LMFDB - Embedded newform 76.7.j.a.29.2

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			29.2
Character	$\chi$	$=$	76.29
Dual form			76.7.j.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18.1708 - 21.6552i) q^{3} +(40.6936 + 14.8113i) q^{5} +(179.977 - 311.730i) q^{7} +(-12.1770 + 69.0593i) q^{9} +O(q^{10})$	\(q+(-18.1708 - 21.6552i) q^{3} +(40.6936 + 14.8113i) q^{5} +(179.977 - 311.730i) q^{7} +(-12.1770 + 69.0593i) q^{9} +(451.055 + 781.249i) q^{11} +(880.095 - 1048.86i) q^{13} +(-418.697 - 1150.36i) q^{15} +(-1025.67 - 5816.84i) q^{17} +(-5697.06 + 3819.60i) q^{19} +(-10020.9 + 1766.96i) q^{21} +(-8881.65 + 3232.66i) q^{23} +(-10532.8 - 8838.11i) q^{25} +(-16130.3 + 9312.81i) q^{27} +(9151.84 + 1613.72i) q^{29} +(-43451.8 - 25086.9i) q^{31} +(8722.04 - 23963.6i) q^{33} +(11941.1 - 10019.7i) q^{35} -37981.8i q^{37} -38705.2 q^{39} +(30507.4 + 36357.3i) q^{41} +(691.795 + 251.793i) q^{43} +(-1518.38 + 2629.91i) q^{45} +(10700.2 - 60683.8i) q^{47} +(-5959.27 - 10321.8i) q^{49} +(-107327. + 127908. i) q^{51} +(-22191.6 - 60971.0i) q^{53} +(6783.75 + 38472.6i) q^{55} +(186234. + 53965.5i) q^{57} +(-103188. + 18194.9i) q^{59} +(-42024.7 + 15295.7i) q^{61} +(19336.3 + 16225.0i) q^{63} +(51349.2 - 29646.5i) q^{65} +(497157. + 87662.2i) q^{67} +(231391. + 133593. i) q^{69} +(-75111.0 + 206366. i) q^{71} +(75180.8 - 63084.2i) q^{73} +388686. i q^{75} +324719. q^{77} +(-167089. - 199129. i) q^{79} +(542808. + 197566. i) q^{81} +(471277. - 816276. i) q^{83} +(44416.7 - 251900. i) q^{85} +(-131351. - 227507. i) q^{87} +(-127638. + 152113. i) q^{89} +(-168563. - 463123. i) q^{91} +(246295. + 1.39681e6i) q^{93} +(-288407. + 71052.6i) q^{95} +(-412609. + 72754.2i) q^{97} +(-59445.0 + 21636.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$

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
$3$	−18.1708	−	21.6552i	−0.672994	−	0.802043i	0.316195	−	0.948694i	$-0.397595\pi$
$3$	−18.1708	−	21.6552i	−0.672994	−	0.802043i	−0.989188	+	0.146652i	$0.953150\pi$
$4$		0			0
$5$	40.6936	+	14.8113i	0.325549	+	0.118490i	0.499624	−	0.866242i	$-0.333471\pi$
$5$	40.6936	+	14.8113i	0.325549	+	0.118490i	−0.174075	+	0.984732i	$0.555694\pi$
$6$		0			0
$7$	179.977	−	311.730i	0.524716	−	0.908834i	−0.474870	−	0.880056i	$-0.657505\pi$
$7$	179.977	−	311.730i	0.524716	−	0.908834i	0.999586	−	0.0287782i	$-0.00916166\pi$
$8$		0			0
$9$	−12.1770	+	69.0593i	−0.0167037	+	0.0947315i
$10$		0			0
$11$	451.055	+	781.249i	0.338884	+	0.586964i	0.984223	−	0.176932i	$-0.0566173\pi$
$11$	451.055	+	781.249i	0.338884	+	0.586964i	−0.645339	+	0.763896i	$0.723284\pi$
$12$		0			0
$13$	880.095	−	1048.86i	0.400590	−	0.477404i	−0.527610	−	0.849487i	$-0.676912\pi$
$13$	880.095	−	1048.86i	0.400590	−	0.477404i	0.928200	+	0.372083i	$0.121356\pi$
$14$		0			0
$15$	−418.697	−	1150.36i	−0.124058	−	0.340847i
$16$		0			0
$17$	−1025.67	−	5816.84i	−0.208766	−	1.18397i	−0.891403	−	0.453212i	$-0.850278\pi$
$17$	−1025.67	−	5816.84i	−0.208766	−	1.18397i	0.682637	−	0.730758i	$-0.260833\pi$
$18$		0			0
$19$	−5697.06	+	3819.60i	−0.830597	+	0.556874i
$19$	−5697.06	+	3819.60i	−0.830597	+	0.556874i
$20$		0			0
$21$	−10020.9	+	1766.96i	−1.08205	+	0.190795i
$22$		0			0
$23$	−8881.65	+	3232.66i	−0.729979	+	0.265691i	−0.680156	−	0.733067i	$-0.738088\pi$
$23$	−8881.65	+	3232.66i	−0.729979	+	0.265691i	−0.0498230	+	0.998758i	$0.515866\pi$
$24$		0			0
$25$	−10532.8	−	8838.11i	−0.674102	−	0.565639i
$26$		0			0
$27$	−16130.3	+	9312.81i	−0.819502	+	0.473140i
$28$		0			0
$29$	9151.84	+	1613.72i	0.375245	+	0.0661657i	0.358090	−	0.933687i	$-0.383428\pi$
$29$	9151.84	+	1613.72i	0.375245	+	0.0661657i	0.0171546	+	0.999853i	$0.494539\pi$
$30$		0			0
$31$	−43451.8	−	25086.9i	−1.45856	−	0.842097i	−0.459615	−	0.888118i	$-0.652013\pi$
$31$	−43451.8	−	25086.9i	−1.45856	−	0.842097i	−0.998940	+	0.0460208i	$0.985346\pi$
$32$		0			0
$33$	8722.04	−	23963.6i	0.242704	−	0.666823i
$34$		0			0
$35$	11941.1	−	10019.7i	0.278509	−	0.233696i
$36$		0			0
$37$		−	37981.8i		−	0.749844i	−0.927056	−	0.374922i	$-0.877670\pi$
$37$		−	37981.8i		−	0.749844i	0.927056	−	0.374922i	$-0.122330\pi$
$38$		0			0
$39$	−38705.2			−0.652493
$40$		0			0
$41$	30507.4	+	36357.3i	0.442643	+	0.527521i	0.940525	−	0.339723i	$-0.110333\pi$
$41$	30507.4	+	36357.3i	0.442643	+	0.527521i	−0.497883	+	0.867244i	$0.665889\pi$
$42$		0			0
$43$	691.795	+	251.793i	0.00870106	+	0.00316693i	0.346367	−	0.938099i	$-0.387415\pi$
$43$	691.795	+	251.793i	0.00870106	+	0.00316693i	−0.337666	+	0.941266i	$0.609637\pi$
$44$		0			0
$45$	−1518.38	+	2629.91i	−0.0166626	+	0.0288605i
$46$		0			0
$47$	10700.2	−	60683.8i	0.103062	−	0.584493i	−0.888915	−	0.458072i	$-0.848540\pi$
$47$	10700.2	−	60683.8i	0.103062	−	0.584493i	0.991977	−	0.126420i	$-0.0403488\pi$
$48$		0			0
$49$	−5959.27	−	10321.8i	−0.0506529	−	0.0877334i
$50$		0			0
$51$	−107327.	+	127908.i	−0.809096	+	0.964243i
$52$		0			0
$53$	−22191.6	−	60971.0i	−0.149060	−	0.409539i	0.842580	−	0.538571i	$-0.181035\pi$
$53$	−22191.6	−	60971.0i	−0.149060	−	0.409539i	−0.991641	+	0.129031i	$0.958813\pi$
$54$		0			0
$55$	6783.75	+	38472.6i	0.0407739	+	0.231240i
$56$		0			0
$57$	186234.	+	53965.5i	1.00562	+	0.291401i
$58$		0			0
$59$	−103188.	+	18194.9i	−0.502429	+	0.0885919i	−0.419118	−	0.907932i	$-0.637661\pi$
$59$	−103188.	+	18194.9i	−0.502429	+	0.0885919i	−0.0833113	+	0.996524i	$0.526550\pi$
$60$		0			0
$61$	−42024.7	+	15295.7i	−0.185146	+	0.0673877i	−0.432930	−	0.901428i	$-0.642520\pi$
$61$	−42024.7	+	15295.7i	−0.185146	+	0.0673877i	0.247783	+	0.968815i	$0.420298\pi$
$62$		0			0
$63$	19336.3	+	16225.0i	0.0773305	+	0.0648880i
$64$		0			0
$65$	51349.2	−	29646.5i	0.186979	−	0.107952i
$66$		0			0
$67$	497157.	+	87662.2i	1.65299	+	0.291466i	0.920915	−	0.389763i	$-0.127443\pi$
$67$	497157.	+	87662.2i	1.65299	+	0.291466i	0.732071	+	0.681229i	$0.238554\pi$
$68$		0			0
$69$	231391.	+	133593.i	0.704366	+	0.406666i
$70$		0			0
$71$	−75111.0	+	206366.i	−0.209859	+	0.576584i	−0.999307	−	0.0372346i	$-0.988145\pi$
$71$	−75111.0	+	206366.i	−0.209859	+	0.576584i	0.789447	+	0.613818i	$0.210367\pi$
$72$		0			0
$73$	75180.8	−	63084.2i	0.193258	−	0.162163i	−0.541024	−	0.841007i	$-0.681963\pi$
$73$	75180.8	−	63084.2i	0.193258	−	0.162163i	0.734282	+	0.678844i	$0.237519\pi$
$74$		0			0
$75$			388686.i			0.921330i
$76$		0			0
$77$	324719.			0.711271
$78$		0			0
$79$	−167089.	−	199129.i	−0.338897	−	0.403881i	0.569500	−	0.821992i	$-0.307137\pi$
$79$	−167089.	−	199129.i	−0.338897	−	0.403881i	−0.908396	+	0.418110i	$0.862693\pi$
$80$		0			0
$81$	542808.	+	197566.i	1.02139	+	0.371755i
$82$		0			0
$83$	471277.	−	816276.i	0.824218	−	1.42759i	−0.0782971	−	0.996930i	$-0.524948\pi$
$83$	471277.	−	816276.i	0.824218	−	1.42759i	0.902515	−	0.430658i	$-0.141718\pi$
$84$		0			0
$85$	44416.7	−	251900.i	0.0723252	−	0.410177i
$86$		0			0
$87$	−131351.	−	227507.i	−0.199469	−	0.345491i
$88$		0			0
