LMFDB - Embedded newform 124.3.o.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,3,Mod(13,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("124.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	124.o (of order $30$, degree $8$, 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:	$3.37875527807$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	124.13
Dual form			124.3.o.a.105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.39545 - 5.38028i) q^{3} +(-3.34056 - 5.78602i) q^{5} +(5.42242 + 6.02221i) q^{7} +(-17.1870 + 19.0881i) q^{9} +O(q^{10})$	\(q+(-2.39545 - 5.38028i) q^{3} +(-3.34056 - 5.78602i) q^{5} +(5.42242 + 6.02221i) q^{7} +(-17.1870 + 19.0881i) q^{9} +(-0.221326 - 1.04126i) q^{11} +(-5.68090 - 0.597086i) q^{13} +(-23.1282 + 31.8333i) q^{15} +(6.60537 - 31.0758i) q^{17} +(0.408005 + 3.88191i) q^{19} +(19.4120 - 43.6001i) q^{21} +(-17.3605 + 5.64077i) q^{23} +(-9.81871 + 17.0065i) q^{25} +(93.4591 + 30.3667i) q^{27} +(-15.0679 - 20.7391i) q^{29} +(-25.5753 - 17.5187i) q^{31} +(-5.07207 + 3.68507i) q^{33} +(16.7307 - 51.4918i) q^{35} +(-26.6567 - 15.3902i) q^{37} +(10.3958 + 31.9951i) q^{39} +(-18.1473 - 8.07968i) q^{41} +(48.6096 - 5.10907i) q^{43} +(167.858 + 35.6794i) q^{45} +(34.4956 + 25.0625i) q^{47} +(-1.74246 + 16.5784i) q^{49} +(-183.019 + 38.9020i) q^{51} +(24.0191 + 21.6269i) q^{53} +(-5.28538 + 4.75897i) q^{55} +(19.9084 - 11.4941i) q^{57} +(29.3539 - 13.0692i) q^{59} -51.2819i q^{61} -208.148 q^{63} +(15.5226 + 34.8644i) q^{65} +(-17.5739 - 30.4389i) q^{67} +(71.9351 + 79.8920i) q^{69} +(33.8518 - 37.5963i) q^{71} +(-10.1420 - 47.7143i) q^{73} +(115.020 + 12.0891i) q^{75} +(5.07054 - 6.97900i) q^{77} +(-7.44319 + 35.0175i) q^{79} +(-36.3318 - 345.674i) q^{81} +(44.2968 - 99.4923i) q^{83} +(-201.871 + 65.5919i) q^{85} +(-75.4879 + 130.749i) q^{87} +(-24.8699 - 8.08071i) q^{89} +(-27.2084 - 37.4492i) q^{91} +(-32.9910 + 179.567i) q^{93} +(21.0978 - 15.3285i) q^{95} +(-45.1501 + 138.958i) q^{97} +(23.6795 + 13.6714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9	$ 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9 + 2 * q^11 - 18 * q^13 + 35 * q^15 + 25 * q^17 - 11 * q^19 + 54 * q^21 + 25 * q^23 - 75 * q^25 + 225 * q^27 + 20 * q^29 + 59 * q^31 - 303 * q^33 - 66 * q^35 - 222 * q^37 - 169 * q^39 + q^41 + 122 * q^43 + 54 * q^45 - 120 * q^47 - 118 * q^49 - 515 * q^51 + 61 * q^53 - 121 * q^55 - 201 * q^57 - 257 * q^59 - 158 * q^63 + 182 * q^65 - q^67 + 510 * q^69 + 459 * q^71 + 253 * q^73 + 651 * q^75 + 670 * q^77 + 385 * q^79 + 974 * q^81 + 375 * q^83 - 370 * q^85 - 344 * q^87 + 245 * q^89 + 960 * q^91 - 212 * q^93 - 851 * q^95 - 797 * q^97 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{11}{30}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.39545	−	5.38028i	−0.798484	−	1.79343i	−0.573804	−	0.818993i	$-0.694533\pi$
$3$	−2.39545	−	5.38028i	−0.798484	−	1.79343i	−0.224680	−	0.974433i	$-0.572134\pi$
$4$		0			0
$5$	−3.34056	−	5.78602i	−0.668112	−	1.15720i	−0.978431	−	0.206572i	$-0.933769\pi$
$5$	−3.34056	−	5.78602i	−0.668112	−	1.15720i	0.310319	−	0.950633i	$-0.399564\pi$
$6$		0			0
$7$	5.42242	+	6.02221i	0.774632	+	0.860316i	0.993310	−	0.115481i	$-0.0368410\pi$
$7$	5.42242	+	6.02221i	0.774632	+	0.860316i	−0.218678	+	0.975797i	$0.570174\pi$
$8$		0			0
$9$	−17.1870	+	19.0881i	−1.90967	+	2.12090i
$10$		0			0
$11$	−0.221326	−	1.04126i	−0.0201205	−	0.0946596i	0.966942	−	0.254998i	$-0.0820748\pi$
$11$	−0.221326	−	1.04126i	−0.0201205	−	0.0946596i	−0.987062	+	0.160338i	$0.948741\pi$
$12$		0			0
$13$	−5.68090	−	0.597086i	−0.436992	−	0.0459297i	−0.116521	−	0.993188i	$-0.537174\pi$
$13$	−5.68090	−	0.597086i	−0.436992	−	0.0459297i	−0.320471	+	0.947258i	$0.603841\pi$
$14$		0			0
$15$	−23.1282	+	31.8333i	−1.54188	+	2.12222i
$16$		0			0
$17$	6.60537	−	31.0758i	0.388551	−	1.82799i	−0.154129	−	0.988051i	$-0.549257\pi$
$17$	6.60537	−	31.0758i	0.388551	−	1.82799i	0.542680	−	0.839939i	$-0.317409\pi$
$18$		0			0
$19$	0.408005	+	3.88191i	0.0214739	+	0.204311i	0.999998	−	0.00182014i	$-0.000579367\pi$
$19$	0.408005	+	3.88191i	0.0214739	+	0.204311i	−0.978524	+	0.206131i	$0.933913\pi$
$20$		0			0
$21$	19.4120	−	43.6001i	0.924381	−	2.07619i
$22$		0			0
$23$	−17.3605	+	5.64077i	−0.754804	+	0.245251i	−0.661047	−	0.750344i	$-0.729888\pi$
$23$	−17.3605	+	5.64077i	−0.754804	+	0.245251i	−0.0937570	+	0.995595i	$0.529888\pi$
$24$		0			0
$25$	−9.81871	+	17.0065i	−0.392749	+	0.680261i
$26$		0			0
$27$	93.4591	+	30.3667i	3.46145	+	1.12469i
$28$		0			0
$29$	−15.0679	−	20.7391i	−0.519581	−	0.715142i	0.465917	−	0.884828i	$-0.345725\pi$
$29$	−15.0679	−	20.7391i	−0.519581	−	0.715142i	−0.985498	+	0.169686i	$0.945725\pi$
$30$		0			0
$31$	−25.5753	−	17.5187i	−0.825009	−	0.565119i
$31$	−25.5753	−	17.5187i	−0.825009	−	0.565119i
$32$		0			0
$33$	−5.07207	+	3.68507i	−0.153699	+	0.111669i
$34$		0			0
$35$	16.7307	−	51.4918i	0.478020	−	1.47120i
$36$		0			0
$37$	−26.6567	−	15.3902i	−0.720450	−	0.415952i	0.0944681	−	0.995528i	$-0.469885\pi$
$37$	−26.6567	−	15.3902i	−0.720450	−	0.415952i	−0.814918	+	0.579576i	$0.803218\pi$
$38$		0			0
$39$	10.3958	+	31.9951i	0.266560	+	0.820387i
$40$		0			0
$41$	−18.1473	−	8.07968i	−0.442616	−	0.197065i	0.173313	−	0.984867i	$-0.444553\pi$
$41$	−18.1473	−	8.07968i	−0.442616	−	0.197065i	−0.615929	+	0.787801i	$0.711219\pi$
$42$		0			0
$43$	48.6096	−	5.10907i	1.13046	−	0.118816i	0.479222	−	0.877694i	$-0.340919\pi$
$43$	48.6096	−	5.10907i	1.13046	−	0.118816i	0.651233	+	0.758878i	$0.274252\pi$
$44$		0			0
$45$	167.858	+	35.6794i	3.73019	+	0.792876i
$46$		0			0
$47$	34.4956	+	25.0625i	0.733948	+	0.533245i	0.890810	−	0.454376i	$-0.150138\pi$
$47$	34.4956	+	25.0625i	0.733948	+	0.533245i	−0.156862	+	0.987621i	$0.550138\pi$
$48$		0			0
$49$	−1.74246	+	16.5784i	−0.0355604	+	0.338334i
$50$		0			0
$51$	−183.019	+	38.9020i	−3.58862	+	0.762784i
$52$		0			0
$53$	24.0191	+	21.6269i	0.453191	+	0.408055i	0.863862	−	0.503729i	$-0.168039\pi$
$53$	24.0191	+	21.6269i	0.453191	+	0.408055i	−0.410671	+	0.911784i	$0.634706\pi$
$54$		0			0
$55$	−5.28538	+	4.75897i	−0.0960977	+	0.0865268i
$56$		0			0
$57$	19.9084	−	11.4941i	0.349270	−	0.201651i
$58$		0			0
$59$	29.3539	−	13.0692i	0.497524	−	0.221512i	−0.142605	−	0.989780i	$-0.545548\pi$
$59$	29.3539	−	13.0692i	0.497524	−	0.221512i	0.640129	+	0.768268i	$0.278881\pi$
$60$		0			0
$61$		−	51.2819i		−	0.840687i	−0.907365	−	0.420344i	$-0.861910\pi$
$61$		−	51.2819i		−	0.840687i	0.907365	−	0.420344i	$-0.138090\pi$
$62$		0			0
$63$	−208.148			−3.30393
$64$		0			0
$65$	15.5226	+	34.8644i	0.238810	+	0.536375i
$66$		0			0
$67$	−17.5739	−	30.4389i	−0.262297	−	0.454312i	0.704555	−	0.709650i	$-0.251147\pi$
$67$	−17.5739	−	30.4389i	−0.262297	−	0.454312i	−0.966852	+	0.255337i	$0.917813\pi$
$68$		0			0
$69$	71.9351	+	79.8920i	1.04254	+	1.15786i
$70$		0			0
$71$	33.8518	−	37.5963i	0.476787	−	0.529525i	−0.455988	−	0.889986i	$-0.650714\pi$
$71$	33.8518	−	37.5963i	0.476787	−	0.529525i	0.932774	+	0.360461i	$0.117381\pi$
