LMFDB - Embedded newform 117.4.g.f.55.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + \cdots + 24920064 $ x^16 + 52x^14 + 1899x^12 + 33440x^10 + 424113x^8 + 2869882x^6 + 13705540x^4 + 21016320*x^2 + 24920064
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.6
Root			$1.37814 + 2.38701i$ of defining polynomial
Character	$\chi$	$=$	117.55
Dual form			117.4.g.f.100.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37814 + 2.38701i) q^{2} +(0.201468 - 0.348954i) q^{4} -0.313209 q^{5} +(-14.2830 + 24.7388i) q^{7} +23.1608 q^{8} +O(q^{10})$	\(q+(1.37814 + 2.38701i) q^{2} +(0.201468 - 0.348954i) q^{4} -0.313209 q^{5} +(-14.2830 + 24.7388i) q^{7} +23.1608 q^{8} +(-0.431646 - 0.747632i) q^{10} +(31.6086 + 54.7478i) q^{11} +(-2.26982 + 46.8172i) q^{13} -78.7357 q^{14} +(30.3071 + 52.4934i) q^{16} +(49.4135 - 85.5867i) q^{17} +(7.24486 - 12.5485i) q^{19} +(-0.0631018 + 0.109295i) q^{20} +(-87.1222 + 150.900i) q^{22} +(-7.19499 - 12.4621i) q^{23} -124.902 q^{25} +(-114.881 + 59.1025i) q^{26} +(5.75514 + 9.96819i) q^{28} +(-98.1415 - 169.986i) q^{29} +118.691 q^{31} +(9.10860 - 15.7766i) q^{32} +272.395 q^{34} +(4.47356 - 7.74843i) q^{35} +(-159.557 - 276.361i) q^{37} +39.9377 q^{38} -7.25418 q^{40} +(173.053 + 299.737i) q^{41} +(34.7427 - 60.1761i) q^{43} +25.4726 q^{44} +(19.8314 - 34.3490i) q^{46} +101.875 q^{47} +(-236.507 - 409.642i) q^{49} +(-172.132 - 298.142i) q^{50} +(15.8797 + 10.2242i) q^{52} +594.823 q^{53} +(-9.90012 - 17.1475i) q^{55} +(-330.806 + 572.972i) q^{56} +(270.505 - 468.529i) q^{58} +(-102.237 + 177.079i) q^{59} +(107.989 - 187.043i) q^{61} +(163.572 + 283.315i) q^{62} +535.125 q^{64} +(0.710929 - 14.6636i) q^{65} +(-34.3025 - 59.4136i) q^{67} +(-19.9105 - 34.4860i) q^{68} +24.6607 q^{70} +(473.121 - 819.469i) q^{71} -779.872 q^{73} +(439.784 - 761.727i) q^{74} +(-2.91922 - 5.05624i) q^{76} -1805.86 q^{77} +240.022 q^{79} +(-9.49245 - 16.4414i) q^{80} +(-476.982 + 826.158i) q^{82} -855.576 q^{83} +(-15.4768 + 26.8065i) q^{85} +191.521 q^{86} +(732.082 + 1268.00i) q^{88} +(632.029 + 1094.71i) q^{89} +(-1125.78 - 724.842i) q^{91} -5.79825 q^{92} +(140.398 + 243.176i) q^{94} +(-2.26916 + 3.93030i) q^{95} +(-331.145 + 573.560i) q^{97} +(651.879 - 1129.09i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 40 q^{4} + 22 q^{7}+O(q^{10}) $ 16 * q - 40 * q^4 + 22 * q^7	$ 16 q - 40 q^{4} + 22 q^{7} - 36 q^{10} + 36 q^{13} - 204 q^{16} - 244 q^{19} - 136 q^{22} + 708 q^{25} + 452 q^{28} + 484 q^{31} - 2584 q^{34} - 1018 q^{37} + 3400 q^{40} - 74 q^{43} + 896 q^{46} - 298 q^{49} - 1676 q^{52} - 1300 q^{55} - 812 q^{58} - 1148 q^{61} + 7272 q^{64} + 2198 q^{67} + 4400 q^{70} - 4352 q^{73} - 6936 q^{76} + 3724 q^{79} - 5436 q^{82} + 890 q^{85} - 3528 q^{88} - 4754 q^{91} + 3104 q^{94} + 4370 q^{97}+O(q^{100}) $ 16 * q - 40 * q^4 + 22 * q^7 - 36 * q^10 + 36 * q^13 - 204 * q^16 - 244 * q^19 - 136 * q^22 + 708 * q^25 + 452 * q^28 + 484 * q^31 - 2584 * q^34 - 1018 * q^37 + 3400 * q^40 - 74 * q^43 + 896 * q^46 - 298 * q^49 - 1676 * q^52 - 1300 * q^55 - 812 * q^58 - 1148 * q^61 + 7272 * q^64 + 2198 * q^67 + 4400 * q^70 - 4352 * q^73 - 6936 * q^76 + 3724 * q^79 - 5436 * q^82 + 890 * q^85 - 3528 * q^88 - 4754 * q^91 + 3104 * q^94 + 4370 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.37814	+	2.38701i	0.487246	+	0.843934i	0.999892	−	0.0146655i	$-0.00466834\pi$
$2$	1.37814	+	2.38701i	0.487246	+	0.843934i	−0.512647	+	0.858600i	$0.671335\pi$
$3$		0			0
$3$		0			0
$4$	0.201468	−	0.348954i	0.0251836	−	0.0436192i
$5$	−0.313209			−0.0280143			−0.0140071	−	0.999902i	$-0.504459\pi$
$5$	−0.313209			−0.0280143			−0.0140071	+	0.999902i	$0.504459\pi$
$6$		0			0
$7$	−14.2830	+	24.7388i	−0.771208	+	1.33577i	0.165693	+	0.986177i	$0.447014\pi$
$7$	−14.2830	+	24.7388i	−0.771208	+	1.33577i	−0.936901	+	0.349595i	$0.886319\pi$
$8$	23.1608			1.02357
$9$		0			0
$10$	−0.431646	−	0.747632i	−0.0136498	−	0.0236422i
$11$	31.6086	+	54.7478i	0.866397	+	1.50064i	0.865654	+	0.500644i	$0.166903\pi$
$11$	31.6086	+	54.7478i	0.866397	+	1.50064i	0.000743312		1.00000i	$0.499763\pi$
$12$		0			0
$13$	−2.26982	+	46.8172i	−0.0484258	+	0.998827i
$13$	−2.26982	+	46.8172i	−0.0484258	+	0.998827i
$14$	−78.7357			−1.50307
$15$		0			0
$16$	30.3071	+	52.4934i	0.473548	+	0.820209i
$17$	49.4135	−	85.5867i	0.704973	−	1.22105i	−0.261729	−	0.965142i	$-0.584292\pi$
$17$	49.4135	−	85.5867i	0.704973	−	1.22105i	0.966701	−	0.255907i	$-0.0823742\pi$
$18$		0			0
$19$	7.24486	−	12.5485i	0.0874782	−	0.151517i	−0.818966	−	0.573842i	$-0.805453\pi$
$19$	7.24486	−	12.5485i	0.0874782	−	0.151517i	0.906445	+	0.422325i	$0.138786\pi$
$20$	−0.0631018	+	0.109295i	−0.000705499	+	0.00122196i
$21$		0			0
$22$	−87.1222	+	150.900i	−0.844296	+	1.46236i
$23$	−7.19499	−	12.4621i	−0.0652286	−	0.112979i	0.831567	−	0.555425i	$-0.187444\pi$
$23$	−7.19499	−	12.4621i	−0.0652286	−	0.112979i	−0.896795	+	0.442446i	$0.854111\pi$
$24$		0			0
$25$	−124.902			−0.999215
$26$	−114.881	+	59.1025i	−0.866539	+	0.445806i
$27$		0			0
$28$	5.75514	+	9.96819i	0.0388435	+	0.0672790i
$29$	−98.1415	−	169.986i	−0.628428	−	1.08847i	−0.987867	−	0.155301i	$-0.950365\pi$
$29$	−98.1415	−	169.986i	−0.628428	−	1.08847i	0.359439	−	0.933169i	$-0.382968\pi$
$30$		0			0
$31$	118.691			0.687661			0.343830	−	0.939032i	$-0.388276\pi$
$31$	118.691			0.687661			0.343830	+	0.939032i	$0.388276\pi$
$32$	9.10860	−	15.7766i	0.0503184	−	0.0871540i
$33$		0			0
$34$	272.395			1.37398
$35$	4.47356	−	7.74843i	0.0216048	−	0.0374207i
$36$		0			0
$37$	−159.557	−	276.361i	−0.708947	−	1.22793i	−0.965248	−	0.261335i	$-0.915837\pi$
$37$	−159.557	−	276.361i	−0.708947	−	1.22793i	0.256302	−	0.966597i	$-0.417496\pi$
$38$	39.9377			0.170493
$39$		0			0
$40$	−7.25418			−0.0286747
$41$	173.053	+	299.737i	0.659180	+	1.14173i	0.980828	+	0.194873i	$0.0624296\pi$
$41$	173.053	+	299.737i	0.659180	+	1.14173i	−0.321649	+	0.946859i	$0.604237\pi$
$42$		0			0
$43$	34.7427	−	60.1761i	0.123214	−	0.213413i	−0.797819	−	0.602897i	$-0.794013\pi$
$43$	34.7427	−	60.1761i	0.123214	−	0.213413i	0.921033	+	0.389483i	$0.127346\pi$
$44$	25.4726			0.0872758
$45$		0			0
$46$	19.8314	−	34.3490i	0.0635647	−	0.110097i
$47$	101.875			0.316170			0.158085	−	0.987426i	$-0.449468\pi$
$47$	101.875			0.316170			0.158085	+	0.987426i	$0.449468\pi$
$48$		0			0
$49$	−236.507	−	409.642i	−0.689525	−	1.19429i
$50$	−172.132	−	298.142i	−0.486863	−	0.843272i
$51$		0			0
$52$	15.8797	+	10.2242i	0.0423485	+	0.0272663i
$53$	594.823			1.54161			0.770804	−	0.637072i	$-0.219855\pi$
$53$	594.823			1.54161			0.770804	+	0.637072i	$0.219855\pi$
$54$		0			0
$55$	−9.90012	−	17.1475i	−0.0242715	−	0.0420394i
$56$	−330.806	+	572.972i	−0.789388	+	1.36726i
$57$		0			0
$58$	270.505	−	468.529i	0.612398	−	1.06070i
$59$	−102.237	+	177.079i	−0.225595	+	0.390741i	−0.956498	−	0.291740i	$-0.905766\pi$
$59$	−102.237	+	177.079i	−0.225595	+	0.390741i	0.730903	+	0.682481i	$0.239099\pi$
$60$		0			0
$61$	107.989	−	187.043i	0.226666	−	0.392596i	−0.730152	−	0.683285i	$-0.760551\pi$
$61$	107.989	−	187.043i	0.226666	−	0.392596i	0.956818	+	0.290688i	$0.0938842\pi$
$62$	163.572	+	283.315i	0.335060	+	0.580340i
$63$		0			0
$64$	535.125			1.04517
$65$	0.710929	−	14.6636i	0.00135661	−	0.0279814i
$66$		0			0