$89$	−127638.	+	152113.i	−0.181055	+	0.215773i	−0.848937	−	0.528494i	$-0.822757\pi$
$89$	−127638.	+	152113.i	−0.181055	+	0.215773i	0.667882	+	0.744267i	$0.267201\pi$
$90$		0			0
$91$	−168563.	−	463123.i	−0.223685	−	0.614571i
$92$		0			0
$93$	246295.	+	1.39681e6i	0.306201	+	1.73655i
$94$		0			0
$95$	−288407.	+	71052.6i	−0.336384	+	0.0828723i
$96$		0			0
$97$	−412609.	+	72754.2i	−0.452089	+	0.0797155i	−0.395057	−	0.918657i	$-0.629275\pi$
$97$	−412609.	+	72754.2i	−0.452089	+	0.0797155i	−0.0570325	+	0.998372i	$0.518164\pi$
$98$		0			0
$99$	−59445.0	+	21636.2i	−0.0612646	+	0.0222985i
$100$		0			0
$101$	−38059.7	−	31935.9i	−0.0369404	−	0.0309967i	0.624131	−	0.781320i	$-0.285453\pi$
$101$	−38059.7	−	31935.9i	−0.0369404	−	0.0309967i	−0.661071	+	0.750323i	$0.729898\pi$
$102$		0			0
$103$	−861685.	+	497494.i	−0.788563	+	0.455277i	−0.839457	−	0.543427i	$-0.817127\pi$
$103$	−861685.	+	497494.i	−0.788563	+	0.455277i	0.0508931	+	0.998704i	$0.483793\pi$
$104$		0			0
$105$	−433958.	−	76518.4i	−0.374869	−	0.0660995i
$106$		0			0
$107$	−1.51337e6	−	873744.i	−1.23536	−	0.713236i	−0.267218	−	0.963636i	$-0.586104\pi$
$107$	−1.51337e6	−	873744.i	−1.23536	−	0.713236i	−0.968142	+	0.250401i	$0.919438\pi$
$108$		0			0
$109$	233335.	−	641082.i	0.180177	−	0.495033i	−0.816420	−	0.577459i	$-0.804044\pi$
$109$	233335.	−	641082.i	0.180177	−	0.495033i	0.996597	+	0.0824256i	$0.0262667\pi$
$110$		0			0
$111$	−822503.	+	690162.i	−0.601407	+	0.504640i
$112$		0			0
$113$		−	353386.i		−	0.244914i	−0.992474	−	0.122457i	$-0.960923\pi$
$113$		−	353386.i		−	0.244914i	0.992474	−	0.122457i	$-0.0390773\pi$
$114$		0			0
$115$	−409306.			−0.269126
$116$		0			0
$117$	61716.3	+	73550.7i	0.0385339	+	0.0459229i
$118$		0			0
$119$	−1.99788e6	−	727170.i	−1.18557	−	0.431514i
$120$		0			0
$121$	478880.	−	829445.i	0.270315	−	0.468200i
$122$		0			0
$123$	232978.	−	1.32128e6i	0.125199	−	0.710036i
$124$		0			0
$125$	−636038.	−	1.10165e6i	−0.325652	−	0.564045i
$126$		0			0
$127$	64878.6	−	77319.4i	0.0316731	−	0.0377465i	−0.749975	−	0.661466i	$-0.769935\pi$
$127$	64878.6	−	77319.4i	0.0316731	−	0.0377465i	0.781648	+	0.623719i	$0.214379\pi$
$128$		0			0
$129$	−7117.88	−	19556.2i	−0.00331575	−	0.00910994i
$130$		0			0
$131$	108653.	+	616200.i	0.0483311	+	0.274099i	0.999391	−	0.0349088i	$-0.0111141\pi$
$131$	108653.	+	616200.i	0.0483311	+	0.274099i	−0.951059	+	0.309008i	$0.900003\pi$
$132$		0			0
$133$	165341.	+	2.46339e6i	0.0702790	+	1.04708i
$134$		0			0
$135$	−794333.	+	140062.i	−0.322850	+	0.0569272i
$136$		0			0
$137$	4.30476e6	−	1.56681e6i	1.67412	−	0.609331i	0.681637	−	0.731690i	$-0.261268\pi$
$137$	4.30476e6	−	1.56681e6i	1.67412	−	0.609331i	0.992486	+	0.122359i	$0.0390460\pi$
$138$		0			0
$139$	−1.41797e6	−	1.18982e6i	−0.527985	−	0.443032i	0.339420	−	0.940635i	$-0.389769\pi$
$139$	−1.41797e6	−	1.18982e6i	−0.527985	−	0.443032i	−0.867405	+	0.497603i	$0.834214\pi$
$140$		0			0
$141$	−1.50855e6	+	870961.i	−0.538148	+	0.310700i
$142$		0			0
$143$	1.21639e6	+	214482.i	0.415972	+	0.0733472i
$144$		0			0
$145$	348520.	+	201218.i	0.114320	+	0.0660030i
$146$		0			0
$147$	−115234.	+	316604.i	−0.0362769	+	0.0996699i
$148$		0			0
$149$	4.84421e6	−	4.06477e6i	1.46441	−	1.22879i	0.543275	−	0.839555i	$-0.317184\pi$
$149$	4.84421e6	−	4.06477e6i	1.46441	−	1.22879i	0.921139	−	0.389234i	$-0.127260\pi$
$150$		0			0
$151$			5.70613e6i			1.65734i	0.559740	+	0.828668i	$0.310901\pi$
$151$			5.70613e6i			1.65734i	−0.559740	+	0.828668i	$0.689099\pi$
$152$		0			0
$153$	414196.			0.115646
$154$		0			0
$155$	−1.39664e6	−	1.66445e6i	−0.375051	−	0.446968i
$156$		0			0
$157$	−3.09392e6	−	1.12610e6i	−0.799485	−	0.290989i	−0.0902122	−	0.995923i	$-0.528755\pi$
$157$	−3.09392e6	−	1.12610e6i	−0.799485	−	0.290989i	−0.709273	+	0.704934i	$0.750977\pi$
$158$		0			0
$159$	−917096.	+	1.58846e6i	−0.228151	+	0.395170i
$160$		0			0
$161$	−590781.	+	3.35048e6i	−0.141563	+	0.802842i
$162$		0			0
$163$	−1.41965e6	−	2.45890e6i	−0.327807	−	0.567778i	0.654270	−	0.756261i	$-0.272976\pi$
$163$	−1.41965e6	−	2.45890e6i	−0.327807	−	0.567778i	−0.982076	+	0.188483i	$0.939643\pi$
$164$		0			0
$165$	709863.	−	845981.i	0.158024	−	0.188325i
$166$		0			0
$167$	1.48824e6	+	4.08889e6i	0.319538	+	0.877923i	0.990633	+	0.136552i	$0.0436020\pi$
$167$	1.48824e6	+	4.08889e6i	0.319538	+	0.877923i	−0.671095	+	0.741371i	$0.734176\pi$
$168$		0			0
$169$	512634.	+	2.90729e6i	0.106206	+	0.602322i
$170$		0			0
$171$	−194405.	−	439946.i	−0.0388795	−	0.0879855i
$172$		0			0
$173$	9.43626e6	−	1.66387e6i	1.82247	−	0.321351i	0.845381	−	0.534163i	$-0.179373\pi$
$173$	9.43626e6	−	1.66387e6i	1.82247	−	0.321351i	0.977093	+	0.212812i	$0.0682622\pi$
$174$		0			0
$175$	−4.65078e6	+	1.69275e6i	−0.867784	+	0.315848i
$176$		0			0
$177$	2.26903e6	+	1.90394e6i	0.409186	+	0.343348i
$178$		0			0
$179$	−2.47613e6	+	1.42960e6i	−0.431733	+	0.249261i	−0.700084	−	0.714060i	$-0.746854\pi$
$179$	−2.47613e6	+	1.42960e6i	−0.431733	+	0.249261i	0.268352	+	0.963321i	$0.413521\pi$
$180$		0			0
$181$	5.46878e6	+	964293.i	0.922262	+	0.162620i	0.614566	−	0.788865i	$-0.289331\pi$
$181$	5.46878e6	+	964293.i	0.922262	+	0.162620i	0.307696	+	0.951485i	$0.400442\pi$
$182$		0			0
$183$	1.09485e6	+	632115.i	0.178650	+	0.103144i
$184$		0			0
$185$	562559.	−	1.54562e6i	0.0888491	−	0.244111i
$186$		0			0
$187$	4.08177e6	−	3.42501e6i	0.624200	−	0.523766i
$188$		0			0
$189$			6.70438e6i			0.993055i
$190$		0			0
$191$	5.02912e6			0.721758			0.360879	−	0.932613i	$-0.382477\pi$
$191$	5.02912e6			0.721758			0.360879	+	0.932613i	$0.382477\pi$
$192$		0			0
$193$	5.35590e6	+	6.38291e6i	0.745007	+	0.887865i	0.996802	−	0.0799155i	$-0.0254650\pi$
$193$	5.35590e6	+	6.38291e6i	0.745007	+	0.887865i	−0.251794	+	0.967781i	$0.581021\pi$
$194$		0			0
$195$	−1.57506e6	−	573273.i	−0.212418	−	0.0773139i
$196$		0			0
$197$	1.34460e6	−	2.32891e6i	0.175871	−	0.304617i	−0.764591	−	0.644515i	$-0.777059\pi$
$197$	1.34460e6	−	2.32891e6i	0.175871	−	0.304617i	0.940462	+	0.339898i	$0.110393\pi$
$198$		0			0
$199$	879101.	−	4.98563e6i	0.111553	−	0.632646i	−0.876847	−	0.480770i	$-0.840357\pi$
$199$	879101.	−	4.98563e6i	0.111553	−	0.632646i	0.988399	−	0.151876i	$-0.0485316\pi$
$200$		0			0
$201$	−7.13542e6	−	1.23589e7i	−0.878681	−	1.52192i
$202$		0			0
$203$	2.15017e6	−	2.56247e6i	0.257030	−	0.306317i
$204$		0			0
$205$	702958.	+	1.93136e6i	0.0815958	+	0.224183i
$206$		0			0
$207$	−115093.	−	652724.i	−0.0129759	−	0.0735900i
$208$		0			0
$209$	−5.55375e6	−	2.72798e6i	−0.608341	−	0.298815i
$210$		0			0
$211$	1.36467e7	−	2.40628e6i	1.45272	−	0.256153i	0.609097	−	0.793096i	$-0.291532\pi$
$211$	1.36467e7	−	2.40628e6i	1.45272	−	0.256153i	0.843619	+	0.536943i	$0.180421\pi$
$212$		0			0
$213$	5.83371e6	−	2.12330e6i	0.603679	−	0.219721i
$214$		0			0
$215$	24422.3	+	20492.7i	0.00245737	+	0.00206198i
$216$		0			0
$217$	−1.56407e7	+	9.03016e6i	−1.53065	+	0.883723i
$218$		0			0
$219$	−2.73220e6	−	481760.i	−0.260123	−	0.0458668i
