$427$	147.884	−	147.884i	0.0167603	−	0.0167603i
$428$		0			0
$429$	−7144.60	+	3494.75i	−0.804066	+	0.393305i
$430$		0			0
$431$	−4734.20			−0.529092			−0.264546	−	0.964373i	$-0.585222\pi$
$431$	−4734.20			−0.529092			−0.264546	+	0.964373i	$0.585222\pi$
$432$		0			0
$433$	−4314.42			−0.478841			−0.239420	−	0.970916i	$-0.576957\pi$
$433$	−4314.42			−0.478841			−0.239420	+	0.970916i	$0.576957\pi$
$434$		0			0
$435$	−2860.93	+	1399.41i	−0.315335	+	0.154245i
$436$		0			0
$437$	−6015.95	+	6015.95i	−0.658539	+	0.658539i
$438$		0			0
$439$	12834.1			1.39531			0.697654	−	0.716435i	$-0.254227\pi$
$439$	12834.1			1.39531			0.697654	+	0.716435i	$0.254227\pi$
$440$		0			0
$441$	−5673.58	+	7296.10i	−0.612632	+	0.787831i
$442$		0			0
$443$	−1859.08	−	1859.08i	−0.199385	−	0.199385i	0.600351	−	0.799736i	$-0.295027\pi$
$443$	−1859.08	−	1859.08i	−0.199385	−	0.199385i	−0.799736	+	0.600351i	$0.795027\pi$
$444$		0			0
$445$	8440.17	−	8440.17i	0.899107	−	0.899107i
$446$		0			0
$447$	342.706	−	998.991i	0.0362628	−	0.105706i
$448$		0			0
$449$		−	8018.01i		−	0.842747i	−0.906887	−	0.421373i	$-0.861548\pi$
$449$		−	8018.01i		−	0.842747i	0.906887	−	0.421373i	$-0.138452\pi$
$450$		0			0
$451$	−11529.1	−	11529.1i	−1.20374	−	1.20374i
$452$		0			0
$453$	6663.22	−	3259.28i	0.691093	−	0.338045i
$454$		0			0
$455$			382.240i			0.0393840i
$456$		0			0
$457$		−	15869.1i		−	1.62434i	−0.583420	−	0.812171i	$-0.698286\pi$
$457$		−	15869.1i		−	1.62434i	0.583420	−	0.812171i	$-0.301714\pi$
$458$		0			0
$459$	10705.9	+	2237.35i	1.08869	+	0.227517i
$460$		0			0
$461$	−2986.52	−	2986.52i	−0.301727	−	0.301727i	0.539962	−	0.841689i	$-0.318438\pi$
$461$	−2986.52	−	2986.52i	−0.301727	−	0.301727i	−0.841689	+	0.539962i	$0.818438\pi$
$462$		0			0
$463$		−	18753.3i		−	1.88238i	−0.337883	−	0.941188i	$-0.609711\pi$
$463$		−	18753.3i		−	1.88238i	0.337883	−	0.941188i	$-0.390289\pi$
$464$		0			0
$465$	18115.7	+	6214.64i	1.80666	+	0.619779i
$466$		0			0
$467$	1865.17	−	1865.17i	0.184817	−	0.184817i	−0.608634	−	0.793451i	$-0.708282\pi$
$467$	1865.17	−	1865.17i	0.184817	−	0.184817i	0.793451	+	0.608634i	$0.208282\pi$
$468$		0			0
$469$	−193.397	−	193.397i	−0.0190410	−	0.0190410i
$470$		0			0
$471$	5313.39	−	15488.6i	0.519805	−	1.51524i
$472$		0			0
$473$	7350.48			0.714536
$474$		0			0
$475$	5283.56	−	5283.56i	0.510372	−	0.510372i
$476$		0			0
$477$	−656.246	−	5245.74i	−0.0629926	−	0.503535i
$478$		0			0
$479$	−15505.8			−1.47907			−0.739536	−	0.673117i	$-0.764955\pi$
$479$	−15505.8			−1.47907			−0.739536	+	0.673117i	$0.764955\pi$
$480$		0			0
$481$	−7079.27			−0.671075
$482$		0			0
$483$	−302.132	−	617.673i	−0.0284627	−	0.0581886i
$484$		0			0
$485$	−5201.10	+	5201.10i	−0.486948	+	0.486948i
$486$		0			0
$487$	−3905.87			−0.363433			−0.181716	−	0.983351i	$-0.558165\pi$
$487$	−3905.87			−0.363433			−0.181716	+	0.983351i	$0.558165\pi$
$488$		0			0
$489$	2905.67	+	996.798i	0.268710	+	0.0921815i
$490$		0			0
$491$	−394.762	−	394.762i	−0.0362839	−	0.0362839i	0.688732	−	0.725016i	$-0.258168\pi$
$491$	−394.762	−	394.762i	−0.0362839	−	0.0362839i	−0.725016	+	0.688732i	$0.758168\pi$
$492$		0			0
$493$	−2074.85	+	2074.85i	−0.189546	+	0.189546i
$494$		0			0
$495$	−14592.2	+	18765.3i	−1.32499	+	1.70391i
$496$		0			0
$497$			554.205i			0.0500191i
$498$		0			0
$499$	−10139.9	−	10139.9i	−0.909665	−	0.909665i	0.0865797	−	0.996245i	$-0.472406\pi$
$499$	−10139.9	−	10139.9i	−0.909665	−	0.909665i	−0.996245	+	0.0865797i	$0.972406\pi$
$500$		0			0
$501$	−8836.77	−	18065.7i	−0.788020	−	1.61101i
$502$		0			0
$503$		−	4295.85i		−	0.380800i	−0.981707	−	0.190400i	$-0.939022\pi$
