LMFDB - Embedded newform 63.4.e.c.46.1

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			46.1
Root			$-2.27818 - 3.94593i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.4.e.c.37.1

$q$-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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.915981	−	0.401223i	$-0.868585\pi$
$2$	−2.27818	−	3.94593i	−0.805459	−	1.39510i	0.110521	−	0.993874i	$-0.464748\pi$
$3$		0			0
$3$		0			0
$4$	−6.38024	+	11.0509i	−0.797530	+	1.38136i
$5$	8.93660	+	15.4786i	0.799314	+	1.38445i	0.920063	+	0.391769i	$0.128137\pi$
$5$	8.93660	+	15.4786i	0.799314	+	1.38445i	−0.120749	+	0.992683i	$0.538530\pi$
$6$		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	−0.933480	−	0.358630i	$-0.883244\pi$
$11$	−5.69708	+	9.86762i	−0.156158	+	0.270473i	0.777322	+	0.629102i	$0.216577\pi$
$12$		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	−0.611081	−	0.791568i	$-0.709265\pi$
$17$	26.6337	−	46.1309i	0.379977	−	0.658140i	0.991059	+	0.133428i	$0.0425984\pi$
$18$		0			0
$19$	21.2111	+	36.7388i	0.256114	+	0.443603i	0.965198	−	0.261522i	$-0.0842244\pi$
$19$	21.2111	+	36.7388i	0.256114	+	0.443603i	−0.709083	+	0.705125i	$0.750891\pi$
$20$	−228.071			−2.54991
$21$		0			0
$22$	51.9159			0.503114
$23$	76.0427	+	131.710i	0.689391	+	1.19406i	0.972035	+	0.234836i	$0.0754553\pi$
$23$	76.0427	+	131.710i	0.689391	+	1.19406i	−0.282644	+	0.959225i	$0.591211\pi$
$24$		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	−0.541481	−	0.840713i	$-0.682136\pi$
$31$	78.9369	−	136.723i	0.457338	−	0.792133i	0.998819	+	0.0485801i	$0.0154696\pi$
$32$	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	0.861834	−	0.507190i	$-0.169316\pi$
$37$	−1.87294	−	3.24403i	−0.00832188	−	0.0144139i	−0.870156	+	0.492776i	$0.835982\pi$
$38$	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	0.881996	−	0.471258i	$-0.156200\pi$
$47$	10.5934	+	18.3484i	0.0328768	+	0.0569444i	−0.849119	+	0.528202i	$0.822866\pi$
$48$		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	−0.525404	−	0.850853i	$-0.676086\pi$
$53$	182.952	−	316.882i	0.474158	−	0.821266i	0.999562	+	0.0295866i	$0.00941909\pi$
$54$		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	−0.963521	−	0.267634i	$-0.913758\pi$
$59$	−113.289	+	196.222i	−0.249982	+	0.432982i	0.713538	+	0.700616i	$0.247091\pi$
$60$		0			0
$61$	−325.987	−	564.626i	−0.684235	−	1.18513i	−0.973677	−	0.227934i	$-0.926803\pi$
$61$	−325.987	−	564.626i	−0.684235	−	1.18513i	0.289442	−	0.957196i	$-0.406530\pi$
$62$	−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	−0.924675	−	0.380756i	$-0.875664\pi$
$67$	−72.7166	+	125.949i	−0.132593	+	0.229658i	0.792082	+	0.610414i	$0.208997\pi$
$68$	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	−0.999907	−	0.0136522i	$-0.995654\pi$
$73$	−304.453	+	527.328i	−0.488130	+	0.845466i	0.511777	+	0.859119i	$0.328988\pi$
$74$	−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	−0.983561	−	0.180574i	$-0.942204\pi$
$79$	−455.119	−	788.289i	−0.648163	−	1.12265i	0.335399	−	0.942076i	$-0.391129\pi$
$80$	−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	0.854609	−	0.519272i	$-0.173797\pi$
