LMFDB - Embedded newform 108.6.b.c.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} + \cdots + 41943040000 $ x^20 - 94x^18 + 5872x^16 - 207192x^14 + 5271952x^12 - 76648960x^10 + 792478720x^8 - 4371873792x^6 + 17152147456x^4 - 32033996800*x^2 + 41943040000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{50}\cdot 3^{40} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.8
Root			$-1.93085 + 1.11477i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.6.b.c.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.63934 + 4.33073i) q^{2} +(-5.51036 - 31.5220i) q^{4} -80.5384i q^{5} -216.819i q^{7} +(156.567 + 90.8555i) q^{8} +O(q^{10})$	\(q+(-3.63934 + 4.33073i) q^{2} +(-5.51036 - 31.5220i) q^{4} -80.5384i q^{5} -216.819i q^{7} +(156.567 + 90.8555i) q^{8} +(348.790 + 293.107i) q^{10} -153.345 q^{11} -945.747 q^{13} +(938.984 + 789.079i) q^{14} +(-963.272 + 347.395i) q^{16} +2184.11i q^{17} -719.706i q^{19} +(-2538.73 + 443.796i) q^{20} +(558.076 - 664.096i) q^{22} +2622.17 q^{23} -3361.43 q^{25} +(3441.90 - 4095.77i) q^{26} +(-6834.57 + 1194.75i) q^{28} +155.049i q^{29} +4909.55i q^{31} +(2001.20 - 5435.96i) q^{32} +(-9458.78 - 7948.73i) q^{34} -17462.3 q^{35} +114.620 q^{37} +(3116.85 + 2619.26i) q^{38} +(7317.35 - 12609.7i) q^{40} -3356.63i q^{41} -13109.4i q^{43} +(844.988 + 4833.74i) q^{44} +(-9542.96 + 11355.9i) q^{46} -9409.97 q^{47} -30203.6 q^{49} +(12233.4 - 14557.4i) q^{50} +(5211.41 + 29811.8i) q^{52} +19619.3i q^{53} +12350.2i q^{55} +(19699.2 - 33946.8i) q^{56} +(-671.476 - 564.277i) q^{58} -21595.2 q^{59} +33298.2 q^{61} +(-21261.9 - 17867.5i) q^{62} +(16258.6 + 28450.0i) q^{64} +76168.9i q^{65} -23493.1i q^{67} +(68847.5 - 12035.2i) q^{68} +(63551.2 - 75624.3i) q^{70} -2402.72 q^{71} +4867.76 q^{73} +(-417.141 + 496.388i) q^{74} +(-22686.6 + 3965.84i) q^{76} +33248.2i q^{77} -11925.5i q^{79} +(27978.7 + 77580.4i) q^{80} +(14536.6 + 12215.9i) q^{82} -83940.6 q^{83} +175905. q^{85} +(56773.1 + 47709.5i) q^{86} +(-24008.8 - 13932.2i) q^{88} -36800.9i q^{89} +205056. i q^{91} +(-14449.1 - 82655.9i) q^{92} +(34246.1 - 40752.0i) q^{94} -57963.9 q^{95} -28249.7 q^{97} +(109921. - 130803. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{4}+O(q^{10}) $ 20 * q + 20 * q^4	$ 20 q + 20 q^{4} + 184 q^{10} - 116 q^{13} - 4168 q^{16} + 696 q^{22} - 15228 q^{25} - 4764 q^{28} - 16520 q^{34} - 6452 q^{37} + 1504 q^{40} - 9336 q^{46} - 44464 q^{49} + 8236 q^{52} - 58736 q^{58} + 84604 q^{61} - 6496 q^{64} + 138696 q^{70} + 85420 q^{73} + 89172 q^{76} + 221200 q^{82} + 180320 q^{85} - 85824 q^{88} - 60936 q^{94} - 219908 q^{97}+O(q^{100}) $ 20 * q + 20 * q^4 + 184 * q^10 - 116 * q^13 - 4168 * q^16 + 696 * q^22 - 15228 * q^25 - 4764 * q^28 - 16520 * q^34 - 6452 * q^37 + 1504 * q^40 - 9336 * q^46 - 44464 * q^49 + 8236 * q^52 - 58736 * q^58 + 84604 * q^61 - 6496 * q^64 + 138696 * q^70 + 85420 * q^73 + 89172 * q^76 + 221200 * q^82 + 180320 * q^85 - 85824 * q^88 - 60936 * q^94 - 219908 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.63934	+	4.33073i	−0.643351	+	0.765571i
$2$	−3.63934	+	4.33073i	−0.643351	+	0.765571i
$3$		0			0
$3$		0			0
$4$	−5.51036	−	31.5220i	−0.172199	−	0.985062i
$5$		−	80.5384i		−	1.44071i	−0.693603	−	0.720357i	$-0.743978\pi$
$5$		−	80.5384i		−	1.44071i	0.693603	−	0.720357i	$-0.256022\pi$
$6$		0			0
$7$		−	216.819i		−	1.67245i	−0.548388	−	0.836224i	$-0.684758\pi$
$7$		−	216.819i		−	1.67245i	0.548388	−	0.836224i	$-0.315242\pi$
$8$	156.567	+	90.8555i	0.864920	+	0.501910i
$9$		0			0
$10$	348.790	+	293.107i	1.10297	+	0.926885i
$11$	−153.345			−0.382110			−0.191055	−	0.981579i	$-0.561191\pi$
$11$	−153.345			−0.382110			−0.191055	+	0.981579i	$0.561191\pi$
$12$		0			0
$13$	−945.747			−1.55209			−0.776044	−	0.630679i	$-0.782777\pi$
$13$	−945.747			−1.55209			−0.776044	+	0.630679i	$0.782777\pi$
$14$	938.984	+	789.079i	1.28038	+	1.07597i
$15$		0			0
$16$	−963.272	+	347.395i	−0.940695	+	0.339253i
$17$			2184.11i			1.83296i	0.400084	+	0.916478i	$0.368981\pi$
$17$			2184.11i			1.83296i	−0.400084	+	0.916478i	$0.631019\pi$
$18$		0			0
$19$		−	719.706i		−	0.457373i	−0.973500	−	0.228687i	$-0.926557\pi$
$19$		−	719.706i		−	0.457373i	0.973500	−	0.228687i	$-0.0734431\pi$
$20$	−2538.73	+	443.796i	−1.41919	+	0.248089i
$21$		0			0
$22$	558.076	−	664.096i	0.245831	−	0.292532i
$23$	2622.17			1.03357			0.516786	−	0.856115i	$-0.327128\pi$
$23$	2622.17			1.03357			0.516786	+	0.856115i	$0.327128\pi$
$24$		0			0
$25$	−3361.43			−1.07566
$26$	3441.90	−	4095.77i	0.998538	−	1.18823i
$27$		0			0
$28$	−6834.57	+	1194.75i	−1.64747	+	0.287994i
$29$			155.049i			0.0342353i	0.999853	+	0.0171177i	$0.00544899\pi$
$29$			155.049i			0.0342353i	−0.999853	+	0.0171177i	$0.994551\pi$
$30$		0			0
$31$			4909.55i			0.917567i	0.888548	+	0.458783i	$0.151715\pi$
$31$			4909.55i			0.917567i	−0.888548	+	0.458783i	$0.848285\pi$
$32$	2001.20	−	5435.96i	0.345475	−	0.938428i
$33$		0			0
$34$	−9458.78	−	7948.73i	−1.40326	−	1.17923i
$35$	−17462.3			−2.40952
$36$		0			0
$37$	114.620			0.0137644			0.00688218	−	0.999976i	$-0.497809\pi$
$37$	114.620			0.0137644			0.00688218	+	0.999976i	$0.497809\pi$
$38$	3116.85	+	2619.26i	0.350152	+	0.294252i
$39$		0			0
$40$	7317.35	−	12609.7i	0.723109	−	1.24610i
$41$		−	3356.63i		−	0.311849i	−0.987769	−	0.155924i	$-0.950164\pi$
$41$		−	3356.63i		−	0.311849i	0.987769	−	0.155924i	$-0.0498356\pi$
$42$		0			0
$43$		−	13109.4i		−	1.08121i	−0.841276	−	0.540606i	$-0.818195\pi$
$43$		−	13109.4i		−	1.08121i	0.841276	−	0.540606i	$-0.181805\pi$
$44$	844.988	+	4833.74i	0.0657989	+	0.376402i
$45$		0			0
$46$	−9542.96	+	11355.9i	−0.664949	+	0.791273i
$47$	−9409.97			−0.621360			−0.310680	−	0.950515i	$-0.600557\pi$
$47$	−9409.97			−0.621360			−0.310680	+	0.950515i	$0.600557\pi$
$48$		0			0
$49$	−30203.6			−1.79708
$50$	12233.4	−	14557.4i	0.692026	−	0.823493i
$51$		0			0
$52$	5211.41	+	29811.8i	0.267268	+	1.52890i
$53$			19619.3i			0.959388i	0.877436	+	0.479694i	$0.159252\pi$
$53$			19619.3i			0.959388i	−0.877436	+	0.479694i	$0.840748\pi$
$54$		0			0
$55$			12350.2i			0.550511i
$56$	19699.2	−	33946.8i	0.839419	−	1.44653i
$57$		0			0
$58$	−671.476	−	564.277i	−0.0262096	−	0.0220253i
$59$	−21595.2			−0.807658			−0.403829	−	0.914835i	$-0.632321\pi$
$59$	−21595.2			−0.807658			−0.403829	+	0.914835i	$0.632321\pi$
$60$		0			0
$61$	33298.2			1.14577			0.572884	−	0.819637i	$-0.305825\pi$
$61$	33298.2			1.14577			0.572884	+	0.819637i	$0.305825\pi$
$62$	−21261.9	−	17867.5i	−0.702463	−	0.590317i
$63$		0			0
$64$	16258.6	+	28450.0i	0.496172	+	0.868224i
$65$			76168.9i			2.23612i
$66$		0			0
$67$		−	23493.1i		−	0.639371i	−0.947524	−	0.319685i	$-0.896423\pi$
$67$		−	23493.1i		−	0.639371i	0.947524	−	0.319685i	$-0.103577\pi$
$68$	68847.5	−	12035.2i	1.80558	−	0.315633i
$69$		0			0