$72$		0			0
$73$	−10.1420	−	47.7143i	−0.138931	−	0.653620i	−0.991403	−	0.130846i	$-0.958231\pi$
$73$	−10.1420	−	47.7143i	−0.138931	−	0.653620i	0.852471	−	0.522774i	$-0.175103\pi$
$74$		0			0
$75$	115.020	+	12.0891i	1.53360	+	0.161188i
$76$		0			0
$77$	5.07054	−	6.97900i	0.0658511	−	0.0906363i
$78$		0			0
$79$	−7.44319	+	35.0175i	−0.0942176	+	0.443259i	0.905599	+	0.424134i	$0.139421\pi$
$79$	−7.44319	+	35.0175i	−0.0942176	+	0.443259i	−0.999817	+	0.0191252i	$0.993912\pi$
$80$		0			0
$81$	−36.3318	−	345.674i	−0.448541	−	4.26758i
$82$		0			0
$83$	44.2968	−	99.4923i	0.533697	−	1.19870i	−0.422603	−	0.906315i	$-0.638883\pi$
$83$	44.2968	−	99.4923i	0.533697	−	1.19870i	0.956300	−	0.292388i	$-0.0944499\pi$
$84$		0			0
$85$	−201.871	+	65.5919i	−2.37495	+	0.771670i
$86$		0			0
$87$	−75.4879	+	130.749i	−0.867677	+	1.50286i
$88$		0			0
$89$	−24.8699	−	8.08071i	−0.279437	−	0.0907944i	0.165946	−	0.986135i	$-0.446932\pi$
$89$	−24.8699	−	8.08071i	−0.279437	−	0.0907944i	−0.445382	+	0.895340i	$0.646932\pi$
$90$		0			0
$91$	−27.2084	−	37.4492i	−0.298994	−	0.411530i
$92$		0			0
$93$	−32.9910	+	179.567i	−0.354742	+	1.93083i
$94$		0			0
$95$	21.0978	−	15.3285i	0.222082	−	0.161352i
$96$		0			0
$97$	−45.1501	+	138.958i	−0.465465	+	1.43256i	0.392931	+	0.919568i	$0.371461\pi$
$97$	−45.1501	+	138.958i	−0.465465	+	1.43256i	−0.858396	+	0.512987i	$0.828539\pi$
$98$		0			0
$99$	23.6795	+	13.6714i	0.239187	+	0.138095i
$100$		0			0
$101$	12.9797	+	39.9475i	0.128512	+	0.395520i	0.994525	−	0.104503i	$-0.0333250\pi$
$101$	12.9797	+	39.9475i	0.128512	+	0.395520i	−0.866012	+	0.500023i	$0.833325\pi$
$102$		0			0
$103$	135.970	+	60.5379i	1.32010	+	0.587747i	0.941250	−	0.337711i	$-0.109653\pi$
$103$	135.970	+	60.5379i	1.32010	+	0.587747i	0.378851	+	0.925458i	$0.376319\pi$
$104$		0			0
$105$	−317.118	+	33.3304i	−3.02017	+	0.317433i
$106$		0			0
$107$	−94.1849	−	20.0196i	−0.880233	−	0.187099i	−0.254440	−	0.967089i	$-0.581891\pi$
$107$	−94.1849	−	20.0196i	−0.880233	−	0.187099i	−0.625793	+	0.779989i	$0.715224\pi$
$108$		0			0
$109$	48.8562	+	35.4961i	0.448222	+	0.325652i	0.788893	−	0.614530i	$-0.210654\pi$
$109$	48.8562	+	35.4961i	0.448222	+	0.325652i	−0.340671	+	0.940182i	$0.610654\pi$
$110$		0			0
$111$	−18.9489	+	180.287i	−0.170711	+	1.62420i
$112$		0			0
$113$	28.8608	−	6.13455i	0.255405	−	0.0542880i	−0.0784296	−	0.996920i	$-0.524991\pi$
$113$	28.8608	−	6.13455i	0.255405	−	0.0542880i	0.333835	+	0.942632i	$0.391657\pi$
$114$		0			0
$115$	90.6314	+	81.6049i	0.788099	+	0.709608i
$116$		0			0
$117$	109.035	−	98.1753i	0.931921	−	0.839105i
$118$		0			0
$119$	222.962	−	128.727i	1.87363	−	1.08174i
$120$		0			0
$121$	109.504	−	48.7542i	0.904990	−	0.402927i
$122$		0			0
$123$			116.992i			0.951152i
$124$		0			0
$125$	−35.8280			−0.286624
$126$		0			0
$127$	70.9502	+	159.357i	0.558663	+	1.25478i	0.943371	+	0.331739i	$0.107635\pi$
$127$	70.9502	+	159.357i	0.558663	+	1.25478i	−0.384708	+	0.923038i	$0.625698\pi$
$128$		0			0
$129$	−143.930	−	249.294i	−1.11574	−	1.93251i
$130$		0			0
$131$	−73.6618	−	81.8098i	−0.562304	−	0.624502i	0.393209	−	0.919449i	$-0.371365\pi$
$131$	−73.6618	−	81.8098i	−0.562304	−	0.624502i	−0.955514	+	0.294947i	$0.904698\pi$
$132$		0			0
$133$	−21.1653	+	23.5064i	−0.159137	+	0.176740i
$134$		0			0
$135$	−136.503	−	642.198i	−1.01114	−	4.75702i
$136$		0			0
$137$	244.810	+	25.7306i	1.78693	+	0.187814i	0.939376	−	0.342888i	$-0.111405\pi$
$137$	244.810	+	25.7306i	1.78693	+	0.187814i	0.847558	+	0.530702i	$0.178072\pi$
$138$		0			0
$139$	48.6130	−	66.9101i	0.349734	−	0.481367i	−0.597519	−	0.801855i	$-0.703847\pi$
$139$	48.6130	−	66.9101i	0.349734	−	0.481367i	0.947253	+	0.320488i	$0.103847\pi$
$140$		0			0
$141$	52.2106	−	245.632i	0.370288	−	1.74207i
$142$		0			0
$143$	0.635609	+	6.04741i	0.00444482	+	0.0422896i
$144$		0			0
$145$	−69.6620	+	156.463i	−0.480427	+	1.07906i
$146$		0			0
$147$	93.3702	−	30.3378i	0.635171	−	0.206380i
$148$		0			0
$149$	75.4862	−	130.746i	0.506619	−	0.877489i	−0.493352	−	0.869830i	$-0.664229\pi$
$149$	75.4862	−	130.746i	0.506619	−	0.877489i	0.999971	−	0.00765945i	$-0.00243810\pi$
$150$		0			0
$151$	192.866	+	62.6658i	1.27726	+	0.415006i	0.867613	−	0.497240i	$-0.165653\pi$
$151$	192.866	+	62.6658i	1.27726	+	0.415006i	0.409643	+	0.912246i	$0.365653\pi$
$152$		0			0
$153$	479.652	+	660.184i	3.13498	+	4.31493i
$154$		0			0
$155$	−15.9277	+	206.502i	−0.102759	+	1.33227i
$156$		0			0
$157$	−170.518	+	123.888i	−1.08610	+	0.789098i	−0.978736	−	0.205122i	$-0.934241\pi$
$157$	−170.518	+	123.888i	−1.08610	+	0.789098i	−0.107363	+	0.994220i	$0.534241\pi$
$158$		0			0
$159$	58.8221	−	181.036i	0.369950	−	1.13859i
$160$		0			0
$161$	−128.106	−	73.9619i	−0.795688	−	0.459391i
$162$		0			0
$163$	−25.0116	−	76.9777i	−0.153445	−	0.472256i	0.844555	−	0.535469i	$-0.179865\pi$
$163$	−25.0116	−	76.9777i	−0.153445	−	0.472256i	−0.998000	+	0.0632132i	$0.979865\pi$
$164$		0			0
$165$	38.2655	+	17.0369i	0.231912	+	0.103254i
$166$		0			0
$167$	66.5328	−	6.99288i	0.398400	−	0.0418735i	0.0967899	−	0.995305i	$-0.469143\pi$
$167$	66.5328	−	6.99288i	0.398400	−	0.0418735i	0.301610	+	0.953431i	$0.402476\pi$
$168$		0			0
$169$	−133.391	−	28.3531i	−0.789295	−	0.167770i
$170$		0			0
$171$	−81.1105	−	58.9303i	−0.474331	−	0.344621i
$172$		0			0
$173$	9.23415	−	87.8571i	0.0533766	−	0.507844i	−0.934872	−	0.354986i	$-0.884486\pi$
$173$	9.23415	−	87.8571i	0.0533766	−	0.507844i	0.988248	−	0.152858i	$-0.0488478\pi$
$174$		0			0
$175$	−155.658	+	33.0861i	−0.889474	+	0.189064i
$176$		0			0
$177$	−140.632	−	126.626i	−0.794530	−	0.715398i
$178$		0			0
$179$	−179.094	+	161.257i	−1.00053	+	0.900877i	−0.995077	−	0.0991080i	$-0.968401\pi$
$179$	−179.094	+	161.257i	−1.00053	+	0.900877i	−0.00544874	+	0.999985i	$0.501734\pi$
$180$		0			0
$181$	180.404	−	104.156i	0.996709	−	0.575450i	0.0894358	−	0.995993i	$-0.471494\pi$
$181$	180.404	−	104.156i	0.996709	−	0.575450i	0.907273	+	0.420543i	$0.138160\pi$
$182$		0			0
$183$	−275.911	+	122.843i	−1.50771	+	0.671276i
$184$		0			0
$185$			205.648i			1.11161i
$186$		0			0
$187$	−33.8198			−0.180855
$188$		0			0
$189$	323.900	+	727.491i	1.71376	+	3.84916i
$190$		0			0
$191$	−48.5957	−	84.1702i	−0.254428	−	0.440682i	0.710312	−	0.703887i	$-0.248554\pi$
$191$	−48.5957	−	84.1702i	−0.254428	−	0.440682i	−0.964740	+	0.263205i	$0.915220\pi$
$192$		0			0
$193$	−122.443	−	135.987i	−0.634422	−	0.704597i	0.337121	−	0.941461i	$-0.390547\pi$
$193$	−122.443	−	135.987i	−0.634422	−	0.704597i	−0.971543	+	0.236865i	$0.923880\pi$
$194$		0			0
$195$	150.396	−	167.032i	0.771263	−	0.856575i
$196$		0			0
$197$	20.9968	+	98.7821i	0.106583	+	0.501432i	0.998762	+	0.0497500i	$0.0158425\pi$
$197$	20.9968	+	98.7821i	0.106583	+	0.501432i	−0.892179	+	0.451682i	$0.850824\pi$
$198$		0			0
$199$	−69.2555	−	7.27904i	−0.348017	−	0.0365781i	−0.0710927	−	0.997470i	$-0.522649\pi$
$199$	−69.2555	−	7.27904i	−0.348017	−	0.0365781i	−0.276925	+	0.960892i	$0.589315\pi$