$89$	−18.8059	−	32.5728i	−0.0223980	−	0.0387945i	−0.877007	+	0.480477i	$0.840463\pi$
$90$		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	−0.200652	−	0.979663i	$-0.564306\pi$
$101$	759.336	−	1315.21i	0.748087	−	1.29572i	0.948739	−	0.316062i	$-0.102361\pi$
$102$		0			0
$103$	525.942	+	910.957i	0.503132	+	0.871450i	0.999993	+	0.00361990i	$0.00115225\pi$
$103$	525.942	+	910.957i	0.503132	+	0.871450i	−0.496862	+	0.867830i	$0.665514\pi$
$104$	−284.116			−0.267883
$105$		0			0
$106$	−1667.19			−1.52766
$107$	383.260	+	663.826i	0.346273	+	0.599762i	0.985584	−	0.169186i	$-0.0541139\pi$
$107$	383.260	+	663.826i	0.346273	+	0.599762i	−0.639312	+	0.768948i	$0.720781\pi$
$108$		0			0
$109$	713.524	−	1235.86i	0.627002	−	1.08600i	−0.361148	−	0.932509i	$-0.617615\pi$
$109$	713.524	−	1235.86i	0.627002	−	1.08600i	0.988150	−	0.153491i	$-0.0490516\pi$
$110$	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	−0.993142	−	0.116914i	$-0.962700\pi$
$131$	−896.351	−	1552.53i	−0.597821	−	1.03546i	0.395321	−	0.918543i	$-0.370633\pi$
$132$		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	−0.474352	−	0.880335i	$-0.657318\pi$
$137$	842.208	−	1458.75i	0.525217	−	0.909702i	0.999569	−	0.0293665i	$-0.00934900\pi$
$138$		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	0.999713	+	0.0239729i	$0.00763155\pi$
$149$	946.887	+	1640.06i	0.520617	+	0.901736i	−0.479095	+	0.877763i	$0.659035\pi$
$150$		0			0
$151$	1005.92	−	1742.31i	0.542124	−	0.938986i	−0.456658	−	0.889642i	$-0.650954\pi$
$151$	1005.92	−	1742.31i	0.542124	−	0.938986i	0.998782	−	0.0493434i	$-0.0157129\pi$
$152$	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	0.286956	−	0.957944i	$-0.407357\pi$
$157$	1914.25	−	3315.58i	0.973082	−	1.68543i	0.686125	−	0.727483i	$-0.259310\pi$
$158$	−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	0.887220	+	0.461347i	$0.152634\pi$
$163$	1754.63	+	3039.11i	0.843148	+	1.46038i	−0.0440718	+	0.999028i	$0.514033\pi$
$164$	−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	−0.799288	−	0.600949i	$-0.794790\pi$
$173$	−2093.61	−	3626.23i	−0.920081	−	1.59363i	−0.120793	−	0.992678i	$-0.538544\pi$
$174$		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	−0.995039	−	0.0994906i	$-0.968279\pi$
$179$	−985.143	+	1706.32i	−0.411358	+	0.712493i	0.583681	+	0.811983i	$0.301612\pi$
$180$		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	0.988186	−	0.153261i	$-0.0489776\pi$
$191$	953.884	+	1652.18i	0.361365	+	0.625902i	−0.626821	+	0.779163i	$0.715644\pi$
$192$		0			0
$193$	−1199.96	+	2078.40i	−0.447540	+	0.775162i	−0.998225	−	0.0595509i	$-0.981033\pi$
$193$	−1199.96	+	2078.40i	−0.447540	+	0.775162i	0.550685	+	0.834713i	$0.314366\pi$
$194$	−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	−0.961742	−	0.273958i	$-0.911667\pi$
$199$	−683.889	+	1184.53i	−0.243616	+	0.421955i	0.718126	+	0.695914i	$0.245000\pi$
$200$	−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	−0.724700	−	0.689065i	$-0.758022\pi$
$227$	801.662	−	1388.52i	0.234397	−	0.405988i	0.959097	+	0.283076i	$0.0913550\pi$
$228$		0			0
$229$	−505.261	−	875.137i	−0.145802	−	0.252536i	0.783870	−	0.620925i	$-0.213243\pi$