$70$	63551.2	−	75624.3i	1.55017	−	1.84466i
$71$	−2402.72			−0.0565662			−0.0282831	−	0.999600i	$-0.509004\pi$
$71$	−2402.72			−0.0565662			−0.0282831	+	0.999600i	$0.509004\pi$
$72$		0			0
$73$	4867.76			0.106911			0.0534555	−	0.998570i	$-0.482976\pi$
$73$	4867.76			0.106911			0.0534555	+	0.998570i	$0.482976\pi$
$74$	−417.141	+	496.388i	−0.00885531	+	0.0105376i
$75$		0			0
$76$	−22686.6	+	3965.84i	−0.450541	+	0.0787592i
$77$			33248.2i			0.639059i
$78$		0			0
$79$		−	11925.5i		−	0.214985i	−0.994206	−	0.107492i	$-0.965718\pi$
$79$		−	11925.5i		−	0.214985i	0.994206	−	0.107492i	$-0.0342821\pi$
$80$	27978.7	+	77580.4i	0.488767	+	1.35527i
$81$		0			0
$82$	14536.6	+	12215.9i	0.238742	+	0.200628i
$83$	−83940.6			−1.33745			−0.668724	−	0.743511i	$-0.733159\pi$
$83$	−83940.6			−1.33745			−0.668724	+	0.743511i	$0.733159\pi$
$84$		0			0
$85$	175905.			2.64077
$86$	56773.1	+	47709.5i	0.827745	+	0.695599i
$87$		0			0
$88$	−24008.8	−	13932.2i	−0.330494	−	0.191785i
$89$		−	36800.9i		−	0.492474i	−0.969210	−	0.246237i	$-0.920806\pi$
$89$		−	36800.9i		−	0.492474i	0.969210	−	0.246237i	$-0.0791941\pi$
$90$		0			0
$91$			205056.i			2.59579i
$92$	−14449.1	−	82655.9i	−0.177980	−	1.01813i
$93$		0			0
$94$	34246.1	−	40752.0i	0.399753	−	0.475696i
$95$	−57963.9			−0.658945
$96$		0			0
$97$	−28249.7			−0.304849			−0.152424	−	0.988315i	$-0.548708\pi$
$97$	−28249.7			−0.304849			−0.152424	+	0.988315i	$0.548708\pi$
$98$	109921.	−	130803.i	1.15616	−	1.37579i
$99$		0			0
$100$	18522.7	+	105959.i	0.185227	+	1.05959i
$101$		−	4051.50i		−	0.0395196i	−0.999805	−	0.0197598i	$-0.993710\pi$
$101$		−	4051.50i		−	0.0395196i	0.999805	−	0.0197598i	$-0.00629015\pi$
$102$		0			0
$103$		−	108384.i		−	1.00663i	−0.864103	−	0.503316i	$-0.832113\pi$
$103$		−	108384.i		−	1.00663i	0.864103	−	0.503316i	$-0.167887\pi$
$104$	−148073.	−	85926.3i	−1.34243	−	0.779009i
$105$		0			0
$106$	−84965.9	−	71401.4i	−0.734480	−	0.617223i
$107$	−94762.1			−0.800157			−0.400079	−	0.916481i	$-0.631017\pi$
$107$	−94762.1			−0.800157			−0.400079	+	0.916481i	$0.631017\pi$
$108$		0			0
$109$	−105703.			−0.852160			−0.426080	−	0.904685i	$-0.640106\pi$
$109$	−105703.			−0.852160			−0.426080	+	0.904685i	$0.640106\pi$
$110$	−53485.2	−	44946.5i	−0.421456	−	0.354172i
$111$		0			0
$112$	75322.0	+	208856.i	0.567383	+	1.57326i
$113$		−	80853.1i		−	0.595663i	−0.954618	−	0.297832i	$-0.903737\pi$
$113$		−	80853.1i		−	0.595663i	0.954618	−	0.297832i	$-0.0962634\pi$
$114$		0			0
$115$		−	211185.i		−	1.48908i
$116$	4887.46	−	854.378i	0.0337239	−	0.00589529i
$117$		0			0
$118$	78592.4	−	93522.9i	0.519607	−	0.618319i
$119$	473557.			3.06552
$120$		0			0
$121$	−137536.			−0.853992
$122$	−121184.	+	144205.i	−0.737131	+	0.877166i
$123$		0			0
$124$	154759.	−	27053.4i	0.903860	−	0.158004i
$125$			19041.9i			0.109002i
$126$		0			0
$127$			47941.0i			0.263753i	0.991266	+	0.131877i	$0.0421003\pi$
$127$			47941.0i			0.263753i	−0.991266	+	0.131877i	$0.957900\pi$
$128$	−182380.	−	33127.8i	−0.983900	−	0.178718i
$129$		0			0
$130$	−329867.	−	277205.i	−1.71191	−	1.43861i
$131$	−301162.			−1.53328			−0.766640	−	0.642077i	$-0.778073\pi$
$131$	−301162.			−1.53328			−0.766640	+	0.642077i	$0.778073\pi$
$132$		0			0
$133$	−156046.			−0.764933
$134$	101742.	+	85499.4i	0.489484	+	0.411340i
$135$		0			0
$136$	−198438.	+	341960.i	−0.919980	+	1.58536i
$137$			134846.i			0.613814i	0.951739	+	0.306907i	$0.0992941\pi$
$137$			134846.i			0.613814i	−0.951739	+	0.306907i	$0.900706\pi$
$138$		0			0
$139$		−	88215.4i		−	0.387264i	−0.981074	−	0.193632i	$-0.937973\pi$
$139$		−	88215.4i		−	0.387264i	0.981074	−	0.193632i	$-0.0620268\pi$
$140$	96223.5	+	550446.i	0.414917	+	2.37353i
$141$		0			0
$142$	8744.31	−	10405.5i	0.0363919	−	0.0433054i
$143$	145026.			0.593068
$144$		0			0
$145$	12487.4			0.0493233
$146$	−17715.5	+	21080.9i	−0.0687813	+	0.0818480i
$147$		0			0
$148$	−631.598	−	3613.05i	−0.00237021	−	0.0135587i
$149$		−	424905.i		−	1.56793i	−0.620806	−	0.783965i	$-0.713194\pi$
$149$		−	424905.i		−	1.56793i	0.620806	−	0.783965i	$-0.286806\pi$
$150$		0			0
$151$			188045.i			0.671150i	0.942014	+	0.335575i	$0.108931\pi$
$151$			188045.i			0.671150i	−0.942014	+	0.335575i	$0.891069\pi$
$152$	65389.2	−	112682.i	0.229560	−	0.395591i
$153$		0			0
$154$	−143989.	−	121002.i	−0.489245	−	0.411139i
$155$	395407.			1.32195
$156$		0			0
$157$	−348168.			−1.12730			−0.563650	−	0.826014i	$-0.690603\pi$
$157$	−348168.			−1.12730			−0.563650	+	0.826014i	$0.690603\pi$
$158$	51645.9	+	43400.9i	0.164586	+	0.138311i
$159$		0			0
$160$	−437803.	−	161174.i	−1.35201	−	0.497730i
$161$		−	568536.i		−	1.72859i
$162$		0			0
$163$		−	25262.9i		−	0.0744756i	−0.999306	−	0.0372378i	$-0.988144\pi$
$163$		−	25262.9i		−	0.0744756i	0.999306	−	0.0372378i	$-0.0118559\pi$
$164$	−105808.	+	18496.2i	−0.307190	+	0.0537000i
$165$		0			0
$166$	305489.	−	363524.i	0.860448	−	1.02391i
$167$	385026.			1.06831			0.534157	−	0.845386i	$-0.320629\pi$
$167$	385026.			1.06831			0.534157	+	0.845386i	$0.320629\pi$
$168$		0			0
$169$	523144.			1.40898
$170$	−640178.	+	761795.i	−1.69894	+	2.02170i
$171$		0			0
$172$	−413233.	+	72237.4i	−1.06506	+	0.186183i
$173$			547742.i			1.39143i	0.718318	+	0.695715i	$0.244912\pi$
$173$			547742.i			1.39143i	−0.718318	+	0.695715i	$0.755088\pi$
$174$		0			0
$175$			728823.i			1.79898i
$176$	147713.	−	53271.4i	0.359449	−	0.129632i
$177$		0			0
$178$	159374.	+	133931.i	0.377024	+	0.316834i
$179$	450824.			1.05166			0.525829	−	0.850590i	$-0.323755\pi$
$179$	450824.			1.05166			0.525829	+	0.850590i	$0.323755\pi$
$180$		0			0
$181$	1585.85			0.00359805			0.00179902	−	0.999998i	$-0.499427\pi$
$181$	1585.85			0.00359805			0.00179902	+	0.999998i	$0.499427\pi$
$182$	−888041.	−	746269.i	−1.98726	−	1.67000i
$183$		0			0
$184$	410545.	+	238238.i	0.893956	+	0.518760i
$185$		−	9231.31i		−	0.0198305i
$186$		0			0
$187$		−	334923.i		−	0.700391i
$188$	51852.3	+	296621.i	0.106998	+	0.612078i
$189$		0			0
$190$	210951.	−	251026.i	0.423933	−	0.504469i
$191$	−310556.			−0.615966			−0.307983	−	0.951392i	$-0.599654\pi$
$191$	−310556.			−0.615966			−0.307983	+	0.951392i	$0.599654\pi$
$192$		0			0
$193$	86770.6			0.167679			0.0838397	−	0.996479i	$-0.473282\pi$
$193$	86770.6			0.167679			0.0838397	+	0.996479i	$0.473282\pi$
$194$	102810.	−	122342.i	0.196125	−	0.233383i
$195$		0			0
$196$	166433.	+	952077.i	0.309456	+	1.77024i
$197$		−	406767.i		−	0.746758i	−0.927679	−	0.373379i	$-0.878199\pi$
$197$		−	406767.i		−	0.746758i	0.927679	−	0.373379i	$-0.121801\pi$
$198$		0			0
$199$		−	1.07477e6i		−	1.92389i	−0.273235	−	0.961947i	$-0.588094\pi$
$199$		−	1.07477e6i		−	1.92389i	0.273235	−	0.961947i	$-0.411906\pi$
$200$	−526290.	−	305404.i	−0.930358	−	0.539884i
$201$		0			0
$202$	17546.0	+	14744.8i	0.0302551	+	0.0254250i
