LMFDB - Embedded newform 88.4.i.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,4,Mod(9,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("88.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	88.i (of order $5$, degree $4$, 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:	$5.19216808051$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 60 x^{14} - 83 x^{13} + 1685 x^{12} - 14618 x^{11} + 106543 x^{10} - 521269 x^{9} + \cdots + 2025 $ x^16 - 4x^15 + 60x^14 - 83x^13 + 1685x^12 - 14618x^11 + 106543x^10 - 521269x^9 + 3907139x^8 - 15948298x^7 + 37290102x^6 - 37052438x^5 + 40742731x^4 + 4262985x^3 + 9787185x^2 + 227475*x + 2025
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.2
Root			$3.98665 + 2.89647i$ of defining polynomial
Character	$\chi$	$=$	88.9
Dual form			88.4.i.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87500 + 1.36227i) q^{3} +(1.88546 + 5.80286i) q^{5} +(-3.69974 - 2.68802i) q^{7} +(-6.68360 + 20.5700i) q^{9} +(-32.6966 + 16.1844i) q^{11} +(-14.6799 + 45.1799i) q^{13} +(-11.4403 - 8.31187i) q^{15} +(19.6589 + 60.5038i) q^{17} +(-14.9266 + 10.8448i) q^{19} +10.5988 q^{21} -51.9123 q^{23} +(71.0089 - 51.5910i) q^{25} +(-34.8272 - 107.187i) q^{27} +(62.4357 + 45.3622i) q^{29} +(33.7328 - 103.819i) q^{31} +(39.2586 - 74.8873i) q^{33} +(8.62246 - 26.5372i) q^{35} +(113.250 + 82.2810i) q^{37} +(-34.0225 - 104.710i) q^{39} +(128.134 - 93.0948i) q^{41} -26.9236 q^{43} -131.967 q^{45} +(208.809 - 151.708i) q^{47} +(-99.5302 - 306.322i) q^{49} +(-119.283 - 86.6641i) q^{51} +(-45.7633 + 140.845i) q^{53} +(-155.564 - 159.218i) q^{55} +(13.2138 - 40.6680i) q^{57} +(587.040 + 426.510i) q^{59} +(149.089 + 458.849i) q^{61} +(80.0201 - 58.1380i) q^{63} -289.851 q^{65} -464.330 q^{67} +(97.3358 - 70.7186i) q^{69} +(281.867 + 867.498i) q^{71} +(-742.094 - 539.163i) q^{73} +(-62.8611 + 193.467i) q^{75} +(164.473 + 28.0108i) q^{77} +(-234.747 + 722.475i) q^{79} +(-261.125 - 189.718i) q^{81} +(215.908 + 664.495i) q^{83} +(-314.029 + 228.155i) q^{85} -178.863 q^{87} -564.403 q^{89} +(175.756 - 127.694i) q^{91} +(78.1801 + 240.613i) q^{93} +(-91.0743 - 66.1694i) q^{95} +(360.762 - 1110.31i) q^{97} +(-114.383 - 780.739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} - q^{5} - 13 q^{7} + 7 q^{9} + 83 q^{11} + 69 q^{13} + 93 q^{15} - 217 q^{17} + 126 q^{19} + 34 q^{21} - 92 q^{23} + 307 q^{25} + 158 q^{27} - 553 q^{29} + 205 q^{31} - 198 q^{33} + 7 q^{35}+ \cdots - 3265 q^{99}+O(q^{100}) $ 16 * q - q^3 - q^5 - 13 * q^7 + 7 * q^9 + 83 * q^11 + 69 * q^13 + 93 * q^15 - 217 * q^17 + 126 * q^19 + 34 * q^21 - 92 * q^23 + 307 * q^25 + 158 * q^27 - 553 * q^29 + 205 * q^31 - 198 * q^33 + 7 * q^35 + 127 * q^37 - 629 * q^39 - 553 * q^41 + 70 * q^43 - 1132 * q^45 + 779 * q^47 + 847 * q^49 - 2176 * q^51 + 1401 * q^53 - 385 * q^55 - 488 * q^57 + 1354 * q^59 - 1623 * q^61 + 256 * q^63 + 1674 * q^65 - 1658 * q^67 + 5470 * q^69 + 1985 * q^71 - 1245 * q^73 + 4114 * q^75 - 2645 * q^77 - 2007 * q^79 + 1966 * q^81 - 2946 * q^83 - 1543 * q^85 - 262 * q^87 - 6410 * q^89 + 3937 * q^91 + 2221 * q^93 - 8359 * q^95 + 6566 * q^97 - 3265 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.87500	+	1.36227i	−0.360844	+	0.262169i	−0.753404	−	0.657558i	$-0.771590\pi$
$3$	−1.87500	+	1.36227i	−0.360844	+	0.262169i	0.392560	+	0.919726i	$0.371590\pi$
$4$		0			0
$5$	1.88546	+	5.80286i	0.168641	+	0.519023i	0.999286	−	0.0377786i	$-0.0120282\pi$
$5$	1.88546	+	5.80286i	0.168641	+	0.519023i	−0.830645	+	0.556802i	$0.812028\pi$
$6$		0			0
$7$	−3.69974	−	2.68802i	−0.199767	−	0.145139i	0.483405	−	0.875397i	$-0.339400\pi$
$7$	−3.69974	−	2.68802i	−0.199767	−	0.145139i	−0.683172	+	0.730258i	$0.739400\pi$
$8$		0			0
$9$	−6.68360	+	20.5700i	−0.247541	+	0.761852i
$10$		0			0
$11$	−32.6966	+	16.1844i	−0.896217	+	0.443617i
$11$	−32.6966	+	16.1844i	−0.896217	+	0.443617i
$12$		0			0
$13$	−14.6799	+	45.1799i	−0.313189	+	0.963897i	0.663304	+	0.748350i	$0.269153\pi$
$13$	−14.6799	+	45.1799i	−0.313189	+	0.963897i	−0.976493	+	0.215547i	$0.930847\pi$
$14$		0			0
$15$	−11.4403	−	8.31187i	−0.196925	−	0.143074i
$16$		0			0
$17$	19.6589	+	60.5038i	0.280469	+	0.863196i	0.987720	+	0.156233i	$0.0499352\pi$
$17$	19.6589	+	60.5038i	0.280469	+	0.863196i	−0.707251	+	0.706963i	$0.750065\pi$
$18$		0			0
$19$	−14.9266	+	10.8448i	−0.180231	+	0.130946i	−0.674243	−	0.738510i	$-0.735530\pi$
$19$	−14.9266	+	10.8448i	−0.180231	+	0.130946i	0.494012	+	0.869455i	$0.335530\pi$
$20$		0			0
$21$	10.5988			0.110136
$22$		0			0
$23$	−51.9123			−0.470629			−0.235315	−	0.971919i	$-0.575612\pi$
$23$	−51.9123			−0.470629			−0.235315	+	0.971919i	$0.575612\pi$
$24$		0			0
$25$	71.0089	−	51.5910i	0.568071	−	0.412728i
$26$		0			0
$27$	−34.8272	−	107.187i	−0.248240	−	0.764006i
$28$		0			0
$29$	62.4357	+	45.3622i	0.399794	+	0.290467i	0.769457	−	0.638699i	$-0.220527\pi$
$29$	62.4357	+	45.3622i	0.399794	+	0.290467i	−0.369663	+	0.929166i	$0.620527\pi$
$30$		0			0
$31$	33.7328	−	103.819i	0.195438	−	0.601497i	−0.804533	−	0.593908i	$-0.797584\pi$
$31$	33.7328	−	103.819i	0.195438	−	0.601497i	0.999971	−	0.00758885i	$-0.00241563\pi$
$32$		0			0
$33$	39.2586	−	74.8873i	0.207092	−	0.395037i
$34$		0			0
$35$	8.62246	−	26.5372i	0.0416418	−	0.128160i
$36$		0			0
$37$	113.250	+	82.2810i	0.503195	+	0.365592i	0.810236	−	0.586104i	$-0.199339\pi$
$37$	113.250	+	82.2810i	0.503195	+	0.365592i	−0.307041	+	0.951696i	$0.599339\pi$
$38$		0			0
$39$	−34.0225	−	104.710i	−0.139691	−	0.429925i
$40$		0			0
$41$	128.134	−	93.0948i	0.488077	−	0.354609i	−0.316367	−	0.948637i	$-0.602463\pi$
$41$	128.134	−	93.0948i	0.488077	−	0.354609i	0.804444	+	0.594028i	$0.202463\pi$
$42$		0			0
$43$	−26.9236			−0.0954838			−0.0477419	−	0.998860i	$-0.515203\pi$
$43$	−26.9236			−0.0954838			−0.0477419	+	0.998860i	$0.515203\pi$
$44$		0			0
$45$	−131.967			−0.437165
$46$		0			0
$47$	208.809	−	151.708i	0.648040	−	0.470828i	−0.214563	−	0.976710i	$-0.568833\pi$
$47$	208.809	−	151.708i	0.648040	−	0.470828i	0.862603	+	0.505882i	$0.168833\pi$
$48$		0			0
$49$	−99.5302	−	306.322i	−0.290176	−	0.893068i
$50$		0			0
$51$	−119.283	−	86.6641i	−0.327509	−	0.237949i
$52$		0			0
$53$	−45.7633	+	140.845i	−0.118605	+	0.365029i	−0.992682	−	0.120759i	$-0.961467\pi$
$53$	−45.7633	+	140.845i	−0.118605	+	0.365029i	0.874077	+	0.485788i	$0.161467\pi$
$54$		0			0
$55$	−155.564	−	159.218i	−0.381386	−	0.390345i
$56$		0			0
$57$	13.2138	−	40.6680i	0.0307056	−	0.0945020i
$58$		0			0
$59$	587.040	+	426.510i	1.29536	+	0.941133i	0.999899	−	0.0142226i	$-0.00452736\pi$
$59$	587.040	+	426.510i	1.29536	+	0.941133i	0.295459	+	0.955355i	$0.404527\pi$
$60$		0			0
$61$	149.089	+	458.849i	0.312933	+	0.963108i	0.976597	+	0.215077i	$0.0690004\pi$
$61$	149.089	+	458.849i	0.312933	+	0.963108i	−0.663664	+	0.748031i	$0.731000\pi$