$220$		0			0
$221$	−7.00372e6	−	4.04360e6i	−0.648861	−	0.374620i
$222$		0			0
$223$	−5.23237e6	+	1.43758e7i	−0.471829	+	1.29634i	0.444453	+	0.895802i	$0.353398\pi$
$223$	−5.23237e6	+	1.43758e7i	−0.471829	+	1.29634i	−0.916281	+	0.400536i	$0.868824\pi$
$224$		0			0
$225$	738612.	−	619769.i	0.0648438	−	0.0544104i
$226$		0			0
$227$			4.56799e6i			0.390524i	0.980751	+	0.195262i	$0.0625557\pi$
$227$			4.56799e6i			0.390524i	−0.980751	+	0.195262i	$0.937444\pi$
$228$		0			0
$229$	−1.88839e7			−1.57248			−0.786240	−	0.617922i	$-0.787975\pi$
$229$	−1.88839e7			−1.57248			−0.786240	+	0.617922i	$0.787975\pi$
$230$		0			0
$231$	−5.90041e6	−	7.03183e6i	−0.478681	−	0.570469i
$232$		0			0
$233$	−1.15903e7	−	4.21852e6i	−0.916276	−	0.333497i	−0.159520	−	0.987195i	$-0.550995\pi$
$233$	−1.15903e7	−	4.21852e6i	−0.916276	−	0.333497i	−0.756756	+	0.653697i	$0.773217\pi$
$234$		0			0
$235$	1.33423e6	−	2.31096e6i	0.102808	−	0.178069i
$236$		0			0
$237$	−1.27602e6	+	7.23669e6i	−0.0958548	+	0.543619i
$238$		0			0
$239$	−7.25128e6	−	1.25596e7i	−0.531154	−	0.919987i	−0.999339	−	0.0363558i	$-0.988425\pi$
$239$	−7.25128e6	−	1.25596e7i	−0.531154	−	0.919987i	0.468184	−	0.883631i	$-0.344908\pi$
$240$		0			0
$241$	3.82187e6	−	4.55473e6i	0.273039	−	0.325395i	−0.612048	−	0.790821i	$-0.709654\pi$
$241$	3.82187e6	−	4.55473e6i	0.273039	−	0.325395i	0.885087	+	0.465425i	$0.154099\pi$
$242$		0			0
$243$	−940979.	−	2.58532e6i	−0.0655784	−	0.180175i
$244$		0			0
$245$	−89625.9	−	508294.i	−0.00609446	−	0.0345634i
$246$		0			0
$247$	−1.00775e6	+	9.33701e6i	−0.0668745	+	0.619608i
$248$		0			0
$249$	−2.62401e7	+	4.62683e6i	−1.69968	+	0.299699i
$250$		0			0
$251$	1.97392e7	−	7.18448e6i	1.24827	−	0.454333i	0.368453	−	0.929646i	$-0.379887\pi$
$251$	1.97392e7	−	7.18448e6i	1.24827	−	0.454333i	0.879817	+	0.475313i	$0.157665\pi$
$252$		0			0
$253$	−6.53162e6	−	5.48068e6i	−0.403329	−	0.338433i
$254$		0			0
$255$	−6.26202e6	+	3.61538e6i	−0.377654	+	0.218038i
$256$		0			0
$257$	6.94771e6	+	1.22507e6i	0.409300	+	0.0721707i	0.374508	−	0.927224i	$-0.377812\pi$
$257$	6.94771e6	+	1.22507e6i	0.409300	+	0.0721707i	0.0347928	+	0.999395i	$0.488923\pi$
$258$		0			0
$259$	−1.18401e7	−	6.83587e6i	−0.681484	−	0.393455i
$260$		0			0
$261$	−222884.	+	612369.i	−0.0125360	+	0.0344423i
$262$		0			0
$263$	1.95721e7	−	1.64230e7i	1.07590	−	0.902786i	0.0803244	−	0.996769i	$-0.474404\pi$
$263$	1.95721e7	−	1.64230e7i	1.07590	−	0.902786i	0.995574	+	0.0939830i	$0.0299599\pi$
$264$		0			0
$265$		−	2.80982e6i		−	0.150987i
$266$		0			0
$267$	5.61332e6			0.294908
$268$		0			0
$269$	−7.37005e6	−	8.78329e6i	−0.378629	−	0.451232i	0.542752	−	0.839893i	$-0.317382\pi$
$269$	−7.37005e6	−	8.78329e6i	−0.378629	−	0.451232i	−0.921381	+	0.388661i	$0.872938\pi$
$270$		0			0
$271$	1.51840e7	+	5.52651e6i	0.762917	+	0.277679i	0.694030	−	0.719946i	$-0.255833\pi$
$271$	1.51840e7	+	5.52651e6i	0.762917	+	0.277679i	0.0688861	+	0.997625i	$0.478055\pi$
$272$		0			0
$273$	−6.96606e6	+	1.20656e7i	−0.342373	+	0.593008i
$274$		0			0
$275$	2.15388e6	−	1.22152e7i	0.103567	−	0.587360i
$276$		0			0
$277$	1.44052e6	+	2.49506e6i	0.0677767	+	0.117393i	0.897922	−	0.440154i	$-0.145076\pi$
$277$	1.44052e6	+	2.49506e6i	0.0677767	+	0.117393i	−0.830146	+	0.557547i	$0.811743\pi$
$278$		0			0
$279$	2.26160e6	−	2.69527e6i	0.104136	−	0.124105i
$280$		0			0
$281$	2.24951e6	+	6.18047e6i	0.101384	+	0.278549i	0.980006	−	0.198968i	$-0.0637590\pi$
$281$	2.24951e6	+	6.18047e6i	0.101384	+	0.278549i	−0.878622	+	0.477517i	$0.841537\pi$
$282$		0			0
$283$	5.98103e6	+	3.39201e7i	0.263886	+	1.49657i	0.772188	+	0.635394i	$0.219162\pi$
$283$	5.98103e6	+	3.39201e7i	0.263886	+	1.49657i	−0.508302	+	0.861179i	$0.669727\pi$
$284$		0			0
$285$	6.77925e6	+	4.95442e6i	0.292851	+	0.214022i
$286$		0			0
$287$	1.68243e7	−	2.96658e6i	0.711690	−	0.125490i
$288$		0			0
$289$	−1.01018e7	+	3.67675e6i	−0.418508	+	0.152325i
$290$		0			0
$291$	9.07296e6	+	7.61312e6i	0.368188	+	0.308947i
$292$		0			0
$293$	3.74355e7	−	2.16134e7i	1.48827	−	0.859252i	0.488358	−	0.872643i	$-0.337596\pi$
$293$	3.74355e7	−	2.16134e7i	1.48827	−	0.859252i	0.999910	+	0.0133914i	$0.00426275\pi$
$294$		0			0
$295$	−4.46860e6	−	787935.i	−0.174063	−	0.0306919i
$296$		0			0
$297$	−1.45512e7	−	8.40117e6i	−0.555432	−	0.320679i
$298$		0			0
$299$	−4.42611e6	+	1.21606e7i	−0.165580	+	0.454928i
$300$		0			0
$301$	202999.	−	170336.i	0.00744379	−	0.00624608i
$302$		0			0
$303$			1.40449e6i			0.0504884i
$304$		0			0
$305$	−1.93669e6			−0.0682589
$306$		0			0
$307$	178771.	+	213050.i	0.00617847	+	0.00736321i	0.769125	−	0.639099i	$-0.220692\pi$
$307$	178771.	+	213050.i	0.00617847	+	0.00736321i	−0.762946	+	0.646462i	$0.776248\pi$
$308$		0			0
$309$	2.64308e7	+	9.62003e6i	0.895850	+	0.326063i
$310$		0			0
$311$	1.05577e7	−	1.82864e7i	0.350983	−	0.607920i	−0.635439	−	0.772151i	$-0.719181\pi$
$311$	1.05577e7	−	1.82864e7i	0.350983	−	0.607920i	0.986422	+	0.164231i	$0.0525142\pi$
$312$		0			0
$313$	1.65039e6	−	9.35984e6i	0.0538213	−	0.305236i	−0.945999	−	0.324168i	$-0.894916\pi$
$313$	1.65039e6	−	9.35984e6i	0.0538213	−	0.305236i	0.999821	+	0.0189324i	$0.00602672\pi$
$314$		0			0
$315$	546549.	+	946651.i	0.0174863	+	0.0302871i
$316$		0			0
$317$	1.11490e7	−	1.32868e7i	0.349991	−	0.417103i	−0.562114	−	0.827060i	$-0.690012\pi$
$317$	1.11490e7	−	1.32868e7i	0.349991	−	0.417103i	0.912105	+	0.409957i	$0.134456\pi$
$318$		0			0
$319$	2.86726e6	+	7.87774e6i	0.0883274	+	0.242678i
$320$		0			0
$321$	8.57811e6	+	4.86489e7i	0.259344	+	1.47081i
$322$		0			0
$323$	2.80613e7	+	2.92213e7i	0.832722	+	0.867145i
$324$		0			0
$325$	−1.85398e7	+	3.26907e6i	−0.540077	+	0.0952301i
$326$		0			0
$327$	−1.81226e7	+	6.59609e6i	−0.518296	+	0.188644i
$328$		0			0
$329$	−1.69912e7	−	1.42573e7i	−0.477129	−	0.400359i
$330$		0			0
$331$	−3.84726e7	+	2.22121e7i	−1.06088	+	0.612500i	−0.925676	−	0.378317i	$-0.876503\pi$
$331$	−3.84726e7	+	2.22121e7i	−1.06088	+	0.612500i	−0.135206	+	0.990818i	$0.543170\pi$
$332$		0			0
$333$	2.62300e6	+	462505.i	0.0710338	+	0.0125252i
$334$		0			0
$335$	1.89327e7	+	1.09308e7i	0.503592	+	0.290749i
$336$		0			0
$337$	−1.16766e7	+	3.20812e7i	−0.305089	+	0.838226i	0.688506	+	0.725231i	$0.258267\pi$
$337$	−1.16766e7	+	3.20812e7i	−0.305089	+	0.838226i	−0.993595	+	0.112996i	$0.963955\pi$
$338$		0			0
$339$	−7.65262e6	+	6.42131e6i	−0.196431	+	0.164826i
$340$		0			0
$341$		−	4.52623e7i		−	1.14149i
$342$		0			0
$343$	3.80582e7			0.943118
$344$		0			0
$345$	7.43744e6	+	8.86359e6i	0.181120	+	0.215850i
$346$		0			0
$347$	7.27757e7	+	2.64882e7i	1.74180	+	0.633963i	0.999354	−	0.0359455i	$-0.0114443\pi$
$347$	7.27757e7	+	2.64882e7i	1.74180	+	0.633963i	0.742444	+	0.669908i	$0.233666\pi$
$348$		0			0
$349$	1.09690e7	−	1.89989e7i	0.258043	−	0.446944i	−0.707675	−	0.706538i	$-0.750256\pi$
$349$	1.09690e7	−	1.89989e7i	0.258043	−	0.446944i	0.965718	+	0.259595i	$0.0835891\pi$
