LMFDB - Embedded newform 76.7.h.a.69.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(65,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("76.65");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9460 x^{18} + 36670708 x^{16} + 75655761912 x^{14} + 90488614064544 x^{12} + \cdots + 10\!\cdots\!00 $ x^20 + 9460x^18 + 36670708x^16 + 75655761912x^14 + 90488614064544x^12 + 64290781142478432x^10 + 26741969359067432592x^8 + 6092313787108272225600x^6 + 632563499034568748983104x^4 + 15152233769669432690883072*x^2 + 103372598905826219735270400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{8}\cdot 19^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.6
Root			$-4.04998i$ of defining polynomial
Character	$\chi$	$=$	76.69
Dual form			76.7.h.a.65.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00739 - 1.15896i) q^{3} +(-67.5013 - 116.916i) q^{5} -157.715 q^{7} +(-361.814 + 626.680i) q^{9} +O(q^{10})$	\(q+(2.00739 - 1.15896i) q^{3} +(-67.5013 - 116.916i) q^{5} -157.715 q^{7} +(-361.814 + 626.680i) q^{9} +663.253 q^{11} +(1630.93 + 941.616i) q^{13} +(-271.002 - 156.463i) q^{15} +(938.453 + 1625.45i) q^{17} +(-2954.88 + 6189.88i) q^{19} +(-316.595 + 182.786i) q^{21} +(-4912.56 + 8508.80i) q^{23} +(-1300.35 + 2252.27i) q^{25} +3367.09i q^{27} +(12606.8 + 7278.51i) q^{29} +44573.3i q^{31} +(1331.41 - 768.687i) q^{33} +(10646.0 + 18439.4i) q^{35} +55050.8i q^{37} +4365.20 q^{39} +(-35438.6 + 20460.5i) q^{41} +(-14840.5 - 25704.5i) q^{43} +97691.5 q^{45} +(-10194.0 + 17656.5i) q^{47} -92774.9 q^{49} +(3767.68 + 2175.27i) q^{51} +(-112309. - 64841.8i) q^{53} +(-44770.4 - 77544.7i) q^{55} +(1242.27 + 15850.1i) q^{57} +(294641. - 170111. i) q^{59} +(-47067.9 + 81524.0i) q^{61} +(57063.5 - 98836.8i) q^{63} -254241. i q^{65} +(154080. + 88958.1i) q^{67} +22773.9i q^{69} +(112740. - 65090.7i) q^{71} +(-364203. - 630818. i) q^{73} +6028.23i q^{75} -104605. q^{77} +(-304428. + 175762. i) q^{79} +(-259860. - 450090. i) q^{81} +106682. q^{83} +(126694. - 219440. i) q^{85} +33742.2 q^{87} +(183457. + 105919. i) q^{89} +(-257222. - 148507. i) q^{91} +(51658.9 + 89475.8i) q^{93} +(923152. - 72353.2i) q^{95} +(736790. - 425386. i) q^{97} +(-239974. + 415647. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9	$ 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9} - 3644 q^{11} - 7140 q^{13} + 9168 q^{15} + 1132 q^{17} + 2110 q^{19} - 8748 q^{21} + 832 q^{23} - 27698 q^{25} - 10920 q^{29} - 30306 q^{33} + 4172 q^{35} + 81144 q^{39} + 109206 q^{41} + 110740 q^{43} - 785440 q^{45} + 107080 q^{47} + 136092 q^{49} + 199872 q^{51} + 254796 q^{53} + 354840 q^{55} + 212268 q^{57} - 610638 q^{59} + 47864 q^{61} - 254476 q^{63} - 839562 q^{67} + 366660 q^{71} + 854482 q^{73} + 763088 q^{77} + 1718592 q^{79} - 1054142 q^{81} + 439612 q^{83} - 400236 q^{85} - 1604736 q^{87} + 478032 q^{89} + 599856 q^{91} + 829380 q^{93} - 1055660 q^{95} - 191286 q^{97} - 2336728 q^{99}+O(q^{100}) $ 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9 - 3644 * q^11 - 7140 * q^13 + 9168 * q^15 + 1132 * q^17 + 2110 * q^19 - 8748 * q^21 + 832 * q^23 - 27698 * q^25 - 10920 * q^29 - 30306 * q^33 + 4172 * q^35 + 81144 * q^39 + 109206 * q^41 + 110740 * q^43 - 785440 * q^45 + 107080 * q^47 + 136092 * q^49 + 199872 * q^51 + 254796 * q^53 + 354840 * q^55 + 212268 * q^57 - 610638 * q^59 + 47864 * q^61 - 254476 * q^63 - 839562 * q^67 + 366660 * q^71 + 854482 * q^73 + 763088 * q^77 + 1718592 * q^79 - 1054142 * q^81 + 439612 * q^83 - 400236 * q^85 - 1604736 * q^87 + 478032 * q^89 + 599856 * q^91 + 829380 * q^93 - 1055660 * q^95 - 191286 * q^97 - 2336728 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	2.00739	−	1.15896i	0.0743476	−	0.0429246i	−0.462365	−	0.886690i	$-0.652999\pi$
$3$	2.00739	−	1.15896i	0.0743476	−	0.0429246i	0.536713	+	0.843765i	$0.319666\pi$
$4$		0			0
$5$	−67.5013	−	116.916i	−0.540010	−	0.935325i	−0.998903	−	0.0468335i	$-0.985087\pi$
$5$	−67.5013	−	116.916i	−0.540010	−	0.935325i	0.458892	−	0.888492i	$-0.348246\pi$
$6$		0			0
$7$	−157.715			−0.459811			−0.229905	−	0.973213i	$-0.573842\pi$
$7$	−157.715			−0.459811			−0.229905	+	0.973213i	$0.573842\pi$
$8$		0			0
$9$	−361.814	+	626.680i	−0.496315	+	0.859643i
$10$		0			0
$11$	663.253			0.498312			0.249156	−	0.968463i	$-0.419847\pi$
$11$	663.253			0.498312			0.249156	+	0.968463i	$0.419847\pi$
$12$		0			0
$13$	1630.93	+	941.616i	0.742343	+	0.428592i	0.822921	−	0.568156i	$-0.192343\pi$
$13$	1630.93	+	941.616i	0.742343	+	0.428592i	−0.0805776	+	0.996748i	$0.525676\pi$
$14$		0			0
$15$	−271.002	−	156.463i	−0.0802970	−	0.0463595i
$16$		0			0
$17$	938.453	+	1625.45i	0.191014	+	0.330846i	0.945587	−	0.325370i	$-0.105489\pi$
$17$	938.453	+	1625.45i	0.191014	+	0.330846i	−0.754572	+	0.656217i	$0.772156\pi$
$18$		0			0
$19$	−2954.88	+	6189.88i	−0.430803	+	0.902446i
$19$	−2954.88	+	6189.88i	−0.430803	+	0.902446i
$20$		0			0
$21$	−316.595	+	182.786i	−0.0341858	+	0.0197372i
$22$		0			0
$23$	−4912.56	+	8508.80i	−0.403761	+	0.699334i	−0.994176	−	0.107765i	$-0.965631\pi$
$23$	−4912.56	+	8508.80i	−0.403761	+	0.699334i	0.590416	+	0.807099i	$0.298964\pi$
$24$		0			0
$25$	−1300.35	+	2252.27i	−0.0832223	+	0.144145i
$26$		0			0
$27$			3367.09i			0.171066i
$28$		0			0
$29$	12606.8	+	7278.51i	0.516903	+	0.298434i	0.735667	−	0.677344i	$-0.236869\pi$
$29$	12606.8	+	7278.51i	0.516903	+	0.298434i	−0.218764	+	0.975778i	$0.570202\pi$
$30$		0			0
$31$			44573.3i			1.49620i	0.663586	+	0.748100i	$0.269034\pi$
$31$			44573.3i			1.49620i	−0.663586	+	0.748100i	$0.730966\pi$
$32$		0			0
$33$	1331.41	−	768.687i	0.0370483	−	0.0213899i
$34$		0			0
$35$	10646.0	+	18439.4i	0.248303	+	0.430073i
$36$		0			0
$37$			55050.8i			1.08682i	0.839467	+	0.543411i	$0.182868\pi$
$37$			55050.8i			1.08682i	−0.839467	+	0.543411i	$0.817132\pi$
$38$		0			0
$39$	4365.20			0.0735886
$40$		0			0
$41$	−35438.6	+	20460.5i	−0.514191	+	0.296868i	−0.734555	−	0.678549i	$-0.762609\pi$
$41$	−35438.6	+	20460.5i	−0.514191	+	0.296868i	0.220364	+	0.975418i	$0.429276\pi$
$42$		0			0
$43$	−14840.5	−	25704.5i	−0.186656	−	0.323298i	0.757477	−	0.652862i	$-0.226432\pi$
$43$	−14840.5	−	25704.5i	−0.186656	−	0.323298i	−0.944133	+	0.329563i	$0.893098\pi$
$44$		0			0
$45$	97691.5			1.07206
$46$		0			0
$47$	−10194.0	+	17656.5i	−0.0981861	+	0.170063i	−0.910934	−	0.412552i	$-0.864637\pi$
$47$	−10194.0	+	17656.5i	−0.0981861	+	0.170063i	0.812748	+	0.582616i	$0.197971\pi$
$48$		0			0
$49$	−92774.9			−0.788574
$50$		0			0
$51$	3767.68	+	2175.27i	0.0284029	+	0.0163984i
$52$		0			0
$53$	−112309.	−	64841.8i	−0.754377	−	0.435540i	0.0728964	−	0.997340i	$-0.476776\pi$
$53$	−112309.	−	64841.8i	−0.754377	−	0.435540i	−0.827273	+	0.561800i	$0.810109\pi$
$54$		0			0
$55$	−44770.4	−	77544.7i	−0.269094	−	0.466084i
$56$		0			0
$57$	1242.27	+	15850.1i	0.00670798	+	0.0855868i
$58$		0			0
$59$	294641.	−	170111.i	1.43462	−	0.828277i	0.437150	−	0.899389i	$-0.355988\pi$