$229$	−505.261	−	875.137i	−0.145802	−	0.252536i	−0.929672	+	0.368389i	$0.879909\pi$
$230$	12385.4			3.55072
$231$		0			0
$232$	−4045.13			−1.14472
$233$	99.1084	+	171.661i	0.0278661	+	0.0482656i	0.879622	−	0.475673i	$-0.157795\pi$
$233$	99.1084	+	171.661i	0.0278661	+	0.0482656i	−0.851756	+	0.523939i	$0.824462\pi$
$234$		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	−0.623605	−	0.781739i	$-0.714333\pi$
$241$	1366.35	−	2366.58i	0.365204	−	0.632551i	0.988809	+	0.149188i	$0.0476660\pi$
$242$	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	0.991595	+	0.129382i	$0.0412994\pi$
$257$	2504.34	+	4337.64i	0.607846	+	1.05282i	−0.383749	+	0.923437i	$0.625367\pi$
$258$		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	0.223249	+	0.974761i	$0.428334\pi$
$263$	−3124.40	+	5411.63i	−0.732544	+	1.26880i	−0.955793	+	0.294042i	$0.905000\pi$
$264$		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	−0.994515	−	0.104595i	$-0.966645\pi$
$269$	−1794.22	+	3107.69i	−0.406676	+	0.704383i	0.587839	+	0.808978i	$0.299979\pi$
$270$		0			0
$271$	991.571	+	1717.45i	0.222264	+	0.384973i	0.955495	−	0.295007i	$-0.0953218\pi$
$271$	991.571	+	1717.45i	0.222264	+	0.384973i	−0.733231	+	0.679980i	$0.761988\pi$
$272$	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	0.121838	+	0.992550i	$0.461121\pi$
$277$	−3681.96	+	6377.33i	−0.798654	+	1.38331i	−0.920493	+	0.390760i	$0.872212\pi$
$278$	−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	−0.802983	−	0.596002i	$-0.796755\pi$
$283$	545.882	−	945.495i	0.114662	−	0.198600i	0.917645	+	0.397402i	$0.130088\pi$
$284$	−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	−0.863553	−	0.504259i	$-0.831766\pi$
$311$	27.0084	−	46.7799i	0.00492446	−	0.00852941i	0.868477	+	0.495729i	$0.165099\pi$
$312$		0			0
$313$	−1886.47	−	3267.46i	−0.340670	−	0.590058i	0.643887	−	0.765120i	$-0.277321\pi$
$313$	−1886.47	−	3267.46i	−0.340670	−	0.590058i	−0.984557	+	0.175063i	$0.943987\pi$
$314$	−17444.1			−3.13511
$315$		0			0
$316$	11615.1			2.06772
$317$	859.618	+	1488.90i	0.152306	+	0.263802i	0.932075	−	0.362266i	$-0.117997\pi$
$317$	859.618	+	1488.90i	0.152306	+	0.263802i	−0.779769	+	0.626068i	$0.784663\pi$
$318$		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	−0.969117	−	0.246603i	$-0.920686\pi$
$331$	−4204.11	−	7281.73i	−0.698123	−	1.20918i	0.270994	−	0.962581i	$-0.412648\pi$
$332$	−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	−0.968492	−	0.249046i	$-0.919883\pi$
$347$	−1735.98	+	3006.81i	−0.268566	+	0.465170i	0.699926	+	0.714216i	$0.253216\pi$
$348$		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	−0.249603	−	0.968348i	$-0.580300\pi$
$353$	4734.20	−	8199.87i	0.713813	−	1.23636i	0.963416	−	0.268012i	$-0.0863666\pi$
$354$		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	0.537450	−	0.843296i	$-0.319388\pi$
$359$	−3139.78	−	5438.25i	−0.461591	−	0.799499i	−0.999040	+	0.0437971i	$0.986054\pi$
$360$		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	−0.167504	−	0.985871i	$-0.553571\pi$
$367$	5413.91	−	9377.17i	0.770038	−	1.33374i	0.937542	−	0.347873i	$-0.113096\pi$
