LMFDB - Embedded newform 97.6.b.a.96.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,6,Mod(96,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.96"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	97.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5572305219$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			96.25
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.13637 q^{2} -26.9093 q^{3} -22.1632 q^{4} -95.4056i q^{5} -84.3974 q^{6} -82.4789i q^{7} -169.876 q^{8} +481.111 q^{9} -299.227i q^{10} -573.103 q^{11} +596.397 q^{12} +288.476i q^{13} -258.684i q^{14} +2567.30i q^{15} +176.431 q^{16} -997.460i q^{17} +1508.94 q^{18} -828.231i q^{19} +2114.50i q^{20} +2219.45i q^{21} -1797.46 q^{22} +3908.18i q^{23} +4571.23 q^{24} -5977.23 q^{25} +904.765i q^{26} -6407.39 q^{27} +1828.00i q^{28} +2949.29i q^{29} +8051.99i q^{30} +5310.23 q^{31} +5989.37 q^{32} +15421.8 q^{33} -3128.40i q^{34} -7868.95 q^{35} -10663.0 q^{36} -15305.2i q^{37} -2597.64i q^{38} -7762.68i q^{39} +16207.1i q^{40} -5087.22i q^{41} +6961.00i q^{42} -4043.83 q^{43} +12701.8 q^{44} -45900.7i q^{45} +12257.5i q^{46} +6271.38 q^{47} -4747.63 q^{48} +10004.2 q^{49} -18746.8 q^{50} +26840.9i q^{51} -6393.55i q^{52} +63.7343 q^{53} -20095.9 q^{54} +54677.2i q^{55} +14011.2i q^{56} +22287.1i q^{57} +9250.05i q^{58} -24044.5i q^{59} -56899.6i q^{60} -39048.8 q^{61} +16654.8 q^{62} -39681.5i q^{63} +13139.1 q^{64} +27522.2 q^{65} +48368.4 q^{66} +57423.9i q^{67} +22106.9i q^{68} -105166. i q^{69} -24679.9 q^{70} +58055.9i q^{71} -81729.0 q^{72} -26907.7 q^{73} -48002.7i q^{74} +160843. q^{75} +18356.3i q^{76} +47268.9i q^{77} -24346.6i q^{78} -86523.1 q^{79} -16832.5i q^{80} +55508.5 q^{81} -15955.4i q^{82} -45441.2i q^{83} -49190.1i q^{84} -95163.3 q^{85} -12682.9 q^{86} -79363.3i q^{87} +97356.2 q^{88} +97809.7 q^{89} -143961. i q^{90} +23793.1 q^{91} -86617.8i q^{92} -142895. q^{93} +19669.4 q^{94} -79017.9 q^{95} -161170. q^{96} +(-10862.2 + 92029.1i) q^{97} +31376.9 q^{98} -275726. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) $ 40 * q - 2 * q^2 + 40 * q^3 + 638 * q^4 - 130 * q^6 + 180 * q^8 + 3300 * q^9 + 382 * q^11 + 2586 * q^12 + 10174 * q^16 + 4738 * q^18 + 1996 * q^22 - 3102 * q^24 - 25178 * q^25 + 3046 * q^27 + 14796 * q^31 + 8128 * q^32 - 9434 * q^33 - 2964 * q^35 + 18124 * q^36 - 45814 * q^43 - 60186 * q^44 - 17866 * q^47 + 69528 * q^48 - 64166 * q^49 + 78812 * q^50 + 117092 * q^53 - 53962 * q^54 - 33546 * q^61 - 148838 * q^62 + 215708 * q^64 + 89628 * q^65 - 17136 * q^66 + 218204 * q^70 - 127452 * q^72 + 25562 * q^73 - 52722 * q^75 - 193912 * q^79 + 175440 * q^81 - 243192 * q^85 + 108918 * q^86 + 155578 * q^88 - 434816 * q^89 - 483858 * q^91 - 66746 * q^93 - 245480 * q^94 + 97106 * q^95 - 306196 * q^96 - 251282 * q^97 - 310510 * q^98 - 562238 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	3.13637			0.554436			0.277218	−	0.960807i	$-0.410588\pi$
$2$	3.13637			0.554436			0.277218	+	0.960807i	$0.410588\pi$
$3$	−26.9093			−1.72623			−0.863116	−	0.505005i	$-0.831491\pi$
$3$	−26.9093			−1.72623			−0.863116	+	0.505005i	$0.831491\pi$
$4$	−22.1632			−0.692600
$5$		−	95.4056i		−	1.70667i	−0.521365	−	0.853334i	$-0.674577\pi$
$5$		−	95.4056i		−	1.70667i	0.521365	−	0.853334i	$-0.325423\pi$
$6$	−84.3974			−0.957086
$7$		−	82.4789i		−	0.636206i	−0.948056	−	0.318103i	$-0.896954\pi$
$7$		−	82.4789i		−	0.636206i	0.948056	−	0.318103i	$-0.103046\pi$
$8$	−169.876			−0.938439
$9$	481.111			1.97988
$10$		−	299.227i		−	0.946238i
$11$	−573.103			−1.42807			−0.714037	−	0.700108i	$-0.753135\pi$
$11$	−573.103			−1.42807			−0.714037	+	0.700108i	$0.753135\pi$
$12$	596.397			1.19559
$13$			288.476i			0.473424i	0.971580	+	0.236712i	$0.0760699\pi$
$13$			288.476i			0.473424i	−0.971580	+	0.236712i	$0.923930\pi$
$14$		−	258.684i		−	0.352736i
$15$			2567.30i			2.94611i
$16$	176.431			0.172296
$17$		−	997.460i		−	0.837092i	−0.908196	−	0.418546i	$-0.862540\pi$
$17$		−	997.460i		−	0.837092i	0.908196	−	0.418546i	$-0.137460\pi$
$18$	1508.94			1.09772
$19$		−	828.231i		−	0.526342i	−0.964749	−	0.263171i	$-0.915232\pi$
$19$		−	828.231i		−	0.526342i	0.964749	−	0.263171i	$-0.0847683\pi$
$20$			2114.50i			1.18204i
$21$			2219.45i			1.09824i
$22$	−1797.46			−0.791776
$23$			3908.18i			1.54048i	0.637757	+	0.770238i	$0.279862\pi$
$23$			3908.18i			1.54048i	−0.637757	+	0.770238i	$0.720138\pi$
$24$	4571.23			1.61996
$25$	−5977.23			−1.91271
$26$			904.765i			0.262484i
$27$	−6407.39			−1.69150
$28$			1828.00i			0.440637i
$29$			2949.29i			0.651212i	0.945506	+	0.325606i	$0.105568\pi$
$29$			2949.29i			0.651212i	−0.945506	+	0.325606i	$0.894432\pi$
$30$			8051.99i			1.63343i
$31$	5310.23			0.992451			0.496225	−	0.868194i	$-0.334719\pi$
$31$	5310.23			0.992451			0.496225	+	0.868194i	$0.334719\pi$
$32$	5989.37			1.03397
$33$	15421.8			2.46519
$34$		−	3128.40i		−	0.464114i
$35$	−7868.95			−1.08579
$36$	−10663.0			−1.37126
$37$		−	15305.2i		−	1.83796i	−0.394309	−	0.918978i	$-0.629016\pi$
$37$		−	15305.2i		−	1.83796i	0.394309	−	0.918978i	$-0.370984\pi$
$38$		−	2597.64i		−	0.291823i
$39$		−	7762.68i		−	0.817241i
$40$			16207.1i			1.60160i
$41$		−	5087.22i		−	0.472630i	−0.971677	−	0.236315i	$-0.924060\pi$
$41$		−	5087.22i		−	0.472630i	0.971677	−	0.236315i	$-0.0759397\pi$
$42$			6961.00i			0.608904i
$43$	−4043.83			−0.333520			−0.166760	−	0.985998i	$-0.553330\pi$
$43$	−4043.83			−0.333520			−0.166760	+	0.985998i	$0.553330\pi$
$44$	12701.8			0.989085
$45$		−	45900.7i		−	3.37900i
$46$			12257.5i			0.854095i
$47$	6271.38			0.414113			0.207056	−	0.978329i	$-0.433612\pi$
$47$	6271.38			0.414113			0.207056	+	0.978329i	$0.433612\pi$
$48$	−4747.63			−0.297423
$49$	10004.2			0.595242
$50$	−18746.8			−1.06048
$51$			26840.9i			1.44502i
$52$		−	6393.55i		−	0.327894i
$53$	63.7343			0.00311662			0.00155831	−	0.999999i	$-0.499504\pi$
$53$	63.7343			0.00311662			0.00155831	+	0.999999i	$0.499504\pi$
$54$	−20095.9			−0.937828
$55$			54677.2i			2.43725i
$56$			14011.2i			0.597041i
$57$			22287.1i			0.908588i
$58$			9250.05i			0.361055i
$59$		−	24044.5i		−	0.899263i	−0.893214	−	0.449631i	$-0.851555\pi$
$59$		−	24044.5i		−	0.899263i	0.893214	−	0.449631i	$-0.148445\pi$
$60$		−	56899.6i		−	2.04047i
$61$	−39048.8			−1.34364			−0.671821	−	0.740714i	$-0.734488\pi$
$61$	−39048.8			−1.34364			−0.671821	+	0.740714i	$0.734488\pi$
$62$	16654.8			0.550251
$63$		−	39681.5i		−	1.25961i
$64$	13139.1			0.400973
$65$	27522.2			0.807978
$66$	48368.4			1.36679
$67$			57423.9i			1.56281i	0.624025	+	0.781404i	$0.285496\pi$
$67$			57423.9i			1.56281i	−0.624025	+	0.781404i	$0.714504\pi$