$203$	33617.6			0.0572568
$204$		0			0
$205$	−270338.			−0.449285
$206$	469380.	+	394445.i	0.770648	+	0.647618i
$207$		0			0
$208$	911011.	−	328548.i	1.46004	−	0.526551i
$209$			110363.i			0.174767i
$210$		0			0
$211$		−	629852.i		−	0.973941i	−0.873419	−	0.486970i	$-0.838102\pi$
$211$		−	629852.i		−	0.973941i	0.873419	−	0.486970i	$-0.161898\pi$
$212$	618440.	−	108110.i	0.945057	−	0.165206i
$213$		0			0
$214$	344872.	−	410389.i	0.514782	−	0.612577i
$215$	−1.05581e6			−1.55772
$216$		0			0
$217$	1.06449e6			1.53458
$218$	384690.	−	457771.i	0.548238	−	0.652389i
$219$		0			0
$220$	389302.	−	68053.9i	0.542288	−	0.0947974i
$221$		−	2.06561e6i		−	2.84491i
$222$		0			0
$223$			1.27771e6i			1.72056i	0.509825	+	0.860278i	$0.329710\pi$
$223$			1.27771e6i			1.72056i	−0.509825	+	0.860278i	$0.670290\pi$
$224$	−1.17862e6	−	433899.i	−1.56947	−	0.577788i
$225$		0			0
$226$	350153.	+	294252.i	0.456023	+	0.383221i
$227$	1.43061e6			1.84271			0.921354	−	0.388724i	$-0.127084\pi$
$227$	1.43061e6			1.84271			0.921354	+	0.388724i	$0.127084\pi$
$228$		0			0
$229$	618971.			0.779977			0.389988	−	0.920820i	$-0.372479\pi$
$229$	618971.			0.779977			0.389988	+	0.920820i	$0.372479\pi$
$230$	914584.	+	768575.i	1.14000	+	0.958002i
$231$		0			0
$232$	−14087.1	+	24275.6i	−0.0171831	+	0.0296108i
$233$			391086.i			0.471936i	0.971761	+	0.235968i	$0.0758260\pi$
$233$			391086.i			0.471936i	−0.971761	+	0.235968i	$0.924174\pi$
$234$		0			0
$235$			757864.i			0.895203i
$236$	118997.	+	680724.i	0.139078	+	0.795593i
$237$		0			0
$238$	−1.72344e6	+	2.05085e6i	−1.97221	+	2.34688i
$239$	−1.39491e6			−1.57961			−0.789806	−	0.613356i	$-0.789819\pi$
$239$	−1.39491e6			−1.57961			−0.789806	+	0.613356i	$0.789819\pi$
$240$		0			0
$241$	−745913.			−0.827266			−0.413633	−	0.910444i	$-0.635740\pi$
$241$	−745913.			−0.827266			−0.413633	+	0.910444i	$0.635740\pi$
$242$	500542.	−	595632.i	0.549417	−	0.653792i
$243$		0			0
$244$	−183485.	−	1.04963e6i	−0.197300	−	1.12865i
$245$			2.43255e6i			2.58908i
$246$		0			0
$247$			680659.i			0.709884i
$248$	−446060.	+	768675.i	−0.460536	+	0.793621i
$249$		0			0
$250$	−82465.1	−	69299.9i	−0.0834488	−	0.0701266i
$251$	−1.22222e6			−1.22452			−0.612260	−	0.790657i	$-0.709739\pi$
$251$	−1.22222e6			−1.22452			−0.612260	+	0.790657i	$0.709739\pi$
$252$		0			0
$253$	−402096.			−0.394938
$254$	−207619.	−	174474.i	−0.201922	−	0.169686i
$255$		0			0
$256$	807209.	−	669272.i	0.769815	−	0.638268i
$257$			1.79287e6i			1.69323i	0.532207	+	0.846614i	$0.321363\pi$
$257$			1.79287e6i			1.69323i	−0.532207	+	0.846614i	$0.678637\pi$
$258$		0			0
$259$		−	24851.8i		−	0.0230202i
$260$	2.40100e6	−	419718.i	2.20271	−	0.385057i
$261$		0			0
$262$	1.09603e6	−	1.30425e6i	0.986438	−	1.17384i
$263$	996371.			0.888243			0.444122	−	0.895967i	$-0.353516\pi$
$263$	996371.			0.888243			0.444122	+	0.895967i	$0.353516\pi$
$264$		0			0
$265$	1.58011e6			1.38220
$266$	567905.	−	675793.i	0.492121	−	0.585611i
$267$		0			0
$268$	−740549.	+	129455.i	−0.629820	+	0.110099i
$269$			2.16053e6i			1.82045i	0.414109	+	0.910227i	$0.364093\pi$
$269$			2.16053e6i			1.82045i	−0.414109	+	0.910227i	$0.635907\pi$
$270$		0			0
$271$		−	1.68130e6i		−	1.39066i	−0.718688	−	0.695332i	$-0.755257\pi$
$271$		−	1.68130e6i		−	1.39066i	0.718688	−	0.695332i	$-0.244743\pi$
$272$	−758749.	−	2.10389e6i	−0.621836	−	1.72425i
$273$		0			0
$274$	−583982.	−	490751.i	−0.469919	−	0.394898i
$275$	515459.			0.411020
$276$		0			0
$277$	1.08867e6			0.852507			0.426254	−	0.904604i	$-0.359833\pi$
$277$	1.08867e6			0.852507			0.426254	+	0.904604i	$0.359833\pi$
$278$	382036.	+	321046.i	0.296478	+	0.249147i
$279$		0			0
$280$	−2.73402e6	−	1.58654e6i	−2.08404	−	1.20936i
$281$		−	728495.i		−	0.550377i	−0.961390	−	0.275189i	$-0.911260\pi$
$281$		−	728495.i		−	0.550377i	0.961390	−	0.275189i	$-0.0887403\pi$
$282$		0			0
$283$		−	733677.i		−	0.544551i	−0.962219	−	0.272276i	$-0.912224\pi$
$283$		−	733677.i		−	0.544551i	0.962219	−	0.272276i	$-0.0877762\pi$
$284$	13239.8	+	75738.4i	0.00974063	+	0.0557212i
$285$		0			0
$286$	−527798.	+	628066.i	−0.381551	+	0.454036i
$287$	−727782.			−0.521551
$288$		0			0
$289$	−3.35048e6			−2.35973
$290$	−45446.0	+	54079.6i	−0.0317322	+	0.0377605i
$291$		0			0
$292$	−26823.1	−	153442.i	−0.0184099	−	0.105314i
$293$		−	400766.i		−	0.272723i	−0.990659	−	0.136361i	$-0.956459\pi$
$293$		−	400766.i		−	0.272723i	0.990659	−	0.136361i	$-0.0435409\pi$
$294$		0			0
$295$			1.73924e6i			1.16360i
$296$	17945.7	+	10413.9i	0.0119051	+	0.00690847i
$297$		0			0
$298$	1.84015e6	+	1.54638e6i	1.20036	+	1.00873i
$299$	−2.47990e6			−1.60419
$300$		0			0
$301$	−2.84236e6			−1.80827
$302$	−814371.	−	684360.i	−0.513813	−	0.431785i
$303$		0			0
$304$	250022.	+	693272.i	0.155165	+	0.430249i
$305$		−	2.68178e6i		−	1.65072i
$306$		0			0
$307$		−	1.18446e6i		−	0.717258i	−0.933480	−	0.358629i	$-0.883244\pi$
$307$		−	1.18446e6i		−	0.717258i	0.933480	−	0.358629i	$-0.116756\pi$
$308$	1.04805e6	−	183210.i	0.629513	−	0.110045i
$309$		0			0
$310$	−1.43902e6	+	1.71240e6i	−0.850479	+	1.01205i
$311$	−2.98276e6			−1.74871			−0.874354	−	0.485289i	$-0.838714\pi$
$311$	−2.98276e6			−1.74871			−0.874354	+	0.485289i	$0.838714\pi$
$312$		0			0
$313$	−2.44466e6			−1.41045			−0.705224	−	0.708984i	$-0.749154\pi$
$313$	−2.44466e6			−1.41045			−0.705224	+	0.708984i	$0.749154\pi$
$314$	1.26710e6	−	1.50782e6i	0.725249	−	0.863028i
$315$		0			0
$316$	−375914.	+	65713.6i	−0.211773	+	0.0370201i
$317$		−	164872.i		−	0.0921508i	−0.998938	−	0.0460754i	$-0.985329\pi$
$317$		−	164872.i		−	0.0921508i	0.998938	−	0.0460754i	$-0.0146715\pi$
$318$		0			0
$319$		−	23776.0i		−	0.0130817i
$320$	2.29131e6	−	1.30944e6i	1.25086	−	0.714842i
$321$		0			0
$322$	2.46217e6	+	2.06910e6i	1.32336	+	1.11209i
$323$	1.57192e6			0.838346
$324$		0			0
$325$	3.17906e6			1.66952
$326$	109407.	+	91940.4i	0.0570164	+	0.0479140i
$327$		0			0
$328$	304968.	−	525538.i	0.156520	−	0.269724i
$329$			2.04026e6i			1.03919i
$330$		0			0
$331$		−	3.03272e6i		−	1.52147i	−0.649065	−	0.760733i	$-0.724840\pi$
$331$		−	3.03272e6i		−	1.52147i	0.649065	−	0.760733i	$-0.275160\pi$
$332$	462543.	+	2.64597e6i	0.230307	+	1.31747i
$333$		0			0
$334$	−1.40124e6	+	1.66744e6i	−0.687300	+	0.817870i
$335$	−1.89209e6			−0.921151
$336$		0			0
$337$	−2.77189e6			−1.32954			−0.664769	−	0.747049i	$-0.731470\pi$
$337$	−2.77189e6			−1.32954			−0.664769	+	0.747049i	$0.731470\pi$
$338$	−1.90390e6	+	2.26559e6i	−0.906468	+	1.07867i
$339$		0			0
$340$	−969299.	−	5.54487e6i	−0.454737	−	2.60132i
$341$		−	752856.i		−	0.350611i
$342$		0			0
$343$			2.90463e6i			1.33308i
$344$	1.19106e6	−	2.05250e6i	0.542671	−	0.935161i
$345$		0			0
$346$	−2.37212e6	−	1.99342e6i	−1.06524	−	0.895177i
$347$	−1.11916e6			−0.498961			−0.249481	−	0.968380i	$-0.580260\pi$
