LMFDB - Embedded newform 76.6.i.a.17.8

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			17.8
Character	$\chi$	$=$	76.17
Dual form			76.6.i.a.9.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.5258 + 18.9014i) q^{3} +(-48.8881 + 17.7938i) q^{5} +(-11.8403 - 20.5081i) q^{7} +(107.952 + 612.226i) q^{9} +O(q^{10})$	\(q+(22.5258 + 18.9014i) q^{3} +(-48.8881 + 17.7938i) q^{5} +(-11.8403 - 20.5081i) q^{7} +(107.952 + 612.226i) q^{9} +(-249.138 + 431.521i) q^{11} +(58.3323 - 48.9466i) q^{13} +(-1437.57 - 523.233i) q^{15} +(282.005 - 1599.33i) q^{17} +(-8.67982 + 1573.54i) q^{19} +(120.918 - 685.758i) q^{21} +(215.101 + 78.2904i) q^{23} +(-320.460 + 268.898i) q^{25} +(-5567.47 + 9643.13i) q^{27} +(-663.534 - 3763.09i) q^{29} +(3299.02 + 5714.07i) q^{31} +(-13768.4 + 5011.27i) q^{33} +(943.768 + 791.916i) q^{35} +11557.4 q^{37} +2239.14 q^{39} +(15195.8 + 12750.8i) q^{41} +(-3675.94 + 1337.93i) q^{43} +(-16171.4 - 28009.7i) q^{45} +(-2753.92 - 15618.2i) q^{47} +(8123.11 - 14069.6i) q^{49} +(36581.8 - 30695.8i) q^{51} +(-16748.1 - 6095.79i) q^{53} +(4501.51 - 25529.4i) q^{55} +(-29937.5 + 35281.1i) q^{57} +(-71.6260 + 406.212i) q^{59} +(40913.3 + 14891.2i) q^{61} +(11277.4 - 9462.85i) q^{63} +(-1980.81 + 3430.87i) q^{65} +(5362.07 + 30409.8i) q^{67} +(3365.52 + 5829.25i) q^{69} +(50445.6 - 18360.7i) q^{71} +(-19969.8 - 16756.6i) q^{73} -12301.1 q^{75} +11799.5 q^{77} +(29658.1 + 24886.1i) q^{79} +(-165724. + 60318.6i) q^{81} +(-6303.15 - 10917.4i) q^{83} +(14671.5 + 83206.1i) q^{85} +(56180.9 - 97308.1i) q^{87} +(62912.6 - 52790.0i) q^{89} +(-1694.47 - 616.738i) q^{91} +(-33690.7 + 191070. i) q^{93} +(-27574.9 - 77081.8i) q^{95} +(15616.6 - 88566.0i) q^{97} +(-291083. - 105946. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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
$3$	22.5258	+	18.9014i	1.44503	+	1.21252i	0.936110	+	0.351708i	$0.114399\pi$
$3$	22.5258	+	18.9014i	1.44503	+	1.21252i	0.508918	+	0.860815i	$0.330046\pi$
$4$		0			0
$5$	−48.8881	+	17.7938i	−0.874537	+	0.318306i	−0.740003	−	0.672603i	$-0.765176\pi$
$5$	−48.8881	+	17.7938i	−0.874537	+	0.318306i	−0.134534	+	0.990909i	$0.542954\pi$
$6$		0			0
$7$	−11.8403	−	20.5081i	−0.0913311	−	0.158190i	0.816740	−	0.577005i	$-0.195779\pi$
$7$	−11.8403	−	20.5081i	−0.0913311	−	0.158190i	−0.908071	+	0.418815i	$0.862445\pi$
$8$		0			0
$9$	107.952	+	612.226i	0.444247	+	2.51945i
$10$		0			0
$11$	−249.138	+	431.521i	−0.620811	+	1.07528i	0.368524	+	0.929618i	$0.379863\pi$
$11$	−249.138	+	431.521i	−0.620811	+	1.07528i	−0.989335	+	0.145657i	$0.953470\pi$
$12$		0			0
$13$	58.3323	−	48.9466i	0.0957307	−	0.0803276i	−0.593666	−	0.804711i	$-0.702320\pi$
$13$	58.3323	−	48.9466i	0.0957307	−	0.0803276i	0.689397	+	0.724384i	$0.257876\pi$
$14$		0			0
$15$	−1437.57	−	523.233i	−1.64968	−	0.600436i
$16$		0			0
$17$	282.005	−	1599.33i	0.236665	−	1.34219i	−0.602414	−	0.798184i	$-0.705794\pi$
$17$	282.005	−	1599.33i	0.236665	−	1.34219i	0.839079	−	0.544010i	$-0.183094\pi$
$18$		0			0
$19$	−8.67982	+	1573.54i	−0.00551603	+	0.999985i
$19$	−8.67982	+	1573.54i	−0.00551603	+	0.999985i
$20$		0			0
$21$	120.918	−	685.758i	0.0598331	−	0.339330i
$22$		0			0
$23$	215.101	+	78.2904i	0.0847858	+	0.0308595i	0.384065	−	0.923306i	$-0.374524\pi$
$23$	215.101	+	78.2904i	0.0847858	+	0.0308595i	−0.299279	+	0.954166i	$0.596746\pi$
$24$		0			0
$25$	−320.460	+	268.898i	−0.102547	+	0.0860472i
$26$		0			0
$27$	−5567.47	+	9643.13i	−1.46977	+	2.54571i
$28$		0			0
$29$	−663.534	−	3763.09i	−0.146510	−	0.830901i	−0.966142	−	0.258011i	$-0.916933\pi$
$29$	−663.534	−	3763.09i	−0.146510	−	0.830901i	0.819632	−	0.572891i	$-0.194178\pi$
$30$		0			0
$31$	3299.02	+	5714.07i	0.616568	+	1.06793i	0.990107	+	0.140312i	$0.0448106\pi$
$31$	3299.02	+	5714.07i	0.616568	+	1.06793i	−0.373540	+	0.927614i	$0.621856\pi$
$32$		0			0
$33$	−13768.4	+	5011.27i	−2.20088	+	0.801056i
$34$		0			0
$35$	943.768	+	791.916i	0.130225	+	0.109272i
$36$		0			0
$37$	11557.4			1.38789			0.693945	−	0.720028i	$-0.255871\pi$
$37$	11557.4			1.38789			0.693945	+	0.720028i	$0.255871\pi$
$38$		0			0
$39$	2239.14			0.235732
$40$		0			0
$41$	15195.8	+	12750.8i	1.41177	+	1.18461i	0.955580	+	0.294731i	$0.0952301\pi$
$41$	15195.8	+	12750.8i	1.41177	+	1.18461i	0.456188	+	0.889883i	$0.349214\pi$
$42$		0			0
$43$	−3675.94	+	1337.93i	−0.303178	+	0.110348i	−0.489129	−	0.872211i	$-0.662685\pi$
$43$	−3675.94	+	1337.93i	−0.303178	+	0.110348i	0.185952	+	0.982559i	$0.440463\pi$
$44$		0			0
$45$	−16171.4	−	28009.7i	−1.19047	−	2.06195i
$46$		0			0
$47$	−2753.92	−	15618.2i	−0.181847	−	1.03131i	−0.929940	−	0.367711i	$-0.880141\pi$
$47$	−2753.92	−	15618.2i	−0.181847	−	1.03131i	0.748093	−	0.663594i	$-0.230970\pi$
$48$		0			0
$49$	8123.11	−	14069.6i	0.483317	−	0.837130i
$50$		0			0
$51$	36581.8	−	30695.8i	1.96943	−	1.65255i
$52$		0			0
$53$	−16748.1	−	6095.79i	−0.818983	−	0.298085i	−0.101654	−	0.994820i	$-0.532413\pi$
$53$	−16748.1	−	6095.79i	−0.818983	−	0.298085i	−0.717329	+	0.696735i	$0.754636\pi$
$54$		0			0
$55$	4501.51	−	25529.4i	0.200656	−	1.13798i
$56$		0			0
$57$	−29937.5	+	35281.1i	−1.22047	+	1.43832i
$58$		0			0
$59$	−71.6260	+	406.212i	−0.00267880	+	0.0151923i	−0.986118	−	0.166047i	$-0.946900\pi$
$59$	−71.6260	+	406.212i	−0.00267880	+	0.0151923i	0.983439	+	0.181239i	$0.0580108\pi$
$60$		0			0
$61$	40913.3	+	14891.2i	1.40780	+	0.512396i	0.930482	−	0.366337i	$-0.119388\pi$
$61$	40913.3	+	14891.2i	1.40780	+	0.512396i	0.477314	+	0.878733i	$0.341610\pi$
$62$		0			0
$63$	11277.4	−	9462.85i	0.357979	−	0.300380i
$64$		0			0
$65$	−1980.81	+	3430.87i	−0.0581513	+	0.100721i
$66$		0			0
$67$	5362.07	+	30409.8i	0.145930	+	0.827611i	0.966616	+	0.256231i	$0.0824808\pi$
$67$	5362.07	+	30409.8i	0.145930	+	0.827611i	−0.820685	+	0.571380i	$0.806408\pi$
$68$		0			0
$69$	3365.52	+	5829.25i	0.0851000	+	0.147398i
$70$		0			0
$71$	50445.6	−	18360.7i	1.18762	−	0.432258i	0.328732	−	0.944423i	$-0.393379\pi$
$71$	50445.6	−	18360.7i	1.18762	−	0.432258i	0.858887	+	0.512165i	$0.171157\pi$
$72$		0			0
$73$	−19969.8	−	16756.6i	−0.438597	−	0.368027i	0.396587	−	0.917997i	$-0.370195\pi$
$73$	−19969.8	−	16756.6i	−0.438597	−	0.368027i	−0.835184	+	0.549970i	$0.814639\pi$
$74$		0			0
$75$	−12301.1			−0.252518
$76$		0			0
$77$	11799.5			0.226797
$78$		0			0
$79$	29658.1	+	24886.1i	0.534658	+	0.448631i	0.869706	−	0.493570i	$-0.164308\pi$
$79$	29658.1	+	24886.1i	0.534658	+	0.448631i	−0.335048	+	0.942201i	$0.608753\pi$
$80$		0			0
$81$	−165724.	+	60318.6i	−2.80655	+	1.02150i
$82$		0			0
$83$	−6303.15	−	10917.4i	−0.100430	−	0.173949i	0.811432	−	0.584447i	$-0.198688\pi$
$83$	−6303.15	−	10917.4i	−0.100430	−	0.173949i	−0.911862	+	0.410497i	$0.865355\pi$
$84$		0			0
$85$	14671.5	+	83206.1i	0.220255	+	1.24913i
$86$		0			0
$87$	56180.9	−	97308.1i	0.795775	−	1.37832i
