LMFDB - Embedded newform 208.4.w.e.49.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 340 x^{18} + 48278 x^{16} + 3724852 x^{14} + 170209937 x^{12} + 4703455168 x^{10} + \cdots + 549543481344 $ x^20 + 340x^18 + 48278x^16 + 3724852x^14 + 170209937x^12 + 4703455168x^10 + 76591569568x^8 + 674465272704x^6 + 2596745246976x^4 + 2244726908928*x^2 + 549543481344
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{40} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.10
Root			$-8.92087i$ of defining polynomial
Character	$\chi$	$=$	208.49
Dual form			208.4.w.e.17.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.96043 + 8.59173i) q^{3} -13.0771i q^{5} +(6.90571 + 3.98702i) q^{7} +(-35.7118 + 61.8547i) q^{9} +O(q^{10})$	\(q+(4.96043 + 8.59173i) q^{3} -13.0771i q^{5} +(6.90571 + 3.98702i) q^{7} +(-35.7118 + 61.8547i) q^{9} +(-46.0142 + 26.5663i) q^{11} +(2.73377 + 46.7924i) q^{13} +(112.355 - 64.8683i) q^{15} +(-14.9143 + 25.8324i) q^{17} +(126.281 + 72.9086i) q^{19} +79.1093i q^{21} +(-0.458532 - 0.794202i) q^{23} -46.0115 q^{25} -440.721 q^{27} +(-31.5119 - 54.5803i) q^{29} +136.687i q^{31} +(-456.501 - 263.561i) q^{33} +(52.1387 - 90.3070i) q^{35} +(165.369 - 95.4757i) q^{37} +(-388.467 + 255.598i) q^{39} +(-18.9665 + 10.9503i) q^{41} +(167.456 - 290.043i) q^{43} +(808.882 + 467.008i) q^{45} -52.8391i q^{47} +(-139.707 - 241.980i) q^{49} -295.926 q^{51} -275.532 q^{53} +(347.411 + 601.734i) q^{55} +1446.63i q^{57} +(353.245 + 203.946i) q^{59} +(401.914 - 696.135i) q^{61} +(-493.231 + 284.767i) q^{63} +(611.910 - 35.7499i) q^{65} +(205.846 - 118.845i) q^{67} +(4.54904 - 7.87917i) q^{69} +(111.080 + 64.1321i) q^{71} -287.235i q^{73} +(-228.237 - 395.318i) q^{75} -423.681 q^{77} +1096.96 q^{79} +(-1221.95 - 2116.48i) q^{81} +16.7794i q^{83} +(337.813 + 195.037i) q^{85} +(312.626 - 541.484i) q^{87} +(77.2306 - 44.5891i) q^{89} +(-167.683 + 334.034i) q^{91} +(-1174.38 + 678.026i) q^{93} +(953.435 - 1651.40i) q^{95} +(1007.72 + 581.807i) q^{97} -3794.92i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.96043	+	8.59173i	0.954636	+	1.65348i	0.735199	+	0.677852i	$0.237089\pi$
$3$	4.96043	+	8.59173i	0.954636	+	1.65348i	0.219438	+	0.975627i	$0.429578\pi$
$4$		0			0
$5$		−	13.0771i		−	1.16965i	−0.811158	−	0.584827i	$-0.801162\pi$
$5$		−	13.0771i		−	1.16965i	0.811158	−	0.584827i	$-0.198838\pi$
$6$		0			0
$7$	6.90571	+	3.98702i	0.372874	+	0.215279i	0.674713	−	0.738080i	$-0.264267\pi$
$7$	6.90571	+	3.98702i	0.372874	+	0.215279i	−0.301840	+	0.953359i	$0.597601\pi$
$8$		0			0
$9$	−35.7118	+	61.8547i	−1.32266	+	2.29091i
$10$		0			0
$11$	−46.0142	+	26.5663i	−1.26125	+	0.728185i	−0.973317	−	0.229464i	$-0.926303\pi$
$11$	−46.0142	+	26.5663i	−1.26125	+	0.728185i	−0.287937	+	0.957649i	$0.592969\pi$
$12$		0			0
$13$	2.73377	+	46.7924i	0.0583240	+	0.998298i
$13$	2.73377	+	46.7924i	0.0583240	+	0.998298i
$14$		0			0
$15$	112.355	−	64.8683i	1.93400	−	1.11659i
$16$		0			0
$17$	−14.9143	+	25.8324i	−0.212780	+	0.368545i	−0.952583	−	0.304278i	$-0.901585\pi$
$17$	−14.9143	+	25.8324i	−0.212780	+	0.368545i	0.739804	+	0.672823i	$0.234918\pi$
$18$		0			0
$19$	126.281	+	72.9086i	1.52479	+	0.880335i	0.999569	+	0.0293672i	$0.00934921\pi$
$19$	126.281	+	72.9086i	1.52479	+	0.880335i	0.525217	+	0.850968i	$0.323984\pi$
$20$		0			0
$21$			79.1093i			0.822051i
$22$		0			0
$23$	−0.458532	−	0.794202i	−0.00415698	−	0.00720011i	0.863939	−	0.503596i	$-0.167990\pi$
$23$	−0.458532	−	0.794202i	−0.00415698	−	0.00720011i	−0.868096	+	0.496396i	$0.834657\pi$
$24$		0			0
$25$	−46.0115			−0.368092
$26$		0			0
$27$	−440.721			−3.14137
$28$		0			0
$29$	−31.5119	−	54.5803i	−0.201780	−	0.349493i	0.747322	−	0.664462i	$-0.231339\pi$
$29$	−31.5119	−	54.5803i	−0.201780	−	0.349493i	−0.949102	+	0.314969i	$0.898006\pi$
$30$		0			0
$31$			136.687i			0.791925i	0.918267	+	0.395962i	$0.129589\pi$
$31$			136.687i			0.791925i	−0.918267	+	0.395962i	$0.870411\pi$
$32$		0			0
$33$	−456.501	−	263.561i	−2.40808	−	1.39030i
$34$		0			0
$35$	52.1387	−	90.3070i	0.251802	−	0.436133i
$36$		0			0
$37$	165.369	−	95.4757i	0.734769	−	0.424219i	−0.0853953	−	0.996347i	$-0.527215\pi$
$37$	165.369	−	95.4757i	0.734769	−	0.424219i	0.820164	+	0.572128i	$0.193882\pi$
$38$		0			0
$39$	−388.467	+	255.598i	−1.59499	+	1.04945i
$40$		0			0
$41$	−18.9665	+	10.9503i	−0.0722458	+	0.0417111i	−0.535688	−	0.844416i	$-0.679948\pi$
$41$	−18.9665	+	10.9503i	−0.0722458	+	0.0417111i	0.463442	+	0.886127i	$0.346614\pi$
$42$		0			0
$43$	167.456	−	290.043i	0.593880	−	1.02863i	−0.399823	−	0.916592i	$-0.630929\pi$
$43$	167.456	−	290.043i	0.593880	−	1.02863i	0.993704	−	0.112039i	$-0.0357381\pi$
$44$		0			0
$45$	808.882	+	467.008i	2.67958	+	1.54706i
$46$		0			0
$47$		−	52.8391i		−	0.163987i	−0.996633	−	0.0819934i	$-0.973871\pi$
$47$		−	52.8391i		−	0.163987i	0.996633	−	0.0819934i	$-0.0261286\pi$
$48$		0			0
$49$	−139.707	−	241.980i	−0.407310	−	0.705482i
$50$		0			0
$51$	−295.926			−0.812509
$52$		0			0
$53$	−275.532			−0.714098			−0.357049	−	0.934086i	$-0.616217\pi$
$53$	−275.532			−0.714098			−0.357049	+	0.934086i	$0.616217\pi$
$54$		0			0
$55$	347.411	+	601.734i	0.851725	+	1.47523i
$56$		0			0
$57$			1446.63i			3.36160i
$58$		0			0
$59$	353.245	+	203.946i	0.779468	+	0.450026i	0.836242	−	0.548361i	$-0.184748\pi$
$59$	353.245	+	203.946i	0.779468	+	0.450026i	−0.0567740	+	0.998387i	$0.518081\pi$
$60$		0			0
$61$	401.914	−	696.135i	0.843603	−	1.46116i	−0.0432258	−	0.999065i	$-0.513763\pi$
$61$	401.914	−	696.135i	0.843603	−	1.46116i	0.886829	−	0.462098i	$-0.152903\pi$
$62$		0			0
$63$	−493.231	+	284.767i	−0.986370	+	0.569481i
$64$		0			0
$65$	611.910	−	35.7499i	1.16766	−	0.0682190i
$66$		0			0
$67$	205.846	−	118.845i	0.375344	−	0.216705i	−0.300447	−	0.953799i	$-0.597136\pi$
$67$	205.846	−	118.845i	0.375344	−	0.216705i	0.675791	+	0.737094i	$0.263802\pi$
$68$		0			0
$69$	4.54904	−	7.87917i	0.00793681	−	0.0137470i
$70$		0			0
$71$	111.080	+	64.1321i	0.185673	+	0.107198i	0.589955	−	0.807436i	$-0.299145\pi$
$71$	111.080	+	64.1321i	0.185673	+	0.107198i	−0.404282	+	0.914634i	$0.632479\pi$
$72$		0			0
$73$		−	287.235i		−	0.460525i	−0.973129	−	0.230262i	$-0.926042\pi$
$73$		−	287.235i		−	0.460525i	0.973129	−	0.230262i	$-0.0739585\pi$
$74$		0			0
$75$	−228.237	−	395.318i	−0.351394	−	0.608632i
$76$		0			0
$77$	−423.681			−0.627051
$78$		0			0
