LMFDB - Embedded newform 15.4.b.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,4,Mod(4,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("15.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	15.b (of order $2$, degree $1$, 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:	$0.885028650086$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 21x^{2} + 100 $ x^4 + 21*x^2 + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.3
Root			$2.70156i$ of defining polynomial
Character	$\chi$	$=$	15.4
Dual form			15.4.b.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.70156i q^{2} +3.00000i q^{3} +5.10469 q^{4} +(-8.10469 - 7.70156i) q^{5} -5.10469 q^{6} -22.2094i q^{7} +22.2984i q^{8} -9.00000 q^{9} +(13.1047 - 13.7906i) q^{10} -1.79063 q^{11} +15.3141i q^{12} +58.2094i q^{13} +37.7906 q^{14} +(23.1047 - 24.3141i) q^{15} +2.89531 q^{16} -18.9844i q^{17} -15.3141i q^{18} -104.837 q^{19} +(-41.3719 - 39.3141i) q^{20} +66.6281 q^{21} -3.04686i q^{22} -49.6125i q^{23} -66.8953 q^{24} +(6.37188 + 124.837i) q^{25} -99.0469 q^{26} -27.0000i q^{27} -113.372i q^{28} +293.466 q^{29} +(41.3719 + 39.3141i) q^{30} +64.4187 q^{31} +183.314i q^{32} -5.37188i q^{33} +32.3031 q^{34} +(-171.047 + 180.000i) q^{35} -45.9422 q^{36} +19.8844i q^{37} -178.388i q^{38} -174.628 q^{39} +(171.733 - 180.722i) q^{40} -165.581 q^{41} +113.372i q^{42} -247.350i q^{43} -9.14059 q^{44} +(72.9422 + 69.3141i) q^{45} +84.4187 q^{46} -384.544i q^{47} +8.68594i q^{48} -150.256 q^{49} +(-212.419 + 10.8422i) q^{50} +56.9531 q^{51} +297.141i q^{52} +463.528i q^{53} +45.9422 q^{54} +(14.5125 + 13.7906i) q^{55} +495.234 q^{56} -314.512i q^{57} +499.350i q^{58} +73.7906 q^{59} +(117.942 - 124.116i) q^{60} -137.350 q^{61} +109.612i q^{62} +199.884i q^{63} -288.758 q^{64} +(448.303 - 471.769i) q^{65} +9.14059 q^{66} -173.906i q^{67} -96.9093i q^{68} +148.837 q^{69} +(-306.281 - 291.047i) q^{70} -594.281 q^{71} -200.686i q^{72} +320.231i q^{73} -33.8345 q^{74} +(-374.512 + 19.1156i) q^{75} -535.163 q^{76} +39.7687i q^{77} -297.141i q^{78} +770.469 q^{79} +(-23.4656 - 22.2984i) q^{80} +81.0000 q^{81} -281.747i q^{82} +173.925i q^{83} +340.116 q^{84} +(-146.209 + 153.862i) q^{85} +420.881 q^{86} +880.397i q^{87} -39.9282i q^{88} -1019.02 q^{89} +(-117.942 + 124.116i) q^{90} +1292.79 q^{91} -253.256i q^{92} +193.256i q^{93} +654.325 q^{94} +(849.675 + 807.412i) q^{95} -549.942 q^{96} -384.375i q^{97} -255.670i q^{98} +16.1156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{4} + 6 q^{5} + 18 q^{6} - 36 q^{9} + 14 q^{10} - 84 q^{11} + 228 q^{14} + 54 q^{15} + 50 q^{16} - 112 q^{19} - 396 q^{20} + 36 q^{21} - 306 q^{24} + 256 q^{25} - 12 q^{26} + 636 q^{29} + 396 q^{30}+ \cdots + 756 q^{99}+O(q^{100}) $ 4 * q - 18 * q^4 + 6 * q^5 + 18 * q^6 - 36 * q^9 + 14 * q^10 - 84 * q^11 + 228 * q^14 + 54 * q^15 + 50 * q^16 - 112 * q^19 - 396 * q^20 + 36 * q^21 - 306 * q^24 + 256 * q^25 - 12 * q^26 + 636 * q^29 + 396 * q^30 + 104 * q^31 - 716 * q^34 - 300 * q^35 + 162 * q^36 - 468 * q^39 + 418 * q^40 - 816 * q^41 + 1116 * q^44 - 54 * q^45 + 184 * q^46 - 140 * q^49 - 696 * q^50 + 612 * q^51 - 162 * q^54 - 864 * q^55 + 60 * q^56 + 372 * q^59 + 126 * q^60 + 680 * q^61 + 958 * q^64 + 948 * q^65 - 1116 * q^66 + 288 * q^69 + 1080 * q^70 - 72 * q^71 - 3132 * q^74 - 576 * q^75 - 2448 * q^76 - 760 * q^79 + 444 * q^80 + 324 * q^81 + 2052 * q^84 - 508 * q^85 + 4296 * q^86 - 2232 * q^89 - 126 * q^90 + 1944 * q^91 + 3232 * q^94 + 2784 * q^95 - 1854 * q^96 + 756 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.70156i			0.601593i	0.953688	+	0.300797i	$0.0972525\pi$
$2$			1.70156i			0.601593i	−0.953688	+	0.300797i	$0.902747\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	5.10469			0.638086
$5$	−8.10469	−	7.70156i	−0.724905	−	0.688849i
$5$	−8.10469	−	7.70156i	−0.724905	−	0.688849i
$6$	−5.10469			−0.347330
$7$		−	22.2094i		−	1.19919i	−0.800302	−	0.599597i	$-0.795328\pi$
$7$		−	22.2094i		−	1.19919i	0.800302	−	0.599597i	$-0.204672\pi$
$8$			22.2984i			0.985461i
$9$	−9.00000			−0.333333
$10$	13.1047	−	13.7906i	0.414407	−	0.436098i
$11$	−1.79063			−0.0490813			−0.0245407	−	0.999699i	$-0.507812\pi$
$11$	−1.79063			−0.0490813			−0.0245407	+	0.999699i	$0.507812\pi$
$12$			15.3141i			0.368399i
$13$			58.2094i			1.24188i	0.783860	+	0.620938i	$0.213248\pi$
$13$			58.2094i			1.24188i	−0.783860	+	0.620938i	$0.786752\pi$
$14$	37.7906			0.721426
$15$	23.1047	−	24.3141i	0.397707	−	0.418524i
$16$	2.89531			0.0452393
$17$		−	18.9844i		−	0.270846i	−0.990788	−	0.135423i	$-0.956761\pi$
$17$		−	18.9844i		−	0.270846i	0.990788	−	0.135423i	$-0.0432394\pi$
$18$		−	15.3141i		−	0.200531i
$19$	−104.837			−1.26586			−0.632931	−	0.774208i	$-0.718148\pi$
$19$	−104.837			−1.26586			−0.632931	+	0.774208i	$0.718148\pi$
$20$	−41.3719	−	39.3141i	−0.462552	−	0.439545i
$21$	66.6281			0.692355
$22$		−	3.04686i		−	0.0295270i
$23$		−	49.6125i		−	0.449779i	−0.974384	−	0.224890i	$-0.927798\pi$
$23$		−	49.6125i		−	0.449779i	0.974384	−	0.224890i	$-0.0722021\pi$
$24$	−66.8953			−0.568956
$25$	6.37188	+	124.837i	0.0509751	+	0.998700i
$26$	−99.0469			−0.747103
$27$		−	27.0000i		−	0.192450i
$28$		−	113.372i		−	0.765188i
$29$	293.466			1.87914			0.939572	−	0.342350i	$-0.111223\pi$
$29$	293.466			1.87914			0.939572	+	0.342350i	$0.111223\pi$
$30$	41.3719	+	39.3141i	0.251781	+	0.239258i
$31$	64.4187			0.373224			0.186612	−	0.982434i	$-0.440249\pi$
$31$	64.4187			0.373224			0.186612	+	0.982434i	$0.440249\pi$
$32$			183.314i			1.01268i
$33$		−	5.37188i		−	0.0283371i
$34$	32.3031			0.162939
$35$	−171.047	+	180.000i	−0.826063	+	0.869302i
$36$	−45.9422			−0.212695
$37$			19.8844i			0.0883505i	0.999024	+	0.0441752i	$0.0140660\pi$
$37$			19.8844i			0.0883505i	−0.999024	+	0.0441752i	$0.985934\pi$
$38$		−	178.388i		−	0.761534i
$39$	−174.628			−0.716997
$40$	171.733	−	180.722i	0.678834	−	0.714366i
$41$	−165.581			−0.630718			−0.315359	−	0.948972i	$-0.602125\pi$
$41$	−165.581			−0.630718			−0.315359	+	0.948972i	$0.602125\pi$
$42$			113.372i			0.416516i
$43$		−	247.350i		−	0.877221i	−0.898677	−	0.438611i	$-0.855471\pi$
$43$		−	247.350i		−	0.877221i	0.898677	−	0.438611i	$-0.144529\pi$
$44$	−9.14059			−0.0313181
$45$	72.9422	+	69.3141i	0.241635	+	0.229616i
$46$	84.4187			0.270584
$47$		−	384.544i		−	1.19344i	−0.802451	−	0.596718i	$-0.796471\pi$
$47$		−	384.544i		−	1.19344i	0.802451	−	0.596718i	$-0.203529\pi$
$48$			8.68594i			0.0261189i
$49$	−150.256			−0.438065
$50$	−212.419	+	10.8422i	−0.600811	+	0.0306662i
$51$	56.9531			0.156373
$52$			297.141i			0.792423i
$53$			463.528i			1.20133i	0.799501	+	0.600665i	$0.205097\pi$
$53$			463.528i			1.20133i	−0.799501	+	0.600665i	$0.794903\pi$
$54$	45.9422			0.115777
$55$	14.5125	+	13.7906i	0.0355793	+	0.0338096i
$56$	495.234			1.18176
$57$		−	314.512i		−	0.730846i
$58$			499.350i			1.13048i
$59$	73.7906			0.162826			0.0814129	−	0.996680i	$-0.474057\pi$
$59$	73.7906			0.162826			0.0814129	+	0.996680i	$0.474057\pi$
$60$	117.942	−	124.116i	0.253771	−	0.267054i
$61$	−137.350			−0.288293			−0.144146	−	0.989556i	$-0.546044\pi$
$61$	−137.350			−0.288293			−0.144146	+	0.989556i	$0.546044\pi$
$62$			109.612i			0.224529i