$503$		−	4295.85i		−	0.380800i	0.981707	−	0.190400i	$-0.0609785\pi$
$504$		0			0
$505$			22843.2i			2.01289i
$506$		0			0
$507$	3186.13	+	6513.67i	0.279095	+	0.570576i
$508$		0			0
$509$	−10770.7	−	10770.7i	−0.937927	−	0.937927i	0.0602555	−	0.998183i	$-0.480808\pi$
$509$	−10770.7	−	10770.7i	−0.937927	−	0.937927i	−0.998183	+	0.0602555i	$0.980808\pi$
$510$		0			0
$511$			1008.62i			0.0873163i
$512$		0			0
$513$	6258.14	−	4094.59i	0.538603	−	0.352399i
$514$		0			0
$515$	1998.36	−	1998.36i	0.170987	−	0.170987i
$516$		0			0
$517$	4682.65	+	4682.65i	0.398342	+	0.398342i
$518$		0			0
$519$	8963.46	+	3074.93i	0.758097	+	0.260067i
$520$		0			0
$521$	16048.6			1.34952			0.674761	−	0.738036i	$-0.264247\pi$
$521$	16048.6			1.34952			0.674761	+	0.738036i	$0.264247\pi$
$522$		0			0
$523$	−16568.1	+	16568.1i	−1.38523	+	1.38523i	−0.550185	+	0.835043i	$0.685443\pi$
$523$	−16568.1	+	16568.1i	−1.38523	+	1.38523i	−0.835043	+	0.550185i	$0.814557\pi$
$524$		0			0
$525$	265.350	+	542.477i	0.0220587	+	0.0450965i
$526$		0			0
$527$	17645.3			1.45852
$528$		0			0
$529$	−13306.3			−1.09363
$530$		0			0
$531$	6379.47	−	798.077i	0.521366	−	0.0652233i
$532$		0			0
$533$	6037.12	−	6037.12i	0.490613	−	0.490613i
$534$		0			0
$535$	4978.95			0.402353
$536$		0			0
$537$	−4214.20	+	12284.4i	−0.338652	+	0.987174i
$538$		0			0
$539$	−13086.7	−	13086.7i	−1.04580	−	1.04580i
$540$		0			0
$541$	−212.644	+	212.644i	−0.0168988	+	0.0168988i	−0.715506	−	0.698607i	$-0.753804\pi$
$541$	−212.644	+	212.644i	−0.0168988	+	0.0168988i	0.698607	+	0.715506i	$0.253804\pi$
$542$		0			0
$543$	2902.34	+	995.653i	0.229376	+	0.0786880i
$544$		0			0
$545$		−	20338.8i		−	1.59856i
$546$		0			0
$547$	−6455.68	−	6455.68i	−0.504616	−	0.504616i	0.408253	−	0.912869i	$-0.366138\pi$
$547$	−6455.68	−	6455.68i	−0.504616	−	0.504616i	−0.912869	+	0.408253i	$0.866138\pi$
$548$		0			0
$549$	845.422	+	6757.92i	0.0657226	+	0.525357i
$550$		0			0
$551$			2006.40i			0.155128i
$552$		0			0
$553$		−	32.7151i		−	0.00251571i
$554$		0			0
$555$	−19006.3	+	9296.86i	−1.45365	+	0.711044i
$556$		0			0
$557$	2281.17	+	2281.17i	0.173530	+	0.173530i	0.788528	−	0.614998i	$-0.210843\pi$
$557$	2281.17	+	2281.17i	0.173530	+	0.173530i	−0.614998	+	0.788528i	$0.710843\pi$
$558$		0			0
$559$			3849.01i			0.291227i
$560$		0			0
$561$	−7106.63	+	20715.9i	−0.534835	+	1.55905i
$562$		0			0
$563$	8170.55	−	8170.55i	0.611630	−	0.611630i	−0.331741	−	0.943371i	$-0.607636\pi$
$563$	8170.55	−	8170.55i	0.611630	−	0.611630i	0.943371	+	0.331741i	$0.107636\pi$
$564$		0			0
$565$	−22059.4	−	22059.4i	−1.64256	−	1.64256i
$566$		0			0
$567$	148.898	+	585.799i	0.0110285	+	0.0433885i
$568$		0			0
$569$	−17007.4			−1.25305			−0.626526	−	0.779400i	$-0.715524\pi$
$569$	−17007.4			−1.25305			−0.626526	+	0.779400i	$0.715524\pi$
$570$		0			0
$571$	−1588.50	+	1588.50i	−0.116421	+	0.116421i	−0.762917	−	0.646496i	$-0.776234\pi$
$571$	−1588.50	+	1588.50i	−0.116421	+	0.116421i	0.646496	+	0.762917i	$0.276234\pi$
$572$		0			0
$573$	5514.69	−	2697.49i	0.402058	−	0.196665i
$574$		0			0
$575$	22372.1			1.62258
$576$		0			0
$577$	−9412.03			−0.679078			−0.339539	−	0.940592i	$-0.610271\pi$
$577$	−9412.03			−0.679078			−0.339539	+	0.940592i	$0.610271\pi$
$578$		0			0
$579$	−8377.86	+	4097.99i	−0.601333	+	0.294139i
$580$		0			0
$581$	−243.520	+	243.520i	−0.0173888	+	0.0173888i
$582$		0			0
$583$	10586.1			0.752029
$584$		0			0
$585$	−9826.27	−	7641.09i	−0.694472	−	0.540034i
$586$		0			0
$587$	−1526.76	−	1526.76i	−0.107353	−	0.107353i	0.651390	−	0.758743i	$-0.274186\pi$