$79$	1096.96			1.56226			0.781128	−	0.624371i	$-0.214645\pi$
$79$	1096.96			1.56226			0.781128	+	0.624371i	$0.214645\pi$
$80$		0			0
$81$	−1221.95	−	2116.48i	−1.67620	−	2.90326i
$82$		0			0
$83$			16.7794i			0.0221901i	0.999938	+	0.0110951i	$0.00353174\pi$
$83$			16.7794i			0.0221901i	−0.999938	+	0.0110951i	$0.996468\pi$
$84$		0			0
$85$	337.813	+	195.037i	0.431071	+	0.248879i
$86$		0			0
$87$	312.626	−	541.484i	0.385253	−	0.667278i
$88$		0			0
$89$	77.2306	−	44.5891i	0.0919823	−	0.0531060i	−0.453303	−	0.891356i	$-0.649755\pi$
$89$	77.2306	−	44.5891i	0.0919823	−	0.0531060i	0.545286	+	0.838250i	$0.316421\pi$
$90$		0			0
$91$	−167.683	+	334.034i	−0.193165	+	0.384795i
$92$		0			0
$93$	−1174.38	+	678.026i	−1.30943	+	0.756000i
$94$		0			0
$95$	953.435	−	1651.40i	1.02969	−	1.78347i
$96$		0			0
$97$	1007.72	+	581.807i	1.05483	+	0.609006i	0.923997	−	0.382399i	$-0.124902\pi$
$97$	1007.72	+	581.807i	1.05483	+	0.609006i	0.130832	+	0.991405i	$0.458235\pi$
$98$		0			0
$99$		−	3794.92i		−	3.85257i
$100$		0			0
$101$	−80.1007	−	138.738i	−0.0789140	−	0.136683i	0.823868	−	0.566782i	$-0.191812\pi$
$101$	−80.1007	−	138.738i	−0.0789140	−	0.136683i	−0.902782	+	0.430099i	$0.858479\pi$
$102$		0			0
$103$	−1766.84			−1.69022			−0.845108	−	0.534595i	$-0.820464\pi$
$103$	−1766.84			−1.69022			−0.845108	+	0.534595i	$0.820464\pi$
$104$		0			0
$105$	1034.52			0.961516
$106$		0			0
$107$	19.6636	+	34.0584i	0.0177659	+	0.0307715i	0.874772	−	0.484535i	$-0.161011\pi$
$107$	19.6636	+	34.0584i	0.0177659	+	0.0307715i	−0.857006	+	0.515307i	$0.827678\pi$
$108$		0			0
$109$		−	619.531i		−	0.544406i	−0.962240	−	0.272203i	$-0.912248\pi$
$109$		−	619.531i		−	0.544406i	0.962240	−	0.272203i	$-0.0877523\pi$
$110$		0			0
$111$	1640.60	+	947.202i	1.40287	+	0.809950i
$112$		0			0
$113$	−779.206	+	1349.62i	−0.648686	+	1.12356i	0.334751	+	0.942307i	$0.391348\pi$
$113$	−779.206	+	1349.62i	−0.648686	+	1.12356i	−0.983437	+	0.181251i	$0.941985\pi$
$114$		0			0
$115$	−10.3859	+	5.99629i	−0.00842164	+	0.00486224i
$116$		0			0
$117$	−2991.96	−	1501.94i	−2.36416	−	1.18679i
$118$		0			0
$119$	−205.988	+	118.927i	−0.158680	+	0.0916138i
$120$		0			0
$121$	746.036	−	1292.17i	0.560508	−	0.970828i
$122$		0			0
$123$	−188.165	−	108.637i	−0.137937	−	0.0796379i
$124$		0			0
$125$		−	1032.94i		−	0.739114i
$126$		0			0
$127$	1204.04	+	2085.46i	0.841270	+	1.45712i	0.888821	+	0.458254i	$0.151525\pi$
$127$	1204.04	+	2085.46i	0.841270	+	1.45712i	−0.0475509	+	0.998869i	$0.515142\pi$
$128$		0			0
$129$	3322.63			2.26776
$130$		0			0
$131$	−1089.53			−0.726659			−0.363329	−	0.931661i	$-0.618360\pi$
$131$	−1089.53			−0.726659			−0.363329	+	0.931661i	$0.618360\pi$
$132$		0			0
$133$	581.375	+	1006.97i	0.379035	+	0.656508i
$134$		0			0
$135$			5763.37i			3.67431i
$136$		0			0
$137$	2278.52	+	1315.50i	1.42093	+	0.820372i	0.996378	−	0.0850334i	$-0.0270997\pi$
$137$	2278.52	+	1315.50i	1.42093	+	0.820372i	0.424548	+	0.905405i	$0.360433\pi$
$138$		0			0
$139$	−691.754	+	1198.15i	−0.422114	+	0.731122i	−0.996146	−	0.0877103i	$-0.972045\pi$
$139$	−691.754	+	1198.15i	−0.422114	+	0.731122i	0.574032	+	0.818833i	$0.305378\pi$
$140$		0			0
$141$	453.979	−	262.105i	0.271149	−	0.156548i
$142$		0			0
$143$	−1368.89	−	2080.49i	−0.800507	−	1.21664i
$144$		0			0
$145$	−713.754	+	412.086i	−0.408786	+	0.236013i
$146$		0			0
$147$	1386.02	−	2400.66i	0.777666	−	1.34696i
$148$		0			0
$149$	1935.77	+	1117.62i	1.06433	+	0.614489i	0.926626	−	0.375985i	$-0.122696\pi$
$149$	1935.77	+	1117.62i	1.06433	+	0.614489i	0.137700	+	0.990474i	$0.456029\pi$
$150$		0			0
$151$			1988.69i			1.07177i	0.844290	+	0.535886i	$0.180022\pi$
$151$			1988.69i			1.07177i	−0.844290	+	0.535886i	$0.819978\pi$
$152$		0			0
$153$	−1065.24	−	1845.04i	−0.562870	−	0.974920i
$154$		0			0
$155$	1787.47			0.926278
$156$		0			0
$157$	−114.693			−0.0583024			−0.0291512	−	0.999575i	$-0.509280\pi$
$157$	−114.693			−0.0583024			−0.0291512	+	0.999575i	$0.509280\pi$
$158$		0			0
$159$	−1366.76	−	2367.29i	−0.681704	−	1.18075i
$160$		0			0
$161$		−	7.31271i		−	0.00357964i
$162$		0			0
$163$	−243.274	−	140.454i	−0.116900	−	0.0674923i	0.440410	−	0.897797i	$-0.354833\pi$
$163$	−243.274	−	140.454i	−0.116900	−	0.0674923i	−0.557310	+	0.830305i	$0.688166\pi$
$164$		0			0
$165$	−3446.62	+	5969.72i	−1.62618	+	2.81662i
$166$		0			0
$167$	−1119.22	+	646.183i	−0.518611	+	0.299420i	−0.736366	−	0.676583i	$-0.763460\pi$
$167$	−1119.22	+	646.183i	−0.518611	+	0.299420i	0.217755	+	0.976003i	$0.430126\pi$
$168$		0			0
$169$	−2182.05	+	255.840i	−0.993197	+	0.116450i
$170$		0			0
$171$	−9019.48	+	5207.40i	−4.03355	+	2.32877i
$172$		0			0
$173$	1441.05	−	2495.98i	0.633302	−	1.09691i	−0.353570	−	0.935408i	$-0.615032\pi$
$173$	1441.05	−	2495.98i	0.633302	−	1.09691i	0.986872	−	0.161503i	$-0.0516342\pi$
$174$		0			0
$175$	−317.742	−	183.448i	−0.137252	−	0.0792423i
$176$		0			0
$177$			4046.65i			1.71844i
$178$		0			0
$179$	−2309.58	−	4000.30i	−0.964390	−	1.67037i	−0.711245	−	0.702944i	$-0.751869\pi$
$179$	−2309.58	−	4000.30i	−0.964390	−	1.67037i	−0.253145	−	0.967428i	$-0.581465\pi$
$180$		0			0
$181$	441.640			0.181364			0.0906819	−	0.995880i	$-0.471095\pi$
$181$	441.640			0.181364			0.0906819	+	0.995880i	$0.471095\pi$
$182$		0			0
$183$	7974.67			3.22134
$184$		0			0
$185$	−1248.55	−	2162.55i	−0.496190	−	0.859426i
$186$		0			0
$187$		−	1584.87i		−	0.619772i
$188$		0			0
$189$	−3043.50	−	1757.16i	−1.17133	−	0.676269i
$190$		0			0
$191$	1433.81	−	2483.43i	0.543176	−	0.940809i	−0.455543	−	0.890214i	$-0.650555\pi$
$191$	1433.81	−	2483.43i	0.543176	−	0.940809i	0.998719	−	0.0505950i	$-0.0161118\pi$
$192$		0			0
$193$	420.283	−	242.650i	0.156749	−	0.0904992i	−0.419574	−	0.907721i	$-0.637820\pi$
$193$	420.283	−	242.650i	0.156749	−	0.0904992i	0.576323	+	0.817222i	$0.304487\pi$
$194$		0			0
$195$	3342.49	+	5080.03i	1.22749	+	1.86558i
$196$		0			0
$197$	3554.43	−	2052.15i	1.28550	−	0.742181i	0.307648	−	0.951500i	$-0.400458\pi$
$197$	3554.43	−	2052.15i	1.28550	−	0.742181i	0.977847	+	0.209319i	$0.0671248\pi$
$198$		0			0
$199$	−1131.10	+	1959.13i	−0.402924	+	0.697885i	−0.994077	−	0.108674i	$-0.965339\pi$
$199$	−1131.10	+	1959.13i	−0.402924	+	0.697885i	0.591153	+	0.806559i	$0.298673\pi$
$200$		0			0
$201$	2042.17	+	1179.05i	0.716634	+	0.413749i
$202$		0			0
$203$		−	502.554i		−	0.173756i
$204$		0			0