$59$	294641.	−	170111.i	1.43462	−	0.828277i	0.997468	+	0.0711112i	$0.0226545\pi$
$60$		0			0
$61$	−47067.9	+	81524.0i	−0.207365	+	0.359167i	−0.950884	−	0.309548i	$-0.899822\pi$
$61$	−47067.9	+	81524.0i	−0.207365	+	0.359167i	0.743519	+	0.668715i	$0.233155\pi$
$62$		0			0
$63$	57063.5	−	98836.8i	0.228211	−	0.395273i
$64$		0			0
$65$		−	254241.i		−	0.925776i
$66$		0			0
$67$	154080.	+	88958.1i	0.512297	+	0.295775i	0.733777	−	0.679390i	$-0.237756\pi$
$67$	154080.	+	88958.1i	0.512297	+	0.295775i	−0.221480	+	0.975165i	$0.571089\pi$
$68$		0			0
$69$			22773.9i			0.0693251i
$70$		0			0
$71$	112740.	−	65090.7i	0.314996	−	0.181863i	−0.334164	−	0.942515i	$-0.608454\pi$
$71$	112740.	−	65090.7i	0.314996	−	0.181863i	0.649160	+	0.760652i	$0.275121\pi$
$72$		0			0
$73$	−364203.	−	630818.i	−0.936213	−	1.62157i	−0.772456	−	0.635069i	$-0.780972\pi$
$73$	−364203.	−	630818.i	−0.936213	−	1.62157i	−0.163758	−	0.986501i	$-0.552362\pi$
$74$		0			0
$75$			6028.23i			0.0142891i
$76$		0			0
$77$	−104605.			−0.229129
$78$		0			0
$79$	−304428.	+	175762.i	−0.617453	+	0.356487i	−0.775877	−	0.630884i	$-0.782692\pi$
$79$	−304428.	+	175762.i	−0.617453	+	0.356487i	0.158424	+	0.987371i	$0.449359\pi$
$80$		0			0
$81$	−259860.	−	450090.i	−0.488972	−	0.846924i
$82$		0			0
$83$	106682.			0.186576			0.0932879	−	0.995639i	$-0.470262\pi$
$83$	106682.			0.186576			0.0932879	+	0.995639i	$0.470262\pi$
$84$		0			0
$85$	126694.	−	219440.i	0.206299	−	0.357321i
$86$		0			0
$87$	33742.2			0.0512407
$88$		0			0
$89$	183457.	+	105919.i	0.260235	+	0.150247i	0.624442	−	0.781071i	$-0.285327\pi$
$89$	183457.	+	105919.i	0.260235	+	0.150247i	−0.364207	+	0.931318i	$0.618660\pi$
$90$		0			0
$91$	−257222.	−	148507.i	−0.341337	−	0.197071i
$92$		0			0
$93$	51658.9	+	89475.8i	0.0642238	+	0.111239i
$94$		0			0
$95$	923152.	−	72353.2i	1.07672	−	0.0843893i
$96$		0			0
$97$	736790.	−	425386.i	0.807288	−	0.466088i	−0.0387253	−	0.999250i	$-0.512330\pi$
$97$	736790.	−	425386.i	0.807288	−	0.466088i	0.846013	+	0.533162i	$0.178996\pi$
$98$		0			0
$99$	−239974.	+	415647.i	−0.247320	+	0.428370i
$100$		0			0
$101$	−729349.	+	1.26327e6i	−0.707899	+	1.22612i	0.257736	+	0.966215i	$0.417023\pi$
$101$	−729349.	+	1.26327e6i	−0.707899	+	1.22612i	−0.965635	+	0.259902i	$0.916310\pi$
$102$		0			0
$103$			1.43922e6i			1.31709i	0.752540	+	0.658546i	$0.228828\pi$
$103$			1.43922e6i			1.31709i	−0.752540	+	0.658546i	$0.771172\pi$
$104$		0			0
$105$	42741.2	+	24676.6i	0.0369214	+	0.0213166i
$106$		0			0
$107$			539515.i			0.440405i	0.975454	+	0.220203i	$0.0706718\pi$
$107$			539515.i			0.440405i	−0.975454	+	0.220203i	$0.929328\pi$
$108$		0			0
$109$	−379927.	+	219351.i	−0.293373	+	0.169379i	−0.639462	−	0.768823i	$-0.720843\pi$
$109$	−379927.	+	219351.i	−0.293373	+	0.169379i	0.346089	+	0.938202i	$0.387510\pi$
$110$		0			0
$111$	63802.0	+	110508.i	0.0466514	+	0.0808027i
$112$		0			0
$113$		−	476422.i		−	0.330184i	−0.986278	−	0.165092i	$-0.947208\pi$
$113$		−	476422.i		−	0.330184i	0.986278	−	0.165092i	$-0.0527922\pi$
$114$		0			0
$115$	1.32642e6			0.872140
$116$		0			0
$117$	−1.18018e6	+	681379.i	−0.736872	+	0.425433i
$118$		0			0
$119$	−148008.	−	256358.i	−0.0878305	−	0.152127i
$120$		0			0
$121$	−1.33166e6			−0.751685
$122$		0			0
$123$	−47425.9	+	82144.1i	−0.0254859	+	0.0441429i
$124$		0			0
$125$	−1.75831e6			−0.900257
$126$		0			0
$127$	2.19908e6	+	1.26964e6i	1.07357	+	0.619826i	0.929155	−	0.369692i	$-0.120537\pi$
$127$	2.19908e6	+	1.26964e6i	1.07357	+	0.619826i	0.144415	+	0.989517i	$0.453870\pi$
$128$		0			0
$129$	−59581.2	−	34399.2i	−0.0277549	−	0.0160243i
$130$		0			0
$131$	1.65749e6	+	2.87086e6i	0.737289	+	1.27702i	0.953712	+	0.300723i	$0.0972278\pi$
$131$	1.65749e6	+	2.87086e6i	0.737289	+	1.27702i	−0.216422	+	0.976300i	$0.569439\pi$
$132$		0			0
$133$	466029.	−	976237.i	0.198088	−	0.414954i
$134$		0			0
$135$	393665.	−	227283.i	0.160002	−	0.0923773i
$136$		0			0
$137$	−1.35065e6	+	2.33940e6i	−0.525269	+	0.909793i	0.474298	+	0.880364i	$0.342702\pi$
$137$	−1.35065e6	+	2.33940e6i	−0.525269	+	0.909793i	−0.999567	+	0.0294281i	$0.990631\pi$
$138$		0			0
$139$	−509855.	+	883094.i	−0.189846	+	0.328823i	−0.945199	−	0.326495i	$-0.894132\pi$
$139$	−509855.	+	883094.i	−0.189846	+	0.328823i	0.755353	+	0.655319i	$0.227466\pi$
$140$		0			0
$141$			47257.9i			0.0168584i
$142$		0			0
$143$	1.08172e6	+	624530.i	0.369918	+	0.213572i
$144$		0			0
$145$		−	1.96524e6i		−	0.644630i
$146$		0			0
$147$	−186235.	+	107523.i	−0.0586286	+	0.0338492i
$148$		0			0
$149$	−18135.9	−	31412.3i	−0.00548252	−	0.00949600i	0.863271	−	0.504740i	$-0.168412\pi$
$149$	−18135.9	−	31412.3i	−0.00548252	−	0.00949600i	−0.868754	+	0.495244i	$0.835078\pi$
$150$		0			0
$151$		−	2.02177e6i		−	0.587220i	−0.955925	−	0.293610i	$-0.905143\pi$
$151$		−	2.02177e6i		−	0.587220i	0.955925	−	0.293610i	$-0.0948567\pi$
$152$		0			0
$153$	−1.35818e6			−0.379213
$154$		0			0
$155$	5.21132e6	−	3.00875e6i	1.39943	−	0.807963i
$156$		0			0
$157$	−2.15733e6	−	3.73660e6i	−0.557465	−	0.965557i	−0.997707	−	0.0676783i	$-0.978441\pi$
$157$	−2.15733e6	−	3.73660e6i	−0.557465	−	0.965557i	0.440242	−	0.897879i	$-0.354892\pi$
$158$		0			0
$159$	−300598.			−0.0747815
$160$		0			0
$161$	774784.	−	1.34197e6i	0.185654	−	0.321561i
$162$		0			0
$163$	−631178.			−0.145743			−0.0728717	−	0.997341i	$-0.523216\pi$
$163$	−631178.			−0.145743			−0.0728717	+	0.997341i	$0.523216\pi$
$164$		0			0
$165$	−179743.	−	103775.i	−0.0400129	−	0.0231015i
$166$		0			0
$167$	−3.31319e6	−	1.91287e6i	−0.711372	−	0.410711i	0.100197	−	0.994968i	$-0.468053\pi$
$167$	−3.31319e6	−	1.91287e6i	−0.711372	−	0.410711i	−0.811569	+	0.584257i	$0.801386\pi$
$168$		0			0
$169$	−640121.	−	1.10872e6i	−0.132618	−	0.229701i
$170$		0			0
$171$	−2.80995e6	−	4.09134e6i	−0.561967	−	0.818234i
$172$		0			0
$173$	865743.	−	499837.i	0.167206	−	0.0965362i	−0.414062	−	0.910249i	$-0.635890\pi$
$173$	865743.	−	499837.i	0.167206	−	0.0965362i	0.581268	+	0.813713i	$0.302557\pi$
$174$		0			0
$175$	205085.	−	355217.i	0.0382665	−	0.0662796i
$176$		0			0
$177$	394305.	−	682956.i	0.0711070	−	0.123161i
$178$		0			0
$179$			472311.i			0.0823511i	0.999152	+	0.0411755i	$0.0131103\pi$
$179$			472311.i			0.0823511i	−0.999152	+	0.0411755i	$0.986890\pi$
$180$		0			0
$181$	−5.22336e6	−	3.01571e6i	−0.880875	−	0.508574i	−0.00992844	−	0.999951i	$-0.503160\pi$
$181$	−5.22336e6	−	3.01571e6i	−0.880875	−	0.508574i	−0.870947	+	0.491377i	$0.836494\pi$
$182$		0			0
$183$			218200.i			0.0356043i
$184$		0			0
$185$	6.43630e6	−	3.71600e6i	1.01653	−	0.586895i
$186$		0			0
$187$	622432.	+	1.07808e6i	0.0951847	+	0.164865i
$188$		0			0
$189$		−	531041.i		−	0.0786579i
$190$		0			0
$191$	7.55505e6			1.08427			0.542135	−	0.840291i	$-0.317616\pi$
$191$	7.55505e6			1.08427			0.542135	+	0.840291i	$0.317616\pi$
$192$		0			0
$193$	−2.94732e6	+	1.70163e6i	−0.409972	+	0.236698i	−0.690778	−	0.723067i	$-0.742732\pi$
$193$	−2.94732e6	+	1.70163e6i	−0.409972	+	0.236698i	0.280805	+	0.959765i	$0.409398\pi$
