LMFDB - Embedded newform 76.5.h.a.69.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,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, 5, names="a")

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

chi := DirichletCharacter("76.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} + \cdots + 90728724573 $ x^12 - 6x^11 + 631x^10 - 3100x^9 + 142264x^8 - 550522x^7 + 14083117x^6 - 40335478x^5 + 638031136x^4 - 1209472584x^3 + 12784623475x^2 - 12186518934*x + 90728724573
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.2
Root			$0.500000 - 9.58497i$ of defining polynomial
Character	$\chi$	$=$	76.69
Dual form			76.5.h.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.05083 + 5.22550i) q^{3} +(-12.7505 - 22.0845i) q^{5} +27.7589 q^{7} +(14.1116 - 24.4421i) q^{9} +O(q^{10})$	\(q+(-9.05083 + 5.22550i) q^{3} +(-12.7505 - 22.0845i) q^{5} +27.7589 q^{7} +(14.1116 - 24.4421i) q^{9} +143.293 q^{11} +(123.911 + 71.5400i) q^{13} +(230.805 + 133.255i) q^{15} +(43.9489 + 76.1217i) q^{17} +(340.586 + 119.675i) q^{19} +(-251.241 + 145.054i) q^{21} +(350.792 - 607.590i) q^{23} +(-12.6488 + 21.9084i) q^{25} -551.569i q^{27} +(-37.5252 - 21.6652i) q^{29} -111.254i q^{31} +(-1296.92 + 748.776i) q^{33} +(-353.939 - 613.040i) q^{35} +1079.87i q^{37} -1495.33 q^{39} +(80.1784 - 46.2910i) q^{41} +(945.995 + 1638.51i) q^{43} -719.720 q^{45} +(1366.72 - 2367.22i) q^{47} -1630.45 q^{49} +(-795.547 - 459.309i) q^{51} +(2153.80 + 1243.50i) q^{53} +(-1827.05 - 3164.54i) q^{55} +(-3707.95 + 696.575i) q^{57} +(-5032.93 + 2905.77i) q^{59} +(1263.85 - 2189.06i) q^{61} +(391.723 - 678.485i) q^{63} -3648.67i q^{65} +(4300.24 + 2482.74i) q^{67} +7332.25i q^{69} +(3720.00 - 2147.74i) q^{71} +(-1588.81 - 2751.89i) q^{73} -264.385i q^{75} +3977.65 q^{77} +(4934.57 - 2848.97i) q^{79} +(4025.27 + 6971.97i) q^{81} +10463.5 q^{83} +(1120.74 - 1941.17i) q^{85} +452.845 q^{87} +(4822.97 + 2784.54i) q^{89} +(3439.63 + 1985.87i) q^{91} +(581.355 + 1006.94i) q^{93} +(-1699.68 - 9047.57i) q^{95} +(-15618.3 + 9017.22i) q^{97} +(2022.10 - 3502.38i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9}+O(q^{10}) $ 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9	$ 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9} + 6 q^{11} - 93 q^{13} - 741 q^{15} - 483 q^{17} - 533 q^{19} + 972 q^{21} + 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} - 1128 q^{35} - 2250 q^{39} - 1692 q^{41} - 63 q^{43} + 7976 q^{45} - 3471 q^{47} + 420 q^{49} + 6741 q^{51} - 3771 q^{53} - 2014 q^{55} + 7617 q^{57} - 9594 q^{59} + 1229 q^{61} + 1514 q^{63} + 7590 q^{67} + 963 q^{71} - 2838 q^{73} - 15408 q^{77} + 11073 q^{79} + 2086 q^{81} - 14202 q^{83} + 9455 q^{85} - 39510 q^{87} + 6525 q^{89} - 7686 q^{91} - 5316 q^{93} + 1521 q^{95} - 34110 q^{97} + 13220 q^{99}+O(q^{100}) $ 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9 + 6 * q^11 - 93 * q^13 - 741 * q^15 - 483 * q^17 - 533 * q^19 + 972 * q^21 + 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 - 1128 * q^35 - 2250 * q^39 - 1692 * q^41 - 63 * q^43 + 7976 * q^45 - 3471 * q^47 + 420 * q^49 + 6741 * q^51 - 3771 * q^53 - 2014 * q^55 + 7617 * q^57 - 9594 * q^59 + 1229 * q^61 + 1514 * q^63 + 7590 * q^67 + 963 * q^71 - 2838 * q^73 - 15408 * q^77 + 11073 * q^79 + 2086 * q^81 - 14202 * q^83 + 9455 * q^85 - 39510 * q^87 + 6525 * q^89 - 7686 * q^91 - 5316 * q^93 + 1521 * q^95 - 34110 * q^97 + 13220 * 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
$3$	−9.05083	+	5.22550i	−1.00565	+	0.580611i	−0.909914	−	0.414796i	$-0.863853\pi$
$3$	−9.05083	+	5.22550i	−1.00565	+	0.580611i	−0.0957331	+	0.995407i	$0.530520\pi$
$4$		0			0
$5$	−12.7505	−	22.0845i	−0.510019	−	0.883378i	−0.999933	−	0.0116075i	$-0.996305\pi$
$5$	−12.7505	−	22.0845i	−0.510019	−	0.883378i	0.489914	−	0.871771i	$-0.337028\pi$
$6$		0			0
$7$	27.7589			0.566508			0.283254	−	0.959045i	$-0.408586\pi$
$7$	27.7589			0.566508			0.283254	+	0.959045i	$0.408586\pi$
$8$		0			0
$9$	14.1116	−	24.4421i	0.174218	−	0.301754i
$10$		0			0
$11$	143.293			1.18424			0.592119	−	0.805850i	$-0.298291\pi$
$11$	143.293			1.18424			0.592119	+	0.805850i	$0.298291\pi$
$12$		0			0
$13$	123.911	+	71.5400i	0.733201	+	0.423314i	0.819592	−	0.572948i	$-0.194200\pi$
$13$	123.911	+	71.5400i	0.733201	+	0.423314i	−0.0863914	+	0.996261i	$0.527534\pi$
$14$		0			0
$15$	230.805	+	133.255i	1.02580	+	0.592245i
$16$		0			0
$17$	43.9489	+	76.1217i	0.152072	+	0.263397i	0.931989	−	0.362486i	$-0.118072\pi$
$17$	43.9489	+	76.1217i	0.152072	+	0.263397i	−0.779917	+	0.625883i	$0.784739\pi$
$18$		0			0
$19$	340.586	+	119.675i	0.943452	+	0.331509i
$19$	340.586	+	119.675i	0.943452	+	0.331509i
$20$		0			0
$21$	−251.241	+	145.054i	−0.569707	+	0.328920i
$22$		0			0
$23$	350.792	−	607.590i	0.663123	−	1.14856i	−0.316667	−	0.948537i	$-0.602564\pi$
$23$	350.792	−	607.590i	0.663123	−	1.14856i	0.979791	−	0.200026i	$-0.0641027\pi$
$24$		0			0
$25$	−12.6488	+	21.9084i	−0.0202381	+	0.0350534i
$26$		0			0
$27$		−	551.569i		−	0.756611i
$28$		0			0
$29$	−37.5252	−	21.6652i	−0.0446197	−	0.0257612i	0.477524	−	0.878619i	$-0.341534\pi$
$29$	−37.5252	−	21.6652i	−0.0446197	−	0.0257612i	−0.522144	+	0.852857i	$0.674868\pi$
$30$		0			0
$31$		−	111.254i		−	0.115769i	−0.998323	−	0.0578843i	$-0.981565\pi$
$31$		−	111.254i		−	0.115769i	0.998323	−	0.0578843i	$-0.0184354\pi$
$32$		0			0
$33$	−1296.92	+	748.776i	−1.19093	+	0.687582i
$34$		0			0
$35$	−353.939	−	613.040i	−0.288929	−	0.500440i
$36$		0			0
$37$			1079.87i			0.788802i	0.918938	+	0.394401i	$0.129048\pi$
$37$			1079.87i			0.788802i	−0.918938	+	0.394401i	$0.870952\pi$
$38$		0			0
$39$	−1495.33			−0.983122
$40$		0			0
$41$	80.1784	−	46.2910i	0.0476969	−	0.0275378i	−0.475962	−	0.879466i	$-0.657900\pi$
$41$	80.1784	−	46.2910i	0.0476969	−	0.0275378i	0.523659	+	0.851928i	$0.324567\pi$
$42$		0			0
$43$	945.995	+	1638.51i	0.511625	+	0.886161i	0.999909	+	0.0134763i	$0.00428978\pi$
$43$	945.995	+	1638.51i	0.511625	+	0.886161i	−0.488284	+	0.872685i	$0.662377\pi$
$44$		0			0
$45$	−719.720			−0.355417
$46$		0			0
$47$	1366.72	−	2367.22i	0.618703	−	1.07163i	−0.371019	−	0.928625i	$-0.620992\pi$
$47$	1366.72	−	2367.22i	0.618703	−	1.07163i	0.989723	−	0.143001i	$-0.0456751\pi$
$48$		0			0
$49$	−1630.45			−0.679069
$50$		0			0
$51$	−795.547	−	459.309i	−0.305862	−	0.176589i
$52$		0			0
$53$	2153.80	+	1243.50i	0.766749	+	0.442683i	0.831714	−	0.555205i	$-0.187360\pi$
$53$	2153.80	+	1243.50i	0.766749	+	0.442683i	−0.0649646	+	0.997888i	$0.520693\pi$
$54$		0			0
$55$	−1827.05	−	3164.54i	−0.603984	−	1.04613i
$56$		0			0
$57$	−3707.95	+	696.575i	−1.14126	+	0.214397i
$58$		0			0
$59$	−5032.93	+	2905.77i	−1.44583	+	0.834750i	−0.998229	−	0.0594837i	$-0.981055\pi$
