LMFDB - Embedded newform 63.4.e.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, 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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$-2.27818 + 3.94593i$ of defining polynomial
Character	$\chi$	$=$	63.37
Dual form			63.4.e.c.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} +(2.26047 - 18.3818i) q^{7} +21.6905 q^{8} +O(q^{10})$	\(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} +(2.26047 - 18.3818i) q^{7} +21.6905 q^{8} +(40.7184 + 70.5264i) q^{10} +(-5.69708 - 9.86762i) q^{11} -13.0987 q^{13} +(67.3835 + 50.7968i) q^{14} +(1.62706 - 2.81815i) q^{16} +(26.6337 + 46.1309i) q^{17} +(21.2111 - 36.7388i) q^{19} -228.071 q^{20} +51.9159 q^{22} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +(29.8412 - 51.6864i) q^{26} +(-217.558 + 92.2999i) q^{28} -186.493 q^{29} +(78.9369 + 136.723i) q^{31} +(94.1753 + 163.116i) q^{32} -242.706 q^{34} +(-264.324 - 199.260i) q^{35} +(-1.87294 + 3.24403i) q^{37} +(96.6457 + 167.395i) q^{38} +(193.839 - 335.739i) q^{40} +39.3230 q^{41} +429.439 q^{43} +(-72.6974 + 125.916i) q^{44} +(346.478 + 600.118i) q^{46} +(10.5934 - 18.3484i) q^{47} +(-332.781 - 83.1031i) q^{49} +885.992 q^{50} +(83.5726 + 144.752i) q^{52} +(182.952 + 316.882i) q^{53} -203.650 q^{55} +(49.0307 - 398.709i) q^{56} +(424.866 - 735.889i) q^{58} +(-113.289 - 196.222i) q^{59} +(-325.987 + 564.626i) q^{61} -719.331 q^{62} -832.161 q^{64} +(-117.058 + 202.750i) q^{65} +(-72.7166 - 125.949i) q^{67} +(339.858 - 588.652i) q^{68} +(1388.44 - 589.055i) q^{70} +368.962 q^{71} +(-304.453 - 527.328i) q^{73} +(-8.53380 - 14.7810i) q^{74} -541.328 q^{76} +(-194.263 + 82.4170i) q^{77} +(-455.119 + 788.289i) q^{79} +(-29.0808 - 50.3694i) q^{80} +(-89.5850 + 155.166i) q^{82} +327.929 q^{83} +952.058 q^{85} +(-978.340 + 1694.53i) q^{86} +(-123.572 - 214.033i) q^{88} +(-18.8059 + 32.5728i) q^{89} +(-29.6092 + 240.777i) q^{91} -1940.68 q^{92} +(48.2676 + 83.6019i) q^{94} +(-379.111 - 656.640i) q^{95} +722.013 q^{97} +(1086.05 - 1123.80i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8}+O(q^{10}) $ 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8	$ 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8} + 55 q^{10} + 35 q^{11} + 124 q^{13} + 326 q^{14} - 241 q^{16} + 48 q^{17} + 202 q^{19} - 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} + 274 q^{26} - 201 q^{28} - 106 q^{29} + 95 q^{31} + 683 q^{32} - 48 q^{34} - 56 q^{35} - 262 q^{37} - 398 q^{38} - 21 q^{40} - 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} - 210 q^{47} - 303 q^{49} + 2756 q^{50} - 324 q^{52} + 393 q^{53} - 2062 q^{55} - 1299 q^{56} + 1249 q^{58} + 1143 q^{59} + 70 q^{61} - 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} + 1944 q^{68} + 3251 q^{70} - 636 q^{71} - 988 q^{73} + 1002 q^{74} - 4680 q^{76} - 1073 q^{77} - 861 q^{79} + 175 q^{80} - 124 q^{82} - 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} + 1766 q^{89} - 654 q^{91} + 1344 q^{92} + 3294 q^{94} - 736 q^{95} + 38 q^{97} + 4267 q^{98}+O(q^{100}) $ 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8 + 55 * q^10 + 35 * q^11 + 124 * q^13 + 326 * q^14 - 241 * q^16 + 48 * q^17 + 202 * q^19 - 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 + 274 * q^26 - 201 * q^28 - 106 * q^29 + 95 * q^31 + 683 * q^32 - 48 * q^34 - 56 * q^35 - 262 * q^37 - 398 * q^38 - 21 * q^40 - 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 - 210 * q^47 - 303 * q^49 + 2756 * q^50 - 324 * q^52 + 393 * q^53 - 2062 * q^55 - 1299 * q^56 + 1249 * q^58 + 1143 * q^59 + 70 * q^61 - 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 + 1944 * q^68 + 3251 * q^70 - 636 * q^71 - 988 * q^73 + 1002 * q^74 - 4680 * q^76 - 1073 * q^77 - 861 * q^79 + 175 * q^80 - 124 * q^82 - 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 + 1766 * q^89 - 654 * q^91 + 1344 * q^92 + 3294 * q^94 - 736 * q^95 + 38 * q^97 + 4267 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.27818	+	3.94593i	−0.805459	+	1.39510i	0.110521	+	0.993874i	$0.464748\pi$
$2$	−2.27818	+	3.94593i	−0.805459	+	1.39510i	−0.915981	+	0.401223i	$0.868585\pi$
$3$		0			0
$3$		0			0
$4$	−6.38024	−	11.0509i	−0.797530	−	1.38136i
$5$	8.93660	−	15.4786i	0.799314	−	1.38445i	−0.120749	−	0.992683i	$-0.538530\pi$
$5$	8.93660	−	15.4786i	0.799314	−	1.38445i	0.920063	−	0.391769i	$-0.128137\pi$
$6$		0			0
$7$	2.26047	−	18.3818i	0.122054	−	0.992523i
$7$	2.26047	−	18.3818i	0.122054	−	0.992523i
$8$	21.6905			0.958592
$9$		0			0
$10$	40.7184	+	70.5264i	1.28763	+	2.23024i
$11$	−5.69708	−	9.86762i	−0.156158	−	0.270473i	0.777322	−	0.629102i	$-0.216577\pi$
$11$	−5.69708	−	9.86762i	−0.156158	−	0.270473i	−0.933480	+	0.358630i	$0.883244\pi$
$12$		0			0
$13$	−13.0987			−0.279455			−0.139728	−	0.990190i	$-0.544623\pi$
$13$	−13.0987			−0.279455			−0.139728	+	0.990190i	$0.544623\pi$
$14$	67.3835	+	50.7968i	1.28636	+	0.969714i
$15$		0			0
$16$	1.62706	−	2.81815i	0.0254228	−	0.0440336i
$17$	26.6337	+	46.1309i	0.379977	+	0.658140i	0.991059	−	0.133428i	$-0.0425984\pi$
$17$	26.6337	+	46.1309i	0.379977	+	0.658140i	−0.611081	+	0.791568i	$0.709265\pi$
$18$		0			0
$19$	21.2111	−	36.7388i	0.256114	−	0.443603i	−0.709083	−	0.705125i	$-0.750891\pi$
$19$	21.2111	−	36.7388i	0.256114	−	0.443603i	0.965198	+	0.261522i	$0.0842244\pi$
$20$	−228.071			−2.54991
$21$		0			0
$22$	51.9159			0.503114
$23$	76.0427	−	131.710i	0.689391	−	1.19406i	−0.282644	−	0.959225i	$-0.591211\pi$
$23$	76.0427	−	131.710i	0.689391	−	1.19406i	0.972035	−	0.234836i	$-0.0754553\pi$
$24$		0			0
$25$	−97.2257	−	168.400i	−0.777806	−	1.34720i
$26$	29.8412	−	51.6864i	0.225090	−	0.389867i
$27$		0			0
$28$	−217.558	+	92.2999i	−1.46838	+	0.622966i
$29$	−186.493			−1.19417			−0.597085	−	0.802178i	$-0.703675\pi$
$29$	−186.493			−1.19417			−0.597085	+	0.802178i	$0.703675\pi$
$30$		0			0
$31$	78.9369	+	136.723i	0.457338	+	0.792133i	0.998819	−	0.0485801i	$-0.0154696\pi$
$31$	78.9369	+	136.723i	0.457338	+	0.792133i	−0.541481	+	0.840713i	$0.682136\pi$
$32$	94.1753	+	163.116i	0.520250	+	0.901099i
$33$		0			0
$34$	−242.706			−1.22423
$35$	−264.324	−	199.260i	−1.27654	−	0.962316i
$36$		0			0
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	−0.870156	−	0.492776i	$-0.835982\pi$
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	0.861834	+	0.507190i	$0.169316\pi$
$38$	96.6457	+	167.395i	0.412579	+	0.714608i
$39$		0			0
$40$	193.839	−	335.739i	0.766216	−	1.32712i
$41$	39.3230			0.149786			0.0748930	−	0.997192i	$-0.476138\pi$
$41$	39.3230			0.149786			0.0748930	+	0.997192i	$0.476138\pi$
$42$		0			0
$43$	429.439			1.52300			0.761498	−	0.648168i	$-0.224464\pi$
$43$	429.439			1.52300			0.761498	+	0.648168i	$0.224464\pi$
$44$	−72.6974	+	125.916i	−0.249080	+	0.431420i
$45$		0			0
$46$	346.478	+	600.118i	1.11055	+	1.92354i
$47$	10.5934	−	18.3484i	0.0328768	−	0.0569444i	−0.849119	−	0.528202i	$-0.822866\pi$
$47$	10.5934	−	18.3484i	0.0328768	−	0.0569444i	0.881996	+	0.471258i	$0.156200\pi$
$48$		0			0
$49$	−332.781	−	83.1031i	−0.970206	−	0.242283i
$50$	885.992			2.50596
$51$		0			0
$52$	83.5726	+	144.752i	0.222874	+	0.386029i
$53$	182.952	+	316.882i	0.474158	+	0.821266i	0.999562	−	0.0295866i	$-0.00941909\pi$
$53$	182.952	+	316.882i	0.474158	+	0.821266i	−0.525404	+	0.850853i	$0.676086\pi$
$54$		0			0
$55$	−203.650			−0.499276
$56$	49.0307	−	398.709i	0.117000	−	0.951425i
$57$		0			0
$58$	424.866	−	735.889i	0.961856	−	1.66598i
$59$	−113.289	−	196.222i	−0.249982	−	0.432982i	0.713538	−	0.700616i	$-0.247091\pi$
