LMFDB - Embedded newform 180.7.f.g.19.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,7,Mod(19,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("180.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	180.f (of order $2$, degree $1$, 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:	$41.4097350516$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.18
Character	$\chi$	$=$	180.19
Dual form			180.7.f.g.19.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.294917 + 7.99456i) q^{2} +(-63.8260 - 4.71546i) q^{4} +(-71.1255 + 102.792i) q^{5} -496.078 q^{7} +(56.5214 - 508.871i) q^{8} +O(q^{10})$	\(q+(-0.294917 + 7.99456i) q^{2} +(-63.8260 - 4.71546i) q^{4} +(-71.1255 + 102.792i) q^{5} -496.078 q^{7} +(56.5214 - 508.871i) q^{8} +(-800.800 - 598.932i) q^{10} -561.571i q^{11} -1584.68i q^{13} +(146.302 - 3965.93i) q^{14} +(4051.53 + 601.938i) q^{16} -4503.06i q^{17} +10102.8i q^{19} +(5024.37 - 6225.41i) q^{20} +(4489.52 + 165.617i) q^{22} -16192.2 q^{23} +(-5507.32 - 14622.2i) q^{25} +(12668.8 + 467.349i) q^{26} +(31662.7 + 2339.24i) q^{28} -2001.00 q^{29} +7380.01i q^{31} +(-6007.10 + 32212.7i) q^{32} +(36000.0 + 1328.03i) q^{34} +(35283.8 - 50992.8i) q^{35} +66699.3i q^{37} +(-80767.5 - 2979.48i) q^{38} +(48287.6 + 42003.6i) q^{40} +97191.8 q^{41} -112822. q^{43} +(-2648.07 + 35842.9i) q^{44} +(4775.36 - 129450. i) q^{46} +196416. q^{47} +128445. q^{49} +(118523. - 39716.3i) q^{50} +(-7472.50 + 101144. i) q^{52} -72076.9i q^{53} +(57724.9 + 39942.0i) q^{55} +(-28039.0 + 252440. i) q^{56} +(590.128 - 15997.1i) q^{58} -141896. i q^{59} +201436. q^{61} +(-59000.0 - 2176.49i) q^{62} +(-255755. - 57524.2i) q^{64} +(162892. + 112711. i) q^{65} -216637. q^{67} +(-21234.0 + 287413. i) q^{68} +(397259. + 297117. i) q^{70} +358449. i q^{71} +411536. i q^{73} +(-533231. - 19670.7i) q^{74} +(47639.3 - 644822. i) q^{76} +278583. i q^{77} -272036. i q^{79} +(-350041. + 373651. i) q^{80} +(-28663.5 + 777005. i) q^{82} -252398. q^{83} +(462878. + 320283. i) q^{85} +(33273.2 - 901965. i) q^{86} +(-285767. - 31740.8i) q^{88} +87241.6 q^{89} +786126. i q^{91} +(1.03349e6 + 76353.9i) q^{92} +(-57926.2 + 1.57026e6i) q^{94} +(-1.03849e6 - 718567. i) q^{95} -130653. i q^{97} +(-37880.4 + 1.02686e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} - 44 q^{5}+O(q^{10}) $ 36 * q - 66 * q^4 - 44 * q^5	$ 36 q - 66 q^{4} - 44 q^{5} - 1422 q^{10} - 15484 q^{14} + 1266 q^{16} + 2188 q^{20} + 13812 q^{25} + 32052 q^{26} + 36920 q^{29} - 156204 q^{34} + 7674 q^{40} - 341848 q^{41} - 74892 q^{44} + 478080 q^{46} + 482556 q^{49} + 191448 q^{50} + 926132 q^{56} - 455976 q^{61} - 618 q^{64} + 624192 q^{65} - 1871304 q^{70} + 612324 q^{74} - 1566456 q^{76} - 2360972 q^{80} + 2280864 q^{85} - 5157592 q^{86} + 1806104 q^{89} - 3121992 q^{94}+O(q^{100}) $ 36 * q - 66 * q^4 - 44 * q^5 - 1422 * q^10 - 15484 * q^14 + 1266 * q^16 + 2188 * q^20 + 13812 * q^25 + 32052 * q^26 + 36920 * q^29 - 156204 * q^34 + 7674 * q^40 - 341848 * q^41 - 74892 * q^44 + 478080 * q^46 + 482556 * q^49 + 191448 * q^50 + 926132 * q^56 - 455976 * q^61 - 618 * q^64 + 624192 * q^65 - 1871304 * q^70 + 612324 * q^74 - 1566456 * q^76 - 2360972 * q^80 + 2280864 * q^85 - 5157592 * q^86 + 1806104 * q^89 - 3121992 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.294917	+	7.99456i	−0.0368646	+	0.999320i
$2$	−0.294917	+	7.99456i	−0.0368646	+	0.999320i
$3$		0			0
$3$		0			0
$4$	−63.8260	−	4.71546i	−0.997282	−	0.0736790i
$5$	−71.1255	+	102.792i	−0.569004	+	0.822335i
$5$	−71.1255	+	102.792i	−0.569004	+	0.822335i
$6$		0			0
$7$	−496.078			−1.44629			−0.723146	−	0.690695i	$-0.757305\pi$
$7$	−496.078			−1.44629			−0.723146	+	0.690695i	$0.757305\pi$
$8$	56.5214	−	508.871i	0.110393	−	0.993888i
$9$		0			0
$10$	−800.800	−	598.932i	−0.800800	−	0.598932i
$11$		−	561.571i		−	0.421917i	−0.977495	−	0.210958i	$-0.932342\pi$
$11$		−	561.571i		−	0.421917i	0.977495	−	0.210958i	$-0.0676585\pi$
$12$		0			0
$13$		−	1584.68i		−	0.721294i	−0.932702	−	0.360647i	$-0.882556\pi$
$13$		−	1584.68i		−	0.721294i	0.932702	−	0.360647i	$-0.117444\pi$
$14$	146.302	−	3965.93i	0.0533169	−	1.44531i
$15$		0			0
$16$	4051.53	+	601.938i	0.989143	+	0.146958i
$17$		−	4503.06i		−	0.916561i	−0.888808	−	0.458281i	$-0.848465\pi$
$17$		−	4503.06i		−	0.916561i	0.888808	−	0.458281i	$-0.151535\pi$
$18$		0			0
$19$			10102.8i			1.47293i	0.676478	+	0.736463i	$0.263505\pi$
$19$			10102.8i			1.47293i	−0.676478	+	0.736463i	$0.736495\pi$
$20$	5024.37	−	6225.41i	0.628046	−	0.778176i
$21$		0			0
$22$	4489.52	+	165.617i	0.421630	+	0.0155538i
$23$	−16192.2			−1.33083			−0.665417	−	0.746472i	$-0.731746\pi$
$23$	−16192.2			−1.33083			−0.665417	+	0.746472i	$0.731746\pi$
$24$		0			0
$25$	−5507.32	−	14622.2i	−0.352469	−	0.935824i
$26$	12668.8	+	467.349i	0.720803	+	0.0265902i
$27$		0			0
$28$	31662.7	+	2339.24i	1.44236	+	0.106561i
$29$	−2001.00			−0.0820451			−0.0410225	−	0.999158i	$-0.513062\pi$
$29$	−2001.00			−0.0820451			−0.0410225	+	0.999158i	$0.513062\pi$
$30$		0			0
$31$			7380.01i			0.247726i	0.992299	+	0.123863i	$0.0395284\pi$
$31$			7380.01i			0.247726i	−0.992299	+	0.123863i	$0.960472\pi$
$32$	−6007.10	+	32212.7i	−0.183322	+	0.983053i
$33$		0			0
$34$	36000.0	+	1328.03i	0.915938	+	0.0337886i
$35$	35283.8	−	50992.8i	0.822946	−	1.18934i
$36$		0			0
$37$			66699.3i			1.31679i	0.752674	+	0.658394i	$0.228764\pi$
$37$			66699.3i			1.31679i	−0.752674	+	0.658394i	$0.771236\pi$
$38$	−80767.5	−	2979.48i	−1.47192	−	0.0542988i
$39$		0			0
$40$	48287.6	+	42003.6i	0.754494	+	0.656307i
$41$	97191.8			1.41019			0.705095	−	0.709113i	$-0.250904\pi$
$41$	97191.8			1.41019			0.705095	+	0.709113i	$0.250904\pi$
$42$		0			0
$43$	−112822.			−1.41902			−0.709512	−	0.704693i	$-0.751085\pi$
$43$	−112822.			−1.41902			−0.709512	+	0.704693i	$0.751085\pi$
$44$	−2648.07	+	35842.9i	−0.0310864	+	0.420770i
$45$		0			0
$46$	4775.36	−	129450.i	0.0490606	−	1.32993i
$47$	196416.			1.89183			0.945916	−	0.324412i	$-0.105167\pi$
$47$	196416.			1.89183			0.945916	+	0.324412i	$0.105167\pi$
$48$		0			0
$49$	128445.			1.09176
$50$	118523.	−	39716.3i	0.948181	−	0.317730i
$51$		0			0
$52$	−7472.50	+	101144.i	−0.0531442	+	0.719333i
$53$		−	72076.9i		−	0.484137i	−0.970259	−	0.242069i	$-0.922174\pi$
$53$		−	72076.9i		−	0.484137i	0.970259	−	0.242069i	$-0.0778260\pi$
$54$		0			0
$55$	57724.9	+	39942.0i	0.346957	+	0.240072i
$56$	−28039.0	+	252440.i	−0.159661	+	1.43745i
$57$		0			0
$58$	590.128	−	15997.1i	0.00302456	−	0.0819893i
$59$		−	141896.i		−	0.690898i	−0.938438	−	0.345449i	$-0.887727\pi$
$59$		−	141896.i		−	0.690898i	0.938438	−	0.345449i	$-0.112273\pi$
$60$		0			0
$61$	201436.			0.887457			0.443728	−	0.896161i	$-0.353656\pi$
$61$	201436.			0.887457			0.443728	+	0.896161i	$0.353656\pi$
$62$	−59000.0	−	2176.49i	−0.247558	−	0.00913233i
$63$		0			0
$64$	−255755.	−	57524.2i	−0.975627	−	0.219437i
$65$	162892.	+	112711.i	0.593145	+	0.410419i
$66$		0			0
$67$	−216637.			−0.720293			−0.360146	−	0.932896i	$-0.617273\pi$
$67$	−216637.			−0.720293			−0.360146	+	0.932896i	$0.617273\pi$
$68$	−21234.0	+	287413.i	−0.0675313	+	0.914070i
$69$		0			0
$70$	397259.	+	297117.i	1.15819	+	0.866231i