$62$		0			0
$63$	80.0201	−	58.1380i	0.160025	−	0.116265i
$64$		0			0
$65$	−289.851			−0.553102
$66$		0			0
$67$	−464.330			−0.846671			−0.423335	−	0.905973i	$-0.639141\pi$
$67$	−464.330			−0.846671			−0.423335	+	0.905973i	$0.639141\pi$
$68$		0			0
$69$	97.3358	−	70.7186i	0.169824	−	0.123384i
$70$		0			0
$71$	281.867	+	867.498i	0.471148	+	1.45004i	0.851083	+	0.525031i	$0.175946\pi$
$71$	281.867	+	867.498i	0.471148	+	1.45004i	−0.379935	+	0.925013i	$0.624054\pi$
$72$		0			0
$73$	−742.094	−	539.163i	−1.18980	−	0.864442i	−0.196559	−	0.980492i	$-0.562977\pi$
$73$	−742.094	−	539.163i	−1.18980	−	0.864442i	−0.993243	+	0.116050i	$0.962977\pi$
$74$		0			0
$75$	−62.8611	+	193.467i	−0.0967810	+	0.297861i
$76$		0			0
$77$	164.473	+	28.0108i	0.243421	+	0.0414562i
$78$		0			0
$79$	−234.747	+	722.475i	−0.334317	+	1.02892i	0.632740	+	0.774364i	$0.281930\pi$
$79$	−234.747	+	722.475i	−0.334317	+	1.02892i	−0.967057	+	0.254558i	$0.918070\pi$
$80$		0			0
$81$	−261.125	−	189.718i	−0.358196	−	0.260244i
$82$		0			0
$83$	215.908	+	664.495i	0.285529	+	0.878769i	0.986239	+	0.165323i	$0.0528666\pi$
$83$	215.908	+	664.495i	0.285529	+	0.878769i	−0.700710	+	0.713446i	$0.747133\pi$
$84$		0			0
$85$	−314.029	+	228.155i	−0.400720	+	0.291140i
$86$		0			0
$87$	−178.863			−0.220415
$88$		0			0
$89$	−564.403			−0.672209			−0.336104	−	0.941825i	$-0.609109\pi$
$89$	−564.403			−0.672209			−0.336104	+	0.941825i	$0.609109\pi$
$90$		0			0
$91$	175.756	−	127.694i	0.202464	−	0.147099i
$92$		0			0
$93$	78.1801	+	240.613i	0.0871709	+	0.268284i
$94$		0			0
$95$	−91.0743	−	66.1694i	−0.0983582	−	0.0714614i
$96$		0			0
$97$	360.762	−	1110.31i	0.377627	−	1.16222i	−0.564062	−	0.825732i	$-0.690762\pi$
$97$	360.762	−	1110.31i	0.377627	−	1.16222i	0.941689	−	0.336484i	$-0.109238\pi$
$98$		0			0
$99$	−114.383	−	780.739i	−0.116120	−	0.792598i
$100$		0			0
$101$	−458.862	+	1412.23i	−0.452064	+	1.39131i	0.422484	+	0.906370i	$0.361158\pi$
$101$	−458.862	+	1412.23i	−0.452064	+	1.39131i	−0.874548	+	0.484939i	$0.838842\pi$
$102$		0			0
$103$	791.019	+	574.709i	0.756712	+	0.549784i	0.897900	−	0.440199i	$-0.145092\pi$
$103$	791.019	+	574.709i	0.756712	+	0.549784i	−0.141188	+	0.989983i	$0.545092\pi$
$104$		0			0
$105$	19.9837	+	61.5034i	0.0185734	+	0.0571631i
$106$		0			0
$107$	988.744	−	718.364i	0.893322	−	0.649037i	−0.0434200	−	0.999057i	$-0.513825\pi$
$107$	988.744	−	718.364i	0.893322	−	0.649037i	0.936742	+	0.350020i	$0.113825\pi$
$108$		0			0
$109$	−250.590			−0.220203			−0.110102	−	0.993920i	$-0.535118\pi$
$109$	−250.590			−0.220203			−0.110102	+	0.993920i	$0.535118\pi$
$110$		0			0
$111$	−324.433			−0.277422
$112$		0			0
$113$	1740.66	−	1264.66i	1.44909	−	1.05283i	0.463051	−	0.886332i	$-0.346755\pi$
$113$	1740.66	−	1264.66i	1.44909	−	1.05283i	0.986042	−	0.166496i	$-0.0532452\pi$
$114$		0			0
$115$	−97.8788	−	301.240i	−0.0793673	−	0.244268i
$116$		0			0
$117$	−831.237	−	603.929i	−0.656820	−	0.477208i
$118$		0			0
$119$	89.9026	−	276.692i	0.0692551	−	0.213145i
$120$		0			0
$121$	807.129	−	1058.35i	0.606408	−	0.795154i
$122$		0			0
$123$	−113.431	+	349.106i	−0.0831526	+	0.255917i
$124$		0			0
$125$	1050.29	+	763.077i	0.751523	+	0.546014i
$126$		0			0
$127$	−551.691	−	1697.93i	−0.385470	−	1.18635i	−0.936139	−	0.351630i	$-0.885628\pi$
$127$	−551.691	−	1697.93i	−0.385470	−	1.18635i	0.550670	−	0.834723i	$-0.314372\pi$
$128$		0			0
$129$	50.4817	−	36.6771i	0.0344548	−	0.0250329i
$130$		0			0
$131$	127.974			0.0853522			0.0426761	−	0.999089i	$-0.486412\pi$
$131$	127.974			0.0853522			0.0426761	+	0.999089i	$0.486412\pi$
$132$		0			0
$133$	84.3754			0.0550096
$134$		0			0
$135$	556.326	−	404.194i	0.354673	−	0.257685i
$136$		0			0
$137$	132.647	+	408.245i	0.0827211	+	0.254589i	0.983860	−	0.178942i	$-0.0572674\pi$
$137$	132.647	+	408.245i	0.0827211	+	0.254589i	−0.901139	+	0.433531i	$0.857267\pi$
$138$		0			0
$139$	−1972.02	−	1432.76i	−1.20334	−	0.874281i	−0.208735	−	0.977972i	$-0.566935\pi$
$139$	−1972.02	−	1432.76i	−1.20334	−	0.874281i	−0.994610	+	0.103692i	$0.966935\pi$
$140$		0			0
$141$	−184.849	+	568.907i	−0.110405	+	0.339791i
$142$		0			0
$143$	−251.231	−	1714.81i	−0.146916	−	1.00280i
$144$		0			0
$145$	−145.510	+	447.835i	−0.0833377	+	0.256487i
$146$		0			0
$147$	603.913	+	438.768i	0.338843	+	0.246184i
$148$		0			0
$149$	861.346	+	2650.95i	0.473585	+	1.45755i	0.847856	+	0.530226i	$0.177893\pi$
$149$	861.346	+	2650.95i	0.473585	+	1.45755i	−0.374271	+	0.927319i	$0.622107\pi$
$150$		0			0
$151$	−1030.25	+	748.520i	−0.555235	+	0.403402i	−0.829712	−	0.558192i	$-0.811495\pi$
$151$	−1030.25	+	748.520i	−0.555235	+	0.403402i	0.274477	+	0.961594i	$0.411495\pi$
$152$		0			0
$153$	−1375.96			−0.727055
$154$		0			0
$155$	666.047			0.345150
$156$		0			0
$157$	2954.08	−	2146.26i	1.50166	−	1.09102i	0.531949	−	0.846777i	$-0.321460\pi$
$157$	2954.08	−	2146.26i	1.50166	−	1.09102i	0.969714	−	0.244245i	$-0.0785401\pi$
$158$		0			0
$159$	−106.062	−	326.427i	−0.0529013	−	0.162813i
$160$		0			0
$161$	192.062	+	139.541i	0.0940162	+	0.0683068i
$162$		0			0
$163$	−521.808	+	1605.96i	−0.250743	+	0.771708i	0.743895	+	0.668296i	$0.232976\pi$
$163$	−521.808	+	1605.96i	−0.250743	+	0.771708i	−0.994639	+	0.103412i	$0.967024\pi$
$164$		0			0
$165$	508.581	+	86.6147i	0.239958	+	0.0408663i
$166$		0			0
$167$	−606.706	+	1867.25i	−0.281128	+	0.865222i	0.706405	+	0.707808i	$0.250316\pi$
$167$	−606.706	+	1867.25i	−0.281128	+	0.865222i	−0.987533	+	0.157414i	$0.949684\pi$
$168$		0			0
$169$	−48.3183	−	35.1053i	−0.0219929	−	0.0159787i
$170$		0			0
$171$	−123.314	−	379.522i	−0.0551466	−	0.169724i
$172$		0			0
$173$	−2008.03	+	1458.92i	−0.882474	+	0.641155i	−0.933905	−	0.357522i	$-0.883622\pi$
$173$	−2008.03	+	1458.92i	−0.882474	+	0.641155i	0.0514311	+	0.998677i	$0.483622\pi$
$174$		0			0
$175$	−401.392			−0.173385
$176$		0			0
$177$	−1681.72			−0.714158
$178$		0			0
$179$	−360.289	+	261.765i	−0.150443	+	0.109303i	−0.660460	−	0.750861i	$-0.729639\pi$
$179$	−360.289	+	261.765i	−0.150443	+	0.109303i	0.510018	+	0.860164i	$0.329639\pi$
$180$		0			0
$181$	428.842	+	1319.84i	0.176108	+	0.542005i	0.999682	−	0.0252033i	$-0.00802332\pi$
$181$	428.842	+	1319.84i	0.176108	+	0.542005i	−0.823574	+	0.567209i	$0.808023\pi$
$182$		0			0
$183$	−904.618	−	657.243i	−0.365417	−	0.265491i
$184$		0			0
$185$	−263.936	+	812.312i	−0.104892	+	0.322824i
$186$		0			0
$187$	−1622.00	−	1660.10i	−0.634290	−	0.649190i
$188$		0			0
$189$	−159.269	+	490.180i	−0.0612969	+	0.188653i
$190$		0			0
$191$	3494.94	+	2539.22i	1.32401	+	0.961946i	0.999873	+	0.0159345i	$0.00507234\pi$
$191$	3494.94	+	2539.22i	1.32401	+	0.961946i	0.324132	+	0.946012i	$0.394928\pi$
$192$		0			0
$193$	565.914	+	1741.70i	0.211064	+	0.649589i	0.999410	+	0.0343560i	$0.0109380\pi$
$193$	565.914	+	1741.70i	0.211064	+	0.649589i	−0.788345	+	0.615233i	$0.789062\pi$
