LMFDB - Embedded newform 124.3.o.a.13.2

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			13.2
Character	$\chi$	$=$	124.13
Dual form			124.3.o.a.105.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21706 - 2.73355i) q^{3} +(4.66965 + 8.08807i) q^{5} +(2.28779 + 2.54085i) q^{7} +(0.0310810 - 0.0345190i) q^{9} +O(q^{10})$	\(q+(-1.21706 - 2.73355i) q^{3} +(4.66965 + 8.08807i) q^{5} +(2.28779 + 2.54085i) q^{7} +(0.0310810 - 0.0345190i) q^{9} +(-1.71359 - 8.06181i) q^{11} +(22.4666 + 2.36133i) q^{13} +(16.4259 - 22.6084i) q^{15} +(0.00817516 - 0.0384611i) q^{17} +(0.299466 + 2.84923i) q^{19} +(4.16118 - 9.34616i) q^{21} +(-9.51173 + 3.09055i) q^{23} +(-31.1112 + 53.8862i) q^{25} +(-25.7444 - 8.36485i) q^{27} +(-1.39940 - 1.92611i) q^{29} +(28.1952 + 12.8854i) q^{31} +(-19.9519 + 14.4959i) q^{33} +(-9.86738 + 30.3687i) q^{35} +(-39.7123 - 22.9279i) q^{37} +(-20.8883 - 64.2875i) q^{39} +(-30.7924 - 13.7096i) q^{41} +(33.6883 - 3.54078i) q^{43} +(0.424329 + 0.0901940i) q^{45} +(29.1665 + 21.1907i) q^{47} +(3.89997 - 37.1057i) q^{49} +(-0.115085 + 0.0244621i) q^{51} +(-48.4701 - 43.6427i) q^{53} +(57.2026 - 51.5054i) q^{55} +(7.42406 - 4.28629i) q^{57} +(-101.244 + 45.0769i) q^{59} +82.6793i q^{61} +0.158815 q^{63} +(85.8124 + 192.738i) q^{65} +(-58.2497 - 100.891i) q^{67} +(20.0245 + 22.2395i) q^{69} +(-51.9813 + 57.7310i) q^{71} +(-19.8778 - 93.5177i) q^{73} +(185.165 + 19.4616i) q^{75} +(16.5635 - 22.7977i) q^{77} +(19.2774 - 90.6930i) q^{79} +(8.42288 + 80.1384i) q^{81} +(29.7799 - 66.8869i) q^{83} +(0.349251 - 0.113479i) q^{85} +(-3.56197 + 6.16952i) q^{87} +(88.7594 + 28.8397i) q^{89} +(45.3991 + 62.4864i) q^{91} +(0.907725 - 92.7553i) q^{93} +(-21.6464 + 15.7270i) q^{95} +(27.8527 - 85.7219i) q^{97} +(-0.331546 - 0.191418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.21706	−	2.73355i	−0.405686	−	0.911185i	−0.994677	−	0.103045i	$-0.967141\pi$
$3$	−1.21706	−	2.73355i	−0.405686	−	0.911185i	0.588991	−	0.808140i	$-0.299525\pi$
$4$		0			0
$5$	4.66965	+	8.08807i	0.933929	+	1.61761i	0.776532	+	0.630078i	$0.216977\pi$
$5$	4.66965	+	8.08807i	0.933929	+	1.61761i	0.157397	+	0.987535i	$0.449690\pi$
$6$		0			0
$7$	2.28779	+	2.54085i	0.326827	+	0.362979i	0.884056	−	0.467380i	$-0.154802\pi$
$7$	2.28779	+	2.54085i	0.326827	+	0.362979i	−0.557229	+	0.830359i	$0.688135\pi$
$8$		0			0
$9$	0.0310810	−	0.0345190i	0.00345345	−	0.00383544i
$10$		0			0
$11$	−1.71359	−	8.06181i	−0.155781	−	0.732891i	−0.984803	−	0.173676i	$-0.944436\pi$
$11$	−1.71359	−	8.06181i	−0.155781	−	0.732891i	0.829022	−	0.559216i	$-0.188898\pi$
$12$		0			0
$13$	22.4666	+	2.36133i	1.72820	+	0.181641i	0.915847	−	0.401528i	$-0.131521\pi$
$13$	22.4666	+	2.36133i	1.72820	+	0.181641i	0.812351	+	0.583168i	$0.198187\pi$
$14$		0			0
$15$	16.4259	−	22.6084i	1.09506	−	1.50722i
$16$		0			0
$17$	0.00817516	−	0.0384611i	0.000480892	−	0.00226242i	−0.977907	−	0.209043i	$-0.932965\pi$
$17$	0.00817516	−	0.0384611i	0.000480892	−	0.00226242i	0.978387	+	0.206780i	$0.0662985\pi$
$18$		0			0
$19$	0.299466	+	2.84923i	0.0157614	+	0.149960i	0.999572	−	0.0292512i	$-0.00931227\pi$
$19$	0.299466	+	2.84923i	0.0157614	+	0.149960i	−0.983811	+	0.179211i	$0.942646\pi$
$20$		0			0
$21$	4.16118	−	9.34616i	0.198151	−	0.445055i
$22$		0			0
$23$	−9.51173	+	3.09055i	−0.413554	+	0.134372i	−0.508402	−	0.861120i	$-0.669763\pi$
$23$	−9.51173	+	3.09055i	−0.413554	+	0.134372i	0.0948481	+	0.995492i	$0.469763\pi$
$24$		0			0
$25$	−31.1112	+	53.8862i	−1.24445	+	2.15545i
$26$		0			0
$27$	−25.7444	−	8.36485i	−0.953495	−	0.309809i
$28$		0			0
$29$	−1.39940	−	1.92611i	−0.0482552	−	0.0664175i	0.784208	−	0.620499i	$-0.213070\pi$
$29$	−1.39940	−	1.92611i	−0.0482552	−	0.0664175i	−0.832463	+	0.554081i	$0.813070\pi$
$30$		0			0
$31$	28.1952	+	12.8854i	0.909521	+	0.415657i
$31$	28.1952	+	12.8854i	0.909521	+	0.415657i
$32$		0			0
$33$	−19.9519	+	14.4959i	−0.604602	+	0.439269i
$34$		0			0
$35$	−9.86738	+	30.3687i	−0.281925	+	0.867677i
$36$		0			0
$37$	−39.7123	−	22.9279i	−1.07331	−	0.619673i	−0.144223	−	0.989545i	$-0.546068\pi$
$37$	−39.7123	−	22.9279i	−1.07331	−	0.619673i	−0.929083	+	0.369872i	$0.879401\pi$
$38$		0			0
$39$	−20.8883	−	64.2875i	−0.535597	−	1.64840i
$40$		0			0
$41$	−30.7924	−	13.7096i	−0.751034	−	0.334382i	−0.00473120	−	0.999989i	$-0.501506\pi$
$41$	−30.7924	−	13.7096i	−0.751034	−	0.334382i	−0.746302	+	0.665607i	$0.768173\pi$
$42$		0			0
$43$	33.6883	−	3.54078i	0.783448	−	0.0823437i	0.295646	−	0.955298i	$-0.404465\pi$
$43$	33.6883	−	3.54078i	0.783448	−	0.0823437i	0.487803	+	0.872954i	$0.337799\pi$
$44$		0			0
$45$	0.424329	+	0.0901940i	0.00942954	+	0.00200431i
$46$		0			0
$47$	29.1665	+	21.1907i	0.620564	+	0.450866i	0.853119	−	0.521717i	$-0.174708\pi$
$47$	29.1665	+	21.1907i	0.620564	+	0.450866i	−0.232554	+	0.972583i	$0.574708\pi$
$48$		0			0
$49$	3.89997	−	37.1057i	0.0795912	−	0.757259i
$50$		0			0
$51$	−0.115085	+	0.0244621i	−0.00225657	+	0.000479649i
$52$		0			0
$53$	−48.4701	−	43.6427i	−0.914531	−	0.823448i	0.0701994	−	0.997533i	$-0.477636\pi$
$53$	−48.4701	−	43.6427i	−0.914531	−	0.823448i	−0.984731	+	0.174085i	$0.944303\pi$
$54$		0			0
$55$	57.2026	−	51.5054i	1.04005	−	0.936462i
$56$		0			0
$57$	7.42406	−	4.28629i	0.130247	−	0.0751980i
$58$		0			0
$59$	−101.244	+	45.0769i	−1.71600	+	0.764014i	−0.718341	+	0.695691i	$0.755098\pi$
$59$	−101.244	+	45.0769i	−1.71600	+	0.764014i	−0.997663	+	0.0683236i	$0.978235\pi$
$60$		0			0
$61$			82.6793i			1.35540i	0.735340	+	0.677699i	$0.237023\pi$
$61$			82.6793i			1.35540i	−0.735340	+	0.677699i	$0.762977\pi$
$62$		0			0
$63$	0.158815			0.00252087
$64$		0			0
$65$	85.8124	+	192.738i	1.32019	+	2.96520i
$66$		0			0
$67$	−58.2497	−	100.891i	−0.869398	−	1.50584i	−0.862613	−	0.505865i	$-0.831173\pi$
$67$	−58.2497	−	100.891i	−0.869398	−	1.50584i	−0.00678541	−	0.999977i	$-0.502160\pi$
$68$		0			0
$69$	20.0245	+	22.2395i	0.290210	+	0.322311i
$70$		0			0
$71$	−51.9813	+	57.7310i	−0.732131	+	0.813113i	−0.988139	−	0.153561i	$-0.950926\pi$
$71$	−51.9813	+	57.7310i	−0.732131	+	0.813113i	0.256009	+	0.966674i	$0.417592\pi$
$72$		0			0
$73$	−19.8778	−	93.5177i	−0.272299	−	1.28106i	−0.875400	−	0.483400i	$-0.839402\pi$
$73$	−19.8778	−	93.5177i	−0.272299	−	1.28106i	0.603101	−	0.797665i	$-0.293931\pi$
$74$		0			0
$75$	185.165	+	19.4616i	2.46887	+	0.259488i
$76$		0			0
$77$	16.5635	−	22.7977i	0.215110	−	0.296074i
$78$		0			0
$79$	19.2774	−	90.6930i	0.244018	−	1.14801i	−0.670007	−	0.742354i	$-0.733709\pi$
$79$	19.2774	−	90.6930i	0.244018	−	1.14801i	0.914025	−	0.405658i	$-0.132958\pi$
$80$		0			0
$81$	8.42288	+	80.1384i	0.103986	+	0.989363i
$82$		0			0
$83$	29.7799	−	66.8869i	0.358795	−	0.805866i	−0.640487	−	0.767969i	$-0.721268\pi$
