LMFDB - Embedded newform 192.4.k.a.47.8

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			47.8
Character	$\chi$	$=$	192.47
Dual form			192.4.k.a.143.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28317 - 4.66767i) q^{3} +(11.5146 + 11.5146i) q^{5} -0.829117 q^{7} +(-16.5743 + 21.3142i) q^{9} +O(q^{10})$	\(q+(-2.28317 - 4.66767i) q^{3} +(11.5146 + 11.5146i) q^{5} -0.829117 q^{7} +(-16.5743 + 21.3142i) q^{9} +(-38.2302 + 38.2302i) q^{11} +(-20.0189 - 20.0189i) q^{13} +(27.4566 - 80.0363i) q^{15} +77.9578i q^{17} +(37.6931 - 37.6931i) q^{19} +(1.89301 + 3.87005i) q^{21} +159.603i q^{23} +140.173i q^{25} +(137.329 + 28.6995i) q^{27} +(-26.6150 + 26.6150i) q^{29} +226.344i q^{31} +(265.732 + 91.1601i) q^{33} +(-9.54698 - 9.54698i) q^{35} +(176.815 - 176.815i) q^{37} +(-47.7351 + 139.148i) q^{39} +301.571 q^{41} +(96.1344 + 96.1344i) q^{43} +(-436.271 + 54.5779i) q^{45} -122.486 q^{47} -342.313 q^{49} +(363.881 - 177.991i) q^{51} +(-138.452 - 138.452i) q^{53} -880.414 q^{55} +(-261.999 - 89.8792i) q^{57} +(-168.375 + 168.375i) q^{59} +(-178.364 - 178.364i) q^{61} +(13.7420 - 17.6719i) q^{63} -461.021i q^{65} +(233.257 - 233.257i) q^{67} +(744.976 - 364.402i) q^{69} -668.427i q^{71} +1216.50i q^{73} +(654.283 - 320.039i) q^{75} +(31.6974 - 31.6974i) q^{77} -39.4578i q^{79} +(-179.586 - 706.534i) q^{81} +(-293.710 - 293.710i) q^{83} +(-897.655 + 897.655i) q^{85} +(184.997 + 63.4635i) q^{87} +732.996 q^{89} +(16.5980 + 16.5980i) q^{91} +(1056.50 - 516.781i) q^{93} +868.044 q^{95} +451.695 q^{97} +(-181.207 - 1448.48i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−2.28317	−	4.66767i	−0.439396	−	0.898293i
$3$	−2.28317	−	4.66767i	−0.439396	−	0.898293i
$4$		0			0
$5$	11.5146	+	11.5146i	1.02990	+	1.02990i	0.999539	+	0.0303606i	$0.00966556\pi$
$5$	11.5146	+	11.5146i	1.02990	+	1.02990i	0.0303606	+	0.999539i	$0.490334\pi$
$6$		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	−0.0491019	+	0.998794i	$0.515636\pi$
$11$	−38.2302	+	38.2302i	−1.04790	+	1.04790i	−0.998794	+	0.0491019i	$0.984364\pi$
$12$		0			0
$13$	−20.0189	−	20.0189i	−0.427096	−	0.427096i	0.460542	−	0.887638i	$-0.347655\pi$
$13$	−20.0189	−	20.0189i	−0.427096	−	0.427096i	−0.887638	+	0.460542i	$0.847655\pi$
$14$		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	−0.441926	−	0.897052i	$-0.645705\pi$
$19$	37.6931	−	37.6931i	0.455126	−	0.455126i	0.897052	+	0.441926i	$0.145705\pi$
$20$		0			0
$21$	1.89301	+	3.87005i	0.0196709	+	0.0402149i
$22$		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
$27$	137.329	+	28.6995i	0.978853	+	0.204563i
$28$		0			0
$29$	−26.6150	+	26.6150i	−0.170424	+	0.170424i	−0.787165	−	0.616742i	$-0.788452\pi$
$29$	−26.6150	+	26.6150i	−0.170424	+	0.170424i	0.616742	+	0.787165i	$0.288452\pi$
$30$		0			0
$31$			226.344i			1.31137i	0.755034	+	0.655686i	$0.227621\pi$
$31$			226.344i			1.31137i	−0.755034	+	0.655686i	$0.772379\pi$
$32$		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	−0.195148	−	0.980774i	$-0.562519\pi$
$37$	176.815	−	176.815i	0.785626	−	0.785626i	0.980774	+	0.195148i	$0.0625188\pi$
$38$		0			0
$39$	−47.7351	+	139.148i	−0.195993	+	0.571322i
$40$		0			0
$41$	301.571			1.14872			0.574359	−	0.818604i	$-0.305251\pi$
$41$	301.571			1.14872			0.574359	+	0.818604i	$0.305251\pi$
$42$		0			0
$43$	96.1344	+	96.1344i	0.340938	+	0.340938i	0.856720	−	0.515782i	$-0.172498\pi$
$43$	96.1344	+	96.1344i	0.340938	+	0.340938i	−0.515782	+	0.856720i	$0.672498\pi$
$44$		0			0
$45$	−436.271	+	54.5779i	−1.44523	+	0.180800i
$46$		0			0
$47$	−122.486			−0.380135			−0.190068	−	0.981771i	$-0.560871\pi$
$47$	−122.486			−0.380135			−0.190068	+	0.981771i	$0.560871\pi$
$48$		0			0
$49$	−342.313			−0.997996
$50$		0			0
$51$	363.881	−	177.991i	0.999089	−	0.488700i
$52$		0			0
$53$	−138.452	−	138.452i	−0.358828	−	0.358828i	0.504553	−	0.863381i	$-0.331657\pi$
$53$	−138.452	−	138.452i	−0.358828	−	0.358828i	−0.863381	+	0.504553i	$0.831657\pi$
$54$		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	$-0.834618\pi$