$368$	−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	0.624915	−	0.780693i	$-0.285134\pi$
$373$	−2619.61	−	4537.30i	−0.363642	−	0.629846i	−0.988557	+	0.150846i	$0.951800\pi$
$374$	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	−0.969058	−	0.246832i	$-0.920610\pi$
$383$	−5234.02	−	9065.59i	−0.698292	−	1.20948i	0.270766	−	0.962645i	$-0.412723\pi$
$384$		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	0.187549	+	0.982255i	$0.439946\pi$
$389$	−5807.02	+	10058.1i	−0.756884	+	1.31096i	−0.944432	+	0.328705i	$0.893388\pi$
$390$		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	0.996323	−	0.0856726i	$-0.0273039\pi$
$397$	3353.65	+	5808.69i	0.423967	+	0.734332i	−0.572356	+	0.820005i	$0.693971\pi$
$398$	6232.10			0.784892
$399$		0			0
$400$	−632.768			−0.0790960
$401$	2763.19	+	4785.98i	0.344107	+	0.596011i	0.985191	−	0.171459i	$-0.0548482\pi$
$401$	2763.19	+	4785.98i	0.344107	+	0.596011i	−0.641084	+	0.767471i	$0.721515\pi$
$402$		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	−0.823406	−	0.567453i	$-0.807929\pi$
$409$	659.453	−	1142.21i	0.0797258	−	0.138089i	0.903132	+	0.429364i	$0.141262\pi$
$410$	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	−0.530579	−	0.847635i	$-0.678026\pi$
$431$	4194.58	−	7265.23i	0.468784	−	0.811958i	0.999363	+	0.0356776i	$0.0113589\pi$
$432$		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	0.592755	+	0.805383i	$0.298040\pi$
$439$	9141.59	+	15833.7i	0.993859	+	1.72142i	0.401104	+	0.916032i	$0.368626\pi$
$440$	−4417.26			−0.478602
$441$		0			0
$442$	3179.12			0.342116
$443$	605.218	+	1048.27i	0.0649092	+	0.112426i	0.896654	−	0.442733i	$-0.145991\pi$
$443$	605.218	+	1048.27i	0.0649092	+	0.112426i	−0.831745	+	0.555159i	$0.812658\pi$
$444$		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	0.987715	+	0.156266i	$0.0499458\pi$
$457$	6146.88	+	10646.7i	0.629188	+	1.08979i	−0.358527	+	0.933519i	$0.616721\pi$
$458$	−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	0.937617	−	0.347671i	$-0.113027\pi$
$467$	1692.59	+	2931.65i	0.167716	+	0.290493i	−0.769900	+	0.638164i	$0.779694\pi$
$468$		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	−0.687470	−	0.726213i	$-0.741279\pi$
$479$	2989.71	−	5178.32i	0.285184	−	0.493953i	0.972654	+	0.232260i	$0.0746120\pi$
$480$		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	−0.838923	−	0.544250i	$-0.816814\pi$
$487$	557.481	−	965.586i	0.0518725	−	0.0898457i	0.890796	+	0.454404i	$0.150148\pi$
$488$	−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	0.911390	−	0.411543i	$-0.135010\pi$
$499$	1106.75	+	1916.95i	0.0992884	+	0.171973i	−0.812102	+	0.583516i	$0.801677\pi$
$500$	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	0.851181	−	0.524872i	$-0.175887\pi$
$509$	−332.584	−	576.053i	−0.0289618	−	0.0501633i	−0.880143	+	0.474709i	$0.842553\pi$
$510$		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	−0.999980	−	0.00630307i	$-0.997994\pi$
$521$	−5880.99	+	10186.2i	−0.494531	+	0.856554i	0.505449	+	0.862857i	$0.331327\pi$
$522$		0			0
$523$	−5061.30	−	8766.43i	−0.423165	−	0.732943i	0.573082	−	0.819498i	$-0.305748\pi$
$523$	−5061.30	−	8766.43i	−0.423165	−	0.732943i	−0.996247	+	0.0865547i	$0.972414\pi$