$59$	−113.289	−	196.222i	−0.249982	−	0.432982i	−0.963521	+	0.267634i	$0.913758\pi$
$60$		0			0
$61$	−325.987	+	564.626i	−0.684235	+	1.18513i	0.289442	+	0.957196i	$0.406530\pi$
$61$	−325.987	+	564.626i	−0.684235	+	1.18513i	−0.973677	+	0.227934i	$0.926803\pi$
$62$	−719.331			−1.47347
$63$		0			0
$64$	−832.161			−1.62532
$65$	−117.058	+	202.750i	−0.223372	+	0.386892i
$66$		0			0
$67$	−72.7166	−	125.949i	−0.132593	−	0.229658i	0.792082	−	0.610414i	$-0.208997\pi$
$67$	−72.7166	−	125.949i	−0.132593	−	0.229658i	−0.924675	+	0.380756i	$0.875664\pi$
$68$	339.858	−	588.652i	0.606086	−	1.04977i
$69$		0			0
$70$	1388.44	−	589.055i	2.37073	−	1.00579i
$71$	368.962			0.616728			0.308364	−	0.951268i	$-0.400218\pi$
$71$	368.962			0.616728			0.308364	+	0.951268i	$0.400218\pi$
$72$		0			0
$73$	−304.453	−	527.328i	−0.488130	−	0.845466i	0.511777	−	0.859119i	$-0.328988\pi$
$73$	−304.453	−	527.328i	−0.488130	−	0.845466i	−0.999907	+	0.0136522i	$0.995654\pi$
$74$	−8.53380	−	14.7810i	−0.0134059	−	0.0232197i
$75$		0			0
$76$	−541.328			−0.817034
$77$	−194.263	+	82.4170i	−0.287510	+	0.121978i
$78$		0			0
$79$	−455.119	+	788.289i	−0.648163	+	1.12265i	0.335399	+	0.942076i	$0.391129\pi$
$79$	−455.119	+	788.289i	−0.648163	+	1.12265i	−0.983561	+	0.180574i	$0.942204\pi$
$80$	−29.0808	−	50.3694i	−0.0406416	−	0.0703933i
$81$		0			0
$82$	−89.5850	+	155.166i	−0.120646	+	0.208966i
$83$	327.929			0.433674			0.216837	−	0.976208i	$-0.430426\pi$
$83$	327.929			0.433674			0.216837	+	0.976208i	$0.430426\pi$
$84$		0			0
$85$	952.058			1.21489
$86$	−978.340	+	1694.53i	−1.22671	+	2.12473i
$87$		0			0
$88$	−123.572	−	214.033i	−0.149691	−	0.259273i
$89$	−18.8059	+	32.5728i	−0.0223980	+	0.0387945i	−0.877007	−	0.480477i	$-0.840463\pi$
$89$	−18.8059	+	32.5728i	−0.0223980	+	0.0387945i	0.854609	+	0.519272i	$0.173797\pi$
$90$		0			0
$91$	−29.6092	+	240.777i	−0.0341086	+	0.277366i
$92$	−1940.68			−2.19924
$93$		0			0
$94$	48.2676	+	83.6019i	0.0529619	+	0.0917327i
$95$	−379.111	−	656.640i	−0.409431	−	0.709156i
$96$		0			0
$97$	722.013			0.755766			0.377883	−	0.925853i	$-0.376652\pi$
$97$	722.013			0.755766			0.377883	+	0.925853i	$0.376652\pi$
$98$	1086.05	−	1123.80i	1.11947	−	1.15838i
$99$		0			0
$100$	−1240.65	+	2148.86i	−1.24065	+	2.14886i
$101$	759.336	+	1315.21i	0.748087	+	1.29572i	0.948739	+	0.316062i	$0.102361\pi$
$101$	759.336	+	1315.21i	0.748087	+	1.29572i	−0.200652	+	0.979663i	$0.564306\pi$
$102$		0			0
$103$	525.942	−	910.957i	0.503132	−	0.871450i	−0.496862	−	0.867830i	$-0.665514\pi$
$103$	525.942	−	910.957i	0.503132	−	0.871450i	0.999993	−	0.00361990i	$-0.00115225\pi$
$104$	−284.116			−0.267883
$105$		0			0
$106$	−1667.19			−1.52766
$107$	383.260	−	663.826i	0.346273	−	0.599762i	−0.639312	−	0.768948i	$-0.720781\pi$
$107$	383.260	−	663.826i	0.346273	−	0.599762i	0.985584	+	0.169186i	$0.0541139\pi$
$108$		0			0
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	0.988150	+	0.153491i	$0.0490516\pi$
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	−0.361148	+	0.932509i	$0.617615\pi$
$110$	463.952	−	803.588i	0.402146	−	0.696538i
$111$		0			0
$112$	−48.1247	−	36.2786i	−0.0406014	−	0.0306072i
$113$	−362.564			−0.301833			−0.150917	−	0.988546i	$-0.548222\pi$
$113$	−362.564			−0.301833			−0.150917	+	0.988546i	$0.548222\pi$
$114$		0			0
$115$	−1359.13	−	2354.08i	−1.10208	−	1.90886i
$116$	1189.87	+	2060.92i	0.952386	+	1.64958i
$117$		0			0
$118$	1032.37			0.805402
$119$	908.173	−	385.297i	0.699597	−	0.296808i
$120$		0			0
$121$	600.587	−	1040.25i	0.451230	−	0.781553i
$122$	−1485.31	−	2572.64i	−1.10225	−	1.90915i
$123$		0			0
$124$	1007.27	−	1744.65i	0.729481	−	1.26350i
$125$	−1241.32			−0.888216
$126$		0			0
$127$	974.777			0.681082			0.340541	−	0.940230i	$-0.389390\pi$
$127$	974.777			0.681082			0.340541	+	0.940230i	$0.389390\pi$
$128$	1142.41	−	1978.72i	0.788875	−	1.36637i
$129$		0			0
$130$	−533.357	−	923.802i	−0.359835	−	0.623252i
$131$	−896.351	+	1552.53i	−0.597821	+	1.03546i	0.395321	+	0.918543i	$0.370633\pi$
$131$	−896.351	+	1552.53i	−0.597821	+	1.03546i	−0.993142	+	0.116914i	$0.962700\pi$
$132$		0			0
$133$	−627.377	−	472.946i	−0.409026	−	0.308343i
$134$	662.647			0.427194
$135$		0			0
$136$	577.697	+	1000.60i	0.364243	+	0.630888i
$137$	842.208	+	1458.75i	0.525217	+	0.909702i	0.999569	+	0.0293665i	$0.00934900\pi$
$137$	842.208	+	1458.75i	0.525217	+	0.909702i	−0.474352	+	0.880335i	$0.657318\pi$
$138$		0			0
$139$	315.089			0.192270			0.0961350	−	0.995368i	$-0.469352\pi$
$139$	315.089			0.192270			0.0961350	+	0.995368i	$0.469352\pi$
$140$	−515.547	+	4192.35i	−0.311226	+	2.53084i
$141$		0			0
$142$	−840.563	+	1455.90i	−0.496750	+	0.860396i
$143$	74.6241	+	129.253i	0.0436390	+	0.0755850i
$144$		0			0
$145$	−1666.62	+	2886.67i	−0.954517	+	1.65327i
$146$	2774.40			1.57268
$147$		0			0
$148$	47.7992			0.0265478
$149$	946.887	−	1640.06i	0.520617	−	0.901736i	−0.479095	−	0.877763i	$-0.659035\pi$
$149$	946.887	−	1640.06i	0.520617	−	0.901736i	0.999713	−	0.0239729i	$-0.00763155\pi$
$150$		0			0
$151$	1005.92	+	1742.31i	0.542124	+	0.938986i	0.998782	+	0.0493434i	$0.0157129\pi$
$151$	1005.92	+	1742.31i	0.542124	+	0.938986i	−0.456658	+	0.889642i	$0.650954\pi$
$152$	460.079	−	796.881i	0.245509	−	0.425234i
$153$		0			0
$154$	117.355	−	954.308i	0.0614071	−	0.499353i
$155$	2821.71			1.46223
$156$		0			0
$157$	1914.25	+	3315.58i	0.973082	+	1.68543i	0.686125	+	0.727483i	$0.259310\pi$
$157$	1914.25	+	3315.58i	0.973082	+	1.68543i	0.286956	+	0.957944i	$0.407357\pi$
$158$	−2073.69	−	3591.73i	−1.04414	−	1.80850i
$159$		0			0
$160$	3366.43			1.66337
$161$	−2249.17	−	1695.53i	−1.10099	−	0.829977i
$162$		0			0
$163$	1754.63	−	3039.11i	0.843148	−	1.46038i	−0.0440718	−	0.999028i	$-0.514033\pi$
$163$	1754.63	−	3039.11i	0.843148	−	1.46038i	0.887220	−	0.461347i	$-0.152634\pi$
$164$	−250.890	−	434.554i	−0.119459	−	0.206909i
$165$		0			0
$166$	−747.083	+	1293.99i	−0.349307	+	0.605017i
$167$	343.008			0.158939			0.0794694	−	0.996837i	$-0.474677\pi$
$167$	343.008			0.158939			0.0794694	+	0.996837i	$0.474677\pi$
$168$		0			0
$169$	−2025.42			−0.921905
$170$	−2168.96	+	3756.75i	−0.978541	+	1.69488i
$171$		0			0
$172$	−2739.92	−	4745.68i	−1.21463	−	2.10381i
$173$	−2093.61	+	3626.23i	−0.920081	+	1.59363i	−0.120793	+	0.992678i	$0.538544\pi$
$173$	−2093.61	+	3626.23i	−0.920081	+	1.59363i	−0.799288	+	0.600949i	$0.794790\pi$
$174$		0			0
$175$	−3315.27	+	1406.52i	−1.43206	+	0.607559i
$176$	−37.0779			−0.0158798
$177$		0			0
$178$	−85.6866	−	148.413i	−0.0360813	−	0.0624947i
$179$	−985.143	−	1706.32i	−0.411358	−	0.712493i	0.583681	−	0.811983i	$-0.301612\pi$
$179$	−985.143	−	1706.32i	−0.411358	−	0.712493i	−0.995039	+	0.0994906i	$0.968279\pi$
$180$		0			0
$181$	−3613.10			−1.48376			−0.741878	−	0.670535i	$-0.766065\pi$
$181$	−3613.10			−1.48376			−0.741878	+	0.670535i	$0.766065\pi$
$182$	−882.634	−	665.370i	−0.359479	−	0.270992i
$183$		0			0
$184$	1649.40	−	2856.85i	0.660845	−	1.14462i
$185$	33.4755	+	57.9812i	0.0133036	+	0.0230425i
$186$		0			0
$187$	303.468	−	525.622i	0.118673	−	0.205547i
$188$	−270.355			−0.104881
$189$		0			0
$190$	3454.74			1.31912
$191$	953.884	−	1652.18i	0.361365	−	0.625902i	−0.626821	−	0.779163i	$-0.715644\pi$
$191$	953.884	−	1652.18i	0.361365	−	0.625902i	0.988186	+	0.153261i	$0.0489776\pi$
$192$		0			0
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	0.550685	−	0.834713i	$-0.314366\pi$
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	−0.998225	+	0.0595509i	$0.981033\pi$
$194$	−1644.88	+	2849.01i	−0.608738	+	1.05437i
