LMFDB - Embedded newform 36.6.b.b.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,6,Mod(35,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, 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("36.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	36.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:	$5.77381751327$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 58x^{6} - 160x^{5} + 805x^{4} - 1348x^{3} + 3024x^{2} - 2376x + 972 $ x^8 - 4x^7 + 58x^6 - 160x^5 + 805x^4 - 1348x^3 + 3024x^2 - 2376*x + 972
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.3
Root			$0.500000 + 5.95281i$ of defining polynomial
Character	$\chi$	$=$	36.35
Dual form			36.6.b.b.35.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.37096 - 4.54276i) q^{2} +(-9.27329 + 30.6269i) q^{4} -6.64357i q^{5} +179.715i q^{7} +(170.390 - 61.1157i) q^{8} +O(q^{10})$	\(q+(-3.37096 - 4.54276i) q^{2} +(-9.27329 + 30.6269i) q^{4} -6.64357i q^{5} +179.715i q^{7} +(170.390 - 61.1157i) q^{8} +(-30.1801 + 22.3952i) q^{10} +330.982 q^{11} +859.304 q^{13} +(816.400 - 605.810i) q^{14} +(-852.012 - 568.024i) q^{16} +1084.90i q^{17} +1830.63i q^{19} +(203.472 + 61.6078i) q^{20} +(-1115.73 - 1503.57i) q^{22} -4675.29 q^{23} +3080.86 q^{25} +(-2896.68 - 3903.61i) q^{26} +(-5504.10 - 1666.54i) q^{28} +4342.37i q^{29} -1909.90i q^{31} +(291.703 + 5785.27i) q^{32} +(4928.44 - 3657.15i) q^{34} +1193.95 q^{35} -898.274 q^{37} +(8316.09 - 6170.96i) q^{38} +(-406.026 - 1132.00i) q^{40} -8605.90i q^{41} +1596.27i q^{43} +(-3069.29 + 10136.9i) q^{44} +(15760.2 + 21238.7i) q^{46} +21449.5 q^{47} -15490.3 q^{49} +(-10385.5 - 13995.6i) q^{50} +(-7968.57 + 26317.8i) q^{52} -16959.7i q^{53} -2198.90i q^{55} +(10983.4 + 30621.6i) q^{56} +(19726.3 - 14637.9i) q^{58} -1642.85 q^{59} -26487.6 q^{61} +(-8676.22 + 6438.20i) q^{62} +(25297.8 - 20827.0i) q^{64} -5708.85i q^{65} -62958.2i q^{67} +(-33227.1 - 10060.6i) q^{68} +(-4024.75 - 5423.81i) q^{70} -19096.4 q^{71} +27565.6 q^{73} +(3028.04 + 4080.64i) q^{74} +(-56066.4 - 16975.9i) q^{76} +59482.3i q^{77} +39826.2i q^{79} +(-3773.71 + 5660.41i) q^{80} +(-39094.5 + 29010.1i) q^{82} -54815.7 q^{83} +7207.62 q^{85} +(7251.46 - 5380.95i) q^{86} +(56396.1 - 20228.2i) q^{88} -49533.2i q^{89} +154429. i q^{91} +(43355.3 - 143189. i) q^{92} +(-72305.4 - 97439.9i) q^{94} +12161.9 q^{95} +153777. q^{97} +(52217.3 + 70368.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 44 q^{4}+O(q^{10}) $ 8 * q + 44 * q^4	$ 8 q + 44 q^{4} - 596 q^{10} + 256 q^{13} - 4216 q^{16} + 9984 q^{22} + 15192 q^{25} - 23232 q^{28} + 23236 q^{34} - 26096 q^{37} - 36104 q^{40} + 84480 q^{46} + 4664 q^{49} - 96368 q^{52} + 126964 q^{58} - 102224 q^{61} - 14608 q^{64} - 28416 q^{70} + 110848 q^{73} + 50688 q^{76} - 240308 q^{82} + 100208 q^{85} + 349056 q^{88} - 287232 q^{94} + 229888 q^{97}+O(q^{100}) $ 8 * q + 44 * q^4 - 596 * q^10 + 256 * q^13 - 4216 * q^16 + 9984 * q^22 + 15192 * q^25 - 23232 * q^28 + 23236 * q^34 - 26096 * q^37 - 36104 * q^40 + 84480 * q^46 + 4664 * q^49 - 96368 * q^52 + 126964 * q^58 - 102224 * q^61 - 14608 * q^64 - 28416 * q^70 + 110848 * q^73 + 50688 * q^76 - 240308 * q^82 + 100208 * q^85 + 349056 * q^88 - 287232 * q^94 + 229888 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.37096	−	4.54276i	−0.595907	−	0.803054i
$2$	−3.37096	−	4.54276i	−0.595907	−	0.803054i
$3$		0			0
$3$		0			0
$4$	−9.27329	+	30.6269i	−0.289790	+	0.957090i
$5$		−	6.64357i		−	0.118844i	−0.998233	−	0.0594219i	$-0.981074\pi$
$5$		−	6.64357i		−	0.118844i	0.998233	−	0.0594219i	$-0.0189257\pi$
$6$		0			0
$7$			179.715i			1.38624i	0.720822	+	0.693120i	$0.243764\pi$
$7$			179.715i			1.38624i	−0.720822	+	0.693120i	$0.756236\pi$
$8$	170.390	−	61.1157i	0.941283	−	0.337619i
$9$		0			0
$10$	−30.1801	+	22.3952i	−0.0954380	+	0.0708199i
$11$	330.982			0.824750			0.412375	−	0.911014i	$-0.364699\pi$
$11$	330.982			0.824750			0.412375	+	0.911014i	$0.364699\pi$
$12$		0			0
$13$	859.304			1.41023			0.705113	−	0.709095i	$-0.250896\pi$
$13$	859.304			1.41023			0.705113	+	0.709095i	$0.250896\pi$
$14$	816.400	−	605.810i	1.11322	−	0.826069i
$15$		0			0
$16$	−852.012	−	568.024i	−0.832043	−	0.554711i
$17$			1084.90i			0.910474i	0.890370	+	0.455237i	$0.150446\pi$
$17$			1084.90i			0.910474i	−0.890370	+	0.455237i	$0.849554\pi$
$18$		0			0
$19$			1830.63i			1.16336i	0.813416	+	0.581682i	$0.197605\pi$
$19$			1830.63i			1.16336i	−0.813416	+	0.581682i	$0.802395\pi$
$20$	203.472	+	61.6078i	0.113744	+	0.0344398i
$21$		0			0
$22$	−1115.73	−	1503.57i	−0.491474	−	0.662319i
$23$	−4675.29			−1.84284			−0.921422	−	0.388563i	$-0.872972\pi$
$23$	−4675.29			−1.84284			−0.921422	+	0.388563i	$0.872972\pi$
$24$		0			0
$25$	3080.86			0.985876
$26$	−2896.68	−	3903.61i	−0.840363	−	1.13249i
$27$		0			0
$28$	−5504.10	−	1666.54i	−1.32676	−	0.401719i
$29$			4342.37i			0.958808i	0.877594	+	0.479404i	$0.159147\pi$
$29$			4342.37i			0.958808i	−0.877594	+	0.479404i	$0.840853\pi$
$30$		0			0
$31$		−	1909.90i		−	0.356949i	−0.983945	−	0.178475i	$-0.942884\pi$
$31$		−	1909.90i		−	0.356949i	0.983945	−	0.178475i	$-0.0571163\pi$
$32$	291.703	+	5785.27i	0.0503578	+	0.998731i
$33$		0			0
$34$	4928.44	−	3657.15i	0.731160	−	0.542558i
$35$	1193.95			0.164746
$36$		0			0
$37$	−898.274			−0.107871			−0.0539355	−	0.998544i	$-0.517177\pi$
$37$	−898.274			−0.107871			−0.0539355	+	0.998544i	$0.517177\pi$
$38$	8316.09	−	6170.96i	0.934243	−	0.693256i
$39$		0			0
$40$	−406.026	−	1132.00i	−0.0401240	−	0.111866i
$41$		−	8605.90i		−	0.799534i	−0.916617	−	0.399767i	$-0.869091\pi$
$41$		−	8605.90i		−	0.799534i	0.916617	−	0.399767i	$-0.130909\pi$
$42$		0			0
$43$			1596.27i			0.131654i	0.997831	+	0.0658271i	$0.0209686\pi$
$43$			1596.27i			0.131654i	−0.997831	+	0.0658271i	$0.979031\pi$
$44$	−3069.29	+	10136.9i	−0.239005	+	0.789360i
$45$		0			0
$46$	15760.2	+	21238.7i	1.09816	+	1.47990i
$47$	21449.5			1.41636			0.708178	−	0.706034i	$-0.249517\pi$
$47$	21449.5			1.41636			0.708178	+	0.706034i	$0.249517\pi$
$48$		0			0
$49$	−15490.3			−0.921660
$50$	−10385.5	−	13995.6i	−0.587490	−	0.791711i
$51$		0			0
$52$	−7968.57	+	26317.8i	−0.408669	+	1.34971i
$53$		−	16959.7i		−	0.829331i	−0.909974	−	0.414666i	$-0.863899\pi$
$53$		−	16959.7i		−	0.829331i	0.909974	−	0.414666i	$-0.136101\pi$
$54$		0			0
$55$		−	2198.90i		−	0.0980165i
$56$	10983.4	+	30621.6i	0.468021	+	1.30484i
$57$		0			0
$58$	19726.3	−	14637.9i	0.769974	−	0.571360i
$59$	−1642.85			−0.0614423			−0.0307211	−	0.999528i	$-0.509780\pi$
$59$	−1642.85			−0.0614423			−0.0307211	+	0.999528i	$0.509780\pi$
$60$		0			0
$61$	−26487.6			−0.911419			−0.455710	−	0.890129i	$-0.650614\pi$
$61$	−26487.6			−0.911419			−0.455710	+	0.890129i	$0.650614\pi$
$62$	−8676.22	+	6438.20i	−0.286650	+	0.212709i
$63$		0			0
$64$	25297.8	−	20827.0i	0.772026	−	0.635591i
$65$		−	5708.85i		−	0.167597i
$66$		0			0