$68$			22106.9i			0.579770i
$69$		−	105166.i		−	2.65922i
$70$	−24679.9			−0.602003
$71$			58055.9i			1.36679i	0.730051	+	0.683393i	$0.239496\pi$
$71$			58055.9i			1.36679i	−0.730051	+	0.683393i	$0.760504\pi$
$72$	−81729.0			−1.85800
$73$	−26907.7			−0.590976			−0.295488	−	0.955346i	$-0.595482\pi$
$73$	−26907.7			−0.590976			−0.295488	+	0.955346i	$0.595482\pi$
$74$		−	48002.7i		−	1.01903i
$75$	160843.			3.30179
$76$			18356.3i			0.364544i
$77$			47268.9i			0.908550i
$78$		−	24346.6i		−	0.453108i
$79$	−86523.1			−1.55978			−0.779892	−	0.625914i	$-0.784726\pi$
$79$	−86523.1			−1.55978			−0.779892	+	0.625914i	$0.784726\pi$
$80$		−	16832.5i		−	0.294052i
$81$	55508.5			0.940041
$82$		−	15955.4i		−	0.262043i
$83$		−	45441.2i		−	0.724027i	−0.932173	−	0.362013i	$-0.882089\pi$
$83$		−	45441.2i		−	0.724027i	0.932173	−	0.362013i	$-0.117911\pi$
$84$		−	49190.1i		−	0.760641i
$85$	−95163.3			−1.42864
$86$	−12682.9			−0.184915
$87$		−	79363.3i		−	1.12414i
$88$	97356.2			1.34016
$89$	97809.7			1.30890			0.654450	−	0.756105i	$-0.272900\pi$
$89$	97809.7			1.30890			0.654450	+	0.756105i	$0.272900\pi$
$90$		−	143961.i		−	1.87344i
$91$	23793.1			0.301195
$92$		−	86617.8i		−	1.06693i
$93$	−142895.			−1.71320
$94$	19669.4			0.229599
$95$	−79017.9			−0.898290
$96$	−161170.			−1.78487
$97$	−10862.2	+	92029.1i	−0.117216	+	0.993106i
$97$	−10862.2	+	92029.1i	−0.117216	+	0.993106i
$98$	31376.9			0.330024
$99$	−275726.			−2.82741
$100$	132475.			1.32475
$101$	33007.0			0.321960			0.160980	−	0.986958i	$-0.448535\pi$
$101$	33007.0			0.321960			0.160980	+	0.986958i	$0.448535\pi$
$102$			84183.0i			0.801169i
$103$	−116401.			−1.08109			−0.540547	−	0.841314i	$-0.681783\pi$
$103$	−116401.			−1.08109			−0.540547	+	0.841314i	$0.681783\pi$
$104$		−	49005.0i		−	0.444280i
$105$	211748.			1.87433
$106$	199.894			0.00172797
$107$			1625.30i			0.0137238i	0.999976	+	0.00686188i	$0.00218422\pi$
$107$			1625.30i			0.0137238i	−0.999976	+	0.00686188i	$0.997816\pi$
$108$	142008.			1.17153
$109$	112304.			0.905378			0.452689	−	0.891669i	$-0.350465\pi$
$109$	112304.			0.905378			0.452689	+	0.891669i	$0.350465\pi$
$110$			171488.i			1.35130i
$111$			411853.i			3.17274i
$112$		−	14551.8i		−	0.109616i
$113$	−48043.4			−0.353946			−0.176973	−	0.984216i	$-0.556631\pi$
$113$	−48043.4			−0.353946			−0.176973	+	0.984216i	$0.556631\pi$
$114$			69900.6i			0.503754i
$115$	372862.			2.62908
$116$		−	65365.7i		−	0.451030i
$117$			138789.i			0.937323i
$118$		−	75412.5i		−	0.498584i
$119$	−82269.4			−0.532563
$120$		−	436121.i		−	2.76474i
$121$	167396.			1.03940
$122$	−122471.			−0.744964
$123$			136894.i			0.815869i
$124$	−117692.			−0.687372
$125$			272119.i			1.55770i
$126$		−	124456.i		−	0.698374i
$127$		−	253036.i		−	1.39211i	−0.717988	−	0.696055i	$-0.754937\pi$
$127$		−	253036.i		−	1.39211i	0.717988	−	0.696055i	$-0.245063\pi$
$128$	−150451.			−0.811652
$129$	108817.			0.575732
$130$	86319.6			0.447972
$131$			369803.i			1.88275i	0.337366	+	0.941374i	$0.390464\pi$
$131$			369803.i			1.88275i	−0.337366	+	0.941374i	$0.609536\pi$
$132$	−341797.			−1.70739
$133$	−68311.6			−0.334862
$134$			180102.i			0.866478i
$135$			611301.i			2.88683i
$136$			169444.i			0.785560i
$137$			68696.5i			0.312704i	0.987701	+	0.156352i	$0.0499734\pi$
$137$			68696.5i			0.312704i	−0.987701	+	0.156352i	$0.950027\pi$
$138$		−	329840.i		−	1.47437i
$139$			176664.i			0.775550i	0.921754	+	0.387775i	$0.126756\pi$
$139$			176664.i			0.775550i	−0.921754	+	0.387775i	$0.873244\pi$
$140$	174401.			0.752020
$141$	−168759.			−0.714855
$142$			182084.i			0.757796i
$143$		−	165326.i		−	0.676085i
$144$	84882.8			0.341125
$145$	281379.			1.11140
$146$	−84392.5			−0.327659
$147$	−269207.			−1.02753
$148$			339213.i			1.27297i
$149$			207858.i			0.767011i	0.923539	+	0.383505i	$0.125283\pi$
$149$			207858.i			0.767011i	−0.923539	+	0.383505i	$0.874717\pi$
$150$	504463.			1.83063
$151$	−516830.			−1.84461			−0.922307	−	0.386458i	$-0.873699\pi$
$151$	−516830.			−1.84461			−0.922307	+	0.386458i	$0.873699\pi$
$152$			140696.i			0.493939i
$153$		−	479888.i		−	1.65734i
$154$			148253.i			0.503733i
$155$		−	506626.i		−	1.69378i
$156$			172046.i			0.566021i
$157$		−	343605.i		−	1.11253i	−0.831006	−	0.556263i	$-0.812235\pi$
$157$		−	343605.i		−	1.11253i	0.831006	−	0.556263i	$-0.187765\pi$
$158$	−271368.			−0.864801
$159$	−1715.05			−0.00538001
$160$		−	571420.i		−	1.76464i
$161$	322342.			0.980060
$162$	174095.			0.521193
$163$	−344327.			−1.01508			−0.507542	−	0.861627i	$-0.669446\pi$
$163$	−344327.			−1.01508			−0.507542	+	0.861627i	$0.669446\pi$
$164$			112749.i			0.327343i
$165$		−	1.47133e6i		−	4.20726i
$166$		−	142520.i		−	0.401427i
$167$	603963.			1.67579			0.837895	−	0.545832i	$-0.183786\pi$
$167$	603963.			1.67579			0.837895	+	0.545832i	$0.183786\pi$
$168$		−	377030.i		−	1.03063i
$169$	288075.			0.775869
$170$	−298467.			−0.792088
$171$		−	398471.i		−	1.04209i
$172$	89624.2			0.230996
$173$			267403.i			0.679284i	0.940555	+	0.339642i	$0.110306\pi$
$173$			267403.i			0.679284i	−0.940555	+	0.339642i	$0.889694\pi$
$174$		−	248912.i		−	0.623266i
$175$			492996.i			1.21688i
$176$	−101113.			−0.246051
$177$			647022.i			1.55234i
$178$	306767.			0.725702
$179$		−	199233.i		−	0.464759i	−0.972625	−	0.232380i	$-0.925349\pi$
$179$		−	199233.i		−	0.464759i	0.972625	−	0.232380i	$-0.0746512\pi$
$180$			1.01731e6i			2.34029i
$181$		−	571624.i		−	1.29692i	−0.761248	−	0.648461i	$-0.775413\pi$
$181$		−	571624.i		−	1.29692i	0.761248	−	0.648461i	$-0.224587\pi$
$182$	74624.0			0.166994
$183$	1.05078e6			2.31944
$184$		−	663904.i		−	1.44564i
$185$	−1.46020e6			−3.13678
$186$	−448169.			−0.949860
$187$			571647.i			1.19543i
$188$	−138994.			−0.286815
$189$			528474.i			1.07614i
$190$	−247829.			−0.498045
$191$	973520.			1.93091			0.965454	−	0.260575i	$-0.0839120\pi$
$191$	973520.			1.93091			0.965454	+	0.260575i	$0.0839120\pi$
$192$	−353563.			−0.692172
$193$	−34733.2			−0.0671200			−0.0335600	−	0.999437i	$-0.510684\pi$
$193$	−34733.2			−0.0671200			−0.0335600	+	0.999437i	$0.510684\pi$
$194$	−34067.8	+	288637.i	−0.0649890	+	0.550614i
$195$	−740603.			−1.39476
$196$	−221726.			−0.412265
$197$	−75425.5			−0.138469			−0.0692345	−	0.997600i	$-0.522056\pi$
$197$	−75425.5			−0.138469			−0.0692345	+	0.997600i	$0.522056\pi$
$198$	−864777.			−1.56762
$199$			354176.i			0.633996i	0.948426	+	0.316998i	$0.102675\pi$
$199$			354176.i			0.633996i	−0.948426	+	0.316998i	$0.897325\pi$
$200$	1.01539e6			1.79497
$201$		−	1.54524e6i		−	2.69777i
$202$	103522.			0.178506
$203$	243254.			0.414305
$204$		−	594882.i		−	1.00082i