$194$		0			0
$195$	543.472	−	394.855i	0.199584	−	0.145006i
$196$		0			0
$197$	−720.368			−0.260529			−0.130264	−	0.991479i	$-0.541583\pi$
$197$	−720.368			−0.260529			−0.130264	+	0.991479i	$0.541583\pi$
$198$		0			0
$199$	−1848.51			−0.658478			−0.329239	−	0.944247i	$-0.606792\pi$
$199$	−1848.51			−0.658478			−0.329239	+	0.944247i	$0.606792\pi$
$200$		0			0
$201$	870.620	−	632.543i	0.305516	−	0.221971i
$202$		0			0
$203$	−109.061	−	335.657i	−0.0377075	−	0.116052i
$204$		0			0
$205$	781.808	+	568.017i	0.266360	+	0.193522i
$206$		0			0
$207$	346.961	−	1067.84i	0.116500	−	0.358550i
$208$		0			0
$209$	312.531	−	596.165i	0.103436	−	0.197309i
$210$		0			0
$211$	−1798.41	+	5534.93i	−0.586766	+	1.80588i	0.00529453	+	0.999986i	$0.498315\pi$
$211$	−1798.41	+	5534.93i	−0.586766	+	1.80588i	−0.592060	+	0.805894i	$0.701685\pi$
$212$		0			0
$213$	−1710.27	−	1242.58i	−0.550167	−	0.399720i
$214$		0			0
$215$	−50.7634	−	156.234i	−0.0161025	−	0.0495583i
$216$		0			0
$217$	−403.869	+	293.428i	−0.126343	+	0.0917935i
$218$		0			0
$219$	2125.91			0.655963
$220$		0			0
$221$	−3022.15			−0.919872
$222$		0			0
$223$	−773.235	+	561.788i	−0.232196	+	0.168700i	−0.697799	−	0.716293i	$-0.745837\pi$
$223$	−773.235	+	561.788i	−0.232196	+	0.168700i	0.465604	+	0.884993i	$0.345837\pi$
$224$		0			0
$225$	586.632	+	1805.47i	0.173817	+	0.534953i
$226$		0			0
$227$	−1667.56	−	1211.55i	−0.487576	−	0.354245i	0.316675	−	0.948534i	$-0.397433\pi$
$227$	−1667.56	−	1211.55i	−0.487576	−	0.354245i	−0.804251	+	0.594289i	$0.797433\pi$
$228$		0			0
$229$	1264.77	−	3892.56i	0.364971	−	1.12326i	−0.585029	−	0.811013i	$-0.698917\pi$
$229$	1264.77	−	3892.56i	0.364971	−	1.12326i	0.949999	−	0.312252i	$-0.101083\pi$
$230$		0			0
$231$	−346.545	+	171.536i	−0.0987055	+	0.0488581i
$232$		0			0
$233$	814.557	−	2506.95i	0.229028	−	0.704874i	−0.768830	−	0.639453i	$-0.779161\pi$
$233$	814.557	−	2506.95i	0.229028	−	0.704874i	0.997858	−	0.0654213i	$-0.0208391\pi$
$234$		0			0
$235$	1274.04	+	925.646i	0.353657	+	0.256947i
$236$		0			0
$237$	−544.056	−	1674.43i	−0.149115	−	0.458928i
$238$		0			0
$239$	5359.80	−	3894.12i	1.45061	−	1.05393i	0.464926	−	0.885349i	$-0.346081\pi$
$239$	5359.80	−	3894.12i	1.45061	−	1.05393i	0.985687	−	0.168583i	$-0.0539193\pi$
$240$		0			0
$241$	19.3078			0.00516069			0.00258034	−	0.999997i	$-0.499179\pi$
$241$	19.3078			0.00516069			0.00258034	+	0.999997i	$0.499179\pi$
$242$		0			0
$243$	3791.04			1.00080
$244$		0			0
$245$	1589.89	−	1155.12i	0.414588	−	0.301216i
$246$		0			0
$247$	−270.847	−	833.582i	−0.0697716	−	0.214735i
$248$		0			0
$249$	−1310.05	−	951.806i	−0.333417	−	0.242242i
$250$		0			0
$251$	282.337	−	868.944i	0.0709998	−	0.218515i	−0.909260	−	0.416229i	$-0.863352\pi$
$251$	282.337	−	868.944i	0.0709998	−	0.218515i	0.980260	+	0.197714i	$0.0633516\pi$
$252$		0			0
$253$	1697.35	−	840.171i	0.421786	−	0.208779i
$254$		0			0
$255$	277.996	−	855.584i	0.0682698	−	0.210113i
$256$		0			0
$257$	−2446.80	−	1777.71i	−0.593880	−	0.431479i	0.249821	−	0.968292i	$-0.419628\pi$
$257$	−2446.80	−	1777.71i	−0.593880	−	0.431479i	−0.843701	+	0.536813i	$0.819628\pi$
$258$		0			0
$259$	−197.823	−	608.836i	−0.0474599	−	0.146067i
$260$		0			0
$261$	−1350.40	+	981.121i	−0.320259	+	0.232681i
$262$		0			0
$263$	302.593			0.0709456			0.0354728	−	0.999371i	$-0.488706\pi$
$263$	302.593			0.0709456			0.0354728	+	0.999371i	$0.488706\pi$
$264$		0			0
$265$	−903.589			−0.209460
$266$		0			0
$267$	1058.26	−	768.868i	0.242563	−	0.176232i
$268$		0			0
$269$	−1677.77	−	5163.63i	−0.380279	−	1.17038i	−0.939847	−	0.341595i	$-0.889033\pi$
$269$	−1677.77	−	5163.63i	−0.380279	−	1.17038i	0.559568	−	0.828785i	$-0.310967\pi$
$270$		0			0
$271$	3238.73	+	2353.08i	0.725974	+	0.527451i	0.888287	−	0.459288i	$-0.151896\pi$
$271$	3238.73	+	2353.08i	0.725974	+	0.527451i	−0.162313	+	0.986739i	$0.551896\pi$
$272$		0			0
$273$	−155.589	+	478.854i	−0.0344933	+	0.106160i
$274$		0			0
$275$	−1486.78	+	2836.09i	−0.326022	+	0.621900i
$276$		0			0
$277$	2269.16	−	6983.77i	0.492205	−	1.51485i	−0.329062	−	0.944308i	$-0.606733\pi$
$277$	2269.16	−	6983.77i	0.492205	−	1.51485i	0.821267	−	0.570544i	$-0.193267\pi$
$278$		0			0
$279$	1910.10	+	1387.77i	0.409873	+	0.297790i
$280$		0			0
$281$	2157.75	+	6640.86i	0.458079	+	1.40982i	0.867482	+	0.497469i	$0.165737\pi$
$281$	2157.75	+	6640.86i	0.458079	+	1.40982i	−0.409402	+	0.912354i	$0.634263\pi$
$282$		0			0
$283$	3459.89	−	2513.76i	0.726746	−	0.528012i	−0.161786	−	0.986826i	$-0.551726\pi$
$283$	3459.89	−	2513.76i	0.726746	−	0.528012i	0.888532	+	0.458814i	$0.151726\pi$
$284$		0			0
$285$	260.905			0.0542270
$286$		0			0
$287$	−724.303			−0.148969
$288$		0			0
$289$	700.459	−	508.914i	0.142573	−	0.103585i
$290$		0			0
$291$	836.113	+	2573.29i	0.168432	+	0.518381i
$292$		0			0
$293$	−4488.77	−	3261.28i	−0.895006	−	0.650260i	0.0421722	−	0.999110i	$-0.486572\pi$
$293$	−4488.77	−	3261.28i	−0.895006	−	0.650260i	−0.937178	+	0.348850i	$0.886572\pi$
$294$		0			0
$295$	−1368.13	+	4210.68i	−0.270020	+	0.831035i
$296$		0			0
$297$	2873.49	+	2940.99i	0.561403	+	0.574591i
$298$		0			0
$299$	762.065	−	2345.40i	0.147396	−	0.453638i
$300$		0			0
$301$	99.6101	+	72.3710i	0.0190745	+	0.0138585i
$302$		0			0
$303$	−1063.47	−	3273.03i	−0.201633	−	0.620563i
$304$		0			0
$305$	−2381.53	+	1730.29i	−0.447102	+	0.324839i
$306$		0			0
$307$	−7074.54			−1.31520			−0.657598	−	0.753369i	$-0.728428\pi$
$307$	−7074.54			−1.31520			−0.657598	+	0.753369i	$0.728428\pi$
$308$		0			0
$309$	−2266.07			−0.417192
$310$		0			0
$311$	−8602.11	+	6249.80i	−1.56843	+	1.13953i	−0.639786	+	0.768553i	$0.720977\pi$
$311$	−8602.11	+	6249.80i	−1.56843	+	1.13953i	−0.928642	+	0.370976i	$0.879023\pi$
$312$		0			0
$313$	788.126	+	2425.60i	0.142324	+	0.438029i	0.996657	−	0.0816969i	$-0.0260339\pi$
$313$	788.126	+	2425.60i	0.142324	+	0.438029i	−0.854333	+	0.519726i	$0.826034\pi$
$314$		0			0
$315$	488.242	+	354.728i	0.0873311	+	0.0634498i
$316$		0			0
$317$	1211.90	−	3729.84i	0.214722	−	0.660847i	−0.784451	−	0.620191i	$-0.787055\pi$
$317$	1211.90	−	3729.84i	0.214722	−	0.660847i	0.999173	−	0.0406561i	$-0.0129448\pi$
$318$		0			0
$319$	−2775.59	−	472.702i	−0.487158	−	0.0829663i
$320$		0			0
$321$	−875.291	+	2693.87i	−0.152193	+	0.468402i
$322$		0			0
$323$	−949.591	−	689.919i	−0.163581	−	0.118849i
$324$		0			0
$325$	1288.48	+	3965.53i	0.219914	+	0.676824i
$326$		0			0
$327$	469.857	−	341.371i	0.0794592	−	0.0577305i
$328$		0			0
$329$	−1180.33			−0.197793
$330$		0			0
$331$	7694.76			1.27777			0.638886	−	0.769302i	$-0.279396\pi$
$331$	7694.76			1.27777			0.638886	+	0.769302i	$0.279396\pi$
$332$		0			0
$333$	−2449.44	+	1779.62i	−0.403089	+	0.292861i
$334$		0			0
$335$	−875.477	−	2694.44i	−0.142783	−	0.439442i
$336$		0			0
$337$	8937.80	+	6493.69i	1.44473	+	1.04966i	0.987028	+	0.160548i	$0.0513261\pi$