$205$	143.199	+	248.028i	0.0487876	+	0.0845026i
$206$		0			0
$207$	65.5001			0.0219931
$208$		0			0
$209$	−7747.64			−2.56419
$210$		0			0
$211$	1071.38	+	1855.68i	0.349557	+	0.605451i	0.986171	−	0.165732i	$-0.0529986\pi$
$211$	1071.38	+	1855.68i	0.349557	+	0.605451i	−0.636613	+	0.771183i	$0.719665\pi$
$212$		0			0
$213$			1272.49i			0.409341i
$214$		0			0
$215$	−3792.93	−	2189.85i	−1.20314	−	0.694635i
$216$		0			0
$217$	−544.972	+	943.920i	−0.170484	+	0.295288i
$218$		0			0
$219$	2467.84	−	1424.81i	0.761468	−	0.439634i
$220$		0			0
$221$	−1249.53	−	627.257i	−0.380328	−	0.190922i
$222$		0			0
$223$	−338.369	+	195.357i	−0.101609	+	0.0586641i	−0.549943	−	0.835202i	$-0.685351\pi$
$223$	−338.369	+	195.357i	−0.101609	+	0.0586641i	0.448334	+	0.893866i	$0.352017\pi$
$224$		0			0
$225$	1643.15	−	2846.03i	0.486860	−	0.843267i
$226$		0			0
$227$	751.920	+	434.121i	0.219853	+	0.126932i	0.605882	−	0.795554i	$-0.292820\pi$
$227$	751.920	+	434.121i	0.219853	+	0.126932i	−0.386029	+	0.922487i	$0.626154\pi$
$228$		0			0
$229$		−	4745.09i		−	1.36928i	−0.728883	−	0.684639i	$-0.759960\pi$
$229$		−	4745.09i		−	1.36928i	0.728883	−	0.684639i	$-0.240040\pi$
$230$		0			0
$231$	−2101.64	−	3640.15i	−0.598606	−	1.03682i
$232$		0			0
$233$	−4316.15			−1.21356			−0.606782	−	0.794868i	$-0.707540\pi$
$233$	−4316.15			−1.21356			−0.606782	+	0.794868i	$0.707540\pi$
$234$		0			0
$235$	−690.984			−0.191808
$236$		0			0
$237$	5441.42	+	9424.82i	1.49139	+	2.58316i
$238$		0			0
$239$			1639.81i			0.443810i	0.975068	+	0.221905i	$0.0712276\pi$
$239$			1639.81i			0.443810i	−0.975068	+	0.221905i	$0.928772\pi$
$240$		0			0
$241$	−2384.58	−	1376.74i	−0.637363	−	0.367982i	0.146235	−	0.989250i	$-0.453284\pi$
$241$	−2384.58	−	1376.74i	−0.637363	−	0.367982i	−0.783598	+	0.621268i	$0.786618\pi$
$242$		0			0
$243$	6173.07	−	10692.1i	1.62964	−	2.82262i
$244$		0			0
$245$	−3164.41	+	1826.97i	−0.825170	+	0.476412i
$246$		0			0
$247$	−3066.34	+	6108.32i	−0.789905	+	1.57353i
$248$		0			0
$249$	−144.164	+	83.2333i	−0.0366909	+	0.0211835i
$250$		0			0
$251$	74.5221	−	129.076i	0.0187402	−	0.0324590i	−0.856503	−	0.516142i	$-0.827368\pi$
$251$	74.5221	−	129.076i	0.0187402	−	0.0324590i	0.875243	+	0.483683i	$0.160701\pi$
$252$		0			0
$253$	42.1980	+	24.3630i	0.0104860	+	0.00605411i
$254$		0			0
$255$			3869.87i			0.950354i
$256$		0			0
$257$	280.232	+	485.376i	0.0680171	+	0.117809i	0.898028	−	0.439937i	$-0.144999\pi$
$257$	280.232	+	485.376i	0.0680171	+	0.117809i	−0.830011	+	0.557747i	$0.811666\pi$
$258$		0			0
$259$	1522.65			0.365301
$260$		0			0
$261$	4501.39			1.06755
$262$		0			0
$263$	1632.81	+	2828.11i	0.382827	+	0.663076i	0.991465	−	0.130372i	$-0.0416172\pi$
$263$	1632.81	+	2828.11i	0.382827	+	0.663076i	−0.608638	+	0.793448i	$0.708284\pi$
$264$		0			0
$265$			3603.17i			0.835248i
$266$		0			0
$267$	766.195	+	442.363i	0.175619	+	0.101394i
$268$		0			0
$269$	1498.18	−	2594.93i	0.339576	−	0.588163i	−0.644777	−	0.764371i	$-0.723050\pi$
$269$	1498.18	−	2594.93i	0.339576	−	0.588163i	0.984353	+	0.176208i	$0.0563832\pi$
$270$		0			0
$271$	3357.60	−	1938.51i	0.752619	−	0.434525i	−0.0740204	−	0.997257i	$-0.523583\pi$
$271$	3357.60	−	1938.51i	0.752619	−	0.434525i	0.826639	+	0.562732i	$0.190250\pi$
$272$		0			0
$273$	−3701.71	+	216.267i	−0.820652	+	0.0479453i
$274$		0			0
$275$	2117.18	−	1222.35i	0.464257	−	0.268039i
$276$		0			0
$277$	−1127.58	+	1953.02i	−0.244583	+	0.423630i	−0.962014	−	0.272999i	$-0.911984\pi$
$277$	−1127.58	+	1953.02i	−0.244583	+	0.423630i	0.717431	+	0.696629i	$0.245318\pi$
$278$		0			0
$279$	−8454.72	−	4881.33i	−1.81423	−	1.04745i
$280$		0			0
$281$			2246.76i			0.476976i	0.971145	+	0.238488i	$0.0766518\pi$
$281$			2246.76i			0.476976i	−0.971145	+	0.238488i	$0.923348\pi$
$282$		0			0
$283$	40.9075	+	70.8538i	0.00859257	+	0.0148828i	0.870290	−	0.492540i	$-0.163932\pi$
$283$	40.9075	+	70.8538i	0.00859257	+	0.0148828i	−0.861697	+	0.507423i	$0.830598\pi$
$284$		0			0
$285$	18917.8			3.93191
$286$		0			0
$287$	−174.637			−0.0359181
$288$		0			0
$289$	2011.63	+	3484.24i	0.409450	+	0.709188i
$290$		0			0
$291$			11544.1i			2.32552i
$292$		0			0
$293$	−4213.63	−	2432.74i	−0.840147	−	0.485059i	0.0171672	−	0.999853i	$-0.494535\pi$
$293$	−4213.63	−	2432.74i	−0.840147	−	0.485059i	−0.857314	+	0.514794i	$0.827869\pi$
$294$		0			0
$295$	2667.03	−	4619.43i	0.526375	−	0.911708i
$296$		0			0
$297$	20279.4	−	11708.3i	3.96206	−	2.28750i
$298$		0			0
$299$	35.9091	−	23.6270i	0.00694540	−	0.00456985i
$300$		0			0
$301$	2312.81	−	1335.30i	0.442885	−	0.255699i
$302$		0			0
$303$	794.668	−	1376.41i	0.150668	−	0.260965i
$304$		0			0
$305$	−9103.45	−	5255.88i	−1.70906	−	0.986724i
$306$		0			0
$307$		−	2675.76i		−	0.497439i	−0.968576	−	0.248720i	$-0.919990\pi$
$307$		−	2675.76i		−	0.497439i	0.968576	−	0.248720i	$-0.0800098\pi$
$308$		0			0
$309$	−8764.31	−	15180.2i	−1.61354	−	2.79474i
$310$		0			0
$311$	−4354.23			−0.793910			−0.396955	−	0.917838i	$-0.629933\pi$
$311$	−4354.23			−0.793910			−0.396955	+	0.917838i	$0.629933\pi$
$312$		0			0
$313$	−27.3938			−0.00494693			−0.00247347	−	0.999997i	$-0.500787\pi$
$313$	−27.3938			−0.00494693			−0.00247347	+	0.999997i	$0.500787\pi$
$314$		0			0
$315$	3723.94	+	6450.05i	0.666096	+	1.15371i
$316$		0			0
$317$		−	3086.31i		−	0.546828i	−0.961896	−	0.273414i	$-0.911847\pi$
$317$		−	3086.31i		−	0.546828i	0.961896	−	0.273414i	$-0.0881528\pi$
$318$		0			0
$319$	2899.99	+	1674.31i	0.508992	+	0.293866i
$320$		0			0
$321$	−195.080	+	337.889i	−0.0339200	+	0.0587511i
$322$		0			0
$323$	−3766.80	+	2174.76i	−0.648887	+	0.374635i
$324$		0			0
$325$	−125.785	−	2152.99i	−0.0214686	−	0.367465i
$326$		0			0
$327$	5322.84	−	3073.14i	0.900164	−	0.519710i
$328$		0			0
$329$	210.670	−	364.892i	0.0353028	−	0.0611463i
$330$		0			0
$331$	−4966.52	−	2867.42i	−0.824727	−	0.476156i	0.0273170	−	0.999627i	$-0.491304\pi$
$331$	−4966.52	−	2867.42i	−0.824727	−	0.476156i	−0.852044	+	0.523471i	$0.824637\pi$
$332$		0			0
$333$			13638.4i			2.24439i
$334$		0			0
$335$	−1554.15	−	2691.87i	−0.253470	−	0.439023i
$336$		0			0
$337$	−5685.20			−0.918969			−0.459484	−	0.888186i	$-0.651966\pi$
$337$	−5685.20			−0.918969			−0.459484	+	0.888186i	$0.651966\pi$
$338$		0			0
$339$	−15460.8			−2.47704
$340$		0			0
$341$	−3631.26	−	6289.53i	−0.576668	−	0.998818i
$342$		0			0
$343$		−	4963.16i		−	0.781298i