$347$	−1.11916e6			−0.498961			−0.249481	+	0.968380i	$0.580260\pi$
$348$		0			0
$349$	2.08395e6			0.915849			0.457925	−	0.888991i	$-0.348593\pi$
$349$	2.08395e6			0.915849			0.457925	+	0.888991i	$0.348593\pi$
$350$	−3.15633e6	−	2.65244e6i	−1.37725	−	1.15738i
$351$		0			0
$352$	−306875.	+	833578.i	−0.132009	+	0.358583i
$353$			2.22872e6i			0.951961i	0.879456	+	0.475980i	$0.157907\pi$
$353$			2.22872e6i			0.951961i	−0.879456	+	0.475980i	$0.842093\pi$
$354$		0			0
$355$			193511.i			0.0814957i
$356$	−1.16004e6	+	202786.i	−0.485117	+	0.0848034i
$357$		0			0
$358$	−1.64070e6	+	1.95239e6i	−0.676585	+	0.805119i
$359$	3.79795e6			1.55530			0.777649	−	0.628699i	$-0.216412\pi$
$359$	3.79795e6			1.55530			0.777649	+	0.628699i	$0.216412\pi$
$360$		0			0
$361$	1.95812e6			0.790810
$362$	−5771.47	+	6867.90i	−0.00231481	+	0.00275456i
$363$		0			0
$364$	6.46377e6	−	1.12993e6i	2.55701	−	0.446992i
$365$		−	392042.i		−	0.154028i
$366$		0			0
$367$			1.00563e6i			0.389737i	0.980829	+	0.194868i	$0.0624280\pi$
$367$			1.00563e6i			0.389737i	−0.980829	+	0.194868i	$0.937572\pi$
$368$	−2.52586e6	+	910928.i	−0.972276	+	0.350642i
$369$		0			0
$370$	39978.3	+	33595.9i	0.0151817	+	0.0127580i
$371$	4.25385e6			1.60453
$372$		0			0
$373$	3.13554e6			1.16692			0.583458	−	0.812143i	$-0.301699\pi$
$373$	3.13554e6			1.16692			0.583458	+	0.812143i	$0.301699\pi$
$374$	1.45046e6	+	1.21890e6i	0.536199	+	0.450597i
$375$		0			0
$376$	−1.47329e6	−	854947.i	−0.537427	−	0.311867i
$377$		−	146637.i		−	0.0531363i
$378$		0			0
$379$		−	1.35382e6i		−	0.484133i	−0.970260	−	0.242066i	$-0.922175\pi$
$379$		−	1.35382e6i		−	0.484133i	0.970260	−	0.242066i	$-0.0778251\pi$
$380$	319402.	+	1.82714e6i	0.113470	+	0.649101i
$381$		0			0
$382$	1.13022e6	−	1.34493e6i	0.396283	−	0.471566i
$383$	3.31845e6			1.15595			0.577974	−	0.816055i	$-0.303843\pi$
$383$	3.31845e6			1.15595			0.577974	+	0.816055i	$0.303843\pi$
$384$		0			0
$385$	2.67775e6			0.920702
$386$	−315788.	+	375780.i	−0.107877	+	0.128370i
$387$		0			0
$388$	155666.	+	890486.i	0.0524946	+	0.300295i
$389$		−	3.73290e6i		−	1.25076i	−0.780322	−	0.625378i	$-0.784945\pi$
$389$		−	3.73290e6i		−	1.25076i	0.780322	−	0.625378i	$-0.215055\pi$
$390$		0			0
$391$			5.72710e6i			1.89449i
$392$	−4.72889e6	−	2.74416e6i	−1.55433	−	0.901974i
$393$		0			0
$394$	1.76160e6	+	1.48036e6i	0.571697	+	0.480428i
$395$	−960458.			−0.309732
$396$		0			0
$397$	−908240.			−0.289217			−0.144609	−	0.989489i	$-0.546192\pi$
$397$	−908240.			−0.289217			−0.144609	+	0.989489i	$0.546192\pi$
$398$	4.65452e6	+	3.91144e6i	1.47288	+	1.23774i
$399$		0			0
$400$	3.23797e6	−	1.16775e6i	1.01187	−	0.364921i
$401$		−	128575.i		−	0.0399297i	−0.999801	−	0.0199649i	$-0.993645\pi$
$401$		−	128575.i		−	0.0399297i	0.999801	−	0.0199649i	$-0.00635544\pi$
$402$		0			0
$403$		−	4.64319e6i		−	1.42414i
$404$	−127711.	+	22325.3i	−0.0389293	+	0.00680524i
$405$		0			0
$406$	−122346.	+	145589.i	−0.0368362	+	0.0438342i
$407$	−17576.4			−0.00525950
$408$		0			0
$409$	4.22625e6			1.24924			0.624622	−	0.780927i	$-0.285253\pi$
$409$	4.22625e6			1.24924			0.624622	+	0.780927i	$0.285253\pi$
$410$	983851.	−	1.17076e6i	0.289048	−	0.343960i
$411$		0			0
$412$	−3.41647e6	+	597233.i	−0.991595	+	0.173341i
$413$			4.68225e6i			1.35077i
$414$		0			0
$415$			6.76044e6i			1.92688i
$416$	−1.89263e6	+	5.14104e6i	−0.536207	+	1.45652i
$417$		0			0
$418$	−477954.	−	401650.i	−0.133797	−	0.112437i
$419$	2.78414e6			0.774739			0.387370	−	0.921924i	$-0.373384\pi$
$419$	2.78414e6			0.774739			0.387370	+	0.921924i	$0.373384\pi$
$420$		0			0
$421$	−2.45303e6			−0.674525			−0.337262	−	0.941411i	$-0.609501\pi$
$421$	−2.45303e6			−0.674525			−0.337262	+	0.941411i	$0.609501\pi$
$422$	2.72772e6	+	2.29225e6i	0.745621	+	0.626586i
$423$		0			0
$424$	−1.78252e6	+	3.07174e6i	−0.481527	+	0.829794i
$425$		−	7.34174e6i		−	1.97164i
$426$		0			0
$427$		−	7.21969e6i		−	1.91624i
$428$	522174.	+	2.98709e6i	0.137786	+	0.788204i
$429$		0			0
$430$	3.84245e6	−	4.57241e6i	1.00216	−	1.19254i
$431$	−1.70611e6			−0.442397			−0.221199	−	0.975229i	$-0.570997\pi$
$431$	−1.70611e6			−0.442397			−0.221199	+	0.975229i	$0.570997\pi$
$432$		0			0
$433$	194630.			0.0498872			0.0249436	−	0.999689i	$-0.492059\pi$
$433$	194630.			0.0498872			0.0249436	+	0.999689i	$0.492059\pi$
$434$	−3.87403e6	+	4.60999e6i	−0.987275	+	1.17483i
$435$		0			0
$436$	582462.	+	3.33197e6i	0.146741	+	0.839431i
$437$		−	1.88719e6i		−	0.472728i
$438$		0			0
$439$		−	550852.i		−	0.136419i	−0.997671	−	0.0682093i	$-0.978271\pi$
$439$		−	550852.i		−	0.136419i	0.997671	−	0.0682093i	$-0.0217286\pi$
$440$	−1.12208e6	+	1.93363e6i	−0.276307	+	0.476148i
$441$		0			0
$442$	8.94561e6	+	7.51748e6i	2.17798	+	1.83028i
$443$	−5.84486e6			−1.41503			−0.707514	−	0.706700i	$-0.750183\pi$
$443$	−5.84486e6			−1.41503			−0.707514	+	0.706700i	$0.750183\pi$
$444$		0			0
$445$	−2.96388e6			−0.709514
$446$	−5.53339e6	−	4.65001e6i	−1.31721	−	1.10692i
$447$		0			0
$448$	6.16850e6	−	3.52517e6i	1.45206	−	0.829822i
$449$		−	3.10126e6i		−	0.725977i	−0.931794	−	0.362989i	$-0.881756\pi$
$449$		−	3.10126e6i		−	0.725977i	0.931794	−	0.362989i	$-0.118244\pi$
$450$		0			0
$451$			514723.i			0.119160i
$452$	−2.54865e6	+	445530.i	−0.586765	+	0.102573i
$453$		0			0
$454$	−5.20648e6	+	6.19558e6i	−1.18551	+	1.41072i
$455$	1.65149e7			3.73979
$456$		0			0
$457$	917472.			0.205496			0.102748	−	0.994707i	$-0.467237\pi$
$457$	917472.			0.205496			0.102748	+	0.994707i	$0.467237\pi$
$458$	−2.25265e6	+	2.68059e6i	−0.501799	+	0.597128i
$459$		0			0
$460$	−6.65697e6	+	1.16371e6i	−1.46684	+	0.256418i
$461$		−	7.26023e6i		−	1.59110i	−0.605886	−	0.795552i	$-0.707181\pi$
$461$		−	7.26023e6i		−	1.59110i	0.605886	−	0.795552i	$-0.292819\pi$
$462$		0			0
$463$		−	7.02175e6i		−	1.52227i	−0.648591	−	0.761137i	$-0.724641\pi$
$463$		−	7.02175e6i		−	1.52227i	0.648591	−	0.761137i	$-0.275359\pi$
$464$	−53863.4	−	149355.i	−0.0116144	−	0.0322050i
$465$		0			0
$466$	−1.69369e6	−	1.42330e6i	−0.361300	−	0.303620i
$467$	−2.85330e6			−0.605417			−0.302709	−	0.953083i	$-0.597891\pi$
$467$	−2.85330e6			−0.605417			−0.302709	+	0.953083i	$0.597891\pi$
$468$		0			0
$469$	−5.09375e6			−1.06931
$470$	−3.28210e6	−	2.75813e6i	−0.685342	−	0.575930i
$471$		0			0
$472$	−3.38110e6	−	1.96204e6i	−0.698559	−	0.405372i
$473$			2.01026e6i			0.413142i
$474$		0			0
$475$			2.41924e6i			0.491978i
$476$	−2.60947e6	−	1.49275e7i	−0.527880	−	3.01973i
$477$		0			0
$478$	5.07655e6	−	6.04096e6i	1.01625	−	1.20931i
$479$	−919797.			−0.183169			−0.0915847	−	0.995797i	$-0.529193\pi$
$479$	−919797.			−0.183169			−0.0915847	+	0.995797i	$0.529193\pi$
$480$		0			0
$481$	−108401.			−0.0213635
$482$	2.71463e6	−	3.23034e6i	0.532223	−	0.633331i
$483$		0			0
$484$	757875.	+	4.33542e6i	0.147056	+	0.841235i
$485$			2.27518e6i			0.439200i