$337$	8937.80	+	6493.69i	1.44473	+	1.04966i	0.457698	+	0.889107i	$0.348674\pi$
$338$		0			0
$339$	−1540.93	+	4742.49i	−0.246878	+	0.759814i
$340$		0			0
$341$	577.301	+	3940.46i	0.0916792	+	0.625771i
$342$		0			0
$343$	−939.883	+	2892.66i	−0.147956	+	0.455362i
$344$		0			0
$345$	593.893	+	431.488i	0.0926786	+	0.0673349i
$346$		0			0
$347$	−3745.17	−	11526.5i	−0.579399	−	1.78321i	−0.620687	−	0.784058i	$-0.713146\pi$
$347$	−3745.17	−	11526.5i	−0.579399	−	1.78321i	0.0412888	−	0.999147i	$-0.486854\pi$
$348$		0			0
$349$	−4899.75	+	3559.87i	−0.751511	+	0.546005i	−0.896295	−	0.443458i	$-0.853751\pi$
$349$	−4899.75	+	3559.87i	−0.751511	+	0.546005i	0.144784	+	0.989463i	$0.453751\pi$
$350$		0			0
$351$	5353.96			0.814169
$352$		0			0
$353$	−1840.84			−0.277558			−0.138779	−	0.990323i	$-0.544318\pi$
$353$	−1840.84			−0.277558			−0.138779	+	0.990323i	$0.544318\pi$
$354$		0			0
$355$	−4502.52	+	3271.27i	−0.673152	+	0.489074i
$356$		0			0
$357$	208.361	+	641.269i	0.0308897	+	0.0950688i
$358$		0			0
$359$	2784.63	+	2023.15i	0.409379	+	0.297431i	0.773350	−	0.633979i	$-0.218579\pi$
$359$	2784.63	+	2023.15i	0.409379	+	0.297431i	−0.363971	+	0.931410i	$0.618579\pi$
$360$		0			0
$361$	−2014.35	+	6199.55i	−0.293680	+	0.903856i
$362$		0			0
$363$	−71.6124	+	3083.93i	−0.0103545	+	0.445908i
$364$		0			0
$365$	1729.50	−	5322.84i	0.248016	−	0.763316i
$366$		0			0
$367$	−3954.19	−	2872.89i	−0.562418	−	0.408620i	0.269925	−	0.962881i	$-0.413001\pi$
$367$	−3954.19	−	2872.89i	−0.562418	−	0.408620i	−0.832343	+	0.554261i	$0.813001\pi$
$368$		0			0
$369$	1058.56	+	3257.93i	0.149341	+	0.459623i
$370$		0			0
$371$	547.906	−	398.077i	0.0766735	−	0.0557066i
$372$		0			0
$373$	9784.78			1.35828			0.679138	−	0.734011i	$-0.262354\pi$
$373$	9784.78			1.35828			0.679138	+	0.734011i	$0.262354\pi$
$374$		0			0
$375$	−3008.81			−0.414331
$376$		0			0
$377$	−2966.01	+	2154.93i	−0.405192	+	0.294389i
$378$		0			0
$379$	−2552.32	−	7855.25i	−0.345921	−	1.06464i	−0.961089	−	0.276239i	$-0.910912\pi$
$379$	−2552.32	−	7855.25i	−0.345921	−	1.06464i	0.615168	−	0.788396i	$-0.289088\pi$
$380$		0			0
$381$	3347.46	+	2432.07i	0.450119	+	0.327031i
$382$		0			0
$383$	2239.86	−	6893.58i	0.298829	−	0.919701i	−0.683079	−	0.730344i	$-0.739360\pi$
$383$	2239.86	−	6893.58i	0.298829	−	0.919701i	0.981908	−	0.189357i	$-0.0606403\pi$
$384$		0			0
$385$	147.565	+	1007.22i	0.0195340	+	0.133332i
$386$		0			0
$387$	179.946	−	553.818i	0.0236361	−	0.0727446i
$388$		0			0
$389$	−8903.37	−	6468.68i	−1.16046	−	0.843123i	−0.170623	−	0.985336i	$-0.554578\pi$
$389$	−8903.37	−	6468.68i	−1.16046	−	0.843123i	−0.989836	+	0.142213i	$0.954578\pi$
$390$		0			0
$391$	−1020.54	−	3140.89i	−0.131997	−	0.406245i
$392$		0			0
$393$	−239.952	+	174.335i	−0.0307989	+	0.0223767i
$394$		0			0
$395$	−4635.03			−0.590414
$396$		0			0
$397$	7715.18			0.975349			0.487675	−	0.873025i	$-0.337845\pi$
$397$	7715.18			0.975349			0.487675	+	0.873025i	$0.337845\pi$
$398$		0			0
$399$	−158.204	+	114.942i	−0.0198499	+	0.0144218i
$400$		0			0
$401$	762.359	+	2346.30i	0.0949386	+	0.292191i	0.987238	−	0.159254i	$-0.0509088\pi$
$401$	762.359	+	2346.30i	0.0949386	+	0.292191i	−0.892299	+	0.451445i	$0.850909\pi$
$402$		0			0
$403$	4195.33	+	3048.09i	0.518572	+	0.376764i
$404$		0			0
$405$	608.567	−	1872.98i	0.0746665	−	0.229800i
$406$		0			0
$407$	−5034.56	−	857.419i	−0.613155	−	0.104424i
$408$		0			0
$409$	2525.13	−	7771.56i	0.305281	−	0.939557i	−0.674292	−	0.738465i	$-0.735551\pi$
$409$	2525.13	−	7771.56i	0.305281	−	0.939557i	0.979572	−	0.201092i	$-0.0644491\pi$
$410$		0			0
$411$	−804.853	−	584.760i	−0.0965949	−	0.0701803i
$412$		0			0
$413$	−1025.43	−	3155.95i	−0.122175	−	0.376015i
$414$		0			0
$415$	−3448.89	+	2505.76i	−0.407950	+	0.296393i
$416$		0			0
$417$	5649.35			0.663429
$418$		0			0
$419$	3563.75			0.415514			0.207757	−	0.978180i	$-0.433384\pi$
$419$	3563.75			0.415514			0.207757	+	0.978180i	$0.433384\pi$
$420$		0			0
$421$	1822.46	−	1324.09i	0.210976	−	0.153283i	−0.477279	−	0.878752i	$-0.658377\pi$
$421$	1822.46	−	1324.09i	0.210976	−	0.153283i	0.688255	+	0.725469i	$0.258377\pi$
$422$		0			0
$423$	1725.05	+	5309.15i	0.198285	+	0.610260i
$424$		0			0
$425$	4517.41	+	3282.09i	0.515592	+	0.374599i
$426$		0			0
$427$	681.803	−	2098.37i	0.0772711	−	0.237816i
$428$		0			0
$429$	2807.09	+	2873.04i	0.315916	+	0.323337i
$430$		0			0
$431$	3282.25	−	10101.7i	0.366822	−	1.12896i	−0.582010	−	0.813181i	$-0.697734\pi$
$431$	3282.25	−	10101.7i	0.366822	−	1.12896i	0.948832	−	0.315781i	$-0.102266\pi$
$432$		0			0
$433$	−14174.5	−	10298.4i	−1.57318	−	1.14298i	−0.924033	−	0.382313i	$-0.875128\pi$
$433$	−14174.5	−	10298.4i	−1.57318	−	1.14298i	−0.649143	−	0.760666i	$-0.724872\pi$
$434$		0			0
$435$	−337.239	−	1037.92i	−0.0371710	−	0.114401i
$436$		0			0
$437$	774.874	−	562.979i	0.0848220	−	0.0616268i
$438$		0			0
$439$	13581.6			1.47657			0.738283	−	0.674491i	$-0.235637\pi$
$439$	13581.6			1.47657			0.738283	+	0.674491i	$0.235637\pi$
$440$		0			0
$441$	6966.28			0.752216
$442$		0			0
$443$	406.616	−	295.424i	0.0436093	−	0.0316840i	−0.565767	−	0.824565i	$-0.691420\pi$
$443$	406.616	−	295.424i	0.0436093	−	0.0316840i	0.609376	+	0.792881i	$0.291420\pi$
$444$		0			0
$445$	−1064.16	−	3275.15i	−0.113362	−	0.348892i
$446$		0			0
$447$	−5226.33	−	3797.15i	−0.553013	−	0.401788i
$448$		0			0
$449$	780.866	−	2403.26i	0.0820742	−	0.252599i	−0.901596	−	0.432579i	$-0.857604\pi$
$449$	780.866	−	2403.26i	0.0820742	−	0.252599i	0.983670	+	0.179981i	$0.0576036\pi$
$450$		0			0
$451$	−2682.85	+	5117.65i	−0.280112	+	0.534326i
$452$		0			0
$453$	912.035	−	2806.95i	0.0945941	−	0.291131i
$454$		0			0
$455$	1072.37	+	779.125i	0.110491	+	0.0802767i
$456$		0			0
$457$	−2123.00	−	6533.92i	−0.217308	−	0.668805i	−0.998982	−	0.0451173i	$-0.985634\pi$
$457$	−2123.00	−	6533.92i	−0.217308	−	0.668805i	0.781674	−	0.623687i	$-0.214366\pi$
$458$		0			0
$459$	5800.56	−	4214.35i	0.589863	−	0.428560i
$460$		0			0
$461$	−6760.39			−0.683000			−0.341500	−	0.939882i	$-0.610935\pi$
$461$	−6760.39			−0.683000			−0.341500	+	0.939882i	$0.610935\pi$
$462$		0			0
$463$	12796.6			1.28447			0.642236	−	0.766507i	$-0.278007\pi$
$463$	12796.6			1.28447			0.642236	+	0.766507i	$0.278007\pi$
$464$		0			0
$465$	−1248.84	+	907.336i	−0.124545	+	0.0904875i
$466$		0			0
$467$	−263.829	−	811.982i	−0.0261425	−	0.0804583i	0.937134	−	0.348970i	$-0.113468\pi$
$467$	−263.829	−	811.982i	−0.0261425	−	0.0804583i	−0.963277	+	0.268511i	$0.913468\pi$
$468$		0			0
$469$	1717.90	+	1248.13i	0.169137	+	0.122885i
$470$		0			0
$471$	−2615.11	+	8048.49i	−0.255835	+	0.787378i
$472$		0			0
$473$	880.308	−	435.742i	0.0855742	−	0.0423582i
$474$		0			0
$475$	−500.427	+	1540.15i	−0.0483392	+	0.148773i
$476$		0			0
$477$	−2591.32	−	1882.70i	−0.248739	−	0.180719i