$83$	29.7799	−	66.8869i	0.358795	−	0.805866i	0.999282	−	0.0378968i	$-0.0120658\pi$
$84$		0			0
$85$	0.349251	−	0.113479i	0.00410884	−	0.00133504i
$86$		0			0
$87$	−3.56197	+	6.16952i	−0.0409422	+	0.0709140i
$88$		0			0
$89$	88.7594	+	28.8397i	0.997296	+	0.324041i	0.761785	−	0.647830i	$-0.224323\pi$
$89$	88.7594	+	28.8397i	0.997296	+	0.324041i	0.235512	+	0.971872i	$0.424323\pi$
$90$		0			0
$91$	45.3991	+	62.4864i	0.498891	+	0.686664i
$92$		0			0
$93$	0.907725	−	92.7553i	0.00976048	−	0.997368i
$94$		0			0
$95$	−21.6464	+	15.7270i	−0.227857	+	0.165547i
$96$		0			0
$97$	27.8527	−	85.7219i	0.287142	−	0.883731i	−0.698607	−	0.715506i	$-0.746196\pi$
$97$	27.8527	−	85.7219i	0.287142	−	0.883731i	0.985749	−	0.168225i	$-0.0538036\pi$
$98$		0			0
$99$	−0.331546	−	0.191418i	−0.00334895	−	0.00193351i
$100$		0			0
$101$	1.30556	+	4.01811i	0.0129264	+	0.0397833i	0.957312	−	0.289058i	$-0.0933420\pi$
$101$	1.30556	+	4.01811i	0.0129264	+	0.0397833i	−0.944385	+	0.328841i	$0.893342\pi$
$102$		0			0
$103$	87.4643	+	38.9416i	0.849168	+	0.378074i	0.784722	−	0.619847i	$-0.212805\pi$
$103$	87.4643	+	38.9416i	0.849168	+	0.378074i	0.0644455	+	0.997921i	$0.479472\pi$
$104$		0			0
$105$	95.0236	−	9.98738i	0.904987	−	0.0951179i
$106$		0			0
$107$	−153.400	−	32.6062i	−1.43365	−	0.304731i	−0.575359	−	0.817901i	$-0.695137\pi$
$107$	−153.400	−	32.6062i	−1.43365	−	0.304731i	−0.858287	+	0.513171i	$0.828471\pi$
$108$		0			0
$109$	−33.7919	−	24.5513i	−0.310018	−	0.225241i	0.421886	−	0.906649i	$-0.361368\pi$
$109$	−33.7919	−	24.5513i	−0.310018	−	0.225241i	−0.731904	+	0.681408i	$0.761368\pi$
$110$		0			0
$111$	−14.3426	+	136.460i	−0.129212	+	1.22937i
$112$		0			0
$113$	23.0878	−	4.90747i	0.204317	−	0.0434290i	−0.104616	−	0.994513i	$-0.533361\pi$
$113$	23.0878	−	4.90747i	0.204317	−	0.0434290i	0.308933	+	0.951084i	$0.400028\pi$
$114$		0			0
$115$	−69.4130	−	62.4997i	−0.603591	−	0.543476i
$116$		0			0
$117$	0.779796	−	0.702131i	0.00666492	−	0.00600112i
$118$		0			0
$119$	0.116427	−	0.0672191i	0.000978378	−	0.000564867i
$120$		0			0
$121$	48.4827	−	21.5859i	0.400683	−	0.178396i
$122$		0			0
$123$			100.858i			0.819984i
$124$		0			0
$125$	−347.631			−2.78105
$126$		0			0
$127$	73.1341	+	164.262i	0.575859	+	1.29340i	0.933177	+	0.359417i	$0.117025\pi$
$127$	73.1341	+	164.262i	0.575859	+	1.29340i	−0.357318	+	0.933983i	$0.616309\pi$
$128$		0			0
$129$	−50.6795	−	87.7794i	−0.392864	−	0.680461i
$130$		0			0
$131$	50.4823	+	56.0663i	0.385361	+	0.427987i	0.904348	−	0.426795i	$-0.140357\pi$
$131$	50.4823	+	56.0663i	0.385361	+	0.427987i	−0.518987	+	0.854782i	$0.673691\pi$
$132$		0			0
$133$	−6.55435	+	7.27935i	−0.0492809	+	0.0547319i
$134$		0			0
$135$	−52.5616	−	247.283i	−0.389345	−	1.83173i
$136$		0			0
$137$	102.595	+	10.7832i	0.748872	+	0.0787096i	0.471273	−	0.881987i	$-0.343795\pi$
$137$	102.595	+	10.7832i	0.748872	+	0.0787096i	0.277599	+	0.960697i	$0.410461\pi$
$138$		0			0
$139$	−44.3467	+	61.0379i	−0.319041	+	0.439122i	−0.938174	−	0.346164i	$-0.887484\pi$
$139$	−44.3467	+	61.0379i	−0.319041	+	0.439122i	0.619133	+	0.785286i	$0.287484\pi$
$140$		0			0
$141$	22.4287	−	105.519i	0.159069	−	0.748359i
$142$		0			0
$143$	−19.4619	−	185.168i	−0.136097	−	1.29488i
$144$		0			0
$145$	9.04379	−	20.3127i	0.0623710	−	0.140087i
$146$		0			0
$147$	−106.177	+	34.4990i	−0.722292	+	0.234687i
$148$		0			0
$149$	−75.0046	+	129.912i	−0.503387	+	0.871891i	0.496606	+	0.867976i	$0.334579\pi$
$149$	−75.0046	+	129.912i	−0.503387	+	0.871891i	−0.999992	+	0.00391484i	$0.998754\pi$
$150$		0			0
$151$	−83.2224	−	27.0406i	−0.551142	−	0.179077i	0.0201898	−	0.999796i	$-0.493573\pi$
$151$	−83.2224	−	27.0406i	−0.551142	−	0.179077i	−0.571332	+	0.820719i	$0.693573\pi$
$152$		0			0
$153$	−0.00107355	−	0.00147761i	−7.01664e−6	−	9.65758e-6i
$154$		0			0
$155$	27.4438	+	288.214i	0.177057	+	1.85945i
$156$		0			0
$157$	−58.8398	+	42.7496i	−0.374776	+	0.272291i	−0.759189	−	0.650871i	$-0.774404\pi$
$157$	−58.8398	+	42.7496i	−0.374776	+	0.272291i	0.384413	+	0.923161i	$0.374404\pi$
$158$		0			0
$159$	−60.3088	+	185.611i	−0.379301	+	1.16737i
$160$		0			0
$161$	−29.6135	−	17.0974i	−0.183935	−	0.106195i
$162$		0			0
$163$	−21.1187	−	64.9967i	−0.129563	−	0.398753i	0.865142	−	0.501527i	$-0.167228\pi$
$163$	−21.1187	−	64.9967i	−0.129563	−	0.398753i	−0.994705	+	0.102774i	$0.967228\pi$
$164$		0			0
$165$	−210.412	−	93.6813i	−1.27522	−	0.567765i
$166$		0			0
$167$	−315.517	+	33.1622i	−1.88932	+	0.198576i	−0.977343	−	0.211660i	$-0.932113\pi$
$167$	−315.517	+	33.1622i	−1.88932	+	0.198576i	−0.911979	+	0.410236i	$0.865446\pi$
$168$		0			0
$169$	333.864	+	70.9650i	1.97553	+	0.419911i
$170$		0			0
$171$	0.107660	+	0.0782198i	0.000629593	+	0.000457426i
$172$		0			0
$173$	27.5528	−	262.147i	0.159264	−	1.51530i	−0.564604	−	0.825362i	$-0.690971\pi$
$173$	27.5528	−	262.147i	0.159264	−	1.51530i	0.723868	−	0.689938i	$-0.242362\pi$
$174$		0			0
$175$	−208.093	+	44.2315i	−1.18910	+	0.252751i
$176$		0			0
$177$	246.440	+	221.896i	1.39232	+	1.25365i
$178$		0			0
$179$	16.5133	−	14.8686i	0.0922530	−	0.0830650i	−0.621714	−	0.783244i	$-0.713563\pi$
$179$	16.5133	−	14.8686i	0.0922530	−	0.0830650i	0.713967	+	0.700179i	$0.246897\pi$
$180$		0			0
$181$	−34.8994	+	20.1492i	−0.192814	+	0.111321i	−0.593299	−	0.804982i	$-0.702175\pi$
$181$	−34.8994	+	20.1492i	−0.192814	+	0.111321i	0.400485	+	0.916303i	$0.368842\pi$
$182$		0			0
$183$	226.008	−	100.625i	1.23502	−	0.549865i
$184$		0			0
$185$		−	428.261i		−	2.31492i
$186$		0			0
$187$	−0.324075			−0.00173302
$188$		0			0
$189$	−37.6439	−	84.5496i	−0.199174	−	0.447352i
$190$		0			0
$191$	147.714	+	255.848i	0.773371	+	1.33952i	0.935705	+	0.352782i	$0.114764\pi$
$191$	147.714	+	255.848i	0.773371	+	1.33952i	−0.162334	+	0.986736i	$0.551902\pi$
$192$		0			0
$193$	165.254	+	183.533i	0.856237	+	0.950948i	0.999248	−	0.0387734i	$-0.0123450\pi$
$193$	165.254	+	183.533i	0.856237	+	0.950948i	−0.143011	+	0.989721i	$0.545678\pi$
$194$		0			0
$195$	422.421	−	469.146i	2.16626	−	2.40587i
$196$		0			0
$197$	−19.5790	−	92.1119i	−0.0993857	−	0.467573i	−0.999491	−	0.0319007i	$-0.989844\pi$
$197$	−19.5790	−	92.1119i	−0.0993857	−	0.467573i	0.900105	−	0.435672i	$-0.143489\pi$
$198$		0			0
$199$	−41.0603	−	4.31561i	−0.206333	−	0.0216865i	0.000798052	−	1.00000i	$-0.499746\pi$
$199$	−41.0603	−	4.31561i	−0.206333	−	0.0216865i	−0.207131	+	0.978313i	$0.566413\pi$
$200$		0			0
$201$	−204.899	+	282.019i	−1.01940	+	1.40308i
$202$		0			0
$203$	1.69242	−	7.96220i	0.00833703	−	0.0392227i
$204$		0			0
$205$	−32.9050	−	313.070i	−0.160512	−	1.52717i
$206$		0			0
$207$	−0.188952	+	0.424393i	−0.000912811	+	0.00205021i
$208$		0			0
$209$	22.4568	−	7.29665i	0.107449	−	0.0349122i
$210$		0			0
$211$	67.5674	−	117.030i	0.320225	−	0.554646i	−0.660310	−	0.750994i	$-0.729575\pi$