$63$			199.884i			0.399731i
$64$	−288.758			−0.563980
$65$	448.303	−	471.769i	0.855464	−	0.900242i
$66$	9.14059			0.0170474
$67$		−	173.906i		−	0.317105i	−0.987351	−	0.158552i	$-0.949317\pi$
$67$		−	173.906i		−	0.317105i	0.987351	−	0.158552i	$-0.0506827\pi$
$68$		−	96.9093i		−	0.172823i
$69$	148.837			0.259680
$70$	−306.281	−	291.047i	−0.522966	−	0.496954i
$71$	−594.281			−0.993355			−0.496677	−	0.867935i	$-0.665447\pi$
$71$	−594.281			−0.993355			−0.496677	+	0.867935i	$0.665447\pi$
$72$		−	200.686i		−	0.328487i
$73$			320.231i			0.513428i	0.966487	+	0.256714i	$0.0826398\pi$
$73$			320.231i			0.513428i	−0.966487	+	0.256714i	$0.917360\pi$
$74$	−33.8345			−0.0531510
$75$	−374.512	+	19.1156i	−0.576600	+	0.0294305i
$76$	−535.163			−0.807728
$77$			39.7687i			0.0588580i
$78$		−	297.141i		−	0.431340i
$79$	770.469			1.09727			0.548636	−	0.836061i	$-0.315147\pi$
$79$	770.469			1.09727			0.548636	+	0.836061i	$0.315147\pi$
$80$	−23.4656	−	22.2984i	−0.0327942	−	0.0311630i
$81$	81.0000			0.111111
$82$		−	281.747i		−	0.379436i
$83$			173.925i			0.230009i	0.993365	+	0.115004i	$0.0366882\pi$
$83$			173.925i			0.230009i	−0.993365	+	0.115004i	$0.963312\pi$
$84$	340.116			0.441782
$85$	−146.209	+	153.862i	−0.186572	+	0.196338i
$86$	420.881			0.527730
$87$			880.397i			1.08492i
$88$		−	39.9282i		−	0.0483677i
$89$	−1019.02			−1.21367			−0.606834	−	0.794829i	$-0.707561\pi$
$89$	−1019.02			−1.21367			−0.606834	+	0.794829i	$0.707561\pi$
$90$	−117.942	+	124.116i	−0.138136	+	0.145366i
$91$	1292.79			1.48925
$92$		−	253.256i		−	0.286998i
$93$			193.256i			0.215481i
$94$	654.325			0.717962
$95$	849.675	+	807.412i	0.917630	+	0.871987i
$96$	−549.942			−0.584669
$97$		−	384.375i		−	0.402344i	−0.979556	−	0.201172i	$-0.935525\pi$
$97$		−	384.375i		−	0.402344i	0.979556	−	0.201172i	$-0.0644750\pi$
$98$		−	255.670i		−	0.263537i
$99$	16.1156			0.0163604
$100$	32.5265	+	637.256i	0.0325265	+	0.637256i
$101$	34.4906			0.0339796			0.0169898	−	0.999856i	$-0.494592\pi$
$101$	34.4906			0.0339796			0.0169898	+	0.999856i	$0.494592\pi$
$102$			96.9093i			0.0940730i
$103$		−	1756.30i		−	1.68013i	−0.542484	−	0.840066i	$-0.682516\pi$
$103$		−	1756.30i		−	1.68013i	0.542484	−	0.840066i	$-0.317484\pi$
$104$	−1297.98			−1.22382
$105$	−540.000	−	513.141i	−0.501891	−	0.476928i
$106$	−788.722			−0.722712
$107$			1361.74i			1.23032i	0.788403	+	0.615159i	$0.210908\pi$
$107$			1361.74i			1.23032i	−0.788403	+	0.615159i	$0.789092\pi$
$108$		−	137.827i		−	0.122800i
$109$	−321.119			−0.282180			−0.141090	−	0.989997i	$-0.545061\pi$
$109$	−321.119			−0.282180			−0.141090	+	0.989997i	$0.545061\pi$
$110$	−23.4656	+	24.6939i	−0.0203396	+	0.0214043i
$111$	−59.6531			−0.0510092
$112$		−	64.3031i		−	0.0542506i
$113$		−	1582.25i		−	1.31721i	−0.752487	−	0.658607i	$-0.771146\pi$
$113$		−	1582.25i		−	1.31721i	0.752487	−	0.658607i	$-0.228854\pi$
$114$	535.163			0.439672
$115$	−382.094	+	402.094i	−0.309830	+	0.326047i
$116$	1498.05			1.19906
$117$		−	523.884i		−	0.413958i
$118$			125.559i			0.0979549i
$119$	−421.631			−0.324797
$120$	542.166	+	515.198i	0.412439	+	0.391925i
$121$	−1327.79			−0.997591
$122$		−	233.709i		−	0.173435i
$123$		−	496.744i		−	0.364145i
$124$	328.837			0.238149
$125$	909.802	−	1060.84i	0.651001	−	0.759077i
$126$	−340.116			−0.240475
$127$			1197.14i			0.836449i	0.908344	+	0.418225i	$0.137348\pi$
$127$			1197.14i			0.836449i	−0.908344	+	0.418225i	$0.862652\pi$
$128$			975.173i			0.673390i
$129$	742.050			0.506464
$130$	802.744	+	762.816i	0.541579	+	0.514641i
$131$	−321.647			−0.214522			−0.107261	−	0.994231i	$-0.534208\pi$
$131$	−321.647			−0.214522			−0.107261	+	0.994231i	$0.534208\pi$
$132$		−	27.4218i		−	0.0180815i
$133$			2328.37i			1.51801i
$134$	295.912			0.190768
$135$	−207.942	+	218.827i	−0.132569	+	0.139508i
$136$	423.322			0.266909
$137$		−	354.291i		−	0.220942i	−0.993879	−	0.110471i	$-0.964764\pi$
$137$		−	354.291i		−	0.220942i	0.993879	−	0.110471i	$-0.0352360\pi$
$138$			253.256i			0.156222i
$139$	−77.2562			−0.0471424			−0.0235712	−	0.999722i	$-0.507504\pi$
$139$	−77.2562			−0.0471424			−0.0235712	+	0.999722i	$0.507504\pi$
$140$	−873.141	+	918.844i	−0.527099	+	0.554689i
$141$	1153.63			0.689030
$142$		−	1011.21i		−	0.597595i
$143$		−	104.231i		−	0.0609529i
$144$	−26.0578			−0.0150798
$145$	−2378.45	−	2260.14i	−1.36220	−	1.29445i
$146$	−544.893			−0.308875
$147$		−	450.769i		−	0.252917i
$148$			101.503i			0.0563752i
$149$	1705.38			0.937651			0.468826	−	0.883291i	$-0.344677\pi$
$149$	1705.38			0.937651			0.468826	+	0.883291i	$0.344677\pi$
$150$	−32.5265	−	637.256i	−0.0177052	−	0.346878i
$151$	758.281			0.408663			0.204331	−	0.978902i	$-0.434498\pi$
$151$	758.281			0.408663			0.204331	+	0.978902i	$0.434498\pi$
$152$		−	2337.71i		−	1.24746i
$153$			170.859i			0.0902821i
$154$	−67.6689			−0.0354086
$155$	−522.094	−	496.125i	−0.270552	−	0.257095i
$156$	−891.422			−0.457506
$157$			1769.05i			0.899273i	0.893212	+	0.449636i	$0.148446\pi$
$157$			1769.05i			0.899273i	−0.893212	+	0.449636i	$0.851554\pi$
$158$			1311.00i			0.660111i
$159$	−1390.58			−0.693588
$160$	1411.80	−	1485.70i	0.697581	−	0.734095i
$161$	−1101.86			−0.539372
$162$			137.827i			0.0668437i
$163$		−	881.719i		−	0.423690i	−0.977303	−	0.211845i	$-0.932053\pi$
$163$		−	881.719i		−	0.423690i	0.977303	−	0.211845i	$-0.0679473\pi$
$164$	−845.240			−0.402452
$165$	−41.3719	+	43.5374i	−0.0195200	+	0.0205417i
$166$	−295.944			−0.138372
$167$			216.900i			0.100504i	0.998737	+	0.0502522i	$0.0160025\pi$
$167$			216.900i			0.100504i	−0.998737	+	0.0502522i	$0.983997\pi$
$168$			1485.70i			0.682289i
$169$	−1191.33			−0.542254
$170$	−261.806	−	248.784i	−0.118116	−	0.112241i
$171$	943.537			0.421954
$172$		−	1262.64i		−	0.559742i
$173$			4125.91i			1.81322i	0.421970	+	0.906610i	$0.361339\pi$
$173$			4125.91i			1.81322i	−0.421970	+	0.906610i	$0.638661\pi$
$174$	−1498.05			−0.652683
$175$	2772.56	−	141.515i	1.19763	−	0.0611289i
$176$	−5.18443			−0.00222040
$177$			221.372i			0.0940075i
$178$		−	1733.93i		−	0.730134i
$179$	3213.14			1.34168			0.670842	−	0.741600i	$-0.265933\pi$
$179$	3213.14			1.34168			0.670842	+	0.741600i	$0.265933\pi$
$180$	372.347	+	353.827i	0.154184	+	0.146515i
$181$	3394.42			1.39395			0.696976	−	0.717095i	$-0.254529\pi$
$181$	3394.42			1.39395			0.696976	+	0.717095i	$0.254529\pi$
$182$			2199.77i			0.895921i
$183$		−	412.050i		−	0.166446i
$184$	1106.28			0.443240
$185$	153.141	−	161.156i	0.0608601	−	0.0640457i
$186$	−328.837			−0.129632
$187$			33.9939i			0.0132935i
$188$		−	1962.98i		−	0.761514i
$189$	−599.653			−0.230785
$190$	−1373.86	+	1445.77i	−0.524581	+	0.552040i
$191$	−3467.49			−1.31361			−0.656804	−	0.754062i	$-0.728092\pi$
$191$	−3467.49			−1.31361			−0.656804	+	0.754062i	$0.728092\pi$
$192$		−	866.273i		−	0.325614i
$193$			1792.14i			0.668401i	0.942502	+	0.334200i	$0.108466\pi$
$193$			1792.14i			0.668401i	−0.942502	+	0.334200i	$0.891534\pi$
$194$	654.038			0.242047
$195$	1415.31	+	1344.91i	0.519755	+	0.493902i
$196$	−767.011			−0.279523
$197$		−	1678.19i		−	0.606935i	−0.952842	−	0.303467i	$-0.901856\pi$
$197$		−	1678.19i		−	0.606935i	0.952842	−	0.303467i	$-0.0981443\pi$
$198$			27.4218i			0.00984233i