$587$	−1526.76	−	1526.76i	−0.107353	−	0.107353i	−0.758743	+	0.651390i	$0.774186\pi$
$588$		0			0
$589$	8531.60	−	8531.60i	0.596839	−	0.596839i
$590$		0			0
$591$	75.6247	−	220.447i	0.00526360	−	0.0153434i
$592$		0			0
$593$		−	4477.09i		−	0.310037i	−0.987912	−	0.155019i	$-0.950456\pi$
$593$		−	4477.09i		−	0.310037i	0.987912	−	0.155019i	$-0.0495437\pi$
$594$		0			0
$595$	744.261	+	744.261i	0.0512802	+	0.0512802i
$596$		0			0
$597$	20221.9	−	9891.43i	1.38631	−	0.678106i
$598$		0			0
$599$		−	15005.4i		−	1.02354i	−0.859121	−	0.511772i	$-0.828989\pi$
$599$		−	15005.4i		−	1.02354i	0.859121	−	0.511772i	$-0.171011\pi$
$600$		0			0
$601$			2400.70i			0.162939i	0.996676	+	0.0814696i	$0.0259613\pi$
$601$			2400.70i			0.162939i	−0.996676	+	0.0814696i	$0.974039\pi$
$602$		0			0
$603$	8837.73	−	1105.61i	0.596849	−	0.0746663i
$604$		0			0
$605$	−18332.5	−	18332.5i	−1.23194	−	1.23194i
$606$		0			0
$607$			6723.04i			0.449555i	0.974410	+	0.224777i	$0.0721655\pi$
$607$			6723.04i			0.449555i	−0.974410	+	0.224777i	$0.927835\pi$
$608$		0			0
$609$	−153.384	−	52.6187i	−0.0102060	−	0.00350118i
$610$		0			0
$611$	−2452.03	+	2452.03i	−0.162354	+	0.162354i
$612$		0			0
$613$	−9705.73	−	9705.73i	−0.639495	−	0.639495i	0.310936	−	0.950431i	$-0.399358\pi$
$613$	−9705.73	−	9705.73i	−0.639495	−	0.639495i	−0.950431	+	0.310936i	$0.899358\pi$
$614$		0			0
$615$	8280.12	−	24136.6i	0.542905	−	1.58257i
$616$		0			0
$617$	−3612.89			−0.235737			−0.117868	−	0.993029i	$-0.537606\pi$
$617$	−3612.89			−0.235737			−0.117868	+	0.993029i	$0.537606\pi$
$618$		0			0
$619$	7079.67	−	7079.67i	0.459703	−	0.459703i	−0.438855	−	0.898558i	$-0.644616\pi$
$619$	7079.67	−	7079.67i	0.459703	−	0.459703i	0.898558	+	0.438855i	$0.144616\pi$
$620$		0			0
$621$	21918.2	+	4580.53i	1.41634	+	0.295991i
$622$		0			0
$623$	607.739			0.0390828
$624$		0			0
$625$	13498.1			0.863879
$626$		0			0
$627$	6580.17	+	13452.4i	0.419117	+	0.856836i
$628$		0			0
$629$	−13784.1	+	13784.1i	−0.873779	+	0.873779i
$630$		0			0
$631$	−11384.1			−0.718217			−0.359108	−	0.933296i	$-0.616919\pi$
$631$	−11384.1			−0.718217			−0.359108	+	0.933296i	$0.616919\pi$
$632$		0			0
$633$	15925.9	+	5463.40i	0.999994	+	0.343050i
$634$		0			0
$635$	494.986	+	494.986i	0.0309337	+	0.0309337i
$636$		0			0
$637$	6852.73	−	6852.73i	0.426240	−	0.426240i
$638$		0			0
$639$	−14247.0	−	11078.7i	−0.882005	−	0.685863i
$640$		0			0
$641$		−	7632.61i		−	0.470312i	−0.971958	−	0.235156i	$-0.924440\pi$
$641$		−	7632.61i		−	0.470312i	0.971958	−	0.235156i	$-0.0755601\pi$
$642$		0			0
$643$	4357.38	+	4357.38i	0.267245	+	0.267245i	0.827989	−	0.560744i	$-0.189485\pi$
$643$	4357.38	+	4357.38i	0.267245	+	0.267245i	−0.560744	+	0.827989i	$0.689485\pi$
$644$		0			0
$645$	5054.71	+	10333.8i	0.308572	+	0.630840i
$646$		0			0
$647$			15886.6i			0.965326i	0.875806	+	0.482663i	$0.160330\pi$
$647$			15886.6i			0.965326i	−0.875806	+	0.482663i	$0.839670\pi$
$648$		0			0
$649$			12874.0i			0.778660i
$650$		0			0
$651$	428.472	+	875.961i	0.0257959	+	0.0527367i
$652$		0			0
$653$	8850.83	+	8850.83i	0.530413	+	0.530413i	0.920695	−	0.390282i	$-0.127622\pi$
$653$	8850.83	+	8850.83i	0.530413	+	0.530413i	−0.390282	+	0.920695i	$0.627622\pi$
$654$		0			0
$655$		−	12816.6i		−	0.764556i
$656$		0			0
$657$	−25928.6	−	20162.6i	−1.53968	−	1.19728i
$658$		0			0
$659$	−8224.56	+	8224.56i	−0.486166	+	0.486166i	−0.907094	−	0.420928i	$-0.861705\pi$
$659$	−8224.56	+	8224.56i	−0.486166	+	0.486166i	0.420928	+	0.907094i	$0.361705\pi$
$660$		0			0
$661$	8586.18	+	8586.18i	0.505240	+	0.505240i	0.913062	−	0.407822i	$-0.133711\pi$