$524$	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	−0.985333	−	0.170644i	$-0.945415\pi$
$541$	−8058.98	−	13958.6i	−0.640449	−	1.10929i	0.344884	−	0.938645i	$-0.387918\pi$
$542$	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	−0.135903	−	0.990722i	$-0.543394\pi$
$557$	10385.6	−	17988.4i	0.790039	−	1.36839i	0.925942	−	0.377665i	$-0.123273\pi$
$558$		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	−0.950664	−	0.310222i	$-0.899597\pi$
$563$	−2760.86	+	4781.95i	−0.206672	+	0.357966i	0.743992	+	0.668188i	$0.232930\pi$
$564$		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	0.971147	−	0.238480i	$-0.0766491\pi$
$569$	3787.40	+	6559.97i	0.279044	+	0.483319i	−0.692103	+	0.721799i	$0.743316\pi$
$570$		0			0
$571$	165.624	−	286.869i	0.0121386	−	0.0210247i	−0.859892	−	0.510476i	$-0.829469\pi$
$571$	165.624	−	286.869i	0.0121386	−	0.0210247i	0.872031	+	0.489451i	$0.162803\pi$
$572$	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	−0.900444	−	0.434972i	$-0.856758\pi$
$577$	−1019.06	+	1765.06i	−0.0735248	+	0.127349i	0.826919	+	0.562321i	$0.190091\pi$
$578$	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	0.749838	−	0.661622i	$-0.230132\pi$
$593$	−2860.12	−	4953.87i	−0.198062	−	0.343054i	−0.947900	+	0.318568i	$0.896798\pi$
$594$		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	−0.373122	−	0.927782i	$-0.621713\pi$
$599$	9044.21	−	15665.0i	0.616922	−	1.06854i	0.990044	−	0.140758i	$-0.0449540\pi$
$600$		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	0.823641	−	0.567111i	$-0.191939\pi$
$607$	−1186.10	−	2054.39i	−0.0793120	−	0.137372i	−0.902953	+	0.429739i	$0.858606\pi$
$608$	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	−0.980567	−	0.196182i	$-0.937146\pi$
$613$	−4862.54	+	8422.16i	−0.320385	+	0.554923i	0.660182	+	0.751105i	$0.270479\pi$
$614$	−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	−0.481062	−	0.876687i	$-0.659749\pi$
$619$	7988.29	−	13836.1i	0.518702	−	0.898418i	0.999764	−	0.0217314i	$-0.00691786\pi$
$620$	−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	−0.822338	−	0.568999i	$-0.807331\pi$
$641$	1324.25	−	2293.67i	0.0815988	−	0.141333i	0.903937	+	0.427666i	$0.140664\pi$
$642$		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	−0.633639	−	0.773628i	$-0.718440\pi$
$647$	5812.07	−	10066.8i	0.353162	−	0.611695i	0.986802	+	0.161934i	$0.0517730\pi$
$648$		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	−0.877135	−	0.480244i	$-0.840548\pi$
$653$	−14258.3	−	24696.1i	−0.854471	−	1.47999i	0.0226638	−	0.999743i	$-0.492785\pi$
$654$		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	0.474653	+	0.880173i	$0.342574\pi$
$661$	−8920.72	+	15451.1i	−0.524926	+	0.909198i	−0.999579	+	0.0290250i	$0.990760\pi$
$662$	−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	−0.992173	−	0.124867i	$-0.960150\pi$
$677$	−10643.4	−	18435.0i	−0.604225	−	1.04655i	0.387949	−	0.921681i	$-0.373184\pi$
$678$		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	0.415755	+	0.909477i	$0.363517\pi$
$683$	−10348.4	+	17924.0i	−0.579753	+	1.00416i	−0.995507	+	0.0946842i	$0.969816\pi$
