LMFDB - Embedded newform 245.6.b.c.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,6,Mod(99,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("245.99");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	245.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:	$39.2940358542$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2408 x^{10} + 1934778 x^{8} + 685997236 x^{6} + 109856760265 x^{4} + 6693959319900 x^{2} + 67265422402500 $ x^12 + 2408x^10 + 1934778x^8 + 685997236x^6 + 109856760265x^4 + 6693959319900*x^2 + 67265422402500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5^{3}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$-35.1720i$ of defining polynomial
Character	$\chi$	$=$	245.99
Dual form			245.6.b.c.99.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.99564i q^{2} +28.1764i q^{3} -16.9390 q^{4} +(55.7986 + 3.39325i) q^{5} +197.112 q^{6} -105.361i q^{8} -550.907 q^{9} +O(q^{10})$	\(q-6.99564i q^{2} +28.1764i q^{3} -16.9390 q^{4} +(55.7986 + 3.39325i) q^{5} +197.112 q^{6} -105.361i q^{8} -550.907 q^{9} +(23.7380 - 390.347i) q^{10} -423.419 q^{11} -477.281i q^{12} -331.590i q^{13} +(-95.6095 + 1572.20i) q^{15} -1279.12 q^{16} +1667.82i q^{17} +3853.95i q^{18} -1441.39 q^{19} +(-945.175 - 57.4785i) q^{20} +2962.09i q^{22} -4043.26i q^{23} +2968.69 q^{24} +(3101.97 + 378.678i) q^{25} -2319.69 q^{26} -8675.69i q^{27} -3927.12 q^{29} +(10998.6 + 668.850i) q^{30} -6311.80 q^{31} +5576.70i q^{32} -11930.4i q^{33} +11667.5 q^{34} +9331.84 q^{36} -201.115i q^{37} +10083.4i q^{38} +9343.01 q^{39} +(357.517 - 5879.00i) q^{40} -6597.82 q^{41} +15333.3i q^{43} +7172.32 q^{44} +(-30739.8 - 1869.37i) q^{45} -28285.2 q^{46} +992.224i q^{47} -36040.9i q^{48} +(2649.10 - 21700.3i) q^{50} -46993.0 q^{51} +5616.83i q^{52} -20282.0i q^{53} -60692.0 q^{54} +(-23626.2 - 1436.77i) q^{55} -40613.0i q^{57} +27472.8i q^{58} +36310.7 q^{59} +(1619.53 - 26631.6i) q^{60} -18931.7 q^{61} +44155.1i q^{62} -1919.15 q^{64} +(1125.17 - 18502.3i) q^{65} -83460.9 q^{66} -46612.4i q^{67} -28251.2i q^{68} +113924. q^{69} -53483.1 q^{71} +58044.1i q^{72} +10030.2i q^{73} -1406.93 q^{74} +(-10669.8 + 87402.2i) q^{75} +24415.7 q^{76} -65360.4i q^{78} +44282.9 q^{79} +(-71373.0 - 4340.37i) q^{80} +110579. q^{81} +46156.0i q^{82} -59266.7i q^{83} +(-5659.33 + 93061.9i) q^{85} +107266. q^{86} -110652. i q^{87} +44611.9i q^{88} -93236.6 q^{89} +(-13077.4 + 215045. i) q^{90} +68488.9i q^{92} -177844. i q^{93} +6941.25 q^{94} +(-80427.3 - 4890.99i) q^{95} -157131. q^{96} +91299.8i q^{97} +233264. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 236 q^{4} - 1280 q^{9}+O(q^{10}) $ 12 * q - 236 * q^4 - 1280 * q^9	$ 12 q - 236 q^{4} - 1280 q^{9} - 12 q^{11} - 820 q^{15} - 4524 q^{16} + 9260 q^{25} + 8372 q^{29} + 27820 q^{30} - 8996 q^{36} + 11484 q^{39} + 51464 q^{44} - 36376 q^{46} + 45700 q^{50} - 198516 q^{51} - 90620 q^{60} + 64156 q^{64} + 137140 q^{65} - 466736 q^{71} + 56824 q^{74} + 107876 q^{79} + 369068 q^{81} + 356780 q^{85} - 76400 q^{86} - 436480 q^{95} + 980088 q^{99}+O(q^{100}) $ 12 * q - 236 * q^4 - 1280 * q^9 - 12 * q^11 - 820 * q^15 - 4524 * q^16 + 9260 * q^25 + 8372 * q^29 + 27820 * q^30 - 8996 * q^36 + 11484 * q^39 + 51464 * q^44 - 36376 * q^46 + 45700 * q^50 - 198516 * q^51 - 90620 * q^60 + 64156 * q^64 + 137140 * q^65 - 466736 * q^71 + 56824 * q^74 + 107876 * q^79 + 369068 * q^81 + 356780 * q^85 - 76400 * q^86 - 436480 * q^95 + 980088 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	6.99564i		−	1.23667i	−0.785916	−	0.618333i	$-0.787808\pi$
$2$		−	6.99564i		−	1.23667i	0.785916	−	0.618333i	$-0.212192\pi$
$3$			28.1764i			1.80751i	0.428046	+	0.903757i	$0.359202\pi$
$3$			28.1764i			1.80751i	−0.428046	+	0.903757i	$0.640798\pi$
$4$	−16.9390			−0.529345
$5$	55.7986	+	3.39325i	0.998156	+	0.0607004i
$5$	55.7986	+	3.39325i	0.998156	+	0.0607004i
$6$	197.112			2.23529
$7$		0			0
$7$		0			0
$8$		−	105.361i		−	0.582043i
$9$	−550.907			−2.26711
$10$	23.7380	−	390.347i	0.0750662	−	1.23439i
$11$	−423.419			−1.05509			−0.527544	−	0.849528i	$-0.676887\pi$
$11$	−423.419			−1.05509			−0.527544	+	0.849528i	$0.676887\pi$
$12$		−	477.281i		−	0.956799i
$13$		−	331.590i		−	0.544181i	−0.962272	−	0.272091i	$-0.912285\pi$
$13$		−	331.590i		−	0.544181i	0.962272	−	0.272091i	$-0.0877151\pi$
$14$		0			0
$15$	−95.6095	+	1572.20i	−0.109717	+	1.80418i
$16$	−1279.12			−1.24914
$17$			1667.82i			1.39967i	0.714304	+	0.699836i	$0.246743\pi$
$17$			1667.82i			1.39967i	−0.714304	+	0.699836i	$0.753257\pi$
$18$			3853.95i			2.80365i
$19$	−1441.39			−0.916001			−0.458001	−	0.888952i	$-0.651434\pi$
$19$	−1441.39			−0.916001			−0.458001	+	0.888952i	$0.651434\pi$
$20$	−945.175	−	57.4785i	−0.528369	−	0.0321315i
$21$		0			0
$22$			2962.09i			1.30479i
$23$		−	4043.26i		−	1.59372i	−0.604165	−	0.796859i	$-0.706493\pi$
$23$		−	4043.26i		−	1.59372i	0.604165	−	0.796859i	$-0.293507\pi$
$24$	2968.69			1.05205
$25$	3101.97	+	378.678i	0.992631	+	0.121177i
$26$	−2319.69			−0.672971
$27$		−	8675.69i		−	2.29031i
$28$		0			0
$29$	−3927.12			−0.867120			−0.433560	−	0.901125i	$-0.642743\pi$
$29$	−3927.12			−0.867120			−0.433560	+	0.901125i	$0.642743\pi$
$30$	10998.6	+	668.850i	2.23117	+	0.135683i
$31$	−6311.80			−1.17964			−0.589819	−	0.807535i	$-0.700801\pi$
$31$	−6311.80			−1.17964			−0.589819	+	0.807535i	$0.700801\pi$
$32$			5576.70i			0.962726i
$33$		−	11930.4i		−	1.90709i
$34$	11667.5			1.73093
$35$		0			0
$36$	9331.84			1.20008
$37$		−	201.115i		−	0.0241513i	−0.999927	−	0.0120757i	$-0.996156\pi$
$37$		−	201.115i		−	0.0241513i	0.999927	−	0.0120757i	$-0.00384389\pi$
$38$			10083.4i			1.13279i
$39$	9343.01			0.983615
$40$	357.517	−	5879.00i	0.0353302	−	0.580970i
$41$	−6597.82			−0.612972			−0.306486	−	0.951875i	$-0.599153\pi$
$41$	−6597.82			−0.612972			−0.306486	+	0.951875i	$0.599153\pi$
$42$		0			0
$43$			15333.3i			1.26463i	0.774710	+	0.632317i	$0.217896\pi$
$43$			15333.3i			1.26463i	−0.774710	+	0.632317i	$0.782104\pi$
$44$	7172.32			0.558506
$45$	−30739.8	−	1869.37i	−2.26293	−	0.137614i
$46$	−28285.2			−1.97090
$47$			992.224i			0.0655187i	0.999463	+	0.0327593i	$0.0104295\pi$
$47$			992.224i			0.0655187i	−0.999463	+	0.0327593i	$0.989571\pi$
$48$		−	36040.9i		−	2.25784i
$49$		0			0
$50$	2649.10	−	21700.3i	0.149855	−	1.22755i
$51$	−46993.0			−2.52993
$52$			5616.83i			0.288060i
$53$		−	20282.0i		−	0.991791i	−0.868382	−	0.495895i	$-0.834840\pi$
$53$		−	20282.0i		−	0.991791i	0.868382	−	0.495895i	$-0.165160\pi$
$54$	−60692.0			−2.83235
$55$	−23626.2	−	1436.77i	−1.05314	−	0.0640442i
$56$		0			0
$57$		−	40613.0i		−	1.65568i
$58$			27472.8i			1.07234i
$59$	36310.7			1.35801			0.679007	−	0.734131i	$-0.262410\pi$
$59$	36310.7			1.35801			0.679007	+	0.734131i	$0.262410\pi$
$60$	1619.53	−	26631.6i	0.0580780	−	0.955034i