$59$	−168.375	+	168.375i	−0.371535	+	0.371535i	0.496501	+	0.868036i	$0.334618\pi$
$60$		0			0
$61$	−178.364	−	178.364i	−0.374379	−	0.374379i	0.494690	−	0.869069i	$-0.335282\pi$
$61$	−178.364	−	178.364i	−0.374379	−	0.374379i	−0.869069	+	0.494690i	$0.835282\pi$
$62$		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	−0.461707	−	0.887033i	$-0.652763\pi$
$67$	233.257	−	233.257i	0.425326	−	0.425326i	0.887033	+	0.461707i	$0.152763\pi$
$68$		0			0
$69$	744.976	−	364.402i	1.29978	−	0.635780i
$70$		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	$0.428971\pi$
$73$			1216.50i			1.95041i	−0.221297	+	0.975207i	$0.571029\pi$
$74$		0			0
$75$	654.283	−	320.039i	1.00733	−	0.492733i
$76$		0			0
$77$	31.6974	−	31.6974i	0.0469123	−	0.0469123i
$78$		0			0
$79$		−	39.4578i		−	0.0561943i	−0.999605	−	0.0280971i	$-0.991055\pi$
$79$		−	39.4578i		−	0.0561943i	0.999605	−	0.0280971i	$-0.00894478\pi$
$80$		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	$-0.338563\pi$
$83$	−293.710	−	293.710i	−0.388419	−	0.388419i	−0.874123	+	0.485704i	$0.838563\pi$
$84$		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	$-0.356217\pi$
$89$	732.996			0.873004			0.436502	+	0.899703i	$0.356217\pi$
$90$		0			0
$91$	16.5980	+	16.5980i	0.0191203	+	0.0191203i
$92$		0			0
$93$	1056.50	−	516.781i	1.17800	−	0.576212i
$94$		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
$99$	−181.207	−	1448.48i	−0.183959	−	1.47049i
$100$		0			0
$101$	−991.920	−	991.920i	−0.977225	−	0.977225i	0.0225216	−	0.999746i	$-0.492831\pi$
$101$	−991.920	−	991.920i	−0.977225	−	0.977225i	−0.999746	+	0.0225216i	$0.992831\pi$
$102$		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	$-0.705893\pi$
$107$	216.201	−	216.201i	0.195336	−	0.195336i	0.797997	+	0.602661i	$0.205893\pi$
$108$		0			0
$109$	−883.171	−	883.171i	−0.776078	−	0.776078i	0.203084	−	0.979161i	$-0.434904\pi$
$109$	−883.171	−	883.171i	−0.776078	−	0.776078i	−0.979161	+	0.203084i	$0.934904\pi$
$110$		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
$117$	758.485	−	94.8871i	0.599333	−	0.0749771i
$118$		0			0
$119$		−	64.6361i		−	0.0497915i
$120$		0			0
$121$		−	1592.10i		−	1.19617i
$122$		0			0
$123$	−688.537	−	1407.63i	−0.504742	−	1.03189i
$124$		0			0
$125$	−174.715	+	174.715i	−0.125016	+	0.125016i
$126$		0			0
$127$			42.9875i			0.0300357i	0.999887	+	0.0150178i	$0.00478050\pi$
$127$			42.9875i			0.0300357i	−0.999887	+	0.0150178i	$0.995219\pi$
$128$		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	$-0.165465\pi$
$131$	556.534	+	556.534i	0.371180	+	0.371180i	−0.496727	+	0.867907i	$0.665465\pi$
$132$		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	$-0.661360\pi$
$137$	−1557.02			−0.970988			−0.485494	+	0.874240i	$0.661360\pi$
$138$		0			0
$139$	682.898	+	682.898i	0.416710	+	0.416710i	0.884068	−	0.467358i	$-0.154794\pi$
$139$	682.898	+	682.898i	0.416710	+	0.416710i	−0.467358	+	0.884068i	$0.654794\pi$
$140$		0			0
$141$	279.655	+	571.722i	0.167030	+	0.341473i
$142$		0			0
$143$	1530.66			0.895104
$144$		0			0
$145$	−612.924			−0.351038
$146$		0			0
$147$	781.557	+	1597.80i	0.438515	+	0.896493i
$148$		0			0
$149$	−143.722	−	143.722i	−0.0790215	−	0.0790215i	0.666491	−	0.745513i	$-0.267795\pi$
$149$	−143.722	−	143.722i	−0.0790215	−	0.0790215i	−0.745513	+	0.666491i	$0.767795\pi$
$150$		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	0.989722	+	0.143003i	$0.0456760\pi$
$157$	2228.30	+	2228.30i	1.13273	+	1.13273i	0.143003	+	0.989722i	$0.454324\pi$
$158$		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	−0.599499	−	0.800375i	$-0.704634\pi$
$163$	418.032	−	418.032i	0.200876	−	0.200876i	0.800375	+	0.599499i	$0.204634\pi$
$164$		0			0
$165$	2010.13	+	4109.48i	0.948416	+	1.93893i
$166$		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
$171$	178.660	+	1428.13i	0.0798977	+	0.638667i
$172$		0			0
$173$	−1289.55	+	1289.55i	−0.566721	+	0.566721i	−0.931208	−	0.364487i	$-0.881244\pi$
$173$	−1289.55	+	1289.55i	−0.566721	+	0.566721i	0.364487	+	0.931208i	$0.381244\pi$
