LMFDB - Embedded newform 48.4.k.a.35.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [48,4,Mod(11,48)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("48.11"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(48, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			35.22
Character	$\chi$	$=$	48.35
Dual form			48.4.k.a.11.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.81978 - 0.221045i) q^{2} +(4.43190 + 2.71261i) q^{3} +(7.90228 - 1.24659i) q^{4} +(-3.17566 - 3.17566i) q^{5} +(13.0966 + 6.66931i) q^{6} -32.3513 q^{7} +(22.0071 - 5.26187i) q^{8} +(12.2835 + 24.0440i) q^{9} +(-9.65662 - 8.25269i) q^{10} +(16.0965 - 16.0965i) q^{11} +(38.4036 + 15.9110i) q^{12} +(-18.2871 - 18.2871i) q^{13} +(-91.2234 + 7.15108i) q^{14} +(-5.45988 - 22.6886i) q^{15} +(60.8920 - 19.7019i) q^{16} -38.5606i q^{17} +(39.9515 + 65.0836i) q^{18} +(-56.2887 + 56.2887i) q^{19} +(-29.0537 - 21.1362i) q^{20} +(-143.378 - 87.7565i) q^{21} +(41.8306 - 48.9467i) q^{22} +197.652i q^{23} +(111.807 + 36.3767i) q^{24} -104.830i q^{25} +(-55.6077 - 47.5232i) q^{26} +(-10.7831 + 139.881i) q^{27} +(-255.649 + 40.3289i) q^{28} +(57.3016 - 57.3016i) q^{29} +(-20.4108 - 62.7698i) q^{30} -148.290i q^{31} +(167.347 - 69.0147i) q^{32} +(115.002 - 27.6746i) q^{33} +(-8.52361 - 108.732i) q^{34} +(102.737 + 102.737i) q^{35} +(127.041 + 174.690i) q^{36} +(-72.5852 + 72.5852i) q^{37} +(-146.279 + 171.164i) q^{38} +(-31.4408 - 130.652i) q^{39} +(-86.5971 - 53.1772i) q^{40} +73.1133 q^{41} +(-423.691 - 215.761i) q^{42} +(226.984 + 226.984i) q^{43} +(107.133 - 147.265i) q^{44} +(37.3476 - 115.364i) q^{45} +(43.6900 + 557.336i) q^{46} +412.986 q^{47} +(323.311 + 77.8597i) q^{48} +703.607 q^{49} +(-23.1722 - 295.598i) q^{50} +(104.600 - 170.897i) q^{51} +(-167.306 - 121.713i) q^{52} +(94.8845 + 94.8845i) q^{53} +(0.514141 + 396.817i) q^{54} -102.234 q^{55} +(-711.958 + 170.228i) q^{56} +(-402.155 + 96.7764i) q^{57} +(148.912 - 174.244i) q^{58} +(-344.070 + 344.070i) q^{59} +(-71.4289 - 172.485i) q^{60} +(-153.024 - 153.024i) q^{61} +(-32.7787 - 418.145i) q^{62} +(-397.386 - 777.856i) q^{63} +(456.625 - 231.597i) q^{64} +116.147i q^{65} +(318.162 - 103.457i) q^{66} +(-603.490 + 603.490i) q^{67} +(-48.0693 - 304.716i) q^{68} +(-536.154 + 875.976i) q^{69} +(312.404 + 266.985i) q^{70} -711.320i q^{71} +(396.840 + 464.506i) q^{72} -687.773i q^{73} +(-188.629 + 220.719i) q^{74} +(284.364 - 464.598i) q^{75} +(-374.640 + 514.978i) q^{76} +(-520.744 + 520.744i) q^{77} +(-117.536 - 361.460i) q^{78} +162.513i q^{79} +(-255.939 - 130.806i) q^{80} +(-427.233 + 590.689i) q^{81} +(206.163 - 16.1613i) q^{82} +(-748.288 - 748.288i) q^{83} +(-1242.41 - 514.743i) q^{84} +(-122.455 + 122.455i) q^{85} +(690.217 + 589.870i) q^{86} +(409.392 - 98.5180i) q^{87} +(269.540 - 438.936i) q^{88} +927.910 q^{89} +(79.8114 - 333.556i) q^{90} +(591.611 + 591.611i) q^{91} +(246.392 + 1561.90i) q^{92} +(402.253 - 657.206i) q^{93} +(1164.53 - 91.2884i) q^{94} +357.508 q^{95} +(928.875 + 148.081i) q^{96} -208.855 q^{97} +(1984.01 - 155.529i) q^{98} +(584.747 + 189.304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33}+ \cdots + 1196 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.81978	−	0.221045i	0.996942	−	0.0781511i
$2$	2.81978	−	0.221045i	0.996942	−	0.0781511i
$3$	4.43190	+	2.71261i	0.852920	+	0.522042i
$3$	4.43190	+	2.71261i	0.852920	+	0.522042i
$4$	7.90228	−	1.24659i	0.987785	−	0.155824i
$5$	−3.17566	−	3.17566i	−0.284040	−	0.284040i	0.550678	−	0.834718i	$-0.314369\pi$
$5$	−3.17566	−	3.17566i	−0.284040	−	0.284040i	−0.834718	+	0.550678i	$0.814369\pi$
$6$	13.0966	+	6.66931i	0.891109	+	0.453789i
$7$	−32.3513			−1.74681			−0.873403	−	0.486998i	$-0.838092\pi$
$7$	−32.3513			−1.74681			−0.873403	+	0.486998i	$0.838092\pi$
$8$	22.0071	−	5.26187i	0.972586	−	0.232544i
$9$	12.2835	+	24.0440i	0.454943	+	0.890520i
$10$	−9.65662	−	8.25269i	−0.305369	−	0.260973i
$11$	16.0965	−	16.0965i	0.441208	−	0.441208i	−0.451210	−	0.892418i	$-0.649007\pi$
$11$	16.0965	−	16.0965i	0.441208	−	0.441208i	0.892418	+	0.451210i	$0.149007\pi$
$12$	38.4036	+	15.9110i	0.923848	+	0.382760i
$13$	−18.2871	−	18.2871i	−0.390148	−	0.390148i	0.484592	−	0.874740i	$-0.338968\pi$
$13$	−18.2871	−	18.2871i	−0.390148	−	0.390148i	−0.874740	+	0.484592i	$0.838968\pi$
$14$	−91.2234	+	7.15108i	−1.74146	+	0.136515i
$15$	−5.45988	−	22.6886i	−0.0939823	−	0.390544i
$16$	60.8920	−	19.7019i	0.951438	−	0.307842i
$17$		−	38.5606i		−	0.550136i	−0.961425	−	0.275068i	$-0.911300\pi$
$17$		−	38.5606i		−	0.550136i	0.961425	−	0.275068i	$-0.0887003\pi$
$18$	39.9515	+	65.0836i	0.523147	+	0.852242i
$19$	−56.2887	+	56.2887i	−0.679658	+	0.679658i	−0.959923	−	0.280264i	$-0.909578\pi$
$19$	−56.2887	+	56.2887i	−0.679658	+	0.679658i	0.280264	+	0.959923i	$0.409578\pi$
$20$	−29.0537	−	21.1362i	−0.324831	−	0.236310i
$21$	−143.378	−	87.7565i	−1.48988	−	0.911907i
$22$	41.8306	−	48.9467i	0.405377	−	0.474339i
$23$			197.652i			1.79189i	0.444169	+	0.895943i	$0.353499\pi$
$23$			197.652i			1.79189i	−0.444169	+	0.895943i	$0.646501\pi$
$24$	111.807	+	36.3767i	0.950935	+	0.309390i
$25$		−	104.830i		−	0.838643i
$26$	−55.6077	−	47.5232i	−0.419445	−	0.358464i
$27$	−10.7831	+	139.881i	−0.0768593	+	0.997042i
$28$	−255.649	+	40.3289i	−1.72547	+	0.272195i
$29$	57.3016	−	57.3016i	0.366919	−	0.366919i	−0.499433	−	0.866352i	$-0.666458\pi$
$29$	57.3016	−	57.3016i	0.366919	−	0.366919i	0.866352	+	0.499433i	$0.166458\pi$
$30$	−20.4108	−	62.7698i	−0.124216	−	0.382005i
$31$		−	148.290i		−	0.859151i	−0.903031	−	0.429575i	$-0.858663\pi$
$31$		−	148.290i		−	0.859151i	0.903031	−	0.429575i	$-0.141337\pi$
$32$	167.347	−	69.0147i	0.924470	−	0.381256i
$33$	115.002	−	27.6746i	0.606644	−	0.145986i
$34$	−8.52361	−	108.732i	−0.0429937	−	0.548453i
$35$	102.737	+	102.737i	0.496162	+	0.496162i
$36$	127.041	+	174.690i	0.588151	+	0.808751i
$37$	−72.5852	+	72.5852i	−0.322512	+	0.322512i	−0.849730	−	0.527218i	$-0.823235\pi$
$37$	−72.5852	+	72.5852i	−0.322512	+	0.322512i	0.527218	+	0.849730i	$0.323235\pi$
$38$	−146.279	+	171.164i	−0.624464	+	0.730696i
$39$	−31.4408	−	130.652i	−0.129091	−	0.536439i
$40$	−86.5971	−	53.1772i	−0.342305	−	0.210201i
$41$	73.1133			0.278497			0.139249	−	0.990257i	$-0.455531\pi$
$41$	73.1133			0.278497			0.139249	+	0.990257i	$0.455531\pi$
$42$	−423.691	−	215.761i	−1.55659	−	0.792682i
$43$	226.984	+	226.984i	0.804993	+	0.804993i	0.983871	−	0.178878i	$-0.0572468\pi$
$43$	226.984	+	226.984i	0.804993	+	0.804993i	−0.178878	+	0.983871i	$0.557247\pi$
$44$	107.133	−	147.265i	0.367067	−	0.504569i
$45$	37.3476	−	115.364i	0.123721	−	0.382165i
$46$	43.6900	+	557.336i	0.140038	+	1.78641i
$47$	412.986			1.28171			0.640853	−	0.767663i	$-0.278581\pi$
$47$	412.986			1.28171			0.640853	+	0.767663i	$0.278581\pi$
$48$	323.311	+	77.8597i	0.972206	+	0.234127i
$49$	703.607			2.05133
$50$	−23.1722	−	295.598i	−0.0655409	−	0.836078i
$51$	104.600	−	170.897i	0.287194	−	0.469222i
$52$	−167.306	−	121.713i	−0.446177	−	0.324588i
$53$	94.8845	+	94.8845i	0.245913	+	0.245913i	0.819291	−	0.573378i	$-0.194367\pi$
$53$	94.8845	+	94.8845i	0.245913	+	0.245913i	−0.573378	+	0.819291i	$0.694367\pi$
$54$	0.514141	+	396.817i	0.00129566	+	0.999999i
$55$	−102.234			−0.250641
$56$	−711.958	+	170.228i	−1.69892	+	0.406209i
$57$	−402.155	+	96.7764i	−0.934504	+	0.224883i
$58$	148.912	−	174.244i	0.337121	−	0.394472i
$59$	−344.070	+	344.070i	−0.759222	+	0.759222i	−0.976181	−	0.216959i	$-0.930386\pi$
$59$	−344.070	+	344.070i	−0.759222	+	0.759222i	0.216959	+	0.976181i	$0.430386\pi$
$60$	−71.4289	−	172.485i	−0.153690	−	0.371129i
$61$	−153.024	−	153.024i	−0.321193	−	0.321193i	0.528032	−	0.849225i	$-0.322930\pi$
$61$	−153.024	−	153.024i	−0.321193	−	0.321193i	−0.849225	+	0.528032i	$0.822930\pi$
$62$	−32.7787	−	418.145i	−0.0671436	−	0.856523i
$63$	−397.386	−	777.856i	−0.794698	−	1.55557i
$64$	456.625	−	231.597i	0.891847	−	0.452338i
$65$			116.147i			0.221635i
$66$	318.162	−	103.457i	0.593380	−	0.192949i
$67$	−603.490	+	603.490i	−1.10042	+	1.10042i	−0.106058	+	0.994360i	$0.533823\pi$
$67$	−603.490	+	603.490i	−1.10042	+	1.10042i	−0.994360	+	0.106058i	$0.966177\pi$
$68$	−48.0693	−	304.716i	−0.0857245	−	0.543416i
$69$	−536.154	+	875.976i	−0.935441	+	1.52833i
$70$	312.404	+	266.985i	0.533421	+	0.455869i
$71$		−	711.320i		−	1.18899i	−0.804100	−	0.594494i	$-0.797353\pi$
$71$		−	711.320i		−	1.18899i	0.804100	−	0.594494i	$-0.202647\pi$
$72$	396.840	+	464.506i	0.649557	+	0.760313i
$73$		−	687.773i		−	1.10271i	−0.834271	−	0.551355i	$-0.814111\pi$
$73$		−	687.773i		−	1.10271i	0.834271	−	0.551355i	$-0.185889\pi$
$74$	−188.629	+	220.719i	−0.296321	+	0.346730i
$75$	284.364	−	464.598i	0.437807	−	0.715295i
$76$	−374.640	+	514.978i	−0.565449	+	0.777263i
$77$	−520.744	+	520.744i	−0.770704	+	0.770704i
$78$	−117.536	−	361.460i	−0.170619	−	0.524709i
$79$			162.513i			0.231445i	0.993282	+	0.115723i	$0.0369184\pi$
$79$			162.513i			0.231445i	−0.993282	+	0.115723i	$0.963082\pi$