$88$		0			0
$89$	62912.6	−	52790.0i	0.841904	−	0.706442i	−0.116087	−	0.993239i	$-0.537035\pi$
$89$	62912.6	−	52790.0i	0.841904	−	0.706442i	0.957991	+	0.286797i	$0.0925906\pi$
$90$		0			0
$91$	−1694.47	−	616.738i	−0.0214502	−	0.00780724i
$92$		0			0
$93$	−33690.7	+	191070.i	−0.403927	+	2.29079i
$94$		0			0
$95$	−27574.9	−	77081.8i	−0.313477	−	0.876280i
$96$		0			0
$97$	15616.6	−	88566.0i	0.168522	−	0.955736i	−0.776836	−	0.629703i	$-0.783177\pi$
$97$	15616.6	−	88566.0i	0.168522	−	0.955736i	0.945358	−	0.326033i	$-0.105712\pi$
$98$		0			0
$99$	−291083.	−	105946.i	−2.98490	−	1.08641i
$100$		0			0
$101$	−111756.	+	93774.2i	−1.09010	+	0.914702i	−0.996720	−	0.0809281i	$-0.974212\pi$
$101$	−111756.	+	93774.2i	−1.09010	+	0.914702i	−0.0933800	+	0.995631i	$0.529767\pi$
$102$		0			0
$103$	91641.9	−	158728.i	0.851140	−	1.47422i	−0.0290406	−	0.999578i	$-0.509245\pi$
$103$	91641.9	−	158728.i	0.851140	−	1.47422i	0.880180	−	0.474639i	$-0.157421\pi$
$104$		0			0
$105$	6290.82	+	35677.0i	0.0556844	+	0.315802i
$106$		0			0
$107$	91255.6	+	158059.i	0.770549	+	1.33463i	0.937262	+	0.348625i	$0.113351\pi$
$107$	91255.6	+	158059.i	0.770549	+	1.33463i	−0.166713	+	0.986005i	$0.553315\pi$
$108$		0			0
$109$	−28283.5	+	10294.4i	−0.228017	+	0.0829914i	−0.453502	−	0.891255i	$-0.649826\pi$
$109$	−28283.5	+	10294.4i	−0.228017	+	0.0829914i	0.225485	+	0.974247i	$0.427603\pi$
$110$		0			0
$111$	260339.	+	218450.i	2.00554	+	1.68285i
$112$		0			0
$113$	−137794.			−1.01516			−0.507580	−	0.861604i	$-0.669460\pi$
$113$	−137794.			−1.01516			−0.507580	+	0.861604i	$0.669460\pi$
$114$		0			0
$115$	−11909.0			−0.0839711
$116$		0			0
$117$	36263.5	+	30428.7i	0.244909	+	0.205503i
$118$		0			0
$119$	−36138.1	+	13153.2i	−0.233937	+	0.0851459i
$120$		0			0
$121$	−43614.5	−	75542.5i	−0.270812	−	0.469059i
$122$		0			0
$123$	101290.	+	574442.i	0.603673	+	3.42360i
$124$		0			0
$125$	92172.1	−	159647.i	0.527624	−	0.913871i
$126$		0			0
$127$	−121219.	+	101715.i	−0.666903	+	0.559598i	−0.912147	−	0.409863i	$-0.865576\pi$
$127$	−121219.	+	101715.i	−0.666903	+	0.559598i	0.245244	+	0.969461i	$0.421132\pi$
$128$		0			0
$129$	−108092.	−	39342.3i	−0.571899	−	0.208154i
$130$		0			0
$131$	−767.380	+	4352.03i	−0.00390690	+	0.0221571i	−0.986699	−	0.162559i	$-0.948025\pi$
$131$	−767.380	+	4352.03i	−0.00390690	+	0.0221571i	0.982792	+	0.184716i	$0.0591364\pi$
$132$		0			0
$133$	32373.0	−	18453.2i	0.158691	−	0.0904571i
$134$		0			0
$135$	100595.	−	570501.i	0.475052	−	2.69415i
$136$		0			0
$137$	−318790.	−	116030.i	−1.45112	−	0.528165i	−0.508217	−	0.861229i	$-0.669695\pi$
$137$	−318790.	−	116030.i	−1.45112	−	0.528165i	−0.942904	+	0.333064i	$0.891918\pi$
$138$		0			0
$139$	−117601.	+	98678.7i	−0.516265	+	0.433198i	−0.863327	−	0.504644i	$-0.831624\pi$
$139$	−117601.	+	98678.7i	−0.516265	+	0.433198i	0.347062	+	0.937842i	$0.387179\pi$
$140$		0			0
$141$	233172.	−	403865.i	0.987707	−	1.71076i
$142$		0			0
$143$	6588.65	+	37366.1i	0.0269436	+	0.152805i
$144$		0			0
$145$	99398.7	+	172164.i	0.392609	+	0.680019i
$146$		0			0
$147$	448915.	−	163392.i	1.71345	−	0.623643i
$148$		0			0
$149$	−287523.	−	241260.i	−1.06098	−	0.890267i	−0.0667739	−	0.997768i	$-0.521271\pi$
$149$	−287523.	−	241260.i	−1.06098	−	0.890267i	−0.994205	+	0.107501i	$0.965715\pi$
$150$		0			0
$151$	286683.			1.02320			0.511599	−	0.859225i	$-0.329053\pi$
$151$	286683.			1.02320			0.511599	+	0.859225i	$0.329053\pi$
$152$		0			0
$153$	1.00959e6			3.48673
$154$		0			0
$155$	−262958.	−	220648.i	−0.879138	−	0.737685i
$156$		0			0
$157$	−293453.	+	106808.i	−0.950145	+	0.345824i	−0.770164	−	0.637846i	$-0.779826\pi$
$157$	−293453.	+	106808.i	−0.950145	+	0.345824i	−0.179981	+	0.983670i	$0.557603\pi$
$158$		0			0
$159$	−262044.	−	453873.i	−0.822018	−	1.42378i
$160$		0			0
$161$	−941.284	−	5338.29i	−0.00286191	−	0.0162307i
$162$		0			0
$163$	142544.	−	246894.i	0.420224	−	0.727849i	−0.575737	−	0.817635i	$-0.695285\pi$
$163$	142544.	−	246894.i	0.420224	−	0.727849i	0.995961	+	0.0897857i	$0.0286182\pi$
$164$		0			0
$165$	583940.	−	489983.i	1.66978	−	1.40111i
$166$		0			0
$167$	−228980.	−	83342.0i	−0.635341	−	0.231245i	0.00421347	−	0.999991i	$-0.498659\pi$
$167$	−228980.	−	83342.0i	−0.635341	−	0.231245i	−0.639554	+	0.768746i	$0.720881\pi$
$168$		0			0
$169$	−63467.5	+	359942.i	−0.170936	+	0.969428i
$170$		0			0
$171$	−964299.	+	164553.i	−2.52186	+	0.430343i
$172$		0			0
$173$	−20409.7	+	115749.i	−0.0518468	+	0.294038i	−0.999695	−	0.0246832i	$-0.992142\pi$
$173$	−20409.7	+	115749.i	−0.0518468	+	0.294038i	0.947848	+	0.318721i	$0.103253\pi$
$174$		0			0
$175$	9308.91	+	3388.17i	0.0229776	+	0.00836315i
$176$		0			0
$177$	−9291.38	+	7796.39i	−0.0222919	+	0.0187051i
$178$		0			0
$179$	−102898.	+	178225.i	−0.240036	+	0.415754i	−0.960724	−	0.277505i	$-0.910493\pi$
$179$	−102898.	+	178225.i	−0.240036	+	0.415754i	0.720688	+	0.693259i	$0.243826\pi$
$180$		0			0
$181$	119372.	+	676995.i	0.270837	+	1.53599i	0.751883	+	0.659297i	$0.229146\pi$
$181$	119372.	+	676995.i	0.270837	+	1.53599i	−0.481046	+	0.876695i	$0.659743\pi$
$182$		0			0
$183$	640139.	+	1.10875e6i	1.41301	+	2.44741i
$184$		0			0
$185$	−565019.	+	205650.i	−1.21376	+	0.441773i
$186$		0			0
$187$	619884.	+	520145.i	1.29630	+	1.08773i
$188$		0			0
$189$	263682.			0.536941
$190$		0			0
$191$	−330878.			−0.656272			−0.328136	−	0.944630i	$-0.606420\pi$
$191$	−330878.			−0.656272			−0.328136	+	0.944630i	$0.606420\pi$
$192$		0			0
$193$	466622.	+	391542.i	0.901720	+	0.756633i	0.970526	−	0.240997i	$-0.0774746\pi$
$193$	466622.	+	391542.i	0.901720	+	0.756633i	−0.0688062	+	0.997630i	$0.521919\pi$
$194$		0			0
$195$	−109467.	+	39842.8i	−0.206157	+	0.0750350i
$196$		0			0
$197$	−467008.	−	808882.i	−0.857352	−	1.48498i	−0.874446	−	0.485123i	$-0.838775\pi$
$197$	−467008.	−	808882.i	−0.857352	−	1.48498i	0.0170936	−	0.999854i	$-0.494559\pi$
$198$		0			0
$199$	−189238.	−	1.07322e6i	−0.338747	−	1.92113i	−0.386537	−	0.922274i	$-0.626329\pi$
$199$	−189238.	−	1.07322e6i	−0.338747	−	1.92113i	0.0477899	−	0.998857i	$-0.484782\pi$
$200$		0			0
$201$	−454002.	+	786354.i	−0.792624	+	1.37287i
$202$		0			0
$203$	−69317.2	+	58164.0i	−0.118059	+	0.0990636i
$204$		0			0
$205$	−969779.	−	352971.i	−1.61171	−	0.586616i
$206$		0			0
$207$	−24710.8	+	140142.i	−0.0400831	+	0.227323i
$208$		0			0
$209$	−676852.	−	395775.i	−1.07183	−	0.626732i
$210$		0			0
$211$	−10652.3	+	60412.4i	−0.0164717	+	0.0934157i	−0.991935	−	0.126745i	$-0.959547\pi$
$211$	−10652.3	+	60412.4i	−0.0164717	+	0.0934157i	0.975464	+	0.220161i	$0.0706581\pi$
$212$		0			0
$213$	1.48337e6	+	539901.i	2.24027	+	0.815390i
$214$		0			0
$215$	155903.	−	130818.i	0.230016	−	0.193006i
$216$		0			0
$217$	78123.0	−	135313.i	0.112624	−	0.195070i
$218$		0			0
$219$	−133111.	−	754912.i	−0.187545	−	1.06362i