$661$	8586.18	+	8586.18i	0.505240	+	0.505240i	−0.407822	+	0.913062i	$0.633711\pi$
$662$		0			0
$663$	−10847.7	−	3721.32i	−0.635429	−	0.217985i
$664$		0			0
$665$	719.710			0.0419687
$666$		0			0
$667$	−4247.85	+	4247.85i	−0.246593	+	0.246593i
$668$		0			0
$669$	−2310.86	−	4724.27i	−0.133547	−	0.273021i
$670$		0			0
$671$	−13637.8			−0.784621
$672$		0			0
$673$	24087.3			1.37964			0.689821	−	0.723980i	$-0.257689\pi$
$673$	24087.3			1.37964			0.689821	+	0.723980i	$0.257689\pi$
$674$		0			0
$675$	−19249.9	−	4022.90i	−1.09767	−	0.229395i
$676$		0			0
$677$	−11065.3	+	11065.3i	−0.628174	+	0.628174i	−0.947608	−	0.319434i	$-0.896507\pi$
$677$	−11065.3	+	11065.3i	−0.628174	+	0.628174i	0.319434	+	0.947608i	$0.396507\pi$
$678$		0			0
$679$	−374.508			−0.0211669
$680$		0			0
$681$	520.469	−	1517.17i	0.0292869	−	0.0853717i
$682$		0			0
$683$	13547.1	+	13547.1i	0.758955	+	0.758955i	0.976132	−	0.217177i	$-0.0696849\pi$
$683$	13547.1	+	13547.1i	0.758955	+	0.758955i	−0.217177	+	0.976132i	$0.569685\pi$
$684$		0			0
$685$	−17928.5	+	17928.5i	−1.00002	+	1.00002i
$686$		0			0
$687$	−3914.46	−	1342.86i	−0.217389	−	0.0745756i
$688$		0			0
$689$			5543.33i			0.306508i
$690$		0			0
$691$	−5857.82	−	5857.82i	−0.322492	−	0.322492i	0.527230	−	0.849722i	$-0.323230\pi$
$691$	−5857.82	−	5857.82i	−0.322492	−	0.322492i	−0.849722	+	0.527230i	$0.823230\pi$
$692$		0			0
$693$	−1200.96	+	150.242i	−0.0658309	+	0.00823550i
$694$		0			0
$695$			15726.6i			0.858338i
$696$		0			0
$697$		−	23509.8i		−	1.27761i
$698$		0			0
$699$	3017.33	−	1475.91i	0.163270	−	0.0798629i
$700$		0			0
$701$	16142.4	+	16142.4i	0.869743	+	0.869743i	0.992444	−	0.122701i	$-0.0391555\pi$
$701$	16142.4	+	16142.4i	0.869743	+	0.869743i	−0.122701	+	0.992444i	$0.539156\pi$
$702$		0			0
$703$			13329.4i			0.715117i
$704$		0			0
$705$	−3363.04	+	9803.29i	−0.179659	+	0.523707i
$706$		0			0
$707$	−822.418	+	822.418i	−0.0437485	+	0.0437485i
$708$		0			0
$709$	12454.7	+	12454.7i	0.659729	+	0.659729i	0.955316	−	0.295587i	$-0.0955153\pi$
$709$	12454.7	+	12454.7i	0.659729	+	0.659729i	−0.295587	+	0.955316i	$0.595515\pi$
$710$		0			0
$711$	841.010	+	653.985i	0.0443605	+	0.0344956i
$712$		0			0
$713$	36125.2			1.89748
$714$		0			0
$715$	17624.9	−	17624.9i	0.921867	−	0.921867i
$716$		0			0
$717$	−4650.63	+	2274.84i	−0.242233	+	0.118487i
$718$		0			0
$719$	6194.00			0.321276			0.160638	−	0.987013i	$-0.448645\pi$
$719$	6194.00			0.321276			0.160638	+	0.987013i	$0.448645\pi$
$720$		0			0
$721$	143.893			0.00743253
$722$		0			0
$723$	21139.5	−	10340.3i	1.08739	−	0.531893i
$724$		0			0
$725$	3730.71	−	3730.71i	0.191111	−	0.191111i
$726$		0			0
$727$	9470.69			0.483148			0.241574	−	0.970382i	$-0.422336\pi$
$727$	9470.69			0.483148			0.241574	+	0.970382i	$0.422336\pi$
$728$		0			0
$729$	−18035.7	−	7882.55i	−0.916308	−	0.400475i
$730$		0			0
$731$	7494.42	+	7494.42i	0.379194	+	0.379194i
$732$		0			0
$733$	−12537.1	+	12537.1i	−0.631744	+	0.631744i	−0.948505	−	0.316761i	$-0.897405\pi$
$733$	−12537.1	+	12537.1i	−0.631744	+	0.631744i	0.316761	+	0.948505i	$0.397405\pi$
$734$		0			0
$735$	9398.75	−	27397.4i	0.471671	−	1.37492i
$736$		0			0
$737$			17834.9i			0.891394i
$738$		0			0
$739$	25128.2	+	25128.2i	1.25082	+	1.25082i	0.955354	+	0.295464i	$0.0954741\pi$
$739$	25128.2	+	25128.2i	1.25082	+	1.25082i	0.295464	+	0.955354i	$0.404526\pi$
$740$		0			0
$741$	−7044.21	+	3445.64i	−0.349225	+	0.170822i
$742$		0			0
$743$			11784.5i			0.581875i	0.956742	+	0.290937i	$0.0939672\pi$
$743$			11784.5i			0.581875i	−0.956742	+	0.290937i	$0.906033\pi$
$744$		0			0
$745$			3309.82i			0.162768i
$746$		0			0