$59$	−5032.93	+	2905.77i	−1.44583	+	0.834750i	−0.447600	+	0.894234i	$0.647721\pi$
$60$		0			0
$61$	1263.85	−	2189.06i	0.339654	−	0.588299i	−0.644713	−	0.764425i	$-0.723023\pi$
$61$	1263.85	−	2189.06i	0.339654	−	0.588299i	0.984368	+	0.176126i	$0.0563565\pi$
$62$		0			0
$63$	391.723	−	678.485i	0.0986957	−	0.170946i
$64$		0			0
$65$		−	3648.67i		−	0.863591i
$66$		0			0
$67$	4300.24	+	2482.74i	0.957950	+	0.553073i	0.895542	−	0.444978i	$-0.146788\pi$
$67$	4300.24	+	2482.74i	0.957950	+	0.553073i	0.0624086	+	0.998051i	$0.480122\pi$
$68$		0			0
$69$			7332.25i			1.54007i
$70$		0			0
$71$	3720.00	−	2147.74i	0.737949	−	0.426055i	−0.0833740	−	0.996518i	$-0.526570\pi$
$71$	3720.00	−	2147.74i	0.737949	−	0.426055i	0.821323	+	0.570463i	$0.193236\pi$
$72$		0			0
$73$	−1588.81	−	2751.89i	−0.298143	−	0.516399i	0.677568	−	0.735460i	$-0.263034\pi$
$73$	−1588.81	−	2751.89i	−0.298143	−	0.516399i	−0.975711	+	0.219061i	$0.929701\pi$
$74$		0			0
$75$		−	264.385i		−	0.0470018i
$76$		0			0
$77$	3977.65			0.670880
$78$		0			0
$79$	4934.57	−	2848.97i	0.790669	−	0.456493i	−0.0495288	−	0.998773i	$-0.515772\pi$
$79$	4934.57	−	2848.97i	0.790669	−	0.456493i	0.840198	+	0.542280i	$0.182439\pi$
$80$		0			0
$81$	4025.27	+	6971.97i	0.613514	+	1.06264i
$82$		0			0
$83$	10463.5			1.51888			0.759439	−	0.650579i	$-0.225474\pi$
$83$	10463.5			1.51888			0.759439	+	0.650579i	$0.225474\pi$
$84$		0			0
$85$	1120.74	−	1941.17i	0.155119	−	0.268674i
$86$		0			0
$87$	452.845			0.0598289
$88$		0			0
$89$	4822.97	+	2784.54i	0.608884	+	0.351539i	0.772528	−	0.634980i	$-0.218992\pi$
$89$	4822.97	+	2784.54i	0.608884	+	0.351539i	−0.163645	+	0.986519i	$0.552325\pi$
$90$		0			0
$91$	3439.63	+	1985.87i	0.415364	+	0.239810i
$92$		0			0
$93$	581.355	+	1006.94i	0.0672165	+	0.116422i
$94$		0			0
$95$	−1699.68	−	9047.57i	−0.188330	−	1.00250i
$96$		0			0
$97$	−15618.3	+	9017.22i	−1.65993	+	0.958361i	−0.687185	+	0.726482i	$0.741154\pi$
$97$	−15618.3	+	9017.22i	−1.65993	+	0.958361i	−0.972745	+	0.231878i	$0.925513\pi$
$98$		0			0
$99$	2022.10	−	3502.38i	0.206315	−	0.357349i
$100$		0			0
$101$	−48.5674	+	84.1212i	−0.00476104	+	0.00824636i	−0.868396	−	0.495871i	$-0.834849\pi$
$101$	−48.5674	+	84.1212i	−0.00476104	+	0.00824636i	0.863635	+	0.504118i	$0.168182\pi$
$102$		0			0
$103$		−	1061.32i		−	0.100040i	−0.998748	−	0.0500198i	$-0.984072\pi$
$103$		−	1061.32i		−	0.100040i	0.998748	−	0.0500198i	$-0.0159285\pi$
$104$		0			0
$105$	6406.87	+	3699.01i	0.581122	+	0.335511i
$106$		0			0
$107$		−	86.6771i		−	0.00757072i	−0.999993	−	0.00378536i	$-0.998795\pi$
$107$		−	86.6771i		−	0.00757072i	0.999993	−	0.00378536i	$-0.00120492\pi$
$108$		0			0
$109$	−17989.3	+	10386.1i	−1.51412	+	0.874179i	−0.514260	+	0.857634i	$0.671933\pi$
$109$	−17989.3	+	10386.1i	−1.51412	+	0.874179i	−0.999863	+	0.0165449i	$0.994733\pi$
$110$		0			0
$111$	−5642.86	−	9773.72i	−0.457987	−	0.793257i
$112$		0			0
$113$		−	18503.4i		−	1.44909i	−0.689227	−	0.724546i	$-0.742050\pi$
$113$		−	18503.4i		−	1.44909i	0.689227	−	0.724546i	$-0.257950\pi$
$114$		0			0
$115$	−17891.1			−1.35282
$116$		0			0
$117$	3497.17	−	2019.09i	0.255473	−	0.147498i
$118$		0			0
$119$	1219.97	+	2113.05i	0.0861500	+	0.149216i
$120$		0			0
$121$	5891.84			0.402421
$122$		0			0
$123$	−483.787	+	837.944i	−0.0319775	+	0.0553866i
$124$		0			0
$125$	−15293.0			−0.978750
$126$		0			0
$127$	16075.2	+	9281.03i	0.996665	+	0.575425i	0.907260	−	0.420571i	$-0.138170\pi$
$127$	16075.2	+	9281.03i	0.996665	+	0.575425i	0.0894051	+	0.995995i	$0.471503\pi$
$128$		0			0
$129$	−17124.1	−	9886.59i	−1.02903	−	0.594111i
$130$		0			0
$131$	−7020.17	−	12159.3i	−0.409077	−	0.708542i	0.585710	−	0.810521i	$-0.300816\pi$
$131$	−7020.17	−	12159.3i	−0.409077	−	0.708542i	−0.994787	+	0.101979i	$0.967483\pi$
$132$		0			0
$133$	9454.29	+	3322.04i	0.534473	+	0.187803i
$134$		0			0
$135$	−12181.1	+	7032.76i	−0.668373	+	0.385886i
$136$		0			0
$137$	8900.54	−	15416.2i	0.474215	−	0.821364i	−0.525349	−	0.850887i	$-0.676065\pi$
$137$	8900.54	−	15416.2i	0.474215	−	0.821364i	0.999564	+	0.0295224i	$0.00939864\pi$
$138$		0			0
$139$	−18227.9	+	31571.7i	−0.943426	+	1.63406i	−0.184554	+	0.982822i	$0.559084\pi$
$139$	−18227.9	+	31571.7i	−0.943426	+	1.63406i	−0.758872	+	0.651240i	$0.774249\pi$
$140$		0			0
$141$			28567.1i			1.43690i
$142$		0			0
$143$	17755.5	+	10251.2i	0.868284	+	0.501304i
$144$		0			0
$145$			1104.96i			0.0525548i
$146$		0			0
$147$	14756.9	−	8519.89i	0.682904	−	0.394275i
$148$		0			0
$149$	−10085.2	−	17468.1i	−0.454268	−	0.786816i	0.544378	−	0.838840i	$-0.316766\pi$
$149$	−10085.2	−	17468.1i	−0.454268	−	0.786816i	−0.998646	+	0.0520247i	$0.983433\pi$
$150$		0			0
$151$			1839.49i			0.0806759i	0.999186	+	0.0403379i	$0.0128434\pi$
$151$			1839.49i			0.0806759i	−0.999186	+	0.0403379i	$0.987157\pi$
$152$		0			0
$153$	2480.76			0.105975
$154$		0			0
$155$	−2456.97	+	1418.54i	−0.102267	+	0.0590441i
$156$		0			0
$157$	−13219.3	−	22896.5i	−0.536301	−	0.928901i	−0.999099	−	0.0424369i	$-0.986488\pi$
$157$	−13219.3	−	22896.5i	−0.536301	−	0.928901i	0.462798	−	0.886464i	$-0.346845\pi$
$158$		0			0
$159$	−25991.5			−1.02811
$160$		0			0
$161$	9737.59	−	16866.0i	0.375664	−	0.650670i
$162$		0			0
$163$	−13879.3			−0.522386			−0.261193	−	0.965287i	$-0.584116\pi$
$163$	−13879.3			−0.522386			−0.261193	+	0.965287i	$0.584116\pi$
$164$		0			0
$165$	33072.6	+	19094.5i	1.21479	+	0.701359i
$166$		0			0
$167$	−13289.5	−	7672.69i	−0.476514	−	0.275115i	0.242449	−	0.970164i	$-0.422049\pi$
$167$	−13289.5	−	7672.69i	−0.476514	−	0.275115i	−0.718962	+	0.695049i	$0.755383\pi$
$168$		0			0
$169$	−4044.56	−	7005.39i	−0.141611	−	0.245278i
$170$		0			0
$171$	7731.34	−	6635.83i	0.264401	−	0.226936i
$172$		0			0
$173$	14804.8	−	8547.56i	0.494664	−	0.285594i	−0.231843	−	0.972753i	$-0.574476\pi$
$173$	14804.8	−	8547.56i	0.494664	−	0.285594i	0.726507	+	0.687159i	$0.241142\pi$
$174$		0			0
$175$	−351.116	+	608.152i	−0.0114650	+	0.0198580i
$176$		0			0
$177$	30368.1	−	52599.2i	0.969330	−	1.67893i
$178$		0			0
$179$			30559.4i			0.953758i	0.878969	+	0.476879i	$0.158232\pi$
$179$			30559.4i			0.953758i	−0.878969	+	0.476879i	$0.841768\pi$
$180$		0			0
$181$	48767.9	+	28156.2i	1.48860	+	0.859441i	0.999915	−	0.0130215i	$-0.00414497\pi$
$181$	48767.9	+	28156.2i	1.48860	+	0.859441i	0.488681	+	0.872463i	$0.337478\pi$
$182$		0			0
$183$			26417.1i			0.788828i
$184$		0			0
$185$	23848.3	−	13768.9i	0.696811	−	0.402304i
$186$		0			0
$187$	6297.56	+	10907.7i	0.180090	+	0.311925i
$188$		0			0
$189$		−	15310.9i		−	0.428626i
$190$		0			0
$191$	−20263.1			−0.555443			−0.277721	−	0.960662i	$-0.589579\pi$
$191$	−20263.1			−0.555443			−0.277721	+	0.960662i	$0.589579\pi$