$67$		−	62958.2i		−	1.71343i	−0.515793	−	0.856713i	$-0.672503\pi$
$67$		−	62958.2i		−	1.71343i	0.515793	−	0.856713i	$-0.327497\pi$
$68$	−33227.1	−	10060.6i	−0.871406	−	0.263847i
$69$		0			0
$70$	−4024.75	−	5423.81i	−0.0981733	−	0.132300i
$71$	−19096.4			−0.449580			−0.224790	−	0.974407i	$-0.572170\pi$
$71$	−19096.4			−0.449580			−0.224790	+	0.974407i	$0.572170\pi$
$72$		0			0
$73$	27565.6			0.605425			0.302713	−	0.953082i	$-0.402108\pi$
$73$	27565.6			0.605425			0.302713	+	0.953082i	$0.402108\pi$
$74$	3028.04	+	4080.64i	0.0642810	+	0.0866262i
$75$		0			0
$76$	−56066.4	−	16975.9i	−1.11344	−	0.337131i
$77$			59482.3i			1.14330i
$78$		0			0
$79$			39826.2i			0.717962i	0.933345	+	0.358981i	$0.116876\pi$
$79$			39826.2i			0.717962i	−0.933345	+	0.358981i	$0.883124\pi$
$80$	−3773.71	+	5660.41i	−0.0659240	+	0.0988832i
$81$		0			0
$82$	−39094.5	+	29010.1i	−0.642068	+	0.476448i
$83$	−54815.7			−0.873393			−0.436697	−	0.899609i	$-0.643852\pi$
$83$	−54815.7			−0.873393			−0.436697	+	0.899609i	$0.643852\pi$
$84$		0			0
$85$	7207.62			0.108204
$86$	7251.46	−	5380.95i	0.105725	−	0.0784536i
$87$		0			0
$88$	56396.1	−	20228.2i	0.776323	−	0.278452i
$89$		−	49533.2i		−	0.662859i	−0.943480	−	0.331429i	$-0.892469\pi$
$89$		−	49533.2i		−	0.662859i	0.943480	−	0.331429i	$-0.107531\pi$
$90$		0			0
$91$			154429.i			1.95491i
$92$	43355.3	−	143189.i	0.534038	−	1.76377i
$93$		0			0
$94$	−72305.4	−	97439.9i	−0.844017	−	1.13741i
$95$	12161.9			0.138259
$96$		0			0
$97$	153777.			1.65944			0.829721	−	0.558178i	$-0.188499\pi$
$97$	153777.			1.65944			0.829721	+	0.558178i	$0.188499\pi$
$98$	52217.3	+	70368.8i	0.549223	+	0.740142i
$99$		0			0
$100$	−28569.7	+	94357.2i	−0.285697	+	0.943572i
$101$			140013.i			1.36573i	0.730545	+	0.682865i	$0.239266\pi$
$101$			140013.i			1.36573i	−0.730545	+	0.682865i	$0.760734\pi$
$102$		0			0
$103$		−	60010.4i		−	0.557357i	−0.960384	−	0.278679i	$-0.910104\pi$
$103$		−	60010.4i		−	0.557357i	0.960384	−	0.278679i	$-0.0898965\pi$
$104$	146417.	−	52516.9i	1.32742	−	0.476119i
$105$		0			0
$106$	−77043.7	+	57170.4i	−0.665998	+	0.494204i
$107$	179304.			1.51401			0.757007	−	0.653407i	$-0.226661\pi$
$107$	179304.			1.51401			0.757007	+	0.653407i	$0.226661\pi$
$108$		0			0
$109$	−5910.47			−0.0476492			−0.0238246	−	0.999716i	$-0.507584\pi$
$109$	−5910.47			−0.0476492			−0.0238246	+	0.999716i	$0.507584\pi$
$110$	−9989.08	+	7412.41i	−0.0787125	+	0.0584087i
$111$		0			0
$112$	102082.	−	153119.i	0.768962	−	1.15341i
$113$		−	74979.0i		−	0.552387i	−0.961102	−	0.276194i	$-0.910927\pi$
$113$		−	74979.0i		−	0.552387i	0.961102	−	0.276194i	$-0.0890731\pi$
$114$		0			0
$115$			31060.6i			0.219011i
$116$	−132993.	−	40268.0i	−0.917666	−	0.277853i
$117$		0			0
$118$	5537.97	+	7463.06i	0.0366139	+	0.0493414i
$119$	−194972.			−1.26214
$120$		0			0
$121$	−51502.0			−0.319787
$122$	89288.6	+	120327.i	0.543121	+	0.731919i
$123$		0			0
$124$	58494.3	+	17711.1i	0.341633	+	0.103440i
$125$		−	41229.1i		−	0.236009i
$126$		0			0
$127$		−	41366.3i		−	0.227582i	−0.993505	−	0.113791i	$-0.963701\pi$
$127$		−	41366.3i		−	0.227582i	0.993505	−	0.113791i	$-0.0362994\pi$
$128$	−179890.	−	44714.5i	−0.970469	−	0.241226i
$129$		0			0
$130$	−25933.9	+	19244.3i	−0.134589	+	0.0998719i
$131$	−147998.			−0.753493			−0.376746	−	0.926316i	$-0.622957\pi$
$131$	−147998.			−0.753493			−0.376746	+	0.926316i	$0.622957\pi$
$132$		0			0
$133$	−328990.			−1.61270
$134$	−286004.	+	212230.i	−1.37597	+	1.02104i
$135$		0			0
$136$	66304.4	+	184857.i	0.307394	+	0.857014i
$137$		−	165677.i		−	0.754155i	−0.926182	−	0.377078i	$-0.876929\pi$
$137$		−	165677.i		−	0.754155i	0.926182	−	0.377078i	$-0.123071\pi$
$138$		0			0
$139$		−	369393.i		−	1.62163i	−0.585303	−	0.810814i	$-0.699025\pi$
$139$		−	369393.i		−	1.62163i	0.585303	−	0.810814i	$-0.300975\pi$
$140$	−11071.8	+	36566.9i	−0.0477418	+	0.157677i
$141$		0			0
$142$	64373.3	+	86750.5i	0.267908	+	0.361037i
$143$	284414.			1.16308
$144$		0			0
$145$	28848.8			0.113948
$146$	−92922.5	−	125224.i	−0.360777	−	0.486189i
$147$		0			0
$148$	8329.95	−	27511.3i	0.0312600	−	0.103242i
$149$			290794.i			1.07305i	0.843885	+	0.536525i	$0.180263\pi$
$149$			290794.i			1.07305i	−0.843885	+	0.536525i	$0.819737\pi$
$150$		0			0
$151$		−	65825.2i		−	0.234936i	−0.993077	−	0.117468i	$-0.962522\pi$
$151$		−	65825.2i		−	0.234936i	0.993077	−	0.117468i	$-0.0374778\pi$
$152$	111880.	+	311921.i	0.392774	+	1.09505i
$153$		0			0
$154$	270214.	−	200512.i	0.918132	−	0.681301i
$155$	−12688.6			−0.0424212
$156$		0			0
$157$	−261354.			−0.846215			−0.423107	−	0.906079i	$-0.639061\pi$
$157$	−261354.			−0.846215			−0.423107	+	0.906079i	$0.639061\pi$
$158$	180921.	−	134252.i	0.576562	−	0.427838i
$159$		0			0
$160$	38434.9	−	1937.95i	0.118693	−	0.00598471i
$161$		−	840217.i		−	2.55462i
$162$		0			0
$163$			17625.9i			0.0519616i	0.999662	+	0.0259808i	$0.00827087\pi$
$163$			17625.9i			0.0519616i	−0.999662	+	0.0259808i	$0.991729\pi$
$164$	263572.	+	79805.0i	0.765226	+	0.231697i
$165$		0			0
$166$	184781.	+	249014.i	0.520461	+	0.701382i
$167$	341458.			0.947428			0.473714	−	0.880679i	$-0.342913\pi$
$167$	341458.			0.947428			0.473714	+	0.880679i	$0.342913\pi$
$168$		0			0
$169$	367110.			0.988735
$170$	−24296.6	−	32742.5i	−0.0644797	−	0.0868938i
$171$		0			0
$172$	−48888.7	−	14802.6i	−0.126005	−	0.0381521i
$173$			728549.i			1.85073i	0.379074	+	0.925366i	$0.376242\pi$
$173$			728549.i			1.85073i	−0.379074	+	0.925366i	$0.623758\pi$
$174$		0			0
$175$			553676.i			1.36666i
$176$	−282001.	−	188006.i	−0.686228	−	0.457498i
$177$		0			0
$178$	−225017.	+	166974.i	−0.532311	+	0.395002i
$179$	143526.			0.334809			0.167404	−	0.985888i	$-0.446461\pi$
$179$	143526.			0.334809			0.167404	+	0.985888i	$0.446461\pi$
$180$		0			0
$181$	−43607.3			−0.0989378			−0.0494689	−	0.998776i	$-0.515753\pi$
$181$	−43607.3			−0.0989378			−0.0494689	+	0.998776i	$0.515753\pi$
$182$	701536.	−	520575.i	1.56990	−	1.16494i
$183$		0			0
$184$	−796624.	+	285733.i	−1.73464	+	0.622180i
$185$			5967.75i			0.0128198i
$186$		0			0
$187$			359082.i			0.750914i
$188$	−198907.	+	656932.i	−0.410446	+	1.35558i
$189$		0			0
$190$	−40997.2	−	55248.5i	−0.0823893	−	0.111029i
$191$	−559151.			−1.10904			−0.554518	−	0.832172i	$-0.687097\pi$
$191$	−559151.			−1.10904			−0.554518	+	0.832172i	$0.687097\pi$
$192$		0			0
$193$	678421.			1.31101			0.655505	−	0.755191i	$-0.272456\pi$
$193$	678421.			1.31101			0.655505	+	0.755191i	$0.272456\pi$
$194$	−518376.	−	698572.i	−0.988873	−	1.33262i
$195$		0			0
$196$	143646.	−	474421.i	0.267088	−	0.882112i
$197$		−	50319.8i		−	0.0923790i	−0.998933	−	0.0461895i	$-0.985292\pi$
$197$		−	50319.8i		−	0.0923790i	0.998933	−	0.0461895i	$-0.0147078\pi$
$198$		0			0
$199$		−	254422.i		−	0.455430i	−0.973728	−	0.227715i	$-0.926875\pi$
$199$		−	254422.i		−	0.455430i	0.973728	−	0.227715i	$-0.0731254\pi$
