LMFDB - Embedded newform 76.7.j.a.13.6

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			13.6
Character	$\chi$	$=$	76.13
Dual form			76.7.j.a.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48422 + 4.07785i) q^{3} +(-10.2967 - 58.3955i) q^{5} +(-54.2532 + 93.9692i) q^{7} +(544.020 + 456.487i) q^{9} +O(q^{10})$	\(q+(-1.48422 + 4.07785i) q^{3} +(-10.2967 - 58.3955i) q^{5} +(-54.2532 + 93.9692i) q^{7} +(544.020 + 456.487i) q^{9} +(-149.837 - 259.525i) q^{11} +(-1260.56 - 3463.37i) q^{13} +(253.411 + 44.6832i) q^{15} +(322.518 - 270.624i) q^{17} +(6488.04 + 2225.15i) q^{19} +(-302.669 - 360.707i) q^{21} +(3117.50 - 17680.2i) q^{23} +(11378.7 - 4141.50i) q^{25} +(-5408.64 + 3122.68i) q^{27} +(26902.0 - 32060.6i) q^{29} +(-7950.76 - 4590.37i) q^{31} +(1280.69 - 225.821i) q^{33} +(6046.01 + 2200.57i) q^{35} -62989.0i q^{37} +15994.1 q^{39} +(-14106.7 + 38757.7i) q^{41} +(-21681.5 - 122962. i) q^{43} +(21055.2 - 36468.7i) q^{45} +(118432. + 99376.6i) q^{47} +(52937.7 + 91690.8i) q^{49} +(624.880 + 1716.84i) q^{51} +(-259093. - 45685.0i) q^{53} +(-13612.3 + 11422.0i) q^{55} +(-18703.5 + 23154.6i) q^{57} +(137971. + 164428. i) q^{59} +(3689.15 - 20922.2i) q^{61} +(-72410.6 + 26355.3i) q^{63} +(-189266. + 109273. i) q^{65} +(-153564. + 183011. i) q^{67} +(67470.3 + 38954.0i) q^{69} +(-14721.9 + 2595.87i) q^{71} +(-142653. - 51921.6i) q^{73} +52547.4i q^{75} +32516.5 q^{77} +(-213385. + 586271. i) q^{79} +(85193.6 + 483157. i) q^{81} +(-113121. + 195931. i) q^{83} +(-19124.1 - 16047.1i) q^{85} +(90809.8 + 157287. i) q^{87} +(-343455. - 943634. i) q^{89} +(393840. + 69444.7i) q^{91} +(30519.5 - 25608.9i) q^{93} +(63133.3 - 401784. i) q^{95} +(-405161. - 482852. i) q^{97} +(36955.5 - 209585. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	−1.48422	+	4.07785i	−0.0549710	+	0.151032i	−0.964139	−	0.265398i	$-0.914497\pi$
$3$	−1.48422	+	4.07785i	−0.0549710	+	0.151032i	0.909168	+	0.416430i	$0.136719\pi$
$4$		0			0
$5$	−10.2967	−	58.3955i	−0.0823737	−	0.467164i	−0.997892	−	0.0648891i	$-0.979331\pi$
$5$	−10.2967	−	58.3955i	−0.0823737	−	0.467164i	0.915519	−	0.402275i	$-0.131780\pi$
$6$		0			0
$7$	−54.2532	+	93.9692i	−0.158173	+	0.273963i	−0.934210	−	0.356724i	$-0.883894\pi$
$7$	−54.2532	+	93.9692i	−0.158173	+	0.273963i	0.776037	+	0.630687i	$0.217227\pi$
$8$		0			0
$9$	544.020	+	456.487i	0.746256	+	0.626183i
$10$		0			0
$11$	−149.837	−	259.525i	−0.112575	−	0.194985i	0.804233	−	0.594314i	$-0.202576\pi$
$11$	−149.837	−	259.525i	−0.112575	−	0.194985i	−0.916808	+	0.399329i	$0.869243\pi$
$12$		0			0
$13$	−1260.56	−	3463.37i	−0.573766	−	1.57641i	−0.798503	−	0.601991i	$-0.794374\pi$
$13$	−1260.56	−	3463.37i	−0.573766	−	1.57641i	0.224737	−	0.974420i	$-0.427848\pi$
$14$		0			0
$15$	253.411	+	44.6832i	0.0750847	+	0.0132395i
$16$		0			0
$17$	322.518	−	270.624i	0.0656458	−	0.0550833i	−0.609374	−	0.792883i	$-0.708579\pi$
$17$	322.518	−	270.624i	0.0656458	−	0.0550833i	0.675020	+	0.737799i	$0.264135\pi$
$18$		0			0
$19$	6488.04	+	2225.15i	0.945916	+	0.324413i
$19$	6488.04	+	2225.15i	0.945916	+	0.324413i
$20$		0			0
$21$	−302.669	−	360.707i	−0.0326821	−	0.0389490i
$22$		0			0
$23$	3117.50	−	17680.2i	0.256226	−	1.45313i	−0.536679	−	0.843786i	$-0.680322\pi$
$23$	3117.50	−	17680.2i	0.256226	−	1.45313i	0.792906	−	0.609345i	$-0.208567\pi$
$24$		0			0
$25$	11378.7	−	4141.50i	0.728236	−	0.265056i
$26$		0			0
$27$	−5408.64	+	3122.68i	−0.274787	+	0.158648i
$28$		0			0
$29$	26902.0	−	32060.6i	1.10304	−	1.31455i	0.158056	−	0.987430i	$-0.449477\pi$
$29$	26902.0	−	32060.6i	1.10304	−	1.31455i	0.944983	−	0.327120i	$-0.106078\pi$
$30$		0			0
$31$	−7950.76	−	4590.37i	−0.266885	−	0.154086i	0.360586	−	0.932726i	$-0.382577\pi$
$31$	−7950.76	−	4590.37i	−0.266885	−	0.154086i	−0.627471	+	0.778640i	$0.715910\pi$
$32$		0			0
$33$	1280.69	−	225.821i	0.0356372	−	0.00628380i
$34$		0			0
$35$	6046.01	+	2200.57i	0.141015	+	0.0513252i
$36$		0			0
$37$		−	62989.0i		−	1.24354i	−0.783200	−	0.621770i	$-0.786414\pi$
$37$		−	62989.0i		−	1.24354i	0.783200	−	0.621770i	$-0.213586\pi$
$38$		0			0
$39$	15994.1			0.269628
$40$		0			0
$41$	−14106.7	+	38757.7i	−0.204679	+	0.562350i	−0.998979	−	0.0451752i	$-0.985615\pi$
$41$	−14106.7	+	38757.7i	−0.204679	+	0.562350i	0.794300	+	0.607525i	$0.207838\pi$
$42$		0			0
$43$	−21681.5	−	122962.i	−0.272699	−	1.54655i	−0.746178	−	0.665747i	$-0.768113\pi$
$43$	−21681.5	−	122962.i	−0.272699	−	1.54655i	0.473479	−	0.880805i	$-0.342998\pi$
$44$		0			0
$45$	21055.2	−	36468.7i	0.231058	−	0.400205i
$46$		0			0
$47$	118432.	+	99376.6i	1.14071	+	0.957173i	0.999462	−	0.0328000i	$-0.0104425\pi$
$47$	118432.	+	99376.6i	1.14071	+	0.957173i	0.141253	+	0.989974i	$0.454887\pi$
$48$		0			0
$49$	52937.7	+	91690.8i	0.449963	+	0.779359i
$50$		0			0
$51$	624.880	+	1716.84i	0.00471071	+	0.0129426i
$52$		0			0
$53$	−259093.	−	45685.0i	−1.74031	−	0.306864i	−0.788841	−	0.614598i	$-0.789318\pi$
$53$	−259093.	−	45685.0i	−1.74031	−	0.306864i	−0.951473	+	0.307734i	$0.900429\pi$
$54$		0			0
$55$	−13612.3	+	11422.0i	−0.0818168	+	0.0686524i
$56$		0			0
$57$	−18703.5	+	23154.6i	−0.100994	+	0.125030i
$58$		0			0
$59$	137971.	+	164428.i	0.671789	+	0.800607i	0.989026	−	0.147739i	$-0.0471995\pi$
$59$	137971.	+	164428.i	0.671789	+	0.800607i	−0.317237	+	0.948346i	$0.602755\pi$
$60$		0			0
$61$	3689.15	−	20922.2i	0.0162531	−	0.0921760i	−0.975602	−	0.219546i	$-0.929542\pi$
$61$	3689.15	−	20922.2i	0.0162531	−	0.0921760i	0.991855	+	0.127370i	$0.0406535\pi$
$62$		0			0
$63$	−72410.6	+	26355.3i	−0.289588	+	0.105401i
$64$		0			0
$65$	−189266.	+	109273.i	−0.689179	+	0.397898i
$66$		0			0
$67$	−153564.	+	183011.i	−0.510582	+	0.608488i	−0.958327	−	0.285673i	$-0.907783\pi$
$67$	−153564.	+	183011.i	−0.510582	+	0.608488i	0.447745	+	0.894161i	$0.352227\pi$
$68$		0			0
$69$	67470.3	+	38954.0i	0.205384	+	0.118578i
$70$		0			0
$71$	−14721.9	+	2595.87i	−0.0411328	+	0.00725283i	−0.194177	−	0.980967i	$-0.562204\pi$
$71$	−14721.9	+	2595.87i	−0.0411328	+	0.00725283i	0.153044	+	0.988219i	$0.451092\pi$
$72$		0			0
$73$	−142653.	−	51921.6i	−0.366702	−	0.133469i	0.152095	−	0.988366i	$-0.451398\pi$
$73$	−142653.	−	51921.6i	−0.366702	−	0.133469i	−0.518797	+	0.854897i	$0.673620\pi$
$74$		0			0
$75$			52547.4i			0.124557i
$76$		0			0
$77$	32516.5			0.0712248
$78$		0			0
$79$	−213385.	+	586271.i	−0.432796	+	1.18910i	0.511293	+	0.859406i	$0.329167\pi$
$79$	−213385.	+	586271.i	−0.432796	+	1.18910i	−0.944089	+	0.329691i	$0.893056\pi$
$80$		0			0
$81$	85193.6	+	483157.i	0.160307	+	0.909145i
$82$		0			0
$83$	−113121.	+	195931.i	−0.197837	+	0.342665i	−0.947827	−	0.318785i	$-0.896725\pi$
$83$	−113121.	+	195931.i	−0.197837	+	0.342665i	0.749990	+	0.661450i	$0.230058\pi$
$84$		0			0
$85$	−19124.1	−	16047.1i	−0.0311405	−	0.0261299i
$86$		0			0
$87$	90809.8	+	157287.i	0.137903	+	0.238856i
$88$		0			0
$89$	−343455.	−	943634.i	−0.487191	−	1.33855i	−0.903213	−	0.429192i	$-0.858798\pi$
