LMFDB - Embedded newform 297.6.e.a.199.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,6,Mod(100,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("297.100");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	297.e (of order $3$, degree $2$, not 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:	$47.6339944845$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			199.21
Character	$\chi$	$=$	297.199
Dual form			297.6.e.a.100.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.74574 + 8.21986i) q^{2} +(-29.0441 + 50.3058i) q^{4} +(15.5606 - 26.9517i) q^{5} +(58.4765 + 101.284i) q^{7} -247.615 q^{8} +O(q^{10})$	\(q+(4.74574 + 8.21986i) q^{2} +(-29.0441 + 50.3058i) q^{4} +(15.5606 - 26.9517i) q^{5} +(58.4765 + 101.284i) q^{7} -247.615 q^{8} +295.386 q^{10} +(-60.5000 - 104.789i) q^{11} +(-149.253 + 258.514i) q^{13} +(-555.028 + 961.338i) q^{14} +(-245.707 - 425.578i) q^{16} -87.2532 q^{17} -1858.45 q^{19} +(903.885 + 1565.58i) q^{20} +(574.234 - 994.603i) q^{22} +(-1369.93 + 2372.79i) q^{23} +(1078.24 + 1867.56i) q^{25} -2833.26 q^{26} -6793.59 q^{28} +(280.459 + 485.769i) q^{29} +(-2163.15 + 3746.69i) q^{31} +(-1629.72 + 2822.76i) q^{32} +(-414.081 - 717.209i) q^{34} +3639.71 q^{35} -11526.9 q^{37} +(-8819.72 - 15276.2i) q^{38} +(-3853.04 + 6673.66i) q^{40} +(133.999 - 232.093i) q^{41} +(-5854.98 - 10141.1i) q^{43} +7028.67 q^{44} -26005.4 q^{46} +(2614.18 + 4527.89i) q^{47} +(1564.50 - 2709.79i) q^{49} +(-10234.1 + 17725.9i) q^{50} +(-8669.84 - 15016.6i) q^{52} +27187.6 q^{53} -3765.66 q^{55} +(-14479.7 - 25079.5i) q^{56} +(-2661.97 + 4610.66i) q^{58} +(-14730.3 + 25513.5i) q^{59} +(-23935.8 - 41458.0i) q^{61} -41063.0 q^{62} -46662.2 q^{64} +(4644.93 + 8045.25i) q^{65} +(25622.9 - 44380.1i) q^{67} +(2534.19 - 4389.34i) q^{68} +(17273.1 + 29917.9i) q^{70} -31329.4 q^{71} -22342.8 q^{73} +(-54703.5 - 94749.3i) q^{74} +(53977.0 - 93490.9i) q^{76} +(7075.66 - 12255.4i) q^{77} +(9637.31 + 16692.3i) q^{79} -15293.4 q^{80} +2543.70 q^{82} +(30197.5 + 52303.6i) q^{83} +(-1357.71 + 2351.62i) q^{85} +(55572.4 - 96254.3i) q^{86} +(14980.7 + 25947.4i) q^{88} +13191.2 q^{89} -34911.2 q^{91} +(-79576.8 - 137831. i) q^{92} +(-24812.4 + 42976.4i) q^{94} +(-28918.5 + 50088.4i) q^{95} +(64142.4 + 111098. i) q^{97} +29698.8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 320 q^{4} + 36 q^{5} + 167 q^{7} - 426 q^{8}+O(q^{10}) $ 46 * q - 320 * q^4 + 36 * q^5 + 167 * q^7 - 426 * q^8	$ 46 q - 320 q^{4} + 36 q^{5} + 167 q^{7} - 426 q^{8} - 1200 q^{10} - 2783 q^{11} + 1871 q^{13} + 1329 q^{14} - 3584 q^{16} - 534 q^{17} - 7282 q^{19} + 1917 q^{20} + 8292 q^{23} - 10049 q^{25} - 19140 q^{26} + 7586 q^{28} + 5970 q^{29} + 9542 q^{31} + 3831 q^{32} + 2982 q^{34} - 6480 q^{35} - 32014 q^{37} - 1221 q^{38} + 40635 q^{40} - 12030 q^{41} + 25943 q^{43} + 77440 q^{44} - 154008 q^{46} - 9756 q^{47} - 6990 q^{49} - 101805 q^{50} + 144446 q^{52} - 107838 q^{53} - 8712 q^{55} + 16602 q^{56} + 95367 q^{58} + 20310 q^{59} + 100247 q^{61} + 30594 q^{62} - 169154 q^{64} - 20931 q^{65} + 84956 q^{67} - 168471 q^{68} + 212292 q^{70} - 72186 q^{71} - 346888 q^{73} - 86619 q^{74} + 340334 q^{76} + 20207 q^{77} + 123113 q^{79} + 30246 q^{80} - 399966 q^{82} - 30672 q^{83} + 268335 q^{85} + 211260 q^{86} + 25773 q^{88} - 65028 q^{89} - 656042 q^{91} + 196731 q^{92} + 230262 q^{94} + 325926 q^{95} + 357002 q^{97} + 428928 q^{98}+O(q^{100}) $ 46 * q - 320 * q^4 + 36 * q^5 + 167 * q^7 - 426 * q^8 - 1200 * q^10 - 2783 * q^11 + 1871 * q^13 + 1329 * q^14 - 3584 * q^16 - 534 * q^17 - 7282 * q^19 + 1917 * q^20 + 8292 * q^23 - 10049 * q^25 - 19140 * q^26 + 7586 * q^28 + 5970 * q^29 + 9542 * q^31 + 3831 * q^32 + 2982 * q^34 - 6480 * q^35 - 32014 * q^37 - 1221 * q^38 + 40635 * q^40 - 12030 * q^41 + 25943 * q^43 + 77440 * q^44 - 154008 * q^46 - 9756 * q^47 - 6990 * q^49 - 101805 * q^50 + 144446 * q^52 - 107838 * q^53 - 8712 * q^55 + 16602 * q^56 + 95367 * q^58 + 20310 * q^59 + 100247 * q^61 + 30594 * q^62 - 169154 * q^64 - 20931 * q^65 + 84956 * q^67 - 168471 * q^68 + 212292 * q^70 - 72186 * q^71 - 346888 * q^73 - 86619 * q^74 + 340334 * q^76 + 20207 * q^77 + 123113 * q^79 + 30246 * q^80 - 399966 * q^82 - 30672 * q^83 + 268335 * q^85 + 211260 * q^86 + 25773 * q^88 - 65028 * q^89 - 656042 * q^91 + 196731 * q^92 + 230262 * q^94 + 325926 * q^95 + 357002 * q^97 + 428928 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	4.74574	+	8.21986i	0.838936	+	1.45308i	0.890785	+	0.454425i	$0.150155\pi$
$2$	4.74574	+	8.21986i	0.838936	+	1.45308i	−0.0518488	+	0.998655i	$0.516511\pi$
$3$		0			0
$3$		0			0
$4$	−29.0441	+	50.3058i	−0.907628	+	1.57206i
$5$	15.5606	−	26.9517i	0.278356	−	0.482127i	−0.692620	−	0.721302i	$-0.743544\pi$
$5$	15.5606	−	26.9517i	0.278356	−	0.482127i	0.970976	+	0.239176i	$0.0768772\pi$
$6$		0			0
$7$	58.4765	+	101.284i	0.451062	+	0.781262i	0.998452	−	0.0556151i	$-0.0177120\pi$
$7$	58.4765	+	101.284i	0.451062	+	0.781262i	−0.547390	+	0.836877i	$0.684379\pi$
$8$	−247.615			−1.36789
$9$		0			0
$10$	295.386			0.934092
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$12$		0			0
$13$	−149.253	+	258.514i	−0.244943	+	0.424254i	−0.962116	−	0.272642i	$-0.912103\pi$
$13$	−149.253	+	258.514i	−0.244943	+	0.424254i	0.717173	+	0.696896i	$0.245436\pi$
$14$	−555.028	+	961.338i	−0.756824	+	1.31086i
$15$		0			0
$16$	−245.707	−	425.578i	−0.239949	−	0.415603i
$17$	−87.2532			−0.0732249			−0.0366125	−	0.999330i	$-0.511657\pi$
$17$	−87.2532			−0.0732249			−0.0366125	+	0.999330i	$0.511657\pi$
$18$		0			0
$19$	−1858.45			−1.18105			−0.590523	−	0.807021i	$-0.701079\pi$
$19$	−1858.45			−1.18105			−0.590523	+	0.807021i	$0.701079\pi$
$20$	903.885	+	1565.58i	0.505287	+	0.875183i
$21$		0			0
$22$	574.234	−	994.603i	0.252949	−	0.438120i
$23$	−1369.93	+	2372.79i	−0.539982	+	0.935276i	0.458922	+	0.888476i	$0.348236\pi$
$23$	−1369.93	+	2372.79i	−0.539982	+	0.935276i	−0.998904	+	0.0467998i	$0.985098\pi$
$24$		0			0
$25$	1078.24	+	1867.56i	0.345036	+	0.597620i
$26$	−2833.26			−0.821966
$27$		0			0
$28$	−6793.59			−1.63759
$29$	280.459	+	485.769i	0.0619261	+	0.107259i	0.895326	−	0.445411i	$-0.146942\pi$
$29$	280.459	+	485.769i	0.0619261	+	0.107259i	−0.833400	+	0.552670i	$0.813609\pi$
$30$		0			0
$31$	−2163.15	+	3746.69i	−0.404280	+	0.700234i	−0.994237	−	0.107200i	$-0.965811\pi$
$31$	−2163.15	+	3746.69i	−0.404280	+	0.700234i	0.589957	+	0.807435i	$0.299145\pi$
$32$	−1629.72	+	2822.76i	−0.281344	+	0.487303i
$33$		0			0
$34$	−414.081	−	717.209i	−0.0614310	−	0.106402i
$35$	3639.71			0.502223
$36$		0			0
$37$	−11526.9			−1.38423			−0.692113	−	0.721789i	$-0.743320\pi$
$37$	−11526.9			−1.38423			−0.692113	+	0.721789i	$0.743320\pi$
$38$	−8819.72	−	15276.2i	−0.990822	−	1.71615i
$39$		0			0
$40$	−3853.04	+	6673.66i	−0.380762	+	0.659499i
$41$	133.999	−	232.093i	0.0124492	−	0.0215627i	−0.859734	−	0.510743i	$-0.829371\pi$
$41$	133.999	−	232.093i	0.0124492	−	0.0215627i	0.872183	+	0.489180i	$0.162704\pi$
$42$		0			0
$43$	−5854.98	−	10141.1i	−0.482897	−	0.836402i	0.516910	−	0.856039i	$-0.327082\pi$
$43$	−5854.98	−	10141.1i	−0.482897	−	0.836402i	−0.999807	+	0.0196378i	$0.993749\pi$
$44$	7028.67			0.547320
$45$		0			0
$46$	−26005.4			−1.81204
$47$	2614.18	+	4527.89i	0.172620	+	0.298986i	0.939335	−	0.343001i	$-0.111443\pi$
$47$	2614.18	+	4527.89i	0.172620	+	0.298986i	−0.766715	+	0.641987i	$0.778110\pi$
$48$		0			0
$49$	1564.50	−	2709.79i	0.0930861	−	0.161230i
$50$	−10234.1	+	17725.9i	−0.578926	+	1.00273i
$51$		0			0
$52$	−8669.84	−	15016.6i	−0.444634	−	0.770129i
$53$	27187.6			1.32948			0.664738	−	0.747076i	$-0.268543\pi$