$220$		0			0
$221$	−61831.7	−	107096.i	−0.0851590	−	0.147500i
$222$		0			0
$223$	−613585.	+	223327.i	−0.826252	+	0.300731i	−0.720320	−	0.693642i	$-0.756005\pi$
$223$	−613585.	+	223327.i	−0.826252	+	0.300731i	−0.105932	+	0.994373i	$0.533783\pi$
$224$		0			0
$225$	−199220.	−	167166.i	−0.262348	−	0.220136i
$226$		0			0
$227$	−301174.			−0.387929			−0.193965	−	0.981009i	$-0.562135\pi$
$227$	−301174.			−0.387929			−0.193965	+	0.981009i	$0.562135\pi$
$228$		0			0
$229$	545924.			0.687929			0.343964	−	0.938983i	$-0.388230\pi$
$229$	545924.			0.687929			0.343964	+	0.938983i	$0.388230\pi$
$230$		0			0
$231$	265793.	+	223027.i	0.327728	+	0.274997i
$232$		0			0
$233$	−357192.	+	130007.i	−0.431035	+	0.156884i	−0.548421	−	0.836203i	$-0.684771\pi$
$233$	−357192.	+	130007.i	−0.431035	+	0.156884i	0.117386	+	0.993086i	$0.462549\pi$
$234$		0			0
$235$	412542.	+	714544.i	0.487302	+	0.844032i
$236$		0			0
$237$	197690.	+	1.12116e6i	0.228620	+	1.29657i
$238$		0			0
$239$	110682.	−	191706.i	0.125337	−	0.217091i	−0.796527	−	0.604602i	$-0.793332\pi$
$239$	110682.	−	191706.i	0.125337	−	0.217091i	0.921865	+	0.387512i	$0.126665\pi$
$240$		0			0
$241$	558534.	−	468665.i	0.619451	−	0.519781i	−0.278180	−	0.960529i	$-0.589731\pi$
$241$	558534.	−	468665.i	0.619451	−	0.519781i	0.897631	+	0.440748i	$0.145287\pi$
$242$		0			0
$243$	−2.33055e6	−	848252.i	−2.53188	−	0.921529i
$244$		0			0
$245$	−146771.	+	832380.i	−0.156216	+	0.885944i
$246$		0			0
$247$	76513.1	+	92213.0i	0.0797983	+	0.0961723i
$248$		0			0
$249$	64369.9	−	365060.i	0.0657937	−	0.373135i
$250$		0			0
$251$	−93535.3	−	34044.1i	−0.0937111	−	0.0341081i	0.294739	−	0.955578i	$-0.404767\pi$
$251$	−93535.3	−	34044.1i	−0.0937111	−	0.0341081i	−0.388450	+	0.921470i	$0.626989\pi$
$252$		0			0
$253$	−87373.9	+	73315.4i	−0.0858184	+	0.0720102i
$254$		0			0
$255$	−1.24222e6	+	2.15159e6i	−1.19632	+	2.07209i
$256$		0			0
$257$	−227931.	−	1.29266e6i	−0.215263	−	1.22082i	−0.880449	−	0.474141i	$-0.842759\pi$
$257$	−227931.	−	1.29266e6i	−0.215263	−	1.22082i	0.665185	−	0.746678i	$-0.268353\pi$
$258$		0			0
$259$	−136843.	−	237019.i	−0.126758	−	0.219550i
$260$		0			0
$261$	2.23223e6	−	812466.i	2.02833	−	0.738251i
$262$		0			0
$263$	749937.	+	629272.i	0.668552	+	0.560982i	0.912636	−	0.408772i	$-0.134043\pi$
$263$	749937.	+	629272.i	0.668552	+	0.560982i	−0.244084	+	0.969754i	$0.578487\pi$
$264$		0			0
$265$	927249.			0.811113
$266$		0			0
$267$	2.41496e6			2.07315
$268$		0			0
$269$	−252872.	−	212185.i	−0.213069	−	0.178786i	0.530007	−	0.847993i	$-0.322189\pi$
$269$	−252872.	−	212185.i	−0.213069	−	0.178786i	−0.743076	+	0.669207i	$0.766634\pi$
$270$		0			0
$271$	1.36465e6	−	496693.i	1.12875	−	0.410833i	0.290914	−	0.956749i	$-0.406041\pi$
$271$	1.36465e6	−	496693.i	1.12875	−	0.410833i	0.837840	+	0.545916i	$0.183818\pi$
$272$		0			0
$273$	−26512.1	−	45920.4i	−0.0215297	−	0.0372905i
$274$		0			0
$275$	−36196.0	−	205278.i	−0.0288622	−	0.163685i
$276$		0			0
$277$	−77794.4	+	134744.i	−0.0609185	+	0.105514i	−0.894876	−	0.446314i	$-0.852736\pi$
$277$	−77794.4	+	134744.i	−0.0609185	+	0.105514i	0.833958	+	0.551828i	$0.186070\pi$
$278$		0			0
$279$	−3.14217e6	+	2.63659e6i	−2.41668	+	2.02783i
$280$		0			0
$281$	1.70452e6	+	620396.i	1.28777	+	0.468709i	0.892993	−	0.450070i	$-0.148601\pi$
$281$	1.70452e6	+	620396.i	1.28777	+	0.468709i	0.394773	+	0.918779i	$0.370823\pi$
$282$		0			0
$283$	71844.5	−	407450.i	0.0533245	−	0.302419i	−0.946468	−	0.322798i	$-0.895376\pi$
$283$	71844.5	−	407450.i	0.0533245	−	0.302419i	0.999792	+	0.0203798i	$0.00648754\pi$
$284$		0			0
$285$	835804.	−	2.25753e6i	0.609526	−	1.64635i
$286$		0			0
$287$	81570.5	−	462609.i	0.0584559	−	0.331520i
$288$		0			0
$289$	−1.14409e6	−	416415.i	−0.805780	−	0.293280i
$290$		0			0
$291$	2.02579e6	−	1.69984e6i	1.40237	−	1.17673i
$292$		0			0
$293$	902920.	−	1.56390e6i	0.614441	−	1.06424i	−0.376042	−	0.926603i	$-0.622715\pi$
$293$	902920.	−	1.56390e6i	0.614441	−	1.06424i	0.990482	−	0.137640i	$-0.0439516\pi$
$294$		0			0
$295$	−3726.39	−	21133.4i	−0.00249306	−	0.0141389i
$296$		0			0
$297$	−2.77414e6	−	4.80495e6i	−1.82489	−	3.16081i
$298$		0			0
$299$	16379.4	−	5961.61i	0.0105955	−	0.00385643i
$300$		0			0
$301$	70962.7	+	59544.8i	0.0451455	+	0.0378815i
$302$		0			0
$303$	−4.28984e6			−2.68432
$304$		0			0
$305$	−2.26515e6			−1.39427
$306$		0			0
$307$	1.60857e6	+	1.34975e6i	0.974082	+	0.817351i	0.983186	−	0.182607i	$-0.0584536\pi$
$307$	1.60857e6	+	1.34975e6i	0.974082	+	0.817351i	−0.00910442	+	0.999959i	$0.502898\pi$
$308$		0			0
$309$	5.06448e6	−	1.84332e6i	3.01744	−	1.09826i
$310$		0			0
$311$	−246857.	−	427570.i	−0.144726	−	0.250672i	0.784545	−	0.620072i	$-0.212897\pi$
$311$	−246857.	−	427570.i	−0.144726	−	0.250672i	−0.929271	+	0.369400i	$0.879563\pi$
$312$		0			0
$313$	−273799.	−	1.55279e6i	−0.157968	−	0.895884i	−0.956021	−	0.293297i	$-0.905248\pi$
$313$	−273799.	−	1.55279e6i	−0.157968	−	0.895884i	0.798053	−	0.602587i	$-0.205863\pi$
$314$		0			0
$315$	−382950.	+	663289.i	−0.217453	+	0.376640i
$316$		0			0
$317$	149077.	−	125090.i	0.0833225	−	0.0699159i	−0.600175	−	0.799869i	$-0.704902\pi$
$317$	149077.	−	125090.i	0.0833225	−	0.0699159i	0.683498	+	0.729953i	$0.260458\pi$
$318$		0			0
$319$	1.78916e6	+	651202.i	0.984403	+	0.358293i
$320$		0			0
$321$	−931935.	+	5.28526e6i	−0.504804	+	2.86289i
$322$		0			0
$323$	2.51416e6	+	457627.i	1.34087	+	0.244065i
$324$		0			0
$325$	−5531.53	+	31370.9i	−0.00290494	+	0.0164747i
$326$		0			0
$327$	−831685.	−	302709.i	−0.430120	−	0.156551i
$328$		0			0
$329$	−287692.	+	241402.i	−0.146534	+	0.122957i
$330$		0			0
$331$	293711.	−	508722.i	0.147350	−	0.255217i	−0.782897	−	0.622151i	$-0.786259\pi$
$331$	293711.	−	508722.i	0.147350	−	0.255217i	0.930247	+	0.366934i	$0.119592\pi$
$332$		0			0
$333$	1.24764e6	+	7.07573e6i	0.616566	+	3.49672i
$334$		0			0
$335$	−803248.	−	1.39127e6i	−0.391055	−	0.677327i
$336$		0			0
$337$	−87014.1	+	31670.5i	−0.0417364	+	0.0151908i	−0.362804	−	0.931865i	$-0.618181\pi$
$337$	−87014.1	+	31670.5i	−0.0417364	+	0.0151908i	0.321068	+	0.947056i	$0.395958\pi$
$338$		0			0
$339$	−3.10392e6	−	2.60450e6i	−1.46694	−	1.23091i
$340$		0			0
$341$	−3.28765e6			−1.53109
$342$		0			0
$343$	−782722.			−0.359230
$344$		0			0
$345$	−268259.	−	225096.i	−0.121341	−	0.101817i
$346$		0			0
$347$	3.77264e6	−	1.37313e6i	1.68198	−	0.612191i	0.688402	−	0.725329i	$-0.258312\pi$
$347$	3.77264e6	−	1.37313e6i	1.68198	−	0.612191i	0.993579	+	0.113138i	$0.0360901\pi$
$348$		0			0
$349$	1.93985e6	+	3.35992e6i	0.852520	+	1.47661i	0.878927	+	0.476956i	$0.158260\pi$
$349$	1.93985e6	+	3.35992e6i	0.852520	+	1.47661i	−0.0264072	+	0.999651i	$0.508407\pi$
$350$		0			0
$351$	147236.	+	835015.i	0.0637889	+	0.361765i
$352$		0			0
$353$	−1.15449e6	+	1.99963e6i	−0.493119	+	0.854108i	−0.999969	−	0.00792689i	$-0.997477\pi$