$199$	−3108.23			−1.10722			−0.553610	−	0.832776i	$-0.686750\pi$
$199$	−3108.23			−1.10722			−0.553610	+	0.832776i	$0.686750\pi$
$200$	−2783.68	+	142.083i	−0.984180	+	0.0502339i
$201$	521.719			0.183081
$202$			58.6878i			0.0204419i
$203$		−	6517.69i		−	2.25346i
$204$	290.728			0.0997795
$205$	1341.98	+	1275.23i	0.457211	+	0.434469i
$206$	2988.46			1.01076
$207$			446.512i			0.149926i
$208$			168.534i			0.0561815i
$209$	187.725			0.0621301
$210$	873.141	−	918.844i	0.286916	−	0.301934i
$211$	−4473.27			−1.45949			−0.729745	−	0.683719i	$-0.760361\pi$
$211$	−4473.27			−1.45949			−0.729745	+	0.683719i	$0.760361\pi$
$212$			2366.17i			0.766551i
$213$		−	1782.84i		−	0.573514i
$214$	−2317.08			−0.740151
$215$	−1904.98	+	2004.69i	−0.604273	+	0.635902i
$216$	602.058			0.189652
$217$		−	1430.70i		−	0.447568i
$218$		−	546.403i		−	0.169757i
$219$	−960.694			−0.296428
$220$	74.0816	+	70.3968i	0.0227026	+	0.0215734i
$221$	1105.07			0.336357
$222$		−	101.503i		−	0.0306868i
$223$		−	1753.42i		−	0.526535i	−0.964723	−	0.263268i	$-0.915200\pi$
$223$		−	1753.42i		−	0.526535i	0.964723	−	0.263268i	$-0.0848003\pi$
$224$	4071.29			1.21440
$225$	−57.3469	−	1123.54i	−0.0169917	−	0.332900i
$226$	2692.29			0.792427
$227$			936.900i			0.273939i	0.990575	+	0.136970i	$0.0437363\pi$
$227$			936.900i			0.273939i	−0.990575	+	0.136970i	$0.956264\pi$
$228$		−	1605.49i		−	0.466342i
$229$	2582.06			0.745096			0.372548	−	0.928013i	$-0.378484\pi$
$229$	2582.06			0.745096			0.372548	+	0.928013i	$0.378484\pi$
$230$	−684.187	−	650.156i	−0.196148	−	0.186391i
$231$	−119.306			−0.0339817
$232$			6543.82i			1.85182i
$233$			2295.01i			0.645284i	0.946521	+	0.322642i	$0.104571\pi$
$233$			2295.01i			0.645284i	−0.946521	+	0.322642i	$0.895429\pi$
$234$	891.422			0.249034
$235$	−2961.59	+	3116.61i	−0.822096	+	0.865128i
$236$	376.678			0.103897
$237$			2311.41i			0.633510i
$238$		−	717.432i		−	0.195396i
$239$	2294.01			0.620866			0.310433	−	0.950595i	$-0.399526\pi$
$239$	2294.01			0.620866			0.310433	+	0.950595i	$0.399526\pi$
$240$	66.8953	−	70.3968i	0.0179920	−	0.0189337i
$241$	382.287			0.102180			0.0510898	−	0.998694i	$-0.483731\pi$
$241$	382.287			0.102180			0.0510898	+	0.998694i	$0.483731\pi$
$242$		−	2259.32i		−	0.600144i
$243$			243.000i			0.0641500i
$244$	−701.128			−0.183956
$245$	1217.78	+	1157.21i	0.317555	+	0.301760i
$246$	845.240			0.219067
$247$		−	6102.52i		−	1.57204i
$248$			1436.44i			0.367798i
$249$	−521.775			−0.132796
$250$	1805.09	+	1548.08i	0.456655	+	0.391638i
$251$	−2259.98			−0.568322			−0.284161	−	0.958777i	$-0.591715\pi$
$251$	−2259.98			−0.568322			−0.284161	+	0.958777i	$0.591715\pi$
$252$			1020.35i			0.255063i
$253$			88.8375i			0.0220758i
$254$	−2037.01			−0.503202
$255$	−461.587	−	438.628i	−0.113356	−	0.107717i
$256$	−3969.38			−0.969087
$257$			92.7843i			0.0225203i	0.999937	+	0.0112602i	$0.00358430\pi$
$257$			92.7843i			0.0225203i	−0.999937	+	0.0112602i	$0.996416\pi$
$258$			1262.64i			0.304685i
$259$	441.619			0.105949
$260$	2288.45	−	2408.23i	0.545859	−	0.574431i
$261$	−2641.19			−0.626382
$262$		−	547.302i		−	0.129055i
$263$		−	568.312i		−	0.133246i	−0.997778	−	0.0666229i	$-0.978778\pi$
$263$		−	568.312i		−	0.133246i	0.997778	−	0.0666229i	$-0.0212224\pi$
$264$	119.785			0.0279251
$265$	3569.89	−	3756.75i	0.827534	−	0.870850i
$266$	−3961.87			−0.913226
$267$		−	3057.07i		−	0.700711i
$268$		−	887.737i		−	0.202340i
$269$	−7582.41			−1.71862			−0.859309	−	0.511458i	$-0.829106\pi$
$269$	−7582.41			−1.71862			−0.859309	+	0.511458i	$0.829106\pi$
$270$	−372.347	−	353.827i	−0.0839271	−	0.0797526i
$271$	7943.69			1.78061			0.890304	−	0.455366i	$-0.150492\pi$
$271$	7943.69			1.78061			0.890304	+	0.455366i	$0.150492\pi$
$272$		−	54.9657i		−	0.0122529i
$273$			3878.38i			0.859818i
$274$	602.847			0.132917
$275$	−11.4097	−	223.537i	−0.00250192	−	0.0490175i
$276$	759.769			0.165698
$277$		−	6823.00i		−	1.47998i	−0.672618	−	0.739990i	$-0.734830\pi$
$277$		−	6823.00i		−	1.47998i	0.672618	−	0.739990i	$-0.265170\pi$
$278$		−	131.456i		−	0.0283605i
$279$	−579.769			−0.124408
$280$	−4013.72	−	3814.08i	−0.856663	−	0.814053i
$281$	3315.86			0.703942			0.351971	−	0.936011i	$-0.385512\pi$
$281$	3315.86			0.703942			0.351971	+	0.936011i	$0.385512\pi$
$282$			1962.98i			0.414516i
$283$			6602.76i			1.38690i	0.720504	+	0.693451i	$0.243910\pi$
$283$			6602.76i			1.38690i	−0.720504	+	0.693451i	$0.756090\pi$
$284$	−3033.62			−0.633846
$285$	−2422.24	+	2549.02i	−0.503442	+	0.529794i
$286$	177.356			0.0366688
$287$			3677.46i			0.756353i
$288$		−	1649.83i		−	0.337559i
$289$	4552.59			0.926642
$290$	3845.77	−	4047.07i	0.778730	−	0.819491i
$291$	1153.12			0.232293
$292$			1634.68i			0.327611i
$293$			5814.14i			1.15927i	0.814877	+	0.579634i	$0.196805\pi$
$293$			5814.14i			1.15927i	−0.814877	+	0.579634i	$0.803195\pi$
$294$	767.011			0.152153
$295$	−598.050	−	568.303i	−0.118033	−	0.112162i
$296$	−443.390			−0.0870660
$297$			48.3469i			0.00944570i
$298$			2901.81i			0.564084i
$299$	2887.91			0.558570
$300$	−1911.77	+	97.5794i	−0.367920	+	0.0187792i
$301$	−5493.49			−1.05196
$302$			1290.26i			0.245849i
$303$			103.472i			0.0196181i
$304$	−303.537			−0.0572667
$305$	1113.18	+	1057.81i	0.208985	+	0.198590i
$306$	−290.728			−0.0543131
$307$			8124.86i			1.51046i	0.655462	+	0.755229i	$0.272474\pi$
$307$			8124.86i			1.51046i	−0.655462	+	0.755229i	$0.727526\pi$
$308$			203.007i			0.0375564i
$309$	5268.91			0.970025
$310$	844.187	−	888.375i	0.154667	−	0.162762i
$311$	7336.26			1.33762			0.668812	−	0.743432i	$-0.266803\pi$
$311$	7336.26			1.33762			0.668812	+	0.743432i	$0.266803\pi$
$312$		−	3893.93i		−	0.706572i
$313$		−	2202.66i		−	0.397768i	−0.980023	−	0.198884i	$-0.936268\pi$
$313$		−	2202.66i		−	0.397768i	0.980023	−	0.198884i	$-0.0637318\pi$
$314$	−3010.15			−0.540996
$315$	1539.42	−	1620.00i	0.275354	−	0.289767i
$316$	3933.00			0.700154
$317$		−	10008.9i		−	1.77336i	−0.462386	−	0.886679i	$-0.653007\pi$
$317$		−	10008.9i		−	1.77336i	0.462386	−	0.886679i	$-0.346993\pi$
$318$		−	2366.17i		−	0.417258i
$319$	−525.488			−0.0922309
$320$	2340.29	+	2223.89i	0.408832	+	0.388497i
$321$	−4085.21			−0.710325
$322$		−	1874.89i		−	0.324483i
$323$			1990.27i			0.342854i
$324$	413.480			0.0708984
$325$	−7266.71	+	370.903i	−1.24026	+	0.0633046i
$326$	1500.30			0.254889
$327$		−	963.356i		−	0.162917i
$328$		−	3692.20i		−	0.621548i
$329$	−8540.47			−1.43116
$330$	−74.0816	−	70.3968i	−0.0123578	−	0.0117431i
$331$	−8695.94			−1.44402			−0.722012	−	0.691881i	$-0.756782\pi$
$331$	−8695.94			−1.44402			−0.722012	+	0.691881i	$0.756782\pi$
$332$			887.832i			0.146765i
$333$		−	178.959i		−	0.0294502i
$334$	−369.069			−0.0604627
$335$	−1339.35	+	1409.46i	−0.218437	+	0.229871i
$336$	192.909			0.0313216
$337$			7400.61i			1.19625i	0.801402	+	0.598126i	$0.204088\pi$
$337$			7400.61i			1.19625i	−0.801402	+	0.598126i	$0.795912\pi$
$338$		−	2027.12i		−	0.326216i
$339$	4746.74			0.760494
$340$	−746.353	+	785.419i	−0.119049	+	0.125280i
$341$	−115.350			−0.0183183
$342$			1605.49i			0.253845i
$343$		−	4280.72i		−	0.673869i
$344$	5515.52			0.864467
$345$	−1206.28	−	1146.28i	−0.188243	−	0.178880i
$346$	−7020.49			−1.09082