$478$		0			0
$479$	−1343.30	−	4134.24i	−0.128135	−	0.394360i	0.866324	−	0.499482i	$-0.166476\pi$
$479$	−1343.30	−	4134.24i	−0.128135	−	0.394360i	−0.994459	+	0.105123i	$0.966476\pi$
$480$		0			0
$481$	−5379.95	+	3908.76i	−0.509989	+	0.370528i
$482$		0			0
$483$	−550.209			−0.0518331
$484$		0			0
$485$	7123.18			0.666901
$486$		0			0
$487$	−9994.13	+	7261.16i	−0.929933	+	0.675636i	−0.945976	−	0.324235i	$-0.894893\pi$
$487$	−9994.13	+	7261.16i	−0.929933	+	0.675636i	0.0160433	+	0.999871i	$0.494893\pi$
$488$		0			0
$489$	−1209.36	−	3722.02i	−0.111839	−	0.344204i
$490$		0			0
$491$	7536.87	+	5475.86i	0.692738	+	0.503303i	0.877559	−	0.479469i	$-0.159171\pi$
$491$	7536.87	+	5475.86i	0.692738	+	0.503303i	−0.184821	+	0.982772i	$0.559171\pi$
$492$		0			0
$493$	−1517.17	+	4669.37i	−0.138600	+	0.426568i
$494$		0			0
$495$	4314.85	−	2135.80i	0.391794	−	0.193934i
$496$		0			0
$497$	1289.01	−	3967.18i	0.116338	−	0.358053i
$498$		0			0
$499$	2367.31	+	1719.95i	0.212375	+	0.154300i	0.688888	−	0.724868i	$-0.258099\pi$
$499$	2367.31	+	1719.95i	0.212375	+	0.154300i	−0.476512	+	0.879168i	$0.658099\pi$
$500$		0			0
$501$	−1406.12	−	4327.59i	−0.125391	−	0.385913i
$502$		0			0
$503$	−9176.67	+	6667.24i	−0.813454	+	0.591009i	−0.914830	−	0.403839i	$-0.867676\pi$
$503$	−9176.67	+	6667.24i	−0.813454	+	0.591009i	0.101376	+	0.994848i	$0.467676\pi$
$504$		0			0
$505$	−9060.15			−0.798359
$506$		0			0
$507$	138.420			0.0121251
$508$		0			0
$509$	−11610.9	+	8435.81i	−1.01109	+	0.734599i	−0.964437	−	0.264312i	$-0.914855\pi$
$509$	−11610.9	+	8435.81i	−1.01109	+	0.734599i	−0.0466516	+	0.998911i	$0.514855\pi$
$510$		0			0
$511$	1296.27	+	3989.52i	0.112219	+	0.345374i
$512$		0			0
$513$	1682.27	+	1222.24i	0.144784	+	0.105192i
$514$		0			0
$515$	−1843.52	+	5673.76i	−0.157738	+	0.485468i
$516$		0			0
$517$	−4372.01	+	8339.78i	−0.371916	+	0.709445i
$518$		0			0
$519$	1777.62	−	5470.96i	0.150345	−	0.462714i
$520$		0			0
$521$	−2122.27	−	1541.92i	−0.178461	−	0.129660i	0.494969	−	0.868911i	$-0.335180\pi$
$521$	−2122.27	−	1541.92i	−0.178461	−	0.129660i	−0.673430	+	0.739251i	$0.735180\pi$
$522$		0			0
$523$	986.726	+	3036.83i	0.0824981	+	0.253903i	0.983794	−	0.179300i	$-0.0573833\pi$
$523$	986.726	+	3036.83i	0.0824981	+	0.253903i	−0.901296	+	0.433203i	$0.857383\pi$
$524$		0			0
$525$	752.611	−	546.804i	0.0625650	−	0.0454561i
$526$		0			0
$527$	6944.58			0.574024
$528$		0			0
$529$	−9472.11			−0.778508
$530$		0			0
$531$	−12696.9	+	9224.80i	−1.03766	+	0.753903i
$532$		0			0
$533$	2325.03	+	7155.70i	0.188946	+	0.581516i
$534$		0			0
$535$	6032.81	+	4383.09i	0.487516	+	0.354201i
$536$		0			0
$537$	318.948	−	981.620i	0.0256306	−	0.0788828i
$538$		0			0
$539$	8211.95	+	8404.85i	0.656240	+	0.671656i
$540$		0			0
$541$	−2489.81	+	7662.84i	−0.197865	+	0.608967i	0.802066	+	0.597236i	$0.203734\pi$
$541$	−2489.81	+	7662.84i	−0.197865	+	0.608967i	−0.999931	+	0.0117314i	$0.996266\pi$
$542$		0			0
$543$	−2602.06	−	1890.51i	−0.205645	−	0.149409i
$544$		0			0
$545$	−472.478	−	1454.14i	−0.0371353	−	0.114291i
$546$		0			0
$547$	−1458.12	+	1059.39i	−0.113976	+	0.0828084i	−0.643313	−	0.765603i	$-0.722441\pi$
$547$	−1458.12	+	1059.39i	−0.113976	+	0.0828084i	0.529337	+	0.848412i	$0.322441\pi$
$548$		0			0
$549$	−10435.0			−0.811209
$550$		0			0
$551$	−1423.90			−0.110091
$552$		0			0
$553$	2810.53	−	2041.97i	0.216122	−	0.157022i
$554$		0			0
$555$	−611.707	−	1882.64i	−0.0467847	−	0.143989i
$556$		0			0
$557$	−694.192	−	504.360i	−0.0528077	−	0.0383670i	0.561068	−	0.827770i	$-0.310391\pi$
$557$	−694.192	−	504.360i	−0.0528077	−	0.0383670i	−0.613876	+	0.789403i	$0.710391\pi$
$558$		0			0
$559$	395.234	−	1216.40i	0.0299045	−	0.0920366i
$560$		0			0
$561$	5302.75	+	903.093i	0.399077	+	0.0679655i
$562$		0			0
$563$	−3427.69	+	10549.4i	−0.256590	+	0.789702i	0.736923	+	0.675977i	$0.236278\pi$
$563$	−3427.69	+	10549.4i	−0.256590	+	0.789702i	−0.993512	+	0.113725i	$0.963722\pi$
$564$		0			0
$565$	10620.6	+	7716.33i	0.790819	+	0.574563i
$566$		0			0
$567$	456.127	+	1403.81i	0.0337840	+	0.103976i
$568$		0			0
$569$	11071.9	−	8044.22i	0.815745	−	0.592674i	−0.0997452	−	0.995013i	$-0.531803\pi$
$569$	11071.9	−	8044.22i	0.815745	−	0.592674i	0.915491	+	0.402339i	$0.131803\pi$
$570$		0			0
$571$	1193.39			0.0874637			0.0437319	−	0.999043i	$-0.486075\pi$
$571$	1193.39			0.0874637			0.0437319	+	0.999043i	$0.486075\pi$
$572$		0			0
$573$	−10012.1			−0.729952
$574$		0			0
$575$	−3686.24	+	2678.21i	−0.267351	+	0.194242i
$576$		0			0
$577$	−3796.06	−	11683.1i	−0.273886	−	0.842934i	−0.989512	−	0.144451i	$-0.953859\pi$
$577$	−3796.06	−	11683.1i	−0.273886	−	0.842934i	0.715626	−	0.698484i	$-0.246141\pi$
$578$		0			0
$579$	−3433.76	−	2494.77i	−0.246463	−	0.179066i
$580$		0			0
$581$	987.373	−	3038.82i	0.0705045	−	0.216991i
$582$		0			0
$583$	−783.192	−	5345.80i	−0.0556372	−	0.379761i
$584$		0			0
$585$	1937.25	−	5962.24i	0.136915	−	0.421382i
$586$		0			0
$587$	−13764.1	−	10000.2i	−0.967809	−	0.703155i	−0.0128580	−	0.999917i	$-0.504093\pi$
$587$	−13764.1	−	10000.2i	−0.967809	−	0.703155i	−0.954951	+	0.296763i	$0.904093\pi$
$588$		0			0
$589$	622.378	+	1915.48i	0.0435393	+	0.134000i
$590$		0			0
$591$	1350.69	−	981.335i	0.0940103	−	0.0683024i
$592$		0			0
$593$	898.618			0.0622291			0.0311145	−	0.999516i	$-0.490094\pi$
$593$	898.618			0.0622291			0.0311145	+	0.999516i	$0.490094\pi$
$594$		0			0
$595$	1775.11			0.122307
$596$		0			0
$597$	3465.95	−	2518.16i	0.237608	−	0.172632i
$598$		0			0
$599$	6515.12	+	20051.5i	0.444409	+	1.36775i	0.883131	+	0.469126i	$0.155431\pi$
$599$	6515.12	+	20051.5i	0.444409	+	1.36775i	−0.438722	+	0.898623i	$0.644569\pi$
$600$		0			0
$601$	−7616.77	−	5533.91i	−0.516963	−	0.375595i	0.298496	−	0.954411i	$-0.403515\pi$
$601$	−7616.77	−	5533.91i	−0.516963	−	0.375595i	−0.815458	+	0.578816i	$0.803515\pi$
$602$		0			0
$603$	3103.40	−	9551.28i	0.209586	−	0.645038i
$604$		0			0
$605$	7663.26	+	2688.18i	0.514969	+	0.180645i
$606$		0			0
$607$	7229.88	−	22251.3i	0.483446	−	1.48789i	−0.350772	−	0.936461i	$-0.614081\pi$
$607$	7229.88	−	22251.3i	0.483446	−	1.48789i	0.834219	−	0.551434i	$-0.185919\pi$
$608$		0			0
$609$	661.745	+	480.786i	0.0440316	+	0.0319909i
$610$		0			0
$611$	3788.89	+	11661.0i	0.250871	+	0.772102i
$612$		0			0
$613$	−9261.58	+	6728.94i	−0.610231	+	0.443359i	−0.849496	−	0.527595i	$-0.823094\pi$
$613$	−9261.58	+	6728.94i	−0.610231	+	0.443359i	0.239264	+	0.970954i	$0.423094\pi$
$614$		0			0
$615$	−2239.68			−0.146850
$616$		0			0
$617$	18827.4			1.22847			0.614233	−	0.789125i	$-0.289465\pi$
$617$	18827.4			1.22847			0.614233	+	0.789125i	$0.289465\pi$
$618$		0			0
$619$	18126.3	−	13169.5i	1.17699	−	0.855134i	0.185162	−	0.982708i	$-0.440719\pi$
$619$	18126.3	−	13169.5i	1.17699	−	0.855134i	0.991829	+	0.127574i	$0.0407191\pi$