$211$	67.5674	−	117.030i	0.320225	−	0.554646i	0.980534	+	0.196348i	$0.0629082\pi$
$212$		0			0
$213$	221.075	+	71.8317i	1.03791	+	0.337238i
$214$		0			0
$215$	185.950	+	255.939i	0.864886	+	1.19041i
$216$		0			0
$217$	31.7649	+	101.119i	0.146382	+	0.465985i
$218$		0			0
$219$	−231.443	+	168.153i	−1.05682	+	0.767824i
$220$		0			0
$221$	0.274487	−	0.844785i	0.00124202	−	0.00382256i
$222$		0			0
$223$	−20.5100	−	11.8414i	−0.0919730	−	0.0531007i	0.453308	−	0.891354i	$-0.350244\pi$
$223$	−20.5100	−	11.8414i	−0.0919730	−	0.0531007i	−0.545281	+	0.838253i	$0.683577\pi$
$224$		0			0
$225$	0.893128	+	2.74877i	0.00396946	+	0.0122167i
$226$		0			0
$227$	304.814	+	135.712i	1.34279	+	0.597850i	0.947220	−	0.320584i	$-0.103879\pi$
$227$	304.814	+	135.712i	1.34279	+	0.597850i	0.395574	+	0.918434i	$0.370546\pi$
$228$		0			0
$229$	99.8590	−	10.4956i	0.436065	−	0.0458323i	0.116047	−	0.993244i	$-0.462978\pi$
$229$	99.8590	−	10.4956i	0.436065	−	0.0458323i	0.320018	+	0.947411i	$0.396311\pi$
$230$		0			0
$231$	−82.4775	−	17.5311i	−0.357045	−	0.0758924i
$232$		0			0
$233$	−42.8134	−	31.1058i	−0.183749	−	0.133501i	0.492108	−	0.870534i	$-0.336226\pi$
$233$	−42.8134	−	31.1058i	−0.183749	−	0.133501i	−0.675857	+	0.737033i	$0.736226\pi$
$234$		0			0
$235$	−35.1946	+	334.854i	−0.149764	+	1.42491i
$236$		0			0
$237$	−271.376	+	57.6827i	−1.14505	+	0.243387i
$238$		0			0
$239$	214.940	+	193.533i	0.899330	+	0.809760i	0.982401	−	0.186783i	$-0.0598062\pi$
$239$	214.940	+	193.533i	0.899330	+	0.809760i	−0.0830712	+	0.996544i	$0.526473\pi$
$240$		0			0
$241$	−211.383	+	190.330i	−0.877108	+	0.789752i	−0.978747	−	0.205069i	$-0.934258\pi$
$241$	−211.383	+	190.330i	−0.877108	+	0.789752i	0.101639	+	0.994821i	$0.467591\pi$
$242$		0			0
$243$	−2.17223	+	1.25413i	−0.00893920	+	0.00516105i
$244$		0			0
$245$	318.325	−	141.727i	1.29928	−	0.578479i
$246$		0			0
$247$			64.7196i			0.262023i
$248$		0			0
$249$	−219.083			−0.879851
$250$		0			0
$251$	−81.9599	−	184.085i	−0.326534	−	0.733406i	0.673449	−	0.739233i	$-0.264812\pi$
$251$	−81.9599	−	184.085i	−0.326534	−	0.733406i	−0.999983	+	0.00582691i	$0.998145\pi$
$252$		0			0
$253$	41.2146	+	71.3858i	0.162904	+	0.282157i
$254$		0			0
$255$	−0.735258	−	0.816587i	−0.00288337	−	0.00320230i
$256$		0			0
$257$	−19.7652	+	21.9515i	−0.0769074	+	0.0854144i	−0.780370	−	0.625318i	$-0.784969\pi$
$257$	−19.7652	+	21.9515i	−0.0769074	+	0.0854144i	0.703463	+	0.710732i	$0.251636\pi$
$258$		0			0
$259$	−32.5971	−	153.357i	−0.125857	−	0.592113i
$260$		0			0
$261$	−0.109982	−	0.0115596i	−0.000421388	−	4.42896e-5i
$262$		0			0
$263$	−32.5278	+	44.7706i	−0.123680	+	0.170231i	−0.866367	−	0.499408i	$-0.833551\pi$
$263$	−32.5278	+	44.7706i	−0.123680	+	0.170231i	0.742687	+	0.669638i	$0.233551\pi$
$264$		0			0
$265$	126.647	−	595.826i	0.477912	−	2.24840i
$266$		0			0
$267$	−29.1904	−	277.728i	−0.109327	−	1.04018i
$268$		0			0
$269$	94.6678	−	212.627i	0.351925	−	0.790437i	−0.647668	−	0.761922i	$-0.724256\pi$
$269$	94.6678	−	212.627i	0.351925	−	0.790437i	0.999593	−	0.0285142i	$-0.00907759\pi$
$270$		0			0
$271$	−63.2847	+	20.5624i	−0.233523	+	0.0758761i	−0.423441	−	0.905924i	$-0.639178\pi$
$271$	−63.2847	+	20.5624i	−0.233523	+	0.0758761i	0.189918	+	0.981800i	$0.439178\pi$
$272$		0			0
$273$	115.557	−	200.150i	0.423285	−	0.733151i
$274$		0			0
$275$	487.732	+	158.474i	1.77357	+	0.576268i
$276$		0			0
$277$	201.925	+	277.927i	0.728973	+	1.00334i	0.999178	+	0.0405420i	$0.0129085\pi$
$277$	201.925	+	277.927i	0.728973	+	1.00334i	−0.270205	+	0.962803i	$0.587092\pi$
$278$		0			0
$279$	1.32113	−	0.572778i	0.00473522	−	0.00205297i
$280$		0			0
$281$	−402.156	+	292.183i	−1.43116	+	1.03980i	−0.441361	+	0.897330i	$0.645504\pi$
$281$	−402.156	+	292.183i	−1.43116	+	1.03980i	−0.989799	+	0.142469i	$0.954496\pi$
$282$		0			0
$283$	160.175	−	492.967i	0.565989	−	1.74193i	−0.0990068	−	0.995087i	$-0.531567\pi$
$283$	160.175	−	492.967i	0.565989	−	1.74193i	0.664996	−	0.746847i	$-0.268433\pi$
$284$		0			0
$285$	69.3355	+	40.0309i	0.243283	+	0.140459i
$286$		0			0
$287$	−35.6124	−	109.604i	−0.124085	−	0.381894i
$288$		0			0
$289$	264.013	+	117.546i	0.913541	+	0.406734i
$290$		0			0
$291$	−268.224	+	28.1915i	−0.921731	+	0.0968779i
$292$		0			0
$293$	−67.8556	−	14.4231i	−0.231589	−	0.0492258i	0.0906552	−	0.995882i	$-0.471104\pi$
$293$	−67.8556	−	14.4231i	−0.231589	−	0.0492258i	−0.322244	+	0.946657i	$0.604437\pi$
$294$		0			0
$295$	−837.359	−	608.377i	−2.83851	−	2.06230i
$296$		0			0
$297$	−23.3205	+	221.880i	−0.0785203	+	0.747071i
$298$		0			0
$299$	−220.994	+	46.9737i	−0.739110	+	0.157103i
$300$		0			0
$301$	86.0683	+	77.4963i	0.285941	+	0.257463i
$302$		0			0
$303$	9.39479	−	8.45910i	0.0310059	−	0.0279178i
$304$		0			0
$305$	−668.715	+	386.083i	−2.19251	+	1.26585i
$306$		0			0
$307$	1.56188	−	0.695394i	0.00508756	−	0.00226513i	−0.404191	−	0.914674i	$-0.632447\pi$
$307$	1.56188	−	0.695394i	0.00508756	−	0.00226513i	0.409279	+	0.912409i	$0.365780\pi$
$308$		0			0
$309$		−	286.483i		−	0.927128i
$310$		0			0
$311$	37.5806			0.120838			0.0604190	−	0.998173i	$-0.480756\pi$
$311$	37.5806			0.120838			0.0604190	+	0.998173i	$0.480756\pi$
$312$		0			0
$313$	−39.6123	−	88.9707i	−0.126557	−	0.284251i	0.839144	−	0.543910i	$-0.183057\pi$
$313$	−39.6123	−	88.9707i	−0.126557	−	0.284251i	−0.965700	+	0.259659i	$0.916390\pi$
$314$		0			0
$315$	0.741608	+	1.28450i	0.00235431	+	0.00407779i
$316$		0			0
$317$	89.7780	+	99.7085i	0.283211	+	0.314538i	0.867919	−	0.496706i	$-0.165457\pi$
$317$	89.7780	+	99.7085i	0.283211	+	0.314538i	−0.584707	+	0.811244i	$0.698791\pi$
$318$		0			0
$319$	−13.1299	+	14.5822i	−0.0411596	+	0.0457124i
$320$		0			0
$321$	97.5658	+	459.011i	0.303943	+	1.42994i
$322$		0			0
$323$	0.112033	+	0.0117751i	0.000346851	+	3.64555e-5i
$324$		0			0
$325$	−826.205	+	1137.17i	−2.54217	+	3.49900i
$326$		0			0
$327$	−25.9855	+	122.252i	−0.0794665	+	0.373860i
$328$		0			0
$329$	12.8845	+	122.588i	0.0391626	+	0.372607i
$330$		0			0
$331$	−231.526	+	520.015i	−0.699473	+	1.57104i	0.116655	+	0.993172i	$0.462783\pi$
$331$	−231.526	+	520.015i	−0.699473	+	1.57104i	−0.816129	+	0.577870i	$0.803884\pi$
$332$		0			0
$333$	−2.02575	+	0.658205i	−0.00608333	+	0.00197659i
$334$		0			0
$335$	544.011	−	942.254i	1.62391	−	2.81270i
$336$		0			0
$337$	75.7383	+	24.6089i	0.224743	+	0.0730233i	0.419224	−	0.907883i	$-0.362302\pi$
$337$	75.7383	+	24.6089i	0.224743	+	0.0730233i	−0.194481	+	0.980906i	$0.562302\pi$
$338$		0			0
$339$	−41.5141	−	57.1392i	−0.122460	−	0.168552i
$340$		0			0
$341$	55.5644	−	249.384i	0.162945	−	0.731332i
$342$		0			0
$343$	238.740	−	173.455i	0.696034	−	0.505699i
$344$		0			0
$345$	−86.3669	+	265.810i	−0.250339	+	0.770464i
$346$		0			0