$200$	524949.	−	188289.i	0.927988	−	0.332851i
$201$		0			0
$202$	636045.	−	471978.i	1.09675	−	0.813848i
$203$	−780387.			−1.32914
$204$		0			0
$205$	−57173.9			−0.0950197
$206$	−272613.	+	202293.i	−0.447588	+	0.332133i
$207$		0			0
$208$	−732138.	−	488105.i	−1.17337	−	0.782267i
$209$			605904.i			0.959485i
$210$		0			0
$211$			284754.i			0.440316i	0.975464	+	0.220158i	$0.0706573\pi$
$211$			284754.i			0.440316i	−0.975464	+	0.220158i	$0.929343\pi$
$212$	519422.	+	157272.i	0.793745	+	0.240332i
$213$		0			0
$214$	−604425.	−	814534.i	−0.902211	−	1.21583i
$215$	10604.9			0.0156463
$216$		0			0
$217$	343237.			0.494817
$218$	19923.9	+	26849.8i	0.0283945	+	0.0382649i
$219$		0			0
$220$	67345.5	+	20391.1i	0.0938106	+	0.0284042i
$221$			932260.i			1.28397i
$222$		0			0
$223$		−	956233.i		−	1.28766i	−0.765168	−	0.643830i	$-0.777344\pi$
$223$		−	956233.i		−	1.28766i	0.765168	−	0.643830i	$-0.222656\pi$
$224$	−1.03970e6	+	52423.4i	−1.38448	+	0.0698079i
$225$		0			0
$226$	−340612.	+	252751.i	−0.443597	+	0.329171i
$227$	506559.			0.652477			0.326239	−	0.945287i	$-0.394219\pi$
$227$	506559.			0.652477			0.326239	+	0.945287i	$0.394219\pi$
$228$		0			0
$229$	19170.8			0.0241575			0.0120788	−	0.999927i	$-0.496155\pi$
$229$	19170.8			0.0241575			0.0120788	+	0.999927i	$0.496155\pi$
$230$	141101.	−	104704.i	0.175877	−	0.130510i
$231$		0			0
$232$	265387.	+	739898.i	0.323712	+	0.902510i
$233$		−	1.34476e6i		−	1.62276i	−0.584519	−	0.811380i	$-0.698717\pi$
$233$		−	1.34476e6i		−	1.62276i	0.584519	−	0.811380i	$-0.301283\pi$
$234$		0			0
$235$		−	142501.i		−	0.168325i
$236$	15234.6	−	50315.3i	0.0178054	−	0.0588058i
$237$		0			0
$238$	657244.	+	885713.i	0.752115	+	1.01356i
$239$	−995047.			−1.12681			−0.563403	−	0.826183i	$-0.690508\pi$
$239$	−995047.			−1.12681			−0.563403	+	0.826183i	$0.690508\pi$
$240$		0			0
$241$	−228924.			−0.253891			−0.126946	−	0.991910i	$-0.540517\pi$
$241$	−228924.			−0.253891			−0.126946	+	0.991910i	$0.540517\pi$
$242$	173611.	+	233961.i	0.190563	+	0.256806i
$243$		0			0
$244$	245627.	−	811233.i	0.264120	−	0.872310i
$245$			102911.i			0.109534i
$246$		0			0
$247$			1.57306e6i			1.64060i
$248$	−116725.	−	325429.i	−0.120513	−	0.335990i
$249$		0			0
$250$	−187294.	+	138982.i	−0.189528	+	0.140639i
$251$	1.37877e6			1.38136			0.690680	−	0.723161i	$-0.257311\pi$
$251$	1.37877e6			1.38136			0.690680	+	0.723161i	$0.257311\pi$
$252$		0			0
$253$	−1.54744e6			−1.51989
$254$	−187917.	+	139444.i	−0.182760	+	0.135617i
$255$		0			0
$256$	403274.	+	967927.i	0.384592	+	0.923087i
$257$		−	1.26490e6i		−	1.19460i	−0.802016	−	0.597302i	$-0.796239\pi$
$257$		−	1.26490e6i		−	1.19460i	0.802016	−	0.597302i	$-0.203761\pi$
$258$		0			0
$259$		−	161433.i		−	0.149535i
$260$	174844.	+	52939.8i	0.160405	+	0.0485679i
$261$		0			0
$262$	498897.	+	672321.i	0.449011	+	0.605095i
$263$	934476.			0.833065			0.416532	−	0.909121i	$-0.363245\pi$
$263$	934476.			0.833065			0.416532	+	0.909121i	$0.363245\pi$
$264$		0			0
$265$	−112673.			−0.0985609
$266$	1.10901e6	+	1.49452e6i	0.961019	+	1.29509i
$267$		0			0
$268$	1.92821e6	+	583830.i	1.63990	+	0.496534i
$269$		−	283680.i		−	0.239028i	−0.992833	−	0.119514i	$-0.961866\pi$
$269$		−	283680.i		−	0.239028i	0.992833	−	0.119514i	$-0.0381336\pi$
$270$		0			0
$271$		−	1.58669e6i		−	1.31241i	−0.754585	−	0.656203i	$-0.772162\pi$
$271$		−	1.58669e6i		−	1.31241i	0.754585	−	0.656203i	$-0.227838\pi$
$272$	616249.	−	924349.i	0.505050	−	0.757554i
$273$		0			0
$274$	−752630.	+	558490.i	−0.605627	+	0.449406i
$275$	1.01971e6			0.813102
$276$		0			0
$277$	−125478.			−0.0982580			−0.0491290	−	0.998792i	$-0.515645\pi$
$277$	−125478.			−0.0982580			−0.0491290	+	0.998792i	$0.515645\pi$
$278$	−1.67806e6	+	1.24521e6i	−1.30225	+	0.966339i
$279$		0			0
$280$	203437.	−	72968.9i	0.155073	−	0.0556215i
$281$			435247.i			0.328829i	0.986391	+	0.164415i	$0.0525735\pi$
$281$			435247.i			0.328829i	−0.986391	+	0.164415i	$0.947427\pi$
$282$		0			0
$283$		−	1.10983e6i		−	0.823739i	−0.911243	−	0.411869i	$-0.864876\pi$
$283$		−	1.10983e6i		−	0.823739i	0.911243	−	0.411869i	$-0.135124\pi$
$284$	177087.	−	584865.i	0.130284	−	0.430288i
$285$		0			0
$286$	−958748.	−	1.29202e6i	−0.693089	−	0.934019i
$287$	1.54661e6			1.10835
$288$		0			0
$289$	242848.			0.171037
$290$	−97248.2	−	131053.i	−0.0679027	−	0.0915067i
$291$		0			0
$292$	−255624.	+	844249.i	−0.175446	+	0.579446i
$293$		−	507271.i		−	0.345200i	−0.984992	−	0.172600i	$-0.944783\pi$
$293$		−	507271.i		−	0.345200i	0.984992	−	0.172600i	$-0.0552168\pi$
$294$		0			0
$295$			10914.4i			0.00730203i
$296$	−153057.	+	54898.6i	−0.101537	+	0.0364193i
$297$		0			0
$298$	1.32101e6	−	980254.i	0.861716	−	0.639437i
$299$	−4.01749e6			−2.59883
$300$		0			0
$301$	−286873.			−0.182504
$302$	−299028.	+	221894.i	−0.188666	+	0.140000i
$303$		0			0
$304$	1.03984e6	−	1.55972e6i	0.645330	−	0.967969i
$305$			175972.i			0.108317i
$306$		0			0
$307$			432378.i			0.261829i	0.991394	+	0.130915i	$0.0417914\pi$
$307$			432378.i			0.261829i	−0.991394	+	0.130915i	$0.958209\pi$
$308$	−1.82176e6	−	551596.i	−1.09424	−	0.331318i
$309$		0			0
$310$	42772.6	+	57641.1i	0.0252791	+	0.0340665i
$311$	−329457.			−0.193151			−0.0965757	−	0.995326i	$-0.530789\pi$
$311$	−329457.			−0.193151			−0.0965757	+	0.995326i	$0.530789\pi$
$312$		0			0
$313$	−1.56877e6			−0.905104			−0.452552	−	0.891738i	$-0.649486\pi$
$313$	−1.56877e6			−0.905104			−0.452552	+	0.891738i	$0.649486\pi$
$314$	881015.	+	1.18727e6i	0.504265	+	0.679556i
$315$		0			0
$316$	−1.21975e6	−	369320.i	−0.687154	−	0.208058i
$317$			83661.3i			0.0467602i	0.999727	+	0.0233801i	$0.00744280\pi$
$317$			83661.3i			0.0467602i	−0.999727	+	0.0233801i	$0.992557\pi$
$318$		0			0
$319$			1.43725e6i			0.790777i
$320$	−138366.	−	168067.i	−0.0755360	−	0.0917506i
$321$		0			0
$322$	−3.81690e6	+	2.83234e6i	−2.05150	+	1.52232i
$323$	−1.98605e6			−1.05921
$324$		0			0
$325$	2.64740e6			1.39031
$326$	80070.2	−	59416.2i	0.0417279	−	0.0309643i
$327$		0			0
$328$	−525955.	−	1.46636e6i	−0.269938	−	0.752587i
$329$			3.85479e6i			1.96341i
$330$		0			0
$331$			180224.i			0.0904157i	0.998978	+	0.0452078i	$0.0143950\pi$
$331$			180224.i			0.0904157i	−0.998978	+	0.0452078i	$0.985605\pi$
$332$	508322.	−	1.67883e6i	0.253101	−	0.835916i
$333$		0			0
$334$	−1.15104e6	−	1.55116e6i	−0.564579	−	0.760835i
$335$	−418268.			−0.203630
$336$		0			0
$337$	1.28853e6			0.618042			0.309021	−	0.951055i	$-0.399999\pi$
$337$	1.28853e6			0.618042			0.309021	+	0.951055i	$0.399999\pi$
$338$	−1.23751e6	−	1.66769e6i	−0.589194	−	0.794007i
$339$		0			0
$340$	−66838.3	+	220747.i	−0.0313565	+	0.103561i
$341$		−	632143.i		−	0.294394i
$342$		0			0
$343$			236624.i			0.108598i
$344$	97556.9	+	271989.i	0.0444490	+	0.123924i
$345$		0			0
$346$	3.30962e6	−	2.45591e6i	1.48624	−	1.10286i
$347$	3.19371e6			1.42387			0.711937	−	0.702243i	$-0.247818\pi$
$347$	3.19371e6			1.42387			0.711937	+	0.702243i	$0.247818\pi$