$195$		0			0
$196$	1204.86	+	4207.74i	0.439087	+	1.53343i
$197$	−1514.32			−0.547668			−0.273834	−	0.961777i	$-0.588292\pi$
$197$	−1514.32			−0.547668			−0.273834	+	0.961777i	$0.588292\pi$
$198$		0			0
$199$	−683.889	−	1184.53i	−0.243616	−	0.421955i	0.718126	−	0.695914i	$-0.245000\pi$
$199$	−683.889	−	1184.53i	−0.243616	−	0.421955i	−0.961742	+	0.273958i	$0.911667\pi$
$200$	−2108.87	−	3652.67i	−0.745598	−	1.29141i
$201$		0			0
$202$	−6919.63			−2.41021
$203$	−421.563	+	3428.08i	−0.145753	+	1.18524i
$204$		0			0
$205$	351.414	−	608.667i	0.119726	−	0.207371i
$206$	2396.38	+	4150.66i	0.810504	+	1.40383i
$207$		0			0
$208$	−21.3123	+	36.9140i	−0.00710453	+	0.0123054i
$209$	−483.366			−0.159977
$210$		0			0
$211$	4302.52			1.40378			0.701891	−	0.712285i	$-0.252339\pi$
$211$	4302.52			1.40378			0.701891	+	0.712285i	$0.252339\pi$
$212$	2334.55	−	4043.57i	0.756311	−	1.30997i
$213$		0			0
$214$	1746.27	+	3024.64i	0.557817	+	0.966167i
$215$	3837.72	−	6647.13i	1.21735	−	2.10851i
$216$		0			0
$217$	2691.64	−	1141.94i	0.842030	−	0.357236i
$218$	−6502.16			−2.02010
$219$		0			0
$220$	1299.34	+	2250.51i	0.398187	+	0.689680i
$221$	−348.866	−	604.253i	−0.106187	−	0.183921i
$222$		0			0
$223$	−1497.19			−0.449592			−0.224796	−	0.974406i	$-0.572172\pi$
$223$	−1497.19			−0.449592			−0.224796	+	0.974406i	$0.572172\pi$
$224$	3211.25	−	1362.39i	0.957861	−	0.406377i
$225$		0			0
$226$	825.987	−	1430.65i	0.243114	−	0.421086i
$227$	801.662	+	1388.52i	0.234397	+	0.405988i	0.959097	−	0.283076i	$-0.0913550\pi$
$227$	801.662	+	1388.52i	0.234397	+	0.405988i	−0.724700	+	0.689065i	$0.758022\pi$
$228$		0			0
$229$	−505.261	+	875.137i	−0.145802	+	0.252536i	−0.929672	−	0.368389i	$-0.879909\pi$
$229$	−505.261	+	875.137i	−0.145802	+	0.252536i	0.783870	+	0.620925i	$0.213243\pi$
$230$	12385.4			3.55072
$231$		0			0
$232$	−4045.13			−1.14472
$233$	99.1084	−	171.661i	0.0278661	−	0.0482656i	−0.851756	−	0.523939i	$-0.824462\pi$
$233$	99.1084	−	171.661i	0.0278661	−	0.0482656i	0.879622	+	0.475673i	$0.157795\pi$
$234$		0			0
$235$	−189.339	−	327.944i	−0.0525578	−	0.0910329i
$236$	−1445.62	+	2503.88i	−0.398736	+	0.690631i
$237$		0			0
$238$	−548.629	+	4461.36i	−0.149422	+	1.21507i
$239$	1201.19			0.325098			0.162549	−	0.986700i	$-0.448028\pi$
$239$	1201.19			0.325098			0.162549	+	0.986700i	$0.448028\pi$
$240$		0			0
$241$	1366.35	+	2366.58i	0.365204	+	0.632551i	0.988809	−	0.149188i	$-0.0476660\pi$
$241$	1366.35	+	2366.58i	0.365204	+	0.632551i	−0.623605	+	0.781739i	$0.714333\pi$
$242$	2736.49	+	4739.74i	0.726894	+	1.25902i
$243$		0			0
$244$	8319.49			2.18279
$245$	−4260.25	+	4408.33i	−1.11093	+	1.14954i
$246$		0			0
$247$	−277.838	+	481.229i	−0.0715724	+	0.123967i
$248$	1712.18	+	2965.58i	0.438401	+	0.759332i
$249$		0			0
$250$	2827.95	−	4898.16i	0.715422	−	1.23915i
$251$	−7565.82			−1.90259			−0.951295	−	0.308281i	$-0.900246\pi$
$251$	−7565.82			−1.90259			−0.951295	+	0.308281i	$0.900246\pi$
$252$		0			0
$253$	−1732.88			−0.430615
$254$	−2220.72	+	3846.40i	−0.548584	+	0.950175i
$255$		0			0
$256$	1876.61	+	3250.38i	0.458156	+	0.793550i
$257$	2504.34	−	4337.64i	0.607846	−	1.05282i	−0.383749	−	0.923437i	$-0.625367\pi$
$257$	2504.34	−	4337.64i	0.607846	−	1.05282i	0.991595	−	0.129382i	$-0.0412994\pi$
$258$		0			0
$259$	55.3973	+	41.7610i	0.0132904	+	0.0100189i
$260$	2987.42			0.712584
$261$		0			0
$262$	−4084.10	−	7073.88i	−0.963041	−	1.66804i
$263$	−3124.40	−	5411.63i	−0.732544	−	1.26880i	−0.955793	−	0.294042i	$-0.905000\pi$
$263$	−3124.40	−	5411.63i	−0.732544	−	1.26880i	0.223249	−	0.974761i	$-0.428334\pi$
$264$		0			0
$265$	6539.88			1.51601
$266$	3295.49	−	1398.13i	0.759622	−	0.322274i
$267$		0			0
$268$	−927.898	+	1607.17i	−0.211494	+	0.366318i
$269$	−1794.22	−	3107.69i	−0.406676	−	0.704383i	0.587839	−	0.808978i	$-0.299979\pi$
$269$	−1794.22	−	3107.69i	−0.406676	−	0.704383i	−0.994515	+	0.104595i	$0.966645\pi$
$270$		0			0
$271$	991.571	−	1717.45i	0.222264	−	0.384973i	−0.733231	−	0.679980i	$-0.761988\pi$
$271$	991.571	−	1717.45i	0.222264	−	0.384973i	0.955495	+	0.295007i	$0.0953218\pi$
$272$	173.338			0.0386404
$273$		0			0
$274$	−7674.81			−1.69216
$275$	−1107.80	+	1918.77i	−0.242920	+	0.420751i
$276$		0			0
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	−0.920493	−	0.390760i	$-0.872212\pi$
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	0.121838	−	0.992550i	$-0.461121\pi$
$278$	−717.831	+	1243.32i	−0.154866	+	0.268235i
$279$		0			0
$280$	−5733.32	−	4322.04i	−1.22368	−	0.922468i
$281$	5312.05			1.12772			0.563861	−	0.825869i	$-0.309315\pi$
$281$	5312.05			1.12772			0.563861	+	0.825869i	$0.309315\pi$
$282$		0			0
$283$	545.882	+	945.495i	0.114662	+	0.198600i	0.917645	−	0.397402i	$-0.130088\pi$
$283$	545.882	+	945.495i	0.114662	+	0.198600i	−0.802983	+	0.596002i	$0.796755\pi$
$284$	−2354.06	−	4077.36i	−0.491859	−	0.851925i
$285$		0			0
$286$	−680.030			−0.140598
$287$	88.8886	−	722.827i	0.0182820	−	0.148666i
$288$		0			0
$289$	1037.79	−	1797.51i	0.211234	−	0.365869i
$290$	−7593.72	−	13152.7i	−1.53765	−	2.66329i
$291$		0			0
$292$	−3884.96	+	6728.95i	−0.778597	+	1.34857i
$293$	7191.86			1.43397			0.716985	−	0.697089i	$-0.245522\pi$
$293$	7191.86			1.43397			0.716985	+	0.697089i	$0.245522\pi$
$294$		0			0
$295$	−4049.67			−0.799257
$296$	−40.6249	+	70.3645i	−0.00797729	+	0.0138171i
$297$		0			0
$298$	4314.36	+	7472.70i	0.838672	+	1.45262i
$299$	−996.058	+	1725.22i	−0.192654	+	0.333687i
$300$		0			0
$301$	970.735	−	7893.85i	0.185888	−	1.51161i
$302$	−9166.69			−1.74663
$303$		0			0
$304$	−69.0236	−	119.552i	−0.0130223	−	0.0225552i
$305$	5826.43	+	10091.7i	1.09384	+	1.89458i
$306$		0			0
$307$	541.355			0.100641			0.0503204	−	0.998733i	$-0.483976\pi$
$307$	541.355			0.100641			0.0503204	+	0.998733i	$0.483976\pi$
$308$	2150.22	+	1620.94i	0.397793	+	0.299875i
$309$		0			0
$310$	−6428.37	+	11134.3i	−1.17776	+	2.03995i
$311$	27.0084	+	46.7799i	0.00492446	+	0.00852941i	0.868477	−	0.495729i	$-0.165099\pi$
$311$	27.0084	+	46.7799i	0.00492446	+	0.00852941i	−0.863553	+	0.504259i	$0.831766\pi$
$312$		0			0
$313$	−1886.47	+	3267.46i	−0.340670	+	0.590058i	−0.984557	−	0.175063i	$-0.943987\pi$
$313$	−1886.47	+	3267.46i	−0.340670	+	0.590058i	0.643887	+	0.765120i	$0.277321\pi$
$314$	−17444.1			−3.13511
$315$		0			0
$316$	11615.1			2.06772
$317$	859.618	−	1488.90i	0.152306	−	0.263802i	−0.779769	−	0.626068i	$-0.784663\pi$
$317$	859.618	−	1488.90i	0.152306	−	0.263802i	0.932075	+	0.362266i	$0.117997\pi$
$318$		0			0
$319$	1062.47	+	1840.25i	0.186479	+	0.322991i
$320$	−7436.70	+	12880.7i	−1.29914	+	2.25017i
$321$		0			0
$322$	11814.5	−	5012.34i	2.04470	−	0.867475i
$323$	2259.72			0.389270
$324$		0			0
$325$	1273.53	+	2205.81i	0.217362	+	0.376482i
$326$	7994.73	+	13847.3i	1.35824	+	2.35255i
$327$		0			0
$328$	852.934			0.143584
$329$	−313.330	−	236.202i	−0.0525059	−	0.0395813i
$330$		0			0
$331$	−4204.11	+	7281.73i	−0.698123	+	1.20918i	0.270994	+	0.962581i	$0.412648\pi$
$331$	−4204.11	+	7281.73i	−0.698123	+	1.20918i	−0.969117	+	0.246603i	$0.920686\pi$
$332$	−2092.27	−	3623.91i	−0.345868	−	0.599060i
$333$		0			0
$334$	−781.436	+	1353.49i	−0.128019	+	0.221735i
$335$	−2599.36			−0.423935
$336$		0			0
$337$	2789.46			0.450894			0.225447	−	0.974255i	$-0.427616\pi$
$337$	2789.46			0.450894			0.225447	+	0.974255i	$0.427616\pi$
$338$	4614.29	−	7992.18i	0.742557	−	1.28615i
$339$		0			0
$340$	−6074.36	−	10521.1i	−0.968907	−	1.67820i
$341$	899.419	−	1557.84i	0.142834	−	0.247395i
$342$		0			0
