LMFDB - Embedded newform 92.6.e.a.85.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,6,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, 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:	$14.7553114228$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.10
Character	$\chi$	$=$	92.85
Dual form			92.6.e.a.13.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(24.2364 - 15.5758i) q^{3} +(-11.6103 - 25.4230i) q^{5} +(-177.640 + 52.1597i) q^{7} +(243.851 - 533.960i) q^{9} +(-474.348 - 547.427i) q^{11} +(166.261 + 48.8187i) q^{13} +(-677.373 - 435.321i) q^{15} +(156.535 - 1088.73i) q^{17} +(395.489 + 2750.69i) q^{19} +(-3492.91 + 4031.04i) q^{21} +(1405.67 - 2111.98i) q^{23} +(1534.91 - 1771.38i) q^{25} +(-1410.45 - 9809.89i) q^{27} +(-467.977 + 3254.85i) q^{29} +(2285.71 + 1468.94i) q^{31} +(-20023.1 - 5879.31i) q^{33} +(3388.50 + 3910.54i) q^{35} +(1856.40 - 4064.95i) q^{37} +(4789.95 - 1406.46i) q^{39} +(-5717.01 - 12518.5i) q^{41} +(7705.63 - 4952.11i) q^{43} -16406.0 q^{45} +8138.79 q^{47} +(14696.3 - 9444.74i) q^{49} +(-13163.9 - 28824.9i) q^{51} +(-18601.5 + 5461.88i) q^{53} +(-8409.90 + 18415.1i) q^{55} +(52429.3 + 60506.6i) q^{57} +(19241.0 + 5649.66i) q^{59} +(46618.8 + 29960.1i) q^{61} +(-15466.5 + 107572. i) q^{63} +(-689.223 - 4793.65i) q^{65} +(-29227.3 + 33730.1i) q^{67} +(1172.66 - 73081.0i) q^{69} +(-7781.03 + 8979.79i) q^{71} +(-5804.95 - 40374.3i) q^{73} +(9610.04 - 66839.3i) q^{75} +(112817. + 72503.0i) q^{77} +(4415.96 + 1296.64i) q^{79} +(-93569.7 - 107985. i) q^{81} +(4630.02 - 10138.3i) q^{83} +(-29496.1 + 8660.83i) q^{85} +(39354.8 + 86174.9i) q^{87} +(60433.9 - 38838.5i) q^{89} -32081.0 q^{91} +78277.2 q^{93} +(65338.9 - 41990.7i) q^{95} +(-3642.12 - 7975.12i) q^{97} +(-407975. + 119792. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{3} - 86 q^{5} - 118 q^{7} - 368 q^{9} - 242 q^{11} + 322 q^{13} - 3717 q^{15} + 2953 q^{17} - 259 q^{19} - 12349 q^{21} - 6038 q^{23} - 1324 q^{25} + 23933 q^{27} + 12677 q^{29} - 4401 q^{31}+ \cdots + 26799 q^{99}+O(q^{100}) $ 100 * q + 2 * q^3 - 86 * q^5 - 118 * q^7 - 368 * q^9 - 242 * q^11 + 322 * q^13 - 3717 * q^15 + 2953 * q^17 - 259 * q^19 - 12349 * q^21 - 6038 * q^23 - 1324 * q^25 + 23933 * q^27 + 12677 * q^29 - 4401 * q^31 - 43115 * q^33 + 10774 * q^35 - 72670 * q^37 - 61242 * q^39 - 30296 * q^41 + 69436 * q^43 + 125954 * q^45 + 79010 * q^47 + 27788 * q^49 - 65954 * q^51 - 60934 * q^53 - 234558 * q^55 + 37333 * q^57 + 392206 * q^59 + 153404 * q^61 + 7889 * q^63 - 178529 * q^65 - 52012 * q^67 - 280729 * q^69 - 166585 * q^71 + 42932 * q^73 + 484227 * q^75 + 434675 * q^77 + 150490 * q^79 - 132170 * q^81 - 236441 * q^83 - 399844 * q^85 + 121816 * q^87 + 151010 * q^89 + 240938 * q^91 - 54450 * q^93 - 281447 * q^95 - 76051 * q^97 + 26799 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

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
$3$	24.2364	−	15.5758i	1.55476	−	0.999186i	0.570744	−	0.821128i	$-0.306655\pi$
$3$	24.2364	−	15.5758i	1.55476	−	0.999186i	0.984020	−	0.178058i	$-0.0569815\pi$
$4$		0			0
$5$	−11.6103	−	25.4230i	−0.207691	−	0.454780i	0.776907	−	0.629616i	$-0.216788\pi$
$5$	−11.6103	−	25.4230i	−0.207691	−	0.454780i	−0.984598	+	0.174836i	$0.944060\pi$
$6$		0			0
$7$	−177.640	+	52.1597i	−1.37024	+	0.402337i	−0.882360	−	0.470576i	$-0.844046\pi$
$7$	−177.640	+	52.1597i	−1.37024	+	0.402337i	−0.487876	+	0.872913i	$0.662228\pi$
$8$		0			0
$9$	243.851	−	533.960i	1.00350	−	2.19737i
$10$		0			0
$11$	−474.348	−	547.427i	−1.18200	−	1.36410i	−0.916526	−	0.399976i	$-0.869018\pi$
$11$	−474.348	−	547.427i	−1.18200	−	1.36410i	−0.265470	−	0.964119i	$-0.585527\pi$
$12$		0			0
$13$	166.261	+	48.8187i	0.272855	+	0.0801175i	0.415298	−	0.909686i	$-0.363677\pi$
$13$	166.261	+	48.8187i	0.272855	+	0.0801175i	−0.142442	+	0.989803i	$0.545496\pi$
$14$		0			0
$15$	−677.373	−	435.321i	−0.777320	−	0.499553i
$16$		0			0
$17$	156.535	−	1088.73i	0.131368	−	0.913685i	−0.812405	−	0.583093i	$-0.801842\pi$
$17$	156.535	−	1088.73i	0.131368	−	0.913685i	0.943774	−	0.330592i	$-0.107249\pi$
$18$		0			0
$19$	395.489	+	2750.69i	0.251334	+	1.74806i	0.590226	+	0.807238i	$0.299039\pi$
$19$	395.489	+	2750.69i	0.251334	+	1.74806i	−0.338892	+	0.940825i	$0.610052\pi$
$20$		0			0
$21$	−3492.91	+	4031.04i	−1.72838	+	1.99466i
$22$		0			0
$23$	1405.67	−	2111.98i	0.554068	−	0.832471i
$23$	1405.67	−	2111.98i	0.554068	−	0.832471i
$24$		0			0
$25$	1534.91	−	1771.38i	0.491172	−	0.566842i
$26$		0			0
$27$	−1410.45	−	9809.89i	−0.372347	−	2.58973i
$28$		0			0
$29$	−467.977	+	3254.85i	−0.103331	+	0.718681i	0.870626	+	0.491946i	$0.163714\pi$
$29$	−467.977	+	3254.85i	−0.103331	+	0.718681i	−0.973956	+	0.226735i	$0.927195\pi$
$30$		0			0
$31$	2285.71	+	1468.94i	0.427186	+	0.274536i	0.736518	−	0.676418i	$-0.236469\pi$
$31$	2285.71	+	1468.94i	0.427186	+	0.274536i	−0.309331	+	0.950954i	$0.600105\pi$
$32$		0			0
$33$	−20023.1	−	5879.31i	−3.20071	−	0.939813i
$34$		0			0
$35$	3388.50	+	3910.54i	0.467560	+	0.539593i
$36$		0			0
$37$	1856.40	−	4064.95i	0.222930	−	0.488148i	−0.764810	−	0.644255i	$-0.777167\pi$
$37$	1856.40	−	4064.95i	0.222930	−	0.488148i	0.987740	+	0.156108i	$0.0498947\pi$
$38$		0			0
$39$	4789.95	−	1406.46i	0.504278	−	0.148069i
$40$		0			0
$41$	−5717.01	−	12518.5i	−0.531140	−	1.16303i	−0.965047	−	0.262077i	$-0.915593\pi$
$41$	−5717.01	−	12518.5i	−0.531140	−	1.16303i	0.433907	−	0.900958i	$-0.357135\pi$
$42$		0			0
$43$	7705.63	−	4952.11i	0.635532	−	0.408431i	−0.182822	−	0.983146i	$-0.558523\pi$
$43$	7705.63	−	4952.11i	0.635532	−	0.408431i	0.818354	+	0.574715i	$0.194887\pi$
$44$		0			0
$45$	−16406.0			−1.20774
$46$		0			0
$47$	8138.79			0.537422			0.268711	−	0.963221i	$-0.413402\pi$
$47$	8138.79			0.537422			0.268711	+	0.963221i	$0.413402\pi$
$48$		0			0
$49$	14696.3	−	9444.74i	0.874415	−	0.561953i
$50$		0			0
$51$	−13163.9	−	28824.9i	−0.708695	−	1.55183i
$52$		0			0
$53$	−18601.5	+	5461.88i	−0.909614	+	0.267087i	−0.702879	−	0.711310i	$-0.748102\pi$
$53$	−18601.5	+	5461.88i	−0.909614	+	0.267087i	−0.206736	+	0.978397i	$0.566284\pi$
$54$		0			0
$55$	−8409.90	+	18415.1i	−0.374873	+	0.820858i
$56$		0			0
$57$	52429.3	+	60506.6i	2.13741	+	2.46670i
$58$		0			0
$59$	19241.0	+	5649.66i	0.719609	+	0.211296i	0.620978	−	0.783828i	$-0.286735\pi$
$59$	19241.0	+	5649.66i	0.719609	+	0.211296i	0.0986310	+	0.995124i	$0.468554\pi$
$60$		0			0
$61$	46618.8	+	29960.1i	1.60412	+	1.03090i	0.965159	+	0.261666i	$0.0842718\pi$
$61$	46618.8	+	29960.1i	1.60412	+	1.03090i	0.638961	+	0.769239i	$0.279365\pi$
$62$		0			0
$63$	−15466.5	+	107572.i	−0.490953	+	3.41465i
$64$		0			0
$65$	−689.223	−	4793.65i	−0.0202337	−	0.140729i
$66$		0			0
$67$	−29227.3	+	33730.1i	−0.795430	+	0.917975i	−0.998121	−	0.0612673i	$-0.980486\pi$
$67$	−29227.3	+	33730.1i	−0.795430	+	0.917975i	0.202691	+	0.979243i	$0.435031\pi$
$68$		0			0
$69$	1172.66	−	73081.0i	0.0296517	−	1.84791i
$70$		0			0
$71$	−7781.03	+	8979.79i	−0.183186	+	0.211407i	−0.839914	−	0.542720i	$-0.817394\pi$
$71$	−7781.03	+	8979.79i	−0.183186	+	0.211407i	0.656728	+	0.754127i	$0.271940\pi$