$194$		0			0
$195$	−294657.	−	510360.i	−0.0397386	−	0.0688293i
$196$		0			0
$197$	5.96004e6			0.779561			0.389781	−	0.920908i	$-0.372551\pi$
$197$	5.96004e6			0.779561			0.389781	+	0.920908i	$0.372551\pi$
$198$		0			0
$199$	−1.27209e6	+	2.20333e6i	−0.161421	+	0.279589i	−0.935379	−	0.353648i	$-0.884941\pi$
$199$	−1.27209e6	+	2.20333e6i	−0.161421	+	0.279589i	0.773957	+	0.633238i	$0.218274\pi$
$200$		0			0
$201$	412397.			0.0507841
$202$		0			0
$203$	−1.98828e6	−	1.14793e6i	−0.237678	−	0.137223i
$204$		0			0
$205$	4.78430e6	+	2.76222e6i	0.555337	+	0.320624i
$206$		0			0
$207$	−3.55486e6	−	6.15720e6i	−0.400785	−	0.694180i
$208$		0			0
$209$	−1.95983e6	+	4.10546e6i	−0.214674	+	0.449700i
$210$		0			0
$211$	−4.29150e6	+	2.47770e6i	−0.456838	+	0.263755i	−0.710714	−	0.703481i	$-0.751628\pi$
$211$	−4.29150e6	+	2.47770e6i	−0.456838	+	0.263755i	0.253876	+	0.967237i	$0.418295\pi$
$212$		0			0
$213$	150876.	−	261324.i	0.0156128	−	0.0270421i
$214$		0			0
$215$	−2.00350e6	+	3.47017e6i	−0.201593	+	0.349169i
$216$		0			0
$217$		−	7.02988e6i		−	0.687969i
$218$		0			0
$219$	−1.46219e6	−	844197.i	−0.139211	−	0.0803732i
$220$		0			0
$221$			3.53465e6i			0.327469i
$222$		0			0
$223$	−1.19236e7	+	6.88407e6i	−1.07521	+	0.620770i	−0.929599	−	0.368572i	$-0.879847\pi$
$223$	−1.19236e7	+	6.88407e6i	−1.07521	+	0.620770i	−0.145606	+	0.989343i	$0.546513\pi$
$224$		0			0
$225$	−940968.	−	1.62980e6i	−0.0826090	−	0.143083i
$226$		0			0
$227$			1.33313e7i			1.13971i	0.821745	+	0.569856i	$0.193001\pi$
$227$			1.33313e7i			1.13971i	−0.821745	+	0.569856i	$0.806999\pi$
$228$		0			0
$229$	−6.50966e6			−0.542066			−0.271033	−	0.962570i	$-0.587365\pi$
$229$	−6.50966e6			−0.542066			−0.271033	+	0.962570i	$0.587365\pi$
$230$		0			0
$231$	−209983.	+	121234.i	−0.0170352	+	0.00983529i
$232$		0			0
$233$	1.06145e7	+	1.83848e7i	0.839134	+	1.45342i	0.890619	+	0.454750i	$0.150271\pi$
$233$	1.06145e7	+	1.83848e7i	0.839134	+	1.45342i	−0.0514849	+	0.998674i	$0.516395\pi$
$234$		0			0
$235$	2.75243e6			0.212086
$236$		0			0
$237$	−407404.	+	705644.i	−0.0306041	+	0.0530079i
$238$		0			0
$239$	2.53033e7			1.85346			0.926731	−	0.375725i	$-0.122606\pi$
$239$	2.53033e7			1.85346			0.926731	+	0.375725i	$0.122606\pi$
$240$		0			0
$241$	−2.47672e6	−	1.42994e6i	−0.176940	−	0.102156i	0.408914	−	0.912573i	$-0.365908\pi$
$241$	−2.47672e6	−	1.42994e6i	−0.176940	−	0.102156i	−0.585854	+	0.810416i	$0.699241\pi$
$242$		0			0
$243$	−3.16903e6	−	1.82964e6i	−0.220855	−	0.127511i
$244$		0			0
$245$	6.26243e6	+	1.08468e7i	0.425838	+	0.737573i
$246$		0			0
$247$	−1.06477e7	+	7.31288e6i	−0.706585	+	0.485286i
$248$		0			0
$249$	214151.	−	123640.i	0.0138715	−	0.00800870i
$250$		0			0
$251$	3.82541e6	−	6.62581e6i	0.241912	−	0.419004i	−0.719347	−	0.694651i	$-0.755559\pi$
$251$	3.82541e6	−	6.62581e6i	0.241912	−	0.419004i	0.961259	+	0.275647i	$0.0888921\pi$
$252$		0			0
$253$	−3.25827e6	+	5.64349e6i	−0.201199	+	0.348487i
$254$		0			0
$255$		−	587334.i		−	0.0354213i
$256$		0			0
$257$	1.02728e7	+	5.93100e6i	0.605186	+	0.349405i	0.771079	−	0.636739i	$-0.219717\pi$
$257$	1.02728e7	+	5.93100e6i	0.605186	+	0.349405i	−0.165893	+	0.986144i	$0.553051\pi$
$258$		0			0
$259$		−	8.68234e6i		−	0.499733i
$260$		0			0
$261$	−9.12259e6	+	5.26693e6i	−0.513094	+	0.296235i
$262$		0			0
$263$	−597610.	−	1.03509e6i	−0.0328512	−	0.0568999i	0.849132	−	0.528180i	$-0.177125\pi$
$263$	−597610.	−	1.03509e6i	−0.0328512	−	0.0568999i	−0.881984	+	0.471280i	$0.843792\pi$
$264$		0			0
$265$			1.75076e7i			0.940784i
$266$		0			0
$267$	491026.			0.0257971
$268$		0			0
$269$	−9.09888e6	+	5.25324e6i	−0.467446	+	0.269880i	−0.715170	−	0.698951i	$-0.753651\pi$
$269$	−9.09888e6	+	5.25324e6i	−0.467446	+	0.269880i	0.247724	+	0.968831i	$0.420317\pi$
$270$		0			0
$271$	−1.62504e6	−	2.81465e6i	−0.0816499	−	0.141422i	0.822309	−	0.569041i	$-0.192686\pi$
$271$	−1.62504e6	−	2.81465e6i	−0.0816499	−	0.141422i	−0.903959	+	0.427620i	$0.859352\pi$
$272$		0			0
$273$	−688458.			−0.0338368
$274$		0			0
$275$	−862460.	+	1.49383e6i	−0.0414707	+	0.0718293i
$276$		0			0
$277$	6.22495e6			0.292885			0.146442	−	0.989219i	$-0.453218\pi$
$277$	6.22495e6			0.292885			0.146442	+	0.989219i	$0.453218\pi$
$278$		0			0
$279$	−2.79332e7	−	1.61272e7i	−1.28620	−	0.742586i
$280$		0			0
$281$	2.80002e7	+	1.61659e7i	1.26195	+	0.728588i	0.973452	−	0.228892i	$-0.0735102\pi$
$281$	2.80002e7	+	1.61659e7i	1.26195	+	0.728588i	0.288500	+	0.957480i	$0.406844\pi$
$282$		0			0
$283$	−6.60210e6	−	1.14352e7i	−0.291288	−	0.504526i	0.682826	−	0.730581i	$-0.260751\pi$
$283$	−6.60210e6	−	1.14352e7i	−0.291288	−	0.504526i	−0.974115	+	0.226055i	$0.927417\pi$
$284$		0			0
$285$	1.76927e6	−	1.21514e6i	0.0764291	−	0.0524919i
$286$		0			0
$287$	5.58920e6	−	3.22693e6i	0.236431	−	0.136503i
$288$		0			0
$289$	1.03074e7	−	1.78529e7i	0.427027	−	0.739633i
$290$		0			0
$291$	986014.	−	1.70783e6i	0.0400133	−	0.0693051i
$292$		0			0
$293$		−	4.25543e7i		−	1.69177i	−0.533368	−	0.845883i	$-0.679074\pi$
$293$		−	4.25543e7i		−	1.69177i	0.533368	−	0.845883i	$-0.320926\pi$
$294$		0			0
$295$	−3.97772e7	−	2.29654e7i	−1.54942	−	0.894557i
$296$		0			0
$297$			2.23323e6i			0.0852441i
$298$		0			0
$299$	−1.60240e7	+	9.25149e6i	−0.599458	+	0.346097i
$300$		0			0
$301$	2.34057e6	+	4.05399e6i	0.0858267	+	0.148656i
$302$		0			0
$303$			3.38116e6i			0.121545i
$304$		0			0
$305$	1.27086e7			0.447917
$306$		0			0
$307$	1.60328e7	−	9.25654e6i	0.554108	−	0.319914i	−0.196669	−	0.980470i	$-0.563013\pi$
$307$	1.60328e7	−	9.25654e6i	0.554108	−	0.319914i	0.750777	+	0.660556i	$0.229679\pi$
$308$		0			0
$309$	1.66801e6	+	2.88908e6i	0.0565357	+	0.0979227i
$310$		0			0
$311$	809497.			0.0269113			0.0134556	−	0.999909i	$-0.495717\pi$
$311$	809497.			0.0269113			0.0134556	+	0.999909i	$0.495717\pi$
$312$		0			0
$313$	2.80059e7	−	4.85077e7i	0.913307	−	1.58189i	0.103946	−	0.994583i	$-0.466853\pi$
$313$	2.80059e7	−	4.85077e7i	0.913307	−	1.58189i	0.809361	−	0.587312i	$-0.199814\pi$
$314$		0			0
$315$	−1.54074e7			−0.492945
$316$		0			0
$317$	2.19986e7	+	1.27009e7i	0.690585	+	0.398710i	0.803831	−	0.594857i	$-0.202791\pi$
$317$	2.19986e7	+	1.27009e7i	0.690585	+	0.398710i	−0.113246	+	0.993567i	$0.536125\pi$
$318$		0			0
$319$	8.36147e6	+	4.82750e6i	0.257579	+	0.148713i
$320$		0			0
$321$	625279.	+	1.08302e6i	0.0189042	+	0.0327431i
$322$		0			0
$323$	−1.28343e7	+	1.00591e6i	−0.380861	+	0.0298505i
$324$		0			0
$325$	−4.24155e6	+	2.44886e6i	−0.123559	+	0.0713368i
$326$		0			0
$327$	−508439.	+	880643.i	−0.0145411	+	0.0251858i
$328$		0			0
$329$	1.60774e6	−	2.78470e6i	0.0451470	−	0.0781970i
$330$		0			0
$331$		−	1.15466e7i		−	0.318399i	−0.987246	−	0.159199i	$-0.949109\pi$
$331$		−	1.15466e7i		−	0.318399i	0.987246	−	0.159199i	$-0.0508912\pi$
$332$		0			0
$333$	−3.44992e7	−	1.99181e7i	−0.934279	−	0.539406i
$334$		0			0
$335$		−	2.40192e7i		−	0.638886i
$336$		0			0