$353$	−1.15449e6	+	1.99963e6i	−0.493119	+	0.854108i	0.506849	+	0.862035i	$0.330810\pi$
$354$		0			0
$355$	−2.13948e6	+	1.79524e6i	−0.901027	+	0.756051i
$356$		0			0
$357$	−1.06265e6	−	386774.i	−0.441286	−	0.160615i
$358$		0			0
$359$	−425197.	+	2.41141e6i	−0.174122	+	0.987497i	0.765030	+	0.643995i	$0.222724\pi$
$359$	−425197.	+	2.41141e6i	−0.174122	+	0.987497i	−0.939152	+	0.343502i	$0.888387\pi$
$360$		0			0
$361$	−2.47595e6	−	27316.1i	−0.999939	−	0.0110319i
$362$		0			0
$363$	445406.	−	2.52602e6i	0.177415	−	1.00617i
$364$		0			0
$365$	1.27445e6	+	463862.i	0.500715	+	0.182245i
$366$		0			0
$367$	1.40540e6	−	1.17927e6i	0.544670	−	0.457032i	−0.328461	−	0.944517i	$-0.606530\pi$
$367$	1.40540e6	−	1.17927e6i	0.544670	−	0.457032i	0.873131	+	0.487485i	$0.162086\pi$
$368$		0			0
$369$	−6.16595e6	+	1.06797e7i	−2.35740	+	4.08314i
$370$		0			0
$371$	73289.6	+	415646.i	0.0276444	+	0.156779i
$372$		0			0
$373$	−1.71907e6	−	2.97751e6i	−0.639765	−	1.10811i	−0.985484	−	0.169767i	$-0.945698\pi$
$373$	−1.71907e6	−	2.97751e6i	−0.639765	−	1.10811i	0.345719	−	0.938338i	$-0.387635\pi$
$374$		0			0
$375$	5.09378e6	−	1.85399e6i	1.87052	−	0.680814i
$376$		0			0
$377$	−222896.	−	187032.i	−0.0807698	−	0.0677739i
$378$		0			0
$379$	3.39640e6			1.21456			0.607282	−	0.794486i	$-0.292260\pi$
$379$	3.39640e6			1.21456			0.607282	+	0.794486i	$0.292260\pi$
$380$		0			0
$381$	−4.65311e6			−1.64222
$382$		0			0
$383$	1.11556e6	+	936063.i	0.388593	+	0.326068i	0.816065	−	0.577961i	$-0.196151\pi$
$383$	1.11556e6	+	936063.i	0.388593	+	0.326068i	−0.427472	+	0.904029i	$0.640596\pi$
$384$		0			0
$385$	−576857.	+	209959.i	−0.198343	+	0.0721908i
$386$		0			0
$387$	−1.21594e6	−	2.10608e6i	−0.412701	−	0.714820i
$388$		0			0
$389$	−488318.	−	2.76939e6i	−0.163617	−	0.927919i	−0.950479	−	0.310789i	$-0.899407\pi$
$389$	−488318.	−	2.76939e6i	−0.163617	−	0.927919i	0.786862	−	0.617129i	$-0.211704\pi$
$390$		0			0
$391$	185871.	−	321939.i	0.0614852	−	0.106496i
$392$		0			0
$393$	−99545.1	+	83528.2i	−0.0325116	+	0.0272805i
$394$		0			0
$395$	−1.89275e6	−	688905.i	−0.610380	−	0.222160i
$396$		0			0
$397$	572592.	−	3.24733e6i	0.182334	−	1.03407i	−0.746998	−	0.664826i	$-0.768506\pi$
$397$	572592.	−	3.24733e6i	0.182334	−	1.03407i	0.929333	−	0.369244i	$-0.120383\pi$
$398$		0			0
$399$	1.07802e6	+	196221.i	0.338995	+	0.0617039i
$400$		0			0
$401$	287604.	−	1.63108e6i	0.0893169	−	0.506541i	−0.907024	−	0.421078i	$-0.861652\pi$
$401$	287604.	−	1.63108e6i	0.0893169	−	0.506541i	0.996341	−	0.0854632i	$-0.0272370\pi$
$402$		0			0
$403$	472124.	+	171839.i	0.144808	+	0.0527059i
$404$		0			0
$405$	7.02864e6	−	5.89773e6i	2.12928	−	1.78668i
$406$		0			0
$407$	−2.87939e6	+	4.98725e6i	−0.861617	+	1.49236i
$408$		0			0
$409$	194113.	+	1.10087e6i	0.0573782	+	0.325408i	0.999963	−	0.00855792i	$-0.00272410\pi$
$409$	194113.	+	1.10087e6i	0.0573782	+	0.325408i	−0.942585	+	0.333966i	$0.891613\pi$
$410$		0			0
$411$	−4.98787e6	−	8.63924e6i	−1.45650	−	2.52273i
$412$		0			0
$413$	9178.68	−	3340.77i	0.00264792	−	0.000963765i
$414$		0			0
$415$	502411.	+	421573.i	0.143199	+	0.120158i
$416$		0			0
$417$	−4.51420e6			−1.27128
$418$		0			0
$419$	3.90731e6			1.08728			0.543642	−	0.839317i	$-0.317045\pi$
$419$	3.90731e6			1.08728			0.543642	+	0.839317i	$0.317045\pi$
$420$		0			0
$421$	1.56283e6	+	1.31137e6i	0.429740	+	0.360594i	0.831853	−	0.554995i	$-0.187280\pi$
$421$	1.56283e6	+	1.31137e6i	0.429740	+	0.360594i	−0.402114	+	0.915590i	$0.631724\pi$
$422$		0			0
$423$	9.26461e6	−	3.37204e6i	2.51754	−	0.916309i
$424$		0			0
$425$	339684.	+	588350.i	0.0912227	+	0.158002i
$426$		0			0
$427$	−179037.	−	1.01537e6i	−0.0475196	−	0.269497i
$428$		0			0
$429$	−557856.	+	966234.i	−0.146345	+	0.253477i
$430$		0			0
$431$	1.74423e6	−	1.46358e6i	0.452282	−	0.379510i	−0.388000	−	0.921659i	$-0.626834\pi$
$431$	1.74423e6	−	1.46358e6i	0.452282	−	0.379510i	0.840282	+	0.542150i	$0.182389\pi$
$432$		0			0
$433$	−4.59913e6	−	1.67395e6i	−1.17884	−	0.429064i	−0.323050	−	0.946382i	$-0.604708\pi$
$433$	−4.59913e6	−	1.67395e6i	−1.17884	−	0.429064i	−0.855793	+	0.517318i	$0.826930\pi$
$434$		0			0
$435$	−1.01509e6	+	5.75688e6i	−0.257207	+	1.45869i
$436$		0			0
$437$	−125060.	+	337790.i	−0.0313267	+	0.0846143i
$438$		0			0
$439$	−945606.	+	5.36280e6i	−0.234180	+	1.32810i	0.610155	+	0.792282i	$0.291107\pi$
$439$	−945606.	+	5.36280e6i	−0.234180	+	1.32810i	−0.844335	+	0.535816i	$0.820004\pi$
$440$		0			0
$441$	9.49072e6	+	3.45434e6i	2.32382	+	0.845801i
$442$		0			0
$443$	−285221.	+	239329.i	−0.0690514	+	0.0579410i	−0.676660	−	0.736296i	$-0.736573\pi$
$443$	−285221.	+	239329.i	−0.0690514	+	0.0579410i	0.607609	+	0.794237i	$0.292129\pi$
$444$		0			0
$445$	−2.13635e6	+	3.70026e6i	−0.511413	+	0.885793i
$446$		0			0
$447$	−1.91652e6	−	1.08691e7i	−0.453675	−	2.57292i
$448$		0			0
$449$	2.17441e6	+	3.76619e6i	0.509009	+	0.881629i	0.999946	+	0.0104341i	$0.00332134\pi$
$449$	2.17441e6	+	3.76619e6i	0.509009	+	0.881629i	−0.490937	+	0.871195i	$0.663345\pi$
$450$		0			0
$451$	−9.28808e6	+	3.38058e6i	−2.15023	+	0.782619i
$452$		0			0
$453$	6.45775e6	+	5.41870e6i	1.47855	+	1.24065i
$454$		0			0
$455$	93813.8			0.0212441
$456$		0			0
$457$	−2.09564e6			−0.469381			−0.234691	−	0.972070i	$-0.575408\pi$
$457$	−2.09564e6			−0.469381			−0.234691	+	0.972070i	$0.575408\pi$
$458$		0			0
$459$	1.38525e7	+	1.16236e7i	3.06899	+	2.57519i
$460$		0			0
$461$	−1.23334e6	+	448898.i	−0.270289	+	0.0983773i	−0.473609	−	0.880735i	$-0.657049\pi$
$461$	−1.23334e6	+	448898.i	−0.270289	+	0.0983773i	0.203320	+	0.979112i	$0.434827\pi$
$462$		0			0
$463$	−3.74714e6	−	6.49024e6i	−0.812359	−	1.40705i	−0.911209	−	0.411944i	$-0.864850\pi$
$463$	−3.74714e6	−	6.49024e6i	−0.812359	−	1.40705i	0.0988502	−	0.995102i	$-0.468484\pi$
$464$		0			0
$465$	−1.75278e6	−	9.94053e6i	−0.375920	−	2.13195i
$466$		0			0
$467$	1.67581e6	−	2.90259e6i	0.355577	−	0.615877i	−0.631640	−	0.775262i	$-0.717618\pi$
$467$	1.67581e6	−	2.90259e6i	0.355577	−	0.615877i	0.987217	+	0.159385i	$0.0509511\pi$
$468$		0			0
$469$	560157.	−	470028.i	0.117592	−	0.0986714i
$470$		0			0
$471$	−8.62908e6	−	3.14073e6i	−1.79231	−	0.652346i
$472$		0			0
$473$	338473.	−	1.91957e6i	0.0695618	−	0.394505i
$474$		0			0
$475$	−420339.	−	506590.i	−0.0854803	−	0.103020i
$476$		0			0
$477$	1.92402e6	−	1.09117e7i	0.387181	−	2.19581i
$478$		0			0
$479$	−2.87821e6	−	1.04758e6i	−0.573171	−	0.208617i	0.0391406	−	0.999234i	$-0.487538\pi$
$479$	−2.87821e6	−	1.04758e6i	−0.573171	−	0.208617i	−0.612312	+	0.790617i	$0.709760\pi$
$480$		0			0
$481$	674169.	−	565695.i	0.132864	−	0.111486i
$482$		0			0
$483$	79697.7	−	138041.i	0.0155446	−	0.0269240i
$484$		0			0
$485$	812463.	+	4.60771e6i	0.156837	+	0.889468i
$486$		0			0