$347$	−21.8281	−	12.6025i	−0.0629052	−	0.0363184i	0.468218	−	0.883613i	$-0.344896\pi$
$347$	−21.8281	−	12.6025i	−0.0629052	−	0.0363184i	−0.531123	+	0.847295i	$0.678230\pi$
$348$		0			0
$349$	−18.0886	−	55.6710i	−0.0518298	−	0.159516i	0.921791	−	0.387686i	$-0.126726\pi$
$349$	−18.0886	−	55.6710i	−0.0518298	−	0.159516i	−0.973621	+	0.228171i	$0.926726\pi$
$350$		0			0
$351$	−558.635	−	248.721i	−1.59155	−	0.708606i
$352$		0			0
$353$	102.146	−	10.7360i	0.289367	−	0.0304137i	0.0412670	−	0.999148i	$-0.486861\pi$
$353$	102.146	−	10.7360i	0.289367	−	0.0304137i	0.248100	+	0.968734i	$0.420194\pi$
$354$		0			0
$355$	−709.667	−	150.844i	−1.99906	−	0.424914i
$356$		0			0
$357$	−0.325445	−	0.236450i	−0.000911612	−	0.000662325i
$358$		0			0
$359$	−20.6472	+	196.445i	−0.0575132	+	0.547201i	0.927390	+	0.374096i	$0.122047\pi$
$359$	−20.6472	+	196.445i	−0.0575132	+	0.547201i	−0.984903	+	0.173106i	$0.944620\pi$
$360$		0			0
$361$	345.083	−	73.3496i	0.955908	−	0.203185i
$362$		0			0
$363$	−118.012	−	106.259i	−0.325103	−	0.292724i
$364$		0			0
$365$	663.555	−	597.467i	1.81796	−	1.63690i
$366$		0			0
$367$	217.006	−	125.288i	0.591296	−	0.341385i	−0.174314	−	0.984690i	$-0.555771\pi$
$367$	217.006	−	125.288i	0.591296	−	0.341385i	0.765610	+	0.643305i	$0.222437\pi$
$368$		0			0
$369$	−1.43030	+	0.636812i	−0.00387616	+	0.00172578i
$370$		0			0
$371$		−	223.001i		−	0.601080i
$372$		0			0
$373$	−140.265			−0.376046			−0.188023	−	0.982165i	$-0.560208\pi$
$373$	−140.265			−0.376046			−0.188023	+	0.982165i	$0.560208\pi$
$374$		0			0
$375$	423.087	+	950.268i	1.12823	+	2.53405i
$376$		0			0
$377$	−26.8915	−	46.5775i	−0.0713303	−	0.123548i
$378$		0			0
$379$	261.913	+	290.884i	0.691063	+	0.767503i	0.981927	−	0.189261i	$-0.0606092\pi$
$379$	261.913	+	290.884i	0.691063	+	0.767503i	−0.290864	+	0.956765i	$0.593943\pi$
$380$		0			0
$381$	360.010	−	399.832i	0.944909	−	1.04943i
$382$		0			0
$383$	−110.525	−	519.978i	−0.288577	−	1.35765i	−0.848541	−	0.529129i	$-0.822519\pi$
$383$	−110.525	−	519.978i	−0.288577	−	1.35765i	0.559965	−	0.828516i	$-0.310815\pi$
$384$		0			0
$385$	261.735	+	27.5095i	0.679831	+	0.0714531i
$386$		0			0
$387$	0.924843	−	1.27294i	0.00238977	−	0.00328924i
$388$		0			0
$389$	43.8890	−	206.481i	0.112825	−	0.530801i	−0.885041	−	0.465513i	$-0.845870\pi$
$389$	43.8890	−	206.481i	0.112825	−	0.530801i	0.997866	−	0.0652881i	$-0.0207966\pi$
$390$		0			0
$391$	0.0411060	+	0.391097i	0.000105130	+	0.00100025i
$392$		0			0
$393$	91.8204	−	206.232i	0.233640	−	0.524763i
$394$		0			0
$395$	823.549	−	267.587i	2.08494	−	0.677437i
$396$		0			0
$397$	−325.111	+	563.108i	−0.818918	+	1.41841i	0.0875618	+	0.996159i	$0.472092\pi$
$397$	−325.111	+	563.108i	−0.818918	+	1.41841i	−0.906480	+	0.422249i	$0.861241\pi$
$398$		0			0
$399$	27.8755	+	9.05731i	0.0698635	+	0.0227000i
$400$		0			0
$401$	−136.333	−	187.646i	−0.339981	−	0.467944i	0.604455	−	0.796640i	$-0.293391\pi$
$401$	−136.333	−	187.646i	−0.339981	−	0.467944i	−0.944436	+	0.328695i	$0.893391\pi$
$402$		0			0
$403$	603.022	+	356.068i	1.49633	+	0.883544i
$404$		0			0
$405$	−608.832	+	442.343i	−1.50329	+	1.09220i
$406$		0			0
$407$	−116.790	+	359.442i	−0.286953	+	0.883149i
$408$		0			0
$409$	−175.862	−	101.534i	−0.429981	−	0.248250i	0.269358	−	0.963040i	$-0.413189\pi$
$409$	−175.862	−	101.534i	−0.429981	−	0.248250i	−0.699339	+	0.714791i	$0.746522\pi$
$410$		0			0
$411$	−95.3880	−	293.574i	−0.232088	−	0.714292i
$412$		0			0
$413$	−346.159	−	154.120i	−0.838158	−	0.373172i
$414$		0			0
$415$	680.047	−	71.4758i	1.63867	−	0.172231i
$416$		0			0
$417$	220.823	+	46.9374i	0.529551	+	0.112560i
$418$		0			0
$419$	19.1027	+	13.8789i	0.0455912	+	0.0331239i	0.610347	−	0.792134i	$-0.291030\pi$
$419$	19.1027	+	13.8789i	0.0455912	+	0.0331239i	−0.564756	+	0.825258i	$0.691030\pi$
$420$		0			0
$421$	36.0260	−	342.764i	0.0855724	−	0.814167i	−0.864604	−	0.502454i	$-0.832431\pi$
$421$	36.0260	−	342.764i	0.0855724	−	0.814167i	0.950176	−	0.311713i	$-0.100903\pi$
$422$		0			0
$423$	1.63801	−	0.348169i	0.00387236	−	0.000823095i
$424$		0			0
$425$	1.81818	+	1.63710i	0.00427808	+	0.00385200i
$426$		0			0
$427$	−210.076	+	189.153i	−0.491980	+	0.442981i
$428$		0			0
$429$	−482.479	+	278.560i	−1.12466	+	0.649323i
$430$		0			0
$431$	589.560	−	262.489i	1.36789	−	0.609023i	0.414302	−	0.910140i	$-0.364026\pi$
$431$	589.560	−	262.489i	1.36789	−	0.609023i	0.953587	+	0.301116i	$0.0973592\pi$
$432$		0			0
$433$		−	156.025i		−	0.360336i	−0.983636	−	0.180168i	$-0.942336\pi$
$433$		−	156.025i		−	0.360336i	0.983636	−	0.180168i	$-0.0576641\pi$
$434$		0			0
$435$	−66.5326			−0.152949
$436$		0			0
$437$	−11.6541	−	26.1756i	−0.0266685	−	0.0598984i
$438$		0			0
$439$	251.171	+	435.040i	0.572143	+	0.990980i	0.996346	+	0.0854132i	$0.0272210\pi$
$439$	251.171	+	435.040i	0.572143	+	0.990980i	−0.424203	+	0.905567i	$0.639446\pi$
$440$		0			0
$441$	−1.15964	−	1.28791i	−0.00262956	−	0.00292042i
$442$		0			0
$443$	259.662	−	288.383i	0.586144	−	0.650978i	−0.375001	−	0.927024i	$-0.622358\pi$
$443$	259.662	−	288.383i	0.586144	−	0.650978i	0.961144	+	0.276046i	$0.0890243\pi$
$444$		0			0
$445$	181.218	+	852.563i	0.407231	+	1.91587i
$446$		0			0
$447$	446.406	+	46.9191i	0.998671	+	0.104965i
$448$		0			0
$449$	322.162	−	443.417i	0.717509	−	0.987567i	−0.282094	−	0.959387i	$-0.591029\pi$
$449$	322.162	−	443.417i	0.717509	−	0.987567i	0.999603	−	0.0281798i	$-0.00897110\pi$
$450$		0			0
$451$	−57.7590	+	271.735i	−0.128069	+	0.602516i
$452$		0			0
$453$	27.3695	+	260.403i	0.0604182	+	0.574841i
$454$		0			0
$455$	−293.397	+	658.980i	−0.644828	+	1.44831i
$456$		0			0
$457$	219.739	−	71.3974i	0.480828	−	0.156231i	−0.0585666	−	0.998284i	$-0.518653\pi$
$457$	219.739	−	71.3974i	0.480828	−	0.156231i	0.539395	+	0.842053i	$0.318653\pi$
$458$		0			0
$459$	−0.532186	+	0.921773i	−0.00115945	+	0.00200822i
$460$		0			0
$461$	−643.076	−	208.948i	−1.39496	−	0.453249i	−0.487401	−	0.873178i	$-0.662055\pi$
$461$	−643.076	−	208.948i	−1.39496	−	0.453249i	−0.907557	+	0.419929i	$0.862055\pi$
$462$		0			0
$463$	3.29587	+	4.53638i	0.00711852	+	0.00979780i	0.812561	−	0.582876i	$-0.198073\pi$
$463$	3.29587	+	4.53638i	0.00711852	+	0.00979780i	−0.805443	+	0.592673i	$0.798073\pi$
$464$		0			0
$465$	754.449	−	425.793i	1.62247	−	0.915683i
$466$		0			0
$467$	−239.828	+	174.245i	−0.513551	+	0.373117i	−0.814169	−	0.580628i	$-0.802807\pi$
$467$	−239.828	+	174.245i	−0.513551	+	0.373117i	0.300618	+	0.953745i	$0.402807\pi$
$468$		0			0
$469$	123.087	−	378.822i	0.262445	−	0.807723i
$470$		0			0
$471$	188.470	+	108.813i	0.400148	+	0.231026i
$472$		0			0
$473$	−86.2730	−	265.521i	−0.182395	−	0.561355i
$474$		0			0
$475$	−162.851	−	72.5059i	−0.342844	−	0.152644i
$476$		0			0
$477$	−3.01301	+	0.316680i	−0.00631657	+	0.000663899i
$478$		0			0
