LMFDB - Embedded newform 76.7.h.a.69.3

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			69.3
Root			$25.0503i$ of defining polynomial
Character	$\chi$	$=$	76.69
Dual form			76.7.h.a.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-23.1942 + 13.3912i) q^{3} +(16.0954 + 27.8780i) q^{5} -416.808 q^{7} +(-5.85193 + 10.1358i) q^{9} +O(q^{10})$	\(q+(-23.1942 + 13.3912i) q^{3} +(16.0954 + 27.8780i) q^{5} -416.808 q^{7} +(-5.85193 + 10.1358i) q^{9} +1031.33 q^{11} +(-2202.37 - 1271.54i) q^{13} +(-746.639 - 431.072i) q^{15} +(3772.21 + 6533.66i) q^{17} +(-1245.17 - 6745.03i) q^{19} +(9667.53 - 5581.55i) q^{21} +(9773.64 - 16928.4i) q^{23} +(7294.38 - 12634.2i) q^{25} -19837.8i q^{27} +(29583.8 + 17080.2i) q^{29} -3711.23i q^{31} +(-23920.8 + 13810.7i) q^{33} +(-6708.68 - 11619.8i) q^{35} -82758.7i q^{37} +68109.7 q^{39} +(-78507.2 + 45326.2i) q^{41} +(10653.4 + 18452.3i) q^{43} -376.756 q^{45} +(46695.0 - 80878.1i) q^{47} +56079.7 q^{49} +(-174987. - 101029. i) q^{51} +(101047. + 58339.5i) q^{53} +(16599.6 + 28751.4i) q^{55} +(119205. + 139772. i) q^{57} +(-20618.2 + 11903.9i) q^{59} +(-158838. + 275115. i) q^{61} +(2439.13 - 4224.70i) q^{63} -81863.6i q^{65} +(-204338. - 117975. i) q^{67} +523523. i q^{69} +(153902. - 88855.3i) q^{71} +(-173594. - 300673. i) q^{73} +390722. i q^{75} -429865. q^{77} +(-225299. + 130077. i) q^{79} +(261386. + 452734. i) q^{81} -615686. q^{83} +(-121430. + 210323. i) q^{85} -914899. q^{87} +(19492.6 + 11254.1i) q^{89} +(917966. + 529988. i) q^{91} +(49697.9 + 86079.2i) q^{93} +(167997. - 143277. i) q^{95} +(874109. - 504667. i) q^{97} +(-6035.26 + 10453.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−23.1942	+	13.3912i	−0.859045	+	0.495970i	−0.863693	−	0.504019i	$-0.831854\pi$
$3$	−23.1942	+	13.3912i	−0.859045	+	0.495970i	0.00464710	+	0.999989i	$0.498521\pi$
$4$		0			0
$5$	16.0954	+	27.8780i	0.128763	+	0.223024i	0.923198	−	0.384326i	$-0.125566\pi$
$5$	16.0954	+	27.8780i	0.128763	+	0.223024i	−0.794435	+	0.607350i	$0.792233\pi$
$6$		0			0
$7$	−416.808			−1.21518			−0.607591	−	0.794250i	$-0.707864\pi$
$7$	−416.808			−1.21518			−0.607591	+	0.794250i	$0.707864\pi$
$8$		0			0
$9$	−5.85193	+	10.1358i	−0.00802734	+	0.0139038i
$10$		0			0
$11$	1031.33			0.774852			0.387426	−	0.921901i	$-0.373364\pi$
$11$	1031.33			0.774852			0.387426	+	0.921901i	$0.373364\pi$
$12$		0			0
$13$	−2202.37	−	1271.54i	−1.00245	−	0.578762i	−0.0934743	−	0.995622i	$-0.529797\pi$
$13$	−2202.37	−	1271.54i	−1.00245	−	0.578762i	−0.908971	+	0.416860i	$0.863131\pi$
$14$		0			0
$15$	−746.639	−	431.072i	−0.221226	−	0.127725i
$16$		0			0
$17$	3772.21	+	6533.66i	0.767802	+	1.32987i	0.938752	+	0.344593i	$0.111983\pi$
$17$	3772.21	+	6533.66i	0.767802	+	1.32987i	−0.170950	+	0.985280i	$0.554684\pi$
$18$		0			0
$19$	−1245.17	−	6745.03i	−0.181537	−	0.983384i
$19$	−1245.17	−	6745.03i	−0.181537	−	0.983384i
$20$		0			0
$21$	9667.53	−	5581.55i	1.04390	−	0.602694i
$22$		0			0
$23$	9773.64	−	16928.4i	0.803291	−	1.39134i	−0.114148	−	0.993464i	$-0.536414\pi$
$23$	9773.64	−	16928.4i	0.803291	−	1.39134i	0.917439	−	0.397877i	$-0.130253\pi$
$24$		0			0
$25$	7294.38	−	12634.2i	0.466840	−	0.808591i
$26$		0			0
$27$		−	19837.8i		−	1.00787i
$28$		0			0
$29$	29583.8	+	17080.2i	1.21300	+	0.700326i	0.963412	−	0.268027i	$-0.0863715\pi$
$29$	29583.8	+	17080.2i	1.21300	+	0.700326i	0.249588	+	0.968352i	$0.419705\pi$
$30$		0			0
$31$		−	3711.23i		−	0.124576i	−0.998058	−	0.0622878i	$-0.980160\pi$
$31$		−	3711.23i		−	0.124576i	0.998058	−	0.0622878i	$-0.0198397\pi$
$32$		0			0
$33$	−23920.8	+	13810.7i	−0.665633	+	0.384303i
$34$		0			0
$35$	−6708.68	−	11619.8i	−0.156471	−	0.271015i
$36$		0			0
$37$		−	82758.7i		−	1.63384i	−0.576754	−	0.816918i	$-0.695681\pi$
$37$		−	82758.7i		−	1.63384i	0.576754	−	0.816918i	$-0.304319\pi$
$38$		0			0
$39$	68109.7			1.14819
$40$		0			0
$41$	−78507.2	+	45326.2i	−1.13909	+	0.657654i	−0.946205	−	0.323568i	$-0.895118\pi$
$41$	−78507.2	+	45326.2i	−1.13909	+	0.657654i	−0.192885	+	0.981221i	$0.561784\pi$
$42$		0			0
$43$	10653.4	+	18452.3i	0.133994	+	0.232084i	0.925213	−	0.379449i	$-0.123886\pi$
$43$	10653.4	+	18452.3i	0.133994	+	0.232084i	−0.791219	+	0.611533i	$0.790553\pi$
$44$		0			0
$45$	−376.756			−0.00413450
$46$		0			0
$47$	46695.0	−	80878.1i	0.449756	−	0.779000i	−0.548614	−	0.836076i	$-0.684844\pi$
$47$	46695.0	−	80878.1i	0.449756	−	0.779000i	0.998370	+	0.0570760i	$0.0181777\pi$
$48$		0			0
$49$	56079.7			0.476669
$50$		0			0
$51$	−174987.	−	101029.i	−1.31915	−	0.761614i
$52$		0			0
$53$	101047.	+	58339.5i	0.678728	+	0.391864i	0.799375	−	0.600832i	$-0.205164\pi$
$53$	101047.	+	58339.5i	0.678728	+	0.391864i	−0.120648	+	0.992695i	$0.538497\pi$
$54$		0			0
$55$	16599.6	+	28751.4i	0.0997722	+	0.172811i
$56$		0			0
$57$	119205.	+	139772.i	0.643678	+	0.754734i
$58$		0			0
$59$	−20618.2	+	11903.9i	−0.100391	+	0.0579609i	−0.549355	−	0.835589i	$-0.685127\pi$
$59$	−20618.2	+	11903.9i	−0.100391	+	0.0579609i	0.448964	+	0.893550i	$0.351793\pi$
$60$		0			0
$61$	−158838.	+	275115.i	−0.699785	+	1.21206i	0.268755	+	0.963208i	$0.413388\pi$
$61$	−158838.	+	275115.i	−0.699785	+	1.21206i	−0.968541	+	0.248855i	$0.919946\pi$
$62$		0			0
$63$	2439.13	−	4224.70i	0.00975468	−	0.0168956i
$64$		0			0
$65$		−	81863.6i		−	0.298092i
$66$		0			0
$67$	−204338.	−	117975.i	−0.679399	−	0.392251i	0.120230	−	0.992746i	$-0.461637\pi$
$67$	−204338.	−	117975.i	−0.679399	−	0.392251i	−0.799629	+	0.600495i	$0.794970\pi$
$68$		0			0
$69$			523523.i			1.59363i
$70$		0			0
$71$	153902.	−	88855.3i	0.430001	−	0.248261i	−0.269346	−	0.963043i	$-0.586808\pi$
$71$	153902.	−	88855.3i	0.430001	−	0.248261i	0.699347	+	0.714782i	$0.253474\pi$
$72$		0			0
$73$	−173594.	−	300673.i	−0.446237	−	0.772905i	0.551900	−	0.833910i	$-0.313903\pi$
$73$	−173594.	−	300673.i	−0.446237	−	0.772905i	−0.998137	+	0.0610047i	$0.980570\pi$
$74$		0			0
$75$			390722.i			0.926155i
$76$		0			0
$77$	−429865.			−0.941587
$78$		0			0
$79$	−225299.	+	130077.i	−0.456961	+	0.263826i	−0.710765	−	0.703429i	$-0.751651\pi$
$79$	−225299.	+	130077.i	−0.456961	+	0.263826i	0.253805	+	0.967255i	$0.418318\pi$
$80$		0			0
$81$	261386.	+	452734.i	0.491844	+	0.851898i
$82$		0			0
$83$	−615686.			−1.07678			−0.538388	−	0.842697i	$-0.680966\pi$
$83$	−615686.			−1.07678			−0.538388	+	0.842697i	$0.680966\pi$
$84$		0			0
$85$	−121430.	+	210323.i	−0.197729	+	0.342477i
$86$		0			0
$87$	−914899.			−1.38936
$88$		0			0
$89$	19492.6	+	11254.1i	0.0276503	+	0.0159639i	0.513761	−	0.857933i	$-0.328252\pi$