$53$	27187.6			1.32948			0.664738	+	0.747076i	$0.268543\pi$
$54$		0			0
$55$	−3765.66			−0.167855
$56$	−14479.7	−	25079.5i	−0.617005	−	1.06868i
$57$		0			0
$58$	−2661.97	+	4610.66i	−0.103904	+	0.179967i
$59$	−14730.3	+	25513.5i	−0.550909	+	0.954203i	0.447300	+	0.894384i	$0.352386\pi$
$59$	−14730.3	+	25513.5i	−0.550909	+	0.954203i	−0.998209	+	0.0598190i	$0.980948\pi$
$60$		0			0
$61$	−23935.8	−	41458.0i	−0.823614	−	1.42654i	−0.902974	−	0.429695i	$-0.858621\pi$
$61$	−23935.8	−	41458.0i	−0.823614	−	1.42654i	0.0793603	−	0.996846i	$-0.474712\pi$
$62$	−41063.0			−1.35666
$63$		0			0
$64$	−46662.2			−1.42402
$65$	4644.93	+	8045.25i	0.136363	+	0.236187i
$66$		0			0
$67$	25622.9	−	44380.1i	0.697334	−	1.20782i	−0.272054	−	0.962282i	$-0.587703\pi$
$67$	25622.9	−	44380.1i	0.697334	−	1.20782i	0.969388	−	0.245535i	$-0.0789637\pi$
$68$	2534.19	−	4389.34i	0.0664610	−	0.115114i
$69$		0			0
$70$	17273.1	+	29917.9i	0.421333	+	0.729771i
$71$	−31329.4			−0.737574			−0.368787	−	0.929514i	$-0.620227\pi$
$71$	−31329.4			−0.737574			−0.368787	+	0.929514i	$0.620227\pi$
$72$		0			0
$73$	−22342.8			−0.490716			−0.245358	−	0.969433i	$-0.578905\pi$
$73$	−22342.8			−0.490716			−0.245358	+	0.969433i	$0.578905\pi$
$74$	−54703.5	−	94749.3i	−1.16128	−	2.01139i
$75$		0			0
$76$	53977.0	−	93490.9i	1.07195	−	1.85667i
$77$	7075.66	−	12255.4i	0.136000	−	0.235559i
$78$		0			0
$79$	9637.31	+	16692.3i	0.173735	+	0.300918i	0.939723	−	0.341937i	$-0.111083\pi$
$79$	9637.31	+	16692.3i	0.173735	+	0.300918i	−0.765988	+	0.642855i	$0.777750\pi$
$80$	−15293.4			−0.267165
$81$		0			0
$82$	2543.70			0.0417764
$83$	30197.5	+	52303.6i	0.481145	+	0.833367i	0.999766	−	0.0216370i	$-0.00688780\pi$
$83$	30197.5	+	52303.6i	0.481145	+	0.833367i	−0.518621	+	0.855004i	$0.673554\pi$
$84$		0			0
$85$	−1357.71	+	2351.62i	−0.0203826	+	0.0353037i
$86$	55572.4	−	96254.3i	0.810239	−	1.40338i
$87$		0			0
$88$	14980.7	+	25947.4i	0.206218	+	0.357180i
$89$	13191.2			0.176526			0.0882632	−	0.996097i	$-0.471868\pi$
$89$	13191.2			0.176526			0.0882632	+	0.996097i	$0.471868\pi$
$90$		0			0
$91$	−34911.2			−0.441938
$92$	−79576.8	−	137831.i	−0.980205	−	1.69777i
$93$		0			0
$94$	−24812.4	+	42976.4i	−0.289634	+	0.501661i
$95$	−28918.5	+	50088.4i	−0.328751	+	0.569414i
$96$		0			0
$97$	64142.4	+	111098.i	0.692175	+	1.19888i	0.971124	+	0.238576i	$0.0766806\pi$
$97$	64142.4	+	111098.i	0.692175	+	1.19888i	−0.278949	+	0.960306i	$0.589986\pi$
$98$	29698.8			0.312373
$99$		0			0
$100$	−125266.			−1.25266
$101$	1.05776	+	1.83209i	1.03177e−5	+	1.78707e-5i	0.866031	−	0.499991i	$-0.166663\pi$
$101$	1.05776	+	1.83209i	1.03177e−5	+	1.78707e-5i	−0.866020	+	0.500009i	$0.833330\pi$
$102$		0			0
$103$	−57024.6	+	98769.6i	−0.529626	+	0.917339i	0.469777	+	0.882785i	$0.344334\pi$
$103$	−57024.6	+	98769.6i	−0.529626	+	0.917339i	−0.999403	+	0.0345541i	$0.988999\pi$
$104$	36957.4	−	64012.0i	0.335056	−	0.580334i
$105$		0			0
$106$	129025.	+	223478.i	1.11535	+	1.93184i
$107$	159266.			1.34482			0.672410	−	0.740179i	$-0.265259\pi$
$107$	159266.			1.34482			0.672410	+	0.740179i	$0.265259\pi$
$108$		0			0
$109$	182112.			1.46815			0.734077	−	0.679066i	$-0.237615\pi$
$109$	182112.			1.46815			0.734077	+	0.679066i	$0.237615\pi$
$110$	−17870.8	−	30953.2i	−0.140820	−	0.243907i
$111$		0			0
$112$	28736.2	−	49772.6i	0.216463	−	0.374926i
$113$	−75792.4	+	131276.i	−0.558379	+	0.967141i	0.439253	+	0.898364i	$0.355243\pi$
$113$	−75792.4	+	131276.i	−0.558379	+	0.967141i	−0.997632	+	0.0687778i	$0.978090\pi$
$114$		0			0
$115$	42633.8	+	73844.0i	0.300614	+	0.520679i
$116$	−32582.7			−0.224824
$117$		0			0
$118$	−279624.			−1.84871
$119$	−5102.26	−	8837.37i	−0.0330290	−	0.0572079i
$120$		0			0
$121$	−7320.50	+	12679.5i	−0.0454545	+	0.0787296i
$122$	227186.	−	393498.i	1.38192	−	2.39355i
$123$		0			0
$124$	−125654.	−	217638.i	−0.733872	−	1.27110i
$125$	164366.			0.940883
$126$		0			0
$127$	55011.8			0.302654			0.151327	−	0.988484i	$-0.451645\pi$
$127$	55011.8			0.302654			0.151327	+	0.988484i	$0.451645\pi$
$128$	−169296.	−	293228.i	−0.913315	−	1.58191i
$129$		0			0
$130$	−44087.2	+	76361.3i	−0.228799	+	0.396292i
$131$	−92581.4	+	160356.i	−0.471352	+	0.816406i	−0.999463	−	0.0327698i	$-0.989567\pi$
$131$	−92581.4	+	160356.i	−0.471352	+	0.816406i	0.528111	+	0.849175i	$0.322901\pi$
$132$		0			0
$133$	−108676.	−	188232.i	−0.532725	−	0.922707i
$134$	486398.			2.34007
$135$		0			0
$136$	21605.2			0.100164
$137$	−112731.	−	195255.i	−0.513145	−	0.888794i	−0.999884	−	0.0152459i	$-0.995147\pi$
$137$	−112731.	−	195255.i	−0.513145	−	0.888794i	0.486739	−	0.873548i	$-0.338186\pi$
$138$		0			0
$139$	92576.1	−	160346.i	0.406407	−	0.703918i	−0.588077	−	0.808805i	$-0.700115\pi$
$139$	92576.1	−	160346.i	0.406407	−	0.703918i	0.994484	+	0.104887i	$0.0334480\pi$
$140$	−105712.	+	183099.i	−0.455832	+	0.789524i
$141$		0			0
$142$	−148681.	−	257523.i	−0.618778	−	1.07175i
$143$	36119.2			0.147706
$144$		0			0
$145$	17456.4			0.0689500
$146$	−106033.	−	183655.i	−0.411679	−	0.713050i
$147$		0			0
$148$	334787.	−	579869.i	1.25636	−	2.17608i
$149$	−164353.	+	284667.i	−0.606473	+	1.05044i	0.385344	+	0.922773i	$0.374083\pi$
$149$	−164353.	+	284667.i	−0.606473	+	1.05044i	−0.991817	+	0.127669i	$0.959250\pi$
$150$		0			0
$151$	−192850.	−	334027.i	−0.688301	−	1.19217i	−0.972387	−	0.233373i	$-0.925024\pi$
$151$	−192850.	−	334027.i	−0.688301	−	1.19217i	0.284087	−	0.958799i	$-0.408310\pi$
$152$	460181.			1.61555
$153$		0			0
$154$	134317.			0.456382
$155$	67319.8	+	116601.i	0.225068	+	0.389829i
$156$		0			0
$157$	−208036.	+	360329.i	−0.673581	+	1.16668i	0.303300	+	0.952895i	$0.401911\pi$
$157$	−208036.	+	360329.i	−0.673581	+	1.16668i	−0.976881	+	0.213782i	$0.931422\pi$
$158$	−91472.4	+	158435.i	−0.291506	+	0.504903i
$159$		0			0
$160$	50718.7	+	87847.4i	0.156628	+	0.271287i
$161$	−320435.			−0.974261
$162$		0			0
$163$	−399837.			−1.17873			−0.589365	−	0.807867i	$-0.700622\pi$
$163$	−399837.			−1.17873			−0.589365	+	0.807867i	$0.700622\pi$
$164$	7783.76	+	13481.9i	0.0225985	+	0.0391418i
$165$		0			0
$166$	−286619.	+	496439.i	−0.807300	+	1.39828i
$167$	249480.	−	432111.i	0.692219	−	1.19896i	−0.278890	−	0.960323i	$-0.589966\pi$
$167$	249480.	−	432111.i	0.692219	−	1.19896i	0.971109	−	0.238636i	$-0.0767003\pi$
$168$		0			0
$169$	141094.	+	244381.i	0.380006	+	0.658190i
$170$	−25773.3			−0.0683988
$171$		0			0
$172$	680210.			1.75316
$173$	170142.	+	294695.i	0.432211	+	0.748612i	0.997063	−	0.0765801i	$-0.0244001\pi$
$173$	170142.	+	294695.i	0.432211	+	0.748612i	−0.564852	+	0.825192i	$0.691067\pi$
$174$		0			0
$175$	−126103.	+	218417.i	−0.311265	+	0.539127i
$176$	−29730.6	+	51494.9i	−0.0723472	+	0.125309i
$177$		0			0
$178$	62602.1	+	108430.i	0.148094	+	0.256507i
$179$	−113031.			−0.263672			−0.131836	−	0.991272i	$-0.542087\pi$
$179$	−113031.			−0.263672			−0.131836	+	0.991272i	$0.542087\pi$
$180$		0			0
$181$	551735.			1.25180			0.625899	−	0.779904i	$-0.284732\pi$
$181$	551735.			1.25180			0.625899	+	0.779904i	$0.284732\pi$
$182$	−165679.	−	286965.i	−0.370758	−	0.642171i
$183$		0			0
$184$	339216.	−	587540.i	0.738639	−	1.27936i
$185$	−179365.	+	310669.i	−0.385308	+	0.667372i
$186$		0			0
$187$	5278.82	+	9143.18i	0.0110391	+	0.0191202i
$188$	−303706.			−0.626698
$189$		0			0
$190$	−548959.			−1.10321
$191$	202328.	+	350443.i	0.401304	+	0.695079i	0.993884	−	0.110433i	$-0.0352238\pi$
$191$	202328.	+	350443.i	0.401304	+	0.695079i	−0.592580	+	0.805512i	$0.701890\pi$
$192$		0			0
$193$	−385212.	+	667207.i	−0.744401	+	1.28934i	0.206074	+	0.978536i	$0.433931\pi$
$193$	−385212.	+	667207.i	−0.744401	+	1.28934i	−0.950474	+	0.310803i	$0.899402\pi$