$205$	−485349.			−0.806622
$206$	−365076.			−0.599398
$207$			1.88027e6i			3.04995i
$208$			50896.0i			0.0815690i
$209$			474662.i			0.751655i
$210$	664119.			1.03920
$211$		−	733549.i		−	1.13429i	−0.823619	−	0.567144i	$-0.808048\pi$
$211$		−	733549.i		−	1.13429i	0.823619	−	0.567144i	$-0.191952\pi$
$212$	−1412.56			−0.00215857
$213$		−	1.56224e6i		−	2.35939i
$214$			5097.52i			0.00760894i
$215$			385804.i			0.569207i
$216$	1.08846e6			1.58737
$217$		−	437982.i		−	0.631403i
$218$	352227.			0.501974
$219$	724068.			1.02016
$220$		−	1.21182e6i		−	1.68804i
$221$	287743.			0.396300
$222$			1.29172e6i			1.75908i
$223$			874658.i			1.17781i	0.808202	+	0.588906i	$0.200441\pi$
$223$			874658.i			1.17781i	−0.808202	+	0.588906i	$0.799559\pi$
$224$		−	493997.i		−	0.657815i
$225$	−2.87571e6			−3.78694
$226$	−150682.			−0.196241
$227$	−438011.			−0.564183			−0.282092	−	0.959387i	$-0.591028\pi$
$227$	−438011.			−0.564183			−0.282092	+	0.959387i	$0.591028\pi$
$228$		−	493954.i		−	0.629288i
$229$	−507797.			−0.639885			−0.319942	−	0.947437i	$-0.603664\pi$
$229$	−507797.			−0.639885			−0.319942	+	0.947437i	$0.603664\pi$
$230$	1.16943e6			1.45766
$231$		−	1.27197e6i		−	1.56837i
$232$		−	501012.i		−	0.611123i
$233$		−	363402.i		−	0.438528i	−0.975666	−	0.219264i	$-0.929634\pi$
$233$		−	363402.i		−	0.438528i	0.975666	−	0.219264i	$-0.0703657\pi$
$234$			435292.i			0.519686i
$235$		−	598325.i		−	0.706753i
$236$			532904.i			0.622830i
$237$	2.32828e6			2.69255
$238$	−258027.			−0.295272
$239$			1.39025e6i			1.57434i	0.616735	+	0.787171i	$0.288455\pi$
$239$			1.39025e6i			1.57434i	−0.616735	+	0.787171i	$0.711545\pi$
$240$			452951.i			0.507602i
$241$	−558025.			−0.618886			−0.309443	−	0.950918i	$-0.600143\pi$
$241$	−558025.			−0.618886			−0.309443	+	0.950918i	$0.600143\pi$
$242$	525015.			0.576279
$243$	63300.5			0.0687688
$244$	865448.			0.930607
$245$		−	954460.i		−	1.01588i
$246$			429348.i			0.452347i
$247$	238924.			0.249183
$248$	−902078.			−0.931354
$249$			1.22279e6i			1.24984i
$250$			853465.i			0.863646i
$251$			1.37652e6i			1.37911i	0.724233	+	0.689556i	$0.242194\pi$
$251$			1.37652e6i			1.37911i	−0.724233	+	0.689556i	$0.757806\pi$
$252$			879469.i			0.872407i
$253$		−	2.23979e6i		−	2.19991i
$254$		−	793615.i		−	0.771836i
$255$	2.56078e6			2.46616
$256$	−892319.			−0.850982
$257$			154904.i			0.146295i	0.997321	+	0.0731473i	$0.0233043\pi$
$257$			154904.i			0.146295i	−0.997321	+	0.0731473i	$0.976696\pi$
$258$	341288.			0.319207
$259$	−1.26236e6			−1.16932
$260$	−609980.			−0.559606
$261$			1.41893e6i			1.28932i
$262$			1.15984e6i			1.04386i
$263$		−	1.65844e6i		−	1.47846i	−0.673451	−	0.739231i	$-0.735189\pi$
$263$		−	1.65844e6i		−	1.47846i	0.673451	−	0.739231i	$-0.264811\pi$
$264$	−2.61979e6			−2.31343
$265$		−	6080.61i		−	0.00531903i
$266$	−214250.			−0.185659
$267$	−2.63199e6			−2.25947
$268$		−	1.27270e6i		−	1.08240i
$269$	−2.15900e6			−1.81916			−0.909582	−	0.415525i	$-0.863598\pi$
$269$	−2.15900e6			−1.81916			−0.909582	+	0.415525i	$0.863598\pi$
$270$			1.91726e6i			1.60056i
$271$			1.31006e6i			1.08360i	0.840508	+	0.541800i	$0.182257\pi$
$271$			1.31006e6i			1.08360i	−0.840508	+	0.541800i	$0.817743\pi$
$272$		−	175983.i		−	0.144227i
$273$	−640257.			−0.519933
$274$			215457.i			0.173374i
$275$	3.42557e6			2.73150
$276$			2.33082e6i			1.84178i
$277$		−	104116.i		−	0.0815303i	−0.999169	−	0.0407652i	$-0.987020\pi$
$277$		−	104116.i		−	0.0815303i	0.999169	−	0.0407652i	$-0.0129796\pi$
$278$			554081.i			0.429993i
$279$	2.55481e6			1.96493
$280$	1.33674e6			1.01895
$281$			2.08313e6i			1.57381i	0.617076	+	0.786903i	$0.288317\pi$
$281$			2.08313e6i			1.57381i	−0.617076	+	0.786903i	$0.711683\pi$
$282$	−529289.			−0.396342
$283$	−1.48615e6			−1.10305			−0.551527	−	0.834157i	$-0.685955\pi$
$283$	−1.48615e6			−1.10305			−0.551527	+	0.834157i	$0.685955\pi$
$284$		−	1.28671e6i		−	0.946636i
$285$	2.12632e6			1.55066
$286$		−	518523.i		−	0.374846i
$287$	−419588.			−0.300690
$288$	2.88155e6			2.04713
$289$	424931.			0.299277
$290$	882506.			0.616202
$291$	292294.	−	2.47644e6i	0.202343	−	1.71433i
$292$	596362.			0.409310
$293$	432344.			0.294212			0.147106	−	0.989121i	$-0.453004\pi$
$293$	432344.			0.294212			0.147106	+	0.989121i	$0.453004\pi$
$294$	−844331.			−0.569698
$295$	−2.29398e6			−1.53474
$296$			2.59998e6i			1.72481i
$297$	3.67209e6			2.41559
$298$			651919.i			0.425258i
$299$	−1.12741e6			−0.729299
$300$	−3.56480e6			−2.28682
$301$			333530.i			0.212187i
$302$	−1.62097e6			−1.02272
$303$	−888194.			−0.555778
$304$		−	146126.i		−	0.0906864i
$305$			3.72548e6i			2.29315i
$306$		−	1.50511e6i		−	0.918890i
$307$	1.87052e6			1.13270			0.566352	−	0.824163i	$-0.308354\pi$
$307$	1.87052e6			1.13270			0.566352	+	0.824163i	$0.308354\pi$
$308$		−	1.04763e6i		−	0.629262i
$309$	3.13227e6			1.86622
$310$		−	1.58896e6i		−	0.939095i
$311$			1.52832e6i			0.896011i	0.894031	+	0.448005i	$0.147865\pi$
$311$			1.52832e6i			0.896011i	−0.894031	+	0.448005i	$0.852135\pi$
$312$			1.31869e6i			0.766931i
$313$	−851146.			−0.491070			−0.245535	−	0.969388i	$-0.578964\pi$
$313$	−851146.			−0.491070			−0.245535	+	0.969388i	$0.578964\pi$
$314$		−	1.07767e6i		−	0.616825i
$315$	−3.78583e6			−2.14974
$316$	1.91763e6			1.08031
$317$			7630.94i			0.00426511i	0.999998	+	0.00213255i	$0.000678813\pi$
$317$			7630.94i			0.00426511i	−0.999998	+	0.00213255i	$0.999321\pi$
$318$	−5379.01			−0.00298287
$319$		−	1.69025e6i		−	0.929979i
$320$		−	1.25354e6i		−	0.684327i
$321$		−	43735.6i		−	0.0236904i
$322$	1.01098e6			0.543381
$323$	−826127.			−0.440596
$324$	−1.23025e6			−0.651073
$325$		−	1.72429e6i		−	0.905526i
$326$	−1.07993e6			−0.562799
$327$	−3.02203e6			−1.56289
$328$			864195.i			0.443534i
$329$		−	517257.i		−	0.263461i
$330$		−	4.61462e6i		−	2.33266i
$331$		−	1.62463e6i		−	0.815052i	−0.913194	−	0.407526i	$-0.866392\pi$
$331$		−	1.62463e6i		−	0.815052i	0.913194	−	0.407526i	$-0.133608\pi$
$332$			1.00712e6i			0.501461i
$333$		−	7.36350e6i		−	3.63893i
$334$	1.89425e6			0.929118
$335$	5.47856e6			2.66719
$336$			391579.i			0.189222i
$337$		−	412404.i		−	0.197810i	−0.995097	−	0.0989050i	$-0.968466\pi$
$337$		−	412404.i		−	0.197810i	0.995097	−	0.0989050i	$-0.0315340\pi$
$338$	903508.			0.430170
$339$	1.29281e6			0.610994
$340$	2.10912e6			0.989475
$341$	−3.04331e6			−1.41729
$342$		−	1.24975e6i		−	0.577774i
$343$		−	2.21136e6i		−	1.01490i
$344$	686947.			0.312988
$345$	−1.00335e7			−4.53840
$346$			838675.i			0.376620i
$347$			258797.i			0.115381i	0.998335	+	0.0576906i	$0.0183737\pi$
$347$			258797.i			0.115381i	−0.998335	+	0.0576906i	$0.981626\pi$