$80$	−255.939	−	130.806i	−0.357685	−	0.182807i
$81$	−427.233	+	590.689i	−0.586053	+	0.810273i
$82$	206.163	−	16.1613i	0.277645	−	0.0217649i
$83$	−748.288	−	748.288i	−0.989582	−	0.989582i	0.0103646	−	0.999946i	$-0.496701\pi$
$83$	−748.288	−	748.288i	−0.989582	−	0.989582i	−0.999946	+	0.0103646i	$0.996701\pi$
$84$	−1242.41	−	514.743i	−1.61378	−	0.668608i
$85$	−122.455	+	122.455i	−0.156260	+	0.156260i
$86$	690.217	+	589.870i	0.865442	+	0.739620i
$87$	409.392	−	98.5180i	0.504499	−	0.121405i
$88$	269.540	−	438.936i	0.326512	−	0.531713i
$89$	927.910			1.10515			0.552575	−	0.833463i	$-0.313645\pi$
$89$	927.910			1.10515			0.552575	+	0.833463i	$0.313645\pi$
$90$	79.8114	−	333.556i	0.0934762	−	0.390665i
$91$	591.611	+	591.611i	0.681513	+	0.681513i
$92$	246.392	+	1561.90i	0.279219	+	1.77000i
$93$	402.253	−	657.206i	0.448513	−	0.732786i
$94$	1164.53	−	91.2884i	1.27779	−	0.100167i
$95$	357.508			0.386100
$96$	928.875	+	148.081i	0.987530	+	0.157432i
$97$	−208.855			−0.218618			−0.109309	−	0.994008i	$-0.534864\pi$
$97$	−208.855			−0.218618			−0.109309	+	0.994008i	$0.534864\pi$
$98$	1984.01	−	155.529i	2.04506	−	0.160314i
$99$	584.747	+	189.304i	0.593629	+	0.192180i
$100$	−130.681	−	828.399i	−0.130681	−	0.828399i
$101$	0.578244	+	0.578244i	0.000569677	+	0.000569677i	0.707392	−	0.706822i	$-0.249872\pi$
$101$	0.578244	+	0.578244i	0.000569677	+	0.000569677i	−0.706822	+	0.707392i	$0.749872\pi$
$102$	257.172	−	505.011i	0.249646	−	0.490231i
$103$	−1063.26			−1.01715			−0.508574	−	0.861018i	$-0.669827\pi$
$103$	−1063.26			−1.01715			−0.508574	+	0.861018i	$0.669827\pi$
$104$	−498.670	−	306.221i	−0.470179	−	0.288726i
$105$	176.634	+	734.004i	0.164169	+	0.682205i
$106$	288.527	+	246.579i	0.264379	+	0.225942i
$107$	528.504	−	528.504i	0.477499	−	0.477499i	−0.426832	−	0.904331i	$-0.640370\pi$
$107$	528.504	−	528.504i	0.477499	−	0.477499i	0.904331	+	0.426832i	$0.140370\pi$
$108$	89.1641	+	1118.82i	0.0794427	+	0.996839i
$109$	−522.214	−	522.214i	−0.458890	−	0.458890i	0.439401	−	0.898291i	$-0.355191\pi$
$109$	−522.214	−	522.214i	−0.458890	−	0.458890i	−0.898291	+	0.439401i	$0.855191\pi$
$110$	−288.278	+	22.5983i	−0.249875	+	0.0195879i
$111$	−518.586	+	124.795i	−0.443441	+	0.106712i
$112$	−1969.94	+	637.381i	−1.66198	+	0.537739i
$113$		−	152.618i		−	0.127054i	−0.997980	−	0.0635269i	$-0.979765\pi$
$113$		−	152.618i		−	0.127054i	0.997980	−	0.0635269i	$-0.0202349\pi$
$114$	−1112.60	+	361.782i	−0.914071	+	0.297228i
$115$	627.677	−	627.677i	0.508967	−	0.508967i
$116$	381.382	−	524.245i	0.305262	−	0.419612i
$117$	215.067	−	664.324i	0.169939	−	0.524930i
$118$	−894.146	+	1046.26i	−0.697566	+	0.816234i
$119$			1247.48i			0.960980i
$120$	−239.540	−	470.580i	−0.182225	−	0.357983i
$121$			812.804i			0.610671i
$122$	−465.320	−	397.670i	−0.345312	−	0.295109i
$123$	324.031	+	198.328i	0.237536	+	0.145387i
$124$	−184.857	−	1171.83i	−0.133876	−	0.848656i
$125$	−729.863	+	729.863i	−0.522248	+	0.522248i
$126$	−1292.48	−	2105.54i	−0.913836	−	1.48870i
$127$			399.802i			0.279344i	0.990198	+	0.139672i	$0.0446048\pi$
$127$			399.802i			0.279344i	−0.990198	+	0.139672i	$0.955395\pi$
$128$	1236.39	−	753.987i	0.853768	−	0.520653i
$129$	390.250	+	1621.69i	0.266354	+	1.10683i
$130$	25.6737	+	327.509i	0.0173210	+	0.220957i
$131$	−1339.67	−	1339.67i	−0.893492	−	0.893492i	0.101358	−	0.994850i	$-0.467681\pi$
$131$	−1339.67	−	1339.67i	−0.893492	−	0.893492i	−0.994850	+	0.101358i	$0.967681\pi$
$132$	874.277	−	362.053i	0.576485	−	0.238732i
$133$	1821.01	−	1821.01i	1.18723	−	1.18723i
$134$	−1568.31	+	1835.10i	−1.01105	+	1.18305i
$135$	478.459	−	409.972i	0.305031	−	0.261369i
$136$	−202.901	−	848.606i	−0.127931	−	0.535054i
$137$	−1598.46			−0.996828			−0.498414	−	0.866939i	$-0.666084\pi$
$137$	−1598.46			−0.996828			−0.498414	+	0.866939i	$0.666084\pi$
$138$	−1318.21	+	2588.57i	−0.813139	+	1.59677i
$139$	−1670.63	−	1670.63i	−1.01943	−	1.01943i	−0.999807	−	0.0196259i	$-0.993752\pi$
$139$	−1670.63	−	1670.63i	−1.01943	−	1.01943i	−0.0196259	−	0.999807i	$-0.506248\pi$
$140$	939.926	+	683.784i	0.567416	+	0.412788i
$141$	1830.31	+	1120.27i	1.09319	+	0.669105i
$142$	−157.233	−	2005.76i	−0.0929207	−	1.18535i
$143$	−588.717			−0.344273
$144$	1221.68	+	1222.08i	0.706989	+	0.707224i
$145$	−363.941			−0.208439
$146$	−152.029	−	1939.37i	−0.0861780	−	1.09934i
$147$	3118.31	+	1908.61i	1.74962	+	1.07088i
$148$	−483.104	+	664.072i	−0.268317	+	0.368827i
$149$	−142.214	−	142.214i	−0.0781919	−	0.0781919i	0.666929	−	0.745121i	$-0.267608\pi$
$149$	−142.214	−	142.214i	−0.0781919	−	0.0781919i	−0.745121	+	0.666929i	$0.767608\pi$
$150$	699.146	−	1372.92i	0.380567	−	0.747322i
$151$	1880.73			1.01359			0.506794	−	0.862067i	$-0.330831\pi$
$151$	1880.73			1.01359			0.506794	+	0.862067i	$0.330831\pi$
$152$	−942.567	+	1534.93i	−0.502976	+	0.819077i
$153$	927.152	−	473.657i	0.489907	−	0.250281i
$154$	−1353.27	+	1583.49i	−0.708116	+	0.828579i
$155$	−470.919	+	470.919i	−0.244033	+	0.244033i
$156$	−411.324	−	993.257i	−0.211104	−	0.509770i
$157$	1585.52	+	1585.52i	0.805976	+	0.805976i	0.984022	−	0.178046i	$-0.0569777\pi$
$157$	1585.52	+	1585.52i	0.805976	+	0.805976i	−0.178046	+	0.984022i	$0.556978\pi$
$158$	35.9227	+	458.251i	0.0180877	+	0.230737i
$159$	163.134	+	677.903i	0.0813670	+	0.338121i
$160$	−750.604	−	312.270i	−0.370878	−	0.154294i
$161$		−	6394.31i		−	3.13008i
$162$	−1074.13	+	1760.05i	−0.520937	+	0.853595i
$163$	−721.338	+	721.338i	−0.346623	+	0.346623i	−0.858850	−	0.512227i	$-0.828821\pi$
$163$	−721.338	+	721.338i	−0.346623	+	0.346623i	0.512227	+	0.858850i	$0.328821\pi$
$164$	577.762	−	91.1426i	0.275095	−	0.0433966i
$165$	−453.092	−	277.322i	−0.213777	−	0.130845i
$166$	−2275.41	−	1944.60i	−1.06389	−	0.909218i
$167$			2199.31i			1.01909i	0.860445	+	0.509544i	$0.170186\pi$
$167$			2199.31i			1.01909i	−0.860445	+	0.509544i	$0.829814\pi$
$168$	−3617.09	−	1176.83i	−1.66110	−	0.540444i
$169$		−	1528.17i		−	0.695569i
$170$	−318.228	+	372.365i	−0.143571	+	0.167994i
$171$	−2044.83	−	661.987i	−0.914456	−	0.296044i
$172$	2076.65	+	1510.73i	0.920597	+	0.669723i
$173$	−450.646	+	450.646i	−0.198046	+	0.198046i	−0.799162	−	0.601116i	$-0.794723\pi$
$173$	−450.646	+	450.646i	−0.198046	+	0.198046i	0.601116	+	0.799162i	$0.294723\pi$
$174$	1132.62	−	368.293i	0.493468	−	0.160461i
$175$			3391.40i			1.46495i
$176$	663.018	−	1297.28i	0.283960	−	0.555604i
$177$	−2458.21	+	591.555i	−1.04390	+	0.251209i
$178$	2616.50	−	205.110i	1.10177	−	0.0863686i
$179$	1160.45	+	1160.45i	0.484559	+	0.484559i	0.906584	−	0.422025i	$-0.138681\pi$
$179$	1160.45	+	1160.45i	0.484559	+	0.484559i	−0.422025	+	0.906584i	$0.638681\pi$
$180$	151.319	−	958.195i	0.0626593	−	0.396776i
$181$	−125.614	+	125.614i	−0.0515847	+	0.0515847i	−0.732429	−	0.680844i	$-0.761613\pi$
$181$	−125.614	+	125.614i	−0.0515847	+	0.0515847i	0.680844	+	0.732429i	$0.261613\pi$
$182$	1798.98	+	1537.44i	0.732689	+	0.626167i
$183$	−263.093	−	1093.29i	−0.106275	−	0.441628i
$184$	1040.02	+	4349.76i	0.416693	+	1.74276i
$185$	461.012			0.183212
$186$	988.992	−	1942.09i	0.389873	−	0.765597i
$187$	−620.691	−	620.691i	−0.242724	−	0.242724i
$188$	3263.53	−	514.826i	1.26605	−	0.199721i
$189$	348.846	−	4525.34i	0.134258	−	1.74164i
$190$	1008.09	−	79.0252i	0.384919	−	0.0301742i
$191$	3729.92			1.41302			0.706512	−	0.707702i	$-0.250268\pi$
$191$	3729.92			1.41302			0.706512	+	0.707702i	$0.250268\pi$
$192$	2651.95	+	212.232i	0.996813	+	0.0797737i
$193$	−3286.88			−1.22588			−0.612941	−	0.790129i	$-0.710014\pi$
$193$	−3286.88			−1.22588			−0.612941	+	0.790129i	$0.710014\pi$
$194$	−588.923	+	46.1662i	−0.217950	+	0.0170853i
$195$	−315.062	+	514.753i	−0.115703	+	0.189037i
$196$	5560.09	−	877.111i	2.02627	−	0.319647i
$197$	1961.53	+	1961.53i	0.709406	+	0.709406i	0.966410	−	0.257004i	$-0.0827355\pi$
$197$	1961.53	+	1961.53i	0.709406	+	0.709406i	−0.257004	+	0.966410i	$0.582736\pi$
$198$	1690.70	+	404.541i	0.606832	+	0.145199i
$199$	−202.789			−0.0722380			−0.0361190	−	0.999347i	$-0.511500\pi$
$199$	−202.789			−0.0722380			−0.0361190	+	0.999347i	$0.511500\pi$
$200$	−551.604	−	2307.01i	−0.195021	−	0.815652i
$201$	−4311.64	+	1037.57i	−1.51303	+	0.364103i
$202$	1.75834	+	1.50270i	0.000612456	+	0.000523414i
$203$	−1853.78	+	1853.78i	−0.640936	+	0.640936i
$204$	613.538	−	1480.87i	0.210570	−	0.508242i
$205$	−232.183	−	232.183i	−0.0791043	−	0.0791043i
$206$	−2998.16	+	235.028i	−1.01404	+	0.0794913i
$207$	−4752.36	+	2427.86i	−1.59571	+	0.815207i
$208$	−1473.83	−	753.248i	−0.491305	−	0.251098i
$209$			1812.10i			0.599741i
$210$	660.316	+	2030.68i	0.216982	+	0.667288i
$211$	2022.16	−	2022.16i	0.659770	−	0.659770i	−0.295556	−	0.955325i	$-0.595505\pi$
$211$	2022.16	−	2022.16i	0.659770	−	0.659770i	0.955325	+	0.295556i	$0.0955048\pi$
$212$	868.086	+	631.521i	0.281228	+	0.204590i
$213$	1929.53	−	3152.50i	0.620702	−	1.01411i
$214$	1373.44	−	1607.09i	0.438722	−	0.513356i
$215$		−	1441.65i		−	0.457300i
$216$	498.732	+	3135.12i	0.157104	+	0.987582i