$194$	−608806.	+	1.05448e6i	−1.16138	+	2.01157i
$195$		0			0
$196$	90878.8	+	157407.i	0.168975	+	0.292673i
$197$	49782.2			0.0913920			0.0456960	−	0.998955i	$-0.485449\pi$
$197$	49782.2			0.0913920			0.0456960	+	0.998955i	$0.485449\pi$
$198$		0			0
$199$	−184700.			−0.330624			−0.165312	−	0.986241i	$-0.552863\pi$
$199$	−184700.			−0.330624			−0.165312	+	0.986241i	$0.552863\pi$
$200$	−266988.	−	462437.i	−0.471973	−	0.817481i
$201$		0			0
$202$	−10.0397	+	17.3892i	−1.73117e−5	+	2.99848e-5i
$203$	−32800.5	+	56812.1i	−0.0558651	+	0.0967611i
$204$		0			0
$205$	−4170.20	−	7223.01i	−0.00693063	−	0.0120042i
$206$	−1.08250e6			−1.77729
$207$		0			0
$208$	146690.			0.235095
$209$	112436.	+	194745.i	0.178049	+	0.308391i
$210$		0			0
$211$	−63323.7	+	109680.i	−0.0979175	+	0.169598i	−0.910822	−	0.412798i	$-0.864551\pi$
$211$	−63323.7	+	109680.i	−0.0979175	+	0.169598i	0.812905	+	0.582396i	$0.197885\pi$
$212$	−789638.	+	1.36769e6i	−1.20667	+	2.09001i
$213$		0			0
$214$	755836.	+	1.30915e6i	1.12822	+	1.95413i
$215$	−364427.			−0.537669
$216$		0			0
$217$	−505974.			−0.729422
$218$	864255.	+	1.49693e6i	1.23169	+	2.13334i
$219$		0			0
$220$	109370.	−	189435.i	0.152350	−	0.263878i
$221$	13022.8	−	22556.2i	0.0179359	−	0.0310659i
$222$		0			0
$223$	−597713.	−	1.03527e6i	−0.804879	−	1.39409i	−0.916373	−	0.400326i	$-0.868897\pi$
$223$	−597713.	−	1.03527e6i	−0.804879	−	1.39409i	0.111494	−	0.993765i	$-0.464437\pi$
$224$	−381201.			−0.507615
$225$		0			0
$226$	−1.43876e6			−1.87378
$227$	453044.	+	784696.i	0.583547	+	1.01073i	0.995055	+	0.0993270i	$0.0316690\pi$
$227$	453044.	+	784696.i	0.583547	+	1.01073i	−0.411508	+	0.911406i	$0.634998\pi$
$228$		0			0
$229$	696081.	−	1.20565e6i	0.877145	−	1.51926i	0.0226839	−	0.999743i	$-0.492779\pi$
$229$	696081.	−	1.20565e6i	0.877145	−	1.51926i	0.854461	−	0.519516i	$-0.173888\pi$
$230$	−404658.	+	700889.i	−0.504393	+	0.873634i
$231$		0			0
$232$	−69445.9	−	120284.i	−0.0847084	−	0.146719i
$233$	1.21924e6			1.47129			0.735646	−	0.677366i	$-0.236879\pi$
$233$	1.21924e6			1.47129			0.735646	+	0.677366i	$0.236879\pi$
$234$		0			0
$235$	162712.			0.192199
$236$	−855654.	−	1.48204e6i	−1.00004	−	1.73212i
$237$		0			0
$238$	48428.0	−	83879.7i	0.0554184	−	0.0959875i
$239$	−687768.	+	1.19125e6i	−0.778838	+	1.34899i	0.153774	+	0.988106i	$0.450857\pi$
$239$	−687768.	+	1.19125e6i	−0.778838	+	1.34899i	−0.932612	+	0.360881i	$0.882476\pi$
$240$		0			0
$241$	778733.	+	1.34881e6i	0.863667	+	1.49591i	0.868365	+	0.495926i	$0.165171\pi$
$241$	778733.	+	1.34881e6i	0.863667	+	1.49591i	−0.00469818	+	0.999989i	$0.501495\pi$
$242$	−138965.			−0.152534
$243$		0			0
$244$	2.78078e6			2.99014
$245$	−48689.0	−	84331.8i	−0.0518221	−	0.0897586i
$246$		0			0
$247$	277379.	−	480435.i	0.289289	−	0.501063i
$248$	535630.	−	927738.i	0.553013	−	0.957847i
$249$		0			0
$250$	780036.	+	1.35106e6i	0.789341	+	1.36718i
$251$	424702.			0.425501			0.212750	−	0.977107i	$-0.431758\pi$
$251$	424702.			0.425501			0.212750	+	0.977107i	$0.431758\pi$
$252$		0			0
$253$	331523.			0.325621
$254$	261072.	+	452189.i	0.253907	+	0.439781i
$255$		0			0
$256$	860270.	−	1.49003e6i	0.820417	−	1.42100i
$257$	970847.	−	1.68156e6i	0.916891	−	1.58810i	0.112783	−	0.993620i	$-0.464024\pi$
$257$	970847.	−	1.68156e6i	0.916891	−	1.58810i	0.804109	−	0.594482i	$-0.202643\pi$
$258$		0			0
$259$	−674051.	−	1.16749e6i	−0.624372	−	1.08144i
$260$	−539631.			−0.495066
$261$		0			0
$262$	−1.75747e6			−1.58174
$263$	813444.	+	1.40893e6i	0.725167	+	1.25603i	0.958905	+	0.283727i	$0.0915709\pi$
$263$	813444.	+	1.40893e6i	0.725167	+	1.25603i	−0.233738	+	0.972300i	$0.575096\pi$
$264$		0			0
$265$	423054.	−	732751.i	0.370068	−	0.640976i
$266$	1.03149e6	−	1.78660e6i	0.893845	−	1.54818i
$267$		0			0
$268$	1.48839e6	+	2.57796e6i	1.26584	+	2.19250i
$269$	1.87130e6			1.57675			0.788374	−	0.615197i	$-0.210923\pi$
$269$	1.87130e6			1.57675			0.788374	+	0.615197i	$0.210923\pi$
$270$		0			0
$271$	−958076.			−0.792459			−0.396229	−	0.918152i	$-0.629681\pi$
$271$	−958076.			−0.792459			−0.396229	+	0.918152i	$0.629681\pi$
$272$	21438.7	+	37133.0i	0.0175702	+	0.0304325i
$273$		0			0
$274$	1.06998e6	−	1.85326e6i	0.860992	−	1.49128i
$275$	130467.	−	225975.i	0.104032	−	0.180189i
$276$		0			0
$277$	381353.	+	660522.i	0.298626	+	0.517235i	0.975822	−	0.218568i	$-0.0701384\pi$
$277$	381353.	+	660522.i	0.298626	+	0.517235i	−0.677196	+	0.735803i	$0.736805\pi$
$278$	1.75737e6			1.36380
$279$		0			0
$280$	−901249.			−0.686989
$281$	191110.	+	331013.i	0.144384	+	0.250080i	0.929143	−	0.369721i	$-0.120547\pi$
$281$	191110.	+	331013.i	0.144384	+	0.250080i	−0.784759	+	0.619801i	$0.787213\pi$
$282$		0			0
$283$	−760030.	+	1.31641e6i	−0.564111	+	0.977069i	0.433021	+	0.901384i	$0.357448\pi$
$283$	−760030.	+	1.31641e6i	−0.564111	+	0.977069i	−0.997132	+	0.0756851i	$0.975886\pi$
$284$	909933.	−	1.57605e6i	0.669443	−	1.15951i
$285$		0			0
$286$	171413.	+	296895.i	0.123916	+	0.214629i
$287$	31343.2			0.0224615
$288$		0			0
$289$	−1.41224e6			−0.994638
$290$	82843.5	+	143489.i	0.0578447	+	0.100190i
$291$		0			0
$292$	648926.	−	1.12397e6i	0.445387	−	0.771434i
$293$	510376.	−	883997.i	0.347313	−	0.601564i	−0.638458	−	0.769657i	$-0.720427\pi$
$293$	510376.	−	883997.i	0.347313	−	0.601564i	0.985771	+	0.168093i	$0.0537608\pi$
$294$		0			0
$295$	458422.	+	794011.i	0.306698	+	0.531216i
$296$	2.85423e6			1.89348
$297$		0			0
$298$	−3.11990e6			−2.03517
$299$	−408933.	−	708293.i	−0.264530	−	0.458179i
$300$		0			0
$301$	684757.	−	1.18603e6i	0.435633	−	0.754538i
$302$	1.83044e6	−	3.17041e6i	1.15488	−	2.00031i
$303$		0			0
$304$	456635.	+	790915.i	0.283390	+	0.490847i
$305$	−1.48982e6			−0.917031
$306$		0			0
$307$	1.79624e6			1.08772			0.543861	−	0.839175i	$-0.316962\pi$
$307$	1.79624e6			1.08772			0.543861	+	0.839175i	$0.316962\pi$
$308$	411012.	+	711894.i	0.246875	+	0.427601i
$309$		0			0
$310$	−638964.	+	1.10672e6i	−0.377635	+	0.654083i
$311$	812523.	−	1.40733e6i	0.476359	−	0.825079i	−0.523274	−	0.852165i	$-0.675289\pi$
$311$	812523.	−	1.40733e6i	0.476359	−	0.825079i	0.999633	+	0.0270859i	$0.00862278\pi$
$312$		0			0
$313$	661468.	+	1.14570e6i	0.381635	+	0.661011i	0.991296	−	0.131651i	$-0.0420278\pi$
$313$	661468.	+	1.14570e6i	0.381635	+	0.661011i	−0.609661	+	0.792662i	$0.708695\pi$
$314$	−3.94914e6			−2.26037
$315$		0			0
$316$	−1.11963e6			−0.630748
$317$	−29078.1	−	50364.7i	−0.0162524	−	0.0281500i	0.857785	−	0.514009i	$-0.171840\pi$
$317$	−29078.1	−	50364.7i	−0.0162524	−	0.0281500i	−0.874037	+	0.485859i	$0.838507\pi$
$318$		0			0
$319$	33935.5	−	58778.0i	0.0186714	−	0.0323399i
$320$	−726090.	+	1.25763e6i	−0.396384	+	0.686556i
$321$		0			0
$322$	−1.52070e6	−	2.63393e6i	−0.817343	−	1.41568i
$323$	162156.			0.0864820
$324$		0			0
$325$	−643721.			−0.338056
$326$	−1.89752e6	−	3.28661e6i	−0.988879	−	1.71279i
$327$		0			0
$328$	−33180.2	+	57469.9i	−0.0170292	+	0.0294955i
$329$	−305736.	+	529550.i	−0.155724	+	0.269723i
$330$		0			0
$331$	316376.	+	547979.i	0.158721	+	0.274912i	0.934408	−	0.356206i	$-0.115930\pi$
$331$	316376.	+	547979.i	0.158721	+	0.274912i	−0.775687	+	0.631118i	$0.782596\pi$
$332$	−3.50824e6			−1.74680
$333$		0			0
$334$	4.73586e6			2.32291
$335$	−797413.	−	1.38116e6i	−0.388214	−	0.672406i
$336$		0			0
$337$	903126.	−	1.56426e6i	0.433185	−	0.750299i	−0.563960	−	0.825802i	$-0.690723\pi$
$337$	903126.	−	1.56426e6i	0.433185	−	0.750299i	0.997146	+	0.0755030i	$0.0240562\pi$
$338$	−1.33919e6	+	2.31954e6i	−0.637601	+	1.10436i
$339$		0			0
$340$	−78866.9	−	136601.i	−0.0369996	−	0.0640852i
$341$	523483.			0.243790
$342$		0			0
$343$	2.33157e6			1.07007