$89$	19492.6	+	11254.1i	0.0276503	+	0.0159639i	−0.486111	+	0.873897i	$0.661585\pi$
$90$		0			0
$91$	917966.	+	529988.i	1.21815	+	0.703302i
$92$		0			0
$93$	49697.9	+	86079.2i	0.0617858	+	0.107016i
$94$		0			0
$95$	167997.	−	143277.i	0.195943	−	0.167111i
$96$		0			0
$97$	874109.	−	504667.i	0.957746	−	0.552955i	0.0622674	−	0.998060i	$-0.480167\pi$
$97$	874109.	−	504667.i	0.957746	−	0.552955i	0.895479	+	0.445105i	$0.146834\pi$
$98$		0			0
$99$	−6035.26	+	10453.4i	−0.00622000	+	0.0107734i
$100$		0			0
$101$	932836.	−	1.61572e6i	0.905401	−	1.56820i	0.0850234	−	0.996379i	$-0.472903\pi$
$101$	932836.	−	1.61572e6i	0.905401	−	1.56820i	0.820378	−	0.571822i	$-0.193763\pi$
$102$		0			0
$103$		−	1.45965e6i		−	1.33579i	−0.744256	−	0.667894i	$-0.767196\pi$
$103$		−	1.45965e6i		−	1.33579i	0.744256	−	0.667894i	$-0.232804\pi$
$104$		0			0
$105$	311205.	+	179674.i	0.268831	+	0.155209i
$106$		0			0
$107$		−	1.53090e6i		−	1.24967i	−0.780758	−	0.624833i	$-0.785167\pi$
$107$		−	1.53090e6i		−	1.24967i	0.780758	−	0.624833i	$-0.214833\pi$
$108$		0			0
$109$	445234.	−	257056.i	0.343802	−	0.198494i	−0.318150	−	0.948040i	$-0.603062\pi$
$109$	445234.	−	257056.i	0.343802	−	0.198494i	0.661952	+	0.749546i	$0.269728\pi$
$110$		0			0
$111$	1.10824e6	+	1.91952e6i	0.810334	+	1.40354i
$112$		0			0
$113$			1.67372e6i			1.15997i	0.814626	+	0.579987i	$0.196942\pi$
$113$			1.67372e6i			1.15997i	−0.814626	+	0.579987i	$0.803058\pi$
$114$		0			0
$115$	629242.			0.413737
$116$		0			0
$117$	25776.2	−	14881.9i	0.0160939	−	0.00929183i
$118$		0			0
$119$	−1.57229e6	−	2.72328e6i	−0.933020	−	1.61604i
$120$		0			0
$121$	−707924.			−0.399605
$122$		0			0
$123$	1.21394e6	−	2.10261e6i	0.652353	−	1.12991i
$124$		0			0
$125$	972603.			0.497973
$126$		0			0
$127$	−1.71650e6	−	991020.i	−0.837976	−	0.483806i	0.0185994	−	0.999827i	$-0.494079\pi$
$127$	−1.71650e6	−	991020.i	−0.837976	−	0.483806i	−0.856576	+	0.516021i	$0.827413\pi$
$128$		0			0
$129$	−494196.	−	285324.i	−0.230213	−	0.132914i
$130$		0			0
$131$	215508.	+	373270.i	0.0958625	+	0.166039i	0.909968	−	0.414678i	$-0.136106\pi$
$131$	215508.	+	373270.i	0.0958625	+	0.166039i	−0.814106	+	0.580717i	$0.802772\pi$
$132$		0			0
$133$	518994.	+	2.81138e6i	0.220601	+	1.19499i
$134$		0			0
$135$	553039.	−	319297.i	0.224778	−	0.129776i
$136$		0			0
$137$	1.09664e6	−	1.89943e6i	0.426483	−	0.738691i	−0.570074	−	0.821593i	$-0.693086\pi$
$137$	1.09664e6	−	1.89943e6i	0.426483	−	0.738691i	0.996558	+	0.0829025i	$0.0264190\pi$
$138$		0			0
$139$	−107067.	+	185445.i	−0.0398667	+	0.0690511i	−0.885270	−	0.465077i	$-0.846027\pi$
$139$	−107067.	+	185445.i	−0.0398667	+	0.0690511i	0.845404	+	0.534128i	$0.179360\pi$
$140$		0			0
$141$			2.50121e6i			0.892261i
$142$		0			0
$143$	−2.27137e6	−	1.31137e6i	−0.776746	−	0.448455i
$144$		0			0
$145$			1.09965e6i			0.360704i
$146$		0			0
$147$	−1.30072e6	+	750974.i	−0.409481	+	0.236414i
$148$		0			0
$149$	875055.	+	1.51564e6i	0.264531	+	0.458181i	0.967441	−	0.253098i	$-0.0814495\pi$
$149$	875055.	+	1.51564e6i	0.264531	+	0.458181i	−0.702910	+	0.711279i	$0.748116\pi$
$150$		0			0
$151$		−	5.24436e6i		−	1.52322i	−0.648038	−	0.761608i	$-0.724410\pi$
$151$		−	5.24436e6i		−	1.52322i	0.648038	−	0.761608i	$-0.275590\pi$
$152$		0			0
$153$	−88298.9			−0.0246536
$154$		0			0
$155$	103462.	−	59733.7i	0.0277834	−	0.0160407i
$156$		0			0
$157$	1.97123e6	+	3.41428e6i	0.509377	+	0.882267i	0.999941	+	0.0108617i	$0.00345745\pi$
$157$	1.97123e6	+	3.41428e6i	0.509377	+	0.882267i	−0.490564	+	0.871405i	$0.663209\pi$
$158$		0			0
$159$	−3.12494e6			−0.777411
$160$		0			0
$161$	−4.07373e6	+	7.05591e6i	−0.976146	+	1.69073i
$162$		0			0
$163$	6.78269e6			1.56617			0.783085	−	0.621914i	$-0.213645\pi$
$163$	6.78269e6			1.56617			0.783085	+	0.621914i	$0.213645\pi$
$164$		0			0
$165$	−770030.	−	444577.i	−0.171418	−	0.0989681i
$166$		0			0
$167$	−2.19102e6	−	1.26499e6i	−0.470432	−	0.271604i	0.245988	−	0.969273i	$-0.420888\pi$
$167$	−2.19102e6	−	1.26499e6i	−0.470432	−	0.271604i	−0.716421	+	0.697668i	$0.754221\pi$
$168$		0			0
$169$	820223.	+	1.42067e6i	0.169931	+	0.294329i
$170$		0			0
$171$	75653.2	+	26850.7i	0.0151300	+	0.00536990i
$172$		0			0
$173$	3.00695e6	−	1.73607e6i	0.580749	−	0.335296i	−0.180682	−	0.983542i	$-0.557830\pi$
$173$	3.00695e6	−	1.73607e6i	0.580749	−	0.335296i	0.761431	+	0.648246i	$0.224497\pi$
$174$		0			0
$175$	−3.04035e6	+	5.26605e6i	−0.567296	+	0.982586i
$176$		0			0
$177$	318816.	−	552206.i	0.0574937	−	0.0995821i
$178$		0			0
$179$			4.13863e6i			0.721602i	0.932643	+	0.360801i	$0.117497\pi$
$179$			4.13863e6i			0.721602i	−0.932643	+	0.360801i	$0.882503\pi$
$180$		0			0
$181$	−9.23288e6	−	5.33060e6i	−1.55705	−	0.898961i	−0.997537	−	0.0701361i	$-0.977657\pi$
$181$	−9.23288e6	−	5.33060e6i	−1.55705	−	0.898961i	−0.559508	−	0.828825i	$-0.689010\pi$
$182$		0			0
$183$		−	8.50812e6i		−	1.38829i
$184$		0			0
$185$	2.30715e6	−	1.33203e6i	0.364385	−	0.210378i
$186$		0			0
$187$	3.89039e6	+	6.73835e6i	0.594933	+	1.03045i
$188$		0			0
$189$			8.26855e6i			1.22474i
$190$		0			0
$191$	−2.71451e6			−0.389575			−0.194788	−	0.980845i	$-0.562402\pi$
$191$	−2.71451e6			−0.389575			−0.194788	+	0.980845i	$0.562402\pi$
$192$		0			0
$193$	−6.71427e6	+	3.87648e6i	−0.933957	+	0.539220i	−0.888061	−	0.459726i	$-0.847948\pi$
$193$	−6.71427e6	+	3.87648e6i	−0.933957	+	0.539220i	−0.0458960	+	0.998946i	$0.514614\pi$
$194$		0			0
$195$	1.09625e6	+	1.89876e6i	0.147845	+	0.256075i
$196$		0			0
$197$	4.02322e6			0.526229			0.263114	−	0.964765i	$-0.415250\pi$
$197$	4.02322e6			0.526229			0.263114	+	0.964765i	$0.415250\pi$
$198$		0			0
$199$	−7.72880e6	+	1.33867e7i	−0.980738	+	1.69869i	−0.321208	+	0.947009i	$0.604089\pi$
$199$	−7.72880e6	+	1.33867e7i	−0.980738	+	1.69869i	−0.659530	+	0.751679i	$0.729245\pi$
$200$		0			0
$201$	6.31928e6			0.778179
$202$		0			0
$203$	−1.23308e7	−	7.11918e6i	−1.47402	−	0.851024i
$204$		0			0
$205$	−2.52721e6	−	1.45908e6i	−0.293345	−	0.169363i
$206$		0			0
$207$	114389.	+	198128.i	0.0128966	+	0.0223375i
$208$		0			0
$209$	−1.28417e6	−	6.95634e6i	−0.140665	−	0.761977i
$210$		0			0
$211$	4.85380e6	−	2.80234e6i	0.516695	−	0.298314i	−0.218886	−	0.975750i	$-0.570242\pi$
$211$	4.85380e6	−	2.80234e6i	0.516695	−	0.298314i	0.735582	+	0.677436i	$0.236909\pi$
$212$		0			0
$213$	−2.37976e6	+	4.12186e6i	−0.246260	+	0.426535i
$214$		0			0
$215$	−342942.	+	593993.i	−0.0345069	+	0.0597676i
$216$		0			0
$217$			1.54687e6i			0.151382i
$218$		0			0
$219$	8.05275e6	+	4.64926e6i	0.766676	+	0.442641i
