LMFDB - Embedded newform 384.4.k.b.287.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,4,Mod(95,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, 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("384.95");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	384.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:	$22.6567334422$
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			287.8
Character	$\chi$	$=$	384.287
Dual form			384.4.k.b.95.8

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−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	−0.0303606	+	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	$-0.492874\pi$
$7$	0.829117			0.0447681			0.0223841	+	0.999749i	$0.492874\pi$
$8$		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	$-0.984364\pi$
$11$	−38.2302	−	38.2302i	−1.04790	−	1.04790i	−0.0491019	−	0.998794i	$-0.515636\pi$
$12$		0			0
$13$	20.0189	−	20.0189i	0.427096	−	0.427096i	−0.460542	−	0.887638i	$-0.652345\pi$
$13$	20.0189	−	20.0189i	0.427096	−	0.427096i	0.887638	+	0.460542i	$0.152345\pi$
$14$		0			0
$15$	−27.4566	−	80.0363i	−0.472618	−	1.37769i
$16$		0			0
$17$		−	77.9578i		−	1.11221i	−0.831113	−	0.556104i	$-0.812296\pi$
$17$		−	77.9578i		−	1.11221i	0.831113	−	0.556104i	$-0.187704\pi$
$18$		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
$21$	−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	$-0.211548\pi$
$29$	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	$0.227621\pi$
$31$			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	$-0.437481\pi$
$37$	−176.815	−	176.815i	−0.785626	−	0.785626i	−0.980774	+	0.195148i	$0.937481\pi$
$38$		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	−0.515782	−	0.856720i	$-0.672498\pi$
$43$	96.1344	−	96.1344i	0.340938	−	0.340938i	0.856720	+	0.515782i	$0.172498\pi$
$44$		0			0
$45$	436.271	+	54.5779i	1.44523	+	0.180800i
$46$		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
$51$	363.881	+	177.991i	0.999089	+	0.488700i
$52$		0			0
$53$	138.452	−	138.452i	0.358828	−	0.358828i	−0.504553	−	0.863381i	$-0.668343\pi$
$53$	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	0.496501	−	0.868036i	$-0.334618\pi$
$59$	−168.375	−	168.375i	−0.371535	−	0.371535i	−0.868036	+	0.496501i	$0.834618\pi$
$60$		0			0
$61$	178.364	−	178.364i	0.374379	−	0.374379i	−0.494690	−	0.869069i	$-0.664718\pi$
$61$	178.364	−	178.364i	0.374379	−	0.374379i	0.869069	+	0.494690i	$0.164718\pi$
$62$		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
$69$	−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	$-0.571029\pi$
$73$		−	1216.50i		−	1.95041i	0.221297	−	0.975207i	$-0.428971\pi$
$74$		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	−0.874123	−	0.485704i	$-0.838563\pi$
$83$	−293.710	+	293.710i	−0.388419	+	0.388419i	0.485704	+	0.874123i	$0.338563\pi$
$84$		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	$-0.507169\pi$
$101$	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	$-0.473546\pi$
$103$	173.550			0.166023			0.0830114	+	0.996549i	$0.473546\pi$
$104$		0			0
$105$	−22.7648	−	66.3595i	−0.0211582	−	0.0616764i
$106$		0			0
$107$	216.201	+	216.201i	0.195336	+	0.195336i	0.797997	−	0.602661i	$-0.205893\pi$
$107$	216.201	+	216.201i	0.195336	+	0.195336i	−0.602661	+	0.797997i	$0.705893\pi$
$108$		0			0
$109$	883.171	−	883.171i	0.776078	−	0.776078i	−0.203084	−	0.979161i	$-0.565096\pi$
$109$	883.171	−	883.171i	0.776078	−	0.776078i	0.979161	+	0.203084i	$0.0650963\pi$
$110$		0			0
$111$	1229.01	−	421.615i	1.05092	−	0.360522i
$112$		0			0
$113$		−	1915.77i		−	1.59487i	−0.603403	−	0.797437i	$-0.706189\pi$
$113$		−	1915.77i		−	1.59487i	0.603403	−	0.797437i	$-0.293811\pi$
$114$		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	−0.496727	−	0.867907i	$-0.665465\pi$
$131$	556.534	−	556.534i	0.371180	−	0.371180i	0.867907	+	0.496727i	$0.165465\pi$
