LMFDB - Embedded newform 76.6.i.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	76.5
Dual form			76.6.i.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77836 + 15.7569i) q^{3} +(40.2412 + 33.7663i) q^{5} +(35.1538 + 60.8882i) q^{7} +(-12.2145 - 4.44570i) q^{9} +O(q^{10})$	\(q+(-2.77836 + 15.7569i) q^{3} +(40.2412 + 33.7663i) q^{5} +(35.1538 + 60.8882i) q^{7} +(-12.2145 - 4.44570i) q^{9} +(-3.62592 + 6.28027i) q^{11} +(11.0176 + 62.4841i) q^{13} +(-643.857 + 540.260i) q^{15} +(-785.685 + 285.966i) q^{17} +(-1237.53 + 971.913i) q^{19} +(-1057.08 + 384.745i) q^{21} +(-1236.08 + 1037.20i) q^{23} +(-63.4653 - 359.930i) q^{25} +(-1840.01 + 3186.99i) q^{27} +(1681.11 + 611.875i) q^{29} +(548.509 + 950.045i) q^{31} +(-88.8833 - 74.5820i) q^{33} +(-641.341 + 3637.23i) q^{35} +6377.82 q^{37} -1015.17 q^{39} +(-174.095 + 987.343i) q^{41} +(-4595.58 - 3856.15i) q^{43} +(-341.409 - 591.338i) q^{45} +(-967.596 - 352.176i) q^{47} +(5931.92 - 10274.4i) q^{49} +(-2323.01 - 13174.5i) q^{51} +(11805.3 - 9905.85i) q^{53} +(-357.973 + 130.291i) q^{55} +(-11876.0 - 22200.0i) q^{57} +(13879.7 - 5051.78i) q^{59} +(23149.4 - 19424.6i) q^{61} +(-158.694 - 899.999i) q^{63} +(-1666.50 + 2886.46i) q^{65} +(24489.9 + 8913.60i) q^{67} +(-12908.7 - 22358.5i) q^{69} +(56395.2 + 47321.2i) q^{71} +(-3760.23 + 21325.3i) q^{73} +5847.70 q^{75} -509.859 q^{77} +(-8530.13 + 48376.7i) q^{79} +(-47524.4 - 39877.7i) q^{81} +(18175.4 + 31480.7i) q^{83} +(-41272.9 - 15022.1i) q^{85} +(-14312.0 + 24789.1i) q^{87} +(-13248.6 - 75136.4i) q^{89} +(-3417.23 + 2867.40i) q^{91} +(-16493.7 + 6003.21i) q^{93} +(-82617.7 - 2676.03i) q^{95} +(-88283.3 + 32132.5i) q^{97} +(72.2088 - 60.5904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	$ 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) $ 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.77836	+	15.7569i	−0.178232	+	1.01080i	0.756115	+	0.654439i	$0.227095\pi$
$3$	−2.77836	+	15.7569i	−0.178232	+	1.01080i	−0.934347	+	0.356365i	$0.884016\pi$
$4$		0			0
$5$	40.2412	+	33.7663i	0.719856	+	0.604031i	0.927345	−	0.374206i	$-0.122085\pi$
$5$	40.2412	+	33.7663i	0.719856	+	0.604031i	−0.207490	+	0.978237i	$0.566529\pi$
$6$		0			0
$7$	35.1538	+	60.8882i	0.271161	+	0.469665i	0.969159	−	0.246435i	$-0.0792591\pi$
$7$	35.1538	+	60.8882i	0.271161	+	0.469665i	−0.697998	+	0.716099i	$0.745926\pi$
$8$		0			0
$9$	−12.2145	−	4.44570i	−0.0502653	−	0.0182951i
$10$		0			0
$11$	−3.62592	+	6.28027i	−0.00903516	+	0.0156494i	−0.870508	−	0.492155i	$-0.836209\pi$
$11$	−3.62592	+	6.28027i	−0.00903516	+	0.0156494i	0.861472	+	0.507804i	$0.169543\pi$
$12$		0			0
$13$	11.0176	+	62.4841i	0.0180813	+	0.102544i	0.992513	−	0.122141i	$-0.0389759\pi$
$13$	11.0176	+	62.4841i	0.0180813	+	0.102544i	−0.974431	+	0.224685i	$0.927865\pi$
$14$		0			0
$15$	−643.857	+	540.260i	−0.738858	+	0.619976i
$16$		0			0
$17$	−785.685	+	285.966i	−0.659366	+	0.239989i	−0.649962	−	0.759966i	$-0.725215\pi$
$17$	−785.685	+	285.966i	−0.659366	+	0.239989i	−0.00940313	+	0.999956i	$0.502993\pi$
$18$		0			0
$19$	−1237.53	+	971.913i	−0.786452	+	0.617651i
$19$	−1237.53	+	971.913i	−0.786452	+	0.617651i
$20$		0			0
$21$	−1057.08	+	384.745i	−0.523068	+	0.190381i
$22$		0			0
$23$	−1236.08	+	1037.20i	−0.487223	+	0.408829i	−0.853030	−	0.521862i	$-0.825238\pi$
$23$	−1236.08	+	1037.20i	−0.487223	+	0.408829i	0.365807	+	0.930691i	$0.380793\pi$
$24$		0			0
$25$	−63.4653	−	359.930i	−0.0203089	−	0.115178i
$26$		0			0
$27$	−1840.01	+	3186.99i	−0.485747	+	0.841338i
$28$		0			0
$29$	1681.11	+	611.875i	0.371195	+	0.135104i	0.520880	−	0.853630i	$-0.325604\pi$
$29$	1681.11	+	611.875i	0.371195	+	0.135104i	−0.149685	+	0.988734i	$0.547826\pi$
$30$		0			0
$31$	548.509	+	950.045i	0.102513	+	0.177558i	0.912719	−	0.408587i	$-0.133978\pi$
$31$	548.509	+	950.045i	0.102513	+	0.177558i	−0.810206	+	0.586145i	$0.800645\pi$
$32$		0			0
$33$	−88.8833	−	74.5820i	−0.0142081	−	0.0119220i
$34$		0			0
$35$	−641.341	+	3637.23i	−0.0884951	+	0.501880i
$36$		0			0
$37$	6377.82			0.765892			0.382946	−	0.923771i	$-0.374909\pi$
$37$	6377.82			0.765892			0.382946	+	0.923771i	$0.374909\pi$
$38$		0			0
$39$	−1015.17			−0.106875
$40$		0			0
$41$	−174.095	+	987.343i	−0.0161744	+	0.0917294i	−0.991826	−	0.127595i	$-0.959274\pi$
$41$	−174.095	+	987.343i	−0.0161744	+	0.0917294i	0.975652	+	0.219324i	$0.0703853\pi$
$42$		0			0
$43$	−4595.58	−	3856.15i	−0.379026	−	0.318041i	0.433294	−	0.901253i	$-0.357351\pi$
$43$	−4595.58	−	3856.15i	−0.379026	−	0.318041i	−0.812320	+	0.583212i	$0.801796\pi$
$44$		0			0
$45$	−341.409	−	591.338i	−0.0251330	−	0.0435316i
$46$		0			0
$47$	−967.596	−	352.176i	−0.0638924	−	0.0232549i	0.309876	−	0.950777i	$-0.399712\pi$
$47$	−967.596	−	352.176i	−0.0638924	−	0.0232549i	−0.373769	+	0.927522i	$0.621935\pi$
$48$		0			0
$49$	5931.92	−	10274.4i	0.352943	−	0.611316i
$50$		0			0
$51$	−2323.01	−	13174.5i	−0.125062	−	0.709263i
$52$		0			0
$53$	11805.3	−	9905.85i	0.577283	−	0.484398i	−0.306771	−	0.951783i	$-0.599249\pi$
$53$	11805.3	−	9905.85i	0.577283	−	0.484398i	0.884053	+	0.467386i	$0.154804\pi$
$54$		0			0
$55$	−357.973	+	130.291i	−0.0159567	+	0.00580777i
$56$		0			0
$57$	−11876.0	−	22200.0i	−0.484153	−	0.905034i
$58$		0			0
$59$	13879.7	−	5051.78i	0.519097	−	0.188936i	−0.0691664	−	0.997605i	$-0.522034\pi$
$59$	13879.7	−	5051.78i	0.519097	−	0.188936i	0.588264	+	0.808669i	$0.299812\pi$
$60$		0			0
$61$	23149.4	−	19424.6i	0.796553	−	0.668388i	−0.150805	−	0.988564i	$-0.548186\pi$
$61$	23149.4	−	19424.6i	0.796553	−	0.668388i	0.947358	+	0.320176i	$0.103742\pi$
$62$		0			0
$63$	−158.694	−	899.999i	−0.00503744	−	0.0285687i
$64$		0			0
$65$	−1666.50	+	2886.46i	−0.0489239	+	0.0847387i
$66$		0			0
$67$	24489.9	+	8913.60i	0.666500	+	0.242586i	0.653040	−	0.757323i	$-0.273493\pi$
$67$	24489.9	+	8913.60i	0.666500	+	0.242586i	0.0134598	+	0.999909i	$0.495715\pi$
$68$		0			0
$69$	−12908.7	−	22358.5i	−0.326407	−	0.565354i
$70$		0			0
$71$	56395.2	+	47321.2i	1.32769	+	1.11406i	0.984612	+	0.174755i	$0.0559133\pi$
$71$	56395.2	+	47321.2i	1.32769	+	1.11406i	0.343076	+	0.939308i	$0.388531\pi$
$72$		0			0
$73$	−3760.23	+	21325.3i	−0.0825861	+	0.468369i	0.915265	+	0.402852i	$0.131981\pi$
$73$	−3760.23	+	21325.3i	−0.0825861	+	0.468369i	−0.997851	+	0.0655174i	$0.979130\pi$
$74$		0			0
$75$	5847.70			0.120042
$76$		0			0
$77$	−509.859			−0.00979994
$78$		0			0
$79$	−8530.13	+	48376.7i	−0.153776	+	0.872105i	0.806121	+	0.591751i	$0.201563\pi$
$79$	−8530.13	+	48376.7i	−0.153776	+	0.872105i	−0.959897	+	0.280354i	$0.909548\pi$
$80$		0			0
$81$	−47524.4	−	39877.7i	−0.804829	−	0.675332i
$82$		0			0
$83$	18175.4	+	31480.7i	0.289594	+	0.501591i	0.973713	−	0.227779i	$-0.0731465\pi$
$83$	18175.4	+	31480.7i	0.289594	+	0.501591i	−0.684119	+	0.729370i	$0.739813\pi$
$84$		0			0
$85$	−41272.9	−	15022.1i	−0.619609	−	0.225519i
$86$		0			0
$87$	−14312.0	+	24789.1i	−0.202722	+	0.351125i