$174$		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	$-0.0752520\pi$
$179$	1767.33	+	1767.33i	0.737970	+	0.737970i	−0.234215	+	0.972185i	$0.575252\pi$
$180$		0			0
$181$	417.552	−	417.552i	0.171472	−	0.171472i	−0.616154	−	0.787626i	$-0.711310\pi$
$181$	417.552	−	417.552i	0.171472	−	0.171472i	0.787626	+	0.616154i	$0.211310\pi$
$182$		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
$189$	−113.862	−	23.7952i	−0.0438214	−	0.00915792i
$190$		0			0
$191$	−1181.47			−0.447580			−0.223790	−	0.974637i	$-0.571843\pi$
$191$	−1181.47			−0.447580			−0.223790	+	0.974637i	$0.571843\pi$
$192$		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
$195$	−2151.89	+	1052.59i	−0.790257	+	0.386551i
$196$		0			0
$197$	−31.7151	−	31.7151i	−0.0114701	−	0.0114701i	0.701348	−	0.712819i	$-0.252582\pi$
$197$	−31.7151	−	31.7151i	−0.0114701	−	0.0114701i	−0.712819	+	0.701348i	$0.752582\pi$
$198$		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	−0.226466	−	0.974019i	$-0.572717\pi$
$211$	2291.21	−	2291.21i	0.747553	−	0.747553i	0.974019	+	0.226466i	$0.0727173\pi$
$212$		0			0
$213$	−3120.00	+	1526.13i	−1.00366	+	0.490934i
$214$		0			0
$215$			2213.90i			0.702265i
$216$		0			0
$217$		−	187.666i		−	0.0587077i
$218$		0			0
$219$	5678.20	−	2777.47i	1.75204	−	0.857004i
$220$		0			0
$221$	1560.63	−	1560.63i	0.475020	−	0.475020i
$222$		0			0
$223$			1012.13i			0.303933i	0.988386	+	0.151966i	$0.0485605\pi$
$223$			1012.13i			0.303933i	−0.988386	+	0.151966i	$0.951439\pi$
$224$		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	$-0.264369\pi$
$227$	−218.272	−	218.272i	−0.0638202	−	0.0638202i	−0.738297	+	0.674476i	$0.764369\pi$
$228$		0			0
$229$	−563.164	+	563.164i	−0.162510	+	0.162510i	−0.783678	−	0.621167i	$-0.786659\pi$
$229$	−563.164	+	563.164i	−0.162510	+	0.162510i	0.621167	+	0.783678i	$0.286659\pi$
$230$		0			0
$231$	−220.323	−	75.5824i	−0.0627541	−	0.0215279i
$232$		0			0
$233$	−646.432			−0.181756			−0.0908781	−	0.995862i	$-0.528967\pi$
$233$	−646.432			−0.181756			−0.0908781	+	0.995862i	$0.528967\pi$
$234$		0			0
$235$	−1410.38	−	1410.38i	−0.391501	−	0.391501i
$236$		0			0
$237$	−184.176	+	90.0888i	−0.0504790	+	0.0246915i
$238$		0			0
$239$	996.350			0.269659			0.134830	−	0.990869i	$-0.456951\pi$
$239$	996.350			0.269659			0.134830	+	0.990869i	$0.456951\pi$
$240$		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
$243$	−2887.84	+	2451.39i	−0.762366	+	0.647146i
$244$		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	$-0.972049\pi$
$251$	−3612.53	+	3612.53i	−0.908449	+	0.908449i	0.0876984	+	0.996147i	$0.472049\pi$
$252$		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
$261$	−126.152	−	1008.40i	−0.0299180	−	0.239151i
$262$		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
$267$	−1673.55	−	3421.38i	−0.383595	−	0.784214i
$268$		0			0
$269$	1316.04	−	1316.04i	0.298290	−	0.298290i	−0.542054	−	0.840344i	$-0.682353\pi$
$269$	1316.04	−	1316.04i	0.298290	−	0.298290i	0.840344	+	0.542054i	$0.182353\pi$
$270$		0			0
$271$		−	4047.05i		−	0.907162i	−0.891215	−	0.453581i	$-0.850146\pi$
$271$		−	4047.05i		−	0.907162i	0.891215	−	0.453581i	$-0.149854\pi$
$272$		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	−0.0238859	−	0.999715i	$-0.507604\pi$
$277$	4498.76	−	4498.76i	0.975829	−	0.975829i	0.999715	+	0.0238859i	$0.00760383\pi$
$278$		0			0
$279$	−4824.33	−	3751.49i	−1.03521	−	0.805002i
$280$		0			0
$281$	2856.76			0.606476			0.303238	−	0.952915i	$-0.401932\pi$
$281$	2856.76			0.606476			0.303238	+	0.952915i	$0.401932\pi$
$282$		0			0
$283$	5461.16	+	5461.16i	1.14711	+	1.14711i	0.987118	+	0.159992i	$0.0511469\pi$
$283$	5461.16	+	5461.16i	1.14711	+	1.14711i	0.159992	+	0.987118i	$0.448853\pi$
$284$		0			0
$285$	−1981.89	−	4051.74i	−0.411919	−	0.842121i
$286$		0			0
$287$	−250.038			−0.0514260
$288$		0			0
$289$	−1164.41			−0.237006
$290$		0			0
$291$	−1031.30	−	2108.36i	−0.207751	−	0.424723i
$292$		0			0
$293$	4624.96	+	4624.96i	0.922162	+	0.922162i	0.997182	−	0.0750205i	$-0.0239022\pi$