$61$	−18931.7			−0.651427			−0.325713	−	0.945469i	$-0.605604\pi$
$61$	−18931.7			−0.651427			−0.325713	+	0.945469i	$0.605604\pi$
$62$			44155.1i			1.45882i
$63$		0			0
$64$	−1919.15			−0.0585679
$65$	1125.17	−	18502.3i	0.0330320	−	0.543178i
$66$	−83460.9			−2.35843
$67$		−	46612.4i		−	1.26857i	−0.773099	−	0.634285i	$-0.781294\pi$
$67$		−	46612.4i		−	1.26857i	0.773099	−	0.634285i	$-0.218706\pi$
$68$		−	28251.2i		−	0.740909i
$69$	113924.			2.88067
$70$		0			0
$71$	−53483.1			−1.25913			−0.629566	−	0.776947i	$-0.716767\pi$
$71$	−53483.1			−1.25913			−0.629566	+	0.776947i	$0.716767\pi$
$72$			58044.1i			1.31955i
$73$			10030.2i			0.220293i	0.993915	+	0.110147i	$0.0351321\pi$
$73$			10030.2i			0.220293i	−0.993915	+	0.110147i	$0.964868\pi$
$74$	−1406.93			−0.0298671
$75$	−10669.8	+	87402.2i	−0.219029	+	1.79419i
$76$	24415.7			0.484881
$77$		0			0
$78$		−	65360.4i		−	1.21640i
$79$	44282.9			0.798303			0.399152	−	0.916885i	$-0.369305\pi$
$79$	44282.9			0.798303			0.399152	+	0.916885i	$0.369305\pi$
$80$	−71373.0	−	4340.37i	−1.24684	−	0.0758232i
$81$	110579.			1.87266
$82$			46156.0i			0.758043i
$83$		−	59266.7i		−	0.944313i	−0.881515	−	0.472156i	$-0.843476\pi$
$83$		−	59266.7i		−	0.944313i	0.881515	−	0.472156i	$-0.156524\pi$
$84$		0			0
$85$	−5659.33	+	93061.9i	−0.0849606	+	1.39709i
$86$	107266.			1.56393
$87$		−	110652.i		−	1.56733i
$88$			44611.9i			0.614107i
$89$	−93236.6			−1.24770			−0.623852	−	0.781543i	$-0.714433\pi$
$89$	−93236.6			−1.24770			−0.623852	+	0.781543i	$0.714433\pi$
$90$	−13077.4	+	215045.i	−0.170183	+	2.79849i
$91$		0			0
$92$			68488.9i			0.843628i
$93$		−	177844.i		−	2.13221i
$94$	6941.25			0.0810248
$95$	−80427.3	−	4890.99i	−0.914312	−	0.0556016i
$96$	−157131.			−1.74014
$97$			91299.8i			0.985236i	0.870246	+	0.492618i	$0.163960\pi$
$97$			91299.8i			0.985236i	−0.870246	+	0.492618i	$0.836040\pi$
$98$		0			0
$99$	233264.			2.39200
$100$	−52544.4	−	6414.44i	−0.525444	−	0.0641444i
$101$	−33257.5			−0.324404			−0.162202	−	0.986758i	$-0.551860\pi$
$101$	−33257.5			−0.324404			−0.162202	+	0.986758i	$0.551860\pi$
$102$			328746.i			3.12868i
$103$		−	57064.8i		−	0.529999i	−0.964249	−	0.265000i	$-0.914628\pi$
$103$		−	57064.8i		−	0.529999i	0.964249	−	0.265000i	$-0.0853718\pi$
$104$	−34936.7			−0.316737
$105$		0			0
$106$	−141885.			−1.22651
$107$			53844.5i			0.454655i	0.973818	+	0.227327i	$0.0729988\pi$
$107$			53844.5i			0.454655i	−0.973818	+	0.227327i	$0.927001\pi$
$108$			146958.i			1.21237i
$109$	−173200.			−1.39631			−0.698154	−	0.715947i	$-0.745995\pi$
$109$	−173200.			−1.39631			−0.698154	+	0.715947i	$0.745995\pi$
$110$	−10051.1	+	165281.i	−0.0792014	+	1.30239i
$111$	5666.69			0.0436538
$112$		0			0
$113$			181689.i			1.33854i	0.743019	+	0.669270i	$0.233393\pi$
$113$			181689.i			1.33854i	−0.743019	+	0.669270i	$0.766607\pi$
$114$	−284114.			−2.04753
$115$	13719.8	−	225608.i	0.0967393	−	1.59078i
$116$	66521.7			0.459006
$117$			182675.i			1.23372i
$118$		−	254017.i		−	1.67941i
$119$		0			0
$120$	165649.	+	10073.5i	1.05011	+	0.0638599i
$121$	18232.7			0.113211
$122$			132440.i			0.805598i
$123$		−	185902.i		−	1.10796i
$124$	106916.			0.624436
$125$	171801.	+	31655.5i	0.983445	+	0.181207i
$126$		0			0
$127$		−	99578.4i		−	0.547843i	−0.961752	−	0.273921i	$-0.911679\pi$
$127$		−	99578.4i		−	0.547843i	0.961752	−	0.273921i	$-0.0883208\pi$
$128$			191880.i			1.03515i
$129$	−432037.			−2.28584
$130$	−129435.	−	7871.29i	−0.671730	−	0.0408496i
$131$	336671.			1.71406			0.857032	−	0.515263i	$-0.172306\pi$
$131$	336671.			1.71406			0.857032	+	0.515263i	$0.172306\pi$
$132$			202090.i			1.00951i
$133$		0			0
$134$	−326084.			−1.56880
$135$	29438.8	−	484091.i	0.139023	−	2.28609i
$136$	175723.			0.814669
$137$			107708.i			0.490284i	0.969487	+	0.245142i	$0.0788346\pi$
$137$			107708.i			0.490284i	−0.969487	+	0.245142i	$0.921165\pi$
$138$		−	796973.i		−	3.56243i
$139$	−340636.			−1.49539			−0.747693	−	0.664044i	$-0.768839\pi$
$139$	−340636.			−1.49539			−0.747693	+	0.664044i	$0.768839\pi$
$140$		0			0
$141$	−27957.3			−0.118426
$142$			374149.i			1.55713i
$143$			140402.i			0.574159i
$144$	704675.			2.83193
$145$	−219128.	−	13325.7i	−0.865522	−	0.0526345i
$146$	70167.6			0.272430
$147$		0			0
$148$			3406.70i			0.0127844i
$149$	412361.			1.52164			0.760821	−	0.648962i	$-0.224797\pi$
$149$	412361.			1.52164			0.760821	+	0.648962i	$0.224797\pi$
$150$	611435.	+	74641.8i	2.21882	+	0.270866i
$151$	−174861.			−0.624095			−0.312048	−	0.950066i	$-0.601015\pi$
$151$	−174861.			−0.624095			−0.312048	+	0.950066i	$0.601015\pi$
$152$			151866.i			0.533152i
$153$		−	918812.i		−	3.17320i
$154$		0			0
$155$	−352190.	−	21417.5i	−1.17746	−	0.0716045i
$156$	−158262.			−0.520672
$157$		−	191923.i		−	0.621411i	−0.950506	−	0.310705i	$-0.899435\pi$
$157$		−	191923.i		−	0.621411i	0.950506	−	0.310705i	$-0.100565\pi$
$158$		−	309787.i		−	0.987235i
$159$	571471.			1.79268
$160$	−18923.2	+	311172.i	−0.0584378	+	0.960950i
$161$		0			0
$162$		−	773571.i		−	2.31586i
$163$		−	68624.4i		−	0.202306i	−0.994871	−	0.101153i	$-0.967747\pi$
$163$		−	68624.4i		−	0.202306i	0.994871	−	0.101153i	$-0.0322532\pi$
$164$	111761.			0.324474
$165$	40482.9	−	665700.i	0.115761	−	1.90357i
$166$	−414609.			−1.16780
$167$		−	394859.i		−	1.09560i	−0.836610	−	0.547798i	$-0.815466\pi$
$167$		−	394859.i		−	1.09560i	0.836610	−	0.547798i	$-0.184534\pi$
$168$		0			0
$169$	261341.			0.703867
$170$	651028.	+	39590.6i	1.72774	+	0.105068i
$171$	794069.			2.07667
$172$		−	259732.i		−	0.669428i
$173$		−	89294.7i		−	0.226835i	−0.993547	−	0.113418i	$-0.963820\pi$
$173$		−	89294.7i		−	0.226835i	0.993547	−	0.113418i	$-0.0361798\pi$
$174$	−774082.			−1.93827
$175$		0			0
$176$	541603.			1.31795
$177$			1.02310e6i			2.45463i
$178$			652250.i			1.54299i
$179$	27971.6			0.0652505			0.0326253	−	0.999468i	$-0.489613\pi$
$179$	27971.6			0.0652505			0.0326253	+	0.999468i	$0.489613\pi$
$180$	520704.	+	31665.3i	1.19787	+	0.0728454i
$181$	117086.			0.265649			0.132825	−	0.991140i	$-0.457595\pi$
$181$	117086.			0.265649			0.132825	+	0.991140i	$0.457595\pi$
$182$		0			0
$183$		−	533427.i		−	1.17746i
$184$	−426002.			−0.927613
$185$	682.435	−	11221.9i	0.00146599	−	0.0241068i
$186$	−1.24413e6			−2.63684
$187$		−	706186.i		−	1.47678i
$188$		−	16807.3i		−	0.0346820i
$189$		0			0
$190$	−34215.6	+	562641.i	−0.0687607	+	1.13070i
$191$	−727677.			−1.44330			−0.721648	−	0.692260i	$-0.756615\pi$
$191$	−727677.			−1.44330			−0.721648	+	0.692260i	$0.756615\pi$
$192$		−	54074.7i		−	0.105862i
$193$			61010.1i			0.117899i	0.998261	+	0.0589493i	$0.0187750\pi$
$193$			61010.1i			0.117899i	−0.998261	+	0.0589493i	$0.981225\pi$
$194$	638701.			1.21841
$195$	521327.	+	31703.2i	0.981801	+	0.0597058i
$196$		0			0
$197$			334020.i			0.613206i	0.951837	+	0.306603i	$0.0991925\pi$
$197$			334020.i			0.613206i	−0.951837	+	0.306603i	$0.900808\pi$