$88$		0			0
$89$	−13248.6	−	75136.4i	−0.177294	−	1.00548i	−0.935462	−	0.353426i	$-0.885017\pi$
$89$	−13248.6	−	75136.4i	−0.177294	−	1.00548i	0.758168	−	0.652059i	$-0.226094\pi$
$90$		0			0
$91$	−3417.23	+	2867.40i	−0.0432585	+	0.0362982i
$92$		0			0
$93$	−16493.7	+	6003.21i	−0.197747	+	0.0719741i
$94$		0			0
$95$	−82617.7	−	2676.03i	−0.939213	−	0.0304216i
$96$		0			0
$97$	−88283.3	+	32132.5i	−0.952685	+	0.346749i	−0.771163	−	0.636638i	$-0.780325\pi$
$97$	−88283.3	+	32132.5i	−0.952685	+	0.346749i	−0.181522	+	0.983387i	$0.558102\pi$
$98$		0			0
$99$	72.2088	−	60.5904i	0.000740461	−	0.000621320i
$100$		0			0
$101$	−4592.13	−	26043.3i	−0.0447931	−	0.254034i	0.954186	−	0.299215i	$-0.0967248\pi$
$101$	−4592.13	−	26043.3i	−0.0447931	−	0.254034i	−0.998979	+	0.0451807i	$0.985614\pi$
$102$		0			0
$103$	−74068.9	+	128291.i	−0.687928	+	1.19153i	0.284579	+	0.958653i	$0.408146\pi$
$103$	−74068.9	+	128291.i	−0.687928	+	1.19153i	−0.972507	+	0.232874i	$0.925187\pi$
$104$		0			0
$105$	−55529.4	−	20211.1i	−0.491530	−	0.178902i
$106$		0			0
$107$	53381.3	+	92459.1i	0.450744	+	0.780711i	0.998432	−	0.0559711i	$-0.0178255\pi$
$107$	53381.3	+	92459.1i	0.450744	+	0.780711i	−0.547689	+	0.836682i	$0.684492\pi$
$108$		0			0
$109$	96357.2	+	80853.3i	0.776816	+	0.651826i	0.942445	−	0.334362i	$-0.108521\pi$
$109$	96357.2	+	80853.3i	0.776816	+	0.651826i	−0.165629	+	0.986188i	$0.552965\pi$
$110$		0			0
$111$	−17719.9	+	100494.i	−0.136507	+	0.774167i
$112$		0			0
$113$	119237.			0.878447			0.439224	−	0.898378i	$-0.355254\pi$
$113$	119237.			0.878447			0.439224	+	0.898378i	$0.355254\pi$
$114$		0			0
$115$	−84763.8			−0.597676
$116$		0			0
$117$	143.211	−	812.191i	0.000967191	−	0.00548521i
$118$		0			0
$119$	−45031.8	−	37786.1i	−0.291509	−	0.244605i
$120$		0			0
$121$	80499.2	+	139429.i	0.499837	+	0.865743i
$122$		0			0
$123$	−15073.7	−	5486.39i	−0.0898376	−	0.0326982i
$124$		0			0
$125$	91679.5	−	158793.i	0.524804	−	0.908987i
$126$		0			0
$127$	−8499.68	−	48204.1i	−0.0467620	−	0.265201i	0.952459	−	0.304667i	$-0.0985452\pi$
$127$	−8499.68	−	48204.1i	−0.0467620	−	0.265201i	−0.999221	+	0.0394666i	$0.987434\pi$
$128$		0			0
$129$	73529.0	−	61698.2i	0.389031	−	0.326436i
$130$		0			0
$131$	203113.	−	73927.1i	1.03409	−	0.376379i	0.231455	−	0.972846i	$-0.425651\pi$
$131$	203113.	−	73927.1i	1.03409	−	0.376379i	0.802638	+	0.596467i	$0.203429\pi$
$132$		0			0
$133$	−102682.	−	41184.6i	−0.503344	−	0.201886i
$134$		0			0
$135$	−181657.	+	66117.7i	−0.857862	+	0.312236i
$136$		0			0
$137$	175862.	−	147566.i	0.800517	−	0.671714i	−0.147807	−	0.989016i	$-0.547221\pi$
$137$	175862.	−	147566.i	0.800517	−	0.671714i	0.948324	+	0.317302i	$0.102777\pi$
$138$		0			0
$139$	−48670.4	−	276024.i	−0.213662	−	1.21174i	−0.883213	−	0.468973i	$-0.844624\pi$
$139$	−48670.4	−	276024.i	−0.213662	−	1.21174i	0.669550	−	0.742767i	$-0.266487\pi$
$140$		0			0
$141$	8237.53	−	14267.8i	0.0348939	−	0.0604379i
$142$		0			0
$143$	−432.366	−	157.368i	−0.00176812	−	0.000643543i
$144$		0			0
$145$	46989.1	+	81387.6i	0.185600	+	0.321468i
$146$		0			0
$147$	145411.	+	122014.i	0.555015	+	0.465713i
$148$		0			0
$149$	61881.8	−	350949.i	0.228348	−	1.29503i	−0.627832	−	0.778349i	$-0.716058\pi$
$149$	61881.8	−	350949.i	0.228348	−	1.29503i	0.856180	−	0.516677i	$-0.172831\pi$
$150$		0			0
$151$	−195866.			−0.699062			−0.349531	−	0.936925i	$-0.613659\pi$
$151$	−195866.			−0.699062			−0.349531	+	0.936925i	$0.613659\pi$
$152$		0			0
$153$	10868.0			0.0375338
$154$		0			0
$155$	−10006.9	+	56752.1i	−0.0334558	+	0.189737i
$156$		0			0
$157$	−107040.	−	89817.1i	−0.346574	−	0.290810i	0.452838	−	0.891593i	$-0.350411\pi$
$157$	−107040.	−	89817.1i	−0.346574	−	0.290810i	−0.799413	+	0.600782i	$0.794856\pi$
$158$		0			0
$159$	123286.	+	213537.i	0.386741	+	0.669855i
$160$		0			0
$161$	−106606.	−	38801.4i	−0.324129	−	0.117973i
$162$		0			0
$163$	155818.	−	269885.i	0.459355	−	0.795626i	−0.539572	−	0.841939i	$-0.681414\pi$
$163$	155818.	−	269885.i	0.459355	−	0.795626i	0.998927	+	0.0463133i	$0.0147473\pi$
$164$		0			0
$165$	−1058.41	−	6002.53i	−0.00302652	−	0.0171642i
$166$		0			0
$167$	176470.	−	148076.i	0.489642	−	0.410859i	−0.364256	−	0.931299i	$-0.618677\pi$
$167$	176470.	−	148076.i	0.489642	−	0.410859i	0.853898	+	0.520440i	$0.174232\pi$
$168$		0			0
$169$	345118.	−	125613.i	0.929504	−	0.338312i
$170$		0			0
$171$	19436.6	−	6369.69i	0.0508312	−	0.0166582i
$172$		0			0
$173$	−287064.	+	104483.i	−0.729228	+	0.265417i	−0.679838	−	0.733362i	$-0.737950\pi$
$173$	−287064.	+	104483.i	−0.729228	+	0.265417i	−0.0493899	+	0.998780i	$0.515728\pi$
$174$		0			0
$175$	19684.4	−	16517.2i	0.0485878	−	0.0407700i
$176$		0			0
$177$	41037.6	+	232736.i	0.0984574	+	0.558380i
$178$		0			0
$179$	250012.	−	433033.i	0.583214	−	1.01016i	−0.411881	−	0.911237i	$-0.635128\pi$
$179$	250012.	−	433033.i	0.583214	−	1.01016i	0.995096	−	0.0989189i	$-0.0315384\pi$
$180$		0			0
$181$	−449764.	−	163701.i	−1.02044	−	0.371410i	−0.223007	−	0.974817i	$-0.571587\pi$
$181$	−449764.	−	163701.i	−1.02044	−	0.371410i	−0.797434	+	0.603407i	$0.793810\pi$
$182$		0			0
$183$	241754.	+	418731.i	0.533638	+	0.924287i
$184$		0			0
$185$	256651.	+	215356.i	0.551332	+	0.462623i
$186$		0			0
$187$	1052.88	−	5971.20i	0.00220179	−	0.0124870i
$188$		0			0
$189$	−258733.			−0.526863
$190$		0			0
$191$	357922.			0.709912			0.354956	−	0.934883i	$-0.384496\pi$
$191$	357922.			0.709912			0.354956	+	0.934883i	$0.384496\pi$
$192$		0			0
$193$	−102588.	+	581805.i	−0.198245	+	1.12430i	0.709476	+	0.704730i	$0.248932\pi$
$193$	−102588.	+	581805.i	−0.198245	+	1.12430i	−0.907721	+	0.419575i	$0.862179\pi$
$194$		0			0
$195$	−40851.4	−	34278.4i	−0.0769344	−	0.0645557i
$196$		0			0
$197$	267040.	+	462528.i	0.490243	+	0.849126i	0.999937	−	0.0112298i	$-0.00357463\pi$
$197$	267040.	+	462528.i	0.490243	+	0.849126i	−0.509694	+	0.860356i	$0.670241\pi$
$198$		0			0
$199$	−686871.	−	250001.i	−1.22954	−	0.447516i	−0.356100	−	0.934448i	$-0.615894\pi$
$199$	−686871.	−	250001.i	−1.22954	−	0.447516i	−0.873440	+	0.486932i	$0.838116\pi$
$200$		0			0
$201$	−208492.	+	361119.i	−0.363999	+	0.630464i
$202$		0			0
$203$	21841.5	+	123870.i	0.0372000	+	0.210972i
$204$		0			0
$205$	−40344.8	+	33853.3i	−0.0670506	+	0.0562621i
$206$		0			0
$207$	19709.2	−	7173.55i	0.0319700	−	0.0116361i
$208$		0			0
$209$	−1616.69	−	11296.1i	−0.00256012	−	0.0178881i
$210$		0			0
$211$	−578994.	+	210737.i	−0.895299	+	0.325862i	−0.748367	−	0.663284i	$-0.769162\pi$
$211$	−578994.	+	210737.i	−0.895299	+	0.325862i	−0.146932	+	0.989147i	$0.546940\pi$
$212$		0			0
$213$	−902320.	+	757136.i	−1.36274	+	1.14347i
$214$		0			0
$215$	−54723.4	−	310352.i	−0.0807378	−	0.457887i
$216$		0			0
$217$	−38564.3	+	66795.4i	−0.0555951	+	0.0962935i
$218$		0			0
$219$	−325573.	−	118499.i	−0.458710	−	0.166957i
$220$		0			0
$221$	−26524.7	−	45942.2i	−0.0365317	−	0.0632748i
$222$		0			0