$67$	−34.3025	−	59.4136i	−0.0625480	−	0.108336i	0.833056	−	0.553189i	$-0.186589\pi$
$67$	−34.3025	−	59.4136i	−0.0625480	−	0.108336i	−0.895604	+	0.444853i	$0.853256\pi$
$68$	−19.9105	−	34.4860i	−0.0355074	−	0.0615007i
$69$		0			0
$70$	24.6607			0.0421075
$71$	473.121	−	819.469i	0.790832	−	1.36976i	−0.134620	−	0.990897i	$-0.542981\pi$
$71$	473.121	−	819.469i	0.790832	−	1.36976i	0.925452	−	0.378864i	$-0.123685\pi$
$72$		0			0
$73$	−779.872			−1.25037			−0.625185	−	0.780476i	$-0.714977\pi$
$73$	−779.872			−1.25037			−0.625185	+	0.780476i	$0.714977\pi$
$74$	439.784	−	761.727i	0.690862	−	1.19661i
$75$		0			0
$76$	−2.91922	−	5.05624i	−0.00440602	−	0.00763145i
$77$	−1805.86			−2.67269
$78$		0			0
$79$	240.022			0.341831			0.170915	−	0.985286i	$-0.445328\pi$
$79$	240.022			0.341831			0.170915	+	0.985286i	$0.445328\pi$
$80$	−9.49245	−	16.4414i	−0.0132661	−	0.0229776i
$81$		0			0
$82$	−476.982	+	826.158i	−0.642365	+	1.11261i
$83$	−855.576			−1.13147			−0.565733	−	0.824588i	$-0.691407\pi$
$83$	−855.576			−1.13147			−0.565733	+	0.824588i	$0.691407\pi$
$84$		0			0
$85$	−15.4768	+	26.8065i	−0.0197493	+	0.0342068i
$86$	191.521			0.240142
$87$		0			0
$88$	732.082	+	1268.00i	0.886821	+	1.53602i
$89$	632.029	+	1094.71i	0.752753	+	1.30381i	0.946484	+	0.322751i	$0.104608\pi$
$89$	632.029	+	1094.71i	0.752753	+	1.30381i	−0.193731	+	0.981055i	$0.562059\pi$
$90$		0			0
$91$	−1125.78	−	724.842i	−1.29686	−	0.834989i
$92$	−5.79825			−0.00657075
$93$		0			0
$94$	140.398	+	243.176i	0.154052	+	0.266826i
$95$	−2.26916	+	3.93030i	−0.00245064	+	0.00424463i
$96$		0			0
$97$	−331.145	+	573.560i	−0.346625	+	0.600373i	−0.985648	−	0.168815i	$-0.946006\pi$
$97$	−331.145	+	573.560i	−0.346625	+	0.600373i	0.639022	+	0.769188i	$0.279339\pi$
$98$	651.879	−	1129.09i	0.671936	−	1.16383i
$99$		0			0
$100$	−25.1638	+	43.5850i	−0.0251638	+	0.0435850i
$101$	−396.785	−	687.252i	−0.390907	−	0.677071i	0.601662	−	0.798751i	$-0.294505\pi$
$101$	−396.785	−	687.252i	−0.390907	−	0.677071i	−0.992569	+	0.121680i	$0.961172\pi$
$102$		0			0
$103$	980.791			0.938254			0.469127	−	0.883131i	$-0.344569\pi$
$103$	980.791			0.938254			0.469127	+	0.883131i	$0.344569\pi$
$104$	−52.5710	+	1084.32i	−0.0495674	+	1.02237i
$105$		0			0
$106$	819.749	+	1419.85i	0.751142	+	1.30102i
$107$	−402.972	−	697.968i	−0.364082	−	0.630609i	0.624546	−	0.780988i	$-0.285284\pi$
$107$	−402.972	−	697.968i	−0.364082	−	0.630609i	−0.988628	+	0.150379i	$0.951951\pi$
$108$		0			0
$109$	845.184			0.742697			0.371348	−	0.928494i	$-0.378896\pi$
$109$	845.184			0.742697			0.371348	+	0.928494i	$0.378896\pi$
$110$	27.2875	−	47.2633i	0.0236523	−	0.0409671i
$111$		0			0
$112$	−1731.50			−1.46082
$113$	28.1887	−	48.8243i	0.0234670	−	0.0406460i	−0.854053	−	0.520185i	$-0.825863\pi$
$113$	28.1887	−	48.8243i	0.0234670	−	0.0406460i	0.877520	+	0.479539i	$0.159196\pi$
$114$		0			0
$115$	2.25354	+	3.90324i	0.00182733	+	0.00316503i
$116$	−79.0896			−0.0633042
$117$		0			0
$118$	−563.585			−0.439680
$119$	1411.54	+	2444.87i	1.08736	+	1.88337i
$120$		0			0
$121$	−1332.71	+	2308.33i	−1.00129	+	1.73428i
$122$	595.296			0.441767
$123$		0			0
$124$	23.9124	−	41.4175i	0.0173177	−	0.0299952i
$125$	78.2716			0.0560066
$126$		0			0
$127$	−833.323	−	1443.36i	−0.582248	−	1.00848i	−0.995212	−	0.0977357i	$-0.968840\pi$
$127$	−833.323	−	1443.36i	−0.582248	−	1.00848i	0.412965	−	0.910747i	$-0.364493\pi$
$128$	664.607	+	1151.13i	0.458934	+	0.794897i
$129$		0			0
$130$	35.9818	−	18.5114i	0.0242755	−	0.0124889i
$131$	602.630			0.401924			0.200962	−	0.979599i	$-0.435593\pi$
$131$	602.630			0.401924			0.200962	+	0.979599i	$0.435593\pi$
$132$		0			0
$133$	206.956	+	358.459i	0.134928	+	0.233702i
$134$	94.5471	−	163.760i	0.0609524	−	0.105573i
$135$		0			0
$136$	1144.46	−	1982.26i	0.721591	−	1.24983i
$137$	210.827	−	365.163i	0.131476	−	0.227722i	−0.792770	−	0.609521i	$-0.791362\pi$
$137$	210.827	−	365.163i	0.131476	−	0.227722i	0.924246	+	0.381799i	$0.124695\pi$
$138$		0			0
$139$	−14.5851	+	25.2622i	−0.00889995	+	0.0154152i	−0.870441	−	0.492273i	$-0.836166\pi$
$139$	−14.5851	+	25.2622i	−0.00889995	+	0.0154152i	0.861541	+	0.507688i	$0.169500\pi$
$140$	−1.80256	−	3.12213i	−0.00108817	−	0.00188477i
$141$		0			0
$142$	2608.10			1.54132
$143$	−2634.88	+	1355.56i	−1.54084	+	0.792710i
$144$		0			0
$145$	30.7388	+	53.2412i	0.0176050	+	0.0304927i
$146$	−1074.77	−	1861.56i	−0.609238	−	1.05523i
$147$		0			0
$148$	−128.583			−0.0714152
$149$	1070.90	−	1854.85i	0.588802	−	1.01983i	−0.405588	−	0.914056i	$-0.632933\pi$
$149$	1070.90	−	1854.85i	0.588802	−	1.01983i	0.994390	−	0.105778i	$-0.0337334\pi$
$150$		0			0
$151$	1459.30			0.786462			0.393231	−	0.919440i	$-0.371357\pi$
$151$	1459.30			0.786462			0.393231	+	0.919440i	$0.371357\pi$
$152$	167.797	−	290.633i	0.0895403	−	0.155088i
$153$		0			0
$154$	−2488.73	−	4310.60i	−1.30226	−	2.25557i
$155$	−37.1750			−0.0192643
$156$		0			0
$157$	2008.20			1.02084			0.510419	−	0.859926i	$-0.329490\pi$
$157$	2008.20			1.02084			0.510419	+	0.859926i	$0.329490\pi$
$158$	330.784	+	572.935i	0.166555	+	0.288482i
$159$		0			0
$160$	−2.85290	+	4.94136i	−0.00140963	+	0.00244156i
$161$	411.063			0.201219
$162$		0			0
$163$	−274.248	+	475.011i	−0.131784	+	0.228256i	−0.924364	−	0.381511i	$-0.875404\pi$
$163$	−274.248	+	475.011i	−0.131784	+	0.228256i	0.792581	+	0.609767i	$0.208737\pi$
$164$	139.459			0.0664019
$165$		0			0
$166$	−1179.10	−	2042.27i	−0.551302	−	0.954883i
$167$	−1981.29	−	3431.69i	−0.918064	−	1.59013i	−0.802352	−	0.596851i	$-0.796418\pi$
$167$	−1981.29	−	3431.69i	−0.918064	−	1.59013i	−0.115712	−	0.993283i	$-0.536915\pi$
$168$		0			0
$169$	−2186.70	−	212.533i	−0.995310	−	0.0967380i
$170$	−85.3165			−0.0384910
$171$		0			0
$172$	−13.9991	−	24.2472i	−0.00620594	−	0.0107490i
$173$	−864.771	+	1497.83i	−0.380042	+	0.658252i	−0.991068	−	0.133358i	$-0.957424\pi$
$173$	−864.771	+	1497.83i	−0.380042	+	0.658252i	0.611026	+	0.791611i	$0.290757\pi$
$174$		0			0
$175$	1783.97	−	3089.93i	0.770603	−	1.33472i
$176$	−1915.93	+	3318.49i	−0.820561	+	1.42125i
$177$		0			0
$178$	−1742.05	+	3017.32i	−0.733551	+	1.27055i
$179$	726.456	+	1258.26i	0.303340	+	0.525400i	0.976890	−	0.213741i	$-0.0685649\pi$
$179$	726.456	+	1258.26i	0.303340	+	0.525400i	−0.673550	+	0.739141i	$0.735232\pi$
$180$		0			0
$181$	−550.329			−0.225998			−0.112999	−	0.993595i	$-0.536046\pi$
$181$	−550.329			−0.225998			−0.112999	+	0.993595i	$0.536046\pi$
$182$	178.716	−	3686.18i	0.0727875	−	1.50131i
$183$		0			0
$184$	−166.642	−	288.632i	−0.0667663	−	0.115643i
$185$	49.9747	+	86.5588i	0.0198606	+	0.0343996i
$186$		0			0
$187$	6247.58			2.44314
$188$	20.5246	−	35.5496i	0.00796228	−	0.0137911i
$189$		0			0
$190$	−12.5089			−0.00477625
$191$	934.340	−	1618.32i	0.353960	−	0.613078i	−0.632979	−	0.774169i	$-0.718168\pi$
$191$	934.340	−	1618.32i	0.353960	−	0.613078i	0.986939	+	0.161091i	$0.0515014\pi$
$192$		0			0
$193$	−2078.26	−	3599.66i	−0.775112	−	1.34253i	−0.934732	−	0.355354i	$-0.884360\pi$
$193$	−2078.26	−	3599.66i	−0.775112	−	1.34253i	0.159620	−	0.987179i	$-0.448973\pi$
$194$	−1825.45			−0.675567
$195$		0			0
$196$	−190.595			−0.0694587
$197$	−761.092	−	1318.25i	−0.275257	−	0.476758i	0.694943	−	0.719065i	$-0.255429\pi$
$197$	−761.092	−	1318.25i	−0.275257	−	0.476758i	−0.970200	+	0.242306i	$0.922096\pi$