$198$		−	1.63184e6i		−	2.95810i
$199$	81600.3			0.146069			0.0730347	−	0.997329i	$-0.476732\pi$
$199$	81600.3			0.146069			0.0730347	+	0.997329i	$0.476732\pi$
$200$	39897.9	−	326827.i	0.0705302	−	0.577754i
$201$	1.31337e6			2.29296
$202$			232658.i			0.401180i
$203$		0			0
$204$	796017.			1.33920
$205$	−368149.	−	22388.1i	−0.611842	−	0.0372076i
$206$	−399205.			−0.655432
$207$			2.22746e6i			3.61313i
$208$			424143.i			0.679758i
$209$	610310.			0.966462
$210$		0			0
$211$	−159693.			−0.246933			−0.123466	−	0.992349i	$-0.539401\pi$
$211$	−159693.			−0.246933			−0.123466	+	0.992349i	$0.539401\pi$
$212$			343557.i			0.525000i
$213$		−	1.50696e6i		−	2.27590i
$214$	376677.			0.562257
$215$	−52029.8	+	855577.i	−0.0767637	+	1.26230i
$216$	−914080.			−1.33306
$217$		0			0
$218$			1.21164e6i			1.72677i
$219$	−282614.			−0.398183
$220$	400205.	+	24337.5i	0.557476	+	0.0339015i
$221$	553032.			0.761675
$222$		−	39642.2i		−	0.0539852i
$223$			772238.i			1.03989i	0.854199	+	0.519947i	$0.174048\pi$
$223$			772238.i			1.03989i	−0.854199	+	0.519947i	$0.825952\pi$
$224$		0			0
$225$	−1.70890e6	−	208616.i	−2.25040	−	0.274721i
$226$	1.27103e6			1.65533
$227$			608158.i			0.783343i	0.920105	+	0.391671i	$0.128103\pi$
$227$			608158.i			0.783343i	−0.920105	+	0.391671i	$0.871897\pi$
$228$			687945.i			0.876429i
$229$	−619832.			−0.781061			−0.390531	−	0.920590i	$-0.627708\pi$
$229$	−619832.			−0.781061			−0.390531	+	0.920590i	$0.627708\pi$
$230$	−1.57827e6	−	95978.8i	−1.96727	−	0.119634i
$231$		0			0
$232$			413766.i			0.504702i
$233$			901162.i			1.08746i	0.839260	+	0.543730i	$0.182988\pi$
$233$			901162.i			1.08746i	−0.839260	+	0.543730i	$0.817012\pi$
$234$	1.27793e6			1.52570
$235$	−3366.87	+	55364.7i	−0.00397701	+	0.0653979i
$236$	−615068.			−0.718859
$237$			1.24773e6i			1.44294i
$238$		0			0
$239$	782664.			0.886299			0.443150	−	0.896448i	$-0.353861\pi$
$239$	782664.			0.886299			0.443150	+	0.896448i	$0.353861\pi$
$240$	122296.	−	2.01103e6i	0.137051	−	2.25367i
$241$	211424.			0.234483			0.117242	−	0.993103i	$-0.462595\pi$
$241$	211424.			0.234483			0.117242	+	0.993103i	$0.462595\pi$
$242$		−	127550.i		−	0.140004i
$243$			1.00752e6i			1.09455i
$244$	320685.			0.344830
$245$		0			0
$246$	−1.30051e6			−1.37017
$247$			477950.i			0.498471i
$248$			665018.i			0.686601i
$249$	1.66992e6			1.70686
$250$	221450.	−	1.20186e6i	0.224092	−	1.21619i
$251$	101441.			0.101632			0.0508158	−	0.998708i	$-0.483818\pi$
$251$	101441.			0.101632			0.0508158	+	0.998708i	$0.483818\pi$
$252$		0			0
$253$			1.71199e6i			1.68151i
$254$	−696615.			−0.677499
$255$	−2.62214e6	−	159459.i	−2.52526	−	0.153567i
$256$	1.28091e6			1.22157
$257$			1.68766e6i			1.59387i	0.604065	+	0.796935i	$0.293547\pi$
$257$			1.68766e6i			1.59387i	−0.604065	+	0.796935i	$0.706453\pi$
$258$			3.02238e6i			2.82683i
$259$		0			0
$260$	−19059.3	+	313411.i	−0.0174853	+	0.287529i
$261$	2.16348e6			1.96585
$262$		−	2.35523e6i		−	2.11973i
$263$		−	605956.i		−	0.540196i	−0.962833	−	0.270098i	$-0.912944\pi$
$263$		−	605956.i		−	0.540196i	0.962833	−	0.270098i	$-0.0870561\pi$
$264$	−1.25700e6			−1.11001
$265$	68821.8	−	1.13170e6i	0.0602021	−	0.989962i
$266$		0			0
$267$		−	2.62707e6i		−	2.25524i
$268$			789570.i			0.671512i
$269$	743325.			0.626323			0.313161	−	0.949700i	$-0.398612\pi$
$269$	743325.			0.626323			0.313161	+	0.949700i	$0.398612\pi$
$270$	−3.38653e6	−	205943.i	−2.82713	−	0.171925i
$271$	1.77909e6			1.47155			0.735773	−	0.677229i	$-0.236819\pi$
$271$	1.77909e6			1.47155			0.735773	+	0.677229i	$0.236819\pi$
$272$		−	2.13334e6i		−	1.74838i
$273$		0			0
$274$	753489.			0.606318
$275$	−1.31343e6	−	160339.i	−1.04731	−	0.127852i
$276$	−1.92977e6			−1.52487
$277$			74238.6i			0.0581340i	0.999577	+	0.0290670i	$0.00925362\pi$
$277$			74238.6i			0.0581340i	−0.999577	+	0.0290670i	$0.990746\pi$
$278$			2.38297e6i			1.84929i
$279$	3.47721e6			2.67437
$280$		0			0
$281$	785384.			0.593357			0.296679	−	0.954977i	$-0.404121\pi$
$281$	785384.			0.593357			0.296679	+	0.954977i	$0.404121\pi$
$282$			195579.i			0.146453i
$283$		−	519822.i		−	0.385823i	−0.981216	−	0.192912i	$-0.938207\pi$
$283$		−	519822.i		−	0.385823i	0.981216	−	0.192912i	$-0.0617930\pi$
$284$	905954.			0.666515
$285$	137810.	−	2.26615e6i	0.100501	−	1.65263i
$286$	982201.			0.710044
$287$		0			0
$288$		−	3.07224e6i		−	2.18260i
$289$	−1.36176e6			−0.959080
$290$	−93222.0	+	1.53294e6i	−0.0650914	+	1.07036i
$291$	−2.57249e6			−1.78083
$292$		−	169902.i		−	0.116611i
$293$			1.12496e6i			0.765539i	0.923844	+	0.382769i	$0.125030\pi$
$293$			1.12496e6i			0.765539i	−0.923844	+	0.382769i	$0.874970\pi$
$294$		0			0
$295$	2.02609e6	+	123211.i	1.35551	+	0.0824320i
$296$	−21189.7			−0.0140571
$297$			3.67345e6i			2.41648i
$298$		−	2.88473e6i		−	1.88176i
$299$	−1.34071e6			−0.867272
$300$	180736.	−	1.48051e6i	0.115942	−	0.949748i
$301$		0			0
$302$			1.22327e6i			0.771798i
$303$		−	937075.i		−	0.586365i
$304$	1.84370e6			1.14421
$305$	−1.05636e6	−	64240.1i	−0.650225	−	0.0395418i
$306$	−6.42768e6			−3.92420
$307$			160689.i			0.0973062i	0.998816	+	0.0486531i	$0.0154929\pi$
$307$			160689.i			0.0973062i	−0.998816	+	0.0486531i	$0.984507\pi$
$308$		0			0
$309$	1.60788e6			0.957981
$310$	−149830.	+	2.46379e6i	−0.0885509	+	1.45613i
$311$	−1.40642e6			−0.824542			−0.412271	−	0.911061i	$-0.635264\pi$
$311$	−1.40642e6			−0.824542			−0.412271	+	0.911061i	$0.635264\pi$
$312$		−	984389.i		−	0.572507i
$313$		−	626967.i		−	0.361729i	−0.983508	−	0.180865i	$-0.942110\pi$
$313$		−	626967.i		−	0.361729i	0.983508	−	0.180865i	$-0.0578896\pi$
$314$	−1.34263e6			−0.768478
$315$		0			0
$316$	−750109.			−0.422578
$317$			1.94856e6i			1.08910i	0.838729	+	0.544549i	$0.183299\pi$
$317$			1.94856e6i			1.08910i	−0.838729	+	0.544549i	$0.816701\pi$
$318$		−	3.99781e6i		−	2.21694i
$319$	1.66282e6			0.914889
$320$	−107086.	−	6512.17i	−0.0584599	−	0.00355509i
$321$	−1.51714e6			−0.821795
$322$		0			0
$323$		−	2.40397e6i		−	1.28210i
$324$	−1.87310e6			−0.991285
$325$	125566.	−	1.02858e6i	0.0659422	−	0.540171i
$326$	−480072.			−0.250186
$327$		−	4.88014e6i		−	2.52385i
$328$			695153.i			0.356776i
$329$		0			0
$330$	−4.65700e6	−	283204.i	−2.35408	−	0.143158i
$331$	788678.			0.395667			0.197833	−	0.980236i	$-0.436609\pi$
$331$	788678.			0.395667			0.197833	+	0.980236i	$0.436609\pi$
$332$			1.00392e6i			0.499867i
$333$			110796.i			0.0547536i
$334$	−2.76229e6			−1.35489
$335$	158168.	−	2.60091e6i	0.0770027	−	1.26623i
$336$		0			0
$337$			844524.i			0.405077i	0.979274	+	0.202538i	$0.0649191\pi$
$337$			844524.i			0.405077i	−0.979274	+	0.202538i	$0.935081\pi$
$338$		−	1.82825e6i		−	0.870449i
$339$	−5.11932e6			−2.41943
$340$	95863.6	−	1.57638e6i	0.0449735	−	0.739543i
$341$	2.67254e6			1.24462
$342$		−	5.55502e6i		−	2.56815i
$343$		0			0
$344$	1.61553e6			0.736071