$747$	−1392.15	−	11128.2i	−0.0681874	−	0.545060i
$748$		0			0
$749$	179.256	+	179.256i	0.00874483	+	0.00874483i
$750$		0			0
$751$			18414.2i			0.894734i	0.894351	+	0.447367i	$0.147638\pi$
$751$			18414.2i			0.894734i	−0.894351	+	0.447367i	$0.852362\pi$
$752$		0			0
$753$	25110.1	+	8614.07i	1.21522	+	0.416885i
$754$		0			0
$755$	−16437.4	+	16437.4i	−0.792343	+	0.792343i
$756$		0			0
$757$	17074.1	+	17074.1i	0.819774	+	0.819774i	0.986075	−	0.166301i	$-0.0531825\pi$
$757$	17074.1	+	17074.1i	0.819774	+	0.819774i	−0.166301	+	0.986075i	$0.553182\pi$
$758$		0			0
$759$	−14549.5	+	42411.8i	−0.695800	+	2.02826i
$760$		0			0
$761$	−24788.6			−1.18080			−0.590399	−	0.807112i	$-0.701030\pi$
$761$	−24788.6			−1.18080			−0.590399	+	0.807112i	$0.701030\pi$
$762$		0			0
$763$	732.253	−	732.253i	0.0347436	−	0.0347436i
$764$		0			0
$765$	−34010.7	+	4254.77i	−1.60740	+	0.201087i
$766$		0			0
$767$	−6741.37			−0.317362
$768$		0			0
$769$	8902.84			0.417483			0.208742	−	0.977971i	$-0.433063\pi$
$769$	8902.84			0.417483			0.208742	+	0.977971i	$0.433063\pi$
$770$		0			0
$771$	−3835.11	−	7840.43i	−0.179141	−	0.366233i
$772$		0			0
$773$	12931.4	−	12931.4i	0.601694	−	0.601694i	−0.339068	−	0.940762i	$-0.610112\pi$
$773$	12931.4	−	12931.4i	0.601694	−	0.601694i	0.940762	+	0.339068i	$0.110112\pi$
$774$		0			0
$775$	−31727.4			−1.47056
$776$		0			0
$777$	−1018.99	−	349.568i	−0.0470479	−	0.0161399i
$778$		0			0
$779$	−11367.1	−	11367.1i	−0.522811	−	0.522811i
$780$		0			0
$781$	25554.1	−	25554.1i	1.17081	−	1.17081i
$782$		0			0
$783$	4418.86	−	2891.19i	0.201682	−	0.131957i
$784$		0			0
$785$			51316.2i			2.33319i
$786$		0			0
$787$	−18783.4	−	18783.4i	−0.850770	−	0.850770i	0.139458	−	0.990228i	$-0.455464\pi$
$787$	−18783.4	−	18783.4i	−0.850770	−	0.850770i	−0.990228	+	0.139458i	$0.955464\pi$
$788$		0			0
$789$	−3594.69	−	7348.92i	−0.162198	−	0.331595i
$790$		0			0
$791$		−	1588.40i		−	0.0713995i
$792$		0			0
$793$		−	7141.30i		−	0.319792i
$794$		0			0
$795$	7279.78	+	14882.6i	0.324764	+	0.663941i
$796$		0			0
$797$	14788.0	+	14788.0i	0.657237	+	0.657237i	0.954725	−	0.297488i	$-0.0961489\pi$
$797$	14788.0	+	14788.0i	0.657237	+	0.657237i	−0.297488	+	0.954725i	$0.596149\pi$
$798$		0			0
$799$			9548.70i			0.422789i
$800$		0			0
$801$	−12148.9	+	15623.2i	−0.535904	+	0.689161i
$802$		0			0
$803$	46507.0	−	46507.0i	2.04383	−	2.04383i
$804$		0			0
$805$	1523.73	+	1523.73i	0.0667136	+	0.0667136i
$806$		0			0
$807$	−9147.55	−	3138.09i	−0.399020	−	0.136885i
$808$		0			0
$809$	−34139.0			−1.48364			−0.741820	−	0.670600i	$-0.766037\pi$
$809$	−34139.0			−1.48364			−0.741820	+	0.670600i	$0.766037\pi$
$810$		0			0
$811$	18395.6	−	18395.6i	0.796494	−	0.796494i	−0.186047	−	0.982541i	$-0.559568\pi$
$811$	18395.6	−	18395.6i	0.796494	−	0.796494i	0.982541	+	0.186047i	$0.0595676\pi$
$812$		0			0
$813$	9240.11	+	18890.3i	0.398604	+	0.814898i
$814$		0			0
$815$	−9626.97			−0.413764
$816$		0			0
$817$	7247.20			0.310340
$818$		0			0
$819$	−78.6726	−	628.873i	−0.00335658	−	0.0268310i
$820$		0			0
$821$	22428.5	−	22428.5i	0.953423	−	0.953423i	−0.0455394	−	0.998963i	$-0.514501\pi$
$821$	22428.5	−	22428.5i	0.953423	−	0.953423i	0.998963	+	0.0455394i	$0.0145007\pi$
$822$		0			0
$823$	34300.0			1.45276			0.726381	−	0.687293i	$-0.241201\pi$
$823$	34300.0			1.45276			0.726381	+	0.687293i	$0.241201\pi$
$824$		0			0
$825$	12778.2	−	37248.6i	0.539249	−	1.57191i
$826$		0			0
$827$	−12181.0	−	12181.0i	−0.512182	−	0.512182i	0.403013	−	0.915194i	$-0.367963\pi$
$827$	−12181.0	−	12181.0i	−0.512182	−	0.512182i	−0.915194	+	0.403013i	$0.867963\pi$
$828$		0			0