$479$	−605.526	−	128.709i	−1.26415	−	0.268703i	−0.473401	−	0.880847i	$-0.656974\pi$
$479$	−605.526	−	128.709i	−1.26415	−	0.268703i	−0.790746	+	0.612144i	$0.790307\pi$
$480$		0			0
$481$	−838.059	−	608.885i	−1.74233	−	1.26587i
$482$		0			0
$483$	−10.6953	+	101.759i	−0.0221434	+	0.210680i
$484$		0			0
$485$	823.387	−	175.016i	1.69770	−	0.360858i
$486$		0			0
$487$	−526.758	−	474.295i	−1.08164	−	0.973912i	−0.0818975	−	0.996641i	$-0.526098\pi$
$487$	−526.758	−	474.295i	−1.08164	−	0.973912i	−0.999742	+	0.0227285i	$0.992765\pi$
$488$		0			0
$489$	−151.969	+	136.834i	−0.310776	+	0.279824i
$490$		0			0
$491$	−566.517	+	327.078i	−1.15380	+	0.666148i	−0.949811	−	0.312825i	$-0.898725\pi$
$491$	−566.517	+	327.078i	−1.15380	+	0.666148i	−0.203991	+	0.978973i	$0.565391\pi$
$492$		0			0
$493$	−0.0855206	+	0.0380762i	−0.000173470	+	7.72337e-5i
$494$		0			0
$495$		−	3.57542i		−	0.00722306i
$496$		0			0
$497$	−265.608			−0.534423
$498$		0			0
$499$	50.6270	+	113.710i	0.101457	+	0.227876i	0.957141	−	0.289623i	$-0.0935299\pi$
$499$	50.6270	+	113.710i	0.101457	+	0.227876i	−0.855684	+	0.517499i	$0.826863\pi$
$500$		0			0
$501$	474.653	+	822.122i	0.947410	+	1.64096i
$502$		0			0
$503$	404.628	+	449.385i	0.804429	+	0.893409i	0.996116	−	0.0880467i	$-0.0280625\pi$
$503$	404.628	+	449.385i	0.804429	+	0.893409i	−0.191687	+	0.981456i	$0.561396\pi$
$504$		0			0
$505$	−26.4022	+	29.3227i	−0.0522817	+	0.0580647i
$506$		0			0
$507$	−212.345	−	999.005i	−0.418826	−	1.97042i
$508$		0			0
$509$	792.987	+	83.3462i	1.55793	+	0.163745i	0.843950	−	0.536421i	$-0.180224\pi$
$509$	792.987	+	83.3462i	1.55793	+	0.163745i	0.713980	+	0.700166i	$0.246891\pi$
$510$		0			0
$511$	192.138	−	264.455i	0.376004	−	0.517525i
$512$		0			0
$513$	16.1238	−	75.8567i	0.0314305	−	0.147869i
$514$		0			0
$515$	93.4651	+	889.261i	0.181486	+	1.72672i
$516$		0			0
$517$	120.856	−	271.447i	0.233764	−	0.525042i
$518$		0			0
$519$	−750.126	+	243.731i	−1.44533	+	0.469616i
$520$		0			0
$521$	−316.046	+	547.408i	−0.606614	+	1.05069i	0.385180	+	0.922842i	$0.374139\pi$
$521$	−316.046	+	547.408i	−0.606614	+	1.05069i	−0.991794	+	0.127845i	$0.959194\pi$
$522$		0			0
$523$	−609.771	−	198.126i	−1.16591	−	0.378827i	−0.338795	−	0.940860i	$-0.610019\pi$
$523$	−609.771	−	198.126i	−1.16591	−	0.378827i	−0.827114	+	0.562033i	$0.810019\pi$
$524$		0			0
$525$	374.170	+	515.000i	0.712704	+	0.980953i
$526$		0			0
$527$	0.726085	−	0.979077i	0.00137777	−	0.00185783i
$528$		0			0
$529$	−347.048	+	252.145i	−0.656046	+	0.476645i
$530$		0			0
$531$	−1.59077	+	4.89589i	−0.00299580	+	0.00922013i
$532$		0			0
$533$	−659.426	−	380.720i	−1.23720	−	0.714296i
$534$		0			0
$535$	−452.603	−	1392.97i	−0.845987	−	2.60368i
$536$		0			0
$537$	−60.7418	−	27.0440i	−0.113113	−	0.0503613i
$538$		0			0
$539$	−305.822	+	32.1432i	−0.567388	+	0.0596348i
$540$		0			0
$541$	−683.314	−	145.243i	−1.26306	−	0.268471i	−0.472759	−	0.881192i	$-0.656742\pi$
$541$	−683.314	−	145.243i	−1.26306	−	0.268471i	−0.790300	+	0.612721i	$0.790075\pi$
$542$		0			0
$543$	97.5534	+	70.8767i	0.179656	+	0.130528i
$544$		0			0
$545$	40.7759	−	387.957i	0.0748182	−	0.711847i
$546$		0			0
$547$	−88.9730	+	18.9118i	−0.162656	+	0.0345737i	−0.288520	−	0.957474i	$-0.593163\pi$
$547$	−88.9730	+	18.9118i	−0.162656	+	0.0345737i	0.125864	+	0.992048i	$0.459830\pi$
$548$		0			0
$549$	2.85401	+	2.56976i	0.00519855	+	0.00468080i
$550$		0			0
$551$	5.06886	−	4.56402i	0.00919938	−	0.00828316i
$552$		0			0
$553$	274.540	−	158.506i	0.496456	−	0.286629i
$554$		0			0
$555$	−1170.67	+	521.218i	−2.10932	+	0.939131i
$556$		0			0
$557$			664.541i			1.19307i	0.802586	+	0.596536i	$0.203457\pi$
$557$			664.541i			1.19307i	−0.802586	+	0.596536i	$0.796543\pi$
$558$		0			0
$559$	765.221			1.36891
$560$		0			0
$561$	0.394418	+	0.885876i	0.000703062	+	0.00157910i
$562$		0			0
$563$	157.543	+	272.872i	0.279827	+	0.484675i	0.971342	−	0.237688i	$-0.0763895\pi$
$563$	157.543	+	272.872i	0.279827	+	0.484675i	−0.691514	+	0.722363i	$0.743056\pi$
$564$		0			0
$565$	147.504	+	163.820i	0.261069	+	0.289947i
$566$		0			0
$567$	−184.350	+	204.741i	−0.325132	+	0.361096i
$568$		0			0
$569$	−170.035	−	799.952i	−0.298831	−	1.40589i	−0.829592	−	0.558370i	$-0.811427\pi$
$569$	−170.035	−	799.952i	−0.298831	−	1.40589i	0.530761	−	0.847522i	$-0.321906\pi$
$570$		0			0
$571$	209.368	+	22.0055i	0.366670	+	0.0385385i	0.286072	−	0.958208i	$-0.407650\pi$
$571$	209.368	+	22.0055i	0.366670	+	0.0385385i	0.0805978	+	0.996747i	$0.474317\pi$
$572$		0			0
$573$	519.598	−	715.166i	0.906803	−	1.24811i
$574$		0			0
$575$	129.384	−	608.702i	0.225015	−	1.05861i
$576$		0			0
$577$	4.93600	+	46.9629i	0.00855459	+	0.0813915i	0.997966	−	0.0637452i	$-0.0203045\pi$
$577$	4.93600	+	46.9629i	0.00855459	+	0.0813915i	−0.989412	+	0.145137i	$0.953638\pi$
$578$		0			0
$579$	300.574	−	675.100i	0.519126	−	1.16598i
$580$		0			0
$581$	238.080	−	77.3568i	0.409776	−	0.133144i
$582$		0			0
$583$	−268.781	+	465.543i	−0.461031	+	0.798529i
$584$		0			0
$585$	9.32025	+	3.02833i	0.0159321	+	0.00517664i
$586$		0			0
$587$	−172.335	−	237.199i	−0.293586	−	0.404086i	0.636589	−	0.771203i	$-0.280345\pi$
$587$	−172.335	−	237.199i	−0.293586	−	0.404086i	−0.930175	+	0.367117i	$0.880345\pi$
$588$		0			0
$589$	−28.2699	+	84.1933i	−0.0479964	+	0.142943i
$590$		0			0
$591$	−227.964	+	165.626i	−0.385726	+	0.280246i
$592$		0			0
$593$	−168.534	+	518.693i	−0.284205	+	0.874693i	0.702431	+	0.711752i	$0.252098\pi$
$593$	−168.534	+	518.693i	−0.284205	+	0.874693i	−0.986636	+	0.162941i	$0.947902\pi$
$594$		0			0
$595$	1.08735	+	0.627779i	0.00182747	+	0.00105509i
$596$		0			0
$597$	38.1757	+	117.493i	0.0639459	+	0.196805i
$598$		0			0
$599$	−181.785	−	80.9360i	−0.303481	−	0.135119i	0.249346	−	0.968414i	$-0.419784\pi$
$599$	−181.785	−	80.9360i	−0.303481	−	0.135119i	−0.552827	+	0.833296i	$0.686451\pi$
$600$		0			0
$601$	582.340	−	61.2064i	0.968952	−	0.101841i	0.393189	−	0.919458i	$-0.371372\pi$
$601$	582.340	−	61.2064i	0.968952	−	0.101841i	0.575763	+	0.817617i	$0.304705\pi$
$602$		0			0
$603$	−5.29313	−	1.12509i	−0.00877800	−	0.00186582i
$604$		0			0
$605$	400.985	+	291.333i	0.662785	+	0.481542i
$606$		0			0
$607$	77.1190	−	733.738i	0.127049	−	1.20879i	−0.726271	−	0.687408i	$-0.758748\pi$
$607$	77.1190	−	733.738i	0.127049	−	1.20879i	0.853321	−	0.521386i	$-0.174585\pi$
$608$		0			0
$609$	−23.8249	+	5.06413i	−0.0391213	+	0.00831549i
$610$		0			0
$611$	605.233	+	544.955i	0.990562	+	0.891906i
$612$		0			0
$613$	−216.410	+	194.856i	−0.353034	+	0.317873i	−0.826498	−	0.562940i	$-0.809670\pi$
$613$	−216.410	+	194.856i	−0.353034	+	0.317873i	0.473464	+	0.880813i	$0.343003\pi$
$614$		0			0
$615$	−815.747	+	470.972i	−1.32642	+	0.765807i
$616$		0			0