$220$		0			0
$221$		−	1.91861e7i		−	1.77750i
$222$		0			0
$223$	1.25394e7	−	7.23963e6i	1.13074	−	0.652833i	0.186619	−	0.982432i	$-0.440247\pi$
$223$	1.25394e7	−	7.23963e6i	1.13074	−	0.652833i	0.944121	+	0.329600i	$0.106914\pi$
$224$		0			0
$225$	85372.4	+	147869.i	0.00749497	+	0.0129817i
$226$		0			0
$227$		−	5.89929e6i		−	0.504338i	−0.967683	−	0.252169i	$-0.918856\pi$
$227$		−	5.89929e6i		−	0.504338i	0.967683	−	0.252169i	$-0.0811440\pi$
$228$		0			0
$229$	1.77108e7			1.47480			0.737399	−	0.675457i	$-0.236054\pi$
$229$	1.77108e7			1.47480			0.737399	+	0.675457i	$0.236054\pi$
$230$		0			0
$231$	9.97039e6	−	5.75641e6i	0.808866	−	0.466999i
$232$		0			0
$233$	−8.80522e6	−	1.52511e7i	−0.696101	−	1.20568i	−0.969808	−	0.243870i	$-0.921583\pi$
$233$	−8.80522e6	−	1.52511e7i	−0.696101	−	1.20568i	0.273707	−	0.961813i	$-0.411750\pi$
$234$		0			0
$235$	3.00629e6			0.231648
$236$		0			0
$237$	3.48376e6	−	6.03406e6i	0.261700	−	0.453278i
$238$		0			0
$239$	−520648.			−0.0381373			−0.0190687	−	0.999818i	$-0.506070\pi$
$239$	−520648.			−0.0381373			−0.0190687	+	0.999818i	$0.506070\pi$
$240$		0			0
$241$	4.93153e6	+	2.84722e6i	0.352314	+	0.203409i	0.665704	−	0.746216i	$-0.268131\pi$
$241$	4.93153e6	+	2.84722e6i	0.352314	+	0.203409i	−0.313390	+	0.949625i	$0.601465\pi$
$242$		0			0
$243$	398969.	+	230345.i	0.0278048	+	0.0160531i
$244$		0			0
$245$	902623.	+	1.56339e6i	0.0613774	+	0.106309i
$246$		0			0
$247$	−5.83426e6	+	1.64383e7i	−0.387164	+	1.09086i
$248$		0			0
$249$	1.42804e7	−	8.24478e6i	0.924999	−	0.534049i
$250$		0			0
$251$	4.86481e6	−	8.42610e6i	0.307642	−	0.532851i	−0.670204	−	0.742177i	$-0.733794\pi$
$251$	4.86481e6	−	8.42610e6i	0.307642	−	0.532851i	0.977846	+	0.209326i	$0.0671269\pi$
$252$		0			0
$253$	1.00798e7	−	1.74588e7i	0.622432	−	1.07808i
$254$		0			0
$255$		−	6.50439e6i		−	0.392271i
$256$		0			0
$257$	−2.82821e7	−	1.63287e7i	−1.66615	−	0.961950i	−0.969686	−	0.244353i	$-0.921424\pi$
$257$	−2.82821e7	−	1.63287e7i	−1.66615	−	0.961950i	−0.696459	−	0.717596i	$-0.745242\pi$
$258$		0			0
$259$			3.44945e7i			1.98541i
$260$		0			0
$261$	−346245.	+	199905.i	−0.0194743	+	0.0112435i
$262$		0			0
$263$	1.33851e7	+	2.31837e7i	0.735792	+	1.27443i	0.954375	+	0.298610i	$0.0965231\pi$
$263$	1.33851e7	+	2.31837e7i	0.735792	+	1.27443i	−0.218583	+	0.975818i	$0.570144\pi$
$264$		0			0
$265$			3.75598e6i			0.201830i
$266$		0			0
$267$	−602822.			−0.0316705
$268$		0			0
$269$	−539234.	+	311327.i	−0.0277026	+	0.0159941i	−0.513787	−	0.857918i	$-0.671758\pi$
$269$	−539234.	+	311327.i	−0.0277026	+	0.0159941i	0.486085	+	0.873912i	$0.338425\pi$
$270$		0			0
$271$	−1.21678e7	−	2.10752e7i	−0.611368	−	1.05892i	−0.991010	−	0.133787i	$-0.957286\pi$
$271$	−1.21678e7	−	2.10752e7i	−0.611368	−	1.05892i	0.379642	−	0.925133i	$-0.376047\pi$
$272$		0			0
$273$	−2.83887e7			−1.39527
$274$		0			0
$275$	7.52289e6	−	1.30300e7i	0.361732	−	0.626538i
$276$		0			0
$277$	3.69111e6			0.173667			0.0868336	−	0.996223i	$-0.472325\pi$
$277$	3.69111e6			0.173667			0.0868336	+	0.996223i	$0.472325\pi$
$278$		0			0
$279$	37616.5	+	21717.9i	0.00173207	+	0.00100001i
$280$		0			0
$281$	−9.07778e6	−	5.24106e6i	−0.409129	−	0.236211i	0.281286	−	0.959624i	$-0.409239\pi$
$281$	−9.07778e6	−	5.24106e6i	−0.409129	−	0.236211i	−0.690416	+	0.723413i	$0.742572\pi$
$282$		0			0
$283$	6.09672e6	+	1.05598e7i	0.268991	+	0.465906i	0.968601	−	0.248619i	$-0.0799766\pi$
$283$	6.09672e6	+	1.05598e7i	0.268991	+	0.465906i	−0.699611	+	0.714524i	$0.746643\pi$
$284$		0			0
$285$	−1.97791e6	+	5.57286e6i	−0.0854420	+	0.240737i
$286$		0			0
$287$	3.27224e7	−	1.88923e7i	1.38420	−	0.799170i
$288$		0			0
$289$	−1.63904e7	+	2.83890e7i	−0.679040	+	1.17613i
$290$		0			0
$291$	−1.35162e7	+	2.34107e7i	−0.548498	+	0.950027i
$292$		0			0
$293$		−	1.16699e7i		−	0.463941i	−0.972723	−	0.231971i	$-0.925483\pi$
$293$		−	1.16699e7i		−	0.463941i	0.972723	−	0.231971i	$-0.0745173\pi$
$294$		0			0
$295$	−663717.	−	383197.i	−0.0258533	−	0.0149264i
$296$		0			0
$297$		−	2.04593e7i		−	0.780946i
$298$		0			0
$299$	−4.30504e7	+	2.48552e7i	−1.61051	+	0.929829i
$300$		0			0
$301$	−4.44043e6	−	7.69106e6i	−0.162827	−	0.282024i
$302$		0			0
$303$			4.99671e7i			1.79621i
$304$		0			0
$305$	−1.02262e7			−0.360426
$306$		0			0
$307$	−2.44066e7	+	1.40911e7i	−0.843513	+	0.487002i	−0.858457	−	0.512886i	$-0.828576\pi$
$307$	−2.44066e7	+	1.40911e7i	−0.843513	+	0.487002i	0.0149438	+	0.999888i	$0.495243\pi$
$308$		0			0
$309$	1.95465e7	+	3.38555e7i	0.662511	+	1.14750i
$310$		0			0
$311$	−5.20873e6			−0.173161			−0.0865807	−	0.996245i	$-0.527594\pi$
$311$	−5.20873e6			−0.173161			−0.0865807	+	0.996245i	$0.527594\pi$
$312$		0			0
$313$	1.98844e7	−	3.44408e7i	0.648455	−	1.12316i	−0.335036	−	0.942205i	$-0.608749\pi$
$313$	1.98844e7	−	3.44408e7i	0.648455	−	1.12316i	0.983492	−	0.180953i	$-0.0579180\pi$
$314$		0			0
$315$	157035.			0.00502417
$316$		0			0
$317$	−1.08077e7	−	6.23984e6i	−0.339278	−	0.195882i	0.320675	−	0.947189i	$-0.396090\pi$
$317$	−1.08077e7	−	6.23984e6i	−0.339278	−	0.195882i	−0.659953	+	0.751307i	$0.729424\pi$
$318$		0			0
$319$	3.05106e7	+	1.76153e7i	0.939895	+	0.542649i
$320$		0			0
$321$	2.05005e7	+	3.55079e7i	0.619797	+	1.07352i
$322$		0			0
$323$	3.93727e7	−	3.35792e7i	1.16839	−	0.996466i
$324$		0			0
$325$	−3.21299e7	+	1.85502e7i	−0.935963	+	0.540379i
$326$		0			0
$327$	−6.88457e6	+	1.19244e7i	−0.196895	+	0.341031i
$328$		0			0
$329$	−1.94628e7	+	3.37106e7i	−0.546535	+	0.946627i
$330$		0			0
$331$		−	4.61322e7i		−	1.27210i	−0.771649	−	0.636048i	$-0.780568\pi$
$331$		−	4.61322e7i		−	1.27210i	0.771649	−	0.636048i	$-0.219432\pi$
$332$		0			0
$333$	838829.	+	484298.i	0.0227165	+	0.0131154i
$334$		0			0
$335$		−	7.59538e6i		−	0.202030i
$336$		0			0
$337$	1.62058e7	−	9.35640e6i	0.423428	−	0.244466i	−0.273115	−	0.961981i	$-0.588054\pi$
$337$	1.62058e7	−	9.35640e6i	0.423428	−	0.244466i	0.696543	+	0.717515i	$0.254721\pi$
$338$		0			0
$339$	−2.24131e7	−	3.88207e7i	−0.575312	−	0.996470i
$340$		0			0
$341$		−	3.82750e6i		−	0.0965277i
$342$		0			0
$343$	2.56626e7			0.635942
$344$		0			0
$345$	−1.45948e7	+	8.42630e6i	−0.355419	+	0.205201i
$346$		0			0
$347$	−6.59302e6	−	1.14195e7i	−0.157796	−	0.273311i	0.776278	−	0.630391i	$-0.217106\pi$
$347$	−6.59302e6	−	1.14195e7i	−0.157796	−	0.273311i	−0.934074	+	0.357080i	$0.883772\pi$
$348$		0			0
$349$	1.78936e7			0.420942			0.210471	−	0.977600i	$-0.432500\pi$
$349$	1.78936e7			0.420942			0.210471	+	0.977600i	$0.432500\pi$
$350$		0			0