$198$		0			0
$199$	−404.065	+	699.861i	−0.143937	+	0.249306i	−0.928976	−	0.370141i	$-0.879309\pi$
$199$	−404.065	+	699.861i	−0.143937	+	0.249306i	0.785039	+	0.619446i	$0.212643\pi$
$200$	−2892.83			−1.02277
$201$		0			0
$202$	1093.65	−	1894.26i	0.380935	−	0.659800i
$203$	5607.01			1.93860
$204$		0			0
$205$	−54.2018	−	93.8803i	−0.0184664	−	0.0319848i
$206$	1351.67	+	2341.15i	0.457160	+	0.791825i
$207$		0			0
$208$	−2526.38	+	1299.74i	−0.842179	+	0.433273i
$209$	916.001			0.303163
$210$		0			0
$211$	2630.02	+	4555.32i	0.858094	+	1.48626i	0.873745	+	0.486384i	$0.161685\pi$
$211$	2630.02	+	4555.32i	0.858094	+	1.48626i	−0.0156511	+	0.999878i	$0.504982\pi$
$212$	119.838	−	207.566i	0.0388232	−	0.0672437i
$213$		0			0
$214$	1110.70	−	1923.79i	0.354795	−	0.614523i
$215$	−10.8817	+	18.8477i	−0.00345176	+	0.00597862i
$216$		0			0
$217$	−1695.26	+	2936.27i	−0.530330	+	0.918558i
$218$	1164.78	+	2017.46i	0.361876	+	0.626787i
$219$		0			0
$220$	−7.97824			−0.00244497
$221$	3894.77	+	2507.67i	1.18548	+	0.763276i
$222$		0			0
$223$	2345.36	+	4062.28i	0.704290	+	1.21987i	0.966947	+	0.254977i	$0.0820678\pi$
$223$	2345.36	+	4062.28i	0.704290	+	1.21987i	−0.262657	+	0.964889i	$0.584599\pi$
$224$	260.196	+	450.672i	0.0776119	+	0.134428i
$225$		0			0
$226$	155.392			0.0457368
$227$	−1780.31	+	3083.58i	−0.520542	+	0.901606i	0.479172	+	0.877721i	$0.340937\pi$
$227$	−1780.31	+	3083.58i	−0.520542	+	0.901606i	−0.999715	+	0.0238849i	$0.992396\pi$
$228$		0			0
$229$	−3144.82			−0.907490			−0.453745	−	0.891131i	$-0.649912\pi$
$229$	−3144.82			−0.907490			−0.453745	+	0.891131i	$0.649912\pi$
$230$	−6.21137	+	10.7584i	−0.00178072	+	0.00308430i
$231$		0			0
$232$	−2273.04	−	3937.02i	−0.643242	−	1.11413i
$233$	−852.543			−0.239708			−0.119854	−	0.992792i	$-0.538243\pi$
$233$	−852.543			−0.239708			−0.119854	+	0.992792i	$0.538243\pi$
$234$		0			0
$235$	−31.9081			−0.00885727
$236$	41.1949	+	71.3517i	0.0113625	+	0.0196805i
$237$		0			0
$238$	−3890.61	+	6738.73i	−1.05962	+	1.83532i
$239$	2189.33			0.592534			0.296267	−	0.955105i	$-0.404258\pi$
$239$	2189.33			0.592534			0.296267	+	0.955105i	$0.404258\pi$
$240$		0			0
$241$	−3164.99	+	5481.92i	−0.845954	+	1.46523i	0.0388369	+	0.999246i	$0.487635\pi$
$241$	−3164.99	+	5481.92i	−0.845954	+	1.46523i	−0.884791	+	0.465989i	$0.845699\pi$
$242$	−7346.65			−1.95149
$243$		0			0
$244$	−43.5128	−	75.3664i	−0.0114165	−	0.0197739i
$245$	74.0762	+	128.304i	0.0193165	+	0.0334572i
$246$		0			0
$247$	571.039	+	367.667i	0.147103	+	0.0947129i
$248$	2748.97			0.703871
$249$		0			0
$250$	107.869	+	186.835i	0.0272890	+	0.0472659i
$251$	1801.49	−	3120.27i	0.453023	−	0.784659i	−0.545549	−	0.838079i	$-0.683679\pi$
$251$	1801.49	−	3120.27i	0.453023	−	0.784659i	0.998572	+	0.0534200i	$0.0170122\pi$
$252$		0			0
$253$	454.848	−	787.819i	0.113028	−	0.195770i
$254$	2296.87	−	3978.29i	0.567395	−	0.982757i
$255$		0			0
$256$	308.657	−	534.610i	0.0753558	−	0.130520i
$257$	−1536.32	−	2660.98i	−0.372891	−	0.645865i	0.617118	−	0.786870i	$-0.288300\pi$
$257$	−1536.32	−	2660.98i	−0.372891	−	0.645865i	−0.990009	+	0.141005i	$0.954967\pi$
$258$		0			0
$259$	9115.80			2.18698
$260$	−4.97367	−	3.20233i	−0.00118636	−	0.000763846i
$261$		0			0
$262$	830.507	+	1438.48i	0.195836	+	0.339197i
$263$	1771.60	+	3068.50i	0.415367	+	0.719437i	0.995467	−	0.0951084i	$-0.0303198\pi$
$263$	1771.60	+	3068.50i	0.415367	+	0.719437i	−0.580100	+	0.814545i	$0.696986\pi$
$264$		0			0
$265$	−186.304			−0.0431871
$266$	−570.429	+	988.012i	−0.131486	+	0.227740i
$267$		0			0
$268$	−27.6435			−0.00630072
$269$	−2949.98	+	5109.52i	−0.668638	+	1.15811i	0.309647	+	0.950852i	$0.399789\pi$
$269$	−2949.98	+	5109.52i	−0.668638	+	1.15811i	−0.978285	+	0.207263i	$0.933544\pi$
$270$		0			0
$271$	1054.76	+	1826.90i	0.236429	+	0.409507i	0.959687	−	0.281071i	$-0.0906896\pi$
$271$	1054.76	+	1826.90i	0.236429	+	0.409507i	−0.723258	+	0.690578i	$0.757356\pi$
$272$	5990.32			1.33535
$273$		0			0
$274$	1162.19			0.256244
$275$	−3947.98	−	6838.10i	−0.865717	−	1.49947i
$276$		0			0
$277$	−3632.50	+	6291.67i	−0.787927	+	1.36473i	0.139308	+	0.990249i	$0.455512\pi$
$277$	−3632.50	+	6291.67i	−0.787927	+	1.36473i	−0.927235	+	0.374480i	$0.877821\pi$
$278$	−80.4012			−0.0173458
$279$		0			0
$280$	103.611	−	179.460i	0.0221141	−	0.0383028i
$281$	−4771.36			−1.01294			−0.506469	−	0.862258i	$-0.669049\pi$
$281$	−4771.36			−1.01294			−0.506469	+	0.862258i	$0.669049\pi$
$282$		0			0
$283$	−1018.13	−	1763.45i	−0.213857	−	0.370411i	0.739061	−	0.673638i	$-0.235269\pi$
$283$	−1018.13	−	1763.45i	−0.213857	−	0.370411i	−0.952918	+	0.303227i	$0.901936\pi$
$284$	−190.638	−	330.194i	−0.0398319	−	0.0689909i
$285$		0			0
$286$	−6866.96	−	4421.33i	−1.41976	−	0.914122i
$287$	−9886.86			−2.03346
$288$		0			0
$289$	−2426.89	−	4203.50i	−0.493973	−	0.855587i
$290$	−84.7247	+	146.747i	−0.0171559	+	0.0297148i
$291$		0			0
$292$	−157.119	+	272.139i	−0.0314888	+	0.0545402i
$293$	1859.51	−	3220.77i	0.370764	−	0.642182i	−0.618920	−	0.785454i	$-0.712429\pi$
$293$	1859.51	−	3220.77i	0.370764	−	0.642182i	0.989683	+	0.143273i	$0.0457626\pi$
$294$		0			0
$295$	32.0215	−	55.4628i	0.00631987	−	0.0109463i
$296$	−3695.47	−	6400.75i	−0.725659	−	1.25688i
$297$		0			0
$298$	5903.39			1.14756
$299$	599.771	−	308.562i	0.116005	−	0.0596810i
$300$		0			0
$301$	992.458	+	1718.99i	0.190048	+	0.329172i
$302$	2011.11	+	3483.35i	0.383200	+	0.663722i
$303$		0			0
$304$	878.282			0.165700
$305$	−33.8232	+	58.5835i	−0.00634987	+	0.0109983i
$306$		0			0
$307$	−7282.24			−1.35381			−0.676905	−	0.736070i	$-0.736679\pi$
$307$	−7282.24			−1.35381			−0.676905	+	0.736070i	$0.736679\pi$
$308$	−363.824	+	630.162i	−0.0673078	+	0.116581i
$309$		0			0
$310$	−51.2323	−	88.7370i	−0.00938645	−	0.0162578i
$311$	4569.28			0.833120			0.416560	−	0.909108i	$-0.363236\pi$
$311$	4569.28			0.833120			0.416560	+	0.909108i	$0.363236\pi$
$312$		0			0
$313$	21.0294			0.00379761			0.00189880	−	0.999998i	$-0.499396\pi$
$313$	21.0294			0.00379761			0.00189880	+	0.999998i	$0.499396\pi$
$314$	2767.57	+	4793.58i	0.497399	+	0.861520i
$315$		0			0
$316$	48.3569	−	83.7566i	0.00860851	−	0.0149104i
$317$	5159.17			0.914095			0.457047	−	0.889442i	$-0.348907\pi$
$317$	5159.17			0.914095			0.457047	+	0.889442i	$0.348907\pi$
$318$		0			0
$319$	6204.24	−	10746.1i	1.08894	−	1.88609i
$320$	−167.606			−0.0292796
$321$		0			0
$322$	566.502	+	981.211i	0.0980433	+	0.169816i
$323$	−715.988	−	1240.13i	−0.123339	−	0.213630i
$324$		0			0
$325$	283.505	−	5847.55i	0.0483878	−	0.998043i
$326$	−1511.80			−0.256844
$327$		0			0
$328$	4008.05	+	6942.15i	0.674719	+	1.16865i
$329$	−1455.08	+	2520.27i	−0.243833	+	0.422331i
$330$		0			0
$331$	3788.76	−	6562.33i	0.629152	−	1.08972i	−0.358570	−	0.933503i	$-0.616736\pi$
$331$	3788.76	−	6562.33i	0.629152	−	1.08972i	0.987722	−	0.156220i	$-0.0499309\pi$
$332$	−172.372	+	298.556i	−0.0284943	+	0.0493536i
$333$		0			0
$334$	5460.98	−	9458.70i	0.894645	−	1.54957i
$335$	10.7438	+	18.6089i	0.00175224	+	0.00303496i
$336$		0			0
$337$	−2109.79			−0.341032			−0.170516	−	0.985355i	$-0.554543\pi$
$337$	−2109.79			−0.341032			−0.170516	+	0.985355i	$0.554543\pi$
$338$	−2506.25	−	5512.56i	−0.403320	−	0.887111i
$339$		0			0
$340$	6.23616	+	10.8013i	0.000994715	+	0.00172290i