$72$		0			0
$73$	−5804.95	−	40374.3i	−0.127495	−	0.886744i	−0.948715	−	0.316133i	$-0.897615\pi$
$73$	−5804.95	−	40374.3i	−0.127495	−	0.886744i	0.821220	−	0.570611i	$-0.193294\pi$
$74$		0			0
$75$	9610.04	−	66839.3i	0.197275	−	1.37208i
$76$		0			0
$77$	112817.	+	72503.0i	2.16844	+	1.39357i
$78$		0			0
$79$	4415.96	+	1296.64i	0.0796081	+	0.0233750i	0.321294	−	0.946979i	$-0.395882\pi$
$79$	4415.96	+	1296.64i	0.0796081	+	0.0233750i	−0.241686	+	0.970355i	$0.577700\pi$
$80$		0			0
$81$	−93569.7	−	107985.i	−1.58461	−	1.82874i
$82$		0			0
$83$	4630.02	−	10138.3i	0.0737714	−	0.161537i	−0.869153	−	0.494543i	$-0.835336\pi$
$83$	4630.02	−	10138.3i	0.0737714	−	0.161537i	0.942925	+	0.333006i	$0.108063\pi$
$84$		0			0
$85$	−29496.1	+	8660.83i	−0.442810	+	0.130021i
$86$		0			0
$87$	39354.8	+	86174.9i	0.557441	+	1.22063i
$88$		0			0
$89$	60433.9	−	38838.5i	0.808734	−	0.519742i	−0.0697214	−	0.997567i	$-0.522211\pi$
$89$	60433.9	−	38838.5i	0.808734	−	0.519742i	0.878455	+	0.477825i	$0.158575\pi$
$90$		0			0
$91$	−32081.0			−0.406110
$92$		0			0
$93$	78277.2			0.938486
$94$		0			0
$95$	65338.9	−	41990.7i	0.742784	−	0.477358i
$96$		0			0
$97$	−3642.12	−	7975.12i	−0.0393029	−	0.0860613i	0.888962	−	0.457981i	$-0.151427\pi$
$97$	−3642.12	−	7975.12i	−0.0393029	−	0.0860613i	−0.928265	+	0.371919i	$0.878700\pi$
$98$		0			0
$99$	−407975.	+	119792.i	−4.18355	+	1.22840i
$100$		0			0
$101$	63774.9	−	139647.i	0.622080	−	1.36216i	−0.291917	−	0.956444i	$-0.594293\pi$
$101$	63774.9	−	139647.i	0.622080	−	1.36216i	0.913997	−	0.405721i	$-0.132980\pi$
$102$		0			0
$103$	−2016.62	−	2327.30i	−0.0187297	−	0.0216152i	0.746307	−	0.665601i	$-0.231825\pi$
$103$	−2016.62	−	2327.30i	−0.0187297	−	0.0216152i	−0.765037	+	0.643986i	$0.777279\pi$
$104$		0			0
$105$	143035.	+	41998.8i	1.26610	+	0.371760i
$106$		0			0
$107$	8073.25	+	5188.37i	0.0681694	+	0.0438098i	0.574282	−	0.818658i	$-0.305281\pi$
$107$	8073.25	+	5188.37i	0.0681694	+	0.0438098i	−0.506112	+	0.862468i	$0.668918\pi$
$108$		0			0
$109$	6058.50	−	42137.8i	0.0488426	−	0.339708i	−0.950718	−	0.310058i	$-0.899652\pi$
$109$	6058.50	−	42137.8i	0.0488426	−	0.339708i	0.999560	−	0.0296500i	$-0.00943926\pi$
$110$		0			0
$111$	−18322.3	−	127435.i	−0.141148	−	0.981703i
$112$		0			0
$113$	−66953.2	+	77268.1i	−0.493259	+	0.569252i	−0.946734	−	0.322018i	$-0.895639\pi$
$113$	−66953.2	+	77268.1i	−0.493259	+	0.569252i	0.453474	+	0.891269i	$0.350184\pi$
$114$		0			0
$115$	−70012.9	−	11215.6i	−0.493666	−	0.0790823i
$116$		0			0
$117$	66610.2	−	76872.2i	0.449859	−	0.519164i
$118$		0			0
$119$	28980.8	+	201566.i	0.187604	+	1.30482i
$120$		0			0
$121$	−51750.2	+	359931.i	−0.321328	+	2.23489i
$122$		0			0
$123$	−333545.	−	214356.i	−1.98788	−	1.27754i
$124$		0			0
$125$	−146656.	−	43062.1i	−0.839509	−	0.246502i
$126$		0			0
$127$	165712.	+	191242.i	0.911684	+	1.05214i	0.998436	+	0.0559094i	$0.0178058\pi$
$127$	165712.	+	191242.i	0.911684	+	1.05214i	−0.0867519	+	0.996230i	$0.527649\pi$
$128$		0			0
$129$	109624.	−	240042.i	0.580003	−	1.27003i
$130$		0			0
$131$	152852.	−	44881.3i	0.778202	−	0.228501i	0.131574	−	0.991306i	$-0.457997\pi$
$131$	152852.	−	44881.3i	0.778202	−	0.228501i	0.646628	+	0.762806i	$0.276179\pi$
$132$		0			0
$133$	−213730.	−	468003.i	−1.04770	−	2.29414i
$134$		0			0
$135$	−233021.	+	149753.i	−1.10042	+	0.707199i
$136$		0			0
$137$	15102.9			0.0687478			0.0343739	−	0.999409i	$-0.489056\pi$
$137$	15102.9			0.0687478			0.0343739	+	0.999409i	$0.489056\pi$
$138$		0			0
$139$	168919.			0.741553			0.370777	−	0.928722i	$-0.379092\pi$
$139$	168919.			0.741553			0.370777	+	0.928722i	$0.379092\pi$
$140$		0			0
$141$	197255.	−	126768.i	0.835564	−	0.536984i
$142$		0			0
$143$	−52141.0	−	114173.i	−0.213226	−	0.466899i
$144$		0			0
$145$	88181.3	−	25892.4i	0.348303	−	0.102271i
$146$		0			0
$147$	209076.	−	457812.i	0.798014	−	1.74741i
$148$		0			0
$149$	89826.5	+	103665.i	0.331466	+	0.382532i	0.896879	−	0.442276i	$-0.145829\pi$
$149$	89826.5	+	103665.i	0.331466	+	0.382532i	−0.565413	+	0.824808i	$0.691283\pi$
$150$		0			0
$151$	87420.1	+	25668.9i	0.312010	+	0.0916145i	0.433989	−	0.900918i	$-0.357106\pi$
$151$	87420.1	+	25668.9i	0.312010	+	0.0916145i	−0.121979	+	0.992533i	$0.538924\pi$
$152$		0			0
$153$	−543165.	−	349071.i	−1.87587	−	1.20555i
$154$		0			0
$155$	10807.0	−	75164.3i	0.0361307	−	0.251294i
$156$		0			0
$157$	−50855.7	−	353709.i	−0.164661	−	1.14524i	−0.889704	−	0.456539i	$-0.849089\pi$
$157$	−50855.7	−	353709.i	−0.164661	−	1.14524i	0.725043	−	0.688704i	$-0.241820\pi$
$158$		0			0
$159$	−365759.	+	422108.i	−1.14737	+	1.32413i
$160$		0			0
$161$	−139543.	+	448490.i	−0.424270	+	1.36360i
$162$		0			0
$163$	−96651.7	+	111542.i	−0.284931	+	0.328828i	−0.880114	−	0.474762i	$-0.842534\pi$
$163$	−96651.7	+	111542.i	−0.284931	+	0.328828i	0.595183	+	0.803590i	$0.297080\pi$
$164$		0			0
$165$	83004.1	+	577306.i	0.237350	+	1.65081i
$166$		0			0
$167$	−61130.7	+	425174.i	−0.169617	+	1.17971i	0.710061	+	0.704140i	$0.248667\pi$
$167$	−61130.7	+	425174.i	−0.169617	+	1.17971i	−0.879678	+	0.475570i	$0.842242\pi$
$168$		0			0
$169$	−287092.	−	184503.i	−0.773222	−	0.496920i
$170$		0			0
$171$	1.56520e6	+	459583.i	4.09335	+	1.20192i
$172$		0			0
$173$	−88165.9	−	101749.i	−0.223968	−	0.258472i	0.632634	−	0.774451i	$-0.281974\pi$
$173$	−88165.9	−	101749.i	−0.223968	−	0.258472i	−0.856601	+	0.515979i	$0.827428\pi$
$174$		0			0
$175$	−180266.	+	394728.i	−0.444959	+	0.974324i
$176$		0			0
$177$	554329.	−	162766.i	1.32995	−	0.390508i
$178$		0			0
$179$	−248107.	−	543278.i	−0.578769	−	1.26733i	−0.941995	−	0.335627i	$-0.891052\pi$
$179$	−248107.	−	543278.i	−0.578769	−	1.26733i	0.363225	−	0.931701i	$-0.381675\pi$
$180$		0			0
$181$	−228088.	+	146583.i	−0.517494	+	0.332573i	−0.773180	−	0.634187i	$-0.781335\pi$
$181$	−228088.	+	146583.i	−0.517494	+	0.332573i	0.255686	+	0.966760i	$0.417699\pi$
$182$		0			0
$183$	1.59652e6			3.52409
$184$		0			0
$185$	−124897.			−0.268300
$186$		0			0
$187$	−670251.	+	430744.i	−1.40163	+	0.900773i
$188$		0			0
$189$	762233.	+	1.66906e6i	1.55215	+	3.39873i
$190$		0			0
$191$	−33698.3	+	9894.71i	−0.0668381	+	0.0196254i	−0.314981	−	0.949098i	$-0.601998\pi$
$191$	−33698.3	+	9894.71i	−0.0668381	+	0.0196254i	0.248143	+	0.968724i	$0.420180\pi$
$192$		0			0
$193$	20589.2	−	45084.0i	0.0397874	−	0.0871222i	−0.888695	−	0.458500i	$-0.848387\pi$
$193$	20589.2	−	45084.0i	0.0397874	−	0.0871222i	0.928482	+	0.371377i	$0.121114\pi$
$194$		0			0
$195$	−91369.0	−	105445.i	−0.172073	−	0.198583i
$196$		0			0
$197$	200888.	+	58986.1i	0.368798	+	0.108289i	0.460880	−	0.887463i	$-0.347534\pi$
$197$	200888.	+	58986.1i	0.368798	+	0.108289i	−0.0920817	+	0.995751i	$0.529352\pi$
$198$		0			0
$199$	−607862.	−	390649.i	−1.08811	−	0.699285i	−0.131692	−	0.991291i	$-0.542041\pi$
$199$	−607862.	−	390649.i	−1.08811	−	0.699285i	−0.956416	+	0.292006i	$0.905677\pi$
$200$		0			0
$201$	−182992.	+	1.27273e6i	−0.319478	+	2.22202i
$202$		0			0
$203$	−86640.9	−	602601.i	−0.147565	−	1.02634i
$204$		0			0
$205$	−251881.	+	290686.i	−0.418611	+	0.483103i