$223$	−250035.	−	209804.i	−0.336696	−	0.282521i	0.458726	−	0.888578i	$-0.348306\pi$
$223$	−250035.	−	209804.i	−0.336696	−	0.282521i	−0.795422	+	0.606056i	$0.792751\pi$
$224$		0			0
$225$	−824.945	+	4678.49i	−0.00108635	+	0.00616098i
$226$		0			0
$227$	−221893.			−0.285811			−0.142906	−	0.989736i	$-0.545645\pi$
$227$	−221893.			−0.285811			−0.142906	+	0.989736i	$0.545645\pi$
$228$		0			0
$229$	54991.2			0.0692954			0.0346477	−	0.999400i	$-0.488969\pi$
$229$	54991.2			0.0692954			0.0346477	+	0.999400i	$0.488969\pi$
$230$		0			0
$231$	1416.57	−	8033.78i	0.00174666	−	0.00990581i
$232$		0			0
$233$	305393.	+	256255.i	0.368527	+	0.309231i	0.808179	−	0.588937i	$-0.200454\pi$
$233$	305393.	+	256255.i	0.368527	+	0.309231i	−0.439651	+	0.898169i	$0.644898\pi$
$234$		0			0
$235$	−27045.5	−	46844.2i	−0.0319466	−	0.0553332i
$236$		0			0
$237$	−738567.	−	268816.i	−0.854120	−	0.310874i
$238$		0			0
$239$	873035.	−	1.51214e6i	0.988637	−	1.71237i	0.364137	−	0.931345i	$-0.381364\pi$
$239$	873035.	−	1.51214e6i	0.988637	−	1.71237i	0.624500	−	0.781025i	$-0.285303\pi$
$240$		0			0
$241$	277967.	+	1.57643e6i	0.308284	+	1.74837i	0.607629	+	0.794221i	$0.292121\pi$
$241$	277967.	+	1.57643e6i	0.308284	+	1.74837i	−0.299345	+	0.954145i	$0.596768\pi$
$242$		0			0
$243$	75357.0	−	63232.0i	0.0818668	−	0.0686944i
$244$		0			0
$245$	585636.	−	213154.i	0.623322	−	0.226871i
$246$		0			0
$247$	−74363.8	−	66617.9i	−0.0775566	−	0.0694782i
$248$		0			0
$249$	−546536.	+	198923.i	−0.558625	+	0.203323i
$250$		0			0
$251$	−371904.	+	312064.i	−0.372603	+	0.312651i	−0.809790	−	0.586720i	$-0.800419\pi$
$251$	−371904.	+	312064.i	−0.372603	+	0.312651i	0.437187	+	0.899370i	$0.355975\pi$
$252$		0			0
$253$	−2031.94	−	11523.7i	−0.00199577	−	0.0113186i
$254$		0			0
$255$	351373.	−	608595.i	0.338390	−	0.586109i
$256$		0			0
$257$	1.21410e6	+	441895.i	1.14662	+	0.417337i	0.844301	−	0.535869i	$-0.180016\pi$
$257$	1.21410e6	+	441895.i	1.14662	+	0.417337i	0.302322	+	0.953206i	$0.402238\pi$
$258$		0			0
$259$	224205.	+	388334.i	0.207680	+	0.359713i
$260$		0			0
$261$	−17813.7	−	14947.4i	−0.0161865	−	0.0135821i
$262$		0			0
$263$	93021.3	−	527550.i	0.0829264	−	0.470299i	−0.914858	−	0.403775i	$-0.867698\pi$
$263$	93021.3	−	527550.i	0.0829264	−	0.470299i	0.997785	−	0.0665242i	$-0.0211910\pi$
$264$		0			0
$265$	809545.			0.708151
$266$		0			0
$267$	1.22072e6			1.04795
$268$		0			0
$269$	166146.	−	942259.i	0.139994	−	0.793943i	−0.831258	−	0.555887i	$-0.812379\pi$
$269$	166146.	−	942259.i	0.139994	−	0.793943i	0.971251	−	0.238056i	$-0.0765102\pi$
$270$		0			0
$271$	403999.	+	338996.i	0.334162	+	0.280395i	0.794393	−	0.607404i	$-0.207789\pi$
$271$	403999.	+	338996.i	0.334162	+	0.280395i	−0.460231	+	0.887799i	$0.652233\pi$
$272$		0			0
$273$	−35686.9	−	61811.6i	−0.0289803	−	0.0501953i
$274$		0			0
$275$	2490.58	+	906.496i	0.00198595	+	0.000722826i
$276$		0			0
$277$	126833.	−	219682.i	0.0993195	−	0.172026i	−0.812084	−	0.583541i	$-0.801667\pi$
$277$	126833.	−	219682.i	0.0993195	−	0.172026i	0.911403	+	0.411515i	$0.135000\pi$
$278$		0			0
$279$	−2476.12	−	14042.8i	−0.00190442	−	0.0108005i
$280$		0			0
$281$	794829.	−	666941.i	0.600493	−	0.503874i	−0.291111	−	0.956689i	$-0.594025\pi$
$281$	794829.	−	666941.i	0.600493	−	0.503874i	0.891604	+	0.452816i	$0.149580\pi$
$282$		0			0
$283$	−2.27598e6	+	828389.i	−1.68928	+	0.614849i	−0.994535	−	0.104404i	$-0.966706\pi$
$283$	−2.27598e6	+	828389.i	−1.68928	+	0.614849i	−0.694748	+	0.719253i	$0.744484\pi$
$284$		0			0
$285$	271708.	−	1.29436e6i	0.198148	−	0.943938i
$286$		0			0
$287$	−66237.6	+	24108.5i	−0.0474679	+	0.0172769i
$288$		0			0
$289$	−552149.	+	463308.i	−0.388876	+	0.326306i
$290$		0			0
$291$	−261025.	−	1.48035e6i	−0.180696	−	1.02478i
$292$		0			0
$293$	806427.	−	1.39677e6i	0.548777	−	0.950510i	−0.449582	−	0.893239i	$-0.648427\pi$
$293$	806427.	−	1.39677e6i	0.548777	−	0.950510i	0.998359	−	0.0572704i	$-0.0182397\pi$
$294$		0			0
$295$	729114.	+	265376.i	0.487798	+	0.177544i
$296$		0			0
$297$	−13343.4	−	23111.5i	−0.00877761	−	0.0152033i
$298$		0			0
$299$	−78427.1	−	65808.1i	−0.0507327	−	0.0425698i
$300$		0			0
$301$	73241.8	−	415375.i	0.0465953	−	0.264255i
$302$		0			0
$303$	423119.			0.264762
$304$		0			0
$305$	1.58746e6			0.977130
$306$		0			0
$307$	171744.	−	974008.i	0.104000	−	0.589816i	−0.887614	−	0.460587i	$-0.847639\pi$
$307$	171744.	−	974008.i	0.104000	−	0.589816i	0.991615	−	0.129229i	$-0.0412501\pi$
$308$		0			0
$309$	−1.81568e6	−	1.52353e6i	−1.08179	−	0.907728i
$310$		0			0
$311$	−571719.	−	990246.i	−0.335183	−	0.580553i	0.648337	−	0.761353i	$-0.275465\pi$
$311$	−571719.	−	990246.i	−0.335183	−	0.580553i	−0.983520	+	0.180800i	$0.942131\pi$
$312$		0			0
$313$	−998156.	−	363299.i	−0.575887	−	0.209606i	0.0376238	−	0.999292i	$-0.488021\pi$
$313$	−998156.	−	363299.i	−0.575887	−	0.209606i	−0.613511	+	0.789686i	$0.710243\pi$
$314$		0			0
$315$	24003.7	−	41575.6i	0.0136302	−	0.0236081i
$316$		0			0
$317$	524502.	+	2.97460e6i	0.293156	+	1.66257i	0.674604	+	0.738180i	$0.264314\pi$
$317$	524502.	+	2.97460e6i	0.293156	+	1.66257i	−0.381448	+	0.924390i	$0.624574\pi$
$318$		0			0
$319$	−9938.31	+	8339.23i	−0.00546809	+	0.00458827i
$320$		0			0
$321$	−1.60518e6	+	584238.i	−0.869483	+	0.316466i
$322$		0			0
$323$	694376.	−	1.11751e6i	0.370330	−	0.595998i
$324$		0			0
$325$	21790.7	−	7931.15i	0.0114436	−	0.00416512i
$326$		0			0
$327$	−1.54171e6	+	1.29365e6i	−0.797322	+	0.669032i
$328$		0			0
$329$	−12571.3	−	71295.5i	−0.00640311	−	0.0363139i
$330$		0			0
$331$	−429959.	+	744712.i	−0.215704	+	0.373610i	−0.953490	−	0.301425i	$-0.902538\pi$
$331$	−429959.	+	744712.i	−0.215704	+	0.373610i	0.737786	+	0.675034i	$0.235871\pi$
$332$		0			0
$333$	−77901.6	−	28353.9i	−0.0384978	−	0.0140120i
$334$		0			0
$335$	684523.	+	1.18563e6i	0.333254	+	0.577214i
$336$		0			0
$337$	2.11720e6	+	1.77654e6i	1.01552	+	0.852120i	0.989058	−	0.147529i	$-0.0471321\pi$
$337$	2.11720e6	+	1.77654e6i	1.01552	+	0.852120i	0.0264600	+	0.999650i	$0.491577\pi$
$338$		0			0
$339$	−331284.	+	1.87881e6i	−0.156567	+	0.887938i
$340$		0			0
$341$	−7955.39			−0.00370489
$342$		0			0
$343$	2.01578e6			0.925140
$344$		0			0
$345$	235505.	−	1.33561e6i	0.106525	−	0.604133i
$346$		0			0
$347$	977391.	+	820128.i	0.435757	+	0.365644i	0.834119	−	0.551585i	$-0.185977\pi$
$347$	977391.	+	820128.i	0.435757	+	0.365644i	−0.398362	+	0.917228i	$0.630421\pi$
$348$		0			0
$349$	−244789.	−	423987.i	−0.107579	−	0.186333i	0.807210	−	0.590265i	$-0.200977\pi$
$349$	−244789.	−	423987.i	−0.107579	−	0.186333i	−0.914789	+	0.403932i	$0.867643\pi$
$350$		0			0
$351$	−219409.	−	79858.2i	−0.0950574	−	0.0345980i
$352$		0			0
$353$	−2.21407e6	+	3.83489e6i	−0.945705	+	1.63801i	−0.191371	+	0.981518i	$0.561293\pi$
$353$	−2.21407e6	+	3.83489e6i	−0.945705	+	1.63801i	−0.754334	+	0.656491i	$0.772040\pi$
$354$		0			0
$355$	671544.	+	3.80852e6i	0.282816	+	1.60393i
$356$		0			0