$71$			358449.i			1.00150i	0.865591	+	0.500751i	$0.166943\pi$
$71$			358449.i			1.00150i	−0.865591	+	0.500751i	$0.833057\pi$
$72$		0			0
$73$			411536.i			1.05789i	0.848657	+	0.528944i	$0.177412\pi$
$73$			411536.i			1.05789i	−0.848657	+	0.528944i	$0.822588\pi$
$74$	−533231.	−	19670.7i	−1.31589	−	0.0485428i
$75$		0			0
$76$	47639.3	−	644822.i	0.108524	−	1.46892i
$77$			278583.i			0.610215i
$78$		0			0
$79$		−	272036.i		−	0.551754i	−0.961193	−	0.275877i	$-0.911032\pi$
$79$		−	272036.i		−	0.551754i	0.961193	−	0.275877i	$-0.0889683\pi$
$80$	−350041.	+	373651.i	−0.683675	+	0.729787i
$81$		0			0
$82$	−28663.5	+	777005.i	−0.0519861	+	1.40923i
$83$	−252398.			−0.441419			−0.220709	−	0.975340i	$-0.570837\pi$
$83$	−252398.			−0.441419			−0.220709	+	0.975340i	$0.570837\pi$
$84$		0			0
$85$	462878.	+	320283.i	0.753720	+	0.521527i
$86$	33273.2	−	901965.i	0.0523117	−	1.41806i
$87$		0			0
$88$	−285767.	−	31740.8i	−0.419338	−	0.0465768i
$89$	87241.6			0.123752			0.0618762	−	0.998084i	$-0.480292\pi$
$89$	87241.6			0.123752			0.0618762	+	0.998084i	$0.480292\pi$
$90$		0			0
$91$			786126.i			1.04320i
$92$	1.03349e6	+	76353.9i	1.32722	+	0.0980545i
$93$		0			0
$94$	−57926.2	+	1.57026e6i	−0.0697416	+	1.89055i
$95$	−1.03849e6	−	718567.i	−1.21124	−	0.838101i
$96$		0			0
$97$		−	130653.i		−	0.143154i	−0.997435	−	0.0715771i	$-0.977197\pi$
$97$		−	130653.i		−	0.143154i	0.997435	−	0.0715771i	$-0.0228032\pi$
$98$	−37880.4	+	1.02686e6i	−0.0402473	+	1.09102i
$99$		0			0
$100$	282560.	+	959250.i	0.282560	+	0.959250i
$101$	1.08656e6			1.05460			0.527300	−	0.849679i	$-0.323204\pi$
$101$	1.08656e6			1.05460			0.527300	+	0.849679i	$0.323204\pi$
$102$		0			0
$103$	1.78249e6			1.63123			0.815616	−	0.578594i	$-0.196398\pi$
$103$	1.78249e6			1.63123			0.815616	+	0.578594i	$0.196398\pi$
$104$	−806398.	−	89568.5i	−0.716885	−	0.0796260i
$105$		0			0
$106$	576224.	+	21256.7i	0.483808	+	0.0178475i
$107$	558410.			0.455829			0.227915	−	0.973681i	$-0.426809\pi$
$107$	558410.			0.455829			0.227915	+	0.973681i	$0.426809\pi$
$108$		0			0
$109$	−453156.			−0.349920			−0.174960	−	0.984576i	$-0.555980\pi$
$109$	−453156.			−0.349920			−0.174960	+	0.984576i	$0.555980\pi$
$110$	−336343.	+	449706.i	−0.252700	+	0.337871i
$111$		0			0
$112$	−2.00987e6	−	298608.i	−1.43059	−	0.212544i
$113$		−	1.83286e6i		−	1.27026i	−0.772403	−	0.635132i	$-0.780946\pi$
$113$		−	1.83286e6i		−	1.27026i	0.772403	−	0.635132i	$-0.219054\pi$
$114$		0			0
$115$	1.15168e6	−	1.66443e6i	0.757250	−	1.09439i
$116$	127716.	+	9435.62i	0.0818221	+	0.00604500i
$117$		0			0
$118$	1.13440e6	+	41847.4i	0.690428	+	0.0254696i
$119$			2.23387e6i			1.32562i
$120$		0			0
$121$	1.45620e6			0.821986
$122$	−59406.8	+	1.61039e6i	−0.0327157	+	0.886853i
$123$		0			0
$124$	34800.2	−	471037.i	0.0182522	−	0.247053i
$125$	1.89476e6	+	473907.i	0.970116	+	0.242640i
$126$		0			0
$127$	−1.99686e6			−0.974847			−0.487423	−	0.873166i	$-0.662063\pi$
$127$	−1.99686e6			−0.974847			−0.487423	+	0.873166i	$0.662063\pi$
$128$	535307.	−	2.02768e6i	0.255254	−	0.966874i
$129$		0			0
$130$	−949118.	+	1.26901e6i	−0.432006	+	0.577612i
$131$		−	596204.i		−	0.265205i	−0.991169	−	0.132602i	$-0.957667\pi$
$131$		−	596204.i		−	0.265205i	0.991169	−	0.132602i	$-0.0423333\pi$
$132$		0			0
$133$		−	5.01178e6i		−	2.13028i
$134$	63890.0	−	1.73192e6i	0.0265533	−	0.719803i
$135$		0			0
$136$	−2.29148e6	−	254519.i	−0.910959	−	0.101182i
$137$		−	4.42870e6i		−	1.72232i	−0.508332	−	0.861161i	$-0.669738\pi$
$137$		−	4.42870e6i		−	1.72232i	0.508332	−	0.861161i	$-0.330262\pi$
$138$		0			0
$139$		−	5.04455e6i		−	1.87836i	−0.343431	−	0.939178i	$-0.611589\pi$
$139$		−	5.04455e6i		−	1.87836i	0.343431	−	0.939178i	$-0.388411\pi$
$140$	−2.49248e6	+	3.08829e6i	−0.908338	+	1.12547i
$141$		0			0
$142$	−2.86564e6	−	105713.i	−1.00082	−	0.0369200i
$143$	−889912.			−0.304326
$144$		0			0
$145$	142322.	−	205686.i	0.0466840	−	0.0674685i
$146$	−3.29005e6	−	121369.i	−1.05717	−	0.0389986i
$147$		0			0
$148$	314518.	−	4.25715e6i	0.0970197	−	1.31321i
$149$	2.31618e6			0.700185			0.350093	−	0.936715i	$-0.386150\pi$
$149$	2.31618e6			0.700185			0.350093	+	0.936715i	$0.386150\pi$
$150$		0			0
$151$			5.72844e6i			1.66382i	0.554912	+	0.831909i	$0.312752\pi$
$151$			5.72844e6i			1.66382i	−0.554912	+	0.831909i	$0.687248\pi$
$152$	5.14102e6	+	571024.i	1.46392	+	0.162601i
$153$		0			0
$154$	−2.22715e6	−	82158.8i	−0.609800	−	0.0224953i
$155$	−758605.	−	524907.i	−0.203714	−	0.140957i
$156$		0			0
$157$		−	214345.i		−	0.0553879i	−0.999616	−	0.0276940i	$-0.991184\pi$
$157$		−	214345.i		−	0.0553879i	0.999616	−	0.0276940i	$-0.00881639\pi$
$158$	2.17481e6	+	80228.0i	0.551379	+	0.0203402i
$159$		0			0
$160$	−2.88394e6	−	2.90862e6i	−0.704088	−	0.710113i
$161$	8.03262e6			1.92477
$162$		0			0
$163$	−5.13155e6			−1.18491			−0.592456	−	0.805603i	$-0.701842\pi$
$163$	−5.13155e6			−1.18491			−0.592456	+	0.805603i	$0.701842\pi$
$164$	−6.20337e6	−	458304.i	−1.40636	−	0.103902i
$165$		0			0
$166$	74436.2	−	2.01781e6i	0.0162727	−	0.441119i
$167$	3.05651e6			0.656260			0.328130	−	0.944633i	$-0.393582\pi$
$167$	3.05651e6			0.656260			0.328130	+	0.944633i	$0.393582\pi$
$168$		0			0
$169$	2.31559e6			0.479735
$170$	−2.69703e6	+	3.60605e6i	−0.548958	+	0.733982i
$171$		0			0
$172$	7.20100e6	+	532009.i	1.41517	+	0.104552i
$173$		−	5.15201e6i		−	0.995034i	−0.867454	−	0.497517i	$-0.834245\pi$
$173$		−	5.15201e6i		−	0.995034i	0.867454	−	0.497517i	$-0.165755\pi$
$174$		0			0
$175$	2.73206e6	+	7.25378e6i	0.509773	+	1.35347i
$176$	338031.	−	2.27522e6i	0.0620039	−	0.417336i
$177$		0			0
$178$	−25729.0	+	697459.i	−0.00456208	+	0.123668i
$179$			1.97052e6i			0.343576i	0.985134	+	0.171788i	$0.0549543\pi$
$179$			1.97052e6i			0.343576i	−0.985134	+	0.171788i	$0.945046\pi$
$180$		0			0
$181$	2.34636e6			0.395694			0.197847	−	0.980233i	$-0.436605\pi$
$181$	2.34636e6			0.395694			0.197847	+	0.980233i	$0.436605\pi$
$182$	−6.28474e6	−	231842.i	−1.04249	−	0.0384572i
$183$		0			0
$184$	−915208.	+	8.23976e6i	−0.146915	+	1.32270i
$185$	−6.85614e6	−	4.74402e6i	−1.08284	−	0.749258i
$186$		0			0
$187$	−2.52879e6			−0.386713
$188$	−1.25364e7	−	926190.i	−1.88669	−	0.139388i
$189$		0			0
$190$	6.05089e6	−	8.09032e6i	0.882183	−	1.17952i
$191$		−	9.12751e6i		−	1.30994i	−0.755654	−	0.654971i	$-0.772681\pi$
$191$		−	9.12751e6i		−	1.30994i	0.755654	−	0.654971i	$-0.227319\pi$
$192$		0			0
$193$		−	1.21768e7i		−	1.69379i	−0.531758	−	0.846896i	$-0.678468\pi$
$193$		−	1.21768e7i		−	1.69379i	0.531758	−	0.846896i	$-0.321532\pi$
$194$	1.04451e6	+	38531.7i	0.143057	+	0.00527732i
$195$		0			0
$196$	−8.19811e6	−	605675.i	−1.08879	−	0.0804399i
$197$			5.33007e6i			0.697162i	0.937279	+	0.348581i	$0.113336\pi$
$197$			5.33007e6i			0.697162i	−0.937279	+	0.348581i	$0.886664\pi$
$198$		0			0
$199$			1.70499e6i			0.216353i	0.994132	+	0.108177i	$0.0345012\pi$
$199$			1.70499e6i			0.216353i	−0.994132	+	0.108177i	$0.965499\pi$
$200$	−7.75211e6	+	1.97605e6i	−0.969014	+	0.247006i
$201$		0			0
$202$	−320444.	+	8.68654e6i	−0.0388774	+	1.05388i
$203$	992651.			0.118661
$204$		0			0
$205$	−6.91281e6	+	9.99052e6i	−0.802404	+	1.15965i