$192$		0			0
$193$	902.539	−	521.081i	0.0242299	−	0.0139891i	−0.487836	−	0.872935i	$-0.662214\pi$
$193$	902.539	−	521.081i	0.0242299	−	0.0139891i	0.512066	+	0.858946i	$0.328880\pi$
$194$		0			0
$195$	19066.1	+	33023.5i	0.501410	+	0.868468i
$196$		0			0
$197$	59986.7			1.54569			0.772845	−	0.634594i	$-0.218833\pi$
$197$	59986.7			1.54569			0.772845	+	0.634594i	$0.218833\pi$
$198$		0			0
$199$	−24312.1	+	42109.9i	−0.613928	+	1.06335i	0.376644	+	0.926358i	$0.377078\pi$
$199$	−24312.1	+	42109.9i	−0.613928	+	1.06335i	−0.990572	+	0.136996i	$0.956255\pi$
$200$		0			0
$201$	−51894.3			−1.28448
$202$		0			0
$203$	−1041.66	−	601.401i	−0.0252774	−	0.0145939i
$204$		0			0
$205$	−2044.62	−	1180.46i	−0.0486526	−	0.0280896i
$206$		0			0
$207$	−9900.51	−	17148.2i	−0.231056	−	0.400200i
$208$		0			0
$209$	48803.6	+	17148.6i	1.11727	+	0.392586i
$210$		0			0
$211$	30887.6	−	17833.0i	0.693777	−	0.400552i	−0.111248	−	0.993793i	$-0.535485\pi$
$211$	30887.6	−	17833.0i	0.693777	−	0.400552i	0.805025	+	0.593240i	$0.202152\pi$
$212$		0			0
$213$	−22446.1	+	38877.7i	−0.494744	+	0.856923i
$214$		0			0
$215$	24123.8	−	41783.6i	0.521877	−	0.903918i
$216$		0			0
$217$		−	3088.27i		−	0.0655838i
$218$		0			0
$219$	28760.0	+	16604.6i	0.599654	+	0.346211i
$220$		0			0
$221$			12576.4i			0.257497i
$222$		0			0
$223$	31201.2	−	18014.0i	0.627425	−	0.362244i	−0.152329	−	0.988330i	$-0.548677\pi$
$223$	31201.2	−	18014.0i	0.627425	−	0.362244i	0.779754	+	0.626086i	$0.215344\pi$
$224$		0			0
$225$	356.991	+	618.326i	0.00705167	+	0.0122139i
$226$		0			0
$227$		−	92863.0i		−	1.80215i	−0.433663	−	0.901075i	$-0.642779\pi$
$227$		−	92863.0i		−	1.80215i	0.433663	−	0.901075i	$-0.357221\pi$
$228$		0			0
$229$	−56402.1			−1.07553			−0.537767	−	0.843094i	$-0.680732\pi$
$229$	−56402.1			−1.07553			−0.537767	+	0.843094i	$0.680732\pi$
$230$		0			0
$231$	−36001.0	+	20785.2i	−0.674669	+	0.389520i
$232$		0			0
$233$	−23210.6	−	40202.0i	−0.427538	−	0.740518i	0.569115	−	0.822258i	$-0.307286\pi$
$233$	−23210.6	−	40202.0i	−0.427538	−	0.740518i	−0.996654	+	0.0817394i	$0.973952\pi$
$234$		0			0
$235$	−69705.1			−1.26220
$236$		0			0
$237$	−29774.6	+	51571.1i	−0.530090	+	0.918142i
$238$		0			0
$239$	−35290.9			−0.617828			−0.308914	−	0.951090i	$-0.599965\pi$
$239$	−35290.9			−0.617828			−0.308914	+	0.951090i	$0.599965\pi$
$240$		0			0
$241$	−96639.8	−	55795.0i	−1.66388	−	0.960642i	−0.970835	−	0.239748i	$-0.922935\pi$
$241$	−96639.8	−	55795.0i	−1.66388	−	0.960642i	−0.693045	−	0.720894i	$-0.743731\pi$
$242$		0			0
$243$	−34172.5	−	19729.5i	−0.578714	−	0.334121i
$244$		0			0
$245$	20788.9	+	36007.5i	0.346338	+	0.599875i
$246$		0			0
$247$	33640.8	+	39194.5i	0.551407	+	0.642439i
$248$		0			0
$249$	−94703.8	+	54677.2i	−1.52746	+	0.881877i
$250$		0			0
$251$	18656.9	−	32314.8i	0.296137	−	0.512924i	−0.679112	−	0.734035i	$-0.737635\pi$
$251$	18656.9	−	32314.8i	0.296137	−	0.512924i	0.975249	+	0.221111i	$0.0709682\pi$
$252$		0			0
$253$	50266.0	−	87063.3i	0.785296	−	1.36017i
$254$		0			0
$255$			23425.6i			0.360256i
$256$		0			0
$257$	−54521.2	−	31477.8i	−0.825466	−	0.476583i	0.0268315	−	0.999640i	$-0.491458\pi$
$257$	−54521.2	−	31477.8i	−0.825466	−	0.476583i	−0.852298	+	0.523057i	$0.824792\pi$
$258$		0			0
$259$			29976.0i			0.446862i
$260$		0			0
$261$	−1059.08	+	611.462i	−0.0155471	+	0.00897612i
$262$		0			0
$263$	43980.5	+	76176.4i	0.635841	+	1.10131i	0.986336	+	0.164745i	$0.0526800\pi$
$263$	43980.5	+	76176.4i	0.635841	+	1.10131i	−0.350495	+	0.936565i	$0.613987\pi$
$264$		0			0
$265$		−	63420.6i		−	0.903106i
$266$		0			0
$267$	−58202.5			−0.816430
$268$		0			0
$269$	−51001.2	+	29445.6i	−0.704816	+	0.406926i	−0.809139	−	0.587618i	$-0.800066\pi$
$269$	−51001.2	+	29445.6i	−0.704816	+	0.406926i	0.104323	+	0.994544i	$0.466733\pi$
$270$		0			0
$271$	44150.5	+	76470.9i	0.601170	+	1.04126i	0.992644	+	0.121068i	$0.0386318\pi$
$271$	44150.5	+	76470.9i	0.601170	+	1.04126i	−0.391475	+	0.920189i	$0.628035\pi$
$272$		0			0
$273$	−41508.6			−0.556946
$274$		0			0
$275$	−1812.48	+	3139.31i	−0.0239667	+	0.0415116i
$276$		0			0
$277$	73761.7			0.961327			0.480664	−	0.876905i	$-0.340396\pi$
$277$	73761.7			0.961327			0.480664	+	0.876905i	$0.340396\pi$
$278$		0			0
$279$	−2719.27	−	1569.97i	−0.0349336	−	0.0201689i
$280$		0			0
$281$	51830.2	+	29924.2i	0.656403	+	0.378975i	0.790905	−	0.611939i	$-0.209610\pi$
$281$	51830.2	+	29924.2i	0.656403	+	0.378975i	−0.134502	+	0.990913i	$0.542943\pi$
$282$		0			0
$283$	−70780.2	−	122595.i	−0.883769	−	1.53073i	−0.847118	−	0.531404i	$-0.821664\pi$
$283$	−70780.2	−	122595.i	−0.883769	−	1.53073i	−0.0366506	−	0.999328i	$-0.511669\pi$
$284$		0			0
$285$	62661.5	+	73006.3i	0.771456	+	0.898816i
$286$		0			0
$287$	2225.66	−	1284.99i	0.0270206	−	0.0156004i
$288$		0			0
$289$	37897.5	−	65640.4i	0.453748	−	0.785915i
$290$		0			0
$291$	94238.9	−	163227.i	1.11287	−	1.92755i
$292$		0			0
$293$			171279.i			1.99512i	0.0697935	+	0.997561i	$0.477766\pi$
$293$			171279.i			1.99512i	−0.0697935	+	0.997561i	$0.522234\pi$
$294$		0			0
$295$	128344.	+	74099.7i	1.47480	+	0.851476i
$296$		0			0
$297$		−	79035.9i		−	0.896007i
$298$		0			0
$299$	86933.9	−	50191.3i	0.972404	−	0.561418i
$300$		0			0
$301$	26259.8	+	45483.2i	0.289840	+	0.502017i
$302$		0			0
$303$		−	1015.15i		−	0.0110572i
$304$		0			0
$305$	−64458.9			−0.692921
$306$		0			0
$307$	23997.7	−	13855.1i	0.254620	−	0.147005i	−0.367258	−	0.930119i	$-0.619703\pi$
$307$	23997.7	−	13855.1i	0.254620	−	0.147005i	0.621878	+	0.783114i	$0.286370\pi$
$308$		0			0
$309$	5545.93	+	9605.83i	0.0580841	+	0.100605i
$310$		0			0
$311$	−189674.			−1.96105			−0.980524	−	0.196401i	$-0.937075\pi$
$311$	−189674.			−1.96105			−0.980524	+	0.196401i	$0.937075\pi$
$312$		0			0
$313$	−79050.5	+	136919.i	−0.806893	+	1.39758i	0.108113	+	0.994139i	$0.465519\pi$
$313$	−79050.5	+	136919.i	−0.806893	+	1.39758i	−0.915006	+	0.403441i	$0.867814\pi$
$314$		0			0
$315$	−19978.6			−0.201347
$316$		0			0
$317$	39512.7	+	22812.7i	0.393204	+	0.227017i	0.683548	−	0.729906i	$-0.260436\pi$
$317$	39512.7	+	22812.7i	0.393204	+	0.227017i	−0.290343	+	0.956923i	$0.593769\pi$
$318$		0			0
$319$	−5377.09	−	3104.46i	−0.0528404	−	0.0305074i
$320$		0			0
$321$	452.931	+	784.500i	0.00439564	+	0.00761347i
$322$		0			0
$323$	5858.52	+	31185.6i	0.0561543	+	0.298915i
$324$		0			0
$325$	−3134.65	+	1809.79i	−0.0296771	+	0.0171341i
$326$		0			0
$327$	108545.	−	188006.i	1.01512	−	1.75823i
$328$		0			0
$329$	37938.5	−	65711.4i	0.350500	−	0.607084i
$330$		0			0
$331$			51241.9i			0.467702i	0.972272	+	0.233851i	$0.0751328\pi$
$331$			51241.9i			0.467702i	−0.972272	+	0.233851i	$0.924867\pi$
$332$		0			0