$132$		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	−0.467358	−	0.884068i	$-0.654794\pi$
$139$	682.898	−	682.898i	0.416710	−	0.416710i	0.884068	+	0.467358i	$0.154794\pi$
$140$		0			0
$141$	−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	$-0.732205\pi$
$149$	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	$-0.625685\pi$
$151$	−1427.53			−0.769340			−0.384670	+	0.923054i	$0.625685\pi$
$152$		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	$0.545676\pi$
$157$	−2228.30	+	2228.30i	−1.13273	+	1.13273i	−0.989722	+	0.143003i	$0.954324\pi$
$158$		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
$165$	−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	$-0.118756\pi$
$173$	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	−0.234215	−	0.972185i	$-0.575252\pi$
$179$	1767.33	−	1767.33i	0.737970	−	0.737970i	0.972185	+	0.234215i	$0.0752520\pi$
$180$		0			0
$181$	−417.552	−	417.552i	−0.171472	−	0.171472i	0.616154	−	0.787626i	$-0.288690\pi$
$181$	−417.552	−	417.552i	−0.171472	−	0.171472i	−0.787626	+	0.616154i	$0.788690\pi$
$182$		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	$-0.428157\pi$
$191$	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
$195$	−2151.89	−	1052.59i	−0.790257	−	0.386551i
$196$		0			0
$197$	31.7151	−	31.7151i	0.0114701	−	0.0114701i	−0.701348	−	0.712819i	$-0.747418\pi$
$197$	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	$-0.780560\pi$
$199$	−4332.32			−1.54327			−0.771634	+	0.636067i	$0.780560\pi$
$200$		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
$213$	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	−0.738297	−	0.674476i	$-0.764369\pi$
$227$	−218.272	+	218.272i	−0.0638202	+	0.0638202i	0.674476	+	0.738297i	$0.264369\pi$
$228$		0			0
$229$	563.164	+	563.164i	0.162510	+	0.162510i	0.783678	−	0.621167i	$-0.213341\pi$
$229$	563.164	+	563.164i	0.162510	+	0.162510i	−0.621167	+	0.783678i	$0.713341\pi$
$230$		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	$-0.543049\pi$
$239$	−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
$243$	−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	0.0876984	−	0.996147i	$-0.472049\pi$
$251$	−3612.53	−	3612.53i	−0.908449	−	0.908449i	−0.996147	+	0.0876984i	$0.972049\pi$
$252$		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	$0.0653453\pi$
$257$			1679.73i			0.407699i	−0.979002	+	0.203850i	$0.934655\pi$
$258$		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	$-0.317647\pi$
$269$	−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	$-0.850146\pi$
$271$		−	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	$-0.492396\pi$
$277$	−4498.76	−	4498.76i	−0.975829	−	0.975829i	−0.999715	+	0.0238859i	$0.992396\pi$
$278$		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	0.159992	−	0.987118i	$-0.448853\pi$
$283$	5461.16	−	5461.16i	1.14711	−	1.14711i	0.987118	−	0.159992i	$-0.0511469\pi$
$284$		0			0
$285$	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	$-0.976098\pi$
$293$	−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
$309$	−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	$-0.807822\pi$
$313$		−	6287.66i		−	1.13546i	0.823214	−	0.567731i	$-0.192178\pi$
$314$		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	$-0.451559\pi$
$317$	−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
$333$	−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	0.927832	−	0.372997i	$-0.121670\pi$
$347$	3586.40	+	3586.40i	0.554835	+	0.554835i	−0.372997	+	0.927832i	$0.621670\pi$
$348$		0			0
$349$	3892.45	−	3892.45i	0.597015	−	0.597015i	−0.342502	−	0.939517i	$-0.611274\pi$
$349$	3892.45	−	3892.45i	0.597015	−	0.597015i	0.939517	+	0.342502i	$0.111274\pi$
$350$		0			0
$351$	2174.65	−	3323.72i	0.330696	−	0.505433i
$352$		0			0
$353$			2306.40i			0.347754i	0.984767	+	0.173877i	$0.0556296\pi$
$353$			2306.40i			0.347754i	−0.984767	+	0.173877i	$0.944370\pi$