$206$	−525686.	+	1.42502e7i	−0.0601347	+	1.63012i
$207$		0			0
$208$	953881.	−	6.42039e6i	0.106000	−	0.713463i
$209$	5.67344e6			0.621452
$210$		0			0
$211$		−	1.25661e7i		−	1.33768i	−0.743407	−	0.668840i	$-0.766791\pi$
$211$		−	1.25661e7i		−	1.33768i	0.743407	−	0.668840i	$-0.233209\pi$
$212$	−339876.	+	4.60039e6i	−0.0356708	+	0.482822i
$213$		0			0
$214$	−164685.	+	4.46425e6i	−0.0168040	+	0.455519i
$215$	8.02455e6	−	1.15972e7i	0.807430	−	1.16691i
$216$		0			0
$217$		−	3.66106e6i		−	0.358285i
$218$	133643.	−	3.62279e6i	0.0128997	−	0.349682i
$219$		0			0
$220$	−3.49601e6	−	2.82154e6i	−0.328325	−	0.264983i
$221$	−7.13593e6			−0.661110
$222$		0			0
$223$	4.78645e6			0.431617			0.215809	−	0.976436i	$-0.430761\pi$
$223$	4.78645e6			0.431617			0.215809	+	0.976436i	$0.430761\pi$
$224$	2.97999e6	−	1.59800e7i	0.265137	−	1.42178i
$225$		0			0
$226$	1.46529e7	+	540541.i	1.26940	+	0.0468278i
$227$	−178099.			−0.0152259			−0.00761296	−	0.999971i	$-0.502423\pi$
$227$	−178099.			−0.0152259			−0.00761296	+	0.999971i	$0.502423\pi$
$228$		0			0
$229$	−1.01777e6			−0.0847505			−0.0423753	−	0.999102i	$-0.513493\pi$
$229$	−1.01777e6			−0.0847505			−0.0423753	+	0.999102i	$0.513493\pi$
$230$	1.29667e7	+	9.69806e6i	1.06573	+	0.797079i
$231$		0			0
$232$	−113099.	+	1.01825e6i	−0.00905723	+	0.0815436i
$233$			2.23582e6i			0.176754i	0.996087	+	0.0883769i	$0.0281680\pi$
$233$			2.23582e6i			0.176754i	−0.996087	+	0.0883769i	$0.971832\pi$
$234$		0			0
$235$	−1.39702e7	+	2.01899e7i	−1.07646	+	1.55572i
$236$	−669104.	+	9.05665e6i	−0.0509047	+	0.689020i
$237$		0			0
$238$	−1.78588e7	−	658806.i	−1.32471	−	0.0488682i
$239$			2.49242e7i			1.82569i	0.408305	+	0.912846i	$0.366120\pi$
$239$			2.49242e7i			1.82569i	−0.408305	+	0.912846i	$0.633880\pi$
$240$		0			0
$241$	−5.64081e6			−0.402986			−0.201493	−	0.979490i	$-0.564579\pi$
$241$	−5.64081e6			−0.402986			−0.201493	+	0.979490i	$0.564579\pi$
$242$	−429457.	+	1.16417e7i	−0.0303022	+	0.821428i
$243$		0			0
$244$	−1.28569e7	−	949862.i	−0.885045	−	0.0653870i
$245$	−9.13568e6	+	1.32031e7i	−0.621216	+	0.897793i
$246$		0			0
$247$	1.60097e7			1.06241
$248$	3.75547e6	+	417129.i	0.246212	+	0.0273473i
$249$		0			0
$250$	−4.34747e6	+	1.50080e7i	−0.278238	+	0.960512i
$251$			8.24054e6i			0.521116i	0.965458	+	0.260558i	$0.0839066\pi$
$251$			8.24054e6i			0.521116i	−0.965458	+	0.260558i	$0.916093\pi$
$252$		0			0
$253$			9.09310e6i			0.561501i
$254$	588907.	−	1.59640e7i	0.0359373	−	0.974184i
$255$		0			0
$256$	1.60526e7	+	4.87754e6i	0.956807	+	0.290724i
$257$		−	1.29601e7i		−	0.763501i	−0.924265	−	0.381750i	$-0.875321\pi$
$257$		−	1.29601e7i		−	0.763501i	0.924265	−	0.381750i	$-0.124679\pi$
$258$		0			0
$259$		−	3.30880e7i		−	1.90446i
$260$	−9.86529e6	−	7.96203e6i	−0.561293	−	0.453006i
$261$		0			0
$262$	4.76639e6	+	175830.i	0.265024	+	0.00977665i
$263$	−6.15939e6			−0.338587			−0.169294	−	0.985566i	$-0.554149\pi$
$263$	−6.15939e6			−0.338587			−0.169294	+	0.985566i	$0.554149\pi$
$264$		0			0
$265$	7.40892e6	+	5.12651e6i	0.398123	+	0.275476i
$266$	4.00670e7	+	1.47806e6i	2.12883	+	0.0785319i
$267$		0			0
$268$	1.38271e7	+	1.02154e6i	0.718335	+	0.0530705i
$269$	−2.56743e6			−0.131899			−0.0659494	−	0.997823i	$-0.521008\pi$
$269$	−2.56743e6			−0.131899			−0.0659494	+	0.997823i	$0.521008\pi$
$270$		0			0
$271$		−	9.66745e6i		−	0.485740i	−0.970059	−	0.242870i	$-0.921911\pi$
$271$		−	9.66745e6i		−	0.485740i	0.970059	−	0.242870i	$-0.0780888\pi$
$272$	2.71057e6	−	1.82443e7i	0.134696	−	0.906610i
$273$		0			0
$274$	3.54055e7	+	1.30610e6i	1.72115	+	0.0634927i
$275$	−8.21143e6	+	3.09275e6i	−0.394840	+	0.148712i
$276$		0			0
$277$			1.59611e7i			0.750972i	0.926828	+	0.375486i	$0.122524\pi$
$277$			1.59611e7i			0.750972i	−0.926828	+	0.375486i	$0.877476\pi$
$278$	4.03290e7	+	1.48772e6i	1.87708	+	0.0692448i
$279$		0			0
$280$	−2.39544e7	−	2.08371e7i	−1.09122	−	0.949211i
$281$	4.28821e7			1.93267			0.966334	−	0.257290i	$-0.0828296\pi$
$281$	4.28821e7			1.93267			0.966334	+	0.257290i	$0.0828296\pi$
$282$		0			0
$283$	−6.36296e6			−0.280737			−0.140369	−	0.990099i	$-0.544829\pi$
$283$	−6.36296e6			−0.280737			−0.140369	+	0.990099i	$0.544829\pi$
$284$	1.69025e6	−	2.28784e7i	0.0737898	−	0.998781i
$285$		0			0
$286$	262450.	−	7.11446e6i	0.0112188	−	0.304119i
$287$	−4.82147e7			−2.03955
$288$		0			0
$289$	3.85998e6			0.159916
$290$	1.60240e6	+	1.19846e6i	0.0657017	+	0.0491395i
$291$		0			0
$292$	1.94058e6	−	2.62667e7i	0.0779441	−	1.05501i
$293$			1.17997e7i			0.469102i	0.972104	+	0.234551i	$0.0753620\pi$
$293$			1.17997e7i			0.469102i	−0.972104	+	0.234551i	$0.924638\pi$
$294$		0			0
$295$	1.45857e7	+	1.00924e7i	0.568149	+	0.393124i
$296$	3.39413e7	+	3.76993e6i	1.30874	+	0.145365i
$297$		0			0
$298$	−683079.	+	1.85168e7i	−0.0258120	+	0.699709i
$299$			2.56596e7i			0.959922i
$300$		0			0
$301$	5.59687e7			2.05232
$302$	−4.57964e7	−	1.68941e6i	−1.66269	−	0.0613359i
$303$		0			0
$304$	−6.08126e6	+	4.09318e7i	−0.216458	+	1.45693i
$305$	−1.43272e7	+	2.07060e7i	−0.504966	+	0.729786i
$306$		0			0
$307$	3.47430e7			1.20075			0.600374	−	0.799719i	$-0.295018\pi$
$307$	3.47430e7			1.20075			0.600374	+	0.799719i	$0.295018\pi$
$308$	1.31365e6	−	1.77809e7i	0.0449600	−	0.608556i
$309$		0			0
$310$	4.42013e6	−	5.90991e6i	0.148371	−	0.198379i
$311$		−	5.00149e7i		−	1.66272i	−0.555737	−	0.831358i	$-0.687564\pi$
$311$		−	5.00149e7i		−	1.66272i	0.555737	−	0.831358i	$-0.312436\pi$
$312$		0			0
$313$			5.15834e7i			1.68220i	0.540882	+	0.841099i	$0.318091\pi$
$313$			5.15834e7i			1.68220i	−0.540882	+	0.841099i	$0.681909\pi$
$314$	1.71360e6	+	63214.0i	0.0553503	+	0.00204185i
$315$		0			0
$316$	−1.28278e6	+	1.73630e7i	−0.0406527	+	0.550254i
$317$			4.05089e7i			1.27166i	0.771827	+	0.635832i	$0.219343\pi$
$317$			4.05089e7i			1.27166i	−0.771827	+	0.635832i	$0.780657\pi$
$318$		0			0
$319$			1.12370e6i			0.0346162i
$320$	2.41037e7	−	2.21981e7i	0.735586	−	0.677431i
$321$		0			0
$322$	−2.36895e6	+	6.42173e7i	−0.0709560	+	1.92347i
$323$	4.54936e7			1.35003
$324$		0			0
$325$	−2.31716e7	+	8.72736e6i	−0.675004	+	0.254234i
$326$	1.51338e6	−	4.10245e7i	0.0436813	−	1.18411i
$327$		0			0
$328$	5.49341e6	−	4.94580e7i	0.155676	−	1.40157i
$329$	−9.74375e7			−2.73614
$330$		0			0
$331$			4.67744e7i			1.28981i	0.764264	+	0.644903i	$0.223102\pi$
$331$			4.67744e7i			1.28981i	−0.764264	+	0.644903i	$0.776898\pi$
$332$	1.61095e7	+	1.19017e6i	0.440219	+	0.0325233i
$333$		0			0
$334$	−901415.	+	2.44354e7i	−0.0241928	+	0.655814i
$335$	1.54084e7	−	2.22686e7i	0.409850	−	0.592322i
$336$		0			0
$337$		−	4.77282e7i		−	1.24705i	−0.781802	−	0.623527i	$-0.785699\pi$
$337$		−	4.77282e7i		−	1.24705i	0.781802	−	0.623527i	$-0.214301\pi$
$338$	−682906.	+	1.85121e7i	−0.0176852	+	0.479409i
$339$		0			0
$340$	−2.80334e7	−	2.26251e7i	−0.713246	−	0.575643i
$341$	4.14440e6			0.104520
$342$		0			0
$343$	−5.35543e6			−0.132713
$344$	−6.37688e6	+	5.74120e7i	−0.156651	+	1.41035i
$345$		0			0
$346$	4.11880e7	+	1.51941e6i	0.994358	+	0.0366815i
$347$	3.93322e7			0.941368			0.470684	−	0.882302i	$-0.344007\pi$
$347$	3.93322e7			0.941368			0.470684	+	0.882302i	$0.344007\pi$
$348$		0			0
$349$	−7.65808e7			−1.80154			−0.900769	−	0.434299i	$-0.856996\pi$
