LMFDB - Embedded newform 76.7.j.a.53.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.10
Character	$\chi$	$=$	76.53
Dual form			76.7.j.a.33.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(48.0588 - 8.47406i) q^{3} +(67.2683 - 56.4448i) q^{5} +(-18.9857 + 32.8842i) q^{7} +(1552.80 - 565.174i) q^{9} +O(q^{10})$	\(q+(48.0588 - 8.47406i) q^{3} +(67.2683 - 56.4448i) q^{5} +(-18.9857 + 32.8842i) q^{7} +(1552.80 - 565.174i) q^{9} +(-443.219 - 767.678i) q^{11} +(2477.96 + 436.932i) q^{13} +(2754.52 - 3282.71i) q^{15} +(-1511.07 - 549.985i) q^{17} +(-6769.01 + 1107.44i) q^{19} +(-633.766 + 1741.26i) q^{21} +(1870.99 + 1569.95i) q^{23} +(-1374.24 + 7793.72i) q^{25} +(39027.4 - 22532.5i) q^{27} +(-7186.37 - 19744.4i) q^{29} +(23317.0 + 13462.1i) q^{31} +(-27805.9 - 33137.8i) q^{33} +(579.006 + 3283.70i) q^{35} -26050.1i q^{37} +122791. q^{39} +(46849.4 - 8260.82i) q^{41} +(66202.0 - 55550.1i) q^{43} +(72553.3 - 125666. i) q^{45} +(-54002.7 + 19655.4i) q^{47} +(58103.6 + 100638. i) q^{49} +(-77280.9 - 13626.7i) q^{51} +(-161217. + 192130. i) q^{53} +(-73146.0 - 26623.0i) q^{55} +(-315926. + 110583. i) q^{57} +(-119006. + 326967. i) q^{59} +(-285390. - 239471. i) q^{61} +(-10895.7 + 61792.8i) q^{63} +(191351. - 110477. i) q^{65} +(62029.2 + 170424. i) q^{67} +(103221. + 59594.8i) q^{69} +(-425274. - 506822. i) q^{71} +(115453. + 654764. i) q^{73} +386203. i q^{75} +33659.2 q^{77} +(-167253. + 29491.2i) q^{79} +(761859. - 639275. i) q^{81} +(-124334. + 215353. i) q^{83} +(-132691. + 48295.6i) q^{85} +(-512683. - 887994. i) q^{87} +(692179. + 122050. i) q^{89} +(-61414.0 + 73190.3i) q^{91} +(1.23466e6 + 449381. i) q^{93} +(-392831. + 456571. i) q^{95} +(40294.4 - 110708. i) q^{97} +(-1.12210e6 - 941556. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	$ 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) $ 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	48.0588	−	8.47406i	1.77996	−	0.313854i	0.815630	−	0.578574i	$-0.196390\pi$
$3$	48.0588	−	8.47406i	1.77996	−	0.313854i	0.964326	+	0.264719i	$0.0852793\pi$
$4$		0			0
$5$	67.2683	−	56.4448i	0.538147	−	0.451559i	−0.332757	−	0.943013i	$-0.607979\pi$
$5$	67.2683	−	56.4448i	0.538147	−	0.451559i	0.870904	+	0.491454i	$0.163534\pi$
$6$		0			0
$7$	−18.9857	+	32.8842i	−0.0553518	+	0.0958722i	−0.892374	−	0.451297i	$-0.850961\pi$
$7$	−18.9857	+	32.8842i	−0.0553518	+	0.0958722i	0.837022	+	0.547170i	$0.184295\pi$
$8$		0			0
$9$	1552.80	−	565.174i	2.13005	−	0.775273i
$10$		0			0
$11$	−443.219	−	767.678i	−0.332997	−	0.576768i	0.650101	−	0.759848i	$-0.274727\pi$
$11$	−443.219	−	767.678i	−0.332997	−	0.576768i	−0.983098	+	0.183080i	$0.941393\pi$
$12$		0			0
$13$	2477.96	+	436.932i	1.12789	+	0.198877i	0.706300	−	0.707912i	$-0.250363\pi$
$13$	2477.96	+	436.932i	1.12789	+	0.198877i	0.421585	+	0.906789i	$0.361474\pi$
$14$		0			0
$15$	2754.52	−	3282.71i	0.816153	−	0.972654i
$16$		0			0
$17$	−1511.07	−	549.985i	−0.307566	−	0.111945i	0.183626	−	0.982996i	$-0.441216\pi$
$17$	−1511.07	−	549.985i	−0.307566	−	0.111945i	−0.491192	+	0.871051i	$0.663439\pi$
$18$		0			0
$19$	−6769.01	+	1107.44i	−0.986880	+	0.161457i
$19$	−6769.01	+	1107.44i	−0.986880	+	0.161457i
$20$		0			0
$21$	−633.766	+	1741.26i	−0.0684339	+	0.188021i
$22$		0			0
$23$	1870.99	+	1569.95i	0.153776	+	0.129033i	0.716429	−	0.697660i	$-0.245775\pi$
$23$	1870.99	+	1569.95i	0.153776	+	0.129033i	−0.562654	+	0.826693i	$0.690220\pi$
$24$		0			0
$25$	−1374.24	+	7793.72i	−0.0879516	+	0.498798i
$26$		0			0
$27$	39027.4	−	22532.5i	1.98280	−	1.14477i
$28$		0			0
$29$	−7186.37	−	19744.4i	−0.294656	−	0.809561i	−0.995370	−	0.0961185i	$-0.969357\pi$
$29$	−7186.37	−	19744.4i	−0.294656	−	0.809561i	0.700714	−	0.713442i	$-0.252865\pi$
$30$		0			0
$31$	23317.0	+	13462.1i	0.782685	+	0.451883i	0.837381	−	0.546620i	$-0.184086\pi$
$31$	23317.0	+	13462.1i	0.782685	+	0.451883i	−0.0546963	+	0.998503i	$0.517419\pi$
$32$		0			0
$33$	−27805.9	−	33137.8i	−0.773741	−	0.922108i
$34$		0			0
$35$	579.006	+	3283.70i	0.0135045	+	0.0765879i
$36$		0			0
$37$		−	26050.1i		−	0.514285i	−0.966373	−	0.257143i	$-0.917219\pi$
$37$		−	26050.1i		−	0.514285i	0.966373	−	0.257143i	$-0.0827810\pi$
$38$		0			0
$39$	122791.			2.07000
$40$		0			0
$41$	46849.4	−	8260.82i	0.679756	−	0.119859i	0.176899	−	0.984229i	$-0.443393\pi$
$41$	46849.4	−	8260.82i	0.679756	−	0.119859i	0.502857	+	0.864370i	$0.332282\pi$
$42$		0			0
$43$	66202.0	−	55550.1i	0.832656	−	0.698682i	−0.123243	−	0.992377i	$-0.539329\pi$
$43$	66202.0	−	55550.1i	0.832656	−	0.698682i	0.955899	+	0.293695i	$0.0948849\pi$
$44$		0			0
$45$	72553.3	−	125666.i	0.796195	−	1.37905i
$46$		0			0
$47$	−54002.7	+	19655.4i	−0.520142	+	0.189316i	−0.588731	−	0.808329i	$-0.700372\pi$
$47$	−54002.7	+	19655.4i	−0.520142	+	0.189316i	0.0685892	+	0.997645i	$0.478150\pi$
$48$		0			0
$49$	58103.6	+	100638.i	0.493872	+	0.855412i
$50$		0			0
$51$	−77280.9	−	13626.7i	−0.582588	−	0.102726i
$52$		0			0
$53$	−161217.	+	192130.i	−1.08288	+	1.29053i	−0.128579	+	0.991699i	$0.541042\pi$
$53$	−161217.	+	192130.i	−1.08288	+	1.29053i	−0.954306	+	0.298832i	$0.903403\pi$
$54$		0			0
$55$	−73146.0	−	26623.0i	−0.439645	−	0.160018i
$56$		0			0
$57$	−315926.	+	110583.i	−1.70593	+	0.597123i
$58$		0			0
$59$	−119006.	+	326967.i	−0.579447	+	1.59202i	0.209669	+	0.977772i	$0.432761\pi$
$59$	−119006.	+	326967.i	−0.579447	+	1.59202i	−0.789116	+	0.614245i	$0.789461\pi$
$60$		0			0
$61$	−285390.	−	239471.i	−1.25733	−	1.05503i	−0.995961	−	0.0897876i	$-0.971381\pi$
$61$	−285390.	−	239471.i	−1.25733	−	1.05503i	−0.261370	−	0.965239i	$-0.584174\pi$
$62$		0			0
$63$	−10895.7	+	61792.8i	−0.0435748	+	0.247125i
$64$		0			0
$65$	191351.	−	110477.i	0.696772	−	0.402282i
$66$		0			0
$67$	62029.2	+	170424.i	0.206239	+	0.566638i	0.999084	−	0.0427855i	$-0.0136232\pi$
$67$	62029.2	+	170424.i	0.206239	+	0.566638i	−0.792845	+	0.609423i	$0.791401\pi$
$68$		0			0
$69$	103221.	+	59594.8i	0.314211	+	0.181410i
$70$		0			0
$71$	−425274.	−	506822.i	−1.18821	−	1.41606i	−0.886546	−	0.462641i	$-0.846902\pi$
$71$	−425274.	−	506822.i	−1.18821	−	1.41606i	−0.301666	−	0.953414i	$-0.597543\pi$
$72$		0			0
$73$	115453.	+	654764.i	0.296780	+	1.68313i	0.659877	+	0.751374i	$0.270608\pi$
$73$	115453.	+	654764.i	0.296780	+	1.68313i	−0.363097	+	0.931751i	$0.618281\pi$
$74$		0			0
$75$			386203.i			0.915443i
$76$		0			0
$77$	33659.2			0.0737279
$78$		0			0
$79$	−167253.	+	29491.2i	−0.339229	+	0.0598152i	−0.340668	−	0.940184i	$-0.610653\pi$
$79$	−167253.	+	29491.2i	−0.339229	+	0.0598152i	0.00143885	+	0.999999i	$0.499542\pi$
$80$		0			0
$81$	761859.	−	639275.i	1.43357	−	1.20291i
$82$		0			0
$83$	−124334.	+	215353.i	−0.217448	+	0.376631i	−0.954027	−	0.299720i	$-0.903107\pi$
$83$	−124334.	+	215353.i	−0.217448	+	0.376631i	0.736579	+	0.676351i	$0.236440\pi$
$84$		0			0
$85$	−132691.	+	48295.6i	−0.216065	+	0.0786413i
$86$		0			0
$87$	−512683.	−	887994.i	−0.778559	−	1.34850i
$88$		0			0
$89$	692179.	+	122050.i	0.981857	+	0.173128i	0.641462	−	0.767155i	$-0.278328\pi$
$89$	692179.	+	122050.i	0.981857	+	0.173128i	0.340395	+	0.940283i	$0.389439\pi$