$354$		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	$-0.0358888\pi$
$373$	6347.59	+	6347.59i	0.881141	+	0.881141i	−0.112509	+	0.993651i	$0.535889\pi$
$374$		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
$381$	−200.652	−	98.1478i	−0.0269808	−	0.0131975i
$382$		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
$387$	−3642.38	−	455.665i	−0.478431	−	0.0598521i
$388$		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	−0.726056	−	0.687636i	$-0.758649\pi$
$397$	−303.909	+	303.909i	−0.0384201	+	0.0384201i	0.687636	+	0.726056i	$0.258649\pi$
$398$		0			0
$399$	−217.228	+	74.5204i	−0.0272556	+	0.00935009i
$400$		0			0
$401$		−	13634.6i		−	1.69795i	−0.528432	−	0.848976i	$-0.677220\pi$
$401$		−	13634.6i		−	1.69795i	0.528432	−	0.848976i	$-0.322780\pi$
$402$		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	$0.0729744\pi$
$409$			3759.45i			0.454506i	−0.973836	+	0.227253i	$0.927026\pi$
$410$		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	−0.433527	−	0.901141i	$-0.642731\pi$
$419$	4010.59	−	4010.59i	0.467614	−	0.467614i	0.901141	+	0.433527i	$0.142731\pi$
$420$		0			0
$421$	−909.573	−	909.573i	−0.105297	−	0.105297i	0.652496	−	0.757792i	$-0.273722\pi$
$421$	−909.573	−	909.573i	−0.105297	−	0.105297i	−0.757792	+	0.652496i	$0.773722\pi$
$422$		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	$-0.585222\pi$
$431$	−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
$435$	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	$-0.745773\pi$
$439$	−12834.1			−1.39531			−0.697654	+	0.716435i	$0.745773\pi$
$440$		0			0
$441$	5673.58	+	7296.10i	0.612632	+	0.787831i
$442$		0			0
$443$	1859.08	+	1859.08i	0.199385	+	0.199385i	0.799736	−	0.600351i	$-0.204973\pi$
$443$	1859.08	+	1859.08i	0.199385	+	0.199385i	−0.600351	+	0.799736i	$0.704973\pi$
$444$		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	$0.138452\pi$
$449$			8018.01i			0.842747i	−0.906887	+	0.421373i	$0.861548\pi$
$450$		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	$-0.698286\pi$
$457$		−	15869.1i		−	1.62434i	0.583420	−	0.812171i	$-0.301714\pi$
$458$		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	$-0.318438\pi$
$461$	−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	$0.390289\pi$
$463$			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	−0.793451	−	0.608634i	$-0.791718\pi$
$467$	−1865.17	+	1865.17i	−0.184817	+	0.184817i	0.608634	+	0.793451i	$0.291718\pi$
$468$		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	$-0.764955\pi$
$479$	−15505.8			−1.47907			−0.739536	+	0.673117i	$0.764955\pi$
$480$		0			0
$481$	−7079.27			−0.671075
$482$		0			0
$483$	−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	$-0.441835\pi$
$487$	3905.87			0.363433			0.181716	+	0.983351i	$0.441835\pi$
$488$		0			0
$489$	−2905.67	+	996.798i	−0.268710	+	0.0921815i
$490$		0			0
$491$	394.762	+	394.762i	0.0362839	+	0.0362839i	0.725016	−	0.688732i	$-0.241832\pi$
$491$	394.762	+	394.762i	0.0362839	+	0.0362839i	−0.688732	+	0.725016i	$0.741832\pi$
$492$		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
$501$	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	$-0.480808\pi$
$509$	−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	$-0.735753\pi$
$521$	−16048.6			−1.34952			−0.674761	+	0.738036i	$0.735753\pi$
$522$		0			0
$523$	−16568.1	+	16568.1i	−1.38523	+	1.38523i	−0.550185	+	0.835043i	$0.685443\pi$
$523$	−16568.1	+	16568.1i	−1.38523	+	1.38523i	−0.835043	+	0.550185i	$0.814557\pi$
$524$		0			0
$525$	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	$-0.746196\pi$
$541$	212.644	−	212.644i	0.0168988	−	0.0168988i	0.715506	+	0.698607i	$0.246196\pi$
$542$		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
$549$	−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	$-0.210843\pi$
$557$	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	−0.943371	−	0.331741i	$-0.892364\pi$