$349$	−7.65808e7			−1.80154			−0.900769	+	0.434299i	$0.856996\pi$
$350$	−5.87965e7	+	1.97024e7i	−1.37135	+	0.459531i
$351$		0			0
$352$	1.80897e7	+	3.37341e6i	0.414767	+	0.0773466i
$353$			1.22834e7i			0.279250i	0.990204	+	0.139625i	$0.0445897\pi$
$353$			1.22834e7i			0.279250i	−0.990204	+	0.139625i	$0.955410\pi$
$354$		0			0
$355$	−3.68456e7	−	2.54949e7i	−0.823570	−	0.569859i
$356$	−5.56829e6	−	411384.i	−0.123416	−	0.00911796i
$357$		0			0
$358$	−1.57535e7	−	581140.i	−0.343342	−	0.0126658i
$359$		−	1.10395e7i		−	0.238598i	−0.992858	−	0.119299i	$-0.961935\pi$
$359$		−	1.10395e7i		−	0.238598i	0.992858	−	0.119299i	$-0.0380647\pi$
$360$		0			0
$361$	−5.50207e7			−1.16951
$362$	−691982.	+	1.87582e7i	−0.0145871	+	0.395425i
$363$		0			0
$364$	3.70695e6	−	5.01753e7i	0.0768621	−	1.04037i
$365$	−4.23025e7	−	2.92707e7i	−0.869937	−	0.601942i
$366$		0			0
$367$	−5.87412e7			−1.18835			−0.594175	−	0.804336i	$-0.702521\pi$
$367$	−5.87412e7			−1.18835			−0.594175	+	0.804336i	$0.702521\pi$
$368$	−6.56034e7	−	9.74673e6i	−1.31638	−	0.195576i
$369$		0			0
$370$	3.99483e7	−	5.34127e7i	0.788667	−	1.05448i
$371$			3.57558e7i			0.700204i
$372$		0			0
$373$			1.24158e7i			0.239247i	0.992819	+	0.119624i	$0.0381688\pi$
$373$			1.24158e7i			0.239247i	−0.992819	+	0.119624i	$0.961831\pi$
$374$	745783.	−	2.02166e7i	0.0142560	−	0.386450i
$375$		0			0
$376$	1.11017e7	−	9.99501e7i	0.208846	−	1.88027i
$377$			3.17095e6i			0.0591786i
$378$		0			0
$379$		−	4.18480e7i		−	0.768701i	−0.923187	−	0.384350i	$-0.874425\pi$
$379$		−	4.18480e7i		−	0.768701i	0.923187	−	0.384350i	$-0.125575\pi$
$380$	6.28940e7	+	5.07602e7i	1.14620	+	0.925066i
$381$		0			0
$382$	7.29704e7	+	2.69185e6i	1.30905	+	0.0482905i
$383$	−5.12412e7			−0.912058			−0.456029	−	0.889965i	$-0.650729\pi$
$383$	−5.12412e7			−0.912058			−0.456029	+	0.889965i	$0.650729\pi$
$384$		0			0
$385$	−2.86361e7	−	1.98144e7i	−0.501801	−	0.347215i
$386$	9.73480e7	+	3.59113e6i	1.69264	+	0.0624410i
$387$		0			0
$388$	−616089.	+	8.33906e6i	−0.0105475	+	0.142765i
$389$	−4.98250e7			−0.846444			−0.423222	−	0.906026i	$-0.639101\pi$
$389$	−4.98250e7			−0.846444			−0.423222	+	0.906026i	$0.639101\pi$
$390$		0			0
$391$			7.29147e7i			1.21979i
$392$	7.25986e6	−	6.53617e7i	0.120523	−	1.08509i
$393$		0			0
$394$	−4.26115e7	−	1.57193e6i	−0.696688	−	0.0257006i
$395$	2.79631e7	+	1.93487e7i	0.453727	+	0.313950i
$396$		0			0
$397$		−	3.92214e7i		−	0.626832i	−0.949616	−	0.313416i	$-0.898527\pi$
$397$		−	3.92214e7i		−	0.626832i	0.949616	−	0.313416i	$-0.101473\pi$
$398$	−1.36307e7	−	502831.i	−0.216206	−	0.00797578i
$399$		0			0
$400$	−1.35114e7	−	6.25575e7i	−0.211116	−	0.977461i
$401$	5.63354e6			0.0873671			0.0436836	−	0.999045i	$-0.486091\pi$
$401$	5.63354e6			0.0873671			0.0436836	+	0.999045i	$0.486091\pi$
$402$		0			0
$403$	1.16950e7			0.178683
$404$	−6.93506e7	−	5.12361e6i	−1.05173	−	0.0777020i
$405$		0			0
$406$	−292749.	+	7.93581e6i	−0.00437439	+	0.118581i
$407$	3.74564e7			0.555575
$408$		0			0
$409$	−2.95973e7			−0.432596			−0.216298	−	0.976327i	$-0.569398\pi$
$409$	−2.95973e7			−0.432596			−0.216298	+	0.976327i	$0.569398\pi$
$410$	−7.78311e7	−	5.82113e7i	−1.12928	−	0.844609i
$411$		0			0
$412$	−1.13769e8	−	8.40526e6i	−1.62680	−	0.120188i
$413$			7.03914e7i			0.999240i
$414$		0			0
$415$	1.79519e7	−	2.59444e7i	0.251169	−	0.362994i
$416$	5.10469e7	+	9.51934e6i	0.709070	+	0.132229i
$417$		0			0
$418$	−1.67319e6	+	4.53567e7i	−0.0229096	+	0.621030i
$419$			1.15258e7i			0.156686i	0.996926	+	0.0783428i	$0.0249629\pi$
$419$			1.15258e7i			0.156686i	−0.996926	+	0.0783428i	$0.975037\pi$
$420$		0			0
$421$	3.57459e7			0.479049			0.239525	−	0.970890i	$-0.423008\pi$
$421$	3.57459e7			0.479049			0.239525	+	0.970890i	$0.423008\pi$
$422$	1.00460e8	+	3.70594e6i	1.33677	+	0.0493130i
$423$		0			0
$424$	−3.66778e7	−	4.07389e6i	−0.481178	−	0.0534456i
$425$	−6.58449e7	+	2.47998e7i	−0.857740	+	0.323059i
$426$		0			0
$427$	−9.99279e7			−1.28352
$428$	−3.56411e7	−	2.63316e6i	−0.454590	−	0.0335851i
$429$		0			0
$430$	9.03481e7	+	6.75729e7i	1.13635	+	0.849899i
$431$			8.20839e6i			0.102524i	0.998685	+	0.0512621i	$0.0163244\pi$
$431$			8.20839e6i			0.102524i	−0.998685	+	0.0512621i	$0.983676\pi$
$432$		0			0
$433$			4.37930e7i			0.539437i	0.962939	+	0.269719i	$0.0869307\pi$
$433$			4.37930e7i			0.539437i	−0.962939	+	0.269719i	$0.913069\pi$
$434$	2.92686e7	+	1.07971e6i	0.358041	+	0.0132080i
$435$		0			0
$436$	2.89232e7	+	2.13684e6i	0.348969	+	0.0257818i
$437$		−	1.63587e8i		−	1.96022i
$438$		0			0
$439$			9.07805e7i			1.07300i	0.843901	+	0.536499i	$0.180254\pi$
$439$			9.07805e7i			1.07300i	−0.843901	+	0.536499i	$0.819746\pi$
$440$	2.35880e7	−	2.71169e7i	0.276907	−	0.318334i
$441$		0			0
$442$	2.10450e6	−	5.70486e7i	0.0243715	−	0.660660i
$443$	4.40997e6			0.0507253			0.0253626	−	0.999678i	$-0.491926\pi$
$443$	4.40997e6			0.0507253			0.0253626	+	0.999678i	$0.491926\pi$
$444$		0			0
$445$	−6.20511e6	+	8.96773e6i	−0.0704156	+	0.101766i
$446$	−1.41160e6	+	3.82655e7i	−0.0159114	+	0.431324i
$447$		0			0
$448$	1.26874e8	+	2.85365e7i	1.41104	+	0.317370i
$449$	7.74897e7			0.856062			0.428031	−	0.903764i	$-0.359207\pi$
$449$	7.74897e7			0.856062			0.428031	+	0.903764i	$0.359207\pi$
$450$		0			0
$451$		−	5.45801e7i		−	0.594983i
$452$	−8.64278e6	+	1.16984e8i	−0.0935919	+	1.26681i
$453$		0			0
$454$	52524.3	−	1.42382e6i	0.000561297	−	0.0152156i
$455$	−8.08074e7	−	5.59136e7i	−0.857861	−	0.593586i
$456$		0			0
$457$		−	1.64079e8i		−	1.71911i	−0.511045	−	0.859554i	$-0.670741\pi$
$457$		−	1.64079e8i		−	1.71911i	0.511045	−	0.859554i	$-0.329259\pi$
$458$	300157.	−	8.13661e6i	0.00312429	−	0.0846929i
$459$		0			0
$460$	−8.13559e7	+	1.00803e8i	−0.835825	+	1.03562i
$461$	1.26212e8			1.28824			0.644121	−	0.764924i	$-0.277223\pi$
$461$	1.26212e8			1.28824			0.644121	+	0.764924i	$0.277223\pi$
$462$		0			0
$463$	3.21664e7			0.324085			0.162043	−	0.986784i	$-0.448192\pi$
$463$	3.21664e7			0.324085			0.162043	+	0.986784i	$0.448192\pi$
$464$	−8.10710e6	−	1.20448e6i	−0.0811543	−	0.0120571i
$465$		0			0
$466$	−1.78744e7	−	659380.i	−0.176634	−	0.00651596i
$467$	1.95660e7			0.192110			0.0960551	−	0.995376i	$-0.469377\pi$
$467$	1.95660e7			0.192110			0.0960551	+	0.995376i	$0.469377\pi$
$468$		0			0
$469$	1.07469e8			1.04175
$470$	−1.57290e8	−	1.17640e8i	−1.51498	−	1.13308i
$471$		0			0
$472$	−7.22066e7	−	8.02015e6i	−0.686675	−	0.0762705i
$473$			6.33578e7i			0.598710i
$474$		0			0
$475$	1.47726e8	−	5.56394e7i	1.37840	−	0.519160i
$476$	1.05337e7	−	1.42579e8i	0.0976700	−	1.32201i
$477$		0			0
$478$	−1.99258e8	−	7.35056e6i	−1.82445	−	0.0673033i
$479$		−	1.93927e8i		−	1.76454i	−0.470743	−	0.882270i	$-0.656014\pi$
$479$		−	1.93927e8i		−	1.76454i	0.470743	−	0.882270i	$-0.343986\pi$
$480$		0			0
$481$	1.05697e8			0.949791
$482$	1.66357e6	−	4.50958e7i	0.0148559	−	0.402712i
$483$		0			0
$484$	−9.29434e7	−	6.86665e6i	−0.819752	−	0.0605632i
$485$	1.34301e7	+	9.29276e6i	0.117721	+	0.0814553i
$486$		0			0
$487$	1.62572e8			1.40754			0.703768	−	0.710430i	$-0.251500\pi$
$487$	1.62572e8			1.40754			0.703768	+	0.710430i	$0.251500\pi$
$488$	1.13854e7	−	1.02505e8i	0.0979693	−	0.882033i