$344$	1.44978e6	+	2.51110e6i	0.660552	+	1.14411i
$345$		0			0
$346$	−1.61490e6	+	2.79709e6i	−0.725196	+	1.25608i
$347$	−7106.83	+	12309.4i	−0.00316849	+	0.00548799i	−0.867605	−	0.497253i	$-0.834342\pi$
$347$	−7106.83	+	12309.4i	−0.00316849	+	0.00548799i	0.864437	+	0.502741i	$0.167675\pi$
$348$		0			0
$349$	2.08151e6	+	3.60529e6i	0.914778	+	1.58444i	0.807225	+	0.590243i	$0.200968\pi$
$349$	2.08151e6	+	3.60529e6i	0.914778	+	1.58444i	0.107553	+	0.994199i	$0.465698\pi$
$350$	−2.39381e6			−1.04453
$351$		0			0
$352$	394392.			0.169657
$353$	−317997.	−	550787.i	−0.135827	−	0.235259i	0.790086	−	0.612996i	$-0.210036\pi$
$353$	−317997.	−	550787.i	−0.135827	−	0.235259i	−0.925913	+	0.377737i	$0.876703\pi$
$354$		0			0
$355$	−487503.	+	844380.i	−0.205308	+	0.355604i
$356$	−383127.	+	663595.i	−0.160220	+	0.277510i
$357$		0			0
$358$	−536414.	−	929096.i	−0.221204	−	0.383136i
$359$	−1.10106e6			−0.450896			−0.225448	−	0.974255i	$-0.572385\pi$
$359$	−1.10106e6			−0.450896			−0.225448	+	0.974255i	$0.572385\pi$
$360$		0			0
$361$	977737.			0.394870
$362$	2.61839e6	+	4.53519e6i	1.05018	+	1.81896i
$363$		0			0
$364$	1.01396e6	−	1.75624e6i	0.401115	−	0.694752i
$365$	−347667.	+	602176.i	−0.136594	+	0.236587i
$366$		0			0
$367$	−681743.	−	1.18081e6i	−0.264214	−	0.457632i	0.703143	−	0.711048i	$-0.251779\pi$
$367$	−681743.	−	1.18081e6i	−0.264214	−	0.457632i	−0.967357	+	0.253416i	$0.918446\pi$
$368$	1.34641e6			0.518272
$369$		0			0
$370$	−3.40487e6			−1.29299
$371$	1.58983e6	+	2.75367e6i	0.599676	+	1.03867i
$372$		0			0
$373$	1.28736e6	−	2.22977e6i	0.479101	−	0.829828i	−0.520611	−	0.853794i	$-0.674296\pi$
$373$	1.28736e6	−	2.22977e6i	0.479101	−	0.829828i	0.999713	+	0.0239657i	$0.00762925\pi$
$374$	−50103.8	+	86782.3i	−0.0185222	+	0.0320813i
$375$		0			0
$376$	−647311.	−	1.12118e6i	−0.236126	−	0.408982i
$377$	−167437.			−0.0606735
$378$		0			0
$379$	−4.33929e6			−1.55174			−0.775872	−	0.630890i	$-0.782690\pi$
$379$	−4.33929e6			−1.55174			−0.775872	+	0.630890i	$0.782690\pi$
$380$	−1.67983e6	−	2.90954e6i	−0.596767	−	1.03363i
$381$		0			0
$382$	−1.92040e6	+	3.32622e6i	−0.673337	+	1.16625i
$383$	537915.	−	931696.i	0.187377	−	0.324547i	−0.756998	−	0.653417i	$-0.773335\pi$
$383$	537915.	−	931696.i	0.187377	−	0.324547i	0.944375	+	0.328871i	$0.106668\pi$
$384$		0			0
$385$	−220203.	−	381402.i	−0.0757130	−	0.131139i
$386$	−7.31247e6			−2.49802
$387$		0			0
$388$	−7.45183e6			−2.51295
$389$	1.69091e6	+	2.92874e6i	0.566561	+	0.981312i	0.996903	+	0.0786463i	$0.0250598\pi$
$389$	1.69091e6	+	2.92874e6i	0.566561	+	0.981312i	−0.430342	+	0.902666i	$0.641607\pi$
$390$		0			0
$391$	119531.	−	207034.i	0.0395401	−	0.0684855i
$392$	−387394.	+	670986.i	−0.127332	+	0.220545i
$393$		0			0
$394$	236253.	+	409203.i	0.0766721	+	0.132800i
$395$	599848.			0.193441
$396$		0			0
$397$	380497.			0.121164			0.0605822	−	0.998163i	$-0.480704\pi$
$397$	380497.			0.121164			0.0605822	+	0.998163i	$0.480704\pi$
$398$	−876537.	−	1.51821e6i	−0.277372	−	0.480423i
$399$		0			0
$400$	529862.	−	917747.i	0.165582	−	0.286796i
$401$	2.37569e6	−	4.11482e6i	0.737785	−	1.27788i	−0.215706	−	0.976458i	$-0.569205\pi$
$401$	2.37569e6	−	4.11482e6i	0.737785	−	1.27788i	0.953491	−	0.301422i	$-0.0974614\pi$
$402$		0			0
$403$	−645714.	−	1.11841e6i	−0.198051	−	0.343035i
$404$	−122.886			−3.74584e−5
$405$		0			0
$406$	−622650.			−0.187469
$407$	697375.	+	1.20789e6i	0.208680	+	0.361444i
$408$		0			0
$409$	110537.	−	191455.i	0.0326737	−	0.0565926i	−0.849226	−	0.528029i	$-0.822931\pi$
$409$	110537.	−	191455.i	0.0326737	−	0.0565926i	0.881900	+	0.471437i	$0.156264\pi$
$410$	39581.4	−	68557.0i	0.0116287	−	0.0201415i
$411$		0			0
$412$	−3.31246e6	−	5.73734e6i	−0.961407	−	1.66521i
$413$	−3.44549e6			−0.993977
$414$		0			0
$415$	1.87956e6			0.535718
$416$	−486481.	−	842610.i	−0.137827	−	0.238723i
$417$		0			0
$418$	−1.06719e6	+	1.84842e6i	−0.298744	+	0.517440i
$419$	3.41745e6	−	5.91919e6i	0.950970	−	1.64713i	0.207637	−	0.978206i	$-0.433423\pi$
$419$	3.41745e6	−	5.91919e6i	0.950970	−	1.64713i	0.743333	−	0.668922i	$-0.233244\pi$
$420$		0			0
$421$	−1.41716e6	−	2.45459e6i	−0.389684	−	0.674953i	0.602723	−	0.797951i	$-0.294082\pi$
$421$	−1.41716e6	−	2.45459e6i	−0.389684	−	0.674953i	−0.992407	+	0.122998i	$0.960749\pi$
$422$	−1.20207e6			−0.328586
$423$		0			0
$424$	−6.73206e6			−1.81858
$425$	−94079.6	−	162951.i	−0.0252652	−	0.0437607i
$426$		0			0
$427$	2.79937e6	−	4.84864e6i	0.743002	−	1.28692i
$428$	−4.62574e6	+	8.01202e6i	−1.22060	+	2.11413i
$429$		0			0
$430$	−1.72948e6	−	2.99554e6i	−0.451070	−	0.781276i
$431$	−3.76956e6			−0.977458			−0.488729	−	0.872436i	$-0.662539\pi$
$431$	−3.76956e6			−0.977458			−0.488729	+	0.872436i	$0.662539\pi$
$432$		0			0
$433$	3.72282e6			0.954229			0.477114	−	0.878841i	$-0.341683\pi$
$433$	3.72282e6			0.954229			0.477114	+	0.878841i	$0.341683\pi$
$434$	−2.40122e6	−	4.15904e6i	−0.611939	−	1.05991i
$435$		0			0
$436$	−5.28927e6	+	9.16128e6i	−1.33254	+	2.30802i
$437$	2.54595e6	−	4.40971e6i	0.637744	−	1.10460i
$438$		0			0
$439$	969399.	+	1.67905e6i	0.240072	+	0.415817i	0.960735	−	0.277469i	$-0.0894957\pi$
$439$	969399.	+	1.67905e6i	0.240072	+	0.415817i	−0.720663	+	0.693286i	$0.756162\pi$
$440$	932435.			0.229608
$441$		0			0
$442$	247211.			0.0601884
$443$	−1.43061e6	−	2.47789e6i	−0.346348	−	0.599892i	0.639250	−	0.768999i	$-0.279245\pi$
$443$	−1.43061e6	−	2.47789e6i	−0.346348	−	0.599892i	−0.985598	+	0.169107i	$0.945912\pi$
$444$		0			0
$445$	205263.	−	355526.i	0.0491372	−	0.0851081i
$446$	5.67318e6	−	9.82624e6i	1.35048	−	2.33911i
$447$		0			0
$448$	−2.72864e6	−	4.72614e6i	−0.642320	−	1.11253i
$449$	−5.25146e6			−1.22932			−0.614659	−	0.788793i	$-0.710706\pi$
$449$	−5.25146e6			−1.22932			−0.614659	+	0.788793i	$0.710706\pi$
$450$		0			0
$451$	−32427.8			−0.00750716
$452$	−4.40264e6	−	7.62560e6i	−1.01360	−	1.75561i
$453$		0			0
$454$	−4.30006e6	+	7.44792e6i	−0.979118	+	1.69588i
$455$	−543238.	+	940916.i	−0.123016	+	0.213070i
$456$		0			0
$457$	−3.88607e6	−	6.73087e6i	−0.870402	−	1.50758i	−0.861581	−	0.507620i	$-0.830525\pi$
$457$	−3.88607e6	−	6.73087e6i	−0.870402	−	1.50758i	−0.00882127	−	0.999961i	$-0.502808\pi$
$458$	1.32137e7			2.94347
$459$		0			0
$460$	−4.95304e6			−1.09138
$461$	−1.76796e6	−	3.06219e6i	−0.387453	−	0.671089i	0.604653	−	0.796489i	$-0.293312\pi$
$461$	−1.76796e6	−	3.06219e6i	−0.387453	−	0.671089i	−0.992106	+	0.125400i	$0.959978\pi$
$462$		0			0
$463$	863078.	−	1.49489e6i	0.187110	−	0.324084i	−0.757175	−	0.653212i	$-0.773421\pi$
$463$	863078.	−	1.49489e6i	0.187110	−	0.324084i	0.944286	+	0.329127i	$0.106755\pi$
$464$	137822.	−	238714.i	0.0297182	−	0.0514734i
$465$		0			0
$466$	5.78619e6	+	1.00220e7i	1.23432	+	2.13791i
$467$	1.55045e6			0.328976			0.164488	−	0.986379i	$-0.447403\pi$
$467$	1.55045e6			0.328976			0.164488	+	0.986379i	$0.447403\pi$
$468$		0			0
$469$	5.99334e6			1.25816
$470$	772191.	+	1.33747e6i	0.161243	+	0.279281i
$471$		0			0
$472$	3.64744e6	−	6.31755e6i	0.753586	−	1.30525i
$473$	−708453.	+	1.22708e6i	−0.145599	+	0.252185i
$474$		0			0
$475$	−2.00385e6	−	3.47077e6i	−0.407503	−	0.705816i
$476$	592762.			0.119912
$477$		0			0
$478$	−1.30559e7			−2.61358
$479$	4.67069e6	+	8.08988e6i	0.930128	+	1.61103i	0.783100	+	0.621896i	$0.213637\pi$
$479$	4.67069e6	+	8.08988e6i	0.930128	+	1.61103i	0.147028	+	0.989132i	$0.453029\pi$
$480$		0			0
$481$	1.72042e6	−	2.97985e6i	0.339056	−	0.587263i
$482$	−7.39133e6	+	1.28022e7i	−1.44912	+	2.50995i
$483$		0			0
$484$	−425235.	−	736528.i	−0.0825116	−	0.142914i
$485$	3.99237e6			0.770684
$486$		0			0
$487$	4.95555e6			0.946825			0.473412	−	0.880841i	$-0.343022\pi$