$337$	2.85821e7	−	1.65019e7i	0.746800	−	0.431165i	−0.0777366	−	0.996974i	$-0.524769\pi$
$337$	2.85821e7	−	1.65019e7i	0.746800	−	0.431165i	0.824536	+	0.565809i	$0.191436\pi$
$338$		0			0
$339$	−552156.	−	956363.i	−0.0141730	−	0.0245484i
$340$		0			0
$341$			2.95634e7i			0.745574i
$342$		0			0
$343$	3.31870e7			0.822406
$344$		0			0
$345$	2.66263e6	−	1.53727e6i	0.0648415	−	0.0374363i
$346$		0			0
$347$	−2.36636e7	−	4.09866e7i	−0.566360	−	0.980964i	−0.996922	−	0.0784029i	$-0.975018\pi$
$347$	−2.36636e7	−	4.09866e7i	−0.566360	−	0.980964i	0.430562	−	0.902561i	$-0.358315\pi$
$348$		0			0
$349$	−4.22347e7			−0.993557			−0.496779	−	0.867877i	$-0.665484\pi$
$349$	−4.22347e7			−0.993557			−0.496779	+	0.867877i	$0.665484\pi$
$350$		0			0
$351$	−3.17051e6	+	5.49148e6i	−0.0733174	+	0.126989i
$352$		0			0
$353$	3.45242e7			0.784873			0.392437	−	0.919779i	$-0.371632\pi$
$353$	3.45242e7			0.784873			0.392437	+	0.919779i	$0.371632\pi$
$354$		0			0
$355$	−1.52202e7	−	8.78741e6i	−0.340202	−	0.196416i
$356$		0			0
$357$	−594219.	−	343073.i	−0.0130600	−	0.00754018i
$358$		0			0
$359$	1.75793e7	+	3.04483e7i	0.379943	+	0.658081i	0.991054	−	0.133465i	$-0.0426102\pi$
$359$	1.75793e7	+	3.04483e7i	0.379943	+	0.658081i	−0.611111	+	0.791545i	$0.709277\pi$
$360$		0			0
$361$	−2.95833e7	−	3.65807e7i	−0.628818	−	0.777553i
$362$		0			0
$363$	−2.67315e6	+	1.54334e6i	−0.0558860	+	0.0322658i
$364$		0			0
$365$	−4.91683e7	+	8.51621e7i	−1.01113	+	1.75133i
$366$		0			0
$367$	−2.33905e7	+	4.05135e7i	−0.473196	+	0.819599i	−0.999529	−	0.0306792i	$-0.990233\pi$
$367$	−2.33905e7	+	4.05135e7i	−0.473196	+	0.819599i	0.526334	+	0.850278i	$0.323566\pi$
$368$		0			0
$369$		−	2.96115e7i		−	0.589361i
$370$		0			0
$371$	1.77129e7	+	1.02265e7i	0.346871	+	0.200266i
$372$		0			0
$373$			1.55608e7i			0.299852i	0.988697	+	0.149926i	$0.0479035\pi$
$373$			1.55608e7i			0.299852i	−0.988697	+	0.149926i	$0.952096\pi$
$374$		0			0
$375$	−3.52962e6	+	2.03782e6i	−0.0669320	+	0.0386432i
$376$		0			0
$377$	1.37071e7	+	2.37414e7i	0.255813	+	0.443081i
$378$		0			0
$379$			2.17858e7i			0.400180i	0.979778	+	0.200090i	$0.0641235\pi$
$379$			2.17858e7i			0.400180i	−0.979778	+	0.200090i	$0.935877\pi$
$380$		0			0
$381$	5.88587e6			0.106423
$382$		0			0
$383$	4.99786e7	−	2.88552e7i	0.889586	−	0.513603i	0.0157792	−	0.999876i	$-0.494977\pi$
$383$	4.99786e7	−	2.88552e7i	0.889586	−	0.513603i	0.873807	+	0.486273i	$0.161644\pi$
$384$		0			0
$385$	7.06098e6	+	1.22300e7i	0.123732	+	0.214310i
$386$		0			0
$387$	2.14780e7			0.370562
$388$		0			0
$389$	−8.42124e6	+	1.45860e7i	−0.143063	+	0.247792i	−0.928649	−	0.370961i	$-0.879028\pi$
$389$	−8.42124e6	+	1.45860e7i	−0.143063	+	0.247792i	0.785586	+	0.618753i	$0.212362\pi$
$390$		0			0
$391$	−1.84408e7			−0.308496
$392$		0			0
$393$	6.65446e6	+	3.84195e6i	0.109631	+	0.0632957i
$394$		0			0
$395$	4.10986e7	+	2.37283e7i	0.666862	+	0.385013i
$396$		0			0
$397$	5.97117e7	+	1.03424e8i	0.954306	+	1.65291i	0.735948	+	0.677038i	$0.236737\pi$
$397$	5.97117e7	+	1.03424e8i	0.954306	+	1.65291i	0.218358	+	0.975869i	$0.429930\pi$
$398$		0			0
$399$	−195925.	−	2.49980e6i	−0.00308440	−	0.0393537i
$400$		0			0
$401$	9.19787e7	−	5.31039e7i	1.42644	−	0.823557i	0.429604	−	0.903018i	$-0.358653\pi$
$401$	9.19787e7	−	5.31039e7i	1.42644	−	0.823557i	0.996838	+	0.0794610i	$0.0253199\pi$
$402$		0			0
$403$	−4.19709e7	+	7.26958e7i	−0.641259	+	1.11069i
$404$		0			0
$405$	−3.50817e7	+	6.07634e7i	−0.528100	+	0.914696i
$406$		0			0
$407$			3.65126e7i			0.541577i
$408$		0			0
$409$	−9.25066e7	−	5.34087e7i	−1.35208	−	0.780624i	−0.363540	−	0.931579i	$-0.618432\pi$
$409$	−9.25066e7	−	5.34087e7i	−1.35208	−	0.780624i	−0.988541	+	0.150954i	$0.951765\pi$
$410$		0			0
$411$			6.26143e6i			0.0901879i
$412$		0			0
$413$	−4.64693e7	+	2.68290e7i	−0.659653	+	0.380851i
$414$		0			0
$415$	−7.20115e6	−	1.24728e7i	−0.100753	−	0.174509i
$416$		0			0
$417$			2.36362e6i			0.0325963i
$418$		0			0
$419$	1.11916e8			1.52142			0.760712	−	0.649090i	$-0.224850\pi$
$419$	1.11916e8			1.52142			0.760712	+	0.649090i	$0.224850\pi$
$420$		0			0
$421$	−9.18429e7	+	5.30255e7i	−1.23083	+	0.710622i	−0.967204	−	0.254002i	$-0.918253\pi$
$421$	−9.18429e7	+	5.30255e7i	−1.23083	+	0.710622i	−0.263629	+	0.964624i	$0.584920\pi$
$422$		0			0
$423$	−7.37664e6	−	1.27767e7i	−0.0974625	−	0.168810i
$424$		0			0
$425$	−4.88127e6			−0.0635866
$426$		0			0
$427$	7.42332e6	−	1.28576e7i	0.0953487	−	0.165149i
$428$		0			0
$429$	2.89523e6			0.0366701
$430$		0			0
$431$	3.68017e6	+	2.12475e6i	0.0459659	+	0.0265384i	0.522807	−	0.852451i	$-0.324885\pi$
$431$	3.68017e6	+	2.12475e6i	0.0459659	+	0.0265384i	−0.476841	+	0.878990i	$0.658218\pi$
$432$		0			0
$433$	−6.89671e7	−	3.98182e7i	−0.849529	−	0.490476i	0.0109628	−	0.999940i	$-0.496510\pi$
$433$	−6.89671e7	−	3.98182e7i	−0.849529	−	0.490476i	−0.860492	+	0.509464i	$0.829844\pi$
$434$		0			0
$435$	−2.27764e6	−	3.94499e6i	−0.0276705	−	0.0479267i
$436$		0			0
$437$	−3.81524e7	−	5.55506e7i	−0.457170	−	0.665647i
$438$		0			0
$439$	6.49923e7	−	3.75233e7i	0.768190	−	0.443515i	−0.0640386	−	0.997947i	$-0.520398\pi$
$439$	6.49923e7	−	3.75233e7i	0.768190	−	0.443515i	0.832229	+	0.554433i	$0.187065\pi$
$440$		0			0
$441$	3.35672e7	−	5.81402e7i	0.391381	−	0.677892i
$442$		0			0
$443$	−7.36600e7	+	1.27583e8i	−0.847268	+	1.46751i	0.0363692	+	0.999338i	$0.488421\pi$
$443$	−7.36600e7	+	1.27583e8i	−0.847268	+	1.46751i	−0.883637	+	0.468173i	$0.844913\pi$
$444$		0			0
$445$		−	2.85987e7i		−	0.324539i
$446$		0			0
$447$	−72811.5	−	42037.7i	−0.000815225	−	0.000470670i
$448$		0			0
$449$		−	6.74787e7i		−	0.745466i	−0.927939	−	0.372733i	$-0.878421\pi$
$449$		−	6.74787e7i		−	0.745466i	0.927939	−	0.372733i	$-0.121579\pi$
$450$		0			0
$451$	−2.35047e7	+	1.35705e7i	−0.256228	+	0.147933i
$452$		0			0
$453$	−2.34316e6	−	4.05847e6i	−0.0252062	−	0.0436584i
$454$		0			0
$455$			4.00977e7i			0.425682i
$456$		0			0
$457$	1.07118e8			1.12231			0.561155	−	0.827711i	$-0.310357\pi$
$457$	1.07118e8			1.12231			0.561155	+	0.827711i	$0.310357\pi$
$458$		0			0
$459$	−5.47303e6	+	3.15985e6i	−0.0565965	+	0.0326760i
$460$		0			0
$461$	−5.19720e7	−	9.00182e7i	−0.530477	−	0.918813i	−0.999368	−	0.0355571i	$-0.988679\pi$
$461$	−5.19720e7	−	9.00182e7i	−0.530477	−	0.918813i	0.468890	−	0.883256i	$-0.344654\pi$
$462$		0			0
$463$	1.04472e8			1.05258			0.526292	−	0.850304i	$-0.323582\pi$
$463$	1.04472e8			1.05258			0.526292	+	0.850304i	$0.323582\pi$
$464$		0			0
$465$	6.97408e6	−	1.20795e7i	0.0693631	−	0.120140i
$466$		0			0
$467$	1.42623e8			1.40035			0.700177	−	0.713969i	$-0.253104\pi$
$467$	1.42623e8			1.40035			0.700177	+	0.713969i	$0.253104\pi$
$468$		0			0
$469$	−2.43007e7	−	1.40300e7i	−0.235560	−	0.136000i
$470$		0			0
$471$	−8.66118e6	−	5.00054e6i	−0.0828924	−	0.0478579i
$472$		0			0
$473$	−9.84300e6	−	1.70486e7i	−0.0930131	−	0.161103i
$474$		0			0
$475$	−1.00989e7	−	1.47042e7i	−0.0942309	−	0.137202i
$476$		0			0
$477$	8.12701e7	−	4.69213e7i	0.748817	−	0.432330i