$343$	−2279.82	+	5929.25i	−0.358889	+	0.933380i
$344$	9314.72			1.45993
$345$		0			0
$346$	−9539.24	−	16522.4i	−1.48217	−	2.56720i
$347$	−1735.98	−	3006.81i	−0.268566	−	0.465170i	0.699926	−	0.714216i	$-0.253216\pi$
$347$	−1735.98	−	3006.81i	−0.268566	−	0.465170i	−0.968492	+	0.249046i	$0.919883\pi$
$348$		0			0
$349$	−6626.12			−1.01630			−0.508149	−	0.861269i	$-0.669670\pi$
$349$	−6626.12			−1.01630			−0.508149	+	0.861269i	$0.669670\pi$
$350$	2002.76	−	16286.1i	0.305863	−	2.48723i
$351$		0			0
$352$	1073.05	−	1858.57i	0.162482	−	0.281427i
$353$	4734.20	+	8199.87i	0.713813	+	1.23636i	0.963416	+	0.268012i	$0.0863666\pi$
$353$	4734.20	+	8199.87i	0.713813	+	1.23636i	−0.249603	+	0.968348i	$0.580300\pi$
$354$		0			0
$355$	3297.27	−	5711.03i	0.492960	−	0.853831i
$356$	479.944			0.0714522
$357$		0			0
$358$	8977.35			1.32533
$359$	−3139.78	+	5438.25i	−0.461591	+	0.799499i	−0.999040	−	0.0437971i	$-0.986054\pi$
$359$	−3139.78	+	5438.25i	−0.461591	+	0.799499i	0.537450	+	0.843296i	$0.319388\pi$
$360$		0			0
$361$	2529.68	+	4381.53i	0.368811	+	0.638800i
$362$	8231.31	−	14257.0i	1.19510	−	2.06998i
$363$		0			0
$364$	2849.71	−	1209.01i	0.410345	−	0.174091i
$365$	−10883.1			−1.56068
$366$		0			0
$367$	5413.91	+	9377.17i	0.770038	+	1.33374i	0.937542	+	0.347873i	$0.113096\pi$
$367$	5413.91	+	9377.17i	0.770038	+	1.33374i	−0.167504	+	0.985871i	$0.553571\pi$
$368$	−247.452	−	428.599i	−0.0350525	−	0.0607127i
$369$		0			0
$370$	−305.053			−0.0428620
$371$	6238.42	−	2646.68i	0.872999	−	0.370374i
$372$		0			0
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	−0.988557	−	0.150846i	$-0.951800\pi$
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	0.624915	+	0.780693i	$0.285134\pi$
$374$	1382.71	+	2394.93i	0.191172	+	0.331120i
$375$		0			0
$376$	229.777	−	397.985i	0.0315155	−	0.0545864i
$377$	2442.81			0.333717
$378$		0			0
$379$	−11050.4			−1.49768			−0.748839	−	0.662751i	$-0.769389\pi$
$379$	−11050.4			−1.49768			−0.748839	+	0.662751i	$0.769389\pi$
$380$	−4837.64	+	8379.03i	−0.653067	+	1.13115i
$381$		0			0
$382$	4346.25	+	7527.92i	0.582129	+	1.00828i
$383$	−5234.02	+	9065.59i	−0.698292	+	1.20948i	0.270766	+	0.962645i	$0.412723\pi$
$383$	−5234.02	+	9065.59i	−0.698292	+	1.20948i	−0.969058	+	0.246832i	$0.920610\pi$
$384$		0			0
$385$	−460.345	+	3743.45i	−0.0609386	+	0.495543i
$386$	10934.9			1.44190
$387$		0			0
$388$	−4606.61	−	7978.88i	−0.602745	−	1.04399i
$389$	−5807.02	−	10058.1i	−0.756884	−	1.31096i	−0.944432	−	0.328705i	$-0.893388\pi$
$389$	−5807.02	−	10058.1i	−0.756884	−	1.31096i	0.187549	−	0.982255i	$-0.439946\pi$
$390$		0			0
$391$	8101.19			1.04781
$392$	−7218.16	−	1802.54i	−0.930031	−	0.232251i
$393$		0			0
$394$	3449.89	−	5975.38i	0.441124	−	0.764049i
$395$	8134.43	+	14089.2i	1.03617	+	1.79470i
$396$		0			0
$397$	3353.65	−	5808.69i	0.423967	−	0.734332i	−0.572356	−	0.820005i	$-0.693971\pi$
$397$	3353.65	−	5808.69i	0.423967	−	0.734332i	0.996323	+	0.0856726i	$0.0273039\pi$
$398$	6232.10			0.784892
$399$		0			0
$400$	−632.768			−0.0790960
$401$	2763.19	−	4785.98i	0.344107	−	0.596011i	−0.641084	−	0.767471i	$-0.721515\pi$
$401$	2763.19	−	4785.98i	0.344107	−	0.596011i	0.985191	+	0.171459i	$0.0548482\pi$
$402$		0			0
$403$	−1033.97	−	1790.89i	−0.127805	−	0.221366i
$404$	9689.49	−	16782.7i	1.19324	−	2.06676i
$405$		0			0
$406$	−12566.6	−	9473.26i	−1.53613	−	1.15800i
$407$	42.6811			0.00519810
$408$		0			0
$409$	659.453	+	1142.21i	0.0797258	+	0.138089i	0.903132	−	0.429364i	$-0.141262\pi$
$409$	659.453	+	1142.21i	0.0797258	+	0.138089i	−0.823406	+	0.567453i	$0.807929\pi$
$410$	1601.17	+	2773.31i	0.192869	+	0.334059i
$411$		0			0
$412$	−13422.5			−1.60505
$413$	−3863.00	+	1638.90i	−0.460256	+	0.195266i
$414$		0			0
$415$	2930.57	−	5075.90i	0.346641	−	0.600401i
$416$	−1233.57	−	2136.61i	−0.145387	−	0.251817i
$417$		0			0
$418$	1101.20	−	1907.33i	0.128855	−	0.223183i
$419$	−3656.13			−0.426286			−0.213143	−	0.977021i	$-0.568370\pi$
$419$	−3656.13			−0.426286			−0.213143	+	0.977021i	$0.568370\pi$
$420$		0			0
$421$	−135.389			−0.0156733			−0.00783663	−	0.999969i	$-0.502495\pi$
$421$	−135.389			−0.0156733			−0.00783663	+	0.999969i	$0.502495\pi$
$422$	−9801.93	+	16977.4i	−1.13069	+	1.95841i
$423$		0			0
$424$	3968.31	+	6873.32i	0.454524	+	0.787259i
$425$	5178.96	−	8970.22i	0.591097	−	1.02381i
$426$		0			0
$427$	9641.94	+	7268.54i	1.09276	+	0.823769i
$428$	−9781.16			−1.10465
$429$		0			0
$430$	17486.1	+	30286.8i	1.96105	+	3.39665i
$431$	4194.58	+	7265.23i	0.468784	+	0.811958i	0.999363	−	0.0356776i	$-0.0113589\pi$
$431$	4194.58	+	7265.23i	0.468784	+	0.811958i	−0.530579	+	0.847635i	$0.678026\pi$
$432$		0			0
$433$	−8243.02			−0.914859			−0.457430	−	0.889246i	$-0.651230\pi$
$433$	−8243.02			−0.914859			−0.457430	+	0.889246i	$0.651230\pi$
$434$	−1626.03	+	13222.6i	−0.179843	+	1.46245i
$435$		0			0
$436$	9104.91	−	15770.2i	1.00011	−	1.73223i
$437$	−3225.91	−	5587.43i	−0.353126	−	0.611632i
$438$		0			0
$439$	9141.59	−	15833.7i	0.993859	−	1.72142i	0.401104	−	0.916032i	$-0.368626\pi$
$439$	9141.59	−	15833.7i	0.993859	−	1.72142i	0.592755	−	0.805383i	$-0.298040\pi$
$440$	−4417.26			−0.478602
$441$		0			0
$442$	3179.12			0.342116
$443$	605.218	−	1048.27i	0.0649092	−	0.112426i	−0.831745	−	0.555159i	$-0.812658\pi$
$443$	605.218	−	1048.27i	0.0649092	−	0.112426i	0.896654	+	0.442733i	$0.145991\pi$
$444$		0			0
$445$	336.122	+	582.180i	0.0358061	+	0.0620179i
$446$	3410.86	−	5907.79i	0.362128	−	0.627224i
$447$		0			0
$448$	−1881.08	+	15296.6i	−0.198376	+	1.61316i
$449$	8301.16			0.872508			0.436254	−	0.899824i	$-0.356305\pi$
$449$	8301.16			0.872508			0.436254	+	0.899824i	$0.356305\pi$
$450$		0			0
$451$	−224.026	−	388.025i	−0.0233902	−	0.0405130i
$452$	2313.24	+	4006.66i	0.240721	+	0.416941i
$453$		0			0
$454$	−7305.34			−0.755190
$455$	3462.30	+	2610.04i	0.356736	+	0.268924i
$456$		0			0
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	−0.358527	−	0.933519i	$-0.616721\pi$
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	0.987715	−	0.156266i	$-0.0499458\pi$
$458$	−2302.15	−	3987.45i	−0.234875	−	0.406815i
$459$		0			0
$460$	−17343.1	+	30039.1i	−1.75788	+	3.04474i
$461$	−19434.2			−1.96343			−0.981717	−	0.190346i	$-0.939039\pi$
$461$	−19434.2			−1.96343			−0.981717	+	0.190346i	$0.939039\pi$
$462$		0			0
$463$	−12491.1			−1.25380			−0.626902	−	0.779098i	$-0.715678\pi$
$463$	−12491.1			−1.25380			−0.626902	+	0.779098i	$0.715678\pi$
$464$	−303.436	+	525.566i	−0.0303592	+	0.0525836i
$465$		0			0
$466$	451.574	+	782.150i	0.0448901	+	0.0777519i
$467$	1692.59	−	2931.65i	0.167716	−	0.290493i	−0.769900	−	0.638164i	$-0.779694\pi$
$467$	1692.59	−	2931.65i	0.167716	−	0.290493i	0.937617	+	0.347671i	$0.113027\pi$
$468$		0			0
$469$	−2479.54	+	1051.96i	−0.244125	+	0.103571i
$470$	1725.39			0.169333
$471$		0			0
$472$	−2457.29	−	4256.14i	−0.239631	−	0.415053i
$473$	−2446.54	−	4237.54i	−0.237827	−	0.411929i
$474$		0			0
$475$	−8249.07			−0.796828
$476$	−10052.2	−	7577.84i	−0.967948	−	0.729684i
$477$		0			0
$478$	−2736.53	+	4739.80i	−0.261853	+	0.453543i
$479$	2989.71	+	5178.32i	0.285184	+	0.493953i	0.972654	−	0.232260i	$-0.0746120\pi$
$479$	2989.71	+	5178.32i	0.285184	+	0.493953i	−0.687470	+	0.726213i	$0.741279\pi$
$480$		0			0
$481$	24.5330	−	42.4925i	0.00232559	−	0.00402804i
$482$	−12451.1			−1.17663
$483$		0			0
$484$	−15327.5			−1.43948
$485$	6452.34	−	11175.8i	0.604094	−	1.04632i
$486$		0			0
$487$	557.481	+	965.586i	0.0518725	+	0.0898457i	0.890796	−	0.454404i	$-0.150148\pi$