$347$		−	7841.44i		−	1.21311i	−0.795040	−	0.606557i	$-0.792550\pi$
$347$		−	7841.44i		−	1.21311i	0.795040	−	0.606557i	$-0.207450\pi$
$348$			4494.15i			0.692275i
$349$	4961.26			0.760946			0.380473	−	0.924792i	$-0.375761\pi$
$349$	4961.26			0.760946			0.380473	+	0.924792i	$0.375761\pi$
$350$	240.797	+	4717.69i	0.0367748	+	0.720489i
$351$	1571.65			0.238999
$352$		−	328.247i		−	0.0497035i
$353$		−	12163.0i		−	1.83392i	−0.398981	−	0.916959i	$-0.630636\pi$
$353$		−	12163.0i		−	1.83392i	0.398981	−	0.916959i	$-0.369364\pi$
$354$	−376.678			−0.0565543
$355$	4816.46	+	4576.89i	0.720088	+	0.684271i
$356$	−5201.80			−0.774424
$357$		−	1264.89i		−	0.187522i
$358$			5467.36i			0.807148i
$359$	−5193.79			−0.763559			−0.381779	−	0.924253i	$-0.624689\pi$
$359$	−5193.79			−0.763559			−0.381779	+	0.924253i	$0.624689\pi$
$360$	−1545.60	+	1626.50i	−0.226278	+	0.238122i
$361$	4131.90			0.602406
$362$			5775.81i			0.838591i
$363$		−	3983.38i		−	0.575959i
$364$	6599.31			0.950268
$365$	2466.28	−	2595.37i	0.353674	−	0.372187i
$366$	701.128			0.100133
$367$			6086.09i			0.865644i	0.901479	+	0.432822i	$0.142482\pi$
$367$			6086.09i			0.865644i	−0.901479	+	0.432822i	$0.857518\pi$
$368$		−	143.644i		−	0.0203477i
$369$	1490.23			0.210239
$370$	274.218	+	260.578i	0.0385295	+	0.0366130i
$371$	10294.7			1.44063
$372$			986.512i			0.137495i
$373$		−	10581.9i		−	1.46893i	−0.678646	−	0.734466i	$-0.737433\pi$
$373$		−	10581.9i		−	1.46893i	0.678646	−	0.734466i	$-0.262567\pi$
$374$	−57.8428			−0.00799727
$375$	3182.53	+	2729.40i	0.438253	+	0.375856i
$376$	8574.72			1.17608
$377$			17082.4i			2.33366i
$378$		−	1020.35i		−	0.138839i
$379$	−11655.2			−1.57964			−0.789822	−	0.613336i	$-0.789827\pi$
$379$	−11655.2			−1.57964			−0.789822	+	0.613336i	$0.789827\pi$
$380$	4337.32	+	4121.59i	0.585526	+	0.556403i
$381$	−3591.42			−0.482924
$382$		−	5900.16i		−	0.790257i
$383$			6364.97i			0.849177i	0.905387	+	0.424588i	$0.139581\pi$
$383$			6364.97i			0.849177i	−0.905387	+	0.424588i	$0.860419\pi$
$384$	−2925.52			−0.388782
$385$	306.281	−	322.313i	0.0405442	−	0.0426665i
$386$	−3049.44			−0.402105
$387$			2226.15i			0.292407i
$388$		−	1962.11i		−	0.256730i
$389$	−6134.33			−0.799545			−0.399773	−	0.916614i	$-0.630911\pi$
$389$	−6134.33			−0.799545			−0.399773	+	0.916614i	$0.630911\pi$
$390$	−2288.45	+	2408.23i	−0.297128	+	0.312681i
$391$	−941.862			−0.121821
$392$		−	3350.48i		−	0.431696i
$393$		−	964.941i		−	0.123855i
$394$	2855.55			0.365128
$395$	−6244.41	−	5933.81i	−0.795418	−	0.755854i
$396$	82.2653			0.0104394
$397$		−	9746.46i		−	1.23214i	−0.787690	−	0.616072i	$-0.788723\pi$
$397$		−	9746.46i		−	1.23214i	0.787690	−	0.616072i	$-0.211277\pi$
$398$		−	5288.85i		−	0.666096i
$399$	−6985.12			−0.876425
$400$	18.4486	+	361.444i	0.00230607	+	0.0451805i
$401$	−1306.44			−0.162695			−0.0813474	−	0.996686i	$-0.525922\pi$
$401$	−1306.44			−0.162695			−0.0813474	+	0.996686i	$0.525922\pi$
$402$			887.737i			0.110140i
$403$			3749.77i			0.463498i
$404$	176.063			0.0216819
$405$	−656.480	−	623.827i	−0.0805450	−	0.0765387i
$406$	11090.2			1.35566
$407$		−	35.6055i		−	0.00433636i
$408$			1269.97i			0.154100i
$409$	3876.93			0.468709			0.234354	−	0.972151i	$-0.424702\pi$
$409$	3876.93			0.468709			0.234354	+	0.972151i	$0.424702\pi$
$410$	−2169.89	+	2283.47i	−0.261374	+	0.275055i
$411$	1062.87			0.127561
$412$		−	8965.38i		−	1.07207i
$413$		−	1638.84i		−	0.195260i
$414$	−759.769			−0.0901947
$415$	1339.49	−	1409.61i	0.158441	−	0.166735i
$416$	−10670.6			−1.25762
$417$		−	231.769i		−	0.0272177i
$418$			319.426i			0.0373771i
$419$	16022.5			1.86814			0.934071	−	0.357088i	$-0.116230\pi$
$419$	16022.5			1.86814			0.934071	+	0.357088i	$0.116230\pi$
$420$	−2756.53	−	2619.42i	−0.320250	−	0.304321i
$421$	−8119.73			−0.939980			−0.469990	−	0.882672i	$-0.655742\pi$
$421$	−8119.73			−0.939980			−0.469990	+	0.882672i	$0.655742\pi$
$422$		−	7611.54i		−	0.878019i
$423$			3460.89i			0.397812i
$424$	−10336.0			−1.18386
$425$	2369.96	−	120.966i	0.270494	−	0.0138064i
$426$	3033.62			0.345022
$427$			3050.46i			0.345719i
$428$			6951.24i			0.785049i
$429$	312.694			0.0351911
$430$	−3411.11	−	3241.44i	−0.382554	−	0.363526i
$431$	−5713.99			−0.638592			−0.319296	−	0.947655i	$-0.603446\pi$
$431$	−5713.99			−0.638592			−0.319296	+	0.947655i	$0.603446\pi$
$432$		−	78.1735i		−	0.00870630i
$433$			6251.34i			0.693811i	0.937900	+	0.346906i	$0.112768\pi$
$433$			6251.34i			0.693811i	−0.937900	+	0.346906i	$0.887232\pi$
$434$	2434.42			0.269254
$435$	6780.43	−	7135.34i	0.747349	−	0.786468i
$436$	−1639.21			−0.180055
$437$			5201.25i			0.569358i
$438$		−	1634.68i		−	0.178329i
$439$	4230.97			0.459984			0.229992	−	0.973192i	$-0.426130\pi$
$439$	4230.97			0.459984			0.229992	+	0.973192i	$0.426130\pi$
$440$	−307.509	+	323.605i	−0.0333180	+	0.0350620i
$441$	1352.31			0.146022
$442$			1880.34i			0.202350i
$443$			6314.29i			0.677203i	0.940930	+	0.338601i	$0.109954\pi$
$443$			6314.29i			0.677203i	−0.940930	+	0.338601i	$0.890046\pi$
$444$	−304.510			−0.0325482
$445$	8258.88	+	7848.08i	0.879794	+	0.836033i
$446$	2983.55			0.316760
$447$			5116.13i			0.541353i
$448$			6413.13i			0.676321i
$449$	9349.71			0.982717			0.491358	−	0.870957i	$-0.336501\pi$
$449$	9349.71			0.982717			0.491358	+	0.870957i	$0.336501\pi$
$450$	1911.77	−	97.5794i	0.200270	−	0.0102221i
$451$	296.494			0.0309565
$452$		−	8076.87i		−	0.840496i
$453$			2274.84i			0.235941i
$454$	−1594.19			−0.164800
$455$	−10477.7	−	9956.53i	−1.07956	−	1.02587i
$456$	7013.14			0.720220
$457$			9547.46i			0.977268i	0.872489	+	0.488634i	$0.162505\pi$
$457$			9547.46i			0.977268i	−0.872489	+	0.488634i	$0.837495\pi$
$458$			4393.53i			0.448245i
$459$	−512.578			−0.0521244
$460$	−1950.47	+	2052.56i	−0.197698	+	0.208046i
$461$	6237.23			0.630145			0.315073	−	0.949068i	$-0.397971\pi$
$461$	6237.23			0.630145			0.315073	+	0.949068i	$0.397971\pi$
$462$		−	203.007i		−	0.0204431i
$463$			6469.98i			0.649428i	0.945812	+	0.324714i	$0.105268\pi$
$463$			6469.98i			0.649428i	−0.945812	+	0.324714i	$0.894732\pi$
$464$	849.675			0.0850111
$465$	1488.37	−	1566.28i	0.148434	−	0.156203i
$466$	−3905.10			−0.388198
$467$		−	7206.64i		−	0.714097i	−0.934086	−	0.357049i	$-0.883783\pi$
$467$		−	7206.64i		−	0.714097i	0.934086	−	0.357049i	$-0.116217\pi$
$468$		−	2674.27i		−	0.264141i
$469$	−3862.35			−0.380270
$470$	−5303.10	−	5039.32i	−0.520455	−	0.494567i
$471$	−5307.16			−0.519195
$472$			1645.42i			0.160458i
$473$			442.912i			0.0430552i
$474$	−3933.00			−0.381115
$475$	−668.012	−	13087.6i	−0.0645274	−	1.26422i
$476$	−2152.29			−0.207248
$477$		−	4171.75i		−	0.400443i
$478$			3903.39i			0.373509i
$479$	10851.8			1.03514			0.517571	−	0.855640i	$-0.326836\pi$
$479$	10851.8			1.03514			0.517571	+	0.855640i	$0.326836\pi$
$480$	4457.11	+	4235.41i	0.423830	+	0.402749i
$481$	−1157.46			−0.109720
$482$			650.485i			0.0614705i
$483$		−	3305.59i		−	0.311407i
$484$	−6777.97			−0.636549
$485$	−2960.29	+	3115.24i	−0.277154	+	0.291661i
$486$	−413.480			−0.0385922
$487$		−	12757.1i		−	1.18702i	−0.804827	−	0.593510i	$-0.797742\pi$
$487$		−	12757.1i		−	1.18702i	0.804827	−	0.593510i	$-0.202258\pi$
$488$		−	3062.69i		−	0.284101i