$293$	4624.96	+	4624.96i	0.922162	+	0.922162i	−0.0750205	+	0.997182i	$0.523902\pi$
$294$		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	−0.823069	−	0.567941i	$-0.807740\pi$
$307$	−1372.35	+	1372.35i	−0.255128	+	0.255128i	0.567941	+	0.823069i	$0.307740\pi$
$308$		0			0
$309$	396.243	+	810.073i	0.0729498	+	0.149137i
$310$		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	$0.192178\pi$
$313$			6287.66i			1.13546i	−0.823214	+	0.567731i	$0.807822\pi$
$314$		0			0
$315$	361.720	−	45.2515i	0.0647004	−	0.00809407i
$316$		0			0
$317$	4723.19	−	4723.19i	0.836848	−	0.836848i	−0.151595	−	0.988443i	$-0.548441\pi$
$317$	4723.19	−	4723.19i	0.836848	−	0.836848i	0.988443	+	0.151595i	$0.0484408\pi$
$318$		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	0.999886	+	0.0151076i	$0.00480907\pi$
$331$	6112.31	+	6112.31i	1.01499	+	1.01499i	0.0151076	+	0.999886i	$0.495191\pi$
$332$		0			0
$333$	838.079	+	6699.23i	0.137917	+	1.10245i
$334$		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
$339$	8942.19	−	4374.03i	1.43266	−	0.700781i
$340$		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	$-0.621670\pi$
$347$	3586.40	−	3586.40i	0.554835	−	0.554835i	0.927832	+	0.372997i	$0.121670\pi$
$348$		0			0
$349$	−3892.45	−	3892.45i	−0.597015	−	0.597015i	0.342502	−	0.939517i	$-0.388726\pi$
$349$	−3892.45	−	3892.45i	−0.597015	−	0.597015i	−0.939517	+	0.342502i	$0.888726\pi$
$350$		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
$357$	−301.700	+	147.575i	−0.0447274	+	0.0218782i
$358$		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
$363$	−7431.41	+	3635.04i	−1.07451	+	0.525593i
$364$		0			0
$365$	−14007.5	+	14007.5i	−2.00873	+	2.00873i
$366$		0			0
$367$			4404.23i			0.626428i	0.949683	+	0.313214i	$0.101406\pi$
$367$			4404.23i			0.626428i	−0.949683	+	0.313214i	$0.898594\pi$
$368$		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	−0.993651	−	0.112509i	$-0.964111\pi$
$373$	−6347.59	+	6347.59i	−0.881141	+	0.881141i	0.112509	+	0.993651i	$0.464111\pi$
$374$		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	−0.999874	−	0.0158460i	$-0.994956\pi$
$379$	−7494.33	−	7494.33i	−1.01572	−	1.01572i	−0.0158460	−	0.999874i	$-0.505044\pi$
$380$		0			0
$381$	200.652	−	98.1478i	0.0269808	−	0.0131975i
$382$		0			0
$383$	−14197.9			−1.89420			−0.947100	−	0.320940i	$-0.896001\pi$
$383$	−14197.9			−1.89420			−0.947100	+	0.320940i	$0.896001\pi$
$384$		0			0
$385$	729.967			0.0966300
$386$		0			0
$387$	−3642.38	+	455.665i	−0.478431	+	0.0598521i
$388$		0			0
$389$	9377.75	+	9377.75i	1.22229	+	1.22229i	0.966816	+	0.255475i	$0.0822318\pi$
$389$	9377.75	+	9377.75i	1.22229	+	1.22229i	0.255475	+	0.966816i	$0.417768\pi$
$390$		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	0.726056	−	0.687636i	$-0.241351\pi$
$397$	303.909	+	303.909i	0.0384201	+	0.0384201i	−0.687636	+	0.726056i	$0.741351\pi$
$398$		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
$405$	6067.60	−	10203.3i	0.744448	−	1.25187i
$406$		0			0
$407$			13519.3i			1.64651i
$408$		0			0
$409$		−	3759.45i		−	0.454506i	−0.973836	−	0.227253i	$-0.927026\pi$
$409$		−	3759.45i		−	0.454506i	0.973836	−	0.227253i	$-0.0729744\pi$
$410$		0			0
$411$	3554.94	+	7267.66i	0.426648	+	0.872232i
$412$		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	$-0.142731\pi$
$419$	4010.59	+	4010.59i	0.467614	+	0.467614i	−0.433527	+	0.901141i	$0.642731\pi$
$420$		0			0
$421$	909.573	−	909.573i	0.105297	−	0.105297i	−0.652496	−	0.757792i	$-0.726278\pi$
$421$	909.573	−	909.573i	0.105297	−	0.105297i	0.757792	+	0.652496i	$0.226278\pi$
$422$		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
$429$	−3494.75	−	7144.60i	−0.393305	−	0.804066i
$430$		0			0
$431$	4734.20			0.529092			0.264546	−	0.964373i	$-0.414778\pi$
$431$	4734.20			0.529092			0.264546	+	0.964373i	$0.414778\pi$
$432$		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
$435$	1399.41	+	2860.93i	0.154245	+	0.315335i
$436$		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	$-0.704973\pi$