$486$		0			0
$487$			5.70621e6i			1.09025i	0.838355	+	0.545124i	$0.183517\pi$
$487$			5.70621e6i			1.09025i	−0.838355	+	0.545124i	$0.816483\pi$
$488$	5.21341e6	+	3.02533e6i	0.990997	+	0.575072i
$489$		0			0
$490$	−1.05347e7	−	8.85287e6i	−1.98213	−	1.66569i
$491$	−2.01852e6			−0.377859			−0.188930	−	0.981991i	$-0.560502\pi$
$491$	−2.01852e6			−0.377859			−0.188930	+	0.981991i	$0.560502\pi$
$492$		0			0
$493$	−338645.			−0.0627519
$494$	−2.94775e6	−	2.47715e6i	−0.543467	−	0.456705i
$495$		0			0
$496$	−1.70556e6	−	4.72923e6i	−0.311287	−	0.863150i
$497$			520955.i			0.0946040i
$498$		0			0
$499$			1.19282e6i			0.214448i	0.994235	+	0.107224i	$0.0341962\pi$
$499$			1.19282e6i			0.214448i	−0.994235	+	0.107224i	$0.965804\pi$
$500$	600238.	−	104928.i	0.107374	−	0.0187700i
$501$		0			0
$502$	4.44808e6	−	5.29310e6i	0.787796	−	0.937457i
$503$	9.18424e6			1.61854			0.809270	−	0.587437i	$-0.199863\pi$
$503$	9.18424e6			1.61854			0.809270	+	0.587437i	$0.199863\pi$
$504$		0			0
$505$	−326302.			−0.0569365
$506$	1.46337e6	−	1.74137e6i	0.254084	−	0.302353i
$507$		0			0
$508$	1.51120e6	−	264172.i	0.259813	−	0.0454180i
$509$		−	1.17272e6i		−	0.200632i	−0.994956	−	0.100316i	$-0.968015\pi$
$509$		−	1.17272e6i		−	0.200632i	0.994956	−	0.100316i	$-0.0319853\pi$
$510$		0			0
$511$		−	1.05542e6i		−	0.178803i
$512$	−39277.0	+	5.93151e6i	−0.00662161	+	0.999978i
$513$		0			0
$514$	−7.76442e6	−	6.52486e6i	−1.29629	−	1.08934i
$515$	−8.72904e6			−1.45027
$516$		0			0
$517$	1.44297e6			0.237428
$518$	107626.	+	90444.3i	0.0176236	+	0.0148101i
$519$		0			0
$520$	−6.92036e6	+	1.19256e7i	−1.12233	+	1.93406i
$521$			6.12848e6i			0.989141i	0.869137	+	0.494571i	$0.164675\pi$
$521$			6.12848e6i			0.989141i	−0.869137	+	0.494571i	$0.835325\pi$
$522$		0			0
$523$		−	6.43682e6i		−	1.02900i	−0.857489	−	0.514502i	$-0.827977\pi$
$523$		−	6.43682e6i		−	1.02900i	0.857489	−	0.514502i	$-0.172023\pi$
$524$	1.65951e6	+	9.49322e6i	0.264029	+	1.51038i
$525$		0			0
$526$	−3.62614e6	+	4.31501e6i	−0.571452	+	0.680013i
$527$	−1.07230e7			−1.68186
$528$		0			0
$529$	439409.			0.0682700
$530$	−5.75056e6	+	6.84302e6i	−0.889242	+	1.05818i
$531$		0			0
$532$	859870.	+	4.91888e6i	0.131721	+	0.753507i
$533$			3.17452e6i			0.484016i
$534$		0			0
$535$			7.63199e6i			1.15280i
$536$	2.13447e6	−	3.67825e6i	0.320907	−	0.553005i
$537$		0			0
$538$	−9.35667e6	−	7.86291e6i	−1.39369	−	1.17119i
$539$	4.63157e6			0.686683
$540$		0			0
$541$	−1.06503e7			−1.56448			−0.782238	−	0.622980i	$-0.785922\pi$
$541$	−1.06503e7			−1.56448			−0.782238	+	0.622980i	$0.785922\pi$
$542$	7.28126e6	+	6.11883e6i	1.06465	+	0.894686i
$543$		0			0
$544$	1.18727e7	+	4.37085e6i	1.72010	+	0.633240i
$545$			8.51315e6i			1.22772i
$546$		0			0
$547$			1.81400e6i			0.259220i	0.991565	+	0.129610i	$0.0413725\pi$
$547$			1.81400e6i			0.259220i	−0.991565	+	0.129610i	$0.958628\pi$
$548$	4.25062e6	−	743051.i	0.604645	−	0.105698i
$549$		0			0
$550$	−1.87593e6	+	2.23231e6i	−0.264430	+	0.314665i
$551$	111590.			0.0156583
$552$		0			0
$553$	−2.58567e6			−0.359551
$554$	−3.96206e6	+	4.71475e6i	−0.548462	+	0.652655i
$555$		0			0
$556$	−2.78072e6	+	486099.i	−0.381479	+	0.0666864i
$557$		−	6.09580e6i		−	0.832517i	−0.909246	−	0.416258i	$-0.863341\pi$
$557$		−	6.09580e6i		−	0.832517i	0.909246	−	0.416258i	$-0.136659\pi$
$558$		0			0
$559$			1.23981e7i			1.67814i
$560$	1.68209e7	−	6.06631e6i	2.26662	−	0.817437i
$561$		0			0
$562$	3.15491e6	+	2.65124e6i	0.421353	+	0.354086i
$563$	2.10559e6			0.279964			0.139982	−	0.990154i	$-0.455296\pi$
$563$	2.10559e6			0.279964			0.139982	+	0.990154i	$0.455296\pi$
$564$		0			0
$565$	−6.51178e6			−0.858181
$566$	3.17735e6	+	2.67010e6i	0.416893	+	0.350338i
$567$		0			0
$568$	−376187.	−	218300.i	−0.0489252	−	0.0283911i
$569$		−	8.26598e6i		−	1.07032i	−0.844751	−	0.535160i	$-0.820251\pi$
$569$		−	8.26598e6i		−	1.07032i	0.844751	−	0.535160i	$-0.179749\pi$
$570$		0			0
$571$		−	6.32978e6i		−	0.812453i	−0.913772	−	0.406227i	$-0.866844\pi$
$571$		−	6.32978e6i		−	0.812453i	0.913772	−	0.406227i	$-0.133156\pi$
$572$	−799144.	−	4.57150e6i	−0.102126	−	0.584209i
$573$		0			0
$574$	2.64865e6	−	3.15182e6i	0.335540	−	0.399284i
$575$	−8.81423e6			−1.11177
$576$		0			0
$577$	1.46843e7			1.83617			0.918087	−	0.396380i	$-0.129734\pi$
$577$	1.46843e7			1.83617			0.918087	+	0.396380i	$0.129734\pi$
$578$	1.21935e7	−	1.45100e7i	1.51813	−	1.80654i
$579$		0			0
$580$	−68810.2	−	393628.i	−0.00849342	−	0.0485866i
$581$			1.81999e7i			2.23681i
$582$		0			0
$583$		−	3.00853e6i		−	0.366592i
$584$	762132.	+	442263.i	0.0924694	+	0.0536597i
$585$		0			0
$586$	1.73561e6	+	1.45852e6i	0.208789	+	0.175457i
$587$	−3.94562e6			−0.472628			−0.236314	−	0.971677i	$-0.575939\pi$
$587$	−3.94562e6			−0.472628			−0.236314	+	0.971677i	$0.575939\pi$
$588$		0			0
$589$	3.53343e6			0.419671
$590$	−7.53218e6	−	6.32970e6i	−0.890822	−	0.748606i
$591$		0			0
$592$	−110410.	+	39818.4i	−0.0129481	+	0.00466960i
$593$			2.10090e6i			0.245341i	0.992447	+	0.122670i	$0.0391458\pi$
$593$			2.10090e6i			0.245341i	−0.992447	+	0.122670i	$0.960854\pi$
$594$		0			0
$595$		−	3.81395e7i		−	4.41655i
$596$	−1.33939e7	+	2.34138e6i	−1.54451	+	0.269996i
$597$		0			0
$598$	9.02522e6	−	1.07398e7i	1.03206	−	1.22813i
$599$	−1.27405e7			−1.45084			−0.725420	−	0.688307i	$-0.758354\pi$
$599$	−1.27405e7			−1.45084			−0.725420	+	0.688307i	$0.758354\pi$
$600$		0			0
$601$	−1.23040e7			−1.38951			−0.694755	−	0.719246i	$-0.744487\pi$
$601$	−1.23040e7			−1.38951			−0.694755	+	0.719246i	$0.744487\pi$
$602$	1.03443e7	−	1.23095e7i	1.16335	−	1.38436i
$603$		0			0
$604$	5.92755e6	−	1.03620e6i	0.661124	−	0.115571i
$605$			1.10769e7i			1.23036i
$606$		0			0
$607$			9.64207e6i			1.06218i	0.847315	+	0.531091i	$0.178218\pi$
$607$			9.64207e6i			1.06218i	−0.847315	+	0.531091i	$0.821782\pi$
$608$	−3.91229e6	−	1.44028e6i	−0.429212	−	0.158011i
$609$		0			0
$610$	1.16141e7	+	9.75993e6i	1.26375	+	1.06199i
$611$	8.89944e6			0.964406
$612$		0			0
$613$	9.91038e6			1.06522			0.532610	−	0.846361i	$-0.321211\pi$
$613$	9.91038e6			1.06522			0.532610	+	0.846361i	$0.321211\pi$
$614$	5.12958e6	+	4.31067e6i	0.549112	+	0.461449i
$615$		0			0
$616$	−3.02078e6	+	5.20557e6i	−0.320750	+	0.552735i
$617$			1.03111e6i			0.109041i	0.998513	+	0.0545207i	$0.0173631\pi$
$617$			1.03111e6i			0.109041i	−0.998513	+	0.0545207i	$0.982637\pi$
$618$		0			0
$619$			3.43026e6i			0.359833i	0.983682	+	0.179917i	$0.0575828\pi$
$619$			3.43026e6i			0.359833i	−0.983682	+	0.179917i	$0.942417\pi$
$620$	−2.17884e6	−	1.24640e7i	−0.227639	−	1.30220i
$621$		0			0
$622$	1.08553e7	−	1.29175e7i	1.12503	−	1.33876i
$623$	−7.97914e6			−0.823637
$624$		0			0
$625$	−8.97087e6			−0.918618
$626$	8.89695e6	−	1.05871e7i	0.907413	−	1.07980i
$627$		0			0
$628$	1.91853e6	+	1.09749e7i	0.194120	+	1.11046i