$345$	6.35681e6	+	386574.i	2.87536	+	0.174858i
$346$	−624674.			−0.280520
$347$		−	2.11031e6i		−	0.940854i	−0.882439	−	0.470427i	$-0.844100\pi$
$347$		−	2.11031e6i		−	0.940854i	0.882439	−	0.470427i	$-0.155900\pi$
$348$			1.87434e6i			0.829660i
$349$	1.40214e6			0.616207			0.308104	−	0.951353i	$-0.400306\pi$
$349$	1.40214e6			0.616207			0.308104	+	0.951353i	$0.400306\pi$
$350$		0			0
$351$	−2.87678e6			−1.24634
$352$		−	2.36128e6i		−	1.01576i
$353$			3.63527e6i			1.55275i	0.630274	+	0.776373i	$0.282942\pi$
$353$			3.63527e6i			1.55275i	−0.630274	+	0.776373i	$0.717058\pi$
$354$	7.15726e6			3.03556
$355$	−2.98429e6	−	181482.i	−1.25681	−	0.0764297i
$356$	1.57934e6			0.660466
$357$		0			0
$358$		−	195679.i		−	0.0806932i
$359$	−382277.			−0.156546			−0.0782729	−	0.996932i	$-0.524941\pi$
$359$	−382277.			−0.156546			−0.0782729	+	0.996932i	$0.524941\pi$
$360$	−196958.	+	3.23878e6i	−0.0800974	+	1.31712i
$361$	−398508.			−0.160942
$362$		−	819093.i		−	0.328520i
$363$			513732.i			0.204630i
$364$		0			0
$365$	−34035.0	+	559670.i	−0.0133719	+	0.219887i
$366$	−3.73166e6			−1.45613
$367$			1.69811e6i			0.658113i	0.944310	+	0.329056i	$0.106731\pi$
$367$			1.69811e6i			0.658113i	−0.944310	+	0.329056i	$0.893269\pi$
$368$			5.17180e6i			1.99078i
$369$	3.63478e6			1.38967
$370$	−78504.8	−	4774.07i	−0.0298120	−	0.00181295i
$371$		0			0
$372$			3.01250e6i			1.12868i
$373$			3.12464e6i			1.16286i	0.813596	+	0.581431i	$0.197507\pi$
$373$			3.12464e6i			1.16286i	−0.813596	+	0.581431i	$0.802493\pi$
$374$	−4.94022e6			−1.82628
$375$	−891936.	+	4.84072e6i	−0.327533	+	1.77759i
$376$	104542.			0.0381347
$377$			1.30220e6i			0.471871i
$378$		0			0
$379$	−274167.			−0.0980433			−0.0490216	−	0.998798i	$-0.515610\pi$
$379$	−274167.			−0.0980433			−0.0490216	+	0.998798i	$0.515610\pi$
$380$	1.36236e6	+	82848.7i	0.483987	+	0.0294325i
$381$	2.80576e6			0.990233
$382$			5.09057e6i			1.78488i
$383$			3.97594e6i			1.38498i	0.721428	+	0.692490i	$0.243486\pi$
$383$			3.97594e6i			1.38498i	−0.721428	+	0.692490i	$0.756514\pi$
$384$	−5.40648e6			−1.87106
$385$		0			0
$386$	426805.			0.145801
$387$		−	8.44722e6i		−	2.86706i
$388$		−	1.54653e6i		−	0.521530i
$389$	138745.			0.0464884			0.0232442	−	0.999730i	$-0.492600\pi$
$389$	138745.			0.0464884			0.0232442	+	0.999730i	$0.492600\pi$
$390$	221784.	−	3.64702e6i	0.0738362	−	1.21416i
$391$	6.74341e6			2.23068
$392$		0			0
$393$			9.48615e6i			3.09819i
$394$	2.33668e6			0.758332
$395$	2.47092e6	+	150263.i	0.796831	+	0.0484573i
$396$	−3.95128e6			−1.26619
$397$		−	2.52038e6i		−	0.802584i	−0.915950	−	0.401292i	$-0.868561\pi$
$397$		−	2.52038e6i		−	0.802584i	0.915950	−	0.401292i	$-0.131439\pi$
$398$		−	570847.i		−	0.180639i
$399$		0			0
$400$	−3.96779e6	−	484374.i	−1.23993	−	0.151367i
$401$	−6.21108e6			−1.92889			−0.964443	−	0.264292i	$-0.914862\pi$
$401$	−6.21108e6			−1.92889			−0.964443	+	0.264292i	$0.914862\pi$
$402$		−	9.18786e6i		−	2.83563i
$403$			2.09293e6i			0.641937i
$404$	563351.			0.171722
$405$	6.17015e6	+	375222.i	1.86921	+	0.113671i
$406$		0			0
$407$			85156.0i			0.0254818i
$408$			4.95123e6i			1.47253i
$409$	58949.2			0.0174249			0.00871244	−	0.999962i	$-0.497227\pi$
$409$	58949.2			0.0174249			0.00871244	+	0.999962i	$0.497227\pi$
$410$	−156619.	+	2.57544e6i	−0.0460135	+	0.756645i
$411$	−3.03483e6			−0.886195
$412$			966623.i			0.280552i
$413$		0			0
$414$	1.55825e7			4.46824
$415$	201107.	−	3.30700e6i	0.0573201	−	0.942571i
$416$	1.84918e6			0.523897
$417$		−	9.59788e6i		−	2.70293i
$418$		−	4.26951e6i		−	1.19519i
$419$	−6.80330e6			−1.89315			−0.946575	−	0.322485i	$-0.895482\pi$
$419$	−6.80330e6			−1.89315			−0.946575	+	0.322485i	$0.895482\pi$
$420$		0			0
$421$	−228574.			−0.0628522			−0.0314261	−	0.999506i	$-0.510005\pi$
$421$	−228574.			−0.0628522			−0.0314261	+	0.999506i	$0.510005\pi$
$422$			1.11715e6i			0.305373i
$423$		−	546623.i		−	0.148538i
$424$	−2.13693e6			−0.577265
$425$	−631565.	+	5.17352e6i	−0.169608	+	1.38936i
$426$	−1.05422e7			−2.81453
$427$		0			0
$428$		−	912074.i		−	0.240669i
$429$	−3.95601e6			−1.03780
$430$	5.98532e6	+	363982.i	1.56105	+	0.0949312i
$431$	−6.41272e6			−1.66283			−0.831417	−	0.555649i	$-0.812470\pi$
$431$	−6.41272e6			−1.66283			−0.831417	+	0.555649i	$0.812470\pi$
$432$			1.10972e7i			2.86092i
$433$			2.60767e6i			0.668394i	0.942503	+	0.334197i	$0.108465\pi$
$433$			2.60767e6i			0.668394i	−0.942503	+	0.334197i	$0.891535\pi$
$434$		0			0
$435$	375470.	−	6.17423e6i	0.0951377	−	1.56444i
$436$	2.93384e6			0.739129
$437$			5.82789e6i			1.45985i
$438$			1.97707e6i			0.492420i
$439$	3.65634e6			0.905494			0.452747	−	0.891639i	$-0.350444\pi$
$439$	3.65634e6			0.905494			0.452747	+	0.891639i	$0.350444\pi$
$440$	−151379.	+	2.48928e6i	−0.0372765	+	0.612974i
$441$		0			0
$442$		−	3.86882e6i		−	0.941938i
$443$		−	2.65258e6i		−	0.642183i	−0.947048	−	0.321092i	$-0.895950\pi$
$443$		−	2.65258e6i		−	0.642183i	0.947048	−	0.321092i	$-0.104050\pi$
$444$	−95988.4			−0.0231079
$445$	−5.20247e6	−	316375.i	−1.24540	−	0.0757361i
$446$	5.40230e6			1.28600
$447$			1.16188e7i			2.75039i
$448$		0			0
$449$	−4.48878e6			−1.05078			−0.525391	−	0.850861i	$-0.676081\pi$
$449$	−4.48878e6			−1.05078			−0.525391	+	0.850861i	$0.676081\pi$
$450$	−1.45940e6	+	1.19548e7i	−0.339738	+	2.78299i
$451$	2.79364e6			0.646740
$452$		−	3.07763e6i		−	0.708550i
$453$		−	4.92695e6i		−	1.12806i
$454$	4.25446e6			0.968734
$455$		0			0
$456$	−4.27903e6			−0.963680
$457$		−	5.96980e6i		−	1.33712i	−0.743659	−	0.668559i	$-0.766912\pi$
$457$		−	5.96980e6i		−	1.33712i	0.743659	−	0.668559i	$-0.233088\pi$
$458$			4.33612e6i			0.965913i
$459$	1.44695e7			3.20568
$460$	−232400.	+	3.82159e6i	−0.0512085	+	0.842072i
$461$	4.10240e6			0.899054			0.449527	−	0.893267i	$-0.351593\pi$
$461$	4.10240e6			0.899054			0.449527	+	0.893267i	$0.351593\pi$
$462$		0			0
$463$		−	7.22818e6i		−	1.56703i	−0.621374	−	0.783514i	$-0.713425\pi$
$463$		−	7.22818e6i		−	1.56703i	0.621374	−	0.783514i	$-0.286575\pi$
$464$	5.02325e6			1.08315
$465$	603468.	−	9.92342e6i	0.129426	−	2.12828i
$466$	6.30421e6			1.34483
$467$			1.88581e6i			0.400134i	0.979782	+	0.200067i	$0.0641160\pi$
$467$			1.88581e6i			0.400134i	−0.979782	+	0.200067i	$0.935884\pi$
$468$		−	3.09435e6i		−	0.653062i
$469$		0			0
$470$	387312.	+	23553.4i	0.0808754	+	0.00491824i
$471$	5.40770e6			1.12321
$472$		−	3.82573e6i		−	0.790423i
$473$		−	6.49242e6i		−	1.33430i
$474$	8.72867e6			1.78444
$475$	−4.47114e6	−	545821.i	−0.909251	−	0.110998i
$476$		0			0
$477$			1.11735e7i			2.24849i
$478$		−	5.47524e6i		−	1.09606i
$479$	1.04308e6			0.207720			0.103860	−	0.994592i	$-0.466881\pi$
$479$	1.04308e6			0.207720			0.103860	+	0.994592i	$0.466881\pi$
$480$	−8.76770e6	−	533186.i	−1.73693	−	0.105627i
$481$	−66687.9			−0.0131427
$482$		−	1.47905e6i		−	0.289978i
$483$		0			0
$484$	−308845.			−0.0599277