$333$	26394.3	+	15238.7i	0.238024	+	0.137423i
$334$		0			0
$335$		−	126625.i		−	1.12831i
$336$		0			0
$337$	7928.49	−	4577.52i	0.0698121	−	0.0403060i	−0.464688	−	0.885475i	$-0.653833\pi$
$337$	7928.49	−	4577.52i	0.0698121	−	0.0403060i	0.534500	+	0.845169i	$0.320500\pi$
$338$		0			0
$339$	96689.7	+	167471.i	0.841358	+	1.45727i
$340$		0			0
$341$		−	15941.8i		−	0.137098i
$342$		0			0
$343$	−111908.			−0.951205
$344$		0			0
$345$	161929.	−	93489.6i	1.36046	−	0.785462i
$346$		0			0
$347$	76816.1	+	133049.i	0.637960	+	1.10498i	0.985880	+	0.167455i	$0.0535548\pi$
$347$	76816.1	+	133049.i	0.637960	+	1.10498i	−0.347920	+	0.937524i	$0.613112\pi$
$348$		0			0
$349$	168335.			1.38205			0.691023	−	0.722832i	$-0.257160\pi$
$349$	168335.			1.38205			0.691023	+	0.722832i	$0.257160\pi$
$350$		0			0
$351$	39459.2	−	68345.4i	0.320283	−	0.554747i
$352$		0			0
$353$	−130340.			−1.04599			−0.522994	−	0.852336i	$-0.675185\pi$
$353$	−130340.			−1.04599			−0.522994	+	0.852336i	$0.675185\pi$
$354$		0			0
$355$	−94863.5	−	54769.5i	−0.752736	−	0.434592i
$356$		0			0
$357$	−22083.5	−	12749.9i	−0.173273	−	0.100039i
$358$		0			0
$359$	−18849.9	−	32649.0i	−0.146258	−	0.253327i	0.783583	−	0.621287i	$-0.213390\pi$
$359$	−18849.9	−	32649.0i	−0.146258	−	0.253327i	−0.929842	+	0.367960i	$0.880056\pi$
$360$		0			0
$361$	101677.	+	81519.2i	0.780203	+	0.625526i
$362$		0			0
$363$	−53326.0	+	30787.8i	−0.404693	+	0.233650i
$364$		0			0
$365$	−40516.0	+	70175.8i	−0.304117	+	0.526747i
$366$		0			0
$367$	48448.8	−	83915.8i	0.359709	−	0.623034i	−0.628203	−	0.778049i	$-0.716209\pi$
$367$	48448.8	−	83915.8i	0.359709	−	0.623034i	0.987912	+	0.155015i	$0.0495427\pi$
$368$		0			0
$369$		−	2612.97i		−	0.0191903i
$370$		0			0
$371$	59787.0	+	34518.0i	0.434369	+	0.250783i
$372$		0			0
$373$			125723.i			0.903644i	0.892108	+	0.451822i	$0.149226\pi$
$373$			125723.i			0.903644i	−0.892108	+	0.451822i	$0.850774\pi$
$374$		0			0
$375$	138414.	−	79913.4i	0.984278	−	0.568273i
$376$		0			0
$377$	−3099.85	−	5369.10i	−0.0218101	−	0.0377762i
$378$		0			0
$379$			7410.05i			0.0515873i	0.999667	+	0.0257936i	$0.00821128\pi$
$379$			7410.05i			0.0515873i	−0.999667	+	0.0257936i	$0.991789\pi$
$380$		0			0
$381$	−193992.			−1.33639
$382$		0			0
$383$	−105519.	+	60921.6i	−0.719340	+	0.415311i	−0.814510	−	0.580150i	$-0.802994\pi$
$383$	−105519.	+	60921.6i	−0.719340	+	0.415311i	0.0951699	+	0.995461i	$0.469661\pi$
$384$		0			0
$385$	−50716.9	−	87844.2i	−0.342161	−	0.592641i
$386$		0			0
$387$	53398.2			0.356537
$388$		0			0
$389$	−129529.	+	224351.i	−0.855990	+	1.48262i	0.0197344	+	0.999805i	$0.493718\pi$
$389$	−129529.	+	224351.i	−0.855990	+	1.48262i	−0.875724	+	0.482812i	$0.839615\pi$
$390$		0			0
$391$	61667.6			0.403370
$392$		0			0
$393$	127077.	+	73367.7i	0.822774	+	0.475029i
$394$		0			0
$395$	−125836.	−	72651.5i	−0.806512	−	0.465640i
$396$		0			0
$397$	−109875.	−	190310.i	−0.697139	−	1.20748i	−0.969454	−	0.245273i	$-0.921122\pi$
$397$	−109875.	−	190310.i	−0.697139	−	1.20748i	0.272315	−	0.962208i	$-0.412211\pi$
$398$		0			0
$399$	−102928.	+	19336.1i	−0.646531	+	0.121457i
$400$		0			0
$401$	−200338.	+	115665.i	−1.24588	+	0.719307i	−0.970284	−	0.241967i	$-0.922207\pi$
$401$	−200338.	+	115665.i	−1.24588	+	0.719307i	−0.275593	+	0.961275i	$0.588874\pi$
$402$		0			0
$403$	7959.08	−	13785.5i	0.0490064	−	0.0848816i
$404$		0			0
$405$	102648.	−	177792.i	0.625807	−	1.08393i
$406$		0			0
$407$			154738.i			0.934130i
$408$		0			0
$409$	36379.7	+	21003.8i	0.217477	+	0.125560i	0.604781	−	0.796392i	$-0.293261\pi$
$409$	36379.7	+	21003.8i	0.217477	+	0.125560i	−0.387305	+	0.921952i	$0.626594\pi$
$410$		0			0
$411$			186039.i			1.10134i
$412$		0			0
$413$	−139709.	+	80660.8i	−0.819073	+	0.472892i
$414$		0			0
$415$	−133415.	−	231082.i	−0.774656	−	1.34174i
$416$		0			0
$417$		−	381000.i		−	2.19105i
$418$		0			0
$419$	−17406.8			−0.0991494			−0.0495747	−	0.998770i	$-0.515787\pi$
$419$	−17406.8			−0.0991494			−0.0495747	+	0.998770i	$0.515787\pi$
$420$		0			0
$421$	−161802.	+	93416.2i	−0.912891	+	0.527058i	−0.881360	−	0.472445i	$-0.843371\pi$
$421$	−161802.	+	93416.2i	−0.912891	+	0.527058i	−0.0315305	+	0.999503i	$0.510038\pi$
$422$		0			0
$423$	−38573.2	−	66810.8i	−0.215578	−	0.373393i
$424$		0			0
$425$	−2223.60			−0.0123106
$426$		0			0
$427$	35083.2	−	60765.8i	0.192417	−	0.333276i
$428$		0			0
$429$	−214270.			−1.16425
$430$		0			0
$431$	9163.54	+	5290.57i	0.0493297	+	0.0284805i	0.524462	−	0.851434i	$-0.324266\pi$
$431$	9163.54	+	5290.57i	0.0493297	+	0.0284805i	−0.475132	+	0.879914i	$0.657600\pi$
$432$		0			0
$433$	−188173.	−	108642.i	−1.00365	−	0.579458i	−0.0943244	−	0.995542i	$-0.530069\pi$
$433$	−188173.	−	108642.i	−1.00365	−	0.579458i	−0.909326	+	0.416083i	$0.863402\pi$
$434$		0			0
$435$	−5773.99	−	10000.8i	−0.0305139	−	0.0528516i
$436$		0			0
$437$	192188.	−	164956.i	1.00638	−	0.863782i
$438$		0			0
$439$	−27000.5	+	15588.7i	−0.140101	+	0.0808875i	−0.568412	−	0.822744i	$-0.692442\pi$
$439$	−27000.5	+	15588.7i	−0.140101	+	0.0808875i	0.428311	+	0.903631i	$0.359109\pi$
$440$		0			0
$441$	−23008.3	+	39851.5i	−0.118306	+	0.204912i
$442$		0			0
$443$	−84484.4	+	146331.i	−0.430496	+	0.745641i	−0.996916	−	0.0784760i	$-0.974995\pi$
$443$	−84484.4	+	146331.i	−0.430496	+	0.745641i	0.566420	+	0.824117i	$0.308328\pi$
$444$		0			0
$445$		−	142017.i		−	0.717166i
$446$		0			0
$447$	182559.	+	105400.i	0.913667	+	0.527506i
$448$		0			0
$449$			240682.i			1.19385i	0.802297	+	0.596926i	$0.203611\pi$
$449$			240682.i			1.19385i	−0.802297	+	0.596926i	$0.796389\pi$
$450$		0			0
$451$	11489.0	−	6633.17i	0.0564845	−	0.0326113i
$452$		0			0
$453$	−9612.25	−	16648.9i	−0.0468413	−	0.0811315i
$454$		0			0
$455$		−	101283.i		−	0.489231i
$456$		0			0
$457$	227190.			1.08782			0.543911	−	0.839143i	$-0.316943\pi$
$457$	227190.			1.08782			0.543911	+	0.839143i	$0.316943\pi$
$458$		0			0
$459$	41986.4	−	24240.8i	0.199289	−	0.115059i
$460$		0			0
$461$	−14069.9	−	24369.7i	−0.0662046	−	0.114670i	0.831023	−	0.556238i	$-0.187756\pi$
$461$	−14069.9	−	24369.7i	−0.0662046	−	0.114670i	−0.897228	+	0.441568i	$0.854422\pi$
$462$		0			0
$463$	81970.7			0.382381			0.191191	−	0.981553i	$-0.438765\pi$
$463$	81970.7			0.382381			0.191191	+	0.981553i	$0.438765\pi$
$464$		0			0
$465$	14825.1	−	25677.8i	0.0685633	−	0.118755i
$466$		0			0
$467$	−126102.			−0.578213			−0.289106	−	0.957297i	$-0.593358\pi$
$467$	−126102.			−0.578213			−0.289106	+	0.957297i	$0.593358\pi$
$468$		0			0
$469$	119370.	+	68918.2i	0.542686	+	0.313320i
$470$		0			0
$471$	239291.	+	138155.i	1.07866	+	0.622764i
$472$		0			0
$473$	135554.	+	234787.i	0.605886	+	1.04943i
$474$		0			0
$475$	−6929.89	+	5947.94i	−0.0307142	+	0.0263621i