$341$	3751.65	+	6498.05i	0.595787	+	1.03193i
$342$		0			0
$343$	3713.98			0.584653
$344$	804.669	−	1393.73i	0.126119	−	0.218444i
$345$		0			0
$346$	−4767.09			−0.740695
$347$	−4053.95	+	7021.65i	−0.627169	+	1.08629i	0.360948	+	0.932586i	$0.382453\pi$
$347$	−4053.95	+	7021.65i	−0.627169	+	1.08629i	−0.988117	+	0.153703i	$0.950880\pi$
$348$		0			0
$349$	−4343.19	−	7522.62i	−0.666148	−	1.15380i	−0.978973	−	0.203991i	$-0.934609\pi$
$349$	−4343.19	−	7522.62i	−0.666148	−	1.15380i	0.312825	−	0.949811i	$-0.398725\pi$
$350$	9834.24			1.50189
$351$		0			0
$352$	1151.64			0.174383
$353$	−4525.12	−	7837.73i	−0.682288	−	1.18176i	−0.974281	−	0.225337i	$-0.927652\pi$
$353$	−4525.12	−	7837.73i	−0.682288	−	1.18176i	0.291993	−	0.956421i	$-0.405682\pi$
$354$		0			0
$355$	−148.186	+	256.665i	−0.0221546	+	0.0383729i
$356$	509.336			0.0758279
$357$		0			0
$358$	−2002.31	+	3468.11i	−0.295602	+	0.511998i
$359$	7043.80			1.03554			0.517768	−	0.855521i	$-0.326763\pi$
$359$	7043.80			1.03554			0.517768	+	0.855521i	$0.326763\pi$
$360$		0			0
$361$	3324.52	+	5758.24i	0.484695	+	0.839517i
$362$	−758.429	−	1313.64i	−0.110116	−	0.190727i
$363$		0			0
$364$	−479.746	+	246.813i	−0.0690811	+	0.0355399i
$365$	244.263			0.0350282
$366$		0			0
$367$	−6912.55	−	11972.9i	−0.983194	−	1.70294i	−0.649703	−	0.760188i	$-0.725107\pi$
$367$	−6912.55	−	11972.9i	−0.983194	−	1.70294i	−0.333491	−	0.942753i	$-0.608227\pi$
$368$	436.118	−	755.378i	0.0617778	−	0.107002i
$369$		0			0
$370$	−137.744	+	238.580i	−0.0193540	+	0.0335221i
$371$	−8495.85	+	14715.2i	−1.18890	+	2.05924i
$372$		0			0
$373$	−3184.09	+	5515.01i	−0.442000	+	0.765567i	−0.997838	−	0.0657238i	$-0.979064\pi$
$373$	−3184.09	+	5515.01i	−0.442000	+	0.765567i	0.555837	+	0.831291i	$0.312398\pi$
$374$	8610.03	+	14913.0i	1.19041	+	2.06185i
$375$		0			0
$376$	2359.51			0.323623
$377$	8181.03	−	4208.87i	1.11762	−	0.574981i
$378$		0			0
$379$	−1225.83	−	2123.20i	−0.166139	−	0.287761i	0.770920	−	0.636932i	$-0.219797\pi$
$379$	−1225.83	−	2123.20i	−0.166139	−	0.287761i	−0.937059	+	0.349171i	$0.886463\pi$
$380$	0.914327	+	1.58366i	0.000123432	+	0.000213790i
$381$		0			0
$382$	5150.60			0.689863
$383$	−5415.47	+	9379.87i	−0.722500	+	1.25141i	0.237494	+	0.971389i	$0.423674\pi$
$383$	−5415.47	+	9379.87i	−0.722500	+	1.25141i	−0.959995	+	0.280018i	$0.909659\pi$
$384$		0			0
$385$	565.613			0.0748735
$386$	5728.27	−	9921.65i	0.755340	−	1.30829i
$387$		0			0
$388$	133.430	+	231.108i	0.0174585	+	0.0302390i
$389$	−4978.07			−0.648838			−0.324419	−	0.945914i	$-0.605169\pi$
$389$	−4978.07			−0.648838			−0.324419	+	0.945914i	$0.605169\pi$
$390$		0			0
$391$	−1422.12			−0.183938
$392$	−5477.70	−	9487.65i	−0.705779	−	1.22245i
$393$		0			0
$394$	2097.78	−	3633.46i	0.268235	−	0.464597i
$395$	−75.1772			−0.00957614
$396$		0			0
$397$	−4725.34	+	8184.52i	−0.597375	+	1.03468i	0.395832	+	0.918323i	$0.370456\pi$
$397$	−4725.34	+	8184.52i	−0.597375	+	1.03468i	−0.993207	+	0.116361i	$0.962877\pi$
$398$	−2227.43			−0.280530
$399$		0			0
$400$	−3785.41	−	6556.52i	−0.473176	−	0.819566i
$401$	−4388.39	−	7600.91i	−0.546498	−	0.946562i	−0.998511	−	0.0545506i	$-0.982627\pi$
$401$	−4388.39	−	7600.91i	−0.546498	−	0.946562i	0.452013	−	0.892011i	$-0.350706\pi$
$402$		0			0
$403$	−269.407	+	5556.76i	−0.0333005	+	0.686854i
$404$	−319.759			−0.0393777
$405$		0			0
$406$	7727.24	+	13384.0i	0.944572	+	1.63605i
$407$	10086.8	−	17470.8i	1.22846	−	2.12775i
$408$		0			0
$409$	2260.10	−	3914.60i	0.273238	−	0.473263i	−0.696451	−	0.717605i	$-0.745239\pi$
$409$	2260.10	−	3914.60i	0.273238	−	0.473263i	0.969689	+	0.244342i	$0.0785719\pi$
$410$	149.395	−	258.760i	0.0179954	−	0.0311689i
$411$		0			0
$412$	197.598	−	342.250i	0.0236286	−	0.0409259i
$413$	−2920.49	−	5058.43i	−0.347961	−	0.602686i
$414$		0			0
$415$	267.974			0.0316972
$416$	717.939	+	462.249i	0.0846150	+	0.0544798i
$417$		0			0
$418$	1262.38	+	2186.50i	0.147715	+	0.255850i
$419$	−6003.22	−	10397.9i	−0.699944	−	1.21234i	−0.968485	−	0.249070i	$-0.919875\pi$
$419$	−6003.22	−	10397.9i	−0.699944	−	1.21234i	0.268541	−	0.963268i	$-0.413458\pi$
$420$		0			0
$421$	−9731.52			−1.12657			−0.563284	−	0.826263i	$-0.690462\pi$
$421$	−9731.52			−1.12657			−0.563284	+	0.826263i	$0.690462\pi$
$422$	−7249.05	+	12555.7i	−0.836205	+	1.44835i
$423$		0			0
$424$	13776.6			1.57795
$425$	−6171.84	+	10689.9i	−0.704420	+	1.22009i
$426$		0			0
$427$	3084.82	+	5343.06i	0.349613	+	0.605547i
$428$	−324.745			−0.0366755
$429$		0			0
$430$	−59.9861			−0.00672741
$431$	2055.51	+	3560.25i	0.229723	+	0.397892i	0.957726	−	0.287682i	$-0.0928846\pi$
$431$	2055.51	+	3560.25i	0.229723	+	0.397892i	−0.728003	+	0.685574i	$0.759551\pi$
$432$		0			0
$433$	−1453.03	+	2516.72i	−0.161266	+	0.279321i	−0.935323	−	0.353795i	$-0.884891\pi$
$433$	−1453.03	+	2516.72i	−0.161266	+	0.279321i	0.774057	+	0.633116i	$0.218224\pi$
$434$	−9345.19			−1.03360
$435$		0			0
$436$	170.278	−	294.930i	0.0187037	−	0.0323958i
$437$	−208.507			−0.0228243
$438$		0			0
$439$	−4437.36	−	7685.73i	−0.482423	−	0.835581i	0.517374	−	0.855760i	$-0.326910\pi$
$439$	−4437.36	−	7685.73i	−0.482423	−	0.835581i	−0.999796	+	0.0201788i	$0.993576\pi$
$440$	−229.295	−	397.150i	−0.0248436	−	0.0430305i
$441$		0			0
$442$	−618.288	+	12752.7i	−0.0665361	+	1.37237i
$443$	12640.5			1.35569			0.677843	−	0.735207i	$-0.262915\pi$
$443$	12640.5			1.35569			0.677843	+	0.735207i	$0.262915\pi$
$444$		0			0
$445$	−197.957	−	342.872i	−0.0210878	−	0.0365252i
$446$	−6464.45	+	11196.8i	−0.686324	+	1.18875i
$447$		0			0
$448$	−7643.18	+	13238.4i	−0.806041	+	1.39610i
$449$	887.147	−	1536.58i	0.0932451	−	0.161505i	−0.815630	−	0.578574i	$-0.803609\pi$
$449$	887.147	−	1536.58i	0.0932451	−	0.161505i	0.908875	+	0.417069i	$0.136943\pi$
$450$		0			0
$451$	−10940.0	+	18948.6i	−1.14222	+	1.97839i
$452$	−11.3583	−	19.6731i	−0.00118197	−	0.00204722i
$453$		0			0
$454$	−9814.04			−1.01453
$455$	352.606	+	227.027i	0.0363306	+	0.0233916i
$456$		0			0
$457$	−3084.41	−	5342.35i	−0.315717	−	0.546837i	0.663873	−	0.747845i	$-0.268912\pi$
$457$	−3084.41	−	5342.35i	−0.315717	−	0.546837i	−0.979590	+	0.201008i	$0.935578\pi$
$458$	−4333.99	−	7506.69i	−0.442171	−	0.765862i
$459$		0			0
$460$	1.81607			0.000184075
$461$	3727.69	−	6456.55i	0.376607	−	0.652302i	−0.613959	−	0.789338i	$-0.710424\pi$
$461$	3727.69	−	6456.55i	0.376607	−	0.652302i	0.990566	+	0.137036i	$0.0437574\pi$
$462$		0			0
$463$	5399.78			0.542006			0.271003	−	0.962578i	$-0.412645\pi$
$463$	5399.78			0.542006			0.271003	+	0.962578i	$0.412645\pi$
$464$	5948.76	−	10303.6i	0.595182	−	1.03088i
$465$		0			0
$466$	−1174.92	−	2035.03i	−0.116797	−	0.202298i
$467$	3992.01			0.395564			0.197782	−	0.980246i	$-0.436626\pi$
$467$	3992.01			0.395564			0.197782	+	0.980246i	$0.436626\pi$
$468$		0			0
$469$	1959.77			0.192950
$470$	−43.9738	−	76.1649i	−0.00431566	−	0.00747495i
$471$		0			0
$472$	−2367.89	+	4101.30i	−0.230913	+	0.399952i
$473$	4392.68			0.427009
$474$		0			0
$475$	−904.897	+	1567.33i	−0.0874095	+	0.151398i
$476$	1137.53			0.109535
$477$		0			0
$478$	3017.19	+	5225.93i	0.288710	+	0.500060i
$479$	−1575.81	−	2729.39i	−0.150315	−	0.260352i	0.781029	−	0.624495i	$-0.214695\pi$
$479$	−1575.81	−	2729.39i	−0.150315	−	0.260352i	−0.931343	+	0.364143i	$0.881362\pi$
$480$		0			0
$481$	13300.6	−	6842.72i	1.26082	−	0.648651i