$443$	1859.08	−	1859.08i	0.199385	−	0.199385i	0.799736	+	0.600351i	$0.204973\pi$
$444$		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
$453$	−3259.28	−	6663.22i	−0.338045	−	0.691093i
$454$		0			0
$455$			382.240i			0.0393840i
$456$		0			0
$457$			15869.1i			1.62434i	0.583420	+	0.812171i	$0.301714\pi$
$457$			15869.1i			1.62434i	−0.583420	+	0.812171i	$0.698286\pi$
$458$		0			0
$459$	−2237.35	+	10705.9i	−0.227517	+	1.08869i
$460$		0			0
$461$	2986.52	−	2986.52i	0.301727	−	0.301727i	−0.539962	−	0.841689i	$-0.681562\pi$
$461$	2986.52	−	2986.52i	0.301727	−	0.301727i	0.841689	+	0.539962i	$0.181562\pi$
$462$		0			0
$463$			18753.3i			1.88238i	0.337883	+	0.941188i	$0.390289\pi$
$463$			18753.3i			1.88238i	−0.337883	+	0.941188i	$0.609711\pi$
$464$		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	$-0.291718\pi$
$467$	−1865.17	−	1865.17i	−0.184817	−	0.184817i	−0.793451	+	0.608634i	$0.791718\pi$
$468$		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
$477$	5245.74	−	656.246i	0.503535	−	0.0629926i
$478$		0			0
$479$	15505.8			1.47907			0.739536	−	0.673117i	$-0.235045\pi$
$479$	15505.8			1.47907			0.739536	+	0.673117i	$0.235045\pi$
$480$		0			0
$481$	−7079.27			−0.671075
$482$		0			0
$483$	−617.673	+	302.132i	−0.0581886	+	0.0284627i
$484$		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	$-0.741832\pi$
$491$	394.762	−	394.762i	0.0362839	−	0.0362839i	0.725016	+	0.688732i	$0.241832\pi$
$492$		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	−0.996245	−	0.0865797i	$-0.972406\pi$
$499$	−10139.9	+	10139.9i	−0.909665	+	0.909665i	0.0865797	+	0.996245i	$0.472406\pi$
$500$		0			0
$501$	−18065.7	+	8836.77i	−1.61101	+	0.788020i
$502$		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
$507$	−6513.67	+	3186.13i	−0.570576	+	0.279095i
$508$		0			0
$509$	10770.7	−	10770.7i	0.937927	−	0.937927i	−0.0602555	−	0.998183i	$-0.519192\pi$
$509$	10770.7	−	10770.7i	0.937927	−	0.937927i	0.998183	+	0.0602555i	$0.0191916\pi$
$510$		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	$-0.735753\pi$
$521$	−16048.6			−1.34952			−0.674761	+	0.738036i	$0.735753\pi$
$522$		0			0
$523$	−16568.1	−	16568.1i	−1.38523	−	1.38523i	−0.835043	−	0.550185i	$-0.814557\pi$
$523$	−16568.1	−	16568.1i	−1.38523	−	1.38523i	−0.550185	−	0.835043i	$-0.685443\pi$
$524$		0			0
$525$	−542.477	+	265.350i	−0.0450965	+	0.0220587i
$526$		0			0
$527$	−17645.3			−1.45852
$528$		0			0
$529$	−13306.3			−1.09363
$530$		0			0
$531$	−798.077	−	6379.47i	−0.0652233	−	0.521366i
$532$		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	0.698607	−	0.715506i	$-0.253804\pi$
$541$	−212.644	−	212.644i	−0.0168988	−	0.0168988i	−0.715506	+	0.698607i	$0.753804\pi$
$542$		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	−0.912869	−	0.408253i	$-0.866138\pi$
$547$	−6455.68	+	6455.68i	−0.504616	+	0.504616i	0.408253	+	0.912869i	$0.366138\pi$
$548$		0			0
$549$	6757.92	−	845.422i	0.525357	−	0.0657226i
$550$		0			0
$551$			2006.40i			0.155128i
$552$		0			0
$553$			32.7151i			0.00251571i
$554$		0			0
$555$	−9296.86	−	19006.3i	−0.711044	−	1.45365i
$556$		0			0
$557$	−2281.17	+	2281.17i	−0.173530	+	0.173530i	−0.788528	−	0.614998i	$-0.789157\pi$
$557$	−2281.17	+	2281.17i	−0.173530	+	0.173530i	0.614998	+	0.788528i	$0.289157\pi$
$558$		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	$-0.392364\pi$
$563$	−8170.55	−	8170.55i	−0.611630	−	0.611630i	−0.943371	+	0.331741i	$0.892364\pi$
$564$		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	$-0.284476\pi$
$569$	17007.4			1.25305			0.626526	+	0.779400i	$0.284476\pi$
$570$		0			0
$571$	−1588.50	−	1588.50i	−0.116421	−	0.116421i	0.646496	−	0.762917i	$-0.276234\pi$
$571$	−1588.50	−	1588.50i	−0.116421	−	0.116421i	−0.762917	+	0.646496i	$0.776234\pi$
$572$		0			0
$573$	2697.49	+	5514.69i	0.196665	+	0.402058i
$574$		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
$579$	4097.99	+	8377.86i	0.294139	+	0.601333i
$580$		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	$-0.725814\pi$