$476$		0			0
$477$	60787.3	−	35095.5i	0.267163	−	0.154246i
$478$		0			0
$479$	−57621.7	+	99803.7i	−0.251139	+	0.434986i	−0.963840	−	0.266482i	$-0.914139\pi$
$479$	−57621.7	+	99803.7i	−0.251139	+	0.434986i	0.712700	+	0.701469i	$0.247472\pi$
$480$		0			0
$481$	−77253.9	+	133808.i	−0.333911	+	0.578350i
$482$		0			0
$483$			203535.i			0.872459i
$484$		0			0
$485$	398281.	+	229947.i	1.69319	+	0.977564i
$486$		0			0
$487$		−	135408.i		−	0.570935i	−0.958388	−	0.285467i	$-0.907851\pi$
$487$		−	135408.i		−	0.570935i	0.958388	−	0.285467i	$-0.0921488\pi$
$488$		0			0
$489$	125619.	−	72526.1i	0.525336	−	0.303303i
$490$		0			0
$491$	−202101.	−	350049.i	−0.838312	−	1.45200i	−0.891305	−	0.453404i	$-0.850210\pi$
$491$	−202101.	−	350049.i	−0.838312	−	1.45200i	0.0529937	−	0.998595i	$-0.483124\pi$
$492$		0			0
$493$		−	3808.64i		−	0.0156702i
$494$		0			0
$495$	−103131.			−0.420899
$496$		0			0
$497$	103263.	−	59619.0i	0.418054	−	0.241363i
$498$		0			0
$499$	220006.	+	381062.i	0.883557	+	1.53037i	0.847359	+	0.531020i	$0.178191\pi$
$499$	220006.	+	381062.i	0.883557	+	1.53037i	0.0361977	+	0.999345i	$0.488475\pi$
$500$		0			0
$501$	160375.			0.638940
$502$		0			0
$503$	140225.	−	242877.i	0.554229	−	0.959953i	−0.443734	−	0.896159i	$-0.646346\pi$
$503$	140225.	−	242877.i	0.554229	−	0.959953i	0.997963	−	0.0637944i	$-0.0203202\pi$
$504$		0			0
$505$	2477.03			0.00971288
$506$		0			0
$507$	73213.2	+	42269.7i	0.284822	+	0.164442i
$508$		0			0
$509$	−87780.5	−	50680.1i	−0.338815	−	0.195615i	0.320933	−	0.947102i	$-0.396004\pi$
$509$	−87780.5	−	50680.1i	−0.338815	−	0.195615i	−0.659748	+	0.751487i	$0.729337\pi$
$510$		0			0
$511$	−44103.5	−	76389.4i	−0.168900	−	0.292544i
$512$		0			0
$513$	66009.0	−	187857.i	0.250824	−	0.713826i
$514$		0			0
$515$	−23438.7	+	13532.3i	−0.0883729	+	0.0510221i
$516$		0			0
$517$	195841.	−	339206.i	0.732692	−	1.26906i
$518$		0			0
$519$	−89330.5	+	154725.i	−0.331638	+	0.574415i
$520$		0			0
$521$			3847.69i			0.0141751i	0.999975	+	0.00708753i	$0.00225605\pi$
$521$			3847.69i			0.0141751i	−0.999975	+	0.00708753i	$0.997744\pi$
$522$		0			0
$523$	126432.	+	72995.3i	0.462223	+	0.266865i	0.712979	−	0.701186i	$-0.247346\pi$
$523$	126432.	+	72995.3i	0.462223	+	0.266865i	−0.250755	+	0.968051i	$0.580679\pi$
$524$		0			0
$525$		−	7339.03i		−	0.0266269i
$526$		0			0
$527$	8468.81	−	4889.47i	0.0304931	−	0.0176052i
$528$		0			0
$529$	−106190.	−	183926.i	−0.379464	−	0.657252i
$530$		0			0
$531$			164021.i			0.581713i
$532$		0			0
$533$	13246.6			0.0466285
$534$		0			0
$535$	−1914.22	+	1105.17i	−0.00668781	+	0.00386121i
$536$		0			0
$537$	−159688.	−	276587.i	−0.553762	−	0.959144i
$538$		0			0
$539$	−233631.			−0.804180
$540$		0			0
$541$	210834.	−	365176.i	0.720355	−	1.24769i	−0.240502	−	0.970649i	$-0.577312\pi$
$541$	210834.	−	365176.i	0.720355	−	1.24769i	0.960857	−	0.277043i	$-0.0893546\pi$
$542$		0			0
$543$	−588520.			−1.99600
$544$		0			0
$545$	458744.	+	264856.i	1.54446	+	0.891696i
$546$		0			0
$547$	86529.9	+	49958.1i	0.289196	+	0.166967i	0.637579	−	0.770385i	$-0.279936\pi$
$547$	86529.9	+	49958.1i	0.289196	+	0.166967i	−0.348383	+	0.937352i	$0.613269\pi$
$548$		0			0
$549$	−35670.1	−	61782.5i	−0.118348	−	0.204984i
$550$		0			0
$551$	−10187.8	−	11869.7i	−0.0335565	−	0.0390963i
$552$		0			0
$553$	136978.	−	79084.3i	0.447920	−	0.258607i
$554$		0			0
$555$	−143898.	+	249239.i	−0.467164	+	0.809152i
$556$		0			0
$557$	−128227.	+	222096.i	−0.413304	+	0.715864i	−0.995249	−	0.0973645i	$-0.968959\pi$
$557$	−128227.	+	222096.i	−0.413304	+	0.715864i	0.581945	+	0.813228i	$0.302292\pi$
$558$		0			0
$559$			270706.i			0.866312i
$560$		0			0
$561$	−113996.	−	65815.7i	−0.362213	−	0.209124i
$562$		0			0
$563$		−	5702.78i		−	0.0179916i	−0.999960	−	0.00899580i	$-0.997137\pi$
$563$		−	5702.78i		−	0.0179916i	0.999960	−	0.00899580i	$-0.00286349\pi$
$564$		0			0
$565$	−408639.	+	235928.i	−1.28010	+	0.739064i
$566$		0			0
$567$	111737.	+	193534.i	0.347560	+	0.601992i
$568$		0			0
$569$		−	264278.i		−	0.816275i	−0.912920	−	0.408138i	$-0.866178\pi$
$569$		−	264278.i		−	0.816275i	0.912920	−	0.408138i	$-0.133822\pi$
$570$		0			0
$571$	−140891.			−0.432126			−0.216063	−	0.976379i	$-0.569322\pi$
$571$	−140891.			−0.432126			−0.216063	+	0.976379i	$0.569322\pi$
$572$		0			0
$573$	183398.	−	105885.i	0.558579	−	0.322496i
$574$		0			0
$575$	8874.20	+	15370.6i	0.0268407	+	0.0464894i
$576$		0			0
$577$	−33455.7			−0.100489			−0.0502445	−	0.998737i	$-0.516000\pi$
$577$	−33455.7			−0.100489			−0.0502445	+	0.998737i	$0.516000\pi$
$578$		0			0
$579$	−5445.82	+	9432.43i	−0.0162445	+	0.0281363i
$580$		0			0
$581$	290456.			0.860456
$582$		0			0
$583$	308624.	+	178184.i	0.908014	+	0.524242i
$584$		0			0
$585$	−89181.2	−	51488.8i	−0.260592	−	0.150453i
$586$		0			0
$587$	−151917.	−	263128.i	−0.440890	−	0.763644i	0.556866	−	0.830602i	$-0.312004\pi$
$587$	−151917.	−	263128.i	−0.440890	−	0.763644i	−0.997756	+	0.0669588i	$0.978670\pi$
$588$		0			0
$589$	13314.3	−	37891.4i	0.0383784	−	0.109222i
$590$		0			0
$591$	−542929.	+	313460.i	−1.55442	+	0.897445i
$592$		0			0
$593$	−130746.	+	226459.i	−0.371809	+	0.643992i	−0.989844	−	0.142158i	$-0.954596\pi$
$593$	−130746.	+	226459.i	−0.371809	+	0.643992i	0.618035	+	0.786151i	$0.287929\pi$
$594$		0			0
$595$	31110.4	−	53884.8i	0.0878763	−	0.152206i
$596$		0			0
$597$		−	508172.i		−	1.42581i
$598$		0			0
$599$	−422627.	−	244004.i	−1.17789	−	0.680053i	−0.222361	−	0.974964i	$-0.571376\pi$
$599$	−422627.	−	244004.i	−1.17789	−	0.680053i	−0.955524	+	0.294912i	$0.904710\pi$
$600$		0			0
$601$			362708.i			1.00417i	0.864818	+	0.502086i	$0.167434\pi$
$601$			362708.i			1.00417i	−0.864818	+	0.502086i	$0.832566\pi$
$602$		0			0
$603$	121367.	−	70071.2i	0.333784	−	0.192710i
$604$		0			0
$605$	−75123.7	−	130118.i	−0.205242	−	0.355490i
$606$		0			0
$607$			560324.i			1.52077i	0.649475	+	0.760383i	$0.274989\pi$
$607$			560324.i			1.52077i	−0.649475	+	0.760383i	$0.725011\pi$
$608$		0			0
$609$	12570.5			0.0338935
$610$		0			0
$611$	338702.	−	195550.i	0.907267	−	0.523811i
$612$		0			0
$613$	−197665.	−	342365.i	−0.526027	−	0.911106i	−0.999540	−	0.0303191i	$-0.990348\pi$
$613$	−197665.	−	342365.i	−0.526027	−	0.911106i	0.473513	−	0.880787i	$-0.342986\pi$
$614$		0			0
$615$	24674.1			0.0652365
$616$		0			0
$617$	−47374.0	+	82054.2i	−0.124443	+	0.215541i	−0.921515	−	0.388343i	$-0.873048\pi$
$617$	−47374.0	+	82054.2i	−0.124443	+	0.215541i	0.797072	+	0.603884i	$0.206381\pi$
$618$		0			0
$619$	255301.			0.666303			0.333151	−	0.942873i	$-0.391888\pi$
$619$	255301.			0.666303			0.333151	+	0.942873i	$0.391888\pi$
$620$		0			0
$621$	−335128.	−	193486.i	−0.869015	−	0.501726i
$622$		0			0