$829$	−29681.5	+	29681.5i	−1.24352	+	1.24352i	−0.284992	+	0.958530i	$0.591991\pi$
$829$	−29681.5	+	29681.5i	−1.24352	+	1.24352i	−0.958530	+	0.284992i	$0.908009\pi$
$830$		0			0
$831$	31270.2	+	10727.3i	1.30536	+	0.447805i
$832$		0			0
$833$		−	26685.9i		−	1.10998i
$834$		0			0
$835$	44566.2	+	44566.2i	1.84704	+	1.84704i
$836$		0			0
$837$	−31083.6	−	6495.94i	−1.28364	−	0.268259i
$838$		0			0
$839$			5645.20i			0.232293i	0.993232	+	0.116147i	$0.0370543\pi$
$839$			5645.20i			0.232293i	−0.993232	+	0.116147i	$0.962946\pi$
$840$		0			0
$841$		−	22972.3i		−	0.941912i
$842$		0			0
$843$	−13334.4	+	6522.46i	−0.544793	+	0.266483i
$844$		0			0
$845$	−16068.5	−	16068.5i	−0.654170	−	0.654170i
$846$		0			0
$847$		−	1320.04i		−	0.0535503i
$848$		0			0
$849$	13022.1	−	37959.6i	0.526406	−	1.53448i
$850$		0			0
$851$	−28220.2	+	28220.2i	−1.13675	+	1.13675i
$852$		0			0
$853$	8393.54	+	8393.54i	0.336916	+	0.336916i	0.855205	−	0.518289i	$-0.173431\pi$
$853$	8393.54	+	8393.54i	0.336916	+	0.336916i	−0.518289	+	0.855205i	$0.673431\pi$
$854$		0			0
$855$	−14387.2	+	18501.6i	−0.575476	+	0.740049i
$856$		0			0
$857$	22054.9			0.879092			0.439546	−	0.898220i	$-0.355139\pi$
$857$	22054.9			0.879092			0.439546	+	0.898220i	$0.355139\pi$
$858$		0			0
$859$	−33958.2	+	33958.2i	−1.34882	+	1.34882i	−0.461884	+	0.886941i	$0.652826\pi$
$859$	−33958.2	+	33958.2i	−1.34882	+	1.34882i	−0.886941	+	0.461884i	$0.847174\pi$
$860$		0			0
$861$	1167.09	−	570.878i	0.0461956	−	0.0225964i
$862$		0			0
$863$	−35981.7			−1.41927			−0.709635	−	0.704569i	$-0.751140\pi$
$863$	−35981.7			−1.41927			−0.709635	+	0.704569i	$0.751140\pi$
$864$		0			0
$865$	−29697.4			−1.16733
$866$		0			0
$867$	−5435.09	+	2658.55i	−0.212901	+	0.104140i
$868$		0			0
$869$	−1508.48	+	1508.48i	−0.0588858	+	0.0588858i
$870$		0			0
$871$	−9339.08			−0.363310
$872$		0			0
$873$	7486.52	−	9627.50i	0.290241	−	0.373244i
$874$		0			0
$875$	−144.859	−	144.859i	−0.00559672	−	0.00559672i
$876$		0			0
$877$	−9471.30	+	9471.30i	−0.364679	+	0.364679i	−0.865532	−	0.500854i	$-0.833020\pi$
$877$	−9471.30	+	9471.30i	−0.364679	+	0.364679i	0.500854	+	0.865532i	$0.333020\pi$
$878$		0			0
$879$	−11028.2	+	32147.4i	−0.423178	+	1.23357i
$880$		0			0
$881$		−	47824.3i		−	1.82888i	−0.404723	−	0.914439i	$-0.632632\pi$
$881$		−	47824.3i		−	1.82888i	0.404723	−	0.914439i	$-0.367368\pi$
$882$		0			0
$883$	25305.1	+	25305.1i	0.964421	+	0.964421i	0.999388	−	0.0349671i	$-0.0111326\pi$
$883$	25305.1	+	25305.1i	0.964421	+	0.964421i	−0.0349671	+	0.999388i	$0.511133\pi$
$884$		0			0
$885$	−18099.1	+	8853.11i	−0.687453	+	0.336264i
$886$		0			0
$887$		−	43498.3i		−	1.64659i	−0.567611	−	0.823297i	$-0.692132\pi$
$887$		−	43498.3i		−	1.64659i	0.567611	−	0.823297i	$-0.307868\pi$
$888$		0			0
$889$			35.6417i			0.00134464i
$890$		0			0
$891$	20145.3	−	33876.6i	0.757456	−	1.27375i
$892$		0			0
$893$	4616.86	+	4616.86i	0.173009	+	0.173009i
$894$		0			0
$895$		−	40700.3i		−	1.52007i
$896$		0			0
$897$	−22208.5	−	7618.69i	−0.826668	−	0.283590i
$898$		0			0
$899$	6024.14	−	6024.14i	0.223489	−	0.223489i
$900$		0			0
$901$	10793.4	+	10793.4i	0.399091	+	0.399091i
$902$		0			0
$903$	−190.061	+	554.028i	−0.00700423	+	0.0204174i
$904$		0			0
$905$	−9615.91			−0.353198
$906$		0			0
$907$	23466.1	−	23466.1i	0.859074	−	0.859074i	−0.132155	−	0.991229i	$-0.542190\pi$
$907$	23466.1	−	23466.1i	0.859074	−	0.859074i	0.991229	+	0.132155i	$0.0421895\pi$
$908$		0			0
$909$	−4701.57	−	37582.3i	−0.171553	−	1.37132i
$910$		0			0
$911$	18223.3			0.662749			0.331375	−	0.943499i	$-0.392488\pi$
$911$	18223.3			0.662749			0.331375	+	0.943499i	$0.392488\pi$