$487$	−412491.	−	714455.i	−0.0788119	−	0.136506i	0.823926	−	0.566698i	$-0.191779\pi$
$487$	−412491.	−	714455.i	−0.0788119	−	0.136506i	−0.902738	+	0.430192i	$0.858446\pi$
$488$		0			0
$489$	7.87755e6	−	2.86719e6i	1.48977	−	0.542231i
$490$		0			0
$491$	702767.	+	589691.i	0.131555	+	0.110388i	0.706191	−	0.708021i	$-0.250412\pi$
$491$	702767.	+	589691.i	0.131555	+	0.110388i	−0.574636	+	0.818409i	$0.694856\pi$
$492$		0			0
$493$	−6.20553e6			−1.14990
$494$		0			0
$495$	1.61157e7			2.95622
$496$		0			0
$497$	−973834.	−	817144.i	−0.176845	−	0.148391i
$498$		0			0
$499$	274714.	−	99987.6i	0.0493889	−	0.0179761i	−0.317208	−	0.948356i	$-0.602745\pi$
$499$	274714.	−	99987.6i	0.0493889	−	0.0179761i	0.366596	+	0.930380i	$0.380523\pi$
$500$		0			0
$501$	−3.58268e6	−	6.20538e6i	−0.637695	−	1.10452i
$502$		0			0
$503$	1.11096e6	+	6.30056e6i	0.195784	+	1.11035i	0.911298	+	0.411749i	$0.135082\pi$
$503$	1.11096e6	+	6.30056e6i	0.195784	+	1.11035i	−0.715513	+	0.698599i	$0.753807\pi$
$504$		0			0
$505$	3.79493e6	−	6.57301e6i	0.662178	−	1.14693i
$506$		0			0
$507$	−8.23304e6	+	6.90834e6i	−1.42246	+	1.19359i
$508$		0			0
$509$	2.35907e6	+	858631.i	0.403595	+	0.146897i	0.535838	−	0.844321i	$-0.319996\pi$
$509$	2.35907e6	+	858631.i	0.403595	+	0.146897i	−0.132243	+	0.991217i	$0.542218\pi$
$510$		0			0
$511$	−107197.	+	607945.i	−0.0181606	+	0.102994i
$512$		0			0
$513$	−1.51255e7	−	8.84432e6i	−2.53756	−	1.48379i
$514$		0			0
$515$	−1.65582e6	+	9.39059e6i	−0.275102	+	1.56018i
$516$		0			0
$517$	7.42570e6	+	2.70273e6i	1.22183	+	0.444710i
$518$		0			0
$519$	−2.64757e6	+	2.22157e6i	−0.431448	+	0.362028i
$520$		0			0
$521$	997031.	−	1.72691e6i	0.160922	−	0.278724i	−0.774278	−	0.632846i	$-0.781887\pi$
$521$	997031.	−	1.72691e6i	0.160922	−	0.278724i	0.935199	+	0.354121i	$0.115220\pi$
$522$		0			0
$523$	−718928.	−	4.07724e6i	−0.114929	−	0.651797i	−0.986785	−	0.162034i	$-0.948195\pi$
$523$	−718928.	−	4.07724e6i	−0.114929	−	0.651797i	0.871856	−	0.489763i	$-0.162917\pi$
$524$		0			0
$525$	145649.	+	252272.i	0.0230627	+	0.0399458i
$526$		0			0
$527$	1.00690e7	−	3.66482e6i	1.57928	−	0.574812i
$528$		0			0
$529$	−4.89039e6	−	4.10352e6i	−0.759808	−	0.637555i
$530$		0			0
$531$	−256426.			−0.0394662
$532$		0			0
$533$	1.51051e6			0.230307
$534$		0			0
$535$	−7.27380e6	−	6.10344e6i	−1.09869	−	0.921914i
$536$		0			0
$537$	−5.68656e6	+	2.06974e6i	−0.850970	+	0.309728i
$538$		0			0
$539$	4.04756e6	+	7.01058e6i	0.600097	+	1.03940i
$540$		0			0
$541$	674489.	+	3.82522e6i	0.0990790	+	0.561905i	0.993421	+	0.114521i	$0.0365332\pi$
$541$	674489.	+	3.82522e6i	0.0990790	+	0.561905i	−0.894342	+	0.447384i	$0.852356\pi$
$542$		0			0
$543$	−1.01072e7	+	1.75061e7i	−1.47106	+	2.54795i
$544$		0			0
$545$	1.19955e6	−	1.00654e6i	0.172993	−	0.145158i
$546$		0			0
$547$	−1.25567e7	−	4.57026e6i	−1.79435	−	0.653089i	−0.998891	−	0.0470773i	$-0.985009\pi$
$547$	−1.25567e7	−	4.57026e6i	−1.79435	−	0.653089i	−0.795456	−	0.606012i	$-0.792768\pi$
$548$		0			0
$549$	−4.70012e6	+	2.66557e7i	−0.665547	+	3.77450i
$550$		0			0
$551$	5.92712e6	−	1.01143e6i	0.831697	−	0.141925i
$552$		0			0
$553$	159204.	−	902891.i	0.0221381	−	0.125552i
$554$		0			0
$555$	−1.66145e7	−	6.04720e6i	−2.28958	−	0.833339i
$556$		0			0
$557$	19710.1	−	16538.7i	0.00269185	−	0.00225873i	−0.641441	−	0.767173i	$-0.721663\pi$
$557$	19710.1	−	16538.7i	0.00269185	−	0.00225873i	0.644133	+	0.764914i	$0.277219\pi$
$558$		0			0
$559$	−148939.	+	257970.i	−0.0201594	+	0.0349172i
$560$		0			0
$561$	4.13192e6	+	2.34333e7i	0.554300	+	3.14359i
$562$		0			0
$563$	755663.	+	1.30885e6i	0.100475	+	0.174027i	0.911880	−	0.410456i	$-0.134630\pi$
$563$	755663.	+	1.30885e6i	0.100475	+	0.174027i	−0.811406	+	0.584484i	$0.801297\pi$
$564$		0			0
$565$	6.73650e6	−	2.45189e6i	0.887796	−	0.323131i
$566$		0			0
$567$	3.19924e6	+	2.68448e6i	0.417917	+	0.350674i
$568$		0			0
$569$	7.05558e6			0.913592			0.456796	−	0.889572i	$-0.348997\pi$
$569$	7.05558e6			0.913592			0.456796	+	0.889572i	$0.348997\pi$
$570$		0			0
$571$	8.81226e6			1.13109			0.565545	−	0.824717i	$-0.308666\pi$
$571$	8.81226e6			1.13109			0.565545	+	0.824717i	$0.308666\pi$
$572$		0			0
$573$	−7.45327e6	−	6.25403e6i	−0.948331	−	0.795745i
$574$		0			0
$575$	−89983.3	+	32751.2i	−0.0113499	+	0.00413103i
$576$		0			0
$577$	3.14468e6	+	5.44674e6i	0.393221	+	0.681079i	0.992872	−	0.119183i	$-0.0380274\pi$
$577$	3.14468e6	+	5.44674e6i	0.393221	+	0.681079i	−0.599651	+	0.800261i	$0.704694\pi$
$578$		0			0
$579$	3.11033e6	+	1.76396e7i	0.385576	+	2.18671i
$580$		0			0
$581$	−149263.	+	258530.i	−0.0183447	+	0.0317740i
$582$		0			0
$583$	6.80305e6	−	5.70843e6i	0.828957	−	0.695577i
$584$		0			0
$585$	−2.31430e6	−	842336.i	−0.279595	−	0.101764i
$586$		0			0
$587$	−1.10917e6	+	6.29042e6i	−0.132863	+	0.753501i	0.843462	+	0.537189i	$0.180514\pi$
$587$	−1.10917e6	+	6.29042e6i	−0.132863	+	0.753501i	−0.976324	+	0.216312i	$0.930597\pi$
$588$		0			0
$589$	−9.01994e6	+	5.14154e6i	−1.07131	+	0.610667i
$590$		0			0
$591$	4.76925e6	−	2.70478e7i	0.561671	−	3.18539i
$592$		0			0
$593$	−5.85296e6	−	2.13030e6i	−0.683501	−	0.248774i	−0.0231510	−	0.999732i	$-0.507370\pi$
$593$	−5.85296e6	−	2.13030e6i	−0.683501	−	0.248774i	−0.660350	+	0.750958i	$0.729592\pi$
$594$		0			0
$595$	1.53268e6	−	1.28607e6i	0.177484	−	0.148927i
$596$		0			0
$597$	1.60226e7	−	2.77520e7i	1.83992	−	3.18683i
$598$		0			0
$599$	22429.3	+	127203.i	0.00255416	+	0.0144854i	0.986058	−	0.166401i	$-0.0532146\pi$
$599$	22429.3	+	127203.i	0.00255416	+	0.0144854i	−0.983504	+	0.180886i	$0.942103\pi$
$600$		0			0
$601$	5.80534e6	+	1.00551e7i	0.655604	+	1.13554i	0.981742	+	0.190217i	$0.0609192\pi$
$601$	5.80534e6	+	1.00551e7i	0.655604	+	1.13554i	−0.326138	+	0.945322i	$0.605747\pi$
$602$		0			0
$603$	−1.80388e7	+	6.56560e6i	−2.02030	+	0.735328i
$604$		0			0
$605$	3.47642e6	+	2.91706e6i	0.386139	+	0.324009i
$606$		0			0
$607$	−5.53530e6			−0.609775			−0.304888	−	0.952388i	$-0.598619\pi$
$607$	−5.53530e6			−0.609775			−0.304888	+	0.952388i	$0.598619\pi$
$608$		0			0
$609$	−2.66080e6			−0.290716
$610$		0			0
$611$	−925103.	−	776253.i	−0.100251	−	0.0841202i
$612$		0			0
$613$	8.03227e6	−	2.92351e6i	0.863351	−	0.314234i	0.127879	−	0.991790i	$-0.459183\pi$
$613$	8.03227e6	−	2.92351e6i	0.863351	−	0.314234i	0.735471	+	0.677556i	$0.236961\pi$
$614$		0			0
$615$	−1.51734e7	−	2.62811e7i	−1.61769	−	2.80192i
$616$		0			0
$617$	458905.	+	2.60258e6i	0.0485299	+	0.275227i	0.999411	−	0.0343311i	$-0.0109301\pi$
$617$	458905.	+	2.60258e6i	0.0485299	+	0.275227i	−0.950881	+	0.309558i	$0.899819\pi$
$618$		0			0
$619$	1.74711e6	−	3.02609e6i	0.183271	−	0.317435i	−0.759721	−	0.650249i	$-0.774665\pi$
$619$	1.74711e6	−	3.02609e6i	0.183271	−	0.317435i	0.942993	+	0.332814i	$0.107998\pi$
$620$		0			0
$621$	−1.95253e6	+	1.63837e6i	−0.203175	+	0.170484i
$622$		0			0