$617$	−175.294	+	78.0459i	−0.284107	+	0.126492i	−0.543843	−	0.839187i	$-0.683031\pi$
$617$	−175.294	+	78.0459i	−0.284107	+	0.126492i	0.259736	+	0.965680i	$0.416365\pi$
$618$		0			0
$619$			696.261i			1.12482i	0.826860	+	0.562408i	$0.190125\pi$
$619$			696.261i			1.12482i	−0.826860	+	0.562408i	$0.809875\pi$
$620$		0			0
$621$	270.725			0.435951
$622$		0			0
$623$	129.786	+	291.503i	0.208324	+	0.467903i
$624$		0			0
$625$	−845.534	−	1464.51i	−1.35285	−	2.34321i
$626$		0			0
$627$	−47.2770	−	52.5064i	−0.0754019	−	0.0837423i
$628$		0			0
$629$	−1.20649	+	1.33994i	−0.00191810	+	0.00213027i
$630$		0			0
$631$	212.103	+	997.866i	0.336138	+	1.58140i	0.743884	+	0.668309i	$0.232982\pi$
$631$	212.103	+	997.866i	0.336138	+	1.58140i	−0.407746	+	0.913095i	$0.633685\pi$
$632$		0			0
$633$	−402.142	−	42.2668i	−0.635295	−	0.0667722i
$634$		0			0
$635$	−987.050	+	1358.56i	−1.55441	+	2.13946i
$636$		0			0
$637$	175.238	−	824.429i	0.275099	−	1.29424i
$638$		0			0
$639$	0.377186	+	3.58868i	0.000590275	+	0.00561609i
$640$		0			0
$641$	−259.863	+	583.662i	−0.405403	+	0.910550i	0.589315	+	0.807903i	$0.299398\pi$
$641$	−259.863	+	583.662i	−0.405403	+	0.910550i	−0.994718	+	0.102647i	$0.967269\pi$
$642$		0			0
$643$	529.017	−	171.888i	0.822733	−	0.267322i	0.132752	−	0.991149i	$-0.457619\pi$
$643$	529.017	−	171.888i	0.822733	−	0.267322i	0.689981	+	0.723827i	$0.257619\pi$
$644$		0			0
$645$	473.310	−	819.798i	0.733815	−	1.27100i
$646$		0			0
$647$	844.092	+	274.262i	1.30462	+	0.423898i	0.877188	−	0.480147i	$-0.159417\pi$
$647$	844.092	+	274.262i	1.30462	+	0.423898i	0.427437	+	0.904045i	$0.359417\pi$
$648$		0			0
$649$	536.892	+	738.968i	0.827260	+	1.13863i
$650$		0			0
$651$	237.754	−	209.898i	0.365213	−	0.322424i
$652$		0			0
$653$	−147.992	+	107.523i	−0.226635	+	0.164660i	−0.695308	−	0.718712i	$-0.744732\pi$
$653$	−147.992	+	107.523i	−0.226635	+	0.164660i	0.468673	+	0.883371i	$0.344732\pi$
$654$		0			0
$655$	−217.733	+	670.114i	−0.332417	+	1.02307i
$656$		0			0
$657$	−3.84596	−	2.22047i	−0.00585382	−	0.00337970i
$658$		0			0
$659$	72.2512	+	222.366i	0.109638	+	0.337430i	0.990791	−	0.135401i	$-0.0432322\pi$
$659$	72.2512	+	222.366i	0.109638	+	0.337430i	−0.881153	+	0.472831i	$0.843232\pi$
$660$		0			0
$661$	702.853	+	312.930i	1.06332	+	0.473420i	0.862420	−	0.506193i	$-0.168947\pi$
$661$	702.853	+	312.930i	1.06332	+	0.473420i	0.200898	+	0.979612i	$0.435614\pi$
$662$		0			0
$663$	−2.64333	+	0.277826i	−0.00398693	+	0.000419043i
$664$		0			0
$665$	−89.4824	−	19.0201i	−0.134560	−	0.0286016i
$666$		0			0
$667$	19.2634	+	13.9957i	0.0288807	+	0.0209831i
$668$		0			0
$669$	−7.40742	+	70.4769i	−0.0110724	+	0.105347i
$670$		0			0
$671$	666.544	−	141.678i	0.993359	−	0.211145i
$672$		0			0
$673$	−262.686	−	236.523i	−0.390321	−	0.351446i	0.450484	−	0.892784i	$-0.351251\pi$
$673$	−262.686	−	236.523i	−0.390321	−	0.351446i	−0.840805	+	0.541338i	$0.817918\pi$
$674$		0			0
$675$	1251.69	−	1127.02i	1.85435	−	1.66967i
$676$		0			0
$677$	680.022	−	392.611i	1.00446	−	0.579927i	0.0948977	−	0.995487i	$-0.469748\pi$
$677$	680.022	−	392.611i	1.00446	−	0.579927i	0.909566	+	0.415560i	$0.136414\pi$
$678$		0			0
$679$	281.528	−	125.344i	0.414621	−	0.184601i
$680$		0			0
$681$		−	998.396i		−	1.46607i
$682$		0			0
$683$	58.8828			0.0862120			0.0431060	−	0.999071i	$-0.486275\pi$
$683$	58.8828			0.0862120			0.0431060	+	0.999071i	$0.486275\pi$
$684$		0			0
$685$	391.869	+	880.152i	0.572072	+	1.28489i
$686$		0			0
$687$	−150.224	−	260.196i	−0.218667	−	0.378743i
$688$		0			0
$689$	−985.903	−	1094.96i	−1.43092	−	1.58920i
$690$		0			0
$691$	59.4773	−	66.0563i	0.0860743	−	0.0955952i	−0.698569	−	0.715543i	$-0.746179\pi$
$691$	59.4773	−	66.0563i	0.0860743	−	0.0955952i	0.784643	+	0.619948i	$0.212846\pi$
$692$		0			0
$693$	−0.272143	−	1.28033i	−0.000392703	−	0.00184752i
$694$		0			0
$695$	−700.762	−	73.6531i	−1.00829	−	0.105976i
$696$		0			0
$697$	−0.779021	+	1.07223i	−0.00111768	+	0.00153835i
$698$		0			0
$699$	−32.9230	+	154.890i	−0.0471001	+	0.221588i
$700$		0			0
$701$	7.33547	+	69.7923i	0.0104643	+	0.0995611i	0.998507	−	0.0546169i	$-0.0173938\pi$
$701$	7.33547	+	69.7923i	0.0104643	+	0.0995611i	−0.988043	+	0.154178i	$0.950727\pi$
$702$		0			0
$703$	53.4344	−	120.016i	0.0760091	−	0.170719i
$704$		0			0
$705$	958.175	−	311.330i	1.35911	−	0.441603i
$706$		0			0
$707$	−7.22256	+	12.5098i	−0.0102158	+	0.0176943i
$708$		0			0
$709$	−29.2646	−	9.50865i	−0.0412759	−	0.0134114i	0.288306	−	0.957538i	$-0.406908\pi$
$709$	−29.2646	−	9.50865i	−0.0412759	−	0.0134114i	−0.329582	+	0.944127i	$0.606908\pi$
$710$		0			0
$711$	−2.53147	−	3.48427i	−0.00356044	−	0.00490052i
$712$		0			0
$713$	−308.008	−	35.4236i	−0.431988	−	0.0496824i
$714$		0			0
$715$	1406.77	−	1022.08i	1.96751	−	1.42948i
$716$		0			0
$717$	267.438	−	823.090i	0.372996	−	1.14796i
$718$		0			0
$719$	14.0844	+	8.13165i	0.0195889	+	0.0113097i	0.509762	−	0.860315i	$-0.329733\pi$
$719$	14.0844	+	8.13165i	0.0195889	+	0.0113097i	−0.490174	+	0.871625i	$0.663067\pi$
$720$		0			0
$721$	101.155	+	311.324i	0.140299	+	0.431795i
$722$		0			0
$723$	777.543	+	346.185i	1.07544	+	0.478817i
$724$		0			0
$725$	147.328	−	15.4848i	0.203211	−	0.0213583i
$726$		0			0
$727$	1319.45	+	280.457i	1.81492	+	0.385773i	0.985061	−	0.172203i	$-0.0550886\pi$
$727$	1319.45	+	280.457i	1.81492	+	0.385773i	0.829857	+	0.557976i	$0.188422\pi$
$728$		0			0
$729$	592.786	+	430.684i	0.813149	+	0.590787i
$730$		0			0
$731$	0.139225	−	1.32463i	0.000190458	−	0.00181209i
$732$		0			0
$733$	−689.831	+	146.628i	−0.941107	+	0.200038i	−0.652826	−	0.757508i	$-0.726417\pi$
$733$	−689.831	+	146.628i	−0.941107	+	0.200038i	−0.288280	+	0.957546i	$0.593083\pi$
$734$		0			0
$735$	−774.839	−	697.668i	−1.05420	−	0.949208i
$736$		0			0
$737$	−713.551	+	642.484i	−0.968183	+	0.871756i
$738$		0			0
$739$	672.990	−	388.551i	0.910677	−	0.525780i	0.0300281	−	0.999549i	$-0.490440\pi$
$739$	672.990	−	388.551i	0.910677	−	0.525780i	0.880649	+	0.473769i	$0.157107\pi$
$740$		0			0
$741$	176.915	−	78.7675i	0.238751	−	0.106299i
$742$		0			0
$743$			717.140i			0.965196i	0.875842	+	0.482598i	$0.160307\pi$
$743$			717.140i			0.965196i	−0.875842	+	0.482598i	$0.839693\pi$
$744$		0			0
$745$	−1400.98			−1.88051
$746$		0			0
$747$	−1.38328	−	3.10689i	−0.00185177	−	0.00415915i
$748$		0			0
$749$	−268.100	−	464.363i	−0.357944	−	0.619977i
$750$		0			0
$751$	434.226	+	482.257i	0.578197	+	0.642153i	0.959303	−	0.282378i	$-0.0911233\pi$
$751$	434.226	+	482.257i	0.578197	+	0.642153i	−0.381106	+	0.924531i	$0.624457\pi$
$752$		0			0
$753$	−403.457	+	448.084i	−0.535799	+	0.595065i
$754$		0			0
$755$	−169.913	−	799.378i	−0.225051	−	1.05878i
$756$		0			0
$757$	543.615	+	57.1363i	0.718118	+	0.0754772i	0.456537	−	0.889704i	$-0.349090\pi$