$482$	−17447.2			−1.64875
$483$		0			0
$484$	536.999	+	930.110i	0.0504319	+	0.0873507i
$485$	103.718	−	179.644i	0.00971046	−	0.0168190i
$486$		0			0
$487$	1954.59	−	3385.45i	0.181870	−	0.315009i	−0.760647	−	0.649166i	$-0.775118\pi$
$487$	1954.59	−	3385.45i	0.181870	−	0.315009i	0.942517	+	0.334157i	$0.108452\pi$
$488$	2501.12	−	4332.07i	0.232009	−	0.401851i
$489$		0			0
$490$	−204.174	+	353.641i	−0.0188238	+	0.0326038i
$491$	−3322.57	−	5754.86i	−0.305388	−	0.528947i	0.671960	−	0.740588i	$-0.265453\pi$
$491$	−3322.57	−	5754.86i	−0.305388	−	0.528947i	−0.977348	+	0.211641i	$0.932119\pi$
$492$		0			0
$493$	−19398.1			−1.77210
$494$	−90.6515	+	1869.77i	−0.00825628	+	0.170293i
$495$		0			0
$496$	3597.17	+	6230.48i	0.325640	+	0.564026i
$497$	13515.1	+	23408.9i	1.21979	+	2.11274i
$498$		0			0
$499$	6111.83			0.548303			0.274151	−	0.961687i	$-0.411603\pi$
$499$	6111.83			0.548303			0.274151	+	0.961687i	$0.411603\pi$
$500$	15.7692	−	27.3131i	0.00141044	−	0.00244296i
$501$		0			0
$502$	9930.79			0.882934
$503$	−5477.03	+	9486.50i	−0.485505	+	0.840919i	−0.999861	−	0.0166575i	$-0.994698\pi$
$503$	−5477.03	+	9486.50i	−0.485505	+	0.840919i	0.514356	+	0.857576i	$0.328031\pi$
$504$		0			0
$505$	124.277	+	215.254i	0.0109510	+	0.0189677i
$506$	2507.37			0.220289
$507$		0			0
$508$	−671.553			−0.0586523
$509$	5560.57	+	9631.18i	0.484220	+	0.838693i	0.999836	−	0.0181268i	$-0.00577025\pi$
$509$	5560.57	+	9631.18i	0.484220	+	0.838693i	−0.515616	+	0.856820i	$0.672437\pi$
$510$		0			0
$511$	11138.9	−	19293.1i	0.964296	−	1.67021i
$512$	12335.2			1.06473
$513$		0			0
$514$	4234.52	−	7334.40i	0.363379	−	0.629390i
$515$	−307.193			−0.0262845
$516$		0			0
$517$	3220.13	+	5577.42i	0.273928	+	0.474458i
$518$	12562.8	+	21759.5i	1.06560	+	1.84567i
$519$		0			0
$520$	16.4657	−	339.620i	0.00138859	−	0.0286410i
$521$	2403.33			0.202096			0.101048	−	0.994882i	$-0.467780\pi$
$521$	2403.33			0.202096			0.101048	+	0.994882i	$0.467780\pi$
$522$		0			0
$523$	−2125.86	−	3682.10i	−0.177739	−	0.307853i	0.763367	−	0.645965i	$-0.223545\pi$
$523$	−2125.86	−	3682.10i	−0.177739	−	0.307853i	−0.941106	+	0.338113i	$0.890212\pi$
$524$	121.411	−	210.290i	0.0101219	−	0.0175316i
$525$		0			0
$526$	−4883.02	+	8457.64i	−0.404772	+	0.701085i
$527$	5864.92	−	10158.3i	0.484782	−	0.839667i
$528$		0			0
$529$	5979.96	−	10357.6i	0.491490	−	0.851286i
$530$	−256.753	−	444.709i	−0.0210427	−	0.0364470i
$531$		0			0
$532$	166.781			0.0135918
$533$	−14425.6	+	7421.51i	−1.17231	+	0.603117i
$534$		0			0
$535$	126.215	+	218.610i	0.0101995	+	0.0176661i
$536$	−794.473	−	1376.07i	−0.0640224	−	0.110890i
$537$		0			0
$538$	−16261.9			−1.30316
$539$	14951.3	−	25896.5i	1.19480	−	2.06946i
$540$		0			0
$541$	−8924.44			−0.709227			−0.354613	−	0.935013i	$-0.615388\pi$
$541$	−8924.44			−0.709227			−0.354613	+	0.935013i	$0.615388\pi$
$542$	−2907.22	+	5035.45i	−0.230398	+	0.399061i
$543$		0			0
$544$	−900.176	−	1559.15i	−0.0709462	−	0.122882i
$545$	−264.719			−0.0208061
$546$		0			0
$547$	−14696.0			−1.14873			−0.574367	−	0.818598i	$-0.694752\pi$
$547$	−14696.0			−1.14873			−0.574367	+	0.818598i	$0.694752\pi$
$548$	−84.9499	−	147.138i	−0.00662204	−	0.0114697i
$549$		0			0
$550$	10881.7	−	18847.7i	0.843633	−	1.46122i
$551$	−2844.09			−0.219895
$552$		0			0
$553$	−3428.23	+	5937.87i	−0.263623	+	0.456608i
$554$	−20024.3			−1.53566
$555$		0			0
$556$	5.87688	+	10.1791i	0.000448265	+	0.000776417i
$557$	−1232.01	−	2133.91i	−0.0937202	−	0.162328i	0.815354	−	0.578963i	$-0.196543\pi$
$557$	−1232.01	−	2133.91i	−0.0937202	−	0.162328i	−0.909074	+	0.416635i	$0.863209\pi$
$558$		0			0
$559$	2738.41	+	1763.14i	0.207196	+	0.133404i
$560$	542.322			0.0409237
$561$		0			0
$562$	−6575.59	−	11389.3i	−0.493549	−	0.854852i
$563$	−9014.61	+	15613.8i	−0.674815	+	1.16881i	0.301708	+	0.953400i	$0.402443\pi$
$563$	−9014.61	+	15613.8i	−0.674815	+	1.16881i	−0.976523	+	0.215413i	$0.930890\pi$
$564$		0			0
$565$	−8.82897	+	15.2922i	−0.000657411	+	0.00113867i
$566$	2806.25	−	4860.57i	0.208402	−	0.360963i
$567$		0			0
$568$	10957.9	−	18979.6i	0.809475	−	1.40205i
$569$	−5962.32	−	10327.0i	−0.439286	−	0.760865i	0.558349	−	0.829606i	$-0.311435\pi$
$569$	−5962.32	−	10327.0i	−0.439286	−	0.760865i	−0.997635	+	0.0687410i	$0.978102\pi$
$570$		0			0
$571$	5834.77			0.427632			0.213816	−	0.976874i	$-0.431411\pi$
$571$	5834.77			0.427632			0.213816	+	0.976874i	$0.431411\pi$
$572$	−57.8182	+	1192.55i	−0.00422640	+	0.0871734i
$573$		0			0
$574$	−13625.5	−	23600.0i	−0.990794	−	1.71611i
$575$	898.667	+	1556.54i	0.0651774	+	0.112891i
$576$		0			0
$577$	15927.5			1.14917			0.574586	−	0.818444i	$-0.305163\pi$
$577$	15927.5			1.14917			0.574586	+	0.818444i	$0.305163\pi$
$578$	6689.19	−	11586.0i	0.481373	−	0.833762i
$579$		0			0
$580$	24.7716			0.00177342
$581$	12220.2	−	21166.0i	0.872596	−	1.51138i
$582$		0			0
$583$	18801.6	+	32565.3i	1.33564	+	2.31340i
$584$	−18062.5			−1.27985
$585$		0			0
$586$	10250.7			0.722612
$587$	6755.55	+	11701.0i	0.475011	+	0.822743i	0.999590	−	0.0286184i	$-0.00911075\pi$
$587$	6755.55	+	11701.0i	0.475011	+	0.822743i	−0.524579	+	0.851362i	$0.675777\pi$
$588$		0			0
$589$	859.898	−	1489.39i	0.0601553	−	0.104192i
$590$	176.520			0.0123173
$591$		0			0
$592$	9671.42	−	16751.4i	0.671441	−	1.16297i
$593$	15830.4			1.09625			0.548126	−	0.836396i	$-0.315341\pi$
$593$	15830.4			1.09625			0.548126	+	0.836396i	$0.315341\pi$
$594$		0			0
$595$	−442.109	−	765.755i	−0.0304617	−	0.0527611i
$596$	−431.505	−	747.388i	−0.0296562	−	0.0513661i
$597$		0			0
$598$	1563.11	+	1006.42i	0.106890	+	0.0688217i
$599$	−5914.12			−0.403413			−0.201706	−	0.979446i	$-0.564649\pi$
$599$	−5914.12			−0.403413			−0.201706	+	0.979446i	$0.564649\pi$
$600$		0			0
$601$	−4946.10	−	8566.89i	−0.335700	−	0.581449i	0.647919	−	0.761709i	$-0.275639\pi$
$601$	−4946.10	−	8566.89i	−0.335700	−	0.581449i	−0.983619	+	0.180260i	$0.942306\pi$
$602$	−2735.49	+	4738.01i	−0.185200	+	0.320775i
$603$		0			0
$604$	294.002	−	509.226i	0.0198059	−	0.0343048i
$605$	417.418	−	722.989i	0.0280503	−	0.0485846i
$606$		0			0
$607$	8391.16	−	14533.9i	0.561098	−	0.971851i	−0.436302	−	0.899800i	$-0.643712\pi$
$607$	8391.16	−	14533.9i	0.561098	−	0.971851i	0.997401	−	0.0720510i	$-0.0229544\pi$
$608$	−131.981	−	228.598i	−0.00880352	−	0.0152481i
$609$		0			0
$610$	−186.452			−0.0123758
$611$	−231.238	+	4769.49i	−0.0153108	+	0.315799i
$612$		0			0
$613$	−6122.83	−	10605.0i	−0.403424	−	0.698750i	0.590713	−	0.806882i	$-0.298847\pi$
$613$	−6122.83	−	10605.0i	−0.403424	−	0.698750i	−0.994137	+	0.108132i	$0.965513\pi$
$614$	−10035.9	−	17382.8i	−0.659638	−	1.14253i
$615$		0			0
$616$	−41825.3			−2.73569
$617$	−5021.86	+	8698.12i	−0.327670	+	0.567542i	−0.982049	−	0.188625i	$-0.939597\pi$
$617$	−5021.86	+	8698.12i	−0.327670	+	0.567542i	0.654379	+	0.756167i	$0.272930\pi$
$618$		0			0
$619$	−9942.69			−0.645607			−0.322803	−	0.946466i	$-0.604625\pi$
$619$	−9942.69			−0.645607			−0.322803	+	0.946466i	$0.604625\pi$
$620$	−7.48959	+	12.9724i	−0.000485144	+	0.000840294i
$621$		0			0
$622$	6297.10	+	10906.9i	0.405934	+	0.703098i
$623$	−36109.1			−2.32212
$624$		0			0
$625$	15588.2			0.997646
$626$	28.9814	+	50.1973i	0.00185037	+	0.00320493i
$627$		0			0
$628$	404.588	−	700.767i	0.0257083	−	0.0445281i