$629$			250343.i			0.0252295i
$630$		0			0
$631$			3.03674e6i			0.303623i	0.988409	+	0.151811i	$0.0485106\pi$
$631$			3.03674e6i			0.303623i	−0.988409	+	0.151811i	$0.951489\pi$
$632$	1.08349e6	−	1.86714e6i	0.107903	−	0.185944i
$633$		0			0
$634$	714016.	+	600026.i	0.0705480	+	0.0592853i
$635$	3.86109e6			0.379993
$636$		0			0
$637$	2.85649e7			2.78923
$638$	102968.	+	86529.2i	0.0100149	+	0.00841610i
$639$		0			0
$640$	−2.66806e6	+	1.46886e7i	−0.257481	+	1.41752i
$641$		−	2.28706e6i		−	0.219853i	−0.993940	−	0.109927i	$-0.964938\pi$
$641$		−	2.28706e6i		−	0.219853i	0.993940	−	0.109927i	$-0.0350616\pi$
$642$		0			0
$643$			1.33547e7i			1.27382i	0.770940	+	0.636908i	$0.219787\pi$
$643$			1.33547e7i			1.27382i	−0.770940	+	0.636908i	$0.780213\pi$
$644$	−1.79214e7	+	3.13284e6i	−1.70277	+	0.297662i
$645$		0			0
$646$	−5.72074e6	+	6.80754e6i	−0.539351	+	0.641813i
$647$	−1.21139e7			−1.13769			−0.568843	−	0.822446i	$-0.692609\pi$
$647$	−1.21139e7			−1.13769			−0.568843	+	0.822446i	$0.692609\pi$
$648$		0			0
$649$	3.31152e6			0.308614
$650$	−1.15697e7	+	1.37676e7i	−1.07409	+	1.27813i
$651$		0			0
$652$	−796337.	+	139208.i	−0.0733631	+	0.0128246i
$653$		−	5.51376e6i		−	0.506017i	−0.967464	−	0.253008i	$-0.918580\pi$
$653$		−	5.51376e6i		−	0.506017i	0.967464	−	0.253008i	$-0.0814200\pi$
$654$		0			0
$655$			2.42551e7i			2.20902i
$656$	1.16608e6	+	3.23335e6i	0.105796	+	0.293354i
$657$		0			0
$658$	−8.83581e6	−	7.42521e6i	−0.795576	−	0.668566i
$659$	7.16100e6			0.642333			0.321166	−	0.947023i	$-0.395925\pi$
$659$	7.16100e6			0.642333			0.321166	+	0.947023i	$0.395925\pi$
$660$		0			0
$661$	−4.29525e6			−0.382371			−0.191186	−	0.981554i	$-0.561233\pi$
$661$	−4.29525e6			−0.382371			−0.191186	+	0.981554i	$0.561233\pi$
$662$	1.31339e7	+	1.10371e7i	1.16479	+	0.978836i
$663$		0			0
$664$	−1.31423e7	−	7.62646e6i	−1.15678	−	0.671279i
$665$			1.25677e7i			1.10205i
$666$		0			0
$667$			406565.i			0.0353847i
$668$	−2.12163e6	−	1.21368e7i	−0.183962	−	1.05235i
$669$		0			0
$670$	6.88598e6	−	8.19414e6i	0.592623	−	0.705207i
$671$	−5.10612e6			−0.437809
$672$		0			0
$673$	8.72112e6			0.742224			0.371112	−	0.928588i	$-0.378977\pi$
$673$	8.72112e6			0.742224			0.371112	+	0.928588i	$0.378977\pi$
$674$	1.00878e7	−	1.20043e7i	0.855359	−	1.01786i
$675$		0			0
$676$	−2.88271e6	−	1.64905e7i	−0.242624	−	1.38793i
$677$		−	1.55598e7i		−	1.30476i	−0.757890	−	0.652382i	$-0.773770\pi$
$677$		−	1.55598e7i		−	1.30476i	0.757890	−	0.652382i	$-0.226230\pi$
$678$		0			0
$679$			6.12507e6i			0.509843i
$680$	2.75409e7	+	1.59819e7i	2.28405	+	1.32543i
$681$		0			0
$682$	3.26041e6	+	2.73990e6i	0.268418	+	0.225566i
$683$	−1.62106e7			−1.32968			−0.664840	−	0.746986i	$-0.731500\pi$
$683$	−1.62106e7			−1.32968			−0.664840	+	0.746986i	$0.731500\pi$
$684$		0			0
$685$	1.08603e7			0.884331
$686$	−1.25792e7	−	1.05710e7i	−1.02057	−	0.857638i
$687$		0			0
$688$	4.55413e6	+	1.26279e7i	0.366804	+	1.01709i
$689$		−	1.85549e7i		−	1.48905i
$690$		0			0
$691$		−	1.77172e7i		−	1.41156i	−0.708429	−	0.705782i	$-0.750596\pi$
$691$		−	1.77172e7i		−	1.41156i	0.708429	−	0.705782i	$-0.249404\pi$
$692$	1.72659e7	−	3.01826e6i	1.37064	−	0.239603i
$693$		0			0
$694$	4.07299e6	−	4.84676e6i	0.321007	−	0.381990i
$695$	−7.10472e6			−0.557937
$696$		0			0
$697$	7.33125e6			0.571605
$698$	−7.58422e6	+	9.02502e6i	−0.589213	+	0.701148i
$699$		0			0
$700$	2.29740e7	−	4.01608e6i	1.77211	−	0.309783i
$701$		−	1.38386e6i		−	0.106364i	−0.998585	−	0.0531821i	$-0.983064\pi$
$701$		−	1.38386e6i		−	0.106364i	0.998585	−	0.0531821i	$-0.0169364\pi$
$702$		0			0
$703$		−	82492.7i		−	0.00629545i
$704$	−2.49317e6	−	4.36267e6i	−0.189592	−	0.331757i
$705$		0			0
$706$	−9.65198e6	−	8.11108e6i	−0.728794	−	0.612445i
$707$	−878444.			−0.0660945
$708$		0			0
$709$	−3.82723e6			−0.285936			−0.142968	−	0.989727i	$-0.545665\pi$
$709$	−3.82723e6			−0.285936			−0.142968	+	0.989727i	$0.545665\pi$
$710$	−838043.	−	704253.i	−0.0623908	−	0.0524304i
$711$		0			0
$712$	3.34356e6	−	5.76181e6i	0.247178	−	0.425950i
$713$			1.28737e7i			0.948371i
$714$		0			0
$715$		−	1.16801e7i		−	0.854442i
$716$	−2.48420e6	−	1.42109e7i	−0.181094	−	1.03595i
$717$		0			0
$718$	−1.38221e7	+	1.64479e7i	−1.00060	+	1.19069i
$719$	1.09144e7			0.787365			0.393682	−	0.919247i	$-0.371201\pi$
$719$	1.09144e7			0.787365			0.393682	+	0.919247i	$0.371201\pi$
$720$		0			0
$721$	−2.34997e7			−1.68354
$722$	−7.12628e6	+	8.48009e6i	−0.508768	+	0.605421i
$723$		0			0
$724$	−8738.63	−	49989.3i	−0.000619580	−	0.00354430i
$725$		−	521187.i		−	0.0368255i
$726$		0			0
$727$			3.42329e6i			0.240219i	0.992761	+	0.120110i	$0.0383246\pi$
$727$			3.42329e6i			0.240219i	−0.992761	+	0.120110i	$0.961675\pi$
$728$	−1.86305e7	+	3.21050e7i	−1.30285	+	2.24515i
$729$		0			0
$730$	1.69783e6	+	1.42677e6i	0.117920	+	0.0990942i
$731$	2.86323e7			1.98181
$732$		0			0
$733$	1.27970e6			0.0879724			0.0439862	−	0.999032i	$-0.485994\pi$
$733$	1.27970e6			0.0879724			0.0439862	+	0.999032i	$0.485994\pi$
$734$	−4.35509e6	−	3.65982e6i	−0.298371	−	0.250737i
$735$		0			0
$736$	5.24749e6	−	1.42540e7i	0.357073	−	0.969932i
$737$			3.60255e6i			0.244310i
$738$		0			0
$739$			73084.4i			0.00492281i	0.999997	+	0.00246141i	$0.000783491\pi$
$739$			73084.4i			0.00492281i	−0.999997	+	0.00246141i	$0.999217\pi$
$740$	−290989.	+	50867.9i	−0.0195343	+	0.00341479i
$741$		0			0
$742$	−1.54812e7	+	1.84222e7i	−1.03227	+	1.22838i
$743$	2.23684e7			1.48649			0.743247	−	0.669017i	$-0.233285\pi$
$743$	2.23684e7			1.48649			0.743247	+	0.669017i	$0.233285\pi$
$744$		0			0
$745$	−3.42212e7			−2.25894
$746$	−1.14113e7	+	1.35792e7i	−0.750737	+	0.893358i
$747$		0			0
$748$	−1.05574e7	+	1.84555e6i	−0.689929	+	0.120607i
$749$			2.05462e7i			1.33822i
$750$		0			0
$751$		−	1.91551e7i		−	1.23932i	−0.784869	−	0.619662i	$-0.787270\pi$
$751$		−	1.91551e7i		−	1.23932i	0.784869	−	0.619662i	$-0.212730\pi$
$752$	9.06436e6	−	3.26898e6i	0.584511	−	0.210798i
$753$		0			0
$754$	635046.	+	533663.i	0.0406796	+	0.0341853i
$755$	1.51448e7			0.966935
$756$		0			0
$757$	−6.56784e6			−0.416565			−0.208283	−	0.978069i	$-0.566787\pi$
$757$	−6.56784e6			−0.416565			−0.208283	+	0.978069i	$0.566787\pi$
$758$	5.86304e6	+	4.92703e6i	0.370638	+	0.311467i
$759$		0			0
$760$	−9.07525e6	−	5.26634e6i	−0.569934	−	0.330731i
$761$		−	1.18923e7i		−	0.744397i	−0.928153	−	0.372199i	$-0.878604\pi$
$761$		−	1.18923e7i		−	0.744397i	0.928153	−	0.372199i	$-0.121396\pi$
$762$		0			0
$763$			2.29185e7i			1.42519i
$764$	1.71128e6	+	9.78935e6i	0.106069	+	0.606765i
$765$		0			0
$766$	−1.20770e7	+	1.43713e7i	−0.743681	+	0.884961i
$767$	2.04236e7			1.25356
$768$		0			0
$769$	2.93438e7			1.78937			0.894686	−	0.446695i	$-0.147399\pi$
$769$	2.93438e7			1.78937			0.894686	+	0.446695i	$0.147399\pi$