$344$		0			0
$345$	−103.037	−	59.4884i	−0.0160792	−	0.00928333i
$346$		0			0
$347$	−3618.67	+	6267.71i	−0.559827	+	0.969650i	0.437683	+	0.899129i	$0.355799\pi$
$347$	−3618.67	+	6267.71i	−0.559827	+	0.969650i	−0.997510	+	0.0705202i	$0.977534\pi$
$348$		0			0
$349$	−4857.11	+	2804.26i	−0.744972	+	0.430110i	−0.823874	−	0.566772i	$-0.808192\pi$
$349$	−4857.11	+	2804.26i	−0.744972	+	0.430110i	0.0789022	+	0.996882i	$0.474859\pi$
$350$		0			0
$351$	−1204.83	−	20622.4i	−0.183217	−	3.13602i
$352$		0			0
$353$	4838.93	−	2793.76i	0.729604	−	0.421237i	−0.0886730	−	0.996061i	$-0.528263\pi$
$353$	4838.93	−	2793.76i	0.729604	−	0.421237i	0.818277	+	0.574823i	$0.194929\pi$
$354$		0			0
$355$	838.664	−	1452.61i	0.125385	−	0.217173i
$356$		0			0
$357$	−2043.58	−	1179.86i	−0.302963	−	0.174916i
$358$		0			0
$359$		−	10159.3i		−	1.49356i	−0.665074	−	0.746778i	$-0.731600\pi$
$359$		−	10159.3i		−	1.49356i	0.665074	−	0.746778i	$-0.268400\pi$
$360$		0			0
$361$	7201.82	+	12473.9i	1.04998	+	1.81862i
$362$		0			0
$363$	14802.6			2.14032
$364$		0			0
$365$	−3756.21			−0.538655
$366$		0			0
$367$	4353.59	+	7540.65i	0.619226	+	1.07253i	0.989627	+	0.143659i	$0.0458867\pi$
$367$	4353.59	+	7540.65i	0.619226	+	1.07253i	−0.370402	+	0.928872i	$0.620780\pi$
$368$		0			0
$369$		−	1564.23i		−	0.220679i
$370$		0			0
$371$	−1902.74	−	1098.55i	−0.266268	−	0.153730i
$372$		0			0
$373$	6387.53	−	11063.5i	0.886686	−	1.53578i	0.0429165	−	0.999079i	$-0.486335\pi$
$373$	6387.53	−	11063.5i	0.886686	−	1.53578i	0.843769	−	0.536706i	$-0.180332\pi$
$374$		0			0
$375$	8874.77	−	5123.85i	1.22211	−	0.705585i
$376$		0			0
$377$	2467.79	−	1623.73i	0.337130	−	0.221820i
$378$		0			0
$379$	2745.24	−	1584.97i	0.372068	−	0.214813i	−0.302294	−	0.953215i	$-0.597752\pi$
$379$	2745.24	−	1584.97i	0.372068	−	0.214813i	0.674361	+	0.738401i	$0.264419\pi$
$380$		0			0
$381$	−11945.1	+	20689.6i	−1.60621	+	2.78204i
$382$		0			0
$383$	−6896.21	−	3981.53i	−0.920053	−	0.531193i	−0.0364007	−	0.999337i	$-0.511589\pi$
$383$	−6896.21	−	3981.53i	−0.920053	−	0.531193i	−0.883652	+	0.468145i	$0.844923\pi$
$384$		0			0
$385$			5540.53i			0.733433i
$386$		0			0
$387$	11960.3	+	20715.9i	1.57100	+	2.72106i
$388$		0			0
$389$	3923.35			0.511367			0.255683	−	0.966761i	$-0.417700\pi$
$389$	3923.35			0.511367			0.255683	+	0.966761i	$0.417700\pi$
$390$		0			0
$391$	27.3548			0.00353809
$392$		0			0
$393$	−5404.52	−	9360.91i	−0.693695	−	1.20151i
$394$		0			0
$395$		−	14345.2i		−	1.82730i
$396$		0			0
$397$	−72.4458	−	41.8266i	−0.00915857	−	0.00528770i	0.495414	−	0.868657i	$-0.335016\pi$
$397$	−72.4458	−	41.8266i	−0.00915857	−	0.00528770i	−0.504572	+	0.863369i	$0.668350\pi$
$398$		0			0
$399$	−5767.75	+	9990.03i	−0.723681	+	1.25345i
$400$		0			0
$401$	7022.74	−	4054.58i	0.874561	−	0.504928i	0.00569993	−	0.999984i	$-0.498186\pi$
$401$	7022.74	−	4054.58i	0.874561	−	0.504928i	0.868861	+	0.495056i	$0.164852\pi$
$402$		0			0
$403$	−6395.90	+	373.671i	−0.790577	+	0.0461883i
$404$		0			0
$405$	−27677.5	+	15979.6i	−3.39582	+	1.96058i
$406$		0			0
$407$	−5072.87	+	8786.47i	−0.617820	+	1.07010i
$408$		0			0
$409$	3143.42	+	1814.85i	0.380029	+	0.219410i	0.677831	−	0.735218i	$-0.262920\pi$
$409$	3143.42	+	1814.85i	0.380029	+	0.219410i	−0.297802	+	0.954628i	$0.596253\pi$
$410$		0			0
$411$			26101.9i			3.13263i
$412$		0			0
$413$	1626.27	+	2816.79i	0.193762	+	0.335605i
$414$		0			0
$415$	219.427			0.0259548
$416$		0			0
$417$	−13725.6			−1.61186
$418$		0			0
$419$	4127.63	+	7149.26i	0.481259	+	0.833566i	0.999769	−	0.0215062i	$-0.00684617\pi$
$419$	4127.63	+	7149.26i	0.481259	+	0.833566i	−0.518509	+	0.855072i	$0.673513\pi$
$420$		0			0
$421$			15097.3i			1.74773i	0.486166	+	0.873867i	$0.338395\pi$
$421$			15097.3i			1.74773i	−0.486166	+	0.873867i	$0.661605\pi$
$422$		0			0
$423$	3268.35	+	1886.98i	0.375680	+	0.216899i
$424$		0			0
$425$	686.230	−	1188.58i	0.0783224	−	0.135658i
$426$		0			0
$427$	5551.00	−	3204.87i	0.629114	−	0.363219i
$428$		0			0
$429$	11084.7	−	22081.3i	1.24749	−	2.48507i
$430$		0			0
$431$	−5722.88	+	3304.11i	−0.639586	+	0.369265i	−0.784455	−	0.620186i	$-0.787057\pi$
$431$	−5722.88	+	3304.11i	−0.639586	+	0.369265i	0.144869	+	0.989451i	$0.453724\pi$
$432$		0			0
$433$	−3374.90	+	5845.49i	−0.374566	+	0.648768i	−0.990262	−	0.139216i	$-0.955542\pi$
$433$	−3374.90	+	5845.49i	−0.374566	+	0.648768i	0.615696	+	0.787984i	$0.288875\pi$
$434$		0			0
$435$	−7081.06	−	4088.25i	−0.780484	−	0.450613i
$436$		0			0
$437$		−	133.724i		−	0.0146382i
$438$		0			0
$439$	−215.512	−	373.278i	−0.0234301	−	0.0405822i	0.854073	−	0.520154i	$-0.174125\pi$
$439$	−215.512	−	373.278i	−0.0234301	−	0.0405822i	−0.877503	+	0.479572i	$0.840792\pi$
$440$		0			0
$441$	19956.8			2.15493
$442$		0			0
$443$	9356.90			1.00352			0.501760	−	0.865007i	$-0.332686\pi$
$443$	9356.90			1.00352			0.501760	+	0.865007i	$0.332686\pi$
$444$		0			0
$445$	−583.098	−	1009.96i	−0.0621157	−	0.107588i
$446$		0			0
$447$			22175.5i			2.34645i
$448$		0			0
$449$	10788.0	+	6228.46i	1.13389	+	0.654653i	0.944911	−	0.327328i	$-0.106148\pi$
$449$	10788.0	+	6228.46i	1.13389	+	0.654653i	0.188981	+	0.981981i	$0.439481\pi$
$450$		0			0
$451$	581.820	−	1007.74i	0.0607469	−	0.105217i
$452$		0			0
$453$	−17086.3	+	9864.79i	−1.77215	+	1.02315i
$454$		0			0
$455$	4368.21	+	2192.82i	0.450077	+	0.225936i
$456$		0			0
$457$	−6516.40	+	3762.24i	−0.667012	+	0.385099i	−0.794943	−	0.606684i	$-0.792499\pi$
$457$	−6516.40	+	3762.24i	−0.667012	+	0.385099i	0.127932	+	0.991783i	$0.459166\pi$
$458$		0			0
$459$	6573.06	−	11384.9i	0.668419	−	1.15773i
$460$		0			0
$461$	−2444.62	−	1411.40i	−0.246979	−	0.142593i	0.371401	−	0.928473i	$-0.378877\pi$
$461$	−2444.62	−	1411.40i	−0.246979	−	0.142593i	−0.618380	+	0.785879i	$0.712211\pi$
$462$		0			0
$463$		−	12108.1i		−	1.21535i	−0.794184	−	0.607677i	$-0.792101\pi$
$463$		−	12108.1i		−	1.21535i	0.794184	−	0.607677i	$-0.207899\pi$
$464$		0			0
$465$	8866.64	+	15357.5i	0.884259	+	1.53158i
$466$		0			0
$467$	9625.77			0.953806			0.476903	−	0.878956i	$-0.341759\pi$
$467$	9625.77			0.953806			0.476903	+	0.878956i	$0.341759\pi$
$468$		0			0
$469$	1895.35			0.186608
$470$		0			0
$471$	−568.926	−	985.408i	−0.0556576	−	0.0964018i
$472$		0			0
$473$			17794.8i			1.72982i
$474$		0			0
$475$	−5810.39	−	3354.63i	−0.561261	−	0.324044i
$476$		0			0