$348$			1.75895e6i			0.778582i
$349$			1.10867e6i			0.487237i	0.969871	+	0.243618i	$0.0783344\pi$
$349$			1.10867e6i			0.487237i	−0.969871	+	0.243618i	$0.921666\pi$
$350$			1.54621e6i			0.674683i
$351$		−	1.84838e6i		−	0.800797i
$352$	−3.43253e6			−1.47658
$353$	878209.			0.375112			0.187556	−	0.982254i	$-0.439943\pi$
$353$	878209.			0.375112			0.187556	+	0.982254i	$0.439943\pi$
$354$			2.02930e6i			0.860672i
$355$	5.53886e6			2.33265
$356$	−2.16778e6			−0.906545
$357$	2.21381e6			0.919327
$358$		−	624866.i		−	0.257679i
$359$			184309.i			0.0754763i	0.999288	+	0.0377381i	$0.0120153\pi$
$359$			184309.i			0.0754763i	−0.999288	+	0.0377381i	$0.987985\pi$
$360$			7.79740e6i			3.17098i
$361$	1.79013e6			0.722965
$362$		−	1.79282e6i		−	0.719061i
$363$	−4.50451e6			−1.79424
$364$	−527333.			−0.208608
$365$			2.56715e6i			1.00860i
$366$	3.29562e6			1.28598
$367$		−	1.96696e6i		−	0.762307i	−0.924512	−	0.381153i	$-0.875527\pi$
$367$		−	1.96696e6i		−	0.762307i	0.924512	−	0.381153i	$-0.124473\pi$
$368$			689523.i			0.265417i
$369$		−	2.44752e6i		−	0.935749i
$370$	−4.57973e6			−1.73914
$371$		−	5256.73i		−	0.00198281i
$372$	3.16700e6			1.18656
$373$			2.42386e6i			0.902060i	0.892509	+	0.451030i	$0.148943\pi$
$373$			2.42386e6i			0.902060i	−0.892509	+	0.451030i	$0.851057\pi$
$374$			1.79289e6i			0.662789i
$375$		−	7.32253e6i		−	2.68895i
$376$	−1.06536e6			−0.388620
$377$	−850798.			−0.308300
$378$			1.65749e6i			0.596652i
$379$	−3.45648e6			−1.23605			−0.618026	−	0.786158i	$-0.712067\pi$
$379$	−3.45648e6			−1.23605			−0.618026	+	0.786158i	$0.712067\pi$
$380$	1.75129e6			0.622156
$381$			6.80903e6i			2.40311i
$382$	3.05331e6			1.07057
$383$		−	2.54854e6i		−	0.887759i	−0.896086	−	0.443880i	$-0.853602\pi$
$383$		−	2.54854e6i		−	0.887759i	0.896086	−	0.443880i	$-0.146398\pi$
$384$	4.04853e6			1.40110
$385$	4.50972e6			1.55059
$386$	−108936.			−0.0372137
$387$	−1.94553e6			−0.660328
$388$	240741.	−	2.03966e6i	0.0811841	−	0.687826i
$389$	157675.			0.0528310			0.0264155	−	0.999651i	$-0.491591\pi$
$389$	157675.			0.0528310			0.0264155	+	0.999651i	$0.491591\pi$
$390$	−2.32280e6			−0.773305
$391$	3.89825e6			1.28952
$392$	−1.69948e6			−0.558598
$393$		−	9.95114e6i		−	3.25006i
$394$	−236562.			−0.0767723
$395$			8.25479e6i			2.66203i
$396$	6.11097e6			1.95827
$397$	−2.97514e6			−0.947395			−0.473698	−	0.880687i	$-0.657081\pi$
$397$	−2.97514e6			−0.947395			−0.473698	+	0.880687i	$0.657081\pi$
$398$			1.11083e6i			0.351510i
$399$	1.83822e6			0.578049
$400$	−1.05457e6			−0.329553
$401$		−	593448.i		−	0.184298i	−0.995745	−	0.0921492i	$-0.970626\pi$
$401$		−	593448.i		−	0.184298i	0.995745	−	0.0921492i	$-0.0293737\pi$
$402$		−	4.84643e6i		−	1.49574i
$403$			1.53187e6i			0.469850i
$404$	−731540.			−0.222990
$405$		−	5.29582e6i		−	1.60434i
$406$	762934.			0.229706
$407$			8.77146e6i			2.62474i
$408$		−	4.55962e6i		−	1.35606i
$409$			4.60575e6i			1.36142i	0.732553	+	0.680709i	$0.238328\pi$
$409$			4.60575e6i			1.36142i	−0.732553	+	0.680709i	$0.761672\pi$
$410$	−1.52223e6			−0.447220
$411$		−	1.84857e6i		−	0.539799i
$412$	2.57982e6			0.748766
$413$	−1.98317e6			−0.572116
$414$			5.89720e6i			1.69101i
$415$	−4.33535e6			−1.23567
$416$			1.72779e6i			0.489505i
$417$		−	4.75389e6i		−	1.33878i
$418$			1.48871e6i			0.416745i
$419$	−1.53664e6			−0.427600			−0.213800	−	0.976877i	$-0.568584\pi$
$419$	−1.53664e6			−0.427600			−0.213800	+	0.976877i	$0.568584\pi$
$420$	−4.69302e6			−1.29816
$421$	−1.00930e6			−0.277534			−0.138767	−	0.990325i	$-0.544314\pi$
$421$	−1.00930e6			−0.277534			−0.138767	+	0.990325i	$0.544314\pi$
$422$		−	2.30068e6i		−	0.628890i
$423$	3.01723e6			0.819893
$424$	−10826.9			−0.00292476
$425$			5.96205e6i			1.60112i
$426$		−	4.89977e6i		−	1.30813i
$427$			3.22070e6i			0.854833i
$428$		−	36021.8i		−	0.00950508i
$429$			4.44881e6i			1.16708i
$430$			1.21002e6i			0.315589i
$431$	13469.7			0.00349274			0.00174637	−	0.999998i	$-0.499444\pi$
$431$	13469.7			0.00349274			0.00174637	+	0.999998i	$0.499444\pi$
$432$	−1.13046e6			−0.291438
$433$		−	1.46966e6i		−	0.376701i	−0.982102	−	0.188350i	$-0.939686\pi$
$433$		−	1.46966e6i		−	0.376701i	0.982102	−	0.188350i	$-0.0603141\pi$
$434$		−	1.37367e6i		−	0.350073i
$435$	−7.57170e6			−1.91854
$436$	−2.48902e6			−0.627065
$437$	3.23688e6			0.810816
$438$	2.27094e6			0.565615
$439$			2.65977e6i			0.658692i	0.944209	+	0.329346i	$0.106828\pi$
$439$			2.65977e6i			0.658692i	−0.944209	+	0.329346i	$0.893172\pi$
$440$		−	9.28833e6i		−	2.28721i
$441$	4.81314e6			1.17851
$442$	902466.			0.219723
$443$		−	1.44305e6i		−	0.349360i	−0.984625	−	0.174680i	$-0.944111\pi$
$443$		−	1.44305e6i		−	0.349360i	0.984625	−	0.174680i	$-0.0558890\pi$
$444$		−	9.12798e6i		−	2.19744i
$445$		−	9.33159e6i		−	2.23386i
$446$			2.74325e6i			0.653022i
$447$		−	5.59332e6i		−	1.32404i
$448$		−	1.08370e6i		−	0.255101i
$449$	−952823.			−0.223047			−0.111523	−	0.993762i	$-0.535573\pi$
$449$	−952823.			−0.223047			−0.111523	+	0.993762i	$0.535573\pi$
$450$	−9.01928e6			−2.09962
$451$			2.91550e6i			0.674950i
$452$	1.06480e6			0.245143
$453$	1.39075e7			3.18423
$454$	−1.37376e6			−0.312804
$455$		−	2.27000e6i		−	0.514041i
$456$		−	3.78604e6i		−	0.852654i
$457$			2.79217e6i			0.625390i	0.949854	+	0.312695i	$0.101232\pi$
$457$			2.79217e6i			0.625390i	−0.949854	+	0.312695i	$0.898768\pi$
$458$	−1.59264e6			−0.354775
$459$			6.39111e6i			1.41594i
$460$	−8.26382e6			−1.82090
$461$	−4.75789e6			−1.04271			−0.521353	−	0.853341i	$-0.674573\pi$
$461$	−4.75789e6			−1.04271			−0.521353	+	0.853341i	$0.674573\pi$
$462$		−	3.98937e6i		−	0.869560i
$463$	−1.49074e6			−0.323183			−0.161592	−	0.986858i	$-0.551663\pi$
$463$	−1.49074e6			−0.323183			−0.161592	+	0.986858i	$0.551663\pi$
$464$			520346.i			0.112201i
$465$			1.36329e7i			2.92386i
$466$		−	1.13976e6i		−	0.243136i
$467$	−649635.			−0.137841			−0.0689203	−	0.997622i	$-0.521955\pi$
$467$	−649635.			−0.137841			−0.0689203	+	0.997622i	$0.521955\pi$
$468$		−	3.07600e6i		−	0.649190i
$469$	4.73626e6			0.994268
$470$		−	1.87657e6i		−	0.391850i
$471$			9.24616e6i			1.92048i
$472$			4.08458e6i			0.843903i
$473$	2.31753e6			0.476291
$474$	7.30232e6			1.49285
$475$			4.95053e6i			1.00674i
$476$	1.82335e6			0.368853
$477$	30663.2			0.00617053
$478$			4.36034e6i			0.872872i
$479$	8.78954e6			1.75036			0.875180	−	0.483797i	$-0.160743\pi$
$479$	8.78954e6			1.75036			0.875180	+	0.483797i	$0.160743\pi$
$480$			1.53765e7i			3.04617i
$481$	4.41518e6			0.870133
$482$	−1.75017e6			−0.343133
$483$	−8.67400e6			−1.69181
$484$	−3.71003e6			−0.719887
$485$	8.78009e6	+	1.03631e6i	1.69490	+	0.200049i