$350$		0			0
$351$	−4.42836e6	+	2.51145e7i	−0.102405	+	0.580768i
$352$		0			0
$353$	−3.78160e7	−	6.54992e7i	−0.859708	−	1.48906i	−0.872207	−	0.489136i	$-0.837312\pi$
$353$	−3.78160e7	−	6.54992e7i	−0.859708	−	1.48906i	0.0124990	−	0.999922i	$-0.496021\pi$
$354$		0			0
$355$	−6.11308e6	+	7.28528e6i	−0.136639	+	0.162840i
$356$		0			0
$357$	2.05562e7	+	5.64777e7i	0.451792	+	1.24129i
$358$		0			0
$359$	−1.35791e7	−	7.70110e7i	−0.293487	−	1.66445i	−0.673290	−	0.739378i	$-0.735120\pi$
$359$	−1.35791e7	−	7.70110e7i	−0.293487	−	1.66445i	0.379804	−	0.925067i	$-0.375992\pi$
$360$		0			0
$361$	1.78672e7	−	4.35210e7i	0.379782	−	0.925076i
$362$		0			0
$363$	−2.66634e7	+	4.70148e6i	−0.557437	+	0.0982911i
$364$		0			0
$365$	3.99374e6	−	1.45360e6i	0.0821298	−	0.0298928i
$366$		0			0
$367$	−4.41039e7	−	3.70076e7i	−0.892234	−	0.748673i	0.0764231	−	0.997075i	$-0.475650\pi$
$367$	−4.41039e7	−	3.70076e7i	−0.892234	−	0.748673i	−0.968657	+	0.248402i	$0.920094\pi$
$368$		0			0
$369$	−2.88229e6	+	1.66409e6i	−0.0573666	+	0.0331206i
$370$		0			0
$371$	−2.30005e7	−	4.05561e6i	−0.450417	−	0.0794207i
$372$		0			0
$373$	8.82867e6	+	5.09723e6i	0.170125	+	0.0982218i	0.582645	−	0.812727i	$-0.302018\pi$
$373$	8.82867e6	+	5.09723e6i	0.170125	+	0.0982218i	−0.412520	+	0.910949i	$0.635351\pi$
$374$		0			0
$375$	−1.22991e7	+	3.37914e7i	−0.233227	+	0.640785i
$376$		0			0
$377$	9.74705e6	−	8.17874e6i	0.181907	−	0.152638i
$378$		0			0
$379$		−	5.59727e7i		−	1.02815i	−0.857744	−	0.514077i	$-0.828134\pi$
$379$		−	5.59727e7i		−	1.02815i	0.857744	−	0.514077i	$-0.171866\pi$
$380$		0			0
$381$	−2.85326e6			−0.0515901
$382$		0			0
$383$	−1.29810e7	−	1.54701e7i	−0.231053	−	0.275358i	0.638044	−	0.770000i	$-0.279744\pi$
$383$	−1.29810e7	−	1.54701e7i	−0.231053	−	0.275358i	−0.869097	+	0.494642i	$0.835299\pi$
$384$		0			0
$385$	1.32140e7	+	4.80949e6i	0.231553	+	0.0842786i
$386$		0			0
$387$	−25812.6	+	44708.8i	−0.000445348	+	0.000771365i
$388$		0			0
$389$	−4.62894e6	+	2.62520e7i	−0.0786381	+	0.445979i	0.919911	+	0.392128i	$0.128261\pi$
$389$	−4.62894e6	+	2.62520e7i	−0.0786381	+	0.445979i	−0.998549	+	0.0538514i	$0.982850\pi$
$390$		0			0
$391$	2.79135e7	+	4.83476e7i	0.466964	+	0.808806i
$392$		0			0
$393$	1.13696e7	−	1.35498e7i	0.187313	−	0.223231i
$394$		0			0
$395$	−3.85011e6	−	1.05781e7i	−0.0624715	−	0.171639i
$396$		0			0
$397$	−2.16627e6	−	1.22855e7i	−0.0346212	−	0.196346i	0.962592	−	0.270956i	$-0.0873399\pi$
$397$	−2.16627e6	−	1.22855e7i	−0.0346212	−	0.196346i	−0.997213	+	0.0746100i	$0.976229\pi$
$398$		0			0
$399$	5.03407e7	−	4.83423e7i	0.792502	−	0.761042i
$400$		0			0
$401$	−1.24567e8	+	2.19646e7i	−1.93184	+	0.340635i	−0.999766	−	0.0216372i	$-0.993112\pi$
$401$	−1.24567e8	+	2.19646e7i	−1.93184	+	0.340635i	−0.932072	+	0.362272i	$0.882001\pi$
$402$		0			0
$403$	−6.45543e7	+	2.34959e7i	−0.986303	+	0.358985i
$404$		0			0
$405$	1.91626e7	+	1.60794e7i	0.288463	+	0.242049i
$406$		0			0
$407$	2.96733e7	−	1.71319e7i	0.440132	−	0.254110i
$408$		0			0
$409$	−1.23587e8	−	2.17918e7i	−1.80636	−	0.318510i	−0.833960	−	0.551825i	$-0.813932\pi$
$409$	−1.23587e8	−	2.17918e7i	−1.80636	−	0.318510i	−0.972401	+	0.233315i	$0.925043\pi$
$410$		0			0
$411$	−1.12150e8	−	6.47501e7i	−1.61538	−	0.932642i
$412$		0			0
$413$	−1.28997e7	+	3.54416e7i	−0.183117	+	0.503110i
$414$		0			0
$415$	3.12681e7	−	2.62370e7i	0.437478	−	0.367088i
$416$		0			0
$417$			5.23262e7i			0.721624i
$418$		0			0
$419$	−7.88780e7			−1.07229			−0.536147	−	0.844125i	$-0.680121\pi$
$419$	−7.88780e7			−1.07229			−0.536147	+	0.844125i	$0.680121\pi$
$420$		0			0
$421$	3.85619e7	+	4.59563e7i	0.516788	+	0.615884i	0.959818	−	0.280623i	$-0.0905410\pi$
$421$	3.85619e7	+	4.59563e7i	0.516788	+	0.615884i	−0.443030	+	0.896507i	$0.646097\pi$
$422$		0			0
$423$	4.06048e6	+	1.47789e6i	0.0536484	+	0.0195264i
$424$		0			0
$425$	−4.06067e7	+	7.03329e7i	−0.528970	+	0.916203i
$426$		0			0
$427$	−2.79535e6	+	1.58532e7i	−0.0359049	+	0.203627i
$428$		0			0
$429$	−1.74582e7	−	3.02384e7i	−0.221119	−	0.382990i
$430$		0			0
$431$	5.40562e7	−	6.44217e7i	0.675171	−	0.804638i	−0.314307	−	0.949321i	$-0.601772\pi$
$431$	5.40562e7	−	6.44217e7i	0.675171	−	0.804638i	0.989478	+	0.144684i	$0.0462165\pi$
$432$		0			0
$433$	1.79027e6	+	4.91872e6i	0.0220523	+	0.0605882i	0.950230	−	0.311548i	$-0.100848\pi$
$433$	1.79027e6	+	4.91872e6i	0.0220523	+	0.0605882i	−0.928178	+	0.372136i	$0.878625\pi$
$434$		0			0
$435$	−1.97549e6	−	1.12036e7i	−0.0239998	−	0.136109i
$436$		0			0
$437$	3.82519e7	−	5.23410e7i	0.458362	−	0.627188i
$438$		0			0
$439$	3.02929e7	−	5.34146e6i	0.358054	−	0.0631345i	0.00827199	−	0.999966i	$-0.497367\pi$
$439$	3.02929e7	−	5.34146e6i	0.358054	−	0.0631345i	0.349782	+	0.936831i	$0.386256\pi$
$440$		0			0
$441$	785378.	−	285854.i	0.00915721	−	0.00333295i
$442$		0			0
$443$	−7.29809e7	−	6.12383e7i	−0.839456	−	0.704388i	0.117985	−	0.993015i	$-0.462357\pi$
$443$	−7.29809e7	−	6.12383e7i	−0.839456	−	0.704388i	−0.957441	+	0.288628i	$0.906801\pi$
$444$		0			0
$445$	−7.44705e6	+	4.29955e6i	−0.0845092	+	0.0487914i
$446$		0			0
$447$	−1.76046e8	−	3.10417e7i	−1.97108	−	0.347555i
$448$		0			0
$449$	4.51922e7	+	2.60917e7i	0.499257	+	0.288246i	0.728407	−	0.685145i	$-0.240261\pi$
$449$	4.51922e7	+	2.60917e7i	0.499257	+	0.288246i	−0.229149	+	0.973391i	$0.573594\pi$
$450$		0			0
$451$	−1.46436e7	+	4.02330e7i	−0.159631	+	0.438584i
$452$		0			0
$453$	1.23567e8	−	1.03685e8i	1.32925	−	1.11538i
$454$		0			0
$455$		−	2.13428e7i		−	0.226577i
$456$		0			0
$457$	9.86379e7			1.03346			0.516732	−	0.856147i	$-0.327148\pi$
$457$	9.86379e7			1.03346			0.516732	+	0.856147i	$0.327148\pi$
$458$		0			0
$459$	7.07154e7	+	8.42753e7i	0.731267	+	0.871490i
$460$		0			0
$461$	1.65163e8	+	6.01143e7i	1.68581	+	0.613586i	0.994088	−	0.108576i	$-0.0346291\pi$
$461$	1.65163e8	+	6.01143e7i	1.68581	+	0.613586i	0.691724	+	0.722162i	$0.256851\pi$
$462$		0			0
$463$	−6.33406e7	+	1.09709e8i	−0.638174	+	1.10535i	0.347659	+	0.937621i	$0.386977\pi$
$463$	−6.33406e7	+	1.09709e8i	−0.638174	+	1.10535i	−0.985833	+	0.167729i	$0.946357\pi$
$464$		0			0
$465$	−1.06658e7	+	6.04890e7i	−0.106081	+	0.601614i
$466$		0			0
$467$	3.61434e7	+	6.26021e7i	0.354877	+	0.614665i	0.987097	−	0.160124i	$-0.0511894\pi$
$467$	3.61434e7	+	6.26021e7i	0.354877	+	0.614665i	−0.632220	+	0.774789i	$0.717856\pi$
$468$		0			0
$469$	1.16804e8	−	1.39202e8i	1.13224	−	1.34935i
$470$		0			0
$471$	3.18334e7	+	8.74615e7i	0.304663	+	0.837055i
$472$		0			0
$473$	115324.	+	654037.i	0.00108978	+	0.00618043i
$474$		0			0
$475$	9.37643e7	+	1.01200e7i	0.874897	+	0.0944279i
$476$		0			0
$477$	4.48084e6	−	790093.i	0.0412861	−	0.00727986i
$478$		0			0
$479$	4.67863e7	−	1.70288e7i	0.425709	−	0.154945i	−0.120276	−	0.992741i	$-0.538378\pi$
$479$	4.67863e7	−	1.70288e7i	0.425709	−	0.154945i	0.545985	+	0.837795i	$0.316156\pi$
$480$		0			0
$481$	−3.98375e7	−	3.34276e7i	−0.357978	−	0.300380i
$482$		0			0