$770$	−9.74527e6	+	1.15966e7i	−0.592334	+	0.704863i
$771$		0			0
$772$	−478138.	−	2.73518e6i	−0.0288742	−	0.165175i
$773$		−	2.17877e7i		−	1.31148i	−0.754986	−	0.655741i	$-0.772356\pi$
$773$		−	2.17877e7i		−	1.31148i	0.754986	−	0.655741i	$-0.227644\pi$
$774$		0			0
$775$		−	1.65031e7i		−	0.986988i
$776$	−4.42297e6	−	2.56664e6i	−0.263670	−	0.153007i
$777$		0			0
$778$	1.61662e7	+	1.35853e7i	0.957542	+	0.804675i
$779$	−2.41579e6			−0.142631
$780$		0			0
$781$	368445.			0.0216145
$782$	−2.48025e7	−	2.08429e7i	−1.45037	−	1.21882i
$783$		0			0
$784$	2.90942e7	−	1.04926e7i	1.69051	−	0.609666i
$785$			2.80409e7i			1.62412i
$786$		0			0
$787$		−	2.15045e7i		−	1.23763i	−0.785536	−	0.618816i	$-0.787613\pi$
$787$		−	2.15045e7i		−	1.23763i	0.785536	−	0.618816i	$-0.212387\pi$
$788$	−1.28221e7	+	2.24143e6i	−0.735603	+	0.128591i
$789$		0			0
$790$	3.49543e6	−	4.15948e6i	0.199266	−	0.237122i
$791$	−1.75305e7			−0.996216
$792$		0			0
$793$	−3.14917e7			−1.77833
$794$	3.30540e6	−	3.93334e6i	0.186068	−	0.221417i
$795$		0			0
$796$	−3.38788e7	+	5.92235e6i	−1.89516	+	0.331292i
$797$			1.17517e7i			0.655322i	0.944795	+	0.327661i	$0.106260\pi$
$797$			1.17517e7i			0.655322i	−0.944795	+	0.327661i	$0.893740\pi$
$798$		0			0
$799$		−	2.05524e7i		−	1.13893i
$800$	−6.72691e6	+	1.82726e7i	−0.371613	+	1.00943i
$801$		0			0
$802$	556824.	+	467930.i	0.0305691	+	0.0256888i
$803$	−746448.			−0.0408517
$804$		0			0
$805$	−4.57890e7			−2.49041
$806$	2.01084e7	+	1.68982e7i	1.09028	+	0.916225i
$807$		0			0
$808$	368101.	−	634333.i	0.0198353	−	0.0341813i
$809$		−	2.46613e7i		−	1.32479i	−0.749157	−	0.662393i	$-0.769541\pi$
$809$		−	2.46613e7i		−	1.32479i	0.749157	−	0.662393i	$-0.230459\pi$
$810$		0			0
$811$			3.20425e7i			1.71070i	0.518047	+	0.855352i	$0.326659\pi$
$811$			3.20425e7i			1.71070i	−0.518047	+	0.855352i	$0.673341\pi$
$812$	−185245.	−	1.05970e6i	−0.00985956	−	0.0564015i
$813$		0			0
$814$	63966.6	−	76118.6i	0.00338370	−	0.00402652i
$815$	−2.03463e6			−0.107298
$816$		0			0
$817$	−9.43489e6			−0.494517
$818$	−1.53808e7	+	1.83027e7i	−0.803702	+	0.956385i
$819$		0			0
$820$	1.48966e6	+	8.52158e6i	0.0773663	+	0.442573i
$821$		−	2.68961e7i		−	1.39262i	−0.717743	−	0.696308i	$-0.754825\pi$
$821$		−	2.68961e7i		−	1.39262i	0.717743	−	0.696308i	$-0.245175\pi$
$822$		0			0
$823$			3.24237e7i			1.66864i	0.551278	+	0.834321i	$0.314140\pi$
$823$			3.24237e7i			1.66864i	−0.551278	+	0.834321i	$0.685860\pi$
$824$	9.84724e6	−	1.69693e7i	0.505239	−	0.870656i
$825$		0			0
$826$	−2.02776e7	−	1.70403e7i	−1.03411	−	0.869016i
$827$	1.20579e6			0.0613065			0.0306533	−	0.999530i	$-0.490241\pi$
$827$	1.20579e6			0.0613065			0.0306533	+	0.999530i	$0.490241\pi$
$828$		0			0
$829$	1.69091e7			0.854545			0.427273	−	0.904123i	$-0.359474\pi$
$829$	1.69091e7			0.854545			0.427273	+	0.904123i	$0.359474\pi$
$830$	−2.92776e7	−	2.46036e7i	−1.47516	−	1.23966i
$831$		0			0
$832$	−1.53765e7	−	2.69065e7i	−0.770103	−	1.34756i
$833$		−	6.59679e7i		−	3.29397i
$834$		0			0
$835$		−	3.10094e7i		−	1.53913i
$836$	3.47887e6	−	608142.i	0.172156	−	0.0300947i
$837$		0			0
$838$	−1.01324e7	+	1.20573e7i	−0.498429	+	0.593118i
$839$	3.21837e6			0.157845			0.0789226	−	0.996881i	$-0.474852\pi$
$839$	3.21837e6			0.157845			0.0789226	+	0.996881i	$0.474852\pi$
$840$		0			0
$841$	2.04871e7			0.998828
$842$	8.92742e6	−	1.06234e7i	0.433956	−	0.516397i
$843$		0			0
$844$	−1.98542e7	+	3.47071e6i	−0.959392	+	0.167711i
$845$		−	4.21332e7i		−	2.02994i
$846$		0			0
$847$			2.98205e7i			1.42826i
$848$	−6.81566e6	−	1.88987e7i	−0.325475	−	0.902492i
$849$		0			0
$850$	3.17950e7	+	2.67191e7i	1.50943	+	1.26845i
$851$	300553.			0.0142264
$852$		0			0
$853$	2.33124e7			1.09702			0.548510	−	0.836144i	$-0.315195\pi$
$853$	2.33124e7			1.09702			0.548510	+	0.836144i	$0.315195\pi$
$854$	3.12665e7	+	2.62749e7i	1.46702	+	1.23281i
$855$		0			0
$856$	−1.48366e7	−	8.60965e6i	−0.692072	−	0.401607i
$857$			1.65961e7i			0.771885i	0.922523	+	0.385943i	$0.126124\pi$
$857$			1.65961e7i			0.771885i	−0.922523	+	0.385943i	$0.873876\pi$
$858$		0			0
$859$			3.87503e6i			0.179181i	0.995979	+	0.0895906i	$0.0285559\pi$
$859$			3.87503e6i			0.179181i	−0.995979	+	0.0895906i	$0.971444\pi$
$860$	5.81788e6	+	3.32812e7i	0.268237	+	1.53445i
$861$		0			0
$862$	6.20910e6	−	7.38867e6i	0.284617	−	0.338687i
$863$	2.73653e7			1.25076			0.625380	−	0.780321i	$-0.284944\pi$
$863$	2.73653e7			1.25076			0.625380	+	0.780321i	$0.284944\pi$
$864$		0			0
$865$	4.41143e7			2.00465
$866$	−708324.	+	842888.i	−0.0320950	+	0.0381922i
$867$		0			0
$868$	−5.86570e6	−	3.35547e7i	−0.264253	−	1.51166i
$869$			1.82871e6i			0.0821478i
$870$		0			0
$871$			2.22185e7i			0.992360i
$872$	−1.65496e7	−	9.60370e6i	−0.737050	−	0.427708i
$873$		0			0
$874$	8.17289e6	+	6.86812e6i	0.361907	+	0.304130i
$875$	4.12864e6			0.182300
$876$		0			0
$877$	4.11018e6			0.180452			0.0902260	−	0.995921i	$-0.471241\pi$
$877$	4.11018e6			0.180452			0.0902260	+	0.995921i	$0.471241\pi$
$878$	2.38559e6	+	2.00474e6i	0.104438	+	0.0877650i
$879$		0			0
$880$	−4.29039e6	−	1.18966e7i	−0.186763	−	0.517863i
$881$			2.51778e7i			1.09289i	0.837494	+	0.546446i	$0.184020\pi$
$881$			2.51778e7i			1.09289i	−0.837494	+	0.546446i	$0.815980\pi$
$882$		0			0
$883$			1.79618e7i			0.775261i	0.921815	+	0.387631i	$0.126706\pi$
$883$			1.79618e7i			0.775261i	−0.921815	+	0.387631i	$0.873294\pi$
$884$	−6.51123e7	+	1.13823e7i	−2.80241	+	0.489890i
$885$		0			0
$886$	2.12714e7	−	2.53125e7i	0.910359	−	1.08330i
$887$	−3.60977e7			−1.54053			−0.770266	−	0.637723i	$-0.779876\pi$
$887$	−3.60977e7			−1.54053			−0.770266	+	0.637723i	$0.779876\pi$
$888$		0			0
$889$	1.03945e7			0.441114
$890$	1.07866e7	−	1.28358e7i	0.456467	−	0.543184i
$891$		0			0
$892$	4.02758e7	−	7.04062e6i	1.69485	−	0.296278i
$893$			6.77241e6i			0.284194i
$894$		0			0
$895$		−	3.63086e7i		−	1.51514i
$896$	−7.18274e6	+	3.95434e7i	−0.298896	+	1.64552i
$897$		0			0
$898$	1.34307e7	+	1.12866e7i	0.555787	+	0.467058i
$899$	−761222.			−0.0314132
$900$		0			0
$901$	−4.28508e7			−1.75852
$902$	−2.22912e6	−	1.87325e6i	−0.0912258	−	0.0766620i
$903$		0			0
$904$	7.34595e6	−	1.26589e7i	0.298969	−	0.515201i
$905$		−	127722.i		−	0.00518376i
$906$		0			0
$907$		−	3.22058e7i		−	1.29992i	−0.759970	−	0.649958i	$-0.774786\pi$
$907$		−	3.22058e7i		−	1.29992i	0.759970	−	0.649958i	$-0.225214\pi$
$908$	−7.88318e6	−	4.50957e7i	−0.317312	−	1.81518i
$909$		0			0
$910$	−6.01033e7	+	7.15214e7i	−2.40600	+	2.86307i
$911$	3.74348e7			1.49444			0.747222	−	0.664574i	$-0.231387\pi$
$911$	3.74348e7			1.49444			0.747222	+	0.664574i	$0.231387\pi$
$912$		0			0
$913$	1.28719e7			0.511052
$914$	−3.33900e6	+	3.97332e6i	−0.132206	+	0.157322i
$915$		0			0
$916$	−3.41075e6	−	1.95112e7i	−0.134311	−	0.768325i
$917$			6.52977e7i			2.56433i
$918$		0			0