$477$	9839.74	−	17042.9i	0.944509	−	1.63594i
$478$		0			0
$479$	890.575	−	514.174i	0.0849508	−	0.0490464i	−0.456923	−	0.889506i	$-0.651048\pi$
$479$	890.575	−	514.174i	0.0849508	−	0.0490464i	0.541874	+	0.840460i	$0.317715\pi$
$480$		0			0
$481$	4919.62	+	7476.99i	0.466352	+	0.708776i
$482$		0			0
$483$	62.8288	−	36.2742i	0.00591886	−	0.00341725i
$484$		0			0
$485$	7608.37	−	13178.1i	0.712327	−	1.23379i
$486$		0			0
$487$	−15009.5	−	8665.76i	−1.39661	−	0.806331i	−0.402571	−	0.915389i	$-0.631883\pi$
$487$	−15009.5	−	8665.76i	−1.39661	−	0.806331i	−0.994035	+	0.109058i	$0.965217\pi$
$488$		0			0
$489$		−	2786.86i		−	0.257722i
$490$		0			0
$491$	−6340.62	−	10982.3i	−0.582786	−	1.00942i	−0.995147	−	0.0983951i	$-0.968629\pi$
$491$	−6340.62	−	10982.3i	−0.582786	−	1.00942i	0.412361	−	0.911021i	$-0.364704\pi$
$492$		0			0
$493$	1879.92			0.171739
$494$		0			0
$495$	−49626.7			−4.50617
$496$		0			0
$497$	511.391	+	885.756i	0.0461550	+	0.0799428i
$498$		0			0
$499$		−	831.545i		−	0.0745993i	−0.999304	−	0.0372996i	$-0.988124\pi$
$499$		−	831.545i		−	0.0745993i	0.999304	−	0.0372996i	$-0.0118756\pi$
$500$		0			0
$501$	−11103.7	−	6410.70i	−0.990169	−	0.571674i
$502$		0			0
$503$	−1435.81	+	2486.90i	−0.127276	+	0.220448i	−0.922620	−	0.385710i	$-0.873957\pi$
$503$	−1435.81	+	2486.90i	−0.127276	+	0.220448i	0.795344	+	0.606158i	$0.207290\pi$
$504$		0			0
$505$	−1814.30	+	1047.49i	−0.159872	+	0.0923021i
$506$		0			0
$507$	−13022.0	−	17478.5i	−1.14069	−	1.53106i
$508$		0			0
$509$	4635.52	−	2676.32i	0.403666	−	0.233057i	−0.284399	−	0.958706i	$-0.591794\pi$
$509$	4635.52	−	2676.32i	0.403666	−	0.233057i	0.688064	+	0.725650i	$0.258461\pi$
$510$		0			0
$511$	1145.21	−	1983.56i	0.0991412	−	0.171718i
$512$		0			0
$513$	−55654.9	−	32132.4i	−4.78991	−	2.76546i
$514$		0			0
$515$			23105.3i			1.97697i
$516$		0			0
$517$	1403.74	+	2431.35i	0.119413	+	0.206829i
$518$		0			0
$519$	28593.0			2.41829
$520$		0			0
$521$	−9231.92			−0.776311			−0.388155	−	0.921594i	$-0.626888\pi$
$521$	−9231.92			−0.776311			−0.388155	+	0.921594i	$0.626888\pi$
$522$		0			0
$523$	1851.54	+	3206.97i	0.154804	+	0.268128i	0.932988	−	0.359909i	$-0.117192\pi$
$523$	1851.54	+	3206.97i	0.154804	+	0.268128i	−0.778184	+	0.628037i	$0.783859\pi$
$524$		0			0
$525$		−	3639.94i		−	0.302590i
$526$		0			0
$527$	−3530.94	−	2038.59i	−0.291860	−	0.168505i
$528$		0			0
$529$	6083.08	−	10536.2i	0.499965	−	0.865966i
$530$		0			0
$531$	−25230.1	+	14566.6i	−2.06194	+	1.19046i
$532$		0			0
$533$	−564.243	−	857.554i	−0.0458538	−	0.0696900i
$534$		0			0
$535$	445.386	−	257.144i	0.0359920	−	0.0207800i
$536$		0			0
$537$	22913.0	−	39686.5i	1.84128	−	3.18920i
$538$		0			0
$539$	12857.0	+	7423.02i	1.02744	+	0.593195i
$540$		0			0
$541$		−	15772.3i		−	1.25343i	−0.779249	−	0.626714i	$-0.784399\pi$
$541$		−	15772.3i		−	1.25343i	0.779249	−	0.626714i	$-0.215601\pi$
$542$		0			0
$543$	2190.73	+	3794.45i	0.173136	+	0.299881i
$544$		0			0
$545$	−8101.69			−0.636767
$546$		0			0
$547$	3326.98			0.260057			0.130029	−	0.991510i	$-0.458493\pi$
$547$	3326.98			0.260057			0.130029	+	0.991510i	$0.458493\pi$
$548$		0			0
$549$	28706.2	+	49720.5i	2.23160	+	3.86525i
$550$		0			0
$551$		−	9189.96i		−	0.710536i
$552$		0			0
$553$	7575.33	+	4373.62i	0.582524	+	0.336320i
$554$		0			0
$555$	12386.7	−	21454.4i	0.947361	−	1.64088i
$556$		0			0
$557$	15869.4	−	9162.18i	1.20719	−	0.696973i	0.245048	−	0.969511i	$-0.421196\pi$
$557$	15869.4	−	9162.18i	1.20719	−	0.696973i	0.962145	+	0.272538i	$0.0878630\pi$
$558$		0			0
$559$	14029.6	+	7042.77i	1.06152	+	0.532875i
$560$		0			0
$561$	13616.8	−	7861.66i	1.02478	−	0.591657i
$562$		0			0
$563$	−5346.17	+	9259.85i	−0.400203	+	0.693172i	−0.993750	−	0.111627i	$-0.964394\pi$
$563$	−5346.17	+	9259.85i	−0.400203	+	0.693172i	0.593547	+	0.804799i	$0.297727\pi$
$564$		0			0
$565$	17649.2	+	10189.8i	1.31417	+	0.758739i
$566$		0			0
$567$		−	19487.7i		−	1.44340i
$568$		0			0
$569$	−11427.7	−	19793.4i	−0.841959	−	1.45832i	−0.888236	−	0.459387i	$-0.848069\pi$
$569$	−11427.7	−	19793.4i	−0.841959	−	1.45832i	0.0462777	−	0.998929i	$-0.485264\pi$
$570$		0			0
$571$	−14250.2			−1.04440			−0.522201	−	0.852823i	$-0.674889\pi$
$571$	−14250.2			−1.04440			−0.522201	+	0.852823i	$0.674889\pi$
$572$		0			0
$573$	28449.2			2.07414
$574$		0			0
$575$	21.0977	+	36.5424i	0.00153015	+	0.00265030i
$576$		0			0
$577$		−	825.523i		−	0.0595615i	−0.999556	−	0.0297808i	$-0.990519\pi$
$577$		−	825.523i		−	0.0595615i	0.999556	−	0.0297808i	$-0.00948091\pi$
$578$		0			0
$579$	4169.57	+	2407.30i	0.299277	+	0.172788i
$580$		0			0
$581$	−66.8999	+	115.874i	−0.00477706	+	0.00827412i
$582$		0			0
$583$	12678.4	−	7319.86i	0.900659	−	0.519996i
$584$		0			0
$585$	−19641.1	+	39126.2i	−1.38814	+	2.76525i
$586$		0			0
$587$	14716.0	−	8496.28i	1.03474	−	0.597409i	0.116402	−	0.993202i	$-0.462864\pi$
$587$	14716.0	−	8496.28i	1.03474	−	0.597409i	0.918340	+	0.395794i	$0.129530\pi$
$588$		0			0
$589$	−9965.64	+	17261.0i	−0.697159	+	1.20752i
$590$		0			0
$591$	35263.0	+	20359.1i	2.45436	+	1.41703i
$592$		0			0
$593$			16385.5i			1.13469i	0.823480	+	0.567345i	$0.192029\pi$
$593$			16385.5i			1.13469i	−0.823480	+	0.567345i	$0.807971\pi$
$594$		0			0
$595$	1555.23	+	2693.73i	0.107157	+	0.185601i
$596$		0			0
$597$	−22443.1			−1.53858
$598$		0			0
$599$	12913.8			0.880874			0.440437	−	0.897783i	$-0.354823\pi$
$599$	12913.8			0.880874			0.440437	+	0.897783i	$0.354823\pi$
$600$		0			0
$601$	−3796.96	−	6576.53i	−0.257706	−	0.446360i	0.707921	−	0.706292i	$-0.249633\pi$
$601$	−3796.96	−	6576.53i	−0.257706	−	0.446360i	−0.965627	+	0.259932i	$0.916300\pi$
$602$		0			0
$603$			16976.7i			1.14651i
$604$		0			0
$605$	−16897.9	−	9756.01i	−1.13553	−	0.655600i
$606$		0			0
$607$	2634.63	−	4563.32i	0.176172	−	0.305139i	−0.764394	−	0.644749i	$-0.776962\pi$
$607$	2634.63	−	4563.32i	0.176172	−	0.305139i	0.940566	+	0.339610i	$0.110295\pi$
$608$		0			0
$609$	4317.81	−	2492.89i	0.287301	−	0.165873i
$610$		0			0
$611$	2472.47	−	144.450i	0.163708	−	0.00956437i
$612$		0			0
$613$	10235.5	−	5909.45i	0.674399	−	0.389365i	−0.123342	−	0.992364i	$-0.539361\pi$
$613$	10235.5	−	5909.45i	0.674399	−	0.389365i	0.797742	+	0.603000i	$0.206028\pi$
$614$		0			0
$615$	−1420.66	+	2460.65i	−0.0931488	+	0.161338i
$616$		0			0
$617$	13494.2	+	7790.89i	0.880480	+	0.508346i	0.870817	−	0.491608i	$-0.163591\pi$