$89$	−343455.	−	943634.i	−0.487191	−	1.33855i	0.416022	−	0.909355i	$-0.363424\pi$
$90$		0			0
$91$	393840.	+	69444.7i	0.522632	+	0.0921541i
$92$		0			0
$93$	30519.5	−	25608.9i	0.0379427	−	0.0318377i
$94$		0			0
$95$	63133.3	−	401784.i	0.0736355	−	0.468621i
$96$		0			0
$97$	−405161.	−	482852.i	−0.443928	−	0.529052i	0.496959	−	0.867774i	$-0.334450\pi$
$97$	−405161.	−	482852.i	−0.443928	−	0.529052i	−0.940887	+	0.338722i	$0.890005\pi$
$98$		0			0
$99$	36955.5	−	209585.i	0.0380868	−	0.216001i
$100$		0			0
$101$	−1.18740e6	+	432180.i	−1.15248	+	0.419469i	−0.846406	−	0.532538i	$-0.821238\pi$
$101$	−1.18740e6	+	432180.i	−1.15248	+	0.419469i	−0.306076	+	0.952007i	$0.599016\pi$
$102$		0			0
$103$	1.70465e6	−	984180.i	1.56000	−	0.900664i	0.562740	−	0.826634i	$-0.309747\pi$
$103$	1.70465e6	−	984180.i	1.56000	−	0.900664i	0.997256	−	0.0740299i	$-0.0235860\pi$
$104$		0			0
$105$	−17947.2	+	21388.6i	−0.0155035	+	0.0184763i
$106$		0			0
$107$	1.57988e6	+	912142.i	1.28965	+	0.744579i	0.978592	−	0.205812i	$-0.0659834\pi$
$107$	1.57988e6	+	912142.i	1.28965	+	0.744579i	0.311058	+	0.950391i	$0.399317\pi$
$108$		0			0
$109$	169505.	−	29888.3i	0.130889	−	0.0230792i	−0.107820	−	0.994170i	$-0.534387\pi$
$109$	169505.	−	29888.3i	0.130889	−	0.0230792i	0.238709	+	0.971091i	$0.423276\pi$
$110$		0			0
$111$	256860.	+	93489.4i	0.187814	+	0.0683586i
$112$		0			0
$113$		−	466113.i		−	0.323039i	−0.986869	−	0.161520i	$-0.948360\pi$
$113$		−	466113.i		−	0.323039i	0.986869	−	0.161520i	$-0.0516395\pi$
$114$		0			0
$115$	−1.06455e6			−0.699957
$116$		0			0
$117$	895213.	−	2.45958e6i	0.558945	−	1.53569i
$118$		0			0
$119$	7932.77	+	44989.0i	0.00470743	+	0.0266972i
$120$		0			0
$121$	840878.	−	1.45644e6i	0.474654	−	0.822125i
$122$		0			0
$123$	−137111.	−	115050.i	−0.0736812	−	0.0618259i
$124$		0			0
$125$	−822261.	−	1.42420e6i	−0.420998	−	0.729189i
$126$		0			0
$127$	318866.	+	876078.i	0.155667	+	0.427693i	0.992870	−	0.119200i	$-0.0380329\pi$
$127$	318866.	+	876078.i	0.155667	+	0.427693i	−0.837203	+	0.546892i	$0.815811\pi$
$128$		0			0
$129$	533600.	+	94088.0i	0.248569	+	0.0438294i
$130$		0			0
$131$	552365.	−	463490.i	0.245704	−	0.206170i	−0.511616	−	0.859214i	$-0.670953\pi$
$131$	552365.	−	463490.i	0.245704	−	0.206170i	0.757320	+	0.653044i	$0.226508\pi$
$132$		0			0
$133$	−561092.	+	488954.i	−0.238495	+	0.207833i
$134$		0			0
$135$	238042.	+	283687.i	0.0967501	+	0.115302i
$136$		0			0
$137$	−194518.	+	1.10317e6i	−0.0756483	+	0.429023i	0.923337	+	0.383990i	$0.125450\pi$
$137$	−194518.	+	1.10317e6i	−0.0756483	+	0.429023i	−0.998986	+	0.0450326i	$0.985661\pi$
$138$		0			0
$139$	3.65679e6	−	1.33096e6i	1.36162	−	0.495589i	0.445065	−	0.895498i	$-0.353181\pi$
$139$	3.65679e6	−	1.33096e6i	1.36162	−	0.495589i	0.916555	+	0.399909i	$0.130958\pi$
$140$		0			0
$141$	−581022.	+	335453.i	−0.207270	+	0.119667i
$142$		0			0
$143$	−709952.	+	846088.i	−0.242785	+	0.289339i
$144$		0			0
$145$	−2.14920e6	−	1.24084e6i	−0.704972	−	0.407016i
$146$		0			0
$147$	−452472.	+	79783.1i	−0.142443	+	0.0251165i
$148$		0			0
$149$	−3.61390e6	−	1.31535e6i	−1.09249	−	0.397634i	−0.267947	−	0.963434i	$-0.586345\pi$
$149$	−3.61390e6	−	1.31535e6i	−1.09249	−	0.397634i	−0.824543	+	0.565800i	$0.808567\pi$
$150$		0			0
$151$			2.78755e6i			0.809640i	0.914396	+	0.404820i	$0.132666\pi$
$151$			2.78755e6i			0.809640i	−0.914396	+	0.404820i	$0.867334\pi$
$152$		0			0
$153$	298993.			0.0834808
$154$		0			0
$155$	−186191.	+	511555.i	−0.0499992	+	0.137372i
$156$		0			0
$157$	−138418.	−	785010.i	−0.0357680	−	0.202851i	0.961687	−	0.274150i	$-0.0883965\pi$
$157$	−138418.	−	785010.i	−0.0357680	−	0.202851i	−0.997455	+	0.0712995i	$0.977285\pi$
$158$		0			0
$159$	570846.	−	988735.i	0.142013	−	0.245974i
$160$		0			0
$161$	1.49226e6	+	1.25216e6i	0.357576	+	0.300042i
$162$		0			0
$163$	2.24002e6	+	3.87983e6i	0.517236	+	0.895879i	0.999800	+	0.0200184i	$0.00637248\pi$
$163$	2.24002e6	+	3.87983e6i	0.517236	+	0.895879i	−0.482563	+	0.875861i	$0.660294\pi$
$164$		0			0
$165$	−26373.8	−	72461.6i	−0.00587113	−	0.0161308i
$166$		0			0
$167$	−2.17988e6	−	384372.i	−0.468040	−	0.0825281i	−0.0653460	−	0.997863i	$-0.520815\pi$
$167$	−2.17988e6	−	384372.i	−0.468040	−	0.0825281i	−0.402694	+	0.915335i	$0.631926\pi$
$168$		0			0
$169$	−6.70838e6	+	5.62900e6i	−1.38982	+	1.16620i
$170$		0			0
$171$	2.51387e6	+	4.17223e6i	0.502753	+	0.834411i
$172$		0			0
$173$	2.48614e6	+	2.96286e6i	0.480161	+	0.572233i	0.950687	−	0.310153i	$-0.100380\pi$
$173$	2.48614e6	+	2.96286e6i	0.480161	+	0.572233i	−0.470526	+	0.882386i	$0.655936\pi$
$174$		0			0
$175$	−228156.	+	1.29394e6i	−0.0425713	+	0.241434i
$176$		0			0
$177$	−875292.	+	318580.i	−0.157846	+	0.0574512i
$178$		0			0
$179$	−4.57104e6	+	2.63909e6i	−0.796996	+	0.460146i	−0.842420	−	0.538822i	$-0.818870\pi$
$179$	−4.57104e6	+	2.63909e6i	−0.796996	+	0.460146i	0.0454235	+	0.998968i	$0.485536\pi$
$180$		0			0
$181$	4.48919e6	−	5.35000e6i	0.757063	−	0.902232i	−0.240596	−	0.970625i	$-0.577343\pi$
$181$	4.48919e6	−	5.35000e6i	0.757063	−	0.902232i	0.997658	+	0.0683930i	$0.0217872\pi$
$182$		0			0
$183$	79842.1	+	46096.8i	0.0130280	+	0.00752173i
$184$		0			0
$185$	−3.67828e6	+	648580.i	−0.580938	+	0.102435i
$186$		0			0
$187$	−118559.	−	43151.8i	−0.0181305	−	0.00659895i
$188$		0			0
$189$		−	677661.i		−	0.100375i
$190$		0			0
$191$	−8.79183e6			−1.26177			−0.630884	−	0.775878i	$-0.717307\pi$
$191$	−8.79183e6			−1.26177			−0.630884	+	0.775878i	$0.717307\pi$
$192$		0			0
$193$	1.53063e6	−	4.20537e6i	0.212911	−	0.584968i	−0.786559	−	0.617515i	$-0.788139\pi$
$193$	1.53063e6	−	4.20537e6i	0.212911	−	0.584968i	0.999470	+	0.0325465i	$0.0103617\pi$
$194$		0			0
$195$	−164686.	−	933982.i	−0.0222103	−	0.125961i
$196$		0			0
$197$	−4.51408e6	+	7.81861e6i	−0.590433	+	1.02266i	0.403742	+	0.914873i	$0.367710\pi$
$197$	−4.51408e6	+	7.81861e6i	−0.590433	+	1.02266i	−0.994174	+	0.107786i	$0.965624\pi$
$198$		0			0
$199$	4.48531e6	+	3.76362e6i	0.569158	+	0.477580i	0.881366	−	0.472433i	$-0.156624\pi$
$199$	4.48531e6	+	3.76362e6i	0.569158	+	0.477580i	−0.312208	+	0.950014i	$0.601069\pi$
$200$		0			0
$201$	−518368.	−	897839.i	−0.0638337	−	0.110563i
$202$		0			0
$203$	1.55319e6	+	4.26735e6i	0.185668	+	0.510117i
$204$		0			0
$205$	2.40853e6	+	424689.i	0.279570	+	0.0492957i
$206$		0			0
$207$	9.76679e6	−	8.19531e6i	1.10114	−	0.923963i
$208$		0			0
$209$	−394665.	−	2.01721e6i	−0.0432304	−	0.220960i
$210$		0			0
$211$	−7.78955e6	−	9.28322e6i	−0.829211	−	0.988215i	−0.999996	−	0.00290652i	$-0.999075\pi$
$211$	−7.78955e6	−	9.28322e6i	−0.829211	−	0.988215i	0.170785	−	0.985308i	$-0.445370\pi$
$212$		0			0
$213$	11264.9	−	63886.5i	0.00116571	−	0.00661105i
$214$		0			0
$215$	−6.95717e6	+	2.53220e6i	−0.700031	+	0.254790i
$216$		0			0
$217$	862708.	−	498085.i	0.0844276	−	0.0487443i
$218$		0			0
$219$	423457.	−	504656.i	0.0403159	−	0.0480467i
$220$		0			0
$221$	−1.34383e6	−	775860.i	−0.124499	−	0.0718797i