$357$	720506.	−	604576.i	0.299204	−	0.251062i
$358$		0			0
$359$	−3.91216e6	+	1.42391e6i	−1.60207	+	0.583105i	−0.979849	−	0.199739i	$-0.935991\pi$
$359$	−3.91216e6	+	1.42391e6i	−1.60207	+	0.583105i	−0.622218	+	0.782844i	$0.713768\pi$
$360$		0			0
$361$	586871.	−	2.40555e6i	0.237014	−	0.971506i
$362$		0			0
$363$	−2.42062e6	+	881032.i	−0.964183	+	0.350934i
$364$		0			0
$365$	−871394.	+	731186.i	−0.342359	+	0.287274i
$366$		0			0
$367$	−275834.	−	1.56433e6i	−0.106901	−	0.606268i	−0.990444	−	0.137917i	$-0.955959\pi$
$367$	−275834.	−	1.56433e6i	−0.106901	−	0.606268i	0.883542	−	0.468351i	$-0.155152\pi$
$368$		0			0
$369$	6515.91	−	11285.9i	0.00249120	−	0.00431489i
$370$		0			0
$371$	1.01815e6	+	370577.i	0.384041	+	0.139779i
$372$		0			0
$373$	−2.07646e6	−	3.59654e6i	−0.772773	−	1.33848i	−0.936037	−	0.351900i	$-0.885536\pi$
$373$	−2.07646e6	−	3.59654e6i	−0.772773	−	1.33848i	0.163264	−	0.986582i	$-0.447798\pi$
$374$		0			0
$375$	2.24737e6	+	1.88577e6i	0.825271	+	0.692484i
$376$		0			0
$377$	−19710.6	+	111784.i	−0.00714243	+	0.0405067i
$378$		0			0
$379$	−189463.			−0.0677525			−0.0338763	−	0.999426i	$-0.510785\pi$
$379$	−189463.			−0.0677525			−0.0338763	+	0.999426i	$0.510785\pi$
$380$		0			0
$381$	783161.			0.276400
$382$		0			0
$383$	561391.	−	3.18380e6i	0.195555	−	1.10905i	−0.716072	−	0.698026i	$-0.754062\pi$
$383$	561391.	−	3.18380e6i	0.195555	−	1.10905i	0.911627	−	0.411019i	$-0.134827\pi$
$384$		0			0
$385$	−20517.3	−	17216.1i	−0.00705454	−	0.00591946i
$386$		0			0
$387$	38989.2	+	67531.3i	0.0132333	+	0.0229207i
$388$		0			0
$389$	−4.28444e6	−	1.55941e6i	−1.43555	−	0.522499i	−0.497037	−	0.867730i	$-0.665579\pi$
$389$	−4.28444e6	−	1.55941e6i	−1.43555	−	0.522499i	−0.938518	+	0.345230i	$0.887801\pi$
$390$		0			0
$391$	674569.	−	1.16839e6i	0.223144	−	0.386496i
$392$		0			0
$393$	600538.	+	3.40582e6i	0.196137	+	1.11235i
$394$		0			0
$395$	−1.97677e6	+	1.65871e6i	−0.637475	+	0.534905i
$396$		0			0
$397$	−4.03179e6	+	1.46745e6i	−1.28387	+	0.467291i	−0.891711	−	0.452605i	$-0.850495\pi$
$397$	−4.03179e6	+	1.46745e6i	−1.28387	+	0.467291i	−0.392161	+	0.919896i	$0.628272\pi$
$398$		0			0
$399$	934229.	−	1.50352e6i	0.293779	−	0.472800i
$400$		0			0
$401$	−1.80152e6	+	655700.i	−0.559472	+	0.203631i	−0.606250	−	0.795274i	$-0.707327\pi$
$401$	−1.80152e6	+	655700.i	−0.559472	+	0.203631i	0.0467778	+	0.998905i	$0.485105\pi$
$402$		0			0
$403$	−53319.4	+	44740.3i	−0.0163540	+	0.0137226i
$404$		0			0
$405$	−565912.	−	3.20945e6i	−0.171440	−	0.972283i
$406$		0			0
$407$	−23125.4	+	40054.4i	−0.00691996	+	0.0119857i
$408$		0			0
$409$	−795761.	−	289633.i	−0.235220	−	0.0856131i	0.221721	−	0.975110i	$-0.428833\pi$
$409$	−795761.	−	289633.i	−0.235220	−	0.0856131i	−0.456941	+	0.889497i	$0.651055\pi$
$410$		0			0
$411$	1.83657e6	+	3.18103e6i	0.536293	+	0.928887i
$412$		0			0
$413$	795517.	+	667518.i	0.229495	+	0.192570i
$414$		0			0
$415$	−331590.	+	1.88054e6i	−0.0945107	+	0.535997i
$416$		0			0
$417$	4.48449e6			1.26291
$418$		0			0
$419$	1.94041e6			0.539955			0.269978	−	0.962867i	$-0.412984\pi$
$419$	1.94041e6			0.539955			0.269978	+	0.962867i	$0.412984\pi$
$420$		0			0
$421$	990773.	−	5.61895e6i	0.272439	−	1.54508i	−0.474543	−	0.880232i	$-0.657387\pi$
$421$	990773.	−	5.61895e6i	0.272439	−	1.54508i	0.746982	−	0.664845i	$-0.231502\pi$
$422$		0			0
$423$	10253.0	+	8603.28i	0.00278612	+	0.00233783i
$424$		0			0
$425$	152791.	+	264642.i	0.0410324	+	0.0710702i
$426$		0			0
$427$	1.99652e6	+	726674.i	0.529912	+	0.192872i
$428$		0			0
$429$	3680.90	−	6375.51i	0.000965631	−	0.00167252i
$430$		0			0
$431$	743956.	+	4.21918e6i	0.192910	+	1.09405i	0.915364	+	0.402627i	$0.131903\pi$
$431$	743956.	+	4.21918e6i	0.192910	+	1.09405i	−0.722454	+	0.691419i	$0.756986\pi$
$432$		0			0
$433$	4.94246e6	−	4.14721e6i	1.26684	−	1.06301i	0.271926	−	0.962318i	$-0.412339\pi$
$433$	4.94246e6	−	4.14721e6i	1.26684	−	1.06301i	0.994918	−	0.100690i	$-0.0321050\pi$
$434$		0			0
$435$	−1.41297e6	+	514278.i	−0.358021	+	0.130309i
$436$		0			0
$437$	521628.	−	2.48493e6i	0.130664	−	0.622459i
$438$		0			0
$439$	−3.94341e6	+	1.43529e6i	−0.976587	+	0.355449i	−0.780512	−	0.625140i	$-0.785042\pi$
$439$	−3.94341e6	+	1.43529e6i	−0.976587	+	0.355449i	−0.196075	+	0.980589i	$0.562820\pi$
$440$		0			0
$441$	−118132.	+	99124.5i	−0.0289249	+	0.0242708i
$442$		0			0
$443$	−1.00039e6	−	5.67348e6i	−0.242191	−	1.37354i	−0.826926	−	0.562311i	$-0.809912\pi$
$443$	−1.00039e6	−	5.67348e6i	−0.242191	−	1.37354i	0.584735	−	0.811225i	$-0.301199\pi$
$444$		0			0
$445$	2.00394e6	−	3.47093e6i	0.479718	−	0.830895i
$446$		0			0
$447$	5.35793e6	+	1.95013e6i	1.26832	+	0.461630i
$448$		0			0
$449$	654996.	+	1.13449e6i	0.153329	+	0.265573i	0.932449	−	0.361301i	$-0.117667\pi$
$449$	654996.	+	1.13449e6i	0.153329	+	0.265573i	−0.779121	+	0.626874i	$0.784334\pi$
$450$		0			0
$451$	−5569.53	−	4673.39i	−0.00128937	−	0.00108191i
$452$		0			0
$453$	544185.	−	3.08623e6i	0.124595	−	0.706615i
$454$		0			0
$455$	−234335.			−0.0530651
$456$		0			0
$457$	7.74242e6			1.73415			0.867074	−	0.498179i	$-0.165998\pi$
$457$	7.74242e6			1.73415			0.867074	+	0.498179i	$0.165998\pi$
$458$		0			0
$459$	534297.	−	3.03015e6i	0.118372	−	0.671324i
$460$		0			0
$461$	−1.97047e6	−	1.65342e6i	−0.431835	−	0.362353i	0.400808	−	0.916162i	$-0.368729\pi$
$461$	−1.97047e6	−	1.65342e6i	−0.431835	−	0.362353i	−0.832644	+	0.553809i	$0.813174\pi$
$462$		0			0
$463$	−8316.26	−	14404.2i	−0.00180292	−	0.00312274i	0.865123	−	0.501561i	$-0.167241\pi$
$463$	−8316.26	−	14404.2i	−0.00180292	−	0.00312274i	−0.866925	+	0.498438i	$0.833907\pi$
$464$		0			0
$465$	−866432.	−	315355.i	−0.185824	−	0.0676345i
$466$		0			0
$467$	2.47925e6	−	4.29419e6i	0.526052	−	0.911149i	−0.473487	−	0.880801i	$-0.657005\pi$
$467$	2.47925e6	−	4.29419e6i	0.526052	−	0.911149i	0.999539	−	0.0303482i	$-0.00966162\pi$
$468$		0			0
$469$	318181.	+	1.80449e6i	0.0667947	+	0.378811i
$470$		0			0
$471$	1.71263e6	−	1.43707e6i	0.355723	−	0.298487i
$472$		0			0
$473$	40880.8	−	14879.4i	0.00840169	−	0.00305797i
$474$		0			0
$475$	428361.	+	383742.i	0.0871115	+	0.0780378i
$476$		0			0
$477$	−188234.	+	68511.6i	−0.0378793	+	0.0137870i
$478$		0			0
$479$	−6.77321e6	+	5.68340e6i	−1.34882	+	1.13180i	−0.369562	+	0.929206i	$0.620492\pi$
$479$	−6.77321e6	+	5.68340e6i	−1.34882	+	1.13180i	−0.979263	+	0.202592i	$0.935063\pi$
$480$		0			0
$481$	70268.5	+	398512.i	0.0138483	+	0.0785379i
$482$		0			0
$483$	907580.	−	1.57197e6i	0.177018	−	0.306604i
$484$		0			0
$485$	−4.63762e6	−	1.68796e6i	−0.895243	−	0.325842i
$486$		0			0
$487$	2.09860e6	+	3.63488e6i	0.400965	+	0.694492i	0.993843	−	0.110801i	$-0.0353415\pi$
$487$	2.09860e6	+	3.63488e6i	0.400965	+	0.694492i	−0.592877	+	0.805293i	$0.702008\pi$
$488$		0			0
$489$	3.81962e6	+	3.20504e6i	0.722350	+	0.606124i
$490$		0			0
$491$	953518.	−	5.40767e6i	0.178495	−	1.01229i	−0.755538	−	0.655105i	$-0.772624\pi$