$623$	−1.82753e6	−	665165.i	−0.188644	−	0.0686609i
$624$		0			0
$625$	−1.43839e6	+	8.15750e6i	−0.147291	+	0.835328i
$626$		0			0
$627$	−7.76592e6	−	2.17085e7i	−0.788904	−	2.20527i
$628$		0			0
$629$	3.25923e6	−	1.84840e7i	0.328465	−	1.86282i
$630$		0			0
$631$	−3.85958e6	−	1.40477e6i	−0.385893	−	0.140453i	0.141786	−	0.989897i	$-0.454715\pi$
$631$	−3.85958e6	−	1.40477e6i	−0.385893	−	0.140453i	−0.527679	+	0.849444i	$0.676938\pi$
$632$		0			0
$633$	−1.38183e6	+	1.15949e6i	−0.137071	+	0.115016i
$634$		0			0
$635$	4.11629e6	−	7.12962e6i	0.405109	−	0.701669i
$636$		0			0
$637$	−214822.	−	1.21831e6i	−0.0209763	−	0.118963i
$638$		0			0
$639$	1.66866e7	+	2.89020e7i	1.61665	+	2.80012i
$640$		0			0
$641$	1.31551e7	−	4.78805e6i	1.26458	−	0.460271i	0.379279	−	0.925282i	$-0.376172\pi$
$641$	1.31551e7	−	4.78805e6i	1.26458	−	0.460271i	0.885305	+	0.465012i	$0.153950\pi$
$642$		0			0
$643$	7.23030e6	+	6.06694e6i	0.689650	+	0.578685i	0.918808	−	0.394704i	$-0.129153\pi$
$643$	7.23030e6	+	6.06694e6i	0.689650	+	0.578685i	−0.229158	+	0.973389i	$0.573597\pi$
$644$		0			0
$645$	5.98447e6			0.566404
$646$		0			0
$647$	1.05805e7			0.993677			0.496838	−	0.867843i	$-0.334494\pi$
$647$	1.05805e7			0.993677			0.496838	+	0.867843i	$0.334494\pi$
$648$		0			0
$649$	−157444.	−	132111.i	−0.0146728	−	0.0123120i
$650$		0			0
$651$	4.31738e6	−	1.57140e6i	0.399271	−	0.145323i
$652$		0			0
$653$	2.44574e6	+	4.23615e6i	0.224454	+	0.388766i	0.956156	−	0.292859i	$-0.0946068\pi$
$653$	2.44574e6	+	4.23615e6i	0.224454	+	0.388766i	−0.731701	+	0.681625i	$0.761273\pi$
$654$		0			0
$655$	−39923.5	−	226417.i	−0.00363601	−	0.0206208i
$656$		0			0
$657$	8.10307e6	−	1.40349e7i	0.732380	−	1.26852i
$658$		0			0
$659$	−2.47928e6	+	2.08036e6i	−0.222388	+	0.186606i	−0.747174	−	0.664628i	$-0.768590\pi$
$659$	−2.47928e6	+	2.08036e6i	−0.222388	+	0.186606i	0.524786	+	0.851234i	$0.324145\pi$
$660$		0			0
$661$	−641155.	−	233362.i	−0.0570768	−	0.0207743i	0.313324	−	0.949646i	$-0.398557\pi$
$661$	−641155.	−	233362.i	−0.0570768	−	0.0207743i	−0.370401	+	0.928872i	$0.620780\pi$
$662$		0			0
$663$	631447.	−	3.58111e6i	0.0557896	−	0.316398i
$664$		0			0
$665$	−1.25430e6	+	1.47818e6i	−0.109989	+	0.129621i
$666$		0			0
$667$	151887.	−	861393.i	0.0132192	−	0.0749698i
$668$		0			0
$669$	−1.80426e7	−	6.56698e6i	−1.55860	−	0.567284i
$670$		0			0
$671$	−1.66189e7	+	1.39449e7i	−1.42494	+	1.19567i
$672$		0			0
$673$	−3.45160e6	+	5.97834e6i	−0.293753	+	0.508795i	−0.974694	−	0.223543i	$-0.928238\pi$
$673$	−3.45160e6	+	5.97834e6i	−0.293753	+	0.508795i	0.680941	+	0.732338i	$0.261571\pi$
$674$		0			0
$675$	−808867.	−	4.58731e6i	−0.0683310	−	0.387524i
$676$		0			0
$677$	−6.02008e6	−	1.04271e7i	−0.504813	−	0.874362i	−0.999985	−	0.00556656i	$-0.998228\pi$
$677$	−6.02008e6	−	1.04271e7i	−0.504813	−	0.874362i	0.495171	−	0.868795i	$-0.335105\pi$
$678$		0			0
$679$	−2.00122e6	+	728385.i	−0.166579	+	0.0606299i
$680$		0			0
$681$	−6.78417e6	−	5.69259e6i	−0.560568	−	0.470373i
$682$		0			0
$683$	9.50286e6			0.779475			0.389738	−	0.920926i	$-0.372566\pi$
$683$	9.50286e6			0.779475			0.389738	+	0.920926i	$0.372566\pi$
$684$		0			0
$685$	1.76497e7			1.43718
$686$		0			0
$687$	1.22973e7	+	1.03187e7i	0.994076	+	0.834129i
$688$		0			0
$689$	−1.27532e6	+	464179.i	−0.102346	+	0.0372510i
$690$		0			0
$691$	1.78911e6	+	3.09883e6i	0.142542	+	0.246890i	0.928453	−	0.371449i	$-0.121139\pi$
$691$	1.78911e6	+	3.09883e6i	0.142542	+	0.246890i	−0.785911	+	0.618339i	$0.787806\pi$
$692$		0			0
$693$	1.27378e6	+	7.22398e6i	0.100754	+	0.571404i
$694$		0			0
$695$	3.99340e6	−	6.91678e6i	0.313604	−	0.543178i
$696$		0			0
$697$	2.46779e7	−	2.07073e7i	1.92410	−	1.61451i
$698$		0			0
$699$	−1.05033e7	−	3.82290e6i	−0.813082	−	0.295938i
$700$		0			0
$701$	85471.0	−	484730.i	0.00656937	−	0.0372568i	−0.981347	−	0.192245i	$-0.938423\pi$
$701$	85471.0	−	484730.i	0.00656937	−	0.0372568i	0.987916	+	0.154989i	$0.0495341\pi$
$702$		0			0
$703$	−100316.	+	1.81860e7i	−0.00765564	+	1.38787i
$704$		0			0
$705$	−4.21302e6	+	2.38932e7i	−0.319243	+	1.81052i
$706$		0			0
$707$	3.24635e6	+	1.18157e6i	0.244257	+	0.0889022i
$708$		0			0
$709$	4.89969e6	−	4.11133e6i	0.366061	−	0.307161i	−0.441140	−	0.897438i	$-0.645426\pi$
$709$	4.89969e6	−	4.11133e6i	0.366061	−	0.307161i	0.807201	+	0.590277i	$0.200981\pi$
$710$		0			0
$711$	−1.20343e7	+	2.08440e7i	−0.892784	+	1.54635i
$712$		0			0
$713$	262266.	+	1.48738e6i	0.0193205	+	0.109572i
$714$		0			0
$715$	−986993.	−	1.70952e6i	−0.0722019	−	0.125057i
$716$		0			0
$717$	6.11669e6	−	2.22629e6i	0.444343	−	0.161728i
$718$		0			0
$719$	7.71278e6	+	6.47179e6i	0.556402	+	0.466877i	0.877102	−	0.480304i	$-0.159474\pi$
$719$	7.71278e6	+	6.47179e6i	0.556402	+	0.466877i	−0.320700	+	0.947181i	$0.603918\pi$
$720$		0			0
$721$	−4.34028e6			−0.310942
$722$		0			0
$723$	2.14398e7			1.52537
$724$		0			0
$725$	1.22452e6	+	1.02750e6i	0.0865210	+	0.0725997i
$726$		0			0
$727$	−2.39359e7	+	8.71194e6i	−1.67963	+	0.611334i	−0.993259	−	0.115919i	$-0.963019\pi$
$727$	−2.39359e7	+	8.71194e6i	−1.67963	+	0.611334i	−0.686369	+	0.727254i	$0.740796\pi$
$728$		0			0
$729$	−1.50366e7	−	2.60442e7i	−1.04793	−	1.81507i
$730$		0			0
$731$	1.10316e6	+	6.25633e6i	0.0763564	+	0.433038i
$732$		0			0
$733$	−8.19144e6	+	1.41880e7i	−0.563119	+	0.975351i	0.434103	+	0.900863i	$0.357065\pi$
$733$	−8.19144e6	+	1.41880e7i	−0.563119	+	0.975351i	−0.997222	+	0.0744874i	$0.976268\pi$
$734$		0			0
$735$	−1.90392e7	+	1.59758e7i	−1.29996	+	1.09080i
$736$		0			0
$737$	−1.44583e7	−	5.26241e6i	−0.980505	−	0.356875i
$738$		0			0
$739$	4.93176e6	−	2.79694e7i	0.332193	−	1.88396i	−0.121165	−	0.992632i	$-0.538663\pi$
$739$	4.93176e6	−	2.79694e7i	0.332193	−	1.88396i	0.453358	−	0.891328i	$-0.350226\pi$
$740$		0			0
$741$	−19435.3	+	3.52337e6i	−0.00130031	+	0.235729i
$742$		0			0
$743$	2.04161e6	−	1.15785e7i	0.135675	−	0.769453i	−0.838712	−	0.544575i	$-0.816691\pi$
$743$	2.04161e6	−	1.15785e7i	0.135675	−	0.769453i	0.974387	−	0.224877i	$-0.0721981\pi$
$744$		0			0
$745$	1.83494e7	+	6.67864e6i	1.21124	+	0.440856i
$746$		0			0
$747$	6.00346e6	−	5.03750e6i	0.393641	−	0.330304i
$748$		0			0
$749$	2.16099e6	−	3.74295e6i	0.140750	−	0.243786i
$750$		0			0
$751$	−5.08778e6	−	2.88543e7i	−0.329177	−	1.86685i	−0.478533	−	0.878070i	$-0.658831\pi$
$751$	−5.08778e6	−	2.88543e7i	−0.329177	−	1.86685i	0.149356	−	0.988783i	$-0.452280\pi$
$752$		0			0
$753$	−1.46347e6	−	2.53481e6i	−0.0940584	−	0.162914i
$754$		0			0
$755$	−1.40154e7	+	5.10119e6i	−0.894824	+	0.325689i
$756$		0			0
$757$	−1.65610e6	−	1.38963e6i	−0.105038	−	0.0881374i	0.588756	−	0.808311i	$-0.299618\pi$
$757$	−1.65610e6	−	1.38963e6i	−0.105038	−	0.0881374i	−0.693794	+	0.720173i	$0.744062\pi$
$758$		0			0
$759$	−3.35392e6			−0.211324
$760$		0			0