$478$		0			0
$479$	−6.64316e7	+	1.15063e8i	−0.604461	+	1.04696i	0.387676	+	0.921796i	$0.373278\pi$
$479$	−6.64316e7	+	1.15063e8i	−0.604461	+	1.04696i	−0.992136	+	0.125161i	$0.960055\pi$
$480$		0			0
$481$	−5.18367e7	+	8.97839e7i	−0.465803	+	0.806795i
$482$		0			0
$483$		−	3.59179e6i		−	0.0318764i
$484$		0			0
$485$	−9.94685e7	−	5.74282e7i	−0.871888	−	0.503384i
$486$		0			0
$487$		−	1.02885e8i		−	0.890769i	−0.895339	−	0.445384i	$-0.853067\pi$
$487$		−	1.02885e8i		−	0.890769i	0.895339	−	0.445384i	$-0.146933\pi$
$488$		0			0
$489$	−1.26702e6	+	731513.i	−0.0108357	+	0.00625598i
$490$		0			0
$491$	−9.41949e7	−	1.63150e8i	−0.795762	−	1.37830i	−0.922354	−	0.386345i	$-0.873737\pi$
$491$	−9.41949e7	−	1.63150e8i	−0.795762	−	1.37830i	0.126593	−	0.991955i	$-0.459596\pi$
$492$		0			0
$493$			2.73222e7i			0.228021i
$494$		0			0
$495$	6.47942e7			0.534221
$496$		0			0
$497$	−1.77809e7	+	1.02658e7i	−0.144838	+	0.0836225i
$498$		0			0
$499$	−7.46714e7	−	1.29335e8i	−0.600970	−	1.04091i	−0.992675	−	0.120819i	$-0.961448\pi$
$499$	−7.46714e7	−	1.29335e8i	−0.600970	−	1.04091i	0.391705	−	0.920091i	$-0.371886\pi$
$500$		0			0
$501$	−8.86780e6			−0.0705184
$502$		0			0
$503$	4.33323e7	−	7.50538e7i	0.340493	−	0.589751i	−0.644032	−	0.764999i	$-0.722739\pi$
$503$	4.33323e7	−	7.50538e7i	0.340493	−	0.589751i	0.984524	+	0.175248i	$0.0560728\pi$
$504$		0			0
$505$	1.96928e8			1.52909
$506$		0			0
$507$	−2.56994e6	−	1.48376e6i	−0.0197197	−	0.0113851i
$508$		0			0
$509$	−1.97185e8	−	1.13845e8i	−1.49527	−	0.863297i	−0.495289	−	0.868728i	$-0.664938\pi$
$509$	−1.97185e8	−	1.13845e8i	−1.49527	−	0.863297i	−0.999985	+	0.00543153i	$0.998271\pi$
$510$		0			0
$511$	5.74403e7	+	9.94895e7i	0.430481	+	0.745615i
$512$		0			0
$513$	−2.08419e7	−	9.94933e6i	−0.154378	−	0.0736956i
$514$		0			0
$515$	1.68268e8	−	9.71494e7i	1.23191	−	0.711244i
$516$		0			0
$517$	−6.76119e6	+	1.17107e7i	−0.0489273	+	0.0847446i
$518$		0			0
$519$	1.15859e6	−	2.00673e6i	0.00828756	−	0.0143545i
$520$		0			0
$521$		−	2.61082e8i		−	1.84614i	−0.384633	−	0.923069i	$-0.625672\pi$
$521$		−	2.61082e8i		−	1.84614i	0.384633	−	0.923069i	$-0.374328\pi$
$522$		0			0
$523$	−1.67558e8	−	9.67397e7i	−1.17128	−	0.676238i	−0.217298	−	0.976105i	$-0.569724\pi$
$523$	−1.67558e8	−	9.67397e7i	−1.17128	−	0.676238i	−0.953981	+	0.299867i	$0.903058\pi$
$524$		0			0
$525$		−	950744.i		−	0.00657030i
$526$		0			0
$527$	−7.24516e7	+	4.18300e7i	−0.495013	+	0.285796i
$528$		0			0
$529$	2.57515e7	+	4.46029e7i	0.173955	+	0.301298i
$530$		0			0
$531$			2.46194e8i			1.64435i
$532$		0			0
$533$	−7.70637e7			−0.508942
$534$		0			0
$535$	6.30778e7	−	3.64180e7i	0.411922	−	0.237823i
$536$		0			0
$537$	547392.	+	948111.i	0.00353489	+	0.00612261i
$538$		0			0
$539$	−6.15333e7			−0.392956
$540$		0			0
$541$	2.19661e6	−	3.80464e6i	0.0138727	−	0.0240282i	−0.859006	−	0.511966i	$-0.828917\pi$
$541$	2.19661e6	−	3.80464e6i	0.0138727	−	0.0240282i	0.872878	+	0.487938i	$0.162251\pi$
$542$		0			0
$543$	−1.39804e7			−0.0873213
$544$		0			0
$545$	5.12911e7	+	2.96129e7i	0.316849	+	0.182933i
$546$		0			0
$547$	2.72400e8	+	1.57270e8i	1.66435	+	0.960914i	0.970599	+	0.240700i	$0.0773771\pi$
$547$	2.72400e8	+	1.57270e8i	1.66435	+	0.960914i	0.693752	+	0.720214i	$0.255956\pi$
$548$		0			0
$549$	−3.40596e7	−	5.89930e7i	−0.205837	−	0.356520i
$550$		0			0
$551$	−8.23045e7	+	5.65271e7i	−0.492004	+	0.337911i
$552$		0			0
$553$	4.80130e7	−	2.77203e7i	0.283912	−	0.163916i
$554$		0			0
$555$	8.61343e6	−	1.49189e7i	0.0503845	−	0.0872685i
$556$		0			0
$557$	−1.57508e8	+	2.72812e8i	−0.911458	+	1.57869i	−0.0994511	+	0.995042i	$0.531709\pi$
$557$	−1.57508e8	+	2.72812e8i	−0.911458	+	1.57869i	−0.812006	+	0.583648i	$0.801625\pi$
$558$		0			0
$559$		−	5.58962e7i		−	0.319998i
$560$		0			0
$561$	2.49892e6	+	1.44275e6i	0.0141535	+	0.00817154i
$562$		0			0
$563$		−	2.94019e7i		−	0.164760i	−0.996601	−	0.0823798i	$-0.973748\pi$
$563$		−	2.94019e7i		−	0.164760i	0.996601	−	0.0823798i	$-0.0262520\pi$
$564$		0			0
$565$	−5.57012e7	+	3.21591e7i	−0.308830	+	0.178303i
$566$		0			0
$567$	4.09838e7	+	7.09861e7i	0.224835	+	0.389425i
$568$		0			0
$569$			2.70816e8i			1.47007i	0.678030	+	0.735034i	$0.262834\pi$
$569$			2.70816e8i			1.47007i	−0.678030	+	0.735034i	$0.737166\pi$
$570$		0			0
$571$	2.83384e8			1.52218			0.761092	−	0.648644i	$-0.224664\pi$
$571$	2.83384e8			1.52218			0.761092	+	0.648644i	$0.224664\pi$
$572$		0			0
$573$	1.51659e7	−	8.75604e6i	0.0806129	−	0.0465419i
$574$		0			0
$575$	−1.27761e7	−	2.21288e7i	−0.0672038	−	0.116400i
$576$		0			0
$577$	1.42647e8			0.742564			0.371282	−	0.928520i	$-0.378918\pi$
$577$	1.42647e8			0.742564			0.371282	+	0.928520i	$0.378918\pi$
$578$		0			0
$579$	−3.94427e6	+	6.83167e6i	−0.0203203	+	0.0351958i
$580$		0			0
$581$	−1.68253e7			−0.0857896
$582$		0			0
$583$	−7.44895e7	−	4.30066e7i	−0.375915	−	0.217035i
$584$		0			0
$585$	1.59328e8	+	9.19880e7i	0.795837	+	0.459477i
$586$		0			0
$587$	8.24985e7	+	1.42892e8i	0.407879	+	0.706468i	0.994652	−	0.103284i	$-0.0329351\pi$
$587$	8.24985e7	+	1.42892e8i	0.407879	+	0.706468i	−0.586773	+	0.809752i	$0.699602\pi$
$588$		0			0
$589$	−2.75903e8	−	1.31709e8i	−1.35024	−	0.644567i
$590$		0			0
$591$	1.19641e7	−	6.90747e6i	0.0579585	−	0.0334624i
$592$		0			0
$593$	−1.74997e7	+	3.03104e7i	−0.0839202	+	0.145354i	−0.904931	−	0.425559i	$-0.860077\pi$
$593$	−1.74997e7	+	3.03104e7i	−0.0839202	+	0.145354i	0.821010	+	0.570913i	$0.193411\pi$
$594$		0			0
$595$	−1.99815e7	+	3.46090e7i	−0.0948587	+	0.164300i
$596$		0			0
$597$			5.89725e6i			0.0277158i
$598$		0			0
$599$	−3.46956e8	−	2.00315e8i	−1.61433	−	0.932037i	−0.988349	−	0.152202i	$-0.951364\pi$
$599$	−3.46956e8	−	2.00315e8i	−1.61433	−	0.932037i	−0.625985	−	0.779835i	$-0.715303\pi$
$600$		0			0
$601$		−	3.29521e7i		−	0.151796i	−0.997116	−	0.0758979i	$-0.975818\pi$
$601$		−	3.29521e7i		−	0.151796i	0.997116	−	0.0758979i	$-0.0241823\pi$
$602$		0			0
$603$	−1.11496e8	+	6.43725e7i	−0.508521	+	0.293595i
$604$		0			0
$605$	8.98885e7	+	1.55691e8i	0.405918	+	0.703070i
$606$		0			0
$607$			2.57448e8i			1.15113i	0.817757	+	0.575564i	$0.195217\pi$
$607$			2.57448e8i			1.15113i	−0.817757	+	0.575564i	$0.804783\pi$
$608$		0			0
$609$	−5.32165e6			−0.0235610
$610$		0			0
$611$	−3.32513e7	+	1.91976e7i	−0.145776	+	0.0841636i
$612$		0			0
$613$	1.30092e8	+	2.25327e8i	0.564768	+	0.978208i	0.997071	+	0.0764791i	$0.0243679\pi$
$613$	1.30092e8	+	2.25327e8i	0.564768	+	0.978208i	−0.432303	+	0.901729i	$0.642299\pi$
$614$		0			0
$615$	1.28052e7			0.0550507
$616$		0			0
$617$	4.88941e7	−	8.46871e7i	0.208162	−	0.360547i	−0.742974	−	0.669321i	$-0.766585\pi$
$617$	4.88941e7	−	8.46871e7i	0.208162	−	0.360547i	0.951136	+	0.308774i	$0.0999186\pi$
$618$		0			0
$619$	−5.99125e7			−0.252607			−0.126304	−	0.991992i	$-0.540311\pi$
$619$	−5.99125e7			−0.252607			−0.126304	+	0.991992i	$0.540311\pi$
$620$		0			0
$621$	−2.86499e7	−	1.65410e7i	−0.119632	−	0.0690696i
$622$		0			0