$919$		−	3.15460e7i		−	1.23213i	−0.787696	−	0.616064i	$-0.788726\pi$
$919$		−	3.15460e7i		−	1.23213i	0.787696	−	0.616064i	$-0.211274\pi$
$920$	1.91873e7	−	3.30646e7i	0.747385	−	1.28794i
$921$		0			0
$922$	3.14421e7	+	2.64225e7i	1.21810	+	1.02364i
$923$	2.27236e6			0.0877957
$924$		0			0
$925$	−385287.			−0.0148057
$926$	3.04093e7	+	2.55546e7i	1.16541	+	0.979357i
$927$		0			0
$928$	842841.	+	310285.i	0.0321274	+	0.0118274i
$929$			3.56283e7i			1.35443i	0.735786	+	0.677214i	$0.236813\pi$
$929$			3.56283e7i			1.35443i	−0.735786	+	0.677214i	$0.763187\pi$
$930$		0			0
$931$			2.17377e7i			0.821938i
$932$	1.23278e7	−	2.15503e6i	0.464886	−	0.0812668i
$933$		0			0
$934$	1.03841e7	−	1.23568e7i	0.389496	−	0.463490i
$935$	−2.69741e7			−1.00906
$936$		0			0
$937$	4.27092e7			1.58918			0.794588	−	0.607149i	$-0.207687\pi$
$937$	4.27092e7			1.58918			0.794588	+	0.607149i	$0.207687\pi$
$938$	1.85379e7	−	2.20596e7i	0.687945	−	0.818637i
$939$		0			0
$940$	2.38894e7	−	4.17610e6i	0.881830	−	0.154153i
$941$			2.64684e7i			0.974435i	0.873281	+	0.487218i	$0.161988\pi$
$941$			2.64684e7i			0.974435i	−0.873281	+	0.487218i	$0.838012\pi$
$942$		0			0
$943$		−	8.80164e6i		−	0.322318i
$944$	2.08020e7	−	7.50207e6i	0.759759	−	0.274000i
$945$		0			0
$946$	−8.70588e6	−	7.31602e6i	−0.316289	−	0.265795i
$947$	−8.86252e6			−0.321131			−0.160566	−	0.987025i	$-0.551332\pi$
$947$	−8.86252e6			−0.321131			−0.160566	+	0.987025i	$0.551332\pi$
$948$		0			0
$949$	−4.60367e6			−0.165935
$950$	−1.04771e7	−	8.80445e6i	−0.376644	−	0.316514i
$951$		0			0
$952$	7.41435e7	+	4.30252e7i	2.65143	+	1.53862i
$953$		−	2.07166e7i		−	0.738901i	−0.929250	−	0.369450i	$-0.879546\pi$
$953$		−	2.07166e7i		−	0.738901i	0.929250	−	0.369450i	$-0.120454\pi$
$954$		0			0
$955$			2.50117e7i			0.887432i
$956$	7.68645e6	+	4.39703e7i	0.272007	+	1.55602i
$957$		0			0
$958$	3.34746e6	−	3.98339e6i	0.117842	−	0.140229i
$959$	2.92372e7			1.02657
$960$		0			0
$961$	4.52545e6			0.158072
$962$	394510.	−	469457.i	0.0137442	−	0.0163553i
$963$		0			0
$964$	4.11025e6	+	2.35127e7i	0.142454	+	0.814909i
$965$		−	6.98837e6i		−	0.241578i
$966$		0			0
$967$			4.43752e7i			1.52607i	0.646358	+	0.763035i	$0.276291\pi$
$967$			4.43752e7i			1.52607i	−0.646358	+	0.763035i	$0.723709\pi$
$968$	−2.15337e7	−	1.24959e7i	−0.738634	−	0.428627i
$969$		0			0
$970$	−9.85320e6	−	8.28017e6i	−0.336239	−	0.282560i
$971$	−2.88625e7			−0.982396			−0.491198	−	0.871048i	$-0.663441\pi$
$971$	−2.88625e7			−0.982396			−0.491198	+	0.871048i	$0.663441\pi$
$972$		0			0
$973$	−1.91268e7			−0.647679
$974$	−2.47120e7	−	2.07669e7i	−0.834663	−	0.701412i
$975$		0			0
$976$	−3.20752e7	+	1.15676e7i	−1.07782	+	0.388705i
$977$			4.81221e6i			0.161290i	0.996743	+	0.0806451i	$0.0256980\pi$
$977$			4.81221e6i			0.161290i	−0.996743	+	0.0806451i	$0.974302\pi$
$978$		0			0
$979$			5.64324e6i			0.188179i
$980$	7.66787e7	−	1.34042e7i	2.55041	−	0.445837i
$981$		0			0
$982$	7.34610e6	−	8.74168e6i	0.243096	−	0.289278i
$983$	2.99778e7			0.989502			0.494751	−	0.869035i	$-0.335259\pi$
$983$	2.99778e7			0.989502			0.494751	+	0.869035i	$0.335259\pi$
$984$		0			0
$985$	−3.27603e7			−1.07587
$986$	1.23244e6	−	1.46658e6i	0.0403715	−	0.0480410i
$987$		0			0
$988$	2.14557e7	−	3.75068e6i	0.699280	−	0.122241i
$989$		−	3.43749e7i		−	1.11751i
$990$		0			0
$991$		−	9.75969e6i		−	0.315683i	−0.987464	−	0.157842i	$-0.949546\pi$
$991$		−	9.75969e6i		−	0.315683i	0.987464	−	0.157842i	$-0.0504536\pi$
$992$	2.66881e7	+	9.82501e6i	0.861070	+	0.316996i
$993$		0			0
$994$	−2.25611e6	−	1.89593e6i	−0.0724261	−	0.0608636i
$995$	−8.65599e7			−2.77178
$996$		0			0
$997$	4.77818e7			1.52238			0.761192	−	0.648527i	$-0.224614\pi$
$997$	4.77818e7			1.52238			0.761192	+	0.648527i	$0.224614\pi$
$998$	−5.16576e6	−	4.34107e6i	−0.164175	−	0.137965i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.b.c.107.8	yes	20
3.2	odd	2	inner	108.6.b.c.107.13	yes	20
4.3	odd	2	inner	108.6.b.c.107.14	yes	20
12.11	even	2	inner	108.6.b.c.107.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.b.c.107.7	✓	20	12.11	even	2	inner
108.6.b.c.107.8	yes	20	1.1	even	1	trivial
108.6.b.c.107.13	yes	20	3.2	odd	2	inner
108.6.b.c.107.14	yes	20	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.63934 + 4.33073i) q^{2} +(-5.51036 - 31.5220i) q^{4} -80.5384i q^{5} -216.819i q^{7} +(156.567 + 90.8555i) q^{8} +O(q^{10})\)	\(q+(-3.63934 + 4.33073i) q^{2} +(-5.51036 - 31.5220i) q^{4} -80.5384i q^{5} -216.819i q^{7} +(156.567 + 90.8555i) q^{8} +(348.790 + 293.107i) q^{10} -153.345 q^{11} -945.747 q^{13} +(938.984 + 789.079i) q^{14} +(-963.272 + 347.395i) q^{16} +2184.11i q^{17} -719.706i q^{19} +(-2538.73 + 443.796i) q^{20} +(558.076 - 664.096i) q^{22} +2622.17 q^{23} -3361.43 q^{25} +(3441.90 - 4095.77i) q^{26} +(-6834.57 + 1194.75i) q^{28} +155.049i q^{29} +4909.55i q^{31} +(2001.20 - 5435.96i) q^{32} +(-9458.78 - 7948.73i) q^{34} -17462.3 q^{35} +114.620 q^{37} +(3116.85 + 2619.26i) q^{38} +(7317.35 - 12609.7i) q^{40} -3356.63i q^{41} -13109.4i q^{43} +(844.988 + 4833.74i) q^{44} +(-9542.96 + 11355.9i) q^{46} -9409.97 q^{47} -30203.6 q^{49} +(12233.4 - 14557.4i) q^{50} +(5211.41 + 29811.8i) q^{52} +19619.3i q^{53} +12350.2i q^{55} +(19699.2 - 33946.8i) q^{56} +(-671.476 - 564.277i) q^{58} -21595.2 q^{59} +33298.2 q^{61} +(-21261.9 - 17867.5i) q^{62} +(16258.6 + 28450.0i) q^{64} +76168.9i q^{65} -23493.1i q^{67} +(68847.5 - 12035.2i) q^{68} +(63551.2 - 75624.3i) q^{70} -2402.72 q^{71} +4867.76 q^{73} +(-417.141 + 496.388i) q^{74} +(-22686.6 + 3965.84i) q^{76} +33248.2i q^{77} -11925.5i q^{79} +(27978.7 + 77580.4i) q^{80} +(14536.6 + 12215.9i) q^{82} -83940.6 q^{83} +175905. q^{85} +(56773.1 + 47709.5i) q^{86} +(-24008.8 - 13932.2i) q^{88} -36800.9i q^{89} +205056. i q^{91} +(-14449.1 - 82655.9i) q^{92} +(34246.1 - 40752.0i) q^{94} -57963.9 q^{95} -28249.7 q^{97} +(109921. - 130803. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{4}+O(q^{10}) \) 20 * q + 20 * q^4	\( 20 q + 20 q^{4} + 184 q^{10} - 116 q^{13} - 4168 q^{16} + 696 q^{22} - 15228 q^{25} - 4764 q^{28} - 16520 q^{34} - 6452 q^{37} + 1504 q^{40} - 9336 q^{46} - 44464 q^{49} + 8236 q^{52} - 58736 q^{58} + 84604 q^{61} - 6496 q^{64} + 138696 q^{70} + 85420 q^{73} + 89172 q^{76} + 221200 q^{82} + 180320 q^{85} - 85824 q^{88} - 60936 q^{94} - 219908 q^{97}+O(q^{100}) \) 20 * q + 20 * q^4 + 184 * q^10 - 116 * q^13 - 4168 * q^16 + 696 * q^22 - 15228 * q^25 - 4764 * q^28 - 16520 * q^34 - 6452 * q^37 + 1504 * q^40 - 9336 * q^46 - 44464 * q^49 + 8236 * q^52 - 58736 * q^58 + 84604 * q^61 - 6496 * q^64 + 138696 * q^70 + 85420 * q^73 + 89172 * q^76 + 221200 * q^82 + 180320 * q^85 - 85824 * q^88 - 60936 * q^94 - 219908 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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