$483$	8.32902e7	−	4.80876e7i	0.739184	−	0.426768i
$484$		0			0
$485$	−1.78682e7	−	3.15064e6i	−0.156623	−	0.0276168i
$486$		0			0
$487$	−1.23024e7	−	7.10279e6i	−0.106513	−	0.0614953i	0.445797	−	0.895134i	$-0.352920\pi$
$487$	−1.23024e7	−	7.10279e6i	−0.106513	−	0.0614953i	−0.552310	+	0.833639i	$0.686254\pi$
$488$		0			0
$489$	−2.74517e7	+	7.54230e7i	−0.234770	+	0.645026i
$490$		0			0
$491$	1.51913e6	−	1.27470e6i	0.0128336	−	0.0107687i	−0.636348	−	0.771402i	$-0.719556\pi$
$491$	1.51913e6	−	1.27470e6i	0.0128336	−	0.0107687i	0.649182	+	0.760633i	$0.275111\pi$
$492$		0			0
$493$		−	5.48899e7i		−	0.458091i
$494$		0			0
$495$	−2.73949e6			−0.0225868
$496$		0			0
$497$	5.08121e7	+	6.05555e7i	0.413903	+	0.493270i
$498$		0			0
$499$	8.64256e7	+	3.14564e7i	0.695570	+	0.253167i	0.665518	−	0.746382i	$-0.268211\pi$
$499$	8.64256e7	+	3.14564e7i	0.695570	+	0.253167i	0.0300518	+	0.999548i	$0.490433\pi$
$500$		0			0
$501$	6.15032e7	−	1.06527e8i	0.489085	−	0.847120i
$502$		0			0
$503$	−2.29460e7	+	1.30133e8i	−0.180303	+	1.02255i	0.751539	+	0.659688i	$0.229312\pi$
$503$	−2.29460e7	+	1.30133e8i	−0.180303	+	1.02255i	−0.931843	+	0.362862i	$0.881799\pi$
$504$		0			0
$505$	−1.07578e6	−	1.86330e6i	−0.00835311	−	0.0144680i
$506$		0			0
$507$	5.36429e7	−	6.39291e7i	0.411612	−	0.490540i
$508$		0			0
$509$	6.27988e7	+	1.72538e8i	0.476210	+	1.30838i	0.912687	+	0.408660i	$0.134004\pi$
$509$	6.27988e7	+	1.72538e8i	0.476210	+	1.30838i	−0.436477	+	0.899715i	$0.643774\pi$
$510$		0			0
$511$	−6.13439e6	−	3.47899e7i	−0.0459736	−	0.260729i
$512$		0			0
$513$	5.63239e7	−	1.14667e8i	0.417196	−	0.849348i
$514$		0			0
$515$	−4.24336e7	+	7.48219e6i	−0.310662	+	0.0547781i
$516$		0			0
$517$	5.22355e7	−	1.90122e7i	0.378002	−	0.137582i
$518$		0			0
$519$	−2.07496e8	−	1.74110e8i	−1.48425	−	1.24543i
$520$		0			0
$521$	−6.99790e7	+	4.04024e7i	−0.494829	+	0.285689i	−0.726575	−	0.687087i	$-0.758889\pi$
$521$	−6.99790e7	+	4.04024e7i	−0.494829	+	0.285689i	0.231747	+	0.972776i	$0.425556\pi$
$522$		0			0
$523$	−1.73842e8	−	3.06531e7i	−1.21521	−	0.214274i	−0.470946	−	0.882162i	$-0.656088\pi$
$523$	−1.73842e8	−	3.06531e7i	−1.21521	−	0.214274i	−0.744262	+	0.667888i	$0.767199\pi$
$524$		0			0
$525$	1.21165e8	+	6.99547e7i	0.837336	+	0.483436i
$526$		0			0
$527$	−1.01360e8	+	2.78483e8i	−0.692521	+	1.90269i
$528$		0			0
$529$	−4.49684e7	+	3.77329e7i	−0.303767	+	0.254891i
$530$		0			0
$531$		−	7.34768e6i		−	0.0490757i
$532$		0			0
$533$	6.49829e7			0.429159
$534$		0			0
$535$	−4.86432e7	−	5.79707e7i	−0.317659	−	0.378571i
$536$		0			0
$537$	7.59515e7	+	2.76441e7i	0.490471	+	0.178517i
$538$		0			0
$539$	5.37591e6	−	9.31135e6i	0.0343309	−	0.0594629i
$540$		0			0
$541$	−1.13037e7	+	6.41063e7i	−0.0713885	+	0.404864i	0.928084	+	0.372372i	$0.121455\pi$
$541$	−1.13037e7	+	6.41063e7i	−0.0713885	+	0.404864i	−0.999472	+	0.0324920i	$0.989656\pi$
$542$		0			0
$543$	−7.84903e7	−	1.35949e8i	−0.490249	−	0.849136i
$544$		0			0
$545$	1.89905e7	−	2.26320e7i	0.117313	−	0.139808i
$546$		0			0
$547$	9.74719e7	+	2.67802e8i	0.595549	+	1.63626i	0.760038	+	0.649879i	$0.225180\pi$
$547$	9.74719e7	+	2.67802e8i	0.595549	+	1.63626i	−0.164489	+	0.986379i	$0.552597\pi$
$548$		0			0
$549$	−544577.	−	3.08845e6i	−0.00329111	−	0.0186648i
$550$		0			0
$551$	−5.83024e7	+	2.57629e7i	−0.348523	+	0.154007i
$552$		0			0
$553$	−9.21469e7	+	1.62480e7i	−0.544886	+	0.0960780i
$554$		0			0
$555$	−4.36928e7	+	1.59029e7i	−0.255582	+	0.0930243i
$556$		0			0
$557$	1.54226e8	+	1.29411e8i	0.892466	+	0.748868i	0.968703	−	0.248222i	$-0.0798461\pi$
$557$	1.54226e8	+	1.29411e8i	0.892466	+	0.748868i	−0.0762369	+	0.997090i	$0.524291\pi$
$558$		0			0
$559$	872940.	−	503992.i	0.00499746	−	0.00288528i
$560$		0			0
$561$	−1.48338e8	−	2.61561e7i	−0.840166	−	0.148144i
$562$		0			0
$563$	−2.50670e8	−	1.44724e8i	−1.40468	−	0.810991i	−0.409810	−	0.912171i	$-0.634405\pi$
$563$	−2.50670e8	−	1.44724e8i	−1.40468	−	0.810991i	−0.994868	+	0.101179i	$0.967738\pi$
$564$		0			0
$565$	5.23409e6	−	1.43805e7i	0.0290199	−	0.0797315i
$566$		0			0
$567$	1.59280e8	−	1.33652e8i	0.873803	−	0.733208i
$568$		0			0
$569$		−	2.25654e8i		−	1.22492i	−0.790503	−	0.612458i	$-0.790181\pi$
$569$		−	2.25654e8i		−	1.22492i	0.790503	−	0.612458i	$-0.209819\pi$
$570$		0			0
$571$	1.09355e8			0.587393			0.293696	−	0.955899i	$-0.405115\pi$
$571$	1.09355e8			0.587393			0.293696	+	0.955899i	$0.405115\pi$
$572$		0			0
$573$	−9.13833e7	−	1.08906e8i	−0.485739	−	0.578881i
$574$		0			0
$575$	1.22120e8	+	4.44479e7i	0.642365	+	0.233802i
$576$		0			0
$577$	−4.18129e6	+	7.24221e6i	−0.0217662	+	0.0377002i	−0.876703	−	0.481031i	$-0.840262\pi$
$577$	−4.18129e6	+	7.24221e6i	−0.0217662	+	0.0377002i	0.854937	+	0.518732i	$0.173596\pi$
$578$		0			0
$579$	4.09018e7	−	2.31966e8i	0.210721	−	1.19506i
$580$		0			0
$581$	−1.69639e8	−	2.93823e8i	−0.864960	−	1.49816i
$582$		0			0
$583$	3.76239e7	−	4.48384e7i	0.189871	−	0.226279i
$584$		0			0
$585$	1.42208e6	+	3.90714e6i	0.00710325	+	0.0195160i
$586$		0			0
$587$	3.46622e7	+	1.96579e8i	0.171373	+	0.971904i	0.942248	+	0.334917i	$0.108708\pi$
$587$	3.46622e7	+	1.96579e8i	0.171373	+	0.971904i	−0.770875	+	0.636987i	$0.780181\pi$
$588$		0			0
$589$	3.43370e8	−	2.30468e7i	1.68041	−	0.112788i
$590$		0			0
$591$	−7.48655e7	+	1.32008e7i	−0.362676	+	0.0639496i
$592$		0			0
$593$	−2.92834e8	+	1.06583e8i	−1.40429	+	0.511121i	−0.929450	−	0.368949i	$-0.879718\pi$
$593$	−2.92834e8	+	1.06583e8i	−1.40429	+	0.511121i	−0.474844	+	0.880070i	$0.657495\pi$
$594$		0			0
$595$	−7.05307e7	−	5.91823e7i	−0.334832	−	0.280958i
$596$		0			0
$597$	−1.23939e8	+	7.15560e7i	−0.582483	+	0.336297i
$598$		0			0
$599$	2.09749e7	+	3.69843e6i	0.0975929	+	0.0172083i	0.222231	−	0.974994i	$-0.428666\pi$
$599$	2.09749e7	+	3.69843e6i	0.0975929	+	0.0172083i	−0.124638	+	0.992202i	$0.539777\pi$
$600$		0			0
$601$	−2.61565e8	−	1.51015e8i	−1.20492	−	0.695658i	−0.243271	−	0.969958i	$-0.578221\pi$
$601$	−2.61565e8	−	1.51015e8i	−1.20492	−	0.695658i	−0.961644	+	0.274300i	$0.911554\pi$
$602$		0			0
$603$	−1.21078e7	+	3.32658e7i	−0.0552220	+	0.151721i
$604$		0			0
$605$	3.17725e7	−	2.66603e7i	0.143478	−	0.120392i
$606$		0			0
$607$			1.69817e8i			0.759301i	0.925130	+	0.379650i	$0.123956\pi$
$607$			1.69817e8i			0.759301i	−0.925130	+	0.379650i	$0.876044\pi$
$608$		0			0
$609$	−9.45610e7			−0.418659
$610$		0			0
$611$	−5.42314e7	−	6.46305e7i	−0.237754	−	0.283344i
$612$		0			0
$613$	9.88419e7	+	3.59755e7i	0.429101	+	0.156180i	0.547537	−	0.836782i	$-0.315566\pi$
$613$	9.88419e7	+	3.59755e7i	0.429101	+	0.156180i	−0.118436	+	0.992962i	$0.537788\pi$
$614$		0			0
$615$	2.90506e7	−	5.03171e7i	0.124891	−	0.216317i
$616$		0			0
$617$	−1.91970e7	+	1.08872e8i	−0.0817294	+	0.463510i	0.916285	+	0.400526i	$0.131173\pi$
$617$	−1.91970e7	+	1.08872e8i	−0.0817294	+	0.463510i	−0.998015	+	0.0629838i	$0.979938\pi$
$618$		0			0
$619$	−1.78705e8	−	3.09526e8i	−0.753467	−	1.30504i	−0.946133	−	0.323779i	$-0.895047\pi$