$485$	−309803.	+	5.09440e6i	−0.0598042	+	0.983420i
$486$	7.04823e6			1.35360
$487$		−	2.92362e6i		−	0.558597i	−0.960204	−	0.279298i	$-0.909898\pi$
$487$		−	2.92362e6i		−	0.558597i	0.960204	−	0.279298i	$-0.0901019\pi$
$488$			1.99467e6i			0.379158i
$489$	1.93359e6			0.365672
$490$		0			0
$491$	−6.66985e6			−1.24857			−0.624284	−	0.781197i	$-0.714609\pi$
$491$	−6.66985e6			−1.24857			−0.624284	+	0.781197i	$0.714609\pi$
$492$			3.14901e6i			0.586491i
$493$		−	6.54972e6i		−	1.21368i
$494$	3.34357e6			0.616442
$495$	1.30158e7	+	791525.i	2.38759	+	0.145195i
$496$	8.07354e6			1.47353
$497$		0			0
$498$		−	1.16822e7i		−	2.11082i
$499$	−5.83720e6			−1.04943			−0.524715	−	0.851278i	$-0.675828\pi$
$499$	−5.83720e6			−1.04943			−0.524715	+	0.851278i	$0.675828\pi$
$500$	−2.91014e6	−	536214.i	−0.520582	−	0.0959208i
$501$	1.11257e7			1.98031
$502$		−	709644.i		−	0.125684i
$503$		−	9.29919e6i		−	1.63880i	−0.573224	−	0.819399i	$-0.694307\pi$
$503$		−	9.29919e6i		−	1.63880i	0.573224	−	0.819399i	$-0.305693\pi$
$504$		0			0
$505$	−1.85572e6	−	112851.i	−0.323806	−	0.0196915i
$506$	1.19765e7			2.07947
$507$			7.36363e6i			1.27225i
$508$			1.68676e6i			0.289998i
$509$	−1.66469e6			−0.284798			−0.142399	−	0.989809i	$-0.545482\pi$
$509$	−1.66469e6			−0.284798			−0.142399	+	0.989809i	$0.545482\pi$
$510$	−1.11552e6	+	1.83436e7i	−0.189912	+	3.12291i
$511$		0			0
$512$		−	2.82064e6i		−	0.475525i
$513$			1.25050e7i			2.09793i
$514$	1.18063e7			1.97109
$515$	193635.	−	3.18414e6i	0.0321711	−	0.529022i
$516$	7.31829e6			1.21000
$517$		−	420127.i		−	0.0691280i
$518$		0			0
$519$	2.51600e6			0.410008
$520$	−1.94942e6	−	118549.i	−0.316153	−	0.0192261i
$521$	−1.10189e7			−1.77846			−0.889230	−	0.457459i	$-0.848759\pi$
$521$	−1.10189e7			−1.77846			−0.889230	+	0.457459i	$0.848759\pi$
$522$		−	1.51349e7i		−	2.43111i
$523$		−	3.95145e6i		−	0.631687i	−0.948811	−	0.315844i	$-0.897712\pi$
$523$		−	3.95145e6i		−	0.631687i	0.948811	−	0.315844i	$-0.102288\pi$
$524$	−5.70288e6			−0.907332
$525$		0			0
$526$	−4.23905e6			−0.668043
$527$		−	1.05269e7i		−	1.65111i
$528$			1.52604e7i			2.38222i
$529$	−9.91158e6			−1.53994
$530$	−7.91701e6	−	481453.i	−1.22425	−	0.0744499i
$531$	−2.00038e7			−3.07876
$532$		0			0
$533$			2.18777e6i			0.333568i
$534$	−1.83780e7			−2.78898
$535$	−182708.	+	3.00445e6i	−0.0275977	+	0.453817i
$536$	−4.91114e6			−0.738363
$537$			788136.i			0.117941i
$538$		−	5.20004e6i		−	0.774553i
$539$		0			0
$540$	−498665.	+	8.20005e6i	−0.0735910	+	1.21013i
$541$	−785720.			−0.115418			−0.0577091	−	0.998333i	$-0.518380\pi$
$541$	−785720.			−0.115418			−0.0577091	+	0.998333i	$0.518380\pi$
$542$		−	1.24459e7i		−	1.81981i
$543$			3.29906e6i			0.480165i
$544$	−9.30092e6			−1.34750
$545$	−9.66432e6	−	587711.i	−1.39373	−	0.0847565i
$546$		0			0
$547$		−	6.70771e6i		−	0.958530i	−0.877670	−	0.479265i	$-0.840903\pi$
$547$		−	6.70771e6i		−	0.958530i	0.877670	−	0.479265i	$-0.159097\pi$
$548$		−	1.82448e6i		−	0.259530i
$549$	1.04296e7			1.47685
$550$	−1.12168e6	+	9.18832e6i	−0.158111	+	1.29518i
$551$	5.66050e6			0.794283
$552$		−	1.20032e7i		−	1.67667i
$553$		0			0
$554$	519347.			0.0718924
$555$	316194.	+	19228.5i	0.0435733	+	0.00264980i
$556$	5.77005e6			0.791576
$557$			1.32024e7i			1.80309i	0.432690	+	0.901543i	$0.357564\pi$
$557$			1.32024e7i			1.80309i	−0.432690	+	0.901543i	$0.642436\pi$
$558$		−	2.43254e7i		−	3.30730i
$559$	5.08438e6			0.688190
$560$		0			0
$561$	1.98977e7			2.66929
$562$		−	5.49427e6i		−	0.733786i
$563$		−	3.49464e6i		−	0.464656i	−0.972638	−	0.232328i	$-0.925366\pi$
$563$		−	3.49464e6i		−	0.464656i	0.972638	−	0.232328i	$-0.0746343\pi$
$564$	473569.			0.0626882
$565$	−616516.	+	1.01380e7i	−0.0812499	+	1.33607i
$566$	−3.63649e6			−0.477135
$567$		0			0
$568$			5.63504e6i			0.732869i
$569$	23578.3			0.00305303			0.00152652	−	0.999999i	$-0.499514\pi$
$569$	23578.3			0.00305303			0.00152652	+	0.999999i	$0.499514\pi$
$570$	−1.58532e7	−	964071.i	−2.04376	−	0.124286i
$571$	−1.18188e7			−1.51699			−0.758493	−	0.651682i	$-0.774064\pi$
$571$	−1.18188e7			−1.51699			−0.758493	+	0.651682i	$0.774064\pi$
$572$		−	2.37827e6i		−	0.303928i
$573$		−	2.05033e7i		−	2.60878i
$574$		0			0
$575$	1.53109e6	−	1.25421e7i	0.193122	−	1.58197i
$576$	1.05727e6			0.132780
$577$			885585.i			0.110737i	0.998466	+	0.0553683i	$0.0176333\pi$
$577$			885585.i			0.110737i	−0.998466	+	0.0553683i	$0.982367\pi$
$578$			9.52637e6i			1.18606i
$579$	−1.71904e6			−0.213103
$580$	3.71182e6	+	225725.i	0.458160	+	0.0278618i
$581$		0			0
$582$			1.79963e7i			2.20229i
$583$			8.58777e6i			1.04643i
$584$	1.05679e6			0.128220
$585$	−619864.	+	1.01930e7i	−0.0748871	+	1.23144i
$586$	7.86980e6			0.946716
$587$			1.20119e7i			1.43886i	0.694567	+	0.719428i	$0.255596\pi$
$587$			1.20119e7i			1.43886i	−0.694567	+	0.719428i	$0.744404\pi$
$588$		0			0
$589$	9.09774e6			1.08055
$590$	861943.	−	1.41738e7i	0.101941	−	1.67632i
$591$	−9.41146e6			−1.10838
$592$			257250.i			0.0301683i
$593$		−	1.90005e6i		−	0.221885i	−0.993827	−	0.110942i	$-0.964613\pi$
$593$		−	1.90005e6i		−	0.221885i	0.993827	−	0.110942i	$-0.0353869\pi$
$594$	2.56982e7			2.98838
$595$		0			0
$596$	−6.98501e6			−0.805474
$597$			2.29920e6i			0.264022i
$598$			9.37910e6i			1.07253i
$599$	9.60719e6			1.09403			0.547015	−	0.837123i	$-0.315764\pi$
$599$	9.60719e6			1.09403			0.547015	+	0.837123i	$0.315764\pi$
$600$	9.20879e6	+	1.12418e6i	1.04430	+	0.127484i
$601$	1.46213e7			1.65120			0.825598	−	0.564259i	$-0.190838\pi$
$601$	1.46213e7			1.65120			0.825598	+	0.564259i	$0.190838\pi$
$602$		0			0
$603$			2.56791e7i			2.87598i
$604$	2.96198e6			0.330362
$605$	1.01736e6	+	61868.3i	0.113002	+	0.00687195i
$606$	−6.55545e6			−0.725138
$607$		−	9.86360e6i		−	1.08658i	−0.839544	−	0.543292i	$-0.817178\pi$
$607$		−	9.86360e6i		−	1.08658i	0.839544	−	0.543292i	$-0.182822\pi$
$608$		−	8.03818e6i		−	0.881858i
$609$		0			0
$610$	−449401.	+	7.38995e6i	−0.0489001	+	0.804112i
$611$	329012.			0.0356540
$612$			1.55638e7i			1.67972i
$613$		−	7.77072e6i		−	0.835237i	−0.908622	−	0.417619i	$-0.862865\pi$
$613$		−	7.77072e6i		−	0.835237i	0.908622	−	0.417619i	$-0.137135\pi$
$614$	1.12412e6			0.120335
$615$	630814.	−	1.03731e7i	0.0672533	−	1.10591i
$616$		0			0
$617$		−	6.58339e6i		−	0.696204i	−0.937457	−	0.348102i	$-0.886826\pi$
$617$		−	6.58339e6i		−	0.696204i	0.937457	−	0.348102i	$-0.113174\pi$
$618$		−	1.12481e7i		−	1.18470i
$619$	1.63347e7			1.71350			0.856751	−	0.515731i	$-0.172479\pi$
$619$	1.63347e7			1.71350			0.856751	+	0.515731i	$0.172479\pi$
$620$	5.96576e6	+	362793.i	0.623285	+	0.0379035i
$621$	−3.50780e7			−3.65011
$622$			9.83879e6i			1.01968i
$623$		0			0
$624$	−1.19508e7			−1.22867
$625$	9.47883e6	+	2.34930e6i	0.970632	+	0.240568i
$626$	−4.38604e6			−0.447339
$627$			1.71963e7i			1.74689i
$628$			3.25100e6i			0.328941i