$200$		0			0
$201$	−121.672	+	167.468i	−0.605335	+	0.833172i
$202$		0			0
$203$	43.1911	−	203.198i	0.212764	−	1.00098i
$204$		0			0
$205$	13.8728	+	131.991i	0.0676723	+	0.643859i
$206$		0			0
$207$	190.703	−	428.326i	0.921272	−	2.06921i
$208$		0			0
$209$	3.95175	−	1.28400i	0.0189079	−	0.00614355i
$210$		0			0
$211$	−26.3082	+	45.5672i	−0.124684	+	0.215958i	−0.921609	−	0.388119i	$-0.873125\pi$
$211$	−26.3082	+	45.5672i	−0.124684	+	0.215958i	0.796926	+	0.604077i	$0.206458\pi$
$212$		0			0
$213$	−283.369	−	92.0721i	−1.33037	−	0.432264i
$214$		0			0
$215$	−191.945	−	264.189i	−0.892765	−	1.22879i
$216$		0			0
$217$	−33.1788	−	249.014i	−0.152898	−	1.14753i
$218$		0			0
$219$	−232.421	+	168.864i	−1.06128	+	0.771068i
$220$		0			0
$221$	−56.0794	+	172.595i	−0.253753	+	0.780971i
$222$		0			0
$223$	152.633	+	88.1228i	0.684454	+	0.395169i	0.801531	−	0.597953i	$-0.204019\pi$
$223$	152.633	+	88.1228i	0.684454	+	0.395169i	−0.117077	+	0.993123i	$0.537353\pi$
$224$		0			0
$225$	−155.868	−	479.711i	−0.692745	−	2.13205i
$226$		0			0
$227$	149.259	+	66.4543i	0.657528	+	0.292750i	0.708249	−	0.705963i	$-0.249485\pi$
$227$	149.259	+	66.4543i	0.657528	+	0.292750i	−0.0507213	+	0.998713i	$0.516152\pi$
$228$		0			0
$229$	54.3153	−	5.70876i	0.237185	−	0.0249291i	0.0148097	−	0.999890i	$-0.495286\pi$
$229$	54.3153	−	5.70876i	0.237185	−	0.0249291i	0.222375	+	0.974961i	$0.428619\pi$
$230$		0			0
$231$	−49.6952	−	10.5630i	−0.215131	−	0.0457274i
$232$		0			0
$233$	33.0039	+	23.9787i	0.141647	+	0.102913i	0.656352	−	0.754455i	$-0.272098\pi$
$233$	33.0039	+	23.9787i	0.141647	+	0.102913i	−0.514705	+	0.857367i	$0.672098\pi$
$234$		0			0
$235$	29.7776	−	283.315i	0.126713	−	1.20560i
$236$		0			0
$237$	206.233	−	43.8363i	0.870183	−	0.184963i
$238$		0			0
$239$	−25.9759	−	23.3888i	−0.108686	−	0.0978611i	0.612996	−	0.790086i	$-0.289964\pi$
$239$	−25.9759	−	23.3888i	−0.108686	−	0.0978611i	−0.721682	+	0.692225i	$0.756631\pi$
$240$		0			0
$241$	226.846	−	204.253i	0.941269	−	0.847522i	−0.0472095	−	0.998885i	$-0.515033\pi$
$241$	226.846	−	204.253i	0.941269	−	0.847522i	0.988478	+	0.151363i	$0.0483662\pi$
$242$		0			0
$243$	−1006.86	+	581.311i	−4.14346	+	2.39223i
$244$		0			0
$245$	101.744	−	45.2992i	0.415280	−	0.184895i
$246$		0			0
$247$		−	22.2963i		−	0.0902685i
$248$		0			0
$249$	−641.407			−2.57593
$250$		0			0
$251$	−106.632	−	239.500i	−0.424830	−	0.954185i	−0.991484	−	0.130229i	$-0.958429\pi$
$251$	−106.632	−	239.500i	−0.424830	−	0.954185i	0.566654	−	0.823956i	$-0.308238\pi$
$252$		0			0
$253$	9.71580	+	16.8283i	0.0384024	+	0.0665149i
$254$		0			0
$255$	836.475	+	929.000i	3.28030	+	3.64314i
$256$		0			0
$257$	67.8607	−	75.3670i	0.264050	−	0.293257i	−0.596511	−	0.802605i	$-0.703447\pi$
$257$	67.8607	−	75.3670i	0.264050	−	0.293257i	0.860561	+	0.509348i	$0.170113\pi$
$258$		0			0
$259$	−51.8605	−	243.984i	−0.200233	−	0.942025i
$260$		0			0
$261$	654.841	+	68.8266i	2.50897	+	0.263703i
$262$		0			0
$263$	−188.255	+	259.111i	−0.715798	+	0.985211i	0.283855	+	0.958867i	$0.408387\pi$
$263$	−188.255	+	259.111i	−0.715798	+	0.985211i	−0.999653	+	0.0263442i	$0.991613\pi$
$264$		0			0
$265$	44.8965	−	211.221i	0.169421	−	0.797061i
$266$		0			0
$267$	16.0981	+	153.164i	0.0602927	+	0.573647i
$268$		0			0
$269$	−125.490	+	281.854i	−0.466504	+	1.04779i	0.515148	+	0.857101i	$0.327737\pi$
$269$	−125.490	+	281.854i	−0.466504	+	1.04779i	−0.981652	+	0.190684i	$0.938930\pi$
$270$		0			0
$271$	−163.322	+	53.0666i	−0.602665	+	0.195818i	−0.594429	−	0.804148i	$-0.702622\pi$
$271$	−163.322	+	53.0666i	−0.602665	+	0.195818i	−0.00823627	+	0.999966i	$0.502622\pi$
$272$		0			0
$273$	−136.311	+	236.097i	−0.499306	+	0.864823i
$274$		0			0
$275$	19.8813	+	6.45981i	0.0722955	+	0.0234902i
$276$		0			0
$277$	−182.384	−	251.030i	−0.658425	−	0.906244i	0.341003	−	0.940062i	$-0.389233\pi$
$277$	−182.384	−	251.030i	−0.658425	−	0.906244i	−0.999428	+	0.0338181i	$0.989233\pi$
$278$		0			0
$279$	773.961	−	187.090i	2.77405	−	0.670573i
$280$		0			0
$281$	−48.6284	+	35.3306i	−0.173055	+	0.125732i	−0.670941	−	0.741511i	$-0.734110\pi$
$281$	−48.6284	+	35.3306i	−0.173055	+	0.125732i	0.497886	+	0.867242i	$0.334110\pi$
$282$		0			0
$283$	−132.554	+	407.960i	−0.468390	+	1.44156i	0.386279	+	0.922382i	$0.373760\pi$
$283$	−132.554	+	407.960i	−0.468390	+	1.44156i	−0.854669	+	0.519173i	$0.826240\pi$
$284$		0			0
$285$	−133.010	−	76.7935i	−0.466703	−	0.269451i
$286$		0			0
$287$	−49.7446	−	153.098i	−0.173326	−	0.533443i
$288$		0			0
$289$	−658.062	−	292.988i	−2.27703	−	1.01380i
$290$		0			0
$291$	855.786	−	89.9468i	2.94085	−	0.309095i
$292$		0			0
$293$	49.9483	+	10.6168i	0.170472	+	0.0362349i	0.292357	−	0.956309i	$-0.405561\pi$
$293$	49.9483	+	10.6168i	0.170472	+	0.0362349i	−0.121885	+	0.992544i	$0.538894\pi$
$294$		0			0
$295$	−173.677	−	126.184i	−0.588737	−	0.427742i
$296$		0			0
$297$	10.9346	−	104.036i	0.0368168	−	0.350288i
$298$		0			0
$299$	101.991	−	21.6789i	0.341108	−	0.0725047i
$300$		0			0
$301$	294.350	+	265.034i	0.977906	+	0.880510i
$302$		0			0
$303$	183.836	−	165.527i	0.606721	−	0.546294i
$304$		0			0
$305$	−296.718	+	171.310i	−0.972847	+	0.561674i
$306$		0			0
$307$	228.251	−	101.624i	0.743488	−	0.331022i	0.000205867	−	1.00000i	$-0.499934\pi$
$307$	228.251	−	101.624i	0.743488	−	0.331022i	0.743283	+	0.668978i	$0.233268\pi$
$308$		0			0
$309$		−	876.574i		−	2.83681i
$310$		0			0
$311$	−202.483			−0.651070			−0.325535	−	0.945530i	$-0.605544\pi$
$311$	−202.483			−0.651070			−0.325535	+	0.945530i	$0.605544\pi$
$312$		0			0
$313$	−121.534	−	272.970i	−0.388287	−	0.872108i	−0.996903	−	0.0786424i	$-0.974941\pi$
$313$	−121.534	−	272.970i	−0.388287	−	0.872108i	0.608616	−	0.793465i	$-0.291725\pi$
$314$		0			0
$315$	695.330	+	1204.35i	2.20740	+	3.82332i
$316$		0			0
$317$	−192.036	−	213.278i	−0.605793	−	0.672801i	0.359749	−	0.933049i	$-0.382862\pi$
$317$	−192.036	−	213.278i	−0.605793	−	0.672801i	−0.965542	+	0.260248i	$0.916196\pi$
$318$		0			0
$319$	−18.2598	+	20.2796i	−0.0572408	+	0.0635724i
$320$		0			0
$321$	117.904	+	554.697i	0.367303	+	1.72803i
$322$		0			0
$323$	123.328	+	12.9623i	0.381822	+	0.0401311i
$324$		0			0
$325$	65.9335	−	90.7496i	0.202872	−	0.279230i
$326$		0			0
$327$	73.9461	−	347.889i	0.226135	−	1.06388i
$328$		0			0
$329$	36.1179	+	343.639i	0.109781	+	1.04450i
$330$		0			0
$331$	62.8213	−	141.099i	0.189792	−	0.426281i	−0.793437	−	0.608652i	$-0.791711\pi$
$331$	62.8213	−	141.099i	0.189792	−	0.426281i	0.983230	+	0.182371i	$0.0583773\pi$
$332$		0			0
$333$	751.918	−	244.313i	2.25801	−	0.733672i
$334$		0			0
$335$	−117.414	+	203.366i	−0.350488	+	0.607064i
$336$		0			0
$337$	499.619	+	162.336i	1.48255	+	0.481709i	0.934873	−	0.354983i	$-0.115513\pi$
$337$	499.619	+	162.336i	1.48255	+	0.481709i	0.547675	+	0.836691i	$0.315513\pi$
$338$		0			0
$339$	−102.140	−	140.584i	−0.301298	−	0.414702i
$340$		0			0
$341$	−12.5810	+	30.5077i	−0.0368943	+	0.0894655i
$342$		0			0
$343$	211.958	−	153.997i	0.617954	−	0.448970i