$761$	−1.81471e7			−1.13592			−0.567958	−	0.823058i	$-0.692266\pi$
$761$	−1.81471e7			−1.13592			−0.567958	+	0.823058i	$0.692266\pi$
$762$		0			0
$763$	546003.	+	458151.i	0.0339535	+	0.0284903i
$764$		0			0
$765$	−4.93571e7	+	1.79645e7i	−3.04927	+	1.10984i
$766$		0			0
$767$	15704.6	+	27201.1i	0.000963913	+	0.00166955i
$768$		0			0
$769$	−2.98304e6	−	1.69177e7i	−0.181904	−	1.03163i	−0.929869	−	0.367892i	$-0.880080\pi$
$769$	−2.98304e6	−	1.69177e7i	−0.181904	−	1.03163i	0.747964	−	0.663739i	$-0.231031\pi$
$770$		0			0
$771$	1.92987e7	−	3.34263e7i	1.16921	−	2.02513i
$772$		0			0
$773$	1.33652e7	−	1.12148e7i	0.804504	−	0.675059i	−0.144786	−	0.989463i	$-0.546249\pi$
$773$	1.33652e7	−	1.12148e7i	0.804504	−	0.675059i	0.949289	+	0.314404i	$0.101805\pi$
$774$		0			0
$775$	−2.59370e6	−	944030.i	−0.155119	−	0.0564588i
$776$		0			0
$777$	1.39749e6	−	7.92556e6i	0.0830417	−	0.470953i
$778$		0			0
$779$	−2.01957e7	+	2.38005e7i	−1.19238	+	1.40521i
$780$		0			0
$781$	−4.64492e6	+	2.63426e7i	−0.272490	+	1.54537i
$782$		0			0
$783$	3.99822e7	+	1.45523e7i	2.33057	+	0.848258i
$784$		0			0
$785$	1.24459e7	−	1.04433e7i	0.720859	−	0.604873i
$786$		0			0
$787$	−7.16214e6	+	1.24052e7i	−0.412198	+	0.713948i	−0.995130	−	0.0985732i	$-0.968572\pi$
$787$	−7.16214e6	+	1.24052e7i	−0.412198	+	0.713948i	0.582932	+	0.812521i	$0.301905\pi$
$788$		0			0
$789$	4.99881e6	+	2.83496e7i	0.285874	+	1.62127i
$790$		0			0
$791$	1.63153e6	+	2.82589e6i	0.0927157	+	0.160588i
$792$		0			0
$793$	3.11544e6	−	1.13393e6i	0.175929	−	0.0640328i
$794$		0			0
$795$	2.08870e7	+	1.75263e7i	1.17208	+	0.983493i
$796$		0			0
$797$	−3.10053e7			−1.72898			−0.864490	−	0.502650i	$-0.832359\pi$
$797$	−3.10053e7			−1.72898			−0.864490	+	0.502650i	$0.832359\pi$
$798$		0			0
$799$	−2.57553e7			−1.42725
$800$		0			0
$801$	3.91110e7	+	3.28180e7i	2.15386	+	1.80730i
$802$		0			0
$803$	1.22061e7	−	4.44265e6i	0.668016	−	0.243138i
$804$		0			0
$805$	141006.	+	244230.i	0.00766917	+	0.0132834i
$806$		0			0
$807$	−1.68555e6	−	9.55926e6i	−0.0911085	−	0.516702i
$808$		0			0
$809$	−7.70017e6	+	1.33371e7i	−0.413646	+	0.716456i	−0.995285	−	0.0969909i	$-0.969078\pi$
$809$	−7.70017e6	+	1.33371e7i	−0.413646	+	0.716456i	0.581639	+	0.813447i	$0.302412\pi$
$810$		0			0
$811$	1.48160e6	−	1.24321e6i	0.0791007	−	0.0663733i	−0.602380	−	0.798209i	$-0.705781\pi$
$811$	1.48160e6	−	1.24321e6i	0.0791007	−	0.0663733i	0.681481	+	0.731836i	$0.261336\pi$
$812$		0			0
$813$	4.01280e7	+	1.46054e7i	2.12922	+	0.774974i
$814$		0			0
$815$	−2.57554e6	+	1.46066e7i	−0.135823	+	0.770291i
$816$		0			0
$817$	−2.07338e6	−	5.79585e6i	−0.108674	−	0.303782i
$818$		0			0
$819$	194662.	−	1.10398e6i	0.0101408	−	0.0575111i
$820$		0			0
$821$	−2.07329e7	−	7.54618e6i	−1.07350	−	0.390723i	−0.256017	−	0.966672i	$-0.582410\pi$
$821$	−2.07329e7	−	7.54618e6i	−1.07350	−	0.390723i	−0.817486	+	0.575949i	$0.804633\pi$
$822$		0			0
$823$	−2.33759e7	+	1.96147e7i	−1.20301	+	1.00945i	−0.203472	+	0.979081i	$0.565222\pi$
$823$	−2.33759e7	+	1.96147e7i	−1.20301	+	1.00945i	−0.999539	+	0.0303648i	$0.990333\pi$
$824$		0			0
$825$	3.06468e6	−	5.30819e6i	0.156766	−	0.271526i
$826$		0			0
$827$	−1.58509e6	−	8.98947e6i	−0.0805914	−	0.457057i	−0.998221	−	0.0596203i	$-0.981011\pi$
$827$	−1.58509e6	−	8.98947e6i	−0.0805914	−	0.457057i	0.917630	−	0.397436i	$-0.130100\pi$
$828$		0			0
$829$	2.18301e6	+	3.78109e6i	0.110324	+	0.191087i	0.915901	−	0.401404i	$-0.131478\pi$
$829$	2.18301e6	+	3.78109e6i	0.110324	+	0.191087i	−0.805577	+	0.592491i	$0.798144\pi$
$830$		0			0
$831$	−4.29922e6	+	1.56479e6i	−0.215967	+	0.0786055i
$832$		0			0
$833$	−2.02112e7	−	1.69592e7i	−1.00921	−	0.846824i
$834$		0			0
$835$	1.26774e7			0.629236
$836$		0			0
$837$	−7.34687e7			−3.62484
$838$		0			0
$839$	−2.72332e7	−	2.28514e7i	−1.33565	−	1.12075i	−0.982720	−	0.185098i	$-0.940740\pi$
$839$	−2.72332e7	−	2.28514e7i	−1.33565	−	1.12075i	−0.352934	−	0.935648i	$-0.614816\pi$
$840$		0			0
$841$	5.55362e6	−	2.02135e6i	0.270761	−	0.0985489i
$842$		0			0
$843$	2.66694e7	+	4.61927e7i	1.29254	+	2.23874i
$844$		0			0
$845$	−3.30194e6	−	1.87262e7i	−0.159084	−	0.902211i
$846$		0			0
$847$	−1.03282e6	+	1.78890e6i	−0.0494670	+	0.0856794i
$848$		0			0
$849$	9.31971e6	−	7.82017e6i	0.443745	−	0.372346i
$850$		0			0
$851$	2.48600e6	+	904832.i	0.117673	+	0.0428296i
$852$		0			0
$853$	−5.41615e6	+	3.07165e7i	−0.254870	+	1.44544i	0.541537	+	0.840677i	$0.317843\pi$
$853$	−5.41615e6	+	3.07165e7i	−0.254870	+	1.44544i	−0.796407	+	0.604761i	$0.793269\pi$
$854$		0			0
$855$	4.42148e7	−	2.52032e7i	2.06848	−	1.17907i
$856$		0			0
$857$	−4.15339e6	+	2.35550e7i	−0.193175	+	1.09555i	0.721819	+	0.692082i	$0.243306\pi$
$857$	−4.15339e6	+	2.35550e7i	−0.193175	+	1.09555i	−0.914994	+	0.403467i	$0.867805\pi$
$858$		0			0
$859$	2.88845e6	+	1.05131e6i	0.133562	+	0.0486125i	0.407936	−	0.913010i	$-0.366249\pi$
$859$	2.88845e6	+	1.05131e6i	0.133562	+	0.0486125i	−0.274374	+	0.961623i	$0.588471\pi$
$860$		0			0
$861$	1.05814e7	−	8.87883e6i	0.486446	−	0.408177i
$862$		0			0
$863$	−4.09307e6	+	7.08941e6i	−0.187078	+	0.324028i	−0.944275	−	0.329158i	$-0.893235\pi$
$863$	−4.09307e6	+	7.08941e6i	−0.187078	+	0.324028i	0.757197	+	0.653187i	$0.226568\pi$
$864$		0			0
$865$	−1.06183e6	−	6.02194e6i	−0.0482520	−	0.273650i
$866$		0			0
$867$	−1.79007e7	−	3.10050e7i	−0.808766	−	1.40082i
$868$		0			0
$869$	−1.81279e7	+	6.59800e6i	−0.814324	+	0.296390i
$870$		0			0
$871$	1.80124e6	+	1.51142e6i	0.0804500	+	0.0675056i
$872$		0			0
$873$	5.59083e7			2.48279
$874$		0			0
$875$	−4.36539e6			−0.192754
$876$		0			0
$877$	9.72151e6	+	8.15732e6i	0.426810	+	0.358136i	0.830747	−	0.556651i	$-0.187914\pi$
$877$	9.72151e6	+	8.15732e6i	0.426810	+	0.358136i	−0.403936	+	0.914787i	$0.632358\pi$
$878$		0			0
$879$	4.98988e7	−	1.81617e7i	2.17830	−	0.792837i
$880$		0			0
$881$	1.28161e7	+	2.21981e7i	0.556307	+	0.963552i	0.997801	+	0.0662879i	$0.0211156\pi$
$881$	1.28161e7	+	2.21981e7i	0.556307	+	0.963552i	−0.441493	+	0.897265i	$0.645551\pi$
$882$		0			0
$883$	−5.23840e6	−	2.97084e7i	−0.226098	−	1.28227i	−0.860575	−	0.509324i	$-0.829895\pi$
$883$	−5.23840e6	−	2.97084e7i	−0.226098	−	1.28227i	0.634477	−	0.772942i	$-0.281216\pi$
$884$		0			0
$885$	315511.	−	546480.i	0.0135412	−	0.0234540i
$886$		0			0
$887$	3.81792e6	−	3.20362e6i	0.162936	−	0.136720i	−0.557674	−	0.830060i	$-0.688306\pi$
$887$	3.81792e6	−	3.20362e6i	0.162936	−	0.136720i	0.720610	+	0.693340i	$0.243862\pi$
$888$		0			0
$889$	3.52126e6	+	1.28163e6i	0.149432	+	0.0543888i
$890$		0			0
$891$	1.52595e7	−	8.65410e7i	0.643941	−	3.65197i
$892$		0			0
$893$	2.45998e7	−	4.19783e6i	1.03229	−	0.176155i
$894$		0			0
$895$	1.85920e6	−	1.05441e7i	0.0775834	−	0.439997i
$896$		0			0
$897$	481641.	+	175303.i	0.0199868	+	0.00727459i
$898$		0			0
$899$	1.93135e7	−	1.62060e7i	0.797008	−	0.668769i