$629$	335423.			0.0338039
$630$		0			0
$631$	7.79392e6			0.779260			0.389630	−	0.920971i	$-0.372603\pi$
$631$	7.79392e6			0.779260			0.389630	+	0.920971i	$0.372603\pi$
$632$		−	4.66569e6i		−	0.464647i
$633$		−	4.49955e6i		−	0.446334i
$634$	1.36315e7			1.34685
$635$	337895.	−	5.55634e6i	0.0332543	−	0.546833i
$636$	−9.68018e6			−0.948944
$637$		0			0
$638$		−	1.16325e7i		−	1.13141i
$639$	2.94642e7			2.85458
$640$	−651098.	+	1.07066e7i	−0.0628343	+	1.03325i
$641$	8.41452e6			0.808880			0.404440	−	0.914564i	$-0.367466\pi$
$641$	8.41452e6			0.808880			0.404440	+	0.914564i	$0.367466\pi$
$642$			1.06134e7i			1.01629i
$643$		−	1.11139e7i		−	1.06008i	−0.847972	−	0.530040i	$-0.822177\pi$
$643$		−	1.11139e7i		−	1.06008i	0.847972	−	0.530040i	$-0.177823\pi$
$644$		0			0
$645$	−2.41070e7	−	1.46601e6i	−2.28163	−	0.138752i
$646$	−1.68173e7			−1.58553
$647$		−	1.17407e7i		−	1.10264i	−0.834294	−	0.551319i	$-0.814125\pi$
$647$		−	1.17407e7i		−	1.10264i	0.834294	−	0.551319i	$-0.185875\pi$
$648$		−	1.16507e7i		−	1.08997i
$649$	−1.53746e7			−1.43283
$650$	−7.19561e6	−	878415.i	−0.668012	−	0.0815485i
$651$		0			0
$652$			1.16243e6i			0.107090i
$653$			2.65462e6i			0.243624i	0.992553	+	0.121812i	$0.0388705\pi$
$653$			2.65462e6i			0.243624i	−0.992553	+	0.121812i	$0.961130\pi$
$654$	−3.41397e7			−3.12116
$655$	1.87858e7	+	1.14241e6i	1.71090	+	0.104044i
$656$	8.43939e6			0.765687
$657$		−	5.52569e6i		−	0.499429i
$658$		0			0
$659$	−780390.			−0.0700000			−0.0350000	−	0.999387i	$-0.511143\pi$
$659$	−780390.			−0.0700000			−0.0350000	+	0.999387i	$0.511143\pi$
$660$	−685742.	+	1.12763e7i	−0.0612775	+	1.00765i
$661$	5.48516e6			0.488299			0.244149	−	0.969738i	$-0.421491\pi$
$661$	5.48516e6			0.488299			0.244149	+	0.969738i	$0.421491\pi$
$662$		−	5.51731e6i		−	0.489308i
$663$			1.55824e7i			1.37674i
$664$	−6.24441e6			−0.549631
$665$		0			0
$666$	775087.			0.0677119
$667$			1.58784e7i			1.38195i
$668$			6.68853e6i			0.579949i
$669$	−2.17588e7			−1.87962
$670$	−1.81950e7	−	1.10649e6i	−1.56591	−	0.0952267i
$671$	8.01605e6			0.687312
$672$		0			0
$673$		−	1.93016e7i		−	1.64269i	−0.570431	−	0.821346i	$-0.693224\pi$
$673$		−	1.93016e7i		−	1.64269i	0.570431	−	0.821346i	$-0.306776\pi$
$674$	5.90799e6			0.500945
$675$	3.28529e6	−	2.69117e7i	0.277533	−	2.27343i
$676$	−4.42686e6			−0.372588
$677$		−	5.50249e6i		−	0.461411i	−0.973024	−	0.230706i	$-0.925897\pi$
$677$		−	5.50249e6i		−	0.461411i	0.973024	−	0.230706i	$-0.0741034\pi$
$678$			3.58130e7i			2.99203i
$679$		0			0
$680$	9.80510e6	+	596273.i	0.813167	+	0.0494507i
$681$	−1.71357e7			−1.41590
$682$		−	1.86961e7i		−	1.53918i
$683$			2.62083e6i			0.214975i	0.994206	+	0.107487i	$0.0342805\pi$
$683$			2.62083e6i			0.214975i	−0.994206	+	0.107487i	$0.965720\pi$
$684$	−1.34508e7			−1.09928
$685$	−365482.	+	6.00997e6i	−0.0297604	+	0.489380i
$686$		0			0
$687$		−	1.74646e7i		−	1.41178i
$688$		−	1.96131e7i		−	1.57970i
$689$	−6.72530e6			−0.539714
$690$	2.70433e6	−	4.44700e7i	0.216241	−	3.55586i
$691$	−1.25949e7			−1.00346			−0.501729	−	0.865025i	$-0.667302\pi$
$691$	−1.25949e7			−1.00346			−0.501729	+	0.865025i	$0.667302\pi$
$692$			1.51257e6i			0.120074i
$693$		0			0
$694$	−1.47630e7			−1.16352
$695$	−1.90070e7	−	1.15586e6i	−1.49263	−	0.0907705i
$696$	−1.16584e7			−0.912255
$697$		−	1.10040e7i		−	0.857960i
$698$		−	9.80885e6i		−	0.762043i
$699$	−2.53915e7			−1.96560
$700$		0			0
$701$	5.04023e6			0.387396			0.193698	−	0.981061i	$-0.437952\pi$
$701$	5.04023e6			0.387396			0.193698	+	0.981061i	$0.437952\pi$
$702$			2.01249e7i			1.54131i
$703$			289884.i			0.0221226i
$704$	812606.			0.0617943
$705$	−1.55998e6	−	94866.1i	−0.118208	−	0.00718850i
$706$	2.54311e7			1.92023
$707$		0			0
$708$		−	1.73304e7i		−	1.29935i
$709$	−6.77185e6			−0.505932			−0.252966	−	0.967475i	$-0.581406\pi$
$709$	−6.77185e6			−0.505932			−0.252966	+	0.967475i	$0.581406\pi$
$710$	−1.26958e6	+	2.08770e7i	−0.0945181	+	1.55425i
$711$	−2.43957e7			−1.80984
$712$			9.82351e6i			0.726217i
$713$			2.55202e7i			1.88001i
$714$		0			0
$715$	−476419.	+	7.83422e6i	−0.0348517	+	0.573101i
$716$	−473812.			−0.0345401
$717$			2.20526e7i			1.60200i
$718$			2.67427e6i			0.193595i
$719$	1.50340e7			1.08456			0.542279	−	0.840199i	$-0.317562\pi$
$719$	1.50340e7			1.08456			0.542279	+	0.840199i	$0.317562\pi$
$720$	3.93199e7	+	2.39114e6i	2.82671	+	0.171899i
$721$		0			0
$722$			2.78782e6i			0.199031i
$723$			5.95716e6i			0.423832i
$724$	−1.98333e6			−0.140620
$725$	−1.21818e7	−	1.48711e6i	−0.860731	−	0.105075i
$726$	3.59389e6			0.253060
$727$		−	1.41880e7i		−	0.995602i	−0.867291	−	0.497801i	$-0.834141\pi$
$727$		−	1.41880e7i		−	0.995602i	0.867291	−	0.497801i	$-0.165859\pi$
$728$		0			0
$729$	−1.51749e6			−0.105756
$730$	3.91525e6	+	238096.i	0.271927	+	0.0165366i
$731$	−2.55732e7			−1.77007
$732$			9.03574e6i			0.623284i
$733$			2.34439e7i			1.61165i	0.592155	+	0.805824i	$0.298277\pi$
$733$			2.34439e7i			1.61165i	−0.592155	+	0.805824i	$0.701723\pi$
$734$	1.18794e7			0.813866
$735$		0			0
$736$	2.25480e7			1.53431
$737$			1.97366e7i			1.33845i
$738$		−	2.54277e7i		−	1.71856i
$739$	−2.00145e6			−0.134813			−0.0674067	−	0.997726i	$-0.521472\pi$
$739$	−2.00145e6			−0.134813			−0.0674067	+	0.997726i	$0.521472\pi$
$740$	−11559.8	+	190089.i	−0.000776017	+	0.0127608i
$741$	−1.34669e7			−0.900993
$742$		0			0
$743$			2.14306e7i			1.42417i	0.702092	+	0.712086i	$0.252250\pi$
$743$			2.14306e7i			1.42417i	−0.702092	+	0.712086i	$0.747750\pi$
$744$	−1.87378e7			−1.24104
$745$	2.30092e7	+	1.39925e6i	1.51884	+	0.0923642i
$746$	2.18589e7			1.43807
$747$			3.26504e7i			2.14086i
$748$			1.19621e7i			0.781725i
$749$		0			0
$750$	3.38640e7	+	6.23967e6i	2.19829	+	0.405050i
$751$	1.29011e6			0.0834696			0.0417348	−	0.999129i	$-0.486712\pi$
$751$	1.29011e6			0.0834696			0.0417348	+	0.999129i	$0.486712\pi$
$752$		−	1.26917e6i		−	0.0818419i
$753$			2.85823e6i			0.183701i
$754$	9.10970e6			0.583547
$755$	−9.75701e6	−	593348.i	−0.622945	−	0.0378828i
$756$		0			0
$757$		−	1.56970e7i		−	0.995584i	−0.867296	−	0.497792i	$-0.834144\pi$
$757$		−	1.56970e7i		−	0.995584i	0.867296	−	0.497792i	$-0.165856\pi$
$758$			1.91798e6i			0.121247i
$759$	−4.82377e7			−3.03936
$760$	−515320.	+	8.47391e6i	−0.0323625	+	0.532169i
$761$	−6.48317e6			−0.405813			−0.202906	−	0.979198i	$-0.565039\pi$
$761$	−6.48317e6			−0.405813			−0.202906	+	0.979198i	$0.565039\pi$
$762$		−	1.96281e7i		−	1.22459i
$763$		0			0
$764$	1.23262e7			0.764002
$765$	3.11776e6	−	5.12684e7i	0.192615	−	3.16735i
$766$	2.78143e7			1.71276
$767$		−	1.20403e7i		−	0.739006i
$768$			3.60914e7i			2.20801i
$769$	−9.95572e6			−0.607095			−0.303548	−	0.952816i	$-0.598171\pi$
$769$	−9.95572e6			−0.607095			−0.303548	+	0.952816i	$0.598171\pi$
$770$		0			0
$771$	−4.75522e7			−2.88094
$772$		−	1.03345e6i		−	0.0624090i