$629$	−31537.1			−1.99915
$630$		0			0
$631$	−5134.31	+	8892.89i	−0.323920	+	0.561047i	−0.981293	−	0.192519i	$-0.938334\pi$
$631$	−5134.31	+	8892.89i	−0.323920	+	0.561047i	0.657373	+	0.753566i	$0.271668\pi$
$632$	5559.11			0.349889
$633$		0			0
$634$	7110.05	+	12315.0i	0.445389	+	0.771436i
$635$	261.004	+	452.073i	0.0163113	+	0.0282519i
$636$		0			0
$637$	19715.1	−	10142.8i	1.22628	−	0.630881i
$638$	34201.2			2.12232
$639$		0			0
$640$	−208.161	−	360.546i	−0.0128567	−	0.0222685i
$641$	6828.72	−	11827.7i	0.420777	−	0.728808i	−0.575238	−	0.817986i	$-0.695091\pi$
$641$	6828.72	−	11827.7i	0.420777	−	0.728808i	0.996016	+	0.0891780i	$0.0284240\pi$
$642$		0			0
$643$	−12335.8	+	21366.2i	−0.756572	+	1.31042i	0.188017	+	0.982166i	$0.439794\pi$
$643$	−12335.8	+	21366.2i	−0.756572	+	1.31042i	−0.944589	+	0.328256i	$0.893539\pi$
$644$	82.8163	−	143.442i	0.00506742	−	0.00877703i
$645$		0			0
$646$	1973.46	−	3418.14i	0.120193	−	0.208181i
$647$	8256.13	+	14300.0i	0.501672	+	0.868922i	0.999998	+	0.00193194i	$0.000614955\pi$
$647$	8256.13	+	14300.0i	0.501672	+	0.868922i	−0.498326	+	0.866990i	$0.666052\pi$
$648$		0			0
$649$	−12926.3			−0.781818
$650$	14348.9	−	7382.01i	0.865859	−	0.445456i
$651$		0			0
$652$	110.504	+	191.399i	0.00663756	+	0.0114966i
$653$	−15297.4	−	26495.8i	−0.916742	−	1.58784i	−0.804330	−	0.594182i	$-0.797476\pi$
$653$	−15297.4	−	26495.8i	−0.916742	−	1.58784i	−0.112412	−	0.993662i	$-0.535858\pi$
$654$		0			0
$655$	−188.749			−0.0112596
$656$	−10489.5	+	18168.3i	−0.624306	+	1.08133i
$657$		0			0
$658$	−8021.19			−0.475226
$659$	1153.89	−	1998.60i	0.0682084	−	0.118140i	−0.829904	−	0.557906i	$-0.811605\pi$
$659$	1153.89	−	1998.60i	0.0682084	−	0.118140i	0.898113	+	0.439765i	$0.144938\pi$
$660$		0			0
$661$	13811.2	+	23921.7i	0.812700	+	1.40764i	0.910968	+	0.412477i	$0.135336\pi$
$661$	13811.2	+	23921.7i	0.812700	+	1.40764i	−0.0982684	+	0.995160i	$0.531330\pi$
$662$	20885.8			1.22621
$663$		0			0
$664$	−19815.9			−1.15814
$665$	−64.8206	−	112.273i	−0.00377991	−	0.00654699i
$666$		0			0
$667$	−1412.25	+	2446.09i	−0.0819830	+	0.141999i
$668$	−1596.67			−0.0924805
$669$		0			0
$670$	−29.6130	+	51.2913i	−0.00170754	+	0.00295754i
$671$	13653.6			0.785530
$672$		0			0
$673$	5652.94	+	9791.17i	0.323781	+	0.560805i	0.981265	−	0.192663i	$-0.0617125\pi$
$673$	5652.94	+	9791.17i	0.323781	+	0.560805i	−0.657484	+	0.753469i	$0.728379\pi$
$674$	−2907.58	−	5036.08i	−0.166166	−	0.287808i
$675$		0			0
$676$	−514.714	+	720.236i	−0.0292851	+	0.0409784i
$677$	15455.8			0.877419			0.438710	−	0.898629i	$-0.355436\pi$
$677$	15455.8			0.877419			0.438710	+	0.898629i	$0.355436\pi$
$678$		0			0
$679$	−9459.47	−	16384.3i	−0.534641	−	0.926025i
$680$	−358.455	+	620.862i	−0.0202149	+	0.0350132i
$681$		0			0
$682$	−10340.6	+	17910.4i	−0.580589	+	1.00561i
$683$	−8420.96	+	14585.5i	−0.471770	+	0.817130i	−0.999478	−	0.0322958i	$-0.989718\pi$
$683$	−8420.96	+	14585.5i	−0.471770	+	0.817130i	0.527708	+	0.849426i	$0.323051\pi$
$684$		0			0
$685$	−66.0329	+	114.372i	−0.00368319	+	0.00637948i
$686$	5118.37	+	8865.28i	0.284869	+	0.493408i
$687$		0			0
$688$	4211.80			0.233391
$689$	−1350.14	+	27847.9i	−0.0746537	+	1.53980i
$690$		0			0
$691$	12520.8	+	21686.6i	0.689310	+	1.19392i	0.972061	+	0.234727i	$0.0754195\pi$
$691$	12520.8	+	21686.6i	0.689310	+	1.19392i	−0.282751	+	0.959193i	$0.591247\pi$
$692$	348.448	+	603.529i	0.0191416	+	0.0331543i
$693$		0			0
$694$	−22347.6			−1.22234
$695$	4.56819	−	7.91234i	0.000249326	−	0.000431845i
$696$		0			0
$697$	34204.7			1.85881
$698$	11971.0	−	20734.4i	0.649155	−	1.12437i
$699$		0			0
$700$	−718.828	−	1245.05i	−0.0388131	−	0.0672262i
$701$	−28309.0			−1.52527			−0.762635	−	0.646829i	$-0.776095\pi$
$701$	−28309.0			−1.52527			−0.762635	+	0.646829i	$0.776095\pi$
$702$		0			0
$703$	−4623.88			−0.248069
$704$	16914.6	+	29296.9i	0.905528	+	1.56842i
$705$		0			0
$706$	12472.5	−	21603.0i	0.664884	−	1.15161i
$707$	22669.1			1.20588
$708$		0			0
$709$	2520.59	−	4365.78i	0.133516	−	0.231256i	−0.791514	−	0.611151i	$-0.790707\pi$
$709$	2520.59	−	4365.78i	0.133516	−	0.231256i	0.925029	+	0.379895i	$0.124040\pi$
$710$	−816.882			−0.0431789
$711$		0			0
$712$	14638.3	+	25354.3i	0.770498	+	1.33454i
$713$	−853.978	−	1479.13i	−0.0448552	−	0.0776914i
$714$		0			0
$715$	825.269	−	424.574i	0.0431655	−	0.0222072i
$716$	585.431			0.0305567
$717$		0			0
$718$	9707.33	+	16813.6i	0.504560	+	0.873924i
$719$	−5919.62	+	10253.1i	−0.307044	+	0.531815i	−0.977714	−	0.209940i	$-0.932673\pi$
$719$	−5919.62	+	10253.1i	−0.307044	+	0.531815i	0.670671	+	0.741755i	$0.266006\pi$
$720$		0			0
$721$	−14008.6	+	24263.6i	−0.723590	+	1.25329i
$722$	−9163.31	+	15871.3i	−0.472331	+	0.818101i
$723$		0			0
$724$	−110.874	+	192.039i	−0.00569143	+	0.00985784i
$725$	12258.1	+	21231.6i	0.627935	+	1.08762i
$726$		0			0
$727$	−31004.9			−1.58172			−0.790858	−	0.611999i	$-0.790365\pi$
$727$	−31004.9			−1.58172			−0.790858	+	0.611999i	$0.790365\pi$
$728$	−26074.1	−	16787.9i	−1.32743	−	0.854673i
$729$		0			0
$730$	336.628	+	583.057i	0.0170674	+	0.0295615i
$731$	−3433.52	−	5947.02i	−0.173725	−	0.300901i
$732$		0			0
$733$	15666.0			0.789411			0.394706	−	0.918808i	$-0.370847\pi$
$733$	15666.0			0.789411			0.394706	+	0.918808i	$0.370847\pi$
$734$	19052.9	−	33000.6i	0.958114	−	1.65950i
$735$		0			0
$736$	−262.145			−0.0131288
$737$	2168.51	−	3755.97i	0.108383	−	0.187724i
$738$		0			0
$739$	16669.7	+	28872.8i	0.829777	+	1.43722i	0.898213	+	0.439561i	$0.144866\pi$
$739$	16669.7	+	28872.8i	0.829777	+	1.43722i	−0.0684357	+	0.997656i	$0.521801\pi$
$740$	40.2733			0.00200064
$741$		0			0
$742$	−46833.8			−2.31715
$743$	−1013.07	−	1754.69i	−0.0500215	−	0.0866397i	0.839931	−	0.542694i	$-0.182596\pi$
$743$	−1013.07	−	1754.69i	−0.0500215	−	0.0866397i	−0.889952	+	0.456054i	$0.849262\pi$
$744$		0			0
$745$	−335.415	+	580.956i	−0.0164949	+	0.0285699i
$746$	−17552.5			−0.861451
$747$		0			0
$748$	1258.69	−	2180.11i	0.0615271	−	0.106568i
$749$	23022.6			1.12313
$750$		0			0
$751$	−17737.4	−	30722.0i	−0.861846	−	1.49276i	−0.870145	−	0.492795i	$-0.835975\pi$
$751$	−17737.4	−	30722.0i	−0.861846	−	1.49276i	0.00829952	−	0.999966i	$-0.497358\pi$
$752$	3087.53	+	5347.76i	0.149722	+	0.259325i
$753$		0			0
$754$	21321.2	+	13727.8i	1.02980	+	0.663044i
$755$	−457.065			−0.0220322
$756$		0			0
$757$	−1199.29	−	2077.23i	−0.0575811	−	0.0997333i	0.835798	−	0.549037i	$-0.185005\pi$
$757$	−1199.29	−	2077.23i	−0.0575811	−	0.0997333i	−0.893379	+	0.449304i	$0.851672\pi$
$758$	3378.73	−	5852.13i	0.161901	−	0.280421i
$759$		0			0
$760$	−52.5555	+	91.0289i	−0.00250841	+	0.00434469i
$761$	2502.53	−	4334.52i	0.119207	−	0.206473i	−0.800246	−	0.599671i	$-0.795298\pi$
$761$	2502.53	−	4334.52i	0.119207	−	0.206473i	0.919454	+	0.393198i	$0.128631\pi$
$762$		0			0
$763$	−12071.7	+	20908.9i	−0.572774	+	0.992074i
$764$	−376.480	−	652.082i	−0.0178280	−	0.0308789i
$765$		0			0
$766$	−29853.1			−1.40814
$767$	−8058.28	−	5188.37i	−0.379358	−	0.244252i
$768$		0			0
$769$	−7054.78	−	12219.2i	−0.330822	−	0.573000i	0.651851	−	0.758347i	$-0.273993\pi$
$769$	−7054.78	−	12219.2i	−0.330822	−	0.573000i	−0.982673	+	0.185346i	$0.940659\pi$
$770$	779.493	+	1350.12i	0.0364818	+	0.0631883i
$771$		0			0
$772$	−1674.82			−0.0780803