$486$	198534.			0.0381279
$487$	−5.12517e6			−0.979233			−0.489617	−	0.871938i	$-0.662863\pi$
$487$	−5.12517e6			−0.979233			−0.489617	+	0.871938i	$0.662863\pi$
$488$	6.63344e6			1.26093
$489$	9.26559e6			1.75227
$490$		−	2.99354e6i		−	0.563241i
$491$	3.16695e6			0.592839			0.296420	−	0.955058i	$-0.404207\pi$
$491$	3.16695e6			0.592839			0.296420	+	0.955058i	$0.404207\pi$
$492$		−	3.03400e6i		−	0.565071i
$493$	2.94180e6			0.545124
$494$	749354.			0.138156
$495$			2.63058e7i			4.82546i
$496$	936888.			0.170995
$497$	4.78839e6			0.869557
$498$			3.83512e6i			0.692956i
$499$		−	2.40107e6i		−	0.431672i	−0.976430	−	0.215836i	$-0.930752\pi$
$499$		−	2.40107e6i		−	0.431672i	0.976430	−	0.215836i	$-0.0692477\pi$
$500$		−	6.03103e6i		−	1.07886i
$501$	−1.62522e7			−2.89280
$502$			4.31728e6i			0.764629i
$503$	−3.03278e6			−0.534467			−0.267233	−	0.963632i	$-0.586109\pi$
$503$	−3.03278e6			−0.534467			−0.267233	+	0.963632i	$0.586109\pi$
$504$			6.74091e6i			1.18207i
$505$		−	3.14905e6i		−	0.549479i
$506$		−	7.02479e6i		−	1.21971i
$507$	−7.75189e6			−1.33933
$508$			5.60810e6i			0.964176i
$509$	−1.48353e6			−0.253806			−0.126903	−	0.991915i	$-0.540504\pi$
$509$	−1.48353e6			−0.253806			−0.126903	+	0.991915i	$0.540504\pi$
$510$	8.03153e6			1.36733
$511$			2.21932e6i			0.375983i
$512$	2.01579e6			0.339837
$513$			5.30680e6i			0.890306i
$514$			485834.i			0.0811111i
$515$			1.11053e7i			1.84507i
$516$	−2.41172e6			−0.398752
$517$	−3.59415e6			−0.591384
$518$	−3.95921e6			−0.648312
$519$		−	7.19564e6i		−	1.17260i
$520$	−4.67535e6			−0.758238
$521$	−2.23871e6			−0.361330			−0.180665	−	0.983545i	$-0.557825\pi$
$521$	−2.23871e6			−0.361330			−0.180665	+	0.983545i	$0.557825\pi$
$522$			4.45029e6i			0.714846i
$523$		−	1.09854e7i		−	1.75616i	−0.478516	−	0.878079i	$-0.658825\pi$
$523$		−	1.09854e7i		−	1.75616i	0.478516	−	0.878079i	$-0.341175\pi$
$524$		−	8.19602e6i		−	1.30399i
$525$		−	1.32662e7i		−	2.10062i
$526$		−	5.20147e6i		−	0.819713i
$527$		−	5.29674e6i		−	0.830772i
$528$	2.72088e6			0.424742
$529$	−8.83752e6			−1.37306
$530$		−	19071.0i		−	0.00294906i
$531$		−	1.15681e7i		−	1.78043i
$532$	1.51400e6			0.231925
$533$	1.46754e6			0.223754
$534$	−8.25488e6			−1.25273
$535$	155062.			0.0234219
$536$		−	9.75492e6i		−	1.46660i
$537$			5.36121e6i			0.802283i
$538$	−6.77141e6			−1.00861
$539$	−5.73345e6			−0.850050
$540$		−	1.35484e7i		−	1.99942i
$541$		−	3.19006e6i		−	0.468604i	−0.972164	−	0.234302i	$-0.924720\pi$
$541$		−	3.19006e6i		−	0.468604i	0.972164	−	0.234302i	$-0.0752805\pi$
$542$			4.10883e6i			0.600787i
$543$			1.53820e7i			2.23879i
$544$		−	5.97416e6i		−	0.865524i
$545$		−	1.07145e7i		−	1.54518i
$546$	−2.00808e6			−0.288270
$547$	1.16662e7			1.66709			0.833546	−	0.552451i	$-0.186307\pi$
$547$	1.16662e7			1.66709			0.833546	+	0.552451i	$0.186307\pi$
$548$		−	1.52253e6i		−	0.216579i
$549$	−1.87868e7			−2.66025
$550$	1.07438e7			1.51444
$551$	2.44269e6			0.342760
$552$			1.78652e7i			2.49551i
$553$			7.13633e6i			0.992344i
$554$		−	326547.i		−	0.0452034i
$555$	3.92930e7			5.41481
$556$		−	3.91543e6i		−	0.537146i
$557$	−5.64098e6			−0.770400			−0.385200	−	0.922833i	$-0.625868\pi$
$557$	−5.64098e6			−0.770400			−0.385200	+	0.922833i	$0.625868\pi$
$558$	8.01281e6			1.08943
$559$		−	1.16655e6i		−	0.157896i
$560$	−1.38833e6			−0.187077
$561$		−	1.53826e7i		−	2.06359i
$562$			6.53347e6i			0.872576i
$563$		−	1.79705e6i		−	0.238940i	−0.992838	−	0.119470i	$-0.961880\pi$
$563$		−	1.79705e6i		−	0.238940i	0.992838	−	0.119470i	$-0.0381196\pi$
$564$	3.74023e6			0.495109
$565$			4.58361e6i			0.604069i
$566$	−4.66111e6			−0.611573
$567$		−	4.57828e6i		−	0.598060i
$568$		−	9.86228e6i		−	1.28265i
$569$			1.01521e7i			1.31454i	0.753655	+	0.657271i	$0.228289\pi$
$569$			1.01521e7i			1.31454i	−0.753655	+	0.657271i	$0.771711\pi$
$570$	6.66891e6			0.859741
$571$	−7.70110e6			−0.988468			−0.494234	−	0.869329i	$-0.664551\pi$
$571$	−7.70110e6			−0.988468			−0.494234	+	0.869329i	$0.664551\pi$
$572$			3.66416e6i			0.468257i
$573$	−2.61967e7			−3.33320
$574$	−1.31598e6			−0.166713
$575$		−	2.33601e7i		−	2.94649i
$576$	6.32134e6			0.793877
$577$		−	1.28734e7i		−	1.60973i	−0.593458	−	0.804865i	$-0.702238\pi$
$577$		−	1.28734e7i		−	1.60973i	0.593458	−	0.804865i	$-0.297762\pi$
$578$	1.33274e6			0.165930
$579$	934647.			0.115865
$580$	−6.23626e6			−0.769758
$581$	−3.74794e6			−0.460630
$582$	916740.	−	7.76702e6i	0.112186	−	0.950488i
$583$	−36526.3			−0.00445076
$584$	4.57097e6			0.554595
$585$	1.32412e7			1.59970
$586$	1.35599e6			0.163122
$587$		−	5.21229e6i		−	0.624358i	−0.950023	−	0.312179i	$-0.898941\pi$
$587$		−	5.21229e6i		−	0.624358i	0.950023	−	0.312179i	$-0.101059\pi$
$588$	5.96649e6			0.711665
$589$		−	4.39810e6i		−	0.522368i
$590$	−7.19477e6			−0.850917
$591$	2.02965e6			0.239030
$592$		−	2.70031e6i		−	0.316672i
$593$	−5.90788e6			−0.689914			−0.344957	−	0.938619i	$-0.612106\pi$
$593$	−5.90788e6			−0.689914			−0.344957	+	0.938619i	$0.612106\pi$
$594$	1.15170e7			1.33929
$595$			7.84896e6i			0.908908i
$596$		−	4.60680e6i		−	0.531232i
$597$		−	9.53063e6i		−	1.09442i
$598$	−3.53598e6			−0.404350
$599$		−	1.10423e7i		−	1.25745i	−0.777627	−	0.628726i	$-0.783577\pi$
$599$		−	1.10423e7i		−	1.25745i	0.777627	−	0.628726i	$-0.216423\pi$
$600$	−2.73233e7			−3.09853
$601$		−	1.73604e6i		−	0.196054i	−0.995184	−	0.0980268i	$-0.968747\pi$
$601$		−	1.73604e6i		−	0.196054i	0.995184	−	0.0980268i	$-0.0312531\pi$
$602$			1.04607e6i			0.117644i
$603$			2.76273e7i			3.09417i
$604$	1.14546e7			1.27758
$605$		−	1.59705e7i		−	1.77391i
$606$	−2.78570e6			−0.308143
$607$	3.32052e6			0.365792			0.182896	−	0.983132i	$-0.441453\pi$
$607$	3.32052e6			0.365792			0.182896	+	0.983132i	$0.441453\pi$
$608$		−	4.96058e6i		−	0.544219i
$609$	−6.54580e6			−0.715186
$610$			1.16845e7i			1.27141i
$611$			1.80914e6i			0.196051i
$612$			1.06359e7i			1.14787i
$613$	1.25673e7			1.35080			0.675401	−	0.737450i	$-0.263970\pi$
$613$	1.25673e7			1.35080			0.675401	+	0.737450i	$0.263970\pi$
$614$	5.86664e6			0.628012
$615$	1.30604e7			1.39242
$616$		−	8.02983e6i		−	0.852618i
$617$	−8.36105e6			−0.884194			−0.442097	−	0.896967i	$-0.645765\pi$
$617$	−8.36105e6			−0.884194			−0.442097	+	0.896967i	$0.645765\pi$
$618$	9.82394e6			1.03470
$619$			1.55012e7i			1.62607i	0.582218	+	0.813033i	$0.302185\pi$
$619$			1.55012e7i			1.62607i	−0.582218	+	0.813033i	$0.697815\pi$
$620$			1.12284e7i			1.17311i
$621$		−	2.50412e7i		−	2.60571i
$622$			4.79337e6i			0.496781i
$623$		−	8.06723e6i		−	0.832731i
$624$		−	1.36958e6i		−	0.140807i
$625$	7.28284e6			0.745762
$626$	−2.66950e6			−0.272267