$773$		−	3.04692e7i		−	1.83406i	−0.398821	−	0.917029i	$-0.630581\pi$
$773$		−	3.04692e7i		−	1.83406i	0.398821	−	0.917029i	$-0.369419\pi$
$774$	−5.90938e7			−3.54560
$775$	−1.95790e7	−	2.39014e6i	−1.17095	−	0.142945i
$776$	9.61944e6			0.573450
$777$		0			0
$778$		−	970613.i		−	0.0574906i
$779$	9.51000e6			0.561483
$780$	−8.83078e6	−	537022.i	−0.519712	−	0.0316050i
$781$	2.26458e7			1.32849
$782$		−	4.71745e7i		−	2.75861i
$783$			3.40705e7i			1.98598i
$784$		0			0
$785$	651245.	−	1.07091e7i	0.0377199	−	0.620265i
$786$	6.63618e7			3.83144
$787$			1.70221e7i			0.979660i	0.871818	+	0.489830i	$0.162941\pi$
$787$			1.70221e7i			0.979660i	−0.871818	+	0.489830i	$0.837059\pi$
$788$		−	5.65798e6i		−	0.324598i
$789$	1.70736e7			0.976412
$790$	1.05119e6	−	1.72857e7i	0.0599256	−	0.985415i
$791$		0			0
$792$		−	2.45770e7i		−	1.39225i
$793$			6.27758e6i			0.354494i
$794$	−1.76317e7			−0.992529
$795$	3.18873e7	+	1.93915e6i	1.78937	+	0.108816i
$796$	−1.38223e6			−0.0773211
$797$			2.90850e7i			1.62190i	0.585118	+	0.810948i	$0.301048\pi$
$797$			2.90850e7i			1.62190i	−0.585118	+	0.810948i	$0.698952\pi$
$798$		0			0
$799$	−1.65485e6			−0.0917046
$800$	−2.11177e6	+	1.72988e7i	−0.116660	+	0.955631i
$801$	5.13647e7			2.82868
$802$			4.34505e7i			2.38539i
$803$		−	4.24697e6i		−	0.232429i
$804$	−2.22472e7			−1.21377
$805$		0			0
$806$	1.46414e7			0.793863
$807$			2.09442e7i			1.13209i
$808$			3.50405e6i			0.188817i
$809$	4.89596e6			0.263006			0.131503	−	0.991316i	$-0.458020\pi$
$809$	4.89596e6			0.263006			0.131503	+	0.991316i	$0.458020\pi$
$810$	2.62492e6	−	4.31642e7i	0.140574	−	2.31159i
$811$	−1.03809e7			−0.554221			−0.277110	−	0.960838i	$-0.589377\pi$
$811$	−1.03809e7			−0.554221			−0.277110	+	0.960838i	$0.589377\pi$
$812$		0			0
$813$			5.01281e7i			2.65984i
$814$	595721.			0.0315124
$815$	232860.	−	3.82915e6i	0.0122801	−	0.201933i
$816$	6.01096e7			3.16023
$817$		−	2.21012e7i		−	1.15841i
$818$		−	412388.i		−	0.0215488i
$819$		0			0
$820$	6.23610e6	+	379233.i	0.323876	+	0.0196957i
$821$	−1.98760e7			−1.02913			−0.514565	−	0.857451i	$-0.672047\pi$
$821$	−1.98760e7			−1.02913			−0.514565	+	0.857451i	$0.672047\pi$
$822$			2.12306e7i			1.09593i
$823$		−	2.82566e7i		−	1.45419i	−0.686538	−	0.727094i	$-0.740871\pi$
$823$		−	2.82566e7i		−	1.45419i	0.686538	−	0.727094i	$-0.259129\pi$
$824$	−6.01241e6			−0.308482
$825$	4.51778e6	−	3.70078e7i	0.231095	−	1.89303i
$826$		0			0
$827$			1.11643e7i			0.567631i	0.958879	+	0.283815i	$0.0916003\pi$
$827$			1.11643e7i			0.567631i	−0.958879	+	0.283815i	$0.908400\pi$
$828$		−	3.77310e7i		−	1.91259i
$829$	2.12115e7			1.07198			0.535988	−	0.844226i	$-0.319939\pi$
$829$	2.12115e7			1.07198			0.535988	+	0.844226i	$0.319939\pi$
$830$	−2.31346e7	−	1.40687e6i	−1.16565	−	0.0708859i
$831$	−2.09177e6			−0.105078
$832$			636373.i			0.0318715i
$833$		0			0
$834$	−6.71433e7			−3.34263
$835$	1.33986e6	−	2.20326e7i	0.0665031	−	1.09358i
$836$	−1.03381e7			−0.511592
$837$			5.47592e7i			2.70174i
$838$			4.75935e7i			2.34120i
$839$	−2.12943e7			−1.04438			−0.522190	−	0.852829i	$-0.674885\pi$
$839$	−2.12943e7			−1.04438			−0.522190	+	0.852829i	$0.674885\pi$
$840$		0			0
$841$	−5.08886e6			−0.248102
$842$			1.59902e6i			0.0777273i
$843$			2.21293e7i			1.07250i
$844$	2.70504e6			0.130713
$845$	1.45825e7	+	886796.i	0.702569	+	0.0427250i
$846$	−3.82398e6			−0.183692
$847$		0			0
$848$			2.59430e7i			1.23888i
$849$	1.46467e7			0.697380
$850$	3.61921e7	+	4.41821e6i	1.71817	+	0.209748i
$851$	−813160.			−0.0384904
$852$			2.55265e7i			1.20474i
$853$		−	1.47529e7i		−	0.694230i	−0.937823	−	0.347115i	$-0.887161\pi$
$853$		−	1.47529e7i		−	0.694230i	0.937823	−	0.347115i	$-0.112839\pi$
$854$		0			0
$855$	4.43079e7	+	2.69448e6i	2.07284	+	0.126055i
$856$	5.67311e6			0.264629
$857$		−	4.03681e7i		−	1.87753i	−0.344563	−	0.938763i	$-0.611973\pi$
$857$		−	4.03681e7i		−	1.87753i	0.344563	−	0.938763i	$-0.388027\pi$
$858$			2.76748e7i			1.28341i
$859$	−2.22445e7			−1.02858			−0.514291	−	0.857616i	$-0.671945\pi$
$859$	−2.22445e7			−1.02858			−0.514291	+	0.857616i	$0.671945\pi$
$860$	881336.	−	1.44927e7i	0.0406345	−	0.668193i
$861$		0			0
$862$			4.48611e7i			2.05637i
$863$		−	3.39032e6i		−	0.154958i	−0.996994	−	0.0774788i	$-0.975313\pi$
$863$		−	3.39032e6i		−	0.154958i	0.996994	−	0.0774788i	$-0.0246870\pi$
$864$	4.83817e7			2.20494
$865$	303000.	−	4.98252e6i	0.0137690	−	0.226417i
$866$	1.82423e7			0.826581
$867$		−	3.83693e7i		−	1.73355i
$868$		0			0
$869$	−1.87502e7			−0.842280
$870$	−4.31927e7	−	2.62666e6i	−1.93469	−	0.117654i
$871$	−1.54562e7			−0.690333
$872$			1.82485e7i			0.812712i
$873$		−	5.02977e7i		−	2.23364i
$874$	4.07698e7			1.80535
$875$		0			0
$876$	4.78721e6			0.210777
$877$		−	2.06439e7i		−	0.906344i	−0.891423	−	0.453172i	$-0.850292\pi$
$877$		−	2.06439e7i		−	0.906344i	0.891423	−	0.453172i	$-0.149708\pi$
$878$		−	2.55785e7i		−	1.11979i
$879$	−3.16972e7			−1.38372
$880$	3.02207e7	+	1.83780e6i	1.31552	+	0.0800002i
$881$	3.88340e6			0.168567			0.0842835	−	0.996442i	$-0.473140\pi$
$881$	3.88340e6			0.168567			0.0842835	+	0.996442i	$0.473140\pi$
$882$		0			0
$883$		−	5.36409e6i		−	0.231523i	−0.993277	−	0.115762i	$-0.963069\pi$
$883$		−	5.36409e6i		−	0.231523i	0.993277	−	0.115762i	$-0.0369308\pi$
$884$	−9.36784e6			−0.403189
$885$	−3.47165e6	+	5.70877e7i	−0.148997	+	2.45010i
$886$	−1.85565e7			−0.794167
$887$		−	3.72663e7i		−	1.59040i	−0.606345	−	0.795202i	$-0.707365\pi$
$887$		−	3.72663e7i		−	1.59040i	0.606345	−	0.795202i	$-0.292635\pi$
$888$		−	597049.i		−	0.0254084i
$889$		0			0
$890$	−2.21325e6	+	3.63946e7i	−0.0936603	+	1.54015i
$891$	−4.68212e7			−1.97582
$892$		−	1.30810e7i		−	0.550463i
$893$		−	1.43018e6i		−	0.0600152i
$894$	8.12813e7			3.40131
$895$	1.56077e6	+	94914.6i	0.0651302	+	0.00396073i
$896$		0			0
$897$		−	3.77762e7i		−	1.56761i
$898$			3.14019e7i			1.29947i
$899$	2.47872e7			1.02289
$900$	2.89471e7	+	3.53376e6i	1.19124	+	0.145422i
$901$	3.38266e7			1.38818
$902$		−	1.95433e7i		−	0.799802i
$903$		0			0
$904$	1.91429e7			0.779089
$905$	6.53324e6	+	397303.i	0.265160	+	0.0161250i
$906$	−3.44672e7			−1.39504
$907$		−	1.38298e7i		−	0.558211i	−0.960260	−	0.279105i	$-0.909962\pi$
$907$		−	1.38298e7i		−	0.558211i	0.960260	−	0.279105i	$-0.0900379\pi$
$908$		−	1.03016e7i		−	0.414659i
$909$	1.83218e7			0.735458
$910$		0			0
$911$	1.68110e7			0.671117			0.335558	−	0.942019i	$-0.391075\pi$
$911$	1.68110e7			0.671117			0.335558	+	0.942019i	$0.391075\pi$
$912$			5.19488e7i			2.06818i
$913$			2.50947e7i			0.996333i
$914$	−4.17626e7			−1.65357
$915$	1.81005e6	−	2.97645e7i	0.0714724	−	1.17529i
$916$	1.04994e7			0.413451
$917$		0			0
$918$		−	1.01223e8i		−	3.96436i
$919$	3.69687e6			0.144393			0.0721964	−	0.997390i	$-0.476999\pi$
$919$	3.69687e6			0.144393			0.0721964	+	0.997390i	$0.476999\pi$
$920$	−2.37703e7	−	1.44553e6i	−0.925903	−	0.0563065i