$217$			4797.37i			1.50077i
$218$	−1587.96	−	1357.09i	−0.493350	−	0.421624i
$219$	1865.66	−	3048.14i	0.575661	−	0.940522i
$220$	−807.883	+	127.445i	−0.247580	+	0.0390560i
$221$	−705.160	+	705.160i	−0.214634	+	0.214634i
$222$	−1434.71	+	466.524i	−0.433745	+	0.141041i
$223$		−	1803.88i		−	0.541688i	−0.962623	−	0.270844i	$-0.912697\pi$
$223$		−	1803.88i		−	0.541688i	0.962623	−	0.270844i	$-0.0873028\pi$
$224$	−5413.89	+	2232.71i	−1.61487	+	0.665980i
$225$	2520.55	−	1287.68i	0.746828	−	0.381535i
$226$	−33.7354	−	430.348i	−0.00992939	−	0.126665i
$227$	−1811.19	−	1811.19i	−0.529573	−	0.529573i	0.390872	−	0.920445i	$-0.372174\pi$
$227$	−1811.19	−	1811.19i	−0.529573	−	0.529573i	−0.920445	+	0.390872i	$0.872174\pi$
$228$	−3057.30	+	1266.08i	−0.888047	+	0.367755i
$229$	−1529.22	+	1529.22i	−0.441281	+	0.441281i	−0.892442	−	0.451161i	$-0.851010\pi$
$229$	−1529.22	+	1529.22i	−0.441281	+	0.441281i	0.451161	+	0.892442i	$0.351010\pi$
$230$	1631.16	−	1908.65i	0.467634	−	0.547187i
$231$	−3720.46	+	895.308i	−1.05969	+	0.255008i
$232$	959.529	−	1562.56i	0.271535	−	0.442185i
$233$	3502.19			0.984703			0.492352	−	0.870396i	$-0.336137\pi$
$233$	3502.19			0.984703			0.492352	+	0.870396i	$0.336137\pi$
$234$	459.595	−	1920.79i	0.128396	−	0.536605i
$235$	−1311.50	−	1311.50i	−0.364056	−	0.364056i
$236$	−2290.02	+	3147.85i	−0.631643	+	0.868253i
$237$	−440.836	+	720.243i	−0.120824	+	0.197404i
$238$	275.750	+	3517.63i	0.0751017	+	0.958041i
$239$	1874.23			0.507254			0.253627	−	0.967302i	$-0.418376\pi$
$239$	1874.23			0.507254			0.253627	+	0.967302i	$0.418376\pi$
$240$	−779.469	−	1273.98i	−0.209644	−	0.342647i
$241$	−627.829			−0.167809			−0.0839046	−	0.996474i	$-0.526739\pi$
$241$	−627.829			−0.167809			−0.0839046	+	0.996474i	$0.526739\pi$
$242$	179.666	+	2291.92i	0.0477247	+	0.608804i
$243$	−3495.76	+	1458.96i	−0.922853	+	0.385153i
$244$	−1400.00	−	1018.48i	−0.367319	−	0.267220i
$245$	−2234.42	−	2234.42i	−0.582660	−	0.582660i
$246$	957.534	+	487.616i	0.248171	+	0.126379i
$247$	2058.71			0.530335
$248$	−780.283	−	3263.43i	−0.199790	−	0.835598i
$249$	−1286.52	−	5346.15i	−0.327430	−	1.36064i
$250$	−1896.72	+	2219.38i	−0.479836	+	0.561465i
$251$	1278.26	−	1278.26i	0.321446	−	0.321446i	−0.527876	−	0.849322i	$-0.677011\pi$
$251$	1278.26	−	1278.26i	0.321446	−	0.321446i	0.849322	+	0.527876i	$0.177011\pi$
$252$	−4109.93	−	5651.46i	−1.02739	−	1.41273i
$253$	3181.52	+	3181.52i	0.790594	+	0.790594i
$254$	88.3740	+	1127.35i	0.0218310	+	0.278489i
$255$	−874.883	+	210.536i	−0.214852	+	0.0517030i
$256$	3319.67	−	2399.37i	0.810467	−	0.585784i
$257$			4587.43i			1.11345i	0.830698	+	0.556724i	$0.187942\pi$
$257$			4587.43i			1.11345i	−0.830698	+	0.556724i	$0.812058\pi$
$258$	1458.88	+	4486.54i	0.352040	+	1.08263i
$259$	2348.22	−	2348.22i	0.563365	−	0.563365i
$260$	144.788	+	917.827i	0.0345361	+	0.218928i
$261$	2081.63	+	673.900i	0.493676	+	0.159821i
$262$	−4073.69	−	3481.44i	−0.960586	−	0.820932i
$263$		−	1063.89i		−	0.249438i	−0.992192	−	0.124719i	$-0.960197\pi$
$263$		−	1063.89i		−	0.249438i	0.992192	−	0.124719i	$-0.0398029\pi$
$264$	2385.24	−	1214.16i	0.556065	−	0.283055i
$265$		−	602.642i		−	0.139698i
$266$	4732.32	−	5537.37i	1.09082	−	1.27638i
$267$	4112.40	+	2517.06i	0.942603	+	0.576935i
$268$	−4016.64	+	5521.25i	−0.915504	+	1.25845i
$269$	−5167.40	+	5167.40i	−1.17123	+	1.17123i	−0.189318	+	0.981916i	$0.560628\pi$
$269$	−5167.40	+	5167.40i	−1.17123	+	1.17123i	−0.981916	+	0.189318i	$0.939372\pi$
$270$	1258.52	−	1261.79i	0.283672	−	0.284408i
$271$		−	6888.32i		−	1.54404i	−0.635597	−	0.772021i	$-0.719246\pi$
$271$		−	6888.32i		−	1.54404i	0.635597	−	0.772021i	$-0.280754\pi$
$272$	−759.715	−	2348.03i	−0.169355	−	0.523420i
$273$	1017.15	+	4226.77i	0.225497	+	0.937054i
$274$	−4507.29	+	353.331i	−0.993779	+	0.0779032i
$275$	−1687.40	−	1687.40i	−0.370016	−	0.370016i
$276$	−3144.86	+	7590.57i	−0.685863	+	1.65543i
$277$	−2142.76	+	2142.76i	−0.464786	+	0.464786i	−0.900221	−	0.435434i	$-0.856595\pi$
$277$	−2142.76	+	2142.76i	−0.464786	+	0.464786i	0.435434	+	0.900221i	$0.356595\pi$
$278$	−5080.10	−	4341.53i	−1.09599	−	0.936646i
$279$	3565.49	−	1821.52i	0.765091	−	0.390865i
$280$	2801.53	+	1720.35i	0.597940	+	0.367181i
$281$	7913.97			1.68010			0.840049	−	0.542510i	$-0.182526\pi$
$281$	7913.97			1.68010			0.840049	+	0.542510i	$0.182526\pi$
$282$	5408.70	+	2754.33i	1.14214	+	0.581625i
$283$	3967.83	+	3967.83i	0.833438	+	0.833438i	0.987985	−	0.154548i	$-0.0493920\pi$
$283$	3967.83	+	3967.83i	0.833438	+	0.833438i	−0.154548	+	0.987985i	$0.549392\pi$
$284$	−886.726	−	5621.05i	−0.185273	−	1.17446i
$285$	1584.44	+	969.780i	0.329312	+	0.201561i
$286$	−1660.05	+	130.133i	−0.343220	+	0.0269053i
$287$	−2365.31			−0.486481
$288$	3714.99	+	3175.96i	0.760097	+	0.649809i
$289$	3426.08			0.697351
$290$	−1026.23	+	80.4473i	−0.207802	+	0.0162897i
$291$	−925.622	−	566.541i	−0.186464	−	0.114128i
$292$	−857.374	−	5434.98i	−0.171829	−	1.08924i
$293$	5006.37	+	5006.37i	0.998209	+	0.998209i	0.999998	−	0.00178897i	$-0.000569447\pi$
$293$	5006.37	+	5006.37i	0.998209	+	0.998209i	−0.00178897	+	0.999998i	$0.500569\pi$
$294$	9214.84	+	4692.57i	1.82796	+	0.930872i
$295$	2185.30			0.431299
$296$	−1215.46	+	1979.32i	−0.238672	+	0.388668i
$297$	2078.03	+	2425.17i	0.405992	+	0.473814i
$298$	−432.446	−	369.575i	−0.0840635	−	0.0718420i
$299$	3614.49	−	3614.49i	0.699101	−	0.699101i
$300$	1667.96	−	4025.87i	0.320999	−	0.774778i
$301$	−7343.22	−	7343.22i	−1.40617	−	1.40617i
$302$	5303.24	−	415.726i	1.01049	−	0.0792130i
$303$	0.994167	+	4.13127i	0.000188493	+	0.000783284i
$304$	−2318.54	+	4536.52i	−0.437425	+	0.855880i
$305$			971.908i			0.182463i
$306$	2509.66	−	1540.55i	0.468849	−	0.287802i
$307$	−1435.75	+	1435.75i	−0.266914	+	0.266914i	−0.827855	−	0.560942i	$-0.810439\pi$
$307$	−1435.75	+	1435.75i	−0.266914	+	0.266914i	0.560942	+	0.827855i	$0.310439\pi$
$308$	−3465.90	+	4764.22i	−0.641196	+	0.881384i
$309$	−4712.27	−	2884.22i	−0.867546	−	0.530995i
$310$	−1223.79	+	1431.98i	−0.224215	+	0.262358i
$311$			3502.88i			0.638681i	0.947640	+	0.319341i	$0.103461\pi$
$311$			3502.88i			0.638681i	−0.947640	+	0.319341i	$0.896539\pi$
$312$	−1379.40	−	2709.84i	−0.250298	−	0.491713i
$313$		−	751.490i		−	0.135708i	−0.997695	−	0.0678542i	$-0.978385\pi$
$313$		−	751.490i		−	0.135708i	0.997695	−	0.0678542i	$-0.0216153\pi$
$314$	4821.28	+	4120.34i	0.866499	+	0.740523i
$315$	−1208.24	+	3732.17i	−0.216117	+	0.667569i
$316$	202.588	+	1284.23i	0.0360648	+	0.228618i
$317$	6924.49	−	6924.49i	1.22687	−	1.22687i	0.261729	−	0.965141i	$-0.415707\pi$
$317$	6924.49	−	6924.49i	1.22687	−	1.22687i	0.965141	−	0.261729i	$-0.0842927\pi$
$318$	609.848	+	1875.48i	0.107543	+	0.330728i
$319$		−	1844.71i		−	0.323775i
$320$	−2185.56	−	714.614i	−0.381802	−	0.124838i
$321$	3775.90	−	908.650i	0.656543	−	0.157994i
$322$	−1413.43	−	18030.5i	−0.244619	−	3.12050i
$323$	2170.52	+	2170.52i	0.373904	+	0.373904i
$324$	−2639.76	+	5200.37i	−0.452634	+	0.891696i
$325$	−1917.04	+	1917.04i	−0.327195	+	0.327195i
$326$	−1874.56	+	2193.46i	−0.318474	+	0.372652i
$327$	−897.836	−	3730.97i	−0.151836	−	0.630957i
$328$	1609.01	−	384.713i	0.270862	−	0.0647629i
$329$	−13360.6			−2.23889
$330$	−1338.92	−	681.832i	−0.223349	−	0.113738i
$331$	3203.80	+	3203.80i	0.532014	+	0.532014i	0.921171	−	0.389157i	$-0.127234\pi$
$331$	3203.80	+	3203.80i	0.532014	+	0.532014i	−0.389157	+	0.921171i	$0.627234\pi$
$332$	−6845.99	−	4980.37i	−1.13169	−	0.823293i
$333$	−2636.84	−	853.644i	−0.433928	−	0.140479i
$334$	486.146	+	6201.56i	0.0796428	+	1.01597i
$335$	3832.96			0.625125
$336$	−10459.5	−	2518.86i	−1.69826	−	0.408974i
$337$	2592.71			0.419091			0.209546	−	0.977799i	$-0.432802\pi$
$337$	2592.71			0.419091			0.209546	+	0.977799i	$0.432802\pi$
$338$	−337.793	−	4309.08i	−0.0543595	−	0.693442i
$339$	413.993	−	676.387i	0.0663274	−	0.108367i
$340$	−815.024	+	1120.33i	−0.130003	+	0.178701i
$341$	−2386.95	−	2386.95i	−0.379064	−	0.379064i
$342$	−5912.29	−	1414.66i	−0.934795	−	0.223672i
$343$	−11666.1			−1.83647
$344$	6189.62	+	3800.90i	0.970121	+	0.595729i
$345$	4484.45	−	1079.16i	0.699810	−	0.168406i
$346$	−1171.11	+	1370.33i	−0.181963	+	0.212918i
$347$	−6043.76	+	6043.76i	−0.935003	+	0.935003i	−0.998013	−	0.0630095i	$-0.979930\pi$
$347$	−6043.76	+	6043.76i	−0.935003	+	0.935003i	0.0630095	+	0.998013i	$0.479930\pi$
$348$	3112.32	−	1288.86i	0.479419	−	0.198535i
$349$	−1836.04	−	1836.04i	−0.281607	−	0.281607i	0.552143	−	0.833750i	$-0.313810\pi$
$349$	−1836.04	−	1836.04i	−0.281607	−	0.281607i	−0.833750	+	0.552143i	$0.813810\pi$
$350$	749.651	+	9562.98i	0.114487	+	1.46047i
$351$	2755.21	−	2360.83i	0.418980	−	0.359007i
$352$	1582.81	−	3804.60i	0.239670	−	0.576096i
$353$		−	7004.62i		−	1.05614i	−0.849200	−	0.528071i	$-0.822915\pi$
$353$		−	7004.62i		−	1.05614i	0.849200	−	0.528071i	$-0.177085\pi$
$354$	−6800.85	+	2211.43i	−1.02108	+	0.332023i
$355$	−2258.91	+	2258.91i	−0.337720	+	0.337720i