$912$		0			0
$913$	22457.2			0.814046
$914$		0			0
$915$	−9378.31	−	19172.8i	−0.338839	−	0.692715i
$916$		0			0
$917$	461.432	−	461.432i	0.0166170	−	0.0166170i
$918$		0			0
$919$	−44782.9			−1.60746			−0.803729	−	0.594996i	$-0.797154\pi$
$919$	−44782.9			−1.60746			−0.803729	+	0.594996i	$0.797154\pi$
$920$		0			0
$921$	−9539.00	−	3272.37i	−0.341282	−	0.117078i
$922$		0			0
$923$	13381.2	+	13381.2i	0.477191	+	0.477191i
$924$		0			0
$925$	24784.7	−	24784.7i	0.880990	−	0.880990i
$926$		0			0
$927$	−2876.46	+	3699.06i	−0.101915	+	0.131061i
$928$		0			0
$929$			16925.2i			0.597737i	0.954294	+	0.298868i	$0.0966092\pi$
$929$			16925.2i			0.597737i	−0.954294	+	0.298868i	$0.903391\pi$
$930$		0			0
$931$	−12902.8	−	12902.8i	−0.454213	−	0.454213i
$932$		0			0
$933$	−7407.48	−	15143.7i	−0.259925	−	0.531386i
$934$		0			0
$935$		−	68635.1i		−	2.40065i
$936$		0			0
$937$			31660.1i			1.10383i	0.833900	+	0.551916i	$0.186103\pi$
$937$			31660.1i			1.10383i	−0.833900	+	0.551916i	$0.813897\pi$
$938$		0			0
$939$	−14355.8	−	29348.7i	−0.498917	−	1.01998i
$940$		0			0
$941$	−2381.85	−	2381.85i	−0.0825143	−	0.0825143i	0.664645	−	0.747159i	$-0.268583\pi$
$941$	−2381.85	−	2381.85i	−0.0825143	−	0.0825143i	−0.747159	+	0.664645i	$0.768583\pi$
$942$		0			0
$943$		−	48131.7i		−	1.66213i
$944$		0			0
$945$	−1037.09	−	1585.07i	−0.0356999	−	0.0545634i
$946$		0			0
$947$	21792.3	−	21792.3i	0.747786	−	0.747786i	−0.226277	−	0.974063i	$-0.572655\pi$
$947$	21792.3	−	21792.3i	0.747786	−	0.747786i	0.974063	+	0.226277i	$0.0726554\pi$
$948$		0			0
$949$	24352.9	+	24352.9i	0.833014	+	0.833014i
$950$		0			0
$951$	−32830.1	−	11262.5i	−1.11944	−	0.384027i
$952$		0			0
$953$	−17854.6			−0.606893			−0.303446	−	0.952849i	$-0.598137\pi$
$953$	−17854.6			−0.606893			−0.303446	+	0.952849i	$0.598137\pi$
$954$		0			0
$955$	−13604.1	+	13604.1i	−0.460963	+	0.460963i
$956$		0			0
$957$	4646.24	+	9498.69i	0.156940	+	0.320846i
$958$		0			0
$959$	−1290.95			−0.0434693
$960$		0			0
$961$	−21440.5			−0.719697
$962$		0			0
$963$	−8191.52	+	1024.77i	−0.274110	+	0.0342914i
$964$		0			0
$965$	20667.3	−	20667.3i	0.689433	−	0.689433i
$966$		0			0
$967$	47141.7			1.56771			0.783854	−	0.620945i	$-0.213251\pi$
$967$	47141.7			1.56771			0.783854	+	0.620945i	$0.213251\pi$
$968$		0			0
$969$	−7006.78	+	20424.8i	−0.232291	+	0.677131i
$970$		0			0
$971$	11615.6	+	11615.6i	0.383896	+	0.383896i	0.872504	−	0.488607i	$-0.162495\pi$
$971$	11615.6	+	11615.6i	0.383896	+	0.383896i	−0.488607	+	0.872504i	$0.662495\pi$
$972$		0			0
$973$	−566.202	+	566.202i	−0.0186553	+	0.0186553i
$974$		0			0
$975$	19504.9	+	6691.19i	0.640672	+	0.219784i
$976$		0			0
$977$		−	4822.57i		−	0.157920i	−0.996878	−	0.0789600i	$-0.974840\pi$
$977$		−	4822.57i		−	0.157920i	0.996878	−	0.0789600i	$-0.0251599\pi$
$978$		0			0
$979$	−28022.6	−	28022.6i	−0.914817	−	0.914817i
$980$		0			0
$981$	4186.12	+	33462.0i	0.136241	+	1.08905i
$982$		0			0
$983$		−	3987.14i		−	0.129369i	−0.997906	−	0.0646846i	$-0.979396\pi$
$983$		−	3987.14i		−	0.129369i	0.997906	−	0.0646846i	$-0.0206041\pi$
$984$		0			0
$985$			730.376i			0.0236261i
$986$		0			0
$987$	−474.025	+	231.867i	−0.0152871	+	0.00747762i
$988$		0			0
$989$	15343.4	+	15343.4i	0.493317	+	0.493317i
$990$		0			0
$991$			42114.2i			1.34995i	0.737840	+	0.674976i	$0.235846\pi$
$991$			42114.2i			1.34995i	−0.737840	+	0.674976i	$0.764154\pi$
$992$		0			0
$993$	14574.8	−	42485.7i	0.465778	−	1.35775i
$994$		0			0
$995$	−49885.1	+	49885.1i	−1.58941	+	1.58941i
$996$		0			0
$997$	−19496.0	−	19496.0i	−0.619304	−	0.619304i	0.326049	−	0.945353i	$-0.394283\pi$