$487$	557.481	+	965.586i	0.0518725	+	0.0898457i	−0.838923	+	0.544250i	$0.816814\pi$
$488$	−7070.80	+	12247.0i	−0.655902	+	1.13606i
$489$		0			0
$490$	−7689.34	−	26853.6i	−0.708916	−	2.47576i
$491$	−1086.23			−0.0998387			−0.0499194	−	0.998753i	$-0.515896\pi$
$491$	−1086.23			−0.0998387			−0.0499194	+	0.998753i	$0.515896\pi$
$492$		0			0
$493$	−4967.00	−	8603.10i	−0.453758	−	0.785932i
$494$	−1265.93	−	2192.66i	−0.115297	−	0.199701i
$495$		0			0
$496$	513.740			0.0465073
$497$	834.028	−	6782.18i	0.0752742	−	0.612117i
$498$		0			0
$499$	1106.75	−	1916.95i	0.0992884	−	0.171973i	−0.812102	−	0.583516i	$-0.801677\pi$
$499$	1106.75	−	1916.95i	0.0992884	−	0.171973i	0.911390	+	0.411543i	$0.135010\pi$
$500$	7919.92	+	13717.7i	0.708379	+	1.22695i
$501$		0			0
$502$	17236.3	−	29854.2i	1.53246	−	2.65430i
$503$	2643.32			0.234314			0.117157	−	0.993113i	$-0.462622\pi$
$503$	2643.32			0.234314			0.117157	+	0.993113i	$0.462622\pi$
$504$		0			0
$505$	27143.5			2.39183
$506$	3947.83	−	6837.84i	0.346843	−	0.600749i
$507$		0			0
$508$	−6219.31	−	10772.2i	−0.543183	−	0.940821i
$509$	−332.584	+	576.053i	−0.0289618	+	0.0501633i	−0.880143	−	0.474709i	$-0.842553\pi$
$509$	−332.584	+	576.053i	−0.0289618	+	0.0501633i	0.851181	+	0.524872i	$0.175887\pi$
$510$		0			0
$511$	−10381.4	+	4404.38i	−0.898724	+	0.381288i
$512$	1177.58			0.101645
$513$		0			0
$514$	11410.7	+	19763.9i	0.979190	+	1.69601i
$515$	−9400.26	−	16281.7i	−0.804320	−	1.39312i
$516$		0			0
$517$	−241.406			−0.0205359
$518$	−290.991	+	123.455i	−0.0246823	+	0.0104716i
$519$		0			0
$520$	−2539.03	+	4397.73i	−0.214123	+	0.370872i
$521$	−5880.99	−	10186.2i	−0.494531	−	0.856554i	0.505449	−	0.862857i	$-0.331327\pi$
$521$	−5880.99	−	10186.2i	−0.494531	−	0.856554i	−0.999980	+	0.00630307i	$0.997994\pi$
$522$		0			0
$523$	−5061.30	+	8766.43i	−0.423165	+	0.732943i	−0.996247	−	0.0865547i	$-0.972414\pi$
$523$	−5061.30	+	8766.43i	−0.423165	+	0.732943i	0.573082	+	0.819498i	$0.305748\pi$
$524$	22875.7			1.90712
$525$		0			0
$526$	28471.9			2.36014
$527$	−4204.76	+	7282.85i	−0.347556	+	0.601985i
$528$		0			0
$529$	−5481.49	−	9494.22i	−0.450521	−	0.780325i
$530$	−14899.0	+	25805.9i	−1.22108	+	2.11497i
$531$		0			0
$532$	−1223.66	+	9950.58i	−0.0997224	+	0.810926i
$533$	−515.079			−0.0418585
$534$		0			0
$535$	−6850.09	−	11864.7i	−0.553561	−	0.958796i
$536$	−1577.26	−	2731.89i	−0.127103	−	0.220148i
$537$		0			0
$538$	16350.3			1.31024
$539$	1075.85	+	3757.20i	0.0859740	+	0.300249i
$540$		0			0
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	0.344884	+	0.938645i	$0.387918\pi$
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	−0.985333	+	0.170644i	$0.945415\pi$
$542$	4517.96	+	7825.34i	0.358050	+	0.620161i
$543$		0			0
$544$	−5016.47	+	8688.78i	−0.395366	+	0.684795i
$545$	25505.9			2.00469
$546$		0			0
$547$	−626.100			−0.0489399			−0.0244699	−	0.999701i	$-0.507790\pi$
$547$	−626.100			−0.0489399			−0.0244699	+	0.999701i	$0.507790\pi$
$548$	10747.0	−	18614.3i	0.837751	−	1.45103i
$549$		0			0
$550$	−5047.56	−	8742.64i	−0.391325	−	0.677795i
$551$	−3955.74	+	6851.54i	−0.305844	+	0.529737i
$552$		0			0
$553$	13461.4	+	10147.8i	1.03515	+	0.780341i
$554$	33552.7			2.57313
$555$		0			0
$556$	−2010.34	−	3482.02i	−0.153341	−	0.265594i
$557$	10385.6	+	17988.4i	0.790039	+	1.36839i	0.925942	+	0.377665i	$0.123273\pi$
$557$	10385.6	+	17988.4i	0.790039	+	1.36839i	−0.135903	+	0.990722i	$0.543394\pi$
$558$		0			0
$559$	−5625.08			−0.425609
$560$	−991.615	+	420.698i	−0.0748275	+	0.0317460i
$561$		0			0
$562$	−12101.8	+	20961.0i	−0.908335	+	1.57328i
$563$	−2760.86	−	4781.95i	−0.206672	−	0.357966i	0.743992	−	0.668188i	$-0.232930\pi$
$563$	−2760.86	−	4781.95i	−0.206672	−	0.357966i	−0.950664	+	0.310222i	$0.899597\pi$
$564$		0			0
$565$	−3240.09	+	5612.00i	−0.241260	+	0.417874i
$566$	−4974.48			−0.369422
$567$		0			0
$568$	8002.95			0.591191
$569$	3787.40	−	6559.97i	0.279044	−	0.483319i	−0.692103	−	0.721799i	$-0.743316\pi$
$569$	3787.40	−	6559.97i	0.279044	−	0.483319i	0.971147	+	0.238480i	$0.0766491\pi$
$570$		0			0
$571$	165.624	+	286.869i	0.0121386	+	0.0210247i	0.872031	−	0.489451i	$-0.162803\pi$
$571$	165.624	+	286.869i	0.0121386	+	0.0210247i	−0.859892	+	0.510476i	$0.829469\pi$
$572$	952.239	−	1649.33i	0.0696068	−	0.120563i
$573$		0			0
$574$	2649.72	+	1997.48i	0.192678	+	0.145250i
$575$	−29573.2			−2.14485
$576$		0			0
$577$	−1019.06	−	1765.06i	−0.0735248	−	0.127349i	0.826919	−	0.562321i	$-0.190091\pi$
$577$	−1019.06	−	1765.06i	−0.0735248	−	0.127349i	−0.900444	+	0.434972i	$0.856758\pi$
$578$	4728.57	+	8190.13i	0.340281	+	0.589385i
$579$		0			0
$580$	42533.6			3.04502
$581$	741.275	−	6027.93i	0.0529316	−	0.430431i
$582$		0			0
$583$	2084.58	−	3610.60i	0.148087	−	0.256494i
$584$	−6603.72	−	11438.0i	−0.467918	−	0.810457i
$585$		0			0
$586$	−16384.4	+	28378.6i	−1.15500	+	2.00053i
$587$	−5232.90			−0.367947			−0.183973	−	0.982931i	$-0.558896\pi$
$587$	−5232.90			−0.367947			−0.183973	+	0.982931i	$0.558896\pi$
$588$		0			0
$589$	6697.36			0.468523
$590$	9225.88	−	15979.7i	0.643769	−	1.11504i
$591$		0			0
$592$	6.09477	+	10.5565i	0.000423131	+	0.000732884i
$593$	−2860.12	+	4953.87i	−0.198062	+	0.343054i	−0.947900	−	0.318568i	$-0.896798\pi$
$593$	−2860.12	+	4953.87i	−0.198062	+	0.343054i	0.749838	+	0.661622i	$0.230132\pi$
$594$		0			0
$595$	2152.10	−	17500.5i	0.148282	−	1.20580i
$596$	−24165.5			−1.66083
$597$		0			0
$598$	−4538.41	−	7860.75i	−0.310350	−	0.537542i
$599$	9044.21	+	15665.0i	0.616922	+	1.06854i	0.990044	+	0.140758i	$0.0449540\pi$
$599$	9044.21	+	15665.0i	0.616922	+	1.06854i	−0.373122	+	0.927782i	$0.621713\pi$
$600$		0			0
$601$	−1821.43			−0.123623			−0.0618117	−	0.998088i	$-0.519688\pi$
$601$	−1821.43			−0.123623			−0.0618117	+	0.998088i	$0.519688\pi$
$602$	28937.1	+	21814.1i	1.95911	+	1.47687i
$603$		0			0
$604$	12836.0	−	22232.6i	0.864719	−	1.49774i
$605$	−10734.4	−	18592.5i	−0.721348	−	1.24941i
$606$		0			0
$607$	−1186.10	+	2054.39i	−0.0793120	+	0.137372i	−0.902953	−	0.429739i	$-0.858606\pi$
$607$	−1186.10	+	2054.39i	−0.0793120	+	0.137372i	0.823641	+	0.567111i	$0.191939\pi$
$608$	7990.26			0.532974
$609$		0			0
$610$	−53094.7			−3.52416
$611$	−138.760	+	240.339i	−0.00918760	+	0.0159134i
$612$		0			0
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	0.660182	−	0.751105i	$-0.270479\pi$
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	−0.980567	+	0.196182i	$0.937146\pi$
$614$	−1233.30	+	2136.15i	−0.0810621	+	0.140404i
$615$		0			0
$616$	−4213.65	+	1787.66i	−0.275605	+	0.116927i
$617$	5329.51			0.347744			0.173872	−	0.984768i	$-0.444372\pi$
$617$	5329.51			0.347744			0.173872	+	0.984768i	$0.444372\pi$
$618$		0			0
$619$	7988.29	+	13836.1i	0.518702	+	0.898418i	0.999764	+	0.0217314i	$0.00691786\pi$
$619$	7988.29	+	13836.1i	0.518702	+	0.898418i	−0.481062	+	0.876687i	$0.659749\pi$
$620$	−18003.2	−	31182.4i	−1.16617	−	2.01986i
$621$		0			0
$622$	−246.120			−0.0158658
$623$	556.236	+	419.316i	0.0357706	+	0.0269656i
$624$		0			0
$625$	1060.03	−	1836.03i	0.0678420	−	0.117506i
$626$	−8595.45	−	14887.8i	−0.548791	−	0.950535i
$627$		0			0
$628$	24426.7	−	42308.4i	1.55212	−	2.68836i
$629$	−199.533			−0.0126485
$630$		0			0
$631$	−4199.98			−0.264974			−0.132487	−	0.991185i	$-0.542296\pi$
$631$	−4199.98			−0.264974			−0.132487	+	0.991185i	$0.542296\pi$
$632$	−9871.73	+	17098.3i	−0.621324	+	1.07616i
$633$		0			0
$634$	3916.74	+	6783.99i	0.245352	+	0.424963i
$635$	8711.19	−	15088.2i	0.544399	−	0.942926i
$636$		0			0
$637$	4358.98	+	1088.54i	0.271129	+	0.0677072i
$638$	−9681.97			−0.600804