$489$	2645.16			0.244618
$490$	−1969.06	+	2072.13i	−0.181537	+	0.191039i
$491$	−7016.52			−0.644911			−0.322455	−	0.946585i	$-0.604508\pi$
$491$	−7016.52			−0.644911			−0.322455	+	0.946585i	$0.604508\pi$
$492$		−	2535.72i		−	0.232356i
$493$		−	5571.26i		−	0.508960i
$494$	10383.8			0.945729
$495$	−130.612	−	124.116i	−0.0118598	−	0.0112699i
$496$	186.512			0.0168844
$497$			13198.6i			1.19122i
$498$		−	887.832i		−	0.0798890i
$499$	−11372.3			−1.02023			−0.510113	−	0.860107i	$-0.670396\pi$
$499$	−11372.3			−1.02023			−0.510113	+	0.860107i	$0.670396\pi$
$500$	4644.25	−	5415.27i	0.415395	−	0.484356i
$501$	−650.700			−0.0580262
$502$		−	3845.50i		−	0.341899i
$503$		−	5587.37i		−	0.495285i	−0.968851	−	0.247643i	$-0.920344\pi$
$503$		−	5587.37i		−	0.495285i	0.968851	−	0.247643i	$-0.0796559\pi$
$504$	−4457.11			−0.393919
$505$	−279.535	−	265.631i	−0.0246320	−	0.0234068i
$506$	−151.163			−0.0132806
$507$		−	3573.99i		−	0.313070i
$508$			6111.03i			0.533726i
$509$	−16256.7			−1.41565			−0.707825	−	0.706388i	$-0.750324\pi$
$509$	−16256.7			−1.41565			−0.707825	+	0.706388i	$0.750324\pi$
$510$	746.353	−	785.419i	0.0648021	−	0.0681940i
$511$	7112.14			0.615699
$512$			1047.24i			0.0903943i
$513$			2830.61i			0.243615i
$514$	−157.878			−0.0135481
$515$	−13526.3	+	14234.3i	−1.15736	+	1.21794i
$516$	3787.93			0.323167
$517$			688.574i			0.0585754i
$518$			751.442i			0.0637384i
$519$	−12377.7			−1.04686
$520$	10519.7	+	9996.46i	0.887153	+	0.843026i
$521$	19748.4			1.66064			0.830320	−	0.557286i	$-0.188157\pi$
$521$	19748.4			1.66064			0.830320	+	0.557286i	$0.188157\pi$
$522$		−	4494.15i		−	0.376827i
$523$		−	7843.44i		−	0.655774i	−0.944717	−	0.327887i	$-0.893663\pi$
$523$		−	7843.44i		−	0.655774i	0.944717	−	0.327887i	$-0.106337\pi$
$524$	−1641.91			−0.136884
$525$	424.546	+	8317.69i	0.0352928	+	0.691455i
$526$	967.019			0.0801597
$527$		−	1222.95i		−	0.101086i
$528$		−	15.5533i		−	0.00128195i
$529$	9705.60			0.797699
$530$	6392.34	+	6074.39i	0.523897	+	0.497839i
$531$	−664.116			−0.0542753
$532$			11885.6i			0.968622i
$533$		−	9638.38i		−	0.783273i
$534$	5201.80			0.421543
$535$	10487.5	−	11036.5i	0.847504	−	0.891865i
$536$	3877.84			0.312495
$537$			9639.42i			0.774622i
$538$		−	12902.0i		−	1.03391i
$539$	269.053			0.0215008
$540$	−1061.48	+	1117.04i	−0.0845904	+	0.0890181i
$541$	7383.29			0.586751			0.293376	−	0.955997i	$-0.405221\pi$
$541$	7383.29			0.586751			0.293376	+	0.955997i	$0.405221\pi$
$542$			13516.7i			1.07120i
$543$			10183.3i			0.804798i
$544$	3480.10			0.274280
$545$	2602.57	+	2473.12i	0.204554	+	0.194379i
$546$	−6599.31			−0.517260
$547$			3354.90i			0.262240i	0.991367	+	0.131120i	$0.0418573\pi$
$547$			3354.90i			0.262240i	−0.991367	+	0.131120i	$0.958143\pi$
$548$		−	1808.54i		−	0.140980i
$549$	1236.15			0.0960976
$550$	380.363	−	19.4143i	0.0294886	−	0.00150514i
$551$	−30766.2			−2.37874
$552$			3318.84i			0.255905i
$553$		−	17111.6i		−	1.31584i
$554$	11609.8			0.890346
$555$	483.469	+	459.422i	0.0369768	+	0.0351376i
$556$	−394.369			−0.0300809
$557$		−	20771.8i		−	1.58012i	−0.613028	−	0.790061i	$-0.710049\pi$
$557$		−	20771.8i		−	1.58012i	0.613028	−	0.790061i	$-0.289951\pi$
$558$		−	986.512i		−	0.0748430i
$559$	14398.1			1.08940
$560$	−495.234	+	521.156i	−0.0373705	+	0.0393266i
$561$	−101.982			−0.00767500
$562$			5642.15i			0.423487i
$563$			7194.86i			0.538592i	0.963057	+	0.269296i	$0.0867910\pi$
$563$			7194.86i			0.538592i	−0.963057	+	0.269296i	$0.913209\pi$
$564$	5888.93			0.439660
$565$	−12185.8	+	12823.6i	−0.907361	+	0.954856i
$566$	−11235.0			−0.834350
$567$		−	1798.96i		−	0.133244i
$568$		−	13251.5i		−	0.978913i
$569$	−11549.5			−0.850931			−0.425466	−	0.904975i	$-0.639890\pi$
$569$	−11549.5			−0.850931			−0.425466	+	0.904975i	$0.639890\pi$
$570$	−4337.32	−	4121.59i	−0.318720	−	0.302867i
$571$	1482.54			0.108655			0.0543277	−	0.998523i	$-0.482698\pi$
$571$	1482.54			0.108655			0.0543277	+	0.998523i	$0.482698\pi$
$572$		−	532.068i		−	0.0388932i
$573$		−	10402.5i		−	0.758412i
$574$	−6257.42			−0.455017
$575$	6193.50	−	316.125i	0.449194	−	0.0229275i
$576$	2598.82			0.187993
$577$			15264.0i			1.10130i	0.834737	+	0.550649i	$0.185620\pi$
$577$			15264.0i			1.10130i	−0.834737	+	0.550649i	$0.814380\pi$
$578$			7746.52i			0.557462i
$579$	−5376.43			−0.385901
$580$	−12141.2	−	11537.3i	−0.869202	−	0.825968i
$581$	3862.76			0.275825
$582$			1962.11i			0.139746i
$583$		−	830.006i		−	0.0589628i
$584$	−7140.66			−0.505963
$585$	−4034.73	+	4245.92i	−0.285155	+	0.300081i
$586$	−9893.12			−0.697408
$587$		−	1736.89i		−	0.122128i	−0.998134	−	0.0610639i	$-0.980551\pi$
$587$		−	1736.89i		−	0.122128i	0.998134	−	0.0610639i	$-0.0194493\pi$
$588$		−	2301.03i		−	0.161383i
$589$	−6753.50			−0.472450
$590$	967.003	−	1017.62i	0.0674761	−	0.0710080i
$591$	5034.57			0.350414
$592$			57.5714i			0.00399691i
$593$		−	11764.8i		−	0.814707i	−0.913271	−	0.407353i	$-0.866452\pi$
$593$		−	11764.8i		−	0.814707i	0.913271	−	0.407353i	$-0.133548\pi$
$594$	−82.2653			−0.00568247
$595$	3417.19	+	3247.22i	0.235447	+	0.223736i
$596$	8705.42			0.598302
$597$		−	9324.69i		−	0.639253i
$598$			4913.96i			0.336032i
$599$	9451.99			0.644737			0.322369	−	0.946614i	$-0.395521\pi$
$599$	9451.99			0.644737			0.322369	+	0.946614i	$0.395521\pi$
$600$	−426.249	−	8351.04i	−0.0290026	−	0.568217i
$601$	−3131.93			−0.212569			−0.106285	−	0.994336i	$-0.533895\pi$
$601$	−3131.93			−0.212569			−0.106285	+	0.994336i	$0.533895\pi$
$602$		−	9347.51i		−	0.632851i
$603$			1565.16i			0.105702i
$604$	3870.79			0.260762
$605$	10761.4	+	10226.1i	0.723159	+	0.687189i
$606$	−176.063			−0.0118021
$607$		−	22700.8i		−	1.51795i	−0.651120	−	0.758975i	$-0.725700\pi$
$607$		−	22700.8i		−	1.51795i	0.651120	−	0.758975i	$-0.274300\pi$
$608$		−	19218.2i		−	1.28191i
$609$	19553.1			1.30103
$610$	−1799.93	+	1894.14i	−0.119470	+	0.125724i
$611$	22384.0			1.48210
$612$			872.184i			0.0576077i
$613$			28911.6i			1.90494i	0.304629	+	0.952471i	$0.401468\pi$
$613$			28911.6i			1.90494i	−0.304629	+	0.952471i	$0.598532\pi$
$614$	−13825.0			−0.908681
$615$	−3825.70	+	4025.95i	−0.250841	+	0.263971i
$616$	−886.780			−0.0580023
$617$			5566.87i			0.363231i	0.983370	+	0.181616i	$0.0581326\pi$
$617$			5566.87i			0.363231i	−0.983370	+	0.181616i	$0.941867\pi$
$618$			8965.38i			0.583560i
$619$	−4150.32			−0.269492			−0.134746	−	0.990880i	$-0.543022\pi$
$619$	−4150.32			−0.269492			−0.134746	+	0.990880i	$0.543022\pi$
$620$	−2665.12	−	2532.56i	−0.172635	−	0.164049i
$621$	−1339.54			−0.0865600
$622$			12483.1i			0.804705i
$623$			22631.9i			1.45542i
$624$	−505.603			−0.0324364
$625$	−15543.8	+	1590.90i	−0.994803	+	0.101818i
$626$	3747.96			0.239295
$627$			563.175i			0.0358709i
$628$			9030.46i			0.573813i
$629$	377.492			0.0239294
$630$	2756.53	+	2619.42i	0.174322	+	0.165651i
$631$	−4090.09			−0.258041			−0.129021	−	0.991642i	$-0.541183\pi$
$631$	−4090.09			−0.258041			−0.129021	+	0.991642i	$0.541183\pi$
$632$			17180.2i			1.08132i
$633$		−	13419.8i		−	0.842637i
$634$	17030.7			1.06684
$635$	9219.85	−	9702.45i	0.576187	−	0.606346i
$636$	−7098.50			−0.442569
$637$		−	8746.32i		−	0.544022i
$638$		−	894.150i		−	0.0554855i