$563$	−8170.55	+	8170.55i	−0.611630	+	0.611630i	0.331741	+	0.943371i	$0.392364\pi$
$564$		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	−0.762917	−	0.646496i	$-0.776234\pi$
$571$	−1588.50	+	1588.50i	−0.116421	+	0.116421i	0.646496	+	0.762917i	$0.276234\pi$
$572$		0			0
$573$	−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	0.758743	−	0.651390i	$-0.225814\pi$
$587$	1526.76	+	1526.76i	0.107353	+	0.107353i	−0.651390	+	0.758743i	$0.725814\pi$
$588$		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	$0.0495437\pi$
$593$			4477.09i			0.310037i	−0.987912	+	0.155019i	$0.950456\pi$
$594$		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	$0.0259613\pi$
$601$			2400.70i			0.162939i	−0.996676	+	0.0814696i	$0.974039\pi$
$602$		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	$-0.100642\pi$
$613$	9705.73	+	9705.73i	0.639495	+	0.639495i	−0.310936	+	0.950431i	$0.600642\pi$
$614$		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	−0.438855	−	0.898558i	$-0.644616\pi$
$619$	7079.67	−	7079.67i	0.459703	−	0.459703i	0.898558	+	0.438855i	$0.144616\pi$
$620$		0			0
$621$	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	$-0.383081\pi$
$631$	11384.1			0.718217			0.359108	+	0.933296i	$0.383081\pi$
$632$		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	$0.0755601\pi$
$641$			7632.61i			0.470312i	−0.971958	+	0.235156i	$0.924440\pi$
$642$		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
$645$	−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	$-0.127622\pi$
$653$	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	−0.420928	−	0.907094i	$-0.638295\pi$
$659$	8224.56	−	8224.56i	0.486166	−	0.486166i	0.907094	+	0.420928i	$0.138295\pi$
$660$		0			0
$661$	−8586.18	−	8586.18i	−0.505240	−	0.505240i	0.407822	−	0.913062i	$-0.366289\pi$
$661$	−8586.18	−	8586.18i	−0.505240	−	0.505240i	−0.913062	+	0.407822i	$0.866289\pi$
$662$		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	$-0.896507\pi$
$677$	−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	0.217177	−	0.976132i	$-0.430315\pi$
$683$	−13547.1	−	13547.1i	−0.758955	−	0.758955i	−0.976132	+	0.217177i	$0.930315\pi$
$684$		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
$693$	−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	$-0.0391555\pi$
$701$	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	0.295587	−	0.955316i	$-0.404485\pi$
$709$	−12454.7	−	12454.7i	−0.659729	−	0.659729i	−0.955316	+	0.295587i	$0.904485\pi$
$710$		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	$-0.448645\pi$
$719$	6194.00			0.321276			0.160638	+	0.987013i	$0.448645\pi$
$720$		0			0
$721$	143.893			0.00743253
$722$		0			0
$723$	−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	$-0.577664\pi$
$727$	−9470.69			−0.483148			−0.241574	+	0.970382i	$0.577664\pi$
$728$		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	$-0.602595\pi$
$733$	12537.1	−	12537.1i	0.631744	−	0.631744i	0.948505	+	0.316761i	$0.102595\pi$
$734$		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
$741$	−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	$-0.446818\pi$
$757$	−17074.1	−	17074.1i	−0.819774	−	0.819774i	−0.986075	+	0.166301i	$0.946818\pi$
$758$		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	$-0.610112\pi$
$773$	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
$789$	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	$-0.0961489\pi$
$797$	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	$-0.233963\pi$
$809$	34139.0			1.48364			0.741820	+	0.670600i	$0.233963\pi$
$810$		0			0
$811$	18395.6	−	18395.6i	0.796494	−	0.796494i	−0.186047	−	0.982541i	$-0.559568\pi$
$811$	18395.6	−	18395.6i	0.796494	−	0.796494i	0.982541	+	0.186047i	$0.0595676\pi$
$812$		0			0
$813$	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	$-0.514501\pi$
$821$	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	$-0.758799\pi$