$639$		0			0
$640$	−20418.6	−	35366.0i	−1.26112	−	2.18432i
$641$	1324.25	+	2293.67i	0.0815988	+	0.141333i	0.903937	−	0.427666i	$-0.140664\pi$
$641$	1324.25	+	2293.67i	0.0815988	+	0.141333i	−0.822338	+	0.568999i	$0.807331\pi$
$642$		0			0
$643$	13.4305			0.000823715			0.000411857	−	1.00000i	$-0.499869\pi$
$643$	13.4305			0.000823715			0.000411857		1.00000i	$0.499869\pi$
$644$	−4386.86	+	35673.2i	−0.268426	+	2.18280i
$645$		0			0
$646$	−5148.06	+	8916.70i	−0.313541	+	0.543070i
$647$	5812.07	+	10066.8i	0.353162	+	0.611695i	0.986802	−	0.161934i	$-0.0517730\pi$
$647$	5812.07	+	10066.8i	0.353162	+	0.611695i	−0.633639	+	0.773628i	$0.718440\pi$
$648$		0			0
$649$	−1290.83	+	2235.78i	−0.0780732	+	0.135227i
$650$	−11605.3			−0.700305
$651$		0			0
$652$	−44779.8			−2.68974
$653$	−14258.3	+	24696.1i	−0.854471	+	1.47999i	0.0226638	+	0.999743i	$0.492785\pi$
$653$	−14258.3	+	24696.1i	−0.854471	+	1.47999i	−0.877135	+	0.480244i	$0.840548\pi$
$654$		0			0
$655$	16020.7	+	27748.6i	0.955694	+	1.65531i
$656$	63.9809	−	110.818i	0.00380798	−	0.00659561i
$657$		0			0
$658$	1645.86	−	698.265i	0.0975111	−	0.0413696i
$659$	−18048.6			−1.06688			−0.533440	−	0.845838i	$-0.679101\pi$
$659$	−18048.6			−1.06688			−0.533440	+	0.845838i	$0.679101\pi$
$660$		0			0
$661$	−8920.72	−	15451.1i	−0.524926	−	0.909198i	−0.999579	−	0.0290250i	$-0.990760\pi$
$661$	−8920.72	−	15451.1i	−0.524926	−	0.909198i	0.474653	−	0.880173i	$-0.342574\pi$
$662$	−19155.5	−	33178.2i	−1.12462	−	1.94790i
$663$		0			0
$664$	7112.94			0.415716
$665$	−12927.2	+	5484.42i	−0.753826	+	0.319815i
$666$		0			0
$667$	−14181.5	+	24563.0i	−0.823251	+	1.42591i
$668$	−2188.47	−	3790.55i	−0.126758	−	0.219552i
$669$		0			0
$670$	5921.81	−	10256.9i	0.341462	−	0.591430i
$671$	7428.68			0.427394
$672$		0			0
$673$	−6826.13			−0.390978			−0.195489	−	0.980706i	$-0.562629\pi$
$673$	−6826.13			−0.390978			−0.195489	+	0.980706i	$0.562629\pi$
$674$	−6354.89	+	11007.0i	−0.363177	+	0.629041i
$675$		0			0
$676$	12922.7	+	22382.8i	0.735246	+	1.27348i
$677$	−10643.4	+	18435.0i	−0.604225	+	1.04655i	0.387949	+	0.921681i	$0.373184\pi$
$677$	−10643.4	+	18435.0i	−0.604225	+	1.04655i	−0.992173	+	0.124867i	$0.960150\pi$
$678$		0			0
$679$	1632.09	−	13271.9i	0.0922443	−	0.750115i
$680$	20650.6			1.16458
$681$		0			0
$682$	4098.08	+	7098.08i	0.230093	+	0.398533i
$683$	−10348.4	−	17924.0i	−0.579753	−	1.00416i	−0.995507	−	0.0946842i	$-0.969816\pi$
$683$	−10348.4	−	17924.0i	−0.579753	−	1.00416i	0.415755	−	0.909477i	$-0.363517\pi$
$684$		0			0
$685$	30105.9			1.67925
$686$	−18202.5	−	22503.9i	−1.01308	−	1.25248i
$687$		0			0
$688$	698.722	−	1210.22i	0.0387188	−	0.0670629i
$689$	−2396.43	−	4150.74i	−0.132506	−	0.229507i
$690$		0			0
$691$	−15671.0	+	27142.9i	−0.862738	+	1.49431i	0.00653825	+	0.999979i	$0.497919\pi$
$691$	−15671.0	+	27142.9i	−0.862738	+	1.49431i	−0.869276	+	0.494327i	$0.835415\pi$
$692$	53430.8			2.93517
$693$		0			0
$694$	15819.5			0.865276
$695$	2815.83	−	4877.16i	0.153684	−	0.266189i
$696$		0			0
$697$	1047.32	+	1814.01i	0.0569153	+	0.0985801i
$698$	15095.5	−	26146.2i	0.818587	−	1.41783i
$699$		0			0
$700$	36695.5	+	27662.7i	1.98137	+	1.49365i
$701$	9213.32			0.496408			0.248204	−	0.968708i	$-0.420160\pi$
$701$	9213.32			0.496408			0.248204	+	0.968708i	$0.420160\pi$
$702$		0			0
$703$	79.4544	+	137.619i	0.00426270	+	0.00738322i
$704$	4740.89	+	8211.46i	0.253805	+	0.439604i
$705$		0			0
$706$	−43141.5			−2.29979
$707$	25892.4	−	10985.0i	1.37734	−	0.584345i
$708$		0			0
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	−0.991696	−	0.128607i	$-0.958949\pi$
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	0.607225	+	0.794530i	$0.292283\pi$
$710$	15023.5	+	26021.6i	0.794118	+	1.37545i
$711$		0			0
$712$	−407.908	+	706.518i	−0.0214705	+	0.0371880i
$713$	24010.3			1.26114
$714$		0			0
$715$	2667.54			0.139525
$716$	−12570.9	+	21773.4i	−0.656140	+	1.13647i
$717$		0			0
$718$	−14306.0	−	24778.7i	−0.743585	−	1.28793i
$719$	12941.2	−	22414.8i	0.671246	−	1.16263i	−0.306306	−	0.951933i	$-0.599093\pi$
$719$	12941.2	−	22414.8i	0.671246	−	1.16263i	0.977551	−	0.210698i	$-0.0675737\pi$
$720$		0			0
$721$	−15556.2	−	11726.9i	−0.803525	−	0.605734i
$722$	−23052.3			−1.18825
$723$		0			0
$724$	23052.4	+	39928.0i	1.18334	+	2.04960i
$725$	18132.0	+	31405.5i	0.928833	+	1.60879i
$726$		0			0
$727$	32181.2			1.64172			0.820862	−	0.571127i	$-0.193494\pi$
$727$	32181.2			1.64172			0.820862	+	0.571127i	$0.193494\pi$
$728$	−642.237	+	5222.56i	−0.0326963	+	0.265881i
$729$		0			0
$730$	24793.7	−	42943.9i	1.25706	−	2.17730i
$731$	11437.5	+	19810.4i	0.578704	+	1.00234i
$732$		0			0
$733$	−10418.1	+	18044.6i	−0.524966	+	0.909268i	0.474611	+	0.880195i	$0.342589\pi$
$733$	−10418.1	+	18044.6i	−0.524966	+	0.909268i	−0.999577	+	0.0290722i	$0.990745\pi$
$734$	−49335.5			−2.48094
$735$		0			0
$736$	28645.4			1.43462
$737$	−828.544	+	1435.08i	−0.0414109	+	0.0717257i
$738$		0			0
$739$	−13217.4	−	22893.3i	−0.657931	−	1.13957i	−0.981150	−	0.193246i	$-0.938098\pi$
$739$	−13217.4	−	22893.3i	−0.657931	−	1.13957i	0.323219	−	0.946324i	$-0.395235\pi$
$740$	427.163	−	739.867i	0.0212200	−	0.0367541i
$741$		0			0
$742$	−3768.64	+	30646.0i	−0.186457	+	1.51624i
$743$	−9954.69			−0.491524			−0.245762	−	0.969330i	$-0.579038\pi$
$743$	−9954.69			−0.491524			−0.245762	+	0.969330i	$0.579038\pi$
$744$		0			0
$745$	−16923.9	−	29313.1i	−0.832274	−	1.44154i
$746$	−11935.9	−	20673.6i	−0.585798	−	1.01463i
$747$		0			0
$748$	−7744.79			−0.378580
$749$	−11336.0	−	8545.57i	−0.553014	−	0.416887i
$750$		0			0
$751$	16602.3	−	28756.0i	0.806692	−	1.39723i	−0.108451	−	0.994102i	$-0.534589\pi$
$751$	16602.3	−	28756.0i	0.806692	−	1.39723i	0.915143	−	0.403129i	$-0.132077\pi$
$752$	−34.4723	−	59.7078i	−0.00167164	−	0.00289537i
$753$		0			0
$754$	−5565.18	+	9639.17i	−0.268796	+	0.465568i
$755$	35958.1			1.73331
$756$		0			0
$757$	1964.06			0.0942998			0.0471499	−	0.998888i	$-0.484986\pi$
$757$	1964.06			0.0942998			0.0471499	+	0.998888i	$0.484986\pi$
$758$	25174.8	−	43604.0i	1.20632	−	2.08941i
$759$		0			0
$760$	−8223.09	−	14242.8i	−0.392477	−	0.679791i
$761$	−19276.9	+	33388.6i	−0.918248	+	1.59045i	−0.116174	+	0.993229i	$0.537063\pi$
$761$	−19276.9	+	33388.6i	−0.918248	+	1.59045i	−0.802075	+	0.597224i	$0.796270\pi$
$762$		0			0
$763$	24330.2	−	10322.2i	1.15441	−	0.489764i
$764$	−24344.0			−1.15280
$765$		0			0
$766$	−23848.1	−	41306.1i	−1.12489	−	1.94837i
$767$	1483.93	+	2570.25i	0.0698588	+	0.120999i
$768$		0			0
$769$	−19715.0			−0.924501			−0.462251	−	0.886749i	$-0.652958\pi$
$769$	−19715.0			−0.924501			−0.462251	+	0.886749i	$0.652958\pi$
$770$	−13722.6	−	10344.8i	−0.642246	−	0.484155i
$771$		0			0
$772$	−15312.1	+	26521.3i	−0.713853	+	1.23643i
$773$	−7350.34	−	12731.2i	−0.342010	−	0.592378i	0.642796	−	0.766037i	$-0.277774\pi$
$773$	−7350.34	−	12731.2i	−0.342010	−	0.592378i	−0.984806	+	0.173659i	$0.944441\pi$
$774$		0			0
$775$	15349.4	−	26585.9i	0.711440	−	1.23225i
$776$	15660.8			0.724471
$777$		0			0
$778$	52917.8			2.43856
$779$	834.086	−	1444.68i	0.0383623	−	0.0664454i
$780$		0			0
$781$	−2102.00	−	3640.78i	−0.0963068	−	0.166808i
$782$	−18456.0	+	31966.7i	−0.843970	+	1.46180i
$783$		0			0
$784$	−775.650	+	802.612i	−0.0353339	+	0.0365621i
$785$	68427.6			3.11119
$786$		0			0
$787$	11959.3	+	20714.1i	0.541681	+	0.938218i	0.998808	+	0.0488169i	$0.0155451\pi$
$787$	11959.3	+	20714.1i	0.541681	+	0.938218i	−0.457127	+	0.889401i	$0.651122\pi$
$788$	9661.69	+	16734.5i	0.436781	+	0.756527i