$773$	6366.85	−	11027.7i	0.296248	−	0.513116i	−0.679027	−	0.734114i	$-0.737598\pi$
$773$	6366.85	−	11027.7i	0.296248	−	0.513116i	0.975274	+	0.220997i	$0.0709312\pi$
$774$		0			0
$775$	−14824.7			−0.687121
$776$	−7669.59	+	13284.1i	−0.354796	+	0.614526i
$777$		0			0
$778$	−6860.46	−	11882.7i	−0.316143	−	0.547576i
$779$	5014.98			0.230655
$780$		0			0
$781$	59818.8			2.74070
$782$	−1959.88	−	3394.60i	−0.0896228	−	0.155231i
$783$		0			0
$784$	14335.7	−	24830.1i	0.653046	−	1.13111i
$785$	−628.986			−0.0285980
$786$		0			0
$787$	−14214.7	+	24620.5i	−0.643834	+	1.11515i	0.340735	+	0.940159i	$0.389324\pi$
$787$	−14214.7	+	24620.5i	−0.643834	+	1.11515i	−0.984569	+	0.174994i	$0.944009\pi$
$788$	−613.344			−0.0277278
$789$		0			0
$790$	−103.605	−	179.448i	−0.00466593	−	0.00808163i
$791$	805.238	+	1394.71i	0.0361959	+	0.0626932i
$792$		0			0
$793$	8511.70	+	5480.30i	0.381159	+	0.245412i
$794$	−26048.7			−1.16427
$795$		0			0
$796$	162.813	+	282.000i	0.00724967	+	0.0125568i
$797$	−5963.36	+	10328.8i	−0.265035	+	0.459054i	−0.967573	−	0.252592i	$-0.918717\pi$
$797$	−5963.36	+	10328.8i	−0.265035	+	0.459054i	0.702538	+	0.711646i	$0.252050\pi$
$798$		0			0
$799$	5034.00	−	8719.14i	0.222891	−	0.386059i
$800$	−1137.68	+	1970.52i	−0.0502789	+	0.0870856i
$801$		0			0
$802$	12095.6	−	20950.2i	0.532557	−	0.922416i
$803$	−24650.7	−	42696.2i	−1.08332	−	1.87636i
$804$		0			0
$805$	−128.749			−0.00563702
$806$	−13635.3	+	7014.91i	−0.595885	+	0.306563i
$807$		0			0
$808$	−9189.87	−	15917.3i	−0.400122	−	0.693032i
$809$	−10002.8	−	17325.4i	−0.434710	−	0.752940i	0.562562	−	0.826755i	$-0.309816\pi$
$809$	−10002.8	−	17325.4i	−0.434710	−	0.752940i	−0.997272	+	0.0738150i	$0.976483\pi$
$810$		0			0
$811$	−5933.84			−0.256924			−0.128462	−	0.991714i	$-0.541004\pi$
$811$	−5933.84			−0.256924			−0.128462	+	0.991714i	$0.541004\pi$
$812$	1129.64	−	1956.59i	0.0488207	−	0.0845600i
$813$		0			0
$814$	55603.8			2.39424
$815$	85.8968	−	148.778i	0.00369182	−	0.00639442i
$816$		0			0
$817$	−503.412	−	871.935i	−0.0215571	−	0.0373380i
$818$	12458.9			0.532537
$819$		0			0
$820$	−43.6798			−0.00186020
$821$	9228.51	+	15984.2i	0.392299	+	0.679481i	0.992752	−	0.120178i	$-0.0383466\pi$
$821$	9228.51	+	15984.2i	0.392299	+	0.679481i	−0.600454	+	0.799660i	$0.705013\pi$
$822$		0			0
$823$	13260.1	−	22967.2i	0.561627	−	0.972767i	−0.435727	−	0.900079i	$-0.643509\pi$
$823$	13260.1	−	22967.2i	0.561627	−	0.972767i	0.997355	−	0.0726886i	$-0.0231579\pi$
$824$	22715.9			0.960372
$825$		0			0
$826$	8049.68	−	13942.4i	0.339085	−	0.587312i
$827$	−25664.8			−1.07915			−0.539573	−	0.841939i	$-0.681414\pi$
$827$	−25664.8			−1.07915			−0.539573	+	0.841939i	$0.681414\pi$
$828$		0			0
$829$	−2181.34	−	3778.20i	−0.0913887	−	0.158290i	0.816707	−	0.577053i	$-0.195797\pi$
$829$	−2181.34	−	3778.20i	−0.0913887	−	0.158290i	−0.908096	+	0.418763i	$0.862464\pi$
$830$	369.306	+	639.656i	0.0154443	+	0.0267504i
$831$		0			0
$832$	−1214.64	+	25053.0i	−0.0506130	+	1.04394i
$833$	−46746.6			−1.94439
$834$		0			0
$835$	620.558	+	1074.84i	0.0257189	+	0.0445465i
$836$	184.545	−	319.642i	0.00763473	−	0.0132237i
$837$		0			0
$838$	16546.5	−	28659.4i	0.682089	−	1.18141i
$839$	17510.1	−	30328.4i	0.720520	−	1.24798i	−0.240272	−	0.970706i	$-0.577237\pi$
$839$	17510.1	−	30328.4i	0.720520	−	1.24798i	0.960792	−	0.277271i	$-0.0894300\pi$
$840$		0			0
$841$	−7069.00	+	12243.9i	−0.289844	+	0.502024i
$842$	−13411.4	−	23229.2i	−0.548915	−	0.950749i
$843$		0			0
$844$	2119.46			0.0864394
$845$	684.893	+	66.5674i	0.0278829	+	0.00271005i
$846$		0			0
$847$	−38070.2	−	65939.6i	−1.54440	−	2.67498i
$848$	18027.4	+	31224.3i	0.730026	+	1.26444i
$849$		0			0
$850$	−34022.6			−1.37290
$851$	−2296.02	+	3976.83i	−0.0924872	+	0.160193i
$852$		0			0
$853$	8318.36			0.333898			0.166949	−	0.985966i	$-0.446608\pi$
$853$	8318.36			0.333898			0.166949	+	0.985966i	$0.446608\pi$
$854$	−8502.61	+	14726.9i	−0.340695	+	0.590100i
$855$		0			0
$856$	−9333.17	−	16165.5i	−0.372665	−	0.645474i
$857$	34832.3			1.38839			0.694193	−	0.719789i	$-0.255761\pi$
$857$	34832.3			1.38839			0.694193	+	0.719789i	$0.255761\pi$
$858$		0			0
$859$	−12571.8			−0.499353			−0.249676	−	0.968329i	$-0.580324\pi$
$859$	−12571.8			−0.499353			−0.249676	+	0.968329i	$0.580324\pi$
$860$	4.38465	+	7.59443i	0.000173855	+	0.000301126i
$861$		0			0
$862$	−5665.57	+	9813.05i	−0.223863	+	0.387742i
$863$	22474.2			0.886480			0.443240	−	0.896403i	$-0.353829\pi$
$863$	22474.2			0.886480			0.443240	+	0.896403i	$0.353829\pi$
$864$		0			0
$865$	270.854	−	469.133i	0.0106466	−	0.0184405i
$866$	−8009.90			−0.314304
$867$		0			0
$868$	683.081	+	1183.13i	0.0267112	+	0.0462651i
$869$	7586.78	+	13140.7i	0.296161	+	0.512966i
$870$		0			0
$871$	2859.44	−	1471.09i	0.111238	−	0.0572283i
$872$	19575.2			0.760205
$873$		0			0
$874$	−287.351	−	497.707i	−0.0111210	−	0.0192622i
$875$	−1117.95	+	1936.35i	−0.0431927	+	0.0748120i
$876$		0			0
$877$	−2692.60	+	4663.72i	−0.103675	+	0.179570i	−0.913196	−	0.407521i	$-0.866393\pi$
$877$	−2692.60	+	4663.72i	−0.103675	+	0.179570i	0.809521	+	0.587090i	$0.199727\pi$
$878$	12230.6	−	21184.0i	0.470117	−	0.814266i
$879$		0			0
$880$	600.087	−	1039.38i	0.0229874	−	0.0398154i
$881$	14886.3	+	25783.9i	0.569278	+	0.986018i	0.996638	+	0.0819365i	$0.0261105\pi$
$881$	14886.3	+	25783.9i	0.569278	+	0.986018i	−0.427360	+	0.904082i	$0.640556\pi$
$882$		0			0
$883$	−27309.6			−1.04082			−0.520409	−	0.853917i	$-0.674220\pi$
$883$	−27309.6			−1.04082			−0.520409	+	0.853917i	$0.674220\pi$
$884$	1659.73	−	853.877i	0.0631480	−	0.0324876i
$885$		0			0
$886$	17420.4	+	30173.0i	0.660552	+	1.14411i
$887$	3264.98	+	5655.12i	0.123594	+	0.214070i	0.921182	−	0.389131i	$-0.127225\pi$
$887$	3264.98	+	5655.12i	0.123594	+	0.214070i	−0.797589	+	0.603202i	$0.793891\pi$
$888$		0			0
$889$	47609.3			1.79614
$890$	545.626	−	945.051i	0.0205499	−	0.0355935i
$891$		0			0
$892$	1890.06			0.0709461
$893$	738.069	−	1278.37i	0.0276579	−	0.0479050i
$894$		0			0
$895$	−227.533	−	394.098i	−0.00849785	−	0.0147187i
$896$	−37970.3			−1.41573
$897$		0			0
$898$	4890.45			0.181733
$899$	−11648.5	−	20175.8i	−0.432145	−	0.748497i
$900$		0			0
$901$	29392.3	−	50909.0i	1.08679	−	1.88238i
$902$	−60307.1			−2.22617
$903$		0			0
$904$	652.874	−	1130.81i	0.0240202	−	0.0416042i
$905$	172.368			0.00633116
$906$		0			0
$907$	−9718.71	−	16833.3i	−0.355793	−	0.616252i	0.631460	−	0.775408i	$-0.282456\pi$
$907$	−9718.71	−	16833.3i	−0.355793	−	0.616252i	−0.987253	+	0.159157i	$0.949123\pi$
$908$	717.351	+	1242.49i	0.0262182	+	0.0454113i
$909$		0			0
$910$	−55.9755	+	1154.55i	−0.00203909	+	0.0420581i
$911$	50234.6			1.82694			0.913472	−	0.406901i	$-0.133391\pi$
$911$	50234.6			1.82694			0.913472	+	0.406901i	$0.133391\pi$
$912$		0			0
$913$	−27043.6	−	46840.9i	−0.980299	−	1.69793i
$914$	8501.48	−	14725.0i	0.307663	−	0.532888i
$915$		0			0
$916$	−633.581	+	1097.39i	−0.0228538	+	0.0395840i
$917$	−8607.35	+	14908.4i	−0.309967	+	0.536878i
$918$		0			0
$919$	−6142.62	+	10639.3i	−0.220486	+	0.381892i	−0.954956	−	0.296749i	$-0.904098\pi$
$919$	−6142.62	+	10639.3i	−0.220486	+	0.381892i	0.734470	+	0.678641i	$0.237431\pi$
$920$	52.1937	+	90.4022i	0.00187041	+	0.00323964i
$921$		0			0
$922$	20549.1			0.734000
$923$	37291.3	+	24010.2i	1.32986	+	0.856236i