$206$		0			0
$207$	−784936.	−	1.26558e6i	−1.27323	−	2.05288i
$208$		0			0
$209$	1.31820e6	−	1.52129e6i	2.08745	−	2.40905i
$210$		0			0
$211$	120877.	+	840718.i	0.186912	+	1.30000i	0.839944	+	0.542673i	$0.182588\pi$
$211$	120877.	+	840718.i	0.186912	+	1.30000i	−0.653032	+	0.757330i	$0.726503\pi$
$212$		0			0
$213$	−48716.8	+	338833.i	−0.0735750	+	0.511725i
$214$		0			0
$215$	−215362.	−	138405.i	−0.317740	−	0.204199i
$216$		0			0
$217$	−482653.	−	141720.i	−0.695802	−	0.204306i
$218$		0			0
$219$	−769553.	−	888111.i	−1.08425	−	1.25129i
$220$		0			0
$221$	79175.9	−	173371.i	0.109047	−	0.238779i
$222$		0			0
$223$	−1.00421e6	+	294862.i	−1.35226	+	0.397060i	−0.876029	−	0.482258i	$-0.839817\pi$
$223$	−1.00421e6	+	294862.i	−1.35226	+	0.397060i	−0.476234	+	0.879318i	$0.657999\pi$
$224$		0			0
$225$	−571557.	−	1.25153e6i	−0.752667	−	1.64811i
$226$		0			0
$227$	456612.	−	293447.i	0.588143	−	0.377977i	−0.212462	−	0.977169i	$-0.568148\pi$
$227$	456612.	−	293447.i	0.588143	−	0.377977i	0.800605	+	0.599193i	$0.204512\pi$
$228$		0			0
$229$	−308741.			−0.389050			−0.194525	−	0.980898i	$-0.562317\pi$
$229$	−308741.			−0.389050			−0.194525	+	0.980898i	$0.562317\pi$
$230$		0			0
$231$	3.86356e6			4.76385
$232$		0			0
$233$	450898.	−	289775.i	0.544113	−	0.349680i	−0.239533	−	0.970888i	$-0.576994\pi$
$233$	450898.	−	289775.i	0.544113	−	0.349680i	0.783645	+	0.621208i	$0.213358\pi$
$234$		0			0
$235$	−94493.6	−	206912.i	−0.111618	−	0.244409i
$236$		0			0
$237$	127223.	−	37356.0i	0.147128	−	0.0432006i
$238$		0			0
$239$	−659967.	+	1.44513e6i	−0.747355	+	1.63648i	0.0237058	+	0.999719i	$0.492454\pi$
$239$	−659967.	+	1.44513e6i	−0.747355	+	1.63648i	−0.771061	+	0.636761i	$0.780274\pi$
$240$		0			0
$241$	−1.03227e6	−	1.19130e6i	−1.14485	−	1.32123i	−0.939502	−	0.342543i	$-0.888712\pi$
$241$	−1.03227e6	−	1.19130e6i	−1.14485	−	1.32123i	−0.205351	−	0.978688i	$-0.565834\pi$
$242$		0			0
$243$	−1.63898e6	−	481248.i	−1.78057	−	0.522821i
$244$		0			0
$245$	−410741.	−	263967.i	−0.437173	−	0.280954i
$246$		0			0
$247$	−68530.4	+	476640.i	−0.0714729	+	0.497105i
$248$		0			0
$249$	−45697.4	−	317833.i	−0.0467082	−	0.324863i
$250$		0			0
$251$	−90689.0	+	104661.i	−0.0908594	+	0.104857i	−0.799359	−	0.600854i	$-0.794827\pi$
$251$	−90689.0	+	104661.i	−0.0908594	+	0.104857i	0.708499	+	0.705712i	$0.249373\pi$
$252$		0			0
$253$	−1.82293e6	+	232311.i	−1.79048	+	0.228175i
$254$		0			0
$255$	−579979.	+	669331.i	−0.558549	+	0.644600i
$256$		0			0
$257$	109810.	+	763743.i	0.103707	+	0.721298i	0.973634	+	0.228117i	$0.0732569\pi$
$257$	109810.	+	763743.i	0.103707	+	0.721298i	−0.869927	+	0.493181i	$0.835834\pi$
$258$		0			0
$259$	−117744.	+	818927.i	−0.109066	+	0.758570i
$260$		0			0
$261$	1.62384e6	+	1.04358e6i	1.47551	+	0.948254i
$262$		0			0
$263$	−1.01354e6	−	297603.i	−0.903550	−	0.265306i	−0.203227	−	0.979132i	$-0.565143\pi$
$263$	−1.01354e6	−	297603.i	−0.903550	−	0.265306i	−0.700324	+	0.713825i	$0.746961\pi$
$264$		0			0
$265$	354825.	+	409490.i	0.310384	+	0.358203i
$266$		0			0
$267$	859759.	−	1.88261e6i	0.738071	−	1.61615i
$268$		0			0
$269$	2.12971e6	−	625341.i	1.79449	−	0.526909i	0.797420	−	0.603425i	$-0.206198\pi$
$269$	2.12971e6	−	625341.i	1.79449	−	0.526909i	0.997068	+	0.0765152i	$0.0243794\pi$
$270$		0			0
$271$	−521724.	−	1.14242e6i	−0.431537	−	0.944934i	−0.993075	−	0.117483i	$-0.962518\pi$
$271$	−521724.	−	1.14242e6i	−0.431537	−	0.944934i	0.561538	−	0.827451i	$-0.310210\pi$
$272$		0			0
$273$	−777526.	+	499686.i	−0.631405	+	0.405780i
$274$		0			0
$275$	−1.69779e6			−1.35379
$276$		0			0
$277$	96290.1			0.0754019			0.0377009	−	0.999289i	$-0.487997\pi$
$277$	96290.1			0.0754019			0.0377009	+	0.999289i	$0.487997\pi$
$278$		0			0
$279$	1.34173e6	−	862276.i	1.03194	−	0.663186i
$280$		0			0
$281$	−61521.2	−	134713.i	−0.0464793	−	0.101775i	0.884968	−	0.465652i	$-0.154180\pi$
$281$	−61521.2	−	134713.i	−0.0464793	−	0.101775i	−0.931447	+	0.363877i	$0.881453\pi$
$282$		0			0
$283$	−930443.	+	273203.i	−0.690596	+	0.202777i	−0.608154	−	0.793819i	$-0.708090\pi$
$283$	−930443.	+	273203.i	−0.690596	+	0.202777i	−0.0824412	+	0.996596i	$0.526272\pi$
$284$		0			0
$285$	929539.	−	2.03541e6i	0.677884	−	1.48436i
$286$		0			0
$287$	1.66853e6	+	1.92558e6i	1.19572	+	1.37993i
$288$		0			0
$289$	201520.	+	59171.6i	0.141930	+	0.0416743i
$290$		0			0
$291$	−212490.	−	136559.i	−0.147098	−	0.0945341i
$292$		0			0
$293$	−261090.	+	1.81592e6i	−0.177673	+	1.23574i	0.684457	+	0.729054i	$0.260039\pi$
$293$	−261090.	+	1.81592e6i	−0.177673	+	1.23574i	−0.862130	+	0.506688i	$0.830870\pi$
$294$		0			0
$295$	−79761.9	−	554756.i	−0.0533630	−	0.371148i
$296$		0			0
$297$	−4.70115e6	+	5.42542e6i	−3.09253	+	3.56897i
$298$		0			0
$299$	336812.	−	282517.i	0.217876	−	0.182754i
$300$		0			0
$301$	−1.11053e6	+	1.28162e6i	−0.706501	+	0.815345i
$302$		0			0
$303$	−629446.	−	4.37789e6i	−0.393869	−	2.73942i
$304$		0			0
$305$	220417.	−	1.53303e6i	0.135674	−	0.943631i
$306$		0			0
$307$	538186.	+	345871.i	0.325901	+	0.209444i	0.693352	−	0.720599i	$-0.256133\pi$
$307$	538186.	+	345871.i	0.325901	+	0.209444i	−0.367451	+	0.930043i	$0.619769\pi$
$308$		0			0
$309$	−85125.0	−	24995.0i	−0.0507179	−	0.0148921i
$310$		0			0
$311$	22719.2	+	26219.3i	0.0133196	+	0.0153716i	0.762370	−	0.647141i	$-0.224036\pi$
$311$	22719.2	+	26219.3i	0.0133196	+	0.0153716i	−0.749051	+	0.662513i	$0.769490\pi$
$312$		0			0
$313$	976201.	−	2.13758e6i	0.563221	−	1.23328i	−0.387109	−	0.922034i	$-0.626526\pi$
$313$	976201.	−	2.13758e6i	0.563221	−	1.23328i	0.950329	−	0.311247i	$-0.100747\pi$
$314$		0			0
$315$	2.91436e6	−	855733.i	1.65488	−	0.485917i
$316$		0			0
$317$	−284547.	−	623070.i	−0.159040	−	0.348248i	0.813291	−	0.581857i	$-0.197674\pi$
$317$	−284547.	−	623070.i	−0.159040	−	0.348248i	−0.972331	+	0.233609i	$0.924946\pi$
$318$		0			0
$319$	2.00378e6	−	1.28775e6i	1.10249	−	0.708525i
$320$		0			0
$321$	276479.			0.149761
$322$		0			0
$323$	3.05666e6			1.63020
$324$		0			0
$325$	341673.	−	219580.i	0.179433	−	0.115314i
$326$		0			0
$327$	−509492.	−	1.11563e6i	−0.263492	−	0.576968i
$328$		0			0
$329$	−1.44577e6	+	424517.i	−0.736394	+	0.216225i
$330$		0			0
$331$	−917769.	+	2.00963e6i	−0.460430	+	1.00820i	0.526960	+	0.849890i	$0.323332\pi$
$331$	−917769.	+	2.00963e6i	−0.460430	+	1.00820i	−0.987389	+	0.158310i	$0.949395\pi$
$332$		0			0
$333$	−1.71784e6	−	1.98249e6i	−0.848928	−	0.979716i
$334$		0			0
$335$	1.19686e6	+	351429.i	0.582680	+	0.171090i
$336$		0			0
$337$	2.76459e6	+	1.77669e6i	1.32604	+	0.852193i	0.995787	−	0.0917004i	$-0.0292302\pi$
$337$	2.76459e6	+	1.77669e6i	1.32604	+	0.852193i	0.330251	+	0.943893i	$0.392867\pi$
$338$		0			0
$339$	−419192.	+	2.91555e6i	−0.198114	+	1.37791i
$340$		0			0
$341$	−280087.	−	1.94805e6i	−0.130439	−	0.907223i
$342$		0			0
$343$	−80324.2	+	92699.1i	−0.0368647	+	0.0425442i
$344$		0			0
$345$	−1.87155e6	+	818678.i	−0.846552	+	0.370310i
$346$		0			0
$347$	1.37439e6	−	1.58613e6i	0.612753	−	0.707154i	−0.361561	−	0.932348i	$-0.617756\pi$
$347$	1.37439e6	−	1.58613e6i	0.612753	−	0.707154i	0.974314	+	0.225194i	$0.0723016\pi$