$90$		0			0
$91$	−61414.0	+	73190.3i	−0.0814973	+	0.0971246i
$92$		0			0
$93$	1.23466e6	+	449381.i	1.53497	+	0.558683i
$94$		0			0
$95$	−392831.	+	456571.i	−0.458178	+	0.532522i
$96$		0			0
$97$	40294.4	−	110708.i	0.0441499	−	0.121301i	−0.915658	−	0.401957i	$-0.868330\pi$
$97$	40294.4	−	110708.i	0.0441499	−	0.121301i	0.959808	+	0.280657i	$0.0905522\pi$
$98$		0			0
$99$	−1.12210e6	−	941556.i	−1.15645	−	0.970378i
$100$		0			0
$101$	−80734.6	+	457869.i	−0.0783602	+	0.444403i	0.920233	+	0.391372i	$0.127999\pi$
$101$	−80734.6	+	457869.i	−0.0783602	+	0.444403i	−0.998593	+	0.0530311i	$0.983112\pi$
$102$		0			0
$103$	−1.74125e6	+	1.00531e6i	−1.59349	+	0.920000i	−0.600785	+	0.799411i	$0.705145\pi$
$103$	−1.74125e6	+	1.00531e6i	−1.59349	+	0.920000i	−0.992702	+	0.120590i	$0.961521\pi$
$104$		0			0
$105$	55652.7	+	152904.i	0.0480749	+	0.132085i
$106$		0			0
$107$	−887189.	−	512219.i	−0.724210	−	0.418123i	0.0920900	−	0.995751i	$-0.470645\pi$
$107$	−887189.	−	512219.i	−0.724210	−	0.418123i	−0.816300	+	0.577628i	$0.803979\pi$
$108$		0			0
$109$	629513.	+	750225.i	0.486100	+	0.579311i	0.952221	−	0.305410i	$-0.0987934\pi$
$109$	629513.	+	750225.i	0.486100	+	0.579311i	−0.466121	+	0.884721i	$0.654349\pi$
$110$		0			0
$111$	−220750.	−	1.25194e6i	−0.161411	−	0.915405i
$112$		0			0
$113$		−	708461.i		−	0.490999i	−0.969397	−	0.245499i	$-0.921048\pi$
$113$		−	708461.i		−	0.490999i	0.969397	−	0.245499i	$-0.0789519\pi$
$114$		0			0
$115$	214474.			0.141020
$116$		0			0
$117$	4.09473e6	−	722012.i	2.55663	−	0.450803i
$118$		0			0
$119$	46774.5	−	39248.5i	0.0277567	−	0.0232907i
$120$		0			0
$121$	492895.	−	853718.i	0.278226	−	0.481902i
$122$		0			0
$123$	2.18153e6	−	794010.i	1.17232	−	0.426688i
$124$		0			0
$125$	1.03351e6	+	1.79009e6i	0.529156	+	0.916525i
$126$		0			0
$127$	−1.69467e6	−	298817.i	−0.827323	−	0.145879i	−0.256075	−	0.966657i	$-0.582429\pi$
$127$	−1.69467e6	−	298817.i	−0.827323	−	0.145879i	−0.571248	+	0.820777i	$0.693541\pi$
$128$		0			0
$129$	2.71085e6	−	3.23067e6i	1.26281	−	1.50496i
$130$		0			0
$131$	2.77147e6	+	1.00873e6i	1.23281	+	0.448706i	0.874559	−	0.484920i	$-0.161151\pi$
$131$	2.77147e6	+	1.00873e6i	1.23281	+	0.448706i	0.358250	+	0.933626i	$0.383373\pi$
$132$		0			0
$133$	92097.1	−	243619.i	0.0391463	−	0.103551i
$134$		0			0
$135$	1.35347e6	−	3.71862e6i	0.550105	−	1.51140i
$136$		0			0
$137$	−2.33156e6	−	1.95641e6i	−0.906745	−	0.760849i	0.0647522	−	0.997901i	$-0.479374\pi$
$137$	−2.33156e6	−	1.95641e6i	−0.906745	−	0.760849i	−0.971497	+	0.237052i	$0.923819\pi$
$138$		0			0
$139$	−838508.	+	4.75541e6i	−0.312221	+	1.77070i	0.275173	+	0.961395i	$0.411265\pi$
$139$	−838508.	+	4.75541e6i	−0.312221	+	1.77070i	−0.587394	+	0.809301i	$0.699846\pi$
$140$		0			0
$141$	−2.42875e6	+	1.40224e6i	−0.866413	+	0.500224i
$142$		0			0
$143$	−762858.	−	2.09593e6i	−0.260877	−	0.716753i
$144$		0			0
$145$	−1.59788e6	−	922538.i	−0.524132	−	0.302608i
$146$		0			0
$147$	3.64521e6	+	4.34419e6i	1.14755	+	1.36759i
$148$		0			0
$149$	−27632.1	−	156710.i	−0.00835325	−	0.0473737i	0.980346	−	0.197285i	$-0.0632124\pi$
$149$	−27632.1	−	156710.i	−0.00835325	−	0.0473737i	−0.988699	+	0.149911i	$0.952101\pi$
$150$		0			0
$151$		−	4.66861e6i		−	1.35599i	−0.735067	−	0.677995i	$-0.762849\pi$
$151$		−	4.66861e6i		−	1.35599i	0.735067	−	0.677995i	$-0.237151\pi$
$152$		0			0
$153$	−2.65723e6			−0.741917
$154$		0			0
$155$	2.32836e6	−	410552.i	0.625251	−	0.110249i
$156$		0			0
$157$	−3.39991e6	+	2.85287e6i	−0.878555	+	0.737195i	−0.965881	−	0.258985i	$-0.916612\pi$
$157$	−3.39991e6	+	2.85287e6i	−0.878555	+	0.737195i	0.0873266	+	0.996180i	$0.472168\pi$
$158$		0			0
$159$	−6.11975e6	+	1.05997e7i	−1.52245	+	2.63696i
$160$		0			0
$161$	−87148.3	+	31719.4i	−0.0208824	+	0.00760059i
$162$		0			0
$163$	194573.	+	337011.i	0.0449284	+	0.0778182i	0.887615	−	0.460586i	$-0.152361\pi$
$163$	194573.	+	337011.i	0.0449284	+	0.0778182i	−0.842687	+	0.538404i	$0.819027\pi$
$164$		0			0
$165$	−3.74091e6	−	659624.i	−0.832772	−	0.146840i
$166$		0			0
$167$	3.27376e6	−	3.90151e6i	0.702906	−	0.837691i	−0.289946	−	0.957043i	$-0.593637\pi$
$167$	3.27376e6	−	3.90151e6i	0.702906	−	0.837691i	0.992852	+	0.119352i	$0.0380818\pi$
$168$		0			0
$169$	1.41368e6	+	514538.i	0.292881	+	0.106600i
$170$		0			0
$171$	−9.88504e6	+	5.54530e6i	−1.97693	+	1.10901i
$172$		0			0
$173$	2.41251e6	−	6.62833e6i	0.465942	−	1.28016i	−0.455010	−	0.890486i	$-0.650364\pi$
$173$	2.41251e6	−	6.62833e6i	0.465942	−	1.28016i	0.920951	−	0.389678i	$-0.127414\pi$
$174$		0			0
$175$	−230199.	−	193160.i	−0.0429526	−	0.0360415i
$176$		0			0
$177$	−2.94856e6	+	1.67221e7i	−0.531728	+	3.01558i
$178$		0			0
$179$	−2.44781e6	+	1.41324e6i	−0.426795	+	0.246410i	−0.697980	−	0.716117i	$-0.745918\pi$
$179$	−2.44781e6	+	1.41324e6i	−0.426795	+	0.246410i	0.271186	+	0.962527i	$0.412584\pi$
$180$		0			0
$181$	1.21378e6	+	3.33483e6i	0.204693	+	0.562390i	0.998980	−	0.0451528i	$-0.0143775\pi$
$181$	1.21378e6	+	3.33483e6i	0.204693	+	0.562390i	−0.794287	+	0.607543i	$0.792155\pi$
$182$		0			0
$183$	−1.57448e7	−	9.09027e6i	−2.56912	−	1.48328i
$184$		0			0
$185$	−1.47039e6	−	1.75235e6i	−0.232230	−	0.276761i
$186$		0			0
$187$	247524.	+	1.40378e6i	0.0378524	+	0.214671i
$188$		0			0
$189$			1.71118e6i			0.253460i
$190$		0			0
$191$	5.33312e6			0.765388			0.382694	−	0.923875i	$-0.374996\pi$
$191$	5.33312e6			0.765388			0.382694	+	0.923875i	$0.374996\pi$
$192$		0			0
$193$	1.16770e7	−	2.05898e6i	1.62428	−	0.286404i	0.713922	−	0.700226i	$-0.246917\pi$
$193$	1.16770e7	−	2.05898e6i	1.62428	−	0.286404i	0.910358	+	0.413821i	$0.135806\pi$
$194$		0			0
$195$	8.25992e6	−	6.93089e6i	1.11397	−	0.934728i
$196$		0			0
$197$	4.45733e6	−	7.72031e6i	0.583010	−	1.00980i	−0.412111	−	0.911134i	$-0.635208\pi$
$197$	4.45733e6	−	7.72031e6i	0.583010	−	1.00980i	0.995120	−	0.0986685i	$-0.0314583\pi$
$198$		0			0
$199$	2.34853e6	−	854794.i	0.298014	−	0.108468i	−0.188686	−	0.982037i	$-0.560423\pi$
$199$	2.34853e6	−	854794.i	0.298014	−	0.108468i	0.486700	+	0.873569i	$0.338201\pi$
$200$		0			0
$201$	4.42523e6	+	7.66472e6i	0.544939	+	0.943861i
$202$		0			0
$203$	785715.	+	138543.i	0.0939241	+	0.0165614i
$204$		0			0
$205$	2.68520e6	−	3.20010e6i	0.311685	−	0.371451i
$206$		0			0
$207$	3.79257e6	+	1.38038e6i	0.427585	+	0.155628i
$208$		0			0
$209$	3.85031e6	+	4.70558e6i	0.421751	+	0.515435i
$210$		0			0
$211$	−410170.	+	1.12693e6i	−0.0436633	+	0.119964i	−0.959608	−	0.281341i	$-0.909221\pi$
$211$	−410170.	+	1.12693e6i	−0.0436633	+	0.119964i	0.915945	+	0.401305i	$0.131443\pi$
$212$		0			0
$213$	−2.47330e7	−	2.07534e7i	−2.55940	−	2.14759i
$214$		0			0
$215$	1.31778e6	−	7.47352e6i	0.132595	−	0.751986i
$216$		0			0
$217$	−885376.	+	511172.i	−0.0866460	+	0.0500251i
$218$		0			0
$219$	1.10970e7	+	3.04888e7i	1.05651	+	2.90274i
$220$		0			0
$221$	−3.50408e6	−	2.02308e6i	−0.324636	−	0.187429i
$222$		0			0
$223$	−7.25368e6	−	8.64459e6i	−0.654099	−	0.779525i	0.332427	−	0.943129i	$-0.392133\pi$
$223$	−7.25368e6	−	8.64459e6i	−0.654099	−	0.779525i	−0.986526	+	0.163604i	$0.947688\pi$
$224$		0			0