$620$		0			0
$621$	1807.96	+	5564.33i	0.116829	+	0.359563i
$622$		0			0
$623$	2088.14	+	1517.12i	0.134285	+	0.0975639i
$624$		0			0
$625$	942.620	−	2901.09i	0.0603277	−	0.185669i
$626$		0			0
$627$	226.141	+	1543.56i	0.0144039	+	0.0983157i
$628$		0			0
$629$	−2751.95	+	8469.62i	−0.174447	+	0.536893i
$630$		0			0
$631$	−2027.51	−	1473.07i	−0.127914	−	0.0929352i	0.521988	−	0.852953i	$-0.325190\pi$
$631$	−2027.51	−	1473.07i	−0.127914	−	0.0929352i	−0.649903	+	0.760017i	$0.725190\pi$
$632$		0			0
$633$	−4168.05	−	12827.9i	−0.261714	−	0.805473i
$634$		0			0
$635$	8812.65	−	6402.77i	0.550739	−	0.400135i
$636$		0			0
$637$	15300.7			0.951706
$638$		0			0
$639$	−19728.3			−1.22135
$640$		0			0
$641$	1323.93	−	961.890i	0.0815788	−	0.0592704i	−0.546248	−	0.837623i	$-0.683945\pi$
$641$	1323.93	−	961.890i	0.0815788	−	0.0592704i	0.627827	+	0.778353i	$0.283945\pi$
$642$		0			0
$643$	−9372.66	−	28846.1i	−0.574839	−	1.76917i	−0.636725	−	0.771091i	$-0.719712\pi$
$643$	−9372.66	−	28846.1i	−0.574839	−	1.76917i	0.0618860	−	0.998083i	$-0.480288\pi$
$644$		0			0
$645$	308.014	+	223.785i	0.0188031	+	0.0136613i
$646$		0			0
$647$	−371.986	+	1144.85i	−0.0226032	+	0.0695655i	−0.961722	−	0.274028i	$-0.911644\pi$
$647$	−371.986	+	1144.85i	−0.0226032	+	0.0695655i	0.939119	+	0.343593i	$0.111644\pi$
$648$		0			0
$649$	−26097.0	−	4444.49i	−1.57842	−	0.268816i
$650$		0			0
$651$	357.527	−	1100.36i	0.0215247	−	0.0662463i
$652$		0			0
$653$	15509.5	+	11268.3i	0.929456	+	0.675289i	0.945860	−	0.324576i	$-0.105222\pi$
$653$	15509.5	+	11268.3i	0.929456	+	0.675289i	−0.0164038	+	0.999865i	$0.505222\pi$
$654$		0			0
$655$	241.290	+	742.615i	0.0143939	+	0.0442998i
$656$		0			0
$657$	16050.5	−	11661.3i	0.953102	−	0.692469i
$658$		0			0
$659$	−2265.97			−0.133945			−0.0669723	−	0.997755i	$-0.521334\pi$
$659$	−2265.97			−0.133945			−0.0669723	+	0.997755i	$0.521334\pi$
$660$		0			0
$661$	9959.70			0.586063			0.293031	−	0.956103i	$-0.405336\pi$
$661$	9959.70			0.586063			0.293031	+	0.956103i	$0.405336\pi$
$662$		0			0
$663$	5666.54	−	4116.98i	0.331931	−	0.241162i
$664$		0			0
$665$	159.087	+	489.619i	0.00927687	+	0.0285513i
$666$		0			0
$667$	−3241.19	−	2354.86i	−0.188155	−	0.136702i
$668$		0			0
$669$	684.511	−	2106.71i	0.0395586	−	0.121749i
$670$		0			0
$671$	−12300.9	−	12589.9i	−0.707706	−	0.724331i
$672$		0			0
$673$	−1928.35	+	5934.85i	−0.110449	+	0.339928i	−0.990971	−	0.134078i	$-0.957193\pi$
$673$	−1928.35	+	5934.85i	−0.110449	+	0.339928i	0.880521	+	0.474007i	$0.157193\pi$
$674$		0			0
$675$	−8002.93	−	5814.47i	−0.456345	−	0.331554i
$676$		0			0
$677$	4908.61	+	15107.2i	0.278661	+	0.857629i	0.988228	+	0.152991i	$0.0488906\pi$
$677$	4908.61	+	15107.2i	0.278661	+	0.857629i	−0.709567	+	0.704638i	$0.751109\pi$
$678$		0			0
$679$	−4319.26	+	3138.12i	−0.244121	+	0.177364i
$680$		0			0
$681$	4777.14			0.268811
$682$		0			0
$683$	−8537.29			−0.478288			−0.239144	−	0.970984i	$-0.576867\pi$
$683$	−8537.29			−0.478288			−0.239144	+	0.970984i	$0.576867\pi$
$684$		0			0
$685$	−2118.89	+	1539.46i	−0.118188	+	0.0858684i
$686$		0			0
$687$	2931.27	+	9021.51i	0.162787	+	0.501008i
$688$		0			0
$689$	−5691.57	−	4135.17i	−0.314705	−	0.228646i
$690$		0			0
$691$	4377.61	−	13472.9i	0.241002	−	0.741727i	−0.755267	−	0.655417i	$-0.772493\pi$
$691$	4377.61	−	13472.9i	0.241002	−	0.741727i	0.996268	−	0.0863091i	$-0.0275073\pi$
$692$		0			0
$693$	−1675.45	+	3195.99i	−0.0918400	+	0.175189i
$694$		0			0
$695$	4595.92	−	14144.8i	0.250839	−	0.772003i
$696$		0			0
$697$	8151.56	+	5922.46i	0.442988	+	0.321849i
$698$		0			0
$699$	1887.84	+	5810.18i	0.102153	+	0.314394i
$700$		0			0
$701$	14064.1	−	10218.1i	0.757764	−	0.550548i	−0.140459	−	0.990086i	$-0.544858\pi$
$701$	14064.1	−	10218.1i	0.757764	−	0.550548i	0.898224	+	0.439538i	$0.144858\pi$
$702$		0			0
$703$	−2582.76			−0.138564
$704$		0			0
$705$	−3649.81			−0.194979
$706$		0			0
$707$	5493.77	−	3991.46i	0.292241	−	0.212326i
$708$		0			0
$709$	−1610.19	−	4955.66i	−0.0852920	−	0.262502i	0.899310	−	0.437311i	$-0.144069\pi$
$709$	−1610.19	−	4955.66i	−0.0852920	−	0.262502i	−0.984602	+	0.174809i	$0.944069\pi$
$710$		0			0
$711$	−13292.4	−	9657.48i	−0.701129	−	0.509400i
$712$		0			0
$713$	−1751.15	+	5389.47i	−0.0919789	+	0.283082i
$714$		0			0
$715$	9477.13	−	4691.07i	0.495699	−	0.245365i
$716$		0			0
$717$	−4744.80	+	14603.0i	−0.247138	+	0.760611i
$718$		0			0
$719$	20925.3	+	15203.1i	1.08537	+	0.788567i	0.978611	−	0.205718i	$-0.0659529\pi$
$719$	20925.3	+	15203.1i	1.08537	+	0.788567i	0.106758	+	0.994285i	$0.465953\pi$
$720$		0			0
$721$	−1381.73	−	4252.54i	−0.0713710	−	0.219657i
$722$		0			0
$723$	−36.2022	+	26.3024i	−0.00186220	+	0.00135297i
$724$		0			0
$725$	6773.78			0.346996
$726$		0			0
$727$	−29046.8			−1.48182			−0.740911	−	0.671603i	$-0.765606\pi$
$727$	−29046.8			−1.48182			−0.740911	+	0.671603i	$0.765606\pi$
$728$		0			0
$729$	−57.8457	+	42.0273i	−0.00293887	+	0.00213521i
$730$		0			0
$731$	−529.287	−	1628.98i	−0.0267803	−	0.0824213i
$732$		0			0
$733$	12582.6	+	9141.78i	0.634036	+	0.460654i	0.857796	−	0.513990i	$-0.171833\pi$
$733$	12582.6	+	9141.78i	0.634036	+	0.460654i	−0.223760	+	0.974644i	$0.571833\pi$
$734$		0			0
$735$	−1407.46	+	4331.70i	−0.0706324	+	0.217384i
$736$		0			0
$737$	15182.0	−	7514.91i	0.758800	−	0.375598i
$738$		0			0
$739$	−11799.8	+	36315.9i	−0.587363	+	1.80772i	0.00220606	+	0.999998i	$0.499298\pi$
$739$	−11799.8	+	36315.9i	−0.587363	+	1.80772i	−0.589569	+	0.807718i	$0.700702\pi$
$740$		0			0
$741$	1643.40	+	1194.00i	0.0814735	+	0.0591940i
$742$		0			0
$743$	5535.39	+	17036.2i	0.273316	+	0.841181i	0.989660	+	0.143433i	$0.0458142\pi$
$743$	5535.39	+	17036.2i	0.273316	+	0.841181i	−0.716344	+	0.697747i	$0.754186\pi$
$744$		0			0
$745$	−13759.0	+	9996.53i	−0.676634	+	0.491604i
$746$		0			0
$747$	−15111.7			−0.740172
$748$		0			0
$749$	−5589.07			−0.272657
$750$		0			0
$751$	32671.5	−	23737.2i	1.58748	−	1.15337i	0.680060	−	0.733156i	$-0.261954\pi$
$751$	32671.5	−	23737.2i	1.58748	−	1.15337i	0.907423	−	0.420218i	$-0.138046\pi$
$752$		0			0
$753$	654.353	+	2013.89i	0.0316679	+	0.0974638i
$754$		0			0
$755$	−6286.05	−	4567.09i	−0.303010	−	0.220150i
$756$		0			0
$757$	−8622.85	+	26538.4i	−0.414006	+	1.27418i	0.499131	+	0.866527i	$0.333653\pi$
$757$	−8622.85	+	26538.4i	−0.414006	+	1.27418i	−0.913137	+	0.407653i	$0.866347\pi$
$758$		0			0
$759$	−2038.00	+	3887.58i	−0.0974636	+	0.185916i
$760$		0			0
$761$	−6276.93	+	19318.4i	−0.299000	+	0.920226i	0.682849	+	0.730560i	$0.260741\pi$
$761$	−6276.93	+	19318.4i	−0.299000	+	0.920226i	−0.981849	+	0.189667i	$0.939259\pi$
$762$		0			0
$763$	927.117	+	673.590i	0.0439894	+	0.0319602i
$764$		0			0
$765$	−2594.32	−	7984.48i	−0.122611	−	0.377359i
$766$		0			0
$767$	−27887.3	+	20261.3i	−1.31285	+	0.953839i
$768$		0			0