$924$		0			0
$925$	19929.0	+	34518.0i	0.708390	+	1.22697i
$926$	7441.64	+	12889.3i	0.264090	+	0.457417i
$927$		0			0
$928$	−3575.72			−0.126486
$929$	−12805.0	+	22178.9i	−0.452227	+	0.783280i	−0.998524	−	0.0543114i	$-0.982704\pi$
$929$	−12805.0	+	22178.9i	−0.452227	+	0.783280i	0.546297	+	0.837591i	$0.316037\pi$
$930$		0			0
$931$	−6853.84			−0.241273
$932$	−171.761	+	297.498i	−0.00603670	+	0.0104559i
$933$		0			0
$934$	5501.55	+	9528.96i	0.192737	+	0.333830i
$935$	−1956.80			−0.0684429
$936$		0			0
$937$	−29893.2			−1.04223			−0.521114	−	0.853487i	$-0.674483\pi$
$937$	−29893.2			−1.04223			−0.521114	+	0.853487i	$0.674483\pi$
$938$	2700.83	+	4677.97i	0.0940140	+	0.162837i
$939$		0			0
$940$	−6.42848	+	11.1345i	−0.000223057	+	0.000386347i
$941$	44960.3			1.55756			0.778780	−	0.627297i	$-0.215839\pi$
$941$	44960.3			1.55756			0.778780	+	0.627297i	$0.215839\pi$
$942$		0			0
$943$	2490.23	−	4313.21i	0.0859947	−	0.148947i
$944$	−12394.0			−0.427320
$945$		0			0
$946$	6053.72	+	10485.3i	0.208058	+	0.360368i
$947$	16798.8	+	29096.4i	0.576439	+	0.998422i	0.995884	+	0.0906410i	$0.0288916\pi$
$947$	16798.8	+	29096.4i	0.576439	+	0.998422i	−0.419444	+	0.907781i	$0.637775\pi$
$948$		0			0
$949$	1770.17	−	36511.4i	0.0605502	−	1.24890i
$950$	−4988.29			−0.170360
$951$		0			0
$952$	32692.5	+	56625.1i	1.11299	+	1.92776i
$953$	12925.1	−	22387.0i	0.439335	−	0.760950i	−0.558303	−	0.829637i	$-0.688547\pi$
$953$	12925.1	−	22387.0i	0.439335	−	0.760950i	0.997638	+	0.0686864i	$0.0218808\pi$
$954$		0			0
$955$	−292.644	+	506.874i	−0.00991595	+	0.0171749i
$956$	441.080	−	763.973i	0.0149221	−	0.0258459i
$957$		0			0
$958$	4343.37	−	7522.94i	0.146480	−	0.253711i
$959$	6022.47	+	10431.2i	0.202790	+	0.351243i
$960$		0			0
$961$	−15703.5			−0.527123
$962$	34663.7	+	22318.4i	1.16175	+	0.747998i
$963$		0			0
$964$	1275.29	+	2208.87i	0.0426082	+	0.0737996i
$965$	650.931	+	1127.45i	0.0217142	+	0.0376101i
$966$		0			0
$967$	6296.49			0.209392			0.104696	−	0.994504i	$-0.466613\pi$
$967$	6296.49			0.209392			0.104696	+	0.994504i	$0.466613\pi$
$968$	−30866.7	+	53462.7i	−1.02489	+	1.77516i
$969$		0			0
$970$	571.749			0.0189255
$971$	3903.21	−	6760.56i	0.129001	−	0.223436i	−0.794289	−	0.607540i	$-0.792156\pi$
$971$	3903.21	−	6760.56i	0.129001	−	0.223436i	0.923290	+	0.384104i	$0.125490\pi$
$972$		0			0
$973$	−416.638	−	721.638i	−0.0137274	−	0.0237766i
$974$	10774.8			0.354462
$975$		0			0
$976$	13091.3			0.429348
$977$	−27846.4	−	48231.4i	−0.911858	−	1.57938i	−0.811438	−	0.584438i	$-0.801315\pi$
$977$	−27846.4	−	48231.4i	−0.911858	−	1.57938i	−0.100420	−	0.994945i	$-0.532019\pi$
$978$		0			0
$979$	−39955.2	+	69204.4i	−1.30437	+	2.25923i
$980$	59.6960			0.00194584
$981$		0			0
$982$	9157.92	−	15862.0i	0.297598	−	0.515454i
$983$	−44635.5			−1.44827			−0.724135	−	0.689658i	$-0.757761\pi$
$983$	−44635.5			−1.44827			−0.724135	+	0.689658i	$0.757761\pi$
$984$		0			0
$985$	238.381	+	412.888i	0.00771112	+	0.0133560i
$986$	−26733.2	−	46303.3i	−0.863447	−	1.49553i
$987$		0			0
$988$	243.345	−	125.193i	0.00783587	−	0.00403129i
$989$	−999.892			−0.0321484
$990$		0			0
$991$	−1942.16	−	3363.92i	−0.0622551	−	0.107829i	0.833218	−	0.552945i	$-0.186496\pi$
$991$	−1942.16	−	3363.92i	−0.0622551	−	0.107829i	−0.895473	+	0.445116i	$0.853163\pi$
$992$	1081.11	−	1872.53i	0.0346020	−	0.0599323i
$993$		0			0
$994$	−37251.5	+	64521.5i	−1.18868	+	2.05885i
$995$	126.557	−	219.203i	0.00403228	−	0.00698412i
$996$		0			0
$997$	9010.72	−	15607.0i	0.286231	−	0.495767i	−0.686676	−	0.726964i	$-0.740931\pi$
$997$	9010.72	−	15607.0i	0.286231	−	0.495767i	0.972907	+	0.231197i	$0.0742642\pi$
$998$	8422.95	+	14589.0i	0.267158	+	0.462731i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.g.f.55.6	yes	16
3.2	odd	2	inner	117.4.g.f.55.3	✓	16
13.3	even	3		1521.4.a.bc.1.3		8
13.9	even	3	inner	117.4.g.f.100.6	yes	16
13.10	even	6		1521.4.a.bd.1.6		8
39.23	odd	6		1521.4.a.bd.1.3		8
39.29	odd	6		1521.4.a.bc.1.6		8
39.35	odd	6	inner	117.4.g.f.100.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.g.f.55.3	✓	16	3.2	odd	2	inner
117.4.g.f.55.6	yes	16	1.1	even	1	trivial
117.4.g.f.100.3	yes	16	39.35	odd	6	inner
117.4.g.f.100.6	yes	16	13.9	even	3	inner
1521.4.a.bc.1.3		8	13.3	even	3
1521.4.a.bc.1.6		8	39.29	odd	6
1521.4.a.bd.1.3		8	39.23	odd	6
1521.4.a.bd.1.6		8	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37814 + 2.38701i) q^{2} +(0.201468 - 0.348954i) q^{4} -0.313209 q^{5} +(-14.2830 + 24.7388i) q^{7} +23.1608 q^{8} +O(q^{10})\)	\(q+(1.37814 + 2.38701i) q^{2} +(0.201468 - 0.348954i) q^{4} -0.313209 q^{5} +(-14.2830 + 24.7388i) q^{7} +23.1608 q^{8} +(-0.431646 - 0.747632i) q^{10} +(31.6086 + 54.7478i) q^{11} +(-2.26982 + 46.8172i) q^{13} -78.7357 q^{14} +(30.3071 + 52.4934i) q^{16} +(49.4135 - 85.5867i) q^{17} +(7.24486 - 12.5485i) q^{19} +(-0.0631018 + 0.109295i) q^{20} +(-87.1222 + 150.900i) q^{22} +(-7.19499 - 12.4621i) q^{23} -124.902 q^{25} +(-114.881 + 59.1025i) q^{26} +(5.75514 + 9.96819i) q^{28} +(-98.1415 - 169.986i) q^{29} +118.691 q^{31} +(9.10860 - 15.7766i) q^{32} +272.395 q^{34} +(4.47356 - 7.74843i) q^{35} +(-159.557 - 276.361i) q^{37} +39.9377 q^{38} -7.25418 q^{40} +(173.053 + 299.737i) q^{41} +(34.7427 - 60.1761i) q^{43} +25.4726 q^{44} +(19.8314 - 34.3490i) q^{46} +101.875 q^{47} +(-236.507 - 409.642i) q^{49} +(-172.132 - 298.142i) q^{50} +(15.8797 + 10.2242i) q^{52} +594.823 q^{53} +(-9.90012 - 17.1475i) q^{55} +(-330.806 + 572.972i) q^{56} +(270.505 - 468.529i) q^{58} +(-102.237 + 177.079i) q^{59} +(107.989 - 187.043i) q^{61} +(163.572 + 283.315i) q^{62} +535.125 q^{64} +(0.710929 - 14.6636i) q^{65} +(-34.3025 - 59.4136i) q^{67} +(-19.9105 - 34.4860i) q^{68} +24.6607 q^{70} +(473.121 - 819.469i) q^{71} -779.872 q^{73} +(439.784 - 761.727i) q^{74} +(-2.91922 - 5.05624i) q^{76} -1805.86 q^{77} +240.022 q^{79} +(-9.49245 - 16.4414i) q^{80} +(-476.982 + 826.158i) q^{82} -855.576 q^{83} +(-15.4768 + 26.8065i) q^{85} +191.521 q^{86} +(732.082 + 1268.00i) q^{88} +(632.029 + 1094.71i) q^{89} +(-1125.78 - 724.842i) q^{91} -5.79825 q^{92} +(140.398 + 243.176i) q^{94} +(-2.26916 + 3.93030i) q^{95} +(-331.145 + 573.560i) q^{97} +(651.879 - 1129.09i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 40 q^{4} + 22 q^{7}+O(q^{10}) \) 16 * q - 40 * q^4 + 22 * q^7	\( 16 q - 40 q^{4} + 22 q^{7} - 36 q^{10} + 36 q^{13} - 204 q^{16} - 244 q^{19} - 136 q^{22} + 708 q^{25} + 452 q^{28} + 484 q^{31} - 2584 q^{34} - 1018 q^{37} + 3400 q^{40} - 74 q^{43} + 896 q^{46} - 298 q^{49} - 1676 q^{52} - 1300 q^{55} - 812 q^{58} - 1148 q^{61} + 7272 q^{64} + 2198 q^{67} + 4400 q^{70} - 4352 q^{73} - 6936 q^{76} + 3724 q^{79} - 5436 q^{82} + 890 q^{85} - 3528 q^{88} - 4754 q^{91} + 3104 q^{94} + 4370 q^{97}+O(q^{100}) \) 16 * q - 40 * q^4 + 22 * q^7 - 36 * q^10 + 36 * q^13 - 204 * q^16 - 244 * q^19 - 136 * q^22 + 708 * q^25 + 452 * q^28 + 484 * q^31 - 2584 * q^34 - 1018 * q^37 + 3400 * q^40 - 74 * q^43 + 896 * q^46 - 298 * q^49 - 1676 * q^52 - 1300 * q^55 - 812 * q^58 - 1148 * q^61 + 7272 * q^64 + 2198 * q^67 + 4400 * q^70 - 4352 * q^73 - 6936 * q^76 + 3724 * q^79 - 5436 * q^82 + 890 * q^85 - 3528 * q^88 - 4754 * q^91 + 3104 * q^94 + 4370 * q^97

Introduction

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