$487$	4.95555e6			0.946825			0.473412	+	0.880841i	$0.343022\pi$
$488$	5.92688e6	+	1.02657e7i	1.12662	+	1.95136i
$489$		0			0
$490$	462130.	−	800433.i	0.0869509	−	0.150603i
$491$	−1.66607e6	+	2.88571e6i	−0.311881	+	0.540194i	−0.978770	−	0.204964i	$-0.934292\pi$
$491$	−1.66607e6	+	2.88571e6i	−0.311881	+	0.540194i	0.666889	+	0.745157i	$0.267626\pi$
$492$		0			0
$493$	−24470.9	−	42384.9i	−0.00453454	−	0.00785405i
$494$	5.26548e6			0.970780
$495$		0			0
$496$	2.12601e6			0.388026
$497$	−1.83203e6	−	3.17317e6i	−0.332692	−	0.576239i
$498$		0			0
$499$	859488.	−	1.48868e6i	0.154521	−	0.267639i	−0.778363	−	0.627814i	$-0.783950\pi$
$499$	859488.	−	1.48868e6i	0.154521	−	0.267639i	0.932885	+	0.360175i	$0.117283\pi$
$500$	−4.77385e6	+	8.26855e6i	−0.853972	+	1.47912i
$501$		0			0
$502$	2.01553e6	+	3.49099e6i	0.356968	+	0.618287i
$503$	7.42097e6			1.30780			0.653899	−	0.756582i	$-0.273132\pi$
$503$	7.42097e6			1.30780			0.653899	+	0.756582i	$0.273132\pi$
$504$		0			0
$505$	65.8371			1.14879e−5
$506$	1.57332e6	+	2.72508e6i	0.273176	+	0.473154i
$507$		0			0
$508$	−1.59777e6	+	2.76741e6i	−0.274697	+	0.475790i
$509$	700378.	−	1.21309e6i	0.119822	−	0.207538i	−0.799875	−	0.600167i	$-0.795101\pi$
$509$	700378.	−	1.21309e6i	0.119822	−	0.207538i	0.919697	+	0.392628i	$0.128434\pi$
$510$		0			0
$511$	−1.30653e6	−	2.26297e6i	−0.221343	−	0.383378i
$512$	5.49556e6			0.926482
$513$		0			0
$514$	1.84295e7			3.07685
$515$	1.77467e6	+	3.07382e6i	0.294849	+	0.510694i
$516$		0			0
$517$	316316.	−	547875.i	0.0520468	−	0.0901478i
$518$	6.39774e6	−	1.10812e7i	1.04762	−	1.81452i
$519$		0			0
$520$	−1.15016e6	−	1.99213e6i	−0.186530	−	0.323079i
$521$	−1.13783e7			−1.83646			−0.918232	−	0.396043i	$-0.870383\pi$
$521$	−1.13783e7			−1.83646			−0.918232	+	0.396043i	$0.870383\pi$
$522$		0			0
$523$	2.86097e6			0.457362			0.228681	−	0.973501i	$-0.426559\pi$
$523$	2.86097e6			0.457362			0.228681	+	0.973501i	$0.426559\pi$
$524$	−5.37788e6	−	9.31477e6i	−0.855624	−	1.48198i
$525$		0			0
$526$	−7.72079e6	+	1.33728e7i	−1.21674	+	2.10745i
$527$	188742.	−	326910.i	0.0296034	−	0.0512746i
$528$		0			0
$529$	−535253.	−	927086.i	−0.0831611	−	0.144039i
$530$	8.03082e6			1.24185
$531$		0			0
$532$	1.26255e7			1.93406
$533$	39999.5	+	69281.2i	0.00609870	+	0.0105633i
$534$		0			0
$535$	2.47827e6	−	4.29250e6i	0.374339	−	0.648374i
$536$	−6.34461e6	+	1.09892e7i	−0.953879	+	1.65217i
$537$		0			0
$538$	8.88069e6	+	1.53818e7i	1.32279	+	2.29114i
$539$	−378609.			−0.0561330
$540$		0			0
$541$	−3.17181e6			−0.465923			−0.232962	−	0.972486i	$-0.574842\pi$
$541$	−3.17181e6			−0.465923			−0.232962	+	0.972486i	$0.574842\pi$
$542$	−4.54678e6	−	7.87525e6i	−0.664822	−	1.15151i
$543$		0			0
$544$	142198.	−	246295.i	0.0206014	−	0.0356827i
$545$	2.83376e6	−	4.90822e6i	0.408669	−	0.707836i
$546$		0			0
$547$	697869.	+	1.20875e6i	0.0997254	+	0.172729i	0.911571	−	0.411143i	$-0.134870\pi$
$547$	697869.	+	1.20875e6i	0.0997254	+	0.172729i	−0.811846	+	0.583872i	$0.801537\pi$
$548$	1.30966e7			1.86298
$549$		0			0
$550$	2.47664e6			0.349106
$551$	−521219.	−	902777.i	−0.0731376	−	0.126678i
$552$		0			0
$553$	−1.12711e6	+	1.95222e6i	−0.156731	+	0.271466i
$554$	−3.61960e6	+	6.26933e6i	−0.501056	+	0.867854i
$555$		0			0
$556$	5.37757e6	+	9.31423e6i	0.737733	+	1.27779i
$557$	2.06079e6			0.281446			0.140723	−	0.990049i	$-0.455057\pi$
$557$	2.06079e6			0.281446			0.140723	+	0.990049i	$0.455057\pi$
$558$		0			0
$559$	3.49549e6			0.473129
$560$	−894304.	−	1.54898e6i	−0.120508	−	0.208726i
$561$		0			0
$562$	−1.81392e6	+	3.14180e6i	−0.242258	+	0.419602i
$563$	−4.71929e6	+	8.17405e6i	−0.627488	+	1.08684i	0.360566	+	0.932734i	$0.382584\pi$
$563$	−4.71929e6	+	8.17405e6i	−0.627488	+	1.08684i	−0.988054	+	0.154108i	$0.950750\pi$
$564$		0			0
$565$	2.35874e6	+	4.08547e6i	0.310856	+	0.538419i
$566$	−1.44276e7			−1.89301
$567$		0			0
$568$	7.75763e6			1.00892
$569$	−1.46618e6	−	2.53950e6i	−0.189848	−	0.328826i	0.755351	−	0.655320i	$-0.227466\pi$
$569$	−1.46618e6	−	2.53950e6i	−0.189848	−	0.328826i	−0.945199	+	0.326494i	$0.894133\pi$
$570$		0			0
$571$	1.76660e6	−	3.05983e6i	0.226750	−	0.392742i	−0.730093	−	0.683348i	$-0.760523\pi$
$571$	1.76660e6	−	3.05983e6i	0.226750	−	0.392742i	0.956843	+	0.290605i	$0.0938567\pi$
$572$	−1.04905e6	+	1.81701e6i	−0.134062	+	0.232203i
$573$		0			0
$574$	148747.	+	257637.i	0.0188438	+	0.0326383i
$575$	−5.90844e6			−0.745253
$576$		0			0
$577$	−9.20959e6			−1.15160			−0.575799	−	0.817592i	$-0.695309\pi$
$577$	−9.20959e6			−1.15160			−0.575799	+	0.817592i	$0.695309\pi$
$578$	−6.70214e6	−	1.16085e7i	−0.834438	−	1.44529i
$579$		0			0
$580$	−507005.	+	878159.i	−0.0625810	+	0.108393i
$581$	−3.53169e6	+	6.11706e6i	−0.434052	+	0.751801i
$582$		0			0
$583$	−1.64485e6	−	2.84896e6i	−0.200426	−	0.347148i
$584$	5.53242e6			0.671248
$585$		0			0
$586$	9.68845e6			1.16549
$587$	7.22910e6	+	1.25212e7i	0.865942	+	1.49986i	0.866109	+	0.499856i	$0.166614\pi$
$587$	7.22910e6	+	1.25212e7i	0.865942	+	1.49986i	−0.000166445		1.00000i	$0.500053\pi$
$588$		0			0
$589$	4.02011e6	−	6.96303e6i	0.477474	−	0.827009i
$590$	−4.35111e6	+	7.53634e6i	−0.514600	+	0.891313i
$591$		0			0
$592$	2.83224e6	+	4.90558e6i	0.332143	+	0.575289i
$593$	1.39039e7			1.62367			0.811837	−	0.583884i	$-0.198468\pi$
$593$	1.39039e7			1.62367			0.811837	+	0.583884i	$0.198468\pi$
$594$		0			0
$595$	−317576.			−0.0367753
$596$	−9.54696e6	−	1.65358e7i	−1.10090	−	1.90682i
$597$		0			0
$598$	3.88138e6	−	6.72274e6i	0.443847	−	0.768765i
$599$	4.52512e6	−	7.83774e6i	0.515304	−	0.892532i	−0.484538	−	0.874770i	$-0.661012\pi$
$599$	4.52512e6	−	7.83774e6i	0.515304	−	0.892532i	0.999842	−	0.0177624i	$-0.00565426\pi$
$600$		0			0
$601$	7.64713e6	+	1.32452e7i	0.863599	+	1.49580i	0.868431	+	0.495810i	$0.165129\pi$
$601$	7.64713e6	+	1.32452e7i	0.863599	+	1.49580i	−0.00483191	+	0.999988i	$0.501538\pi$
$602$	1.29987e7			1.46187
$603$		0			0
$604$	2.24047e7			2.49888
$605$	227822.	+	394600.i	0.0253051	+	0.0438297i
$606$		0			0
$607$	1.60479e6	−	2.77958e6i	0.176786	−	0.306202i	−0.763992	−	0.645226i	$-0.776763\pi$
$607$	1.60479e6	−	2.77958e6i	0.176786	−	0.306202i	0.940778	+	0.339024i	$0.110097\pi$
$608$	3.02875e6	−	5.24595e6i	0.332281	−	0.575527i
$609$		0			0
$610$	−7.07030e6	−	1.22461e7i	−0.769331	−	1.33252i
$611$	−1.56070e6			−0.169128
$612$		0			0
$613$	1.25901e6			0.135325			0.0676625	−	0.997708i	$-0.478446\pi$
$613$	1.25901e6			0.135325			0.0676625	+	0.997708i	$0.478446\pi$
$614$	8.52448e6	+	1.47648e7i	0.912529	+	1.58055i
$615$		0			0
$616$	−1.75204e6	+	3.03462e6i	−0.186034	+	0.322221i
$617$	1.50348e6	−	2.60410e6i	0.158996	−	0.275388i	−0.775511	−	0.631334i	$-0.782508\pi$
$617$	1.50348e6	−	2.60410e6i	0.158996	−	0.275388i	0.934507	+	0.355946i	$0.115841\pi$
$618$		0			0
$619$	2.37067e6	+	4.10613e6i	0.248682	+	0.430731i	0.963161	−	0.268927i	$-0.0866691\pi$
$619$	2.37067e6	+	4.10613e6i	0.248682	+	0.430731i	−0.714478	+	0.699658i	$0.753336\pi$
$620$	−7.82096e6			−0.817111
$621$		0			0
$622$	1.54241e7			1.59854
$623$	771376.	+	1.33606e6i	0.0796244	+	0.137913i
$624$		0			0
$625$	−811870.	+	1.40620e6i	−0.0831355	+	0.143995i
$626$	−6.27831e6	+	1.08744e7i	−0.640335	+	1.10909i
$627$		0			0
$628$	−1.20844e7	−	2.09309e7i	−1.22272	−	2.11782i
$629$	1.00576e6			0.101360
$630$		0			0
$631$	−1.87105e7			−1.87074			−0.935369	−	0.353673i	$-0.884932\pi$
$631$	−1.87105e7			−1.87074			−0.935369	+	0.353673i	$0.884932\pi$
$632$	−2.38635e6	−	4.13327e6i	−0.237652	−	0.411625i
$633$		0			0
$634$	275994.	−	478035.i	0.0272694	−	0.0472321i
$635$	856015.	−	1.48266e6i	0.0842456	−	0.145918i
$636$		0			0
$637$	467012.	+	808889.i	0.0456016	+	0.0789842i