$344$		0			0
$345$	221.954	−	683.103i	0.643344	−	1.98001i
$346$		0			0
$347$	−530.894	−	306.512i	−1.52995	−	0.883320i	−0.999363	−	0.0356919i	$-0.988637\pi$
$347$	−530.894	−	306.512i	−1.52995	−	0.883320i	−0.530591	−	0.847628i	$-0.678030\pi$
$348$		0			0
$349$	150.379	+	462.819i	0.430886	+	1.32613i	0.897245	+	0.441534i	$0.145566\pi$
$349$	150.379	+	462.819i	0.430886	+	1.32613i	−0.466359	+	0.884596i	$0.654434\pi$
$350$		0			0
$351$	−512.800	−	228.313i	−1.46097	−	0.650465i
$352$		0			0
$353$	269.571	−	28.3331i	0.763657	−	0.0802636i	0.285311	−	0.958435i	$-0.407903\pi$
$353$	269.571	−	28.3331i	0.763657	−	0.0802636i	0.478346	+	0.878171i	$0.341236\pi$
$354$		0			0
$355$	−330.617	−	70.2749i	−0.931316	−	0.197957i
$356$		0			0
$357$	−1226.68	−	891.238i	−3.43609	−	2.49647i
$358$		0			0
$359$	−12.8028	+	121.810i	−0.0356623	+	0.339304i	0.962114	+	0.272649i	$0.0878996\pi$
$359$	−12.8028	+	121.810i	−0.0356623	+	0.339304i	−0.997776	+	0.0666559i	$0.978767\pi$
$360$		0			0
$361$	338.209	−	71.8884i	0.936866	−	0.199137i
$362$		0			0
$363$	−524.622	−	472.372i	−1.44524	−	1.30130i
$364$		0			0
$365$	−242.196	+	218.074i	−0.663551	+	0.597464i
$366$		0			0
$367$	−180.039	+	103.945i	−0.490569	+	0.283230i	−0.724810	−	0.688948i	$-0.758073\pi$
$367$	−180.039	+	103.945i	−0.490569	+	0.283230i	0.234242	+	0.972178i	$0.424739\pi$
$368$		0			0
$369$	466.122	−	207.531i	1.26320	−	0.562415i
$370$		0			0
$371$			261.918i			0.705980i
$372$		0			0
$373$	646.609			1.73354			0.866768	−	0.498712i	$-0.166194\pi$
$373$	646.609			1.73354			0.866768	+	0.498712i	$0.166194\pi$
$374$		0			0
$375$	85.8243	+	192.765i	0.228865	+	0.514039i
$376$		0			0
$377$	73.2159	+	126.814i	0.194207	+	0.336376i
$378$		0			0
$379$	217.846	+	241.943i	0.574792	+	0.638372i	0.958503	−	0.285082i	$-0.0920207\pi$
$379$	217.846	+	241.943i	0.574792	+	0.638372i	−0.383711	+	0.923453i	$0.625354\pi$
$380$		0			0
$381$	687.425	−	763.463i	1.80427	−	2.00384i
$382$		0			0
$383$	33.2062	+	156.223i	0.0867002	+	0.407892i	1.00000		0.000603966i	$0.000192248\pi$
$383$	33.2062	+	156.223i	0.0867002	+	0.407892i	−0.913300	+	0.407288i	$0.866474\pi$
$384$		0			0
$385$	−57.3191	−	6.02448i	−0.148881	−	0.0156480i
$386$		0			0
$387$	−737.930	+	1015.67i	−1.90680	+	2.62448i
$388$		0			0
$389$	−56.9181	+	267.778i	−0.146319	+	0.688376i	0.842432	+	0.538803i	$0.181123\pi$
$389$	−56.9181	+	267.778i	−0.146319	+	0.688376i	−0.988751	+	0.149573i	$0.952210\pi$
$390$		0			0
$391$	60.6190	+	576.751i	0.155036	+	1.47507i
$392$		0			0
$393$	−263.706	+	592.292i	−0.671007	+	1.50711i
$394$		0			0
$395$	227.476	−	73.9116i	0.575890	−	0.187118i
$396$		0			0
$397$	91.2557	−	158.060i	0.229863	−	0.398135i	−0.727904	−	0.685679i	$-0.759505\pi$
$397$	91.2557	−	158.060i	0.229863	−	0.398135i	0.957767	+	0.287544i	$0.0928388\pi$
$398$		0			0
$399$	177.171	+	57.5665i	0.444039	+	0.144277i
$400$		0			0
$401$	238.684	+	328.521i	0.595223	+	0.819254i	0.995260	−	0.0972448i	$-0.0310030\pi$
$401$	238.684	+	328.521i	0.595223	+	0.819254i	−0.400038	+	0.916499i	$0.631003\pi$
$402$		0			0
$403$	134.830	+	114.793i	0.334567	+	0.284845i
$404$		0			0
$405$	−1878.71	+	1364.96i	−4.63879	+	3.37028i
$406$		0			0
$407$	−10.1254	+	31.1626i	−0.0248780	+	0.0765667i
$408$		0			0
$409$	−13.7075	−	7.91401i	−0.0335146	−	0.0193496i	0.483149	−	0.875538i	$-0.339493\pi$
$409$	−13.7075	−	7.91401i	−0.0335146	−	0.0193496i	−0.516664	+	0.856188i	$0.672826\pi$
$410$		0			0
$411$	−447.993	−	1378.78i	−1.09001	−	3.35470i
$412$		0			0
$413$	237.875	+	105.909i	0.575968	+	0.256438i
$414$		0			0
$415$	−723.641	+	76.0578i	−1.74371	+	0.183272i
$416$		0			0
$417$	−476.445	−	101.271i	−1.14255	−	0.242857i
$418$		0			0
$419$	−119.244	−	86.6359i	−0.284592	−	0.206768i	0.436326	−	0.899789i	$-0.356280\pi$
$419$	−119.244	−	86.6359i	−0.284592	−	0.206768i	−0.720918	+	0.693021i	$0.756280\pi$
$420$		0			0
$421$	−49.5670	+	471.599i	−0.117736	+	1.12019i	0.762940	+	0.646469i	$0.223755\pi$
$421$	−49.5670	+	471.599i	−0.117736	+	1.12019i	−0.880677	+	0.473718i	$0.842912\pi$
$422$		0			0
$423$	−1071.27	+	227.706i	−2.53255	+	0.538311i
$424$		0			0
$425$	463.635	+	417.459i	1.09091	+	0.982257i
$426$		0			0
$427$	308.831	−	278.072i	0.723257	−	0.651223i
$428$		0			0
$429$	31.0142	−	17.9060i	0.0722941	−	0.0417390i
$430$		0			0
$431$	288.652	−	128.516i	0.669726	−	0.298181i	−0.0435636	−	0.999051i	$-0.513871\pi$
$431$	288.652	−	128.516i	0.669726	−	0.298181i	0.713290	+	0.700869i	$0.247204\pi$
$432$		0			0
$433$		−	661.393i		−	1.52747i	−0.645532	−	0.763733i	$-0.723364\pi$
$433$		−	661.393i		−	1.52747i	0.645532	−	0.763733i	$-0.276636\pi$
$434$		0			0
$435$	1008.69			2.31882
$436$		0			0
$437$	−28.9801	−	65.0903i	−0.0663160	−	0.148948i
$438$		0			0
$439$	−73.2655	−	126.900i	−0.166892	−	0.289065i	0.770434	−	0.637520i	$-0.220040\pi$
$439$	−73.2655	−	126.900i	−0.166892	−	0.289065i	−0.937325	+	0.348455i	$0.886706\pi$
$440$		0			0
$441$	−286.502	−	318.193i	−0.649664	−	0.721525i
$442$		0			0
$443$	−453.732	+	503.921i	−1.02423	+	1.13752i	−0.0338064	+	0.999428i	$0.510763\pi$
$443$	−453.732	+	503.921i	−1.02423	+	1.13752i	−0.990420	+	0.138090i	$0.955904\pi$
$444$		0			0
$445$	36.3241	+	170.892i	0.0816273	+	0.384026i
$446$		0			0
$447$	−884.272	−	92.9408i	−1.97824	−	0.207921i
$448$		0			0
$449$	−395.976	+	545.014i	−0.881907	+	1.21384i	0.0939823	+	0.995574i	$0.470040\pi$
$449$	−395.976	+	545.014i	−0.881907	+	1.21384i	−0.975889	+	0.218267i	$0.929960\pi$
$450$		0			0
$451$	−4.39655	+	20.6842i	−0.00974846	+	0.0458629i
$452$		0			0
$453$	−124.841	−	1187.78i	−0.275587	−	2.62204i
$454$		0			0
$455$	−125.791	+	282.530i	−0.276463	+	0.620945i
$456$		0			0
$457$	199.256	−	64.7423i	0.436009	−	0.141668i	−0.0827843	−	0.996567i	$-0.526381\pi$
$457$	199.256	−	64.7423i	0.436009	−	0.141668i	0.518794	+	0.854899i	$0.326381\pi$
$458$		0			0
$459$	1561.00	−	2703.73i	3.40088	−	5.89049i
$460$		0			0
$461$	−479.579	−	155.825i	−1.04030	−	0.338014i	−0.261446	−	0.965218i	$-0.584199\pi$
$461$	−479.579	−	155.825i	−1.04030	−	0.338014i	−0.778855	+	0.627204i	$0.784199\pi$
$462$		0			0
$463$	391.203	+	538.445i	0.844932	+	1.16295i	0.984957	+	0.172801i	$0.0552817\pi$
$463$	391.203	+	538.445i	0.844932	+	1.16295i	−0.140025	+	0.990148i	$0.544718\pi$
$464$		0			0
$465$	1149.19	−	408.969i	2.47137	−	0.879504i
$466$		0			0
$467$	414.130	−	300.883i	0.886788	−	0.644289i	−0.0482506	−	0.998835i	$-0.515365\pi$
$467$	414.130	−	300.883i	0.886788	−	0.644289i	0.935039	+	0.354546i	$0.115365\pi$
$468$		0			0
$469$	88.0164	−	270.887i	0.187668	−	0.577583i
$470$		0			0
$471$	1075.02	+	620.663i	2.28242	+	1.31776i
$472$		0			0
$473$	−16.0784	−	49.4842i	−0.0339924	−	0.104618i
$474$		0			0
$475$	−70.0238	−	31.1766i	−0.147418	−	0.0656349i
$476$		0			0
$477$	−825.633	+	86.7775i	−1.73089	+	0.181924i
$478$		0			0
$479$	−811.025	−	172.389i	−1.69316	−	0.359893i	−0.742435	−	0.669918i	$-0.766329\pi$
$479$	−811.025	−	172.389i	−1.69316	−	0.359893i	−0.950728	+	0.310026i	$0.899662\pi$
$480$		0			0