$587$	1526.76	−	1526.76i	0.107353	−	0.107353i	0.758743	+	0.651390i	$0.225814\pi$
$588$		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
$597$	−9891.43	−	20221.9i	−0.678106	−	1.38631i
$598$		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	$-0.974039\pi$
$601$		−	2400.70i		−	0.162939i	0.996676	−	0.0814696i	$-0.0259613\pi$
$602$		0			0
$603$	1105.61	+	8837.73i	0.0746663	+	0.596849i
$604$		0			0
$605$	18332.5	−	18332.5i	1.23194	−	1.23194i
$606$		0			0
$607$		−	6723.04i		−	0.449555i	−0.974410	−	0.224777i	$-0.927835\pi$
$607$		−	6723.04i		−	0.449555i	0.974410	−	0.224777i	$-0.0721655\pi$
$608$		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	−0.950431	−	0.310936i	$-0.899358\pi$
$613$	−9705.73	+	9705.73i	−0.639495	+	0.639495i	0.310936	+	0.950431i	$0.399358\pi$
$614$		0			0
$615$	8280.12	−	24136.6i	0.542905	−	1.58257i
$616$		0			0
$617$	3612.89			0.235737			0.117868	−	0.993029i	$-0.462394\pi$
$617$	3612.89			0.235737			0.117868	+	0.993029i	$0.462394\pi$
$618$		0			0
$619$	7079.67	+	7079.67i	0.459703	+	0.459703i	0.898558	−	0.438855i	$-0.144616\pi$
$619$	7079.67	+	7079.67i	0.459703	+	0.459703i	−0.438855	+	0.898558i	$0.644616\pi$
$620$		0			0
$621$	−4580.53	+	21918.2i	−0.295991	+	1.41634i
$622$		0			0
$623$	−607.739			−0.0390828
$624$		0			0
$625$	13498.1			0.863879
$626$		0			0
$627$	13452.4	−	6580.17i	0.856836	−	0.419117i
$628$		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	−0.560744	−	0.827989i	$-0.689485\pi$
$643$	4357.38	−	4357.38i	0.267245	−	0.267245i	0.827989	+	0.560744i	$0.189485\pi$
$644$		0			0
$645$	10333.8	−	5054.71i	0.630840	−	0.308572i
$646$		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
$651$	−875.961	+	428.472i	−0.0527367	+	0.0257959i
$652$		0			0
$653$	−8850.83	+	8850.83i	−0.530413	+	0.530413i	−0.920695	−	0.390282i	$-0.872378\pi$
$653$	−8850.83	+	8850.83i	−0.530413	+	0.530413i	0.390282	+	0.920695i	$0.372378\pi$
$654$		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	$-0.138295\pi$
$659$	8224.56	+	8224.56i	0.486166	+	0.486166i	−0.420928	+	0.907094i	$0.638295\pi$
$660$		0			0
$661$	8586.18	−	8586.18i	0.505240	−	0.505240i	−0.407822	−	0.913062i	$-0.633711\pi$
$661$	8586.18	−	8586.18i	0.505240	−	0.505240i	0.913062	+	0.407822i	$0.133711\pi$
$662$		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
$669$	4724.27	−	2310.86i	0.273021	−	0.133547i
$670$		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
$675$	−4022.90	+	19249.9i	−0.229395	+	1.09767i
$676$		0			0
$677$	11065.3	+	11065.3i	0.628174	+	0.628174i	0.947608	−	0.319434i	$-0.103493\pi$
$677$	11065.3	+	11065.3i	0.628174	+	0.628174i	−0.319434	+	0.947608i	$0.603493\pi$
$678$		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	$-0.930315\pi$
$683$	−13547.1	+	13547.1i	−0.758955	+	0.758955i	0.217177	+	0.976132i	$0.430315\pi$
$684$		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	−0.849722	−	0.527230i	$-0.823230\pi$
$691$	−5857.82	+	5857.82i	−0.322492	+	0.322492i	0.527230	+	0.849722i	$0.323230\pi$
$692$		0			0
$693$	150.242	+	1200.96i	0.00823550	+	0.0658309i
$694$		0			0
$695$			15726.6i			0.858338i
$696$		0			0
$697$			23509.8i			1.27761i
$698$		0			0
$699$	1475.91	+	3017.33i	0.0798629	+	0.163270i
$700$		0			0
$701$	−16142.4	+	16142.4i	−0.869743	+	0.869743i	−0.992444	−	0.122701i	$-0.960844\pi$
$701$	−16142.4	+	16142.4i	−0.869743	+	0.869743i	0.122701	+	0.992444i	$0.460844\pi$
$702$		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	−0.295587	−	0.955316i	$-0.595515\pi$
$709$	12454.7	−	12454.7i	0.659729	−	0.659729i	0.955316	+	0.295587i	$0.0955153\pi$
$710$		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
$717$	−2274.84	−	4650.63i	−0.118487	−	0.242233i
$718$		0			0
$719$	−6194.00			−0.321276			−0.160638	−	0.987013i	$-0.551355\pi$
$719$	−6194.00			−0.321276			−0.160638	+	0.987013i	$0.551355\pi$
$720$		0			0
$721$	143.893			0.00743253
$722$		0			0
$723$	−10340.3	−	21139.5i	−0.531893	−	1.08739i
$724$		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	0.316761	−	0.948505i	$-0.397405\pi$