$351$	−2.52246e7	+	4.36902e7i	−0.583314	+	1.01033i
$352$		0			0
$353$	−5.32161e7			−1.20982			−0.604908	−	0.796295i	$-0.706790\pi$
$353$	−5.32161e7			−1.20982			−0.604908	+	0.796295i	$0.706790\pi$
$354$		0			0
$355$	4.95422e6	+	2.86032e6i	0.110736	+	0.0639336i
$356$		0			0
$357$	7.29360e7	+	4.21096e7i	1.60301	+	0.925500i
$358$		0			0
$359$	−1.09170e7	−	1.89088e7i	−0.235950	−	0.408678i	0.723598	−	0.690222i	$-0.242487\pi$
$359$	−1.09170e7	−	1.89088e7i	−0.235950	−	0.408678i	−0.959548	+	0.281543i	$0.909154\pi$
$360$		0			0
$361$	−4.39450e7	+	1.67974e7i	−0.934088	+	0.357042i
$362$		0			0
$363$	1.64198e7	−	9.47995e6i	0.343279	−	0.198192i
$364$		0			0
$365$	5.58811e6	−	9.67890e6i	0.114918	−	0.199043i
$366$		0			0
$367$	−2.13394e7	+	3.69610e7i	−0.431702	+	0.747730i	−0.997020	−	0.0771428i	$-0.975420\pi$
$367$	−2.13394e7	+	3.69610e7i	−0.431702	+	0.747730i	0.565318	+	0.824873i	$0.308754\pi$
$368$		0			0
$369$		−	1.06098e6i		−	0.0211168i
$370$		0			0
$371$	−4.21171e7	−	2.43163e7i	−0.824778	−	0.476186i
$372$		0			0
$373$		−	1.98749e7i		−	0.382982i	−0.981494	−	0.191491i	$-0.938668\pi$
$373$		−	1.98749e7i		−	0.382982i	0.981494	−	0.191491i	$-0.0613323\pi$
$374$		0			0
$375$	−2.25588e7	+	1.30243e7i	−0.427781	+	0.246980i
$376$		0			0
$377$	−4.34364e7	−	7.52341e7i	−0.810644	−	1.40408i
$378$		0			0
$379$			3.89370e7i			0.715229i	0.933869	+	0.357614i	$0.116410\pi$
$379$			3.89370e7i			0.715229i	−0.933869	+	0.357614i	$0.883590\pi$
$380$		0			0
$381$	5.30837e7			0.959813
$382$		0			0
$383$	2.64933e7	−	1.52959e7i	0.471563	−	0.272257i	−0.245331	−	0.969439i	$-0.578897\pi$
$383$	2.64933e7	−	1.52959e7i	0.471563	−	0.272257i	0.716894	+	0.697182i	$0.245563\pi$
$384$		0			0
$385$	−6.91884e6	−	1.19838e7i	−0.121241	−	0.209996i
$386$		0			0
$387$	−249373.			−0.00430245
$388$		0			0
$389$	4.19252e7	−	7.26165e7i	0.712240	−	1.23364i	−0.251775	−	0.967786i	$-0.581014\pi$
$389$	4.19252e7	−	7.26165e7i	0.712240	−	1.23364i	0.964015	−	0.265849i	$-0.0856524\pi$
$390$		0			0
$391$	1.47473e8			2.46707
$392$		0			0
$393$	−9.99707e6	−	5.77181e6i	−0.164700	−	0.0950899i
$394$		0			0
$395$	−7.25256e6	−	4.18727e6i	−0.117679	−	0.0679421i
$396$		0			0
$397$	1.65611e7	+	2.86846e7i	0.264678	+	0.458435i	0.967479	−	0.252951i	$-0.0814012\pi$
$397$	1.65611e7	+	2.86846e7i	0.264678	+	0.458435i	−0.702802	+	0.711386i	$0.748068\pi$
$398$		0			0
$399$	−4.96854e7	−	5.82579e7i	−0.782186	−	0.917140i
$400$		0			0
$401$	4.29281e7	−	2.47846e7i	0.665746	−	0.384369i	−0.128717	−	0.991681i	$-0.541086\pi$
$401$	4.29281e7	−	2.47846e7i	0.665746	−	0.384369i	0.794463	+	0.607313i	$0.207752\pi$
$402$		0			0
$403$	−4.71898e6	+	8.17352e6i	−0.0720997	+	0.124880i
$404$		0			0
$405$	−8.41421e6	+	1.45738e7i	−0.126663	+	0.219386i
$406$		0			0
$407$		−	8.53513e7i		−	1.26598i
$408$		0			0
$409$	−2.55251e7	−	1.47369e7i	−0.373076	−	0.215395i	0.301726	−	0.953395i	$-0.402437\pi$
$409$	−2.55251e7	−	1.47369e7i	−0.373076	−	0.215395i	−0.674801	+	0.738000i	$0.735771\pi$
$410$		0			0
$411$			5.87412e7i			0.846092i
$412$		0			0
$413$	8.59384e6	−	4.96166e6i	0.121994	−	0.0704331i
$414$		0			0
$415$	−9.90970e6	−	1.71641e7i	−0.138649	−	0.240147i
$416$		0			0
$417$		−	5.73501e6i		−	0.0790908i
$418$		0			0
$419$	1.15129e8			1.56510			0.782551	−	0.622587i	$-0.213918\pi$
$419$	1.15129e8			1.56510			0.782551	+	0.622587i	$0.213918\pi$
$420$		0			0
$421$	3.61568e7	−	2.08751e7i	0.484555	−	0.279758i	−0.237758	−	0.971325i	$-0.576412\pi$
$421$	3.61568e7	−	2.08751e7i	0.484555	−	0.279758i	0.722313	+	0.691566i	$0.243079\pi$
$422$		0			0
$423$	546511.	+	946586.i	0.00722068	+	0.0125066i
$424$		0			0
$425$	1.10064e8			1.43376
$426$		0			0
$427$	6.62049e7	−	1.14670e8i	0.850367	−	1.47288i
$428$		0			0
$429$	7.02435e7			0.889681
$430$		0			0
$431$	1.50216e7	+	8.67271e6i	0.187622	+	0.108324i	0.590869	−	0.806768i	$-0.298785\pi$
$431$	1.50216e7	+	8.67271e6i	0.187622	+	0.108324i	−0.403247	+	0.915091i	$0.632118\pi$
$432$		0			0
$433$	−8.51933e7	−	4.91864e7i	−1.04940	−	0.605872i	−0.126920	−	0.991913i	$-0.540509\pi$
$433$	−8.51933e7	−	4.91864e7i	−1.04940	−	0.605872i	−0.922482	+	0.386041i	$0.873842\pi$
$434$		0			0
$435$	−1.47256e7	−	2.55056e7i	−0.178898	−	0.309861i
$436$		0			0
$437$	−1.26353e8	−	4.48448e7i	−1.51405	−	0.537363i
$438$		0			0
$439$	−9.74476e7	+	5.62614e7i	−1.15180	+	0.664993i	−0.949325	−	0.314295i	$-0.898232\pi$
$439$	−9.74476e7	+	5.62614e7i	−1.15180	+	0.664993i	−0.202476	+	0.979287i	$0.564899\pi$
$440$		0			0
$441$	−328174.	+	568414.i	−0.00382639	+	0.00662749i
$442$		0			0
$443$	−7.45590e7	+	1.29140e8i	−0.857608	+	1.48542i	0.0165958	+	0.999862i	$0.494717\pi$
$443$	−7.45590e7	+	1.29140e8i	−0.857608	+	1.48542i	−0.874204	+	0.485559i	$0.838616\pi$
$444$		0			0
$445$			724554.i			0.00822225i
$446$		0			0
$447$	−4.05925e7	−	2.34361e7i	−0.454488	−	0.262399i
$448$		0			0
$449$			7.59293e7i			0.838824i	0.907796	+	0.419412i	$0.137764\pi$
$449$			7.59293e7i			0.838824i	−0.907796	+	0.419412i	$0.862236\pi$
$450$		0			0
$451$	−8.09667e7	+	4.67461e7i	−0.882626	+	0.509584i
$452$		0			0
$453$	7.02282e7	+	1.21639e8i	0.755470	+	1.30851i
$454$		0			0
$455$			3.41214e7i			0.362237i
$456$		0			0
$457$	1.72025e6			0.0180237			0.00901183	−	0.999959i	$-0.497131\pi$
$457$	1.72025e6			0.0180237			0.00901183	+	0.999959i	$0.497131\pi$
$458$		0			0
$459$	1.29614e8	−	7.48324e7i	1.34033	−	0.773841i
$460$		0			0
$461$	7.62328e6	+	1.32039e7i	0.0778107	+	0.134772i	0.902305	−	0.431098i	$-0.141874\pi$
$461$	7.62328e6	+	1.32039e7i	0.0778107	+	0.134772i	−0.824494	+	0.565870i	$0.808540\pi$
$462$		0			0
$463$	5.27757e7			0.531730			0.265865	−	0.964010i	$-0.414342\pi$
$463$	5.27757e7			0.531730			0.265865	+	0.964010i	$0.414342\pi$
$464$		0			0
$465$	−1.59981e6	+	2.77095e6i	−0.0159115	+	0.0275594i
$466$		0			0
$467$	−1.38878e8			−1.36358			−0.681792	−	0.731546i	$-0.738799\pi$
$467$	−1.38878e8			−1.36358			−0.681792	+	0.731546i	$0.738799\pi$
$468$		0			0
$469$	8.51697e7	+	4.91727e7i	0.825594	+	0.476657i
$470$		0			0
$471$	−9.14425e7	−	5.27944e7i	−0.875156	−	0.505272i
$472$		0			0
$473$	1.09872e7	+	1.90304e7i	0.103825	+	0.179831i
$474$		0			0
$475$	−9.43010e7	−	3.34691e7i	−0.879904	−	0.312294i
$476$		0			0
$477$	−1.18264e6	+	682797.i	−0.0108968	+	0.00629124i
$478$		0			0
$479$	−4.54257e7	+	7.86797e7i	−0.413328	+	0.715906i	−0.995251	−	0.0973381i	$-0.968967\pi$
$479$	−4.54257e7	+	7.86797e7i	−0.413328	+	0.715906i	0.581923	+	0.813244i	$0.302301\pi$
$480$		0			0
$481$	−1.05231e8	+	1.82265e8i	−0.945602	+	1.63783i
$482$		0			0
$483$		−	2.18208e8i		−	1.93656i