$489$		0			0
$490$	−1.02858e8	−	7.69296e7i	−0.874281	−	0.653891i
$491$			1.55899e8i			1.31704i	0.752564	+	0.658519i	$0.228817\pi$
$491$			1.55899e8i			1.31704i	−0.752564	+	0.658519i	$0.771183\pi$
$492$		0			0
$493$			9.01062e6i			0.0751993i
$494$	−4.72154e6	+	1.27991e8i	−0.0391654	+	1.06169i
$495$		0			0
$496$	−4.44231e6	+	2.99003e7i	−0.0364053	+	0.245037i
$497$		−	1.77819e8i		−	1.44847i
$498$		0			0
$499$			5.34345e7i			0.430051i	0.976608	+	0.215026i	$0.0689835\pi$
$499$			5.34345e7i			0.430051i	−0.976608	+	0.215026i	$0.931017\pi$
$500$	−1.18700e8	−	3.91822e7i	−0.949602	−	0.313458i
$501$		0			0
$502$	−6.58795e7	−	2.43027e6i	−0.520762	−	0.0192107i
$503$	−1.13337e8			−0.890565			−0.445283	−	0.895390i	$-0.646897\pi$
$503$	−1.13337e8			−0.890565			−0.445283	+	0.895390i	$0.646897\pi$
$504$		0			0
$505$	−7.72819e7	+	1.11689e8i	−0.600072	+	0.867235i
$506$	−7.26954e7	−	2.68171e6i	−0.561119	−	0.0206995i
$507$		0			0
$508$	1.27452e8	+	9.41611e6i	0.972197	+	0.0718258i
$509$	1.55905e8			1.18224			0.591120	−	0.806584i	$-0.298686\pi$
$509$	1.55905e8			1.18224			0.591120	+	0.806584i	$0.298686\pi$
$510$		0			0
$511$		−	2.04154e8i		−	1.53001i
$512$	−4.37280e7	+	1.26895e8i	−0.325799	+	0.945439i
$513$		0			0
$514$	1.03610e8	+	3.82215e6i	0.762982	+	0.0281461i
$515$	−1.26781e8	+	1.83226e8i	−0.928178	+	1.34142i
$516$		0			0
$517$		−	1.10301e8i		−	0.798195i
$518$	2.64524e8	+	9.75821e6i	1.90317	+	0.0702071i
$519$		0			0
$520$	6.65624e7	−	7.65206e7i	0.473390	−	0.544212i
$521$	1.28940e8			0.911750			0.455875	−	0.890044i	$-0.349326\pi$
$521$	1.28940e8			0.911750			0.455875	+	0.890044i	$0.349326\pi$
$522$		0			0
$523$	5.74458e7			0.401562			0.200781	−	0.979636i	$-0.435652\pi$
$523$	5.74458e7			0.401562			0.200781	+	0.979636i	$0.435652\pi$
$524$	−2.81137e6	+	3.80533e7i	−0.0195400	+	0.264484i
$525$		0			0
$526$	1.81651e6	−	4.92416e7i	0.0124819	−	0.338357i
$527$	3.32327e7			0.227056
$528$		0			0
$529$	1.14153e8			0.771117
$530$	−4.31692e7	+	5.77192e7i	−0.289966	+	0.387697i
$531$		0			0
$532$	−2.36328e7	+	3.19882e8i	−0.156957	+	2.12449i
$533$		−	1.54018e8i		−	1.01716i
$534$		0			0
$535$	−3.97172e7	+	5.74000e7i	−0.259369	+	0.374844i
$536$	−1.22446e7	+	1.10240e8i	−0.0795155	+	0.715890i
$537$		0			0
$538$	757177.	−	2.05254e7i	0.00486240	−	0.131809i
$539$		−	7.21308e7i		−	0.460632i
$540$		0			0
$541$	−8.81969e7			−0.557008			−0.278504	−	0.960435i	$-0.589839\pi$
$541$	−8.81969e7			−0.557008			−0.278504	+	0.960435i	$0.589839\pi$
$542$	7.72870e7	+	2.85109e6i	0.485410	+	0.0179066i
$543$		0			0
$544$	1.45056e8	+	2.70503e7i	0.901028	+	0.168026i
$545$	3.22310e7	−	4.65808e7i	0.199106	−	0.287751i
$546$		0			0
$547$	−2.52994e8			−1.54578			−0.772892	−	0.634538i	$-0.781190\pi$
$547$	−2.52994e8			−1.54578			−0.772892	+	0.634538i	$0.781190\pi$
$548$	−2.08834e7	+	2.82666e8i	−0.126899	+	1.71764i
$549$		0			0
$550$	−2.23035e7	−	6.65589e7i	−0.134056	−	0.400054i
$551$		−	2.02157e7i		−	0.120846i
$552$		0			0
$553$			1.34951e8i			0.797998i
$554$	−1.27602e8	−	4.70720e6i	−0.750462	−	0.0276843i
$555$		0			0
$556$	−2.37874e7	+	3.21974e8i	−0.138395	+	1.87325i
$557$			2.32228e8i			1.34384i	0.740622	+	0.671922i	$0.234531\pi$
$557$			2.32228e8i			1.34384i	−0.740622	+	0.671922i	$0.765469\pi$
$558$		0			0
$559$			1.78788e8i			1.02353i
$560$	1.73648e8	−	1.85360e8i	0.988793	−	1.05549i
$561$		0			0
$562$	−1.26467e7	+	3.42824e8i	−0.0712470	+	1.93135i
$563$	2.04220e8			1.14439			0.572193	−	0.820119i	$-0.306093\pi$
$563$	2.04220e8			1.14439			0.572193	+	0.820119i	$0.306093\pi$
$564$		0			0
$565$	1.88403e8	+	1.30363e8i	1.04458	+	0.722786i
$566$	1.87654e6	−	5.08691e7i	0.0103493	−	0.280547i
$567$		0			0
$568$	1.82404e8	+	2.02600e7i	0.995382	+	0.110559i
$569$	−1.10819e8			−0.601558			−0.300779	−	0.953694i	$-0.597247\pi$
$569$	−1.10819e8			−0.601558			−0.300779	+	0.953694i	$0.597247\pi$
$570$		0			0
$571$		−	1.80433e8i		−	0.969186i	−0.874740	−	0.484593i	$-0.838968\pi$
$571$		−	1.80433e8i		−	0.969186i	0.874740	−	0.484593i	$-0.161032\pi$
$572$	5.67996e7	+	4.19634e6i	0.303499	+	0.0224224i
$573$		0			0
$574$	1.42193e7	−	3.85455e8i	0.0751871	−	2.03816i
$575$	8.91760e7	+	2.36767e8i	0.469077	+	1.24543i
$576$		0			0
$577$		−	1.16278e8i		−	0.605297i	−0.953102	−	0.302648i	$-0.902129\pi$
$577$		−	1.16278e8i		−	0.605297i	0.953102	−	0.302648i	$-0.0978708\pi$
$578$	−1.13837e6	+	3.08588e7i	−0.00589523	+	0.159807i
$579$		0			0
$580$	−1.00538e7	+	1.24570e7i	−0.0515281	+	0.0638455i
$581$	1.25209e8			0.638421
$582$		0			0
$583$	−4.04763e7			−0.204266
$584$	2.09419e8	+	2.32606e7i	1.05142	+	0.116784i
$585$		0			0
$586$	−9.43332e7	−	3.47992e6i	−0.468783	−	0.0172932i
$587$	−8.67855e7			−0.429075			−0.214537	−	0.976716i	$-0.568824\pi$
$587$	−8.67855e7			−0.429075			−0.214537	+	0.976716i	$0.568824\pi$
$588$		0			0
$589$	−7.45588e7			−0.364882
$590$	−8.49860e7	+	1.13630e8i	−0.413801	+	0.553271i
$591$		0			0
$592$	−4.01488e7	+	2.70234e8i	−0.193512	+	1.30249i
$593$			1.04689e8i			0.502038i	0.967982	+	0.251019i	$0.0807657\pi$
$593$			1.04689e8i			0.502038i	−0.967982	+	0.251019i	$0.919234\pi$
$594$		0			0
$595$	−2.29624e8	−	1.58885e8i	−1.09010	−	0.754280i
$596$	−1.47832e8	−	1.09218e7i	−0.698282	−	0.0515890i
$597$		0			0
$598$	−2.05137e8	−	7.56743e6i	−0.959269	−	0.0353871i
$599$			6.77750e7i			0.315347i	0.987491	+	0.157674i	$0.0503994\pi$
$599$			6.77750e7i			0.315347i	−0.987491	+	0.157674i	$0.949601\pi$
$600$		0			0
$601$	2.94031e8			1.35447			0.677236	−	0.735766i	$-0.263177\pi$
$601$	2.94031e8			1.35447			0.677236	+	0.735766i	$0.263177\pi$
$602$	−1.65061e7	+	4.47445e8i	−0.0756580	+	2.05093i
$603$		0			0
$604$	2.70122e7	−	3.65624e8i	0.122588	−	1.65930i
$605$	−1.03573e8	+	1.49685e8i	−0.467714	+	0.675948i
$606$		0			0
$607$	1.77492e8			0.793618			0.396809	−	0.917901i	$-0.370118\pi$
$607$	1.77492e8			0.793618			0.396809	+	0.917901i	$0.370118\pi$
$608$	−3.25438e8	−	6.06885e7i	−1.44796	−	0.270020i
$609$		0			0
$610$	−1.61310e8	−	1.20646e8i	−0.710675	−	0.531527i
$611$		−	3.11256e8i		−	1.36457i
$612$		0			0
$613$			1.82426e8i			0.791962i	0.918259	+	0.395981i	$0.129595\pi$
$613$			1.82426e8i			0.791962i	−0.918259	+	0.395981i	$0.870405\pi$
$614$	−1.02463e7	+	2.77755e8i	−0.0442651	+	1.19993i
$615$		0			0
$616$	1.41763e8	+	1.57459e7i	0.606485	+	0.0673637i
$617$		−	2.51870e8i		−	1.07231i	−0.844119	−	0.536156i	$-0.819876\pi$
$617$		−	2.51870e8i		−	1.07231i	0.844119	−	0.536156i	$-0.180124\pi$
$618$		0			0
$619$			2.50301e8i			1.05534i	0.849450	+	0.527669i	$0.176934\pi$
$619$			2.50301e8i			1.05534i	−0.849450	+	0.527669i	$0.823066\pi$
$620$	4.59436e7	+	3.70799e7i	0.192775	+	0.155584i
$621$		0			0
$622$	3.99847e8	+	1.47502e7i	1.66159	+	0.0612953i
$623$	−4.32787e7			−0.178982
$624$		0			0
$625$	−1.83479e8	+	1.61059e8i	−0.751532	+	0.659697i
$626$	−4.12387e8	−	1.52128e7i	−1.68105	−	0.0620135i
$627$		0			0
$628$	−1.01074e6	+	1.36808e7i	−0.00408093	+	0.0552374i
$629$	3.00351e8			1.20692
$630$		0			0
$631$			2.44022e8i			0.971272i	0.874161	+	0.485636i	$0.161412\pi$
$631$			2.44022e8i			0.971272i	−0.874161	+	0.485636i	$0.838588\pi$
$632$	−1.38431e8	−	1.53759e7i	−0.548382	−	0.0609100i
$633$		0			0