$348$		0			0
$349$	577625.	+	4.01747e6i	0.253853	+	1.76559i	0.574611	+	0.818427i	$0.305153\pi$
$349$	577625.	+	4.01747e6i	0.253853	+	1.76559i	−0.320758	+	0.947161i	$0.603938\pi$
$350$		0			0
$351$	244403.	−	1.69986e6i	0.105886	−	0.736453i
$352$		0			0
$353$	1.66258e6	+	1.06848e6i	0.710145	+	0.456382i	0.845196	−	0.534456i	$-0.179484\pi$
$353$	1.66258e6	+	1.06848e6i	0.710145	+	0.456382i	−0.135051	+	0.990839i	$0.543120\pi$
$354$		0			0
$355$	318633.	+	93559.0i	0.134190	+	0.0394017i
$356$		0			0
$357$	3.84194e6	+	4.43383e6i	1.59544	+	1.84123i
$358$		0			0
$359$	−1.21615e6	+	2.66300e6i	−0.498025	+	1.09052i	0.479082	+	0.877770i	$0.340970\pi$
$359$	−1.21615e6	+	2.66300e6i	−0.498025	+	1.09052i	−0.977106	+	0.212751i	$0.931758\pi$
$360$		0			0
$361$	−5.03407e6	+	1.47814e6i	−2.03307	+	0.596962i
$362$		0			0
$363$	4.35196e6	+	9.52947e6i	1.73348	+	3.79579i
$364$		0			0
$365$	−959038.	+	616336.i	−0.376794	+	0.242151i
$366$		0			0
$367$	3.49428e6			1.35423			0.677115	−	0.735877i	$-0.263230\pi$
$367$	3.49428e6			1.35423			0.677115	+	0.735877i	$0.263230\pi$
$368$		0			0
$369$	−8.07847e6			−3.08861
$370$		0			0
$371$	3.01947e6	−	1.94049e6i	1.13893	−	0.731944i
$372$		0			0
$373$	−421640.	−	923262.i	−0.156917	−	0.343600i	0.814803	−	0.579739i	$-0.196845\pi$
$373$	−421640.	−	923262.i	−0.156917	−	0.343600i	−0.971719	+	0.236139i	$0.924118\pi$
$374$		0			0
$375$	−4.22514e6	+	1.24061e6i	−1.55154	+	0.455573i
$376$		0			0
$377$	−236704.	+	518309.i	−0.0857733	+	0.187817i
$378$		0			0
$379$	1.95508e6	+	2.25629e6i	0.699145	+	0.806857i	0.988637	−	0.150324i	$-0.0480316\pi$
$379$	1.95508e6	+	2.25629e6i	0.699145	+	0.806857i	−0.289491	+	0.957181i	$0.593486\pi$
$380$		0			0
$381$	6.99499e6	+	2.05391e6i	2.46874	+	0.724886i
$382$		0			0
$383$	222381.	+	142916.i	0.0774642	+	0.0497832i	0.578800	−	0.815470i	$-0.303521\pi$
$383$	222381.	+	142916.i	0.0774642	+	0.0497832i	−0.501335	+	0.865253i	$0.667158\pi$
$384$		0			0
$385$	533405.	−	3.70992e6i	0.183403	−	1.27559i
$386$		0			0
$387$	−765199.	−	5.32208e6i	−0.259715	−	1.80636i
$388$		0			0
$389$	2.77116e6	−	3.19808e6i	0.928511	−	1.07156i	−0.0687531	−	0.997634i	$-0.521902\pi$
$389$	2.77116e6	−	3.19808e6i	0.928511	−	1.07156i	0.997264	−	0.0739248i	$-0.0235525\pi$
$390$		0			0
$391$	−2.07933e6	−	1.86099e6i	−0.687830	−	0.615604i
$392$		0			0
$393$	3.00551e6	−	3.46855e6i	0.981606	−	1.13283i
$394$		0			0
$395$	−18306.0	−	127321.i	−0.00590338	−	0.0410589i
$396$		0			0
$397$	467511.	−	3.25161e6i	0.148873	−	1.03543i	−0.769196	−	0.639013i	$-0.779343\pi$
$397$	467511.	−	3.25161e6i	0.148873	−	1.03543i	0.918069	−	0.396420i	$-0.129748\pi$
$398$		0			0
$399$	−1.24695e7	−	8.01369e6i	−3.92119	−	2.52000i
$400$		0			0
$401$	1.57602e6	+	462761.i	0.489441	+	0.143713i	0.517135	−	0.855904i	$-0.326998\pi$
$401$	1.57602e6	+	462761.i	0.489441	+	0.143713i	−0.0276945	+	0.999616i	$0.508817\pi$
$402$		0			0
$403$	308313.	+	355813.i	0.0945649	+	0.109134i
$404$		0			0
$405$	−1.65893e6	+	3.63256e6i	−0.502564	+	1.10046i
$406$		0			0
$407$	−3.10585e6	+	911959.i	−0.929382	+	0.272891i
$408$		0			0
$409$	126234.	+	276414.i	0.0373138	+	0.0817057i	0.927371	−	0.374143i	$-0.122063\pi$
$409$	126234.	+	276414.i	0.0373138	+	0.0817057i	−0.890057	+	0.455849i	$0.849336\pi$
$410$		0			0
$411$	366039.	−	235239.i	0.106887	−	0.0686919i
$412$		0			0
$413$	−3.71264e6			−1.07105
$414$		0			0
$415$	−311502.			−0.0887853
$416$		0			0
$417$	4.09399e6	−	2.63105e6i	1.15294	−	0.740950i
$418$		0			0
$419$	2.62270e6	+	5.74290e6i	0.729815	+	1.59807i	0.799617	+	0.600511i	$0.205036\pi$
$419$	2.62270e6	+	5.74290e6i	0.729815	+	1.59807i	−0.0698016	+	0.997561i	$0.522237\pi$
$420$		0			0
$421$	4.88974e6	−	1.43576e6i	1.34456	−	0.394799i	0.471267	−	0.881991i	$-0.343797\pi$
$421$	4.88974e6	−	1.43576e6i	1.34456	−	0.394799i	0.873295	+	0.487191i	$0.161979\pi$
$422$		0			0
$423$	1.98465e6	−	4.34579e6i	0.539304	−	1.18091i
$424$		0			0
$425$	−1.68828e6	−	1.94838e6i	−0.453391	−	0.523241i
$426$		0			0
$427$	−9.84407e6	−	2.89048e6i	−2.61279	−	0.767185i
$428$		0			0
$429$	−3.04204e6	−	1.95500e6i	−0.798035	−	0.512866i
$430$		0			0
$431$	52449.2	−	364792.i	0.0136002	−	0.0945915i	−0.981891	−	0.189448i	$-0.939330\pi$
$431$	52449.2	−	364792.i	0.0136002	−	0.0945915i	0.995491	+	0.0948565i	$0.0302392\pi$
$432$		0			0
$433$	283016.	+	1.96842e6i	0.0725423	+	0.504543i	0.993405	+	0.114656i	$0.0365767\pi$
$433$	283016.	+	1.96842e6i	0.0725423	+	0.504543i	−0.920863	+	0.389887i	$0.872514\pi$
$434$		0			0
$435$	1.73390e6	−	2.00103e6i	0.439341	−	0.507026i
$436$		0			0
$437$	6.36531e6	+	3.03129e6i	1.59447	+	0.759319i
$438$		0			0
$439$	−4.57773e6	+	5.28298e6i	−1.13367	+	1.30833i	−0.188386	+	0.982095i	$0.560326\pi$
$439$	−4.57773e6	+	5.28298e6i	−1.13367	+	1.30833i	−0.945289	+	0.326235i	$0.894220\pi$
$440$		0			0
$441$	−1.45940e6	−	1.01503e7i	−0.357337	−	2.48533i
$442$		0			0
$443$	−24311.1	+	169087.i	−0.00588565	+	0.0409356i	−0.992553	−	0.121817i	$-0.961128\pi$
$443$	−24311.1	+	169087.i	−0.00588565	+	0.0409356i	0.986667	+	0.162752i	$0.0520371\pi$
$444$		0			0
$445$	−1.68904e6	−	1.08548e6i	−0.404335	−	0.259850i
$446$		0			0
$447$	3.79174e6	+	1.11335e6i	0.897572	+	0.263551i
$448$		0			0
$449$	−4.02808e6	−	4.64865e6i	−0.942936	−	1.08821i	−0.995977	−	0.0896140i	$-0.971437\pi$
$449$	−4.02808e6	−	4.64865e6i	−0.942936	−	1.08821i	0.0530404	−	0.998592i	$-0.483109\pi$
$450$		0			0
$451$	−4.14111e6	+	9.06777e6i	−0.958685	+	2.09923i
$452$		0			0
$453$	2.51856e6	−	739515.i	0.576642	−	0.169317i
$454$		0			0
$455$	372469.	+	815593.i	0.0843454	+	0.184691i
$456$		0			0
$457$	829653.	−	533186.i	0.185826	−	0.119423i	−0.444420	−	0.895818i	$-0.646590\pi$
$457$	829653.	−	533186.i	0.185826	−	0.119423i	0.630246	+	0.776395i	$0.282954\pi$
$458$		0			0
$459$	−1.09011e7			−2.41511
$460$		0			0
$461$	491966.			0.107816			0.0539079	−	0.998546i	$-0.482832\pi$
$461$	491966.			0.107816			0.0539079	+	0.998546i	$0.482832\pi$
$462$		0			0
$463$	5.43537e6	−	3.49310e6i	1.17836	−	0.757284i	0.203273	−	0.979122i	$-0.434842\pi$
$463$	5.43537e6	−	3.49310e6i	1.17836	−	0.757284i	0.975083	+	0.221838i	$0.0712057\pi$
$464$		0			0
$465$	−908820.	−	1.99004e6i	−0.194915	−	0.426804i
$466$		0			0
$467$	3.58693e6	−	1.05322e6i	0.761081	−	0.223474i	0.121913	−	0.992541i	$-0.461097\pi$
$467$	3.58693e6	−	1.05322e6i	0.761081	−	0.223474i	0.639168	+	0.769067i	$0.279279\pi$
$468$		0			0
$469$	3.43258e6	−	7.51630e6i	0.720591	−	1.57787i
$470$		0			0
$471$	−6.74185e6	−	7.78051e6i	−1.40032	−	1.61605i
$472$		0			0
$473$	−6.36608e6	−	1.86925e6i	−1.30833	−	0.384162i
$474$		0			0
$475$	5.47956e6	+	3.52150e6i	1.11432	+	0.716133i
$476$		0			0
$477$	−1.61956e6	+	1.12643e7i	−0.325913	+	2.26678i
$478$		0			0
$479$	563815.	+	3.92142e6i	0.112279	+	0.780916i	0.965694	+	0.259684i	$0.0836184\pi$
$479$	563815.	+	3.92142e6i	0.112279	+	0.780916i	−0.853415	+	0.521232i	$0.825473\pi$
$480$		0			0
$481$	507093.	−	585217.i	0.0999367	−	0.115333i
$482$		0			0
$483$	3.60357e6	+	1.30433e7i	0.702855	+	2.54401i
$484$		0			0
$485$	−160465.	+	185187.i	−0.0309761	+	0.0357483i