$484$		0			0
$485$	2.81382e7	+	1.62456e7i	0.246644	+	0.142400i
$486$		0			0
$487$		−	1.87686e8i		−	1.62497i	−0.582982	−	0.812485i	$-0.698114\pi$
$487$		−	1.87686e8i		−	1.62497i	0.582982	−	0.812485i	$-0.301886\pi$
$488$		0			0
$489$	−1.57319e8	+	9.08283e7i	−1.34541	+	0.776774i
$490$		0			0
$491$	2.02654e7	+	3.51008e7i	0.171203	+	0.296532i	0.938841	−	0.344352i	$-0.111901\pi$
$491$	2.02654e7	+	3.51008e7i	0.171203	+	0.296532i	−0.767638	+	0.640884i	$0.778568\pi$
$492$		0			0
$493$			2.57721e8i			2.15085i
$494$		0			0
$495$	−388559.			−0.00320362
$496$		0			0
$497$	−6.41475e7	+	3.70356e7i	−0.522529	+	0.301682i
$498$		0			0
$499$	1.24558e7	+	2.15741e7i	0.100247	+	0.173633i	0.911786	−	0.410665i	$-0.134703\pi$
$499$	1.24558e7	+	2.15741e7i	0.100247	+	0.173633i	−0.811539	+	0.584298i	$0.801370\pi$
$500$		0			0
$501$	6.77587e7			0.538830
$502$		0			0
$503$	−8.03746e7	+	1.39213e8i	−0.631561	+	1.09389i	0.355672	+	0.934611i	$0.384252\pi$
$503$	−8.03746e7	+	1.39213e8i	−0.631561	+	1.09389i	−0.987233	+	0.159284i	$0.949081\pi$
$504$		0			0
$505$	6.00574e7			0.466329
$506$		0			0
$507$	−3.80489e7	−	2.19675e7i	−0.291956	−	0.168561i
$508$		0			0
$509$	1.47616e8	+	8.52261e7i	1.11939	+	0.646278i	0.941244	−	0.337727i	$-0.109658\pi$
$509$	1.47616e8	+	8.52261e7i	1.11939	+	0.646278i	0.178142	+	0.984005i	$0.442991\pi$
$510$		0			0
$511$	7.23552e7	+	1.25323e8i	0.542260	+	0.939221i
$512$		0			0
$513$	−1.33807e8	+	2.47014e7i	−0.991119	+	0.182965i
$514$		0			0
$515$	4.06922e7	−	2.34936e7i	0.297913	−	0.172000i
$516$		0			0
$517$	4.81578e7	−	8.34118e7i	0.348494	−	0.603609i
$518$		0			0
$519$	−4.64960e7	+	8.05334e7i	−0.332593	+	0.576068i
$520$		0			0
$521$			1.49534e8i			1.05737i	0.848818	+	0.528686i	$0.177315\pi$
$521$			1.49534e8i			1.05737i	−0.848818	+	0.528686i	$0.822685\pi$
$522$		0			0
$523$	−2.38622e8	−	1.37768e8i	−1.66803	−	0.963039i	−0.968697	−	0.248247i	$-0.920146\pi$
$523$	−2.38622e8	−	1.37768e8i	−1.66803	−	0.963039i	−0.699337	−	0.714793i	$-0.746521\pi$
$524$		0			0
$525$		−	1.62856e8i		−	1.12545i
$526$		0			0
$527$	2.42480e7	−	1.39996e7i	0.165670	−	0.0956495i
$528$		0			0
$529$	−1.17030e8	−	2.02702e8i	−0.790553	−	1.36928i
$530$		0			0
$531$		−	278644.i		−	0.00186109i
$532$		0			0
$533$	2.30536e8			1.52250
$534$		0			0
$535$	4.26783e7	−	2.46403e7i	0.278706	−	0.160911i
$536$		0			0
$537$	−5.54212e7	−	9.59924e7i	−0.357893	−	0.619889i
$538$		0			0
$539$	5.78365e7			0.369348
$540$		0			0
$541$	5.62958e7	−	9.75071e7i	0.355536	−	0.615807i	−0.631673	−	0.775235i	$-0.717632\pi$
$541$	5.62958e7	−	9.75071e7i	0.355536	−	0.615807i	0.987210	+	0.159428i	$0.0509649\pi$
$542$		0			0
$543$	2.85533e8			1.78343
$544$		0			0
$545$	1.43324e7	+	8.27482e6i	0.0885380	+	0.0511175i
$546$		0			0
$547$	1.98558e8	+	1.14637e8i	1.21318	+	0.700429i	0.963450	−	0.267887i	$-0.0863253\pi$
$547$	1.98558e8	+	1.14637e8i	1.21318	+	0.700429i	0.249729	+	0.968316i	$0.419659\pi$
$548$		0			0
$549$	−1.85902e6	−	3.21991e6i	−0.0112348	−	0.0194593i
$550$		0			0
$551$	7.83700e7	−	2.20812e8i	0.468484	−	1.31998i
$552$		0			0
$553$	9.39065e7	−	5.42170e7i	0.555291	−	0.320597i
$554$		0			0
$555$	−3.56750e7	+	6.17909e7i	−0.208682	+	0.361448i
$556$		0			0
$557$	−1.42830e8	+	2.47388e8i	−0.826520	+	1.43157i	0.0742326	+	0.997241i	$0.476349\pi$
$557$	−1.42830e8	+	2.47388e8i	−0.826520	+	1.43157i	−0.900752	+	0.434333i	$0.856984\pi$
$558$		0			0
$559$		−	5.41851e7i		−	0.310202i
$560$		0			0
$561$	−1.80469e8	−	1.04194e8i	−1.02215	−	0.590138i
$562$		0			0
$563$			1.94396e8i			1.08934i	0.838651	+	0.544670i	$0.183345\pi$
$563$			1.94396e8i			1.08934i	−0.838651	+	0.544670i	$0.816655\pi$
$564$		0			0
$565$	−4.66600e7	+	2.69392e7i	−0.258702	+	0.149362i
$566$		0			0
$567$	−1.08948e8	−	1.88703e8i	−0.597680	−	1.03521i
$568$		0			0
$569$			2.84193e8i			1.54269i	0.636420	+	0.771343i	$0.280414\pi$
$569$			2.84193e8i			1.54269i	−0.636420	+	0.771343i	$0.719586\pi$
$570$		0			0
$571$	−6.01264e7			−0.322966			−0.161483	−	0.986875i	$-0.551628\pi$
$571$	−6.01264e7			−0.322966			−0.161483	+	0.986875i	$0.551628\pi$
$572$		0			0
$573$	6.29609e7	−	3.63505e7i	0.334663	−	0.193218i
$574$		0			0
$575$	−1.42585e8	−	2.46965e8i	−0.750017	−	1.29907i
$576$		0			0
$577$	−2.50087e8			−1.30186			−0.650929	−	0.759138i	$-0.725621\pi$
$577$	−2.50087e8			−1.30186			−0.650929	+	0.759138i	$0.725621\pi$
$578$		0			0
$579$	1.03822e8	−	1.79824e8i	0.534874	−	0.926429i
$580$		0			0
$581$	2.56623e8			1.30848
$582$		0			0
$583$	1.04213e8	+	6.01671e7i	0.525913	+	0.303636i
$584$		0			0
$585$	829757.	+	479060.i	0.00414460	+	0.00239289i
$586$		0			0
$587$	9.84333e7	+	1.70492e8i	0.486663	+	0.842924i	0.999882	−	0.0153329i	$-0.00488080\pi$
$587$	9.84333e7	+	1.70492e8i	0.486663	+	0.842924i	−0.513220	+	0.858257i	$0.671547\pi$
$588$		0			0
$589$	−2.50324e7	+	4.62110e6i	−0.122506	+	0.0226151i
$590$		0			0
$591$	−9.33154e7	+	5.38757e7i	−0.452055	+	0.260994i
$592$		0			0
$593$	−8.73896e7	+	1.51363e8i	−0.419079	+	0.725866i	−0.995847	−	0.0910422i	$-0.970980\pi$
$593$	−8.73896e7	+	1.51363e8i	−0.419079	+	0.725866i	0.576768	+	0.816908i	$0.304314\pi$
$594$		0			0
$595$	5.06131e7	−	8.76644e7i	0.240277	−	0.416172i
$596$		0			0
$597$		−	4.13991e8i		−	1.94567i
$598$		0			0
$599$	−9.46476e7	−	5.46448e7i	−0.440381	−	0.254254i	0.263378	−	0.964693i	$-0.415163\pi$
$599$	−9.46476e7	−	5.46448e7i	−0.440381	−	0.254254i	−0.703759	+	0.710438i	$0.748497\pi$
$600$		0			0
$601$		−	2.11871e8i		−	0.975994i	−0.872845	−	0.487997i	$-0.837728\pi$
$601$		−	2.11871e8i		−	0.975994i	0.872845	−	0.487997i	$-0.162272\pi$
$602$		0			0
$603$	2.39154e6	−	1.38076e6i	0.0109075	−	0.00629746i
$604$		0			0
$605$	−1.13943e7	−	1.97355e7i	−0.0514543	−	0.0891214i
$606$		0			0
$607$		−	5.43070e7i		−	0.242823i	−0.992602	−	0.121411i	$-0.961258\pi$
$607$		−	5.43070e7i		−	0.242823i	0.992602	−	0.121411i	$-0.0387421\pi$
$608$		0			0
$609$	3.81337e8			1.68833
$610$		0			0
$611$	−2.05679e8	+	1.18749e8i	−0.901711	+	0.520603i
$612$		0			0
$613$	1.71413e8	+	2.96897e8i	0.744155	+	1.28891i	0.950588	+	0.310454i	$0.100481\pi$
$613$	1.71413e8	+	2.96897e8i	0.744155	+	1.28891i	−0.206433	+	0.978461i	$0.566186\pi$
$614$		0			0
$615$	7.81554e7			0.335996
$616$		0			0
$617$	1.67520e8	−	2.90153e8i	0.713200	−	1.23530i	−0.250450	−	0.968129i	$-0.580579\pi$
$617$	1.67520e8	−	2.90153e8i	0.713200	−	1.23530i	0.963650	−	0.267169i	$-0.0860880\pi$
$618$		0			0
$619$	−1.09542e8			−0.461856			−0.230928	−	0.972971i	$-0.574176\pi$
$619$	−1.09542e8			−0.461856			−0.230928	+	0.972971i	$0.574176\pi$