$348$		0			0
$349$	3.20922e6			1.41038			0.705189	−	0.709020i	$-0.250862\pi$
$349$	3.20922e6			1.41038			0.705189	+	0.709020i	$0.250862\pi$
$350$	2.51522e6	−	1.86642e6i	1.09750	−	0.814402i
$351$		0			0
$352$	96548.5	+	1.91482e6i	0.0415326	+	0.823704i
$353$		−	1.22806e6i		−	0.524543i	−0.964994	−	0.262272i	$-0.915528\pi$
$353$		−	1.22806e6i		−	0.524543i	0.964994	−	0.262272i	$-0.0844717\pi$
$354$		0			0
$355$			126869.i			0.0534298i
$356$	1.51705e6	+	459335.i	0.634416	+	0.192090i
$357$		0			0
$358$	−483819.	−	652002.i	−0.199515	−	0.268869i
$359$	−1.74974e6			−0.716535			−0.358268	−	0.933619i	$-0.616632\pi$
$359$	−1.74974e6			−0.716535			−0.358268	+	0.933619i	$0.616632\pi$
$360$		0			0
$361$	−875091.			−0.353415
$362$	146998.	+	198097.i	0.0589577	+	0.0794524i
$363$		0			0
$364$	−4.72969e6	−	1.43207e6i	−1.87103	−	0.566514i
$365$		−	183134.i		−	0.0719511i
$366$		0			0
$367$			2.52629e6i			0.979078i	0.871981	+	0.489539i	$0.162835\pi$
$367$			2.52629e6i			0.979078i	−0.871981	+	0.489539i	$0.837165\pi$
$368$	3.98340e6	+	2.65567e6i	1.53333	+	1.02225i
$369$		0			0
$370$	27110.0	−	20117.0i	0.0102950	−	0.00763941i
$371$	3.04790e6			1.14965
$372$		0			0
$373$	−245568.			−0.0913903			−0.0456951	−	0.998955i	$-0.514550\pi$
$373$	−245568.			−0.0913903			−0.0456951	+	0.998955i	$0.514550\pi$
$374$	1.63122e6	−	1.21045e6i	0.603024	−	0.447475i
$375$		0			0
$376$	3.65479e6	−	1.31090e6i	1.33319	−	0.478190i
$377$			3.73142e6i			1.35214i
$378$		0			0
$379$			3.97839e6i			1.42269i	0.702844	+	0.711344i	$0.251913\pi$
$379$			3.97839e6i			1.42269i	−0.702844	+	0.711344i	$0.748087\pi$
$380$	−112781.	+	372481.i	−0.0400660	+	0.132326i
$381$		0			0
$382$	1.88487e6	+	2.54008e6i	0.660882	+	0.890615i
$383$	−64277.0			−0.0223902			−0.0111951	−	0.999937i	$-0.503564\pi$
$383$	−64277.0			−0.0223902			−0.0111951	+	0.999937i	$0.503564\pi$
$384$		0			0
$385$	395175.			0.135874
$386$	−2.28693e6	−	3.08190e6i	−0.781240	−	1.05281i
$387$		0			0
$388$	−1.42602e6	+	4.70971e6i	−0.480890	+	1.58824i
$389$		−	3.49951e6i		−	1.17256i	−0.810110	−	0.586278i	$-0.800593\pi$
$389$		−	3.49951e6i		−	1.17256i	0.810110	−	0.586278i	$-0.199407\pi$
$390$		0			0
$391$		−	5.07222e6i		−	1.67786i
$392$	−2.63940e6	+	946702.i	−0.867542	+	0.311170i
$393$		0			0
$394$	−228591.	+	169626.i	−0.0741853	+	0.0550493i
$395$	264588.			0.0853253
$396$		0			0
$397$	−1.45518e6			−0.463385			−0.231692	−	0.972789i	$-0.574426\pi$
$397$	−1.45518e6			−0.463385			−0.231692	+	0.972789i	$0.574426\pi$
$398$	−1.15578e6	+	857645.i	−0.365735	+	0.271394i
$399$		0			0
$400$	−2.62493e6	−	1.75000e6i	−0.820292	−	0.546876i
$401$		−	2.60333e6i		−	0.808478i	−0.914653	−	0.404239i	$-0.867536\pi$
$401$		−	2.60333e6i		−	0.808478i	0.914653	−	0.404239i	$-0.132464\pi$
$402$		0			0
$403$		−	1.64119e6i		−	0.503379i
$404$	−4.28816e6	−	1.29838e6i	−1.30713	−	0.395775i
$405$		0			0
$406$	2.63065e6	+	3.54511e6i	0.792042	+	1.06737i
$407$	−297312.			−0.0889666
$408$		0			0
$409$	−3.68957e6			−1.09061			−0.545303	−	0.838239i	$-0.683585\pi$
$409$	−3.68957e6			−1.09061			−0.545303	+	0.838239i	$0.683585\pi$
$410$	192731.	+	259727.i	0.0566229	+	0.0763059i
$411$		0			0
$412$	1.83793e6	+	556494.i	0.533441	+	0.161517i
$413$		−	295244.i		−	0.0851737i
$414$		0			0
$415$			364172.i			0.103797i
$416$	250662.	+	4.97131e6i	0.0710158	+	1.40844i
$417$		0			0
$418$	2.75247e6	−	2.04248e6i	0.770518	−	0.571763i
$419$	−4.32190e6			−1.20265			−0.601326	−	0.799004i	$-0.705361\pi$
$419$	−4.32190e6			−1.20265			−0.601326	+	0.799004i	$0.705361\pi$
$420$		0			0
$421$	−326613.			−0.0898106			−0.0449053	−	0.998991i	$-0.514299\pi$
$421$	−326613.			−0.0898106			−0.0449053	+	0.998991i	$0.514299\pi$
$422$	1.29357e6	−	959895.i	0.353597	−	0.262387i
$423$		0			0
$424$	−1.03650e6	−	2.88977e6i	−0.279998	−	0.780635i
$425$			3.34243e6i			0.897615i
$426$		0			0
$427$		−	4.76021e6i		−	1.26345i
$428$	−1.66274e6	+	5.49152e6i	−0.438747	+	1.44905i
$429$		0			0
$430$	−35748.7	−	48175.6i	−0.00932373	−	0.0125648i
$431$	−566316.			−0.146847			−0.0734235	−	0.997301i	$-0.523392\pi$
$431$	−566316.			−0.146847			−0.0734235	+	0.997301i	$0.523392\pi$
$432$		0			0
$433$	−4.80805e6			−1.23239			−0.616196	−	0.787593i	$-0.711327\pi$
$433$	−4.80805e6			−1.23239			−0.616196	+	0.787593i	$0.711327\pi$
$434$	−1.15704e6	−	1.55924e6i	−0.294865	−	0.397365i
$435$		0			0
$436$	54809.4	−	181019.i	0.0138083	−	0.0456046i
$437$		−	8.55870e6i		−	2.14390i
$438$		0			0
$439$		−	2.12964e6i		−	0.527407i	−0.964604	−	0.263703i	$-0.915056\pi$
$439$		−	2.12964e6i		−	0.527407i	0.964604	−	0.263703i	$-0.0849440\pi$
$440$	−134387.	−	374672.i	−0.0330923	−	0.0922612i
$441$		0			0
$442$	4.23503e6	−	3.14261e6i	1.03110	−	0.765129i
$443$	6.85174e6			1.65879			0.829395	−	0.558663i	$-0.188685\pi$
$443$	6.85174e6			1.65879			0.829395	+	0.558663i	$0.188685\pi$
$444$		0			0
$445$	−329077.			−0.0787767
$446$	−4.34393e6	+	3.22342e6i	−1.03406	+	0.767326i
$447$		0			0
$448$	3.74292e6	+	4.54638e6i	0.881081	+	1.07021i
$449$			7.28148e6i			1.70453i	0.523113	+	0.852263i	$0.324770\pi$
$449$			7.28148e6i			1.70453i	−0.523113	+	0.852263i	$0.675230\pi$
$450$		0			0
$451$		−	2.84840e6i		−	0.659416i
$452$	2.29637e6	+	695302.i	0.528684	+	0.160076i
$453$		0			0
$454$	−1.70759e6	−	2.30117e6i	−0.388816	−	0.523974i
$455$	1.02596e6			0.232329
$456$		0			0
$457$	−3.67151e6			−0.822345			−0.411172	−	0.911558i	$-0.634881\pi$
$457$	−3.67151e6			−0.822345			−0.411172	+	0.911558i	$0.634881\pi$
$458$	−64624.1	−	87088.5i	−0.0143956	−	0.0193998i
$459$		0			0
$460$	−951290.	−	288034.i	−0.209613	−	0.0634672i
$461$		−	3.01233e6i		−	0.660161i	−0.943953	−	0.330080i	$-0.892924\pi$
$461$		−	3.01233e6i		−	0.660161i	0.943953	−	0.330080i	$-0.107076\pi$
$462$		0			0
$463$		−	2.96920e6i		−	0.643705i	−0.946790	−	0.321853i	$-0.895694\pi$
$463$		−	2.96920e6i		−	0.643705i	0.946790	−	0.321853i	$-0.104306\pi$
$464$	2.46657e6	−	3.69975e6i	0.531861	−	0.797770i
$465$		0			0
$466$	−6.10891e6	+	4.53312e6i	−1.30316	+	0.967014i
$467$	−6.57558e6			−1.39522			−0.697609	−	0.716479i	$-0.745753\pi$
$467$	−6.57558e6			−1.39522			−0.697609	+	0.716479i	$0.745753\pi$
$468$		0			0
$469$	1.13145e7			2.37522
$470$	−647349.	+	480366.i	−0.135174	+	0.100306i
$471$		0			0
$472$	−279925.	+	100404.i	−0.0578345	+	0.0207441i
$473$			528336.i			0.108582i
$474$		0			0
$475$			5.63991e6i			1.14693i
$476$	1.80804e6	−	5.97140e6i	0.365754	−	1.20798i
$477$		0			0
$478$	3.35426e6	+	4.52026e6i	0.671471	+	0.904885i
$479$	6.46607e6			1.28766			0.643830	−	0.765168i	$-0.277344\pi$
$479$	6.46607e6			1.28766			0.643830	+	0.765168i	$0.277344\pi$
$480$		0			0
$481$	−771891.			−0.152122
$482$	771692.	+	1.03994e6i	0.151296	+	0.203888i
$483$		0			0
$484$	477593.	−	1.57735e6i	0.0926711	−	0.306065i
$485$		−	1.02163e6i		−	0.197215i
$486$		0			0
$487$			8.82689e6i			1.68650i	0.537525	+	0.843248i	$0.319359\pi$