$491$	953518.	−	5.40767e6i	0.178495	−	1.01229i	0.934032	−	0.357188i	$-0.116265\pi$
$492$		0			0
$493$	−1.49580e6			−0.277176
$494$		0			0
$495$	4951.68			0.000908322
$496$		0			0
$497$	−898795.	+	5.09732e6i	−0.163219	+	0.925659i
$498$		0			0
$499$	−3.86248e6	−	3.24100e6i	−0.694408	−	0.582677i	0.225769	−	0.974181i	$-0.427511\pi$
$499$	−3.86248e6	−	3.24100e6i	−0.694408	−	0.582677i	−0.920177	+	0.391504i	$0.871955\pi$
$500$		0			0
$501$	1.84291e6	+	3.19202e6i	0.328028	+	0.568160i
$502$		0			0
$503$	−5.04191e6	−	1.83511e6i	−0.888537	−	0.323401i	−0.142887	−	0.989739i	$-0.545639\pi$
$503$	−5.04191e6	−	1.83511e6i	−0.888537	−	0.323401i	−0.745650	+	0.666338i	$0.767861\pi$
$504$		0			0
$505$	694594.	−	1.20307e6i	0.121200	−	0.209924i
$506$		0			0
$507$	1.02040e6	+	5.78699e6i	0.176300	+	0.999845i
$508$		0			0
$509$	−2.41100e6	+	2.02307e6i	−0.412480	+	0.346112i	−0.825294	−	0.564704i	$-0.808990\pi$
$509$	−2.41100e6	+	2.02307e6i	−0.412480	+	0.346112i	0.412814	+	0.910815i	$0.364546\pi$
$510$		0			0
$511$	−1.43065e6	+	520712.i	−0.242370	+	0.0882156i
$512$		0			0
$513$	−820404.	−	5.73232e6i	−0.137637	−	0.961695i
$514$		0			0
$515$	−7.31254e6	+	2.66155e6i	−1.21493	+	0.442197i
$516$		0			0
$517$	5720.18	−	4799.80i	0.000941204	−	0.000789764i
$518$		0			0
$519$	−848753.	−	4.81352e6i	−0.138313	−	0.784412i
$520$		0			0
$521$	919613.	−	1.59282e6i	0.148426	−	0.257082i	−0.782220	−	0.623003i	$-0.785913\pi$
$521$	919613.	−	1.59282e6i	0.148426	−	0.257082i	0.930646	+	0.365921i	$0.119246\pi$
$522$		0			0
$523$	−278721.	−	101446.i	−0.0445569	−	0.0162174i	0.319646	−	0.947537i	$-0.396436\pi$
$523$	−278721.	−	101446.i	−0.0445569	−	0.0162174i	−0.364202	+	0.931320i	$0.618658\pi$
$524$		0			0
$525$	205569.	+	356056.i	0.0325506	+	0.0563793i
$526$		0			0
$527$	−702636.	−	589581.i	−0.110206	−	0.0924735i
$528$		0			0
$529$	−665535.	+	3.77444e6i	−0.103403	+	0.586426i
$530$		0			0
$531$	−191991.			−0.0295492
$532$		0			0
$533$	−63611.4			−0.00969877
$534$		0			0
$535$	−973881.	+	5.52316e6i	−0.147103	+	0.834263i
$536$		0			0
$537$	6.12863e6	+	5.14253e6i	0.917123	+	0.769557i
$538$		0			0
$539$	43017.3	+	74508.1i	0.00637780	+	0.0110467i
$540$		0			0
$541$	−1.01239e7	−	3.68479e6i	−1.48714	−	0.541276i	−0.534449	−	0.845201i	$-0.679481\pi$
$541$	−1.01239e7	−	3.68479e6i	−1.48714	−	0.541276i	−0.952696	+	0.303924i	$0.901703\pi$
$542$		0			0
$543$	3.82901e6	−	6.63205e6i	0.557298	−	0.965268i
$544$		0			0
$545$	1.14741e6	+	6.50726e6i	0.165473	+	0.938441i
$546$		0			0
$547$	3.74973e6	−	3.14640e6i	0.535836	−	0.449620i	−0.334275	−	0.942476i	$-0.608491\pi$
$547$	3.74973e6	−	3.14640e6i	0.535836	−	0.449620i	0.870111	+	0.492856i	$0.164047\pi$
$548$		0			0
$549$	−369113.	+	134346.i	−0.0522672	+	0.0190237i
$550$		0			0
$551$	−2.67512e6	+	876680.i	−0.375374	+	0.123016i
$552$		0			0
$553$	−3.24544e6	+	1.18124e6i	−0.451295	+	0.164258i
$554$		0			0
$555$	−4.10640e6	+	3.44568e6i	−0.565886	+	0.474835i
$556$		0			0
$557$	1.73011e6	+	9.81194e6i	0.236285	+	1.34004i	0.839891	+	0.542755i	$0.182619\pi$
$557$	1.73011e6	+	9.81194e6i	0.236285	+	1.34004i	−0.603606	+	0.797283i	$0.706270\pi$
$558$		0			0
$559$	190316.	−	329636.i	0.0257599	−	0.0446175i
$560$		0			0
$561$	91162.2	+	33180.3i	0.0122295	+	0.00445116i
$562$		0			0
$563$	3.71859e6	+	6.44079e6i	0.494433	+	0.856383i	0.999979	−	0.00641628i	$-0.00204238\pi$
$563$	3.71859e6	+	6.44079e6i	0.494433	+	0.856383i	−0.505546	+	0.862799i	$0.668709\pi$
$564$		0			0
$565$	4.79824e6	+	4.02621e6i	0.632355	+	0.530609i
$566$		0			0
$567$	757417.	−	4.29552e6i	0.0989412	−	0.561124i
$568$		0			0
$569$	−9.96643e6			−1.29050			−0.645251	−	0.763970i	$-0.723247\pi$
$569$	−9.96643e6			−1.29050			−0.645251	+	0.763970i	$0.723247\pi$
$570$		0			0
$571$	8.23703e6			1.05726			0.528628	−	0.848853i	$-0.322707\pi$
$571$	8.23703e6			1.05726			0.528628	+	0.848853i	$0.322707\pi$
$572$		0			0
$573$	−994436.	+	5.63973e6i	−0.126529	+	0.717582i
$574$		0			0
$575$	451766.	+	379077.i	0.0569829	+	0.0478143i
$576$		0			0
$577$	6.13919e6	+	1.06334e7i	0.767664	+	1.32963i	0.938826	+	0.344391i	$0.111914\pi$
$577$	6.13919e6	+	1.06334e7i	0.767664	+	1.32963i	−0.171162	+	0.985243i	$0.554752\pi$
$578$		0			0
$579$	−8.88240e6	−	3.23293e6i	−1.10112	−	0.400774i
$580$		0			0
$581$	−1.27787e6	+	2.21334e6i	−0.157053	+	0.272024i
$582$		0			0
$583$	19406.3	+	110058.i	0.00236467	+	0.0134107i
$584$		0			0
$585$	33187.7	−	27847.8i	0.00400947	−	0.00336435i
$586$		0			0
$587$	1.28069e7	−	4.66132e6i	1.53408	−	0.558359i	0.569462	−	0.822017i	$-0.307151\pi$
$587$	1.28069e7	−	4.66132e6i	1.53408	−	0.558359i	0.964616	+	0.263658i	$0.0849292\pi$
$588$		0			0
$589$	−1.60216e6	−	642608.i	−0.190290	−	0.0763235i
$590$		0			0
$591$	−8.02993e6	+	2.92265e6i	−0.945677	+	0.344198i
$592$		0			0
$593$	−6.35943e6	+	5.33619e6i	−0.742645	+	0.623153i	−0.933547	−	0.358456i	$-0.883303\pi$
$593$	−6.35943e6	+	5.33619e6i	−0.742645	+	0.623153i	0.190902	+	0.981609i	$0.438859\pi$
$594$		0			0
$595$	−536231.	−	3.04112e6i	−0.0620954	−	0.352161i
$596$		0			0
$597$	5.84760e6	−	1.01283e7i	0.671494	−	1.16306i
$598$		0			0
$599$	−3.24075e6	−	1.17953e6i	−0.369044	−	0.134321i	0.150839	−	0.988558i	$-0.451802\pi$
$599$	−3.24075e6	−	1.17953e6i	−0.369044	−	0.134321i	−0.519883	+	0.854237i	$0.674025\pi$
$600$		0			0
$601$	−645751.	−	1.11847e6i	−0.0729255	−	0.126311i	0.827257	−	0.561824i	$-0.189900\pi$
$601$	−645751.	−	1.11847e6i	−0.0729255	−	0.126311i	−0.900182	+	0.435513i	$0.856567\pi$
$602$		0			0
$603$	−259504.	−	217750.i	−0.0290637	−	0.0243873i
$604$		0			0
$605$	−1.46862e6	+	8.32894e6i	−0.163125	+	0.925127i
$606$		0			0
$607$	2.91456e6			0.321071			0.160536	−	0.987030i	$-0.448678\pi$
$607$	2.91456e6			0.321071			0.160536	+	0.987030i	$0.448678\pi$
$608$		0			0
$609$	−2.01248e6			−0.219881
$610$		0			0
$611$	11344.8	−	64339.5i	0.00122940	−	0.00697228i
$612$		0			0
$613$	−6.50460e6	−	5.45801e6i	−0.699149	−	0.586656i	0.222382	−	0.974960i	$-0.428617\pi$
$613$	−6.50460e6	−	5.45801e6i	−0.699149	−	0.586656i	−0.921531	+	0.388304i	$0.873061\pi$
$614$		0			0
$615$	−421330.	−	729764.i	−0.0449194	−	0.0778027i
$616$		0			0
$617$	−1.06557e7	−	3.87837e6i	−1.12686	−	0.410144i	−0.289710	−	0.957114i	$-0.593559\pi$
$617$	−1.06557e7	−	3.87837e6i	−1.12686	−	0.410144i	−0.837152	+	0.546970i	$0.815781\pi$
$618$		0			0
$619$	7.60032e6	−	1.31641e7i	0.797270	−	1.38091i	−0.124119	−	0.992267i	$-0.539610\pi$
$619$	7.60032e6	−	1.31641e7i	0.797270	−	1.38091i	0.921388	−	0.388644i	$-0.127056\pi$
$620$		0			0
$621$	−1.03113e6	−	5.84783e6i	−0.107296	−	0.608507i
$622$		0			0
$623$	4.10918e6	−	3.44801e6i	0.424165	−	0.355917i
$624$		0			0
$625$	7.97791e6	−	2.90372e6i	0.816938	−	0.297341i
$626$		0			0
$627$	182483.	+	5910.73i	0.0185376	+	0.000600444i
$628$		0			0
$629$	−5.01096e6	+	1.82384e6i	−0.505003	+	0.183806i
$630$		0			0
$631$	121650.	−	102077.i	0.0121630	−	0.0102059i	−0.636686	−	0.771123i	$-0.719695\pi$