$757$	543.615	+	57.1363i	0.718118	+	0.0754772i	0.261581	+	0.965182i	$0.415756\pi$
$758$		0			0
$759$	144.976	−	199.543i	0.191010	−	0.262902i
$760$		0			0
$761$	−95.5361	+	449.462i	−0.125540	+	0.590621i	0.869734	+	0.493520i	$0.164290\pi$
$761$	−95.5361	+	449.462i	−0.125540	+	0.590621i	−0.995275	+	0.0971003i	$0.969043\pi$
$762$		0			0
$763$	−14.9278	−	142.028i	−0.0195646	−	0.186145i
$764$		0			0
$765$	0.00693792	−	0.0155828i	9.06918e−6	−	2.03697e-5i
$766$		0			0
$767$	−2381.05	+	773.651i	−3.10437	+	1.00867i
$768$		0			0
$769$	−150.884	+	261.339i	−0.196208	+	0.339843i	−0.947296	−	0.320360i	$-0.896196\pi$
$769$	−150.884	+	261.339i	−0.196208	+	0.339843i	0.751088	+	0.660203i	$0.229530\pi$
$770$		0			0
$771$	84.0610	+	27.3131i	0.109029	+	0.0354255i
$772$		0			0
$773$	269.949	+	371.553i	0.349222	+	0.480663i	0.947107	−	0.320919i	$-0.103992\pi$
$773$	269.949	+	371.553i	0.349222	+	0.480663i	−0.597884	+	0.801582i	$0.703992\pi$
$774$		0			0
$775$	−1571.53	+	1118.45i	−2.02778	+	1.44316i
$776$		0			0
$777$	−379.538	+	275.750i	−0.488466	+	0.354891i
$778$		0			0
$779$	29.8407	−	91.8402i	0.0383064	−	0.117895i
$780$		0			0
$781$	554.491	+	320.136i	0.709976	+	0.409905i
$782$		0			0
$783$	19.9150	+	61.2922i	0.0254343	+	0.0782787i
$784$		0			0
$785$	−620.523	−	276.275i	−0.790475	−	0.351942i
$786$		0			0
$787$	52.0847	−	5.47432i	0.0661813	−	0.00695594i	−0.0713799	−	0.997449i	$-0.522740\pi$
$787$	52.0847	−	5.47432i	0.0661813	−	0.00695594i	0.137561	+	0.990493i	$0.456074\pi$
$788$		0			0
$789$	161.971	+	34.4280i	0.205287	+	0.0436350i
$790$		0			0
$791$	65.2893	+	47.4355i	0.0825402	+	0.0599690i
$792$		0			0
$793$	−195.233	+	1857.52i	−0.246196	+	2.34240i
$794$		0			0
$795$	−1782.86	+	378.958i	−2.24259	+	0.476677i
$796$		0			0
$797$	653.328	+	588.259i	0.819734	+	0.738092i	0.968025	−	0.250852i	$-0.0807107\pi$
$797$	653.328	+	588.259i	0.819734	+	0.738092i	−0.148292	+	0.988944i	$0.547377\pi$
$798$		0			0
$799$	1.05346	−	0.948539i	0.00131847	−	0.00118716i
$800$		0			0
$801$	3.75425	−	2.16752i	0.00468695	−	0.00270601i
$802$		0			0
$803$	−719.859	+	320.502i	−0.896462	+	0.399131i
$804$		0			0
$805$		−	319.354i		−	0.396713i
$806$		0			0
$807$	−696.445			−0.863005
$808$		0			0
$809$	−129.416	−	290.674i	−0.159971	−	0.359300i	0.815722	−	0.578445i	$-0.196340\pi$
$809$	−129.416	−	290.674i	−0.159971	−	0.359300i	−0.975692	+	0.219144i	$0.929673\pi$
$810$		0			0
$811$	293.546	+	508.437i	0.361956	+	0.626926i	0.988283	−	0.152634i	$-0.0487757\pi$
$811$	293.546	+	508.437i	0.361956	+	0.626926i	−0.626327	+	0.779561i	$0.715442\pi$
$812$		0			0
$813$	133.230	+	147.966i	0.163874	+	0.182001i
$814$		0			0
$815$	427.081	−	474.321i	0.524026	−	0.581990i
$816$		0			0
$817$	20.1770	+	94.9254i	0.0246965	+	0.116188i
$818$		0			0
$819$	3.56802	+	0.375014i	0.00435656	+	0.000457892i
$820$		0			0
$821$	445.657	−	613.395i	0.542823	−	0.747131i	−0.446194	−	0.894936i	$-0.647221\pi$
$821$	445.657	−	613.395i	0.542823	−	0.747131i	0.989017	+	0.147805i	$0.0472208\pi$
$822$		0			0
$823$	45.8529	−	215.721i	0.0557143	−	0.262115i	−0.941471	−	0.337095i	$-0.890556\pi$
$823$	45.8529	−	215.721i	0.0557143	−	0.262115i	0.997185	+	0.0749794i	$0.0238891\pi$
$824$		0			0
$825$	−160.401	−	1526.11i	−0.194425	−	1.84983i
$826$		0			0
$827$	478.036	−	1073.69i	0.578036	−	1.29829i	−0.353769	−	0.935333i	$-0.615100\pi$
$827$	478.036	−	1073.69i	0.578036	−	1.29829i	0.931805	−	0.362958i	$-0.118233\pi$
$828$		0			0
$829$	−420.692	+	136.691i	−0.507469	+	0.164887i	−0.551551	−	0.834141i	$-0.685964\pi$
$829$	−420.692	+	136.691i	−0.507469	+	0.164887i	0.0440818	+	0.999028i	$0.485964\pi$
$830$		0			0
$831$	513.973	−	890.227i	0.618499	−	1.07127i
$832$		0			0
$833$	−1.39524	−	0.453342i	−0.00167496	−	0.000544228i
$834$		0			0
$835$	−1741.57	−	2397.07i	−2.08571	−	2.87074i
$836$		0			0
$837$	−618.082	−	567.574i	−0.738450	−	0.678105i
$838$		0			0
$839$	833.786	−	605.781i	0.993786	−	0.722028i	0.0330391	−	0.999454i	$-0.489481\pi$
$839$	833.786	−	605.781i	0.993786	−	0.722028i	0.960747	+	0.277426i	$0.0894814\pi$
$840$		0			0
$841$	258.132	−	794.448i	0.306934	−	0.944647i
$842$		0			0
$843$	1288.15	+	743.712i	1.52805	+	0.882220i
$844$		0			0
$845$	985.058	+	3031.70i	1.16575	+	3.58781i
$846$		0			0
$847$	165.765	+	73.8032i	0.195708	+	0.0871349i
$848$		0			0
$849$	−1542.50	+	162.123i	−1.81684	+	0.190957i
$850$		0			0
$851$	448.592	+	95.3513i	0.527136	+	0.112046i
$852$		0			0
$853$	−972.347	−	706.451i	−1.13991	−	0.828196i	−0.152807	−	0.988256i	$-0.548831\pi$
$853$	−972.347	−	706.451i	−1.13991	−	0.828196i	−0.987107	+	0.160060i	$0.948831\pi$
$854$		0			0
$855$	−0.129911	+	1.23602i	−0.000151943	+	0.00144564i
$856$		0			0
$857$	246.655	−	52.4282i	0.287812	−	0.0611764i	−0.0617432	−	0.998092i	$-0.519666\pi$
$857$	246.655	−	52.4282i	0.287812	−	0.0611764i	0.349555	+	0.936916i	$0.386333\pi$
$858$		0			0
$859$	471.061	+	424.145i	0.548383	+	0.493766i	0.896111	−	0.443829i	$-0.146380\pi$
$859$	471.061	+	424.145i	0.548383	+	0.493766i	−0.347729	+	0.937595i	$0.613047\pi$
$860$		0			0
$861$	−256.265	+	230.742i	−0.297637	+	0.267993i
$862$		0			0
$863$	−224.016	+	129.336i	−0.259579	+	0.149868i	−0.624142	−	0.781311i	$-0.714552\pi$
$863$	−224.016	+	129.336i	−0.259579	+	0.149868i	0.364564	+	0.931178i	$0.381218\pi$
$864$		0			0
$865$	2248.92	−	1001.29i	2.59991	−	1.15755i
$866$		0			0
$867$		−	864.755i		−	0.997411i
$868$		0			0
$869$	−764.183			−0.879382
$870$		0			0
$871$	−1070.43	−	2404.23i	−1.22897	−	2.76031i
$872$		0			0
$873$	−2.09334	−	3.62577i	−0.00239787	−	0.00415324i
$874$		0			0
$875$	−795.307	−	883.278i	−0.908922	−	1.00946i
$876$		0			0
$877$	−580.394	+	644.593i	−0.661795	+	0.734998i	−0.976814	−	0.214087i	$-0.931322\pi$
$877$	−580.394	+	644.593i	−0.661795	+	0.734998i	0.315020	+	0.949085i	$0.397989\pi$
$878$		0			0
$879$	43.1576	+	203.041i	0.0490986	+	0.230991i
$880$		0			0
$881$	−370.956	−	38.9890i	−0.421062	−	0.0442554i	−0.108372	−	0.994110i	$-0.534564\pi$
$881$	−370.956	−	38.9890i	−0.421062	−	0.0442554i	−0.312691	+	0.949855i	$0.601230\pi$
$882$		0			0
$883$	−189.737	+	261.151i	−0.214878	+	0.295754i	−0.902826	−	0.430006i	$-0.858512\pi$
$883$	−189.737	+	261.151i	−0.214878	+	0.295754i	0.687948	+	0.725760i	$0.258512\pi$
$884$		0			0
$885$	−643.918	+	3029.40i	−0.727591	+	3.42305i
$886$		0			0
$887$	−41.7428	−	397.156i	−0.0470607	−	0.447752i	−0.992526	−	0.122031i	$-0.961059\pi$
$887$	−41.7428	−	397.156i	−0.0470607	−	0.447752i	0.945466	−	0.325722i	$-0.105607\pi$
$888$		0			0
$889$	−250.049	+	561.620i	−0.281270	+	0.631743i
$890$		0			0
$891$	631.627	−	205.228i	0.708896	−	0.230334i
$892$		0			0
$893$	−51.6429	+	89.4481i	−0.0578308	+	0.100166i
$894$		0			0
$895$	197.370	+	64.1293i	0.220525	+	0.0716529i
$896$		0			0
$897$	397.367	+	546.929i	0.442996	+	0.609732i
$898$		0			0