$481$	142.244	+	103.347i	0.295726	+	0.214858i
$482$		0			0
$483$	−91.0641	+	866.417i	−0.188538	+	1.79382i
$484$		0			0
$485$	954.840	−	202.958i	1.96874	−	0.418469i
$486$		0			0
$487$	−8.09779	−	7.29128i	−0.0166279	−	0.0149718i	0.660775	−	0.750584i	$-0.270228\pi$
$487$	−8.09779	−	7.29128i	−0.0166279	−	0.0149718i	−0.677403	+	0.735612i	$0.736895\pi$
$488$		0			0
$489$	−354.247	+	318.966i	−0.724432	+	0.652282i
$490$		0			0
$491$	−319.409	+	184.411i	−0.650526	+	0.375582i	−0.788658	−	0.614832i	$-0.789224\pi$
$491$	−319.409	+	184.411i	−0.650526	+	0.375582i	0.138131	+	0.990414i	$0.455890\pi$
$492$		0			0
$493$	−744.014	+	331.256i	−1.50916	+	0.671920i
$494$		0			0
$495$		−	182.680i		−	0.369051i
$496$		0			0
$497$	409.972			0.824893
$498$		0			0
$499$	−89.8876	−	201.891i	−0.180135	−	0.404591i	0.800798	−	0.598934i	$-0.204409\pi$
$499$	−89.8876	−	201.891i	−0.180135	−	0.404591i	−0.980934	+	0.194344i	$0.937742\pi$
$500$		0			0
$501$	−197.000	−	341.214i	−0.393213	−	0.681065i
$502$		0			0
$503$	182.519	+	202.707i	0.362860	+	0.402997i	0.896736	−	0.442566i	$-0.145932\pi$
$503$	182.519	+	202.707i	0.362860	+	0.402997i	−0.533876	+	0.845563i	$0.679265\pi$
$504$		0			0
$505$	187.778	−	208.548i	0.371837	−	0.412967i
$506$		0			0
$507$	166.984	+	785.598i	0.329357	+	1.54950i
$508$		0			0
$509$	−23.2819	−	2.44702i	−0.0457404	−	0.00480751i	0.0816306	−	0.996663i	$-0.473987\pi$
$509$	−23.2819	−	2.44702i	−0.0457404	−	0.00480751i	−0.127371	+	0.991855i	$0.540654\pi$
$510$		0			0
$511$	232.351	−	319.804i	0.454699	−	0.625840i
$512$		0			0
$513$	−79.7489	+	375.189i	−0.155456	+	0.731363i
$514$		0			0
$515$	−103.944	−	988.959i	−0.201832	−	1.92031i
$516$		0			0
$517$	18.4617	−	41.4657i	0.0357093	−	0.0802044i
$518$		0			0
$519$	−494.815	+	160.775i	−0.953401	+	0.309779i
$520$		0			0
$521$	−69.9456	+	121.149i	−0.134253	+	0.232532i	−0.925312	−	0.379207i	$-0.876197\pi$
$521$	−69.9456	+	121.149i	−0.134253	+	0.232532i	0.791059	+	0.611740i	$0.209530\pi$
$522$		0			0
$523$	530.765	+	172.456i	1.01485	+	0.329744i	0.768783	−	0.639510i	$-0.220863\pi$
$523$	530.765	+	172.456i	1.01485	+	0.329744i	0.246064	+	0.969254i	$0.420863\pi$
$524$		0			0
$525$	550.884	+	758.227i	1.04930	+	1.44424i
$526$		0			0
$527$	−713.342	+	679.056i	−1.35359	+	1.28853i
$528$		0			0
$529$	−158.401	+	115.085i	−0.299436	+	0.217553i
$530$		0			0
$531$	−255.039	+	784.931i	−0.480300	+	1.47821i
$532$		0			0
$533$	98.2684	+	56.7353i	0.184368	+	0.106445i
$534$		0			0
$535$	198.797	+	611.833i	0.371582	+	1.14361i
$536$		0			0
$537$	1296.62	+	577.292i	2.41456	+	1.07503i
$538$		0			0
$539$	17.6480	−	1.85488i	0.0327421	−	0.00344133i
$540$		0			0
$541$	−810.014	−	172.174i	−1.49725	−	0.318251i	−0.614813	−	0.788673i	$-0.710768\pi$
$541$	−810.014	−	172.174i	−1.49725	−	0.318251i	−0.882442	+	0.470422i	$0.844102\pi$
$542$		0			0
$543$	−992.540	−	721.123i	−1.82788	−	1.32803i
$544$		0			0
$545$	42.1742	−	401.260i	0.0773838	−	0.736257i
$546$		0			0
$547$	532.745	−	113.239i	0.973940	−	0.207017i	0.306656	−	0.951820i	$-0.400790\pi$
$547$	532.745	−	113.239i	0.973940	−	0.207017i	0.667284	+	0.744803i	$0.267457\pi$
$548$		0			0
$549$	978.874	+	881.382i	1.78301	+	1.60543i
$550$		0			0
$551$	74.3596	−	66.9537i	0.134954	−	0.121513i
$552$		0			0
$553$	−251.243	+	145.055i	−0.454327	+	0.262306i
$554$		0			0
$555$	1106.44	−	492.620i	1.99359	−	0.887604i
$556$		0			0
$557$			553.181i			0.993143i	0.867996	+	0.496571i	$0.165408\pi$
$557$			553.181i			0.993143i	−0.867996	+	0.496571i	$0.834592\pi$
$558$		0			0
$559$	−279.197			−0.499457
$560$		0			0
$561$	81.0138	+	181.960i	0.144410	+	0.324349i
$562$		0			0
$563$	319.423	+	553.257i	0.567359	+	0.982695i	0.996826	+	0.0796122i	$0.0253682\pi$
$563$	319.423	+	553.257i	0.567359	+	0.982695i	−0.429467	+	0.903083i	$0.641298\pi$
$564$		0			0
$565$	−131.906	−	146.496i	−0.233462	−	0.259285i
$566$		0			0
$567$	1884.71	−	2093.19i	3.32401	−	3.69169i
$568$		0			0
$569$	−116.578	−	548.455i	−0.204882	−	0.963892i	−0.953617	−	0.301023i	$-0.902672\pi$
$569$	−116.578	−	548.455i	−0.204882	−	0.963892i	0.748735	−	0.662869i	$-0.230661\pi$
$570$		0			0
$571$	416.822	+	43.8098i	0.729986	+	0.0767246i	0.462227	−	0.886761i	$-0.347050\pi$
$571$	416.822	+	43.8098i	0.729986	+	0.0767246i	0.267759	+	0.963486i	$0.413717\pi$
$572$		0			0
$573$	−336.450	+	463.084i	−0.587173	+	0.808174i
$574$		0			0
$575$	74.5280	−	350.627i	0.129614	−	0.609785i
$576$		0			0
$577$	−28.8049	−	274.060i	−0.0499218	−	0.474974i	−0.990711	−	0.135983i	$-0.956581\pi$
$577$	−28.8049	−	274.060i	−0.0499218	−	0.474974i	0.940789	−	0.338992i	$-0.110086\pi$
$578$		0			0
$579$	−438.341	+	984.530i	−0.757066	+	1.70040i
$580$		0			0
$581$	839.360	−	272.725i	1.44468	−	0.469406i
$582$		0			0
$583$	17.2031	−	29.7966i	0.0295079	−	0.0511091i
$584$		0			0
$585$	−932.282	−	302.917i	−1.59364	−	0.517807i
$586$		0			0
$587$	−258.508	−	355.806i	−0.440389	−	0.606143i	0.529910	−	0.848054i	$-0.322226\pi$
$587$	−258.508	−	355.806i	−0.440389	−	0.606143i	−0.970298	+	0.241911i	$0.922226\pi$
$588$		0			0
$589$	57.5711	−	106.429i	0.0977438	−	0.180694i
$590$		0			0
$591$	481.178	−	349.596i	0.814176	−	0.591533i
$592$		0			0
$593$	212.675	−	654.547i	0.358643	−	1.10379i	−0.595224	−	0.803560i	$-0.702937\pi$
$593$	212.675	−	654.547i	0.358643	−	1.10379i	0.953867	−	0.300230i	$-0.0970634\pi$
$594$		0			0
$595$	−1489.64	−	860.043i	−2.50360	−	1.44545i
$596$		0			0
$597$	126.735	+	390.050i	0.212286	+	0.653350i
$598$		0			0
$599$	−74.4791	−	33.1602i	−0.124339	−	0.0553593i	0.343624	−	0.939107i	$-0.388345\pi$
$599$	−74.4791	−	33.1602i	−0.124339	−	0.0553593i	−0.467963	+	0.883748i	$0.655012\pi$
$600$		0			0
$601$	−462.129	+	48.5717i	−0.768934	+	0.0808182i	−0.480869	−	0.876793i	$-0.659679\pi$
$601$	−462.129	+	48.5717i	−0.768934	+	0.0808182i	−0.288065	+	0.957611i	$0.593012\pi$
$602$		0			0
$603$	883.064	+	187.701i	1.46445	+	0.311279i
$604$		0			0
$605$	−647.897	−	470.725i	−1.07090	−	0.778058i
$606$		0			0
$607$	−54.4691	+	518.239i	−0.0897350	+	0.853771i	0.853377	+	0.521295i	$0.174551\pi$
$607$	−54.4691	+	518.239i	−0.0897350	+	0.853771i	−0.943112	+	0.332476i	$0.892116\pi$
$608$		0			0
$609$	−1196.72	+	254.372i	−1.96506	+	0.417687i
$610$		0			0
$611$	−181.001	−	162.974i	−0.296238	−	0.266734i
$612$		0			0
$613$	715.677	−	644.398i	1.16750	−	1.05122i	0.169661	−	0.985503i	$-0.445733\pi$
$613$	715.677	−	644.398i	1.16750	−	1.05122i	0.997838	−	0.0657184i	$-0.0209339\pi$
$614$		0			0
$615$	676.917	−	390.818i	1.10068	−	0.635477i
$616$		0			0
$617$	1013.21	−	451.109i	1.64215	−	0.731134i	0.642763	−	0.766065i	$-0.277788\pi$
$617$	1013.21	−	451.109i	1.64215	−	0.731134i	0.999390	+	0.0349311i	$0.0111212\pi$
$618$		0			0
$619$		−	382.118i		−	0.617315i	−0.951173	−	0.308657i	$-0.900120\pi$
$619$		−	382.118i		−	0.617315i	0.951173	−	0.308657i	$-0.0998797\pi$
$620$		0			0
$621$	−1793.79			−2.88855
$622$		0			0
$623$	−86.1912	−	193.589i	−0.138349	−	0.310736i
$624$		0			0
$625$	365.154	+	632.464i	0.584246	+	1.01194i
$626$		0			0