$769$	−19314.1			−0.905701			−0.452850	−	0.891587i	$-0.649593\pi$
$769$	−19314.1			−0.905701			−0.452850	+	0.891587i	$0.649593\pi$
$770$		0			0
$771$	7009.47			0.327419
$772$		0			0
$773$	−3935.29	+	2859.16i	−0.183108	+	0.133036i	−0.675563	−	0.737302i	$-0.736100\pi$
$773$	−3935.29	+	2859.16i	−0.183108	+	0.133036i	0.492455	+	0.870338i	$0.336100\pi$
$774$		0			0
$775$	−2960.79	−	9112.36i	−0.137232	−	0.422356i
$776$		0			0
$777$	1200.32	+	872.082i	0.0554198	+	0.0402648i
$778$		0			0
$779$	−903.008	+	2779.17i	−0.0415323	+	0.127823i
$780$		0			0
$781$	−23256.0	−	23802.3i	−1.06551	−	1.09054i
$782$		0			0
$783$	2687.78	−	8272.14i	0.122674	−	0.377551i
$784$		0			0
$785$	18024.3	+	13095.4i	0.819507	+	0.595407i
$786$		0			0
$787$	5052.14	+	15548.9i	0.228830	+	0.704267i	0.997880	+	0.0650785i	$0.0207298\pi$
$787$	5052.14	+	15548.9i	0.228830	+	0.704267i	−0.769050	+	0.639189i	$0.779270\pi$
$788$		0			0
$789$	−567.363	+	412.213i	−0.0256003	+	0.0185997i
$790$		0			0
$791$	−9839.42			−0.442288
$792$		0			0
$793$	−22919.4			−1.02634
$794$		0			0
$795$	1694.23	−	1230.93i	0.0755826	−	0.0549140i
$796$		0			0
$797$	1544.91	+	4754.75i	0.0686619	+	0.211320i	0.979500	−	0.201444i	$-0.0645635\pi$
$797$	1544.91	+	4754.75i	0.0686619	+	0.211320i	−0.910838	+	0.412764i	$0.864563\pi$
$798$		0			0
$799$	13283.9	+	9651.30i	0.588172	+	0.427332i
$800$		0			0
$801$	3772.24	−	11609.8i	0.166399	−	0.512124i
$802$		0			0
$803$	32990.0	+	5618.41i	1.44980	+	0.246911i
$804$		0			0
$805$	−447.612	+	1377.61i	−0.0195978	+	0.0603159i
$806$		0			0
$807$	10180.1	+	7396.25i	0.444059	+	0.322628i
$808$		0			0
$809$	−1001.12	−	3081.13i	−0.0435074	−	0.133902i	0.926943	−	0.375201i	$-0.122426\pi$
$809$	−1001.12	−	3081.13i	−0.0435074	−	0.133902i	−0.970451	+	0.241299i	$0.922426\pi$
$810$		0			0
$811$	−13745.1	+	9986.39i	−0.595136	+	0.432392i	−0.844149	−	0.536109i	$-0.819894\pi$
$811$	−13745.1	+	9986.39i	−0.595136	+	0.432392i	0.249013	+	0.968500i	$0.419894\pi$
$812$		0			0
$813$	−9278.15			−0.400245
$814$		0			0
$815$	−10303.0			−0.442820
$816$		0			0
$817$	401.877	−	291.981i	0.0172092	−	0.0125032i
$818$		0			0
$819$	1451.99	+	4468.76i	0.0619494	+	0.190661i
$820$		0			0
$821$	−28185.9	−	20478.2i	−1.19816	−	0.870517i	−0.204061	−	0.978958i	$-0.565414\pi$
$821$	−28185.9	−	20478.2i	−1.19816	−	0.870517i	−0.994103	+	0.108441i	$0.965414\pi$
$822$		0			0
$823$	−855.025	+	2631.50i	−0.0362142	+	0.111456i	−0.967530	−	0.252758i	$-0.918662\pi$
$823$	−855.025	+	2631.50i	−0.0362142	+	0.111456i	0.931315	+	0.364214i	$0.118662\pi$
$824$		0			0
$825$	−1075.80	−	7343.06i	−0.0453996	−	0.309882i
$826$		0			0
$827$	−10220.6	+	31455.7i	−0.429751	+	1.32264i	0.468620	+	0.883400i	$0.344751\pi$
$827$	−10220.6	+	31455.7i	−0.429751	+	1.32264i	−0.898371	+	0.439237i	$0.855249\pi$
$828$		0			0
$829$	5208.77	+	3784.39i	0.218225	+	0.158549i	0.691527	−	0.722351i	$-0.256938\pi$
$829$	5208.77	+	3784.39i	0.218225	+	0.158549i	−0.473303	+	0.880900i	$0.656938\pi$
$830$		0			0
$831$	5259.08	+	16185.8i	0.219537	+	0.675667i
$832$		0			0
$833$	16577.0	−	12043.9i	0.689508	−	0.500957i
$834$		0			0
$835$	−11979.3			−0.496480
$836$		0			0
$837$	−12302.8			−0.508062
$838$		0			0
$839$	22453.9	−	16313.7i	0.923953	−	0.671291i	−0.0205520	−	0.999789i	$-0.506542\pi$
$839$	22453.9	−	16313.7i	0.923953	−	0.671291i	0.944505	+	0.328498i	$0.106542\pi$
$840$		0			0
$841$	−5696.12	−	17530.9i	−0.233553	−	0.718802i
$842$		0			0
$843$	−13092.4	−	9512.19i	−0.534907	−	0.388633i
$844$		0			0
$845$	112.609	−	346.574i	0.00458445	−	0.0141095i
$846$		0			0
$847$	−5831.03	+	1746.04i	−0.236548	+	0.0708319i
$848$		0			0
$849$	−3062.89	+	9426.60i	−0.123814	+	0.381060i
$850$		0			0
$851$	−5879.08	−	4271.40i	−0.236818	−	0.172058i
$852$		0			0
$853$	−3222.19	−	9916.87i	−0.129338	−	0.398062i	0.865328	−	0.501206i	$-0.167110\pi$
$853$	−3222.19	−	9916.87i	−0.129338	−	0.398062i	−0.994667	+	0.103143i	$0.967110\pi$
$854$		0			0
$855$	1969.81	−	1431.15i	0.0787907	−	0.0572448i
$856$		0			0
$857$	26763.2			1.06676			0.533379	−	0.845876i	$-0.320922\pi$
$857$	26763.2			1.06676			0.533379	+	0.845876i	$0.320922\pi$
$858$		0			0
$859$	29313.2			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$859$	29313.2			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$860$		0			0
$861$	1358.07	−	986.695i	0.0537548	−	0.0390551i
$862$		0			0
$863$	14478.5	+	44560.4i	0.571095	+	1.75765i	0.649106	+	0.760698i	$0.275143\pi$
$863$	14478.5	+	44560.4i	0.571095	+	1.75765i	−0.0780101	+	0.996953i	$0.524857\pi$
$864$		0			0
$865$	−12252.0	−	8901.59i	−0.481596	−	0.349900i
$866$		0			0
$867$	−620.086	+	1908.43i	−0.0242898	+	0.0747562i
$868$		0			0
$869$	−4017.44	−	27421.7i	−0.156827	−	1.07045i
$870$		0			0
$871$	6816.30	−	20978.4i	0.265168	−	0.816104i
$872$		0			0
$873$	20427.9	+	14841.7i	0.791959	+	0.575392i
$874$		0			0
$875$	−1834.62	−	5646.37i	−0.0708816	−	0.218151i
$876$		0			0
$877$	29738.4	−	21606.2i	1.14503	−	0.831914i	0.157219	−	0.987564i	$-0.449747\pi$
$877$	29738.4	−	21606.2i	1.14503	−	0.831914i	0.987812	+	0.155649i	$0.0497470\pi$
$878$		0			0
$879$	12859.2			0.493436
$880$		0			0
$881$	8902.03			0.340428			0.170214	−	0.985407i	$-0.445554\pi$
$881$	8902.03			0.340428			0.170214	+	0.985407i	$0.445554\pi$
$882$		0			0
$883$	37666.0	−	27366.0i	1.43552	−	1.04296i	0.446562	−	0.894753i	$-0.352648\pi$
$883$	37666.0	−	27366.0i	1.43552	−	1.04296i	0.988956	−	0.148212i	$-0.0473519\pi$
$884$		0			0
$885$	−3170.83	−	9758.80i	−0.120436	−	0.370665i
$886$		0			0
$887$	−13879.4	−	10084.0i	−0.525393	−	0.381721i	0.293239	−	0.956039i	$-0.405267\pi$
$887$	−13879.4	−	10084.0i	−0.525393	−	0.381721i	−0.818632	+	0.574319i	$0.805267\pi$
$888$		0			0
$889$	−2522.95	+	7764.84i	−0.0951823	+	0.292941i
$890$		0			0
$891$	11608.4	+	1976.98i	0.436470	+	0.0743336i
$892$		0			0
$893$	−1471.55	+	4528.97i	−0.0551440	+	0.169716i
$894$		0			0
$895$	−2198.30	−	1597.16i	−0.0821016	−	0.0596503i
$896$		0			0
$897$	1766.19	+	5435.76i	0.0657427	+	0.202335i
$898$		0			0
$899$	6815.58	−	4951.81i	0.252850	−	0.183706i
$900$		0			0
$901$	−9421.32			−0.348357
$902$		0			0
$903$	−285.358			−0.0105162
$904$		0			0
$905$	−6850.28	+	4977.02i	−0.251614	+	0.182809i
$906$		0			0
$907$	−6020.17	−	18528.2i	−0.220393	−	0.678300i	−0.998727	−	0.0504492i	$-0.983935\pi$
$907$	−6020.17	−	18528.2i	−0.220393	−	0.678300i	0.778334	−	0.627851i	$-0.216065\pi$
$908$		0			0
$909$	−25982.8	−	18877.6i	−0.948068	−	0.688812i
$910$		0			0
$911$	16441.2	−	50600.9i	0.597939	−	1.84027i	0.0584238	−	0.998292i	$-0.481393\pi$
$911$	16441.2	−	50600.9i	0.597939	−	1.84027i	0.539515	−	0.841976i	$-0.318607\pi$
$912$		0			0
$913$	−17813.9	−	18232.4i	−0.645733	−	0.660902i
$914$		0			0
$915$	2108.27	−	6488.58i	0.0761718	−	0.234433i
$916$		0			0
$917$	−473.470	−	343.996i	−0.0170506	−	0.0123880i
$918$		0			0