$639$	5348.53			0.331118
$640$	7510.36	−	7903.47i	0.463864	−	0.488144i
$641$	3909.35			0.240890			0.120445	−	0.992720i	$-0.461568\pi$
$641$	3909.35			0.240890			0.120445	+	0.992720i	$0.461568\pi$
$642$		−	6951.24i		−	0.427327i
$643$			30539.5i			1.87303i	0.350624	+	0.936516i	$0.385969\pi$
$643$			30539.5i			1.87303i	−0.350624	+	0.936516i	$0.614031\pi$
$644$	−5624.66			−0.344166
$645$	−6014.08	−	5714.94i	−0.367138	−	0.348877i
$646$	−3386.58			−0.206259
$647$			12707.7i			0.772167i	0.922464	+	0.386083i	$0.126172\pi$
$647$			12707.7i			0.772167i	−0.922464	+	0.386083i	$0.873828\pi$
$648$			1806.17i			0.109496i
$649$	−132.132			−0.00799170
$650$	−631.115	−	12364.8i	−0.0380836	−	0.746132i
$651$	4292.10			0.258403
$652$		−	4500.90i		−	0.270351i
$653$			12777.6i			0.765737i	0.923803	+	0.382869i	$0.125064\pi$
$653$			12777.6i			0.765737i	−0.923803	+	0.382869i	$0.874936\pi$
$654$	1639.21			0.0980095
$655$	2606.85	+	2477.18i	0.155508	+	0.147773i
$656$	−479.410			−0.0285332
$657$		−	2882.08i		−	0.171143i
$658$		−	14532.1i		−	0.860976i
$659$	−23563.5			−1.39287			−0.696435	−	0.717620i	$-0.745232\pi$
$659$	−23563.5			−1.39287			−0.696435	+	0.717620i	$0.745232\pi$
$660$	−211.190	+	222.245i	−0.0124554	+	0.0131074i
$661$	−4361.31			−0.256634			−0.128317	−	0.991733i	$-0.540958\pi$
$661$	−4361.31			−0.256634			−0.128317	+	0.991733i	$0.540958\pi$
$662$		−	14796.7i		−	0.868715i
$663$			3315.21i			0.194196i
$664$	−3878.25			−0.226665
$665$	17932.1	−	18870.7i	1.04568	−	1.10042i
$666$	304.510			0.0177170
$667$		−	14559.6i		−	0.845200i
$668$			1107.21i			0.0641304i
$669$	5260.25			0.303995
$670$	−2398.28	−	2278.99i	−0.138289	−	0.131410i
$671$	245.943			0.0141498
$672$			12213.9i			0.701131i
$673$		−	8203.52i		−	0.469870i	−0.972011	−	0.234935i	$-0.924512\pi$
$673$		−	8203.52i		−	0.469870i	0.972011	−	0.234935i	$-0.0754877\pi$
$674$	−12592.6			−0.719657
$675$	3370.61	−	172.041i	0.192200	−	0.00981015i
$676$	−6081.37			−0.346004
$677$		−	28057.1i		−	1.59279i	−0.604774	−	0.796397i	$-0.706737\pi$
$677$		−	28057.1i		−	1.59279i	0.604774	−	0.796397i	$-0.293263\pi$
$678$			8076.87i			0.457508i
$679$	−8536.73			−0.482488
$680$	−3430.89	−	3260.24i	−0.193483	−	0.183860i
$681$	−2810.70			−0.158159
$682$		−	196.275i		−	0.0110202i
$683$		−	3344.62i		−	0.187377i	−0.995602	−	0.0936885i	$-0.970134\pi$
$683$		−	3344.62i		−	0.187377i	0.995602	−	0.0936885i	$-0.0298658\pi$
$684$	4816.46			0.269243
$685$	−2728.59	+	2871.41i	−0.152196	+	0.160162i
$686$	7283.91			0.405395
$687$			7746.17i			0.430182i
$688$		−	716.156i		−	0.0396849i
$689$	−26981.7			−1.49190
$690$	1950.47	−	2052.56i	0.107613	−	0.113246i
$691$	12964.8			0.713757			0.356879	−	0.934151i	$-0.383841\pi$
$691$	12964.8			0.713757			0.356879	+	0.934151i	$0.383841\pi$
$692$			21061.5i			1.15699i
$693$		−	357.918i		−	0.0196193i
$694$	13342.7			0.729801
$695$	626.138	+	594.994i	0.0341737	+	0.0324740i
$696$	−19631.5			−1.06915
$697$			3143.46i			0.170828i
$698$			8441.90i			0.457780i
$699$	−6885.03			−0.372555
$700$	14153.1	−	722.392i	0.764193	−	0.0390055i
$701$	−16162.1			−0.870806			−0.435403	−	0.900236i	$-0.643394\pi$
$701$	−16162.1			−0.870806			−0.435403	+	0.900236i	$0.643394\pi$
$702$			2674.27i			0.143780i
$703$		−	2084.63i		−	0.111839i
$704$	517.058			0.0276809
$705$	−9349.82	−	8884.76i	−0.499482	−	0.474638i
$706$	20696.2			1.10327
$707$		−	766.014i		−	0.0407481i
$708$			1130.03i			0.0599849i
$709$	14244.4			0.754529			0.377265	−	0.926105i	$-0.376865\pi$
$709$	14244.4			0.754529			0.377265	+	0.926105i	$0.376865\pi$
$710$	−7787.87	+	8195.51i	−0.411653	+	0.433200i
$711$	−6934.22			−0.365757
$712$		−	22722.7i		−	1.19602i
$713$		−	3195.97i		−	0.167868i
$714$	2152.29			0.112812
$715$	−802.744	+	844.762i	−0.0419873	+	0.0441850i
$716$	16402.1			0.856109
$717$			6882.02i			0.358457i
$718$		−	8837.55i		−	0.459352i
$719$	27638.5			1.43358			0.716790	−	0.697289i	$-0.245611\pi$
$719$	27638.5			1.43358			0.716790	+	0.697289i	$0.245611\pi$
$720$	211.190	+	200.686i	0.0109314	+	0.0103877i
$721$	−39006.4			−2.01480
$722$			7030.68i			0.362403i
$723$			1146.86i			0.0589934i
$724$	17327.4			0.889460
$725$	1869.93	+	36635.5i	0.0957895	+	1.87670i
$726$	6777.97			0.346493
$727$			2525.52i			0.128840i	0.997923	+	0.0644199i	$0.0205197\pi$
$727$			2525.52i			0.128840i	−0.997923	+	0.0644199i	$0.979480\pi$
$728$			28827.3i			1.46760i
$729$	−729.000			−0.0370370
$730$	4416.19	+	4196.53i	0.223905	+	0.212768i
$731$	−4695.79			−0.237592
$732$		−	2103.39i		−	0.106207i
$733$		−	8400.27i		−	0.423289i	−0.977347	−	0.211645i	$-0.932118\pi$
$733$		−	8400.27i		−	0.423289i	0.977347	−	0.211645i	$-0.0678820\pi$
$734$	−10355.9			−0.520765
$735$	−3471.62	+	3653.34i	−0.174221	+	0.183341i
$736$	9094.67			0.455481
$737$			311.401i			0.0155639i
$738$			2535.72i			0.126479i
$739$	19689.1			0.980074			0.490037	−	0.871702i	$-0.336983\pi$
$739$	19689.1			0.980074			0.490037	+	0.871702i	$0.336983\pi$
$740$	781.735	−	822.653i	0.0388340	−	0.0408667i
$741$	18307.6			0.907619
$742$			17517.0i			0.866671i
$743$		−	22526.6i		−	1.11227i	−0.831091	−	0.556137i	$-0.812283\pi$
$743$		−	22526.6i		−	1.11227i	0.831091	−	0.556137i	$-0.187717\pi$
$744$	−4309.31			−0.212348
$745$	−13821.6	−	13134.1i	−0.679708	−	0.645900i
$746$	18005.8			0.883699
$747$		−	1565.32i		−	0.0766696i
$748$			173.528i			0.00848239i
$749$	30243.3			1.47539
$750$	−4644.25	+	5415.27i	−0.226112	+	0.263650i
$751$	34691.1			1.68562			0.842808	−	0.538215i	$-0.180901\pi$
$751$	34691.1			1.68562			0.842808	+	0.538215i	$0.180901\pi$
$752$		−	1113.37i		−	0.0539902i
$753$		−	6779.95i		−	0.328121i
$754$	−29066.8			−1.40392
$755$	−6145.63	−	5839.95i	−0.296242	−	0.281507i
$756$	−3061.04			−0.147261
$757$		−	6619.98i		−	0.317843i	−0.987291	−	0.158922i	$-0.949198\pi$
$757$		−	6619.98i		−	0.317843i	0.987291	−	0.158922i	$-0.0508017\pi$
$758$		−	19832.0i		−	0.950303i
$759$	−266.512			−0.0127454
$760$	−18004.0	+	18946.4i	−0.859309	+	0.904288i
$761$	−29368.7			−1.39897			−0.699483	−	0.714649i	$-0.746586\pi$
$761$	−29368.7			−1.39897			−0.699483	+	0.714649i	$0.746586\pi$
$762$		−	6111.03i		−	0.290524i
$763$			7131.84i			0.338388i
$764$	−17700.5			−0.838194
$765$	1315.88	−	1384.76i	0.0621907	−	0.0654460i
$766$	−10830.4			−0.510859
$767$			4295.31i			0.202209i
$768$		−	11908.1i		−	0.559503i
$769$	−32677.4			−1.53235			−0.766174	−	0.642633i	$-0.777842\pi$
$769$	−32677.4			−1.53235			−0.766174	+	0.642633i	$0.777842\pi$
$770$	548.435	+	521.156i	0.0256678	+	0.0243911i
$771$	−278.353			−0.0130021
$772$			9148.33i			0.426497i
$773$		−	28047.5i		−	1.30504i	−0.757770	−	0.652522i	$-0.773711\pi$
$773$		−	28047.5i		−	1.30504i	0.757770	−	0.652522i	$-0.226289\pi$
$774$	−3787.93			−0.175910
$775$	410.469	+	8041.87i	0.0190251	+	0.372739i
$776$	8570.96			0.396494
$777$			1324.86i			0.0611699i
$778$		−	10438.0i		−	0.481001i
$779$	17359.1			0.798402
$780$	7224.69	+	6865.34i	0.331648	+	0.315152i
$781$	1064.14			0.0487552
$782$		−	1602.64i		−	0.0732867i
$783$		−	7923.57i		−	0.361642i
$784$	−435.039			−0.0198177
$785$	13624.5	−	14337.6i	0.619463	−	0.651887i
$786$	1641.91			0.0745100
$787$			22172.1i			1.00426i	0.864793	+	0.502128i	$0.167449\pi$