$627$		−	1.27728e7i		−	1.29753i
$628$			7.61539e6i			0.770536i
$629$	−1.52663e7			−1.53854
$630$	−1.18738e7			−1.19189
$631$	−7.04697e6			−0.704578			−0.352289	−	0.935891i	$-0.614597\pi$
$631$	−7.04697e6			−0.704578			−0.352289	+	0.935891i	$0.614597\pi$
$632$	1.46982e7			1.46376
$633$			1.97393e7i			1.95804i
$634$			23933.4i			0.00236473i
$635$	−2.41411e7			−2.37587
$636$	38010.9			0.00372619
$637$			2.88598e6i			0.281802i
$638$		−	5.30123e6i		−	0.515614i
$639$			2.79313e7i			2.70607i
$640$			1.43539e7i			1.38522i
$641$			4.69321e6i			0.451154i	0.974225	+	0.225577i	$0.0724268\pi$
$641$			4.69321e6i			0.451154i	−0.974225	+	0.225577i	$0.927573\pi$
$642$		−	137171.i		−	0.0131348i
$643$	2.48309e6			0.236846			0.118423	−	0.992963i	$-0.462216\pi$
$643$	2.48309e6			0.236846			0.118423	+	0.992963i	$0.462216\pi$
$644$	−7.14414e6			−0.678790
$645$		−	1.03817e7i		−	0.982584i
$646$	−2.59104e6			−0.244282
$647$	−1.55196e7			−1.45754			−0.728770	−	0.684759i	$-0.759908\pi$
$647$	−1.55196e7			−1.45754			−0.728770	+	0.684759i	$0.759908\pi$
$648$	−9.42954e6			−0.882171
$649$			1.37800e7i			1.28421i
$650$		−	5.40799e6i		−	0.502056i
$651$			1.17858e7i			1.08995i
$652$	7.63139e6			0.703047
$653$			1.85659e6i			0.170386i	0.996364	+	0.0851930i	$0.0271507\pi$
$653$			1.85659e6i			0.170386i	−0.996364	+	0.0851930i	$0.972849\pi$
$654$	−9.47818e6			−0.866524
$655$	3.52813e7			3.21322
$656$		−	897543.i		−	0.0814321i
$657$	−1.29456e7			−1.17006
$658$		−	1.62231e6i		−	0.146072i
$659$		−	2.75691e6i		−	0.247291i	−0.992326	−	0.123646i	$-0.960541\pi$
$659$		−	2.75691e6i		−	0.247291i	0.992326	−	0.123646i	$-0.0394586\pi$
$660$			3.26093e7i			2.91395i
$661$	−865188.			−0.0770206			−0.0385103	−	0.999258i	$-0.512261\pi$
$661$	−865188.			−0.0770206			−0.0385103	+	0.999258i	$0.512261\pi$
$662$		−	5.09544e6i		−	0.451894i
$663$	−7.74296e6			−0.684105
$664$			7.71935e6i			0.679455i
$665$			6.51731e6i			0.571497i
$666$		−	2.30946e7i		−	2.01755i
$667$	−1.15263e7			−1.00318
$668$	−1.33858e7			−1.16065
$669$		−	2.35364e7i		−	2.03318i
$670$	1.71828e7			1.47879
$671$	2.23790e7			1.91882
$672$			1.32931e7i			1.13554i
$673$	1.73987e6			0.148074			0.0740369	−	0.997256i	$-0.476412\pi$
$673$	1.73987e6			0.148074			0.0740369	+	0.997256i	$0.476412\pi$
$674$		−	1.29345e6i		−	0.109673i
$675$	3.82985e7			3.23535
$676$	−6.38466e6			−0.537367
$677$	9.14719e6			0.767037			0.383518	−	0.923533i	$-0.374712\pi$
$677$	9.14719e6			0.767037			0.383518	+	0.923533i	$0.374712\pi$
$678$	4.05474e6			0.338757
$679$	7.59046e6	+	895901.i	0.631820	+	0.0745737i
$680$	1.61659e7			1.34069
$681$	1.17866e7			0.973912
$682$	−9.54492e6			−0.785799
$683$	−8.73714e6			−0.716668			−0.358334	−	0.933594i	$-0.616655\pi$
$683$	−8.73714e6			−0.716668			−0.358334	+	0.933594i	$0.616655\pi$
$684$			8.83139e6i			0.721754i
$685$	6.55403e6			0.533681
$686$		−	6.93563e6i		−	0.562699i
$687$	1.36645e7			1.10459
$688$	−713456.			−0.0574640
$689$			18385.8i			0.00147548i
$690$	−3.14686e7			−2.51626
$691$	5.58931e6			0.445311			0.222655	−	0.974897i	$-0.428528\pi$
$691$	5.58931e6			0.445311			0.222655	+	0.974897i	$0.428528\pi$
$692$		−	5.92652e6i		−	0.470473i
$693$			2.27416e7i			1.79882i
$694$			811682.i			0.0639716i
$695$	1.68547e7			1.32361
$696$			1.34819e7i			1.05494i
$697$	−5.07430e6			−0.395634
$698$			3.47720e6i			0.270142i
$699$			9.77890e6i			0.757002i
$700$		−	1.09264e7i		−	0.842812i
$701$	1.82704e7			1.40428			0.702138	−	0.712041i	$-0.252229\pi$
$701$	1.82704e7			1.40428			0.702138	+	0.712041i	$0.252229\pi$
$702$		−	5.79718e6i		−	0.443991i
$703$	−1.26763e7			−0.967392
$704$	−7.53004e6			−0.572619
$705$			1.61005e7i			1.22002i
$706$	2.75439e6			0.207976
$707$		−	2.72238e6i		−	0.204833i
$708$		−	1.43401e7i		−	1.07515i
$709$		−	910191.i		−	0.0680013i	−0.999422	−	0.0340006i	$-0.989175\pi$
$709$		−	910191.i		−	0.0680013i	0.999422	−	0.0340006i	$-0.0108248\pi$
$710$	1.73719e7			1.29331
$711$	−4.16272e7			−3.08818
$712$	−1.66155e7			−1.22832
$713$			2.07533e7i			1.52885i
$714$	6.94332e6			0.509708
$715$	−1.57730e7			−1.15385
$716$			4.41564e6i			0.321892i
$717$		−	3.74107e7i		−	2.71768i
$718$			578060.i			0.0418468i
$719$		−	2.34684e7i		−	1.69301i	−0.532377	−	0.846507i	$-0.678701\pi$
$719$		−	2.34684e7i		−	1.69301i	0.532377	−	0.846507i	$-0.321299\pi$
$720$		−	8.09829e6i		−	0.582187i
$721$			9.60062e6i			0.687798i
$722$	5.61451e6			0.400838
$723$	1.50161e7			1.06834
$724$			1.26690e7i			0.898249i
$725$		−	1.76286e7i		−	1.24558i
$726$	−1.41278e7			−0.994792
$727$	−1.22924e7			−0.862585			−0.431293	−	0.902212i	$-0.641942\pi$
$727$	−1.22924e7			−0.862585			−0.431293	+	0.902212i	$0.641942\pi$
$728$	−4.04188e6			−0.282654
$729$	−1.51919e7			−1.05875
$730$			8.05152e6i			0.559204i
$731$			4.03355e6i			0.279186i
$732$	−2.32886e7			−1.60644
$733$	2.69653e7			1.85373			0.926864	−	0.375397i	$-0.122494\pi$
$733$	2.69653e7			1.85373			0.926864	+	0.375397i	$0.122494\pi$
$734$		−	6.16910e6i		−	0.422651i
$735$			2.56839e7i			1.75365i
$736$			2.34075e7i			1.59280i
$737$		−	3.29098e7i		−	2.23181i
$738$		−	7.67630e6i		−	0.518813i
$739$			5.81245e6i			0.391515i	0.980652	+	0.195757i	$0.0627165\pi$
$739$			5.81245e6i			0.391515i	−0.980652	+	0.195757i	$0.937283\pi$
$740$	3.23628e7			2.17253
$741$	−6.42929e6			−0.430148
$742$		−	16487.0i		−	0.00109934i
$743$	−2.63049e7			−1.74810			−0.874048	−	0.485839i	$-0.838514\pi$
$743$	−2.63049e7			−1.74810			−0.874048	+	0.485839i	$0.838514\pi$
$744$	2.42743e7			1.60773
$745$	1.98308e7			1.30903
$746$			7.60211e6i			0.500135i
$747$		−	2.18622e7i		−	1.43349i
$748$		−	1.26695e7i		−	0.827955i
$749$	134053.			0.00873113
$750$		−	2.29661e7i		−	1.49085i
$751$	−1.95041e7			−1.26190			−0.630950	−	0.775823i	$-0.717335\pi$
$751$	−1.95041e7			−1.26190			−0.630950	+	0.775823i	$0.717335\pi$
$752$	1.10647e6			0.0713499
$753$		−	3.70413e7i		−	2.38067i
$754$	−2.66841e6			−0.170932
$755$			4.93085e7i			3.14814i
$756$		−	1.17127e7i		−	0.745336i
$757$		−	1.03926e7i		−	0.659147i	−0.944130	−	0.329574i	$-0.893095\pi$
$757$		−	1.03926e7i		−	0.659147i	0.944130	−	0.329574i	$-0.106905\pi$
$758$	−1.08408e7			−0.685312
$759$			6.02711e7i			3.79756i
$760$	1.34232e7			0.842990
$761$			1.36330e7i			0.853357i	0.904403	+	0.426678i	$0.140316\pi$
$761$			1.36330e7i			0.853357i	−0.904403	+	0.426678i	$0.859684\pi$
$762$			2.13556e7i			1.33237i
$763$		−	9.26273e6i		−	0.576007i
$764$	−2.15763e7			−1.33735
$765$	−4.57841e7			−2.82853
$766$		−	7.99316e6i		−	0.492206i
$767$	6.93626e6			0.425733
$768$	2.40117e7			1.46899
$769$			1.49522e7i			0.911779i	0.890036	+	0.455890i	$0.150679\pi$
$769$			1.49522e7i			0.911779i	−0.890036	+	0.455890i	$0.849321\pi$