$222$		0			0
$223$	7.01101e6	−	1.23623e6i	0.632217	−	0.111477i	0.151649	−	0.988434i	$-0.451542\pi$
$223$	7.01101e6	−	1.23623e6i	0.632217	−	0.111477i	0.480568	+	0.876958i	$0.340431\pi$
$224$		0			0
$225$	8.08078e6	+	2.94116e6i	0.709424	+	0.258209i
$226$		0			0
$227$		−	4.73355e6i		−	0.404678i	−0.979316	−	0.202339i	$-0.935146\pi$
$227$		−	4.73355e6i		−	0.404678i	0.979316	−	0.202339i	$-0.0648542\pi$
$228$		0			0
$229$	2.12959e7			1.77333			0.886664	−	0.462414i	$-0.153017\pi$
$229$	2.12959e7			1.77333			0.886664	+	0.462414i	$0.153017\pi$
$230$		0			0
$231$	−48261.5	+	132597.i	−0.00391530	+	0.0107572i
$232$		0			0
$233$	265231.	+	1.50420e6i	0.0209679	+	0.118915i	0.993495	−	0.113874i	$-0.0363260\pi$
$233$	265231.	+	1.50420e6i	0.0209679	+	0.118915i	−0.972527	+	0.232789i	$0.925215\pi$
$234$		0			0
$235$	4.58369e6	−	7.93918e6i	0.353192	−	0.611747i
$236$		0			0
$237$	−2.07402e6	−	1.74031e6i	−0.155800	−	0.130732i
$238$		0			0
$239$	761473.	+	1.31891e6i	0.0557777	+	0.0966099i	0.892566	−	0.450917i	$-0.148903\pi$
$239$	761473.	+	1.31891e6i	0.0557777	+	0.0966099i	−0.836788	+	0.547527i	$0.815570\pi$
$240$		0			0
$241$	−4.25763e6	−	1.16977e7i	−0.304170	−	0.835701i	−0.993764	−	0.111505i	$-0.964433\pi$
$241$	−4.25763e6	−	1.16977e7i	−0.304170	−	0.835701i	0.689593	−	0.724197i	$-0.257789\pi$
$242$		0			0
$243$	−6.58038e6	−	1.16030e6i	−0.458598	−	0.0808632i
$244$		0			0
$245$	4.80925e6	−	4.03544e6i	0.327023	−	0.274405i
$246$		0			0
$247$	−472072.	−	2.52754e7i	−0.0313269	−	1.67729i
$248$		0			0
$249$	−631082.	−	752094.i	−0.0408778	−	0.0487163i
$250$		0			0
$251$	1.34991e6	−	7.65573e6i	0.0853659	−	0.484134i	−0.911911	−	0.410388i	$-0.865393\pi$
$251$	1.34991e6	−	7.65573e6i	0.0853659	−	0.484134i	0.997277	−	0.0737463i	$-0.0234955\pi$
$252$		0			0
$253$	−5.05558e6	+	1.84008e6i	−0.312183	+	0.113625i
$254$		0			0
$255$	93821.8	−	54168.1i	0.00565827	−	0.00326680i
$256$		0			0
$257$	−9.79997e6	+	1.16791e7i	−0.577332	+	0.688037i	−0.973118	−	0.230305i	$-0.926027\pi$
$257$	−9.79997e6	+	1.16791e7i	−0.577332	+	0.688037i	0.395787	+	0.918342i	$0.370472\pi$
$258$		0			0
$259$	5.91903e6	+	3.41736e6i	0.340684	+	0.196694i
$260$		0			0
$261$	2.92705e7	−	5.16118e6i	1.64630	−	0.290287i
$262$		0			0
$263$	−2.47547e7	−	9.00998e6i	−1.36079	−	0.495286i	−0.444490	−	0.895784i	$-0.646615\pi$
$263$	−2.47547e7	−	9.00998e6i	−1.36079	−	0.495286i	−0.916298	+	0.400497i	$0.868837\pi$
$264$		0			0
$265$			1.56003e7i			0.838290i
$266$		0			0
$267$	4.35776e6			0.228944
$268$		0			0
$269$	3.11105e6	−	8.54754e6i	0.159827	−	0.439121i	−0.833769	−	0.552114i	$-0.813821\pi$
$269$	3.11105e6	−	8.54754e6i	0.159827	−	0.439121i	0.993596	+	0.112992i	$0.0360436\pi$
$270$		0			0
$271$	4.36924e6	+	2.47792e7i	0.219532	+	1.24503i	0.872866	+	0.487959i	$0.162259\pi$
$271$	4.36924e6	+	2.47792e7i	0.219532	+	1.24503i	−0.653334	+	0.757070i	$0.726630\pi$
$272$		0			0
$273$	−867729.	+	1.50295e6i	−0.0426478	+	0.0738681i
$274$		0			0
$275$	−2.77977e6	−	2.33250e6i	−0.133663	−	0.112156i
$276$		0			0
$277$	1.24592e6	+	2.15800e6i	0.0586207	+	0.101534i	0.893846	−	0.448373i	$-0.147996\pi$
$277$	1.24592e6	+	2.15800e6i	0.0586207	+	0.101534i	−0.835226	+	0.549907i	$0.814663\pi$
$278$		0			0
$279$	−2.22993e6	−	6.12668e6i	−0.102678	−	0.282106i
$280$		0			0
$281$	−274478.	−	48397.9i	−0.0123705	−	0.00218126i	0.167459	−	0.985879i	$-0.446444\pi$
$281$	−274478.	−	48397.9i	−0.0123705	−	0.00218126i	−0.179830	+	0.983698i	$0.557555\pi$
$282$		0			0
$283$	1.26563e7	−	1.06199e7i	0.558405	−	0.468557i	−0.319371	−	0.947630i	$-0.603471\pi$
$283$	1.26563e7	−	1.06199e7i	0.558405	−	0.468557i	0.877775	+	0.479073i	$0.159027\pi$
$284$		0			0
$285$	1.54471e6	+	853782.i	0.0667287	+	0.0368818i
$286$		0			0
$287$	−2.87670e6	−	3.42832e6i	−0.121688	−	0.145023i
$288$		0			0
$289$	−4.16066e6	+	2.35963e7i	−0.172373	+	0.977576i
$290$		0			0
$291$	2.57034e6	−	935529.i	0.104307	−	0.0379645i
$292$		0			0
$293$	−2.06958e7	+	1.19488e7i	−0.822773	+	0.475028i	−0.851372	−	0.524563i	$-0.824229\pi$
$293$	−2.06958e7	+	1.19488e7i	−0.822773	+	0.475028i	0.0285985	+	0.999591i	$0.490896\pi$
$294$		0			0
$295$	8.18121e6	−	9.74998e6i	0.318677	−	0.379785i
$296$		0			0
$297$	1.62082e6	+	935783.i	0.0618681	+	0.0357195i
$298$		0			0
$299$	−6.51631e7	+	1.14900e7i	−2.43774	+	0.429840i
$300$		0			0
$301$	1.27309e7	+	4.63367e6i	0.466831	+	0.169913i
$302$		0			0
$303$		−	5.48350e6i		−	0.197120i
$304$		0			0
$305$	−1.25975e6			−0.0444001
$306$		0			0
$307$	−21067.7	+	57882.9i	−0.000728117	+	0.00200049i	−0.940056	−	0.341020i	$-0.889228\pi$
$307$	−21067.7	+	57882.9i	−0.000728117	+	0.00200049i	0.939328	+	0.343020i	$0.111450\pi$
$308$		0			0
$309$	1.48327e6	+	8.41204e6i	0.0502742	+	0.285119i
$310$		0			0
$311$	−1.48987e7	+	2.58052e7i	−0.495297	+	0.857880i	−0.999985	−	0.00542175i	$-0.998274\pi$
$311$	−1.48987e7	+	2.58052e7i	−0.495297	+	0.857880i	0.504688	+	0.863302i	$0.331608\pi$
$312$		0			0
$313$	2.98192e7	+	2.50213e7i	0.972441	+	0.815975i	0.982932	−	0.183970i	$-0.0588949\pi$
$313$	2.98192e7	+	2.50213e7i	0.972441	+	0.815975i	−0.0104907	+	0.999945i	$0.503339\pi$
$314$		0			0
$315$	2.28462e6	+	3.95708e6i	0.0730942	+	0.126603i
$316$		0			0
$317$	1.69511e7	+	4.65728e7i	0.532133	+	1.46202i	0.856527	+	0.516102i	$0.172617\pi$
$317$	1.69511e7	+	4.65728e7i	0.532133	+	1.46202i	−0.324394	+	0.945922i	$0.605160\pi$
$318$		0			0
$319$	−1.23514e7	−	2.17789e6i	−0.380491	−	0.0670909i
$320$		0			0
$321$	−6.06446e6	+	5.08868e6i	−0.183348	+	0.153847i
$322$		0			0
$323$	2.69469e6	−	1.03817e6i	0.0799651	−	0.0308079i
$324$		0			0
$325$	−2.86871e7	−	3.41880e7i	−0.835674	−	0.995918i
$326$		0			0
$327$	−129702.	+	735576.i	−0.00370939	+	0.0210370i
$328$		0			0
$329$	−1.57637e7	+	5.73751e6i	−0.442660	+	0.161115i
$330$		0			0
$331$	−4.06311e7	+	2.34584e7i	−1.12040	+	0.646865i	−0.941504	−	0.337002i	$-0.890587\pi$
$331$	−4.06311e7	+	2.34584e7i	−1.12040	+	0.646865i	−0.178900	+	0.983867i	$0.557254\pi$
$332$		0			0
$333$	2.87537e7	−	3.42673e7i	0.778684	−	0.927999i
$334$		0			0
$335$	1.22682e7	+	7.08305e6i	0.326322	+	0.188402i
$336$		0			0
$337$	−2.60320e6	+	459015.i	−0.0680171	+	0.0119932i	−0.207553	−	0.978224i	$-0.566550\pi$
$337$	−2.60320e6	+	459015.i	−0.0680171	+	0.0119932i	0.139536	+	0.990217i	$0.455439\pi$
$338$		0			0
$339$	1.90074e6	+	691812.i	0.0487891	+	0.0177578i
$340$		0			0
$341$			2.75123e6i			0.0693846i
$342$		0			0
$343$	−2.42538e7			−0.601032
$344$		0			0
$345$	1.58002e6	−	4.34107e6i	0.0384773	−	0.105716i
$346$		0			0
$347$	−690013.	−	3.91326e6i	−0.0165146	−	0.0936592i	0.975436	−	0.220281i	$-0.0706975\pi$
$347$	−690013.	−	3.91326e6i	−0.0165146	−	0.0936592i	−0.991951	+	0.126622i	$0.959586\pi$
$348$		0			0
$349$	2.54666e7	−	4.41094e7i	0.599093	−	1.03766i	−0.393863	−	0.919169i	$-0.628861\pi$
$349$	2.54666e7	−	4.41094e7i	0.599093	−	1.03766i	0.992955	−	0.118490i	$-0.0378053\pi$
$350$		0			0
$351$	1.76329e7	+	1.47958e7i	0.407759	+	0.342150i