$684$		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	−0.869276	−	0.494327i	$-0.835415\pi$
$691$	−15671.0	−	27142.9i	−0.862738	−	1.49431i	0.00653825	−	0.999979i	$-0.497919\pi$
$692$	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	0.607225	−	0.794530i	$-0.292283\pi$
$709$	−7258.27	−	12571.7i	−0.384471	−	0.665923i	−0.991696	+	0.128607i	$0.958949\pi$
$710$	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	0.977551	+	0.210698i	$0.0675737\pi$
$719$	12941.2	+	22414.8i	0.671246	+	1.16263i	−0.306306	+	0.951933i	$0.599093\pi$
$720$		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	−0.999577	−	0.0290722i	$-0.990745\pi$
$733$	−10418.1	−	18044.6i	−0.524966	−	0.909268i	0.474611	−	0.880195i	$-0.342589\pi$
$734$	−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	0.323219	+	0.946324i	$0.395235\pi$
$739$	−13217.4	+	22893.3i	−0.657931	+	1.13957i	−0.981150	+	0.193246i	$0.938098\pi$
$740$	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	0.915143	+	0.403129i	$0.132077\pi$
$751$	16602.3	+	28756.0i	0.806692	+	1.39723i	−0.108451	+	0.994102i	$0.534589\pi$
$752$	−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	−0.802075	−	0.597224i	$-0.796270\pi$
$761$	−19276.9	−	33388.6i	−0.918248	−	1.59045i	−0.116174	−	0.993229i	$-0.537063\pi$
$762$		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	−0.984806	−	0.173659i	$-0.944441\pi$
$773$	−7350.34	+	12731.2i	−0.342010	+	0.592378i	0.642796	+	0.766037i	$0.277774\pi$
$774$		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	−0.457127	−	0.889401i	$-0.651122\pi$
$787$	11959.3	−	20714.1i	0.541681	−	0.938218i	0.998808	−	0.0488169i	$-0.0155451\pi$
$788$	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	0.290962	+	0.956734i	$0.406025\pi$
$809$	−15717.8	+	27224.0i	−0.683075	+	1.18312i	−0.974038	+	0.226386i	$0.927309\pi$
$810$		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	0.807599	−	0.589732i	$-0.200767\pi$
$821$	−2515.29	−	4356.60i	−0.106923	−	0.185197i	−0.914522	+	0.404535i	$0.867433\pi$
$822$		0			0
$823$	6992.59	−	12111.5i	0.296168	−	0.512978i	−0.679088	−	0.734057i	$-0.737625\pi$
$823$	6992.59	−	12111.5i	0.296168	−	0.512978i	0.975256	+	0.221079i	$0.0709578\pi$
$824$	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	−0.574909	−	0.818218i	$-0.694962\pi$
$829$	10052.2	−	17410.9i	0.421143	−	0.729441i	0.996052	+	0.0887769i	$0.0282958\pi$
$830$	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	−0.754428	−	0.656383i	$-0.772086\pi$
$857$	4797.64	−	8309.76i	0.191230	−	0.331220i	0.945658	+	0.325162i	$0.105419\pi$
$858$		0			0
$859$	−10920.4	−	18914.7i	−0.433760	−	0.751295i	0.563433	−	0.826162i	$-0.309480\pi$
$859$	−10920.4	−	18914.7i	−0.433760	−	0.751295i	−0.997194	+	0.0748666i	$0.976147\pi$
$860$	−97942.3			−3.88350
$861$		0			0
$862$	−38224.1			−1.51035
$863$	−13265.8	−	22977.1i	−0.523260	−	0.906313i	−0.999634	−	0.0270699i	$-0.991382\pi$
$863$	−13265.8	−	22977.1i	−0.523260	−	0.906313i	0.476374	−	0.879243i	$-0.341951\pi$
$864$		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	0.924269	−	0.381741i	$-0.124675\pi$
$877$	3416.23	+	5917.09i	0.131537	+	0.227829i	−0.792732	+	0.609570i	$0.791342\pi$