$634$	−3.23851e8	−	1.19467e7i	−1.27080	−	0.0468794i
$635$	1.42028e8	−	2.05261e8i	0.554692	−	0.801650i
$636$		0			0
$637$		−	2.03544e8i		−	0.787480i
$638$	−8.98351e6	−	331399.i	−0.0345927	−	0.00127611i
$639$		0			0
$640$	1.70355e8	+	1.99245e8i	0.649853	+	0.760060i
$641$	−2.17104e8			−0.824317			−0.412159	−	0.911112i	$-0.635225\pi$
$641$	−2.17104e8			−0.824317			−0.412159	+	0.911112i	$0.635225\pi$
$642$		0			0
$643$	7.06668e7			0.265817			0.132908	−	0.991128i	$-0.457568\pi$
$643$	7.06668e7			0.265817			0.132908	+	0.991128i	$0.457568\pi$
$644$	−5.12690e8	−	3.78775e7i	−1.91954	−	0.141815i
$645$		0			0
$646$	−1.34168e7	+	3.63701e8i	−0.0497682	+	1.34911i
$647$	1.10253e8			0.407077			0.203539	−	0.979067i	$-0.434756\pi$
$647$	1.10253e8			0.407077			0.203539	+	0.979067i	$0.434756\pi$
$648$		0			0
$649$	−7.96846e7			−0.291501
$650$	−6.29377e7	−	1.87821e8i	−0.229177	−	0.683917i
$651$		0			0
$652$	3.27527e8	+	2.41976e7i	1.18169	+	0.0873032i
$653$		−	2.64139e8i		−	0.948622i	−0.880357	−	0.474311i	$-0.842697\pi$
$653$		−	2.64139e8i		−	0.948622i	0.880357	−	0.474311i	$-0.157303\pi$
$654$		0			0
$655$	6.12849e7	+	4.24053e7i	0.218087	+	0.150902i
$656$	3.93775e8	+	5.85034e7i	1.39488	+	0.207238i
$657$		0			0
$658$	2.87359e7	−	7.78970e8i	0.100867	−	2.73428i
$659$		−	3.71991e8i		−	1.29980i	−0.760020	−	0.649900i	$-0.774811\pi$
$659$		−	3.71991e8i		−	1.29980i	0.760020	−	0.649900i	$-0.225189\pi$
$660$		0			0
$661$	8.07649e6			0.0279652			0.0139826	−	0.999902i	$-0.495549\pi$
$661$	8.07649e6			0.0279652			0.0139826	+	0.999902i	$0.495549\pi$
$662$	−3.73941e8	−	1.37946e7i	−1.28893	−	0.0475482i
$663$		0			0
$664$	−1.42659e7	+	1.28438e8i	−0.0487297	+	0.438721i
$665$	5.15170e8	+	3.56465e8i	1.75180	+	1.21214i
$666$		0			0
$667$	3.24007e7			0.109188
$668$	−1.95085e8	−	1.44128e7i	−0.654476	−	0.0483526i
$669$		0			0
$670$	1.73483e8	+	1.29751e8i	0.576810	+	0.431407i
$671$		−	1.13121e8i		−	0.374433i
$672$		0			0
$673$		−	4.68686e8i		−	1.53758i	−0.639504	−	0.768788i	$-0.720860\pi$
$673$		−	4.68686e8i		−	1.53758i	0.639504	−	0.768788i	$-0.279140\pi$
$674$	3.81566e8	+	1.40758e7i	1.24621	+	0.0459721i
$675$		0			0
$676$	−1.47795e8	−	1.09191e7i	−0.478431	−	0.0353464i
$677$		−	4.87718e8i		−	1.57182i	−0.618340	−	0.785911i	$-0.712195\pi$
$677$		−	4.87718e8i		−	1.57182i	0.618340	−	0.785911i	$-0.287805\pi$
$678$		0			0
$679$			6.48141e7i			0.207043i
$680$	1.89145e8	−	2.17442e8i	0.601545	−	0.691540i
$681$		0			0
$682$	−1.22225e6	+	3.31327e7i	−0.00385308	+	0.104449i
$683$	1.37472e8			0.431473			0.215736	−	0.976452i	$-0.430785\pi$
$683$	1.37472e8			0.431473			0.215736	+	0.976452i	$0.430785\pi$
$684$		0			0
$685$	4.55234e8	+	3.14994e8i	1.41633	+	0.980009i
$686$	1.57941e6	−	4.28143e7i	0.00489239	−	0.132622i
$687$		0			0
$688$	−4.57103e8	−	6.79121e7i	−1.40362	−	0.208536i
$689$	−1.14219e8			−0.349205
$690$		0			0
$691$		−	3.91195e7i		−	0.118566i	−0.998241	−	0.0592829i	$-0.981119\pi$
$691$		−	3.91195e7i		−	0.118566i	0.998241	−	0.0592829i	$-0.0188814\pi$
$692$	−2.42941e7	+	3.28832e8i	−0.0733132	+	0.992330i
$693$		0			0
$694$	−1.15997e7	+	3.14443e8i	−0.0347031	+	0.940728i
$695$	5.18538e8	+	3.58796e8i	1.54464	+	1.06879i
$696$		0			0
$697$		−	4.37661e8i		−	1.29253i
$698$	2.25849e7	−	6.12230e8i	0.0664129	−	1.80031i
$699$		0			0
$700$	−1.40172e8	−	4.75863e8i	−0.408664	−	1.38735i
$701$	−7.90495e7			−0.229480			−0.114740	−	0.993396i	$-0.536604\pi$
$701$	−7.90495e7			−0.229480			−0.114740	+	0.993396i	$0.536604\pi$
$702$		0			0
$703$	−6.73849e8			−1.93953
$704$	−3.23039e7	+	1.43624e8i	−0.0925843	+	0.411633i
$705$		0			0
$706$	−9.82002e7	−	3.62257e6i	−0.279060	−	0.0102944i
$707$	−5.39017e8			−1.52526
$708$		0			0
$709$	3.79297e8			1.06424			0.532121	−	0.846668i	$-0.321395\pi$
$709$	3.79297e8			1.06424			0.532121	+	0.846668i	$0.321395\pi$
$710$	2.14687e8	−	2.87046e8i	0.599832	−	0.802003i
$711$		0			0
$712$	4.93102e6	−	4.43947e7i	0.0136614	−	0.122996i
$713$		−	1.19499e8i		−	0.329682i
$714$		0			0
$715$	6.32954e7	−	9.14757e7i	0.173163	−	0.250258i
$716$	9.29192e6	−	1.25771e8i	0.0253143	−	0.342642i
$717$		0			0
$718$	8.82560e7	+	3.25573e6i	0.238436	+	0.00879581i
$719$		−	9.42836e7i		−	0.253659i	−0.991925	−	0.126829i	$-0.959520\pi$
$719$		−	9.42836e7i		−	0.253659i	0.991925	−	0.126829i	$-0.0404801\pi$
$720$		0			0
$721$	−8.84255e8			−2.35924
$722$	1.62265e7	−	4.39866e8i	0.0431135	−	1.16872i
$723$		0			0
$724$	−1.49759e8	−	1.10642e7i	−0.394619	−	0.0291544i
$725$	1.10201e7	+	2.92591e7i	0.0289183	+	0.0767797i
$726$		0			0
$727$	3.70399e8			0.963977			0.481988	−	0.876178i	$-0.339915\pi$
$727$	3.70399e8			0.963977			0.481988	+	0.876178i	$0.339915\pi$
$728$	4.00037e8	+	4.44330e7i	1.03683	+	0.115162i
$729$		0			0
$730$	2.46482e8	−	3.29558e8i	0.633603	−	0.847156i
$731$			5.08046e8i			1.30062i
$732$		0			0
$733$			2.70421e8i			0.686639i	0.939219	+	0.343320i	$0.111551\pi$
$733$			2.70421e8i			0.686639i	−0.939219	+	0.343320i	$0.888449\pi$
$734$	1.73238e7	−	4.69610e8i	0.0438080	−	1.18754i
$735$		0			0
$736$	9.72684e7	−	5.21596e8i	0.243971	−	1.30828i
$737$			1.21657e8i			0.303904i
$738$		0			0
$739$		−	1.34877e8i		−	0.334199i	−0.985940	−	0.167099i	$-0.946560\pi$
$739$		−	1.34877e8i		−	0.334199i	0.985940	−	0.167099i	$-0.0534400\pi$
$740$	4.15230e8	+	3.35122e8i	1.02469	+	0.827004i
$741$		0			0
$742$	−2.85852e8	−	1.05450e7i	−0.699728	−	0.0258127i
$743$	−3.91308e8			−0.954008			−0.477004	−	0.878901i	$-0.658277\pi$
$743$	−3.91308e8			−0.954008			−0.477004	+	0.878901i	$0.658277\pi$
$744$		0			0
$745$	−1.64739e8	+	2.38084e8i	−0.398408	+	0.575787i
$746$	−9.92586e7	−	3.66161e6i	−0.239085	−	0.00881975i
$747$		0			0
$748$	1.61403e8	+	1.19244e7i	0.385661	+	0.0284926i
$749$	−2.77015e8			−0.659262
$750$		0			0
$751$		−	2.95353e8i		−	0.697303i	−0.937253	−	0.348651i	$-0.886640\pi$
$751$		−	2.95353e8i		−	0.697303i	0.937253	−	0.348651i	$-0.113360\pi$
$752$	7.95784e8	+	1.18230e8i	1.87129	+	0.278019i
$753$		0			0
$754$	−2.53503e7	−	935165.i	−0.0591384	−	0.00218159i
$755$	−5.88837e8	−	4.07438e8i	−1.36821	−	0.946719i
$756$		0			0
$757$		−	4.40767e8i		−	1.01607i	−0.861338	−	0.508033i	$-0.830373\pi$
$757$		−	4.40767e8i		−	1.01607i	0.861338	−	0.508033i	$-0.169627\pi$
$758$	3.34557e8	+	1.23417e7i	0.768178	+	0.0283378i
$759$		0			0
$760$	−4.24354e8	+	4.87840e8i	−0.966691	+	1.11131i
$761$	−8.11422e8			−1.84117			−0.920583	−	0.390548i	$-0.872286\pi$
$761$	−8.11422e8			−1.84117			−0.920583	+	0.390548i	$0.872286\pi$
$762$		0			0
$763$	2.24801e8			0.506086
$764$	−4.30404e7	+	5.82573e8i	−0.0965153	+	1.30638i
$765$		0			0
$766$	1.51119e7	−	4.09651e8i	0.0336226	−	0.911438i
$767$	−2.24860e8			−0.498340
$768$		0			0
$769$	−4.57333e8			−1.00567			−0.502833	−	0.864383i	$-0.667709\pi$
$769$	−4.57333e8			−1.00567			−0.502833	+	0.864383i	$0.667709\pi$
$770$	1.66852e8	−	2.23089e8i	0.365477	−	0.488660i
$771$		0			0
$772$	−5.74191e7	+	7.77195e8i	−0.124797	+	1.68919i
$773$			7.52735e8i			1.62969i	0.579682	+	0.814843i	$0.303177\pi$
$773$			7.52735e8i			1.62969i	−0.579682	+	0.814843i	$0.696823\pi$
$774$		0			0
$775$	1.07912e8	−	4.06441e7i	0.231828	−	0.0873158i
$776$	−6.64855e7	−	7.38469e6i	−0.142279	−	0.0158033i
$777$		0			0
$778$	1.46942e7	−	3.98329e8i	0.0312038	−	0.845869i