$225$	2.27088e6	+	1.28788e7i	0.199364	+	1.13065i
$226$		0			0
$227$		−	1.60470e7i		−	1.37188i	−0.727659	−	0.685939i	$-0.759392\pi$
$227$		−	1.60470e7i		−	1.37188i	0.727659	−	0.685939i	$-0.240608\pi$
$228$		0			0
$229$	8.76151e6			0.729579			0.364790	−	0.931090i	$-0.381141\pi$
$229$	8.76151e6			0.729579			0.364790	+	0.931090i	$0.381141\pi$
$230$		0			0
$231$	1.61762e6	−	285231.i	0.131232	−	0.0231398i
$232$		0			0
$233$	1.51211e7	−	1.26881e7i	1.19540	−	1.00306i	0.195654	−	0.980673i	$-0.437317\pi$
$233$	1.51211e7	−	1.26881e7i	1.19540	−	1.00306i	0.999749	−	0.0223896i	$-0.00712744\pi$
$234$		0			0
$235$	−2.52323e6	+	4.37036e6i	−0.194425	+	0.336755i
$236$		0			0
$237$	−7.78807e6	+	2.83463e6i	−0.585039	+	0.212937i
$238$		0			0
$239$	2.94636e6	+	5.10325e6i	0.215820	+	0.373812i	0.953526	−	0.301311i	$-0.0974241\pi$
$239$	2.94636e6	+	5.10325e6i	0.215820	+	0.373812i	−0.737706	+	0.675123i	$0.764091\pi$
$240$		0			0
$241$	3.93878e6	+	694513.i	0.281391	+	0.0496169i	0.312562	−	0.949897i	$-0.398813\pi$
$241$	3.93878e6	+	694513.i	0.281391	+	0.0496169i	−0.0311713	+	0.999514i	$0.509924\pi$
$242$		0			0
$243$	1.00797e7	−	1.20125e7i	0.702470	−	0.837171i
$244$		0			0
$245$	9.58905e6	+	3.49013e6i	0.652044	+	0.237325i
$246$		0			0
$247$	−1.72572e7	−	213409.i	−1.14520	−	0.0141619i
$248$		0			0
$249$	−4.15043e6	+	1.14032e7i	−0.268841	+	0.738634i
$250$		0			0
$251$	−1.11946e7	−	9.39341e6i	−0.707927	−	0.594021i	0.216090	−	0.976374i	$-0.430670\pi$
$251$	−1.11946e7	−	9.39341e6i	−0.707927	−	0.594021i	−0.924017	+	0.382352i	$0.875114\pi$
$252$		0			0
$253$	375955.	−	2.13215e6i	0.0232153	−	0.131660i
$254$		0			0
$255$	−5.96771e6	+	3.44546e6i	−0.359905	+	0.207791i
$256$		0			0
$257$	−1.61504e6	−	4.43730e6i	−0.0951448	−	0.261408i	0.882986	−	0.469400i	$-0.155530\pi$
$257$	−1.61504e6	−	4.43730e6i	−0.0951448	−	0.261408i	−0.978131	+	0.207991i	$0.933307\pi$
$258$		0			0
$259$	856635.	+	494579.i	0.0493057	+	0.0284666i
$260$		0			0
$261$	−2.23180e7	−	2.65976e7i	−1.25526	−	1.49596i
$262$		0			0
$263$	−1.31619e6	−	7.46448e6i	−0.0723521	−	0.410329i	−0.999376	−	0.0353264i	$-0.988753\pi$
$263$	−1.31619e6	−	7.46448e6i	−0.0723521	−	0.410329i	0.927024	−	0.375003i	$-0.122358\pi$
$264$		0			0
$265$			2.20241e7i			1.18348i
$266$		0			0
$267$	3.42995e7			1.80200
$268$		0			0
$269$	2.13939e7	−	3.77232e6i	1.09909	−	0.193799i	0.405446	−	0.914119i	$-0.367116\pi$
$269$	2.13939e7	−	3.77232e6i	1.09909	−	0.193799i	0.693642	+	0.720320i	$0.256005\pi$
$270$		0			0
$271$	9.45889e6	−	7.93695e6i	0.475261	−	0.398791i	−0.373448	−	0.927651i	$-0.621825\pi$
$271$	9.45889e6	−	7.93695e6i	0.475261	−	0.398791i	0.848709	+	0.528860i	$0.177380\pi$
$272$		0			0
$273$	−2.33126e6	+	4.03787e6i	−0.114579	+	0.198456i
$274$		0			0
$275$	6.59216e6	−	2.39935e6i	0.316978	−	0.115371i
$276$		0			0
$277$	3.45650e6	+	5.98683e6i	0.162629	+	0.281681i	0.935811	−	0.352503i	$-0.114669\pi$
$277$	3.45650e6	+	5.98683e6i	0.162629	+	0.281681i	−0.773182	+	0.634184i	$0.781336\pi$
$278$		0			0
$279$	4.38150e7	+	7.72577e6i	2.01749	+	0.355737i
$280$		0			0
$281$	2.23063e7	−	2.65836e7i	1.00533	−	1.19810i	0.0252109	−	0.999682i	$-0.491974\pi$
$281$	2.23063e7	−	2.65836e7i	1.00533	−	1.19810i	0.980117	−	0.198421i	$-0.0635813\pi$
$282$		0			0
$283$	−1.28921e7	−	4.69234e6i	−0.568806	−	0.207028i	0.0415764	−	0.999135i	$-0.486762\pi$
$283$	−1.28921e7	−	4.69234e6i	−0.568806	−	0.207028i	−0.610382	+	0.792107i	$0.708984\pi$
$284$		0			0
$285$	−1.50100e7	+	2.52711e7i	−0.648403	+	1.09167i
$286$		0			0
$287$	−617818.	+	1.69744e6i	−0.0261345	+	0.0718041i
$288$		0			0
$289$	−1.65096e7	−	1.38532e7i	−0.683979	−	0.573927i
$290$		0			0
$291$	998355.	−	5.66195e6i	0.0405141	−	0.229767i
$292$		0			0
$293$	2.15763e7	−	1.24571e7i	0.857776	−	0.495237i	−0.00549090	−	0.999985i	$-0.501748\pi$
$293$	2.15763e7	−	1.24571e7i	0.857776	−	0.495237i	0.863267	+	0.504748i	$0.168414\pi$
$294$		0			0
$295$	1.04502e7	+	2.87118e7i	0.407062	+	1.11839i
$296$		0			0
$297$	−3.45954e7	−	1.99736e7i	−1.32053	−	0.762409i
$298$		0			0
$299$	3.95028e6	+	4.70776e6i	0.147780	+	0.176117i
$300$		0			0
$301$	569828.	+	3.23165e6i	0.0208951	+	0.118502i
$302$		0			0
$303$			2.26888e7i			0.815611i
$304$		0			0
$305$	−3.27146e7			−1.15303
$306$		0			0
$307$	−4.29116e6	+	756647.i	−0.148306	+	0.0261504i	−0.247308	−	0.968937i	$-0.579546\pi$
$307$	−4.29116e6	+	756647.i	−0.148306	+	0.0261504i	0.0990021	+	0.995087i	$0.468435\pi$
$308$		0			0
$309$	−7.51632e7	+	6.30694e7i	−2.54759	+	2.13768i
$310$		0			0
$311$	4.65524e6	−	8.06311e6i	0.154761	−	0.268054i	−0.778211	−	0.628003i	$-0.783873\pi$
$311$	4.65524e6	−	8.06311e6i	0.154761	−	0.268054i	0.932972	+	0.359949i	$0.117206\pi$
$312$		0			0
$313$	−4.35942e7	+	1.58670e7i	−1.42166	+	0.517442i	−0.934529	−	0.355887i	$-0.884179\pi$
$313$	−4.35942e7	+	1.58670e7i	−1.42166	+	0.517442i	−0.487131	+	0.873329i	$0.661957\pi$
$314$		0			0
$315$	2.75495e6	+	4.77171e6i	0.0881417	+	0.152666i
$316$		0			0
$317$	−3.89381e7	−	6.86583e6i	−1.22235	−	0.215534i	−0.475015	−	0.879978i	$-0.657557\pi$
$317$	−3.89381e7	−	6.86583e6i	−1.22235	−	0.215534i	−0.747338	+	0.664444i	$0.768668\pi$
$318$		0			0
$319$	−1.19722e7	+	1.42679e7i	−0.368809	+	0.439529i
$320$		0			0
$321$	−4.69778e7	−	1.70985e7i	−1.42029	−	0.516944i
$322$		0			0
$323$	1.08375e7	+	2.04944e6i	0.321605	+	0.0608173i
$324$		0			0
$325$	−6.81065e6	+	1.87121e7i	−0.198399	+	0.545096i
$326$		0			0
$327$	3.66111e7	+	3.07204e7i	1.04706	+	0.878584i
$328$		0			0
$329$	378928.	−	2.14901e6i	0.0106407	−	0.0603462i
$330$		0			0
$331$	−5.24089e7	+	3.02583e7i	−1.44518	+	0.834374i	−0.998188	−	0.0601649i	$-0.980837\pi$
$331$	−5.24089e7	+	3.02583e7i	−1.44518	+	0.834374i	−0.446990	+	0.894539i	$0.647504\pi$
$332$		0			0
$333$	−1.47228e7	−	4.04507e7i	−0.398712	−	1.09545i
$334$		0			0
$335$	1.37921e7	+	7.96289e6i	0.366857	+	0.211805i
$336$		0			0
$337$	4.67437e7	+	5.57070e7i	1.22133	+	1.45553i	0.849801	+	0.527104i	$0.176722\pi$
$337$	4.67437e7	+	5.57070e7i	1.22133	+	1.45553i	0.371530	+	0.928421i	$0.378833\pi$
$338$		0			0
$339$	−6.00354e6	−	3.40478e7i	−0.154102	−	0.873956i
$340$		0			0
$341$		−	2.38665e7i		−	0.601903i
$342$		0			0
$343$	−8.87984e6			−0.220051
$344$		0			0
$345$	1.03073e7	−	1.81746e6i	0.251009	−	0.0442597i
$346$		0			0
$347$	2.74415e6	−	2.30262e6i	0.0656779	−	0.0551103i	−0.609358	−	0.792895i	$-0.708573\pi$
$347$	2.74415e6	−	2.30262e6i	0.0656779	−	0.0551103i	0.675036	+	0.737785i	$0.264128\pi$
$348$		0			0
$349$	2.00092e6	−	3.46570e6i	0.0470710	−	0.0815294i	−0.841530	−	0.540210i	$-0.818345\pi$
$349$	2.00092e6	−	3.46570e6i	0.0470710	−	0.0815294i	0.888601	+	0.458681i	$0.151678\pi$
$350$		0			0
$351$	1.06554e8	−	3.87824e7i	2.46404	−	0.896836i
$352$		0			0
$353$	2.40118e7	+	4.15897e7i	0.545885	+	0.945501i	0.998551	+	0.0538205i	$0.0171399\pi$
$353$	2.40118e7	+	4.15897e7i	0.545885	+	0.945501i	−0.452665	+	0.891680i	$0.649527\pi$
$354$		0			0
$355$	−5.72149e7	−	1.00885e7i	−1.27886	−	0.225498i
$356$		0			0
$357$	1.91533e6	−	2.28261e6i	0.0420959	−	0.0501679i
$358$		0			0
$359$	−3.55485e7	−	1.29386e7i	−0.768313	−	0.279643i	−0.0720221	−	0.997403i	$-0.522945\pi$