$486$		0			0
$487$	−209376.	−	1.45624e6i	−0.0400041	−	0.278234i	0.959994	−	0.280019i	$-0.0903409\pi$
$487$	−209376.	−	1.45624e6i	−0.0400041	−	0.278234i	−0.999998	+	0.00178505i	$0.999432\pi$
$488$		0			0
$489$	−605134.	+	4.20880e6i	−0.114440	+	0.795950i
$490$		0			0
$491$	−3.96413e6	−	2.54759e6i	−0.742069	−	0.476899i	0.114181	−	0.993460i	$-0.463576\pi$
$491$	−3.96413e6	−	2.54759e6i	−0.742069	−	0.476899i	−0.856250	+	0.516561i	$0.827212\pi$
$492$		0			0
$493$	3.47039e6	+	1.01900e6i	0.643074	+	0.188824i
$494$		0			0
$495$	7.78217e6	+	8.98110e6i	1.42754	+	1.64747i
$496$		0			0
$497$	913837.	−	2.00102e6i	0.165950	−	0.363380i
$498$		0			0
$499$	540526.	−	158713.i	0.0971774	−	0.0285339i	−0.232782	−	0.972529i	$-0.574783\pi$
$499$	540526.	−	158713.i	0.0971774	−	0.0285339i	0.329960	+	0.943995i	$0.392965\pi$
$500$		0			0
$501$	5.14082e6	+	1.12568e7i	0.915036	+	2.00365i
$502$		0			0
$503$	−35181.4	+	22609.7i	−0.00620001	+	0.00398451i	−0.543737	−	0.839256i	$-0.682991\pi$
$503$	−35181.4	+	22609.7i	−0.00620001	+	0.00398451i	0.537537	+	0.843240i	$0.319355\pi$
$504$		0			0
$505$	−4.29070e6			−0.748685
$506$		0			0
$507$	−9.83184e6			−1.69869
$508$		0			0
$509$	−2.93127e6	+	1.88382e6i	−0.501490	+	0.322288i	−0.766812	−	0.641872i	$-0.778158\pi$
$509$	−2.93127e6	+	1.88382e6i	−0.501490	+	0.322288i	0.265322	+	0.964160i	$0.414522\pi$
$510$		0			0
$511$	3.13711e6	+	6.86930e6i	0.531468	+	1.16375i
$512$		0			0
$513$	2.64261e7	−	7.75941e6i	4.43343	−	1.30177i
$514$		0			0
$515$	−35753.4	+	78289.0i	−0.00594018	+	0.0130072i
$516$		0			0
$517$	−3.86062e6	−	4.45540e6i	−0.635230	−	0.733095i
$518$		0			0
$519$	−3.72164e6	−	1.09277e6i	−0.606479	−	0.178078i
$520$		0			0
$521$	−485166.	−	311797.i	−0.0783062	−	0.0503244i	0.500902	−	0.865504i	$-0.333002\pi$
$521$	−485166.	−	311797.i	−0.0783062	−	0.0503244i	−0.579208	+	0.815180i	$0.696638\pi$
$522$		0			0
$523$	1.51018e6	−	1.05035e7i	0.241420	−	1.67911i	−0.403589	−	0.914940i	$-0.632238\pi$
$523$	1.51018e6	−	1.05035e7i	0.241420	−	1.67911i	0.645010	−	0.764174i	$-0.276853\pi$
$524$		0			0
$525$	1.77920e6	+	1.23746e7i	0.281725	+	1.95944i
$526$		0			0
$527$	1.95707e6	−	2.25858e6i	0.306958	−	0.354248i
$528$		0			0
$529$	−2.48454e6	−	5.93747e6i	−0.386017	−	0.922492i
$530$		0			0
$531$	7.70862e6	−	8.89622e6i	1.18643	−	1.36921i
$532$		0			0
$533$	−339379.	−	2.36044e6i	−0.0517449	−	0.359894i
$534$		0			0
$535$	38170.9	−	265484.i	0.00576564	−	0.0401009i
$536$		0			0
$537$	−1.44752e7	−	9.30263e6i	−2.16615	−	1.39210i
$538$		0			0
$539$	−1.21415e7	−	3.56506e6i	−1.80011	−	0.528560i
$540$		0			0
$541$	3.57204e6	+	4.12236e6i	0.524715	+	0.605553i	0.954805	−	0.297233i	$-0.0960637\pi$
$541$	3.57204e6	+	4.12236e6i	0.524715	+	0.605553i	−0.430090	+	0.902786i	$0.641518\pi$
$542$		0			0
$543$	−3.24488e6	+	7.10529e6i	−0.472279	+	1.03415i
$544$		0			0
$545$	−1.14161e6	+	335206.i	−0.164636	+	0.0483416i
$546$		0			0
$547$	999654.	+	2.18894e6i	0.142850	+	0.312799i	0.967511	−	0.252829i	$-0.0813611\pi$
$547$	999654.	+	2.18894e6i	0.142850	+	0.312799i	−0.824661	+	0.565628i	$0.808634\pi$
$548$		0			0
$549$	2.73655e7	−	1.75868e7i	3.87501	−	2.49032i
$550$		0			0
$551$	−9.13816e6			−1.28227
$552$		0			0
$553$	−852082.			−0.118486
$554$		0			0
$555$	−3.02704e6	+	1.94536e6i	−0.417143	+	0.268082i
$556$		0			0
$557$	−3.62365e6	−	7.93469e6i	−0.494890	−	1.08366i	−0.978097	−	0.208152i	$-0.933255\pi$
$557$	−3.62365e6	−	7.93469e6i	−0.494890	−	1.08366i	0.483207	−	0.875506i	$-0.339472\pi$
$558$		0			0
$559$	1.52290e6	−	447165.i	0.206131	−	0.0605254i
$560$		0			0
$561$	−9.53528e6	+	2.08794e7i	−1.27916	+	2.80098i
$562$		0			0
$563$	150078.	+	173199.i	0.0199547	+	0.0230290i	0.765639	−	0.643270i	$-0.222423\pi$
$563$	150078.	+	173199.i	0.0199547	+	0.0230290i	−0.745684	+	0.666299i	$0.767877\pi$
$564$		0			0
$565$	2.74173e6	+	805044.i	0.361330	+	0.106096i
$566$		0			0
$567$	2.22542e7	+	1.43019e7i	2.90706	+	1.86825i
$568$		0			0
$569$	−2.00840e6	+	1.39687e7i	−0.260058	+	1.80874i	0.272288	+	0.962216i	$0.412220\pi$
$569$	−2.00840e6	+	1.39687e7i	−0.260058	+	1.80874i	−0.532346	+	0.846527i	$0.678689\pi$
$570$		0			0
$571$	−810676.	−	5.63838e6i	−0.104054	−	0.723709i	−0.973335	−	0.229390i	$-0.926327\pi$
$571$	−810676.	−	5.63838e6i	−0.104054	−	0.723709i	0.869281	−	0.494318i	$-0.164582\pi$
$572$		0			0
$573$	−662606.	+	764689.i	−0.0843081	+	0.0972967i
$574$		0			0
$575$	−1.58354e6	−	5.73167e6i	−0.199737	−	0.722956i
$576$		0			0
$577$	2.59709e6	−	2.99720e6i	0.324748	−	0.374780i	−0.569775	−	0.821801i	$-0.692970\pi$
$577$	2.59709e6	−	2.99720e6i	0.324748	−	0.374780i	0.894523	+	0.447021i	$0.147515\pi$
$578$		0			0
$579$	−203211.	−	1.41336e6i	−0.0251913	−	0.175210i
$580$		0			0
$581$	−293663.	+	2.04247e6i	−0.0360918	+	0.251024i
$582$		0			0
$583$	1.18136e7	+	7.59211e6i	1.43949	+	0.925105i
$584$		0			0
$585$	−2.72768e6	−	800920.i	−0.329537	−	0.0967608i
$586$		0			0
$587$	−4.52282e6	−	5.21961e6i	−0.541768	−	0.625234i	0.417177	−	0.908825i	$-0.363020\pi$
$587$	−4.52282e6	−	5.21961e6i	−0.541768	−	0.625234i	−0.958945	+	0.283591i	$0.908474\pi$
$588$		0			0
$589$	−3.13661e6	+	6.86823e6i	−0.372540	+	0.815749i
$590$		0			0
$591$	5.78755e6	−	1.69938e6i	0.681595	−	0.200134i
$592$		0			0
$593$	6.03383e6	+	1.32122e7i	0.704622	+	1.54291i	0.834276	+	0.551348i	$0.185886\pi$
$593$	6.03383e6	+	1.32122e7i	0.704622	+	1.54291i	−0.129653	+	0.991559i	$0.541386\pi$
$594$		0			0
$595$	4.78793e6	−	3.07702e6i	0.554441	−	0.356318i
$596$		0			0
$597$	−2.08170e7			−2.39047
$598$		0			0
$599$	−2.05140e6			−0.233606			−0.116803	−	0.993155i	$-0.537265\pi$
$599$	−2.05140e6			−0.233606			−0.116803	+	0.993155i	$0.537265\pi$
$600$		0			0
$601$	2.58635e6	−	1.66214e6i	0.292079	−	0.187708i	−0.386393	−	0.922334i	$-0.626279\pi$
$601$	2.58635e6	−	1.66214e6i	0.292079	−	0.187708i	0.678472	+	0.734627i	$0.262643\pi$
$602$		0			0
$603$	1.08834e7	+	2.38313e7i	1.21891	+	2.66904i
$604$		0			0
$605$	9.75134e6	−	2.86325e6i	1.08312	−	0.318032i
$606$		0			0
$607$	490863.	−	1.07484e6i	0.0540740	−	0.118406i	−0.880666	−	0.473737i	$-0.842905\pi$
$607$	490863.	−	1.07484e6i	0.0540740	−	0.118406i	0.934740	+	0.355331i	$0.115632\pi$
$608$		0			0
$609$	−1.14858e7	−	1.32554e7i	−1.25493	−	1.44827i
$610$		0			0
$611$	1.35316e6	+	397325.i	0.146638	+	0.0430569i
$612$		0			0
$613$	4794.26	+	3081.08i	0.000515312	+	0.000331171i	0.540898	−	0.841088i	$-0.318084\pi$
$613$	4794.26	+	3081.08i	0.000515312	+	0.000331171i	−0.540383	+	0.841419i	$0.681721\pi$
$614$		0			0
$615$	−1.57702e6	+	1.09684e7i	−0.168132	+	1.16938i
$616$		0			0
$617$	1.22623e6	+	8.52858e6i	0.129675	+	0.901912i	0.945965	+	0.324269i	$0.105118\pi$
$617$	1.22623e6	+	8.52858e6i	0.129675	+	0.901912i	−0.816290	+	0.577643i	$0.803973\pi$
$618$		0			0
$619$	−1.63649e6	+	1.88861e6i	−0.171667	+	0.198114i	−0.835063	−	0.550154i	$-0.814569\pi$
$619$	−1.63649e6	+	1.88861e6i	−0.171667	+	0.198114i	0.663396	+	0.748268i	$0.269114\pi$
$620$		0			0
$621$	−2.27009e7	−	1.08106e7i	−2.36218	−	1.12492i
$622$		0			0
$623$	−8.70966e6	+	1.00515e7i	−0.899044	+	1.03755i
$624$		0			0
$625$	−434449.	−	3.02166e6i	−0.0444876	−	0.309418i