$638$	644196.			0.0626566
$639$		0			0
$640$	−1.05373e7			−1.01691
$641$	−1.65985e6	−	2.87495e6i	−0.159560	−	0.276367i	0.775150	−	0.631777i	$-0.217674\pi$
$641$	−1.65985e6	−	2.87495e6i	−0.159560	−	0.276367i	−0.934710	+	0.355411i	$0.884341\pi$
$642$		0			0
$643$	−2.28458e6	+	3.95700e6i	−0.217911	+	0.377432i	−0.954169	−	0.299268i	$-0.903257\pi$
$643$	−2.28458e6	+	3.95700e6i	−0.217911	+	0.377432i	0.736258	+	0.676700i	$0.236591\pi$
$644$	9.30675e6	−	1.61198e7i	0.884267	−	1.53160i
$645$		0			0
$646$	769548.	+	1.33290e6i	0.0725529	+	0.125665i
$647$	4.49477e6			0.422130			0.211065	−	0.977472i	$-0.432307\pi$
$647$	4.49477e6			0.422130			0.211065	+	0.977472i	$0.432307\pi$
$648$		0			0
$649$	3.56472e6			0.332211
$650$	−3.05493e6	−	5.29130e6i	−0.283608	−	0.491223i
$651$		0			0
$652$	1.16129e7	−	2.01141e7i	1.06985	−	1.85303i
$653$	8.09599e6	−	1.40227e7i	0.742997	−	1.28691i	−0.208128	−	0.978102i	$-0.566737\pi$
$653$	8.09599e6	−	1.40227e7i	0.742997	−	1.28691i	0.951125	−	0.308807i	$-0.0999296\pi$
$654$		0			0
$655$	2.88124e6	+	4.99045e6i	0.262407	+	0.454503i
$656$	−131698.			−0.0119487
$657$		0			0
$658$	−5.80378e6			−0.522572
$659$	7.60226e6	+	1.31675e7i	0.681914	+	1.18111i	0.974396	+	0.224838i	$0.0721853\pi$
$659$	7.60226e6	+	1.31675e7i	0.681914	+	1.18111i	−0.292482	+	0.956271i	$0.594481\pi$
$660$		0			0
$661$	−7.19470e6	+	1.24616e7i	−0.640485	+	1.10935i	0.344839	+	0.938662i	$0.387934\pi$
$661$	−7.19470e6	+	1.24616e7i	−0.640485	+	1.10935i	−0.985325	+	0.170692i	$0.945400\pi$
$662$	−3.00288e6	+	5.20113e6i	−0.266313	+	0.461268i
$663$		0			0
$664$	−7.47737e6	−	1.29512e7i	−0.658155	−	1.13996i
$665$	−6.76422e6			−0.593149
$666$		0			0
$667$	−1.53684e6			−0.133756
$668$	1.44918e7	+	2.51006e7i	1.25656	+	2.17642i
$669$		0			0
$670$	7.56863e6	−	1.31092e7i	0.651373	−	1.12821i
$671$	−2.89623e6	+	5.01642e6i	−0.248329	+	0.430118i
$672$		0			0
$673$	−4.31351e6	−	7.47123e6i	−0.367108	−	0.635849i	0.622004	−	0.783014i	$-0.286319\pi$
$673$	−4.31351e6	−	7.47123e6i	−0.367108	−	0.635849i	−0.989112	+	0.147165i	$0.952985\pi$
$674$	1.71440e7			1.45366
$675$		0			0
$676$	−1.63917e7			−1.37962
$677$	−2.56325e6	−	4.43968e6i	−0.214941	−	0.372289i	0.738313	−	0.674458i	$-0.235623\pi$
$677$	−2.56325e6	−	4.43968e6i	−0.214941	−	0.372289i	−0.953254	+	0.302169i	$0.902289\pi$
$678$		0			0
$679$	−7.50164e6	+	1.29932e7i	−0.624427	+	1.08154i
$680$	336190.	−	582298.i	0.0278812	−	0.0482917i
$681$		0			0
$682$	2.48431e6	+	4.30296e6i	0.204524	+	0.354247i
$683$	−1.64537e7			−1.34962			−0.674809	−	0.737992i	$-0.735774\pi$
$683$	−1.64537e7			−1.34962			−0.674809	+	0.737992i	$0.735774\pi$
$684$		0			0
$685$	−7.01661e6			−0.571348
$686$	1.10650e7	+	1.91652e7i	0.897724	+	1.55490i
$687$		0			0
$688$	−2.87722e6	+	4.98350e6i	−0.231741	+	0.401387i
$689$	−4.05783e6	+	7.02836e6i	−0.325646	+	0.564035i
$690$		0			0
$691$	−1.30312e6	−	2.25706e6i	−0.103822	−	0.179824i	0.809435	−	0.587210i	$-0.199774\pi$
$691$	−1.30312e6	−	2.25706e6i	−0.103822	−	0.179824i	−0.913256	+	0.407386i	$0.866440\pi$
$692$	−1.97665e7			−1.56915
$693$		0			0
$694$	−134909.			−0.0106326
$695$	−2.88107e6	−	4.99016e6i	−0.226252	−	0.391880i
$696$		0			0
$697$	−11691.8	+	20250.9i	−0.000911593	+	0.00157893i
$698$	−1.97567e7	+	3.42195e7i	−1.53488	+	2.65849i
$699$		0			0
$700$	−7.32510e6	−	1.26874e7i	−0.565026	−	0.978654i
$701$	787564.			0.0605328			0.0302664	−	0.999542i	$-0.490364\pi$
$701$	787564.			0.0605328			0.0302664	+	0.999542i	$0.490364\pi$
$702$		0			0
$703$	2.14221e7			1.63483
$704$	2.82306e6	+	4.88969e6i	0.214679	+	0.371834i
$705$		0			0
$706$	3.01826e6	−	5.22779e6i	0.227901	−	0.394735i
$707$	−123.708	+	214.268i	−9.30782e−6	+	1.61216e-5i
$708$		0			0
$709$	−2.20266e6	−	3.81511e6i	−0.164563	−	0.285031i	0.771937	−	0.635699i	$-0.219288\pi$
$709$	−2.20266e6	−	3.81511e6i	−0.164563	−	0.285031i	−0.936500	+	0.350668i	$0.885955\pi$
$710$	−9.25425e6			−0.688962
$711$		0			0
$712$	−3.26635e6			−0.241470
$713$	−5.92674e6	−	1.02654e7i	−0.436608	−	0.756228i
$714$		0			0
$715$	562036.	−	973475.i	0.0411149	−	0.0712131i
$716$	3.28287e6	−	5.68610e6i	0.239316	−	0.414507i
$717$		0			0
$718$	−5.22536e6	−	9.05060e6i	−0.378273	−	0.655188i
$719$	−2.82520e6			−0.203810			−0.101905	−	0.994794i	$-0.532494\pi$
$719$	−2.82520e6			−0.203810			−0.101905	+	0.994794i	$0.532494\pi$
$720$		0			0
$721$	−1.33384e7			−0.955577
$722$	4.64008e6	+	8.03686e6i	0.331271	+	0.573777i
$723$		0			0
$724$	−1.60246e7	+	2.77555e7i	−1.13617	+	1.96790i
$725$	−604802.	+	1.04755e6i	−0.0427335	+	0.0740166i
$726$		0			0
$727$	3.76578e6	+	6.52252e6i	0.264252	+	0.457698i	0.967367	−	0.253378i	$-0.0815415\pi$
$727$	3.76578e6	+	6.52252e6i	0.264252	+	0.457698i	−0.703115	+	0.711076i	$0.748208\pi$
$728$	8.64455e6			0.604524
$729$		0			0
$730$	−6.59974e6			−0.458374
$731$	510866.	+	884845.i	0.0353601	+	0.0612455i
$732$		0			0
$733$	1.07102e7	−	1.85507e7i	0.736273	−	1.27526i	−0.217889	−	0.975974i	$-0.569917\pi$
$733$	1.07102e7	−	1.85507e7i	0.736273	−	1.27526i	0.954162	−	0.299289i	$-0.0967495\pi$
$734$	6.47075e6	−	1.12077e7i	0.443317	−	0.767848i
$735$		0			0
$736$	−4.46521e6	−	7.73397e6i	−0.303842	−	0.526269i
$737$	−6.20073e6			−0.420508
$738$		0			0
$739$	−1.49241e7			−1.00526			−0.502628	−	0.864503i	$-0.667633\pi$
$739$	−1.49241e7			−1.00526			−0.502628	+	0.864503i	$0.667633\pi$
$740$	−1.04190e7	−	1.80462e7i	−0.699432	−	1.21145i
$741$		0			0
$742$	−1.50899e7	+	2.61364e7i	−1.00618	+	1.74276i
$743$	−4.36677e6	+	7.56347e6i	−0.290194	+	0.502631i	−0.973855	−	0.227169i	$-0.927053\pi$
$743$	−4.36677e6	+	7.56347e6i	−0.290194	+	0.502631i	0.683662	+	0.729799i	$0.260386\pi$
$744$		0			0
$745$	5.11485e6	+	8.85918e6i	0.337631	+	0.584794i
$746$	2.44379e7			1.60774
$747$		0			0
$748$	−613274.			−0.0400775
$749$	9.31333e6	+	1.61312e7i	0.606597	+	1.05066i
$750$		0			0
$751$	−1.12334e7	+	1.94568e7i	−0.726792	+	1.25884i	0.231440	+	0.972849i	$0.425656\pi$
$751$	−1.12334e7	+	1.94568e7i	−0.726792	+	1.25884i	−0.958232	+	0.285991i	$0.907677\pi$
$752$	1.28465e6	−	2.22507e6i	0.0828398	−	0.143483i
$753$		0			0
$754$	−794614.	−	1.37631e6i	−0.0509012	−	0.0881634i
$755$	−1.20035e7			−0.766370
$756$		0			0
$757$	−2.32097e7			−1.47207			−0.736037	−	0.676942i	$-0.763305\pi$
$757$	−2.32097e7			−1.47207			−0.736037	+	0.676942i	$0.763305\pi$
$758$	−2.05931e7	−	3.56683e7i	−1.30181	−	2.25481i
$759$		0			0
$760$	7.16068e6	−	1.24027e7i	0.449697	−	0.778898i
$761$	−1.29087e7	+	2.23585e7i	−0.808018	+	1.39953i	0.106217	+	0.994343i	$0.466126\pi$
$761$	−1.29087e7	+	2.23585e7i	−0.808018	+	1.39953i	−0.914235	+	0.405185i	$0.867207\pi$
$762$		0			0
$763$	1.06493e7	+	1.84450e7i	0.662228	+	1.14701i
$764$	−2.35058e7			−1.45694
$765$		0			0
$766$	1.02112e7			0.628790
$767$	−4.39707e6	−	7.61595e6i	−0.269883	−	0.467451i
$768$		0			0
$769$	−1.03983e7	+	1.80104e7i	−0.634085	+	1.09827i	0.352623	+	0.935765i	$0.385290\pi$
$769$	−1.03983e7	+	1.80104e7i	−0.634085	+	1.09827i	−0.986708	+	0.162502i	$0.948044\pi$
$770$	2.09005e6	−	3.62007e6i	0.127037	−	0.220034i
$771$		0			0
$772$	−2.23763e7	−	3.87568e7i	−1.35128	−	2.34048i
$773$	924553.			0.0556523			0.0278261	−	0.999613i	$-0.491142\pi$
$773$	924553.			0.0556523			0.0278261	+	0.999613i	$0.491142\pi$
$774$		0			0
$775$	−9.32956e6			−0.557965
$776$	−1.58826e7	−	2.75095e7i	−0.946822	−	1.63994i
$777$		0			0
$778$	−1.60492e7	+	2.77981e7i	−0.950617	+	1.64652i
$779$	−249031.	+	431334.i	−0.0147031	+	0.0254665i
$780$		0			0
$781$	1.89543e6	+	3.28297e6i	0.111193	+	0.192593i
$782$	2.26905e6			0.132687
$783$		0			0
$784$	−1.53763e6			−0.0893435
$785$	6.47433e6	+	1.12139e7i	0.374991	+	0.649503i
$786$		0			0