$352$		0			0
$353$	1.27843e7	+	2.21431e7i	0.290639	+	0.503401i	0.973961	−	0.226716i	$-0.0727990\pi$
$353$	1.27843e7	+	2.21431e7i	0.290639	+	0.503401i	−0.683322	+	0.730117i	$0.739466\pi$
$354$		0			0
$355$	303174.	+	832964.i	0.00677652	+	0.0186183i
$356$		0			0
$357$	−195232.	−	34424.7i	−0.00429089	−	0.000756599i
$358$		0			0
$359$	−3.51661e7	+	2.95078e7i	−0.760047	+	0.637755i	−0.938139	−	0.346259i	$-0.887452\pi$
$359$	−3.51661e7	+	2.95078e7i	−0.760047	+	0.637755i	0.178092	+	0.984014i	$0.443008\pi$
$360$		0			0
$361$	3.71433e7	+	2.88737e7i	0.789513	+	0.613734i
$362$		0			0
$363$	4.69112e6	+	5.59065e6i	0.0980746	+	0.116881i
$364$		0			0
$365$	−1.56313e6	+	8.86494e6i	−0.0321452	+	0.182304i
$366$		0			0
$367$	5.63021e7	−	2.04923e7i	1.13901	−	0.414564i	0.297452	−	0.954737i	$-0.403863\pi$
$367$	5.63021e7	−	2.04923e7i	1.13901	−	0.414564i	0.841554	+	0.540172i	$0.181641\pi$
$368$		0			0
$369$	−2.53667e7	+	1.46455e7i	−0.504877	+	0.291491i
$370$		0			0
$371$	1.83496e7	−	2.18682e7i	0.359339	−	0.428244i
$372$		0			0
$373$	1.14080e7	+	6.58643e6i	0.219829	+	0.126918i	0.605871	−	0.795563i	$-0.292825\pi$
$373$	1.14080e7	+	6.58643e6i	0.219829	+	0.126918i	−0.386042	+	0.922481i	$0.626158\pi$
$374$		0			0
$375$	7.02808e6	−	1.23924e6i	0.133273	−	0.0234997i
$376$		0			0
$377$	−1.44949e8	−	5.27573e7i	−2.70516	−	0.984597i
$378$		0			0
$379$		−	1.51006e7i		−	0.277381i	−0.990336	−	0.138690i	$-0.955711\pi$
$379$		−	1.51006e7i		−	0.277381i	0.990336	−	0.138690i	$-0.0442893\pi$
$380$		0			0
$381$	−4.04578e6			−0.0731523
$382$		0			0
$383$	3.20701e7	−	8.81120e7i	0.570827	−	1.56833i	−0.232374	−	0.972626i	$-0.574649\pi$
$383$	3.20701e7	−	8.81120e7i	0.570827	−	1.56833i	0.803201	−	0.595708i	$-0.203128\pi$
$384$		0			0
$385$	−334813.	−	1.89882e6i	−0.00586705	−	0.0332737i
$386$		0			0
$387$	4.43353e7	−	7.67910e7i	0.764921	−	1.32488i
$388$		0			0
$389$	2.06225e7	+	1.73043e7i	0.350341	+	0.293971i	0.800927	−	0.598762i	$-0.204340\pi$
$389$	2.06225e7	+	1.73043e7i	0.350341	+	0.293971i	−0.450586	+	0.892733i	$0.648785\pi$
$390$		0			0
$391$	−3.77926e6	−	6.54586e6i	−0.0632231	−	0.109506i
$392$		0			0
$393$	1.07021e6	+	2.94038e6i	0.0176316	+	0.0484425i
$394$		0			0
$395$	3.64328e7	+	6.42408e6i	0.591155	+	0.104237i
$396$		0			0
$397$	8.01633e7	−	6.72650e7i	1.28116	−	1.07502i	0.288080	−	0.957606i	$-0.406983\pi$
$397$	8.01633e7	−	6.72650e7i	1.28116	−	1.07502i	0.993083	−	0.117416i	$-0.0374612\pi$
$398$		0			0
$399$	−1.16110e6	−	3.01376e6i	−0.0182790	−	0.0474450i
$400$		0			0
$401$	−3.43339e7	−	4.09176e7i	−0.532464	−	0.634566i	0.431016	−	0.902344i	$-0.358155\pi$
$401$	−3.43339e7	−	4.09176e7i	−0.532464	−	0.634566i	−0.963481	+	0.267778i	$0.913711\pi$
$402$		0			0
$403$	−5.87573e6	+	3.33229e7i	−0.0897732	+	0.509129i
$404$		0			0
$405$	2.73370e7	−	9.94986e6i	0.411515	−	0.149779i
$406$		0			0
$407$	−1.63472e7	+	9.43807e6i	−0.242471	+	0.139991i
$408$		0			0
$409$	−2.53764e7	+	3.02424e7i	−0.370902	+	0.442024i	−0.918921	−	0.394442i	$-0.870938\pi$
$409$	−2.53764e7	+	3.02424e7i	−0.370902	+	0.442024i	0.548019	+	0.836466i	$0.315382\pi$
$410$		0			0
$411$	−4.20985e6	−	2.43056e6i	−0.0606375	−	0.0350091i
$412$		0			0
$413$	−2.29366e7	+	4.04433e6i	−0.325595	+	0.0574112i
$414$		0			0
$415$	1.26063e7	+	4.58831e6i	0.176377	+	0.0641961i
$416$		0			0
$417$			1.68873e7i			0.232890i
$418$		0			0
$419$	1.11380e8			1.51413			0.757067	−	0.653337i	$-0.226631\pi$
$419$	1.11380e8			1.51413			0.757067	+	0.653337i	$0.226631\pi$
$420$		0			0
$421$	3.82929e7	−	1.05209e8i	0.513182	−	1.40996i	−0.364720	−	0.931117i	$-0.618835\pi$
$421$	3.82929e7	−	1.05209e8i	0.513182	−	1.40996i	0.877902	−	0.478840i	$-0.158943\pi$
$422$		0			0
$423$	1.90655e7	+	1.08126e8i	0.251899	+	1.42859i
$424$		0			0
$425$	2.54903e6	−	4.41506e6i	0.0332054	−	0.0575135i
$426$		0			0
$427$	1.76589e6	+	1.48176e6i	0.0226820	+	0.0190324i
$428$		0			0
$429$	−2.39650e6	−	4.15086e6i	−0.0303533	−	0.0525734i
$430$		0			0
$431$	−1.77277e7	−	4.87066e7i	−0.221422	−	0.608353i	0.778389	−	0.627782i	$-0.216037\pi$
$431$	−1.77277e7	−	4.87066e7i	−0.221422	−	0.608353i	−0.999811	+	0.0194295i	$0.993815\pi$
$432$		0			0
$433$	−5.73042e7	−	1.01043e7i	−0.705867	−	0.124463i	−0.190820	−	0.981625i	$-0.561115\pi$
$433$	−5.73042e7	−	1.01043e7i	−0.705867	−	0.124463i	−0.515047	+	0.857162i	$0.672226\pi$
$434$		0			0
$435$	8.24983e6	−	6.92243e6i	0.100225	−	0.0840990i
$436$		0			0
$437$	5.95676e7	−	1.07773e8i	0.713783	−	1.29142i
$438$		0			0
$439$	−9.89507e6	−	1.17925e7i	−0.116957	−	0.139384i	0.704389	−	0.709814i	$-0.251221\pi$
$439$	−9.89507e6	−	1.17925e7i	−0.116957	−	0.139384i	−0.821346	+	0.570430i	$0.806777\pi$
$440$		0			0
$441$	−1.30565e7	+	7.40470e7i	−0.152234	+	0.863360i
$442$		0			0
$443$	−1.52760e8	+	5.56000e7i	−1.75711	+	0.639534i	−0.999907	−	0.0136513i	$-0.995655\pi$
$443$	−1.52760e8	+	5.56000e7i	−1.75711	+	0.639534i	−0.757198	+	0.653185i	$0.773432\pi$
$444$		0			0
$445$	−5.15676e7	+	2.97726e7i	−0.585190	+	0.337859i
$446$		0			0
$447$	1.07276e7	−	1.27847e7i	0.120110	−	0.143142i
$448$		0			0
$449$	1.37310e8	+	7.92762e7i	1.51693	+	0.875798i	0.999802	+	0.0198880i	$0.00633096\pi$
$449$	1.37310e8	+	7.92762e7i	1.51693	+	0.875798i	0.517125	+	0.855910i	$0.327002\pi$
$450$		0			0
$451$	1.21723e7	−	2.14630e6i	0.132691	−	0.0233971i
$452$		0			0
$453$	−1.13672e7	−	4.13733e6i	−0.122281	−	0.0445067i
$454$		0			0
$455$		−	2.37136e7i		−	0.251746i
$456$		0			0
$457$	−5.72003e7			−0.599307			−0.299654	−	0.954048i	$-0.596871\pi$
$457$	−5.72003e7			−0.599307			−0.299654	+	0.954048i	$0.596871\pi$
$458$		0			0
$459$	−899308.	+	2.47083e6i	−0.00929973	+	0.0255508i
$460$		0			0
$461$	−5.20370e6	−	2.95116e7i	−0.0531140	−	0.301225i	0.946666	−	0.322218i	$-0.104428\pi$
$461$	−5.20370e6	−	2.95116e7i	−0.0531140	−	0.301225i	−0.999780	+	0.0209931i	$0.993317\pi$
$462$		0			0
$463$	−1.30767e6	+	2.26496e6i	−0.0131752	+	0.0228201i	−0.872538	−	0.488547i	$-0.837527\pi$
$463$	−1.30767e6	+	2.26496e6i	−0.0131752	+	0.0228201i	0.859363	+	0.511367i	$0.170861\pi$
$464$		0			0
$465$	−1.80970e6	−	1.51852e6i	−0.0179989	−	0.0151029i
$466$		0			0
$467$	6.36187e7	+	1.10191e8i	0.624647	+	1.08192i	0.988609	+	0.150506i	$0.0480903\pi$
$467$	6.36187e7	+	1.10191e8i	0.624647	+	1.08192i	−0.363962	+	0.931414i	$0.618576\pi$
$468$		0			0
$469$	−8.86603e6	−	2.43592e7i	−0.0859430	−	0.236127i
$470$		0			0
$471$	3.40660e6	+	600675.i	0.0326030	+	0.00574879i
$472$		0			0
$473$	−2.86629e7	+	2.40511e7i	−0.270855	+	0.227275i
$474$		0			0
$475$	8.30407e7	−	1.55096e6i	0.774837	−	0.0144717i
$476$		0			0
$477$	−1.20097e8	−	1.43126e8i	−1.10657	−	1.31875i
$478$		0			0
$479$	−2.99238e7	+	1.69706e8i	−0.272276	+	1.54415i	0.475207	+	0.879874i	$0.342373\pi$
$479$	−2.99238e7	+	1.69706e8i	−0.272276	+	1.54415i	−0.747483	+	0.664281i	$0.768738\pi$
$480$		0			0
$481$	−2.18155e8	+	7.94018e7i	−1.96033	+	0.713502i
$482$		0			0
$483$	−7.32096e6	+	4.22676e6i	−0.0649721	+	0.0375116i
$484$		0			0