$623$	133880.	+	77295.7i	0.344937	+	0.199150i
$624$		0			0
$625$	202898.	+	351430.i	0.519419	+	0.899660i
$626$		0			0
$627$	−531322.	+	99814.2i	−1.35152	+	0.253897i
$628$		0			0
$629$	−82201.5	+	47459.1i	−0.207768	+	0.119955i
$630$		0			0
$631$	392479.	−	679794.i	0.985730	−	1.70733i	0.347084	−	0.937834i	$-0.387172\pi$
$631$	392479.	−	679794.i	0.985730	−	1.70733i	0.638646	−	0.769501i	$-0.279495\pi$
$632$		0			0
$633$	−186372.	+	322807.i	−0.465130	+	0.805629i
$634$		0			0
$635$		−	473350.i		−	1.17391i
$636$		0			0
$637$	−202030.	−	116642.i	−0.497894	−	0.287459i
$638$		0			0
$639$		−	121233.i		−	0.296906i
$640$		0			0
$641$	−55185.8	+	31861.5i	−0.134311	+	0.0775444i	−0.565650	−	0.824646i	$-0.691375\pi$
$641$	−55185.8	+	31861.5i	−0.134311	+	0.0775444i	0.431339	+	0.902190i	$0.358041\pi$
$642$		0			0
$643$	−114558.	−	198420.i	−0.277079	−	0.479915i	0.693579	−	0.720381i	$-0.256033\pi$
$643$	−114558.	−	198420.i	−0.277079	−	0.479915i	−0.970657	+	0.240466i	$0.922700\pi$
$644$		0			0
$645$			504235.i			1.21203i
$646$		0			0
$647$	439341.			1.04953			0.524763	−	0.851248i	$-0.324154\pi$
$647$	439341.			1.04953			0.524763	+	0.851248i	$0.324154\pi$
$648$		0			0
$649$	−721183.	+	416375.i	−1.71221	+	0.988543i
$650$		0			0
$651$	16137.8	+	27951.4i	0.0380786	+	0.0659541i
$652$		0			0
$653$	296297.			0.694866			0.347433	−	0.937705i	$-0.387053\pi$
$653$	296297.			0.694866			0.347433	+	0.937705i	$0.387053\pi$
$654$		0			0
$655$	−179021.	+	310073.i	−0.417274	+	0.722739i
$656$		0			0
$657$	−89682.7			−0.207768
$658$		0			0
$659$	−642280.	−	370820.i	−1.47895	−	0.853872i	−0.479233	−	0.877688i	$-0.659085\pi$
$659$	−642280.	−	370820.i	−1.47895	−	0.853872i	−0.999716	+	0.0238155i	$0.992419\pi$
$660$		0			0
$661$	−287667.	−	166084.i	−0.658395	−	0.380125i	0.133270	−	0.991080i	$-0.457452\pi$
$661$	−287667.	−	166084.i	−0.658395	−	0.380125i	−0.791665	+	0.610955i	$0.790786\pi$
$662$		0			0
$663$	−65718.0	−	113827.i	−0.149505	−	0.258951i
$664$		0			0
$665$	−47181.1	−	251150.i	−0.106690	−	0.567924i
$666$		0			0
$667$	−26327.1	+	15199.9i	−0.0591767	+	0.0341657i
$668$		0			0
$669$	−188265.	+	326084.i	−0.420646	+	0.728580i
$670$		0			0
$671$	181101.	−	313677.i	0.402232	−	0.696686i
$672$		0			0
$673$		−	40533.1i		−	0.0894912i	−0.998998	−	0.0447456i	$-0.985752\pi$
$673$		−	40533.1i		−	0.0894912i	0.998998	−	0.0447456i	$-0.0142477\pi$
$674$		0			0
$675$	12084.0	+	6976.69i	0.0265218	+	0.0153123i
$676$		0			0
$677$		−	392617.i		−	0.856627i	−0.903630	−	0.428314i	$-0.859108\pi$
$677$		−	392617.i		−	0.856627i	0.903630	−	0.428314i	$-0.140892\pi$
$678$		0			0
$679$	−433546.	+	250308.i	−0.940363	+	0.542919i
$680$		0			0
$681$	485255.	+	840487.i	1.04635	+	1.81233i
$682$		0			0
$683$		−	509603.i		−	1.09242i	−0.837648	−	0.546211i	$-0.816070\pi$
$683$		−	509603.i		−	1.09242i	0.837648	−	0.546211i	$-0.183930\pi$
$684$		0			0
$685$	−453944.			−0.967434
$686$		0			0
$687$	510485.	−	294729.i	1.08161	−	0.624466i
$688$		0			0
$689$	177919.	+	308165.i	0.374787	+	0.649150i
$690$		0			0
$691$	753165.			1.57737			0.788686	−	0.614796i	$-0.210762\pi$
$691$	753165.			1.57737			0.788686	+	0.614796i	$0.210762\pi$
$692$		0			0
$693$	56131.2	−	97222.0i	0.116879	−	0.202441i
$694$		0			0
$695$	929659.			1.92466
$696$		0			0
$697$	7047.50	+	4068.88i	0.0145067	+	0.00837547i
$698$		0			0
$699$	420151.	+	242574.i	0.859906	+	0.496467i
$700$		0			0
$701$	286342.	+	495960.i	0.582706	+	1.00928i	0.995157	+	0.0982968i	$0.0313395\pi$
$701$	286342.	+	495960.i	0.582706	+	1.00928i	−0.412451	+	0.910980i	$0.635327\pi$
$702$		0			0
$703$	−129233.	+	367789.i	−0.261495	+	0.744197i
$704$		0			0
$705$	630888.	−	364244.i	1.26933	−	0.732848i
$706$		0			0
$707$	−1348.18	+	2335.11i	−0.00269717	+	0.00467163i
$708$		0			0
$709$	−84487.5	+	146337.i	−0.168074	+	0.291112i	−0.937743	−	0.347331i	$-0.887088\pi$
$709$	−84487.5	+	146337.i	−0.168074	+	0.291112i	0.769669	+	0.638443i	$0.220421\pi$
$710$		0			0
$711$		−	160815.i		−	0.318117i
$712$		0			0
$713$	−67596.5	−	39026.9i	−0.132967	−	0.0767688i
$714$		0			0
$715$		−	522829.i		−	1.02270i
$716$		0			0
$717$	319412.	−	184413.i	0.621317	−	0.358717i
$718$		0			0
$719$	−6416.59	−	11113.9i	−0.0124121	−	0.0214985i	0.859753	−	0.510711i	$-0.170618\pi$
$719$	−6416.59	−	11113.9i	−0.0124121	−	0.0214985i	−0.872165	+	0.489212i	$0.837284\pi$
$720$		0			0
$721$		−	29461.1i		−	0.0566732i
$722$		0			0
$723$	1.16623e6			2.23104
$724$		0			0
$725$	949.297	−	548.077i	0.00180603	−	0.00104271i
$726$		0			0
$727$	385862.	+	668332.i	0.730067	+	1.26451i	0.956854	+	0.290569i	$0.0938447\pi$
$727$	385862.	+	668332.i	0.730067	+	1.26451i	−0.226787	+	0.973944i	$0.572822\pi$
$728$		0			0
$729$	−239708.			−0.451052
$730$		0			0
$731$	−83150.8	+	144021.i	−0.155608	+	0.269521i
$732$		0			0
$733$	598661.			1.11423			0.557113	−	0.830437i	$-0.311909\pi$
$733$	598661.			1.11423			0.557113	+	0.830437i	$0.311909\pi$
$734$		0			0
$735$	−376314.	−	217265.i	−0.696588	−	0.402175i
$736$		0			0
$737$	616193.	+	355759.i	1.13444	+	0.654970i
$738$		0			0
$739$	−56363.8	−	97624.9i	−0.103207	−	0.178761i	0.809797	−	0.586710i	$-0.199577\pi$
$739$	−56363.8	−	97624.9i	−0.103207	−	0.178761i	−0.913004	+	0.407950i	$0.866244\pi$
$740$		0			0
$741$	−509288.	−	178953.i	−0.927528	−	0.325914i
$742$		0			0
$743$	444706.	−	256751.i	0.805555	−	0.465088i	−0.0398546	−	0.999205i	$-0.512689\pi$
$743$	444706.	−	256751.i	0.805555	−	0.465088i	0.845410	+	0.534118i	$0.179356\pi$
$744$		0			0
$745$	−257182.	+	445453.i	−0.463370	+	0.802581i
$746$		0			0
$747$	147658.	−	255751.i	0.264616	−	0.458328i
$748$		0			0
$749$		−	2406.06i		−	0.00428887i
$750$		0			0
$751$	−740064.	−	427276.i	−1.31217	−	0.757580i	−0.329713	−	0.944081i	$-0.606952\pi$
$751$	−740064.	−	427276.i	−1.31217	−	0.757580i	−0.982455	+	0.186501i	$0.940285\pi$
$752$		0			0
$753$			389967.i			0.687761i
$754$		0			0
$755$	40624.2	−	23454.4i	0.0712673	−	0.0411462i
$756$		0			0
$757$	−74063.5	−	128282.i	−0.129245	−	0.223858i	0.794139	−	0.607736i	$-0.207922\pi$
$757$	−74063.5	−	128282.i	−0.129245	−	0.223858i	−0.923384	+	0.383877i	$0.874589\pi$
$758$		0			0
$759$			1.05066e6i			1.82380i
$760$		0			0
$761$	262528.			0.453322			0.226661	−	0.973974i	$-0.427219\pi$
$761$	262528.			0.453322			0.226661	+	0.973974i	$0.427219\pi$
$762$		0			0
$763$	−499363.	+	288307.i	−0.857762	+	0.495229i
$764$		0			0
$765$	−31630.9	−	54786.3i	−0.0540491	−	0.0936158i
$766$		0			0
$767$	−831514.			−1.41344
$768$		0			0
$769$	−23000.9	+	39838.8i	−0.0388949	+	0.0673680i	−0.884818	−	0.465938i	$-0.845717\pi$
$769$	−23000.9	+	39838.8i	−0.0388949	+	0.0673680i	0.845923	+	0.533306i	$0.179050\pi$
$770$		0			0
$771$	657950.			1.10684
$772$		0			0