$878$	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	0.893987	+	0.448093i	$0.147897\pi$
$887$	22059.7	+	38208.5i	0.835054	+	1.44636i	−0.0589333	+	0.998262i	$0.518770\pi$
$888$		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	0.300764	+	0.953698i	$0.402758\pi$
$907$	−18452.9	+	31961.4i	−0.675545	+	1.17008i	−0.976309	+	0.216380i	$0.930575\pi$
$908$	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	0.777024	−	0.629470i	$-0.216728\pi$
$919$	−4363.50	−	7557.80i	−0.156625	−	0.271283i	−0.933650	+	0.358188i	$0.883395\pi$
$920$	−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	0.984926	−	0.172979i	$-0.0553392\pi$
$929$	9702.54	+	16805.3i	0.342659	+	0.593502i	−0.642267	+	0.766481i	$0.722006\pi$
$930$		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	0.487140	+	0.873324i	$0.338040\pi$
$941$	−14801.0	+	25636.1i	−0.512751	+	0.888111i	−0.999891	+	0.0147865i	$0.995293\pi$
$942$		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	0.958474	−	0.285180i	$-0.0920535\pi$
$947$	6768.71	+	11723.8i	0.232264	+	0.402292i	−0.726210	+	0.687473i	$0.758720\pi$
$948$		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	0.658826	−	0.752295i	$-0.271053\pi$
$971$	−9745.65	−	16880.0i	−0.322094	−	0.557882i	−0.980920	+	0.194413i	$0.937720\pi$
$972$		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	−0.912588	−	0.408881i	$-0.865919\pi$
$977$	−3120.78	+	5405.35i	−0.102193	+	0.177004i	0.810395	+	0.585884i	$0.199253\pi$
$978$		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	0.268382	−	0.963313i	$-0.413511\pi$
$983$	29847.3	−	51697.0i	0.968444	−	1.67739i	0.700062	−	0.714082i	$-0.253155\pi$
$984$		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	−0.963362	−	0.268203i	$-0.913570\pi$
$991$	−7780.82	+	13476.8i	−0.249411	+	0.431992i	0.713952	+	0.700195i	$0.246904\pi$
$992$	−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	−0.979613	−	0.200892i	$-0.935616\pi$
$997$	−9942.47	+	17220.9i	−0.315829	+	0.547031i	0.663785	+	0.747924i	$0.268949\pi$
$998$	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.46.1		6
3.2	odd	2		21.4.e.b.4.3	✓	6
7.2	even	3	inner	63.4.e.c.37.1		6
7.3	odd	6		441.4.a.t.1.3		3
7.4	even	3		441.4.a.s.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
12.11	even	2		336.4.q.k.193.1		6
21.2	odd	6		21.4.e.b.16.3	yes	6
21.5	even	6		147.4.e.n.79.3		6
21.11	odd	6		147.4.a.l.1.1		3
21.17	even	6		147.4.a.m.1.1		3
21.20	even	2		147.4.e.n.67.3		6
84.11	even	6		2352.4.a.ci.1.3		3
84.23	even	6		336.4.q.k.289.1		6
84.59	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	3.2	odd	2
21.4.e.b.16.3	yes	6	21.2	odd	6
63.4.e.c.37.1		6	7.2	even	3	inner
63.4.e.c.46.1		6	1.1	even	1	trivial
147.4.a.l.1.1		3	21.11	odd	6
147.4.a.m.1.1		3	21.17	even	6
147.4.e.n.67.3		6	21.20	even	2
147.4.e.n.79.3		6	21.5	even	6
336.4.q.k.193.1		6	12.11	even	2
336.4.q.k.289.1		6	84.23	even	6
441.4.a.s.1.3		3	7.4	even	3
441.4.a.t.1.3		3	7.3	odd	6
441.4.e.w.226.1		6	7.5	odd	6
441.4.e.w.361.1		6	7.6	odd	2
2352.4.a.cg.1.1		3	84.59	odd	6
2352.4.a.ci.1.3		3	84.11	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

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