$921$	−4.52763e6			−0.175882
$922$		−	2.86989e7i		−	1.11183i
$923$			1.77345e7i			0.685196i
$924$		0			0
$925$	76157.9	−	623854.i	0.00292658	−	0.0239733i
$926$	−5.05658e7			−1.93789
$927$			3.14374e7i			1.20156i
$928$		−	2.19004e7i		−	0.834799i
$929$	−4.38026e7			−1.66518			−0.832589	−	0.553892i	$-0.813142\pi$
$929$	−4.38026e7			−1.66518			−0.832589	+	0.553892i	$0.813142\pi$
$930$	−6.94207e7	−	4.22165e6i	−2.63198	−	0.160057i
$931$		0			0
$932$		−	1.52648e7i		−	0.575641i
$933$		−	3.96277e7i		−	1.49037i
$934$	1.31924e7			0.494832
$935$	2.39627e6	−	3.94042e7i	0.0896409	−	1.47405i
$936$	1.92469e7			0.718076
$937$		−	222461.i		−	0.00827762i	−0.999991	−	0.00413881i	$-0.998683\pi$
$937$		−	222461.i		−	0.00827762i	0.999991	−	0.00413881i	$-0.00131743\pi$
$938$		0			0
$939$	1.76656e7			0.653830
$940$	57031.5	−	937826.i	0.00210521	−	0.0346180i
$941$	3.90168e7			1.43641			0.718204	−	0.695832i	$-0.244964\pi$
$941$	3.90168e7			1.43641			0.718204	+	0.695832i	$0.244964\pi$
$942$		−	3.78304e7i		−	1.38903i
$943$			2.66767e7i			0.976905i
$944$	−4.64457e7			−1.69635
$945$		0			0
$946$	−4.54186e7			−1.65008
$947$			6.36923e6i			0.230787i	0.993320	+	0.115394i	$0.0368129\pi$
$947$			6.36923e6i			0.230787i	−0.993320	+	0.115394i	$0.963187\pi$
$948$		−	2.11353e7i		−	0.763816i
$949$	3.32591e6			0.119880
$950$	−3.81837e6	+	3.12785e7i	−0.137268	+	1.12444i
$951$	−5.49034e7			−1.96856
$952$		0			0
$953$		−	2.69493e7i		−	0.961203i	−0.876939	−	0.480601i	$-0.840418\pi$
$953$		−	2.69493e7i		−	0.961203i	0.876939	−	0.480601i	$-0.159582\pi$
$954$	7.81656e7			2.78064
$955$	−4.06034e7	−	2.46919e6i	−1.44063	−	0.0876086i
$956$	−1.32576e7			−0.469158
$957$			4.68522e7i			1.65367i
$958$		−	7.29700e6i		−	0.256880i
$959$		0			0
$960$	183489.	−	3.01729e6i	0.00642588	−	0.105667i
$961$	1.12097e7			0.391548
$962$			466525.i			0.0162531i
$963$		−	2.96633e7i		−	1.03075i
$964$	−3.58132e6			−0.124123
$965$	−207023.	+	3.40428e6i	−0.00715649	+	0.117681i
$966$		0			0
$967$			4.94426e7i			1.70034i	0.526510	+	0.850169i	$0.323500\pi$
$967$			4.94426e7i			1.70034i	−0.526510	+	0.850169i	$0.676500\pi$
$968$		−	1.92102e6i		−	0.0658936i
$969$	6.77350e7			2.31741
$970$	3.56386e7	+	2.16727e6i	1.21616	+	0.0739579i
$971$	2.41232e7			0.821084			0.410542	−	0.911842i	$-0.365340\pi$
$971$	2.41232e7			0.821084			0.410542	+	0.911842i	$0.365340\pi$
$972$		−	1.70664e7i		−	0.579396i
$973$		0			0
$974$	−2.04526e7			−0.690798
$975$	2.89817e7	+	3.53799e6i	0.976367	+	0.119191i
$976$	2.42159e7			0.813722
$977$		−	3.53366e7i		−	1.18437i	−0.805801	−	0.592186i	$-0.798265\pi$
$977$		−	3.53366e7i		−	1.18437i	0.805801	−	0.592186i	$-0.201735\pi$
$978$		−	1.35267e7i		−	0.452214i
$979$	3.94781e7			1.31644
$980$		0			0
$981$	9.54170e7			3.16558
$982$			4.66599e7i			1.54406i
$983$			2.86857e7i			0.946852i	0.880834	+	0.473426i	$0.156983\pi$
$983$			2.86857e7i			0.946852i	−0.880834	+	0.473426i	$0.843017\pi$
$984$	−1.95869e7			−0.644878
$985$	−1.13341e6	+	1.86378e7i	−0.0372219	+	0.612076i
$986$	−4.58195e7			−1.50092
$987$		0			0
$988$		−	8.09601e6i		−	0.263863i
$989$	6.19965e7			2.01547
$990$	5.53723e6	−	9.10541e7i	0.179558	−	2.95265i
$991$	−4.46529e7			−1.44433			−0.722163	−	0.691723i	$-0.756852\pi$
$991$	−4.46529e7			−1.44433			−0.722163	+	0.691723i	$0.756852\pi$
$992$		−	3.51990e7i		−	1.13567i
$993$			2.22221e7i			0.715173i
$994$		0			0
$995$	4.55318e6	+	276891.i	0.145800	+	0.00886646i
$996$	−2.82869e7			−0.903517
$997$		−	1.35119e7i		−	0.430505i	−0.976558	−	0.215253i	$-0.930943\pi$
$997$		−	1.35119e7i		−	0.430505i	0.976558	−	0.215253i	$-0.0690575\pi$
$998$			4.08350e7i			1.29780i
$999$	−1.74481e6			−0.0553140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.b.c.99.4	yes	12
5.4	even	2	inner	245.6.b.c.99.9	yes	12
7.6	odd	2	inner	245.6.b.c.99.3	✓	12
35.34	odd	2	inner	245.6.b.c.99.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.b.c.99.3	✓	12	7.6	odd	2	inner
245.6.b.c.99.4	yes	12	1.1	even	1	trivial
245.6.b.c.99.9	yes	12	5.4	even	2	inner
245.6.b.c.99.10	yes	12	35.34	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.99564i q^{2} +28.1764i q^{3} -16.9390 q^{4} +(55.7986 + 3.39325i) q^{5} +197.112 q^{6} -105.361i q^{8} -550.907 q^{9} +O(q^{10})\)	\(q-6.99564i q^{2} +28.1764i q^{3} -16.9390 q^{4} +(55.7986 + 3.39325i) q^{5} +197.112 q^{6} -105.361i q^{8} -550.907 q^{9} +(23.7380 - 390.347i) q^{10} -423.419 q^{11} -477.281i q^{12} -331.590i q^{13} +(-95.6095 + 1572.20i) q^{15} -1279.12 q^{16} +1667.82i q^{17} +3853.95i q^{18} -1441.39 q^{19} +(-945.175 - 57.4785i) q^{20} +2962.09i q^{22} -4043.26i q^{23} +2968.69 q^{24} +(3101.97 + 378.678i) q^{25} -2319.69 q^{26} -8675.69i q^{27} -3927.12 q^{29} +(10998.6 + 668.850i) q^{30} -6311.80 q^{31} +5576.70i q^{32} -11930.4i q^{33} +11667.5 q^{34} +9331.84 q^{36} -201.115i q^{37} +10083.4i q^{38} +9343.01 q^{39} +(357.517 - 5879.00i) q^{40} -6597.82 q^{41} +15333.3i q^{43} +7172.32 q^{44} +(-30739.8 - 1869.37i) q^{45} -28285.2 q^{46} +992.224i q^{47} -36040.9i q^{48} +(2649.10 - 21700.3i) q^{50} -46993.0 q^{51} +5616.83i q^{52} -20282.0i q^{53} -60692.0 q^{54} +(-23626.2 - 1436.77i) q^{55} -40613.0i q^{57} +27472.8i q^{58} +36310.7 q^{59} +(1619.53 - 26631.6i) q^{60} -18931.7 q^{61} +44155.1i q^{62} -1919.15 q^{64} +(1125.17 - 18502.3i) q^{65} -83460.9 q^{66} -46612.4i q^{67} -28251.2i q^{68} +113924. q^{69} -53483.1 q^{71} +58044.1i q^{72} +10030.2i q^{73} -1406.93 q^{74} +(-10669.8 + 87402.2i) q^{75} +24415.7 q^{76} -65360.4i q^{78} +44282.9 q^{79} +(-71373.0 - 4340.37i) q^{80} +110579. q^{81} +46156.0i q^{82} -59266.7i q^{83} +(-5659.33 + 93061.9i) q^{85} +107266. q^{86} -110652. i q^{87} +44611.9i q^{88} -93236.6 q^{89} +(-13077.4 + 215045. i) q^{90} +68488.9i q^{92} -177844. i q^{93} +6941.25 q^{94} +(-80427.3 - 4890.99i) q^{95} -157131. q^{96} +91299.8i q^{97} +233264. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 236 q^{4} - 1280 q^{9}+O(q^{10}) \) 12 * q - 236 * q^4 - 1280 * q^9	\( 12 q - 236 q^{4} - 1280 q^{9} - 12 q^{11} - 820 q^{15} - 4524 q^{16} + 9260 q^{25} + 8372 q^{29} + 27820 q^{30} - 8996 q^{36} + 11484 q^{39} + 51464 q^{44} - 36376 q^{46} + 45700 q^{50} - 198516 q^{51} - 90620 q^{60} + 64156 q^{64} + 137140 q^{65} - 466736 q^{71} + 56824 q^{74} + 107876 q^{79} + 369068 q^{81} + 356780 q^{85} - 76400 q^{86} - 436480 q^{95} + 980088 q^{99}+O(q^{100}) \) 12 * q - 236 * q^4 - 1280 * q^9 - 12 * q^11 - 820 * q^15 - 4524 * q^16 + 9260 * q^25 + 8372 * q^29 + 27820 * q^30 - 8996 * q^36 + 11484 * q^39 + 51464 * q^44 - 36376 * q^46 + 45700 * q^50 - 198516 * q^51 - 90620 * q^60 + 64156 * q^64 + 137140 * q^65 - 466736 * q^71 + 56824 * q^74 + 107876 * q^79 + 369068 * q^81 + 356780 * q^85 - 76400 * q^86 - 436480 * q^95 + 980088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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