$620$		0			0
$621$	−3.35823e8	−	1.93888e8i	−1.40228	−	0.809609i
$622$		0			0
$623$	−8.12468e6	−	4.69079e6i	−0.0336002	−	0.0193991i
$624$		0			0
$625$	−9.83202e7	−	1.70296e8i	−0.402720	−	0.697531i
$626$		0			0
$627$	1.22939e8	+	1.44150e8i	0.498755	+	0.584807i
$628$		0			0
$629$	5.40717e8	−	3.12183e8i	2.17279	−	1.25446i
$630$		0			0
$631$	2.71363e7	−	4.70015e7i	0.108010	−	0.187078i	−0.806954	−	0.590614i	$-0.798886\pi$
$631$	2.71363e7	−	4.70015e7i	0.108010	−	0.187078i	0.914964	+	0.403536i	$0.132219\pi$
$632$		0			0
$633$	−7.50534e7	+	1.29996e8i	−0.295910	+	0.512531i
$634$		0			0
$635$		−	6.38033e7i		−	0.249185i
$636$		0			0
$637$	−1.23508e8	−	7.13075e7i	−0.477835	−	0.275878i
$638$		0			0
$639$			2.07990e6i			0.00797150i
$640$		0			0
$641$	6.38613e7	−	3.68703e7i	0.242473	−	0.139992i	−0.373840	−	0.927493i	$-0.621959\pi$
$641$	6.38613e7	−	3.68703e7i	0.242473	−	0.139992i	0.616313	+	0.787501i	$0.288626\pi$
$642$		0			0
$643$	1.87704e8	+	3.25113e8i	0.706058	+	1.22293i	0.966308	+	0.257387i	$0.0828616\pi$
$643$	1.87704e8	+	3.25113e8i	0.706058	+	1.22293i	−0.260250	+	0.965541i	$0.583805\pi$
$644$		0			0
$645$		−	1.83696e7i		−	0.0684575i
$646$		0			0
$647$	2.40689e8			0.888677			0.444338	−	0.895859i	$-0.353439\pi$
$647$	2.40689e8			0.888677			0.444338	+	0.895859i	$0.353439\pi$
$648$		0			0
$649$	−2.12642e7	+	1.22769e7i	−0.0777883	+	0.0449111i
$650$		0			0
$651$	−2.07144e7	−	3.58785e7i	−0.0750811	−	0.130044i
$652$		0			0
$653$	−3.56641e8			−1.28083			−0.640415	−	0.768029i	$-0.721238\pi$
$653$	−3.56641e8			−1.28083			−0.640415	+	0.768029i	$0.721238\pi$
$654$		0			0
$655$	−6.93735e6	+	1.20158e7i	−0.0246871	+	0.0427593i
$656$		0			0
$657$	4.06343e6			0.0143284
$658$		0			0
$659$	−1.01901e7	−	5.88327e6i	−0.0356060	−	0.0205571i	0.482091	−	0.876121i	$-0.339877\pi$
$659$	−1.01901e7	−	5.88327e6i	−0.0356060	−	0.0205571i	−0.517697	+	0.855564i	$0.673211\pi$
$660$		0			0
$661$	−4.28807e7	−	2.47572e7i	−0.148476	−	0.0857229i	0.423921	−	0.905699i	$-0.360653\pi$
$661$	−4.28807e7	−	2.47572e7i	−0.148476	−	0.0857229i	−0.572398	+	0.819976i	$0.693987\pi$
$662$		0			0
$663$	2.56924e8	+	4.45006e8i	0.881586	+	1.52695i
$664$		0			0
$665$	−7.00223e7	+	5.97188e7i	−0.238107	+	0.203070i
$666$		0			0
$667$	5.78284e8	−	3.33872e8i	1.94878	−	1.12513i
$668$		0			0
$669$	−1.93895e8	+	3.35835e8i	−0.647571	+	1.12163i
$670$		0			0
$671$	−1.63814e8	+	2.83734e8i	−0.542230	+	0.939170i
$672$		0			0
$673$		−	4.83173e8i		−	1.58510i	−0.609806	−	0.792551i	$-0.708752\pi$
$673$		−	4.83173e8i		−	1.58510i	0.609806	−	0.792551i	$-0.291248\pi$
$674$		0			0
$675$	−2.50636e8	−	1.44705e8i	−0.814951	−	0.470512i
$676$		0			0
$677$			8.39581e7i			0.270581i	0.990806	+	0.135290i	$0.0431967\pi$
$677$			8.39581e7i			0.270581i	−0.990806	+	0.135290i	$0.956803\pi$
$678$		0			0
$679$	−3.64335e8	+	2.10349e8i	−1.16384	+	0.671941i
$680$		0			0
$681$	7.89985e7	+	1.36829e8i	0.250137	+	0.433250i
$682$		0			0
$683$			2.28817e8i			0.718170i	0.933305	+	0.359085i	$0.116911\pi$
$683$			2.28817e8i			0.718170i	−0.933305	+	0.359085i	$0.883089\pi$
$684$		0			0
$685$	7.06032e7			0.219661
$686$		0			0
$687$	−4.10789e8	+	2.37169e8i	−1.26692	+	0.731456i
$688$		0			0
$689$	−1.48362e8	−	2.56970e8i	−0.453591	−	0.785643i
$690$		0			0
$691$	3.98311e8			1.20723			0.603613	−	0.797277i	$-0.293727\pi$
$691$	3.98311e8			1.20723			0.603613	+	0.797277i	$0.293727\pi$
$692$		0			0
$693$	2.51554e6	−	4.35705e6i	0.00755843	−	0.0130916i
$694$		0			0
$695$	−6.89312e6			−0.0205334
$696$		0			0
$697$	−5.92292e8	−	3.41960e8i	−1.74919	−	1.00990i
$698$		0			0
$699$	4.08461e8	+	2.35825e8i	1.19597	+	0.690491i
$700$		0			0
$701$	2.02008e8	+	3.49889e8i	0.586429	+	1.01572i	0.994696	+	0.102862i	$0.0328000\pi$
$701$	2.02008e8	+	3.49889e8i	0.586429	+	1.01572i	−0.408267	+	0.912863i	$0.633867\pi$
$702$		0			0
$703$	−5.58210e8	+	1.03048e8i	−1.60669	+	0.296602i
$704$		0			0
$705$	−6.97286e7	+	4.02578e7i	−0.198996	+	0.114890i
$706$		0			0
$707$	−3.88813e8	+	6.73444e8i	−1.10023	+	1.90565i
$708$		0			0
$709$	2.06420e8	−	3.57529e8i	0.579178	−	1.00317i	−0.416395	−	0.909184i	$-0.636707\pi$
$709$	2.06420e8	−	3.57529e8i	0.579178	−	1.00317i	0.995574	−	0.0939828i	$-0.0299599\pi$
$710$		0			0
$711$		−	3.04480e6i		−	0.00847129i
$712$		0			0
$713$	−6.28254e7	−	3.62723e7i	−0.173327	−	0.100071i
$714$		0			0
$715$		−	8.44282e7i		−	0.230977i
$716$		0			0
$717$	1.20760e7	−	6.97209e6i	0.0327617	−	0.0189150i
$718$		0			0
$719$	9.86032e7	+	1.70786e8i	0.265280	+	0.459478i	0.967637	−	0.252347i	$-0.0812023\pi$
$719$	9.86032e7	+	1.70786e8i	0.265280	+	0.459478i	−0.702357	+	0.711825i	$0.747869\pi$
$720$		0			0
$721$			6.08394e8i			1.62323i
$722$		0			0
$723$	−1.52511e8			−0.403539
$724$		0			0
$725$	4.31592e8	−	2.49179e8i	1.13255	−	0.653880i
$726$		0			0
$727$	−2.35592e8	−	4.08057e8i	−0.613136	−	1.06198i	−0.990709	−	0.136002i	$-0.956574\pi$
$727$	−2.35592e8	−	4.08057e8i	−0.613136	−	1.06198i	0.377573	−	0.925980i	$-0.376759\pi$
$728$		0			0
$729$	−3.93439e8			−1.01554
$730$		0			0
$731$	−8.03740e7	+	1.39212e8i	−0.205761	+	0.356389i
$732$		0			0
$733$	−3.72655e8			−0.946226			−0.473113	−	0.881002i	$-0.656870\pi$
$733$	−3.72655e8			−0.946226			−0.473113	+	0.881002i	$0.656870\pi$
$734$		0			0
$735$	−4.18713e7	−	2.41744e7i	−0.105452	−	0.0608827i
$736$		0			0
$737$	−2.10739e8	−	1.21670e8i	−0.526433	−	0.303936i
$738$		0			0
$739$	2.10429e8	+	3.64474e8i	0.521401	+	0.903094i	0.999690	+	0.0248910i	$0.00792386\pi$
$739$	2.10429e8	+	3.64474e8i	0.521401	+	0.903094i	−0.478289	+	0.878203i	$0.658743\pi$
$740$		0			0
$741$	−8.48079e7	−	4.59402e8i	−0.208440	−	1.12912i
$742$		0			0
$743$	1.60325e8	−	9.25638e7i	0.390873	−	0.225671i	−0.291665	−	0.956520i	$-0.594209\pi$
$743$	1.60325e8	−	9.25638e7i	0.390873	−	0.225671i	0.682538	+	0.730850i	$0.260876\pi$
$744$		0			0
$745$	−2.81687e7	+	4.87896e7i	−0.0681236	+	0.117994i
$746$		0			0
$747$	3.60295e6	−	6.24050e6i	0.00864364	−	0.0149712i
$748$		0			0
$749$			6.38089e8i			1.51857i
$750$		0			0
$751$	−2.79041e8	−	1.61104e8i	−0.658791	−	0.380353i	0.133025	−	0.991113i	$-0.457531\pi$
$751$	−2.79041e8	−	1.61104e8i	−0.658791	−	0.380353i	−0.791816	+	0.610759i	$0.790864\pi$
$752$		0			0
$753$			2.60583e8i			0.610324i
$754$		0			0
$755$	1.46202e8	−	8.44099e7i	0.339714	−	0.196134i
$756$		0			0
$757$	1.61102e7	+	2.79037e7i	0.0371376	+	0.0643241i	0.883997	−	0.467493i	$-0.154843\pi$
$757$	1.61102e7	+	2.79037e7i	0.0371376	+	0.0643241i	−0.846859	+	0.531817i	$0.821509\pi$
$758$		0			0
$759$			5.39924e8i			1.23483i
$760$		0			0