$779$			9.81909e8i			2.07711i
$780$		0			0
$781$	2.01295e8			0.422551
$782$	−5.82921e8	−	2.15038e7i	−1.21896	−	0.0449670i
$783$		0			0
$784$	5.20397e8	+	7.73157e7i	1.07991	+	0.160442i
$785$	2.20330e7	+	1.52454e7i	0.0455474	+	0.0315160i
$786$		0			0
$787$	2.11025e8			0.432921			0.216461	−	0.976291i	$-0.430549\pi$
$787$	2.11025e8			0.432921			0.216461	+	0.976291i	$0.430549\pi$
$788$	2.51337e7	−	3.40197e8i	0.0513663	−	0.695267i
$789$		0			0
$790$	−1.62931e8	+	2.17847e8i	−0.330463	+	0.441845i
$791$			9.09242e8i			1.83717i
$792$		0			0
$793$		−	3.19212e8i		−	0.640117i
$794$	3.13558e8	+	1.15670e7i	0.626406	+	0.0231079i
$795$		0			0
$796$	8.03983e6	−	1.08823e8i	0.0159407	−	0.215765i
$797$			2.07292e8i			0.409456i	0.978819	+	0.204728i	$0.0656310\pi$
$797$			2.07292e8i			0.409456i	−0.978819	+	0.204728i	$0.934369\pi$
$798$		0			0
$799$		−	8.84472e8i		−	1.73398i
$800$	5.04105e8	−	8.95684e7i	0.984579	−	0.174938i
$801$		0			0
$802$	−1.66142e6	+	4.50377e7i	−0.00322075	+	0.0873078i
$803$	2.31107e8			0.446340
$804$		0			0
$805$	−5.71324e8	+	8.25688e8i	−1.09520	+	1.58281i
$806$	−3.44904e6	+	9.34962e7i	−0.00658709	+	0.178562i
$807$		0			0
$808$	6.14137e7	−	5.52917e8i	0.116421	−	1.04816i
$809$	−4.26907e8			−0.806283			−0.403142	−	0.915138i	$-0.632082\pi$
$809$	−4.26907e8			−0.806283			−0.403142	+	0.915138i	$0.632082\pi$
$810$		0			0
$811$			6.62743e8i			1.24246i	0.783628	+	0.621230i	$0.213367\pi$
$811$			6.62743e8i			1.24246i	−0.783628	+	0.621230i	$0.786633\pi$
$812$	−6.33570e7	−	4.68081e6i	−0.118339	−	0.00874284i
$813$		0			0
$814$	−1.10465e7	+	2.99447e8i	−0.0204810	+	0.555197i
$815$	3.64984e8	−	5.27482e8i	0.674220	−	0.974394i
$816$		0			0
$817$		−	1.13982e9i		−	2.09012i
$818$	8.72874e6	−	2.36617e8i	0.0159475	−	0.432302i
$819$		0			0
$820$	4.88327e8	−	6.05058e8i	0.885665	−	1.09738i
$821$	−5.73913e8			−1.03709			−0.518545	−	0.855050i	$-0.673526\pi$
$821$	−5.73913e8			−1.03709			−0.518545	+	0.855050i	$0.673526\pi$
$822$		0			0
$823$	5.19180e8			0.931362			0.465681	−	0.884953i	$-0.345809\pi$
$823$	5.19180e8			0.931362			0.465681	+	0.884953i	$0.345809\pi$
$824$	1.00749e8	−	9.07058e8i	0.180077	−	1.62126i
$825$		0			0
$826$	−5.62749e8	−	2.07596e7i	−0.998560	−	0.0368366i
$827$	4.62996e8			0.818580			0.409290	−	0.912404i	$-0.365776\pi$
$827$	4.62996e8			0.818580			0.409290	+	0.912404i	$0.365776\pi$
$828$		0			0
$829$	−7.20209e8			−1.26414			−0.632069	−	0.774912i	$-0.717794\pi$
$829$	−7.20209e8			−1.26414			−0.632069	+	0.774912i	$0.717794\pi$
$830$	2.02120e8	+	1.51169e8i	0.353488	+	0.264380i
$831$		0			0
$832$	−9.11575e7	+	4.05290e8i	−0.158279	+	0.703713i
$833$		−	5.78394e8i		−	1.00067i
$834$		0			0
$835$	−2.17396e8	+	3.14184e8i	−0.373415	+	0.539665i
$836$	−3.62113e8	−	2.67529e7i	−0.619763	−	0.0457880i
$837$		0			0
$838$	−9.21438e7	−	3.39915e6i	−0.156579	−	0.00577615i
$839$		−	3.84875e8i		−	0.651680i	−0.945425	−	0.325840i	$-0.894353\pi$
$839$		−	3.84875e8i		−	0.651680i	0.945425	−	0.325840i	$-0.105647\pi$
$840$		0			0
$841$	−5.90819e8			−0.993269
$842$	−1.05421e7	+	2.85773e8i	−0.0176599	+	0.478723i
$843$		0			0
$844$	−5.92548e7	+	8.02042e8i	−0.0985589	+	1.33404i
$845$	−1.64698e8	+	2.38024e8i	−0.272971	+	0.394503i
$846$		0			0
$847$	−7.22388e8			−1.18883
$848$	4.33859e7	−	2.92022e8i	0.0711477	−	0.478881i
$849$		0			0
$850$	−1.78845e8	−	5.33715e8i	−0.291219	−	0.869066i
$851$		−	1.08001e9i		−	1.75243i
$852$		0			0
$853$			5.38061e8i			0.866931i	0.901170	+	0.433466i	$0.142709\pi$
$853$			5.38061e8i			0.866931i	−0.901170	+	0.433466i	$0.857291\pi$
$854$	2.94704e7	−	7.98880e8i	0.0473165	−	1.28265i
$855$		0			0
$856$	3.15621e7	−	2.84159e8i	0.0503205	−	0.453043i
$857$		−	3.71687e8i		−	0.590521i	−0.955417	−	0.295261i	$-0.904594\pi$
$857$		−	3.71687e8i		−	0.590521i	0.955417	−	0.295261i	$-0.0954065\pi$
$858$		0			0
$859$		−	3.70545e7i		−	0.0584603i	−0.999573	−	0.0292302i	$-0.990694\pi$
$859$		−	3.70545e7i		−	0.0584603i	0.999573	−	0.0292302i	$-0.00930557\pi$
$860$	−5.66861e8	+	7.02365e8i	−0.891213	+	1.10425i
$861$		0			0
$862$	−6.56225e7	−	2.42079e6i	−0.102454	−	0.00377951i
$863$	2.37470e7			0.0369468			0.0184734	−	0.999829i	$-0.494119\pi$
$863$	2.37470e7			0.0369468			0.0184734	+	0.999829i	$0.494119\pi$
$864$		0			0
$865$	5.29584e8	+	3.66439e8i	0.818251	+	0.566178i
$866$	−3.50106e8	−	1.29153e7i	−0.539071	−	0.0198861i
$867$		0			0
$868$	−1.72636e7	+	2.33671e8i	−0.0263981	+	0.357311i
$869$	−1.52768e8			−0.232794
$870$		0			0
$871$			3.43302e8i			0.519543i
$872$	−2.56130e7	+	2.30598e8i	−0.0386288	+	0.347781i
$873$		0			0
$874$	1.30781e9	+	4.82445e7i	1.95889	+	0.0722626i
$875$	−9.39948e8	−	2.35095e8i	−1.40307	−	0.350929i
$876$		0			0
$877$			9.70223e8i			1.43838i	0.694815	+	0.719189i	$0.255486\pi$
$877$			9.70223e8i			1.43838i	−0.694815	+	0.719189i	$0.744514\pi$
$878$	−7.25751e8	−	2.67727e7i	−1.07227	−	0.0395556i
$879$		0			0
$880$	2.09832e8	+	1.96573e8i	0.307909	+	0.288454i
$881$	−3.34234e8			−0.488791			−0.244396	−	0.969676i	$-0.578590\pi$
$881$	−3.34234e8			−0.488791			−0.244396	+	0.969676i	$0.578590\pi$
$882$		0			0
$883$	1.04292e9			1.51485			0.757426	−	0.652921i	$-0.226457\pi$
$883$	1.04292e9			1.51485			0.757426	+	0.652921i	$0.226457\pi$
$884$	4.55458e8	+	3.36492e7i	0.659313	+	0.0487099i
$885$		0			0
$886$	−1.30057e6	+	3.52558e7i	−0.00186997	+	0.0506908i
$887$	2.82542e8			0.404867			0.202434	−	0.979296i	$-0.435115\pi$
$887$	2.82542e8			0.404867			0.202434	+	0.979296i	$0.435115\pi$
$888$		0			0
$889$	9.90598e8			1.40991
$890$	−6.98631e7	−	5.22518e7i	−0.0991009	−	0.0741193i
$891$		0			0
$892$	−3.05500e8	−	2.25703e7i	−0.430444	−	0.0318011i
$893$			1.98435e9i			2.78653i
$894$		0			0
$895$	−2.02554e8	−	1.40154e8i	−0.282534	−	0.195496i
$896$	−2.65554e8	+	1.00589e9i	−0.369172	+	1.39838i
$897$		0			0
$898$	−2.28530e7	+	6.19497e8i	−0.0315584	+	0.855480i
$899$		−	1.47674e7i		−	0.0203247i
$900$		0			0
$901$	−3.24567e8			−0.443742
$902$	4.36344e8	+	1.60966e7i	0.594579	+	0.0219338i
$903$		0			0
$904$	−9.32689e8	−	1.03596e8i	−1.26250	−	0.140229i
$905$	−1.66886e8	+	2.41187e8i	−0.225152	+	0.325393i
$906$		0			0
$907$	−6.77657e7			−0.0908214			−0.0454107	−	0.998968i	$-0.514460\pi$
$907$	−6.77657e7			−0.0908214			−0.0454107	+	0.998968i	$0.514460\pi$
$908$	1.13673e7	+	839818.i	0.0151845	+	0.00112183i
$909$		0			0
$910$	4.70836e8	−	6.29530e8i	0.624807	−	0.835395i
$911$		−	9.61421e7i		−	0.127162i	−0.997977	−	0.0635812i	$-0.979748\pi$
$911$		−	9.61421e7i		−	0.127162i	0.997977	−	0.0635812i	$-0.0202522\pi$
$912$		0			0
$913$			1.41739e8i			0.186242i
$914$	1.31174e9	+	4.83895e7i	1.71794	+	0.0633742i
$915$		0			0
$916$	6.49601e7	+	4.79924e6i	0.0845202	+	0.00624434i
$917$			2.95764e8i			0.383563i
$918$		0			0
$919$		−	5.40889e8i		−	0.696885i	−0.937330	−	0.348443i	$-0.886711\pi$
$919$		−	5.40889e8i		−	0.696885i	0.937330	−	0.348443i	$-0.113289\pi$
$920$	−7.81885e8	−	6.80133e8i	−1.00411	−	0.873435i
$921$		0			0
$922$	−3.72220e7	+	1.00901e9i	−0.0474905	+	1.28737i
$923$	5.68028e8			0.722378
$924$		0			0
$925$	9.75293e8	−	3.67334e8i	1.23228	−	0.464127i
$926$	−9.48641e6	+	2.57156e8i	−0.0119473	+	0.323865i
$927$		0			0
$928$	1.20202e7	−	6.44575e7i	0.0150407	−	0.0806547i