$487$			8.82689e6i			1.68650i	−0.537525	+	0.843248i	$0.680641\pi$
$488$	−4.51323e6	+	1.61881e6i	−0.857903	+	0.307713i
$489$		0			0
$490$	467501.	−	346909.i	0.0879613	−	0.0652718i
$491$	−1.16252e6			−0.217618			−0.108809	−	0.994063i	$-0.534704\pi$
$491$	−1.16252e6			−0.217618			−0.108809	+	0.994063i	$0.534704\pi$
$492$		0			0
$493$	−4.71104e6			−0.872970
$494$	7.14605e6	−	5.30273e6i	1.31749	−	0.977648i
$495$		0			0
$496$	−1.08487e6	+	1.62726e6i	−0.198004	+	0.296997i
$497$		−	3.43191e6i		−	0.623225i
$498$		0			0
$499$			7.39018e6i			1.32863i	0.747454	+	0.664314i	$0.231276\pi$
$499$			7.39018e6i			1.32863i	−0.747454	+	0.664314i	$0.768724\pi$
$500$	1.26272e6	+	382329.i	0.225882	+	0.0683931i
$501$		0			0
$502$	−4.64777e6	−	6.26341e6i	−0.823162	−	1.10931i
$503$	−992910.			−0.174981			−0.0874903	−	0.996165i	$-0.527885\pi$
$503$	−992910.			−0.174981			−0.0874903	+	0.996165i	$0.527885\pi$
$504$		0			0
$505$	930186.			0.162309
$506$	5.21634e6	+	7.02962e6i	0.905711	+	1.22055i
$507$		0			0
$508$	1.26692e6	+	383601.i	0.217816	+	0.0659509i
$509$			7.94817e6i			1.35979i	0.733308	+	0.679897i	$0.237975\pi$
$509$			7.94817e6i			1.35979i	−0.733308	+	0.679897i	$0.762025\pi$
$510$		0			0
$511$			4.95394e6i			0.839264i
$512$	3.03764e6	−	5.09482e6i	0.512107	−	0.858922i
$513$		0			0
$514$	−5.74614e6	+	4.26393e6i	−0.959331	+	0.711873i
$515$	−398684.			−0.0662385
$516$		0			0
$517$	7.09940e6			1.16814
$518$	−733351.	+	544184.i	−0.120085	+	0.0891089i
$519$		0			0
$520$	−348900.	−	972733.i	−0.0565839	−	0.157756i
$521$			8.14816e6i			1.31512i	0.753402	+	0.657560i	$0.228411\pi$
$521$			8.14816e6i			1.31512i	−0.753402	+	0.657560i	$0.771589\pi$
$522$		0			0
$523$		−	8.41689e6i		−	1.34554i	−0.739851	−	0.672771i	$-0.765104\pi$
$523$		−	8.41689e6i		−	1.34554i	0.739851	−	0.672771i	$-0.234896\pi$
$524$	1.37243e6	−	4.53273e6i	0.218355	−	0.721160i
$525$		0			0
$526$	−3.15008e6	−	4.24510e6i	−0.496429	−	0.668996i
$527$	2.07205e6			0.324993
$528$		0			0
$529$	1.54220e7			2.39608
$530$	379816.	+	511846.i	0.0587331	+	0.0791497i
$531$		0			0
$532$	3.05082e6	−	1.00759e7i	0.467345	−	1.54350i
$533$		−	7.39509e6i		−	1.12752i
$534$		0			0
$535$		−	1.19122e6i		−	0.179931i
$536$	−3.84773e6	−	1.07275e7i	−0.578486	−	1.61282i
$537$		0			0
$538$	−1.28869e6	+	956274.i	−0.191952	+	0.142438i
$539$	−5.12702e6			−0.760139
$540$		0			0
$541$	−3.05821e6			−0.449235			−0.224618	−	0.974447i	$-0.572113\pi$
$541$	−3.05821e6			−0.449235			−0.224618	+	0.974447i	$0.572113\pi$
$542$	−7.20793e6	+	5.34865e6i	−1.05393	+	0.782071i
$543$		0			0
$544$	−6.27644e6	+	316469.i	−0.909319	+	0.0458495i
$545$			39266.6i			0.00566281i
$546$		0			0
$547$		−	8.63839e6i		−	1.23442i	−0.786797	−	0.617212i	$-0.788262\pi$
$547$		−	8.63839e6i		−	1.23442i	0.786797	−	0.617212i	$-0.211738\pi$
$548$	5.07417e6	+	1.53637e6i	0.721794	+	0.218547i
$549$		0			0
$550$	−3.43740e6	−	4.63229e6i	−0.484533	−	0.652964i
$551$	−7.94925e6			−1.11544
$552$		0			0
$553$	−7.15735e6			−0.995267
$554$	422981.	+	570016.i	0.0585526	+	0.0789064i
$555$		0			0
$556$	1.13134e7	+	3.42549e6i	1.55204	+	0.469932i
$557$			1.12443e7i			1.53566i	0.640656	+	0.767828i	$0.278663\pi$
$557$			1.12443e7i			1.53566i	−0.640656	+	0.767828i	$0.721337\pi$
$558$		0			0
$559$			1.37168e6i			0.185662i
$560$	−1.01726e6	−	678190.i	−0.137076	−	0.0913864i
$561$		0			0
$562$	1.97722e6	−	1.46720e6i	0.264067	−	0.195951i
$563$	8.98556e6			1.19474			0.597371	−	0.801965i	$-0.296212\pi$
$563$	8.98556e6			1.19474			0.597371	+	0.801965i	$0.296212\pi$
$564$		0			0
$565$	−498129.			−0.0656478
$566$	−5.04168e6	+	3.74118e6i	−0.661506	+	0.490872i
$567$		0			0
$568$	−3.25385e6	+	1.16709e6i	−0.423182	+	0.151787i
$569$			3.96103e6i			0.512893i	0.966558	+	0.256447i	$0.0825518\pi$
$569$			3.96103e6i			0.512893i	−0.966558	+	0.256447i	$0.917448\pi$
$570$		0			0
$571$			1.13704e7i			1.45944i	0.683749	+	0.729718i	$0.260348\pi$
$571$			1.13704e7i			1.45944i	−0.683749	+	0.729718i	$0.739652\pi$
$572$	−2.63745e6	+	8.71072e6i	−0.337050	+	1.11318i
$573$		0			0
$574$	−5.21354e6	−	7.02586e6i	−0.660470	−	0.890061i
$575$	−1.44039e7			−1.81682
$576$		0			0
$577$	−7.78266e6			−0.973169			−0.486585	−	0.873633i	$-0.661757\pi$
$577$	−7.78266e6			−0.973169			−0.486585	+	0.873633i	$0.661757\pi$
$578$	−818629.	−	1.10320e6i	−0.101922	−	0.137352i
$579$		0			0
$580$	−267524.	+	883550.i	−0.0330211	+	0.109059i
$581$		−	9.85118e6i		−	1.21073i
$582$		0			0
$583$		−	5.61335e6i		−	0.683991i
$584$	4.69691e6	−	1.68469e6i	0.569876	−	0.204403i
$585$		0			0
$586$	−2.30441e6	+	1.70999e6i	−0.277214	+	0.205707i
$587$	−6.91862e6			−0.828751			−0.414375	−	0.910106i	$-0.636000\pi$
$587$	−6.91862e6			−0.828751			−0.414375	+	0.910106i	$0.636000\pi$
$588$		0			0
$589$	3.49631e6			0.415262
$590$	49581.4	−	36791.9i	0.00586393	−	0.00435133i
$591$		0			0
$592$	765341.	+	510241.i	0.0897533	+	0.0598372i
$593$		−	1.33982e7i		−	1.56462i	−0.622890	−	0.782310i	$-0.714041\pi$
$593$		−	1.33982e7i		−	1.56462i	0.622890	−	0.782310i	$-0.285959\pi$
$594$		0			0
$595$			1.29531e6i			0.149997i
$596$	−8.90611e6	−	2.69662e6i	−1.02701	−	0.310959i
$597$		0			0
$598$	1.35428e7	+	1.82505e7i	1.54866	+	2.08700i
$599$	7.73898e6			0.881286			0.440643	−	0.897682i	$-0.354751\pi$
$599$	7.73898e6			0.881286			0.440643	+	0.897682i	$0.354751\pi$
$600$		0			0
$601$	−9.33823e6			−1.05458			−0.527289	−	0.849686i	$-0.676791\pi$
$601$	−9.33823e6			−1.05458			−0.527289	+	0.849686i	$0.676791\pi$
$602$	967036.	+	1.30319e6i	0.108755	+	0.146561i
$603$		0			0
$604$	2.01602e6	+	610416.i	0.224855	+	0.0680821i
$605$			342157.i			0.0380047i
$606$		0			0
$607$		−	1.38412e7i		−	1.52476i	−0.647128	−	0.762381i	$-0.724030\pi$
$607$		−	1.38412e7i		−	1.52476i	0.647128	−	0.762381i	$-0.275970\pi$
$608$	−1.05907e7	+	534000.i	−1.16189	+	0.0585844i
$609$		0			0
$610$	799400.	−	593195.i	0.0869840	−	0.0645466i
$611$	1.84316e7			1.99738
$612$		0			0
$613$	−3.03062e6			−0.325747			−0.162874	−	0.986647i	$-0.552076\pi$
$613$	−3.03062e6			−0.325747			−0.162874	+	0.986647i	$0.552076\pi$
$614$	1.96419e6	−	1.45753e6i	0.210263	−	0.156026i
$615$		0			0
$616$	3.63530e6	+	1.01352e7i	0.386001	+	1.07617i
$617$			5.14315e6i			0.543896i	0.962312	+	0.271948i	$0.0876679\pi$
$617$			5.14315e6i			0.543896i	−0.962312	+	0.271948i	$0.912332\pi$
$618$		0			0
$619$			1.97207e6i			0.206869i	0.994636	+	0.103434i	$0.0329832\pi$
$619$			1.97207e6i			0.206869i	−0.994636	+	0.103434i	$0.967017\pi$
$620$	117665.	−	388611.i	0.0122933	−	0.0406010i
$621$		0			0
$622$	1.11059e6	+	1.49664e6i	0.115100	+	0.155111i
$623$	8.90183e6			0.918881
$624$		0			0
$625$	9.35379e6			0.957828
$626$	5.28826e6	+	7.12654e6i	0.539357	+	0.726847i
$627$		0			0
$628$	2.42361e6	−	8.00447e6i	0.245225	−	0.809904i
$629$		−	974538.i		−	0.0982137i
$630$		0			0
$631$		−	5.50415e6i		−	0.550322i	−0.961398	−	0.275161i	$-0.911269\pi$
$631$		−	5.50415e6i		−	0.550322i	0.961398	−	0.275161i	$-0.0887311\pi$