$623$	−2.89340e7	−	1.67051e7i	−0.119659	−	0.0690850i
$624$		0			0
$625$	1.39006e8	+	2.40766e8i	0.569370	+	0.986178i
$626$		0			0
$627$	823940.	+	1.05126e7i	0.00334267	+	0.0426489i
$628$		0			0
$629$	−8.94823e7	+	5.16626e7i	−0.359571	+	0.207599i
$630$		0			0
$631$	−1.54628e8	+	2.67823e8i	−0.615459	+	1.06601i	0.374845	+	0.927088i	$0.377696\pi$
$631$	−1.54628e8	+	2.67823e8i	−0.615459	+	1.06601i	−0.990304	+	0.138919i	$0.955637\pi$
$632$		0			0
$633$	−5.74313e6	+	9.94740e6i	−0.0226432	+	0.0392192i
$634$		0			0
$635$		−	3.42809e8i		−	1.33885i
$636$		0			0
$637$	−1.51309e8	−	8.73584e7i	−0.585392	−	0.337976i
$638$		0			0
$639$			9.42028e7i			0.361045i
$640$		0			0
$641$	−2.16111e7	+	1.24772e7i	−0.0820547	+	0.0473743i	−0.540466	−	0.841366i	$-0.681752\pi$
$641$	−2.16111e7	+	1.24772e7i	−0.0820547	+	0.0473743i	0.458411	+	0.888740i	$0.348419\pi$
$642$		0			0
$643$	3.80849e7	+	6.59650e7i	0.143258	+	0.248131i	0.928722	−	0.370777i	$-0.120909\pi$
$643$	3.80849e7	+	6.59650e7i	0.143258	+	0.248131i	−0.785463	+	0.618908i	$0.787575\pi$
$644$		0			0
$645$			9.28797e6i			0.0346132i
$646$		0			0
$647$	2.48962e8			0.919223			0.459611	−	0.888120i	$-0.347989\pi$
$647$	2.48962e8			0.919223			0.459611	+	0.888120i	$0.347989\pi$
$648$		0			0
$649$	1.95421e8	−	1.12827e8i	0.714888	−	0.412741i
$650$		0			0
$651$	−8.14739e6	−	1.41117e7i	−0.0295308	−	0.0511489i
$652$		0			0
$653$	−1.68447e8			−0.604957			−0.302478	−	0.953156i	$-0.597814\pi$
$653$	−1.68447e8			−0.604957			−0.302478	+	0.953156i	$0.597814\pi$
$654$		0			0
$655$	2.23766e8	−	3.87574e8i	0.796288	−	1.37921i
$656$		0			0
$657$	5.27094e8			1.85863
$658$		0			0
$659$	−4.22259e8	−	2.43791e8i	−1.47544	−	0.851848i	−0.475828	−	0.879538i	$-0.657852\pi$
$659$	−4.22259e8	−	2.43791e8i	−1.47544	−	0.851848i	−0.999617	+	0.0276901i	$0.991185\pi$
$660$		0			0
$661$	4.64303e8	+	2.68065e8i	1.60767	+	0.928189i	0.989890	+	0.141838i	$0.0453011\pi$
$661$	4.64303e8	+	2.68065e8i	1.60767	+	0.928189i	0.617780	+	0.786351i	$0.288032\pi$
$662$		0			0
$663$	4.09654e6	+	7.09541e6i	0.0140565	+	0.0243465i
$664$		0			0
$665$	−1.45595e8	+	1.14112e7i	−0.495087	+	0.0388031i
$666$		0			0
$667$	−1.23863e8	+	7.15122e7i	−0.417410	+	0.240992i
$668$		0			0
$669$	−1.59568e7	+	2.76380e7i	−0.0532926	+	0.0923056i
$670$		0			0
$671$	−3.12180e7	+	5.40711e7i	−0.103332	+	0.178977i
$672$		0			0
$673$		−	4.41464e8i		−	1.44827i	−0.689657	−	0.724136i	$-0.742239\pi$
$673$		−	4.41464e8i		−	1.44827i	0.689657	−	0.724136i	$-0.257761\pi$
$674$		0			0
$675$	−7.58359e6	−	4.37839e6i	−0.0246583	−	0.0142365i
$676$		0			0
$677$		−	1.65511e8i		−	0.533411i	−0.963778	−	0.266705i	$-0.914065\pi$
$677$		−	1.65511e8i		−	0.533411i	0.963778	−	0.266705i	$-0.0859351\pi$
$678$		0			0
$679$	−1.16203e8	+	6.70898e7i	−0.371200	+	0.214312i
$680$		0			0
$681$	1.54505e7	+	2.67611e7i	0.0489217	+	0.0847349i
$682$		0			0
$683$			4.54816e7i			0.142749i	0.997450	+	0.0713746i	$0.0227386\pi$
$683$			4.54816e7i			0.142749i	−0.997450	+	0.0713746i	$0.977261\pi$
$684$		0			0
$685$	3.64683e8			1.13460
$686$		0			0
$687$	−1.30674e7	+	7.54447e6i	−0.0403013	+	0.0232680i
$688$		0			0
$689$	−1.22112e8	−	2.11505e8i	−0.373338	−	0.646640i
$690$		0			0
$691$	−5.31210e8			−1.61002			−0.805012	−	0.593259i	$-0.797841\pi$
$691$	−5.31210e8			−1.61002			−0.805012	+	0.593259i	$0.797841\pi$
$692$		0			0
$693$	3.78475e7	−	6.55538e7i	0.113720	−	0.196969i
$694$		0			0
$695$	1.37663e8			0.410076
$696$		0			0
$697$	−6.65149e7	−	3.84024e7i	−0.196436	−	0.113412i
$698$		0			0
$699$	4.26148e7	+	2.46037e7i	0.124775	+	0.0720391i
$700$		0			0
$701$	8.35008e6	+	1.44628e7i	0.0242402	+	0.0419853i	0.877891	−	0.478860i	$-0.158950\pi$
$701$	8.35008e6	+	1.44628e7i	0.0242402	+	0.0419853i	−0.853651	+	0.520846i	$0.825617\pi$
$702$		0			0
$703$	−3.40758e8	−	1.62668e8i	−0.980798	−	0.468206i
$704$		0			0
$705$	5.52518e6	−	3.18997e6i	0.0157681	−	0.00910372i
$706$		0			0
$707$	1.15029e8	−	1.99237e8i	0.325500	−	0.563782i
$708$		0			0
$709$	−9.83758e7	+	1.70392e8i	−0.276026	+	0.478091i	−0.970393	−	0.241530i	$-0.922351\pi$
$709$	−9.83758e7	+	1.70392e8i	−0.276026	+	0.478091i	0.694368	+	0.719621i	$0.255684\pi$
$710$		0			0
$711$		−	2.54372e8i		−	0.707719i
$712$		0			0
$713$	−3.79265e8	−	2.18969e8i	−1.04634	−	0.604107i
$714$		0			0
$715$		−	1.68626e8i		−	0.461325i
$716$		0			0
$717$	5.07935e7	−	2.93257e7i	0.137801	−	0.0795592i
$718$		0			0
$719$	−3.21686e8	−	5.57176e8i	−0.865456	−	1.49901i	−0.866594	−	0.499015i	$-0.833695\pi$
$719$	−3.21686e8	−	5.57176e8i	−0.865456	−	1.49901i	0.00113745	−	0.999999i	$-0.499638\pi$
$720$		0			0
$721$		−	2.26987e8i		−	0.605614i
$722$		0			0
$723$	−6.62898e6			−0.0175401
$724$		0			0
$725$	−3.27863e7	+	1.89292e7i	−0.0860357	+	0.0496728i
$726$		0			0
$727$	1.69697e8	+	2.93923e8i	0.441642	+	0.764946i	0.997811	−	0.0661227i	$-0.0210629\pi$
$727$	1.69697e8	+	2.93923e8i	0.441642	+	0.764946i	−0.556170	+	0.831069i	$0.687730\pi$
$728$		0			0
$729$	3.70394e8			0.956051
$730$		0			0
$731$	2.78542e7	−	4.82449e7i	0.0713081	−	0.123509i
$732$		0			0
$733$	2.34275e8			0.594859			0.297429	−	0.954744i	$-0.403871\pi$
$733$	2.34275e8			0.594859			0.297429	+	0.954744i	$0.403871\pi$
$734$		0			0
$735$	2.51422e7	+	1.45159e7i	0.0633201	+	0.0365579i
$736$		0			0
$737$	1.02194e8	+	5.90018e7i	0.255284	+	0.147388i
$738$		0			0
$739$	7.82975e7	+	1.35615e8i	0.194006	+	0.336028i	0.946574	−	0.322486i	$-0.104519\pi$
$739$	7.82975e7	+	1.35615e8i	0.194006	+	0.336028i	−0.752568	+	0.658514i	$0.771185\pi$
$740$		0			0
$741$	−1.28986e7	+	2.70201e7i	−0.0317022	+	0.0664097i
$742$		0			0
$743$	2.87300e8	−	1.65873e8i	0.700438	−	0.404398i	−0.107072	−	0.994251i	$-0.534148\pi$
$743$	2.87300e8	−	1.65873e8i	0.700438	−	0.404398i	0.807511	+	0.589853i	$0.200814\pi$
$744$		0			0
$745$	−2.44839e6	+	4.24074e6i	−0.00592123	+	0.0102559i
$746$		0			0
$747$	−3.85989e7	+	6.68552e7i	−0.0926004	+	0.160389i
$748$		0			0
$749$		−	8.50897e7i		−	0.202503i
$750$		0			0
$751$	−4.86019e8	−	2.80603e8i	−1.14745	−	0.662480i	−0.199185	−	0.979962i	$-0.563830\pi$
$751$	−4.86019e8	−	2.80603e8i	−1.14745	−	0.662480i	−0.948264	+	0.317481i	$0.897163\pi$
$752$		0			0
$753$		−	1.77341e7i		−	0.0415359i
$754$		0			0
$755$	−2.36376e8	+	1.36472e8i	−0.549242	+	0.317105i
$756$		0			0
$757$	1.95303e8	+	3.38275e8i	0.450216	+	0.779798i	0.998399	−	0.0565609i	$-0.0180135\pi$
$757$	1.95303e8	+	3.38275e8i	0.450216	+	0.779798i	−0.548183	+	0.836359i	$0.684680\pi$
$758$		0			0
$759$			1.51049e7i			0.0345455i
$760$		0			0
$761$	2.49233e8			0.565524			0.282762	−	0.959190i	$-0.408749\pi$
$761$	2.49233e8			0.565524			0.282762	+	0.959190i	$0.408749\pi$
$762$		0			0
$763$	5.99202e7	−	3.45949e7i	0.134896	−	0.0778823i
$764$		0			0
$765$	9.16790e7	+	1.58793e8i	0.204779	+	0.354688i
$766$		0			0
$767$	6.40716e8			1.41997
$768$		0			0
$769$	−3.77735e7	+	6.54256e7i	−0.0830630	+	0.143869i	−0.904564	−	0.426337i	$-0.859804\pi$
$769$	−3.77735e7	+	6.54256e7i	−0.0830630	+	0.143869i	0.821501	+	0.570207i	$0.193137\pi$