$619$	−1.78705e8	−	3.09526e8i	−0.753467	−	1.30504i	0.192666	−	0.981264i	$-0.438287\pi$
$620$		0			0
$621$	1.13158e8	−	1.34857e8i	0.472510	−	0.563116i
$622$		0			0
$623$	2.44463e7	+	6.71656e7i	0.101099	+	0.277768i
$624$		0			0
$625$	2.77404e7	+	1.57324e8i	0.113625	+	0.644398i
$626$		0			0
$627$	4.18414e7	+	1.69837e8i	0.169747	+	0.689016i
$628$		0			0
$629$	−2.20934e8	+	3.89567e7i	−0.887792	+	0.156542i
$630$		0			0
$631$	9.88954e7	−	3.59950e7i	0.393630	−	0.143270i	−0.137619	−	0.990485i	$-0.543945\pi$
$631$	9.88954e7	−	3.59950e7i	0.393630	−	0.143270i	0.531249	+	0.847216i	$0.321723\pi$
$632$		0			0
$633$	−3.00081e8	−	2.51797e8i	−1.18311	−	0.992751i
$634$		0			0
$635$	3.78534e6	−	2.18547e6i	0.0147837	−	0.00853539i
$636$		0			0
$637$	−1.60708e7	−	2.83371e6i	−0.0621753	−	0.0109632i
$638$		0			0
$639$	−1.33368e7	−	7.70003e6i	−0.0511152	−	0.0295114i
$640$		0			0
$641$	−1.71073e8	+	4.70019e8i	−0.649542	+	1.78460i	−0.0301171	+	0.999546i	$0.509588\pi$
$641$	−1.71073e8	+	4.70019e8i	−0.649542	+	1.78460i	−0.619425	+	0.785056i	$0.712634\pi$
$642$		0			0
$643$	3.76968e8	−	3.16314e8i	1.41799	−	1.18983i	0.465578	−	0.885007i	$-0.345846\pi$
$643$	3.76968e8	−	3.16314e8i	1.41799	−	1.18983i	0.952408	−	0.304825i	$-0.0985980\pi$
$644$		0			0
$645$		−	901238.i		−	0.00335862i
$646$		0			0
$647$	−3.22687e8			−1.19143			−0.595716	−	0.803195i	$-0.703132\pi$
$647$	−3.22687e8			−1.19143			−0.595716	+	0.803195i	$0.703132\pi$
$648$		0			0
$649$	−6.07584e7	−	7.24090e7i	−0.222265	−	0.264886i
$650$		0			0
$651$	4.79754e8	+	1.74616e8i	1.73890	+	0.632909i
$652$		0			0
$653$	−2.25243e8	+	3.90133e8i	−0.808932	+	1.40111i	0.104672	+	0.994507i	$0.466621\pi$
$653$	−2.25243e8	+	3.90133e8i	−0.808932	+	1.40111i	−0.913604	+	0.406605i	$0.866713\pi$
$654$		0			0
$655$	−4.70523e6	+	2.66847e7i	−0.0167439	+	0.0949595i
$656$		0			0
$657$	3.44107e6	+	5.96011e6i	0.0121338	+	0.0210164i
$658$		0			0
$659$	1.19731e7	−	1.42690e7i	0.0418360	−	0.0498582i	−0.744721	−	0.667376i	$-0.767417\pi$
$659$	1.19731e7	−	1.42690e7i	0.0418360	−	0.0498582i	0.786557	+	0.617518i	$0.211862\pi$
$660$		0			0
$661$	−1.63569e8	−	4.49401e8i	−0.566364	−	1.55607i	−0.810137	−	0.586240i	$-0.800608\pi$
$661$	−1.63569e8	−	4.49401e8i	−0.566364	−	1.55607i	0.243773	−	0.969832i	$-0.421615\pi$
$662$		0			0
$663$	3.96986e7	+	2.25142e8i	0.136218	+	0.772531i
$664$		0			0
$665$	−2.97576e7	+	1.02693e8i	−0.101189	+	0.349202i
$666$		0			0
$667$	−8.65001e7	+	1.52523e7i	−0.291500	+	0.0513994i
$668$		0			0
$669$	4.06387e8	−	1.47913e8i	1.35726	−	0.494001i
$670$		0			0
$671$	−3.09052e7	−	2.59325e7i	−0.102297	−	0.0858376i
$672$		0			0
$673$	−3.09972e8	+	1.78963e8i	−1.01690	+	0.587107i	−0.913204	−	0.407503i	$-0.866400\pi$
$673$	−3.09972e8	+	1.78963e8i	−1.01690	+	0.587107i	−0.103694	+	0.994609i	$0.533066\pi$
$674$		0			0
$675$	2.52205e8	+	4.44706e7i	0.820054	+	0.144598i
$676$		0			0
$677$	−1.56997e8	−	9.06421e7i	−0.505970	−	0.292122i	0.225206	−	0.974311i	$-0.427695\pi$
$677$	−1.56997e8	−	9.06421e7i	−0.505970	−	0.292122i	−0.731175	+	0.682190i	$0.761028\pi$
$678$		0			0
$679$	−5.15807e7	+	1.41717e8i	−0.164770	+	0.452702i
$680$		0			0
$681$	9.89205e7	−	8.30041e7i	0.313217	−	0.262820i
$682$		0			0
$683$		−	3.01027e8i		−	0.944808i	−0.881382	−	0.472404i	$-0.843386\pi$
$683$		−	3.01027e8i		−	0.944808i	0.881382	−	0.472404i	$-0.156614\pi$
$684$		0			0
$685$	1.98383e8			0.617209
$686$		0			0
$687$	3.43136e8	+	4.08933e8i	1.05827	+	1.26120i
$688$		0			0
$689$	−8.34806e7	−	3.03844e7i	−0.255228	−	0.0928953i
$690$		0			0
$691$	3.20424e8	−	5.54991e8i	0.971162	−	1.68210i	0.279101	−	0.960262i	$-0.409963\pi$
$691$	3.20424e8	−	5.54991e8i	0.971162	−	1.68210i	0.692060	−	0.721840i	$-0.256703\pi$
$692$		0			0
$693$	−3.95410e6	+	2.24248e7i	−0.0118809	+	0.0673797i
$694$		0			0
$695$	−4.00795e7	−	6.94198e7i	−0.119390	−	0.206790i
$696$		0			0
$697$	1.80194e8	−	2.14747e8i	0.532160	−	0.634204i
$698$		0			0
$699$	1.19252e8	+	3.27643e8i	0.349169	+	0.959334i
$700$		0			0
$701$	7.74532e7	+	4.39259e8i	0.224846	+	1.27517i	0.862979	+	0.505239i	$0.168596\pi$
$701$	7.74532e7	+	4.39259e8i	0.224846	+	1.27517i	−0.638133	+	0.769926i	$0.720293\pi$
$702$		0			0
$703$	1.45075e8	+	2.16385e8i	0.417569	+	0.622818i
$704$		0			0
$705$	−7.42883e7	+	1.30990e7i	−0.212008	+	0.0373828i
$706$		0			0
$707$	−1.68053e7	+	6.11662e6i	−0.0475540	+	0.0173083i
$708$		0			0
$709$	2.19435e8	+	1.84127e8i	0.615696	+	0.516630i	0.896447	−	0.443150i	$-0.146139\pi$
$709$	2.19435e8	+	1.84127e8i	0.615696	+	0.516630i	−0.280751	+	0.959781i	$0.590584\pi$
$710$		0			0
$711$	1.57864e7	−	9.11426e6i	0.0439211	−	0.0253579i
$712$		0			0
$713$	4.67022e8	+	8.23485e7i	1.28845	+	0.227189i
$714$		0			0
$715$	4.63225e7	+	2.67443e7i	0.126728	+	0.0731667i
$716$		0			0
$717$	−1.40218e8	+	3.85246e8i	−0.380405	+	1.04515i
$718$		0			0
$719$	4.84586e8	−	4.06616e8i	1.30372	−	1.09395i	0.314231	−	0.949346i	$-0.398253\pi$
$719$	4.84586e8	−	4.06616e8i	1.30372	−	1.09395i	0.989489	−	0.144605i	$-0.0461912\pi$
$720$		0			0
$721$			3.58151e8i			0.955564i
$722$		0			0
$723$	−1.68080e8			−0.444735
$724$		0			0
$725$	−8.21327e7	−	9.78820e7i	−0.215527	−	0.256855i
$726$		0			0
$727$	1.48118e8	+	5.39107e7i	0.385484	+	0.140305i	0.527490	−	0.849561i	$-0.323133\pi$
$727$	1.48118e8	+	5.39107e7i	0.385484	+	0.140305i	−0.142007	+	0.989866i	$0.545355\pi$
$728$		0			0
$729$	1.71664e8	−	2.97331e8i	0.443096	−	0.767464i
$730$		0			0
$731$	755088.	−	4.28232e6i	0.00193306	−	0.0109629i
$732$		0			0
$733$	−2.93269e8	−	5.07956e8i	−0.744652	−	1.28978i	−0.950357	−	0.311162i	$-0.899282\pi$
$733$	−2.93269e8	−	5.07956e8i	−0.744652	−	1.28978i	0.205705	−	0.978614i	$-0.434051\pi$
$734$		0			0
$735$	−9.37860e6	+	1.11770e7i	−0.0236198	+	0.0281490i
$736$		0			0
$737$	1.55759e8	+	4.27944e8i	0.389090	+	1.06902i
$738$		0			0
$739$	−1.08543e7	−	6.15578e7i	−0.0268948	−	0.152528i	0.968403	−	0.249391i	$-0.0802303\pi$
$739$	−1.08543e7	−	6.15578e7i	−0.0268948	−	0.152528i	−0.995298	+	0.0968627i	$0.969119\pi$
$740$		0			0
$741$	2.20506e8	−	1.47838e8i	0.541958	−	0.363356i
$742$		0			0
$743$	7.37754e8	−	1.30086e8i	1.79864	−	0.317150i	0.828557	−	0.559905i	$-0.189162\pi$
$743$	7.37754e8	−	1.30086e8i	1.79864	−	0.317150i	0.970088	+	0.242756i	$0.0780513\pi$
$744$		0			0
$745$	2.57333e8	−	9.36614e7i	0.622338	−	0.226512i
$746$		0			0
$747$	5.06327e7	+	4.24859e7i	0.121470	+	0.101925i
$748$		0			0
$749$	−5.44745e8	+	3.14509e8i	−1.29643	+	0.748492i
$750$		0			0
$751$	−2.56973e8	−	4.53113e7i	−0.606692	−	0.106976i	−0.138141	−	0.990413i	$-0.544113\pi$
$751$	−2.56973e8	−	4.53113e7i	−0.606692	−	0.106976i	−0.468551	+	0.883437i	$0.655224\pi$
$752$		0			0
$753$	−5.14259e8	−	2.96908e8i	−1.20447	−	0.695403i
$754$		0			0
$755$	−8.45150e7	+	2.32203e8i	−0.196378	+	0.539544i
$756$		0			0
$757$	1.66909e8	−	1.40054e8i	0.384763	−	0.322854i	−0.429806	−	0.902921i	$-0.641418\pi$
$757$	1.66909e8	−	1.40054e8i	0.384763	−	0.322854i	0.814569	+	0.580067i	$0.196974\pi$