$773$	−590492.	−	340921.i	−0.988224	−	0.570551i	−0.0834809	−	0.996509i	$-0.526604\pi$
$773$	−590492.	−	340921.i	−0.988224	−	0.570551i	−0.904743	+	0.425958i	$0.859937\pi$
$774$		0			0
$775$	2437.38	+	1407.22i	0.00405808	+	0.00234293i
$776$		0			0
$777$	−156639.	−	271307.i	−0.259453	−	0.449386i
$778$		0			0
$779$	32847.5	−	6170.74i	0.0541287	−	0.0101686i
$780$		0			0
$781$	533050.	−	307756.i	0.873908	−	0.504551i
$782$		0			0
$783$	−11949.8	+	20697.7i	−0.0194912	+	0.0337597i
$784$		0			0
$785$	−337104.	+	583881.i	−0.547047	+	0.947513i
$786$		0			0
$787$		−	356499.i		−	0.575584i	−0.957693	−	0.287792i	$-0.907079\pi$
$787$		−	356499.i		−	0.575584i	0.957693	−	0.287792i	$-0.0929212\pi$
$788$		0			0
$789$	−796120.	−	459640.i	−1.27886	−	0.738352i
$790$		0			0
$791$		−	513635.i		−	0.820921i
$792$		0			0
$793$	313211.	−	180832.i	0.498070	−	0.287561i
$794$		0			0
$795$	331404.	+	574009.i	0.524353	+	0.908206i
$796$		0			0
$797$			356520.i			0.561265i	0.959815	+	0.280632i	$0.0905442\pi$
$797$			356520.i			0.561265i	−0.959815	+	0.280632i	$0.909456\pi$
$798$		0			0
$799$	240262.			0.376350
$800$		0			0
$801$	136120.	−	78588.9i	0.212157	−	0.122489i
$802$		0			0
$803$	−227665.	−	394327.i	−0.353073	−	0.611540i
$804$		0			0
$805$	−496635.			−0.766383
$806$		0			0
$807$	307735.	−	533013.i	0.472531	−	0.818448i
$808$		0			0
$809$	146248.			0.223456			0.111728	−	0.993739i	$-0.464361\pi$
$809$	146248.			0.223456			0.111728	+	0.993739i	$0.464361\pi$
$810$		0			0
$811$	−1.09333e6	−	631237.i	−1.66231	−	0.959733i	−0.971610	−	0.236588i	$-0.923971\pi$
$811$	−1.09333e6	−	631237.i	−1.66231	−	0.959733i	−0.690696	−	0.723145i	$-0.742696\pi$
$812$		0			0
$813$	−799197.	−	461417.i	−1.20913	−	0.698091i
$814$		0			0
$815$	176967.	+	306516.i	0.266427	+	0.461465i
$816$		0			0
$817$	126104.	+	671266.i	0.188923	+	1.00566i
$818$		0			0
$819$	97077.6	−	56047.8i	0.144728	−	0.0835585i
$820$		0			0
$821$	−86526.3	+	149868.i	−0.128370	+	0.222343i	−0.923045	−	0.384692i	$-0.874308\pi$
$821$	−86526.3	+	149868.i	−0.128370	+	0.222343i	0.794676	+	0.607034i	$0.207641\pi$
$822$		0			0
$823$	−164144.	+	284306.i	−0.242340	+	0.419745i	−0.961380	−	0.275223i	$-0.911248\pi$
$823$	−164144.	+	284306.i	−0.242340	+	0.419745i	0.719040	+	0.694968i	$0.244582\pi$
$824$		0			0
$825$		−	37884.5i		−	0.0556613i
$826$		0			0
$827$	−894676.	−	516541.i	−1.30814	−	0.755256i	−0.326356	−	0.945247i	$-0.605821\pi$
$827$	−894676.	−	516541.i	−1.30814	−	0.755256i	−0.981786	+	0.189991i	$0.939154\pi$
$828$		0			0
$829$		−	876630.i		−	1.27558i	−0.770211	−	0.637789i	$-0.779849\pi$
$829$		−	876630.i		−	1.27558i	0.770211	−	0.637789i	$-0.220151\pi$
$830$		0			0
$831$	−667604.	+	385441.i	−0.966756	+	0.558157i
$832$		0			0
$833$	−71656.2	−	124112.i	−0.103268	−	0.178865i
$834$		0			0
$835$			391322.i			0.561256i
$836$		0			0
$837$	−61364.0			−0.0875917
$838$		0			0
$839$	228597.	−	131981.i	0.324748	−	0.187493i	−0.328759	−	0.944414i	$-0.606630\pi$
$839$	228597.	−	131981.i	0.324748	−	0.187493i	0.653507	+	0.756921i	$0.273297\pi$
$840$		0			0
$841$	−352702.	−	610897.i	−0.498673	−	0.863726i
$842$		0			0
$843$	−625475.			−0.880147
$844$		0			0
$845$	−103140.	+	178644.i	−0.144449	+	0.250193i
$846$		0			0
$847$	163551.			0.227974
$848$		0			0
$849$	1.28124e6	+	739723.i	1.77752	+	1.02625i
$850$		0			0
$851$	656118.	+	378810.i	0.905989	+	0.523073i
$852$		0			0
$853$	537972.	+	931795.i	0.739370	+	1.28063i	0.952779	+	0.303664i	$0.0982099\pi$
$853$	537972.	+	931795.i	0.739370	+	1.28063i	−0.213409	+	0.976963i	$0.568457\pi$
$854$		0			0
$855$	−245127.	−	86132.5i	−0.335319	−	0.117824i
$856$		0			0
$857$	346531.	−	200070.i	0.471824	−	0.272408i	−0.245179	−	0.969478i	$-0.578847\pi$
$857$	346531.	−	200070.i	0.471824	−	0.272408i	0.717003	+	0.697070i	$0.245513\pi$
$858$		0			0
$859$	−274871.	+	476090.i	−0.372514	+	0.645213i	−0.989952	−	0.141407i	$-0.954837\pi$
$859$	−274871.	+	476090.i	−0.372514	+	0.645213i	0.617438	+	0.786620i	$0.288171\pi$
$860$		0			0
$861$	−13429.4	+	23260.4i	−0.0181155	+	0.0313769i
$862$		0			0
$863$		−	443814.i		−	0.595908i	−0.954580	−	0.297954i	$-0.903696\pi$
$863$		−	443814.i		−	0.595908i	0.954580	−	0.297954i	$-0.0963042\pi$
$864$		0			0
$865$	−377536.	−	217971.i	−0.504576	−	0.291317i
$866$		0			0
$867$			792133.i			1.05380i
$868$		0			0
$869$	707088.	−	408238.i	0.936341	−	0.540597i
$870$		0			0
$871$	355231.	+	615278.i	0.468246	+	0.811027i
$872$		0			0
$873$			508991.i			0.667854i
$874$		0			0
$875$	−424516.			−0.554469
$876$		0			0
$877$	−919656.	+	530964.i	−1.19571	+	0.690344i	−0.959596	−	0.281381i	$-0.909207\pi$
$877$	−919656.	+	530964.i	−1.19571	+	0.690344i	−0.236115	+	0.971725i	$0.575874\pi$
$878$		0			0
$879$	−895020.	−	1.55022e6i	−1.15839	−	2.00639i
$880$		0			0
$881$	−337096.			−0.434312			−0.217156	−	0.976137i	$-0.569678\pi$
$881$	−337096.			−0.434312			−0.217156	+	0.976137i	$0.569678\pi$
$882$		0			0
$883$	−23184.8	+	40157.3i	−0.0297360	+	0.0515043i	−0.880510	−	0.474027i	$-0.842800\pi$
$883$	−23184.8	+	40157.3i	−0.0297360	+	0.0515043i	0.850774	+	0.525531i	$0.176133\pi$
$884$		0			0
$885$	−1.54883e6			−1.97751
$886$		0			0
$887$	−94128.5	−	54345.1i	−0.119639	−	0.0690738i	0.438986	−	0.898494i	$-0.355338\pi$
$887$	−94128.5	−	54345.1i	−0.119639	−	0.0690738i	−0.558625	+	0.829420i	$0.688671\pi$
$888$		0			0
$889$	446230.	+	257631.i	0.564618	+	0.325982i
$890$		0			0
$891$	576792.	+	999033.i	0.726547	+	1.25842i
$892$		0			0
$893$	748781.	−	642681.i	0.938971	−	0.805921i
$894$		0			0
$895$	674887.	−	389646.i	0.842529	−	0.486434i
$896$		0			0
$897$	−524549.	+	908546.i	−0.651931	+	1.12918i
$898$		0			0
$899$	−2410.33	+	4174.81i	−0.00298234	+	0.00516556i
$900$		0			0
$901$			218601.i			0.269279i
$902$		0			0
$903$	−475345.	−	274441.i	−0.582953	−	0.336568i
$904$		0			0
$905$		−	1.43602e6i		−	1.75332i
$906$		0			0
$907$	−930792.	+	537393.i	−1.13146	+	0.653247i	−0.944301	−	0.329083i	$-0.893260\pi$
$907$	−930792.	+	537393.i	−1.13146	+	0.653247i	−0.187156	+	0.982330i	$0.559927\pi$
$908$		0			0
$909$	1370.73	+	2374.18i	0.00165892	+	0.00287333i
$910$		0			0
$911$			586315.i			0.706471i	0.935534	+	0.353235i	$0.114919\pi$
$911$			586315.i			0.706471i	−0.935534	+	0.353235i	$0.885081\pi$
$912$		0			0
$913$	1.49935e6			1.79871
$914$		0			0
$915$	583407.	−	336830.i	0.696834	−	0.402317i
$916$		0			0
$917$	−194872.	−	337528.i	−0.231745	−	0.401394i
$918$		0			0
$919$	678021.			0.802809			0.401405	−	0.915901i	$-0.368522\pi$
$919$	678021.			0.802809			0.401405	+	0.915901i	$0.368522\pi$
$920$		0			0
$921$	−144799.	+	250800.i	−0.170705	+	0.295671i
$922$		0			0
$923$	614598.			0.721420
$924$		0			0
$925$	−23658.2	−	13659.1i	−0.0276502	−	0.0159638i
$926$		0			0