$631$	121650.	−	102077.i	0.0121630	−	0.0102059i	0.648849	+	0.760917i	$0.275251\pi$
$632$		0			0
$633$	−1.71190e6	−	9.70864e6i	−0.169812	−	0.963051i
$634$		0			0
$635$	1.28564e6	−	2.22679e6i	0.126527	−	0.219152i
$636$		0			0
$637$	707342.	+	257451.i	0.0690686	+	0.0251389i
$638$		0			0
$639$	−478461.	−	828718.i	−0.0463547	−	0.0802888i
$640$		0			0
$641$	3.71382e6	+	3.11627e6i	0.357007	+	0.299564i	0.803596	−	0.595175i	$-0.202917\pi$
$641$	3.71382e6	+	3.11627e6i	0.357007	+	0.299564i	−0.446590	+	0.894739i	$0.647362\pi$
$642$		0			0
$643$	1.96268e6	−	1.11309e7i	0.187207	−	1.06170i	−0.735880	−	0.677112i	$-0.763231\pi$
$643$	1.96268e6	−	1.11309e7i	0.187207	−	1.06170i	0.923087	−	0.384591i	$-0.125658\pi$
$644$		0			0
$645$	5.04222e6			0.477224
$646$		0			0
$647$	2.58004e6			0.242306			0.121153	−	0.992634i	$-0.461341\pi$
$647$	2.58004e6			0.242306			0.121153	+	0.992634i	$0.461341\pi$
$648$		0			0
$649$	−18599.9	+	105485.i	−0.00173340	+	0.00983061i
$650$		0			0
$651$	−945341.	−	793235.i	−0.0874251	−	0.0733583i
$652$		0			0
$653$	2.67083e6	+	4.62601e6i	0.245111	+	0.424545i	0.962163	−	0.272475i	$-0.0878422\pi$
$653$	2.67083e6	+	4.62601e6i	0.245111	+	0.424545i	−0.717052	+	0.697020i	$0.754509\pi$
$654$		0			0
$655$	1.06697e7	+	3.88347e6i	0.971742	+	0.353685i
$656$		0			0
$657$	140735.	−	243760.i	0.0127200	−	0.0220318i
$658$		0			0
$659$	−966779.	−	5.48288e6i	−0.0867189	−	0.491807i	−0.996972	−	0.0777559i	$-0.975225\pi$
$659$	−966779.	−	5.48288e6i	−0.0867189	−	0.491807i	0.910254	−	0.414051i	$-0.135887\pi$
$660$		0			0
$661$	6.60238e6	−	5.54005e6i	0.587756	−	0.493186i	−0.299728	−	0.954025i	$-0.596896\pi$
$661$	6.60238e6	−	5.54005e6i	0.587756	−	0.493186i	0.887484	+	0.460839i	$0.152452\pi$
$662$		0			0
$663$	797600.	−	290303.i	0.0704695	−	0.0256488i
$664$		0			0
$665$	−2.74139e6	−	5.12451e6i	−0.240390	−	0.449364i
$666$		0			0
$667$	−2.71263e6	+	987316.i	−0.236089	+	0.0859294i
$668$		0			0
$669$	4.00054e6	−	3.35685e6i	0.345584	−	0.289979i
$670$		0			0
$671$	38054.3	+	215817.i	0.00326285	+	0.0185045i
$672$		0			0
$673$	−3.92629e6	+	6.80054e6i	−0.334153	+	0.578770i	−0.983322	−	0.181875i	$-0.941783\pi$
$673$	−3.92629e6	+	6.80054e6i	−0.334153	+	0.578770i	0.649169	+	0.760644i	$0.275117\pi$
$674$		0			0
$675$	1.26387e6	+	460010.i	0.106768	+	0.0388605i
$676$		0			0
$677$	7.89025e6	+	1.36663e7i	0.661636	+	1.14599i	0.980186	+	0.198081i	$0.0634709\pi$
$677$	7.89025e6	+	1.36663e7i	0.661636	+	1.14599i	−0.318550	+	0.947906i	$0.603196\pi$
$678$		0			0
$679$	−5.05999e6	−	4.24583e6i	−0.421187	−	0.353418i
$680$		0			0
$681$	616499.	−	3.49634e6i	0.0509407	−	0.288899i
$682$		0			0
$683$	8.20735e6			0.673211			0.336605	−	0.941646i	$-0.390721\pi$
$683$	8.20735e6			0.673211			0.336605	+	0.941646i	$0.390721\pi$
$684$		0			0
$685$	1.20597e7			0.981993
$686$		0			0
$687$	−152785.	+	866489.i	−0.0123507	+	0.0700440i
$688$		0			0
$689$	749025.	+	628507.i	0.0601102	+	0.0504385i
$690$		0			0
$691$	6.92809e6	+	1.19998e7i	0.551974	+	0.956046i	0.998132	+	0.0610923i	$0.0194584\pi$
$691$	6.92809e6	+	1.19998e7i	0.551974	+	0.956046i	−0.446159	+	0.894954i	$0.647208\pi$
$692$		0			0
$693$	6227.65	+	2266.68i	0.000492596	+	0.000179290i
$694$		0			0
$695$	7.36175e6	−	1.27509e7i	0.578122	−	1.00134i
$696$		0			0
$697$	−145563.	−	825526.i	−0.0113493	−	0.0643649i
$698$		0			0
$699$	−4.88628e6	+	4.10007e6i	−0.378256	+	0.317394i
$700$		0			0
$701$	2.66065e6	−	968397.i	0.204500	−	0.0744318i	−0.237740	−	0.971329i	$-0.576406\pi$
$701$	2.66065e6	−	968397.i	0.204500	−	0.0744318i	0.442239	+	0.896897i	$0.354184\pi$
$702$		0			0
$703$	−7.89275e6	+	6.19868e6i	−0.602338	+	0.473054i
$704$		0			0
$705$	813260.	−	296002.i	0.0616249	−	0.0224296i
$706$		0			0
$707$	1.42430e6	−	1.19513e6i	0.107165	−	0.0899219i
$708$		0			0
$709$	−1.03547e6	−	5.87244e6i	−0.0773610	−	0.438736i	−0.998745	−	0.0500827i	$-0.984052\pi$
$709$	−1.03547e6	−	5.87244e6i	−0.0773610	−	0.438736i	0.921384	−	0.388653i	$-0.127060\pi$
$710$		0			0
$711$	319259.	−	552973.i	0.0236848	−	0.0410233i
$712$		0			0
$713$	−1.66339e6	−	605423.i	−0.122538	−	0.0446000i
$714$		0			0
$715$	−12085.2	−	20932.1i	−0.000884072	−	0.00153126i
$716$		0			0
$717$	2.14010e7	+	1.79576e7i	1.55466	+	1.30452i
$718$		0			0
$719$	1.76543e6	−	1.00122e7i	0.127358	−	0.722285i	−0.852521	−	0.522693i	$-0.824927\pi$
$719$	1.76543e6	−	1.00122e7i	0.127358	−	0.722285i	0.979879	−	0.199592i	$-0.0639616\pi$
$720$		0			0
$721$	−1.04152e7			−0.746157
$722$		0			0
$723$	−2.56119e7			−1.82220
$724$		0			0
$725$	113540.	−	643915.i	0.00802236	−	0.0454971i
$726$		0			0
$727$	−5.26074e6	−	4.41429e6i	−0.369157	−	0.309760i	0.439271	−	0.898355i	$-0.355237\pi$
$727$	−5.26074e6	−	4.41429e6i	−0.369157	−	0.309760i	−0.808428	+	0.588595i	$0.799681\pi$
$728$		0			0
$729$	−6.75073e6	−	1.16926e7i	−0.470470	−	0.814877i
$730$		0			0
$731$	4.71340e6	+	1.71554e6i	0.326243	+	0.118743i
$732$		0			0
$733$	−3.53199e6	+	6.11758e6i	−0.242806	+	0.420552i	−0.961512	−	0.274761i	$-0.911401\pi$
$733$	−3.53199e6	+	6.11758e6i	−0.242806	+	0.420552i	0.718707	+	0.695314i	$0.244734\pi$
$734$		0			0
$735$	1.73153e6	+	9.82001e6i	0.118226	+	0.670492i
$736$		0			0
$737$	−144778.	+	121483.i	−0.00981826	+	0.00823849i
$738$		0			0
$739$	−1.53724e7	+	5.59508e6i	−1.03545	+	0.376873i	−0.803154	−	0.595772i	$-0.796846\pi$
$739$	−1.53724e7	+	5.59508e6i	−1.03545	+	0.376873i	−0.232297	+	0.972645i	$0.574624\pi$
$740$		0			0
$741$	1.25630e6	−	986652.i	0.0840519	−	0.0660113i
$742$		0			0
$743$	−2.54803e6	+	927406.i	−0.169329	+	0.0616308i	−0.425294	−	0.905055i	$-0.639829\pi$
$743$	−2.54803e6	+	927406.i	−0.169329	+	0.0616308i	0.255964	+	0.966686i	$0.417607\pi$
$744$		0			0
$745$	1.43405e7	−	1.20331e7i	0.946613	−	0.794303i
$746$		0			0
$747$	−82048.9	−	465323.i	−0.00537987	−	0.0305107i
$748$		0			0
$749$	−3.75311e6	+	6.50058e6i	−0.244448	+	0.423397i
$750$		0			0
$751$	−1.33227e7	−	4.84905e6i	−0.861968	−	0.313731i	−0.127058	−	0.991895i	$-0.540554\pi$
$751$	−1.33227e7	−	4.84905e6i	−0.861968	−	0.313731i	−0.734910	+	0.678164i	$0.762776\pi$
$752$		0			0
$753$	−3.88387e6	−	6.72706e6i	−0.249619	−	0.432353i
$754$		0			0
$755$	−7.88186e6	−	6.61366e6i	−0.503224	−	0.422255i
$756$		0			0
$757$	−3.08319e6	+	1.74856e7i	−0.195551	+	1.10903i	0.716080	+	0.698018i	$0.245935\pi$
$757$	−3.08319e6	+	1.74856e7i	−0.195551	+	1.10903i	−0.911631	+	0.411009i	$0.865177\pi$
$758$		0			0
$759$	187223.			0.0117966
$760$		0			0
$761$	−5.72589e6			−0.358411			−0.179206	−	0.983812i	$-0.557353\pi$
$761$	−5.72589e6			−0.358411			−0.179206	+	0.983812i	$0.557353\pi$
$762$		0			0
$763$	−1.53569e6	+	8.70932e6i	−0.0954974	+	0.541593i
$764$		0			0
$765$	437343.	+	366974.i	0.0270189	+	0.0226716i
$766$		0			0
$767$	468577.	+	811599.i	0.0287603	+	0.0498142i
$768$		0			0
$769$	−6.16979e6	−	2.24562e6i	−0.376231	−	0.136937i	0.146981	−	0.989139i	$-0.453044\pi$
$769$	−6.16979e6	−	2.24562e6i	−0.376231	−	0.136937i	−0.523212	+	0.852202i	$0.675266\pi$
$770$		0			0