$758$		0			0
$759$			2.41032e8i			0.551250i
$760$		0			0
$761$	5.96010e7			0.135238			0.0676191	−	0.997711i	$-0.478460\pi$
$761$	5.96010e7			0.135238			0.0676191	+	0.997711i	$0.478460\pi$
$762$		0			0
$763$	−1.57850e8	−	1.88118e8i	−0.355361	−	0.423503i
$764$		0			0
$765$	1.68552e7	+	6.13477e6i	0.0376486	+	0.0137030i
$766$		0			0
$767$	−7.17318e7	+	1.24243e8i	−0.158974	+	0.275351i
$768$		0			0
$769$	8.06199e7	−	4.57218e8i	0.177281	−	1.00541i	−0.758196	−	0.652026i	$-0.773919\pi$
$769$	8.06199e7	−	4.57218e8i	0.177281	−	1.00541i	0.935478	−	0.353386i	$-0.114970\pi$
$770$		0			0
$771$	−9.97166e7	−	1.72714e8i	−0.217573	−	0.376847i
$772$		0			0
$773$	2.45464e8	−	2.92532e8i	0.531434	−	0.633338i	−0.431811	−	0.901964i	$-0.642125\pi$
$773$	2.45464e8	−	2.92532e8i	0.531434	−	0.633338i	0.963244	+	0.268626i	$0.0865697\pi$
$774$		0			0
$775$	2.35951e8	+	6.48269e8i	0.506892	+	1.39268i
$776$		0			0
$777$	6.71122e7	+	3.80612e8i	0.143067	+	0.811372i
$778$		0			0
$779$	−3.12673e8	−	9.06037e7i	−0.661420	−	0.191661i
$780$		0			0
$781$	−1.95102e8	+	3.44018e7i	−0.409552	+	0.0722151i
$782$		0			0
$783$	−1.62650e8	+	5.91997e7i	−0.338819	+	0.123320i
$784$		0			0
$785$	−1.09224e8	−	9.16498e7i	−0.225792	−	0.189462i
$786$		0			0
$787$	2.71653e7	−	1.56839e7i	0.0557302	−	0.0321758i	−0.471876	−	0.881665i	$-0.656423\pi$
$787$	2.71653e7	−	1.56839e7i	0.0557302	−	0.0321758i	0.527606	+	0.849489i	$0.323090\pi$
$788$		0			0
$789$	−7.11284e8	−	1.25419e8i	−1.44815	−	0.255347i
$790$		0			0
$791$	−1.10161e8	−	6.36014e7i	−0.222586	−	0.128510i
$792$		0			0
$793$	−2.09427e7	+	5.75396e7i	−0.0419965	+	0.115384i
$794$		0			0
$795$	−6.08470e7	+	5.10567e7i	−0.121098	+	0.101613i
$796$		0			0
$797$			5.61520e8i			1.10915i	0.832134	+	0.554575i	$0.187119\pi$
$797$			5.61520e8i			1.10915i	−0.832134	+	0.554575i	$0.812881\pi$
$798$		0			0
$799$	−3.63963e8			−0.713538
$800$		0			0
$801$	−8.95057e6	−	1.06669e7i	−0.0174162	−	0.0207558i
$802$		0			0
$803$	8.31951e7	+	3.02805e7i	0.160676	+	0.0584813i
$804$		0			0
$805$	−7.36659e7	+	1.27593e8i	−0.141214	+	0.244591i
$806$		0			0
$807$	−5.62834e7	+	3.19199e8i	−0.107093	+	0.607353i
$808$		0			0
$809$	−4.46354e8	−	7.73108e8i	−0.843013	−	1.46014i	−0.887336	−	0.461124i	$-0.847446\pi$
$809$	−4.46354e8	−	7.73108e8i	−0.843013	−	1.46014i	0.0443231	−	0.999017i	$-0.485887\pi$
$810$		0			0
$811$	−3.67936e8	+	4.38489e8i	−0.689778	+	0.822045i	−0.991329	−	0.131405i	$-0.958051\pi$
$811$	−3.67936e8	+	4.38489e8i	−0.689778	+	0.822045i	0.301551	+	0.953450i	$0.402496\pi$
$812$		0			0
$813$	−1.56228e8	−	4.29232e8i	−0.290728	−	0.798768i
$814$		0			0
$815$	−2.13512e7	−	1.21088e8i	−0.0394411	−	0.223681i
$816$		0			0
$817$	−4.90295e6	+	1.20790e6i	−0.00899065	+	0.00221495i
$818$		0			0
$819$	3.40355e7	−	6.00138e6i	0.0619556	−	0.0109244i
$820$		0			0
$821$	1.02256e8	−	3.72181e7i	0.184781	−	0.0672549i	−0.247972	−	0.968767i	$-0.579764\pi$
$821$	1.02256e8	−	3.72181e7i	0.184781	−	0.0672549i	0.432754	+	0.901512i	$0.357542\pi$
$822$		0			0
$823$	−4.18823e8	−	3.51434e8i	−0.751331	−	0.630442i	0.184524	−	0.982828i	$-0.440926\pi$
$823$	−4.18823e8	−	3.51434e8i	−0.751331	−	0.630442i	−0.935855	+	0.352387i	$0.885370\pi$
$824$		0			0
$825$	−3.03661e8	+	1.75319e8i	−0.540788	+	0.312224i
$826$		0			0
$827$	−2.85266e8	−	5.03000e7i	−0.504351	−	0.0889307i	−0.0843168	−	0.996439i	$-0.526871\pi$
$827$	−2.85266e8	−	5.03000e7i	−0.504351	−	0.0889307i	−0.420034	+	0.907508i	$0.637982\pi$
$828$		0			0
$829$	4.71872e7	+	2.72436e7i	0.0828249	+	0.0478190i	0.540840	−	0.841125i	$-0.318106\pi$
$829$	4.71872e7	+	2.72436e7i	0.0828249	+	0.0478190i	−0.458016	+	0.888944i	$0.651440\pi$
$830$		0			0
$831$	2.78554e7	−	7.65320e7i	0.0485407	−	0.133364i
$832$		0			0
$833$	−5.39278e7	+	4.52508e7i	−0.0932991	+	0.0782873i
$834$		0			0
$835$			1.88435e8i			0.323669i
$836$		0			0
$837$	9.34519e8			1.59372
$838$		0			0
$839$	−5.01275e8	−	5.97396e8i	−0.848770	−	1.01153i	−0.999736	−	0.0229862i	$-0.992683\pi$
$839$	−5.01275e8	−	5.97396e8i	−0.848770	−	1.01153i	0.150965	−	0.988539i	$-0.451762\pi$
$840$		0			0
$841$	−4.77799e8	−	1.73905e8i	−0.803262	−	0.292363i
$842$		0			0
$843$	9.29636e7	−	1.61018e8i	0.155178	−	0.268776i
$844$		0			0
$845$	−2.21997e7	+	1.25901e8i	−0.0367941	+	0.208670i
$846$		0			0
$847$	−1.72375e8	−	2.98563e8i	−0.283677	−	0.491344i
$848$		0			0
$849$	6.25865e8	−	7.45876e8i	1.02272	−	1.21883i
$850$		0			0
$851$	1.22782e8	+	3.37342e8i	0.199226	+	0.547370i
$852$		0			0
$853$	−9.69524e7	−	5.49844e8i	−0.156211	−	0.885916i	−0.957670	−	0.287867i	$-0.907054\pi$
$853$	−9.69524e7	−	5.49844e8i	−0.156211	−	0.885916i	0.801459	−	0.598049i	$-0.204057\pi$
$854$		0			0
$855$	−1.39490e6	−	2.07824e7i	−0.00223175	−	0.0332504i
$856$		0			0
$857$	3.64855e8	−	6.43338e7i	0.579666	−	0.102211i	0.123875	−	0.992298i	$-0.460468\pi$
$857$	3.64855e8	−	6.43338e7i	0.579666	−	0.102211i	0.455791	+	0.890087i	$0.349357\pi$
$858$		0			0
$859$	−1.26302e8	+	4.59702e7i	−0.199265	+	0.0725266i	−0.439725	−	0.898133i	$-0.644924\pi$
$859$	−1.26302e8	+	4.59702e7i	−0.199265	+	0.0725266i	0.240460	+	0.970659i	$0.422702\pi$
$860$		0			0
$861$	−3.69953e8	−	3.10427e8i	−0.579612	−	0.486352i
$862$		0			0
$863$	4.29635e8	−	2.48050e8i	0.668447	−	0.385928i	−0.127041	−	0.991897i	$-0.540548\pi$
$863$	4.29635e8	−	2.48050e8i	0.668447	−	0.385928i	0.795488	+	0.605970i	$0.207215\pi$
$864$		0			0
$865$	4.08639e8	+	7.20542e7i	0.631382	+	0.111330i
$866$		0			0
$867$	2.63178e8	+	1.51946e8i	0.403824	+	0.233148i
$868$		0			0
$869$	8.02032e7	−	2.20357e8i	0.122217	−	0.335789i
$870$		0			0
$871$	5.29491e8	−	4.44295e8i	0.801316	−	0.672384i
$872$		0			0
$873$		−	2.93804e7i		−	0.0441586i
$874$		0			0
$875$	−4.57890e8			−0.683498
$876$		0			0
$877$	5.13057e8	+	6.11437e8i	0.760618	+	0.906469i	0.997887	−	0.0649746i	$-0.0206966\pi$
$877$	5.13057e8	+	6.11437e8i	0.760618	+	0.906469i	−0.237269	+	0.971444i	$0.576252\pi$
$878$		0			0
$879$	−1.14828e9	−	4.17938e8i	−1.69075	−	0.615383i
$880$		0			0
$881$	−5.17847e8	+	8.96937e8i	−0.757310	+	1.31170i	0.186908	+	0.982377i	$0.440153\pi$
$881$	−5.17847e8	+	8.96937e8i	−0.757310	+	1.31170i	−0.944218	+	0.329322i	$0.893180\pi$
$882$		0			0
$883$	−1.60800e8	+	9.11941e8i	−0.233563	+	1.32460i	0.612057	+	0.790813i	$0.290342\pi$
$883$	−1.60800e8	+	9.11941e8i	−0.233563	+	1.32460i	−0.845620	+	0.533786i	$0.820769\pi$
$884$		0			0
$885$	6.41353e7	+	1.11086e8i	0.0925268	+	0.160261i
$886$		0			0
$887$	3.48129e8	−	4.14884e8i	0.498849	−	0.594505i	−0.456596	−	0.889674i	$-0.650931\pi$
$887$	3.48129e8	−	4.14884e8i	0.498849	−	0.594505i	0.955445	+	0.295169i	$0.0953759\pi$
$888$		0			0
$889$	−1.24261e7	−	3.41404e7i	−0.0176860	−	0.0485918i
$890$		0			0
$891$	9.04878e7	+	5.13182e8i	0.127925	+	0.725501i
$892$		0			0
$893$	1.70828e8	+	3.86590e8i	0.239886	+	0.542870i
$894$		0			0
$895$	−1.21937e8	+	2.15008e7i	−0.170085	+	0.0299906i
$896$		0			0
$897$	3.43766e8	−	1.25121e8i	0.476306	−	0.173361i