$359$	−3.55485e7	−	1.29386e7i	−0.768313	−	0.279643i	−0.696290	+	0.717760i	$0.745167\pi$
$360$		0			0
$361$	4.45931e7	−	1.49925e7i	0.947863	−	0.318678i
$362$		0			0
$363$	1.64535e7	−	4.52055e7i	0.343983	−	0.945086i
$364$		0			0
$365$	4.47244e7	+	3.75282e7i	0.919741	+	0.771754i
$366$		0			0
$367$	4.43147e6	−	2.51321e7i	0.0896499	−	0.508430i	−0.906606	−	0.421978i	$-0.861336\pi$
$367$	4.43147e6	−	2.51321e7i	0.0896499	−	0.508430i	0.996256	−	0.0864518i	$-0.0275529\pi$
$368$		0			0
$369$	6.80791e7	−	3.93055e7i	1.35499	−	0.782302i
$370$		0			0
$371$	−3.25724e6	−	8.94920e6i	−0.0637864	−	0.175252i
$372$		0			0
$373$	−4.11580e7	−	2.37626e7i	−0.793099	−	0.457896i	0.0479536	−	0.998850i	$-0.484730\pi$
$373$	−4.11580e7	−	2.37626e7i	−0.793099	−	0.457896i	−0.841052	+	0.540954i	$0.818063\pi$
$374$		0			0
$375$	6.48385e7	+	7.72715e7i	1.22953	+	1.46530i
$376$		0			0
$377$	−9.18061e6	−	5.20658e7i	−0.171336	−	0.971692i
$378$		0			0
$379$			4.33231e7i			0.795796i	0.917430	+	0.397898i	$0.130260\pi$
$379$			4.33231e7i			0.795796i	−0.917430	+	0.397898i	$0.869740\pi$
$380$		0			0
$381$	−8.39762e7			−1.51838
$382$		0			0
$383$	−8.14642e7	+	1.43643e7i	−1.45001	+	0.255675i	−0.842525	−	0.538658i	$-0.818932\pi$
$383$	−8.14642e7	+	1.43643e7i	−1.45001	+	0.255675i	−0.607483	+	0.794333i	$0.707821\pi$
$384$		0			0
$385$	2.26420e6	−	1.89989e6i	0.0396764	−	0.0332925i
$386$		0			0
$387$	7.14032e7	−	1.23674e8i	1.23193	−	2.13376i
$388$		0			0
$389$	1.02120e8	−	3.71685e7i	1.73484	−	0.631431i	0.735886	−	0.677105i	$-0.236766\pi$
$389$	1.02120e8	−	3.71685e7i	1.73484	−	0.631431i	0.998956	+	0.0456745i	$0.0145437\pi$
$390$		0			0
$391$	−1.96375e6	−	3.40132e6i	−0.0328516	−	0.0569006i
$392$		0			0
$393$	1.41741e8	+	2.49928e7i	2.33517	+	0.411754i
$394$		0			0
$395$	−9.58621e6	+	1.14244e7i	−0.155545	+	0.185371i
$396$		0			0
$397$	1.67651e6	+	610200.i	0.0267938	+	0.00975216i	0.355382	−	0.934721i	$-0.384351\pi$
$397$	1.67651e6	+	610200.i	0.0267938	+	0.00975216i	−0.328588	+	0.944473i	$0.606573\pi$
$398$		0			0
$399$	2.36164e6	−	1.24885e7i	0.0371787	−	0.196603i
$400$		0			0
$401$	−3.73049e6	+	1.02494e7i	−0.0578540	+	0.158953i	−0.965253	−	0.261318i	$-0.915843\pi$
$401$	−3.73049e6	+	1.02494e7i	−0.0578540	+	0.158953i	0.907399	+	0.420271i	$0.138065\pi$
$402$		0			0
$403$	5.18966e7	+	4.35464e7i	0.792910	+	0.665330i
$404$		0			0
$405$	1.51652e7	−	8.60060e7i	0.228288	−	1.29468i
$406$		0			0
$407$	−1.99981e7	+	1.15459e7i	−0.296623	+	0.171255i
$408$		0			0
$409$	−2.52503e7	−	6.93747e7i	−0.369060	−	1.01398i	−0.975720	−	0.219023i	$-0.929713\pi$
$409$	−2.52503e7	−	6.93747e7i	−0.369060	−	1.01398i	0.606660	−	0.794962i	$-0.292509\pi$
$410$		0			0
$411$	−1.28631e8	−	7.42650e7i	−1.85276	−	1.06969i
$412$		0			0
$413$	−8.49262e6	−	1.01211e7i	−0.120557	−	0.143674i
$414$		0			0
$415$	3.79181e6	+	2.15044e7i	0.0530521	+	0.300873i
$416$		0			0
$417$			2.35645e8i			3.24975i
$418$		0			0
$419$	−1.11060e8			−1.50978			−0.754891	−	0.655850i	$-0.772310\pi$
$419$	−1.11060e8			−1.50978			−0.754891	+	0.655850i	$0.772310\pi$
$420$		0			0
$421$	6.21344e6	−	1.09560e6i	0.0832694	−	0.0146826i	−0.131858	−	0.991269i	$-0.542094\pi$
$421$	6.21344e6	−	1.09560e6i	0.0832694	−	0.0146826i	0.215128	+	0.976586i	$0.430983\pi$
$422$		0			0
$423$	−7.27469e7	+	6.10419e7i	−0.961155	+	0.806505i
$424$		0			0
$425$	6.36301e6	−	1.10211e7i	0.0828888	−	0.143568i
$426$		0			0
$427$	1.32931e7	−	4.83830e6i	0.170743	−	0.0621455i
$428$		0			0
$429$	−5.44231e7	−	9.42636e7i	−0.689305	−	1.19391i
$430$		0			0
$431$	1.11045e8	+	1.95802e7i	1.38697	+	0.244560i	0.816777	−	0.576953i	$-0.195759\pi$
$431$	1.11045e8	+	1.95802e7i	1.38697	+	0.244560i	0.570190	+	0.821513i	$0.306870\pi$
$432$		0			0
$433$	−2.93314e7	+	3.49558e7i	−0.361301	+	0.430582i	−0.915820	−	0.401590i	$-0.868458\pi$
$433$	−2.93314e7	+	3.49558e7i	−0.361301	+	0.430582i	0.554519	+	0.832171i	$0.312902\pi$
$434$		0			0
$435$	−8.46100e7	−	3.07955e7i	−1.02791	−	0.374128i
$436$		0			0
$437$	−1.44034e7	−	8.55498e6i	−0.172591	−	0.102512i
$438$		0			0
$439$	−3.72471e7	+	1.02336e8i	−0.440250	+	1.20958i	0.499078	+	0.866557i	$0.333672\pi$
$439$	−3.72471e7	+	1.02336e8i	−0.440250	+	1.20958i	−0.939328	+	0.343020i	$0.888550\pi$
$440$		0			0
$441$	1.47102e8	+	1.23433e8i	1.71515	+	1.43918i
$442$		0			0
$443$	2.20418e7	−	1.25005e8i	0.253534	−	1.43786i	−0.546275	−	0.837606i	$-0.683955\pi$
$443$	2.20418e7	−	1.25005e8i	0.253534	−	1.43786i	0.799809	−	0.600255i	$-0.204934\pi$
$444$		0			0
$445$	5.34508e7	−	3.08598e7i	0.606560	−	0.350198i
$446$		0			0
$447$	−2.65593e6	−	7.29712e6i	−0.0297368	−	0.0817013i
$448$		0			0
$449$	1.36289e8	+	7.86867e7i	1.50565	+	0.869285i	0.999979	+	0.00655618i	$0.00208691\pi$
$449$	1.36289e8	+	7.86867e7i	1.50565	+	0.869285i	0.505667	+	0.862729i	$0.331246\pi$
$450$		0			0
$451$	−2.71062e7	−	3.23039e7i	−0.295487	−	0.352148i
$452$		0			0
$453$	−3.95621e7	−	2.24368e8i	−0.425583	−	2.41360i
$454$		0			0
$455$			8.38989e6i			0.0890681i
$456$		0			0
$457$	1.07893e8			1.13043			0.565214	−	0.824944i	$-0.308794\pi$
$457$	1.07893e8			1.13043			0.565214	+	0.824944i	$0.308794\pi$
$458$		0			0
$459$	−7.13657e7	+	1.25837e7i	−0.737992	+	0.130128i
$460$		0			0
$461$	−9.90650e6	+	8.31254e6i	−0.101115	+	0.0848459i	−0.691944	−	0.721951i	$-0.743245\pi$
$461$	−9.90650e6	+	8.31254e6i	−0.101115	+	0.0848459i	0.590828	+	0.806797i	$0.298801\pi$
$462$		0			0
$463$	7.59240e7	−	1.31504e8i	0.764956	−	1.32494i	−0.175315	−	0.984512i	$-0.556094\pi$
$463$	7.59240e7	−	1.31504e8i	0.764956	−	1.32494i	0.940270	−	0.340429i	$-0.110572\pi$
$464$		0			0
$465$	1.08419e8	−	3.94613e7i	1.07832	−	0.392475i
$466$		0			0
$467$	2.91973e7	+	5.05711e7i	0.286676	+	0.496537i	0.973014	−	0.230745i	$-0.0741163\pi$
$467$	2.91973e7	+	5.05711e7i	0.286676	+	0.496537i	−0.686338	+	0.727283i	$0.740783\pi$
$468$		0			0
$469$	−6.78190e6	−	1.19583e6i	−0.0657405	−	0.0115918i
$470$		0			0
$471$	−1.39220e8	+	1.65916e8i	−1.33242	+	1.58791i
$472$		0			0
$473$	−7.19865e7	−	2.62010e7i	−0.680249	−	0.247590i
$474$		0			0
$475$	671216.	−	5.42777e7i	0.00626298	−	0.506454i
$476$		0			0
$477$	−1.41750e8	+	3.89456e8i	−1.30608	+	3.58842i
$478$		0			0
$479$	−1.36099e8	−	1.14200e8i	−1.23836	−	1.03911i	−0.997650	−	0.0685109i	$-0.978175\pi$
$479$	−1.36099e8	−	1.14200e8i	−1.23836	−	1.03911i	−0.240710	−	0.970597i	$-0.577380\pi$
$480$		0			0
$481$	1.13821e7	−	6.45512e7i	0.102279	−	0.580055i
$482$		0			0
$483$	−3.91945e6	+	2.26290e6i	−0.0347844	+	0.0200828i
$484$		0			0
$485$	−3.53836e6	−	9.72155e6i	−0.0310153	−	0.0852139i
$486$		0			0
$487$	3.52703e7	+	2.03633e7i	0.305367	+	0.176304i	0.644851	−	0.764308i	$-0.276919\pi$
$487$	3.52703e7	+	2.03633e7i	0.305367	+	0.176304i	−0.339485	+	0.940612i	$0.610253\pi$
$488$		0			0
$489$	1.22068e7	+	1.45475e7i	0.104394	+	0.124412i
$490$		0			0
$491$	1.75340e7	+	9.94403e7i	0.148128	+	0.840074i	0.964802	+	0.262976i	$0.0847040\pi$
$491$	1.75340e7	+	9.94403e7i	0.148128	+	0.840074i	−0.816675	+	0.577098i	$0.804185\pi$
$492$		0			0
$493$			3.37876e7i			0.281979i
$494$		0			0
$495$	−1.28628e8			−1.06052
$496$		0			0
$497$	2.47405e7	−	4.36242e6i	0.201530	−	0.0355352i