$771$	−1.03361e7	+	1.79026e7i	−0.626210	+	1.08463i
$772$		0			0
$773$	−1.65472e6	−	9.38441e6i	−0.0996040	−	0.564882i	−0.993239	−	0.116088i	$-0.962965\pi$
$773$	−1.65472e6	−	9.38441e6i	−0.0996040	−	0.564882i	0.893635	−	0.448795i	$-0.148147\pi$
$774$		0			0
$775$	307138.	−	257719.i	0.0183687	−	0.0154132i
$776$		0			0
$777$	−6.74185e6	+	2.45383e6i	−0.400614	+	0.145812i
$778$		0			0
$779$	−744163.	−	1.39107e6i	−0.0439364	−	0.0821309i
$780$		0			0
$781$	−501674.	+	182594.i	−0.0294302	+	0.0107117i
$782$		0			0
$783$	−5.04329e6	+	4.23183e6i	−0.293975	+	0.246674i
$784$		0			0
$785$	−1.27461e6	−	7.22869e6i	−0.0738251	−	0.418683i
$786$		0			0
$787$	−1.33773e7	+	2.31702e7i	−0.769898	+	1.33350i	0.167720	+	0.985835i	$0.446359\pi$
$787$	−1.33773e7	+	2.31702e7i	−0.769898	+	1.33350i	−0.937618	+	0.347667i	$0.886974\pi$
$788$		0			0
$789$	8.05409e6	+	2.93145e6i	0.460600	+	0.167645i
$790$		0			0
$791$	4.19164e6	+	7.26014e6i	0.238201	+	0.412576i
$792$		0			0
$793$	1.46878e6	+	1.23246e6i	0.0829420	+	0.0695966i
$794$		0			0
$795$	−2.24921e6	+	1.27559e7i	−0.126215	+	0.715802i
$796$		0			0
$797$	−3.69953e6			−0.206301			−0.103150	−	0.994666i	$-0.532892\pi$
$797$	−3.69953e6			−0.206301			−0.103150	+	0.994666i	$0.532892\pi$
$798$		0			0
$799$	860936.			0.0477094
$800$		0			0
$801$	−172210.	+	976650.i	−0.00948367	+	0.0537846i
$802$		0			0
$803$	−120294.	−	100939.i	−0.00658350	−	0.00552421i
$804$		0			0
$805$	−2.97977e6	−	5.16111e6i	−0.162066	−	0.280707i
$806$		0			0
$807$	1.43854e7	+	5.23587e6i	0.777570	+	0.283012i
$808$		0			0
$809$	−8.48134e6	+	1.46901e7i	−0.455610	+	0.789140i	−0.998723	−	0.0505199i	$-0.983912\pi$
$809$	−8.48134e6	+	1.46901e7i	−0.455610	+	0.789140i	0.543113	+	0.839660i	$0.317245\pi$
$810$		0			0
$811$	1.46378e6	+	8.30152e6i	0.0781492	+	0.443206i	0.998626	+	0.0524082i	$0.0166897\pi$
$811$	1.46378e6	+	8.30152e6i	0.0781492	+	0.443206i	−0.920477	+	0.390798i	$0.872199\pi$
$812$		0			0
$813$	−6.46397e6	+	5.42391e6i	−0.342983	+	0.287797i
$814$		0			0
$815$	1.53833e7	−	5.59907e6i	0.811252	−	0.295272i
$816$		0			0
$817$	9.43501e6	+	305605.i	0.494524	+	0.0160179i
$818$		0			0
$819$	54487.2	−	19831.7i	0.00283847	−	0.00103312i
$820$		0			0
$821$	1.44000e7	−	1.20830e7i	0.745596	−	0.625629i	−0.188738	−	0.982027i	$-0.560440\pi$
$821$	1.44000e7	−	1.20830e7i	0.745596	−	0.625629i	0.934334	+	0.356398i	$0.115995\pi$
$822$		0			0
$823$	4.86829e6	+	2.76095e7i	0.250540	+	1.42088i	0.807266	+	0.590187i	$0.200946\pi$
$823$	4.86829e6	+	2.76095e7i	0.250540	+	1.42088i	−0.556726	+	0.830696i	$0.687943\pi$
$824$		0			0
$825$	−21203.3	+	36725.1i	−0.00108460	+	0.00187857i
$826$		0			0
$827$	1.23672e7	+	4.50129e6i	0.628793	+	0.228862i	0.636706	−	0.771107i	$-0.280297\pi$
$827$	1.23672e7	+	4.50129e6i	0.628793	+	0.228862i	−0.00791307	+	0.999969i	$0.502519\pi$
$828$		0			0
$829$	−1.28807e7	−	2.23101e7i	−0.650961	−	1.12750i	−0.982890	−	0.184193i	$-0.941033\pi$
$829$	−1.28807e7	−	2.23101e7i	−0.650961	−	1.12750i	0.331930	−	0.943304i	$-0.392300\pi$
$830$		0			0
$831$	3.10911e6	+	2.60885e6i	0.156183	+	0.131053i
$832$		0			0
$833$	−1.72250e6	+	9.76876e6i	−0.0860094	+	0.487783i
$834$		0			0
$835$	1.21013e7			0.600643
$836$		0			0
$837$	−4.03704e6			−0.199182
$838$		0			0
$839$	5.75337e6	−	3.26290e7i	0.282174	−	1.60029i	−0.433033	−	0.901378i	$-0.642557\pi$
$839$	5.75337e6	−	3.26290e7i	0.282174	−	1.60029i	0.715207	−	0.698912i	$-0.246332\pi$
$840$		0			0
$841$	−1.32607e7	−	1.11271e7i	−0.646512	−	0.542488i
$842$		0			0
$843$	8.30058e6	+	1.43770e7i	0.402290	+	0.696787i
$844$		0			0
$845$	1.81295e7	+	6.59858e6i	0.873460	+	0.317913i
$846$		0			0
$847$	−5.65971e6	+	9.80290e6i	−0.271072	+	0.469511i
$848$		0			0
$849$	−6.72933e6	−	3.81639e7i	−0.320407	−	1.81712i
$850$		0			0
$851$	−7.88351e6	+	6.61505e6i	−0.373161	+	0.313119i
$852$		0			0
$853$	−2.15066e7	+	7.82775e6i	−1.01204	+	0.368353i	−0.794217	−	0.607635i	$-0.792119\pi$
$853$	−2.15066e7	+	7.82775e6i	−1.01204	+	0.368353i	−0.217825	+	0.975988i	$0.569896\pi$
$854$		0			0
$855$	997233.	+	399980.i	0.0466532	+	0.0187121i
$856$		0			0
$857$	3.06077e7	−	1.11403e7i	1.42357	−	0.518136i	0.488487	−	0.872571i	$-0.337549\pi$
$857$	3.06077e7	−	1.11403e7i	1.42357	−	0.518136i	0.935081	+	0.354434i	$0.115327\pi$
$858$		0			0
$859$	4.19842e6	−	3.52289e6i	0.194135	−	0.162898i	−0.540539	−	0.841319i	$-0.681780\pi$
$859$	4.19842e6	−	3.52289e6i	0.194135	−	0.162898i	0.734674	+	0.678421i	$0.237335\pi$
$860$		0			0
$861$	−195843.	−	1.11068e6i	−0.00900326	−	0.0510600i
$862$		0			0
$863$	8.64328e6	−	1.49706e7i	0.395050	−	0.684246i	−0.598058	−	0.801453i	$-0.704061\pi$
$863$	8.64328e6	−	1.49706e7i	0.395050	−	0.684246i	0.993108	+	0.117207i	$0.0373941\pi$
$864$		0			0
$865$	−1.50798e7	−	5.48859e6i	−0.685259	−	0.249414i
$866$		0			0
$867$	−5.76622e6	−	9.98738e6i	−0.260521	−	0.451236i
$868$		0			0
$869$	−272890.	−	228982.i	−0.0122585	−	0.0102861i
$870$		0			0
$871$	−287137.	+	1.62844e6i	−0.0128246	+	0.0727320i
$872$		0			0
$873$	1.22118e6			0.0542308
$874$		0			0
$875$	1.28915e7			0.569225
$876$		0			0
$877$	3.31736e6	−	1.88137e7i	0.145644	−	0.825991i	−0.821203	−	0.570636i	$-0.806697\pi$
$877$	3.31736e6	−	1.88137e7i	0.145644	−	0.825991i	0.966847	−	0.255355i	$-0.0821922\pi$
$878$		0			0
$879$	1.97682e7	+	1.65875e7i	0.862969	+	0.724117i
$880$		0			0
$881$	−1.94256e7	−	3.36461e7i	−0.843206	−	1.46048i	−0.887170	−	0.461443i	$-0.847332\pi$
$881$	−1.94256e7	−	3.36461e7i	−0.843206	−	1.46048i	0.0439635	−	0.999033i	$-0.486001\pi$
$882$		0			0
$883$	118260.	+	43043.1i	0.00510430	+	0.00185781i	0.344571	−	0.938760i	$-0.388024\pi$
$883$	118260.	+	43043.1i	0.00510430	+	0.00185781i	−0.339467	+	0.940618i	$0.610247\pi$
$884$		0			0
$885$	−6.20723e6	+	1.07512e7i	−0.266404	+	0.461424i
$886$		0			0
$887$	−400669.	−	2.27231e6i	−0.0170992	−	0.0969746i	0.975064	−	0.221925i	$-0.0712340\pi$
$887$	−400669.	−	2.27231e6i	−0.0170992	−	0.0969746i	−0.992163	+	0.124950i	$0.960123\pi$
$888$		0			0
$889$	2.63626e6	−	2.21209e6i	0.111875	−	0.0938745i
$890$		0			0
$891$	422762.	−	153873.i	0.0178403	−	0.00649333i
$892$		0			0
$893$	1.53972e6	−	504590.i	0.0646118	−	0.0211743i
$894$		0			0
$895$	2.46827e7	−	8.98377e6i	1.03000	−	0.374888i
$896$		0			0
$897$	1.25483e6	−	1.05293e6i	0.0520719	−	0.0436935i
$898$		0			0
$899$	340796.	+	1.93275e6i	0.0140636	+	0.0797584i
$900$		0			0
$901$	−6.44254e6	+	1.11588e7i	−0.264390	+	0.457937i
$902$		0			0
$903$	6.34151e6	+	2.30812e6i	0.258806	+	0.0941975i
$904$		0			0
$905$	−1.25714e7	−	2.17744e7i	−0.510227	−	0.883739i
$906$		0			0
$907$	−3.31664e7	−	2.78299e7i	−1.33869	−	1.12330i	−0.981960	−	0.189089i	$-0.939446\pi$
$907$	−3.31664e7	−	2.78299e7i	−1.33869	−	1.12330i	−0.356732	−	0.934207i	$-0.616109\pi$
$908$		0			0
$909$	−59690.2	+	338520.i	−0.00239604	+	0.0135886i
$910$		0			0
$911$	9.62251e6			0.384142			0.192071	−	0.981381i	$-0.438480\pi$
$911$	9.62251e6			0.384142			0.192071	+	0.981381i	$0.438480\pi$