$485$	−2.40246e7	+	2.86314e7i	−0.210586	+	0.250967i
$486$		0			0
$487$	5.67561e7	+	3.27681e7i	0.491389	+	0.283704i	0.725151	−	0.688590i	$-0.241770\pi$
$487$	5.67561e7	+	3.27681e7i	0.491389	+	0.283704i	−0.233761	+	0.972294i	$0.575103\pi$
$488$		0			0
$489$	−1.91460e7	+	3.37596e6i	−0.163739	+	0.0288716i
$490$		0			0
$491$	−9.58041e7	−	3.48699e7i	−0.809356	−	0.294582i	−0.0959984	−	0.995381i	$-0.530604\pi$
$491$	−9.58041e7	−	3.48699e7i	−0.809356	−	0.294582i	−0.713358	+	0.700800i	$0.752827\pi$
$492$		0			0
$493$		−	1.76204e7i		−	0.147054i
$494$		0			0
$495$	−1.26194e7			−0.104045
$496$		0			0
$497$	554778.	−	1.52424e6i	0.00451908	−	0.0124161i
$498$		0			0
$499$	3.84358e7	+	2.17980e8i	0.309338	+	1.75435i	0.602345	+	0.798235i	$0.294233\pi$
$499$	3.84358e7	+	2.17980e8i	0.309338	+	1.75435i	−0.293007	+	0.956110i	$0.594656\pi$
$500$		0			0
$501$	4.80282e6	−	8.31874e6i	0.0381930	−	0.0661522i
$502$		0			0
$503$	1.37967e8	+	1.15768e8i	1.08410	+	0.909669i	0.996255	−	0.0864653i	$-0.0275572\pi$
$503$	1.37967e8	+	1.15768e8i	1.08410	+	0.909669i	0.0878461	+	0.996134i	$0.472002\pi$
$504$		0			0
$505$	3.74637e7	+	6.48890e7i	0.290895	+	0.503845i
$506$		0			0
$507$	−1.29975e7	−	3.57104e7i	−0.0997326	−	0.274013i
$508$		0			0
$509$	5.65120e7	+	9.96459e6i	0.428536	+	0.0755625i	0.383756	−	0.923434i	$-0.374630\pi$
$509$	5.65120e7	+	9.96459e6i	0.428536	+	0.0755625i	0.0447797	+	0.998997i	$0.485741\pi$
$510$		0			0
$511$	1.26184e7	−	1.05881e7i	0.0945676	−	0.0793516i
$512$		0			0
$513$	−4.20398e7	+	8.22503e6i	−0.311393	+	0.0609236i
$514$		0			0
$515$	−7.50240e7	−	8.94101e7i	−0.549261	−	0.654583i
$516$		0			0
$517$	8.04517e6	−	4.56264e7i	0.0582188	−	0.330175i
$518$		0			0
$519$	−1.57721e7	+	5.74056e6i	−0.112820	+	0.0410632i
$520$		0			0
$521$	−1.49649e8	+	8.64000e7i	−1.05818	+	0.610943i	−0.924929	−	0.380139i	$-0.875876\pi$
$521$	−1.49649e8	+	8.64000e7i	−1.05818	+	0.610943i	−0.133254	+	0.991082i	$0.542543\pi$
$522$		0			0
$523$	5.02460e7	−	5.98809e7i	0.351234	−	0.418584i	−0.561282	−	0.827624i	$-0.689692\pi$
$523$	5.02460e7	−	5.98809e7i	0.351234	−	0.418584i	0.912517	+	0.409040i	$0.134136\pi$
$524$		0			0
$525$	−4.93784e6	−	2.85087e6i	−0.0341240	−	0.0197015i
$526$		0			0
$527$	−3.80653e6	+	671194.i	−0.0260074	+	0.00458581i
$528$		0			0
$529$	−1.63764e8	−	5.96052e7i	−1.10624	−	0.402640i
$530$		0			0
$531$			1.52434e8i			1.01812i
$532$		0			0
$533$	1.52015e8			1.00393
$534$		0			0
$535$	3.69975e7	−	1.01650e8i	0.241608	−	0.663812i
$536$		0			0
$537$	−3.97741e6	−	2.25570e7i	−0.0256849	−	0.145666i
$538$		0			0
$539$	1.58640e7	−	2.74773e7i	0.101309	−	0.175472i
$540$		0			0
$541$	1.81326e8	+	1.52151e8i	1.14517	+	0.960910i	0.999596	−	0.0284382i	$-0.00905337\pi$
$541$	1.81326e8	+	1.52151e8i	1.14517	+	0.960910i	0.145572	+	0.989348i	$0.453498\pi$
$542$		0			0
$543$	1.51536e7	+	2.62468e7i	0.0946490	+	0.163937i
$544$		0			0
$545$	−3.49068e6	−	9.59057e6i	−0.0215636	−	0.0592454i
$546$		0			0
$547$	−2.14136e8	−	3.77580e7i	−1.30836	−	0.230700i	−0.524381	−	0.851484i	$-0.675703\pi$
$547$	−2.14136e8	−	3.77580e7i	−1.30836	−	0.230700i	−0.783982	+	0.620784i	$0.786814\pi$
$548$		0			0
$549$	1.15577e7	−	9.69805e6i	0.0698480	−	0.0586094i
$550$		0			0
$551$	2.45881e8	−	1.48149e8i	1.46984	−	0.885614i
$552$		0			0
$553$	−4.35146e7	−	5.18587e7i	−0.257312	−	0.306652i
$554$		0			0
$555$	2.81455e6	−	1.59621e7i	0.0164638	−	0.0933708i
$556$		0			0
$557$	2.22017e8	−	8.08077e7i	1.28476	−	0.467614i	0.392755	−	0.919643i	$-0.371522\pi$
$557$	2.22017e8	−	8.08077e7i	1.28476	−	0.467614i	0.892003	+	0.452030i	$0.149300\pi$
$558$		0			0
$559$	−3.98531e8	+	2.30092e8i	−2.28154	+	1.31725i
$560$		0			0
$561$	351934.	−	419418.i	0.00199330	−	0.00237552i
$562$		0			0
$563$	4.65704e7	+	2.68875e7i	0.260967	+	0.150669i	0.624775	−	0.780804i	$-0.285191\pi$
$563$	4.65704e7	+	2.68875e7i	0.260967	+	0.150669i	−0.363809	+	0.931474i	$0.618524\pi$
$564$		0			0
$565$	−2.72189e7	+	4.79943e6i	−0.150912	+	0.0266099i
$566$		0			0
$567$	−5.00239e7	−	1.82072e7i	−0.274428	−	0.0998837i
$568$		0			0
$569$		−	7.26953e7i		−	0.394611i	−0.980342	−	0.197306i	$-0.936781\pi$
$569$		−	7.26953e7i		−	0.394611i	0.980342	−	0.197306i	$-0.0632192\pi$
$570$		0			0
$571$	2.04269e8			1.09722			0.548610	−	0.836078i	$-0.315157\pi$
$571$	2.04269e8			1.09722			0.548610	+	0.836078i	$0.315157\pi$
$572$		0			0
$573$	1.30490e7	−	3.58518e7i	0.0693606	−	0.190567i
$574$		0			0
$575$	−3.77497e7	−	2.14089e8i	−0.198568	−	1.12614i
$576$		0			0
$577$	1.42587e8	−	2.46968e8i	0.742253	−	1.28562i	−0.209215	−	0.977870i	$-0.567091\pi$
$577$	1.42587e8	−	2.46968e8i	0.742253	−	1.28562i	0.951467	−	0.307750i	$-0.0995760\pi$
$578$		0			0
$579$	1.48771e7	+	1.24834e7i	0.0766447	+	0.0643126i
$580$		0			0
$581$	−1.22743e7	−	2.12598e7i	−0.0625849	−	0.108400i
$582$		0			0
$583$	2.69652e7	+	7.40862e7i	0.136081	+	0.373880i
$584$		0			0
$585$	−1.52846e8	−	2.69509e7i	−0.763461	−	0.134619i
$586$		0			0
$587$	1.63730e8	−	1.37386e8i	0.809495	−	0.679247i	−0.140992	−	0.990011i	$-0.545029\pi$
$587$	1.63730e8	−	1.37386e8i	0.809495	−	0.679247i	0.950487	+	0.310764i	$0.100585\pi$
$588$		0			0
$589$	−4.13706e7	−	4.74741e7i	−0.202463	−	0.232333i
$590$		0			0
$591$	−2.51833e7	−	3.00122e7i	−0.121997	−	0.145391i
$592$		0			0
$593$	−1.43121e7	+	8.11682e7i	−0.0686342	+	0.389244i	0.931068	+	0.364845i	$0.118878\pi$
$593$	−1.43121e7	+	8.11682e7i	−0.0686342	+	0.389244i	−0.999702	+	0.0243985i	$0.992233\pi$
$594$		0			0
$595$	2.54547e6	−	926477.i	0.0120842	−	0.00439829i
$596$		0			0
$597$	−2.20046e7	+	1.27044e7i	−0.103417	+	0.0597078i
$598$		0			0
$599$	1.82445e8	−	2.17429e8i	0.848890	−	1.01167i	−0.150843	−	0.988558i	$-0.548199\pi$
$599$	1.82445e8	−	2.17429e8i	0.848890	−	1.01167i	0.999733	−	0.0231098i	$-0.00735673\pi$
$600$		0			0
$601$	−2.83689e7	−	1.63788e7i	−0.130683	−	0.0754498i	0.433233	−	0.901282i	$-0.357373\pi$
$601$	−2.83689e7	−	1.63788e7i	−0.130683	−	0.0754498i	−0.563916	+	0.825832i	$0.690706\pi$
$602$		0			0
$603$	−1.67084e8	+	2.94614e7i	−0.762049	+	0.134370i
$604$		0			0
$605$	−9.37081e7	−	3.41070e7i	−0.423166	−	0.154020i
$606$		0			0
$607$		−	1.72002e8i		−	0.769073i	−0.923110	−	0.384536i	$-0.874361\pi$
$607$		−	1.72002e8i		−	0.769073i	0.923110	−	0.384536i	$-0.125639\pi$
$608$		0			0
$609$	−1.97069e7			−0.0872501
$610$		0			0
$611$	1.94887e8	−	5.35446e8i	0.854394	−	2.34743i
$612$		0			0
$613$	5.34637e7	+	3.03208e8i	0.232101	+	1.31631i	0.848633	+	0.528982i	$0.177426\pi$
$613$	5.34637e7	+	3.03208e8i	0.232101	+	1.31631i	−0.616532	+	0.787330i	$0.711463\pi$
$614$		0			0
$615$	−5.30660e6	+	9.19130e6i	−0.0228134	+	0.0395140i
$616$		0			0
$617$	2.22119e8	+	1.86380e8i	0.945648	+	0.793493i	0.978559	−	0.205965i	$-0.0660334\pi$
$617$	2.22119e8	+	1.86380e8i	0.945648	+	0.793493i	−0.0329113	+	0.999458i	$0.510478\pi$
$618$		0			0
$619$	1.55810e8	+	2.69871e8i	0.656937	+	1.13785i	0.981404	+	0.191952i	$0.0614817\pi$
$619$	1.55810e8	+	2.69871e8i	0.656937	+	1.13785i	−0.324467	+	0.945897i	$0.605185\pi$