$997$	−19496.0	−	19496.0i	−0.619304	−	0.619304i	−0.945353	+	0.326049i	$0.894283\pi$
$998$		0			0
$999$	29356.3	−	19207.4i	0.929723	−	0.608302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.4.k.a.143.19		44
3.2	odd	2	inner	192.4.k.a.143.8		44
4.3	odd	2		48.4.k.a.11.12	yes	44
8.3	odd	2		384.4.k.b.287.19		44
8.5	even	2		384.4.k.a.287.4		44
12.11	even	2		48.4.k.a.11.11	✓	44
16.3	odd	4	inner	192.4.k.a.47.8		44
16.5	even	4		384.4.k.b.95.8		44
16.11	odd	4		384.4.k.a.95.15		44
16.13	even	4		48.4.k.a.35.11	yes	44
24.5	odd	2		384.4.k.a.287.15		44
24.11	even	2		384.4.k.b.287.8		44
48.5	odd	4		384.4.k.b.95.19		44
48.11	even	4		384.4.k.a.95.4		44
48.29	odd	4		48.4.k.a.35.12	yes	44
48.35	even	4	inner	192.4.k.a.47.19		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.11	✓	44	12.11	even	2
48.4.k.a.11.12	yes	44	4.3	odd	2
48.4.k.a.35.11	yes	44	16.13	even	4
48.4.k.a.35.12	yes	44	48.29	odd	4
192.4.k.a.47.8		44	16.3	odd	4	inner
192.4.k.a.47.19		44	48.35	even	4	inner
192.4.k.a.143.8		44	3.2	odd	2	inner
192.4.k.a.143.19		44	1.1	even	1	trivial
384.4.k.a.95.4		44	48.11	even	4
384.4.k.a.95.15		44	16.11	odd	4
384.4.k.a.287.4		44	8.5	even	2
384.4.k.a.287.15		44	24.5	odd	2
384.4.k.b.95.8		44	16.5	even	4
384.4.k.b.95.19		44	48.5	odd	4
384.4.k.b.287.8		44	24.11	even	2
384.4.k.b.287.19		44	8.3	odd	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.66767 - 2.28317i) q^{3} +(-11.5146 + 11.5146i) q^{5} -0.829117 q^{7} +(16.5743 - 21.3142i) q^{9} +O(q^{10})\)	\(q+(4.66767 - 2.28317i) q^{3} +(-11.5146 + 11.5146i) q^{5} -0.829117 q^{7} +(16.5743 - 21.3142i) q^{9} +(38.2302 + 38.2302i) q^{11} +(-20.0189 + 20.0189i) q^{13} +(-27.4566 + 80.0363i) q^{15} +77.9578i q^{17} +(37.6931 + 37.6931i) q^{19} +(-3.87005 + 1.89301i) q^{21} +159.603i q^{23} -140.173i q^{25} +(28.6995 - 137.329i) q^{27} +(26.6150 + 26.6150i) q^{29} -226.344i q^{31} +(265.732 + 91.1601i) q^{33} +(9.54698 - 9.54698i) q^{35} +(176.815 + 176.815i) q^{37} +(-47.7351 + 139.148i) q^{39} -301.571 q^{41} +(96.1344 - 96.1344i) q^{43} +(54.5779 + 436.271i) q^{45} +122.486 q^{47} -342.313 q^{49} +(177.991 + 363.881i) q^{51} +(138.452 - 138.452i) q^{53} -880.414 q^{55} +(261.999 + 89.8792i) q^{57} +(168.375 + 168.375i) q^{59} +(-178.364 + 178.364i) q^{61} +(-13.7420 + 17.6719i) q^{63} -461.021i q^{65} +(233.257 + 233.257i) q^{67} +(364.402 + 744.976i) q^{69} -668.427i q^{71} -1216.50i q^{73} +(-320.039 - 654.283i) q^{75} +(-31.6974 - 31.6974i) q^{77} +39.4578i q^{79} +(-179.586 - 706.534i) q^{81} +(293.710 - 293.710i) q^{83} +(-897.655 - 897.655i) q^{85} +(184.997 + 63.4635i) q^{87} -732.996 q^{89} +(16.5980 - 16.5980i) q^{91} +(-516.781 - 1056.50i) q^{93} -868.044 q^{95} +451.695 q^{97} +(1448.48 - 181.207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{3} + 8 q^{7}+O(q^{10}) \) 44 * q + 2 * q^3 + 8 * q^7	\( 44 q + 2 q^{3} + 8 q^{7} - 4 q^{13} - 20 q^{19} - 56 q^{21} + 134 q^{27} - 4 q^{33} - 4 q^{37} - 596 q^{39} + 436 q^{43} - 252 q^{45} + 972 q^{49} + 648 q^{51} - 280 q^{55} - 916 q^{61} + 1636 q^{67} + 52 q^{69} - 1454 q^{75} - 4 q^{81} + 736 q^{85} - 1284 q^{87} - 424 q^{91} - 2084 q^{93} - 8 q^{97} - 1196 q^{99}+O(q^{100}) \) 44 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 - 20 * q^19 - 56 * q^21 + 134 * q^27 - 4 * q^33 - 4 * q^37 - 596 * q^39 + 436 * q^43 - 252 * q^45 + 972 * q^49 + 648 * q^51 - 280 * q^55 - 916 * q^61 + 1636 * q^67 + 52 * q^69 - 1454 * q^75 - 4 * q^81 + 736 * q^85 - 1284 * q^87 - 424 * q^91 - 2084 * q^93 - 8 * q^97 - 1196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more