$787$	5.39495e6	−	9.34432e6i	0.310492	−	0.537788i	−0.667977	−	0.744182i	$-0.732840\pi$
$787$	5.39495e6	−	9.34432e6i	0.310492	−	0.537788i	0.978469	+	0.206394i	$0.0661729\pi$
$788$	−1.44588e6	+	2.50433e6i	−0.0829499	+	0.143674i
$789$		0			0
$790$	2.84672e6	+	4.93067e6i	0.162285	+	0.281085i
$791$	−1.77283e7			−1.00745
$792$		0			0
$793$	1.42900e7			0.806953
$794$	1.80574e6	+	3.12764e6i	0.101649	+	0.176062i
$795$		0			0
$796$	5.36444e6	−	9.29148e6i	0.300083	−	0.519759i
$797$	1.62806e7	−	2.81989e7i	0.907874	−	1.57248i	0.0908608	−	0.995864i	$-0.471038\pi$
$797$	1.62806e7	−	2.81989e7i	0.907874	−	1.57248i	0.817013	−	0.576620i	$-0.195629\pi$
$798$		0			0
$799$	−228095.	−	395073.i	−0.0126401	−	0.0218932i
$800$	−7.02890e6			−0.388295
$801$		0			0
$802$	4.50977e7			2.47582
$803$	1.35174e6	+	2.34128e6i	0.0739782	+	0.128134i
$804$		0			0
$805$	−4.98616e6	+	8.63627e6i	−0.271192	+	0.469717i
$806$	6.12878e6	−	1.06154e7i	0.332305	−	0.575569i
$807$		0			0
$808$	−261.916	−	453.653i	−1.41135e−5	−	2.44453e-5i
$809$	1.54392e7			0.829381			0.414691	−	0.909963i	$-0.363890\pi$
$809$	1.54392e7			0.829381			0.414691	+	0.909963i	$0.363890\pi$
$810$		0			0
$811$	−2.26720e6			−0.121043			−0.0605213	−	0.998167i	$-0.519276\pi$
$811$	−2.26720e6			−0.121043			−0.0605213	+	0.998167i	$0.519276\pi$
$812$	−1.90532e6	−	3.30011e6i	−0.101409	−	0.175646i
$813$		0			0
$814$	−6.61912e6	+	1.14647e7i	−0.350138	+	0.606457i
$815$	−6.22169e6	+	1.07763e7i	−0.328106	+	0.568297i
$816$		0			0
$817$	1.08812e7	+	1.88468e7i	0.570323	+	0.987829i
$818$	2.09832e6			0.109645
$819$		0			0
$820$	484479.			0.0251617
$821$	16005.1	+	27721.6i	0.000828706	+	0.00143536i	0.866439	−	0.499282i	$-0.166403\pi$
$821$	16005.1	+	27721.6i	0.000828706	+	0.00143536i	−0.865611	+	0.500718i	$0.833070\pi$
$822$		0			0
$823$	−9.75278e6	+	1.68923e7i	−0.501913	+	0.869339i	0.498084	+	0.867129i	$0.334037\pi$
$823$	−9.75278e6	+	1.68923e7i	−0.501913	+	0.869339i	−0.999998	+	0.00221067i	$0.999296\pi$
$824$	1.41202e7	−	2.44569e7i	0.724473	−	1.25482i
$825$		0			0
$826$	−1.63514e7	−	2.83215e7i	−0.833883	−	1.44433i
$827$	2.10239e7			1.06893			0.534464	−	0.845191i	$-0.320513\pi$
$827$	2.10239e7			1.06893			0.534464	+	0.845191i	$0.320513\pi$
$828$		0			0
$829$	−1.28560e7			−0.649711			−0.324855	−	0.945764i	$-0.605316\pi$
$829$	−1.28560e7			−0.649711			−0.324855	+	0.945764i	$0.605316\pi$
$830$	8.91991e6	+	1.54497e7i	0.449433	+	0.778441i
$831$		0			0
$832$	6.96447e6	−	1.20628e7i	0.348803	−	0.604144i
$833$	−136507.	+	236438.i	−0.00681622	+	0.0118060i
$834$		0			0
$835$	−7.76409e6	−	1.34478e7i	−0.385367	−	0.667475i
$836$	−1.30624e7			−0.646410
$837$		0			0
$838$	6.48732e7			3.19121
$839$	−4.73751e6	−	8.20561e6i	−0.232351	−	0.402445i	0.726148	−	0.687538i	$-0.241309\pi$
$839$	−4.73751e6	−	8.20561e6i	−0.232351	−	0.402445i	−0.958500	+	0.285094i	$0.907975\pi$
$840$		0			0
$841$	1.00983e7	−	1.74907e7i	0.492330	−	0.852741i
$842$	1.34509e7	−	2.32977e7i	0.653840	−	1.13248i
$843$		0			0
$844$	−3.67836e6	−	6.37111e6i	−0.177745	−	0.307864i
$845$	8.78199e6			0.423108
$846$		0			0
$847$	−1.71231e6			−0.0820113
$848$	−6.68019e6	−	1.15704e7i	−0.319006	−	0.552535i
$849$		0			0
$850$	892955.	−	1.54664e6i	0.0423918	−	0.0734248i
$851$	1.57910e7	−	2.73508e7i	0.747457	−	1.29463i
$852$		0			0
$853$	−9.99292e6	−	1.73082e7i	−0.470240	−	0.814480i	0.529181	−	0.848509i	$-0.322499\pi$
$853$	−9.99292e6	−	1.73082e7i	−0.470240	−	0.814480i	−0.999421	+	0.0340294i	$0.989166\pi$
$854$	5.31402e7			2.49332
$855$		0			0
$856$	−3.94368e7			−1.83957
$857$	−8.84095e6	−	1.53130e7i	−0.411194	−	0.712209i	0.583826	−	0.811879i	$-0.301555\pi$
$857$	−8.84095e6	−	1.53130e7i	−0.411194	−	0.712209i	−0.995021	+	0.0996692i	$0.968222\pi$
$858$		0			0
$859$	−5.68007e6	+	9.83817e6i	−0.262646	+	0.454916i	−0.966944	−	0.254988i	$-0.917928\pi$
$859$	−5.68007e6	+	9.83817e6i	−0.262646	+	0.454916i	0.704298	+	0.709904i	$0.251262\pi$
$860$	1.05845e7	−	1.83328e7i	0.488003	−	0.845246i
$861$		0			0
$862$	−1.78894e7	−	3.09853e7i	−0.820025	−	1.42032i
$863$	−1.40682e6			−0.0643002			−0.0321501	−	0.999483i	$-0.510235\pi$
$863$	−1.40682e6			−0.0643002			−0.0321501	+	0.999483i	$0.510235\pi$
$864$		0			0
$865$	1.05900e7			0.481235
$866$	1.76675e7	+	3.06011e7i	0.800537	+	1.38657i
$867$		0			0
$868$	1.46956e7	−	2.54535e7i	0.662044	−	1.14669i
$869$	1.16611e6	−	2.01977e6i	0.0523832	−	0.0907303i
$870$		0			0
$871$	7.64858e6	+	1.32477e7i	0.341614	+	0.591692i
$872$	−4.50937e7			−2.00828
$873$		0			0
$874$	4.83296e7			2.14010
$875$	9.61152e6	+	1.66476e7i	0.424397	+	0.735077i
$876$		0			0
$877$	−8.63790e6	+	1.49613e7i	−0.379236	+	0.656856i	−0.990951	−	0.134222i	$-0.957146\pi$
$877$	−8.63790e6	+	1.49613e7i	−0.379236	+	0.656856i	0.611715	+	0.791078i	$0.290480\pi$
$878$	−9.20103e6	+	1.59367e7i	−0.402810	+	0.697687i
$879$		0			0
$880$	925250.	+	1.60258e6i	0.0402766	+	0.0697611i
$881$	−4.17144e7			−1.81070			−0.905349	−	0.424669i	$-0.860391\pi$
$881$	−4.17144e7			−1.81070			−0.905349	+	0.424669i	$0.860391\pi$
$882$		0			0
$883$	−1.85206e7			−0.799378			−0.399689	−	0.916651i	$-0.630882\pi$
$883$	−1.85206e7			−0.799378			−0.399689	+	0.916651i	$0.630882\pi$
$884$	756471.	+	1.31025e6i	0.0325583	+	0.0563926i
$885$		0			0
$886$	1.35786e7	−	2.35189e7i	0.581128	−	1.00654i
$887$	−3.92294e6	+	6.79473e6i	−0.167418	+	0.289977i	−0.937511	−	0.347955i	$-0.886876\pi$
$887$	−3.92294e6	+	6.79473e6i	−0.167418	+	0.289977i	0.770093	+	0.637931i	$0.220210\pi$
$888$		0			0
$889$	3.21690e6	+	5.57183e6i	0.136516	+	0.236452i
$890$	3.89650e6			0.164892
$891$		0			0
$892$	6.94401e7			2.92212
$893$	−4.85832e6	−	8.41486e6i	−0.203872	−	0.353117i
$894$		0			0
$895$	−1.75882e6	+	3.04637e6i	−0.0733946	+	0.127123i
$896$	1.97996e7	−	3.42939e7i	0.823923	−	1.42708i
$897$		0			0
$898$	−2.49220e7	−	4.31662e7i	−1.03132	−	1.78630i
$899$	−2.42670e6			−0.100142
$900$		0			0
$901$	−2.37220e6			−0.0973508
$902$	−153894.	−	266552.i	−0.00629803	−	0.0109085i
$903$		0			0
$904$	1.87674e7	−	3.25060e7i	0.763804	−	1.32295i
$905$	8.58531e6	−	1.48702e7i	0.348445	−	0.603525i
$906$		0			0
$907$	737386.	+	1.27719e6i	0.0297630	+	0.0515510i	0.880523	−	0.474003i	$-0.157191\pi$
$907$	737386.	+	1.27719e6i	0.0297630	+	0.0515510i	−0.850760	+	0.525554i	$0.823858\pi$
$908$	−5.26330e7			−2.11857
$909$		0			0
$910$	−1.03123e7			−0.412810
$911$	4.55928e6	+	7.89690e6i	0.182012	+	0.315254i	0.942566	−	0.334021i	$-0.108406\pi$
$911$	4.55928e6	+	7.89690e6i	0.182012	+	0.315254i	−0.760554	+	0.649275i	$0.775072\pi$
$912$		0			0
$913$	3.65390e6	−	6.32874e6i	0.145071	−	0.251270i
$914$	3.68845e7	−	6.38859e7i	1.46042	−	2.52953i
$915$		0			0
$916$	4.04341e7	+	7.00339e7i	1.59224	+	2.75784i
$917$	−2.16553e7			−0.850436
$918$		0			0
$919$	−1.76427e7			−0.689091			−0.344546	−	0.938770i	$-0.611967\pi$
$919$	−1.76427e7			−0.689091			−0.344546	+	0.938770i	$0.611967\pi$
$920$	−1.05568e7	−	1.82849e7i	−0.411209	−	0.712235i
$921$		0			0
$922$	1.67805e7	−	2.90647e7i	0.650097	−	1.12600i
$923$	4.67600e6	−	8.09907e6i	0.180664	−	0.312918i
$924$		0			0
$925$	−1.24287e7	−	2.15271e7i	−0.477608	−	0.827241i
$926$	1.63838e7			0.627894
$927$		0			0
$928$	−1.82828e6			−0.0696903
$929$	1.05878e7	+	1.83386e7i	0.402499	+	0.697150i	0.994027	−	0.109135i	$-0.0348082\pi$
$929$	1.05878e7	+	1.83386e7i	0.402499	+	0.697150i	−0.591527	+	0.806285i	$0.701475\pi$
$930$		0			0
$931$	−2.90754e6	+	5.03601e6i	−0.109939	+	0.190420i
$932$	−3.54117e7	+	6.13348e7i	−1.33539	+	2.31296i
$933$		0			0
$934$	7.35801e6	+	1.27445e7i	0.275990	+	0.478029i
$935$	328566.			0.0122912
$936$		0			0
$937$	−3.58889e7			−1.33540			−0.667700	−	0.744430i	$-0.732721\pi$
$937$	−3.58889e7			−1.33540			−0.667700	+	0.744430i	$0.732721\pi$