$498$		0			0
$499$	−515356.	+	432435.i	−0.00414768	+	0.00348032i	−0.644859	−	0.764301i	$-0.723084\pi$
$499$	−515356.	+	432435.i	−0.00414768	+	0.00348032i	0.640711	+	0.767782i	$0.278640\pi$
$500$		0			0
$501$	1.24271e8	−	2.15244e8i	0.988229	−	1.71166i
$502$		0			0
$503$	−6.24463e7	+	2.27286e7i	−0.490685	+	0.178595i	−0.575500	−	0.817802i	$-0.695192\pi$
$503$	−6.24463e7	+	2.27286e7i	−0.490685	+	0.178595i	0.0848146	+	0.996397i	$0.472970\pi$
$504$		0			0
$505$	2.04134e7	+	3.53571e7i	0.158505	+	0.274538i
$506$		0			0
$507$	7.23000e7	+	1.27484e7i	0.554772	+	0.0978213i
$508$		0			0
$509$	−1.38810e7	+	1.65427e7i	−0.105261	+	0.125445i	−0.816103	−	0.577907i	$-0.803870\pi$
$509$	−1.38810e7	+	1.65427e7i	−0.105261	+	0.125445i	0.710842	+	0.703352i	$0.248314\pi$
$510$		0			0
$511$	−2.37233e7	−	8.63458e6i	−0.177792	−	0.0647111i
$512$		0			0
$513$	−2.39223e8	+	1.95743e8i	−1.77195	+	1.44989i
$514$		0			0
$515$	−6.03862e7	+	1.65910e8i	−0.442096	+	1.21465i
$516$		0			0
$517$	3.90240e7	+	3.27451e7i	0.282397	+	0.236959i
$518$		0			0
$519$	5.97737e7	−	3.38993e8i	0.427571	−	2.42487i
$520$		0			0
$521$	−9.19026e7	+	5.30600e7i	−0.649852	+	0.375192i	−0.788400	−	0.615163i	$-0.789090\pi$
$521$	−9.19026e7	+	5.30600e7i	−0.649852	+	0.375192i	0.138547	+	0.990356i	$0.455757\pi$
$522$		0			0
$523$	−2.28817e7	−	6.28669e7i	−0.159949	−	0.439457i	0.833667	−	0.552267i	$-0.186237\pi$
$523$	−2.28817e7	−	6.28669e7i	−0.159949	−	0.439457i	−0.993617	+	0.112810i	$0.964015\pi$
$524$		0			0
$525$	−1.26999e7	−	7.33232e6i	−0.0877655	−	0.0506714i
$526$		0			0
$527$	−2.78297e7	−	3.31661e7i	−0.190141	−	0.226601i
$528$		0			0
$529$	−2.46703e7	−	1.39912e8i	−0.166651	−	0.945123i
$530$		0			0
$531$			5.74974e8i			3.84030i
$532$		0			0
$533$	1.19701e8			0.790524
$534$		0			0
$535$	−8.85918e7	+	1.56211e7i	−0.578538	+	0.102012i
$536$		0			0
$537$	−1.05663e8	+	8.86618e7i	−0.682339	+	0.572550i
$538$		0			0
$539$	5.15052e7	−	8.92096e7i	0.328916	−	0.569699i
$540$		0			0
$541$	−4.29585e7	+	1.56356e7i	−0.271305	+	0.0987469i	−0.474090	−	0.880476i	$-0.657223\pi$
$541$	−4.29585e7	+	1.56356e7i	−0.271305	+	0.0987469i	0.202785	+	0.979223i	$0.435001\pi$
$542$		0			0
$543$	8.65923e7	+	1.49982e8i	0.540854	+	0.936786i
$544$		0			0
$545$	8.46926e7	+	1.49336e7i	0.523186	+	0.0922518i
$546$		0			0
$547$	4.13662e7	−	4.92983e7i	0.252746	−	0.301211i	−0.624721	−	0.780848i	$-0.714787\pi$
$547$	4.13662e7	−	4.92983e7i	0.252746	−	0.301211i	0.877467	+	0.479637i	$0.159232\pi$
$548$		0			0
$549$	−5.78498e8	−	2.10556e8i	−3.49611	−	1.27248i
$550$		0			0
$551$	7.05102e7	+	1.25691e8i	0.421500	+	0.751365i
$552$		0			0
$553$	2.20562e6	−	6.05989e6i	0.0130423	−	0.0358335i
$554$		0			0
$555$	−8.55148e7	−	7.17555e7i	−0.500222	−	0.419736i
$556$		0			0
$557$	2.51532e6	−	1.42651e7i	0.0145555	−	0.0825483i	−0.976665	−	0.214770i	$-0.931100\pi$
$557$	2.51532e6	−	1.42651e7i	0.0145555	−	0.0825483i	0.991220	+	0.132221i	$0.0422110\pi$
$558$		0			0
$559$	1.88318e8	−	1.08725e8i	1.07809	−	0.622437i
$560$		0			0
$561$	2.37914e7	+	6.53664e7i	0.134751	+	0.370225i
$562$		0			0
$563$	−1.76845e8	−	1.02102e8i	−0.990987	−	0.572147i	−0.0854178	−	0.996345i	$-0.527223\pi$
$563$	−1.76845e8	−	1.02102e8i	−0.990987	−	0.572147i	−0.905569	+	0.424199i	$0.860556\pi$
$564$		0			0
$565$	−3.99889e7	−	4.76570e7i	−0.221715	−	0.264229i
$566$		0			0
$567$	6.55763e6	+	3.71902e7i	0.0359747	+	0.204023i
$568$		0			0
$569$		−	1.81985e8i		−	0.987868i	−0.869499	−	0.493934i	$-0.835558\pi$
$569$		−	1.81985e8i		−	0.987868i	0.869499	−	0.493934i	$-0.164442\pi$
$570$		0			0
$571$	1.18975e8			0.639068			0.319534	−	0.947575i	$-0.396474\pi$
$571$	1.18975e8			0.639068			0.319534	+	0.947575i	$0.396474\pi$
$572$		0			0
$573$	2.56303e8	−	4.51932e7i	1.36236	−	0.240220i
$574$		0			0
$575$	−1.48069e7	+	1.24245e7i	−0.0778863	+	0.0653544i
$576$		0			0
$577$	2.49564e7	−	4.32258e7i	0.129914	−	0.225017i	−0.793729	−	0.608271i	$-0.791863\pi$
$577$	2.49564e7	−	4.32258e7i	0.129914	−	0.225017i	0.923643	+	0.383254i	$0.125197\pi$
$578$		0			0
$579$	5.43737e8	−	1.97904e8i	2.80126	−	1.01957i
$580$		0			0
$581$	−4.72113e6	−	8.17724e6i	−0.0240723	−	0.0416944i
$582$		0			0
$583$	2.18948e8	+	3.86065e7i	1.10493	+	0.194830i
$584$		0			0
$585$	2.34692e8	−	2.79695e8i	1.17228	−	1.39707i
$586$		0			0
$587$	1.77795e8	+	6.47121e7i	0.879033	+	0.319942i	0.741820	−	0.670600i	$-0.233963\pi$
$587$	1.77795e8	+	6.47121e7i	0.879033	+	0.319942i	0.137214	+	0.990541i	$0.456185\pi$
$588$		0			0
$589$	−1.72741e8	−	6.53027e7i	−0.845375	−	0.319584i
$590$		0			0
$591$	1.48791e8	−	4.08801e8i	0.720801	−	1.98038i
$592$		0			0
$593$	2.95979e8	+	2.48356e8i	1.41937	+	1.19100i	0.951674	+	0.307109i	$0.0993615\pi$
$593$	2.95979e8	+	2.48356e8i	1.41937	+	1.19100i	0.467700	+	0.883887i	$0.345083\pi$
$594$		0			0
$595$	931070.	−	5.28036e6i	0.00442009	−	0.0250676i
$596$		0			0
$597$	1.05624e8	−	6.09819e7i	0.496408	−	0.286601i
$598$		0			0
$599$	1.97544e7	+	5.42748e7i	0.0919143	+	0.252533i	0.977128	−	0.212652i	$-0.0682101\pi$
$599$	1.97544e7	+	5.42748e7i	0.0919143	+	0.252533i	−0.885214	+	0.465185i	$0.845988\pi$
$600$		0			0
$601$	−1.06235e8	−	6.13347e7i	−0.489377	−	0.282542i	0.234939	−	0.972010i	$-0.424511\pi$
$601$	−1.06235e8	−	6.13347e7i	−0.489377	−	0.282542i	−0.724316	+	0.689468i	$0.757844\pi$
$602$		0			0
$603$	1.92638e8	+	2.29577e8i	0.878598	+	1.04707i
$604$		0			0
$605$	−1.50318e7	−	8.52496e7i	−0.0678805	−	0.384969i
$606$		0			0
$607$			1.20152e8i			0.537237i	0.963247	+	0.268618i	$0.0865671\pi$
$607$			1.20152e8i			0.537237i	−0.963247	+	0.268618i	$0.913433\pi$
$608$		0			0
$609$	3.89346e7			0.172379
$610$		0			0
$611$	−1.42405e8	+	2.51098e7i	−0.624312	+	0.110083i
$612$		0			0
$613$	−4.68770e7	+	3.93344e7i	−0.203506	+	0.170762i	−0.738845	−	0.673875i	$-0.764628\pi$
$613$	−4.68770e7	+	3.93344e7i	−0.203506	+	0.170762i	0.535339	+	0.844638i	$0.320184\pi$
$614$		0			0
$615$	1.01930e8	−	1.76548e8i	0.438203	−	0.758990i
$616$		0			0
$617$	−2.49180e7	+	9.06939e6i	−0.106086	+	0.0386120i	−0.394518	−	0.918888i	$-0.629088\pi$
$617$	−2.49180e7	+	9.06939e6i	−0.106086	+	0.0386120i	0.288432	+	0.957500i	$0.406866\pi$
$618$		0			0
$619$	−1.92830e8	−	3.33991e8i	−0.813022	−	1.40819i	−0.910740	−	0.412980i	$-0.864488\pi$
$619$	−1.92830e8	−	3.33991e8i	−0.813022	−	1.40819i	0.0977184	−	0.995214i	$-0.468846\pi$
$620$		0			0
$621$	1.08395e8	+	1.91129e7i	0.452619	+	0.0798089i
$622$		0			0
$623$	−1.71550e7	+	2.04445e7i	−0.0709457	+	0.0845498i
$624$		0			0
$625$	5.43653e7	+	1.97874e7i	0.222680	+	0.0810490i
$626$		0			0
$627$	2.24916e8	+	1.93517e8i	0.912470	+	0.785084i
$628$		0			0
$629$	−1.43272e7	+	3.93636e7i	−0.0575716	+	0.158177i
$630$		0			0
$631$	−2.46280e8	−	2.06653e8i	−0.980258	−	0.822534i	0.00386995	−	0.999993i	$-0.498768\pi$
$631$	−2.46280e8	−	2.06653e8i	−0.980258	−	0.822534i	−0.984128	+	0.177458i	$0.943213\pi$
$632$		0			0
$633$	−1.01626e7	+	5.76349e7i	−0.0400676	+	0.227234i
$634$		0			0
$635$	−1.30865e8	+	7.55547e7i	−0.511094	+	0.295080i
$636$		0			0
$637$	1.00006e8	+	2.74766e8i	0.386910	+	1.06303i
$638$		0			0
$639$	−9.46809e8	−	5.46641e8i	−3.62877	−	2.09507i