$898$		0			0
$899$	−3.57181e8	−	2.99710e8i	−0.491597	−	0.412499i
$900$		0			0
$901$	−3.31897e8	+	1.91621e8i	−0.453763	+	0.261980i
$902$		0			0
$903$	−7.37732e6	−	1.30082e6i	−0.0100192	−	0.00176666i
$904$		0			0
$905$	2.08262e8	+	1.20240e8i	0.280973	+	0.162220i
$906$		0			0
$907$	5.33048e6	−	1.46454e7i	0.00714405	−	0.0196281i	−0.936069	−	0.351816i	$-0.885564\pi$
$907$	5.33048e6	−	1.46454e7i	0.00714405	−	0.0196281i	0.943213	+	0.332187i	$0.107787\pi$
$908$		0			0
$909$	2.66892e6	−	2.23949e6i	0.00355340	−	0.00298166i
$910$		0			0
$911$		−	4.69164e8i		−	0.620540i	−0.950648	−	0.310270i	$-0.899581\pi$
$911$		−	4.69164e8i		−	0.620540i	0.950648	−	0.310270i	$-0.100419\pi$
$912$		0			0
$913$	8.50287e8			1.11726
$914$		0			0
$915$	3.51912e7	+	4.19392e7i	0.0459378	+	0.0547466i
$916$		0			0
$917$	2.11643e8	+	7.70318e7i	0.274471	+	0.0998992i
$918$		0			0
$919$	7.31203e6	−	1.26648e7i	0.00942088	−	0.0163174i	−0.861277	−	0.508137i	$-0.830335\pi$
$919$	7.31203e6	−	1.26648e7i	0.00942088	−	0.0163174i	0.870697	+	0.491819i	$0.163668\pi$
$920$		0			0
$921$	1.36523e6	−	7.74261e6i	0.00174754	−	0.00991079i
$922$		0			0
$923$	1.50343e8	+	2.60402e8i	0.191196	+	0.331161i
$924$		0			0
$925$	−3.35688e8	+	4.00057e8i	−0.424141	+	0.505471i
$926$		0			0
$927$	−2.38638e7	−	6.55653e7i	−0.0299572	−	0.0823066i
$928$		0			0
$929$	−2.01336e7	−	1.14183e8i	−0.0251116	−	0.142415i	0.969674	−	0.244401i	$-0.0785913\pi$
$929$	−2.01336e7	−	1.14183e8i	−0.0251116	−	0.142415i	−0.994786	+	0.101986i	$0.967480\pi$
$930$		0			0
$931$	7.33753e7	+	3.60417e7i	0.0909286	+	0.0446638i
$932$		0			0
$933$	−5.87836e8	+	1.03651e8i	−0.723787	+	0.127623i
$934$		0			0
$935$	2.16831e8	−	7.89200e7i	0.265269	−	0.0965500i
$936$		0			0
$937$	5.10543e8	+	4.28396e8i	0.620602	+	0.520747i	0.897993	−	0.440010i	$-0.145025\pi$
$937$	5.10543e8	+	4.28396e8i	0.620602	+	0.520747i	−0.277391	+	0.960757i	$0.589470\pi$
$938$		0			0
$939$	−2.32678e8	+	1.34337e8i	−0.281034	+	0.162255i
$940$		0			0
$941$	−2.14572e8	−	3.78348e7i	−0.257516	−	0.0454070i	0.0433997	−	0.999058i	$-0.486181\pi$
$941$	−2.14572e8	−	3.78348e7i	−0.257516	−	0.0454070i	−0.300916	+	0.953651i	$0.597292\pi$
$942$		0			0
$943$	−3.88486e8	−	2.24293e8i	−0.463277	−	0.267473i
$944$		0			0
$945$	−9.93004e7	+	2.72826e8i	−0.117667	+	0.323288i
$946$		0			0
$947$	−2.80228e8	+	2.35139e8i	−0.329960	+	0.276869i	−0.792684	−	0.609633i	$-0.791317\pi$
$947$	−2.80228e8	+	2.35139e8i	−0.329960	+	0.276869i	0.462724	+	0.886503i	$0.346872\pi$
$948$		0			0
$949$		−	1.34374e8i		−	0.157223i
$950$		0			0
$951$	−4.90314e8			−0.570076
$952$		0			0
$953$	6.99232e8	+	8.33312e8i	0.807872	+	0.962784i	0.999827	−	0.0186199i	$-0.00592724\pi$
$953$	6.99232e8	+	8.33312e8i	0.807872	+	0.962784i	−0.191955	+	0.981404i	$0.561483\pi$
$954$		0			0
$955$	2.04653e8	+	7.44876e7i	0.234968	+	0.0855213i
$956$		0			0
$957$	1.18493e8	−	2.05236e8i	0.135194	−	0.234163i
$958$		0			0
$959$	2.86340e8	−	1.62391e9i	0.324658	−	1.84123i
$960$		0			0
$961$	8.14956e8	+	1.41154e9i	0.918256	+	1.59047i
$962$		0			0
$963$	7.87684e7	−	9.38726e7i	0.0882010	−	0.105114i
$964$		0			0
$965$	1.23412e8	+	3.39072e8i	0.137333	+	0.377320i
$966$		0			0
$967$	8.49043e7	+	4.81516e8i	0.0938967	+	0.532514i	0.995080	+	0.0990760i	$0.0315887\pi$
$967$	8.49043e7	+	4.81516e8i	0.0938967	+	0.532514i	−0.901183	+	0.433438i	$0.857300\pi$
$968$		0			0
$969$	1.22894e8	−	1.13865e9i	0.135071	−	1.25146i
$970$		0			0
$971$	5.58169e8	−	9.84202e7i	0.609688	−	0.107505i	0.139725	−	0.990190i	$-0.455378\pi$
$971$	5.58169e8	−	9.84202e7i	0.609688	−	0.107505i	0.469964	+	0.882686i	$0.344267\pi$
$972$		0			0
$973$	−6.26103e8	+	2.27883e8i	−0.679685	+	0.247385i
$974$		0			0
$975$	4.07676e8	+	3.42081e8i	0.439847	+	0.369075i
$976$		0			0
$977$	5.96459e8	−	3.44366e8i	0.639583	−	0.369263i	−0.144871	−	0.989451i	$-0.546277\pi$
$977$	5.96459e8	−	3.44366e8i	0.639583	−	0.369263i	0.784454	+	0.620187i	$0.212943\pi$
$978$		0			0
$979$	−1.76410e8	−	3.11059e7i	−0.188008	−	0.0331508i
$980$		0			0
$981$	4.14313e7	+	2.39204e7i	0.0438856	+	0.0253374i
$982$		0			0
$983$	2.28539e8	−	6.27906e8i	0.240603	−	0.661050i	−0.759344	−	0.650690i	$-0.774480\pi$
$983$	2.28539e8	−	6.27906e8i	0.240603	−	0.661050i	0.999946	−	0.0103605i	$-0.00329789\pi$
$984$		0			0
$985$	8.92108e7	−	7.48567e7i	0.0933488	−	0.0783289i
$986$		0			0
$987$			6.27013e8i			0.652116i
$988$		0			0
$989$	−6.95824e6			−0.00719301
$990$		0			0
$991$	2.89568e8	+	3.45094e8i	0.297529	+	0.354582i	0.894011	−	0.448045i	$-0.147880\pi$
$991$	2.89568e8	+	3.45094e8i	0.297529	+	0.354582i	−0.596482	+	0.802627i	$0.703435\pi$
$992$		0			0
$993$	1.18009e9	+	4.29516e8i	1.20522	+	0.438664i
$994$		0			0
$995$	1.09617e8	−	1.89863e8i	0.111278	−	0.192739i
$996$		0			0
$997$	−1.77375e8	+	1.00594e9i	−0.178981	+	1.01505i	0.754467	+	0.656338i	$0.227896\pi$
$997$	−1.77375e8	+	1.00594e9i	−0.178981	+	1.01505i	−0.933448	+	0.358713i	$0.883216\pi$
$998$		0			0
$999$	3.53718e8	+	6.12657e8i	0.354781	+	0.614498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.29.2	yes	60
19.2	odd	18	inner	76.7.j.a.21.2	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.21.2	✓	60	19.2	odd	18	inner
76.7.j.a.29.2	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)

\(f(q)\)	\(=\)	\(q+(-18.1708 - 21.6552i) q^{3} +(40.6936 + 14.8113i) q^{5} +(179.977 - 311.730i) q^{7} +(-12.1770 + 69.0593i) q^{9} +O(q^{10})\)	\(q+(-18.1708 - 21.6552i) q^{3} +(40.6936 + 14.8113i) q^{5} +(179.977 - 311.730i) q^{7} +(-12.1770 + 69.0593i) q^{9} +(451.055 + 781.249i) q^{11} +(880.095 - 1048.86i) q^{13} +(-418.697 - 1150.36i) q^{15} +(-1025.67 - 5816.84i) q^{17} +(-5697.06 + 3819.60i) q^{19} +(-10020.9 + 1766.96i) q^{21} +(-8881.65 + 3232.66i) q^{23} +(-10532.8 - 8838.11i) q^{25} +(-16130.3 + 9312.81i) q^{27} +(9151.84 + 1613.72i) q^{29} +(-43451.8 - 25086.9i) q^{31} +(8722.04 - 23963.6i) q^{33} +(11941.1 - 10019.7i) q^{35} -37981.8i q^{37} -38705.2 q^{39} +(30507.4 + 36357.3i) q^{41} +(691.795 + 251.793i) q^{43} +(-1518.38 + 2629.91i) q^{45} +(10700.2 - 60683.8i) q^{47} +(-5959.27 - 10321.8i) q^{49} +(-107327. + 127908. i) q^{51} +(-22191.6 - 60971.0i) q^{53} +(6783.75 + 38472.6i) q^{55} +(186234. + 53965.5i) q^{57} +(-103188. + 18194.9i) q^{59} +(-42024.7 + 15295.7i) q^{61} +(19336.3 + 16225.0i) q^{63} +(51349.2 - 29646.5i) q^{65} +(497157. + 87662.2i) q^{67} +(231391. + 133593. i) q^{69} +(-75111.0 + 206366. i) q^{71} +(75180.8 - 63084.2i) q^{73} +388686. i q^{75} +324719. q^{77} +(-167089. - 199129. i) q^{79} +(542808. + 197566. i) q^{81} +(471277. - 816276. i) q^{83} +(44416.7 - 251900. i) q^{85} +(-131351. - 227507. i) q^{87} +(-127638. + 152113. i) q^{89} +(-168563. - 463123. i) q^{91} +(246295. + 1.39681e6i) q^{93} +(-288407. + 71052.6i) q^{95} +(-412609. + 72754.2i) q^{97} +(-59445.0 + 21636.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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