$627$	−16.3745	−	18.1858i	−0.0261157	−	0.0290044i
$628$		0			0
$629$	−654.341	+	726.720i	−1.04029	+	1.15536i
$630$		0			0
$631$	−243.447	−	1145.33i	−0.385812	−	1.81510i	−0.557767	−	0.829998i	$-0.688342\pi$
$631$	−243.447	−	1145.33i	−0.385812	−	1.81510i	0.171955	−	0.985105i	$-0.444992\pi$
$632$		0			0
$633$	308.184	+	32.3915i	0.486863	+	0.0511714i
$634$		0			0
$635$	685.029	−	942.861i	1.07879	−	1.48482i
$636$		0			0
$637$	19.7974	−	93.1396i	0.0310792	−	0.146216i
$638$		0			0
$639$	135.830	+	1292.33i	0.212566	+	2.02243i
$640$		0			0
$641$	−251.324	+	564.483i	−0.392081	+	0.880628i	0.604390	+	0.796689i	$0.293417\pi$
$641$	−251.324	+	564.483i	−0.392081	+	0.880628i	−0.996471	+	0.0839395i	$0.973250\pi$
$642$		0			0
$643$	222.693	−	72.3573i	0.346334	−	0.112531i	−0.130684	−	0.991424i	$-0.541717\pi$
$643$	222.693	−	72.3573i	0.346334	−	0.112531i	0.477019	+	0.878893i	$0.341717\pi$
$644$		0			0
$645$	−961.615	+	1665.57i	−1.49088	+	2.58227i
$646$		0			0
$647$	516.265	+	167.745i	0.797936	+	0.259265i	0.679480	−	0.733694i	$-0.262206\pi$
$647$	516.265	+	167.745i	0.797936	+	0.259265i	0.118456	+	0.992959i	$0.462206\pi$
$648$		0			0
$649$	−20.1052	−	27.6724i	−0.0309787	−	0.0426385i
$650$		0			0
$651$	−1260.28	+	775.011i	−1.93592	+	1.19049i
$652$		0			0
$653$	723.602	−	525.728i	1.10812	−	0.805096i	0.125753	−	0.992062i	$-0.459865\pi$
$653$	723.602	−	525.728i	1.10812	−	0.805096i	0.982366	+	0.186965i	$0.0598653\pi$
$654$		0			0
$655$	−227.281	+	699.500i	−0.346994	+	1.06794i
$656$		0			0
$657$	1085.08	+	626.474i	1.65157	+	0.953537i
$658$		0			0
$659$	34.1774	+	105.187i	0.0518626	+	0.159617i	0.973633	−	0.228119i	$-0.0732575\pi$
$659$	34.1774	+	105.187i	0.0518626	+	0.159617i	−0.921771	+	0.387735i	$0.873257\pi$
$660$		0			0
$661$	−400.536	−	178.330i	−0.605955	−	0.269788i	0.0807390	−	0.996735i	$-0.474272\pi$
$661$	−400.536	−	178.330i	−0.605955	−	0.269788i	−0.686694	+	0.726947i	$0.740939\pi$
$662$		0			0
$663$	1062.94	−	111.720i	1.60323	−	0.168506i
$664$		0			0
$665$	206.713	+	43.9381i	0.310846	+	0.0660724i
$666$		0			0
$667$	378.570	+	275.047i	0.567571	+	0.412365i
$668$		0			0
$669$	108.499	−	1032.30i	0.162181	−	1.54305i
$670$		0			0
$671$	−53.3976	+	11.3500i	−0.0795791	+	0.0169151i
$672$		0			0
$673$	20.1543	+	18.1470i	0.0299470	+	0.0269644i	0.683968	−	0.729512i	$-0.260253\pi$
$673$	20.1543	+	18.1470i	0.0299470	+	0.0269644i	−0.654021	+	0.756476i	$0.726919\pi$
$674$		0			0
$675$	−1434.08	+	1291.25i	−2.12456	+	1.91296i
$676$		0			0
$677$	−625.154	+	360.933i	−0.923418	+	0.533136i	−0.884724	−	0.466115i	$-0.845653\pi$
$677$	−625.154	+	360.933i	−0.923418	+	0.533136i	−0.0386944	+	0.999251i	$0.512320\pi$
$678$		0			0
$679$	−1081.66	+	481.585i	−1.59301	+	0.709256i
$680$		0			0
$681$		−	962.242i		−	1.41298i
$682$		0			0
$683$	−998.271			−1.46160			−0.730798	−	0.682593i	$-0.760852\pi$
$683$	−998.271			−1.46160			−0.730798	+	0.682593i	$0.760852\pi$
$684$		0			0
$685$	−668.925	−	1502.43i	−0.976534	−	2.19333i
$686$		0			0
$687$	−160.824	−	278.556i	−0.234097	−	0.405467i
$688$		0			0
$689$	−123.537	−	137.202i	−0.179299	−	0.199132i
$690$		0			0
$691$	−298.173	+	331.155i	−0.431509	+	0.479240i	−0.919208	−	0.393772i	$-0.871170\pi$
$691$	−298.173	+	331.155i	−0.431509	+	0.479240i	0.487699	+	0.873012i	$0.337836\pi$
$692$		0			0
$693$	46.0684	+	216.735i	0.0664768	+	0.312749i
$694$		0			0
$695$	−549.538	−	57.7588i	−0.790702	−	0.0831061i
$696$		0			0
$697$	−370.952	+	510.572i	−0.532212	+	0.732527i
$698$		0			0
$699$	49.9529	−	235.010i	0.0714633	−	0.336208i
$700$		0			0
$701$	11.7611	+	111.899i	0.0167775	+	0.159628i	0.999703	−	0.0243775i	$-0.00776037\pi$
$701$	11.7611	+	111.899i	0.0167775	+	0.159628i	−0.982925	+	0.184005i	$0.941094\pi$
$702$		0			0
$703$	48.8674	−	109.758i	0.0695126	−	0.156128i
$704$		0			0
$705$	−1595.64	+	518.456i	−2.26332	+	0.735399i
$706$		0			0
$707$	−170.191	+	294.779i	−0.240722	+	0.416944i
$708$		0			0
$709$	295.801	+	96.1117i	0.417209	+	0.135559i	0.510097	−	0.860117i	$-0.329610\pi$
$709$	295.801	+	96.1117i	0.417209	+	0.135559i	−0.0928874	+	0.995677i	$0.529610\pi$
$710$		0			0
$711$	−540.490	−	743.921i	−0.760184	−	1.04630i
$712$		0			0
$713$	542.819	+	159.869i	0.761316	+	0.224220i
$714$		0			0
$715$	32.8672	−	23.8794i	0.0459681	−	0.0333978i
$716$		0			0
$717$	−63.6141	+	195.784i	−0.0887227	+	0.273060i
$718$		0			0
$719$	279.673	+	161.469i	0.388974	+	0.224574i	0.681716	−	0.731617i	$-0.261234\pi$
$719$	279.673	+	161.469i	0.388974	+	0.224574i	−0.292741	+	0.956192i	$0.594567\pi$
$720$		0			0
$721$	372.717	+	1147.10i	0.516944	+	1.59099i
$722$		0			0
$723$	−1642.33	−	731.215i	−2.27156	−	1.01136i
$724$		0			0
$725$	500.647	−	52.6201i	0.690548	−	0.0725795i
$726$		0			0
$727$	1169.29	+	248.540i	1.60838	+	0.341871i	0.922546	−	0.385888i	$-0.126105\pi$
$727$	1169.29	+	248.540i	1.60838	+	0.341871i	0.685832	+	0.727759i	$0.259438\pi$
$728$		0			0
$729$	3008.73	+	2185.97i	4.12721	+	2.99859i
$730$		0			0
$731$	162.316	−	1544.33i	0.222046	−	2.11263i
$732$		0			0
$733$	764.803	−	162.564i	1.04339	−	0.221779i	0.345822	−	0.938300i	$-0.387600\pi$
$733$	764.803	−	162.564i	1.04339	−	0.221779i	0.697565	+	0.716521i	$0.254267\pi$
$734$		0			0
$735$	−487.444	−	438.897i	−0.663190	−	0.597139i
$736$		0			0
$737$	−27.8051	+	25.0359i	−0.0377275	+	0.0339700i
$738$		0			0
$739$	−283.629	+	163.753i	−0.383801	+	0.221588i	−0.679471	−	0.733703i	$-0.737791\pi$
$739$	−283.629	+	163.753i	−0.383801	+	0.221588i	0.295670	+	0.955290i	$0.404457\pi$
$740$		0			0
$741$	−119.960	+	53.4098i	−0.161890	+	0.0720780i
$742$		0			0
$743$		−	5.81914i		−	0.00783195i	−0.999992	−	0.00391598i	$-0.998754\pi$
$743$		−	5.81914i		−	0.00783195i	0.999992	−	0.00391598i	$-0.00124650\pi$
$744$		0			0
$745$	−1008.67			−1.35391
$746$		0			0
$747$	1137.79	+	2555.52i	1.52314	+	3.42104i
$748$		0			0
$749$	−390.148	−	675.756i	−0.520892	−	0.902211i
$750$		0			0
$751$	603.107	+	669.818i	0.803072	+	0.891902i	0.996004	−	0.0893106i	$-0.0284664\pi$
$751$	603.107	+	669.818i	0.803072	+	0.891902i	−0.192932	+	0.981212i	$0.561800\pi$
$752$		0			0
$753$	−1033.15	+	1147.42i	−1.37204	+	1.52380i
$754$		0			0
$755$	−281.694	−	1325.26i	−0.373104	−	1.75532i
$756$		0			0
$757$	−201.631	−	21.1922i	−0.266355	−	0.0279950i	−0.0295905	−	0.999562i	$-0.509420\pi$
$757$	−201.631	−	21.1922i	−0.266355	−	0.0279950i	−0.236765	+	0.971567i	$0.576087\pi$
$758$		0			0
$759$	67.2669	−	92.5850i	0.0886257	−	0.121983i
$760$		0			0
$761$	292.345	−	1375.38i	0.384159	−	1.80733i	−0.182305	−	0.983242i	$-0.558356\pi$
$761$	292.345	−	1375.38i	0.384159	−	1.80733i	0.566465	−	0.824086i	$-0.308311\pi$
$762$		0			0
$763$	51.1540	+	486.697i	0.0670432	+	0.637873i
$764$		0			0
$765$	2217.53	−	4980.66i	2.89874	−	6.51067i
$766$		0			0
$767$	−174.560	+	56.7180i	−0.227588	+	0.0739478i
$768$		0			0
$769$	−170.080	+	294.587i	−0.221170	+	0.383079i	−0.955164	−	0.296078i	$-0.904321\pi$
$769$	−170.080	+	294.587i	−0.221170	+	0.383079i	0.733993	+	0.679157i	$0.237654\pi$
$770$		0			0