$640$		0			0
$641$	1.53986e8	+	1.83513e8i	0.584664	+	0.696775i	0.974571	−	0.224079i	$-0.0719374\pi$
$641$	1.53986e8	+	1.83513e8i	0.584664	+	0.696775i	−0.389907	+	0.920854i	$0.627493\pi$
$642$		0			0
$643$	6.38340e7	+	3.62021e8i	0.240115	+	1.36176i	0.831569	+	0.555421i	$0.187443\pi$
$643$	6.38340e7	+	3.62021e8i	0.240115	+	1.36176i	−0.591454	+	0.806339i	$0.701446\pi$
$644$		0			0
$645$		−	3.70336e8i		−	1.38012i
$646$		0			0
$647$	−4.83260e8			−1.78430			−0.892150	−	0.451739i	$-0.850804\pi$
$647$	−4.83260e8			−1.78430			−0.892150	+	0.451739i	$0.850804\pi$
$648$		0			0
$649$	3.03751e8	−	5.35595e7i	1.11118	−	0.195931i
$650$		0			0
$651$	−3.82184e7	+	3.20691e7i	−0.138526	+	0.116237i
$652$		0			0
$653$	−1.98735e8	+	3.44219e8i	−0.713731	+	1.23622i	0.249716	+	0.968319i	$0.419663\pi$
$653$	−1.98735e8	+	3.44219e8i	−0.713731	+	1.23622i	−0.963447	+	0.267899i	$0.913671\pi$
$654$		0			0
$655$	2.43370e8	−	8.85793e7i	0.866049	−	0.315216i
$656$		0			0
$657$	5.49331e8	+	9.51469e8i	1.93704	+	3.35505i
$658$		0			0
$659$	−2.55538e8	−	4.50583e7i	−0.892893	−	0.157441i	−0.291667	−	0.956520i	$-0.594210\pi$
$659$	−2.55538e8	−	4.50583e7i	−0.892893	−	0.157441i	−0.601226	+	0.799079i	$0.705321\pi$
$660$		0			0
$661$	2.50816e8	−	2.98911e8i	0.868462	−	1.03499i	−0.130589	−	0.991437i	$-0.541687\pi$
$661$	2.50816e8	−	2.98911e8i	0.868462	−	1.03499i	0.999051	−	0.0435564i	$-0.0138688\pi$
$662$		0			0
$663$	−1.85545e8	−	6.75330e7i	−0.636663	−	0.231726i
$664$		0			0
$665$	−7.55579e6	−	2.15862e7i	−0.0256930	−	0.0734026i
$666$		0			0
$667$	1.75520e7	−	4.82237e7i	0.0591492	−	0.162511i
$668$		0			0
$669$	−4.21858e8	−	3.53981e8i	−1.40892	−	1.18223i
$670$		0			0
$671$	−5.73461e7	+	3.25226e8i	−0.189817	+	1.07651i
$672$		0			0
$673$	−4.14931e8	+	2.39561e8i	−1.36123	+	0.785905i	−0.989787	−	0.142552i	$-0.954469\pi$
$673$	−4.14931e8	+	2.39561e8i	−1.36123	+	0.785905i	−0.371440	+	0.928457i	$0.621136\pi$
$674$		0			0
$675$	1.21979e8	+	3.35134e8i	0.396618	+	1.08970i
$676$		0			0
$677$	−3.84922e8	−	2.22235e8i	−1.24053	−	0.716220i	−0.271328	−	0.962487i	$-0.587463\pi$
$677$	−3.84922e8	−	2.22235e8i	−1.24053	−	0.716220i	−0.969202	+	0.246267i	$0.920796\pi$
$678$		0			0
$679$	2.87552e6	+	3.42691e6i	0.00918560	+	0.0109470i
$680$		0			0
$681$	−1.35983e8	−	7.71198e8i	−0.430570	−	2.44188i
$682$		0			0
$683$			5.54542e8i			1.74049i	0.492618	+	0.870246i	$0.336040\pi$
$683$			5.54542e8i			1.74049i	−0.492618	+	0.870246i	$0.663960\pi$
$684$		0			0
$685$	−2.67269e8			−0.831530
$686$		0			0
$687$	4.21068e8	−	7.42456e7i	1.29862	−	0.228982i
$688$		0			0
$689$	−4.83437e8	+	4.05652e8i	−1.47803	+	1.24021i
$690$		0			0
$691$	8.54369e7	−	1.47981e8i	0.258947	−	0.448510i	−0.707013	−	0.707201i	$-0.749958\pi$
$691$	8.54369e7	−	1.47981e8i	0.258947	−	0.448510i	0.965960	+	0.258691i	$0.0832911\pi$
$692$		0			0
$693$	5.22662e7	−	1.90233e7i	0.157044	−	0.0571593i
$694$		0			0
$695$	2.12014e8	+	3.67218e8i	0.631552	+	1.09388i
$696$		0			0
$697$	−7.53362e7	−	1.32838e7i	−0.222487	−	0.0392305i
$698$		0			0
$699$	6.19181e8	−	7.37911e8i	1.81295	−	2.16059i
$700$		0			0
$701$	844593.	+	307407.i	0.00245185	+	0.000892400i	0.343246	−	0.939246i	$-0.388474\pi$
$701$	844593.	+	307407.i	0.00245185	+	0.000892400i	−0.340794	+	0.940138i	$0.610696\pi$
$702$		0			0
$703$	2.88488e7	+	1.76333e8i	0.0830352	+	0.507538i
$704$		0			0
$705$	−8.42286e7	+	2.31416e8i	−0.240377	+	0.660430i
$706$		0			0
$707$	−1.35238e7	−	1.13478e7i	−0.0382685	−	0.0321111i
$708$		0			0
$709$	−1.32870e7	+	7.53541e7i	−0.0372810	+	0.211431i	−0.997758	−	0.0669294i	$-0.978680\pi$
$709$	−1.32870e7	+	7.53541e7i	−0.0372810	+	0.211431i	0.960477	+	0.278360i	$0.0897909\pi$
$710$		0			0
$711$	−2.43043e8	+	1.40321e8i	−0.676200	+	0.390404i
$712$		0			0
$713$	2.24911e7	+	6.17937e7i	0.0620500	+	0.170481i
$714$		0			0
$715$	−1.69621e8	−	9.79306e7i	−0.464046	−	0.267917i
$716$		0			0
$717$	1.84844e8	+	2.20288e8i	0.501473	+	0.597633i
$718$		0			0
$719$	−2.06640e7	−	1.17191e8i	−0.0555940	−	0.315289i	0.944311	−	0.329054i	$-0.106730\pi$
$719$	−2.06640e7	−	1.17191e8i	−0.0555940	−	0.315289i	−0.999905	+	0.0137643i	$0.995619\pi$
$720$		0			0
$721$		−	7.63459e7i		−	0.203695i
$722$		0			0
$723$	1.95178e8			0.516436
$724$		0			0
$725$	1.63758e8	−	2.88750e7i	0.429723	−	0.0757718i
$726$		0			0
$727$	3.23119e8	−	2.71129e8i	0.840930	−	0.705624i	−0.116843	−	0.993150i	$-0.537277\pi$
$727$	3.23119e8	−	2.71129e8i	0.840930	−	0.705624i	0.957773	+	0.287527i	$0.0928330\pi$
$728$		0			0
$729$	2.01143e7	−	3.48390e7i	0.0519185	−	0.0899254i
$730$		0			0
$731$	−1.30588e8	+	4.75300e7i	−0.334311	+	0.121679i
$732$		0			0
$733$	1.01560e8	+	1.75906e8i	0.257875	+	0.446652i	0.965672	−	0.259763i	$-0.0836444\pi$
$733$	1.01560e8	+	1.75906e8i	0.257875	+	0.446652i	−0.707798	+	0.706415i	$0.750311\pi$
$734$		0			0
$735$	4.90414e8	+	8.64732e7i	1.23510	+	0.217781i
$736$		0			0
$737$	1.03338e8	−	1.23153e8i	0.258141	−	0.307641i
$738$		0			0
$739$	3.95342e8	+	1.43893e8i	0.979578	+	0.356537i	0.781676	−	0.623684i	$-0.214365\pi$
$739$	3.95342e8	+	1.43893e8i	0.979578	+	0.356537i	0.197902	+	0.980222i	$0.436587\pi$
$740$		0			0
$741$	−8.31170e8	+	1.35983e8i	−2.04285	+	0.334217i
$742$		0			0
$743$	2.00195e8	−	5.50032e8i	0.488076	−	1.34098i	−0.414344	−	0.910120i	$-0.635989\pi$
$743$	2.00195e8	−	5.50032e8i	0.488076	−	1.34098i	0.902420	−	0.430857i	$-0.141789\pi$
$744$		0			0
$745$	−1.07042e7	−	8.98190e6i	−0.0258873	−	0.0217220i
$746$		0			0
$747$	−7.13544e7	+	4.04671e8i	−0.171182	+	0.970823i
$748$		0			0
$749$	3.36878e7	−	1.94496e7i	0.0801727	−	0.0462877i
$750$		0			0
$751$	2.13062e8	+	5.85383e8i	0.503021	+	1.38204i	0.888310	+	0.459243i	$0.151879\pi$
$751$	2.13062e8	+	5.85383e8i	0.503021	+	1.38204i	−0.385289	+	0.922796i	$0.625898\pi$
$752$		0			0
$753$	−6.17601e8	−	3.56572e8i	−1.44651	−	0.835146i
$754$		0			0
$755$	−2.63519e8	−	3.14049e8i	−0.612309	−	0.729721i
$756$		0			0
$757$	−8.41402e7	−	4.77183e8i	−0.193962	−	1.10001i	−0.913890	−	0.405962i	$-0.866936\pi$
$757$	−8.41402e7	−	4.77183e8i	−0.193962	−	1.10001i	0.719928	−	0.694049i	$-0.244175\pi$
$758$		0			0
$759$		−	1.05654e8i		−	0.241636i
$760$		0			0
$761$	3.73543e8			0.847591			0.423795	−	0.905758i	$-0.360698\pi$
$761$	3.73543e8			0.847591			0.423795	+	0.905758i	$0.360698\pi$
$762$		0			0
$763$	−3.66222e7	+	6.45749e6i	−0.0824463	+	0.0145375i
$764$		0			0
$765$	−1.78748e8	+	1.49987e8i	−0.399260	+	0.335019i
$766$		0			0
$767$	−4.37755e8	+	7.58215e8i	−0.970165	+	1.68037i
$768$		0			0
$769$	−3.95634e8	+	1.43999e8i	−0.869990	+	0.316650i	−0.738163	−	0.674622i	$-0.764306\pi$
$769$	−3.95634e8	+	1.43999e8i	−0.869990	+	0.316650i	−0.131827	+	0.991273i	$0.542084\pi$
$770$		0			0
$771$	−1.15219e8	−	1.99565e8i	−0.251398	−	0.435434i
$772$		0			0
$773$	−1.02327e8	−	1.80430e7i	−0.221540	−	0.0390634i	0.0617764	−	0.998090i	$-0.480323\pi$
$773$	−1.02327e8	−	1.80430e7i	−0.221540	−	0.0390634i	−0.283316	+	0.959027i	$0.591435\pi$
$774$		0			0
$775$	−1.36963e8	+	1.63226e8i	−0.294237	+	0.350658i
$776$		0			0
$777$	4.53600e7	+	1.65097e7i	0.0966962	+	0.0351946i
$778$		0			0