$617$	13494.2	+	7790.89i	0.880480	+	0.508346i	0.00966362	+	0.999953i	$0.496924\pi$
$618$		0			0
$619$			14605.8i			0.948393i	0.880419	+	0.474197i	$0.157261\pi$
$619$			14605.8i			0.948393i	−0.880419	+	0.474197i	$0.842739\pi$
$620$		0			0
$621$	202.085	+	350.022i	0.0130586	+	0.0226182i
$622$		0			0
$623$	711.110			0.0457304
$624$		0			0
$625$	−19259.4			−1.23260
$626$		0			0
$627$	−38431.7	−	66565.6i	−2.44787	−	4.23983i
$628$		0			0
$629$			5695.82i			0.361061i
$630$		0			0
$631$	−2139.86	−	1235.45i	−0.135002	−	0.0779435i	0.430978	−	0.902363i	$-0.358169\pi$
$631$	−2139.86	−	1235.45i	−0.135002	−	0.0779435i	−0.565980	+	0.824419i	$0.691502\pi$
$632$		0			0
$633$	−10629.0	+	18410.0i	−0.667400	+	1.15597i
$634$		0			0
$635$	27271.8	−	15745.4i	1.70433	−	0.983996i
$636$		0			0
$637$	10940.9	−	7198.76i	0.680525	−	0.447763i
$638$		0			0
$639$	−7933.74	+	4580.55i	−0.491164	+	0.283574i
$640$		0			0
$641$	−5113.13	+	8856.20i	−0.315065	+	0.545708i	−0.979451	−	0.201681i	$-0.935360\pi$
$641$	−5113.13	+	8856.20i	−0.315065	+	0.545708i	0.664387	+	0.747389i	$0.268693\pi$
$642$		0			0
$643$	14533.9	+	8391.17i	0.891388	+	0.514643i	0.874396	−	0.485213i	$-0.161258\pi$
$643$	14533.9	+	8391.17i	0.891388	+	0.514643i	0.0169917	+	0.999856i	$0.494591\pi$
$644$		0			0
$645$		−	43450.4i		−	2.65249i
$646$		0			0
$647$	−13451.5	−	23298.7i	−0.817363	−	1.41571i	−0.907619	−	0.419796i	$-0.862102\pi$
$647$	−13451.5	−	23298.7i	−0.817363	−	1.41571i	0.0902557	−	0.995919i	$-0.471232\pi$
$648$		0			0
$649$	−21672.4			−1.31081
$650$		0			0
$651$	−10813.2			−0.651003
$652$		0			0
$653$	13652.4	+	23646.6i	0.818162	+	1.41710i	0.907035	+	0.421054i	$0.138340\pi$
$653$	13652.4	+	23646.6i	0.818162	+	1.41710i	−0.0888738	+	0.996043i	$0.528327\pi$
$654$		0			0
$655$			14247.9i			0.849940i
$656$		0			0
$657$	17766.8	+	10257.7i	1.05502	+	0.609118i
$658$		0			0
$659$	1311.03	−	2270.77i	0.0774970	−	0.134229i	−0.824672	−	0.565611i	$-0.808641\pi$
$659$	1311.03	−	2270.77i	0.0774970	−	0.134229i	0.902169	+	0.431382i	$0.141974\pi$
$660$		0			0
$661$	−19228.2	+	11101.4i	−1.13145	+	0.653243i	−0.944299	−	0.329088i	$-0.893259\pi$
$661$	−19228.2	+	11101.4i	−1.13145	+	0.653243i	−0.187151	+	0.982331i	$0.559925\pi$
$662$		0			0
$663$	−808.995	−	13847.1i	−0.0473888	−	0.811125i
$664$		0			0
$665$	13168.3	−	7602.72i	0.767887	−	0.443340i
$666$		0			0
$667$	−28.8985	+	50.0537i	−0.00167759	+	0.00290567i
$668$		0			0
$669$	−3356.91	−	1938.11i	−0.194000	−	0.112006i
$670$		0			0
$671$			42709.4i			2.45720i
$672$		0			0
$673$	−14782.6	−	25604.2i	−0.846698	−	1.46652i	−0.884139	−	0.467225i	$-0.845254\pi$
$673$	−14782.6	−	25604.2i	−0.846698	−	1.46652i	0.0374410	−	0.999299i	$-0.488079\pi$
$674$		0			0
$675$	20278.2			1.15631
$676$		0			0
$677$	−18866.9			−1.07107			−0.535536	−	0.844512i	$-0.679890\pi$
$677$	−18866.9			−1.07107			−0.535536	+	0.844512i	$0.679890\pi$
$678$		0			0
$679$	4639.35	+	8035.59i	0.262212	+	0.454164i
$680$		0			0
$681$			8613.71i			0.484696i
$682$		0			0
$683$	−21372.4	−	12339.3i	−1.19735	−	0.691291i	−0.237388	−	0.971415i	$-0.576291\pi$
$683$	−21372.4	−	12339.3i	−1.19735	−	0.691291i	−0.959964	+	0.280123i	$0.909625\pi$
$684$		0			0
$685$	17203.0	−	29796.5i	0.959552	−	1.66199i
$686$		0			0
$687$	40768.5	−	23537.7i	2.26407	−	1.30716i
$688$		0			0
$689$	−753.241	−	12892.8i	−0.0416491	−	0.712882i
$690$		0			0
$691$	417.904	−	241.277i	0.0230070	−	0.0132831i	−0.488452	−	0.872591i	$-0.662438\pi$
$691$	417.904	−	241.277i	0.0230070	−	0.0132831i	0.511459	+	0.859307i	$0.329105\pi$
$692$		0			0
$693$	15130.4	−	26206.7i	0.829375	−	1.43652i
$694$		0			0
$695$	15668.4	+	9046.16i	0.855161	+	0.493727i
$696$		0			0
$697$		−	653.268i		−	0.0355011i
$698$		0			0
$699$	−21410.0	−	37083.2i	−1.15851	−	2.00660i
$700$		0			0
$701$	17704.2			0.953894			0.476947	−	0.878932i	$-0.341743\pi$
$701$	17704.2			0.953894			0.476947	+	0.878932i	$0.341743\pi$
$702$		0			0
$703$	27844.0			1.49382
$704$		0			0
$705$	−3427.58	−	5936.75i	−0.183107	−	0.317150i
$706$		0			0
$707$		−	1277.45i		−	0.0679540i
$708$		0			0
$709$	5929.81	+	3423.58i	0.314102	+	0.181347i	0.648761	−	0.760992i	$-0.275288\pi$
$709$	5929.81	+	3423.58i	0.314102	+	0.181347i	−0.334658	+	0.942340i	$0.608621\pi$
$710$		0			0
$711$	−39174.6	+	67852.4i	−2.06633	+	3.57899i
$712$		0			0
$713$	108.557	−	62.6753i	0.00570194	−	0.00329202i
$714$		0			0
$715$	−27206.8	+	17901.2i	−1.42304	+	0.936317i
$716$		0			0
$717$	−14088.8	+	8134.19i	−0.733831	+	0.423677i
$718$		0			0
$719$	−5338.29	+	9246.18i	−0.276891	+	0.479589i	−0.970610	−	0.240656i	$-0.922637\pi$
$719$	−5338.29	+	9246.18i	−0.276891	+	0.479589i	0.693720	+	0.720245i	$0.255971\pi$
$720$		0			0
$721$	−12201.3	−	7044.44i	−0.630237	−	0.363868i
$722$		0			0
$723$		−	27316.9i		−	1.40515i
$724$		0			0
$725$	1449.91	+	2511.32i	0.0742735	+	0.128646i
$726$		0			0
$727$	−1862.62			−0.0950219			−0.0475109	−	0.998871i	$-0.515129\pi$
$727$	−1862.62			−0.0950219			−0.0475109	+	0.998871i	$0.515129\pi$
$728$		0			0
$729$	56499.1			2.87045
$730$		0			0
$731$	4995.00	+	8651.59i	0.252731	+	0.437743i
$732$		0			0
$733$			21157.6i			1.06613i	0.846075	+	0.533064i	$0.178960\pi$
$733$			21157.6i			1.06613i	−0.846075	+	0.533064i	$0.821040\pi$
$734$		0			0
$735$	−31393.7	−	18125.2i	−1.57547	−	0.909601i
$736$		0			0
$737$	−6314.54	+	10937.1i	−0.315603	+	0.546640i
$738$		0			0
$739$	−12971.4	+	7489.05i	−0.645685	+	0.372786i	−0.786801	−	0.617207i	$-0.788264\pi$
$739$	−12971.4	+	7489.05i	−0.645685	+	0.372786i	0.141116	+	0.989993i	$0.454931\pi$
$740$		0			0
$741$	−67691.4	+	3954.77i	−3.35588	+	0.196062i
$742$		0			0
$743$	−20676.3	+	11937.5i	−1.02092	+	0.589426i	−0.914369	−	0.404882i	$-0.867313\pi$
$743$	−20676.3	+	11937.5i	−1.02092	+	0.589426i	−0.106546	+	0.994308i	$0.533979\pi$
$744$		0			0
$745$	14615.2	−	25314.3i	0.718740	−	1.24489i
$746$		0			0
$747$	−1037.89	−	599.224i	−0.0508357	−	0.0293500i
$748$		0			0
$749$			313.596i			0.0152985i
$750$		0			0
$751$	−19389.1	−	33582.8i	−0.942099	−	1.63176i	−0.761457	−	0.648215i	$-0.775516\pi$
$751$	−19389.1	−	33582.8i	−0.942099	−	1.63176i	−0.180642	−	0.983549i	$-0.557818\pi$
$752$		0			0
$753$	1478.65			0.0715604
$754$		0			0
$755$	26006.4			1.25360
$756$		0			0
$757$	−15543.1	−	26921.4i	−0.746265	−	1.29257i	−0.949602	−	0.313459i	$-0.898512\pi$
$757$	−15543.1	−	26921.4i	−0.746265	−	1.29257i	0.203337	−	0.979109i	$-0.434821\pi$