$929$	1.21327e9			1.51325			0.756626	−	0.653848i	$-0.226846\pi$
$929$	1.21327e9			1.51325			0.756626	+	0.653848i	$0.226846\pi$
$930$		0			0
$931$			1.29765e9i			1.60808i
$932$	1.05429e7	−	1.42703e8i	0.0130231	−	0.176273i
$933$		0			0
$934$	−5.77033e6	+	1.56421e8i	−0.00708207	+	0.191980i
$935$	1.79862e8	−	2.59939e8i	0.220041	−	0.318007i
$936$		0			0
$937$			4.32441e8i			0.525663i	0.964842	+	0.262832i	$0.0846564\pi$
$937$			4.32441e8i			0.525663i	−0.964842	+	0.262832i	$0.915344\pi$
$938$	−3.16944e7	+	8.59168e8i	−0.0384038	+	1.04105i
$939$		0			0
$940$	9.86865e8	−	1.22277e9i	1.18816	−	1.47218i
$941$	−1.21123e9			−1.45364			−0.726821	−	0.686827i	$-0.759003\pi$
$941$	−1.21123e9			−1.45364			−0.726821	+	0.686827i	$0.759003\pi$
$942$		0			0
$943$	−1.57375e9			−1.87673
$944$	8.54125e7	−	5.74895e8i	0.101533	−	0.683396i
$945$		0			0
$946$	−5.06518e8	−	1.86853e7i	−0.598303	−	0.0220712i
$947$	6.93040e8			0.816034			0.408017	−	0.912974i	$-0.366220\pi$
$947$	6.93040e8			0.816034			0.408017	+	0.912974i	$0.366220\pi$
$948$		0			0
$949$	6.52154e8			0.763047
$950$	4.01246e8	+	1.19741e9i	0.467993	+	1.39660i
$951$		0			0
$952$	1.13675e9	+	1.26262e8i	1.31751	+	0.146339i
$953$		−	3.68416e8i		−	0.425657i	−0.977090	−	0.212828i	$-0.931732\pi$
$953$		−	3.68416e8i		−	0.425657i	0.977090	−	0.212828i	$-0.0682675\pi$
$954$		0			0
$955$	9.38233e8	+	6.49198e8i	1.07721	+	0.745362i
$956$	1.17529e8	−	1.59081e9i	0.134515	−	1.82073i
$957$		0			0
$958$	1.55036e9	+	5.71923e7i	1.76334	+	0.0650490i
$959$			2.19698e9i			2.49098i
$960$		0			0
$961$	8.33039e8			0.938632
$962$	−3.11718e7	+	8.45002e8i	−0.0350136	+	0.949145i
$963$		0			0
$964$	3.60031e8	+	2.65990e7i	0.401891	+	0.0296916i
$965$	1.25167e9	+	8.66079e8i	1.39286	+	0.963775i
$966$		0			0
$967$	−1.15287e9			−1.27497			−0.637485	−	0.770463i	$-0.720025\pi$
$967$	−1.15287e9			−1.27497			−0.637485	+	0.770463i	$0.720025\pi$
$968$	8.23064e7	−	7.41017e8i	0.0907418	−	0.816962i
$969$		0			0
$970$	−7.82523e7	+	1.04627e8i	−0.0857397	+	0.114638i
$971$		−	4.34130e8i		−	0.474201i	−0.971485	−	0.237100i	$-0.923803\pi$
$971$		−	4.34130e8i		−	0.474201i	0.971485	−	0.237100i	$-0.0761971\pi$
$972$		0			0
$973$			2.50249e9i			2.71665i
$974$	−4.79452e7	+	1.29969e9i	−0.0518882	+	1.40658i
$975$		0			0
$976$	8.16123e8	+	1.21252e8i	0.877821	+	0.130418i
$977$		−	1.16648e9i		−	1.25082i	−0.780297	−	0.625410i	$-0.784932\pi$
$977$		−	1.16648e9i		−	1.25082i	0.780297	−	0.625410i	$-0.215068\pi$
$978$		0			0
$979$		−	4.89924e7i		−	0.0522132i
$980$	6.45353e8	−	7.99620e8i	0.685676	−	0.849582i
$981$		0			0
$982$	−1.24634e9	−	4.59771e7i	−1.31614	−	0.0485520i
$983$	−4.61997e8			−0.486384			−0.243192	−	0.969978i	$-0.578194\pi$
$983$	−4.61997e8			−0.486384			−0.243192	+	0.969978i	$0.578194\pi$
$984$		0			0
$985$	−5.47887e8	−	3.79104e8i	−0.573301	−	0.396688i
$986$	−7.20360e7	−	2.65738e6i	−0.0751482	−	0.00277219i
$987$		0			0
$988$	−1.02184e9	−	7.54932e7i	−1.05952	−	0.0782775i
$989$	1.82685e9			1.88848
$990$		0			0
$991$		−	1.16310e9i		−	1.19508i	−0.801841	−	0.597538i	$-0.796146\pi$
$991$		−	1.16310e9i		−	1.19508i	0.801841	−	0.597538i	$-0.203854\pi$
$992$	−2.37730e8	−	4.43324e7i	−0.243528	−	0.0454137i
$993$		0			0
$994$	1.42158e9	+	5.24417e7i	1.44748	+	0.0533971i
$995$	−1.75259e8	−	1.21269e8i	−0.177915	−	0.123106i
$996$		0			0
$997$		−	1.47436e9i		−	1.48771i	−0.668343	−	0.743853i	$-0.732996\pi$
$997$		−	1.47436e9i		−	1.48771i	0.668343	−	0.743853i	$-0.267004\pi$
$998$	−4.27185e8	−	1.57587e7i	−0.429759	−	0.0158537i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.7.f.g.19.18		36
3.2	odd	2		60.7.f.a.19.19	yes	36
4.3	odd	2	inner	180.7.f.g.19.20		36
5.4	even	2	inner	180.7.f.g.19.19		36
12.11	even	2		60.7.f.a.19.17	✓	36
15.14	odd	2		60.7.f.a.19.18	yes	36
20.19	odd	2	inner	180.7.f.g.19.17		36
60.59	even	2		60.7.f.a.19.20	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.17	✓	36	12.11	even	2
60.7.f.a.19.18	yes	36	15.14	odd	2
60.7.f.a.19.19	yes	36	3.2	odd	2
60.7.f.a.19.20	yes	36	60.59	even	2
180.7.f.g.19.17		36	20.19	odd	2	inner
180.7.f.g.19.18		36	1.1	even	1	trivial
180.7.f.g.19.19		36	5.4	even	2	inner
180.7.f.g.19.20		36	4.3	odd	2	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	180.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.294917 + 7.99456i) q^{2} +(-63.8260 - 4.71546i) q^{4} +(-71.1255 + 102.792i) q^{5} -496.078 q^{7} +(56.5214 - 508.871i) q^{8} +O(q^{10})\)	\(q+(-0.294917 + 7.99456i) q^{2} +(-63.8260 - 4.71546i) q^{4} +(-71.1255 + 102.792i) q^{5} -496.078 q^{7} +(56.5214 - 508.871i) q^{8} +(-800.800 - 598.932i) q^{10} -561.571i q^{11} -1584.68i q^{13} +(146.302 - 3965.93i) q^{14} +(4051.53 + 601.938i) q^{16} -4503.06i q^{17} +10102.8i q^{19} +(5024.37 - 6225.41i) q^{20} +(4489.52 + 165.617i) q^{22} -16192.2 q^{23} +(-5507.32 - 14622.2i) q^{25} +(12668.8 + 467.349i) q^{26} +(31662.7 + 2339.24i) q^{28} -2001.00 q^{29} +7380.01i q^{31} +(-6007.10 + 32212.7i) q^{32} +(36000.0 + 1328.03i) q^{34} +(35283.8 - 50992.8i) q^{35} +66699.3i q^{37} +(-80767.5 - 2979.48i) q^{38} +(48287.6 + 42003.6i) q^{40} +97191.8 q^{41} -112822. q^{43} +(-2648.07 + 35842.9i) q^{44} +(4775.36 - 129450. i) q^{46} +196416. q^{47} +128445. q^{49} +(118523. - 39716.3i) q^{50} +(-7472.50 + 101144. i) q^{52} -72076.9i q^{53} +(57724.9 + 39942.0i) q^{55} +(-28039.0 + 252440. i) q^{56} +(590.128 - 15997.1i) q^{58} -141896. i q^{59} +201436. q^{61} +(-59000.0 - 2176.49i) q^{62} +(-255755. - 57524.2i) q^{64} +(162892. + 112711. i) q^{65} -216637. q^{67} +(-21234.0 + 287413. i) q^{68} +(397259. + 297117. i) q^{70} +358449. i q^{71} +411536. i q^{73} +(-533231. - 19670.7i) q^{74} +(47639.3 - 644822. i) q^{76} +278583. i q^{77} -272036. i q^{79} +(-350041. + 373651. i) q^{80} +(-28663.5 + 777005. i) q^{82} -252398. q^{83} +(462878. + 320283. i) q^{85} +(33273.2 - 901965. i) q^{86} +(-285767. - 31740.8i) q^{88} +87241.6 q^{89} +786126. i q^{91} +(1.03349e6 + 76353.9i) q^{92} +(-57926.2 + 1.57026e6i) q^{94} +(-1.03849e6 - 718567. i) q^{95} -130653. i q^{97} +(-37880.4 + 1.02686e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} - 44 q^{5}+O(q^{10}) \) 36 * q - 66 * q^4 - 44 * q^5	\( 36 q - 66 q^{4} - 44 q^{5} - 1422 q^{10} - 15484 q^{14} + 1266 q^{16} + 2188 q^{20} + 13812 q^{25} + 32052 q^{26} + 36920 q^{29} - 156204 q^{34} + 7674 q^{40} - 341848 q^{41} - 74892 q^{44} + 478080 q^{46} + 482556 q^{49} + 191448 q^{50} + 926132 q^{56} - 455976 q^{61} - 618 q^{64} + 624192 q^{65} - 1871304 q^{70} + 612324 q^{74} - 1566456 q^{76} - 2360972 q^{80} + 2280864 q^{85} - 5157592 q^{86} + 1806104 q^{89} - 3121992 q^{94}+O(q^{100}) \) 36 * q - 66 * q^4 - 44 * q^5 - 1422 * q^10 - 15484 * q^14 + 1266 * q^16 + 2188 * q^20 + 13812 * q^25 + 32052 * q^26 + 36920 * q^29 - 156204 * q^34 + 7674 * q^40 - 341848 * q^41 - 74892 * q^44 + 478080 * q^46 + 482556 * q^49 + 191448 * q^50 + 926132 * q^56 - 455976 * q^61 - 618 * q^64 + 624192 * q^65 - 1871304 * q^70 + 612324 * q^74 - 1566456 * q^76 - 2360972 * q^80 + 2280864 * q^85 - 5157592 * q^86 + 1806104 * q^89 - 3121992 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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