$919$	3800.15	+	11695.7i	0.136404	+	0.419809i	0.995806	−	0.0914922i	$-0.0291637\pi$
$919$	3800.15	+	11695.7i	0.136404	+	0.419809i	−0.859402	+	0.511301i	$0.829164\pi$
$920$		0			0
$921$	13264.8	−	9637.43i	0.474581	−	0.344803i
$922$		0			0
$923$	−43331.3			−1.54525
$924$		0			0
$925$	12286.7			0.436741
$926$		0			0
$927$	−17108.6	+	12430.1i	−0.606171	+	0.440409i
$928$		0			0
$929$	11760.7	+	36195.8i	0.415347	+	1.27831i	0.911940	+	0.410323i	$0.134584\pi$
$929$	11760.7	+	36195.8i	0.415347	+	1.27831i	−0.496594	+	0.867983i	$0.665416\pi$
$930$		0			0
$931$	4807.65	+	3492.96i	0.169242	+	0.122962i
$932$		0			0
$933$	7615.07	−	23436.8i	0.267209	−	0.822386i
$934$		0			0
$935$	6575.10	−	12542.3i	0.229977	−	0.438691i
$936$		0			0
$937$	−12909.9	+	39732.6i	−0.450105	+	1.38528i	0.426683	+	0.904401i	$0.359682\pi$
$937$	−12909.9	+	39732.6i	−0.450105	+	1.38528i	−0.876787	+	0.480878i	$0.840318\pi$
$938$		0			0
$939$	−4782.06	−	3474.37i	−0.166195	−	0.120747i
$940$		0			0
$941$	−9980.78	−	30717.7i	−0.345764	−	1.06415i	−0.961173	−	0.275945i	$-0.911009\pi$
$941$	−9980.78	−	30717.7i	−0.345764	−	1.06415i	0.615409	−	0.788208i	$-0.288991\pi$
$942$		0			0
$943$	−6651.74	+	4832.77i	−0.229703	+	0.166889i
$944$		0			0
$945$	−3144.74			−0.108252
$946$		0			0
$947$	1027.50			0.0352579			0.0176290	−	0.999845i	$-0.494388\pi$
$947$	1027.50			0.0352579			0.0176290	+	0.999845i	$0.494388\pi$
$948$		0			0
$949$	35253.2	−	25612.9i	1.20587	−	0.876113i
$950$		0			0
$951$	2808.73	+	8644.38i	0.0957721	+	0.294756i
$952$		0			0
$953$	−29825.9	−	21669.8i	−1.01380	−	0.736571i	−0.0488000	−	0.998809i	$-0.515540\pi$
$953$	−29825.9	−	21669.8i	−1.01380	−	0.736571i	−0.965003	+	0.262237i	$0.915540\pi$
$954$		0			0
$955$	−8145.17	+	25068.3i	−0.275991	+	0.849413i
$956$		0			0
$957$	5848.19	−	2894.79i	0.197539	−	0.0977798i
$958$		0			0
$959$	606.611	−	1866.96i	0.0204260	−	0.0628647i
$960$		0			0
$961$	14461.0	+	10506.5i	0.485415	+	0.352674i
$962$		0			0
$963$	8168.39	+	25139.7i	0.273336	+	0.841242i
$964$		0			0
$965$	−9039.86	+	6567.84i	−0.301558	+	0.219095i
$966$		0			0
$967$	58557.8			1.94735			0.973677	−	0.227931i	$-0.0731960\pi$
$967$	58557.8			1.94735			0.973677	+	0.227931i	$0.0731960\pi$
$968$		0			0
$969$	2720.34			0.0901857
$970$		0			0
$971$	14372.1	−	10442.0i	0.474999	−	0.345107i	−0.324387	−	0.945924i	$-0.605158\pi$
$971$	14372.1	−	10442.0i	0.474999	−	0.345107i	0.799386	+	0.600817i	$0.205158\pi$
$972$		0			0
$973$	3444.69	+	10601.7i	0.113496	+	0.349305i
$974$		0			0
$975$	−7818.01	−	5680.12i	−0.256797	−	0.186574i
$976$		0			0
$977$	−5685.90	+	17499.4i	−0.186191	+	0.573036i	−0.999967	−	0.00814260i	$-0.997408\pi$
$977$	−5685.90	+	17499.4i	−0.186191	+	0.573036i	0.813776	+	0.581178i	$0.197408\pi$
$978$		0			0
$979$	18454.0	−	9134.53i	0.602444	−	0.298203i
$980$		0			0
$981$	1674.84	−	5154.64i	0.0545093	−	0.167762i
$982$		0			0
$983$	−10004.6	−	7268.76i	−0.324615	−	0.235847i	0.413527	−	0.910492i	$-0.364297\pi$
$983$	−10004.6	−	7268.76i	−0.324615	−	0.235847i	−0.738142	+	0.674645i	$0.764297\pi$
$984$		0			0
$985$	−1358.23	−	4180.20i	−0.0439358	−	0.135220i
$986$		0			0
$987$	2213.12	−	1607.93i	0.0713723	−	0.0518550i
$988$		0			0
$989$	1397.66			0.0449375
$990$		0			0
$991$	−54570.4			−1.74923			−0.874615	−	0.484818i	$-0.838886\pi$
$991$	−54570.4			−1.74923			−0.874615	+	0.484818i	$0.838886\pi$
$992$		0			0
$993$	−14427.7	+	10482.3i	−0.461077	+	0.334992i
$994$		0			0
$995$	−3485.29	−	10726.6i	−0.111046	−	0.341766i
$996$		0			0
$997$	33039.6	+	24004.7i	1.04952	+	0.762523i	0.972122	−	0.234477i	$-0.0753376\pi$
$997$	33039.6	+	24004.7i	1.04952	+	0.762523i	0.0774017	+	0.997000i	$0.475338\pi$
$998$		0			0
$999$	4875.28	−	15004.6i	0.154401	−	0.475199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.4.i.a.9.2	✓	16
4.3	odd	2		176.4.m.e.97.3		16
11.4	even	5		968.4.a.n.1.6		8
11.5	even	5	inner	88.4.i.a.49.2	yes	16
11.7	odd	10		968.4.a.o.1.6		8
44.7	even	10		1936.4.a.bv.1.3		8
44.15	odd	10		1936.4.a.bw.1.3		8
44.27	odd	10		176.4.m.e.49.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.4.i.a.9.2	✓	16	1.1	even	1	trivial
88.4.i.a.49.2	yes	16	11.5	even	5	inner
176.4.m.e.49.3		16	44.27	odd	10
176.4.m.e.97.3		16	4.3	odd	2
968.4.a.n.1.6		8	11.4	even	5
968.4.a.o.1.6		8	11.7	odd	10
1936.4.a.bv.1.3		8	44.7	even	10
1936.4.a.bw.1.3		8	44.15	odd	10

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	88.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87500 + 1.36227i) q^{3} +(1.88546 + 5.80286i) q^{5} +(-3.69974 - 2.68802i) q^{7} +(-6.68360 + 20.5700i) q^{9} +(-32.6966 + 16.1844i) q^{11} +(-14.6799 + 45.1799i) q^{13} +(-11.4403 - 8.31187i) q^{15} +(19.6589 + 60.5038i) q^{17} +(-14.9266 + 10.8448i) q^{19} +10.5988 q^{21} -51.9123 q^{23} +(71.0089 - 51.5910i) q^{25} +(-34.8272 - 107.187i) q^{27} +(62.4357 + 45.3622i) q^{29} +(33.7328 - 103.819i) q^{31} +(39.2586 - 74.8873i) q^{33} +(8.62246 - 26.5372i) q^{35} +(113.250 + 82.2810i) q^{37} +(-34.0225 - 104.710i) q^{39} +(128.134 - 93.0948i) q^{41} -26.9236 q^{43} -131.967 q^{45} +(208.809 - 151.708i) q^{47} +(-99.5302 - 306.322i) q^{49} +(-119.283 - 86.6641i) q^{51} +(-45.7633 + 140.845i) q^{53} +(-155.564 - 159.218i) q^{55} +(13.2138 - 40.6680i) q^{57} +(587.040 + 426.510i) q^{59} +(149.089 + 458.849i) q^{61} +(80.0201 - 58.1380i) q^{63} -289.851 q^{65} -464.330 q^{67} +(97.3358 - 70.7186i) q^{69} +(281.867 + 867.498i) q^{71} +(-742.094 - 539.163i) q^{73} +(-62.8611 + 193.467i) q^{75} +(164.473 + 28.0108i) q^{77} +(-234.747 + 722.475i) q^{79} +(-261.125 - 189.718i) q^{81} +(215.908 + 664.495i) q^{83} +(-314.029 + 228.155i) q^{85} -178.863 q^{87} -564.403 q^{89} +(175.756 - 127.694i) q^{91} +(78.1801 + 240.613i) q^{93} +(-91.0743 - 66.1694i) q^{95} +(360.762 - 1110.31i) q^{97} +(-114.383 - 780.739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} - q^{5} - 13 q^{7} + 7 q^{9} + 83 q^{11} + 69 q^{13} + 93 q^{15} - 217 q^{17} + 126 q^{19} + 34 q^{21} - 92 q^{23} + 307 q^{25} + 158 q^{27} - 553 q^{29} + 205 q^{31} - 198 q^{33} + 7 q^{35}+ \cdots - 3265 q^{99}+O(q^{100}) \) 16 * q - q^3 - q^5 - 13 * q^7 + 7 * q^9 + 83 * q^11 + 69 * q^13 + 93 * q^15 - 217 * q^17 + 126 * q^19 + 34 * q^21 - 92 * q^23 + 307 * q^25 + 158 * q^27 - 553 * q^29 + 205 * q^31 - 198 * q^33 + 7 * q^35 + 127 * q^37 - 629 * q^39 - 553 * q^41 + 70 * q^43 - 1132 * q^45 + 779 * q^47 + 847 * q^49 - 2176 * q^51 + 1401 * q^53 - 385 * q^55 - 488 * q^57 + 1354 * q^59 - 1623 * q^61 + 256 * q^63 + 1674 * q^65 - 1658 * q^67 + 5470 * q^69 + 1985 * q^71 - 1245 * q^73 + 4114 * q^75 - 2645 * q^77 - 2007 * q^79 + 1966 * q^81 - 2946 * q^83 - 1543 * q^85 - 262 * q^87 - 6410 * q^89 + 3937 * q^91 + 2221 * q^93 - 8359 * q^95 + 6566 * q^97 - 3265 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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