$899$	−14.6377	−	72.3387i	−0.0162822	−	0.0804658i
$900$		0			0
$901$	−2.07480	+	1.50743i	−0.00230277	+	0.00167306i
$902$		0			0
$903$	107.090	−	329.590i	0.118594	−	0.364994i
$904$		0			0
$905$	−325.936	−	188.179i	−0.360150	−	0.207933i
$906$		0			0
$907$	49.8439	+	153.404i	0.0549547	+	0.169133i	0.974767	−	0.223226i	$-0.0716589\pi$
$907$	49.8439	+	153.404i	0.0549547	+	0.169133i	−0.919812	+	0.392359i	$0.871659\pi$
$908$		0			0
$909$	0.179280	+	0.0798204i	0.000197227	+	8.78112e-5i
$910$		0			0
$911$	−851.814	+	89.5292i	−0.935032	+	0.0982758i	−0.559775	−	0.828645i	$-0.689112\pi$
$911$	−851.814	+	89.5292i	−0.935032	+	0.0982758i	−0.375257	+	0.926921i	$0.622446\pi$
$912$		0			0
$913$	−590.259	−	125.464i	−0.646505	−	0.137419i
$914$		0			0
$915$	1869.24	+	1358.08i	2.04289	+	1.48425i
$916$		0			0
$917$	−26.9630	+	256.536i	−0.0294035	+	0.279756i
$918$		0			0
$919$	−258.290	+	54.9012i	−0.281055	+	0.0597402i	−0.346282	−	0.938130i	$-0.612556\pi$
$919$	−258.290	+	54.9012i	−0.281055	+	0.0597402i	0.0652272	+	0.997870i	$0.479223\pi$
$920$		0			0
$921$	−3.80179	−	3.42315i	−0.00412790	−	0.00371678i
$922$		0			0
$923$	−1304.16	+	1174.27i	−1.41296	+	1.27224i
$924$		0			0
$925$	2470.99	−	1426.63i	2.67135	−	1.54230i
$926$		0			0
$927$	4.06271	−	1.80883i	0.00438264	−	0.00195128i
$928$		0			0
$929$			418.814i			0.450822i	0.974264	+	0.225411i	$0.0723726\pi$
$929$			418.814i			0.450822i	−0.974264	+	0.225411i	$0.927627\pi$
$930$		0			0
$931$	106.891			0.114813
$932$		0			0
$933$	−45.7378	−	102.729i	−0.0490222	−	0.110106i
$934$		0			0
$935$	−1.51332	−	2.62114i	−0.00161852	−	0.00280336i
$936$		0			0
$937$	357.977	+	397.574i	0.382046	+	0.424305i	0.903242	−	0.429132i	$-0.141181\pi$
$937$	357.977	+	397.574i	0.382046	+	0.424305i	−0.521196	+	0.853437i	$0.674514\pi$
$938$		0			0
$939$	−194.996	+	216.565i	−0.207663	+	0.230633i
$940$		0			0
$941$	−77.7968	−	366.005i	−0.0826746	−	0.388954i	0.917282	−	0.398238i	$-0.130378\pi$
$941$	−77.7968	−	366.005i	−0.0826746	−	0.388954i	−0.999957	+	0.00928412i	$0.997045\pi$
$942$		0			0
$943$	335.259	+	35.2372i	0.355524	+	0.0373671i
$944$		0			0
$945$	508.059	−	699.283i	0.537628	−	0.739982i
$946$		0			0
$947$	252.782	−	1189.25i	0.266929	−	1.25580i	−0.616543	−	0.787321i	$-0.711467\pi$
$947$	252.782	−	1189.25i	0.266929	−	1.25580i	0.883473	−	0.468483i	$-0.155199\pi$
$948$		0			0
$949$	−225.760	−	2147.96i	−0.237892	−	2.26339i
$950$		0			0
$951$	163.294	−	366.764i	0.171707	−	0.385661i
$952$		0			0
$953$	−1444.31	+	469.283i	−1.51554	+	0.492428i	−0.944504	−	0.328500i	$-0.893457\pi$
$953$	−1444.31	+	469.283i	−1.51554	+	0.492428i	−0.571032	+	0.820928i	$0.693457\pi$
$954$		0			0
$955$	−1379.54	+	2389.44i	−1.44455	+	2.50203i
$956$		0			0
$957$	55.8412	+	18.1439i	0.0583503	+	0.0189592i
$958$		0			0
$959$	207.318	+	285.349i	0.216182	+	0.297549i
$960$		0			0
$961$	628.935	+	726.610i	0.654459	+	0.756098i
$962$		0			0
$963$	−5.89337	+	4.28178i	−0.00611980	+	0.00444629i
$964$		0			0
$965$	−712.749	+	2193.62i	−0.738600	+	2.27318i
$966$		0			0
$967$	−981.130	−	566.456i	−1.01461	−	0.585787i	−0.102074	−	0.994777i	$-0.532548\pi$
$967$	−981.130	−	566.456i	−1.01461	−	0.585787i	−0.912539	+	0.408990i	$0.865881\pi$
$968$		0			0
$969$	−0.104162	−	0.320579i	−0.000107495	−	0.000330835i
$970$		0			0
$971$	30.2495	+	13.4680i	0.0311530	+	0.0138702i	0.422254	−	0.906478i	$-0.361239\pi$
$971$	30.2495	+	13.4680i	0.0311530	+	0.0138702i	−0.391101	+	0.920348i	$0.627906\pi$
$972$		0			0
$973$	−256.544	+	26.9639i	−0.263663	+	0.0277121i
$974$		0			0
$975$	4114.07	+	874.472i	4.21956	+	0.896894i
$976$		0			0
$977$	1146.45	+	832.945i	1.17344	+	0.852554i	0.991417	−	0.130740i	$-0.0417354\pi$
$977$	1146.45	+	832.945i	1.17344	+	0.852554i	0.182023	+	0.983294i	$0.441735\pi$
$978$		0			0
$979$	80.4027	−	764.980i	0.0821273	−	0.781389i
$980$		0			0
$981$	−1.89777	+	0.403384i	−0.00193453	+	0.000411197i
$982$		0			0
$983$	458.445	+	412.786i	0.466374	+	0.419925i	0.868523	−	0.495650i	$-0.165070\pi$
$983$	458.445	+	412.786i	0.466374	+	0.419925i	−0.402149	+	0.915574i	$0.631737\pi$
$984$		0			0
$985$	653.580	−	588.486i	0.663533	−	0.597448i
$986$		0			0
$987$	319.419	−	184.417i	0.323626	−	0.186846i
$988$		0			0
$989$	−309.491	+	137.794i	−0.312933	+	0.139327i
$990$		0			0
$991$		−	897.405i		−	0.905555i	−0.891623	−	0.452778i	$-0.850433\pi$
$991$		−	897.405i		−	0.905555i	0.891623	−	0.452778i	$-0.149567\pi$
$992$		0			0
$993$	1703.27			1.71528
$994$		0			0
$995$	−156.832	−	352.250i	−0.157620	−	0.354021i
$996$		0			0
$997$	−493.426	−	854.639i	−0.494911	−	0.857210i	0.505072	−	0.863077i	$-0.331466\pi$
$997$	−493.426	−	854.639i	−0.494911	−	0.857210i	−0.999983	+	0.00586678i	$0.998133\pi$
$998$		0			0
$999$	830.579	+	922.452i	0.831411	+	0.923375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.3.o.a.13.2	✓	40
31.12	odd	30	inner	124.3.o.a.105.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.3.o.a.13.2	✓	40	1.1	even	1	trivial
124.3.o.a.105.2	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)

\(f(q)\)	\(=\)	\(q+(-1.21706 - 2.73355i) q^{3} +(4.66965 + 8.08807i) q^{5} +(2.28779 + 2.54085i) q^{7} +(0.0310810 - 0.0345190i) q^{9} +O(q^{10})\)	\(q+(-1.21706 - 2.73355i) q^{3} +(4.66965 + 8.08807i) q^{5} +(2.28779 + 2.54085i) q^{7} +(0.0310810 - 0.0345190i) q^{9} +(-1.71359 - 8.06181i) q^{11} +(22.4666 + 2.36133i) q^{13} +(16.4259 - 22.6084i) q^{15} +(0.00817516 - 0.0384611i) q^{17} +(0.299466 + 2.84923i) q^{19} +(4.16118 - 9.34616i) q^{21} +(-9.51173 + 3.09055i) q^{23} +(-31.1112 + 53.8862i) q^{25} +(-25.7444 - 8.36485i) q^{27} +(-1.39940 - 1.92611i) q^{29} +(28.1952 + 12.8854i) q^{31} +(-19.9519 + 14.4959i) q^{33} +(-9.86738 + 30.3687i) q^{35} +(-39.7123 - 22.9279i) q^{37} +(-20.8883 - 64.2875i) q^{39} +(-30.7924 - 13.7096i) q^{41} +(33.6883 - 3.54078i) q^{43} +(0.424329 + 0.0901940i) q^{45} +(29.1665 + 21.1907i) q^{47} +(3.89997 - 37.1057i) q^{49} +(-0.115085 + 0.0244621i) q^{51} +(-48.4701 - 43.6427i) q^{53} +(57.2026 - 51.5054i) q^{55} +(7.42406 - 4.28629i) q^{57} +(-101.244 + 45.0769i) q^{59} +82.6793i q^{61} +0.158815 q^{63} +(85.8124 + 192.738i) q^{65} +(-58.2497 - 100.891i) q^{67} +(20.0245 + 22.2395i) q^{69} +(-51.9813 + 57.7310i) q^{71} +(-19.8778 - 93.5177i) q^{73} +(185.165 + 19.4616i) q^{75} +(16.5635 - 22.7977i) q^{77} +(19.2774 - 90.6930i) q^{79} +(8.42288 + 80.1384i) q^{81} +(29.7799 - 66.8869i) q^{83} +(0.349251 - 0.113479i) q^{85} +(-3.56197 + 6.16952i) q^{87} +(88.7594 + 28.8397i) q^{89} +(45.3991 + 62.4864i) q^{91} +(0.907725 - 92.7553i) q^{93} +(-21.6464 + 15.7270i) q^{95} +(27.8527 - 85.7219i) q^{97} +(-0.331546 - 0.191418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} - 3 q^{5} + 19 q^{7} - 2 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more