$761$	2.44863e8			0.555609			0.277804	−	0.960638i	$-0.410393\pi$
$761$	2.44863e8			0.555609			0.277804	+	0.960638i	$0.410393\pi$
$762$		0			0
$763$	−1.85577e8	+	1.07143e8i	−0.417783	+	0.241207i
$764$		0			0
$765$	−1.42120e6	−	2.46160e6i	−0.00317447	−	0.00549835i
$766$		0			0
$767$	6.05454e7			0.134182
$768$		0			0
$769$	−3.36566e8	+	5.82949e8i	−0.740101	+	1.28189i	0.212348	+	0.977194i	$0.431889\pi$
$769$	−3.36566e8	+	5.82949e8i	−0.740101	+	1.28189i	−0.952449	+	0.304698i	$0.901444\pi$
$770$		0			0
$771$	8.74643e8			1.90839
$772$		0			0
$773$	3.72024e8	+	2.14788e8i	0.805439	+	0.465021i	0.845370	−	0.534182i	$-0.179380\pi$
$773$	3.72024e8	+	2.14788e8i	0.805439	+	0.465021i	−0.0399303	+	0.999202i	$0.512714\pi$
$774$		0			0
$775$	−4.68886e7	−	2.70711e7i	−0.100731	−	0.0581569i
$776$		0			0
$777$	−4.61922e8	−	8.00072e8i	−0.984704	−	1.70556i
$778$		0			0
$779$	4.03481e8	+	4.73095e8i	0.853514	+	1.00077i
$780$		0			0
$781$	1.58723e8	−	9.16390e7i	0.333187	−	0.192365i
$782$		0			0
$783$	3.38835e8	−	5.86879e8i	0.705834	−	1.22254i
$784$		0			0
$785$	−6.34555e7	+	1.09908e8i	−0.131178	+	0.227207i
$786$		0			0
$787$		−	8.19240e8i		−	1.68069i	−0.542054	−	0.840344i	$-0.682353\pi$
$787$		−	8.19240e8i		−	1.68069i	0.542054	−	0.840344i	$-0.317647\pi$
$788$		0			0
$789$	−6.20915e8	−	3.58485e8i	−1.26416	−	0.729861i
$790$		0			0
$791$		−	6.97620e8i		−	1.40958i
$792$		0			0
$793$	6.99641e8	−	4.03938e8i	1.40299	−	0.810018i
$794$		0			0
$795$	−5.02971e7	−	8.71171e7i	−0.100102	−	0.173381i
$796$		0			0
$797$		−	4.18496e8i		−	0.826639i	−0.910586	−	0.413320i	$-0.864369\pi$
$797$		−	4.18496e8i		−	0.826639i	0.910586	−	0.413320i	$-0.135631\pi$
$798$		0			0
$799$	7.04573e8			1.38129
$800$		0			0
$801$	−228139.	+	131716.i	−0.000443917	+	0.000256296i
$802$		0			0
$803$	−1.79032e8	−	3.10093e8i	−0.345768	−	0.598887i
$804$		0			0
$805$	−2.62273e8			−0.502766
$806$		0			0
$807$	8.33808e6	−	1.44420e7i	0.0158652	−	0.0274793i
$808$		0			0
$809$	9.48582e8			1.79155			0.895776	−	0.444506i	$-0.146621\pi$
$809$	9.48582e8			1.79155			0.895776	+	0.444506i	$0.146621\pi$
$810$		0			0
$811$	−1.45076e8	−	8.37595e7i	−0.271977	−	0.157026i	0.357809	−	0.933795i	$-0.383524\pi$
$811$	−1.45076e8	−	8.37595e7i	−0.271977	−	0.157026i	−0.629786	+	0.776769i	$0.716857\pi$
$812$		0			0
$813$	5.64443e8	+	3.25881e8i	1.05039	+	0.606440i
$814$		0			0
$815$	1.09170e8	+	1.89088e8i	0.201665	+	0.349294i
$816$		0			0
$817$	1.11196e8	−	9.48339e7i	0.203903	−	0.173899i
$818$		0			0
$819$	−1.07437e7	+	6.20290e6i	−0.0195571	+	0.0112913i
$820$		0			0
$821$	−1.42132e8	+	2.46179e8i	−0.256839	+	0.444859i	−0.965394	−	0.260798i	$-0.916014\pi$
$821$	−1.42132e8	+	2.46179e8i	−0.256839	+	0.444859i	0.708554	+	0.705657i	$0.249348\pi$
$822$		0			0
$823$	2.26163e7	−	3.91726e7i	0.0405716	−	0.0702721i	−0.845027	−	0.534724i	$-0.820415\pi$
$823$	2.26163e7	−	3.91726e7i	0.0405716	−	0.0702721i	0.885598	+	0.464452i	$0.153749\pi$
$824$		0			0
$825$			4.02962e8i			0.717633i
$826$		0			0
$827$	−7.86623e8	−	4.54157e8i	−1.39075	−	0.802952i	−0.397355	−	0.917665i	$-0.630072\pi$
$827$	−7.86623e8	−	4.54157e8i	−1.39075	−	0.802952i	−0.993399	+	0.114713i	$0.963405\pi$
$828$		0			0
$829$		−	6.63682e8i		−	1.16492i	−0.812859	−	0.582460i	$-0.802090\pi$
$829$		−	6.63682e8i		−	1.16492i	0.812859	−	0.582460i	$-0.197910\pi$
$830$		0			0
$831$	−8.56124e7	+	4.94284e7i	−0.149188	+	0.0861337i
$832$		0			0
$833$	2.11544e8	+	3.66406e8i	0.365988	+	0.633909i
$834$		0			0
$835$		−	8.14418e7i		−	0.139890i
$836$		0			0
$837$	−7.36228e7			−0.125556
$838$		0			0
$839$	4.92376e7	−	2.84273e7i	0.0833702	−	0.0481338i	−0.457735	−	0.889088i	$-0.651339\pi$
$839$	4.92376e7	−	2.84273e7i	0.0833702	−	0.0481338i	0.541106	+	0.840955i	$0.318006\pi$
$840$		0			0
$841$	2.86058e8	+	4.95466e8i	0.480912	+	0.832964i
$842$		0			0
$843$	2.80736e8			0.468614
$844$		0			0
$845$	−2.64036e7	+	4.57324e7i	−0.0437616	+	0.0757973i
$846$		0			0
$847$	2.95068e8			0.485593
$848$		0			0
$849$	−2.82818e8	−	1.63285e8i	−0.462150	−	0.266823i
$850$		0			0
$851$	−1.40098e9	−	8.08854e8i	−2.27322	−	1.31245i
$852$		0			0
$853$	−4.80813e7	−	8.32793e7i	−0.0774692	−	0.134181i	0.824688	−	0.565588i	$-0.191351\pi$
$853$	−4.80813e7	−	8.32793e7i	−0.0774692	−	0.134181i	−0.902157	+	0.431407i	$0.858017\pi$
$854$		0			0
$855$	469123.	+	2.54123e6i	0.000750566	+	0.00406580i
$856$		0			0
$857$	3.37812e8	−	1.95036e8i	0.536701	−	0.309864i	−0.207040	−	0.978332i	$-0.566383\pi$
$857$	3.37812e8	−	1.95036e8i	0.536701	−	0.309864i	0.743741	+	0.668468i	$0.233050\pi$
$858$		0			0
$859$	−1.21544e8	+	2.10520e8i	−0.191758	+	0.332135i	−0.945833	−	0.324654i	$-0.894752\pi$
$859$	−1.21544e8	+	2.10520e8i	−0.191758	+	0.332135i	0.754075	+	0.656789i	$0.228086\pi$
$860$		0			0
$861$	−5.05981e8	+	8.76384e8i	−0.792728	+	1.37305i
$862$		0			0
$863$		−	4.58699e8i		−	0.713667i	−0.934168	−	0.356833i	$-0.883856\pi$
$863$		−	4.58699e8i		−	0.713667i	0.934168	−	0.356833i	$-0.116144\pi$
$864$		0			0
$865$	9.67961e7	+	5.58852e7i	0.149558	+	0.0863473i
$866$		0			0
$867$		−	8.77947e8i		−	1.34713i
$868$		0			0
$869$	−2.32358e8	+	1.34152e8i	−0.354077	+	0.204426i
$870$		0			0
$871$	3.00019e8	+	5.19648e8i	0.454040	+	0.786420i
$872$		0			0
$873$			1.18131e7i			0.0177550i
$874$		0			0
$875$	−4.05389e8			−0.605128
$876$		0			0
$877$	4.02974e8	−	2.32657e8i	0.597418	−	0.344919i	−0.170607	−	0.985339i	$-0.554573\pi$
$877$	4.02974e8	−	2.32657e8i	0.597418	−	0.344919i	0.768025	+	0.640420i	$0.221240\pi$
$878$		0			0
$879$	1.56273e8	+	2.70674e8i	0.230101	+	0.398547i
$880$		0			0
$881$	−1.32256e8			−0.193414			−0.0967070	−	0.995313i	$-0.530831\pi$
$881$	−1.32256e8			−0.193414			−0.0967070	+	0.995313i	$0.530831\pi$
$882$		0			0
$883$	1.39786e8	−	2.42117e8i	0.203041	−	0.351677i	−0.746466	−	0.665423i	$-0.768251\pi$
$883$	1.39786e8	−	2.42117e8i	0.203041	−	0.351677i	0.949507	+	0.313747i	$0.101584\pi$
$884$		0			0
$885$	2.05259e7			0.0296123
$886$		0			0
$887$	5.75020e8	+	3.31988e8i	0.823972	+	0.475720i	0.851784	−	0.523893i	$-0.175521\pi$
$887$	5.75020e8	+	3.31988e8i	0.823972	+	0.475720i	−0.0278124	+	0.999613i	$0.508854\pi$
$888$		0			0
$889$	7.15449e8	+	4.13065e8i	1.01829	+	0.587913i
$890$		0			0
$891$	2.69575e8	+	4.66917e8i	0.381106	+	0.660095i
$892$		0			0
$893$	−6.03668e8	−	2.14253e8i	−0.847703	−	0.300865i
$894$		0			0
$895$	−1.15377e8	+	6.66129e7i	−0.160935	+	0.0929157i
$896$		0			0
$897$	6.65680e8	−	1.15299e9i	0.922334	−	1.59753i
$898$		0			0
$899$	6.33888e7	−	1.09793e8i	0.0872435	−	0.151110i
$900$		0			0
$901$			8.80275e8i			1.20349i