$900$		0			0
$901$	−1.44722e7	+	2.50666e7i	−0.593913	+	1.02869i
$902$		0			0
$903$	473012.	+	2.68258e6i	0.0193042	+	0.109480i
$904$		0			0
$905$	−1.78822e7	−	3.09729e7i	−0.725772	−	1.25707i
$906$		0			0
$907$	3.61210e7	−	1.31470e7i	1.45795	−	0.530649i	0.513147	−	0.858301i	$-0.328480\pi$
$907$	3.61210e7	−	1.31470e7i	1.45795	−	0.530649i	0.944798	+	0.327652i	$0.106257\pi$
$908$		0			0
$909$	−6.94753e7	−	5.82967e7i	−2.78882	−	2.34010i
$910$		0			0
$911$	−3.61370e7			−1.44263			−0.721316	−	0.692606i	$-0.756463\pi$
$911$	−3.61370e7			−1.44263			−0.721316	+	0.692606i	$0.756463\pi$
$912$		0			0
$913$	6.28142e6			0.249391
$914$		0			0
$915$	−5.10241e7	−	4.28143e7i	−2.01476	−	1.69058i
$916$		0			0
$917$	98337.7	−	35792.0i	0.00386186	−	0.00140560i
$918$		0			0
$919$	−1.53088e7	−	2.65156e7i	−0.597932	−	1.03565i	−0.993126	−	0.117051i	$-0.962656\pi$
$919$	−1.53088e7	−	2.65156e7i	−0.597932	−	1.03565i	0.395194	−	0.918598i	$-0.370677\pi$
$920$		0			0
$921$	1.07222e7	+	6.08085e7i	0.416518	+	2.36219i
$922$		0			0
$923$	2.04391e6	−	3.54016e6i	0.0789693	−	0.136779i
$924$		0			0
$925$	−3.70367e6	+	3.10775e6i	−0.142324	+	0.119424i
$926$		0			0
$927$	1.07071e8	+	3.89705e7i	4.09233	+	1.48949i
$928$		0			0
$929$	2.61804e6	−	1.48477e7i	0.0995263	−	0.564442i	−0.893740	−	0.448586i	$-0.851928\pi$
$929$	2.61804e6	−	1.48477e7i	0.0995263	−	0.564442i	0.993266	−	0.115856i	$-0.0369610\pi$
$930$		0			0
$931$	2.20686e7	+	1.29042e7i	0.834451	+	0.487928i
$932$		0			0
$933$	2.52099e6	−	1.42973e7i	0.0948130	−	0.537711i
$934$		0			0
$935$	−3.95604e7	−	1.43988e7i	−1.47990	−	0.538638i
$936$		0			0
$937$	3.21132e6	−	2.69462e6i	0.119491	−	0.100265i	−0.581084	−	0.813843i	$-0.697371\pi$
$937$	3.21132e6	−	2.69462e6i	0.119491	−	0.100265i	0.700575	+	0.713579i	$0.252927\pi$
$938$		0			0
$939$	2.31823e7	−	4.01529e7i	0.858010	−	1.48612i
$940$		0			0
$941$	11234.2	+	63712.4i	0.000413588	+	0.00234558i	0.985014	−	0.172475i	$-0.0551765\pi$
$941$	11234.2	+	63712.4i	0.000413588	+	0.00234558i	−0.984600	+	0.174821i	$0.944065\pi$
$942$		0			0
$943$	2.27037e6	+	3.93239e6i	0.0831413	+	0.144005i
$944$		0			0
$945$	−1.28909e7	+	4.69192e6i	−0.469575	+	0.170911i
$946$		0			0
$947$	2.45999e7	+	2.06418e7i	0.891370	+	0.747948i	0.968484	−	0.249074i	$-0.0801262\pi$
$947$	2.45999e7	+	2.06418e7i	0.891370	+	0.747948i	−0.0771143	+	0.997022i	$0.524571\pi$
$948$		0			0
$949$	−1.98506e6			−0.0715499
$950$		0			0
$951$	5.72245e6			0.205178
$952$		0			0
$953$	−3.20006e7	−	2.68517e7i	−1.14137	−	0.957722i	−0.141886	−	0.989883i	$-0.545317\pi$
$953$	−3.20006e7	−	2.68517e7i	−1.14137	−	0.957722i	−0.999483	+	0.0321607i	$0.989761\pi$
$954$		0			0
$955$	1.61760e7	−	5.88758e6i	0.573934	−	0.208895i
$956$		0			0
$957$	2.79936e7	+	4.84864e7i	0.988051	+	1.71135i
$958$		0			0
$959$	1.39503e6	+	7.91161e6i	0.0489820	+	0.277791i
$960$		0			0
$961$	−7.45248e6	+	1.29081e7i	−0.260311	+	0.450872i
$962$		0			0
$963$	−8.69169e7	+	7.29320e7i	−3.02022	+	2.53427i
$964$		0			0
$965$	−2.97793e7	−	1.08388e7i	−1.02943	−	0.374681i
$966$		0			0
$967$	−955654.	+	5.41978e6i	−0.0328651	+	0.186387i	−0.996821	−	0.0796754i	$-0.974612\pi$
$967$	−955654.	+	5.41978e6i	−0.0328651	+	0.186387i	0.963956	+	0.266062i	$0.0857227\pi$
$968$		0			0
$969$	4.79835e7	+	5.78293e7i	1.64166	+	1.97851i
$970$		0			0
$971$	−4.30864e6	+	2.44355e7i	−0.146653	+	0.831712i	0.819372	+	0.573263i	$0.194323\pi$
$971$	−4.30864e6	+	2.44355e7i	−0.146653	+	0.831712i	−0.966025	+	0.258449i	$0.916788\pi$
$972$		0			0
$973$	3.41614e6	+	1.24337e6i	0.115679	+	0.0421036i
$974$		0			0
$975$	−717553.	+	602099.i	−0.0241737	+	0.0202841i
$976$		0			0
$977$	1.20836e7	−	2.09294e7i	0.405004	−	0.701488i	−0.589318	−	0.807901i	$-0.700603\pi$
$977$	1.20836e7	−	2.09294e7i	0.405004	−	0.701488i	0.994322	+	0.106414i	$0.0339367\pi$
$978$		0			0
$979$	7.10599e6	+	4.03001e7i	0.236956	+	1.34385i
$980$		0			0
$981$	−9.35574e6	−	1.62046e7i	−0.310389	−	0.537609i
$982$		0			0
$983$	−1.90913e7	+	6.94867e6i	−0.630161	+	0.229360i	−0.637302	−	0.770615i	$-0.719949\pi$
$983$	−1.90913e7	+	6.94867e6i	−0.630161	+	0.229360i	0.00714013	+	0.999975i	$0.497727\pi$
$984$		0			0
$985$	3.72243e7	+	3.12349e7i	1.22246	+	1.02577i
$986$		0			0
$987$	−1.10433e7			−0.360833
$988$		0			0
$989$	−895446.			−0.0291104
$990$		0			0
$991$	−7.10005e6	−	5.95765e6i	−0.229656	−	0.192704i	0.520697	−	0.853741i	$-0.325672\pi$
$991$	−7.10005e6	−	5.95765e6i	−0.229656	−	0.192704i	−0.750353	+	0.661037i	$0.770116\pi$
$992$		0			0
$993$	1.62316e7	−	5.90781e6i	0.522381	−	0.190131i
$994$		0			0
$995$	2.83482e7	+	4.91006e7i	0.907754	+	1.57228i
$996$		0			0
$997$	−6.33362e6	−	3.59197e7i	−0.201797	−	1.14445i	−0.902401	−	0.430896i	$-0.858197\pi$
$997$	−6.33362e6	−	3.59197e7i	−0.201797	−	1.14445i	0.700605	−	0.713550i	$-0.252914\pi$
$998$		0			0
$999$	−6.43453e7	+	1.11449e8i	−2.03987	+	3.53316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.i.a.17.8	yes	48
19.9	even	9	inner	76.6.i.a.9.8	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.i.a.9.8	✓	48	19.9	even	9	inner
76.6.i.a.17.8	yes	48	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(22.5258 + 18.9014i) q^{3} +(-48.8881 + 17.7938i) q^{5} +(-11.8403 - 20.5081i) q^{7} +(107.952 + 612.226i) q^{9} +O(q^{10})\)	\(q+(22.5258 + 18.9014i) q^{3} +(-48.8881 + 17.7938i) q^{5} +(-11.8403 - 20.5081i) q^{7} +(107.952 + 612.226i) q^{9} +(-249.138 + 431.521i) q^{11} +(58.3323 - 48.9466i) q^{13} +(-1437.57 - 523.233i) q^{15} +(282.005 - 1599.33i) q^{17} +(-8.67982 + 1573.54i) q^{19} +(120.918 - 685.758i) q^{21} +(215.101 + 78.2904i) q^{23} +(-320.460 + 268.898i) q^{25} +(-5567.47 + 9643.13i) q^{27} +(-663.534 - 3763.09i) q^{29} +(3299.02 + 5714.07i) q^{31} +(-13768.4 + 5011.27i) q^{33} +(943.768 + 791.916i) q^{35} +11557.4 q^{37} +2239.14 q^{39} +(15195.8 + 12750.8i) q^{41} +(-3675.94 + 1337.93i) q^{43} +(-16171.4 - 28009.7i) q^{45} +(-2753.92 - 15618.2i) q^{47} +(8123.11 - 14069.6i) q^{49} +(36581.8 - 30695.8i) q^{51} +(-16748.1 - 6095.79i) q^{53} +(4501.51 - 25529.4i) q^{55} +(-29937.5 + 35281.1i) q^{57} +(-71.6260 + 406.212i) q^{59} +(40913.3 + 14891.2i) q^{61} +(11277.4 - 9462.85i) q^{63} +(-1980.81 + 3430.87i) q^{65} +(5362.07 + 30409.8i) q^{67} +(3365.52 + 5829.25i) q^{69} +(50445.6 - 18360.7i) q^{71} +(-19969.8 - 16756.6i) q^{73} -12301.1 q^{75} +11799.5 q^{77} +(29658.1 + 24886.1i) q^{79} +(-165724. + 60318.6i) q^{81} +(-6303.15 - 10917.4i) q^{83} +(14671.5 + 83206.1i) q^{85} +(56180.9 - 97308.1i) q^{87} +(62912.6 - 52790.0i) q^{89} +(-1694.47 - 616.738i) q^{91} +(-33690.7 + 191070. i) q^{93} +(-27574.9 - 77081.8i) q^{95} +(15616.6 - 88566.0i) q^{97} +(-291083. - 105946. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) 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

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