$632$	2.43400e6	+	6.78600e6i	0.242398	+	0.675805i
$633$		0			0
$634$	380053.	−	282019.i	0.0375510	−	0.0278647i
$635$	−274820.			−0.0270467
$636$		0			0
$637$	−1.33109e7			−1.29975
$638$	6.52906e6	−	4.84489e6i	0.635037	−	0.471230i
$639$		0			0
$640$	−297064.	+	1.19511e6i	−0.0286682	+	0.115334i
$641$		−	1.69518e7i		−	1.62956i	−0.579770	−	0.814780i	$-0.696858\pi$
$641$		−	1.69518e7i		−	1.62956i	0.579770	−	0.814780i	$-0.303142\pi$
$642$		0			0
$643$			9.41918e6i			0.898433i	0.893423	+	0.449217i	$0.148297\pi$
$643$			9.41918e6i			0.898433i	−0.893423	+	0.449217i	$0.851703\pi$
$644$	2.57332e7	+	7.79158e6i	2.44501	+	0.740305i
$645$		0			0
$646$	6.69488e6	+	9.02213e6i	0.631192	+	0.850605i
$647$	1.21977e7			1.14556			0.572778	−	0.819711i	$-0.305866\pi$
$647$	1.21977e7			1.14556			0.572778	+	0.819711i	$0.305866\pi$
$648$		0			0
$649$	−543753.			−0.0506745
$650$	−8.92427e6	−	1.20265e7i	−0.828494	−	1.11649i
$651$		0			0
$652$	−539827.	−	163450.i	−0.0497319	−	0.0150580i
$653$			2.02858e6i			0.186169i	0.995658	+	0.0930847i	$0.0296727\pi$
$653$			2.02858e6i			0.186169i	−0.995658	+	0.0930847i	$0.970327\pi$
$654$		0			0
$655$			983239.i			0.0895480i
$656$	−4.88836e6	+	7.33233e6i	−0.443510	+	0.665247i
$657$		0			0
$658$	1.75114e7	−	1.29943e7i	1.57672	−	1.17001i
$659$	−313352.			−0.0281073			−0.0140536	−	0.999901i	$-0.504474\pi$
$659$	−313352.			−0.0281073			−0.0140536	+	0.999901i	$0.504474\pi$
$660$		0			0
$661$	−1.05415e7			−0.938427			−0.469213	−	0.883085i	$-0.655462\pi$
$661$	−1.05415e7			−0.938427			−0.469213	+	0.883085i	$0.655462\pi$
$662$	818716.	−	607529.i	0.0726086	−	0.0538793i
$663$		0			0
$664$	−9.34007e6	+	3.35010e6i	−0.822110	+	0.294875i
$665$			2.18567e6i			0.191660i
$666$		0			0
$667$		−	2.03018e7i		−	1.76693i
$668$	−3.16644e6	+	1.04578e7i	−0.274555	+	0.906774i
$669$		0			0
$670$	1.40996e6	+	1.90009e6i	0.121345	+	0.163526i
$671$	−8.76692e6			−0.751693
$672$		0			0
$673$	1.21080e7			1.03047			0.515236	−	0.857049i	$-0.327704\pi$
$673$	1.21080e7			1.03047			0.515236	+	0.857049i	$0.327704\pi$
$674$	−4.34356e6	−	5.85346e6i	−0.368296	−	0.496321i
$675$		0			0
$676$	−3.40432e6	+	1.12435e7i	−0.286526	+	0.946309i
$677$			8.96603e6i			0.751846i	0.926651	+	0.375923i	$0.122674\pi$
$677$			8.96603e6i			0.751846i	−0.926651	+	0.375923i	$0.877326\pi$
$678$		0			0
$679$			2.76360e7i			2.30039i
$680$	1.22811e6	−	440498.i	0.101851	−	0.0365319i
$681$		0			0
$682$	−2.87167e6	+	2.13093e6i	−0.236414	+	0.175431i
$683$	−4.61704e6			−0.378715			−0.189357	−	0.981908i	$-0.560640\pi$
$683$	−4.61704e6			−0.378715			−0.189357	+	0.981908i	$0.560640\pi$
$684$		0			0
$685$	−1.10069e6			−0.0896267
$686$	1.07492e6	−	797649.i	0.0872103	−	0.0647145i
$687$		0			0
$688$	906718.	−	1.36004e6i	0.0730300	−	0.109542i
$689$		−	1.45735e7i		−	1.16954i
$690$		0			0
$691$		−	6.89862e6i		−	0.549626i	−0.961498	−	0.274813i	$-0.911384\pi$
$691$		−	6.89862e6i		−	0.549626i	0.961498	−	0.274813i	$-0.0886159\pi$
$692$	−2.23132e7	−	6.75605e6i	−1.77132	−	0.536324i
$693$		0			0
$694$	−1.07659e7	−	1.45082e7i	−0.848496	−	1.14345i
$695$	−2.45409e6			−0.192721
$696$		0			0
$697$	9.33655e6			0.727955
$698$	−1.08181e7	−	1.45787e7i	−0.840453	−	1.13261i
$699$		0			0
$700$	−1.69574e7	−	5.13440e6i	−1.30802	−	0.396045i
$701$			1.70003e7i			1.30666i	0.757074	+	0.653329i	$0.226628\pi$
$701$			1.70003e7i			1.30666i	−0.757074	+	0.653329i	$0.773372\pi$
$702$		0			0
$703$		−	1.64440e6i		−	0.125493i
$704$	8.37310e6	−	6.89337e6i	0.636729	−	0.524204i
$705$		0			0
$706$	−5.57876e6	+	4.13973e6i	−0.421236	+	0.312579i
$707$	−2.51624e7			−1.89323
$708$		0			0
$709$	5.83646e6			0.436048			0.218024	−	0.975943i	$-0.430039\pi$
$709$	5.83646e6			0.436048			0.218024	+	0.975943i	$0.430039\pi$
$710$	576333.	−	427669.i	0.0429070	−	0.0318392i
$711$		0			0
$712$	−3.02725e6	−	8.43998e6i	−0.223794	−	0.623938i
$713$			8.92934e6i			0.657802i
$714$		0			0
$715$		−	1.88953e6i		−	0.138225i
$716$	−1.33095e6	+	4.39574e6i	−0.0970243	+	0.320442i
$717$		0			0
$718$	5.89830e6	+	7.94865e6i	0.426988	+	0.575416i
$719$	−5.51019e6			−0.397506			−0.198753	−	0.980050i	$-0.563689\pi$
$719$	−5.51019e6			−0.397506			−0.198753	+	0.980050i	$0.563689\pi$
$720$		0			0
$721$	1.07848e7			0.772631
$722$	2.94990e6	+	3.97533e6i	0.210603	+	0.283811i
$723$		0			0
$724$	404383.	−	1.33555e6i	0.0286712	−	0.0946924i
$725$			1.33782e7i			0.945266i
$726$		0			0
$727$			1.65851e6i			0.116381i	0.998305	+	0.0581905i	$0.0185331\pi$
$727$			1.65851e6i			0.116381i	−0.998305	+	0.0581905i	$0.981467\pi$
$728$	9.43806e6	+	2.63133e7i	0.660016	+	1.84012i
$729$		0			0
$730$	−831934.	+	617337.i	−0.0577806	+	0.0428761i
$731$	−1.73179e6			−0.119868
$732$		0			0
$733$	−1.66917e7			−1.14747			−0.573733	−	0.819042i	$-0.694505\pi$
$733$	−1.66917e7			−1.14747			−0.573733	+	0.819042i	$0.694505\pi$
$734$	1.14763e7	−	8.51601e6i	0.786253	−	0.583440i
$735$		0			0
$736$	−1.36380e6	−	2.70478e7i	−0.0928015	−	1.84051i
$737$		−	2.08380e7i		−	1.41315i
$738$		0			0
$739$			1.66267e7i			1.11994i	0.828513	+	0.559970i	$0.189187\pi$
$739$			1.66267e7i			1.11994i	−0.828513	+	0.559970i	$0.810813\pi$
$740$	−182774.	−	55340.7i	−0.0122697	−	0.00371505i
$741$		0			0
$742$	−1.02744e7	−	1.38459e7i	−0.685085	−	0.923232i
$743$	1.33945e6			0.0890134			0.0445067	−	0.999009i	$-0.485828\pi$
$743$	1.33945e6			0.0890134			0.0445067	+	0.999009i	$0.485828\pi$
$744$		0			0
$745$	1.93191e6			0.127525
$746$	827800.	+	1.11556e6i	0.0544601	+	0.0733913i
$747$		0			0
$748$	−1.09976e7	−	3.32987e6i	−0.718692	−	0.217607i
$749$			3.22235e7i			2.09879i
$750$		0			0
$751$		−	4.23540e6i		−	0.274028i	−0.990569	−	0.137014i	$-0.956250\pi$
$751$		−	4.23540e6i		−	0.274028i	0.990569	−	0.137014i	$-0.0437505\pi$
$752$	−1.82752e7	−	1.21838e7i	−1.17847	−	0.785668i
$753$		0			0
$754$	1.69509e7	−	1.25784e7i	1.08584	−	0.805747i
$755$	−437314.			−0.0279207
$756$		0			0
$757$	2.28026e7			1.44625			0.723127	−	0.690715i	$-0.242704\pi$
$757$	2.28026e7			1.44625			0.723127	+	0.690715i	$0.242704\pi$
$758$	1.80729e7	−	1.34110e7i	1.14249	−	0.847789i
$759$		0			0
$760$	2.07227e6	−	743282.i	0.130140	−	0.0466788i
$761$			6.15417e6i			0.385219i	0.981275	+	0.192610i	$0.0616951\pi$
$761$			6.15417e6i			0.385219i	−0.981275	+	0.192610i	$0.938305\pi$
$762$		0			0
$763$		−	1.06220e6i		−	0.0660532i
$764$	5.18516e6	−	1.71250e7i	0.321388	−	1.06145i
$765$		0			0
$766$	216675.	+	291995.i	0.0133425	+	0.0179806i
$767$	−1.41171e6			−0.0866474
$768$		0			0
$769$	2.84019e7			1.73194			0.865968	−	0.500099i	$-0.166703\pi$
$769$	2.84019e7			1.73194			0.865968	+	0.500099i	$0.166703\pi$
$770$	−1.33212e6	−	1.79518e6i	−0.0809684	−	0.109114i
$771$		0			0
$772$	−6.29119e6	+	2.07779e7i	−0.379918	+	1.25475i
$773$		−	3.13266e7i		−	1.88566i	−0.333268	−	0.942832i	$-0.608151\pi$
$773$		−	3.13266e7i		−	1.88566i	0.333268	−	0.942832i	$-0.391849\pi$
$774$		0			0