$771$	−568.052	−	184.571i	−0.736774	−	0.239392i
$772$		0			0
$773$	34.7185	+	47.7859i	0.0449140	+	0.0618188i	0.830883	−	0.556447i	$-0.187836\pi$
$773$	34.7185	+	47.7859i	0.0449140	+	0.0618188i	−0.785969	+	0.618266i	$0.787836\pi$
$774$		0			0
$775$	549.048	−	262.935i	0.708449	−	0.339272i
$776$		0			0
$777$	−1188.47	+	863.477i	−1.52957	+	1.11130i
$778$		0			0
$779$	23.9604	−	73.7425i	0.0307579	−	0.0946630i
$780$		0			0
$781$	−46.6396	−	26.9274i	−0.0597178	−	0.0344781i
$782$		0			0
$783$	−778.449	−	2395.82i	−0.994188	−	3.05980i
$784$		0			0
$785$	1286.45	+	572.763i	1.63878	+	0.729634i
$786$		0			0
$787$	−1411.89	+	148.396i	−1.79402	+	0.188559i	−0.942148	−	0.335197i	$-0.891197\pi$
$787$	−1411.89	+	148.396i	−1.79402	+	0.188559i	−0.851868	+	0.523756i	$0.824530\pi$
$788$		0			0
$789$	1845.04	+	392.176i	2.33846	+	0.497054i
$790$		0			0
$791$	193.439	+	140.542i	0.244550	+	0.177676i
$792$		0			0
$793$	−30.6197	+	291.327i	−0.0386125	+	0.367374i
$794$		0			0
$795$	−1243.98	+	264.415i	−1.56475	+	0.332598i
$796$		0			0
$797$	−785.355	−	707.137i	−0.985389	−	0.887248i	0.00823831	−	0.999966i	$-0.497378\pi$
$797$	−785.355	−	707.137i	−0.985389	−	0.887248i	−0.993627	+	0.112718i	$0.964044\pi$
$798$		0			0
$799$	1006.69	−	906.431i	1.25994	−	1.13446i
$800$		0			0
$801$	581.683	−	335.835i	0.726196	−	0.419270i
$802$		0			0
$803$	−47.4381	+	21.1208i	−0.0590760	+	0.0263023i
$804$		0			0
$805$			988.298i			1.22770i
$806$		0			0
$807$	1817.06			2.25162
$808$		0			0
$809$	−48.2307	−	108.328i	−0.0596177	−	0.133904i	0.881280	−	0.472595i	$-0.156683\pi$
$809$	−48.2307	−	108.328i	−0.0596177	−	0.133904i	−0.940898	+	0.338691i	$0.890016\pi$
$810$		0			0
$811$	−47.8717	−	82.9163i	−0.0590280	−	0.102240i	0.835001	−	0.550248i	$-0.185467\pi$
$811$	−47.8717	−	82.9163i	−0.0590280	−	0.102240i	−0.894029	+	0.448008i	$0.852133\pi$
$812$		0			0
$813$	676.743	+	751.600i	0.832403	+	0.924477i
$814$		0			0
$815$	−361.842	+	401.867i	−0.443978	+	0.493088i
$816$		0			0
$817$	39.6659	+	186.613i	0.0485506	+	0.228413i
$818$		0			0
$819$	1182.47	+	124.282i	1.44379	+	0.151749i
$820$		0			0
$821$	−592.233	+	815.138i	−0.721355	+	0.992860i	0.278123	+	0.960546i	$0.410288\pi$
$821$	−592.233	+	815.138i	−0.721355	+	0.992860i	−0.999478	+	0.0323146i	$0.989712\pi$
$822$		0			0
$823$	43.9914	−	206.963i	0.0534525	−	0.251474i	−0.943306	−	0.331924i	$-0.892302\pi$
$823$	43.9914	−	206.963i	0.0534525	−	0.251474i	0.996759	+	0.0804497i	$0.0256356\pi$
$824$		0			0
$825$	−12.8690	−	122.441i	−0.0155988	−	0.148413i
$826$		0			0
$827$	430.482	−	966.878i	0.520534	−	1.16914i	−0.441761	−	0.897133i	$-0.645646\pi$
$827$	430.482	−	966.878i	0.520534	−	1.16914i	0.962295	−	0.272006i	$-0.0876872\pi$
$828$		0			0
$829$	−386.332	+	125.527i	−0.466022	+	0.151420i	−0.532610	−	0.846361i	$-0.678789\pi$
$829$	−386.332	+	125.527i	−0.466022	+	0.151420i	0.0665880	+	0.997781i	$0.478789\pi$
$830$		0			0
$831$	−913.717	+	1582.60i	−1.09954	+	1.90446i
$832$		0			0
$833$	503.677	+	163.655i	0.604655	+	0.196464i
$834$		0			0
$835$	−262.718	−	361.600i	−0.314632	−	0.433054i
$836$		0			0
$837$	−1858.26	−	2413.92i	−2.22014	−	2.88401i
$838$		0			0
$839$	414.598	−	301.223i	0.494158	−	0.359027i	−0.312623	−	0.949877i	$-0.601208\pi$
$839$	414.598	−	301.223i	0.494158	−	0.359027i	0.806781	+	0.590851i	$0.201208\pi$
$840$		0			0
$841$	56.8123	−	174.850i	0.0675533	−	0.207908i
$842$		0			0
$843$	306.575	+	177.001i	0.363672	+	0.209966i
$844$		0			0
$845$	281.549	+	866.518i	0.333194	+	1.02547i
$846$		0			0
$847$	887.384	+	395.089i	1.04768	+	0.466457i
$848$		0			0
$849$	2512.47	−	264.071i	2.95932	−	0.311037i
$850$		0			0
$851$	549.585	+	116.818i	0.645811	+	0.137271i
$852$		0			0
$853$	−57.0025	−	41.4147i	−0.0668259	−	0.0485518i	0.553871	−	0.832603i	$-0.313150\pi$
$853$	−57.0025	−	41.4147i	−0.0668259	−	0.0485518i	−0.620697	+	0.784051i	$0.713150\pi$
$854$		0			0
$855$	−70.0171	+	666.168i	−0.0818913	+	0.779144i
$856$		0			0
$857$	1041.37	−	221.350i	1.21513	−	0.258284i	0.444625	−	0.895717i	$-0.353337\pi$
$857$	1041.37	−	221.350i	1.21513	−	0.258284i	0.770506	+	0.637433i	$0.220004\pi$
$858$		0			0
$859$	267.521	+	240.877i	0.311433	+	0.280415i	0.809993	−	0.586440i	$-0.199471\pi$
$859$	267.521	+	240.877i	0.311433	+	0.280415i	−0.498560	+	0.866855i	$0.666138\pi$
$860$		0			0
$861$	−704.549	+	634.379i	−0.818291	+	0.736793i
$862$		0			0
$863$	1380.05	−	796.771i	1.59913	−	0.923257i	0.607472	−	0.794341i	$-0.292183\pi$
$863$	1380.05	−	796.771i	1.59913	−	0.923257i	0.991655	−	0.128916i	$-0.0411498\pi$
$864$		0			0
$865$	−539.190	+	240.063i	−0.623341	+	0.277529i
$866$		0			0
$867$			4242.39i			4.89318i
$868$		0			0
$869$	38.1095			0.0438544
$870$		0			0
$871$	81.6610	+	183.414i	0.0937554	+	0.210578i
$872$		0			0
$873$	−1876.44	−	3250.10i	−2.14942	−	3.72291i
$874$		0			0
$875$	−194.275	−	215.764i	−0.222028	−	0.246587i
$876$		0			0
$877$	−748.765	+	831.588i	−0.853780	+	0.948219i	−0.999153	−	0.0411582i	$-0.986895\pi$
$877$	−748.765	+	831.588i	−0.853780	+	0.948219i	0.145373	+	0.989377i	$0.453562\pi$
$878$		0			0
$879$	−62.5273	−	294.168i	−0.0711346	−	0.334662i
$880$		0			0
$881$	277.688	+	29.1862i	0.315196	+	0.0331285i	0.260806	−	0.965391i	$-0.416012\pi$
$881$	277.688	+	29.1862i	0.315196	+	0.0331285i	0.0543904	+	0.998520i	$0.482678\pi$
$882$		0			0
$883$	405.255	−	557.785i	0.458952	−	0.631694i	−0.515339	−	0.856986i	$-0.672334\pi$
$883$	405.255	−	557.785i	0.458952	−	0.631694i	0.974291	+	0.225293i	$0.0723339\pi$
$884$		0			0
$885$	−262.869	+	1236.70i	−0.297027	+	1.39740i
$886$		0			0
$887$	36.1527	+	343.970i	0.0407584	+	0.387791i	0.995817	+	0.0913726i	$0.0291254\pi$
$887$	36.1527	+	343.970i	0.0407584	+	0.387791i	−0.955058	+	0.296418i	$0.904208\pi$
$888$		0			0
$889$	−574.958	+	1291.38i	−0.646747	+	1.45262i
$890$		0			0
$891$	−351.894	+	114.337i	−0.394942	+	0.128325i
$892$		0			0
$893$	−83.2159	+	144.134i	−0.0931869	+	0.161404i
$894$		0			0
$895$	1531.31	+	497.553i	1.71096	+	0.555926i
$896$		0			0
$897$	−360.954	−	496.810i	−0.402401	−	0.553857i
$898$		0			0
$899$	22.0425	+	794.378i	0.0245189	+	0.883624i
$900$		0			0
$901$	830.730	−	603.560i	0.922008	−	0.669878i
$902$		0			0
$903$	720.853	−	2218.56i	0.798287	−	2.45687i
$904$		0			0
$905$	−1205.30	−	695.882i	−1.33183	−	0.768931i
$906$		0			0
$907$	208.638	+	642.121i	0.230031	+	0.707962i	0.997742	+	0.0671658i	$0.0213956\pi$
$907$	208.638	+	642.121i	0.230031	+	0.707962i	−0.767711	+	0.640796i	$0.778604\pi$
$908$		0			0
$909$	−985.605	−	438.819i	−1.08427	−	0.482750i
$910$		0			0
$911$	−322.684	+	33.9154i	−0.354208	+	0.0372288i	−0.279962	−	0.960011i	$-0.590322\pi$
$911$	−322.684	+	33.9154i	−0.354208	+	0.0372288i	−0.0742464	+	0.997240i	$0.523655\pi$
$912$		0			0
$913$	−113.401	−	24.1041i	−0.124207	−	0.0264010i
$914$		0			0
$915$	1632.47	+	1186.06i	1.78412	+	1.29624i
$916$		0			0
$917$	93.2500	−	887.214i	0.101690	−	0.967518i
$918$		0			0
$919$	−1347.53	+	286.426i	−1.46630	+	0.311672i	−0.870782	−	0.491669i	$-0.836387\pi$