$787$			22172.1i			1.00426i	−0.864793	+	0.502128i	$0.832551\pi$
$788$		−	8566.64i		−	0.387276i
$789$	1704.94			0.0769295
$790$	10096.7	−	10625.2i	0.454717	−	0.478518i
$791$	−35140.7			−1.57960
$792$			359.354i			0.0161226i
$793$		−	7995.06i		−	0.358024i
$794$	16584.2			0.741249
$795$	11270.2	+	10709.7i	0.502786	+	0.477777i
$796$	−15866.5			−0.706501
$797$			24170.3i			1.07422i	0.843511	+	0.537112i	$0.180485\pi$
$797$			24170.3i			1.07422i	−0.843511	+	0.537112i	$0.819515\pi$
$798$		−	11885.6i		−	0.527251i
$799$	−7300.32			−0.323238
$800$	−22884.5	+	1168.06i	−1.01136	+	0.0516212i
$801$	9171.22			0.404556
$802$		−	2222.99i		−	0.0978761i
$803$		−	573.415i		−	0.0251997i
$804$	2663.21			0.116821
$805$	8930.25	+	8486.06i	0.390994	+	0.371546i
$806$	−6380.47			−0.278837
$807$		−	22747.2i		−	0.992244i
$808$			769.085i			0.0334856i
$809$	−15304.2			−0.665102			−0.332551	−	0.943085i	$-0.607909\pi$
$809$	−15304.2			−0.665102			−0.332551	+	0.943085i	$0.607909\pi$
$810$	1061.48	−	1117.04i	0.0460452	−	0.0484553i
$811$	−27002.2			−1.16914			−0.584572	−	0.811342i	$-0.698738\pi$
$811$	−27002.2			−1.16914			−0.584572	+	0.811342i	$0.698738\pi$
$812$		−	33270.7i		−	1.43790i
$813$			23831.1i			1.02803i
$814$	60.5849			0.00260872
$815$	−6790.61	+	7146.05i	−0.291859	+	0.307135i
$816$	164.897			0.00707421
$817$			25931.5i			1.11044i
$818$			6596.84i			0.281972i
$819$	−11635.1			−0.496416
$820$	6850.41	+	6509.67i	0.291740	+	0.277229i
$821$	25061.4			1.06535			0.532673	−	0.846321i	$-0.321188\pi$
$821$	25061.4			1.06535			0.532673	+	0.846321i	$0.321188\pi$
$822$			1808.54i			0.0767398i
$823$		−	24896.4i		−	1.05448i	−0.849718	−	0.527238i	$-0.823228\pi$
$823$		−	24896.4i		−	1.05448i	0.849718	−	0.527238i	$-0.176772\pi$
$824$	39162.8			1.65571
$825$	670.612	−	34.2290i	0.0283003	−	0.00144449i
$826$	2788.59			0.117467
$827$			20063.2i			0.843612i	0.906686	+	0.421806i	$0.138604\pi$
$827$			20063.2i			0.843612i	−0.906686	+	0.421806i	$0.861396\pi$
$828$			2279.31i			0.0956659i
$829$	13884.2			0.581687			0.290844	−	0.956771i	$-0.406064\pi$
$829$	13884.2			0.581687			0.290844	+	0.956771i	$0.406064\pi$
$830$	2398.53	+	2279.23i	0.100306	+	0.0953172i
$831$	20469.0			0.854467
$832$		−	16808.4i		−	0.700393i
$833$			2852.52i			0.118648i
$834$	394.369			0.0163740
$835$	1670.47	−	1757.91i	0.0692323	−	0.0728561i
$836$	958.277			0.0396444
$837$		−	1739.31i		−	0.0718270i
$838$			27263.3i			1.12386i
$839$	13678.1			0.562838			0.281419	−	0.959585i	$-0.409195\pi$
$839$	13678.1			0.562838			0.281419	+	0.959585i	$0.409195\pi$
$840$	11442.2	−	12041.2i	0.469994	−	0.494594i
$841$	61733.1			2.53118
$842$		−	13816.2i		−	0.565485i
$843$			9947.59i			0.406421i
$844$	−22834.6			−0.931280
$845$	9655.36	+	9175.11i	0.393082	+	0.373531i
$846$	−5888.93			−0.239321
$847$			29489.5i			1.19630i
$848$			1342.06i			0.0543473i
$849$	−19808.3			−0.800728
$850$	205.832	+	4032.64i	0.00830584	+	0.162727i
$851$	986.512			0.0397382
$852$		−	9100.86i		−	0.365951i
$853$			29802.9i			1.19629i	0.801390	+	0.598143i	$0.204094\pi$
$853$			29802.9i			1.19629i	−0.801390	+	0.598143i	$0.795906\pi$
$854$	−5190.54			−0.207982
$855$	−7647.07	−	7266.71i	−0.305877	−	0.290662i
$856$	−30364.6			−1.21243
$857$		−	22045.2i		−	0.878706i	−0.898314	−	0.439353i	$-0.855208\pi$
$857$		−	22045.2i		−	0.878706i	0.898314	−	0.439353i	$-0.144792\pi$
$858$			532.068i			0.0211708i
$859$	−33609.5			−1.33497			−0.667487	−	0.744622i	$-0.732630\pi$
$859$	−33609.5			−1.33497			−0.667487	+	0.744622i	$0.732630\pi$
$860$	−9724.33	+	10233.3i	−0.385578	+	0.405760i
$861$	−11032.4			−0.436681
$862$		−	9722.70i		−	0.384172i
$863$			33775.6i			1.33226i	0.745838	+	0.666128i	$0.232049\pi$
$863$			33775.6i			1.33226i	−0.745838	+	0.666128i	$0.767951\pi$
$864$	4949.48			0.194890
$865$	31775.9	−	33439.2i	1.24903	−	1.31441i
$866$	−10637.0			−0.417392
$867$			13657.8i			0.534997i
$868$		−	7303.27i		−	0.285587i
$869$	−1379.62			−0.0538556
$870$	12141.2	+	11537.3i	0.473133	+	0.449600i
$871$	10123.0			0.393805
$872$		−	7160.44i		−	0.278077i
$873$			3459.37i			0.134115i
$874$	−8850.25			−0.342522
$875$	−23560.6	−	20206.1i	−0.910280	−	0.780676i
$876$	−4904.04			−0.189146
$877$		−	12637.0i		−	0.486570i	−0.969955	−	0.243285i	$-0.921775\pi$
$877$		−	12637.0i		−	0.486570i	0.969955	−	0.243285i	$-0.0782250\pi$
$878$			7199.25i			0.276723i
$879$	−17442.4			−0.669304
$880$	42.0182	+	39.9282i	0.00160958	+	0.00152952i
$881$	−6579.45			−0.251609			−0.125804	−	0.992055i	$-0.540151\pi$
$881$	−6579.45			−0.251609			−0.125804	+	0.992055i	$0.540151\pi$
$882$			2301.03i			0.0878456i
$883$		−	50442.1i		−	1.92244i	−0.275786	−	0.961219i	$-0.588938\pi$
$883$		−	50442.1i		−	1.92244i	0.275786	−	0.961219i	$-0.411062\pi$
$884$	5641.03			0.214625
$885$	1704.91	−	1794.15i	0.0647569	−	0.0681465i
$886$	−10744.2			−0.407401
$887$		−	984.823i		−	0.0372797i	−0.999826	−	0.0186399i	$-0.994066\pi$
$887$		−	984.823i		−	0.0372797i	0.999826	−	0.0186399i	$-0.00593360\pi$
$888$		−	1330.17i		−	0.0502676i
$889$	26587.7			1.00306
$890$	−13354.0	+	14053.0i	−0.502952	+	0.529278i
$891$	−145.041			−0.00545348
$892$		−	8950.64i		−	0.335975i
$893$			40314.6i			1.51072i
$894$	−8705.42			−0.325674
$895$	−26041.5	−	24746.2i	−0.972594	−	0.924217i
$896$	21658.0			0.807525
$897$			8663.74i			0.322490i
$898$			15909.1i			0.591196i
$899$	18904.7			0.701342
$900$	−292.738	−	5735.31i	−0.0108422	−	0.212419i
$901$	8799.79			0.325376
$902$			504.503i			0.0186232i
$903$		−	16480.5i		−	0.607348i
$904$	35281.6			1.29806
$905$	−27510.7	−	26142.3i	−1.01048	−	0.960221i
$906$	−3870.79			−0.141941
$907$		−	43679.9i		−	1.59908i	−0.600612	−	0.799541i	$-0.705076\pi$
$907$		−	43679.9i		−	1.59908i	0.600612	−	0.799541i	$-0.294924\pi$
$908$			4782.58i			0.174797i
$909$	−310.415			−0.0113265
$910$	16941.7	−	17828.4i	0.617154	−	0.649458i
$911$	−10364.3			−0.376930			−0.188465	−	0.982080i	$-0.560351\pi$
$911$	−10364.3			−0.376930			−0.188465	+	0.982080i	$0.560351\pi$
$912$		−	910.612i		−	0.0330629i
$913$		−	311.435i		−	0.0112891i
$914$	−16245.6			−0.587918
$915$	−3173.43	+	3339.54i	−0.114656	+	0.120658i
$916$	13180.6			0.475435
$917$			7143.58i			0.257254i
$918$		−	872.184i		−	0.0313577i
$919$	−11451.9			−0.411059			−0.205530	−	0.978651i	$-0.565892\pi$
$919$	−11451.9			−0.411059			−0.205530	+	0.978651i	$0.565892\pi$
$920$	−8966.06	−	8520.09i	−0.321307	−	0.305325i
$921$	−24374.6			−0.872063
$922$			10613.0i			0.379091i
$923$		−	34592.7i		−	1.23362i
$924$	−609.020			−0.0216832
$925$	−2482.31	+	126.701i	−0.0882356	+	0.00450367i
$926$	−11009.1			−0.390692
$927$			15806.7i			0.560044i
$928$			53796.4i			1.90297i
$929$	27701.8			0.978326			0.489163	−	0.872192i	$-0.337302\pi$
$929$	27701.8			0.978326			0.489163	+	0.872192i	$0.337302\pi$
$930$	2665.12	+	2532.56i	0.0939708	+	0.0892968i
$931$	15752.5			0.554529
$932$			11715.3i			0.411746i
$933$			22008.8i			0.772277i
$934$	12262.5			0.429596
$935$	261.806	−	275.510i	0.00915721	−	0.00963652i
$936$	11681.8			0.407940
$937$			5878.01i			0.204937i	0.994736	+	0.102469i	$0.0326741\pi$
$937$			5878.01i			0.204937i	−0.994736	+	0.102469i	$0.967326\pi$
$938$		−	6572.03i		−	0.228768i
$939$	6607.97			0.229652
$940$	−15118.0	+	15909.3i	−0.524568	+	0.552026i