$356$	7332.60	−	1156.73i	1.09165	−	0.172209i
$357$	−3383.94	+	5528.72i	−0.501673	+	0.819639i
$358$	3528.72	+	3015.70i	0.520946	+	0.445208i
$359$		−	3792.90i		−	0.557609i	−0.960348	−	0.278805i	$-0.910062\pi$
$359$		−	3792.90i		−	0.557609i	0.960348	−	0.278805i	$-0.0899382\pi$
$360$	214.883	−	2735.34i	0.0314592	−	0.400459i
$361$			522.169i			0.0761291i
$362$	−326.438	+	381.970i	−0.0473955	+	0.0554583i
$363$	−2204.82	+	3602.26i	−0.318796	+	0.520854i
$364$	5412.57	+	3937.58i	0.779384	+	0.566992i
$365$	−2184.14	+	2184.14i	−0.313213	+	0.313213i
$366$	−983.529	−	3024.66i	−0.140464	−	0.431972i
$367$		−	4167.61i		−	0.592773i	−0.955068	−	0.296386i	$-0.904218\pi$
$367$		−	4167.61i		−	0.592773i	0.955068	−	0.296386i	$-0.0957816\pi$
$368$	3894.12	+	12035.5i	0.551617	+	1.70487i
$369$	898.086	+	1757.94i	0.126700	+	0.248007i
$370$	1299.95	−	101.904i	0.182652	−	0.0143182i
$371$	−3069.64	−	3069.64i	−0.429562	−	0.429562i
$372$	2359.45	−	5694.87i	0.328849	−	0.793724i
$373$	−5292.64	+	5292.64i	−0.734698	+	0.734698i	−0.971547	−	0.236848i	$-0.923886\pi$
$373$	−5292.64	+	5292.64i	−0.734698	+	0.734698i	0.236848	+	0.971547i	$0.423886\pi$
$374$	−1887.41	−	1613.01i	−0.260951	−	0.223013i
$375$	−5214.52	+	1254.85i	−0.718071	+	0.172800i
$376$	9088.63	−	2173.08i	1.24657	−	0.298053i
$377$	−2095.76			−0.286305
$378$	−16.6331	−	12837.5i	−0.00226327	−	1.74680i
$379$	−4863.55	−	4863.55i	−0.659165	−	0.659165i	0.296017	−	0.955183i	$-0.404341\pi$
$379$	−4863.55	−	4863.55i	−0.659165	−	0.659165i	−0.955183	+	0.296017i	$0.904341\pi$
$380$	2825.12	−	445.667i	0.381384	−	0.0601637i
$381$	−1084.51	+	1771.88i	−0.145829	+	0.238258i
$382$	10517.5	−	824.479i	1.40870	−	0.110429i
$383$	−6729.11			−0.897759			−0.448879	−	0.893592i	$-0.648177\pi$
$383$	−6729.11			−0.897759			−0.448879	+	0.893592i	$0.648177\pi$
$384$	7524.82	+	12.2478i	0.999999	+	0.00162765i
$385$	3307.41			0.437821
$386$	−9268.28	+	726.549i	−1.22213	+	0.0958040i
$387$	−2669.46	+	8245.76i	−0.350636	+	1.08309i
$388$	−1650.43	+	260.357i	−0.215948	+	0.0340660i
$389$	−1689.70	−	1689.70i	−0.220234	−	0.220234i	0.588363	−	0.808597i	$-0.299773\pi$
$389$	−1689.70	−	1689.70i	−0.220234	−	0.220234i	−0.808597	+	0.588363i	$0.799773\pi$
$390$	−774.622	+	1521.13i	−0.100576	+	0.197501i
$391$	7621.59			0.985781
$392$	15484.3	−	3702.29i	1.99510	−	0.477025i
$393$	−2303.28	−	9571.28i	−0.295636	−	1.22852i
$394$	5964.65	+	5097.48i	0.762677	+	0.651795i
$395$	516.087	−	516.087i	0.0657397	−	0.0657397i
$396$	4856.82	+	766.995i	0.616324	+	0.0973307i
$397$	8515.47	+	8515.47i	1.07652	+	1.07652i	0.996819	+	0.0797039i	$0.0253975\pi$
$397$	8515.47	+	8515.47i	1.07652	+	1.07652i	0.0797039	+	0.996819i	$0.474603\pi$
$398$	−571.821	+	44.8255i	−0.0720170	+	0.00564548i
$399$	13010.2	−	3130.84i	1.63240	−	0.392828i
$400$	−2065.35	−	6383.33i	−0.258169	−	0.797916i
$401$			4257.88i			0.530246i	0.964215	+	0.265123i	$0.0854125\pi$
$401$			4257.88i			0.530246i	−0.964215	+	0.265123i	$0.914588\pi$
$402$	−11928.5	+	3878.79i	−1.47995	+	0.481235i
$403$	−2711.79	+	2711.79i	−0.335196	+	0.335196i
$404$	5.29028	+	3.84861i	0.000651488	+	0.000473949i
$405$	3232.57	−	519.081i	0.396612	−	0.0636873i
$406$	−4817.48	+	5637.02i	−0.588886	+	0.689065i
$407$			2336.74i			0.284589i
$408$	1402.70	−	4311.33i	0.170206	−	0.523144i
$409$		−	5141.14i		−	0.621548i	−0.950484	−	0.310774i	$-0.899412\pi$
$409$		−	5141.14i		−	0.621548i	0.950484	−	0.310774i	$-0.100588\pi$
$410$	−706.028	−	603.382i	−0.0850444	−	0.0726803i
$411$	−7084.20	−	4335.99i	−0.850214	−	0.520386i
$412$	−8402.19	+	1325.46i	−1.00472	+	0.158496i
$413$	11131.1	−	11131.1i	1.32621	−	1.32621i
$414$	−12863.9	+	7896.50i	−1.52712	+	0.937420i
$415$			4752.62i			0.562161i
$416$	−4322.36	−	1798.21i	−0.509426	−	0.211934i
$417$	−2872.30	−	11935.9i	−0.337307	−	1.40168i
$418$	400.556	+	5109.73i	0.0468704	+	0.597907i
$419$	9514.69	+	9514.69i	1.10936	+	1.10936i	0.993234	+	0.116129i	$0.0370487\pi$
$419$	9514.69	+	9514.69i	1.10936	+	1.10936i	0.116129	+	0.993234i	$0.462951\pi$
$420$	2310.82	+	5580.11i	0.268467	+	0.648290i
$421$	−942.451	+	942.451i	−0.109103	+	0.109103i	−0.759551	−	0.650448i	$-0.774581\pi$
$421$	−942.451	+	942.451i	−0.109103	+	0.109103i	0.650448	+	0.759551i	$0.274581\pi$
$422$	5255.06	−	6149.03i	0.606190	−	0.709313i
$423$	5072.90	+	9929.86i	0.583104	+	1.14139i
$424$	2587.40	+	1588.86i	0.296357	+	0.181986i
$425$	−4042.32			−0.461367
$426$	4744.01	−	9315.85i	0.539550	−	1.05952i
$427$	4950.54	+	4950.54i	0.561062	+	0.561062i
$428$	3517.56	−	4835.21i	0.397260	−	0.546072i
$429$	−2609.13	−	1596.96i	−0.293637	−	0.179725i
$430$	−318.669	−	4065.12i	−0.0357385	−	0.455902i
$431$	−106.218			−0.0118709			−0.00593543	−	0.999982i	$-0.501889\pi$
$431$	−106.218			−0.0118709			−0.00593543	+	0.999982i	$0.501889\pi$
$432$	2099.31	+	8730.09i	0.233804	+	0.972284i
$433$	4043.15			0.448733			0.224367	−	0.974505i	$-0.427969\pi$
$433$	4043.15			0.448733			0.224367	+	0.974505i	$0.427969\pi$
$434$	1060.43	+	13527.5i	0.117287	+	1.49618i
$435$	−1612.95	−	987.231i	−0.177782	−	0.108814i
$436$	−4777.67	−	3475.69i	−0.524791	−	0.381779i
$437$	−11125.6	−	11125.6i	−1.21787	−	1.21787i
$438$	4586.97	−	9007.47i	0.500398	−	0.982634i
$439$	−2283.39			−0.248246			−0.124123	−	0.992267i	$-0.539612\pi$
$439$	−2283.39			−0.248246			−0.124123	+	0.992267i	$0.539612\pi$
$440$	−2249.88	+	537.944i	−0.243770	+	0.0582851i
$441$	8642.73	+	16917.6i	0.933239	+	1.82675i
$442$	−1832.52	+	2144.27i	−0.197204	+	0.230752i
$443$	3308.60	−	3308.60i	0.354845	−	0.354845i	−0.507064	−	0.861909i	$-0.669269\pi$
$443$	3308.60	−	3308.60i	0.354845	−	0.354845i	0.861909	+	0.507064i	$0.169269\pi$
$444$	−3942.44	+	1632.63i	−0.421396	+	0.174507i
$445$	−2946.73	−	2946.73i	−0.313906	−	0.313906i
$446$	−398.737	−	5086.53i	−0.0423335	−	0.540031i
$447$	−244.506	−	1016.05i	−0.0258719	−	0.107511i
$448$	−14772.4	+	7492.47i	−1.55788	+	0.790147i
$449$		−	5247.10i		−	0.551506i	−0.961229	−	0.275753i	$-0.911073\pi$
$449$		−	5247.10i		−	0.551506i	0.961229	−	0.275753i	$-0.0889272\pi$
$450$	6822.74	−	4188.12i	0.714727	−	0.438734i
$451$	1176.87	−	1176.87i	0.122875	−	0.122875i
$452$	−190.252	−	1206.03i	−0.0197980	−	0.125502i
$453$	8335.21	+	5101.69i	0.864509	+	0.529136i
$454$	−5507.52	−	4706.81i	−0.569341	−	0.486567i
$455$		−	3757.51i		−	0.387154i
$456$	−8341.05	+	4245.86i	−0.856590	+	0.436032i
$457$		−	682.527i		−	0.0698627i	−0.999390	−	0.0349314i	$-0.988879\pi$
$457$		−	682.527i		−	0.0698627i	0.999390	−	0.0349314i	$-0.0111213\pi$
$458$	−3974.02	+	4650.07i	−0.405445	+	0.474418i
$459$	5393.89	+	415.801i	0.548508	+	0.0422831i
$460$	4177.62	−	5742.54i	0.423441	−	0.582059i
$461$	−5158.76	+	5158.76i	−0.521187	+	0.521187i	−0.917930	−	0.396743i	$-0.870141\pi$
$461$	−5158.76	+	5158.76i	−0.521187	+	0.521187i	0.396743	+	0.917930i	$0.370141\pi$
$462$	−10293.0	+	3346.96i	−1.03652	+	0.337044i
$463$			4260.25i			0.427625i	0.976875	+	0.213813i	$0.0685882\pi$
$463$			4260.25i			0.427625i	−0.976875	+	0.213813i	$0.931412\pi$
$464$	2360.26	−	4618.16i	0.236147	−	0.462053i
$465$	−3364.49	+	809.645i	−0.335536	+	0.0807449i
$466$	9875.38	−	774.140i	0.981691	−	0.0769556i
$467$	−501.947	−	501.947i	−0.0497374	−	0.0497374i	0.681801	−	0.731538i	$-0.261197\pi$
$467$	−501.947	−	501.947i	−0.0497374	−	0.0497374i	−0.731538	+	0.681801i	$0.761197\pi$
$468$	871.374	−	5517.78i	0.0860669	−	0.544999i
$469$	19523.7	−	19523.7i	1.92222	−	1.92222i
$470$	−3988.05	−	3408.25i	−0.391394	−	0.334491i
$471$	2725.96	+	11327.8i	0.266679	+	1.10819i
$472$	−5761.53	+	9382.44i	−0.561856	+	0.914961i
$473$	7307.30			0.710338
$474$	−1083.85	+	2128.37i	−0.105027	+	0.206243i
$475$	5900.76	+	5900.76i	0.569991	+	0.569991i
$476$	1555.11	+	9857.97i	0.149744	+	0.949242i
$477$	−1115.90	+	3446.92i	−0.107114	+	0.330867i
$478$	5284.91	−	414.288i	0.505703	−	0.0396425i
$479$	−15980.7			−1.52438			−0.762190	−	0.647353i	$-0.775876\pi$
$479$	−15980.7			−1.52438			−0.762190	+	0.647353i	$0.775876\pi$
$480$	−2479.54	−	3420.05i	−0.235781	−	0.325215i
$481$	2654.74			0.251655
$482$	−1770.34	+	138.778i	−0.167296	+	0.0131145i
$483$	17345.3	−	28339.0i	1.63403	−	2.66970i
$484$	1013.24	+	6423.00i	0.0951574	+	0.603212i
$485$	663.251	+	663.251i	0.0620963	+	0.0620963i
$486$	−9534.77	+	4886.65i	−0.889930	+	0.456097i
$487$	1901.65			0.176945			0.0884723	−	0.996079i	$-0.471802\pi$
$487$	1901.65			0.176945			0.0884723	+	0.996079i	$0.471802\pi$
$488$	−4172.82	−	2562.43i	−0.387079	−	0.237696i
$489$	−5153.61	+	1240.19i	−0.476593	+	0.114690i
$490$	−6794.46	−	5806.65i	−0.626413	−	0.535342i
$491$	−5271.77	+	5271.77i	−0.484545	+	0.484545i	−0.906580	−	0.422035i	$-0.861316\pi$
$491$	−5271.77	+	5271.77i	−0.484545	+	0.484545i	0.422035	+	0.906580i	$0.361316\pi$
$492$	2807.82	+	1163.31i	0.257289	+	0.106598i
$493$	−2209.58	−	2209.58i	−0.201855	−	0.201855i
$494$	5805.11	−	455.067i	0.528713	−	0.0414462i
$495$	−1255.79	−	2458.13i	−0.114028	−	0.223201i
$496$	−2921.59	−	9029.68i	−0.264482	−	0.817428i
$497$			23012.1i			2.07693i
$498$	−4809.44	−	14790.6i	−0.432764	−	1.33089i