$938$	2.84428e7	+	4.92644e7i	1.05552	+	1.82821i
$939$		0			0
$940$	−4.72584e6	+	8.18539e6i	−0.174445	+	0.302148i
$941$	−2.70130e6	+	4.67879e6i	−0.0994487	+	0.172250i	−0.911457	−	0.411396i	$-0.865041\pi$
$941$	−2.70130e6	+	4.67879e6i	−0.0994487	+	0.172250i	0.812008	+	0.583646i	$0.198375\pi$
$942$		0			0
$943$	367139.	+	635904.i	0.0134447	+	0.0232869i
$944$	1.44773e7			0.528760
$945$		0			0
$946$	−1.34485e7			−0.488593
$947$	−1.91462e7	−	3.31622e7i	−0.693757	−	1.20162i	−0.970598	−	0.240706i	$-0.922621\pi$
$947$	−1.91462e7	−	3.31622e7i	−0.693757	−	1.20162i	0.276841	−	0.960916i	$-0.410712\pi$
$948$		0			0
$949$	3.33473e6	−	5.77592e6i	0.120197	−	0.208188i
$950$	1.90195e7	−	3.29427e7i	0.683739	−	1.18427i
$951$		0			0
$952$	1.26340e6	+	2.18827e6i	0.0451802	+	0.0782544i
$953$	2.85647e7			1.01882			0.509410	−	0.860524i	$-0.329864\pi$
$953$	2.85647e7			1.01882			0.509410	+	0.860524i	$0.329864\pi$
$954$		0			0
$955$	1.25934e7			0.446821
$956$	−3.99512e7	−	6.91975e7i	−1.41379	−	2.44876i
$957$		0			0
$958$	−4.43318e7	+	7.67849e7i	−1.56064	+	2.70310i
$959$	1.31842e7	−	2.28357e7i	0.462921	−	0.801802i
$960$		0			0
$961$	4.95613e6	+	8.58426e6i	0.173115	+	0.299843i
$962$	3.26587e7			1.13779
$963$		0			0
$964$	−9.04704e7			−3.13555
$965$	1.19882e7	+	2.07642e7i	0.414417	+	0.717791i
$966$		0			0
$967$	−4.27802e6	+	7.40974e6i	−0.147122	+	0.254822i	−0.930162	−	0.367148i	$-0.880334\pi$
$967$	−4.27802e6	+	7.40974e6i	−0.147122	+	0.254822i	0.783041	+	0.621970i	$0.213668\pi$
$968$	1.81267e6	−	3.13963e6i	0.0621770	−	0.107694i
$969$		0			0
$970$	1.89467e7	+	3.28167e7i	0.646555	+	1.11987i
$971$	−1.38864e7			−0.472654			−0.236327	−	0.971674i	$-0.575944\pi$
$971$	−1.38864e7			−0.472654			−0.236327	+	0.971674i	$0.575944\pi$
$972$		0			0
$973$	2.16541e7			0.733260
$974$	2.35178e7	+	4.07340e7i	0.794326	+	1.37581i
$975$		0			0
$976$	−1.17624e7	+	2.03731e7i	−0.395250	+	0.684593i
$977$	−2.14141e7	+	3.70902e7i	−0.717733	+	1.24315i	0.244164	+	0.969734i	$0.421487\pi$
$977$	−2.14141e7	+	3.70902e7i	−0.717733	+	1.24315i	−0.961896	+	0.273415i	$0.911847\pi$
$978$		0			0
$979$	−798069.	−	1.38230e6i	−0.0266124	−	0.0460940i
$980$	5.65651e6			0.188141
$981$		0			0
$982$	−3.16269e7			−1.04659
$983$	−5.41898e6	−	9.38595e6i	−0.178868	−	0.309809i	0.762625	−	0.646841i	$-0.223910\pi$
$983$	−5.41898e6	−	9.38595e6i	−0.178868	−	0.309809i	−0.941493	+	0.337032i	$0.890577\pi$
$984$		0			0
$985$	774639.	−	1.34171e6i	0.0254395	−	0.0440625i
$986$	232265.	−	402295.i	0.00760837	−	0.0131781i
$987$		0			0
$988$	1.61125e7	+	2.79076e7i	0.525133	+	0.909557i
$989$	3.20837e7			1.04302
$990$		0			0
$991$	3.64184e7			1.17798			0.588989	−	0.808141i	$-0.299526\pi$
$991$	3.64184e7			1.17798			0.588989	+	0.808141i	$0.299526\pi$
$992$	−7.05066e6	−	1.22121e7i	−0.227484	−	0.394014i
$993$		0			0
$994$	1.73887e7	−	3.01181e7i	0.558214	−	0.966855i
$995$	−2.87404e6	+	4.97797e6i	−0.0920310	+	0.159402i
$996$		0			0
$997$	5.54985e6	+	9.61262e6i	0.176825	+	0.306270i	0.940791	−	0.338986i	$-0.110084\pi$
$997$	5.54985e6	+	9.61262e6i	0.176825	+	0.306270i	−0.763966	+	0.645256i	$0.776751\pi$
$998$	1.63156e7			0.518534
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.6.e.a.199.21		46
3.2	odd	2		99.6.e.a.67.3	yes	46
9.2	odd	6		99.6.e.a.34.3	✓	46
9.4	even	3		891.6.a.e.1.3		23
9.5	odd	6		891.6.a.f.1.21		23
9.7	even	3	inner	297.6.e.a.100.21		46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.6.e.a.34.3	✓	46	9.2	odd	6
99.6.e.a.67.3	yes	46	3.2	odd	2
297.6.e.a.100.21		46	9.7	even	3	inner
297.6.e.a.199.21		46	1.1	even	1	trivial
891.6.a.e.1.3		23	9.4	even	3
891.6.a.f.1.21		23	9.5	odd	6

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.74574 + 8.21986i) q^{2} +(-29.0441 + 50.3058i) q^{4} +(15.5606 - 26.9517i) q^{5} +(58.4765 + 101.284i) q^{7} -247.615 q^{8} +O(q^{10})\)	\(q+(4.74574 + 8.21986i) q^{2} +(-29.0441 + 50.3058i) q^{4} +(15.5606 - 26.9517i) q^{5} +(58.4765 + 101.284i) q^{7} -247.615 q^{8} +295.386 q^{10} +(-60.5000 - 104.789i) q^{11} +(-149.253 + 258.514i) q^{13} +(-555.028 + 961.338i) q^{14} +(-245.707 - 425.578i) q^{16} -87.2532 q^{17} -1858.45 q^{19} +(903.885 + 1565.58i) q^{20} +(574.234 - 994.603i) q^{22} +(-1369.93 + 2372.79i) q^{23} +(1078.24 + 1867.56i) q^{25} -2833.26 q^{26} -6793.59 q^{28} +(280.459 + 485.769i) q^{29} +(-2163.15 + 3746.69i) q^{31} +(-1629.72 + 2822.76i) q^{32} +(-414.081 - 717.209i) q^{34} +3639.71 q^{35} -11526.9 q^{37} +(-8819.72 - 15276.2i) q^{38} +(-3853.04 + 6673.66i) q^{40} +(133.999 - 232.093i) q^{41} +(-5854.98 - 10141.1i) q^{43} +7028.67 q^{44} -26005.4 q^{46} +(2614.18 + 4527.89i) q^{47} +(1564.50 - 2709.79i) q^{49} +(-10234.1 + 17725.9i) q^{50} +(-8669.84 - 15016.6i) q^{52} +27187.6 q^{53} -3765.66 q^{55} +(-14479.7 - 25079.5i) q^{56} +(-2661.97 + 4610.66i) q^{58} +(-14730.3 + 25513.5i) q^{59} +(-23935.8 - 41458.0i) q^{61} -41063.0 q^{62} -46662.2 q^{64} +(4644.93 + 8045.25i) q^{65} +(25622.9 - 44380.1i) q^{67} +(2534.19 - 4389.34i) q^{68} +(17273.1 + 29917.9i) q^{70} -31329.4 q^{71} -22342.8 q^{73} +(-54703.5 - 94749.3i) q^{74} +(53977.0 - 93490.9i) q^{76} +(7075.66 - 12255.4i) q^{77} +(9637.31 + 16692.3i) q^{79} -15293.4 q^{80} +2543.70 q^{82} +(30197.5 + 52303.6i) q^{83} +(-1357.71 + 2351.62i) q^{85} +(55572.4 - 96254.3i) q^{86} +(14980.7 + 25947.4i) q^{88} +13191.2 q^{89} -34911.2 q^{91} +(-79576.8 - 137831. i) q^{92} +(-24812.4 + 42976.4i) q^{94} +(-28918.5 + 50088.4i) q^{95} +(64142.4 + 111098. i) q^{97} +29698.8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 320 q^{4} + 36 q^{5} + 167 q^{7} - 426 q^{8}+O(q^{10}) \) 46 * q - 320 * q^4 + 36 * q^5 + 167 * q^7 - 426 * q^8	\( 46 q - 320 q^{4} + 36 q^{5} + 167 q^{7} - 426 q^{8} - 1200 q^{10} - 2783 q^{11} + 1871 q^{13} + 1329 q^{14} - 3584 q^{16} - 534 q^{17} - 7282 q^{19} + 1917 q^{20} + 8292 q^{23} - 10049 q^{25} - 19140 q^{26} + 7586 q^{28} + 5970 q^{29} + 9542 q^{31} + 3831 q^{32} + 2982 q^{34} - 6480 q^{35} - 32014 q^{37} - 1221 q^{38} + 40635 q^{40} - 12030 q^{41} + 25943 q^{43} + 77440 q^{44} - 154008 q^{46} - 9756 q^{47} - 6990 q^{49} - 101805 q^{50} + 144446 q^{52} - 107838 q^{53} - 8712 q^{55} + 16602 q^{56} + 95367 q^{58} + 20310 q^{59} + 100247 q^{61} + 30594 q^{62} - 169154 q^{64} - 20931 q^{65} + 84956 q^{67} - 168471 q^{68} + 212292 q^{70} - 72186 q^{71} - 346888 q^{73} - 86619 q^{74} + 340334 q^{76} + 20207 q^{77} + 123113 q^{79} + 30246 q^{80} - 399966 q^{82} - 30672 q^{83} + 268335 q^{85} + 211260 q^{86} + 25773 q^{88} - 65028 q^{89} - 656042 q^{91} + 196731 q^{92} + 230262 q^{94} + 325926 q^{95} + 357002 q^{97} + 428928 q^{98}+O(q^{100}) \) 46 * q - 320 * q^4 + 36 * q^5 + 167 * q^7 - 426 * q^8 - 1200 * q^10 - 2783 * q^11 + 1871 * q^13 + 1329 * q^14 - 3584 * q^16 - 534 * q^17 - 7282 * q^19 + 1917 * q^20 + 8292 * q^23 - 10049 * q^25 - 19140 * q^26 + 7586 * q^28 + 5970 * q^29 + 9542 * q^31 + 3831 * q^32 + 2982 * q^34 - 6480 * q^35 - 32014 * q^37 - 1221 * q^38 + 40635 * q^40 - 12030 * q^41 + 25943 * q^43 + 77440 * q^44 - 154008 * q^46 - 9756 * q^47 - 6990 * q^49 - 101805 * q^50 + 144446 * q^52 - 107838 * q^53 - 8712 * q^55 + 16602 * q^56 + 95367 * q^58 + 20310 * q^59 + 100247 * q^61 + 30594 * q^62 - 169154 * q^64 - 20931 * q^65 + 84956 * q^67 - 168471 * q^68 + 212292 * q^70 - 72186 * q^71 - 346888 * q^73 - 86619 * q^74 + 340334 * q^76 + 20207 * q^77 + 123113 * q^79 + 30246 * q^80 - 399966 * q^82 - 30672 * q^83 + 268335 * q^85 + 211260 * q^86 + 25773 * q^88 - 65028 * q^89 - 656042 * q^91 + 196731 * q^92 + 230262 * q^94 + 325926 * q^95 + 357002 * q^97 + 428928 * q^98

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