$626$		0			0
$627$	8.25323e6	−	5.74025e7i	0.838407	−	5.83125i
$628$		0			0
$629$	−4.13503e6	−	2.65742e6i	−0.416728	−	0.267815i
$630$		0			0
$631$	1.61988e7	+	4.75641e6i	1.61961	+	0.475560i	0.960914	−	0.276849i	$-0.0892901\pi$
$631$	1.61988e7	+	4.75641e6i	1.61961	+	0.475560i	0.658696	+	0.752409i	$0.271108\pi$
$632$		0			0
$633$	1.60245e7	+	1.84932e7i	1.58955	+	1.83444i
$634$		0			0
$635$	2.93797e6	−	6.43325e6i	0.289143	−	0.633135i
$636$		0			0
$637$	2.90450e6	−	852839.i	0.283611	−	0.0832757i
$638$		0			0
$639$	2.89743e6	+	6.34449e6i	0.280712	+	0.614674i
$640$		0			0
$641$	−1.03665e6	+	666215.i	−0.0996523	+	0.0640426i	−0.589518	−	0.807755i	$-0.700682\pi$
$641$	−1.03665e6	+	666215.i	−0.0996523	+	0.0640426i	0.489866	+	0.871798i	$0.337046\pi$
$642$		0			0
$643$	9.16430e6			0.874121			0.437061	−	0.899432i	$-0.356020\pi$
$643$	9.16430e6			0.874121			0.437061	+	0.899432i	$0.356020\pi$
$644$		0			0
$645$	−7.37535e6			−0.698045
$646$		0			0
$647$	−1.13990e7	+	7.32566e6i	−1.07054	+	0.687996i	−0.952354	−	0.304995i	$-0.901345\pi$
$647$	−1.13990e7	+	7.32566e6i	−1.07054	+	0.687996i	−0.118189	+	0.992991i	$0.537709\pi$
$648$		0			0
$649$	−6.03414e6	−	1.32129e7i	−0.562346	−	1.23137i
$650$		0			0
$651$	−1.39051e7	+	4.08292e6i	−1.28595	+	0.377588i
$652$		0			0
$653$	−7.57374e6	+	1.65842e7i	−0.695068	+	1.52199i	0.150782	+	0.988567i	$0.451821\pi$
$653$	−7.57374e6	+	1.65842e7i	−0.695068	+	1.52199i	−0.845851	+	0.533420i	$0.820907\pi$
$654$		0			0
$655$	−2.91567e6	−	3.36486e6i	−0.265543	−	0.306453i
$656$		0			0
$657$	−2.29738e7	−	6.74572e6i	−2.07644	−	0.609698i
$658$		0			0
$659$	−1.45171e6	−	932957.i	−0.130217	−	0.0836851i	0.473911	−	0.880573i	$-0.342842\pi$
$659$	−1.45171e6	−	932957.i	−0.130217	−	0.0836851i	−0.604127	+	0.796888i	$0.706478\pi$
$660$		0			0
$661$	2.20073e6	−	1.53064e7i	0.195913	−	1.36261i	−0.620077	−	0.784541i	$-0.712899\pi$
$661$	2.20073e6	−	1.53064e7i	0.195913	−	1.36261i	0.815990	−	0.578065i	$-0.196192\pi$
$662$		0			0
$663$	−781451.	−	5.43511e6i	−0.0690427	−	0.480203i
$664$		0			0
$665$	−9.41656e6	+	1.08673e7i	−0.825730	+	0.952943i
$666$		0			0
$667$	6.21635e6	+	5.56360e6i	0.541029	+	0.484218i
$668$		0			0
$669$	−1.97456e7	+	2.27877e7i	−1.70571	+	1.96850i
$670$		0			0
$671$	−5.71259e6	−	3.97319e7i	−0.489809	−	3.40670i
$672$		0			0
$673$	2.45481e6	−	1.70736e7i	0.208920	−	1.45307i	−0.567768	−	0.823188i	$-0.692193\pi$
$673$	2.45481e6	−	1.70736e7i	0.208920	−	1.45307i	0.776689	−	0.629885i	$-0.216898\pi$
$674$		0			0
$675$	−1.95420e7	−	1.25589e7i	−1.65086	−	1.06094i
$676$		0			0
$677$	8.37912e6	+	2.46033e6i	0.702630	+	0.206311i	0.613483	−	0.789708i	$-0.289768\pi$
$677$	8.37912e6	+	2.46033e6i	0.702630	+	0.206311i	0.0891469	+	0.996018i	$0.471586\pi$
$678$		0			0
$679$	1.06296e6	+	1.22673e6i	0.0884799	+	0.102111i
$680$		0			0
$681$	6.49597e6	−	1.42242e7i	0.536755	−	1.17533i
$682$		0			0
$683$	2.19114e7	−	6.43378e6i	1.79729	−	0.527733i	0.799916	−	0.600112i	$-0.204877\pi$
$683$	2.19114e7	−	6.43378e6i	1.79729	−	0.527733i	0.997377	+	0.0723789i	$0.0230591\pi$
$684$		0			0
$685$	−175349.	−	383960.i	−0.0142783	−	0.0312651i
$686$		0			0
$687$	−7.48275e6	+	4.80887e6i	−0.604881	+	0.388733i
$688$		0			0
$689$	−3.35934e6			−0.269591
$690$		0			0
$691$	−1.57937e7			−1.25831			−0.629157	−	0.777279i	$-0.716600\pi$
$691$	−1.57937e7			−1.25831			−0.629157	+	0.777279i	$0.716600\pi$
$692$		0			0
$693$	6.62242e7	−	4.25597e7i	5.23822	−	3.36640i
$694$		0			0
$695$	−1.96120e6	−	4.29443e6i	−0.154014	−	0.337243i
$696$		0			0
$697$	−1.45241e7	+	4.26467e6i	−1.13242	+	0.332509i
$698$		0			0
$699$	6.41467e6	−	1.40462e7i	0.496571	−	1.08734i
$700$		0			0
$701$	−5.56092e6	−	6.41764e6i	−0.427416	−	0.493265i	0.500666	−	0.865641i	$-0.333089\pi$
$701$	−5.56092e6	−	6.41764e6i	−0.427416	−	0.493265i	−0.928082	+	0.372376i	$0.878543\pi$
$702$		0			0
$703$	1.19156e7	+	3.49874e6i	0.909343	+	0.267007i
$704$		0			0
$705$	−5.51300e6	−	3.54299e6i	−0.417749	−	0.268471i
$706$		0			0
$707$	−4.04498e6	+	2.81334e7i	−0.304346	+	2.11677i
$708$		0			0
$709$	167404.	+	1.16432e6i	0.0125070	+	0.0869878i	0.995119	−	0.0986835i	$-0.0314631\pi$
$709$	167404.	+	1.16432e6i	0.0125070	+	0.0869878i	−0.982612	+	0.185671i	$0.940554\pi$
$710$		0			0
$711$	1.76919e6	−	2.04176e6i	0.131250	−	0.151471i
$712$		0			0
$713$	6.31531e6	−	2.76253e6i	0.465234	−	0.203509i
$714$		0			0
$715$	−2.29724e6	+	2.65116e6i	−0.168051	+	0.193941i
$716$		0			0
$717$	6.51374e6	+	4.53041e7i	0.473187	+	3.29109i
$718$		0			0
$719$	−2.20077e6	+	1.53067e7i	−0.158764	+	1.10423i	0.742151	+	0.670233i	$0.233806\pi$
$719$	−2.20077e6	+	1.53067e7i	−0.158764	+	1.10423i	−0.900915	+	0.433996i	$0.857103\pi$
$720$		0			0
$721$	479623.	+	308235.i	0.0343607	+	0.0220823i
$722$		0			0
$723$	−4.35739e7	−	1.27944e7i	−3.10013	−	0.910281i
$724$		0			0
$725$	5.04729e6	+	5.82488e6i	0.356626	+	0.411568i
$726$		0			0
$727$	−2.22342e6	+	4.86861e6i	−0.156022	+	0.341640i	−0.971460	−	0.237204i	$-0.923769\pi$
$727$	−2.22342e6	+	4.86861e6i	−0.156022	+	0.341640i	0.815438	+	0.578845i	$0.196496\pi$
$728$		0			0
$729$	−1.39042e7	+	4.08263e6i	−0.969005	+	0.284526i
$730$		0			0
$731$	−4.18529e6	−	9.16451e6i	−0.289689	−	0.634331i
$732$		0			0
$733$	8.38402e6	−	5.38808e6i	0.576358	−	0.370403i	−0.219751	−	0.975556i	$-0.570524\pi$
$733$	8.38402e6	−	5.38808e6i	0.576358	−	0.370403i	0.796109	+	0.605153i	$0.206888\pi$
$734$		0			0
$735$	−1.40664e7			−0.960426
$736$		0			0
$737$	3.23287e7			2.19240
$738$		0			0
$739$	4.80917e6	−	3.09066e6i	0.323936	−	0.208181i	−0.368558	−	0.929605i	$-0.620148\pi$
$739$	4.80917e6	−	3.09066e6i	0.323936	−	0.208181i	0.692494	+	0.721424i	$0.256512\pi$
$740$		0			0
$741$	5.76310e6	+	1.26194e7i	0.385577	+	0.844295i
$742$		0			0
$743$	5.34775e6	−	1.57024e6i	0.355385	−	0.104350i	−0.0991667	−	0.995071i	$-0.531618\pi$
$743$	5.34775e6	−	1.57024e6i	0.355385	−	0.104350i	0.454552	+	0.890720i	$0.349800\pi$
$744$		0			0
$745$	1.59257e6	−	3.48724e6i	0.105125	−	0.230192i
$746$		0			0
$747$	−4.28443e6	−	4.94449e6i	−0.280925	−	0.324205i
$748$		0			0
$749$	−1.70475e6	−	500561.i	−0.111034	−	0.0326026i
$750$		0			0
$751$	1.30002e7	+	8.35475e6i	0.841108	+	0.540547i	0.888790	−	0.458315i	$-0.151547\pi$
$751$	1.30002e7	+	8.35475e6i	0.841108	+	0.540547i	−0.0476818	+	0.998863i	$0.515183\pi$
$752$		0			0
$753$	−567801.	+	3.94914e6i	−0.0364929	+	0.253814i
$754$		0			0
$755$	−362393.	−	2.52050e6i	−0.0231373	−	0.160923i
$756$		0			0
$757$	−1.37683e7	+	1.58895e7i	−0.873256	+	1.00779i	0.126619	+	0.991951i	$0.459588\pi$
$757$	−1.37683e7	+	1.58895e7i	−0.873256	+	1.00779i	−0.999875	+	0.0158397i	$0.994958\pi$
$758$		0			0
$759$	−4.05628e7	+	3.40239e7i	−2.55578	+	2.14378i
$760$		0			0
$761$	1.07563e7	−	1.24134e7i	0.673286	−	0.777014i	−0.311601	−	0.950213i	$-0.600865\pi$
$761$	1.07563e7	−	1.24134e7i	0.673286	−	0.777014i	0.984887	+	0.173199i	$0.0554105\pi$
$762$		0			0
$763$	1.12167e6	+	7.80135e6i	0.0697512	+	0.485130i
$764$		0			0
$765$	−2.56812e6	+	1.78617e7i	−0.158658	+	1.10349i
$766$		0			0
$767$	2.92322e6	+	1.87864e6i	0.179421	+	0.115307i
$768$		0			0