$779$	−3.07976e8	+	1.07800e8i	−0.651485	+	0.228038i
$780$		0			0
$781$	−2.00586e8	+	5.51106e8i	−0.421064	+	1.15686i
$782$		0			0
$783$	−7.25355e8	−	6.08645e8i	−1.51100	−	1.26788i
$784$		0			0
$785$	−6.76769e7	+	3.83815e8i	−0.139905	+	0.793438i
$786$		0			0
$787$	8.69392e7	−	5.01944e7i	0.178357	−	0.102975i	−0.408163	−	0.912909i	$-0.633831\pi$
$787$	8.69392e7	−	5.01944e7i	0.178357	−	0.102975i	0.586521	+	0.809934i	$0.300497\pi$
$788$		0			0
$789$	−1.26509e8	−	3.47580e8i	−0.257567	−	0.707659i
$790$		0			0
$791$	2.32971e7	+	1.34506e7i	0.0470731	+	0.0271777i
$792$		0			0
$793$	−6.02554e8	−	7.18096e8i	−1.20831	−	1.44000i
$794$		0			0
$795$	1.86634e8	+	1.05845e9i	0.371440	+	2.10654i
$796$		0			0
$797$			5.80507e8i			1.14665i	0.819327	+	0.573327i	$0.194347\pi$
$797$			5.80507e8i			1.14665i	−0.819327	+	0.573327i	$0.805653\pi$
$798$		0			0
$799$	9.24122e7			0.181171
$800$		0			0
$801$	1.14380e9	−	2.01682e8i	2.22562	−	0.392437i
$802$		0			0
$803$	4.51477e8	−	3.78834e8i	0.871945	−	0.731649i
$804$		0			0
$805$	−4.07193e6	+	7.05278e6i	−0.00780571	+	0.0135199i
$806$		0			0
$807$	9.96197e8	−	3.62586e8i	1.89550	−	0.689907i
$808$		0			0
$809$	−2.51011e8	−	4.34764e8i	−0.474075	−	0.821122i	0.525484	−	0.850803i	$-0.323884\pi$
$809$	−2.51011e8	−	4.34764e8i	−0.474075	−	0.821122i	−0.999559	+	0.0296810i	$0.990551\pi$
$810$		0			0
$811$	3.62124e8	+	6.38522e7i	0.678883	+	0.119705i	0.502448	−	0.864607i	$-0.332433\pi$
$811$	3.62124e8	+	6.38522e7i	0.678883	+	0.119705i	0.176434	+	0.984312i	$0.443544\pi$
$812$		0			0
$813$	3.87325e8	−	4.61596e8i	0.720781	−	0.858994i
$814$		0			0
$815$	3.21111e7	+	1.16875e7i	0.0593175	+	0.0215898i
$816$		0			0
$817$	−3.86604e8	+	4.49333e8i	−0.708924	+	0.823953i
$818$		0			0
$819$	−5.39985e7	+	1.48360e8i	−0.0982947	+	0.270063i
$820$		0			0
$821$	−6.44362e8	−	5.40684e8i	−1.16439	−	0.977043i	−0.164439	−	0.986387i	$-0.552581\pi$
$821$	−6.44362e8	−	5.40684e8i	−1.16439	−	0.977043i	−0.999956	+	0.00934391i	$0.997026\pi$
$822$		0			0
$823$	1.46113e8	−	8.28647e8i	0.262113	−	1.48652i	−0.515018	−	0.857179i	$-0.672215\pi$
$823$	1.46113e8	−	8.28647e8i	0.262113	−	1.48652i	0.777131	−	0.629338i	$-0.216674\pi$
$824$		0			0
$825$	2.96479e8	−	1.71172e8i	0.527998	−	0.304840i
$826$		0			0
$827$	2.42883e8	+	6.67316e8i	0.429418	+	1.17982i	0.946167	+	0.323680i	$0.104920\pi$
$827$	2.42883e8	+	6.67316e8i	0.429418	+	1.17982i	−0.516748	+	0.856138i	$0.672858\pi$
$828$		0			0
$829$	7.43876e8	+	4.29477e8i	1.30568	+	0.753835i	0.981372	−	0.192116i	$-0.0615351\pi$
$829$	7.43876e8	+	4.29477e8i	1.30568	+	0.753835i	0.324309	+	0.945951i	$0.394868\pi$
$830$		0			0
$831$	2.16848e8	+	2.58429e8i	0.377878	+	0.450338i
$832$		0			0
$833$	−3.24491e7	−	1.84028e8i	−0.0561394	−	0.318382i
$834$		0			0
$835$		−	4.47235e8i		−	0.768204i
$836$		0			0
$837$	1.21333e9			2.06921
$838$		0			0
$839$	6.65889e8	−	1.17414e8i	1.12750	−	0.198808i	0.421367	−	0.906890i	$-0.361550\pi$
$839$	6.65889e8	−	1.17414e8i	1.12750	−	0.198808i	0.706130	+	0.708082i	$0.250439\pi$
$840$		0			0
$841$	1.17464e8	−	9.85642e7i	0.197478	−	0.165703i
$842$		0			0
$843$	8.46741e8	−	1.46660e9i	1.41341	−	2.44810i
$844$		0			0
$845$	1.24139e8	−	4.51829e7i	0.205749	−	0.0748865i
$846$		0			0
$847$	1.87159e7	+	3.24168e7i	0.0308006	+	0.0533483i
$848$		0			0
$849$	−6.59342e8	−	1.16260e8i	−1.07743	−	0.189979i
$850$		0			0
$851$	4.08972e7	−	4.87394e7i	0.0663598	−	0.0790846i
$852$		0			0
$853$	−1.57936e8	−	5.74841e7i	−0.254469	−	0.0926192i	0.211636	−	0.977349i	$-0.432121\pi$
$853$	−1.57936e8	−	5.74841e7i	−0.254469	−	0.0926192i	−0.466105	+	0.884729i	$0.654343\pi$
$854$		0			0
$855$	−3.51947e8	+	9.30982e8i	−0.563091	+	1.48951i
$856$		0			0
$857$	−3.55088e7	+	9.75596e7i	−0.0564149	+	0.154999i	−0.964699	−	0.263356i	$-0.915171\pi$
$857$	−3.55088e7	+	9.75596e7i	−0.0564149	+	0.154999i	0.908284	+	0.418354i	$0.137393\pi$
$858$		0			0
$859$	−3.05335e8	−	2.56206e8i	−0.481722	−	0.404213i	0.369327	−	0.929300i	$-0.379588\pi$
$859$	−3.05335e8	−	2.56206e8i	−0.481722	−	0.404213i	−0.851049	+	0.525087i	$0.824033\pi$
$860$		0			0
$861$	−1.53074e7	+	8.68124e7i	−0.0239823	+	0.136011i
$862$		0			0
$863$	−3.63164e8	+	2.09673e8i	−0.565028	+	0.326219i	−0.755161	−	0.655539i	$-0.772441\pi$
$863$	−3.63164e8	+	2.09673e8i	−0.565028	+	0.326219i	0.190133	+	0.981758i	$0.439108\pi$
$864$		0			0
$865$	−2.11849e8	−	5.82050e8i	−0.327324	−	0.899316i
$866$		0			0
$867$	−9.10824e8	−	5.25865e8i	−1.39758	−	0.806894i
$868$		0			0
$869$	9.67695e7	+	1.15325e8i	0.147462	+	0.175738i
$870$		0			0
$871$	7.92425e7	+	4.49406e8i	0.119923	+	0.680119i
$872$		0			0
$873$		−	1.94681e8i		−	0.292605i
$874$		0			0
$875$	−7.84874e7			−0.117159
$876$		0			0
$877$	−2.48851e8	+	4.38791e7i	−0.368927	+	0.0650517i	−0.355038	−	0.934852i	$-0.615532\pi$
$877$	−2.48851e8	+	4.38791e7i	−0.368927	+	0.0650517i	−0.0138885	+	0.999904i	$0.504421\pi$
$878$		0			0
$879$	9.31369e8	−	7.81511e8i	1.37137	−	1.15072i
$880$		0			0
$881$	4.36544e8	−	7.56117e8i	0.638411	−	1.10576i	−0.347370	−	0.937728i	$-0.612925\pi$
$881$	4.36544e8	−	7.56117e8i	0.638411	−	1.10576i	0.985781	−	0.168033i	$-0.0537414\pi$
$882$		0			0
$883$	−1.44076e8	+	5.24396e7i	−0.209272	+	0.0761688i	−0.444529	−	0.895764i	$-0.646629\pi$
$883$	−1.44076e8	+	5.24396e7i	−0.209272	+	0.0761688i	0.235257	+	0.971933i	$0.424407\pi$
$884$		0			0
$885$	7.45532e8	+	1.29130e9i	1.07556	+	1.86293i
$886$		0			0
$887$	1.13594e9	+	2.00297e8i	1.62774	+	0.287014i	0.911642	−	0.410986i	$-0.134816\pi$
$887$	1.13594e9	+	2.00297e8i	1.62774	+	0.287014i	0.716097	+	0.698001i	$0.245927\pi$
$888$		0			0
$889$	4.20009e7	−	5.00547e7i	0.0597796	−	0.0712426i
$890$		0			0
$891$	−8.28428e8	−	3.01523e8i	−1.17117	−	0.426273i
$892$		0			0
$893$	3.43778e8	−	1.92852e8i	0.482751	−	0.270813i
$894$		0			0
$895$	−8.48898e7	+	2.33233e8i	−0.118409	+	0.325327i
$896$		0			0
$897$	2.29740e8	+	1.92775e8i	0.318316	+	0.267099i
$898$		0			0
$899$	9.82357e7	−	5.57122e8i	0.135204	−	0.766781i
$900$		0			0
$901$	3.49279e8	−	2.01656e8i	0.477527	−	0.275700i
$902$		0			0
$903$	5.47705e7	+	1.50481e8i	0.0743846	+	0.204370i
$904$		0			0
$905$	2.69883e8	+	1.55817e8i	0.364107	+	0.210217i
$906$		0			0
$907$	2.01287e8	+	2.39884e8i	0.269770	+	0.321499i	0.883873	−	0.467726i	$-0.154927\pi$
$907$	2.01287e8	+	2.39884e8i	0.269770	+	0.321499i	−0.614103	+	0.789226i	$0.710482\pi$
$908$		0			0
$909$	1.33411e8	+	7.56609e8i	0.177623	+	1.00735i
$910$		0			0
$911$		−	4.32880e8i		−	0.572548i	−0.958148	−	0.286274i	$-0.907583\pi$
$911$		−	4.32880e8i		−	0.572548i	0.958148	−	0.286274i	$-0.0924168\pi$
$912$		0			0
$913$	2.20429e8			0.289638
$914$		0			0
$915$	−1.57223e9	+	2.77226e8i	−2.05235	+	0.361885i
$916$		0			0
$917$	−8.57894e7	+	7.19859e7i	−0.111257	+	0.0933554i
$918$		0			0
$919$	−3.10570e8	+	5.37923e8i	−0.400141	+	0.693064i	−0.993743	−	0.111695i	$-0.964372\pi$
$919$	−3.10570e8	+	5.37923e8i	−0.400141	+	0.693064i	0.593602	+	0.804759i	$0.297705\pi$
$920$		0			0
$921$	−1.99816e8	+	7.27271e7i	−0.255771	+	0.0930931i
$922$		0			0
$923$	−8.32367e8	−	1.44170e9i	−1.05855	−	1.83346i
$924$		0			0
$925$	2.03027e8	+	3.57992e7i	0.256525	+	0.0452322i
$926$		0			0