$770$	1.41441e7			0.859705
$771$		−	4.16835e6i		−	0.252539i
$772$	769800.			0.0464873
$773$	1.27499e6			0.0767463			0.0383732	−	0.999263i	$-0.487782\pi$
$773$	1.27499e6			0.0767463			0.0383732	+	0.999263i	$0.487782\pi$
$774$	−6.10188e6			−0.366110
$775$	−3.17405e7			−1.89827
$776$	1.84522e6	−	1.56335e7i	0.110000	−	0.931970i
$777$	3.39691e7			2.01852
$778$	494526.			0.0292914
$779$	−4.21339e6			−0.248765
$780$	1.64141e7			0.966010
$781$		−	3.32720e7i		−	1.95187i
$782$	1.22263e7			0.714956
$783$		−	1.88972e7i		−	1.10152i
$784$	1.76506e6			0.102558
$785$	−3.27818e7			−1.89871
$786$		−	3.12104e7i		−	1.80195i
$787$	−2.63718e7			−1.51776			−0.758880	−	0.651230i	$-0.774253\pi$
$787$	−2.63718e7			−1.51776			−0.758880	+	0.651230i	$0.774253\pi$
$788$	1.67167e6			0.0959037
$789$			4.46275e7i			2.55217i
$790$			2.58900e7i			1.47593i
$791$			3.96257e6i			0.225183i
$792$	4.68391e7			2.65336
$793$		−	1.12646e7i		−	0.636113i
$794$	−9.33113e6			−0.525270
$795$			163625.i			0.00918188i
$796$		−	7.84968e6i		−	0.439106i
$797$			1.94980e7i			1.08729i	0.839316	+	0.543643i	$0.182956\pi$
$797$			1.94980e7i			1.08729i	−0.839316	+	0.543643i	$0.817044\pi$
$798$	5.76532e6			0.320491
$799$		−	6.25545e6i		−	0.346651i
$800$	−3.57999e7			−1.97768
$801$	4.70573e7			2.59147
$802$		−	1.86127e6i		−	0.102182i
$803$	1.54209e7			0.843958
$804$			3.42474e7i			1.86848i
$805$		−	3.07533e7i		−	1.67264i
$806$			4.80451e6i			0.260502i
$807$	5.80972e7			3.14030
$808$	−5.60708e6			−0.302140
$809$	2.75267e7			1.47871			0.739354	−	0.673317i	$-0.235131\pi$
$809$	2.75267e7			1.47871			0.739354	+	0.673317i	$0.235131\pi$
$810$		−	1.66096e7i		−	0.889503i
$811$	−1.19960e7			−0.640451			−0.320226	−	0.947341i	$-0.603759\pi$
$811$	−1.19960e7			−0.640451			−0.320226	+	0.947341i	$0.603759\pi$
$812$	−5.39129e6			−0.286948
$813$		−	3.52529e7i		−	1.87054i
$814$			2.75105e7i			1.45525i
$815$			3.28507e7i			1.73241i
$816$			4.73557e6i			0.248970i
$817$			3.34922e6i			0.175545i
$818$			1.44453e7i			0.754820i
$819$	1.14471e7			0.596330
$820$	1.07569e7			0.558666
$821$			3.24705e7i			1.68125i	0.541620	+	0.840623i	$0.317811\pi$
$821$			3.24705e7i			1.68125i	−0.541620	+	0.840623i	$0.682189\pi$
$822$		−	5.79780e6i		−	0.299284i
$823$	−7.77043e6			−0.399894			−0.199947	−	0.979807i	$-0.564077\pi$
$823$	−7.77043e6			−0.399894			−0.199947	+	0.979807i	$0.564077\pi$
$824$	1.97737e7			1.01454
$825$	−9.21797e7			−4.71520
$826$	−6.21994e6			−0.317202
$827$		−	1.29252e7i		−	0.657163i	−0.944476	−	0.328581i	$-0.893430\pi$
$827$		−	1.29252e7i		−	0.657163i	0.944476	−	0.328581i	$-0.106570\pi$
$828$		−	4.16727e7i		−	2.11240i
$829$	4.33588e6			0.219125			0.109562	−	0.993980i	$-0.465055\pi$
$829$	4.33588e6			0.219125			0.109562	+	0.993980i	$0.465055\pi$
$830$	−1.35972e7			−0.685102
$831$			2.80170e6i			0.140740i
$832$			3.79030e6i			0.189830i
$833$		−	9.97882e6i		−	0.498272i
$834$		−	1.49099e7i		−	0.742268i
$835$		−	5.76215e7i		−	2.86002i
$836$		−	1.05200e7i		−	0.520597i
$837$	−3.40247e7			−1.67873
$838$	−4.81947e6			−0.237077
$839$			1.88783e7i			0.925889i	0.886387	+	0.462944i	$0.153207\pi$
$839$			1.88783e7i			0.925889i	−0.886387	+	0.462944i	$0.846793\pi$
$840$	−3.59708e7			−1.75894
$841$	1.18128e7			0.575923
$842$	−3.16554e6			−0.153875
$843$		−	5.60557e7i		−	2.71676i
$844$			1.62578e7i			0.785608i
$845$		−	2.74840e7i		−	1.32415i
$846$	9.46313e6			0.454579
$847$		−	1.38066e7i		−	0.661271i
$848$	11244.7			0.000536980
$849$	3.99913e7			1.90413
$850$			1.86992e7i			0.887718i
$851$	5.98155e7			2.83133
$852$			3.46243e7i			1.63411i
$853$		−	1.49671e7i		−	0.704313i	−0.935941	−	0.352156i	$-0.885448\pi$
$853$		−	1.49671e7i		−	0.704313i	0.935941	−	0.352156i	$-0.114552\pi$
$854$			1.01013e7i			0.473950i
$855$	−3.80164e7			−1.77851
$856$		−	276098.i		−	0.0128789i
$857$	−1.32117e7			−0.614476			−0.307238	−	0.951633i	$-0.599405\pi$
$857$	−1.32117e7			−0.614476			−0.307238	+	0.951633i	$0.599405\pi$
$858$			1.39531e7i			0.647072i
$859$			5.96714e6i			0.275920i	0.990438	+	0.137960i	$0.0440546\pi$
$859$			5.96714e6i			0.275920i	−0.990438	+	0.137960i	$0.955945\pi$
$860$		−	8.55065e6i		−	0.394233i
$861$	1.12908e7			0.519060
$862$	42246.0			0.00193650
$863$		−	2.95311e7i		−	1.34975i	−0.737933	−	0.674874i	$-0.764198\pi$
$863$		−	2.95311e7i		−	1.34975i	0.737933	−	0.674874i	$-0.235802\pi$
$864$	−3.83762e7			−1.74895
$865$	2.55118e7			1.15931
$866$		−	4.60939e6i		−	0.208857i
$867$	−1.14346e7			−0.516622
$868$			9.70708e6i			0.437310i
$869$	4.95866e7			2.22749
$870$	−2.37476e7			−1.06371
$871$	−1.65654e7			−0.739872
$872$	−1.90777e7			−0.849642
$873$	−5.22591e6	+	4.42762e7i	−0.232074	+	1.96623i
$874$	1.01520e7			0.449546
$875$	2.24441e7			0.991018
$876$	−1.60477e7			−0.706565
$877$	−2.61066e7			−1.14618			−0.573088	−	0.819494i	$-0.694255\pi$
$877$	−2.61066e7			−1.14618			−0.573088	+	0.819494i	$0.694255\pi$
$878$			8.34200e6i			0.365203i
$879$	−1.16341e7			−0.507878
$880$			9.64675e6i			0.419928i
$881$	−3.31155e7			−1.43745			−0.718724	−	0.695296i	$-0.755273\pi$
$881$	−3.31155e7			−1.43745			−0.718724	+	0.695296i	$0.755273\pi$
$882$	1.50958e7			0.653407
$883$		−	3.70375e6i		−	0.159860i	−0.996800	−	0.0799300i	$-0.974530\pi$
$883$		−	3.70375e6i		−	0.159860i	0.996800	−	0.0799300i	$-0.0254697\pi$
$884$	−6.37730e6			−0.274477
$885$	6.17295e7			2.64932
$886$		−	4.52594e6i		−	0.193698i
$887$			6.14035e6i			0.262050i	0.991379	+	0.131025i	$0.0418268\pi$
$887$			6.14035e6i			0.262050i	−0.991379	+	0.131025i	$0.958173\pi$
$888$		−	6.99637e7i		−	2.97742i
$889$	−2.08702e7			−0.885669
$890$		−	2.92673e7i		−	1.23853i
$891$	−3.18121e7			−1.34245
$892$		−	1.93852e7i		−	0.815753i
$893$		−	5.19416e6i		−	0.217965i
$894$		−	1.75427e7i		−	0.734095i
$895$	−1.90079e7			−0.793190
$896$			1.24090e7i			0.516378i
$897$	3.03379e7			1.25894
$898$	−2.98840e6			−0.123665
$899$			1.56614e7i			0.646295i
$900$	6.37350e7			2.62284
$901$		−	63572.4i		−	0.00260889i
$902$			9.14407e6i			0.374217i
$903$		−	8.97507e6i		−	0.366284i
$904$	8.16140e6			0.332157
$905$	−5.45361e7			−2.21341
$906$	4.36191e7			1.76545
$907$		−	9.76379e6i		−	0.394094i	−0.980394	−	0.197047i	$-0.936865\pi$
$907$		−	9.76379e6i		−	0.394094i	0.980394	−	0.197047i	$-0.0631352\pi$
$908$	9.70773e6			0.390754
$909$	1.58800e7			0.637442
$910$		−	7.11955e6i		−	0.285003i
$911$			3.27943e7i			1.30919i	0.755981	+	0.654594i	$0.227160\pi$
$911$			3.27943e7i			1.30919i	−0.755981	+	0.654594i	$0.772840\pi$
$912$			3.93214e6i			0.156546i
$913$			2.60425e7i			1.03396i
$914$			8.75725e6i			0.346739i
$915$		−	1.00250e8i		−	3.95851i
$916$	1.12544e7			0.443184