$499$	29.4722	−	29.4722i	0.00264400	−	0.00264400i	−0.705784	−	0.708428i	$-0.749405\pi$
$499$	29.4722	−	29.4722i	0.00264400	−	0.00264400i	0.708428	+	0.705784i	$0.249405\pi$
$500$	−4857.74	+	6677.43i	−0.434490	+	0.597247i
$501$	−5965.87	+	9747.11i	−0.532007	+	0.869200i
$502$	3321.85	−	3886.95i	0.295341	−	0.345584i
$503$		−	11304.7i		−	1.00209i	−0.865421	−	0.501045i	$-0.832949\pi$
$503$		−	11304.7i		−	1.00209i	0.865421	−	0.501045i	$-0.167051\pi$
$504$	−12838.3	−	15027.4i	−1.13465	−	1.32812i
$505$		−	3.67261i		−	0.000323622i
$506$	9674.43	+	8267.91i	0.849962	+	0.726390i
$507$	4145.32	−	6772.68i	0.363117	−	0.593264i
$508$	498.390	+	3159.34i	0.0435285	+	0.275931i
$509$	−2527.57	+	2527.57i	−0.220103	+	0.220103i	−0.808542	−	0.588439i	$-0.799743\pi$
$509$	−2527.57	+	2527.57i	−0.220103	+	0.220103i	0.588439	+	0.808542i	$0.299743\pi$
$510$	−2420.44	+	787.052i	−0.210154	+	0.0683358i
$511$			22250.4i			1.92622i
$512$	8830.37	−	7499.49i	0.762209	−	0.647331i
$513$	−7266.76	−	8480.69i	−0.625410	−	0.729886i
$514$	1014.03	+	12935.5i	0.0870172	+	1.11004i
$515$	3376.56	+	3376.56i	0.288911	+	0.288911i
$516$	5105.45	+	12328.5i	0.435572	+	1.05181i
$517$	6647.64	−	6647.64i	0.565499	−	0.565499i
$518$	6102.41	−	7140.53i	0.517614	−	0.605670i
$519$	−3219.65	+	774.790i	−0.272306	+	0.0655289i
$520$	611.152	+	2556.06i	0.0515399	+	0.215559i
$521$	−55.5878			−0.00467437			−0.00233719	−	0.999997i	$-0.500744\pi$
$521$	−55.5878			−0.00467437			−0.00233719	+	0.999997i	$0.500744\pi$
$522$	6018.68	+	1440.12i	0.504656	+	0.120751i
$523$	−14970.9	−	14970.9i	−1.25169	−	1.25169i	−0.954963	−	0.296723i	$-0.904106\pi$
$523$	−14970.9	−	14970.9i	−1.25169	−	1.25169i	−0.296723	−	0.954963i	$-0.595894\pi$
$524$	−12256.5	−	8916.41i	−1.02181	−	0.743350i
$525$	−9199.55	+	15030.3i	−0.764764	+	1.24948i
$526$	−235.167	−	2999.93i	−0.0194939	−	0.248675i
$527$	−5718.14			−0.472650
$528$	6457.45	−	3950.91i	0.532243	−	0.325646i
$529$	−26899.5			−2.21086
$530$	−133.211	−	1699.32i	−0.0109176	−	0.139271i
$531$	−12499.2	−	4046.46i	−1.02151	−	0.330700i
$532$	12120.1	−	16660.2i	0.987730	−	1.35773i
$533$	−1337.03	−	1337.03i	−0.108655	−	0.108655i
$534$	12152.4	+	6188.52i	0.984808	+	0.501505i
$535$	−3356.70			−0.271258
$536$	−10105.6	+	16456.5i	−0.814355	+	1.32615i
$537$	1995.15	+	8290.85i	0.160329	+	0.666250i
$538$	−13428.7	+	15713.1i	−1.07612	+	1.25918i
$539$	11325.6	−	11325.6i	0.905063	−	0.905063i
$540$	3269.84	−	3836.15i	0.260577	−	0.305707i
$541$	1527.27	+	1527.27i	0.121372	+	0.121372i	0.765184	−	0.643812i	$-0.222648\pi$
$541$	1527.27	+	1527.27i	0.121372	+	0.121372i	−0.643812	+	0.765184i	$0.722648\pi$
$542$	−1522.63	−	19423.5i	−0.120669	−	1.53932i
$543$	−897.452	+	215.967i	−0.0709270	+	0.0170682i
$544$	−2661.24	−	6452.99i	−0.209743	−	0.508584i
$545$			3316.75i			0.260686i
$546$	3802.44	+	11693.7i	0.298039	+	0.916565i
$547$	−8402.23	+	8402.23i	−0.656770	+	0.656770i	−0.954615	−	0.297844i	$-0.903732\pi$
$547$	−8402.23	+	8402.23i	−0.656770	+	0.656770i	0.297844	+	0.954615i	$0.403732\pi$
$548$	−12631.5	+	1992.63i	−0.984651	+	0.155330i
$549$	1799.66	−	5559.00i	0.139904	−	0.432154i
$550$	−5131.09	−	4385.11i	−0.397801	−	0.339967i
$551$			6450.86i			0.498759i
$552$	−7189.93	+	22098.9i	−0.554391	+	1.70397i
$553$		−	5257.52i		−	0.404290i
$554$	−5568.45	+	6515.74i	−0.427041	+	0.499688i
$555$	2043.16	+	1250.55i	0.156265	+	0.0956446i
$556$	−15284.4	−	11119.2i	−1.16583	−	0.848128i
$557$	11345.5	−	11345.5i	0.863060	−	0.863060i	−0.128633	−	0.991692i	$-0.541059\pi$
$557$	11345.5	−	11345.5i	0.863060	−	0.863060i	0.991692	+	0.128633i	$0.0410588\pi$
$558$	9651.25	−	5924.40i	0.732205	−	0.449462i
$559$		−	8301.74i		−	0.628133i
$560$	8279.95	+	4231.74i	0.624807	+	0.319328i
$561$	−1067.15	−	4434.53i	−0.0803119	−	0.333736i
$562$	22315.6	−	1749.34i	1.67496	−	0.131302i
$563$	6452.36	+	6452.36i	0.483010	+	0.483010i	0.906092	−	0.423082i	$-0.139052\pi$
$563$	6452.36	+	6452.36i	0.483010	+	0.483010i	−0.423082	+	0.906092i	$0.639052\pi$
$564$	15860.2	+	6571.04i	1.18410	+	0.490586i
$565$	−484.662	+	484.662i	−0.0360883	+	0.0360883i
$566$	12065.5	+	10311.3i	0.896023	+	0.765755i
$567$	13821.5	−	19109.5i	1.02372	−	1.41539i
$568$	−3742.87	−	15654.1i	−0.276492	−	1.15639i
$569$	8010.89			0.590218			0.295109	−	0.955464i	$-0.404644\pi$
$569$	8010.89			0.590218			0.295109	+	0.955464i	$0.404644\pi$
$570$	4682.13	+	2384.33i	0.344057	+	0.175208i
$571$	−13548.1	−	13548.1i	−0.992946	−	0.992946i	0.00702892	−	0.999975i	$-0.497763\pi$
$571$	−13548.1	−	13548.1i	−0.992946	−	0.992946i	−0.999975	+	0.00702892i	$0.997763\pi$
$572$	−4652.21	+	733.891i	−0.340067	+	0.0536460i
$573$	16530.6	+	10117.8i	1.20519	+	0.737658i
$574$	−6669.65	+	522.840i	−0.484993	+	0.0380190i
$575$	20720.0			1.50275
$576$	11177.5	+	8134.31i	0.808556	+	0.588419i
$577$	3085.97			0.222652			0.111326	−	0.993784i	$-0.464490\pi$
$577$	3085.97			0.222652			0.111326	+	0.993784i	$0.464490\pi$
$578$	9660.79	−	757.318i	0.695218	−	0.0544987i
$579$	−14567.1	−	8916.04i	−1.04558	−	0.639962i
$580$	−2875.96	+	453.687i	−0.205893	+	0.0324798i
$581$	24208.1	+	24208.1i	1.72861	+	1.72861i
$582$	−2735.28	−	1392.92i	−0.194813	−	0.0992066i
$583$	3054.62			0.216997
$584$	−3618.97	−	15135.9i	−0.256428	−	1.07248i
$585$	−2792.65	+	1426.69i	−0.197371	+	0.100831i
$586$	15223.5	+	13010.2i	1.07317	+	0.917145i
$587$	7599.07	−	7599.07i	0.534323	−	0.534323i	−0.387533	−	0.921856i	$-0.626673\pi$
$587$	7599.07	−	7599.07i	0.534323	−	0.534323i	0.921856	+	0.387533i	$0.126673\pi$
$588$	27021.0	+	11195.1i	1.89512	+	0.785168i
$589$	8347.05	+	8347.05i	0.583929	+	0.583929i
$590$	6162.06	−	483.049i	0.429980	−	0.0337065i
$591$	3372.43	+	14014.1i	0.234726	+	0.975406i
$592$	−2989.79	+	5849.92i	−0.207567	+	0.406132i
$593$			13043.4i			0.903253i	0.892207	+	0.451627i	$0.149156\pi$
$593$			13043.4i			0.903253i	−0.892207	+	0.451627i	$0.850844\pi$
$594$	6395.65	+	6379.10i	0.441779	+	0.440636i
$595$	3961.59	−	3961.59i	0.272957	−	0.272957i
$596$	−1301.09	−	946.529i	−0.0894209	−	0.0650526i
$597$	−898.742	−	550.089i	−0.0616132	−	0.0377113i
$598$	9393.08	−	10991.0i	0.642327	−	0.751598i
$599$		−	12441.1i		−	0.848630i	−0.905515	−	0.424315i	$-0.860515\pi$
$599$		−	12441.1i		−	0.848630i	0.905515	−	0.424315i	$-0.139485\pi$
$600$	3813.38	−	11720.7i	0.259467	−	0.797495i
$601$		−	556.990i		−	0.0378038i	−0.999821	−	0.0189019i	$-0.993983\pi$
$601$		−	556.990i		−	0.0378038i	0.999821	−	0.0189019i	$-0.00601702\pi$
$602$	−22329.4	−	19083.1i	−1.51176	−	1.29197i
$603$	−21923.3	−	7097.39i	−1.48057	−	0.479317i
$604$	14862.1	−	2344.51i	1.00121	−	0.157941i
$605$	2581.19	−	2581.19i	0.173455	−	0.173455i
$606$	3.71652	+	11.4295i	0.000249131	+	0.000766158i
$607$			10080.8i			0.674080i	0.941490	+	0.337040i	$0.109426\pi$
$607$			10080.8i			0.674080i	−0.941490	+	0.337040i	$0.890574\pi$
$608$	−5534.99	+	13304.5i	−0.369200	+	0.887447i
$609$	−13244.4	+	3187.18i	−0.881262	+	0.212071i
$610$	214.835	+	2740.56i	0.0142597	+	0.181905i
$611$	−7552.31	−	7552.31i	−0.500055	−	0.500055i
$612$	6736.15	−	4898.75i	0.444923	−	0.323563i
$613$	−13360.3	+	13360.3i	−0.880290	+	0.880290i	−0.993564	−	0.113274i	$-0.963866\pi$
$613$	−13360.3	+	13360.3i	−0.880290	+	0.880290i	0.113274	+	0.993564i	$0.463866\pi$
$614$	−3731.13	+	4365.86i	−0.245238	+	0.286957i
$615$	−399.190	−	1658.84i	−0.0261738	−	0.108765i
$616$	−8719.97	+	14200.1i	−0.570353	+	0.928799i
$617$	−28317.5			−1.84768			−0.923840	−	0.382779i	$-0.874967\pi$
$617$	−28317.5			−1.84768			−0.923840	+	0.382779i	$0.874967\pi$
$618$	−13925.1	−	7091.22i	−0.906390	−	0.461571i
$619$	5399.53	+	5399.53i	0.350606	+	0.350606i	0.860335	−	0.509729i	$-0.170254\pi$
$619$	5399.53	+	5399.53i	0.350606	+	0.350606i	−0.509729	+	0.860335i	$0.670254\pi$
$620$	−3134.29	+	4308.38i	−0.203026	+	0.279078i
$621$	−27647.8	−	2131.30i	−1.78659	−	0.137723i
$622$	774.292	+	9877.32i	0.0499136	+	0.636728i
$623$	−30019.1			−1.93048
$624$	−4488.58	−	7336.24i	−0.287960	−	0.470648i
$625$	−8468.19			−0.541964
$626$	−166.113	−	2119.03i	−0.0106058	−	0.135293i
$627$	−4915.54	+	8031.06i	−0.313090	+	0.511531i
$628$	14505.7	+	10552.7i	0.921721	+	0.670540i
$629$	2798.92	+	2798.92i	0.177425	+	0.177425i
$630$	−2582.00	+	10791.0i	−0.163285	+	0.682417i
$631$	−6123.81			−0.386347			−0.193174	−	0.981165i	$-0.561878\pi$
$631$	−6123.81			−0.386347			−0.193174	+	0.981165i	$0.561878\pi$
$632$	855.124	+	3576.45i	0.0538212	+	0.225100i
$633$	14447.4	−	3476.68i	0.907158	−	0.218303i
$634$	17994.9	−	21056.1i	1.12724	−	1.31900i
$635$	1269.63	−	1269.63i	0.0793447	−	0.0793447i
$636$	2134.20	+	5153.62i	0.133060	+	0.321312i
$637$	−12866.9	−	12866.9i	−0.800323	−	0.800323i
$638$	−407.764	−	5201.68i	−0.0253034	−	0.322785i
$639$	17103.0	−	8737.47i	1.05882	−	0.540922i
$640$	−6320.76	−	1531.94i	−0.390390	−	0.0946178i
$641$		−	20240.4i		−	1.24719i	−0.781748	−	0.623594i	$-0.785672\pi$
$641$		−	20240.4i		−	1.24719i	0.781748	−	0.623594i	$-0.214328\pi$
$642$	10446.3	−	3396.83i	0.642188	−	0.208820i