$769$	2.23043e7	+	6.54914e6i	1.36011	+	0.399364i	0.878801	−	0.477189i	$-0.158344\pi$
$769$	2.23043e7	+	6.54914e6i	1.36011	+	0.399364i	0.481307	+	0.876552i	$0.340162\pi$
$770$		0			0
$771$	1.45573e7	+	1.68000e7i	0.881951	+	1.01783i
$772$		0			0
$773$	−3.96240e6	+	8.67644e6i	−0.238512	+	0.522267i	−0.990599	−	0.136796i	$-0.956320\pi$
$773$	−3.96240e6	+	8.67644e6i	−0.238512	+	0.522267i	0.752088	+	0.659063i	$0.229047\pi$
$774$		0			0
$775$	6.11042e6	−	1.79418e6i	0.365440	−	0.107303i
$776$		0			0
$777$	9.90173e6	+	2.16818e7i	0.588381	+	1.28837i
$778$		0			0
$779$	3.21735e7	−	2.06766e7i	1.89956	−	1.22078i
$780$		0			0
$781$	8.60670e6			0.504904
$782$		0			0
$783$	3.25898e7			1.89967
$784$		0			0
$785$	−8.40189e6	+	5.39957e6i	−0.486634	+	0.312741i
$786$		0			0
$787$	4.44303e6	+	9.72889e6i	0.255707	+	0.559920i	0.993332	−	0.115291i	$-0.0367799\pi$
$787$	4.44303e6	+	9.72889e6i	0.255707	+	0.559920i	−0.737625	+	0.675211i	$0.764053\pi$
$788$		0			0
$789$	−2.92000e7	+	8.57388e6i	−1.66990	+	0.490326i
$790$		0			0
$791$	7.86327e6	−	1.72182e7i	0.446850	−	0.978465i
$792$		0			0
$793$	6.28829e6	+	7.25707e6i	0.355099	+	0.409806i
$794$		0			0
$795$	1.49778e7	+	4.39788e6i	0.840485	+	0.246789i
$796$		0			0
$797$	−1.61788e7	−	1.03975e7i	−0.902197	−	0.579807i	0.00524410	−	0.999986i	$-0.498331\pi$
$797$	−1.61788e7	−	1.03975e7i	−0.902197	−	0.579807i	−0.907441	+	0.420180i	$0.861967\pi$
$798$		0			0
$799$	1.27401e6	−	8.86092e6i	0.0706001	−	0.491034i
$800$		0			0
$801$	−6.00132e6	−	4.17401e7i	−0.330495	−	2.29865i
$802$		0			0
$803$	−1.93484e7	+	2.23293e7i	−1.05891	+	1.22204i
$804$		0			0
$805$	1.30221e7	−	1.65951e6i	0.708256	−	0.0902589i
$806$		0			0
$807$	4.18764e7	−	4.83279e7i	2.26353	−	2.61225i
$808$		0			0
$809$	235223.	+	1.63601e6i	0.0126360	+	0.0878851i	0.995164	−	0.0982320i	$-0.0313187\pi$
$809$	235223.	+	1.63601e6i	0.0126360	+	0.0878851i	−0.982528	+	0.186117i	$0.940410\pi$
$810$		0			0
$811$	−3.46220e6	+	2.40801e7i	−0.184842	+	1.28560i	0.660276	+	0.751023i	$0.270439\pi$
$811$	−3.46220e6	+	2.40801e7i	−0.184842	+	1.28560i	−0.845118	+	0.534580i	$0.820470\pi$
$812$		0			0
$813$	−3.04387e7	−	1.95618e7i	−1.61510	−	1.03796i
$814$		0			0
$815$	3.95788e6	+	1.16214e6i	0.208722	+	0.0612864i
$816$		0			0
$817$	1.66692e7	+	1.92373e7i	0.873695	+	1.00830i
$818$		0			0
$819$	−7.82298e6	+	1.71299e7i	−0.407533	+	0.892372i
$820$		0			0
$821$	−2.04891e7	+	6.01614e6i	−1.06088	+	0.311501i	−0.765204	−	0.643788i	$-0.777362\pi$
$821$	−2.04891e7	+	6.01614e6i	−1.06088	+	0.311501i	−0.295672	+	0.955289i	$0.595544\pi$
$822$		0			0
$823$	4.75055e6	+	1.04023e7i	0.244481	+	0.535338i	0.991599	−	0.129354i	$-0.0412903\pi$
$823$	4.75055e6	+	1.04023e7i	0.244481	+	0.535338i	−0.747118	+	0.664691i	$0.768563\pi$
$824$		0			0
$825$	−4.11482e7	+	2.64443e7i	−2.10482	+	1.35269i
$826$		0			0
$827$	2.44806e7			1.24468			0.622342	−	0.782746i	$-0.286181\pi$
$827$	2.44806e7			1.24468			0.622342	+	0.782746i	$0.286181\pi$
$828$		0			0
$829$	−2.25593e7			−1.14009			−0.570046	−	0.821612i	$-0.693075\pi$
$829$	−2.25593e7			−1.14009			−0.570046	+	0.821612i	$0.693075\pi$
$830$		0			0
$831$	2.33372e6	−	1.49979e6i	0.117232	−	0.0753405i
$832$		0			0
$833$	−7.98225e6	−	1.74787e7i	−0.398577	−	0.872763i
$834$		0			0
$835$	1.15189e7	−	3.38226e6i	0.571736	−	0.167877i
$836$		0			0
$837$	1.11862e7	−	2.44944e7i	0.551912	−	1.20852i
$838$		0			0
$839$	2.02229e6	+	2.33385e6i	0.0991832	+	0.114464i	0.803171	−	0.595749i	$-0.203145\pi$
$839$	2.02229e6	+	2.33385e6i	0.0991832	+	0.114464i	−0.703988	+	0.710212i	$0.748599\pi$
$840$		0			0
$841$	9.30524e6	+	2.73226e6i	0.453667	+	0.133209i
$842$		0			0
$843$	−3.58931e6	−	2.30671e6i	−0.173957	−	0.111795i
$844$		0			0
$845$	−1.35739e6	+	9.44086e6i	−0.0653978	+	0.454852i
$846$		0			0
$847$	−9.58100e6	−	6.66373e7i	−0.458883	−	3.19160i
$848$		0			0
$849$	−1.82952e7	+	2.11138e7i	−0.871101	+	1.00530i
$850$		0			0
$851$	−5.97560e6	−	9.63465e6i	−0.282851	−	0.456050i
$852$		0			0
$853$	1.77720e7	−	2.05100e7i	0.836302	−	0.965144i	−0.163469	−	0.986548i	$-0.552268\pi$
$853$	1.77720e7	−	2.05100e7i	0.836302	−	0.965144i	0.999771	+	0.0214045i	$0.00681377\pi$
$854$		0			0
$855$	−6.48840e6	−	4.51278e7i	−0.303545	−	2.11120i
$856$		0			0
$857$	−3.50349e6	+	2.43673e7i	−0.162948	+	1.13333i	0.730092	+	0.683349i	$0.239477\pi$
$857$	−3.50349e6	+	2.43673e7i	−0.162948	+	1.13333i	−0.893039	+	0.449978i	$0.851432\pi$
$858$		0			0
$859$	−3.91771e6	−	2.51776e6i	−0.181154	−	0.116421i	0.446921	−	0.894574i	$-0.352521\pi$
$859$	−3.91771e6	−	2.51776e6i	−0.181154	−	0.116421i	−0.628075	+	0.778153i	$0.716157\pi$
$860$		0			0
$861$	7.04316e7	+	2.06806e7i	3.23787	+	0.950724i
$862$		0			0
$863$	−2.72827e7	−	3.14859e7i	−1.24698	−	1.43909i	−0.854596	−	0.519294i	$-0.826195\pi$
$863$	−2.72827e7	−	3.14859e7i	−1.24698	−	1.43909i	−0.392386	−	0.919801i	$-0.628350\pi$
$864$		0			0
$865$	−1.56313e6	+	3.42277e6i	−0.0710320	+	0.155538i
$866$		0			0
$867$	5.80575e6	−	1.70472e6i	0.262308	−	0.0770204i
$868$		0			0
$869$	−1.38489e6	−	3.03248e6i	−0.0622106	−	0.136222i
$870$		0			0
$871$	−6.50603e6	+	4.18117e6i	−0.290583	+	0.186747i
$872$		0			0
$873$	−5.14653e6			−0.228549
$874$		0			0
$875$	2.82981e7			1.24950
$876$		0			0
$877$	−9.16170e6	+	5.88787e6i	−0.402232	+	0.258499i	−0.726080	−	0.687610i	$-0.758660\pi$
$877$	−9.16170e6	+	5.88787e6i	−0.402232	+	0.258499i	0.323848	+	0.946109i	$0.395023\pi$
$878$		0			0
$879$	2.19565e7	+	4.80780e7i	0.958496	+	2.09881i
$880$		0			0
$881$	3.63174e7	−	1.06637e7i	1.57643	−	0.462881i	0.627565	−	0.778565i	$-0.284052\pi$
$881$	3.63174e7	−	1.06637e7i	1.57643	−	0.462881i	0.948865	+	0.315683i	$0.102234\pi$
$882$		0			0
$883$	1.56389e7	−	3.42445e7i	0.675002	−	1.47805i	−0.192851	−	0.981228i	$-0.561774\pi$
$883$	1.56389e7	−	3.42445e7i	0.675002	−	1.47805i	0.867853	−	0.496820i	$-0.165499\pi$
$884$		0			0
$885$	−1.05739e7	−	1.22029e7i	−0.453813	−	0.523728i
$886$		0			0
$887$	−1.71192e7	−	5.02665e6i	−0.730591	−	0.214521i	−0.104780	−	0.994495i	$-0.533414\pi$
$887$	−1.71192e7	−	5.02665e6i	−0.730591	−	0.214521i	−0.625811	+	0.779974i	$0.715232\pi$
$888$		0			0
$889$	−3.94121e7	−	2.53286e7i	−1.67254	−	1.07487i
$890$		0			0
$891$	−1.47294e7	+	1.02445e8i	−0.621571	+	4.32312i
$892$		0			0
$893$	3.21880e6	+	2.23873e7i	0.135072	+	0.939448i
$894$		0			0
$895$	−1.09311e7	+	1.26152e7i	−0.456150	+	0.526425i
$896$		0			0
$897$	3.76268e6	−	1.20933e7i	0.156141	−	0.501837i
$898$		0			0
$899$	−5.85084e6	+	6.75223e6i	−0.241445	+	0.278643i
$900$		0			0
$901$	3.03471e6	+	2.11069e7i	0.124539	+	0.866188i
$902$		0			0
$903$	−6.95298e6	+	4.83590e7i	−0.283760	+	1.97359i
$904$		0			0
$905$	6.37474e6	+	4.09680e6i	0.258727	+	0.166273i
$906$		0			0
$907$	2.20599e7	+	6.47736e6i	0.890399	+	0.261445i	0.694769	−	0.719233i	$-0.255507\pi$
$907$	2.20599e7	+	6.47736e6i	0.890399	+	0.261445i	0.195630	+	0.980678i	$0.437325\pi$
$908$		0			0
$909$	−5.90146e7	−	6.81064e7i	−2.36891	−	2.73387i
$910$		0			0
$911$	−1.39637e7	+	3.05762e7i	−0.557447	+	1.22064i	0.395769	+	0.918350i	$0.370478\pi$
$911$	−1.39637e7	+	3.05762e7i	−0.557447	+	1.22064i	−0.953216	+	0.302289i	$0.902249\pi$