$917$	3.05009e7			1.19781
$918$			2.00449e7i			0.785048i
$919$			2.89871e6i			0.113218i	0.998396	+	0.0566091i	$0.0180289\pi$
$919$			2.89871e6i			0.113218i	−0.998396	+	0.0566091i	$0.981971\pi$
$920$	−6.33402e7			−2.46723
$921$	−5.03344e7			−1.95531
$922$	−1.49225e7			−0.578114
$923$	−1.67477e7			−0.647070
$924$			2.81910e7i			1.08625i
$925$			9.14828e7i			3.51548i
$926$	−4.67550e6			−0.179185
$927$	−5.60017e7			−2.14043
$928$			1.76644e7i			0.673331i
$929$			1.61081e7i			0.612356i	0.951974	+	0.306178i	$0.0990504\pi$
$929$			1.61081e7i			0.612356i	−0.951974	+	0.306178i	$0.900950\pi$
$930$			4.27579e7i			1.62110i
$931$		−	8.28582e6i		−	0.313301i
$932$			8.05416e6i			0.303725i
$933$		−	4.11260e7i		−	1.54672i
$934$	−2.03749e6			−0.0764238
$935$	5.45383e7			2.04020
$936$		−	2.35768e7i		−	0.879621i
$937$	3.43022e7			1.27636			0.638181	−	0.769887i	$-0.279687\pi$
$937$	3.43022e7			1.27636			0.638181	+	0.769887i	$0.279687\pi$
$938$	1.48546e7			0.551258
$939$	2.29037e7			0.847701
$940$			1.32608e7i			0.489498i
$941$		−	2.31090e7i		−	0.850759i	−0.905015	−	0.425379i	$-0.860141\pi$
$941$		−	2.31090e7i		−	0.850759i	0.905015	−	0.425379i	$-0.139859\pi$
$942$			2.89993e7i			1.06478i
$943$	1.98818e7			0.728074
$944$		−	4.24220e6i		−	0.154939i
$945$	5.04194e7			1.83662
$946$	7.26862e6			0.264073
$947$		−	2.58367e7i		−	0.936188i	−0.883679	−	0.468094i	$-0.844941\pi$
$947$		−	2.58367e7i		−	0.936188i	0.883679	−	0.468094i	$-0.155059\pi$
$948$	−5.16021e7			−1.86486
$949$		−	7.76223e6i		−	0.279783i
$950$			1.55267e7i			0.558174i
$951$		−	205343.i		−	0.00736256i
$952$	1.39756e7			0.499778
$953$			2.20350e6i			0.0785925i	0.999228	+	0.0392963i	$0.0125116\pi$
$953$			2.20350e6i			0.0785925i	−0.999228	+	0.0392963i	$0.987488\pi$
$954$	96171.1			0.00342116
$955$		−	9.28793e7i		−	3.29542i
$956$		−	3.08125e7i		−	1.09039i
$957$			4.54833e7i			1.60536i
$958$	2.75672e7			0.970463
$959$	5.66601e6			0.198944
$960$			3.37319e7i			1.18131i
$961$	−430639.			−0.0150420
$962$	1.38476e7			0.482433
$963$			781947.i			0.0271714i
$964$	1.23676e7			0.428641
$965$			3.31374e6i			0.114551i
$966$	−2.72048e7			−0.938001
$967$	−3.08694e7			−1.06160			−0.530801	−	0.847496i	$-0.678109\pi$
$967$	−3.08694e7			−1.06160			−0.530801	+	0.847496i	$0.678109\pi$
$968$	−2.84365e7			−0.975411
$969$	2.22305e7			0.760571
$970$	2.75376e7	+	3.25026e6i	0.939715	+	0.110915i
$971$	−4.35503e6			−0.148232			−0.0741162	−	0.997250i	$-0.523614\pi$
$971$	−4.35503e6			−0.148232			−0.0741162	+	0.997250i	$0.523614\pi$
$972$	−1.40294e6			−0.0476293
$973$	1.45710e7			0.493410
$974$	−1.60744e7			−0.542923
$975$			4.63993e7i			1.56315i
$976$	−6.88942e6			−0.231504
$977$			1.48921e7i			0.499137i	0.968357	+	0.249568i	$0.0802888\pi$
$977$			1.48921e7i			0.499137i	−0.968357	+	0.249568i	$0.919711\pi$
$978$	2.90603e7			0.971522
$979$	−5.60550e7			−1.86921
$980$			2.11539e7i			0.703599i
$981$	5.40307e7			1.79254
$982$	9.93270e6			0.328692
$983$		−	1.63068e7i		−	0.538250i	−0.963105	−	0.269125i	$-0.913266\pi$
$983$		−	1.63068e7i		−	0.538250i	0.963105	−	0.269125i	$-0.0867345\pi$
$984$		−	2.32549e7i		−	0.765643i
$985$			7.19602e6i			0.236321i
$986$	9.22655e6			0.302237
$987$			1.39190e7i			0.454795i
$988$	−5.29533e6			−0.172584
$989$		−	1.58040e7i		−	0.513779i
$990$			8.25046e7i			2.67541i
$991$			5.16770e7i			1.67153i	0.549089	+	0.835764i	$0.314975\pi$
$991$			5.16770e7i			1.67153i	−0.549089	+	0.835764i	$0.685025\pi$
$992$	3.18049e7			1.02616
$993$			4.37177e7i			1.40697i
$994$	1.50181e7			0.482114
$995$	3.37904e7			1.08202
$996$		−	2.71010e7i		−	0.865639i
$997$	3.39384e7			1.08132			0.540658	−	0.841242i	$-0.318175\pi$
$997$	3.39384e7			1.08132			0.540658	+	0.841242i	$0.318175\pi$
$998$		−	7.53064e6i		−	0.239335i
$999$			9.80664e7i			3.10890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.25	✓	40
97.96	even	2	inner	97.6.b.a.96.26	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.25	✓	40	1.1	even	1	trivial
97.6.b.a.96.26	yes	40	97.96	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	97.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.13637 q^{2} -26.9093 q^{3} -22.1632 q^{4} -95.4056i q^{5} -84.3974 q^{6} -82.4789i q^{7} -169.876 q^{8} +481.111 q^{9} -299.227i q^{10} -573.103 q^{11} +596.397 q^{12} +288.476i q^{13} -258.684i q^{14} +2567.30i q^{15} +176.431 q^{16} -997.460i q^{17} +1508.94 q^{18} -828.231i q^{19} +2114.50i q^{20} +2219.45i q^{21} -1797.46 q^{22} +3908.18i q^{23} +4571.23 q^{24} -5977.23 q^{25} +904.765i q^{26} -6407.39 q^{27} +1828.00i q^{28} +2949.29i q^{29} +8051.99i q^{30} +5310.23 q^{31} +5989.37 q^{32} +15421.8 q^{33} -3128.40i q^{34} -7868.95 q^{35} -10663.0 q^{36} -15305.2i q^{37} -2597.64i q^{38} -7762.68i q^{39} +16207.1i q^{40} -5087.22i q^{41} +6961.00i q^{42} -4043.83 q^{43} +12701.8 q^{44} -45900.7i q^{45} +12257.5i q^{46} +6271.38 q^{47} -4747.63 q^{48} +10004.2 q^{49} -18746.8 q^{50} +26840.9i q^{51} -6393.55i q^{52} +63.7343 q^{53} -20095.9 q^{54} +54677.2i q^{55} +14011.2i q^{56} +22287.1i q^{57} +9250.05i q^{58} -24044.5i q^{59} -56899.6i q^{60} -39048.8 q^{61} +16654.8 q^{62} -39681.5i q^{63} +13139.1 q^{64} +27522.2 q^{65} +48368.4 q^{66} +57423.9i q^{67} +22106.9i q^{68} -105166. i q^{69} -24679.9 q^{70} +58055.9i q^{71} -81729.0 q^{72} -26907.7 q^{73} -48002.7i q^{74} +160843. q^{75} +18356.3i q^{76} +47268.9i q^{77} -24346.6i q^{78} -86523.1 q^{79} -16832.5i q^{80} +55508.5 q^{81} -15955.4i q^{82} -45441.2i q^{83} -49190.1i q^{84} -95163.3 q^{85} -12682.9 q^{86} -79363.3i q^{87} +97356.2 q^{88} +97809.7 q^{89} -143961. i q^{90} +23793.1 q^{91} -86617.8i q^{92} -142895. q^{93} +19669.4 q^{94} -79017.9 q^{95} -161170. q^{96} +(-10862.2 + 92029.1i) q^{97} +31376.9 q^{98} -275726. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 + 40 * q^3 + 638 * q^4 - 130 * q^6 + 180 * q^8 + 3300 * q^9 + 382 * q^11 + 2586 * q^12 + 10174 * q^16 + 4738 * q^18 + 1996 * q^22 - 3102 * q^24 - 25178 * q^25 + 3046 * q^27 + 14796 * q^31 + 8128 * q^32 - 9434 * q^33 - 2964 * q^35 + 18124 * q^36 - 45814 * q^43 - 60186 * q^44 - 17866 * q^47 + 69528 * q^48 - 64166 * q^49 + 78812 * q^50 + 117092 * q^53 - 53962 * q^54 - 33546 * q^61 - 148838 * q^62 + 215708 * q^64 + 89628 * q^65 - 17136 * q^66 + 218204 * q^70 - 127452 * q^72 + 25562 * q^73 - 52722 * q^75 - 193912 * q^79 + 175440 * q^81 - 243192 * q^85 + 108918 * q^86 + 155578 * q^88 - 434816 * q^89 - 483858 * q^91 - 66746 * q^93 - 245480 * q^94 + 97106 * q^95 - 306196 * q^96 - 251282 * q^97 - 310510 * q^98 - 562238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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