$758$		0			0
$759$			483.405i			0.0231179i
$760$		0			0
$761$	22293.5	+	12871.2i	1.06194	+	0.613113i	0.925969	−	0.377599i	$-0.123250\pi$
$761$	22293.5	+	12871.2i	1.06194	+	0.613113i	0.135974	+	0.990712i	$0.456584\pi$
$762$		0			0
$763$	2470.08	−	4278.30i	0.117199	−	0.202995i
$764$		0			0
$765$	−24127.9	+	13930.2i	−1.14032	+	0.658364i
$766$		0			0
$767$	−8577.43	+	17086.7i	−0.403798	+	0.804388i
$768$		0			0
$769$	−16462.0	+	9504.35i	−0.771958	+	0.445690i	−0.833573	−	0.552410i	$-0.813708\pi$
$769$	−16462.0	+	9504.35i	−0.771958	+	0.445690i	0.0616146	+	0.998100i	$0.480375\pi$
$770$		0			0
$771$	−2780.15	+	4815.36i	−0.129863	+	0.224930i
$772$		0			0
$773$	31509.8	+	18192.2i	1.46614	+	0.846478i	0.999283	−	0.0378528i	$-0.0120518\pi$
$773$	31509.8	+	18192.2i	1.46614	+	0.846478i	0.466860	+	0.884331i	$0.345385\pi$
$774$		0			0
$775$		−	6289.16i		−	0.291501i
$776$		0			0
$777$	7553.02	+	13082.2i	0.348730	+	0.604018i
$778$		0			0
$779$	−3193.50			−0.146879
$780$		0			0
$781$	−6815.01			−0.312241
$782$		0			0
$783$	13888.0	+	24054.7i	0.633865	+	1.09789i
$784$		0			0
$785$			1499.85i			0.0681937i
$786$		0			0
$787$	8379.12	+	4837.69i	0.379522	+	0.219117i	0.677610	−	0.735421i	$-0.263016\pi$
$787$	8379.12	+	4837.69i	0.379522	+	0.219117i	−0.298089	+	0.954538i	$0.596349\pi$
$788$		0			0
$789$	−16198.9	+	28057.3i	−0.730921	+	1.26599i
$790$		0			0
$791$	−10762.0	+	6213.42i	−0.483756	+	0.279297i
$792$		0			0
$793$	33672.6	+	16903.4i	1.50788	+	0.756946i
$794$		0			0
$795$	−30957.4	+	17873.3i	−1.38106	+	0.797358i
$796$		0			0
$797$	−16453.8	+	28498.8i	−0.731271	+	1.26660i	0.225069	+	0.974343i	$0.427739\pi$
$797$	−16453.8	+	28498.8i	−0.731271	+	1.26660i	−0.956340	+	0.292256i	$0.905594\pi$
$798$		0			0
$799$	1364.96	+	788.060i	0.0604365	+	0.0348930i
$800$		0			0
$801$			6369.44i			0.280965i
$802$		0			0
$803$	7630.77	+	13216.9i	0.335347	+	0.580839i
$804$		0			0
$805$	−95.6292			−0.00418694
$806$		0			0
$807$	29726.6			1.29669
$808$		0			0
$809$	−6717.93	−	11635.8i	−0.291953	−	0.505677i	0.682319	−	0.731055i	$-0.260972\pi$
$809$	−6717.93	−	11635.8i	−0.291953	−	0.505677i	−0.974271	+	0.225378i	$0.927638\pi$
$810$		0			0
$811$			4276.62i			0.185169i	0.995705	+	0.0925847i	$0.0295129\pi$
$811$			4276.62i			0.185169i	−0.995705	+	0.0925847i	$0.970487\pi$
$812$		0			0
$813$	33310.3	+	19231.7i	1.43695	+	0.829626i
$814$		0			0
$815$	−1836.74	+	3181.33i	−0.0789427	+	0.136733i
$816$		0			0
$817$	42293.2	−	24418.0i	1.81108	−	1.04563i
$818$		0			0
$819$	−14673.3	−	22301.0i	−0.626041	−	0.951477i
$820$		0			0
$821$	−13381.4	+	7725.77i	−0.568837	+	0.328418i	−0.756685	−	0.653780i	$-0.773182\pi$
$821$	−13381.4	+	7725.77i	−0.568837	+	0.328418i	0.187848	+	0.982198i	$0.439849\pi$
$822$		0			0
$823$	10604.9	−	18368.3i	0.449167	−	0.777981i	−0.549165	−	0.835714i	$-0.685054\pi$
$823$	10604.9	−	18368.3i	0.449167	−	0.777981i	0.998332	+	0.0577335i	$0.0183874\pi$
$824$		0			0
$825$	21004.3	+	12126.8i	0.886393	+	0.511759i
$826$		0			0
$827$		−	9065.79i		−	0.381195i	−0.981668	−	0.190597i	$-0.938957\pi$
$827$		−	9065.79i		−	0.381195i	0.981668	−	0.190597i	$-0.0610425\pi$
$828$		0			0
$829$	−1004.46	−	1739.78i	−0.0420826	−	0.0728891i	0.844217	−	0.536002i	$-0.180066\pi$
$829$	−1004.46	−	1739.78i	−0.0420826	−	0.0728891i	−0.886300	+	0.463113i	$0.846733\pi$
$830$		0			0
$831$	−22373.0			−0.933950
$832$		0			0
$833$	8334.56			0.346669
$834$		0			0
$835$	8450.22	+	14636.2i	0.350218	+	0.606595i
$836$		0			0
$837$		−	60240.8i		−	2.48772i
$838$		0			0
$839$	−15848.7	−	9150.27i	−0.652156	−	0.376523i	0.137126	−	0.990554i	$-0.456214\pi$
$839$	−15848.7	−	9150.27i	−0.652156	−	0.376523i	−0.789282	+	0.614031i	$0.789547\pi$
$840$		0			0
$841$	10208.5	−	17681.6i	0.418570	−	0.724984i
$842$		0			0
$843$	−19303.5	+	11144.9i	−0.788670	+	0.455339i
$844$		0			0
$845$	3345.65	+	28535.0i	0.136206	+	1.16170i
$846$		0			0
$847$	10303.8	−	5948.91i	0.417997	−	0.241331i
$848$		0			0
$849$	−405.838	+	702.931i	−0.0164056	+	0.0284152i
$850$		0			0
$851$	−151.654	−	87.5574i	−0.00610885	−	0.00352694i
$852$		0			0
$853$		−	24134.0i		−	0.968737i	−0.874864	−	0.484369i	$-0.839049\pi$
$853$		−	24134.0i		−	0.968737i	0.874864	−	0.484369i	$-0.160951\pi$
$854$		0			0
$855$	68097.8	+	117949.i	2.72386	+	4.71786i
$856$		0			0
$857$	−44247.3			−1.76366			−0.881831	−	0.471565i	$-0.843689\pi$
$857$	−44247.3			−1.76366			−0.881831	+	0.471565i	$0.843689\pi$
$858$		0			0
$859$	−3684.50			−0.146348			−0.0731742	−	0.997319i	$-0.523313\pi$
$859$	−3684.50			−0.146348			−0.0731742	+	0.997319i	$0.523313\pi$
$860$		0			0
$861$	−866.274	−	1500.43i	−0.0342887	−	0.0593897i
$862$		0			0
$863$			10915.4i			0.430549i	0.976554	+	0.215275i	$0.0690647\pi$
$863$			10915.4i			0.430549i	−0.976554	+	0.215275i	$0.930935\pi$
$864$		0			0
$865$	−32640.2	−	18844.8i	−1.28301	−	0.740745i
$866$		0			0
$867$	−19957.1	+	34566.7i	−0.781751	+	1.35403i
$868$		0			0
$869$	−50475.9	+	29142.3i	−1.97040	+	1.13761i
$870$		0			0
$871$	6123.78	+	9307.11i	0.238228	+	0.362066i
$872$		0			0
$873$	−71975.0	+	41554.8i	−2.79036	+	1.61102i
$874$		0			0
$875$	4118.36	−	7133.21i	0.159116	−	0.275596i
$876$		0			0
$877$	−34436.5	−	19881.9i	−1.32593	−	0.765524i	−0.341259	−	0.939969i	$-0.610853\pi$
$877$	−34436.5	−	19881.9i	−1.32593	−	0.765524i	−0.984667	+	0.174446i	$0.944187\pi$
$878$		0			0
$879$		−	48269.8i		−	1.85222i
$880$		0			0
$881$	21303.2	+	36898.2i	0.814669	+	1.41105i	0.909566	+	0.415561i	$0.136415\pi$
$881$	21303.2	+	36898.2i	0.814669	+	1.41105i	−0.0948967	+	0.995487i	$0.530252\pi$
$882$		0			0
$883$	−33991.7			−1.29548			−0.647742	−	0.761860i	$-0.724286\pi$
$883$	−33991.7			−1.29548			−0.647742	+	0.761860i	$0.724286\pi$
$884$		0			0
$885$	52918.5			2.00999
$886$		0			0
$887$	−21552.9	−	37330.7i	−0.815868	−	1.41313i	−0.908703	−	0.417444i	$-0.862926\pi$
$887$	−21552.9	−	37330.7i	−0.815868	−	1.41313i	0.0928342	−	0.995682i	$-0.470407\pi$
$888$		0			0
$889$			19202.1i			0.724430i
$890$		0			0
$891$	112454.	+	64925.4i	4.22823	+	2.44117i
$892$		0			0
$893$	3852.43	−	6672.60i	0.144363	−	0.250045i
$894$		0			0
$895$	−52312.5	+	30202.6i	−1.95376	+	1.12800i
$896$		0			0
$897$	381.121	+	191.321i	0.0141865	+	0.00712153i
$898$		0			0
$899$	7460.40	−	4307.26i	0.276772	−	0.159795i
$900$		0			0
$901$	4109.37	−	7117.64i	0.151946	−	0.263177i
$902$		0			0