$770$		0			0
$771$	2.74953e7			0.0599922
$772$		0			0
$773$	−3.13593e8	−	1.81053e8i	−0.678935	−	0.391984i	0.120518	−	0.992711i	$-0.461544\pi$
$773$	−3.13593e8	−	1.81053e8i	−0.678935	−	0.391984i	−0.799454	+	0.600728i	$0.794878\pi$
$774$		0			0
$775$	−1.00391e8	−	5.79608e7i	−0.215670	−	0.124517i
$776$		0			0
$777$	−1.00625e7	−	1.74288e7i	−0.0214508	−	0.0371539i
$778$		0			0
$779$	−2.19312e7	−	2.79819e8i	−0.0463926	−	0.591922i
$780$		0			0
$781$	7.47754e7	−	4.31716e7i	0.156966	−	0.0906244i
$782$		0			0
$783$	−2.45074e7	+	4.24480e7i	−0.0510519	+	0.0884244i
$784$		0			0
$785$	−2.91245e8	+	5.04451e8i	−0.602073	+	1.04282i
$786$		0			0
$787$			1.64248e8i			0.336958i	0.985705	+	0.168479i	$0.0538855\pi$
$787$			1.64248e8i			0.336958i	−0.985705	+	0.168479i	$0.946114\pi$
$788$		0			0
$789$	−2.39927e6	−	1.38522e6i	−0.00488481	−	0.00282025i
$790$		0			0
$791$			7.51389e7i			0.151822i
$792$		0			0
$793$	−1.53529e8	+	8.86399e7i	−0.307872	+	0.177750i
$794$		0			0
$795$	2.02907e7	+	3.51446e7i	0.0403828	+	0.0699450i
$796$		0			0
$797$			9.70129e8i			1.91626i	0.286334	+	0.958130i	$0.407563\pi$
$797$			9.70129e8i			1.91626i	−0.286334	+	0.958130i	$0.592437\pi$
$798$		0			0
$799$	−3.82663e7			−0.0750198
$800$		0			0
$801$	−1.32755e8	+	7.66460e7i	−0.258317	+	0.149139i
$802$		0			0
$803$	−2.41559e8	−	4.18392e8i	−0.466526	−	0.808047i
$804$		0			0
$805$	−2.09196e8			−0.401019
$806$		0			0
$807$	−1.21766e7	+	2.10906e7i	−0.0231690	+	0.0401299i
$808$		0			0
$809$	−7.15238e7			−0.135084			−0.0675421	−	0.997716i	$-0.521516\pi$
$809$	−7.15238e7			−0.135084			−0.0675421	+	0.997716i	$0.521516\pi$
$810$		0			0
$811$	5.24400e8	+	3.02762e8i	0.983105	+	0.567596i	0.903206	−	0.429207i	$-0.141207\pi$
$811$	5.24400e8	+	3.02762e8i	0.983105	+	0.567596i	0.0798987	+	0.996803i	$0.474540\pi$
$812$		0			0
$813$	−6.52416e6	−	3.76672e6i	−0.0121410	−	0.00700958i
$814$		0			0
$815$	4.26053e7	+	7.37946e7i	0.0787030	+	0.136318i
$816$		0			0
$817$	2.02959e8	−	1.59072e7i	0.372172	−	0.0291694i
$818$		0			0
$819$	1.86133e8	−	1.07464e8i	0.338822	−	0.195619i
$820$		0			0
$821$	−1.75853e8	+	3.04586e8i	−0.317775	+	0.550403i	−0.980024	−	0.198881i	$-0.936269\pi$
$821$	−1.75853e8	+	3.04586e8i	−0.317775	+	0.550403i	0.662248	+	0.749285i	$0.269602\pi$
$822$		0			0
$823$	−1.55920e8	+	2.70062e8i	−0.279707	+	0.484467i	−0.971312	−	0.237809i	$-0.923571\pi$
$823$	−1.55920e8	+	2.70062e8i	−0.279707	+	0.484467i	0.691605	+	0.722276i	$0.256904\pi$
$824$		0			0
$825$			3.99824e6i			0.00712045i
$826$		0			0
$827$	5.29596e8	+	3.05762e8i	0.936328	+	0.540589i	0.888807	−	0.458281i	$-0.151535\pi$
$827$	5.29596e8	+	3.05762e8i	0.936328	+	0.540589i	0.0475205	+	0.998870i	$0.484868\pi$
$828$		0			0
$829$		−	3.77043e8i		−	0.661801i	−0.943666	−	0.330901i	$-0.892647\pi$
$829$		−	3.77043e8i		−	0.661801i	0.943666	−	0.330901i	$-0.107353\pi$
$830$		0			0
$831$	1.24959e7	−	7.21450e6i	0.0217753	−	0.0125720i
$832$		0			0
$833$	−8.70649e7	−	1.50801e8i	−0.150629	−	0.260897i
$834$		0			0
$835$			5.16485e8i			0.887153i
$836$		0			0
$837$	−1.50082e8			−0.255949
$838$		0			0
$839$	−5.39759e8	+	3.11630e8i	−0.913932	+	0.527659i	−0.881694	−	0.471821i	$-0.843597\pi$
$839$	−5.39759e8	+	3.11630e8i	−0.913932	+	0.527659i	−0.0322380	+	0.999480i	$0.510263\pi$
$840$		0			0
$841$	−1.91458e8	−	3.31615e8i	−0.321874	−	0.557502i
$842$		0			0
$843$	7.49430e7			0.125097
$844$		0			0
$845$	−8.64180e7	+	1.49680e8i	−0.143230	+	0.248082i
$846$		0			0
$847$	2.10022e8			0.345633
$848$		0			0
$849$	−2.65059e7	−	1.53032e7i	−0.0433132	−	0.0250069i
$850$		0			0
$851$	−4.68416e8	−	2.70440e8i	−0.760052	−	0.438816i
$852$		0			0
$853$	1.71599e8	+	2.97218e8i	0.276482	+	0.478881i	0.970508	−	0.241069i	$-0.0774980\pi$
$853$	1.71599e8	+	2.97218e8i	0.276482	+	0.478881i	−0.694026	+	0.719950i	$0.744165\pi$
$854$		0			0
$855$	−2.88667e8	+	6.04699e8i	−0.461847	+	0.967477i
$856$		0			0
$857$	5.92761e8	−	3.42231e8i	0.941753	−	0.543721i	0.0512436	−	0.998686i	$-0.483682\pi$
$857$	5.92761e8	−	3.42231e8i	0.941753	−	0.543721i	0.890509	+	0.454965i	$0.150348\pi$
$858$		0			0
$859$	−1.92731e8	+	3.33821e8i	−0.304070	+	0.526664i	−0.977054	−	0.212993i	$-0.931679\pi$
$859$	−1.92731e8	+	3.33821e8i	−0.304070	+	0.526664i	0.672984	+	0.739657i	$0.265012\pi$
$860$		0			0
$861$	7.47979e6	−	1.29554e7i	0.0117187	−	0.0202974i
$862$		0			0
$863$			3.96015e8i			0.616141i	0.951364	+	0.308070i	$0.0996832\pi$
$863$			3.96015e8i			0.616141i	−0.951364	+	0.308070i	$0.900317\pi$
$864$		0			0
$865$	−1.16878e8	−	6.74793e7i	−0.180586	−	0.104261i
$866$		0			0
$867$		−	4.77836e7i		−	0.0733199i
$868$		0			0
$869$	−2.01913e8	+	1.16575e8i	−0.307684	+	0.177642i
$870$		0			0
$871$	1.67529e8	+	2.90169e8i	0.253533	+	0.439133i
$872$		0			0
$873$			6.15641e8i			0.925305i
$874$		0			0
$875$	2.77313e8			0.413948
$876$		0			0
$877$	9.31135e8	−	5.37591e8i	1.38043	−	0.796991i	0.388219	−	0.921567i	$-0.373090\pi$
$877$	9.31135e8	−	5.37591e8i	1.38043	−	0.796991i	0.992210	+	0.124576i	$0.0397571\pi$
$878$		0			0
$879$	−4.93189e7	−	8.54229e7i	−0.0726185	−	0.125779i
$880$		0			0
$881$	2.86646e8			0.419197			0.209598	−	0.977788i	$-0.432784\pi$
$881$	2.86646e8			0.419197			0.209598	+	0.977788i	$0.432784\pi$
$882$		0			0
$883$	−1.55440e8	+	2.69229e8i	−0.225777	+	0.391057i	−0.956552	−	0.291561i	$-0.905825\pi$
$883$	−1.55440e8	+	2.69229e8i	−0.225777	+	0.391057i	0.730775	+	0.682618i	$0.239159\pi$
$884$		0			0
$885$	−1.06464e8			−0.153594
$886$		0			0
$887$	1.10008e9	+	6.35131e8i	1.57635	+	0.910106i	0.995363	+	0.0961940i	$0.0306669\pi$
$887$	1.10008e9	+	6.35131e8i	1.57635	+	0.910106i	0.580988	+	0.813912i	$0.302666\pi$
$888$		0			0
$889$	−3.46828e8	−	2.00241e8i	−0.493639	−	0.285003i
$890$		0			0
$891$	−1.72353e8	−	2.98524e8i	−0.243661	−	0.422033i
$892$		0			0
$893$	−7.91695e7	−	1.15272e8i	−0.111174	−	0.161871i
$894$		0			0
$895$	5.52206e7	−	3.18816e7i	0.0770251	−	0.0444704i
$896$		0			0
$897$	−2.14443e7	+	3.71426e7i	−0.0297122	+	0.0514630i
$898$		0			0
$899$	−3.24427e8	+	5.61924e8i	−0.446517	+	0.773390i
$900$		0			0
$901$		−	2.43404e8i		−	0.332777i
$902$		0			0
$903$	9.39686e6	+	5.42528e6i	0.0127620	+	0.00736815i
$904$		0			0
$905$			8.14257e8i			1.09854i
$906$		0			0
$907$	4.11830e8	−	2.37770e8i	0.551946	−	0.318666i	−0.197961	−	0.980210i	$-0.563432\pi$
$907$	4.11830e8	−	2.37770e8i	0.551946	−	0.318666i	0.749906	+	0.661544i	$0.230099\pi$
$908$		0			0
$909$	−5.27777e8	−	9.14136e8i	−0.702682	−	1.21708i
$910$		0			0
$911$		−	8.78484e8i		−	1.16193i	−0.813930	−	0.580963i	$-0.802676\pi$
$911$		−	8.78484e8i		−	1.16193i	0.813930	−	0.580963i	$-0.197324\pi$
$912$		0			0
$913$	7.07569e7			0.0929730
$914$		0			0
$915$	2.55110e7	−	1.47288e7i	0.0333016	−	0.0192267i
$916$		0			0
$917$	−2.61412e8	−	4.52778e8i	−0.339014	−	0.587189i
$918$		0			0
$919$	−1.74546e8			−0.224886			−0.112443	−	0.993658i	$-0.535868\pi$
$919$	−1.74546e8			−0.224886			−0.112443	+	0.993658i	$0.535868\pi$
$920$		0			0