$823$	−34300.0			−1.45276			−0.726381	+	0.687293i	$0.758799\pi$
$824$		0			0
$825$	−12778.2	−	37248.6i	−0.539249	−	1.57191i
$826$		0			0
$827$	12181.0	+	12181.0i	0.512182	+	0.512182i	0.915194	−	0.403013i	$-0.132037\pi$
$827$	12181.0	+	12181.0i	0.512182	+	0.512182i	−0.403013	+	0.915194i	$0.632037\pi$
$828$		0			0
$829$	29681.5	−	29681.5i	1.24352	−	1.24352i	0.284992	−	0.958530i	$-0.408009\pi$
$829$	29681.5	−	29681.5i	1.24352	−	1.24352i	0.958530	−	0.284992i	$-0.0919910\pi$
$830$		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	$-0.326569\pi$
$853$	−8393.54	−	8393.54i	−0.336916	−	0.336916i	−0.855205	+	0.518289i	$0.826569\pi$
$854$		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	−0.461884	+	0.886941i	$0.652826\pi$
$859$	−33958.2	+	33958.2i	−1.34882	+	1.34882i	−0.886941	+	0.461884i	$0.847174\pi$
$860$		0			0
$861$	−570.878	+	1167.09i	−0.0225964	+	0.0461956i
$862$		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
$867$	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	$-0.666980\pi$
$877$	9471.30	−	9471.30i	0.364679	−	0.364679i	0.865532	+	0.500854i	$0.166980\pi$
$878$		0			0
$879$	−11028.2	−	32147.4i	−0.423178	−	1.23357i
$880$		0			0
$881$			47824.3i			1.82888i	0.404723	+	0.914439i	$0.367368\pi$
$881$			47824.3i			1.82888i	−0.404723	+	0.914439i	$0.632632\pi$
$882$		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
$885$	−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	−0.132155	−	0.991229i	$-0.542190\pi$
$907$	23466.1	−	23466.1i	0.859074	−	0.859074i	0.991229	+	0.132155i	$0.0421895\pi$
$908$		0			0
$909$	−37582.3	−	4701.57i	−1.37132	−	0.171553i
$910$		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
$915$	−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	$-0.202846\pi$
$919$	44782.9			1.60746			0.803729	+	0.594996i	$0.202846\pi$
$920$		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	$-0.903391\pi$
$929$		−	16925.2i		−	0.597737i	0.954294	−	0.298868i	$-0.0966092\pi$
$930$		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	$0.186103\pi$
$937$			31660.1i			1.10383i	−0.833900	+	0.551916i	$0.813897\pi$
$938$		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	$-0.268583\pi$
$941$	−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	−0.974063	−	0.226277i	$-0.927345\pi$
$947$	−21792.3	+	21792.3i	−0.747786	+	0.747786i	0.226277	+	0.974063i	$0.427345\pi$
$948$		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	$-0.786749\pi$
$967$	−47141.7			−1.56771			−0.783854	+	0.620945i	$0.786749\pi$
$968$		0			0
$969$	7006.78	+	20424.8i	0.232291	+	0.677131i
$970$		0			0
$971$	−11615.6	−	11615.6i	−0.383896	−	0.383896i	0.488607	−	0.872504i	$-0.337505\pi$
$971$	−11615.6	−	11615.6i	−0.383896	−	0.383896i	−0.872504	+	0.488607i	$0.837505\pi$
$972$		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	$0.0251599\pi$
$977$			4822.57i			0.157920i	−0.996878	+	0.0789600i	$0.974840\pi$
$978$		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	$-0.105717\pi$
$997$	19496.0	+	19496.0i	0.619304	+	0.619304i	−0.326049	+	0.945353i	$0.605717\pi$
$998$		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	384.4.k.b.287.8		44
3.2	odd	2	inner	384.4.k.b.287.19		44
4.3	odd	2		384.4.k.a.287.15		44
8.3	odd	2		192.4.k.a.143.8		44
8.5	even	2		48.4.k.a.11.11	✓	44
12.11	even	2		384.4.k.a.287.4		44
16.3	odd	4	inner	384.4.k.b.95.19		44
16.5	even	4		192.4.k.a.47.19		44
16.11	odd	4		48.4.k.a.35.12	yes	44
16.13	even	4		384.4.k.a.95.4		44
24.5	odd	2		48.4.k.a.11.12	yes	44
24.11	even	2		192.4.k.a.143.19		44
48.5	odd	4		192.4.k.a.47.8		44
48.11	even	4		48.4.k.a.35.11	yes	44
48.29	odd	4		384.4.k.a.95.15		44
48.35	even	4	inner	384.4.k.b.95.8		44

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

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	384.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

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