$733$	−12537.1	−	12537.1i	−0.631744	−	0.631744i	−0.948505	+	0.316761i	$0.897405\pi$
$734$		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	0.295464	−	0.955354i	$-0.404526\pi$
$739$	25128.2	−	25128.2i	1.25082	−	1.25082i	0.955354	−	0.295464i	$-0.0954741\pi$
$740$		0			0
$741$	3445.64	+	7044.21i	0.170822	+	0.349225i
$742$		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
$747$	11128.2	−	1392.15i	0.545060	−	0.0681874i
$748$		0			0
$749$	−179.256	+	179.256i	−0.00874483	+	0.00874483i
$750$		0			0
$751$		−	18414.2i		−	0.894734i	−0.894351	−	0.447367i	$-0.852362\pi$
$751$		−	18414.2i		−	0.894734i	0.894351	−	0.447367i	$-0.147638\pi$
$752$		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	−0.166301	−	0.986075i	$-0.553182\pi$
$757$	17074.1	−	17074.1i	0.819774	−	0.819774i	0.986075	+	0.166301i	$0.0531825\pi$
$758$		0			0
$759$	−14549.5	+	42411.8i	−0.695800	+	2.02826i
$760$		0			0
$761$	24788.6			1.18080			0.590399	−	0.807112i	$-0.298970\pi$
$761$	24788.6			1.18080			0.590399	+	0.807112i	$0.298970\pi$
$762$		0			0
$763$	732.253	+	732.253i	0.0347436	+	0.0347436i
$764$		0			0
$765$	−4254.77	−	34010.7i	−0.201087	−	1.60740i
$766$		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
$771$	−7840.43	+	3835.11i	−0.366233	+	0.179141i
$772$		0			0
$773$	−12931.4	−	12931.4i	−0.601694	−	0.601694i	0.339068	−	0.940762i	$-0.389888\pi$
$773$	−12931.4	−	12931.4i	−0.601694	−	0.601694i	−0.940762	+	0.339068i	$0.889888\pi$
$774$		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	−0.990228	−	0.139458i	$-0.955464\pi$
$787$	−18783.4	+	18783.4i	−0.850770	+	0.850770i	0.139458	+	0.990228i	$0.455464\pi$
$788$		0			0
$789$	−7348.92	+	3594.69i	−0.331595	+	0.162198i
$790$		0			0
$791$		−	1588.40i		−	0.0713995i
$792$		0			0
$793$			7141.30i			0.319792i
$794$		0			0
$795$	−14882.6	+	7279.78i	−0.663941	+	0.324764i
$796$		0			0
$797$	−14788.0	+	14788.0i	−0.657237	+	0.657237i	−0.954725	−	0.297488i	$-0.903851\pi$
$797$	−14788.0	+	14788.0i	−0.657237	+	0.657237i	0.297488	+	0.954725i	$0.403851\pi$
$798$		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	$-0.233963\pi$
$809$	34139.0			1.48364			0.741820	+	0.670600i	$0.233963\pi$
$810$		0			0
$811$	18395.6	+	18395.6i	0.796494	+	0.796494i	0.982541	−	0.186047i	$-0.0595676\pi$
$811$	18395.6	+	18395.6i	0.796494	+	0.796494i	−0.186047	+	0.982541i	$0.559568\pi$
$812$		0			0
$813$	−18890.3	+	9240.11i	−0.814898	+	0.398604i
$814$		0			0
$815$	9626.97			0.413764
$816$		0			0
$817$	7247.20			0.310340
$818$		0			0
$819$	−628.873	+	78.6726i	−0.0268310	+	0.00335658i
$820$		0			0
$821$	−22428.5	−	22428.5i	−0.953423	−	0.953423i	0.0455394	−	0.998963i	$-0.485499\pi$
$821$	−22428.5	−	22428.5i	−0.953423	−	0.953423i	−0.998963	+	0.0455394i	$0.985499\pi$
$822$		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	$-0.632037\pi$
$827$	12181.0	−	12181.0i	0.512182	−	0.512182i	0.915194	+	0.403013i	$0.132037\pi$
$828$		0			0
$829$	−29681.5	−	29681.5i	−1.24352	−	1.24352i	−0.958530	−	0.284992i	$-0.908009\pi$
$829$	−29681.5	−	29681.5i	−1.24352	−	1.24352i	−0.284992	−	0.958530i	$-0.591991\pi$
$830$		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
$837$	−6495.94	+	31083.6i	−0.268259	+	1.28364i
$838$		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
$843$	−6522.46	−	13334.4i	−0.266483	−	0.544793i
$844$		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	−0.518289	−	0.855205i	$-0.673431\pi$
$853$	8393.54	−	8393.54i	0.336916	−	0.336916i	0.855205	+	0.518289i	$0.173431\pi$
$854$		0			0
$855$	−14387.2	+	18501.6i	−0.575476	+	0.740049i
$856$		0			0
$857$	−22054.9			−0.879092			−0.439546	−	0.898220i	$-0.644861\pi$
$857$	−22054.9			−0.879092			−0.439546	+	0.898220i	$0.644861\pi$
$858$		0			0
$859$	−33958.2	−	33958.2i	−1.34882	−	1.34882i	−0.886941	−	0.461884i	$-0.847174\pi$
$859$	−33958.2	−	33958.2i	−1.34882	−	1.34882i	−0.461884	−	0.886941i	$-0.652826\pi$
$860$		0			0
$861$	570.878	+	1167.09i	0.0225964	+	0.0461956i
$862$		0			0