$775$		−	5.88414e6i		−	0.351908i
$776$	2.62021e7	−	9.39819e6i	1.56200	−	0.560260i
$777$		0			0
$778$	−1.58974e7	+	1.17967e7i	−0.941625	+	0.698734i
$779$	1.57542e7			0.930149
$780$		0			0
$781$	−6.32058e6			−0.370791
$782$	−2.30419e7	+	1.70982e7i	−1.34741	+	0.999850i
$783$		0			0
$784$	1.31980e7	+	8.79888e6i	0.766861	+	0.511255i
$785$			1.73633e6i			0.100567i
$786$		0			0
$787$		−	4.70960e6i		−	0.271049i	−0.990774	−	0.135524i	$-0.956728\pi$
$787$		−	4.70960e6i		−	0.271049i	0.990774	−	0.135524i	$-0.0432719\pi$
$788$	1.54114e6	+	466630.i	0.0884151	+	0.0267705i
$789$		0			0
$790$	−891916.	−	1.20196e6i	−0.0508459	−	0.0685208i
$791$	1.34748e7			0.765741
$792$		0			0
$793$	−2.27609e7			−1.28531
$794$	4.90536e6	+	6.61055e6i	0.276134	+	0.372123i
$795$		0			0
$796$	7.79215e6	+	2.35933e6i	0.435887	+	0.131979i
$797$			1.91999e7i			1.07066i	0.844642	+	0.535331i	$0.179813\pi$
$797$			1.91999e7i			1.07066i	−0.844642	+	0.535331i	$0.820187\pi$
$798$		0			0
$799$			2.32706e7i			1.28956i
$800$	898698.	+	1.78236e7i	0.0496465	+	0.984625i
$801$		0			0
$802$	−1.18263e7	+	8.77572e6i	−0.649251	+	0.481778i
$803$	9.12372e6			0.499325
$804$		0			0
$805$	−5.58205e6			−0.303601
$806$	−7.45551e6	+	5.53237e6i	−0.404240	+	0.299967i
$807$		0			0
$808$	8.55698e6	+	2.38569e7i	0.461097	+	1.28554i
$809$		−	1.77520e7i		−	0.953621i	−0.879006	−	0.476810i	$-0.841793\pi$
$809$		−	1.77520e7i		−	0.953621i	0.879006	−	0.476810i	$-0.158207\pi$
$810$		0			0
$811$			2.82756e7i			1.50959i	0.655958	+	0.754797i	$0.272265\pi$
$811$			2.82756e7i			1.50959i	−0.655958	+	0.754797i	$0.727735\pi$
$812$	7.23675e6	−	2.39008e7i	0.385171	−	1.27210i
$813$		0			0
$814$	1.00223e6	+	1.35062e6i	0.0530158	+	0.0714450i
$815$	117099.			0.00617532
$816$		0			0
$817$	−2.92217e6			−0.153162
$818$	1.24374e7	+	1.67608e7i	0.649899	+	0.875815i
$819$		0			0
$820$	530190.	−	1.75106e6i	0.0275358	−	0.0909424i
$821$		−	1.11741e7i		−	0.578567i	−0.957244	−	0.289283i	$-0.906583\pi$
$821$		−	1.11741e7i		−	0.578567i	0.957244	−	0.289283i	$-0.0934169\pi$
$822$		0			0
$823$		−	1.44872e7i		−	0.745564i	−0.927919	−	0.372782i	$-0.878404\pi$
$823$		−	1.44872e7i		−	0.745564i	0.927919	−	0.372782i	$-0.121596\pi$
$824$	−3.66758e6	−	1.02252e7i	−0.188175	−	0.524631i
$825$		0			0
$826$	−1.34122e6	+	995254.i	−0.0683990	+	0.0507556i
$827$	3.05054e6			0.155100			0.0775502	−	0.996988i	$-0.475290\pi$
$827$	3.05054e6			0.155100			0.0775502	+	0.996988i	$0.475290\pi$
$828$		0			0
$829$	−2.64275e7			−1.33558			−0.667789	−	0.744350i	$-0.732759\pi$
$829$	−2.64275e7			−1.33558			−0.667789	+	0.744350i	$0.732759\pi$
$830$	1.65435e6	−	1.22761e6i	0.0833549	−	0.0618536i
$831$		0			0
$832$	2.17385e7	−	1.78968e7i	1.08873	−	0.896326i
$833$		−	1.68055e7i		−	0.839147i
$834$		0			0
$835$		−	2.26850e6i		−	0.112596i
$836$	−1.85569e7	−	5.61872e6i	−0.918313	−	0.278049i
$837$		0			0
$838$	1.45690e7	+	1.96334e7i	0.716669	+	0.965794i
$839$	−2.10948e7			−1.03460			−0.517298	−	0.855805i	$-0.673062\pi$
$839$	−2.10948e7			−1.03460			−0.517298	+	0.855805i	$0.673062\pi$
$840$		0			0
$841$	1.65498e6			0.0806869
$842$	1.10100e6	+	1.48372e6i	0.0535188	+	0.0721227i
$843$		0			0
$844$	−8.72114e6	−	2.64061e6i	−0.421422	−	0.127599i
$845$		−	2.43893e6i		−	0.117505i
$846$		0			0
$847$		−	9.25566e6i		−	0.443301i
$848$	−9.63350e6	+	1.44499e7i	−0.460039	+	0.690040i
$849$		0			0
$850$	1.51838e7	−	1.12672e7i	0.720833	−	0.534895i
$851$	4.19969e6			0.198789
$852$		0			0
$853$	−2.93887e6			−0.138295			−0.0691477	−	0.997606i	$-0.522028\pi$
$853$	−2.93887e6			−0.138295			−0.0691477	+	0.997606i	$0.522028\pi$
$854$	−2.16245e7	+	1.60465e7i	−1.01461	+	0.752896i
$855$		0			0
$856$	3.05516e7	−	1.09583e7i	1.42512	−	0.511161i
$857$		−	6.72685e6i		−	0.312867i	−0.987688	−	0.156434i	$-0.950000\pi$
$857$		−	6.72685e6i		−	0.312867i	0.987688	−	0.156434i	$-0.0499997\pi$
$858$		0			0
$859$		−	3.89806e7i		−	1.80246i	−0.433343	−	0.901229i	$-0.642666\pi$
$859$		−	3.89806e7i		−	1.80246i	0.433343	−	0.901229i	$-0.357334\pi$
$860$	−98342.5	+	324796.i	−0.00453414	+	0.0149749i
$861$		0			0
$862$	1.90903e6	+	2.57263e6i	0.0875072	+	0.117926i
$863$	2.44524e7			1.11762			0.558811	−	0.829295i	$-0.311258\pi$
$863$	2.44524e7			1.11762			0.558811	+	0.829295i	$0.311258\pi$
$864$		0			0
$865$	4.84017e6			0.219948
$866$	1.62077e7	+	2.18418e7i	0.734391	+	0.989677i
$867$		0			0
$868$	−3.18294e6	+	1.05123e7i	−0.143393	+	0.473585i
$869$			1.31818e7i			0.592139i
$870$		0			0
$871$		−	5.41003e7i		−	2.41632i
$872$	−1.00709e6	+	361222.i	−0.0448514	+	0.0160873i
$873$		0			0
$874$	−3.88801e7	+	2.88510e7i	−1.72167	+	1.27756i
$875$	7.40947e6			0.327165
$876$		0			0
$877$	−3.78282e7			−1.66080			−0.830399	−	0.557170i	$-0.811887\pi$
$877$	−3.78282e7			−1.66080			−0.830399	+	0.557170i	$0.811887\pi$
$878$	−9.67446e6	+	7.17894e6i	−0.423536	+	0.314285i
$879$		0			0
$880$	−1.24903e6	+	1.87349e6i	−0.0543708	+	0.0815540i
$881$		−	1.64482e7i		−	0.713966i	−0.934111	−	0.356983i	$-0.883805\pi$
$881$		−	1.64482e7i		−	0.713966i	0.934111	−	0.356983i	$-0.116195\pi$
$882$		0			0
$883$		−	4.90395e6i		−	0.211663i	−0.994384	−	0.105831i	$-0.966250\pi$
$883$		−	4.90395e6i		−	0.211663i	0.994384	−	0.105831i	$-0.0337504\pi$
$884$	−2.85522e7	−	8.64511e6i	−1.22888	−	0.372083i
$885$		0			0
$886$	−2.30969e7	−	3.11258e7i	−0.988484	−	1.33210i
$887$	−2.63366e7			−1.12396			−0.561981	−	0.827150i	$-0.689960\pi$
$887$	−2.63366e7			−1.12396			−0.561981	+	0.827150i	$0.689960\pi$
$888$		0			0
$889$	7.43412e6			0.315483
$890$	1.10931e6	+	1.49492e6i	0.0469436	+	0.0632619i
$891$		0			0
$892$	2.92864e7	+	8.86742e6i	1.23241	+	0.373152i
$893$			3.92660e7i			1.64774i
$894$		0			0
$895$		−	953523.i		−	0.0397900i
$896$	8.03585e6	−	3.23288e7i	0.334396	−	1.34530i
$897$		0			0
$898$	3.30780e7	−	2.45456e7i	1.36883	−	1.01574i
$899$	8.29350e6			0.342246
$900$		0			0
$901$	1.83996e7			0.755085
$902$	−1.29396e7	+	9.60183e6i	−0.529546	+	0.392950i
$903$		0			0
$904$	−4.58239e6	−	1.27757e7i	−0.186497	−	0.519953i
$905$			289708.i			0.0117582i
$906$		0			0
$907$			4.22305e7i			1.70454i	0.523099	+	0.852272i	$0.324776\pi$
$907$			4.22305e7i			1.70454i	−0.523099	+	0.852272i	$0.675224\pi$
$908$	−4.69747e6	+	1.55143e7i	−0.189082	+	0.624480i
$909$		0			0
$910$	−3.45848e6	−	4.66070e6i	−0.138446	−	0.186573i
$911$	−1.45518e7			−0.580925			−0.290463	−	0.956886i	$-0.593809\pi$
$911$	−1.45518e7			−0.580925			−0.290463	+	0.956886i	$0.593809\pi$
$912$		0			0
$913$	−1.81430e7			−0.720331
$914$	1.23765e7	+	1.66788e7i	0.490041	+	0.660387i
$915$		0			0
$916$	−177777.	+	587143.i	−0.00700061	+	0.0231209i
$917$		−	2.65975e7i		−	1.04452i
$918$		0			0
$919$			2.00944e7i			0.784849i	0.919784	+	0.392424i	$0.128364\pi$
$919$			2.00944e7i			0.784849i	−0.919784	+	0.392424i	$0.871636\pi$
$920$	1.89829e6	+	5.29243e6i	0.0739423	+	0.206151i
$921$		0			0
$922$	−1.36843e7	+	1.01544e7i	−0.530144	+	0.393394i
$923$	−1.64097e7			−0.634009