$789$		0			0
$790$	−74126.9			−3.33837
$791$	−819.566	+	6664.58i	−0.0368400	+	0.299577i
$792$		0			0
$793$	4269.99	−	7395.84i	0.191213	−	0.331191i
$794$	15280.5	+	26466.5i	0.682976	+	1.18295i
$795$		0			0
$796$	−8726.75	+	15115.2i	−0.388582	+	0.673044i
$797$	−38252.7			−1.70010			−0.850051	−	0.526700i	$-0.823429\pi$
$797$	−38252.7			−1.70010			−0.850051	+	0.526700i	$0.823429\pi$
$798$		0			0
$799$	1128.57			0.0499698
$800$	18312.5	−	31718.2i	0.809307	−	1.40176i
$801$		0			0
$802$	12590.1	+	21806.7i	0.554329	+	0.960126i
$803$	−3468.98	+	6008.45i	−0.152450	+	0.264052i
$804$		0			0
$805$	−46344.4	+	19661.9i	−2.02910	+	0.860857i
$806$	9422.27			0.411769
$807$		0			0
$808$	16470.3	+	28527.5i	0.717110	+	1.24207i
$809$	−15717.8	−	27224.0i	−0.683075	−	1.18312i	−0.974038	−	0.226386i	$-0.927309\pi$
$809$	−15717.8	−	27224.0i	−0.683075	−	1.18312i	0.290962	−	0.956734i	$-0.406025\pi$
$810$		0			0
$811$	11467.0			0.496501			0.248250	−	0.968696i	$-0.420144\pi$
$811$	11467.0			0.496501			0.248250	+	0.968696i	$0.420144\pi$
$812$	40573.0	−	17213.3i	1.75349	−	0.743928i
$813$		0			0
$814$	−97.2354	+	168.417i	−0.00418686	+	0.00725185i
$815$	−31360.8	−	54318.6i	−1.34788	−	2.33460i
$816$		0			0
$817$	9108.88	−	15777.1i	0.390061	−	0.675605i
$818$	−6009.42			−0.256864
$819$		0			0
$820$	−8968.42			−0.381940
$821$	−2515.29	+	4356.60i	−0.106923	+	0.185197i	−0.914522	−	0.404535i	$-0.867433\pi$
$821$	−2515.29	+	4356.60i	−0.106923	+	0.185197i	0.807599	+	0.589732i	$0.200767\pi$
$822$		0			0
$823$	6992.59	+	12111.5i	0.296168	+	0.512978i	0.975256	−	0.221079i	$-0.0709578\pi$
$823$	6992.59	+	12111.5i	0.296168	+	0.512978i	−0.679088	+	0.734057i	$0.737625\pi$
$824$	11407.9	−	19759.1i	0.482298	−	0.835364i
$825$		0			0
$826$	2333.65	−	18976.8i	0.0983025	−	0.799380i
$827$	13939.5			0.586125			0.293063	−	0.956093i	$-0.405326\pi$
$827$	13939.5			0.586125			0.293063	+	0.956093i	$0.405326\pi$
$828$		0			0
$829$	10052.2	+	17410.9i	0.421143	+	0.729441i	0.996052	−	0.0887769i	$-0.0282958\pi$
$829$	10052.2	+	17410.9i	0.421143	+	0.729441i	−0.574909	+	0.818218i	$0.694962\pi$
$830$	13352.8	+	23127.7i	0.558411	+	0.967197i
$831$		0			0
$832$	10900.2			0.454203
$833$	−5029.55	−	17564.8i	−0.209200	−	0.730593i
$834$		0			0
$835$	3065.33	−	5309.31i	0.127042	−	0.220043i
$836$	3083.99	+	5341.62i	0.127586	+	0.220986i
$837$		0			0
$838$	8329.33	−	14426.8i	0.343356	−	0.594710i
$839$	−15949.5			−0.656302			−0.328151	−	0.944625i	$-0.606425\pi$
$839$	−15949.5			−0.656302			−0.328151	+	0.944625i	$0.606425\pi$
$840$		0			0
$841$	10390.8			0.426043
$842$	308.440	−	534.235i	0.0126242	−	0.0218657i
$843$		0			0
$844$	−27451.1	−	47546.7i	−1.11956	−	1.93913i
$845$	−18100.4	+	31350.8i	−0.736891	+	1.27633i
$846$		0			0
$847$	−17764.0	−	13391.3i	−0.720635	−	0.543248i
$848$	1190.70			0.0482177
$849$		0			0
$850$	23597.2	+	40871.6i	0.952210	+	1.64928i
$851$	284.847	+	493.369i	0.0114741	+	0.0198737i
$852$		0			0
$853$	11802.0			0.473730			0.236865	−	0.971543i	$-0.423880\pi$
$853$	11802.0			0.473730			0.236865	+	0.971543i	$0.423880\pi$
$854$	−50647.3	+	21487.4i	−2.02941	+	0.860986i
$855$		0			0
$856$	8313.09	−	14398.7i	0.331934	−	0.574927i
$857$	4797.64	+	8309.76i	0.191230	+	0.331220i	0.945658	−	0.325162i	$-0.105419\pi$
$857$	4797.64	+	8309.76i	0.191230	+	0.331220i	−0.754428	+	0.656383i	$0.772086\pi$
$858$		0			0
$859$	−10920.4	+	18914.7i	−0.433760	+	0.751295i	−0.997194	−	0.0748666i	$-0.976147\pi$
$859$	−10920.4	+	18914.7i	−0.433760	+	0.751295i	0.563433	+	0.826162i	$0.309480\pi$
$860$	−97942.3			−3.88350
$861$		0			0
$862$	−38224.1			−1.51035
$863$	−13265.8	+	22977.1i	−0.523260	+	0.906313i	0.476374	+	0.879243i	$0.341951\pi$
$863$	−13265.8	+	22977.1i	−0.523260	+	0.906313i	−0.999634	+	0.0270699i	$0.991382\pi$
$864$		0			0
$865$	37419.5	+	64812.4i	1.47087	+	2.54762i
$866$	18779.1	−	32526.4i	0.736882	−	1.27632i
$867$		0			0
$868$	−29792.8	−	22459.2i	−1.16502	−	0.878242i
$869$	10371.4			0.404862
$870$		0			0
$871$	952.491	+	1649.76i	0.0370539	+	0.0641792i
$872$	15476.7	+	26806.4i	0.601039	+	1.04103i
$873$		0			0
$874$	29396.8			1.13771
$875$	−2805.97	+	22817.7i	−0.108410	+	0.881576i
$876$		0			0
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	−0.792732	−	0.609570i	$-0.791342\pi$
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	0.924269	+	0.381741i	$0.124675\pi$
$878$	41652.4	+	72144.1i	1.60103	+	2.77306i
$879$		0			0
$880$	−331.351	+	573.916i	−0.0126930	+	0.0219849i
$881$	3994.77			0.152766			0.0763832	−	0.997079i	$-0.475663\pi$
$881$	3994.77			0.152766			0.0763832	+	0.997079i	$0.475663\pi$
$882$		0			0
$883$	13727.0			0.523161			0.261580	−	0.965182i	$-0.415756\pi$
$883$	13727.0			0.523161			0.261580	+	0.965182i	$0.415756\pi$
$884$	−4451.69	+	7710.56i	−0.169374	+	0.293364i
$885$		0			0
$886$	2757.59	+	4776.29i	0.104563	+	0.181109i
$887$	22059.7	−	38208.5i	0.835054	−	1.44636i	−0.0589333	−	0.998262i	$-0.518770\pi$
$887$	22059.7	−	38208.5i	0.835054	−	1.44636i	0.893987	−	0.448093i	$-0.147897\pi$
$888$		0			0
$889$	2203.46	−	17918.1i	0.0831288	−	0.675990i
$890$	−3062.99			−0.115361
$891$		0			0
$892$	9552.40	+	16545.2i	0.358563	+	0.621049i
$893$	−449.398	−	778.380i	−0.0168405	−	0.0291685i
$894$		0			0
$895$	−35215.3			−1.31522
$896$	−33790.0	−	25472.4i	−1.25987	−	0.949749i
$897$		0			0
$898$	−18911.6	+	32755.8i	−0.702769	+	1.21723i
$899$	−14721.2	−	25497.9i	−0.546140	−	0.945942i
$900$		0			0
$901$	−9745.37	+	16879.5i	−0.360339	+	0.624125i
$902$	2041.49			0.0753594
$903$		0			0
$904$	−7864.18			−0.289335
$905$	−32288.9	+	55925.9i	−1.18599	+	2.05419i
$906$		0			0
$907$	−18452.9	−	31961.4i	−0.675545	−	1.17008i	−0.976309	−	0.216380i	$-0.930575\pi$
$907$	−18452.9	−	31961.4i	−0.675545	−	1.17008i	0.300764	−	0.953698i	$-0.402758\pi$
$908$	10229.6	−	17718.2i	0.373878	−	0.647575i
$909$		0			0
$910$	−18186.8	+	7715.83i	−0.662512	+	0.281074i
$911$	3169.56			0.115271			0.0576356	−	0.998338i	$-0.481644\pi$
$911$	3169.56			0.115271			0.0576356	+	0.998338i	$0.481644\pi$
$912$		0			0
$913$	−1868.24	−	3235.88i	−0.0677214	−	0.117297i
$914$	28007.4	+	48510.3i	1.01357	+	1.75556i
$915$		0			0
$916$	12894.7			0.465124
$917$	26512.0	+	19986.0i	0.954749	+	0.719733i
$918$		0			0
$919$	−4363.50	+	7557.80i	−0.156625	+	0.271283i	−0.933650	−	0.358188i	$-0.883395\pi$
$919$	−4363.50	+	7557.80i	−0.156625	+	0.271283i	0.777024	+	0.629470i	$0.216728\pi$
$920$	−29480.1	−	51061.0i	−1.05645	−	1.82982i
$921$		0			0
$922$	44274.8	−	76686.2i	1.58147	−	2.73918i
$923$	−4832.91			−0.172348
$924$		0			0
$925$	728.392			0.0258912
$926$	28457.1	−	49289.1i	1.00989	−	1.74918i
$927$		0			0
$928$	−17563.1	−	30420.1i	−0.621267	−	1.07607i
$929$	9702.54	−	16805.3i	0.342659	−	0.593502i	−0.642267	−	0.766481i	$-0.722006\pi$
$929$	9702.54	−	16805.3i	0.342659	−	0.593502i	0.984926	+	0.172979i	$0.0553392\pi$
$930$		0			0
$931$	−10111.8	+	10463.2i	−0.355961	+	0.368334i
$932$	−2529.34			−0.0888963
$933$		0			0
$934$	7712.04	+	13357.6i	0.270177	+	0.467961i
$935$	−5423.95	−	9394.55i	−0.189713	−	0.328593i
$936$		0			0
$937$	−615.692			−0.0214662			−0.0107331	−	0.999942i	$-0.503417\pi$
$937$	−615.692			−0.0214662			−0.0107331	+	0.999942i	$0.503417\pi$
$938$	1497.90	−	12180.6i	0.0521407	−	0.424000i
$939$		0			0
$940$	−2416.05	+	4184.72i	−0.0838329	+	0.145203i
$941$	−14801.0	−	25636.1i	−0.512751	−	0.888111i	−0.999891	−	0.0147865i	$-0.995293\pi$
$941$	−14801.0	−	25636.1i	−0.512751	−	0.888111i	0.487140	−	0.873324i	$-0.338040\pi$
$942$		0			0
$943$	2990.23	−	5179.23i	0.103261	−	0.178854i