$620$		0			0
$621$	3.83483e7	+	1.05361e8i	0.160129	+	0.439952i
$622$		0			0
$623$	1.07306e8	+	1.89210e7i	0.443772	+	0.0782490i
$624$		0			0
$625$	7.02370e7	−	5.89359e7i	0.287691	−	0.241401i
$626$		0			0
$627$	8.81167e6	+	1.38460e6i	0.0357483	+	0.00561722i
$628$		0			0
$629$	−1.70464e7	−	2.03151e7i	−0.0684984	−	0.0816332i
$630$		0			0
$631$	−5.71437e7	+	3.24078e8i	−0.227447	+	1.28992i	0.630505	+	0.776186i	$0.282848\pi$
$631$	−5.71437e7	+	3.24078e8i	−0.227447	+	1.28992i	−0.857952	+	0.513731i	$0.828263\pi$
$632$		0			0
$633$	4.94170e7	−	1.79863e7i	0.194834	−	0.0709138i
$634$		0			0
$635$	4.78758e7	−	2.76411e7i	0.186980	−	0.107953i
$636$		0			0
$637$	2.50828e8	−	2.98925e8i	0.970415	−	1.15650i
$638$		0			0
$639$	−9.19399e6	−	5.30815e6i	−0.0352372	−	0.0203442i
$640$		0			0
$641$	−1.80113e8	+	3.17588e7i	−0.683867	+	0.120584i	−0.504779	−	0.863249i	$-0.668426\pi$
$641$	−1.80113e8	+	3.17588e7i	−0.683867	+	0.120584i	−0.179088	+	0.983833i	$0.557315\pi$
$642$		0			0
$643$	−3.85399e8	−	1.40274e8i	−1.44970	−	0.527647i	−0.507192	−	0.861833i	$-0.669317\pi$
$643$	−3.85399e8	−	1.40274e8i	−1.44970	−	0.527647i	−0.942507	+	0.334185i	$0.891539\pi$
$644$		0			0
$645$		−	3.21286e7i		−	0.119733i
$646$		0			0
$647$	−3.00921e8			−1.11107			−0.555533	−	0.831495i	$-0.687486\pi$
$647$	−3.00921e8			−1.11107			−0.555533	+	0.831495i	$0.687486\pi$
$648$		0			0
$649$	2.19999e7	−	6.04443e7i	0.0804799	−	0.221117i
$650$		0			0
$651$	750670.	+	4.25726e6i	0.00272086	+	0.0154308i
$652$		0			0
$653$	1.02171e8	−	1.76965e8i	0.366933	−	0.635547i	−0.622151	−	0.782897i	$-0.713741\pi$
$653$	1.02171e8	−	1.76965e8i	0.366933	−	0.635547i	0.989084	+	0.147350i	$0.0470743\pi$
$654$		0			0
$655$	−3.27533e7	−	2.74833e7i	−0.116555	−	0.0978012i
$656$		0			0
$657$	−5.39048e7	−	9.33658e7i	−0.190078	−	0.329224i
$658$		0			0
$659$	9.67943e7	+	2.65940e8i	0.338215	+	0.929239i	0.985901	+	0.167331i	$0.0535149\pi$
$659$	9.67943e7	+	2.65940e8i	0.338215	+	0.929239i	−0.647685	+	0.761908i	$0.724263\pi$
$660$		0			0
$661$	1.66901e8	+	2.94292e7i	0.577903	+	0.101900i	0.454957	−	0.890513i	$-0.349655\pi$
$661$	1.66901e8	+	2.94292e7i	0.577903	+	0.101900i	0.122946	+	0.992413i	$0.460766\pi$
$662$		0			0
$663$	5.15837e6	−	4.32839e6i	0.0176999	−	0.0148520i
$664$		0			0
$665$	3.43302e7	+	2.77306e7i	0.116738	+	0.0942964i
$666$		0			0
$667$	−4.82972e8	−	5.75583e8i	−1.62759	−	1.93968i
$668$		0			0
$669$	−5.36469e6	+	3.04247e7i	−0.0179171	+	0.101613i
$670$		0			0
$671$	−5.98260e6	+	2.17749e6i	−0.0198026	+	0.00720755i
$672$		0			0
$673$	−3.38823e8	+	1.95619e8i	−1.11155	+	0.641751i	−0.939229	−	0.343291i	$-0.888458\pi$
$673$	−3.38823e8	+	1.95619e8i	−1.11155	+	0.641751i	−0.172316	+	0.985042i	$0.555125\pi$
$674$		0			0
$675$	−4.86106e7	+	5.79318e7i	−0.158059	+	0.188367i
$676$		0			0
$677$	3.44170e8	+	1.98707e8i	1.10919	+	0.640393i	0.938620	−	0.344952i	$-0.112105\pi$
$677$	3.44170e8	+	1.98707e8i	1.10919	+	0.640393i	0.170573	+	0.985345i	$0.445438\pi$
$678$		0			0
$679$	6.73545e7	−	1.18764e7i	0.215158	−	0.0379381i
$680$		0			0
$681$	1.93027e7	+	7.02561e6i	0.0611191	+	0.0222455i
$682$		0			0
$683$			4.57229e8i			1.43506i	0.696525	+	0.717532i	$0.254728\pi$
$683$			4.57229e8i			1.43506i	−0.696525	+	0.717532i	$0.745272\pi$
$684$		0			0
$685$	6.64230e7			0.206655
$686$		0			0
$687$	−3.16077e7	+	8.68414e7i	−0.0974816	+	0.267828i
$688$		0			0
$689$	1.68379e8	+	9.54923e8i	0.514789	+	2.91952i
$690$		0			0
$691$	−2.05612e8	+	3.56130e8i	−0.623181	+	1.07938i	0.365709	+	0.930729i	$0.380827\pi$
$691$	−2.05612e8	+	3.56130e8i	−0.623181	+	1.07938i	−0.988890	+	0.148652i	$0.952507\pi$
$692$		0			0
$693$	1.76896e7	+	1.48434e7i	0.0531519	+	0.0445997i
$694$		0			0
$695$	−1.15375e8	−	1.99836e8i	−0.343683	−	0.595277i
$696$		0			0
$697$	5.93914e6	+	1.63177e7i	0.0175398	+	0.0481903i
$698$		0			0
$699$	−6.52755e6	−	1.15098e6i	−0.0191126	−	0.00337006i
$700$		0			0
$701$	1.59937e8	−	1.34203e8i	0.464297	−	0.389591i	−0.380412	−	0.924817i	$-0.624218\pi$
$701$	1.59937e8	−	1.34203e8i	0.464297	−	0.389591i	0.844709	+	0.535226i	$0.179773\pi$
$702$		0			0
$703$	1.40160e8	−	4.08675e8i	0.403420	−	1.17628i
$704$		0			0
$705$	2.55716e7	+	3.04750e7i	0.0729778	+	0.0869715i
$706$		0			0
$707$	2.38088e7	−	1.35027e8i	0.0673720	−	0.382086i
$708$		0			0
$709$	−4.28921e8	+	1.56115e8i	−1.20348	+	0.438031i	−0.864438	−	0.502740i	$-0.832325\pi$
$709$	−4.28921e8	+	1.56115e8i	−1.20348	+	0.438031i	−0.339043	+	0.940771i	$0.610103\pi$
$710$		0			0
$711$	−3.83711e8	+	2.21536e8i	−1.06757	+	0.616361i
$712$		0			0
$713$	−1.05945e8	+	1.26261e8i	−0.292290	+	0.348337i
$714$		0			0
$715$	5.67179e7	+	3.27461e7i	0.155168	+	0.0895863i
$716$		0			0
$717$	−6.50851e6	+	1.14763e6i	−0.0176573	+	0.00311346i
$718$		0			0
$719$	−1.59270e8	−	5.79694e7i	−0.428496	−	0.155960i	0.118764	−	0.992922i	$-0.462107\pi$
$719$	−1.59270e8	−	5.79694e7i	−0.428496	−	0.155960i	−0.547260	+	0.836963i	$0.684329\pi$
$720$		0			0
$721$			2.13580e8i			0.569841i
$722$		0			0
$723$	5.40209e7			0.142938
$724$		0			0
$725$	1.73331e8	−	4.76222e8i	0.454842	−	1.24967i
$726$		0			0
$727$	1.89960e7	+	1.07732e8i	0.0494379	+	0.280376i	0.999498	−	0.0316918i	$-0.0100895\pi$
$727$	1.89960e7	+	1.07732e8i	0.0494379	+	0.280376i	−0.950060	+	0.312068i	$0.898978\pi$
$728$		0			0
$729$	−1.64329e8	+	2.84627e8i	−0.424163	+	0.734671i
$730$		0			0
$731$	−4.02691e7	−	3.37898e7i	−0.103091	−	0.0865035i
$732$		0			0
$733$	9.90834e7	+	1.71617e8i	0.251587	+	0.435762i	0.963963	−	0.266036i	$-0.0857141\pi$
$733$	9.90834e7	+	1.71617e8i	0.251587	+	0.435762i	−0.712376	+	0.701798i	$0.752381\pi$
$734$		0			0
$735$	9.31795e6	+	2.56009e7i	0.0234670	+	0.0644752i
$736$		0			0
$737$	7.05053e7	+	1.24320e7i	0.176124	+	0.0310555i
$738$		0			0
$739$	1.03985e8	−	8.72537e7i	0.257654	−	0.216197i	−0.504806	−	0.863233i	$-0.668436\pi$
$739$	1.03985e8	−	8.72537e7i	0.257654	−	0.216197i	0.762460	+	0.647035i	$0.223991\pi$
$740$		0			0
$741$	1.03770e8	+	3.55892e7i	0.255045	+	0.0874708i
$742$		0			0
$743$	−1.54725e8	−	1.84394e8i	−0.377219	−	0.449553i	0.543715	−	0.839270i	$-0.317017\pi$
$743$	−1.54725e8	−	1.84394e8i	−0.377219	−	0.449553i	−0.920935	+	0.389717i	$0.872573\pi$
$744$		0			0
$745$	−3.95994e7	+	2.24579e8i	−0.0957679	+	0.543127i
$746$		0			0
$747$	−1.50980e8	+	5.49523e7i	−0.362208	+	0.131833i
$748$		0			0
$749$	−1.71427e8	+	9.89732e7i	−0.407974	+	0.235544i
$750$		0			0
$751$	−2.95147e8	+	3.51742e8i	−0.696817	+	0.830434i	−0.992162	−	0.124957i	$-0.960121\pi$
$751$	−2.95147e8	+	3.51742e8i	−0.696817	+	0.830434i	0.295345	+	0.955391i	$0.404565\pi$
$752$		0			0
$753$	2.92154e7	+	1.68675e7i	0.0684269	+	0.0395063i
$754$		0			0
$755$	1.62780e8	−	2.87026e7i	0.378235	−	0.0666930i
$756$		0			0
$757$	−4.49888e8	−	1.63746e8i	−1.03709	−	0.377470i	−0.233314	−	0.972401i	$-0.574957\pi$
$757$	−4.49888e8	−	1.63746e8i	−1.03709	−	0.377470i	−0.803777	+	0.594931i	$0.797179\pi$
$758$		0			0
$759$		−	2.33470e7i		−	0.0533956i