$927$	−2.13564e9	+	2.54516e9i	−2.68095	+	3.19503i
$928$		0			0
$929$	3.26804e8	+	1.18947e8i	0.407606	+	0.148356i	0.537682	−	0.843148i	$-0.319300\pi$
$929$	3.26804e8	+	1.18947e8i	0.407606	+	0.148356i	−0.130076	+	0.991504i	$0.541522\pi$
$930$		0			0
$931$	−5.04754e8	−	6.16876e8i	−0.625505	−	0.764449i
$932$		0			0
$933$	1.55398e8	−	4.26952e8i	0.191338	−	0.525696i
$934$		0			0
$935$	9.58866e7	+	8.04584e7i	0.117307	+	0.0984321i
$936$		0			0
$937$	−1.30348e8	+	7.39238e8i	−0.158447	+	0.898598i	0.797119	+	0.603822i	$0.206356\pi$
$937$	−1.30348e8	+	7.39238e8i	−0.158447	+	0.898598i	−0.955566	+	0.294776i	$0.904755\pi$
$938$		0			0
$939$	−1.96063e9	+	1.13197e9i	−2.36809	+	1.36722i
$940$		0			0
$941$	−1.63392e8	−	4.48916e8i	−0.196093	−	0.538761i	0.802207	−	0.597046i	$-0.203659\pi$
$941$	−1.63392e8	−	4.48916e8i	−0.196093	−	0.538761i	−0.998300	+	0.0582852i	$0.981437\pi$
$942$		0			0
$943$	1.00624e8	+	5.80952e7i	0.119996	+	0.0692795i
$944$		0			0
$945$	9.65871e7	+	1.15108e8i	0.114452	+	0.136399i
$946$		0			0
$947$	−3.39589e7	−	1.92591e8i	−0.0399856	−	0.226770i	0.958266	−	0.285878i	$-0.0922853\pi$
$947$	−3.39589e7	−	1.92591e8i	−0.0399856	−	0.226770i	−0.998252	+	0.0591085i	$0.981174\pi$
$948$		0			0
$949$			1.67293e9i			1.95739i
$950$		0			0
$951$	−1.92950e9			−2.24338
$952$		0			0
$953$	1.04166e8	−	1.83673e7i	0.120350	−	0.0212210i	−0.113149	−	0.993578i	$-0.536094\pi$
$953$	1.04166e8	−	1.83673e7i	0.120350	−	0.0212210i	0.233499	+	0.972357i	$0.424982\pi$
$954$		0			0
$955$	3.58750e8	−	3.01027e8i	0.411891	−	0.345617i
$956$		0			0
$957$	−4.54462e8	+	7.87151e8i	−0.518515	+	0.898095i
$958$		0			0
$959$	1.08601e8	−	3.95276e7i	0.123134	−	0.0448172i
$960$		0			0
$961$	−8.12982e7	−	1.40813e8i	−0.0916032	−	0.158661i
$962$		0			0
$963$	−1.66712e9	−	2.93959e8i	−1.86676	−	0.329160i
$964$		0			0
$965$	6.69276e8	−	7.97612e8i	0.744772	−	0.887585i
$966$		0			0
$967$	4.52946e8	+	1.64859e8i	0.500919	+	0.182320i	0.580107	−	0.814540i	$-0.303011\pi$
$967$	4.52946e8	+	1.64859e8i	0.500919	+	0.182320i	−0.0791885	+	0.996860i	$0.525233\pi$
$968$		0			0
$969$	5.38206e8	+	6.65563e6i	0.591530	+	0.00731506i
$970$		0			0
$971$	−1.18042e8	+	3.24319e8i	−0.128938	+	0.354254i	−0.987317	−	0.158762i	$-0.949250\pi$
$971$	−1.18042e8	+	3.24319e8i	−0.128938	+	0.354254i	0.858379	+	0.513016i	$0.171472\pi$
$972$		0			0
$973$	−1.40458e8	−	1.17858e8i	−0.152478	−	0.127945i
$974$		0			0
$975$	−1.68744e8	+	9.56996e8i	−0.182060	+	1.03251i
$976$		0			0
$977$	1.53353e9	−	8.85386e8i	1.64441	−	0.949399i	0.665168	−	0.746694i	$-0.268360\pi$
$977$	1.53353e9	−	8.85386e8i	1.64441	−	0.949399i	0.979240	−	0.202705i	$-0.0649734\pi$
$978$		0			0
$979$	−2.13092e8	−	5.85465e8i	−0.227101	−	0.623954i
$980$		0			0
$981$	1.40152e9	+	8.09167e8i	1.48454	+	0.857099i
$982$		0			0
$983$	3.50307e8	+	4.17480e8i	0.368798	+	0.439517i	0.918245	−	0.396012i	$-0.129606\pi$
$983$	3.50307e8	+	4.17480e8i	0.368798	+	0.439517i	−0.549447	+	0.835528i	$0.685162\pi$
$984$		0			0
$985$	−1.35935e8	−	7.70926e8i	−0.142240	−	0.806685i
$986$		0			0
$987$		−	1.06490e8i		−	0.110753i
$988$		0			0
$989$	2.11074e8			0.218195
$990$		0			0
$991$	−4.63085e8	+	8.16544e7i	−0.475817	+	0.0838993i	−0.406413	−	0.913689i	$-0.633221\pi$
$991$	−4.63085e8	+	8.16544e7i	−0.475817	+	0.0838993i	−0.0694034	+	0.997589i	$0.522110\pi$
$992$		0			0
$993$	−2.26230e9	+	1.89830e9i	−2.31048	+	1.93872i
$994$		0			0
$995$	1.09733e8	−	1.90063e8i	0.111395	−	0.192942i
$996$		0			0
$997$	2.63595e8	−	9.59409e7i	0.265982	−	0.0968096i	−0.205587	−	0.978639i	$-0.565910\pi$
$997$	2.63595e8	−	9.59409e7i	0.265982	−	0.0968096i	0.471569	+	0.881829i	$0.343688\pi$
$998$		0			0
$999$	−5.86973e8	−	1.01667e9i	−0.588738	−	1.01972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.53.10	yes	60
19.14	odd	18	inner	76.7.j.a.33.10	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.33.10	✓	60	19.14	odd	18	inner
76.7.j.a.53.10	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(48.0588 - 8.47406i) q^{3} +(67.2683 - 56.4448i) q^{5} +(-18.9857 + 32.8842i) q^{7} +(1552.80 - 565.174i) q^{9} +O(q^{10})\)	\(q+(48.0588 - 8.47406i) q^{3} +(67.2683 - 56.4448i) q^{5} +(-18.9857 + 32.8842i) q^{7} +(1552.80 - 565.174i) q^{9} +(-443.219 - 767.678i) q^{11} +(2477.96 + 436.932i) q^{13} +(2754.52 - 3282.71i) q^{15} +(-1511.07 - 549.985i) q^{17} +(-6769.01 + 1107.44i) q^{19} +(-633.766 + 1741.26i) q^{21} +(1870.99 + 1569.95i) q^{23} +(-1374.24 + 7793.72i) q^{25} +(39027.4 - 22532.5i) q^{27} +(-7186.37 - 19744.4i) q^{29} +(23317.0 + 13462.1i) q^{31} +(-27805.9 - 33137.8i) q^{33} +(579.006 + 3283.70i) q^{35} -26050.1i q^{37} +122791. q^{39} +(46849.4 - 8260.82i) q^{41} +(66202.0 - 55550.1i) q^{43} +(72553.3 - 125666. i) q^{45} +(-54002.7 + 19655.4i) q^{47} +(58103.6 + 100638. i) q^{49} +(-77280.9 - 13626.7i) q^{51} +(-161217. + 192130. i) q^{53} +(-73146.0 - 26623.0i) q^{55} +(-315926. + 110583. i) q^{57} +(-119006. + 326967. i) q^{59} +(-285390. - 239471. i) q^{61} +(-10895.7 + 61792.8i) q^{63} +(191351. - 110477. i) q^{65} +(62029.2 + 170424. i) q^{67} +(103221. + 59594.8i) q^{69} +(-425274. - 506822. i) q^{71} +(115453. + 654764. i) q^{73} +386203. i q^{75} +33659.2 q^{77} +(-167253. + 29491.2i) q^{79} +(761859. - 639275. i) q^{81} +(-124334. + 215353. i) q^{83} +(-132691. + 48295.6i) q^{85} +(-512683. - 887994. i) q^{87} +(692179. + 122050. i) q^{89} +(-61414.0 + 73190.3i) q^{91} +(1.23466e6 + 449381. i) q^{93} +(-392831. + 456571. i) q^{95} +(40294.4 - 110708. i) q^{97} +(-1.12210e6 - 941556. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9} + 1680 q^{11} - 2940 q^{13} + 2496 q^{15} - 5112 q^{17} - 15792 q^{19} - 32076 q^{21} - 19272 q^{23} + 58896 q^{25} - 124830 q^{27} + 126840 q^{29} + 30780 q^{31} - 274470 q^{33} - 226284 q^{35} + 178968 q^{39} + 83394 q^{41} + 418848 q^{43} - 95472 q^{45} - 498696 q^{47} - 744330 q^{49} + 1334538 q^{51} + 458004 q^{53} - 260136 q^{55} - 981984 q^{57} - 523362 q^{59} - 644172 q^{61} + 926832 q^{63} + 1337220 q^{65} + 1719114 q^{67} + 1333800 q^{69} - 1895220 q^{71} - 1189704 q^{73} + 1337256 q^{77} + 147432 q^{79} + 272130 q^{81} + 442800 q^{83} + 1479096 q^{85} + 1300572 q^{87} - 301596 q^{89} + 661008 q^{91} + 3576 q^{93} - 5709984 q^{95} + 1386630 q^{97} + 3822798 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 216 * q^7 + 690 * q^9 + 1680 * q^11 - 2940 * q^13 + 2496 * q^15 - 5112 * q^17 - 15792 * q^19 - 32076 * q^21 - 19272 * q^23 + 58896 * q^25 - 124830 * q^27 + 126840 * q^29 + 30780 * q^31 - 274470 * q^33 - 226284 * q^35 + 178968 * q^39 + 83394 * q^41 + 418848 * q^43 - 95472 * q^45 - 498696 * q^47 - 744330 * q^49 + 1334538 * q^51 + 458004 * q^53 - 260136 * q^55 - 981984 * q^57 - 523362 * q^59 - 644172 * q^61 + 926832 * q^63 + 1337220 * q^65 + 1719114 * q^67 + 1333800 * q^69 - 1895220 * q^71 - 1189704 * q^73 + 1337256 * q^77 + 147432 * q^79 + 272130 * q^81 + 442800 * q^83 + 1479096 * q^85 + 1300572 * q^87 - 301596 * q^89 + 661008 * q^91 + 3576 * q^93 - 5709984 * q^95 + 1386630 * q^97 + 3822798 * q^99

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