$944$	−737.310			−0.0254210
$945$		0			0
$946$	22294.7			0.766240
$947$	6768.71	−	11723.8i	0.232264	−	0.402292i	−0.726210	−	0.687473i	$-0.758720\pi$
$947$	6768.71	−	11723.8i	0.232264	−	0.402292i	0.958474	+	0.285180i	$0.0920535\pi$
$948$		0			0
$949$	3987.93	+	6907.29i	0.136411	+	0.236270i
$950$	18792.9	−	32550.3i	0.641813	−	1.11165i
$951$		0			0
$952$	19698.7	−	8357.27i	0.670628	−	0.284518i
$953$	−33468.5			−1.13762			−0.568810	−	0.822469i	$-0.692596\pi$
$953$	−33468.5			−1.13762			−0.568810	+	0.822469i	$0.692596\pi$
$954$		0			0
$955$	−17049.0	−	29529.7i	−0.577688	−	1.00058i
$956$	−7663.86	−	13274.2i	−0.259275	−	0.449078i
$957$		0			0
$958$	−27244.4			−0.918817
$959$	28718.2	−	12183.8i	0.967005	−	0.410257i
$960$		0			0
$961$	2433.44	−	4214.85i	0.0816838	−	0.141480i
$962$	111.781	+	193.611i	0.00374634	+	0.00648885i
$963$		0			0
$964$	17435.2	−	30198.7i	0.582521	−	1.00896i
$965$	−42894.4			−1.43090
$966$		0			0
$967$	−55733.5			−1.85343			−0.926715	−	0.375764i	$-0.877380\pi$
$967$	−55733.5			−1.85343			−0.926715	+	0.375764i	$0.877380\pi$
$968$	13027.0	−	22563.4i	0.432545	−	0.749190i
$969$		0			0
$970$	29399.2	+	50920.9i	0.973146	+	1.68554i
$971$	−9745.65	+	16880.0i	−0.322094	+	0.557882i	−0.980920	−	0.194413i	$-0.937720\pi$
$971$	−9745.65	+	16880.0i	−0.322094	+	0.557882i	0.658826	+	0.752295i	$0.271053\pi$
$972$		0			0
$973$	712.251	−	5791.91i	0.0234673	−	0.190832i
$974$	−5080.18			−0.167125
$975$		0			0
$976$	1060.80	+	1837.36i	0.0347903	+	0.0602586i
$977$	−3120.78	−	5405.35i	−0.102193	−	0.177004i	0.810395	−	0.585884i	$-0.199253\pi$
$977$	−3120.78	−	5405.35i	−0.102193	−	0.177004i	−0.912588	+	0.408881i	$0.865919\pi$
$978$		0			0
$979$	428.554			0.0139905
$980$	75897.4	+	18953.4i	2.47393	+	0.617799i
$981$		0			0
$982$	2474.63	−	4286.18i	0.0804160	−	0.139285i
$983$	29847.3	+	51697.0i	0.968444	+	1.67739i	0.700062	+	0.714082i	$0.253155\pi$
$983$	29847.3	+	51697.0i	0.968444	+	1.67739i	0.268382	+	0.963313i	$0.413511\pi$
$984$		0			0
$985$	−13532.8	+	23439.6i	−0.437758	+	0.758220i
$986$	45263.0			1.46193
$987$		0			0
$988$	7090.68			0.228324
$989$	32655.7	−	56561.3i	1.04994	−	1.81855i
$990$		0			0
$991$	−7780.82	−	13476.8i	−0.249411	−	0.431992i	0.713952	−	0.700195i	$-0.246904\pi$
$991$	−7780.82	−	13476.8i	−0.249411	−	0.431992i	−0.963362	+	0.268203i	$0.913570\pi$
$992$	−14867.8	+	25751.8i	−0.475860	+	0.824214i
$993$		0			0
$994$	24861.9	+	18742.1i	0.793333	+	0.598050i
$995$	−24446.6			−0.778903
$996$		0			0
$997$	−9942.47	−	17220.9i	−0.315829	−	0.547031i	0.663785	−	0.747924i	$-0.268949\pi$
$997$	−9942.47	−	17220.9i	−0.315829	−	0.547031i	−0.979613	+	0.200892i	$0.935616\pi$
$998$	5042.76	+	8734.31i	0.159946	+	0.277034i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.e.c.37.1		6
3.2	odd	2		21.4.e.b.16.3	yes	6
7.2	even	3		441.4.a.s.1.3		3
7.3	odd	6		441.4.e.w.361.1		6
7.4	even	3	inner	63.4.e.c.46.1		6
7.5	odd	6		441.4.a.t.1.3		3
7.6	odd	2		441.4.e.w.226.1		6
12.11	even	2		336.4.q.k.289.1		6
21.2	odd	6		147.4.a.l.1.1		3
21.5	even	6		147.4.a.m.1.1		3
21.11	odd	6		21.4.e.b.4.3	✓	6
21.17	even	6		147.4.e.n.67.3		6
21.20	even	2		147.4.e.n.79.3		6
84.11	even	6		336.4.q.k.193.1		6
84.23	even	6		2352.4.a.ci.1.3		3
84.47	odd	6		2352.4.a.cg.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.3	✓	6	21.11	odd	6
21.4.e.b.16.3	yes	6	3.2	odd	2
63.4.e.c.37.1		6	1.1	even	1	trivial
63.4.e.c.46.1		6	7.4	even	3	inner
147.4.a.l.1.1		3	21.2	odd	6
147.4.a.m.1.1		3	21.5	even	6
147.4.e.n.67.3		6	21.17	even	6
147.4.e.n.79.3		6	21.20	even	2
336.4.q.k.193.1		6	84.11	even	6
336.4.q.k.289.1		6	12.11	even	2
441.4.a.s.1.3		3	7.2	even	3
441.4.a.t.1.3		3	7.5	odd	6
441.4.e.w.226.1		6	7.6	odd	2
441.4.e.w.361.1		6	7.3	odd	6
2352.4.a.cg.1.1		3	84.47	odd	6
2352.4.a.ci.1.3		3	84.23	even	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} +(2.26047 - 18.3818i) q^{7} +21.6905 q^{8} +O(q^{10})\)	\(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(8.93660 - 15.4786i) q^{5} +(2.26047 - 18.3818i) q^{7} +21.6905 q^{8} +(40.7184 + 70.5264i) q^{10} +(-5.69708 - 9.86762i) q^{11} -13.0987 q^{13} +(67.3835 + 50.7968i) q^{14} +(1.62706 - 2.81815i) q^{16} +(26.6337 + 46.1309i) q^{17} +(21.2111 - 36.7388i) q^{19} -228.071 q^{20} +51.9159 q^{22} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +(29.8412 - 51.6864i) q^{26} +(-217.558 + 92.2999i) q^{28} -186.493 q^{29} +(78.9369 + 136.723i) q^{31} +(94.1753 + 163.116i) q^{32} -242.706 q^{34} +(-264.324 - 199.260i) q^{35} +(-1.87294 + 3.24403i) q^{37} +(96.6457 + 167.395i) q^{38} +(193.839 - 335.739i) q^{40} +39.3230 q^{41} +429.439 q^{43} +(-72.6974 + 125.916i) q^{44} +(346.478 + 600.118i) q^{46} +(10.5934 - 18.3484i) q^{47} +(-332.781 - 83.1031i) q^{49} +885.992 q^{50} +(83.5726 + 144.752i) q^{52} +(182.952 + 316.882i) q^{53} -203.650 q^{55} +(49.0307 - 398.709i) q^{56} +(424.866 - 735.889i) q^{58} +(-113.289 - 196.222i) q^{59} +(-325.987 + 564.626i) q^{61} -719.331 q^{62} -832.161 q^{64} +(-117.058 + 202.750i) q^{65} +(-72.7166 - 125.949i) q^{67} +(339.858 - 588.652i) q^{68} +(1388.44 - 589.055i) q^{70} +368.962 q^{71} +(-304.453 - 527.328i) q^{73} +(-8.53380 - 14.7810i) q^{74} -541.328 q^{76} +(-194.263 + 82.4170i) q^{77} +(-455.119 + 788.289i) q^{79} +(-29.0808 - 50.3694i) q^{80} +(-89.5850 + 155.166i) q^{82} +327.929 q^{83} +952.058 q^{85} +(-978.340 + 1694.53i) q^{86} +(-123.572 - 214.033i) q^{88} +(-18.8059 + 32.5728i) q^{89} +(-29.6092 + 240.777i) q^{91} -1940.68 q^{92} +(48.2676 + 83.6019i) q^{94} +(-379.111 - 656.640i) q^{95} +722.013 q^{97} +(1086.05 - 1123.80i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8}+O(q^{10}) \) 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8	\( 6 q + q^{2} - 25 q^{4} + 11 q^{5} - 13 q^{7} - 78 q^{8} + 55 q^{10} + 35 q^{11} + 124 q^{13} + 326 q^{14} - 241 q^{16} + 48 q^{17} + 202 q^{19} - 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} + 274 q^{26} - 201 q^{28} - 106 q^{29} + 95 q^{31} + 683 q^{32} - 48 q^{34} - 56 q^{35} - 262 q^{37} - 398 q^{38} - 21 q^{40} - 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} - 210 q^{47} - 303 q^{49} + 2756 q^{50} - 324 q^{52} + 393 q^{53} - 2062 q^{55} - 1299 q^{56} + 1249 q^{58} + 1143 q^{59} + 70 q^{61} - 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} + 1944 q^{68} + 3251 q^{70} - 636 q^{71} - 988 q^{73} + 1002 q^{74} - 4680 q^{76} - 1073 q^{77} - 861 q^{79} + 175 q^{80} - 124 q^{82} - 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} + 1766 q^{89} - 654 q^{91} + 1344 q^{92} + 3294 q^{94} - 736 q^{95} + 38 q^{97} + 4267 q^{98}+O(q^{100}) \) 6 * q + q^2 - 25 * q^4 + 11 * q^5 - 13 * q^7 - 78 * q^8 + 55 * q^10 + 35 * q^11 + 124 * q^13 + 326 * q^14 - 241 * q^16 + 48 * q^17 + 202 * q^19 - 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 + 274 * q^26 - 201 * q^28 - 106 * q^29 + 95 * q^31 + 683 * q^32 - 48 * q^34 - 56 * q^35 - 262 * q^37 - 398 * q^38 - 21 * q^40 - 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 - 210 * q^47 - 303 * q^49 + 2756 * q^50 - 324 * q^52 + 393 * q^53 - 2062 * q^55 - 1299 * q^56 + 1249 * q^58 + 1143 * q^59 + 70 * q^61 - 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 + 1944 * q^68 + 3251 * q^70 - 636 * q^71 - 988 * q^73 + 1002 * q^74 - 4680 * q^76 - 1073 * q^77 - 861 * q^79 + 175 * q^80 - 124 * q^82 - 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 + 1766 * q^89 - 654 * q^91 + 1344 * q^92 + 3294 * q^94 - 736 * q^95 + 38 * q^97 + 4267 * q^98

Introduction

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