$924$		0			0
$925$	−2.76746e6			−0.106347
$926$	−1.34884e7	+	1.00090e7i	−0.516930	+	0.383588i
$927$		0			0
$928$	−2.51218e7	+	1.26668e6i	−0.957592	+	0.0482834i
$929$		−	1.29812e7i		−	0.493486i	−0.969081	−	0.246743i	$-0.920640\pi$
$929$		−	1.29812e7i		−	0.493486i	0.969081	−	0.246743i	$-0.0793603\pi$
$930$		0			0
$931$		−	2.83570e7i		−	1.07223i
$932$	4.11858e7	+	1.24703e7i	1.55313	+	0.470260i
$933$		0			0
$934$	2.21660e7	+	2.98713e7i	0.831420	+	1.12043i
$935$	2.38559e6			0.0892415
$936$		0			0
$937$	−7.80840e6			−0.290545			−0.145272	−	0.989392i	$-0.546406\pi$
$937$	−7.80840e6			−0.290545			−0.145272	+	0.989392i	$0.546406\pi$
$938$	−3.81407e7	−	5.13991e7i	−1.41541	−	1.90743i
$939$		0			0
$940$	4.36437e6	+	1.32146e6i	0.161102	+	0.0487790i
$941$		−	1.20841e7i		−	0.444877i	−0.974947	−	0.222439i	$-0.928598\pi$
$941$		−	1.20841e7i		−	0.444877i	0.974947	−	0.222439i	$-0.0714017\pi$
$942$		0			0
$943$			4.02351e7i			1.47342i
$944$	1.39973e6	+	933176.i	0.0511226	+	0.0340827i
$945$		0			0
$946$	2.40010e6	−	1.78100e6i	0.0871970	−	0.0647046i
$947$	−3.47876e7			−1.26052			−0.630261	−	0.776384i	$-0.717052\pi$
$947$	−3.47876e7			−1.26052			−0.630261	+	0.776384i	$0.717052\pi$
$948$		0			0
$949$	2.36872e7			0.853786
$950$	2.56207e7	−	1.90119e7i	0.921048	−	0.683465i
$951$		0			0
$952$	−3.32214e7	+	1.19159e7i	−1.18803	+	0.426121i
$953$			4.27521e7i			1.52484i	0.647081	+	0.762421i	$0.275989\pi$
$953$			4.27521e7i			1.52484i	−0.647081	+	0.762421i	$0.724011\pi$
$954$		0			0
$955$			3.71476e6i			0.131802i
$956$	9.22736e6	−	3.04752e7i	0.326537	−	1.07845i
$957$		0			0
$958$	−2.17968e7	−	2.93738e7i	−0.767326	−	1.03406i
$959$	2.97746e7			1.04544
$960$		0			0
$961$	2.49814e7			0.872587
$962$	2.60201e6	+	3.50651e6i	0.0906507	+	0.122162i
$963$		0			0
$964$	2.12287e6	−	7.01122e6i	0.0735752	−	0.242997i
$965$		−	4.50714e6i		−	0.155805i
$966$		0			0
$967$			4.96089e7i			1.70606i	0.521864	+	0.853029i	$0.325237\pi$
$967$			4.96089e7i			1.70606i	−0.521864	+	0.853029i	$0.674763\pi$
$968$	−8.77545e6	+	3.14758e6i	−0.301010	+	0.107966i
$969$		0			0
$970$	−4.64101e6	+	3.44387e6i	−0.158374	+	0.117522i
$971$	3.55351e7			1.20951			0.604755	−	0.796411i	$-0.293271\pi$
$971$	3.55351e7			1.20951			0.604755	+	0.796411i	$0.293271\pi$
$972$		0			0
$973$	6.63853e7			2.24797
$974$	4.00984e7	−	2.97551e7i	1.35435	−	1.00499i
$975$		0			0
$976$	2.25678e7	+	1.50456e7i	0.758340	+	0.505574i
$977$			2.92180e7i			0.979297i	0.871920	+	0.489648i	$0.162875\pi$
$977$			2.92180e7i			0.979297i	−0.871920	+	0.489648i	$0.837125\pi$
$978$		0			0
$979$		−	1.63946e7i		−	0.546693i
$980$	−3.15185e6	−	954325.i	−0.104834	−	0.0317418i
$981$		0			0
$982$	3.91879e6	+	5.28103e6i	0.129680	+	0.174759i
$983$	1.11835e7			0.369141			0.184570	−	0.982819i	$-0.440911\pi$
$983$	1.11835e7			0.369141			0.184570	+	0.982819i	$0.440911\pi$
$984$		0			0
$985$	−334303.			−0.0109787
$986$	1.58807e7	+	2.14011e7i	0.520209	+	0.701042i
$987$		0			0
$988$	−4.81781e7	−	1.45875e7i	−1.57021	−	0.475431i
$989$		−	7.46301e6i		−	0.242618i
$990$		0			0
$991$			4.19480e6i			0.135683i	0.997696	+	0.0678417i	$0.0216113\pi$
$991$			4.19480e6i			0.135683i	−0.997696	+	0.0678417i	$0.978389\pi$
$992$	1.10493e7	−	557125.i	0.356497	−	0.0179752i
$993$		0			0
$994$	−1.55903e7	+	1.15688e7i	−0.500483	+	0.371384i
$995$	−1.69027e6			−0.0541250
$996$		0			0
$997$	−1.78454e7			−0.568575			−0.284288	−	0.958739i	$-0.591757\pi$
$997$	−1.78454e7			−0.568575			−0.284288	+	0.958739i	$0.591757\pi$
$998$	3.35718e7	−	2.49120e7i	1.06696	−	0.791738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.6.b.b.35.3	✓	8
3.2	odd	2	inner	36.6.b.b.35.6	yes	8
4.3	odd	2	inner	36.6.b.b.35.5	yes	8
8.3	odd	2		576.6.c.c.575.5		8
8.5	even	2		576.6.c.c.575.6		8
12.11	even	2	inner	36.6.b.b.35.4	yes	8
24.5	odd	2		576.6.c.c.575.4		8
24.11	even	2		576.6.c.c.575.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.b.b.35.3	✓	8	1.1	even	1	trivial
36.6.b.b.35.4	yes	8	12.11	even	2	inner
36.6.b.b.35.5	yes	8	4.3	odd	2	inner
36.6.b.b.35.6	yes	8	3.2	odd	2	inner
576.6.c.c.575.3		8	24.11	even	2
576.6.c.c.575.4		8	24.5	odd	2
576.6.c.c.575.5		8	8.3	odd	2
576.6.c.c.575.6		8	8.5	even	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	36.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.37096 - 4.54276i) q^{2} +(-9.27329 + 30.6269i) q^{4} -6.64357i q^{5} +179.715i q^{7} +(170.390 - 61.1157i) q^{8} +O(q^{10})\)	\(q+(-3.37096 - 4.54276i) q^{2} +(-9.27329 + 30.6269i) q^{4} -6.64357i q^{5} +179.715i q^{7} +(170.390 - 61.1157i) q^{8} +(-30.1801 + 22.3952i) q^{10} +330.982 q^{11} +859.304 q^{13} +(816.400 - 605.810i) q^{14} +(-852.012 - 568.024i) q^{16} +1084.90i q^{17} +1830.63i q^{19} +(203.472 + 61.6078i) q^{20} +(-1115.73 - 1503.57i) q^{22} -4675.29 q^{23} +3080.86 q^{25} +(-2896.68 - 3903.61i) q^{26} +(-5504.10 - 1666.54i) q^{28} +4342.37i q^{29} -1909.90i q^{31} +(291.703 + 5785.27i) q^{32} +(4928.44 - 3657.15i) q^{34} +1193.95 q^{35} -898.274 q^{37} +(8316.09 - 6170.96i) q^{38} +(-406.026 - 1132.00i) q^{40} -8605.90i q^{41} +1596.27i q^{43} +(-3069.29 + 10136.9i) q^{44} +(15760.2 + 21238.7i) q^{46} +21449.5 q^{47} -15490.3 q^{49} +(-10385.5 - 13995.6i) q^{50} +(-7968.57 + 26317.8i) q^{52} -16959.7i q^{53} -2198.90i q^{55} +(10983.4 + 30621.6i) q^{56} +(19726.3 - 14637.9i) q^{58} -1642.85 q^{59} -26487.6 q^{61} +(-8676.22 + 6438.20i) q^{62} +(25297.8 - 20827.0i) q^{64} -5708.85i q^{65} -62958.2i q^{67} +(-33227.1 - 10060.6i) q^{68} +(-4024.75 - 5423.81i) q^{70} -19096.4 q^{71} +27565.6 q^{73} +(3028.04 + 4080.64i) q^{74} +(-56066.4 - 16975.9i) q^{76} +59482.3i q^{77} +39826.2i q^{79} +(-3773.71 + 5660.41i) q^{80} +(-39094.5 + 29010.1i) q^{82} -54815.7 q^{83} +7207.62 q^{85} +(7251.46 - 5380.95i) q^{86} +(56396.1 - 20228.2i) q^{88} -49533.2i q^{89} +154429. i q^{91} +(43355.3 - 143189. i) q^{92} +(-72305.4 - 97439.9i) q^{94} +12161.9 q^{95} +153777. q^{97} +(52217.3 + 70368.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 44 q^{4}+O(q^{10}) \) 8 * q + 44 * q^4	\( 8 q + 44 q^{4} - 596 q^{10} + 256 q^{13} - 4216 q^{16} + 9984 q^{22} + 15192 q^{25} - 23232 q^{28} + 23236 q^{34} - 26096 q^{37} - 36104 q^{40} + 84480 q^{46} + 4664 q^{49} - 96368 q^{52} + 126964 q^{58} - 102224 q^{61} - 14608 q^{64} - 28416 q^{70} + 110848 q^{73} + 50688 q^{76} - 240308 q^{82} + 100208 q^{85} + 349056 q^{88} - 287232 q^{94} + 229888 q^{97}+O(q^{100}) \) 8 * q + 44 * q^4 - 596 * q^10 + 256 * q^13 - 4216 * q^16 + 9984 * q^22 + 15192 * q^25 - 23232 * q^28 + 23236 * q^34 - 26096 * q^37 - 36104 * q^40 + 84480 * q^46 + 4664 * q^49 - 96368 * q^52 + 126964 * q^58 - 102224 * q^61 - 14608 * q^64 - 28416 * q^70 + 110848 * q^73 + 50688 * q^76 - 240308 * q^82 + 100208 * q^85 + 349056 * q^88 - 287232 * q^94 + 229888 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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