$643$	12470.6	−	12470.6i	0.764842	−	0.764842i	−0.212352	−	0.977193i	$-0.568112\pi$
$643$	12470.6	−	12470.6i	0.764842	−	0.764842i	0.977193	+	0.212352i	$0.0681122\pi$
$644$	−7971.11	−	50529.6i	−0.487742	−	3.09184i
$645$	3910.63	−	6389.24i	0.238730	−	0.390040i
$646$	6600.17	+	5640.61i	0.401982	+	0.343540i
$647$			7081.47i			0.430296i	0.976581	+	0.215148i	$0.0690234\pi$
$647$			7081.47i			0.430296i	−0.976581	+	0.215148i	$0.930977\pi$
$648$	−6294.03	+	15247.4i	−0.381563	+	0.924343i
$649$			11076.7i			0.669949i
$650$	−4981.88	+	5829.38i	−0.300623	+	0.351765i
$651$	−13013.4	+	21261.5i	−0.783465	+	1.28004i
$652$	−4801.00	+	6599.43i	−0.288377	+	0.396401i
$653$	−4674.02	+	4674.02i	−0.280105	+	0.280105i	−0.833151	−	0.553046i	$-0.813465\pi$
$653$	−4674.02	+	4674.02i	−0.280105	+	0.280105i	0.553046	+	0.833151i	$0.313465\pi$
$654$	−3356.41	−	10322.0i	−0.200682	−	0.617161i
$655$			8508.67i			0.507575i
$656$	4452.02	−	1440.47i	0.264973	−	0.0857330i
$657$	16536.9	−	8448.24i	0.981985	−	0.501670i
$658$	−37674.0	+	2953.30i	−2.23205	+	0.174972i
$659$	20967.1	+	20967.1i	1.23939	+	1.23939i	0.960249	+	0.279146i	$0.0900512\pi$
$659$	20967.1	+	20967.1i	1.23939	+	1.23939i	0.279146	+	0.960249i	$0.409949\pi$
$660$	−3926.17	−	1626.65i	−0.231554	−	0.0959354i
$661$	17021.5	−	17021.5i	1.00160	−	1.00160i	0.00160195	−	0.999999i	$-0.499490\pi$
$661$	17021.5	−	17021.5i	1.00160	−	1.00160i	0.999999	−	0.00160195i	$-0.000509918\pi$
$662$	9742.17	+	8325.81i	0.571964	+	0.488809i
$663$	−5038.02	+	1212.37i	−0.295114	+	0.0710176i
$664$	−20405.0	−	12530.3i	−1.19257	−	0.732332i
$665$	−11565.8			−0.674442
$666$	−7623.99	−	1824.22i	−0.443579	−	0.106137i
$667$	11325.8	+	11325.8i	0.657477	+	0.657477i
$668$	2741.64	+	17379.5i	0.158798	+	1.00664i
$669$	4893.22	−	7994.60i	0.282784	−	0.462016i
$670$	10808.1	−	847.255i	0.623213	−	0.0488542i
$671$	−4926.32			−0.283426
$672$	−30050.3	−	4790.61i	−1.72502	−	0.275003i
$673$	5131.88			0.293937			0.146969	−	0.989141i	$-0.453048\pi$
$673$	5131.88			0.293937			0.146969	+	0.989141i	$0.453048\pi$
$674$	7310.85	−	573.104i	0.417809	−	0.0327524i
$675$	14663.8	+	1130.39i	0.836162	+	0.0644575i
$676$	−1905.00	−	12076.0i	−0.108386	−	0.687073i
$677$	−7945.30	−	7945.30i	−0.451053	−	0.451053i	0.444651	−	0.895704i	$-0.353328\pi$
$677$	−7945.30	−	7945.30i	−0.451053	−	0.451053i	−0.895704	+	0.444651i	$0.853328\pi$
$678$	1017.86	−	1998.77i	0.0576556	−	0.113219i
$679$	6756.72			0.381884
$680$	−2050.54	+	3339.23i	−0.115639	+	0.188314i
$681$	−3113.96	−	12940.1i	−0.175224	−	0.728143i
$682$	−7258.30	−	6203.05i	−0.407529	−	0.348280i
$683$	−14603.2	+	14603.2i	−0.818121	+	0.818121i	−0.985836	−	0.167714i	$-0.946361\pi$
$683$	−14603.2	+	14603.2i	−0.818121	+	0.818121i	0.167714	+	0.985836i	$0.446361\pi$
$684$	−16984.0	−	2682.14i	−0.949416	−	0.149933i
$685$	5076.16	+	5076.16i	0.283139	+	0.283139i
$686$	−32895.8	+	2578.73i	−1.83085	+	0.143522i
$687$	−10925.5	+	2629.16i	−0.606745	+	0.146010i
$688$	18293.5	+	9349.50i	1.01371	+	0.518090i
$689$		−	3470.32i		−	0.191885i
$690$	12406.6	−	4034.25i	0.684509	−	0.222581i
$691$	5956.77	−	5956.77i	0.327940	−	0.327940i	−0.523863	−	0.851803i	$-0.675510\pi$
$691$	5956.77	−	5956.77i	0.327940	−	0.327940i	0.851803	+	0.523863i	$0.175510\pi$
$692$	−2999.36	+	4122.90i	−0.164767	+	0.226487i
$693$	−18917.3	−	6124.25i	−1.03695	−	0.335701i
$694$	−15706.1	+	18378.0i	−0.859072	+	1.00522i
$695$			10610.7i			0.579119i
$696$	8491.15	−	4322.26i	0.462437	−	0.235395i
$697$		−	2819.29i		−	0.153211i
$698$	−5583.06	−	4771.37i	−0.302754	−	0.258738i
$699$	15521.3	+	9500.07i	0.839872	+	0.514057i
$700$	4227.69	+	26799.8i	0.228274	+	1.44705i
$701$	19922.3	−	19922.3i	1.07340	−	1.07340i	0.0763183	−	0.997084i	$-0.475683\pi$
$701$	19922.3	−	19922.3i	1.07340	−	1.07340i	0.997084	−	0.0763183i	$-0.0243165\pi$
$702$	7247.22	−	7266.03i	0.389642	−	0.390653i
$703$		−	8171.45i		−	0.438395i
$704$	3622.17	−	11078.0i	0.193914	−	0.593065i
$705$	−2254.85	−	9370.06i	−0.120458	−	0.500563i
$706$	−1548.33	−	19751.5i	−0.0825387	−	1.05291i
$707$	−18.7069	−	18.7069i	−0.000995115	−	0.000995115i
$708$	−18688.1	+	7739.03i	−0.992006	+	0.410806i
$709$	−6339.66	+	6339.66i	−0.335812	+	0.335812i	−0.854789	−	0.518976i	$-0.826313\pi$
$709$	−6339.66	+	6339.66i	−0.335812	+	0.335812i	0.518976	+	0.854789i	$0.326313\pi$
$710$	−5870.30	+	6868.94i	−0.310294	+	0.363080i
$711$	−3907.48	+	1996.23i	−0.206107	+	0.105295i
$712$	20420.6	−	4882.54i	1.07485	−	0.256996i
$713$	29309.9			1.53950
$714$	−8319.86	+	16337.8i	−0.436083	+	0.856338i
$715$	1869.57	+	1869.57i	0.0977871	+	0.0977871i
$716$	10616.8	+	7723.59i	0.554146	+	0.403134i
$717$	8306.39	+	5084.06i	0.432647	+	0.264808i
$718$	−838.401	−	10695.1i	−0.0435778	−	0.555904i
$719$	23861.1			1.23765			0.618824	−	0.785530i	$-0.287610\pi$
$719$	23861.1			1.23765			0.618824	+	0.785530i	$0.287610\pi$
$720$	1.28823	−	7760.56i	6.66796e−5	−	0.401693i
$721$	34397.9			1.77676
$722$	115.423	+	1472.40i	0.00594957	+	0.0758962i
$723$	−2782.47	−	1703.06i	−0.143128	−	0.0876035i
$724$	−836.049	+	1149.23i	−0.0429164	+	0.0589927i
$725$	−6006.95	−	6006.95i	−0.307714	−	0.307714i
$726$	−5420.84	+	10644.9i	−0.277116	+	0.544175i
$727$	13991.5			0.713776			0.356888	−	0.934147i	$-0.383838\pi$
$727$	13991.5			0.713776			0.356888	+	0.934147i	$0.383838\pi$
$728$	16132.6	+	9906.66i	0.821312	+	0.504348i
$729$	−19450.5	−	3016.70i	−0.988185	−	0.153264i
$730$	−5675.98	+	6641.57i	−0.287777	+	0.336733i
$731$	8752.62	−	8752.62i	0.442856	−	0.442856i
$732$	−3441.92	−	8311.47i	−0.173794	−	0.419673i
$733$	11874.1	+	11874.1i	0.598334	+	0.598334i	0.939869	−	0.341535i	$-0.110947\pi$
$733$	11874.1	+	11874.1i	0.598334	+	0.598334i	−0.341535	+	0.939869i	$0.610947\pi$
$734$	−921.228	−	11751.7i	−0.0463258	−	0.590960i
$735$	−3841.60	−	15963.8i	−0.192789	−	0.801135i
$736$	13640.9	+	33076.5i	0.683167	+	1.65654i
$737$			19428.2i			0.971026i
$738$	2920.98	+	4758.48i	0.145695	+	0.237347i
$739$	−24843.0	+	24843.0i	−1.23662	+	1.23662i	−0.275253	+	0.961372i	$0.588762\pi$
$739$	−24843.0	+	24843.0i	−1.23662	+	1.23662i	−0.961372	+	0.275253i	$0.911238\pi$
$740$	3643.04	−	574.694i	0.180974	−	0.0285489i
$741$	9124.00	+	5584.49i	0.452333	+	0.276857i
$742$	−9334.22	−	7977.16i	−0.461819	−	0.394678i
$743$			12479.8i			0.616204i	0.951353	+	0.308102i	$0.0996939\pi$
$743$			12479.8i			0.616204i	−0.951353	+	0.308102i	$0.900306\pi$
$744$	5394.29	−	16579.8i	0.265812	−	0.816997i
$745$			903.245i			0.0444192i
$746$	−13754.1	+	16094.0i	−0.675034	+	0.789869i
$747$	8800.30	−	27183.4i	0.431039	−	1.33145i
$748$	−5678.62	−	4131.12i	−0.277582	−	0.201937i
$749$	−17097.8	+	17097.8i	−0.834098	+	0.834098i
$750$	−14426.4	+	4691.02i	−0.702370	+	0.228389i
$751$		−	34126.2i		−	1.65817i	−0.559124	−	0.829084i	$-0.688862\pi$
$751$		−	34126.2i		−	1.65817i	0.559124	−	0.829084i	$-0.311138\pi$
$752$	25147.6	−	8136.59i	1.21946	−	0.394563i
$753$	9132.53	−	2197.69i	0.441976	−	0.106359i
$754$	−5909.57	+	463.256i	−0.285430	+	0.0223751i
$755$	−5972.57	−	5972.57i	−0.287899	−	0.287899i
$756$	−2884.57	−	36195.3i	−0.138771	−	1.74129i
$757$	−7341.39	+	7341.39i	−0.352480	+	0.352480i	−0.861032	−	0.508551i	$-0.830181\pi$
$757$	−7341.39	+	7341.39i	−0.352480	+	0.352480i	0.508551	+	0.861032i	$0.330181\pi$
$758$	−14789.2	−	12639.1i	−0.708664	−	0.605635i
$759$	5469.94	+	22730.4i	0.261589	+	1.08704i
$760$	7867.71	−	1881.16i	0.375515	−	0.0897853i
$761$	18960.2			0.903162			0.451581	−	0.892230i	$-0.350860\pi$
$761$	18960.2			0.903162			0.451581	+	0.892230i	$0.350860\pi$
$762$	−2666.40	+	5236.03i	−0.126763	+	0.248926i
$763$	16894.3	+	16894.3i	0.801592	+	0.801592i
$764$	29474.9	−	4649.69i	1.39576	−	0.220183i
$765$	−4448.50	−	1440.15i	−0.210243	−	0.0680635i
$766$	−18974.6	+	1487.44i	−0.895013	+	0.0701609i
$767$	12584.1			0.592418
$768$	21221.0	−	1628.79i	0.997067	−	0.0765283i
$769$	12020.7			0.563692			0.281846	−	0.959460i	$-0.409053\pi$
$769$	12020.7			0.563692			0.281846	+	0.959460i	$0.409053\pi$
$770$	9326.16	−	731.086i	0.436482	−	0.0342162i
$771$	−12443.9	+	20331.0i	−0.581267	+	0.949681i
$772$	−25973.9	+	4097.41i	−1.21091	+	0.191022i
$773$	−18559.5	−	18559.5i	−0.863568	−	0.863568i	0.128183	−	0.991751i	$-0.459086\pi$
$773$	−18559.5	−	18559.5i	−0.863568	−	0.863568i	−0.991751	+	0.128183i	$0.959086\pi$
$774$	−5704.60	+	23841.3i	−0.264919	+	1.10718i
$775$	−15545.3			−0.720520
$776$	−4596.28	+	1098.97i	−0.212625	+	0.0508384i
$777$	16776.9	−	4037.27i	0.774606	−	0.186405i
$778$	−5138.06	−	4391.07i	−0.236772	−	0.202349i
$779$	−4115.45	+	4115.45i	−0.189283	+	0.189283i
$780$	−1848.02	+	4460.47i	−0.0848331	+	0.204757i
$781$	−11449.8	−	11449.8i	−0.524590	−	0.524590i
$782$	21491.2	−	1684.71i	0.982766	−	0.0770399i
$783$	7397.53	+	8633.30i	0.337632	+	0.394034i
$784$	42844.0	−	13862.4i	1.95171	−	0.631485i
$785$		−	10070.1i		−	0.457858i
$786$	−8610.41	−	26479.7i	−0.390742	−	1.20166i
$787$	6934.87	−	6934.87i	0.314106	−	0.314106i	−0.532392	−	0.846498i	$-0.678707\pi$
$787$	6934.87	−	6934.87i	0.314106	−	0.314106i	0.846498	+	0.532392i	$0.178707\pi$