$903$	22945.1	+	13247.4i	0.845587	+	0.488200i
$904$		0			0
$905$		−	5775.39i		−	0.212133i
$906$		0			0
$907$	−12731.1	−	22051.0i	−0.466075	−	0.807266i	0.533174	−	0.846006i	$-0.320999\pi$
$907$	−12731.1	−	22051.0i	−0.466075	−	0.807266i	−0.999249	+	0.0387394i	$0.987666\pi$
$908$		0			0
$909$	11442.2			0.417506
$910$		0			0
$911$	−25207.3			−0.916747			−0.458374	−	0.888760i	$-0.651568\pi$
$911$	−25207.3			−0.916747			−0.458374	+	0.888760i	$0.651568\pi$
$912$		0			0
$913$	−445.767	−	772.092i	−0.0161585	−	0.0279874i
$914$		0			0
$915$		−	104286.i		−	3.76785i
$916$		0			0
$917$	−7523.95	−	4343.96i	−0.270952	−	0.156434i
$918$		0			0
$919$	−2845.03	+	4927.74i	−0.102121	+	0.176878i	−0.912558	−	0.408947i	$-0.865896\pi$
$919$	−2845.03	+	4927.74i	−0.102121	+	0.176878i	0.810438	+	0.585825i	$0.199229\pi$
$920$		0			0
$921$	22989.4	−	13272.9i	0.822505	−	0.474873i
$922$		0			0
$923$	−2697.22	+	5373.02i	−0.0961866	+	0.191609i
$924$		0			0
$925$	−7608.86	+	4392.98i	−0.270462	+	0.156152i
$926$		0			0
$927$	63097.2	−	109288.i	2.23558	−	3.87214i
$928$		0			0
$929$	19008.8	+	10974.7i	0.671321	+	0.387587i	0.796577	−	0.604537i	$-0.206642\pi$
$929$	19008.8	+	10974.7i	0.671321	+	0.387587i	−0.125256	+	0.992124i	$0.539975\pi$
$930$		0			0
$931$		−	40743.5i		−	1.43428i
$932$		0			0
$933$	−21598.9	−	37410.4i	−0.757895	−	1.31271i
$934$		0			0
$935$	−20725.6			−0.724919
$936$		0			0
$937$	36285.1			1.26508			0.632541	−	0.774527i	$-0.282012\pi$
$937$	36285.1			1.26508			0.632541	+	0.774527i	$0.282012\pi$
$938$		0			0
$939$	−135.885	−	235.360i	−0.00472252	−	0.00817964i
$940$		0			0
$941$		−	18017.2i		−	0.624170i	−0.950054	−	0.312085i	$-0.898973\pi$
$941$		−	18017.2i		−	0.624170i	0.950054	−	0.312085i	$-0.101027\pi$
$942$		0			0
$943$	17.3936	+	10.0422i	0.000600649	+	0.000346785i
$944$		0			0
$945$	−22978.7	+	39800.2i	−0.791001	+	1.37005i
$946$		0			0
$947$	40360.8	−	23302.3i	1.38495	−	0.799603i	0.392211	−	0.919875i	$-0.371710\pi$
$947$	40360.8	−	23302.3i	1.38495	−	0.799603i	0.992741	+	0.120273i	$0.0383769\pi$
$948$		0			0
$949$	13440.4	−	785.236i	0.459741	−	0.0268597i
$950$		0			0
$951$	26516.7	−	15309.4i	0.904168	−	0.522021i
$952$		0			0
$953$	−4905.45	+	8496.49i	−0.166740	+	0.288802i	−0.937272	−	0.348599i	$-0.886657\pi$
$953$	−4905.45	+	8496.49i	−0.166740	+	0.288802i	0.770532	+	0.637402i	$0.219991\pi$
$954$		0			0
$955$	−32476.1	−	18750.1i	−1.10042	−	0.635328i
$956$		0			0
$957$			33221.2i			1.12214i
$958$		0			0
$959$	10489.9	+	18169.0i	0.353217	+	0.611790i
$960$		0			0
$961$	11107.7			0.372855
$962$		0			0
$963$	−2808.89			−0.0939931
$964$		0			0
$965$	−3173.17	−	5496.09i	−0.105853	−	0.183342i
$966$		0			0
$967$		−	10999.6i		−	0.365796i	−0.983132	−	0.182898i	$-0.941452\pi$
$967$		−	10999.6i		−	0.365796i	0.983132	−	0.182898i	$-0.0585478\pi$
$968$		0			0
$969$	−37369.9	−	21575.5i	−1.23890	−	0.715280i
$970$		0			0
$971$	12479.0	−	21614.3i	0.412431	−	0.714351i	−0.582724	−	0.812670i	$-0.698013\pi$
$971$	12479.0	−	21614.3i	0.412431	−	0.714351i	0.995155	+	0.0983187i	$0.0313464\pi$
$972$		0			0
$973$	−9554.11	+	5516.07i	−0.314790	+	0.181744i
$974$		0			0
$975$	17873.9	−	11760.5i	0.587101	−	0.386293i
$976$		0			0
$977$	14493.6	−	8367.89i	0.474608	−	0.274015i	−0.243559	−	0.969886i	$-0.578315\pi$
$977$	14493.6	−	8367.89i	0.474608	−	0.274015i	0.718167	+	0.695871i	$0.244982\pi$
$978$		0			0
$979$	−2369.14	+	4103.46i	−0.0773421	+	0.133960i
$980$		0			0
$981$	38320.9	+	22124.6i	1.24719	+	0.720065i
$982$		0			0
$983$			10160.6i			0.329677i	0.986321	+	0.164838i	$0.0527102\pi$
$983$			10160.6i			0.329677i	−0.986321	+	0.164838i	$0.947290\pi$
$984$		0			0
$985$	−26836.2	−	46481.7i	−0.868095	−	1.50359i
$986$		0			0
$987$	4180.07			0.134805
$988$		0			0
$989$	−307.137			−0.00987500
$990$		0			0
$991$	18489.5	+	32024.8i	0.592673	+	1.02654i	0.993871	+	0.110548i	$0.0352605\pi$
$991$	18489.5	+	32024.8i	0.592673	+	1.02654i	−0.401198	+	0.915991i	$0.631406\pi$
$992$		0			0
$993$		−	56894.6i		−	1.81822i
$994$		0			0
$995$	25619.8	+	14791.6i	0.816284	+	0.471282i
$996$		0			0
$997$	−6139.86	+	10634.5i	−0.195036	+	0.337813i	−0.946912	−	0.321492i	$-0.895816\pi$
$997$	−6139.86	+	10634.5i	−0.195036	+	0.337813i	0.751876	+	0.659304i	$0.229149\pi$
$998$		0			0
$999$	−72881.5	+	42078.2i	−2.30818	+	1.33263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.w.e.49.10		20
4.3	odd	2		104.4.o.a.49.1	yes	20
13.4	even	6	inner	208.4.w.e.17.10		20
52.11	even	12		1352.4.a.p.1.10		10
52.15	even	12		1352.4.a.o.1.10		10
52.43	odd	6		104.4.o.a.17.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.4.o.a.17.1	✓	20	52.43	odd	6
104.4.o.a.49.1	yes	20	4.3	odd	2
208.4.w.e.17.10		20	13.4	even	6	inner
208.4.w.e.49.10		20	1.1	even	1	trivial
1352.4.a.o.1.10		10	52.15	even	12
1352.4.a.p.1.10		10	52.11	even	12

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.96043 + 8.59173i) q^{3} -13.0771i q^{5} +(6.90571 + 3.98702i) q^{7} +(-35.7118 + 61.8547i) q^{9} +O(q^{10})\)	\(q+(4.96043 + 8.59173i) q^{3} -13.0771i q^{5} +(6.90571 + 3.98702i) q^{7} +(-35.7118 + 61.8547i) q^{9} +(-46.0142 + 26.5663i) q^{11} +(2.73377 + 46.7924i) q^{13} +(112.355 - 64.8683i) q^{15} +(-14.9143 + 25.8324i) q^{17} +(126.281 + 72.9086i) q^{19} +79.1093i q^{21} +(-0.458532 - 0.794202i) q^{23} -46.0115 q^{25} -440.721 q^{27} +(-31.5119 - 54.5803i) q^{29} +136.687i q^{31} +(-456.501 - 263.561i) q^{33} +(52.1387 - 90.3070i) q^{35} +(165.369 - 95.4757i) q^{37} +(-388.467 + 255.598i) q^{39} +(-18.9665 + 10.9503i) q^{41} +(167.456 - 290.043i) q^{43} +(808.882 + 467.008i) q^{45} -52.8391i q^{47} +(-139.707 - 241.980i) q^{49} -295.926 q^{51} -275.532 q^{53} +(347.411 + 601.734i) q^{55} +1446.63i q^{57} +(353.245 + 203.946i) q^{59} +(401.914 - 696.135i) q^{61} +(-493.231 + 284.767i) q^{63} +(611.910 - 35.7499i) q^{65} +(205.846 - 118.845i) q^{67} +(4.54904 - 7.87917i) q^{69} +(111.080 + 64.1321i) q^{71} -287.235i q^{73} +(-228.237 - 395.318i) q^{75} -423.681 q^{77} +1096.96 q^{79} +(-1221.95 - 2116.48i) q^{81} +16.7794i q^{83} +(337.813 + 195.037i) q^{85} +(312.626 - 541.484i) q^{87} +(77.2306 - 44.5891i) q^{89} +(-167.683 + 334.034i) q^{91} +(-1174.38 + 678.026i) q^{93} +(953.435 - 1651.40i) q^{95} +(1007.72 + 581.807i) q^{97} -3794.92i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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