$921$	2.14560e7	−	3.71629e7i	0.0274644	−	0.0475697i
$922$		0			0
$923$	2.45162e8			0.311780
$924$		0			0
$925$	−1.23989e8	−	7.15852e7i	−0.156660	−	0.0904479i
$926$		0			0
$927$	−9.01932e8	−	5.20730e8i	−1.13223	−	0.653693i
$928$		0			0
$929$	−3.76167e8	−	6.51541e8i	−0.469174	−	0.812633i	0.530205	−	0.847870i	$-0.322115\pi$
$929$	−3.76167e8	−	6.51541e8i	−0.469174	−	0.812633i	−0.999379	+	0.0352361i	$0.988782\pi$
$930$		0			0
$931$	2.74139e8	−	5.74265e8i	0.339720	−	0.711645i
$932$		0			0
$933$	1.62497e6	−	938178.i	0.00200079	−	0.00115516i
$934$		0			0
$935$	8.40299e7	−	1.45544e8i	0.102801	−	0.178057i
$936$		0			0
$937$	9.98837e7	−	1.73004e8i	0.121416	−	0.210299i	−0.798910	−	0.601450i	$-0.794590\pi$
$937$	9.98837e7	−	1.73004e8i	0.121416	−	0.210299i	0.920326	+	0.391152i	$0.127923\pi$
$938$		0			0
$939$		−	1.29832e8i		−	0.156813i
$940$		0			0
$941$	−2.44786e8	−	1.41327e8i	−0.293777	−	0.169612i	0.345867	−	0.938284i	$-0.387585\pi$
$941$	−2.44786e8	−	1.41327e8i	−0.293777	−	0.169612i	−0.639644	+	0.768671i	$0.720918\pi$
$942$		0			0
$943$		−	4.02053e8i		−	0.479455i
$944$		0			0
$945$	−6.20870e7	+	3.58459e7i	−0.0735707	+	0.0424761i
$946$		0			0
$947$	4.72862e8	+	8.19020e8i	0.556781	+	0.964372i	0.997763	+	0.0668565i	$0.0212970\pi$
$947$	4.72862e8	+	8.19020e8i	0.556781	+	0.964372i	−0.440982	+	0.897516i	$0.645370\pi$
$948$		0			0
$949$		−	1.37176e9i		−	1.60501i
$950$		0			0
$951$	5.88796e7			0.0684578
$952$		0			0
$953$	−8.01361e8	+	4.62666e8i	−0.925868	+	0.534550i	−0.885503	−	0.464635i	$-0.846186\pi$
$953$	−8.01361e8	+	4.62666e8i	−0.925868	+	0.534550i	−0.0403659	+	0.999185i	$0.512852\pi$
$954$		0			0
$955$	−5.09976e8	−	8.83304e8i	−0.585517	−	1.01415i
$956$		0			0
$957$	2.23796e7			0.0255339
$958$		0			0
$959$	2.13018e8	−	3.68958e8i	0.241524	−	0.418332i
$960$		0			0
$961$	−1.09927e9			−1.23861
$962$		0			0
$963$	−3.38103e8	−	1.95204e8i	−0.378591	−	0.218580i
$964$		0			0
$965$	3.97895e8	+	2.29725e8i	0.442779	+	0.255638i
$966$		0			0
$967$	6.16567e8	+	1.06793e9i	0.681869	+	1.18103i	0.974410	+	0.224778i	$0.0721659\pi$
$967$	6.16567e8	+	1.06793e9i	0.681869	+	1.18103i	−0.292541	+	0.956253i	$0.594501\pi$
$968$		0			0
$969$	−2.45977e7	+	1.68938e7i	−0.0270348	+	0.0185676i
$970$		0			0
$971$	1.33730e9	−	7.72089e8i	1.46073	−	0.843353i	0.461685	−	0.887044i	$-0.347245\pi$
$971$	1.33730e9	−	7.72089e8i	1.46073	−	0.843353i	0.999045	+	0.0436905i	$0.0139116\pi$
$972$		0			0
$973$	8.04118e7	−	1.39277e8i	0.0872934	−	0.151197i
$974$		0			0
$975$	−5.67628e6	+	9.83161e6i	−0.00612421	+	0.0106074i
$976$		0			0
$977$			1.13693e9i			1.21913i	0.792738	+	0.609563i	$0.208655\pi$
$977$			1.13693e9i			1.21913i	−0.792738	+	0.609563i	$0.791345\pi$
$978$		0			0
$979$	1.21679e8	+	7.02512e7i	0.129678	+	0.0748696i
$980$		0			0
$981$		−	3.17456e8i		−	0.336261i
$982$		0			0
$983$	8.90792e8	−	5.14299e8i	0.937812	−	0.541446i	0.0485383	−	0.998821i	$-0.484544\pi$
$983$	8.90792e8	−	5.14299e8i	0.937812	−	0.541446i	0.889274	+	0.457375i	$0.151210\pi$
$984$		0			0
$985$	−4.02310e8	−	6.96822e8i	−0.420971	−	0.729143i
$986$		0			0
$987$		−	7.45328e6i		−	0.00775168i
$988$		0			0
$989$	2.91619e8			0.301458
$990$		0			0
$991$	−7.38328e7	+	4.26274e7i	−0.0758627	+	0.0437994i	−0.537452	−	0.843295i	$-0.680613\pi$
$991$	−7.38328e7	+	4.26274e7i	−0.0758627	+	0.0437994i	0.461589	+	0.887094i	$0.347280\pi$
$992$		0			0
$993$	−1.33821e7	−	2.31785e7i	−0.0136671	−	0.0236722i
$994$		0			0
$995$	3.43472e8			0.348676
$996$		0			0
$997$	4.80725e8	−	8.32640e8i	0.485077	−	0.840179i	−0.514776	−	0.857325i	$-0.672125\pi$
$997$	4.80725e8	−	8.32640e8i	0.485077	−	0.840179i	0.999853	+	0.0171463i	$0.00545809\pi$
$998$		0			0
$999$	−1.85361e8			−0.185918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.h.a.69.6	yes	20
3.2	odd	2		684.7.y.c.145.7		20
19.8	odd	6	inner	76.7.h.a.65.6	✓	20
57.8	even	6		684.7.y.c.217.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.h.a.65.6	✓	20	19.8	odd	6	inner
76.7.h.a.69.6	yes	20	1.1	even	1	trivial
684.7.y.c.145.7		20	3.2	odd	2
684.7.y.c.217.7		20	57.8	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.00739 - 1.15896i) q^{3} +(-67.5013 - 116.916i) q^{5} -157.715 q^{7} +(-361.814 + 626.680i) q^{9} +O(q^{10})\)	\(q+(2.00739 - 1.15896i) q^{3} +(-67.5013 - 116.916i) q^{5} -157.715 q^{7} +(-361.814 + 626.680i) q^{9} +663.253 q^{11} +(1630.93 + 941.616i) q^{13} +(-271.002 - 156.463i) q^{15} +(938.453 + 1625.45i) q^{17} +(-2954.88 + 6189.88i) q^{19} +(-316.595 + 182.786i) q^{21} +(-4912.56 + 8508.80i) q^{23} +(-1300.35 + 2252.27i) q^{25} +3367.09i q^{27} +(12606.8 + 7278.51i) q^{29} +44573.3i q^{31} +(1331.41 - 768.687i) q^{33} +(10646.0 + 18439.4i) q^{35} +55050.8i q^{37} +4365.20 q^{39} +(-35438.6 + 20460.5i) q^{41} +(-14840.5 - 25704.5i) q^{43} +97691.5 q^{45} +(-10194.0 + 17656.5i) q^{47} -92774.9 q^{49} +(3767.68 + 2175.27i) q^{51} +(-112309. - 64841.8i) q^{53} +(-44770.4 - 77544.7i) q^{55} +(1242.27 + 15850.1i) q^{57} +(294641. - 170111. i) q^{59} +(-47067.9 + 81524.0i) q^{61} +(57063.5 - 98836.8i) q^{63} -254241. i q^{65} +(154080. + 88958.1i) q^{67} +22773.9i q^{69} +(112740. - 65090.7i) q^{71} +(-364203. - 630818. i) q^{73} +6028.23i q^{75} -104605. q^{77} +(-304428. + 175762. i) q^{79} +(-259860. - 450090. i) q^{81} +106682. q^{83} +(126694. - 219440. i) q^{85} +33742.2 q^{87} +(183457. + 105919. i) q^{89} +(-257222. - 148507. i) q^{91} +(51658.9 + 89475.8i) q^{93} +(923152. - 72353.2i) q^{95} +(736790. - 425386. i) q^{97} +(-239974. + 415647. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9} - 3644 q^{11} - 7140 q^{13} + 9168 q^{15} + 1132 q^{17} + 2110 q^{19} - 8748 q^{21} + 832 q^{23} - 27698 q^{25} - 10920 q^{29} - 30306 q^{33} + 4172 q^{35} + 81144 q^{39} + 109206 q^{41} + 110740 q^{43} - 785440 q^{45} + 107080 q^{47} + 136092 q^{49} + 199872 q^{51} + 254796 q^{53} + 354840 q^{55} + 212268 q^{57} - 610638 q^{59} + 47864 q^{61} - 254476 q^{63} - 839562 q^{67} + 366660 q^{71} + 854482 q^{73} + 763088 q^{77} + 1718592 q^{79} - 1054142 q^{81} + 439612 q^{83} - 400236 q^{85} - 1604736 q^{87} + 478032 q^{89} + 599856 q^{91} + 829380 q^{93} - 1055660 q^{95} - 191286 q^{97} - 2336728 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 - 56 * q^5 + 464 * q^7 + 2200 * q^9 - 3644 * q^11 - 7140 * q^13 + 9168 * q^15 + 1132 * q^17 + 2110 * q^19 - 8748 * q^21 + 832 * q^23 - 27698 * q^25 - 10920 * q^29 - 30306 * q^33 + 4172 * q^35 + 81144 * q^39 + 109206 * q^41 + 110740 * q^43 - 785440 * q^45 + 107080 * q^47 + 136092 * q^49 + 199872 * q^51 + 254796 * q^53 + 354840 * q^55 + 212268 * q^57 - 610638 * q^59 + 47864 * q^61 - 254476 * q^63 - 839562 * q^67 + 366660 * q^71 + 854482 * q^73 + 763088 * q^77 + 1718592 * q^79 - 1054142 * q^81 + 439612 * q^83 - 400236 * q^85 - 1604736 * q^87 + 478032 * q^89 + 599856 * q^91 + 829380 * q^93 - 1055660 * q^95 - 191286 * q^97 - 2336728 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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