$788$	17945.7	+	13055.3i	0.811283	+	0.590198i
$789$	2885.92	−	4715.05i	0.130217	−	0.212751i
$790$	1341.17	−	1569.33i	0.0604010	−	0.0706762i
$791$			4937.38i			0.221938i
$792$	13864.7	+	1089.18i	0.622045	+	0.0488666i
$793$			5596.74i			0.250626i
$794$	25894.0	+	22129.4i	1.15736	+	0.989099i
$795$	1634.73	−	2670.85i	0.0729284	−	0.119151i
$796$	−1602.50	+	252.796i	−0.0713556	+	0.0112564i
$797$	−1033.71	+	1033.71i	−0.0459424	+	0.0459424i	−0.729705	−	0.683762i	$-0.760342\pi$
$797$	−1033.71	+	1033.71i	−0.0459424	+	0.0459424i	0.683762	+	0.729705i	$0.260342\pi$
$798$	35993.9	−	11704.1i	1.59671	−	0.519200i
$799$		−	15925.0i		−	0.705113i
$800$	−7234.83	−	17543.0i	−0.319737	−	0.775300i
$801$	11398.0	+	22310.7i	0.502780	+	0.984158i
$802$	941.182	+	12006.3i	0.0414393	+	0.528624i
$803$	−11070.8	−	11070.8i	−0.486524	−	0.486524i
$804$	−32778.3	+	13574.0i	−1.43781	+	0.595422i
$805$	−20306.2	+	20306.2i	−0.889067	+	0.889067i
$806$	−7047.22	+	8246.07i	−0.307975	+	0.360367i
$807$	−36918.5	+	8884.24i	−1.61040	+	0.387534i
$808$	15.7681	+	9.68282i	0.000686535	+	0.000421585i
$809$	−28378.6			−1.23330			−0.616649	−	0.787239i	$-0.711510\pi$
$809$	−28378.6			−1.23330			−0.616649	+	0.787239i	$0.711510\pi$
$810$	9000.40	−	2178.24i	0.390422	−	0.0944882i
$811$	−18955.2	−	18955.2i	−0.820723	−	0.820723i	0.165489	−	0.986212i	$-0.447080\pi$
$811$	−18955.2	−	18955.2i	−0.820723	−	0.820723i	−0.986212	+	0.165489i	$0.947080\pi$
$812$	−12338.2	+	16960.0i	−0.533233	+	0.732980i
$813$	18685.3	−	30528.3i	0.806056	−	1.31694i
$814$	516.524	+	6589.08i	0.0222410	+	0.283719i
$815$	4581.45			0.196909
$816$	3002.32	−	12467.0i	0.128802	−	0.534845i
$817$	−25553.2			−1.09424
$818$	−1136.42	−	14496.9i	−0.0485746	−	0.619647i
$819$	−6957.69	+	21491.8i	−0.296851	+	0.916951i
$820$	−2124.21	−	1545.34i	−0.0904644	−	0.0658117i
$821$	−26166.4	−	26166.4i	−1.11232	−	1.11232i	−0.992836	−	0.119482i	$-0.961877\pi$
$821$	−26166.4	−	26166.4i	−1.11232	−	1.11232i	−0.119482	−	0.992836i	$-0.538123\pi$
$822$	−20934.3	−	10660.6i	−0.888282	−	0.452350i
$823$	−22421.9			−0.949672			−0.474836	−	0.880074i	$-0.657493\pi$
$823$	−22421.9			−0.949672			−0.474836	+	0.880074i	$0.657493\pi$
$824$	−23399.3	+	5594.75i	−0.989264	+	0.236532i
$825$	−2901.13	−	12055.7i	−0.122430	−	0.508757i
$826$	28926.8	−	33847.7i	1.21851	−	1.42580i
$827$	−32421.5	+	32421.5i	−1.36325	+	1.36325i	−0.493501	+	0.869745i	$0.664283\pi$
$827$	−32421.5	+	32421.5i	−1.36325	+	1.36325i	−0.869745	+	0.493501i	$0.835717\pi$
$828$	−34528.0	+	25109.9i	−1.44919	+	1.05390i
$829$	508.732	+	508.732i	0.0213136	+	0.0213136i	0.717683	−	0.696370i	$-0.245203\pi$
$829$	508.732	+	508.732i	0.0213136	+	0.0213136i	−0.696370	+	0.717683i	$0.745203\pi$
$830$	1050.54	+	13401.3i	0.0439335	+	0.560442i
$831$	−15309.0	+	3684.02i	−0.639063	+	0.153787i
$832$	−12585.6	−	4115.11i	−0.524431	−	0.171473i
$833$		−	27131.5i		−	1.12851i
$834$	−10737.6	−	33021.5i	−0.445818	−	1.37103i
$835$	6984.26	−	6984.26i	0.289461	−	0.289461i
$836$	2258.96	+	14319.8i	0.0934542	+	0.592415i
$837$	20743.0	+	1599.02i	0.856609	+	0.0660338i
$838$	28932.5	+	24726.1i	1.19267	+	1.01927i
$839$		−	28733.8i		−	1.18236i	−0.806539	−	0.591181i	$-0.798662\pi$
$839$		−	28733.8i		−	1.18236i	0.806539	−	0.591181i	$-0.201338\pi$
$840$	7749.44	+	15223.9i	0.318311	+	0.625326i
$841$			17822.0i			0.730741i
$842$	−2449.18	+	2865.83i	−0.100243	+	0.117296i
$843$	35073.9	+	21467.5i	1.43299	+	0.877083i
$844$	13458.9	−	18500.5i	0.548902	−	0.754518i
$845$	−4852.94	+	4852.94i	−0.197569	+	0.197569i
$846$	16499.4	+	26878.6i	0.670521	+	1.09232i
$847$		−	26295.3i		−	1.06672i
$848$	7647.11	+	3908.31i	0.309673	+	0.158269i
$849$	6821.84	+	28348.2i	0.275765	+	1.14595i
$850$	−11398.4	+	893.533i	−0.459956	+	0.0360564i
$851$	−14346.6	−	14346.6i	−0.577904	−	0.577904i
$852$	11317.8	−	27317.3i	0.455097	−	1.09844i
$853$	−32516.7	+	32516.7i	−1.30522	+	1.30522i	−0.380390	+	0.924826i	$0.624210\pi$
$853$	−32516.7	+	32516.7i	−1.30522	+	1.30522i	−0.924826	+	0.380390i	$0.875790\pi$
$854$	15053.7	+	12865.1i	0.603194	+	0.515498i
$855$	4391.43	+	8595.93i	0.175654	+	0.343830i
$856$	8849.92	−	14411.8i	0.353369	−	0.575448i
$857$	17192.8			0.685292			0.342646	−	0.939465i	$-0.388677\pi$
$857$	17192.8			0.685292			0.342646	+	0.939465i	$0.388677\pi$
$858$	−7710.18	−	3926.34i	−0.306784	−	0.156227i
$859$	28319.0	+	28319.0i	1.12483	+	1.12483i	0.991005	+	0.133827i	$0.0427266\pi$
$859$	28319.0	+	28319.0i	1.12483	+	1.12483i	0.133827	+	0.991005i	$0.457273\pi$
$860$	−1797.15	−	11392.3i	−0.0712584	−	0.451714i
$861$	−10482.8	−	6416.17i	−0.414929	−	0.253963i
$862$	−299.511	+	23.4789i	−0.0118346	+	0.000927721i
$863$	−25432.8			−1.00318			−0.501589	−	0.865106i	$-0.667251\pi$
$863$	−25432.8			−1.00318			−0.501589	+	0.865106i	$0.667251\pi$
$864$	7849.34	+	24152.9i	0.309074	+	0.951038i
$865$	2862.20			0.112506
$866$	11400.8	−	893.717i	0.447361	−	0.0350690i
$867$	15184.1	+	9293.64i	0.594784	+	0.364047i
$868$	5980.38	+	37910.2i	0.233856	+	1.48244i
$869$	2615.90	+	2615.90i	0.102115	+	0.102115i
$870$	−4766.38	−	2427.24i	−0.185742	−	0.0945874i
$871$	22072.1			0.858652
$872$	−14240.2	−	8744.60i	−0.553023	−	0.339598i
$873$	−2565.46	−	5021.71i	−0.0994589	−	0.194684i
$874$	−33830.9	−	28912.4i	−1.30932	−	1.11897i
$875$	23612.0	−	23612.0i	0.912266	−	0.912266i
$876$	10943.2	−	26413.0i	0.422073	−	1.01874i
$877$	−34340.0	−	34340.0i	−1.32221	−	1.32221i	−0.911982	−	0.410231i	$-0.865448\pi$
$877$	−34340.0	−	34340.0i	−1.32221	−	1.32221i	−0.410231	−	0.911982i	$-0.634552\pi$
$878$	−6438.64	+	504.730i	−0.247487	+	0.0194007i
$879$	8607.39	+	35768.1i	0.330285	+	1.37250i
$880$	−6225.25	+	2014.20i	−0.238469	+	0.0771577i
$881$		−	1486.40i		−	0.0568423i	−0.999596	−	0.0284211i	$-0.990952\pi$
$881$		−	1486.40i		−	0.0568423i	0.999596	−	0.0284211i	$-0.00904795\pi$
$882$	28110.1	+	45793.3i	1.07315	+	1.74823i
$883$	26569.1	−	26569.1i	1.01260	−	1.01260i	0.0126765	−	0.999920i	$-0.495965\pi$
$883$	26569.1	−	26569.1i	1.01260	−	1.01260i	0.999920	−	0.0126765i	$-0.00403517\pi$
$884$	−4693.32	+	6451.42i	−0.178567	+	0.245458i
$885$	9685.03	+	5927.87i	0.367863	+	0.225156i
$886$	8598.17	−	10060.9i	0.326028	−	0.381491i
$887$		−	24047.1i		−	0.910284i	−0.890419	−	0.455142i	$-0.849588\pi$
$887$		−	24047.1i		−	0.910284i	0.890419	−	0.455142i	$-0.150412\pi$
$888$	−10755.9	+	5475.10i	−0.406469	+	0.206906i
$889$		−	12934.1i		−	0.487959i
$890$	−8960.47	−	7657.76i	−0.337478	−	0.288414i
$891$	2631.08	+	16385.0i	0.0989274	+	0.616070i
$892$	−2248.70	−	14254.7i	−0.0844081	−	0.535071i
$893$	−23246.4	+	23246.4i	−0.871123	+	0.871123i
$894$	−914.044	−	2810.98i	−0.0341949	−	0.105160i
$895$		−	7370.39i		−	0.275268i
$896$	−39998.8	+	24392.5i	−1.49137	+	0.909481i
$897$	25823.7	−	6214.34i	0.961237	−	0.231316i
$898$	−1159.84	−	14795.7i	−0.0431008	−	0.549819i
$899$	−8497.26	−	8497.26i	−0.315238	−	0.315238i
$900$	18312.8	−	13317.7i	0.678253	−	0.493248i
$901$	3658.80	−	3658.80i	0.135286	−	0.135286i
$902$	3058.37	−	3578.65i	0.112896	−	0.132102i
$903$	−12625.1	−	52463.7i	−0.465268	−	1.93343i
$904$	−803.055	−	3358.68i	−0.0295456	−	0.123571i
$905$	797.817			0.0293042
$906$	24631.1	+	12543.2i	0.903217	+	0.459955i
$907$	−20817.3	−	20817.3i	−0.762101	−	0.762101i	0.214601	−	0.976702i	$-0.431155\pi$
$907$	−20817.3	−	20817.3i	−0.762101	−	0.762101i	−0.976702	+	0.214601i	$0.931155\pi$
$908$	−16570.4	−	12054.7i	−0.605625	−	0.440584i
$909$	−6.80048	+	21.0062i	−0.000248138	+	0.000766480i
$910$	−830.578	−	10595.3i	−0.0302565	−	0.385970i
$911$	9545.92			0.347168			0.173584	−	0.984819i	$-0.444465\pi$
$911$	9545.92			0.347168			0.173584	+	0.984819i	$0.444465\pi$
$912$	−22581.4	+	13816.1i	−0.819894	+	0.501642i
$913$	−24089.7			−0.873222
$914$	−150.869	−	1924.57i	−0.00545985	−	0.0696491i
$915$	−2636.41	+	4307.40i	−0.0952536	+	0.155626i
$916$	−10178.0	+	13990.6i	−0.367129	+	0.504653i
$917$	43340.0	+	43340.0i	1.56076	+	1.56076i
$918$	15301.5	−	19.8256i	0.550135	−	0.000712789i
$919$	−12290.4			−0.441156			−0.220578	−	0.975369i	$-0.570794\pi$
$919$	−12290.4			−0.441156			−0.220578	+	0.975369i	$0.570794\pi$
$920$	10510.6	−	17116.1i	0.376657	−	0.613371i
$921$	−10257.7	+	2468.47i	−0.366996	+	0.0883157i
$922$	−13406.2	+	15686.9i	−0.478862	+	0.560325i
$923$	−13008.0	+	13008.0i	−0.463881	+	0.463881i
$924$	−28284.0	+	11712.9i	−1.00701	+	0.417019i
$925$	7609.13	+	7609.13i	0.270472	+	0.270472i
$926$	941.705	+	12012.9i	0.0334194	+	0.426317i
$927$	−13060.5	−	25565.1i	−0.462745	−	0.905791i
$928$	5634.59	−	13543.9i	0.199315	−	0.479095i
$929$			26256.0i			0.927268i	0.886027	+	0.463634i	$0.153455\pi$
$929$			26256.0i			0.927268i	−0.886027	+	0.463634i	$0.846545\pi$
$930$	−9308.13	+	3026.72i	−0.328200	+	0.106720i
$931$	−39605.1	+	39605.1i	−1.39420	+	1.39420i
$932$	27675.2	−	4365.80i	0.972675	−	0.153441i
$933$	−9501.94	+	15524.4i	−0.333419	+	0.544744i
$934$	−1526.33	−	1304.43i	−0.0534723	−	0.0456982i
$935$			3942.21i			0.137887i
$936$	1237.41	−	15751.5i	0.0432114	−	0.550058i