$919$	−1347.53	+	286.426i	−1.46630	+	0.311672i	−0.595519	+	0.803341i	$0.703054\pi$
$920$		0			0
$921$	−1093.53	−	984.618i	−1.18733	−	1.06907i
$922$		0			0
$923$	−214.757	+	193.368i	−0.232673	+	0.209500i
$924$		0			0
$925$	523.468	−	302.225i	0.565912	−	0.326729i
$926$		0			0
$927$	−3492.48	+	1554.95i	−3.76750	+	1.67740i
$928$		0			0
$929$		−	921.369i		−	0.991785i	−0.868384	−	0.495893i	$-0.834841\pi$
$929$		−	921.369i		−	0.991785i	0.868384	−	0.495893i	$-0.165159\pi$
$930$		0			0
$931$	−65.0666			−0.0698890
$932$		0			0
$933$	485.038	+	1089.41i	0.519870	+	1.16765i
$934$		0			0
$935$	112.977	+	195.682i	0.120831	+	0.209286i
$936$		0			0
$937$	−718.811	−	798.321i	−0.767141	−	0.851996i	0.225355	−	0.974277i	$-0.427646\pi$
$937$	−718.811	−	798.321i	−0.767141	−	0.851996i	−0.992496	+	0.122280i	$0.960979\pi$
$938$		0			0
$939$	−1177.52	+	1307.77i	−1.25402	+	1.39273i
$940$		0			0
$941$	20.3862	+	95.9096i	0.0216644	+	0.101923i	0.987651	−	0.156668i	$-0.0500752\pi$
$941$	20.3862	+	95.9096i	0.0216644	+	0.101923i	−0.965987	+	0.258591i	$0.916742\pi$
$942$		0			0
$943$	360.621	+	37.9028i	0.382419	+	0.0401938i
$944$		0			0
$945$	3127.27	−	4304.32i	3.30928	−	4.55484i
$946$		0			0
$947$	8.69995	−	40.9300i	0.00918685	−	0.0432207i	−0.973315	−	0.229471i	$-0.926300\pi$
$947$	8.69995	−	40.9300i	0.00918685	−	0.0432207i	0.982502	+	0.186251i	$0.0596336\pi$
$948$		0			0
$949$	29.1260	+	277.115i	0.0306913	+	0.292008i
$950$		0			0
$951$	−687.480	+	1544.11i	−0.722902	+	1.62367i
$952$		0			0
$953$	33.6146	−	10.9221i	0.0352724	−	0.0114607i	−0.291328	−	0.956623i	$-0.594097\pi$
$953$	33.6146	−	10.9221i	0.0352724	−	0.0114607i	0.326600	+	0.945163i	$0.394097\pi$
$954$		0			0
$955$	−324.674	+	562.352i	−0.339973	+	0.588850i
$956$		0			0
$957$	152.850	+	49.6641i	0.159718	+	0.0518956i
$958$		0			0
$959$	1172.51	+	1613.82i	1.22264	+	1.68282i
$960$		0			0
$961$	347.191	+	896.091i	0.361281	+	0.932457i
$962$		0			0
$963$	2000.89	−	1453.73i	2.07777	−	1.50959i
$964$		0			0
$965$	−377.795	+	1162.73i	−0.391498	+	1.20491i
$966$		0			0
$967$	−1416.30	−	817.703i	−1.46464	−	0.845608i	−0.465415	−	0.885092i	$-0.654095\pi$
$967$	−1416.30	−	817.703i	−1.46464	−	0.845608i	−0.999220	+	0.0394846i	$0.987428\pi$
$968$		0			0
$969$	−225.687	−	694.592i	−0.232907	−	0.716813i
$970$		0			0
$971$	759.770	+	338.271i	0.782462	+	0.348374i	0.758782	−	0.651345i	$-0.225795\pi$
$971$	759.770	+	338.271i	0.782462	+	0.348374i	0.0236801	+	0.999720i	$0.492462\pi$
$972$		0			0
$973$	666.547	−	70.0569i	0.685043	−	0.0720009i
$974$		0			0
$975$	−646.198	−	137.354i	−0.662768	−	0.140876i
$976$		0			0
$977$	−1417.62	−	1029.96i	−1.45100	−	1.05421i	−0.985597	−	0.169111i	$-0.945910\pi$
$977$	−1417.62	−	1029.96i	−1.45100	−	1.05421i	−0.465400	−	0.885100i	$-0.654090\pi$
$978$		0			0
$979$	−2.90974	+	27.6843i	−0.00297216	+	0.0282782i
$980$		0			0
$981$	−1517.24	+	322.500i	−1.54663	+	0.328746i
$982$		0			0
$983$	792.363	+	713.446i	0.806066	+	0.725785i	0.965212	−	0.261470i	$-0.0842074\pi$
$983$	792.363	+	713.446i	0.806066	+	0.725785i	−0.159146	+	0.987255i	$0.550874\pi$
$984$		0			0
$985$	501.414	−	451.476i	0.509050	−	0.458351i
$986$		0			0
$987$	1762.35	−	1017.50i	1.78557	−	1.03090i
$988$		0			0
$989$	−815.067	+	362.891i	−0.824133	+	0.366927i
$990$		0			0
$991$		−	1060.14i		−	1.06977i	−0.844925	−	0.534884i	$-0.820355\pi$
$991$		−	1060.14i		−	1.06977i	0.844925	−	0.534884i	$-0.179645\pi$
$992$		0			0
$993$	−909.636			−0.916048
$994$		0			0
$995$	189.236	+	425.030i	0.190186	+	0.427166i
$996$		0			0
$997$	248.657	+	430.686i	0.249405	+	0.431982i	0.963361	−	0.268209i	$-0.0864316\pi$
$997$	248.657	+	430.686i	0.249405	+	0.431982i	−0.713956	+	0.700191i	$0.753098\pi$
$998$		0			0
$999$	−2023.96	−	2247.83i	−2.02598	−	2.25008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.o.a.13.1	✓	40
31.12	odd	30	inner	124.3.o.a.105.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.o.a.13.1	✓	40	1.1	even	1	trivial
124.3.o.a.105.1	yes	40	31.12	odd	30	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.o (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.39545 - 5.38028i) q^{3} +(-3.34056 - 5.78602i) q^{5} +(5.42242 + 6.02221i) q^{7} +(-17.1870 + 19.0881i) q^{9} +O(q^{10})\)	\(q+(-2.39545 - 5.38028i) q^{3} +(-3.34056 - 5.78602i) q^{5} +(5.42242 + 6.02221i) q^{7} +(-17.1870 + 19.0881i) q^{9} +(-0.221326 - 1.04126i) q^{11} +(-5.68090 - 0.597086i) q^{13} +(-23.1282 + 31.8333i) q^{15} +(6.60537 - 31.0758i) q^{17} +(0.408005 + 3.88191i) q^{19} +(19.4120 - 43.6001i) q^{21} +(-17.3605 + 5.64077i) q^{23} +(-9.81871 + 17.0065i) q^{25} +(93.4591 + 30.3667i) q^{27} +(-15.0679 - 20.7391i) q^{29} +(-25.5753 - 17.5187i) q^{31} +(-5.07207 + 3.68507i) q^{33} +(16.7307 - 51.4918i) q^{35} +(-26.6567 - 15.3902i) q^{37} +(10.3958 + 31.9951i) q^{39} +(-18.1473 - 8.07968i) q^{41} +(48.6096 - 5.10907i) q^{43} +(167.858 + 35.6794i) q^{45} +(34.4956 + 25.0625i) q^{47} +(-1.74246 + 16.5784i) q^{49} +(-183.019 + 38.9020i) q^{51} +(24.0191 + 21.6269i) q^{53} +(-5.28538 + 4.75897i) q^{55} +(19.9084 - 11.4941i) q^{57} +(29.3539 - 13.0692i) q^{59} -51.2819i q^{61} -208.148 q^{63} +(15.5226 + 34.8644i) q^{65} +(-17.5739 - 30.4389i) q^{67} +(71.9351 + 79.8920i) q^{69} +(33.8518 - 37.5963i) q^{71} +(-10.1420 - 47.7143i) q^{73} +(115.020 + 12.0891i) q^{75} +(5.07054 - 6.97900i) q^{77} +(-7.44319 + 35.0175i) q^{79} +(-36.3318 - 345.674i) q^{81} +(44.2968 - 99.4923i) q^{83} +(-201.871 + 65.5919i) q^{85} +(-75.4879 + 130.749i) q^{87} +(-24.8699 - 8.08071i) q^{89} +(-27.2084 - 37.4492i) q^{91} +(-32.9910 + 179.567i) q^{93} +(21.0978 - 15.3285i) q^{95} +(-45.1501 + 138.958i) q^{97} +(23.6795 + 13.6714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9} + 2 q^{11} - 18 q^{13} + 35 q^{15} + 25 q^{17} - 11 q^{19} + 54 q^{21} + 25 q^{23} - 75 q^{25} + 225 q^{27} + 20 q^{29} + 59 q^{31} - 303 q^{33} - 66 q^{35} - 222 q^{37} - 169 q^{39} + q^{41} + 122 q^{43} + 54 q^{45} - 120 q^{47} - 118 q^{49} - 515 q^{51} + 61 q^{53} - 121 q^{55} - 201 q^{57} - 257 q^{59} - 158 q^{63} + 182 q^{65} - q^{67} + 510 q^{69} + 459 q^{71} + 253 q^{73} + 651 q^{75} + 670 q^{77} + 385 q^{79} + 974 q^{81} + 375 q^{83} - 370 q^{85} - 344 q^{87} + 245 q^{89} + 960 q^{91} - 212 q^{93} - 851 q^{95} - 797 q^{97} - 21 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 - 3 * q^5 + 19 * q^7 - 2 * q^9 + 2 * q^11 - 18 * q^13 + 35 * q^15 + 25 * q^17 - 11 * q^19 + 54 * q^21 + 25 * q^23 - 75 * q^25 + 225 * q^27 + 20 * q^29 + 59 * q^31 - 303 * q^33 - 66 * q^35 - 222 * q^37 - 169 * q^39 + q^41 + 122 * q^43 + 54 * q^45 - 120 * q^47 - 118 * q^49 - 515 * q^51 + 61 * q^53 - 121 * q^55 - 201 * q^57 - 257 * q^59 - 158 * q^63 + 182 * q^65 - q^67 + 510 * q^69 + 459 * q^71 + 253 * q^73 + 651 * q^75 + 670 * q^77 + 385 * q^79 + 974 * q^81 + 375 * q^83 - 370 * q^85 - 344 * q^87 + 245 * q^89 + 960 * q^91 - 212 * q^93 - 851 * q^95 - 797 * q^97 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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