$912$		0			0
$913$	−263610.			−0.0104661
$914$		0			0
$915$	−4.41053e6	+	2.50134e7i	−0.174156	+	0.987687i
$916$		0			0
$917$	1.16415e7	+	9.76836e6i	0.457177	+	0.383617i
$918$		0			0
$919$	−1.25389e7	−	2.17181e7i	−0.489747	−	0.848268i	0.510183	−	0.860066i	$-0.329578\pi$
$919$	−1.25389e7	−	2.17181e7i	−0.489747	−	0.848268i	−0.999930	+	0.0117984i	$0.996244\pi$
$920$		0			0
$921$	1.48701e7	+	5.41229e6i	0.577652	+	0.210248i
$922$		0			0
$923$	−2.33548e6	+	4.04517e6i	−0.0902343	+	0.156290i
$924$		0			0
$925$	−404770.	−	2.29557e6i	−0.0155544	−	0.0882136i
$926$		0			0
$927$	1.47506e6	−	1.23772e6i	0.0563779	−	0.0473067i
$928$		0			0
$929$	6.55316e6	−	2.38516e6i	0.249122	−	0.0906729i	−0.214441	−	0.976737i	$-0.568793\pi$
$929$	6.55316e6	−	2.38516e6i	0.249122	−	0.0906729i	0.463563	+	0.886064i	$0.346571\pi$
$930$		0			0
$931$	2.64487e6	+	1.84802e7i	0.100007	+	0.698767i
$932$		0			0
$933$	1.71916e7	−	6.25724e6i	0.646566	−	0.235331i
$934$		0			0
$935$	243995.	−	204736.i	0.00912750	−	0.00765888i
$936$		0			0
$937$	950257.	+	5.38917e6i	0.0353583	+	0.200527i	0.997370	−	0.0724823i	$-0.0230921\pi$
$937$	950257.	+	5.38917e6i	0.0353583	+	0.200527i	−0.962011	+	0.273009i	$0.911981\pi$
$938$		0			0
$939$	8.49769e6	−	1.47184e7i	0.314512	−	0.544751i
$940$		0			0
$941$	3.39623e7	+	1.23613e7i	1.25033	+	0.455081i	0.880512	−	0.474024i	$-0.157199\pi$
$941$	3.39623e7	+	1.23613e7i	1.25033	+	0.455081i	0.369814	+	0.929106i	$0.379421\pi$
$942$		0			0
$943$	−808873.	−	1.40101e6i	−0.0296211	−	0.0513053i
$944$		0			0
$945$	−1.04117e7	−	8.73647e6i	−0.379265	−	0.318241i
$946$		0			0
$947$	6.29391e6	−	3.56946e7i	0.228058	−	1.29338i	−0.628693	−	0.777653i	$-0.716410\pi$
$947$	6.29391e6	−	3.56946e7i	0.228058	−	1.29338i	0.856751	−	0.515730i	$-0.172479\pi$
$948$		0			0
$949$	−1.37392e6			−0.0495218
$950$		0			0
$951$	−4.83276e7			−1.73278
$952$		0			0
$953$	2.66162e6	−	1.50948e7i	0.0949323	−	0.538388i	−0.899836	−	0.436229i	$-0.856314\pi$
$953$	2.66162e6	−	1.50948e7i	0.0949323	−	0.538388i	0.994768	−	0.102159i	$-0.0325750\pi$
$954$		0			0
$955$	1.44032e7	+	1.20857e7i	0.511035	+	0.428809i
$956$		0			0
$957$	−103788.	−	179766.i	−0.00366326	−	0.00634495i
$958$		0			0
$959$	1.51672e7	+	5.52042e6i	0.532549	+	0.193832i
$960$		0			0
$961$	1.37129e7	−	2.37514e7i	0.478982	−	0.829621i
$962$		0			0
$963$	−240978.	−	1.36666e6i	−0.00837360	−	0.0474890i
$964$		0			0
$965$	−2.37737e7	+	1.99485e7i	−0.821823	+	0.689591i
$966$		0			0
$967$	−8.89865e6	+	3.23884e6i	−0.306026	+	0.111384i	−0.490468	−	0.871459i	$-0.663174\pi$
$967$	−8.89865e6	+	3.23884e6i	−0.306026	+	0.111384i	0.184443	+	0.982843i	$0.440952\pi$
$968$		0			0
$969$	1.56792e7	+	1.40460e7i	0.536433	+	0.480557i
$970$		0			0
$971$	4.44853e7	−	1.61913e7i	1.51415	−	0.551105i	0.554470	−	0.832204i	$-0.312921\pi$
$971$	4.44853e7	−	1.61913e7i	1.51415	−	0.551105i	0.959679	+	0.281099i	$0.0906989\pi$
$972$		0			0
$973$	1.50956e7	−	1.26667e7i	0.511174	−	0.428926i
$974$		0			0
$975$	64427.8	+	365388.i	0.00217051	+	0.0123096i
$976$		0			0
$977$	−1.41728e7	+	2.45480e7i	−0.475028	+	0.822773i	−0.999591	−	0.0285986i	$-0.990896\pi$
$977$	−1.41728e7	+	2.45480e7i	−0.475028	+	0.822773i	0.524563	+	0.851372i	$0.324229\pi$
$978$		0			0
$979$	519915.	+	189234.i	0.0173371	+	0.00631018i
$980$		0			0
$981$	−817502.	−	1.41595e6i	−0.0271217	−	0.0469761i
$982$		0			0
$983$	−2.16729e7	−	1.81857e7i	−0.715373	−	0.600269i	0.210728	−	0.977545i	$-0.432417\pi$
$983$	−2.16729e7	−	1.81857e7i	−0.715373	−	0.600269i	−0.926101	+	0.377276i	$0.876861\pi$
$984$		0			0
$985$	−4.87185e6	+	2.76296e7i	−0.159994	+	0.907370i
$986$		0			0
$987$	1.15832e6			0.0378474
$988$		0			0
$989$	9.68010e6			0.314695
$990$		0			0
$991$	−3.68528e6	+	2.09003e7i	−0.119203	+	0.676033i	0.865380	+	0.501116i	$0.167077\pi$
$991$	−3.68528e6	+	2.09003e7i	−0.119203	+	0.676033i	−0.984583	+	0.174917i	$0.944034\pi$
$992$		0			0
$993$	−1.05397e7	−	8.84389e6i	−0.339201	−	0.284623i
$994$		0			0
$995$	−1.91989e7	−	3.32534e7i	−0.614778	−	1.06483i
$996$		0			0
$997$	4.68264e7	+	1.70434e7i	1.49194	+	0.543023i	0.953960	−	0.299932i	$-0.0969641\pi$
$997$	4.68264e7	+	1.70434e7i	1.49194	+	0.543023i	0.537983	+	0.842956i	$0.319186\pi$
$998$		0			0
$999$	−1.17352e7	+	2.03260e7i	−0.372030	+	0.644375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.5.2	✓	48
19.4	even	9	inner	76.6.i.a.61.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.5.2	✓	48	1.1	even	1	trivial
76.6.i.a.61.2	yes	48	19.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.77836 + 15.7569i) q^{3} +(40.2412 + 33.7663i) q^{5} +(35.1538 + 60.8882i) q^{7} +(-12.2145 - 4.44570i) q^{9} +O(q^{10})\)	\(q+(-2.77836 + 15.7569i) q^{3} +(40.2412 + 33.7663i) q^{5} +(35.1538 + 60.8882i) q^{7} +(-12.2145 - 4.44570i) q^{9} +(-3.62592 + 6.28027i) q^{11} +(11.0176 + 62.4841i) q^{13} +(-643.857 + 540.260i) q^{15} +(-785.685 + 285.966i) q^{17} +(-1237.53 + 971.913i) q^{19} +(-1057.08 + 384.745i) q^{21} +(-1236.08 + 1037.20i) q^{23} +(-63.4653 - 359.930i) q^{25} +(-1840.01 + 3186.99i) q^{27} +(1681.11 + 611.875i) q^{29} +(548.509 + 950.045i) q^{31} +(-88.8833 - 74.5820i) q^{33} +(-641.341 + 3637.23i) q^{35} +6377.82 q^{37} -1015.17 q^{39} +(-174.095 + 987.343i) q^{41} +(-4595.58 - 3856.15i) q^{43} +(-341.409 - 591.338i) q^{45} +(-967.596 - 352.176i) q^{47} +(5931.92 - 10274.4i) q^{49} +(-2323.01 - 13174.5i) q^{51} +(11805.3 - 9905.85i) q^{53} +(-357.973 + 130.291i) q^{55} +(-11876.0 - 22200.0i) q^{57} +(13879.7 - 5051.78i) q^{59} +(23149.4 - 19424.6i) q^{61} +(-158.694 - 899.999i) q^{63} +(-1666.50 + 2886.46i) q^{65} +(24489.9 + 8913.60i) q^{67} +(-12908.7 - 22358.5i) q^{69} +(56395.2 + 47321.2i) q^{71} +(-3760.23 + 21325.3i) q^{73} +5847.70 q^{75} -509.859 q^{77} +(-8530.13 + 48376.7i) q^{79} +(-47524.4 - 39877.7i) q^{81} +(18175.4 + 31480.7i) q^{83} +(-41272.9 - 15022.1i) q^{85} +(-14312.0 + 24789.1i) q^{87} +(-13248.6 - 75136.4i) q^{89} +(-3417.23 + 2867.40i) q^{91} +(-16493.7 + 6003.21i) q^{93} +(-82617.7 - 2676.03i) q^{95} +(-88283.3 + 32132.5i) q^{97} +(72.2088 - 60.5904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 - 177 * q^7 + 33 * q^9 - 237 * q^11 + 2049 * q^13 + 2085 * q^15 - 609 * q^17 - 6012 * q^19 + 3591 * q^21 + 14100 * q^23 + 11802 * q^25 - 861 * q^27 - 10575 * q^29 - 6546 * q^31 - 21234 * q^33 - 231 * q^35 + 20052 * q^37 + 72204 * q^39 - 3249 * q^41 - 34677 * q^43 - 34956 * q^45 + 4461 * q^47 - 41139 * q^49 + 12099 * q^51 - 24291 * q^53 - 61767 * q^55 - 64470 * q^57 - 20100 * q^59 + 95490 * q^61 + 86403 * q^63 - 57915 * q^65 - 64452 * q^67 - 99315 * q^69 - 115536 * q^71 - 16362 * q^73 + 236250 * q^75 + 26688 * q^77 + 29799 * q^79 + 180327 * q^81 + 52347 * q^83 + 204618 * q^85 + 69414 * q^87 + 47394 * q^89 - 249384 * q^91 - 462126 * q^93 + 412869 * q^95 - 229974 * q^97 - 692274 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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