$902$		0			0
$903$	2.05985e8	+	1.18925e8i	0.279751	+	0.161514i
$904$		0			0
$905$		−	3.43192e8i		−	0.463011i
$906$		0			0
$907$	−1.19797e9	+	6.91650e8i	−1.60555	+	0.926967i	−0.615206	+	0.788366i	$0.710927\pi$
$907$	−1.19797e9	+	6.91650e8i	−1.60555	+	0.926967i	−0.990348	+	0.138601i	$0.955740\pi$
$908$		0			0
$909$	1.09178e7	+	1.89101e7i	0.0145359	+	0.0251770i
$910$		0			0
$911$		−	6.82463e8i		−	0.902660i	−0.892357	−	0.451330i	$-0.850950\pi$
$911$		−	6.82463e8i		−	0.902660i	0.892357	−	0.451330i	$-0.149050\pi$
$912$		0			0
$913$	−6.34974e8			−0.834342
$914$		0			0
$915$	2.37189e8	−	1.36941e8i	0.309622	−	0.178760i
$916$		0			0
$917$	−8.98252e7	−	1.55582e8i	−0.116490	−	0.201767i
$918$		0			0
$919$	9.54832e8			1.23021			0.615107	−	0.788444i	$-0.289113\pi$
$919$	9.54832e8			1.23021			0.615107	+	0.788444i	$0.289113\pi$
$920$		0			0
$921$	3.77394e8	−	6.53666e8i	0.483077	−	0.836714i
$922$		0			0
$923$	−4.51932e8			−0.574736
$924$		0			0
$925$	−1.04559e9	−	6.03673e8i	−1.32110	−	0.762740i
$926$		0			0
$927$	1.47948e7	+	8.54178e6i	0.0185725	+	0.0107228i
$928$		0			0
$929$	1.23210e8	+	2.13406e8i	0.153674	+	0.266170i	0.932575	−	0.360976i	$-0.117556\pi$
$929$	1.23210e8	+	2.13406e8i	0.153674	+	0.266170i	−0.778902	+	0.627146i	$0.784223\pi$
$930$		0			0
$931$	−6.98284e7	−	3.78259e8i	−0.0865333	−	0.468749i
$932$		0			0
$933$	1.20813e8	−	6.97512e7i	0.148753	−	0.0858829i
$934$		0			0
$935$	−1.25234e8	+	2.16912e8i	−0.153211	+	0.265369i
$936$		0			0
$937$	−1.71223e8	+	2.96566e8i	−0.208134	+	0.360498i	−0.951127	−	0.308801i	$-0.900072\pi$
$937$	−1.71223e8	+	2.96566e8i	−0.208134	+	0.360498i	0.742993	+	0.669299i	$0.233406\pi$
$938$		0			0
$939$			1.06510e9i			1.28646i
$940$		0			0
$941$	1.28870e9	+	7.44033e8i	1.54662	+	0.892943i	0.998396	+	0.0566124i	$0.0180299\pi$
$941$	1.28870e9	+	7.44033e8i	1.54662	+	0.892943i	0.548226	+	0.836330i	$0.315303\pi$
$942$		0			0
$943$			1.77201e9i			2.11315i
$944$		0			0
$945$	−2.30511e8	+	1.33085e8i	−0.273147	+	0.157701i
$946$		0			0
$947$	−4.37325e8	−	7.57470e8i	−0.514938	−	0.891898i	−0.999850	−	0.0173352i	$-0.994482\pi$
$947$	−4.37325e8	−	7.57470e8i	−0.514938	−	0.891898i	0.484912	−	0.874563i	$-0.338852\pi$
$948$		0			0
$949$			8.82926e8i			1.03306i
$950$		0			0
$951$	3.34235e8			0.388607
$952$		0			0
$953$	−1.75798e8	+	1.01497e8i	−0.203112	+	0.117267i	−0.598106	−	0.801417i	$-0.704080\pi$
$953$	−1.75798e8	+	1.01497e8i	−0.203112	+	0.117267i	0.394994	+	0.918684i	$0.370747\pi$
$954$		0			0
$955$	−4.36910e7	−	7.56751e7i	−0.0501628	−	0.0868846i
$956$		0			0
$957$	−9.43561e8			−1.07655
$958$		0			0
$959$	−4.57088e8	+	7.91699e8i	−0.518255	+	0.897644i
$960$		0			0
$961$	8.73730e8			0.984481
$962$		0			0
$963$	1.55169e7	+	8.95869e6i	0.0173751	+	0.0100315i
$964$		0			0
$965$	−2.16137e8	−	1.24787e8i	−0.240518	−	0.138863i
$966$		0			0
$967$	−2.80016e8	−	4.85002e8i	−0.309673	−	0.536370i	0.668618	−	0.743606i	$-0.266886\pi$
$967$	−2.80016e8	−	4.85002e8i	−0.309673	−	0.536370i	−0.978291	+	0.207237i	$0.933553\pi$
$968$		0			0
$969$	−4.63555e8	+	1.30609e9i	−0.509483	+	1.43550i
$970$		0			0
$971$	−6.67300e8	+	3.85266e8i	−0.728892	+	0.420826i	−0.818017	−	0.575195i	$-0.804926\pi$
$971$	−6.67300e8	+	3.85266e8i	−0.728892	+	0.420826i	0.0891247	+	0.996020i	$0.471593\pi$
$972$		0			0
$973$	4.46263e7	−	7.72949e7i	0.0484453	−	0.0839098i
$974$		0			0
$975$	4.96818e8	−	8.60514e8i	0.536023	−	0.928420i
$976$		0			0
$977$		−	1.03135e9i		−	1.10592i	−0.833207	−	0.552961i	$-0.813498\pi$
$977$		−	1.03135e9i		−	1.10592i	0.833207	−	0.552961i	$-0.186502\pi$
$978$		0			0
$979$	2.01033e7	+	1.16066e7i	0.0214249	+	0.0123697i
$980$		0			0
$981$			6.01709e6i			0.00637353i
$982$		0			0
$983$	−3.53560e7	+	2.04128e7i	−0.0372223	+	0.0214903i	−0.518496	−	0.855080i	$-0.673508\pi$
$983$	−3.53560e7	+	2.04128e7i	−0.0372223	+	0.0214903i	0.481273	+	0.876571i	$0.340174\pi$
$984$		0			0
$985$	6.47552e7	+	1.12159e8i	0.0677588	+	0.117362i
$986$		0			0
$987$		−	1.04252e9i		−	1.08426i
$988$		0			0
$989$	4.16492e8			0.430544
$990$		0			0
$991$	−4.76946e8	+	2.75365e8i	−0.490059	+	0.282936i	−0.724599	−	0.689171i	$-0.757975\pi$
$991$	−4.76946e8	+	2.75365e8i	−0.490059	+	0.282936i	0.234540	+	0.972106i	$0.424642\pi$
$992$		0			0
$993$	6.17765e8	+	1.07000e9i	0.630922	+	1.09279i
$994$		0			0
$995$	−4.97592e8			−0.505131
$996$		0			0
$997$	−3.65102e8	+	6.32375e8i	−0.368408	+	0.638101i	−0.989317	−	0.145782i	$-0.953430\pi$
$997$	−3.65102e8	+	6.32375e8i	−0.368408	+	0.638101i	0.620909	+	0.783883i	$0.286764\pi$
$998$		0			0
$999$	−1.64175e9			−1.64669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.h.a.69.3	yes	20
3.2	odd	2		684.7.y.c.145.5		20
19.8	odd	6	inner	76.7.h.a.65.3	✓	20
57.8	even	6		684.7.y.c.217.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.h.a.65.3	✓	20	19.8	odd	6	inner
76.7.h.a.69.3	yes	20	1.1	even	1	trivial
684.7.y.c.145.5		20	3.2	odd	2
684.7.y.c.217.5		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)

\(f(q)\)	\(=\)	\(q+(-23.1942 + 13.3912i) q^{3} +(16.0954 + 27.8780i) q^{5} -416.808 q^{7} +(-5.85193 + 10.1358i) q^{9} +O(q^{10})\)	\(q+(-23.1942 + 13.3912i) q^{3} +(16.0954 + 27.8780i) q^{5} -416.808 q^{7} +(-5.85193 + 10.1358i) q^{9} +1031.33 q^{11} +(-2202.37 - 1271.54i) q^{13} +(-746.639 - 431.072i) q^{15} +(3772.21 + 6533.66i) q^{17} +(-1245.17 - 6745.03i) q^{19} +(9667.53 - 5581.55i) q^{21} +(9773.64 - 16928.4i) q^{23} +(7294.38 - 12634.2i) q^{25} -19837.8i q^{27} +(29583.8 + 17080.2i) q^{29} -3711.23i q^{31} +(-23920.8 + 13810.7i) q^{33} +(-6708.68 - 11619.8i) q^{35} -82758.7i q^{37} +68109.7 q^{39} +(-78507.2 + 45326.2i) q^{41} +(10653.4 + 18452.3i) q^{43} -376.756 q^{45} +(46695.0 - 80878.1i) q^{47} +56079.7 q^{49} +(-174987. - 101029. i) q^{51} +(101047. + 58339.5i) q^{53} +(16599.6 + 28751.4i) q^{55} +(119205. + 139772. i) q^{57} +(-20618.2 + 11903.9i) q^{59} +(-158838. + 275115. i) q^{61} +(2439.13 - 4224.70i) q^{63} -81863.6i q^{65} +(-204338. - 117975. i) q^{67} +523523. i q^{69} +(153902. - 88855.3i) q^{71} +(-173594. - 300673. i) q^{73} +390722. i q^{75} -429865. q^{77} +(-225299. + 130077. i) q^{79} +(261386. + 452734. i) q^{81} -615686. q^{83} +(-121430. + 210323. i) q^{85} -914899. q^{87} +(19492.6 + 11254.1i) q^{89} +(917966. + 529988. i) q^{91} +(49697.9 + 86079.2i) q^{93} +(167997. - 143277. i) q^{95} +(874109. - 504667. i) q^{97} +(-6035.26 + 10453.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} - 56 q^{5} + 464 q^{7} + 2200 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more