$760$		0			0
$761$	2.83137e8			0.642456			0.321228	−	0.947002i	$-0.395904\pi$
$761$	2.83137e8			0.642456			0.321228	+	0.947002i	$0.395904\pi$
$762$		0			0
$763$	−6.38759e6	+	1.75498e7i	−0.0143802	+	0.0395092i
$764$		0			0
$765$	−3.07864e6	−	1.74598e7i	−0.00687662	−	0.0389992i
$766$		0			0
$767$	3.95553e8	−	6.85119e8i	0.876636	−	1.51838i
$768$		0			0
$769$	3.34186e8	+	2.80416e8i	0.734868	+	0.616628i	0.931454	−	0.363859i	$-0.118541\pi$
$769$	3.34186e8	+	2.80416e8i	0.734868	+	0.616628i	−0.196586	+	0.980487i	$0.562985\pi$
$770$		0			0
$771$	−3.30805e7	−	5.72972e7i	−0.0721788	−	0.125017i
$772$		0			0
$773$	−1.08240e8	−	2.97387e8i	−0.234342	−	0.643849i	−1.00000		0.000600907i	$-0.999809\pi$
$773$	−1.08240e8	−	2.97387e8i	−0.234342	−	0.643849i	0.765658	−	0.643248i	$-0.222413\pi$
$774$		0			0
$775$	−1.09480e8	−	1.93043e7i	−0.235196	−	0.0414715i
$776$		0			0
$777$	−2.27206e7	+	1.90648e7i	−0.0484347	+	0.0406415i
$778$		0			0
$779$	−1.77766e8	+	2.20072e8i	−0.376042	+	0.465535i
$780$		0			0
$781$	2.87957e6	+	3.43174e6i	0.00604470	+	0.00720379i
$782$		0			0
$783$	−4.53884e7	+	2.57410e8i	−0.0945495	+	0.536217i
$784$		0			0
$785$	−4.44158e7	+	1.61660e7i	−0.0918182	+	0.0334191i
$786$		0			0
$787$	3.85266e8	−	2.22433e8i	0.790380	−	0.456326i	−0.0497160	−	0.998763i	$-0.515832\pi$
$787$	3.85266e8	−	2.22433e8i	0.790380	−	0.456326i	0.840096	+	0.542437i	$0.182498\pi$
$788$		0			0
$789$	7.34827e7	−	8.75733e7i	0.149608	−	0.178296i
$790$		0			0
$791$	4.38003e7	+	2.52881e7i	0.0885008	+	0.0510960i
$792$		0			0
$793$	−7.71118e7	+	1.35969e7i	−0.154633	+	0.0272659i
$794$		0			0
$795$	−6.36155e7	−	2.31542e7i	−0.126608	−	0.0460816i
$796$		0			0
$797$		−	3.80132e8i		−	0.750861i	−0.926851	−	0.375430i	$-0.877495\pi$
$797$		−	3.80132e8i		−	0.750861i	0.926851	−	0.375430i	$-0.122505\pi$
$798$		0			0
$799$	6.50903e7			0.127607
$800$		0			0
$801$	2.43911e8	−	6.70139e8i	0.474606	−	1.30397i
$802$		0			0
$803$	7.89977e6	+	4.48018e7i	0.0152570	+	0.0865265i
$804$		0			0
$805$	5.77551e7	−	1.00035e8i	0.110714	−	0.191762i
$806$		0			0
$807$	3.02381e7	+	2.53728e7i	0.0575353	+	0.0482779i
$808$		0			0
$809$	3.62284e8	+	6.27493e8i	0.684231	+	1.18512i	0.973678	+	0.227929i	$0.0731955\pi$
$809$	3.62284e8	+	6.27493e8i	0.684231	+	1.18512i	−0.289446	+	0.957194i	$0.593471\pi$
$810$		0			0
$811$	−2.92391e7	−	8.03337e7i	−0.0548152	−	0.150604i	0.909263	−	0.416222i	$-0.136646\pi$
$811$	−2.92391e7	−	8.03337e7i	−0.0548152	−	0.150604i	−0.964078	+	0.265618i	$0.914424\pi$
$812$		0			0
$813$	−1.07531e8	−	1.89606e7i	−0.200106	−	0.0352842i
$814$		0			0
$815$	2.03500e8	−	1.70757e8i	0.375916	−	0.315431i
$816$		0			0
$817$	1.32938e8	−	8.46024e8i	0.243771	−	1.55137i
$818$		0			0
$819$	1.82557e8	+	2.17562e8i	0.332312	+	0.396034i
$820$		0			0
$821$	−7.03681e7	+	3.99077e8i	−0.127159	+	0.721153i	0.852844	+	0.522167i	$0.174876\pi$
$821$	−7.03681e7	+	3.99077e8i	−0.127159	+	0.721153i	−0.980002	+	0.198986i	$0.936235\pi$
$822$		0			0
$823$	2.14296e8	−	7.79973e7i	0.384427	−	0.139920i	−0.142575	−	0.989784i	$-0.545538\pi$
$823$	2.14296e8	−	7.79973e7i	0.384427	−	0.139920i	0.527002	+	0.849864i	$0.323316\pi$
$824$		0			0
$825$	1.36374e7	−	7.87353e6i	0.0242867	−	0.0140219i
$826$		0			0
$827$	7.07627e8	−	8.43317e8i	1.25109	−	1.49099i	0.449298	−	0.893382i	$-0.351674\pi$
$827$	7.07627e8	−	8.43317e8i	1.25109	−	1.49099i	0.801790	−	0.597606i	$-0.203881\pi$
$828$		0			0
$829$	2.54920e7	+	1.47178e7i	0.0447445	+	0.0258333i	0.522205	−	0.852820i	$-0.325109\pi$
$829$	2.54920e7	+	1.47178e7i	0.0447445	+	0.0258333i	−0.477461	+	0.878653i	$0.658443\pi$
$830$		0			0
$831$	−1.06492e7	+	1.87774e6i	−0.0185573	+	0.00327215i
$832$		0			0
$833$	4.18871e7	+	1.52457e7i	0.0724678	+	0.0263761i
$834$		0			0
$835$			1.31253e8i			0.225450i
$836$		0			0
$837$	5.73370e7			0.0977820
$838$		0			0
$839$	−1.05496e8	+	2.89849e8i	−0.178629	+	0.490779i	−0.996401	−	0.0847632i	$-0.972987\pi$
$839$	−1.05496e8	+	2.89849e8i	−0.178629	+	0.490779i	0.817772	+	0.575542i	$0.195209\pi$
$840$		0			0
$841$	−2.00872e8	−	1.13920e9i	−0.337700	−	1.91519i
$842$		0			0
$843$	604744.	−	1.04745e6i	0.00100946	−	0.00174843i
$844$		0			0
$845$	3.97783e8	+	3.33779e8i	0.659289	+	0.553209i
$846$		0			0
$847$	9.12406e7	+	1.58033e8i	0.150154	+	0.260075i
$848$		0			0
$849$	2.45218e7	+	6.73730e7i	0.0400708	+	0.110094i
$850$		0			0
$851$	−1.11366e9	−	1.96369e8i	−1.80703	−	0.318628i
$852$		0			0
$853$	−2.99545e8	+	2.51348e8i	−0.482631	+	0.404975i	−0.851377	−	0.524555i	$-0.824232\pi$
$853$	−2.99545e8	+	2.51348e8i	−0.482631	+	0.404975i	0.368746	+	0.929530i	$0.379787\pi$
$854$		0			0
$855$	2.17755e8	−	1.89759e8i	0.348393	−	0.303602i
$856$		0			0
$857$	−4.24517e8	−	5.05920e8i	−0.674455	−	0.803784i	0.314928	−	0.949116i	$-0.398020\pi$
$857$	−4.24517e8	−	5.05920e8i	−0.674455	−	0.803784i	−0.989383	+	0.145331i	$0.953575\pi$
$858$		0			0
$859$	8.69923e7	−	4.93358e8i	0.137246	−	0.778363i	−0.836023	−	0.548695i	$-0.815125\pi$
$859$	8.69923e7	−	4.93358e8i	0.137246	−	0.778363i	0.973269	−	0.229668i	$-0.0737641\pi$
$860$		0			0
$861$	1.82498e7	−	6.64240e6i	0.0285923	−	0.0104068i
$862$		0			0
$863$	−6.22220e8	+	3.59239e8i	−0.968081	+	0.558922i	−0.898651	−	0.438665i	$-0.855451\pi$
$863$	−6.22220e8	+	3.59239e8i	−0.968081	+	0.558922i	−0.0694301	+	0.997587i	$0.522118\pi$
$864$		0			0
$865$	1.47419e8	−	1.75687e8i	0.227774	−	0.271451i
$866$		0			0
$867$	−9.00469e7	−	5.19886e7i	−0.138169	−	0.0797720i
$868$		0			0
$869$	1.84125e8	−	3.24662e7i	0.280578	−	0.0494734i
$870$		0			0
$871$	8.27412e8	+	3.01153e8i	1.25218	+	0.455757i
$872$		0			0
$873$		−	4.47632e8i		−	0.672788i
$874$		0			0
$875$	1.78441e8			0.266361
$876$		0			0
$877$	−9.31784e7	+	2.56006e8i	−0.138139	+	0.379534i	−0.989401	−	0.145206i	$-0.953615\pi$
$877$	−9.31784e7	+	2.56006e8i	−0.138139	+	0.379534i	0.851262	+	0.524740i	$0.175838\pi$
$878$		0			0
$879$	−1.80081e7	−	1.02129e8i	−0.0265156	−	0.150377i
$880$		0			0
$881$	9.05577e7	−	1.56850e8i	0.132433	−	0.229381i	−0.792181	−	0.610287i	$-0.791054\pi$
$881$	9.05577e7	−	1.56850e8i	0.132433	−	0.229381i	0.924614	+	0.380905i	$0.124388\pi$
$882$		0			0
$883$	5.79151e8	+	4.85966e8i	0.841221	+	0.705868i	0.957838	−	0.287309i	$-0.0927607\pi$
$883$	5.79151e8	+	4.85966e8i	0.841221	+	0.705868i	−0.116617	+	0.993177i	$0.537205\pi$
$884$		0			0
$885$	2.76163e7	+	4.78328e7i	0.0398415	+	0.0690075i
$886$		0			0
$887$	−2.06055e8	−	5.66131e8i	−0.295265	−	0.811233i	−0.995275	−	0.0971002i	$-0.969043\pi$
$887$	−2.06055e8	−	5.66131e8i	−0.295265	−	0.811233i	0.700010	−	0.714133i	$-0.253179\pi$
$888$		0			0
$889$	−9.96239e7	−	1.75664e7i	−0.141794	−	0.0250021i
$890$		0			0
$891$	1.12626e8	−	9.45045e7i	0.159223	−	0.133604i
$892$		0			0
$893$	5.47266e8	+	9.08289e8i	0.768501	+	1.27547i
$894$		0			0
$895$	2.01178e8	+	2.39755e8i	0.280615	+	0.334424i
$896$		0			0
$897$	4.98616e7	−	2.82779e8i	0.0690858	−	0.391805i
$898$		0			0
$899$	−3.61061e8	+	1.31416e8i	−0.496938	+	0.180871i