$927$	−25940.9	−	14977.0i	−0.0301874	−	0.0174287i
$928$		0			0
$929$	−364161.	−	630746.i	−0.421951	−	0.730841i	0.574179	−	0.818730i	$-0.305321\pi$
$929$	−364161.	−	630746.i	−0.421951	−	0.730841i	−0.996130	+	0.0878888i	$0.971988\pi$
$930$		0			0
$931$	−555307.	−	195123.i	−0.640669	−	0.225118i
$932$		0			0
$933$	1.71671e6	−	991143.i	1.97212	−	1.13861i
$934$		0			0
$935$	160594.	−	278156.i	0.183698	−	0.318175i
$936$		0			0
$937$	−338424.	+	586168.i	−0.385463	+	0.667641i	−0.991833	−	0.127541i	$-0.959292\pi$
$937$	−338424.	+	586168.i	−0.385463	+	0.667641i	0.606370	+	0.795182i	$0.292625\pi$
$938$		0			0
$939$		−	1.65231e6i		−	1.87396i
$940$		0			0
$941$	−211702.	−	122226.i	−0.239081	−	0.138034i	0.375673	−	0.926752i	$-0.377412\pi$
$941$	−211702.	−	122226.i	−0.239081	−	0.138034i	−0.614754	+	0.788719i	$0.710745\pi$
$942$		0			0
$943$		−	64954.1i		−	0.0730438i
$944$		0			0
$945$	−338134.	+	195222.i	−0.378639	+	0.218607i
$946$		0			0
$947$	392652.	+	680093.i	0.437832	+	0.758348i	0.997522	−	0.0703543i	$-0.0224130\pi$
$947$	392652.	+	680093.i	0.437832	+	0.758348i	−0.559690	+	0.828702i	$0.689080\pi$
$948$		0			0
$949$		−	454653.i		−	0.504832i
$950$		0			0
$951$	−476830.			−0.527233
$952$		0			0
$953$	−504490.	+	291268.i	−0.555478	+	0.320705i	−0.751329	−	0.659928i	$-0.770587\pi$
$953$	−504490.	+	291268.i	−0.555478	+	0.320705i	0.195850	+	0.980634i	$0.437253\pi$
$954$		0			0
$955$	258364.	+	447500.i	0.283286	+	0.490666i
$956$		0			0
$957$	64889.5			0.0708517
$958$		0			0
$959$	247069.	−	427936.i	0.268646	−	0.465309i
$960$		0			0
$961$	911144.			0.986598
$962$		0			0
$963$	−2118.57	−	1223.16i	−0.00228450	−	0.00131895i
$964$		0			0
$965$	−23015.6	−	13288.1i	−0.0247154	−	0.0142694i
$966$		0			0
$967$	378832.	+	656157.i	0.405130	+	0.701705i	0.994337	−	0.106277i	$-0.0338930\pi$
$967$	378832.	+	656157.i	0.405130	+	0.701705i	−0.589207	+	0.807982i	$0.700560\pi$
$968$		0			0
$969$	−215984.	−	251641.i	−0.230025	−	0.268000i
$970$		0			0
$971$	−412390.	+	238093.i	−0.437390	+	0.252527i	−0.702490	−	0.711694i	$-0.747928\pi$
$971$	−412390.	+	238093.i	−0.437390	+	0.252527i	0.265100	+	0.964221i	$0.414595\pi$
$972$		0			0
$973$	−505987.	+	876395.i	−0.534458	+	0.925709i
$974$		0			0
$975$	18914.1	−	32760.2i	0.0198965	−	0.0344617i
$976$		0			0
$977$			439217.i			0.460140i	0.973174	+	0.230070i	$0.0738955\pi$
$977$			439217.i			0.460140i	−0.973174	+	0.230070i	$0.926105\pi$
$978$		0			0
$979$	691097.	+	399005.i	0.721063	+	0.416306i
$980$		0			0
$981$			586261.i			0.609191i
$982$		0			0
$983$	−469744.	+	271207.i	−0.486132	+	0.280668i	−0.722968	−	0.690881i	$-0.757223\pi$
$983$	−469744.	+	271207.i	−0.486132	+	0.280668i	0.236837	+	0.971549i	$0.423889\pi$
$984$		0			0
$985$	−764859.	−	1.32477e6i	−0.788331	−	1.36543i
$986$		0			0
$987$			792990.i			0.814017i
$988$		0			0
$989$	1.32739e6			1.35708
$990$		0			0
$991$	560235.	−	323452.i	0.570457	−	0.329354i	−0.186875	−	0.982384i	$-0.559836\pi$
$991$	560235.	−	323452.i	0.570457	−	0.329354i	0.757332	+	0.653030i	$0.226502\pi$
$992$		0			0
$993$	−267764.	−	463781.i	−0.271553	−	0.470343i
$994$		0			0
$995$	1.23996e6			1.25246
$996$		0			0
$997$	581238.	−	1.00673e6i	0.584741	−	1.01280i	−0.410166	−	0.912011i	$-0.634529\pi$
$997$	581238.	−	1.00673e6i	0.584741	−	1.01280i	0.994908	−	0.100791i	$-0.0321373\pi$
$998$		0			0
$999$	595623.			0.596816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.h.a.69.2	yes	12
3.2	odd	2		684.5.y.c.145.5		12
4.3	odd	2		304.5.r.b.145.5		12
19.8	odd	6	inner	76.5.h.a.65.2	✓	12
57.8	even	6		684.5.y.c.217.5		12
76.27	even	6		304.5.r.b.65.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.2	✓	12	19.8	odd	6	inner
76.5.h.a.69.2	yes	12	1.1	even	1	trivial
304.5.r.b.65.5		12	76.27	even	6
304.5.r.b.145.5		12	4.3	odd	2
684.5.y.c.145.5		12	3.2	odd	2
684.5.y.c.217.5		12	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.05083 + 5.22550i) q^{3} +(-12.7505 - 22.0845i) q^{5} +27.7589 q^{7} +(14.1116 - 24.4421i) q^{9} +O(q^{10})\)	\(q+(-9.05083 + 5.22550i) q^{3} +(-12.7505 - 22.0845i) q^{5} +27.7589 q^{7} +(14.1116 - 24.4421i) q^{9} +143.293 q^{11} +(123.911 + 71.5400i) q^{13} +(230.805 + 133.255i) q^{15} +(43.9489 + 76.1217i) q^{17} +(340.586 + 119.675i) q^{19} +(-251.241 + 145.054i) q^{21} +(350.792 - 607.590i) q^{23} +(-12.6488 + 21.9084i) q^{25} -551.569i q^{27} +(-37.5252 - 21.6652i) q^{29} -111.254i q^{31} +(-1296.92 + 748.776i) q^{33} +(-353.939 - 613.040i) q^{35} +1079.87i q^{37} -1495.33 q^{39} +(80.1784 - 46.2910i) q^{41} +(945.995 + 1638.51i) q^{43} -719.720 q^{45} +(1366.72 - 2367.22i) q^{47} -1630.45 q^{49} +(-795.547 - 459.309i) q^{51} +(2153.80 + 1243.50i) q^{53} +(-1827.05 - 3164.54i) q^{55} +(-3707.95 + 696.575i) q^{57} +(-5032.93 + 2905.77i) q^{59} +(1263.85 - 2189.06i) q^{61} +(391.723 - 678.485i) q^{63} -3648.67i q^{65} +(4300.24 + 2482.74i) q^{67} +7332.25i q^{69} +(3720.00 - 2147.74i) q^{71} +(-1588.81 - 2751.89i) q^{73} -264.385i q^{75} +3977.65 q^{77} +(4934.57 - 2848.97i) q^{79} +(4025.27 + 6971.97i) q^{81} +10463.5 q^{83} +(1120.74 - 1941.17i) q^{85} +452.845 q^{87} +(4822.97 + 2784.54i) q^{89} +(3439.63 + 1985.87i) q^{91} +(581.355 + 1006.94i) q^{93} +(-1699.68 - 9047.57i) q^{95} +(-15618.3 + 9017.22i) q^{97} +(2022.10 - 3502.38i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9}+O(q^{10}) \) 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9	\( 12 q - 12 q^{3} + 9 q^{5} - 52 q^{7} + 136 q^{9} + 6 q^{11} - 93 q^{13} - 741 q^{15} - 483 q^{17} - 533 q^{19} + 972 q^{21} + 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} - 1128 q^{35} - 2250 q^{39} - 1692 q^{41} - 63 q^{43} + 7976 q^{45} - 3471 q^{47} + 420 q^{49} + 6741 q^{51} - 3771 q^{53} - 2014 q^{55} + 7617 q^{57} - 9594 q^{59} + 1229 q^{61} + 1514 q^{63} + 7590 q^{67} + 963 q^{71} - 2838 q^{73} - 15408 q^{77} + 11073 q^{79} + 2086 q^{81} - 14202 q^{83} + 9455 q^{85} - 39510 q^{87} + 6525 q^{89} - 7686 q^{91} - 5316 q^{93} + 1521 q^{95} - 34110 q^{97} + 13220 q^{99}+O(q^{100}) \) 12 * q - 12 * q^3 + 9 * q^5 - 52 * q^7 + 136 * q^9 + 6 * q^11 - 93 * q^13 - 741 * q^15 - 483 * q^17 - 533 * q^19 + 972 * q^21 + 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 - 1128 * q^35 - 2250 * q^39 - 1692 * q^41 - 63 * q^43 + 7976 * q^45 - 3471 * q^47 + 420 * q^49 + 6741 * q^51 - 3771 * q^53 - 2014 * q^55 + 7617 * q^57 - 9594 * q^59 + 1229 * q^61 + 1514 * q^63 + 7590 * q^67 + 963 * q^71 - 2838 * q^73 - 15408 * q^77 + 11073 * q^79 + 2086 * q^81 - 14202 * q^83 + 9455 * q^85 - 39510 * q^87 + 6525 * q^89 - 7686 * q^91 - 5316 * q^93 + 1521 * q^95 - 34110 * q^97 + 13220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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