$912$		0			0
$913$	−7.74624e6	+	2.27450e6i	−0.307549	+	0.0903045i
$914$		0			0
$915$	−1.85361e7	−	4.05883e7i	−0.731922	−	1.60269i
$916$		0			0
$917$	−2.48116e7	+	1.59454e7i	−0.974385	+	0.626199i
$918$		0			0
$919$	−2.17303e7			−0.848745			−0.424372	−	0.905488i	$-0.639505\pi$
$919$	−2.17303e7			−0.848745			−0.424372	+	0.905488i	$0.639505\pi$
$920$		0			0
$921$	1.84309e7			0.715973
$922$		0			0
$923$	−1.73206e6	+	1.11313e6i	−0.0669206	+	0.0430073i
$924$		0			0
$925$	−4.35117e6	−	9.52774e6i	−0.167206	−	0.366130i
$926$		0			0
$927$	−1.73444e6	+	509278.i	−0.0662918	+	0.0194650i
$928$		0			0
$929$	−9.28376e6	+	2.03286e7i	−0.352927	+	0.772802i	0.647020	+	0.762473i	$0.276015\pi$
$929$	−9.28376e6	+	2.03286e7i	−0.352927	+	0.772802i	−0.999947	+	0.0103290i	$0.996712\pi$
$930$		0			0
$931$	3.17917e7	+	3.66896e7i	1.20210	+	1.38730i
$932$		0			0
$933$	959016.	+	281592.i	0.0360680	+	0.0105905i
$934$		0			0
$935$	1.87326e7	+	1.20387e7i	0.700759	+	0.450351i
$936$		0			0
$937$	−5.35015e6	+	3.72111e7i	−0.199075	+	1.38460i	0.607900	+	0.794014i	$0.292012\pi$
$937$	−5.35015e6	+	3.72111e7i	−0.199075	+	1.38460i	−0.806975	+	0.590585i	$0.798897\pi$
$938$		0			0
$939$	−9.63492e6	−	6.70123e7i	−0.356602	−	2.48022i
$940$		0			0
$941$	8.24316e6	−	9.51312e6i	0.303473	−	0.350226i	−0.583446	−	0.812152i	$-0.698296\pi$
$941$	8.24316e6	−	9.51312e6i	0.303473	−	0.350226i	0.886919	+	0.461926i	$0.152841\pi$
$942$		0			0
$943$	−3.44750e7	−	5.52268e6i	−1.26248	−	0.202242i
$944$		0			0
$945$	3.35826e7	−	3.87564e7i	1.22331	−	1.41177i
$946$		0			0
$947$	−2.43527e6	−	1.69377e7i	−0.0882415	−	0.613733i	−0.985173	−	0.171564i	$-0.945118\pi$
$947$	−2.43527e6	−	1.69377e7i	−0.0882415	−	0.613733i	0.896932	−	0.442169i	$-0.145791\pi$
$948$		0			0
$949$	1.00588e6	−	6.99607e6i	0.0362562	−	0.252167i
$950$		0			0
$951$	−1.66012e7	−	1.06689e7i	−0.595234	−	0.382534i
$952$		0			0
$953$	−2.07448e7	−	6.09122e6i	−0.739907	−	0.217256i	−0.110005	−	0.993931i	$-0.535087\pi$
$953$	−2.07448e7	−	6.09122e6i	−0.739907	−	0.217256i	−0.629902	+	0.776675i	$0.716905\pi$
$954$		0			0
$955$	642799.	+	741830.i	0.0228069	+	0.0263206i
$956$		0			0
$957$	2.85066e7	−	6.24208e7i	1.00616	−	2.20318i
$958$		0			0
$959$	−2.68287e6	+	787763.i	−0.0942006	+	0.0276598i
$960$		0			0
$961$	−8.82628e6	−	1.93269e7i	−0.308297	−	0.675076i
$962$		0			0
$963$	4.73905e6	−	3.04560e6i	0.164674	−	0.105830i
$964$		0			0
$965$	−1.38521e6			−0.0478849
$966$		0			0
$967$	2.84035e7			0.976801			0.488400	−	0.872620i	$-0.337581\pi$
$967$	2.84035e7			0.976801			0.488400	+	0.872620i	$0.337581\pi$
$968$		0			0
$969$	7.40822e7	−	4.76098e7i	2.53457	−	1.62887i
$970$		0			0
$971$	2.00841e6	+	4.39780e6i	0.0683603	+	0.149688i	0.940728	−	0.339162i	$-0.110144\pi$
$971$	2.00841e6	+	4.39780e6i	0.0683603	+	0.149688i	−0.872368	+	0.488851i	$0.837416\pi$
$972$		0			0
$973$	−3.00068e7	+	8.81079e6i	−1.01610	+	0.298354i
$974$		0			0
$975$	4.86078e6	−	1.06436e7i	0.163755	−	0.358573i
$976$		0			0
$977$	1.65359e7	+	1.90835e7i	0.554233	+	0.639619i	0.961864	−	0.273528i	$-0.0881906\pi$
$977$	1.65359e7	+	1.90835e7i	0.554233	+	0.639619i	−0.407631	+	0.913147i	$0.633645\pi$
$978$		0			0
$979$	−4.99280e7	−	1.46602e7i	−1.66490	−	0.488858i
$980$		0			0
$981$	−2.10225e7	−	1.35103e7i	−0.697448	−	0.448223i
$982$		0			0
$983$	8.31932e6	−	5.78621e7i	0.274602	−	1.90990i	−0.123115	−	0.992392i	$-0.539288\pi$
$983$	8.31932e6	−	5.78621e7i	0.274602	−	1.90990i	0.397717	−	0.917508i	$-0.369802\pi$
$984$		0			0
$985$	−832766.	−	5.79201e6i	−0.0273484	−	0.190213i
$986$		0			0
$987$	−2.84281e7	+	3.28078e7i	−0.928870	+	1.07197i
$988$		0			0
$989$	372832.	−	2.32351e7i	0.0121205	−	0.755361i
$990$		0			0
$991$	−3.06596e7	+	3.53830e7i	−0.991704	+	1.14449i	−0.00219726	+	0.999998i	$0.500699\pi$
$991$	−3.06596e7	+	3.53830e7i	−0.991704	+	1.14449i	−0.989506	+	0.144489i	$0.953846\pi$
$992$		0			0
$993$	9.05820e6	+	6.30012e7i	0.291520	+	2.02757i
$994$		0			0
$995$	−2.87401e6	+	1.99892e7i	−0.0920303	+	0.640085i
$996$		0			0
$997$	−4.45381e7	−	2.86229e7i	−1.41904	−	0.911961i	−0.999992	−	0.00399569i	$-0.998728\pi$
$997$	−4.45381e7	−	2.86229e7i	−1.41904	−	0.911961i	−0.419046	−	0.907965i	$-0.637636\pi$
$998$		0			0
$999$	−4.24951e7	−	1.24777e7i	−1.34718	−	0.395567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.6.e.a.85.10	yes	100
23.13	even	11	inner	92.6.e.a.13.10	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.6.e.a.13.10	✓	100	23.13	even	11	inner
92.6.e.a.85.10	yes	100	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(24.2364 - 15.5758i) q^{3} +(-11.6103 - 25.4230i) q^{5} +(-177.640 + 52.1597i) q^{7} +(243.851 - 533.960i) q^{9} +(-474.348 - 547.427i) q^{11} +(166.261 + 48.8187i) q^{13} +(-677.373 - 435.321i) q^{15} +(156.535 - 1088.73i) q^{17} +(395.489 + 2750.69i) q^{19} +(-3492.91 + 4031.04i) q^{21} +(1405.67 - 2111.98i) q^{23} +(1534.91 - 1771.38i) q^{25} +(-1410.45 - 9809.89i) q^{27} +(-467.977 + 3254.85i) q^{29} +(2285.71 + 1468.94i) q^{31} +(-20023.1 - 5879.31i) q^{33} +(3388.50 + 3910.54i) q^{35} +(1856.40 - 4064.95i) q^{37} +(4789.95 - 1406.46i) q^{39} +(-5717.01 - 12518.5i) q^{41} +(7705.63 - 4952.11i) q^{43} -16406.0 q^{45} +8138.79 q^{47} +(14696.3 - 9444.74i) q^{49} +(-13163.9 - 28824.9i) q^{51} +(-18601.5 + 5461.88i) q^{53} +(-8409.90 + 18415.1i) q^{55} +(52429.3 + 60506.6i) q^{57} +(19241.0 + 5649.66i) q^{59} +(46618.8 + 29960.1i) q^{61} +(-15466.5 + 107572. i) q^{63} +(-689.223 - 4793.65i) q^{65} +(-29227.3 + 33730.1i) q^{67} +(1172.66 - 73081.0i) q^{69} +(-7781.03 + 8979.79i) q^{71} +(-5804.95 - 40374.3i) q^{73} +(9610.04 - 66839.3i) q^{75} +(112817. + 72503.0i) q^{77} +(4415.96 + 1296.64i) q^{79} +(-93569.7 - 107985. i) q^{81} +(4630.02 - 10138.3i) q^{83} +(-29496.1 + 8660.83i) q^{85} +(39354.8 + 86174.9i) q^{87} +(60433.9 - 38838.5i) q^{89} -32081.0 q^{91} +78277.2 q^{93} +(65338.9 - 41990.7i) q^{95} +(-3642.12 - 7975.12i) q^{97} +(-407975. + 119792. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{3} - 86 q^{5} - 118 q^{7} - 368 q^{9} - 242 q^{11} + 322 q^{13} - 3717 q^{15} + 2953 q^{17} - 259 q^{19} - 12349 q^{21} - 6038 q^{23} - 1324 q^{25} + 23933 q^{27} + 12677 q^{29} - 4401 q^{31}+ \cdots + 26799 q^{99}+O(q^{100}) \) 100 * q + 2 * q^3 - 86 * q^5 - 118 * q^7 - 368 * q^9 - 242 * q^11 + 322 * q^13 - 3717 * q^15 + 2953 * q^17 - 259 * q^19 - 12349 * q^21 - 6038 * q^23 - 1324 * q^25 + 23933 * q^27 + 12677 * q^29 - 4401 * q^31 - 43115 * q^33 + 10774 * q^35 - 72670 * q^37 - 61242 * q^39 - 30296 * q^41 + 69436 * q^43 + 125954 * q^45 + 79010 * q^47 + 27788 * q^49 - 65954 * q^51 - 60934 * q^53 - 234558 * q^55 + 37333 * q^57 + 392206 * q^59 + 153404 * q^61 + 7889 * q^63 - 178529 * q^65 - 52012 * q^67 - 280729 * q^69 - 166585 * q^71 + 42932 * q^73 + 484227 * q^75 + 434675 * q^77 + 150490 * q^79 - 132170 * q^81 - 236441 * q^83 - 399844 * q^85 + 121816 * q^87 + 151010 * q^89 + 240938 * q^91 - 54450 * q^93 - 281447 * q^95 - 76051 * q^97 + 26799 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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