$941$	−28786.0			−0.997234			−0.498617	−	0.866823i	$-0.666159\pi$
$941$	−28786.0			−0.997234			−0.498617	+	0.866823i	$0.666159\pi$
$942$		−	9030.46i		−	0.312344i
$943$			8214.90i			0.283684i
$944$	213.647			0.00736612
$945$	4860.00	+	4618.27i	0.167297	+	0.158976i
$946$	−753.642			−0.0259017
$947$			1695.04i			0.0581641i	0.999577	+	0.0290821i	$0.00925841\pi$
$947$			1695.04i			0.0581641i	−0.999577	+	0.0290821i	$0.990742\pi$
$948$			11799.0i			0.404234i
$949$	−18640.5			−0.637613
$950$	22269.4	−	1136.66i	0.760543	−	0.0388192i
$951$	30026.6			1.02385
$952$		−	9401.72i		−	0.320075i
$953$			31929.4i			1.08530i	0.839958	+	0.542651i	$0.182580\pi$
$953$			31929.4i			1.08530i	−0.839958	+	0.542651i	$0.817420\pi$
$954$	7098.50			0.240904
$955$	28102.9	+	26705.1i	0.952241	+	0.904877i
$956$	11710.2			0.396166
$957$		−	1576.46i		−	0.0532495i
$958$			18465.1i			0.622735i
$959$	−7868.57			−0.264952
$960$	−6671.66	+	7020.87i	−0.224299	+	0.236039i
$961$	−25641.2			−0.860704
$962$		−	1969.48i		−	0.0660069i
$963$		−	12255.6i		−	0.410106i
$964$	1951.46			0.0651994
$965$	13802.3	−	14524.8i	0.460427	−	0.484527i
$966$	5624.66			0.187340
$967$			10897.1i			0.362385i	0.983448	+	0.181193i	$0.0579957\pi$
$967$			10897.1i			0.362385i	−0.983448	+	0.181193i	$0.942004\pi$
$968$		−	29607.7i		−	0.983087i
$969$	−5970.82			−0.197947
$970$	−5300.77	−	5037.11i	−0.175461	−	0.166734i
$971$	7041.97			0.232737			0.116368	−	0.993206i	$-0.462875\pi$
$971$	7041.97			0.232737			0.116368	+	0.993206i	$0.462875\pi$
$972$			1240.44i			0.0409332i
$973$			1715.81i			0.0565328i
$974$	21707.0			0.714103
$975$	−1112.71	−	21800.1i	−0.0365490	−	0.716065i
$976$	−397.671			−0.0130422
$977$			37607.6i			1.23150i	0.787943	+	0.615749i	$0.211146\pi$
$977$			37607.6i			1.23150i	−0.787943	+	0.615749i	$0.788854\pi$
$978$			4500.90i			0.147160i
$979$	1824.69			0.0595684
$980$	6216.38	+	5907.18i	0.202628	+	0.192549i
$981$	2890.07			0.0940599
$982$		−	11939.0i		−	0.387974i
$983$		−	25297.7i		−	0.820826i	−0.911900	−	0.410413i	$-0.865385\pi$
$983$		−	25297.7i		−	0.820826i	0.911900	−	0.410413i	$-0.134615\pi$
$984$	11076.6			0.358851
$985$	−12924.7	+	13601.2i	−0.418086	+	0.439970i
$986$	9479.85			0.306187
$987$		−	25621.4i		−	0.826281i
$988$		−	31151.5i		−	1.00310i
$989$	−12271.6			−0.394556
$990$	211.190	−	222.245i	0.00677987	−	0.00713475i
$991$	−41686.5			−1.33624			−0.668120	−	0.744053i	$-0.732901\pi$
$991$	−41686.5			−1.33624			−0.668120	+	0.744053i	$0.732901\pi$
$992$			11808.9i			0.377955i
$993$		−	26087.8i		−	0.833708i
$994$	−22458.3			−0.716633
$995$	25191.2	+	23938.2i	0.802629	+	0.762707i
$996$	−2663.50			−0.0847351
$997$		−	25465.9i		−	0.808939i	−0.914551	−	0.404470i	$-0.867456\pi$
$997$		−	25465.9i		−	0.808939i	0.914551	−	0.404470i	$-0.132544\pi$
$998$		−	19350.6i		−	0.613761i
$999$	536.878			0.0170031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.4.b.a.4.3	yes	4
3.2	odd	2		45.4.b.b.19.2		4
4.3	odd	2		240.4.f.f.49.1		4
5.2	odd	4		75.4.a.f.1.1		2
5.3	odd	4		75.4.a.c.1.2		2
5.4	even	2	inner	15.4.b.a.4.2	✓	4
8.3	odd	2		960.4.f.p.769.4		4
8.5	even	2		960.4.f.q.769.2		4
12.11	even	2		720.4.f.j.289.4		4
15.2	even	4		225.4.a.i.1.2		2
15.8	even	4		225.4.a.o.1.1		2
15.14	odd	2		45.4.b.b.19.3		4
20.3	even	4		1200.4.a.bt.1.2		2
20.7	even	4		1200.4.a.bn.1.1		2
20.19	odd	2		240.4.f.f.49.3		4
40.19	odd	2		960.4.f.p.769.2		4
40.29	even	2		960.4.f.q.769.4		4
60.59	even	2		720.4.f.j.289.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.b.a.4.2	✓	4	5.4	even	2	inner
15.4.b.a.4.3	yes	4	1.1	even	1	trivial
45.4.b.b.19.2		4	3.2	odd	2
45.4.b.b.19.3		4	15.14	odd	2
75.4.a.c.1.2		2	5.3	odd	4
75.4.a.f.1.1		2	5.2	odd	4
225.4.a.i.1.2		2	15.2	even	4
225.4.a.o.1.1		2	15.8	even	4
240.4.f.f.49.1		4	4.3	odd	2
240.4.f.f.49.3		4	20.19	odd	2
720.4.f.j.289.3		4	60.59	even	2
720.4.f.j.289.4		4	12.11	even	2
960.4.f.p.769.2		4	40.19	odd	2
960.4.f.p.769.4		4	8.3	odd	2
960.4.f.q.769.2		4	8.5	even	2
960.4.f.q.769.4		4	40.29	even	2
1200.4.a.bn.1.1		2	20.7	even	4
1200.4.a.bt.1.2		2	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	15.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.70156i q^{2} +3.00000i q^{3} +5.10469 q^{4} +(-8.10469 - 7.70156i) q^{5} -5.10469 q^{6} -22.2094i q^{7} +22.2984i q^{8} -9.00000 q^{9} +(13.1047 - 13.7906i) q^{10} -1.79063 q^{11} +15.3141i q^{12} +58.2094i q^{13} +37.7906 q^{14} +(23.1047 - 24.3141i) q^{15} +2.89531 q^{16} -18.9844i q^{17} -15.3141i q^{18} -104.837 q^{19} +(-41.3719 - 39.3141i) q^{20} +66.6281 q^{21} -3.04686i q^{22} -49.6125i q^{23} -66.8953 q^{24} +(6.37188 + 124.837i) q^{25} -99.0469 q^{26} -27.0000i q^{27} -113.372i q^{28} +293.466 q^{29} +(41.3719 + 39.3141i) q^{30} +64.4187 q^{31} +183.314i q^{32} -5.37188i q^{33} +32.3031 q^{34} +(-171.047 + 180.000i) q^{35} -45.9422 q^{36} +19.8844i q^{37} -178.388i q^{38} -174.628 q^{39} +(171.733 - 180.722i) q^{40} -165.581 q^{41} +113.372i q^{42} -247.350i q^{43} -9.14059 q^{44} +(72.9422 + 69.3141i) q^{45} +84.4187 q^{46} -384.544i q^{47} +8.68594i q^{48} -150.256 q^{49} +(-212.419 + 10.8422i) q^{50} +56.9531 q^{51} +297.141i q^{52} +463.528i q^{53} +45.9422 q^{54} +(14.5125 + 13.7906i) q^{55} +495.234 q^{56} -314.512i q^{57} +499.350i q^{58} +73.7906 q^{59} +(117.942 - 124.116i) q^{60} -137.350 q^{61} +109.612i q^{62} +199.884i q^{63} -288.758 q^{64} +(448.303 - 471.769i) q^{65} +9.14059 q^{66} -173.906i q^{67} -96.9093i q^{68} +148.837 q^{69} +(-306.281 - 291.047i) q^{70} -594.281 q^{71} -200.686i q^{72} +320.231i q^{73} -33.8345 q^{74} +(-374.512 + 19.1156i) q^{75} -535.163 q^{76} +39.7687i q^{77} -297.141i q^{78} +770.469 q^{79} +(-23.4656 - 22.2984i) q^{80} +81.0000 q^{81} -281.747i q^{82} +173.925i q^{83} +340.116 q^{84} +(-146.209 + 153.862i) q^{85} +420.881 q^{86} +880.397i q^{87} -39.9282i q^{88} -1019.02 q^{89} +(-117.942 + 124.116i) q^{90} +1292.79 q^{91} -253.256i q^{92} +193.256i q^{93} +654.325 q^{94} +(849.675 + 807.412i) q^{95} -549.942 q^{96} -384.375i q^{97} -255.670i q^{98} +16.1156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{4} + 6 q^{5} + 18 q^{6} - 36 q^{9} + 14 q^{10} - 84 q^{11} + 228 q^{14} + 54 q^{15} + 50 q^{16} - 112 q^{19} - 396 q^{20} + 36 q^{21} - 306 q^{24} + 256 q^{25} - 12 q^{26} + 636 q^{29} + 396 q^{30}+ \cdots + 756 q^{99}+O(q^{100}) \) 4 * q - 18 * q^4 + 6 * q^5 + 18 * q^6 - 36 * q^9 + 14 * q^10 - 84 * q^11 + 228 * q^14 + 54 * q^15 + 50 * q^16 - 112 * q^19 - 396 * q^20 + 36 * q^21 - 306 * q^24 + 256 * q^25 - 12 * q^26 + 636 * q^29 + 396 * q^30 + 104 * q^31 - 716 * q^34 - 300 * q^35 + 162 * q^36 - 468 * q^39 + 418 * q^40 - 816 * q^41 + 1116 * q^44 - 54 * q^45 + 184 * q^46 - 140 * q^49 - 696 * q^50 + 612 * q^51 - 162 * q^54 - 864 * q^55 + 60 * q^56 + 372 * q^59 + 126 * q^60 + 680 * q^61 + 958 * q^64 + 948 * q^65 - 1116 * q^66 + 288 * q^69 + 1080 * q^70 - 72 * q^71 - 3132 * q^74 - 576 * q^75 - 2448 * q^76 - 760 * q^79 + 444 * q^80 + 324 * q^81 + 2052 * q^84 - 508 * q^85 + 4296 * q^86 - 2232 * q^89 - 126 * q^90 + 1944 * q^91 + 3232 * q^94 + 2784 * q^95 - 1854 * q^96 + 756 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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