$900$		0			0
$901$	−9.59254e7	+	5.53826e7i	−0.131147	+	0.0757179i
$902$		0			0
$903$	−3.77908e7	+	4.50374e7i	−0.0513243	+	0.0611660i
$904$		0			0
$905$	−3.58640e8	−	2.07061e8i	−0.483853	−	0.279353i
$906$		0			0
$907$	−3.20686e8	+	5.65456e7i	−0.429792	+	0.0757839i	−0.384359	−	0.923184i	$-0.625578\pi$
$907$	−3.20686e8	+	5.65456e7i	−0.429792	+	0.0757839i	−0.0454323	+	0.998967i	$0.514467\pi$
$908$		0			0
$909$	−8.43256e8	−	3.06920e8i	−1.12271	−	0.408633i
$910$		0			0
$911$			4.57033e7i			0.0604494i	0.999543	+	0.0302247i	$0.00962229\pi$
$911$			4.57033e7i			0.0604494i	−0.999543	+	0.0302247i	$0.990378\pi$
$912$		0			0
$913$	6.77986e7			0.0890858
$914$		0			0
$915$	1.86974e6	−	5.13707e6i	0.00244072	−	0.00670582i
$916$		0			0
$917$	1.35862e7	+	7.70511e7i	0.0176193	+	0.0999243i
$918$		0			0
$919$	−2.63865e8	+	4.57028e8i	−0.339966	+	0.588839i	−0.984426	−	0.175800i	$-0.943749\pi$
$919$	−2.63865e8	+	4.57028e8i	−0.339966	+	0.588839i	0.644460	+	0.764638i	$0.277082\pi$
$920$		0			0
$921$	−204769.	−	171822.i	−0.000262111	−	0.000219937i
$922$		0			0
$923$	2.75484e7	+	4.77152e7i	0.0350341	+	0.0606808i
$924$		0			0
$925$	−2.60869e8	−	7.16732e8i	−0.329608	−	0.905590i
$926$		0			0
$927$	1.37663e9	+	2.42737e8i	1.72814	+	0.304717i
$928$		0			0
$929$	−3.04318e8	+	2.55353e8i	−0.379559	+	0.318488i	−0.812529	−	0.582920i	$-0.801910\pi$
$929$	−3.04318e8	+	2.55353e8i	−0.379559	+	0.318488i	0.432970	+	0.901408i	$0.357466\pi$
$930$		0			0
$931$	1.39436e8	+	7.12687e8i	0.172793	+	0.883181i
$932$		0			0
$933$	−8.31170e7	−	9.90550e7i	−0.102340	−	0.121964i
$934$		0			0
$935$	−1.29911e6	+	7.36762e6i	−0.00158932	+	0.00901348i
$936$		0			0
$937$	1.76206e8	−	6.41337e7i	0.214191	−	0.0779592i	−0.232696	−	0.972550i	$-0.574755\pi$
$937$	1.76206e8	−	6.41337e7i	0.214191	−	0.0779592i	0.446887	+	0.894590i	$0.352533\pi$
$938$		0			0
$939$	−1.46291e8	+	8.44613e7i	−0.176694	+	0.102014i
$940$		0			0
$941$	−8.00902e8	+	9.54477e8i	−0.961192	+	1.14550i	0.0281071	+	0.999605i	$0.491052\pi$
$941$	−8.00902e8	+	9.54477e8i	−0.961192	+	1.14550i	−0.989299	+	0.145900i	$0.953392\pi$
$942$		0			0
$943$	6.41269e8	+	3.70237e8i	0.764724	+	0.441514i
$944$		0			0
$945$	−3.95723e7	+	6.97767e6i	−0.0468917	+	0.00826828i
$946$		0			0
$947$	−6.56153e8	−	2.38820e8i	−0.772601	−	0.281204i	−0.0745173	−	0.997220i	$-0.523742\pi$
$947$	−6.56153e8	−	2.38820e8i	−0.772601	−	0.281204i	−0.698084	+	0.716016i	$0.745964\pi$
$948$		0			0
$949$			5.59512e8i			0.654653i
$950$		0			0
$951$	−2.15076e8			−0.250064
$952$		0			0
$953$	−2.63356e8	+	7.23566e8i	−0.304274	+	0.835986i	0.689471	+	0.724313i	$0.257843\pi$
$953$	−2.63356e8	+	7.23566e8i	−0.304274	+	0.835986i	−0.993745	+	0.111673i	$0.964379\pi$
$954$		0			0
$955$	9.05269e7	+	5.13404e8i	0.103936	+	0.589453i
$956$		0			0
$957$	2.72133e7	−	4.71348e7i	0.0310488	−	0.0537781i
$958$		0			0
$959$	−9.31107e7	−	7.81291e7i	−0.105571	−	0.0885844i
$960$		0			0
$961$	−4.01609e8	−	6.95607e8i	−0.452515	−	0.783779i
$962$		0			0
$963$	4.43104e8	+	1.21742e9i	0.496165	+	1.36320i
$964$		0			0
$965$	−2.61335e8	−	4.60805e7i	−0.290815	−	0.0512785i
$966$		0			0
$967$	−7.80410e8	+	6.54842e8i	−0.863065	+	0.724197i	−0.962626	−	0.270834i	$-0.912700\pi$
$967$	−7.80410e8	+	6.54842e8i	−0.863065	+	0.724197i	0.0995614	+	0.995031i	$0.468256\pi$
$968$		0			0
$969$	234013.	+	1.25294e7i	0.000257199	+	0.0137708i
$970$		0			0
$971$	2.25110e8	+	2.68275e8i	0.245888	+	0.293037i	0.874846	−	0.484402i	$-0.160963\pi$
$971$	2.25110e8	+	2.68275e8i	0.245888	+	0.293037i	−0.628958	+	0.777439i	$0.716518\pi$
$972$		0			0
$973$	−7.33229e7	+	4.15835e8i	−0.0795978	+	0.451422i
$974$		0			0
$975$	1.81991e8	−	6.62395e7i	0.196353	−	0.0714666i
$976$		0			0
$977$	7.87732e8	−	4.54797e8i	0.844685	−	0.487679i	−0.0141689	−	0.999900i	$-0.504510\pi$
$977$	7.87732e8	−	4.54797e8i	0.844685	−	0.487679i	0.858854	+	0.512220i	$0.171177\pi$
$978$		0			0
$979$	−1.93434e8	+	2.30526e8i	−0.206151	+	0.245681i
$980$		0			0
$981$	1.05858e8	+	6.11169e7i	0.112128	+	0.0647373i
$982$		0			0
$983$	4.47181e8	−	7.88500e7i	0.470785	−	0.0830121i	0.0667777	−	0.997768i	$-0.478728\pi$
$983$	4.47181e8	−	7.88500e7i	0.470785	−	0.0830121i	0.404007	+	0.914756i	$0.367617\pi$
$984$		0			0
$985$	5.03052e8	+	1.83096e8i	0.526386	+	0.191589i
$986$		0			0
$987$		−	7.27976e7i		−	0.0757122i
$988$		0			0
$989$	−2.24159e9			−2.31722
$990$		0			0
$991$	2.53545e8	−	6.96609e8i	0.260516	−	0.715761i	−0.738617	−	0.674125i	$-0.764521\pi$
$991$	2.53545e8	−	6.96609e8i	0.260516	−	0.715761i	0.999133	−	0.0416359i	$-0.0132569\pi$
$992$		0			0
$993$	−3.53544e7	−	2.00505e8i	−0.0361074	−	0.204775i
$994$		0			0
$995$	1.73595e8	−	3.00675e8i	0.176225	−	0.305230i
$996$		0			0
$997$	−8.68788e8	−	7.29000e8i	−0.876654	−	0.735600i	0.0888339	−	0.996046i	$-0.471686\pi$
$997$	−8.68788e8	−	7.29000e8i	−0.876654	−	0.735600i	−0.965488	+	0.260446i	$0.916130\pi$
$998$		0			0
$999$	1.96694e8	+	3.40685e8i	0.197286	+	0.341709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.j.a.13.6	✓	60
19.3	odd	18	inner	76.7.j.a.41.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.j.a.13.6	✓	60	1.1	even	1	trivial
76.7.j.a.41.6	yes	60	19.3	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.48422 + 4.07785i) q^{3} +(-10.2967 - 58.3955i) q^{5} +(-54.2532 + 93.9692i) q^{7} +(544.020 + 456.487i) q^{9} +O(q^{10})\)	\(q+(-1.48422 + 4.07785i) q^{3} +(-10.2967 - 58.3955i) q^{5} +(-54.2532 + 93.9692i) q^{7} +(544.020 + 456.487i) q^{9} +(-149.837 - 259.525i) q^{11} +(-1260.56 - 3463.37i) q^{13} +(253.411 + 44.6832i) q^{15} +(322.518 - 270.624i) q^{17} +(6488.04 + 2225.15i) q^{19} +(-302.669 - 360.707i) q^{21} +(3117.50 - 17680.2i) q^{23} +(11378.7 - 4141.50i) q^{25} +(-5408.64 + 3122.68i) q^{27} +(26902.0 - 32060.6i) q^{29} +(-7950.76 - 4590.37i) q^{31} +(1280.69 - 225.821i) q^{33} +(6046.01 + 2200.57i) q^{35} -62989.0i q^{37} +15994.1 q^{39} +(-14106.7 + 38757.7i) q^{41} +(-21681.5 - 122962. i) q^{43} +(21055.2 - 36468.7i) q^{45} +(118432. + 99376.6i) q^{47} +(52937.7 + 91690.8i) q^{49} +(624.880 + 1716.84i) q^{51} +(-259093. - 45685.0i) q^{53} +(-13612.3 + 11422.0i) q^{55} +(-18703.5 + 23154.6i) q^{57} +(137971. + 164428. i) q^{59} +(3689.15 - 20922.2i) q^{61} +(-72410.6 + 26355.3i) q^{63} +(-189266. + 109273. i) q^{65} +(-153564. + 183011. i) q^{67} +(67470.3 + 38954.0i) q^{69} +(-14721.9 + 2595.87i) q^{71} +(-142653. - 51921.6i) q^{73} +52547.4i q^{75} +32516.5 q^{77} +(-213385. + 586271. i) q^{79} +(85193.6 + 483157. i) q^{81} +(-113121. + 195931. i) q^{83} +(-19124.1 - 16047.1i) q^{85} +(90809.8 + 157287. i) q^{87} +(-343455. - 943634. i) q^{89} +(393840. + 69444.7i) q^{91} +(30519.5 - 25608.9i) q^{93} +(63133.3 - 401784. i) q^{95} +(-405161. - 482852. i) q^{97} +(36955.5 - 209585. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 216 q^{7} + 690 q^{9}+O(q^{10}) \) 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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