$937$		−	9723.86i		−	0.339023i	−0.985528	−	0.169512i	$-0.945781\pi$
$937$		−	9723.86i		−	0.339023i	0.985528	−	0.169512i	$-0.0542190\pi$
$938$	50736.8	−	59368.0i	1.76611	−	2.06656i
$939$	2038.50	−	3330.53i	0.0708455	−	0.115748i
$940$	−11998.8	−	8728.96i	−0.416337	−	0.302880i
$941$	24237.0	−	24237.0i	0.839644	−	0.839644i	−0.149168	−	0.988812i	$-0.547660\pi$
$941$	24237.0	−	24237.0i	0.839644	−	0.839644i	0.988812	+	0.149168i	$0.0476596\pi$
$942$	10190.5	+	31339.2i	0.352469	+	1.08396i
$943$			14451.0i			0.499035i
$944$	−14172.3	+	27729.9i	−0.488632	+	0.956073i
$945$	−15478.8	+	13263.1i	−0.532830	+	0.456560i
$946$	20605.0	−	1615.24i	0.708166	−	0.0555137i
$947$	−26385.5	−	26385.5i	−0.905399	−	0.905399i	0.0904976	−	0.995897i	$-0.471154\pi$
$947$	−26385.5	−	26385.5i	−0.905399	−	0.905399i	−0.995897	+	0.0904976i	$0.971154\pi$
$948$	−2585.76	+	6241.10i	−0.0885880	+	0.213820i
$949$	−12577.4	+	12577.4i	−0.430220	+	0.430220i
$950$	17943.2	+	15334.5i	0.612793	+	0.523702i
$951$	49472.1	−	11905.2i	1.68690	−	0.405943i
$952$	6564.10	+	27453.5i	0.223470	+	0.934636i
$953$	−11928.6			−0.405464			−0.202732	−	0.979234i	$-0.564982\pi$
$953$	−11928.6			−0.405464			−0.202732	+	0.979234i	$0.564982\pi$
$954$	−2384.66	+	9966.20i	−0.0809288	+	0.338226i
$955$	−11845.0	−	11845.0i	−0.401355	−	0.401355i
$956$	14810.7	−	2336.40i	0.501058	−	0.0790425i
$957$	5003.99	−	8175.59i	0.169024	−	0.276154i
$958$	−45062.1	+	3532.46i	−1.51972	+	0.119132i
$959$	51712.2			1.74126
$960$	−7747.72	−	9095.68i	−0.260476	−	0.305794i
$961$	7801.07			0.261860
$962$	7485.78	−	586.817i	0.250885	−	0.0196671i
$963$	19199.2	+	6215.51i	0.642458	+	0.207988i
$964$	−4961.28	+	782.647i	−0.165759	+	0.0261487i
$965$	10438.0	+	10438.0i	0.348199	+	0.348199i
$966$	42645.7	−	83743.6i	1.42040	−	2.78924i
$967$	52495.5			1.74575			0.872876	−	0.487943i	$-0.162252\pi$
$967$	52495.5			1.74575			0.872876	+	0.487943i	$0.162252\pi$
$968$	4276.87	+	17887.5i	0.142008	+	0.593930i
$969$	3731.75	+	15507.3i	0.123716	+	0.514104i
$970$	2016.83	+	1723.61i	0.0667593	+	0.0570535i
$971$	8668.87	−	8668.87i	0.286506	−	0.286506i	−0.549191	−	0.835697i	$-0.685064\pi$
$971$	8668.87	−	8668.87i	0.286506	−	0.286506i	0.835697	+	0.549191i	$0.185064\pi$
$972$	−25805.8	+	15886.9i	−0.851564	+	0.524251i
$973$	54047.1	+	54047.1i	1.78075	+	1.78075i
$974$	5362.23	−	420.350i	0.176403	−	0.0138284i
$975$	−13696.3	+	3295.95i	−0.449880	+	0.108261i
$976$	−12332.8	−	6303.10i	−0.404472	−	0.206719i
$977$		−	34992.7i		−	1.14587i	−0.819600	−	0.572936i	$-0.805804\pi$
$977$		−	34992.7i		−	1.14587i	0.819600	−	0.572936i	$-0.194196\pi$
$978$	−14257.9	+	4636.23i	−0.466173	+	0.151585i
$979$	14936.1	−	14936.1i	0.487600	−	0.487600i
$980$	−20442.4	−	14871.6i	−0.666335	−	0.484750i
$981$	6141.54	−	18970.7i	0.199882	−	0.617420i
$982$	−13699.9	+	16030.5i	−0.445195	+	0.520931i
$983$			60755.5i			1.97131i	0.168767	+	0.985656i	$0.446021\pi$
$983$			60755.5i			1.97131i	−0.168767	+	0.985656i	$0.553979\pi$
$984$	8174.56	+	2659.62i	0.264833	+	0.0861642i
$985$		−	12458.3i		−	0.402999i
$986$	−6718.94	−	5742.11i	−0.217013	−	0.185463i
$987$	−59213.0	−	36242.2i	−1.90960	−	1.16880i
$988$	16268.5	−	2566.38i	0.523857	−	0.0826390i
$989$	−44863.9	+	44863.9i	−1.44246	+	1.44246i
$990$	−4084.41	−	6653.78i	−0.131122	−	0.213607i
$991$		−	1498.28i		−	0.0480268i	−0.999712	−	0.0240134i	$-0.992356\pi$
$991$		−	1498.28i		−	0.0480268i	0.999712	−	0.0240134i	$-0.00764444\pi$
$992$	−10234.2	−	24815.9i	−0.327556	−	0.794259i
$993$	5508.25	+	22889.6i	0.176031	+	0.731499i
$994$	5086.71	+	64889.0i	0.162314	+	2.07058i
$995$	643.990	+	643.990i	0.0205185	+	0.0205185i
$996$	−16830.9	−	40643.0i	−0.535450	−	1.29300i
$997$	43616.9	−	43616.9i	1.38552	−	1.38552i	0.551033	−	0.834484i	$-0.314234\pi$
$997$	43616.9	−	43616.9i	1.38552	−	1.38552i	0.834484	−	0.551033i	$-0.185766\pi$
$998$	76.5904	−	89.6197i	0.00242928	−	0.00284255i
$999$	−9370.60	−	10936.0i	−0.296770	−	0.346346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.k.a.35.22	yes	44
3.2	odd	2	inner	48.4.k.a.35.1	yes	44
4.3	odd	2		192.4.k.a.47.4		44
8.3	odd	2		384.4.k.a.95.19		44
8.5	even	2		384.4.k.b.95.4		44
12.11	even	2		192.4.k.a.47.16		44
16.3	odd	4		384.4.k.b.287.16		44
16.5	even	4		192.4.k.a.143.16		44
16.11	odd	4	inner	48.4.k.a.11.1	✓	44
16.13	even	4		384.4.k.a.287.7		44
24.5	odd	2		384.4.k.b.95.16		44
24.11	even	2		384.4.k.a.95.7		44
48.5	odd	4		192.4.k.a.143.4		44
48.11	even	4	inner	48.4.k.a.11.22	yes	44
48.29	odd	4		384.4.k.a.287.19		44
48.35	even	4		384.4.k.b.287.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.k.a.11.1	✓	44	16.11	odd	4	inner
48.4.k.a.11.22	yes	44	48.11	even	4	inner
48.4.k.a.35.1	yes	44	3.2	odd	2	inner
48.4.k.a.35.22	yes	44	1.1	even	1	trivial
192.4.k.a.47.4		44	4.3	odd	2
192.4.k.a.47.16		44	12.11	even	2
192.4.k.a.143.4		44	48.5	odd	4
192.4.k.a.143.16		44	16.5	even	4
384.4.k.a.95.7		44	24.11	even	2
384.4.k.a.95.19		44	8.3	odd	2
384.4.k.a.287.7		44	16.13	even	4
384.4.k.a.287.19		44	48.29	odd	4
384.4.k.b.95.4		44	8.5	even	2
384.4.k.b.95.16		44	24.5	odd	2
384.4.k.b.287.4		44	48.35	even	4
384.4.k.b.287.16		44	16.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.81978 - 0.221045i) q^{2} +(4.43190 + 2.71261i) q^{3} +(7.90228 - 1.24659i) q^{4} +(-3.17566 - 3.17566i) q^{5} +(13.0966 + 6.66931i) q^{6} -32.3513 q^{7} +(22.0071 - 5.26187i) q^{8} +(12.2835 + 24.0440i) q^{9} +(-9.65662 - 8.25269i) q^{10} +(16.0965 - 16.0965i) q^{11} +(38.4036 + 15.9110i) q^{12} +(-18.2871 - 18.2871i) q^{13} +(-91.2234 + 7.15108i) q^{14} +(-5.45988 - 22.6886i) q^{15} +(60.8920 - 19.7019i) q^{16} -38.5606i q^{17} +(39.9515 + 65.0836i) q^{18} +(-56.2887 + 56.2887i) q^{19} +(-29.0537 - 21.1362i) q^{20} +(-143.378 - 87.7565i) q^{21} +(41.8306 - 48.9467i) q^{22} +197.652i q^{23} +(111.807 + 36.3767i) q^{24} -104.830i q^{25} +(-55.6077 - 47.5232i) q^{26} +(-10.7831 + 139.881i) q^{27} +(-255.649 + 40.3289i) q^{28} +(57.3016 - 57.3016i) q^{29} +(-20.4108 - 62.7698i) q^{30} -148.290i q^{31} +(167.347 - 69.0147i) q^{32} +(115.002 - 27.6746i) q^{33} +(-8.52361 - 108.732i) q^{34} +(102.737 + 102.737i) q^{35} +(127.041 + 174.690i) q^{36} +(-72.5852 + 72.5852i) q^{37} +(-146.279 + 171.164i) q^{38} +(-31.4408 - 130.652i) q^{39} +(-86.5971 - 53.1772i) q^{40} +73.1133 q^{41} +(-423.691 - 215.761i) q^{42} +(226.984 + 226.984i) q^{43} +(107.133 - 147.265i) q^{44} +(37.3476 - 115.364i) q^{45} +(43.6900 + 557.336i) q^{46} +412.986 q^{47} +(323.311 + 77.8597i) q^{48} +703.607 q^{49} +(-23.1722 - 295.598i) q^{50} +(104.600 - 170.897i) q^{51} +(-167.306 - 121.713i) q^{52} +(94.8845 + 94.8845i) q^{53} +(0.514141 + 396.817i) q^{54} -102.234 q^{55} +(-711.958 + 170.228i) q^{56} +(-402.155 + 96.7764i) q^{57} +(148.912 - 174.244i) q^{58} +(-344.070 + 344.070i) q^{59} +(-71.4289 - 172.485i) q^{60} +(-153.024 - 153.024i) q^{61} +(-32.7787 - 418.145i) q^{62} +(-397.386 - 777.856i) q^{63} +(456.625 - 231.597i) q^{64} +116.147i q^{65} +(318.162 - 103.457i) q^{66} +(-603.490 + 603.490i) q^{67} +(-48.0693 - 304.716i) q^{68} +(-536.154 + 875.976i) q^{69} +(312.404 + 266.985i) q^{70} -711.320i q^{71} +(396.840 + 464.506i) q^{72} -687.773i q^{73} +(-188.629 + 220.719i) q^{74} +(284.364 - 464.598i) q^{75} +(-374.640 + 514.978i) q^{76} +(-520.744 + 520.744i) q^{77} +(-117.536 - 361.460i) q^{78} +162.513i q^{79} +(-255.939 - 130.806i) q^{80} +(-427.233 + 590.689i) q^{81} +(206.163 - 16.1613i) q^{82} +(-748.288 - 748.288i) q^{83} +(-1242.41 - 514.743i) q^{84} +(-122.455 + 122.455i) q^{85} +(690.217 + 589.870i) q^{86} +(409.392 - 98.5180i) q^{87} +(269.540 - 438.936i) q^{88} +927.910 q^{89} +(79.8114 - 333.556i) q^{90} +(591.611 + 591.611i) q^{91} +(246.392 + 1561.90i) q^{92} +(402.253 - 657.206i) q^{93} +(1164.53 - 91.2884i) q^{94} +357.508 q^{95} +(928.875 + 148.081i) q^{96} -208.855 q^{97} +(1984.01 - 155.529i) q^{98} +(584.747 + 189.304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + 56 q^{10} - 80 q^{12} - 4 q^{13} - 112 q^{16} + 52 q^{18} + 20 q^{19} - 56 q^{21} - 40 q^{22} - 120 q^{24} - 134 q^{27} - 296 q^{28} - 332 q^{30} - 4 q^{33}+ \cdots + 1196 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 4 * q^4 + 28 * q^6 - 8 * q^7 + 56 * q^10 - 80 * q^12 - 4 * q^13 - 112 * q^16 + 52 * q^18 + 20 * q^19 - 56 * q^21 - 40 * q^22 - 120 * q^24 - 134 * q^27 - 296 * q^28 - 332 * q^30 - 4 * q^33 + 520 * q^34 - 604 * q^36 - 4 * q^37 + 596 * q^39 + 632 * q^40 + 696 * q^42 - 436 * q^43 - 252 * q^45 + 664 * q^46 + 1200 * q^48 + 972 * q^49 - 648 * q^51 + 320 * q^52 + 1592 * q^54 + 280 * q^55 - 424 * q^58 + 800 * q^60 - 916 * q^61 - 2056 * q^64 - 668 * q^66 - 1636 * q^67 + 52 * q^69 - 5192 * q^70 - 3704 * q^72 + 1454 * q^75 - 568 * q^76 - 4932 * q^78 - 4 * q^81 + 768 * q^82 - 2096 * q^84 + 736 * q^85 + 1284 * q^87 + 8864 * q^88 + 2672 * q^90 + 424 * q^91 - 2084 * q^93 + 5616 * q^94 + 8008 * q^96 - 8 * q^97 + 1196 * q^99

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