$863$	35981.7			1.41927			0.709635	−	0.704569i	$-0.248860\pi$
$863$	35981.7			1.41927			0.709635	+	0.704569i	$0.248860\pi$
$864$		0			0
$865$	−29697.4			−1.16733
$866$		0			0
$867$	2658.55	+	5435.09i	0.104140	+	0.212901i
$868$		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	0.500854	−	0.865532i	$-0.333020\pi$
$877$	−9471.30	−	9471.30i	−0.364679	−	0.364679i	−0.865532	+	0.500854i	$0.833020\pi$
$878$		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	−0.0349671	−	0.999388i	$-0.511133\pi$
$883$	25305.1	−	25305.1i	0.964421	−	0.964421i	0.999388	+	0.0349671i	$0.0111326\pi$
$884$		0			0
$885$	8853.11	+	18099.1i	0.336264	+	0.687453i
$886$		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
$891$	33876.6	+	20145.3i	1.27375	+	0.757456i
$892$		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	0.991229	−	0.132155i	$-0.0421895\pi$
$907$	23466.1	+	23466.1i	0.859074	+	0.859074i	−0.132155	+	0.991229i	$0.542190\pi$
$908$		0			0
$909$	37582.3	−	4701.57i	1.37132	−	0.171553i
$910$		0			0
$911$	−18223.3			−0.662749			−0.331375	−	0.943499i	$-0.607512\pi$
$911$	−18223.3			−0.662749			−0.331375	+	0.943499i	$0.607512\pi$
$912$		0			0
$913$	22457.2			0.814046
$914$		0			0
$915$	−19172.8	+	9378.31i	−0.692715	+	0.338839i
$916$		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
$933$	−15143.7	+	7407.48i	−0.531386	+	0.259925i
$934$		0			0
$935$		−	68635.1i		−	2.40065i
$936$		0			0
$937$		−	31660.1i		−	1.10383i	−0.833900	−	0.551916i	$-0.813897\pi$
$937$		−	31660.1i		−	1.10383i	0.833900	−	0.551916i	$-0.186103\pi$
$938$		0			0
$939$	29348.7	−	14355.8i	1.01998	−	0.498917i
$940$		0			0
$941$	2381.85	−	2381.85i	0.0825143	−	0.0825143i	−0.664645	−	0.747159i	$-0.731417\pi$
$941$	2381.85	−	2381.85i	0.0825143	−	0.0825143i	0.747159	+	0.664645i	$0.231417\pi$
$942$		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	$-0.427345\pi$
$947$	−21792.3	−	21792.3i	−0.747786	−	0.747786i	−0.974063	+	0.226277i	$0.927345\pi$
$948$		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	$-0.401863\pi$
$953$	17854.6			0.606893			0.303446	+	0.952849i	$0.401863\pi$
$954$		0			0
$955$	−13604.1	−	13604.1i	−0.460963	−	0.460963i
$956$		0			0
$957$	−9498.69	+	4646.24i	−0.320846	+	0.156940i
$958$		0			0
$959$	1290.95			0.0434693
$960$		0			0
$961$	−21440.5			−0.719697
$962$		0			0
$963$	1024.77	+	8191.52i	0.0342914	+	0.274110i
$964$		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	$-0.837505\pi$
$971$	−11615.6	+	11615.6i	−0.383896	+	0.383896i	0.488607	+	0.872504i	$0.337505\pi$
$972$		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
$981$	33462.0	−	4186.12i	1.08905	−	0.136241i
$982$		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
$987$	−231.867	−	474.025i	−0.00747762	−	0.0152871i
$988$		0			0
$989$	−15343.4	+	15343.4i	−0.493317	+	0.493317i
$990$		0			0
$991$		−	42114.2i		−	1.34995i	−0.737840	−	0.674976i	$-0.764154\pi$
$991$		−	42114.2i		−	1.34995i	0.737840	−	0.674976i	$-0.235846\pi$
$992$		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	−0.945353	−	0.326049i	$-0.894283\pi$
$997$	−19496.0	+	19496.0i	−0.619304	+	0.619304i	0.326049	+	0.945353i	$0.394283\pi$
$998$		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.47.8		44
3.2	odd	2	inner	192.4.k.a.47.19		44
4.3	odd	2		48.4.k.a.35.11	yes	44
8.3	odd	2		384.4.k.b.95.8		44
8.5	even	2		384.4.k.a.95.15		44
12.11	even	2		48.4.k.a.35.12	yes	44
16.3	odd	4		384.4.k.a.287.4		44
16.5	even	4		48.4.k.a.11.12	yes	44
16.11	odd	4	inner	192.4.k.a.143.19		44
16.13	even	4		384.4.k.b.287.19		44
24.5	odd	2		384.4.k.a.95.4		44
24.11	even	2		384.4.k.b.95.19		44
48.5	odd	4		48.4.k.a.11.11	✓	44
48.11	even	4	inner	192.4.k.a.143.8		44
48.29	odd	4		384.4.k.b.287.8		44
48.35	even	4		384.4.k.a.287.15		44

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

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)

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

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Database

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