LMFDB - Embedded newform 97.6.b.a.96.4

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			96.4
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-9.84944 q^{2} -20.3089 q^{3} +65.0114 q^{4} +53.6529i q^{5} +200.031 q^{6} +56.8568i q^{7} -325.144 q^{8} +169.450 q^{9} -528.451i q^{10} +27.0752 q^{11} -1320.31 q^{12} -1023.69i q^{13} -560.007i q^{14} -1089.63i q^{15} +1122.12 q^{16} -221.046i q^{17} -1668.99 q^{18} +216.145i q^{19} +3488.05i q^{20} -1154.70i q^{21} -266.676 q^{22} -1613.08i q^{23} +6603.30 q^{24} +246.365 q^{25} +10082.7i q^{26} +1493.72 q^{27} +3696.34i q^{28} +4691.91i q^{29} +10732.2i q^{30} +186.878 q^{31} -647.628 q^{32} -549.867 q^{33} +2177.18i q^{34} -3050.53 q^{35} +11016.2 q^{36} -13902.2i q^{37} -2128.91i q^{38} +20789.9i q^{39} -17444.9i q^{40} +10059.8i q^{41} +11373.1i q^{42} -7968.97 q^{43} +1760.20 q^{44} +9091.48i q^{45} +15887.9i q^{46} +15189.1 q^{47} -22788.9 q^{48} +13574.3 q^{49} -2426.56 q^{50} +4489.20i q^{51} -66551.4i q^{52} -1616.19 q^{53} -14712.3 q^{54} +1452.66i q^{55} -18486.6i q^{56} -4389.66i q^{57} -46212.7i q^{58} +11300.6i q^{59} -70838.4i q^{60} -12641.6 q^{61} -1840.64 q^{62} +9634.37i q^{63} -29529.0 q^{64} +54923.8 q^{65} +5415.88 q^{66} +31988.1i q^{67} -14370.5i q^{68} +32759.8i q^{69} +30046.0 q^{70} +36346.6i q^{71} -55095.6 q^{72} -86187.4 q^{73} +136929. i q^{74} -5003.40 q^{75} +14051.9i q^{76} +1539.41i q^{77} -204769. i q^{78} +93058.4 q^{79} +60204.9i q^{80} -71512.1 q^{81} -99083.8i q^{82} +47630.2i q^{83} -75068.4i q^{84} +11859.8 q^{85} +78489.8 q^{86} -95287.3i q^{87} -8803.34 q^{88} -9609.52 q^{89} -89546.0i q^{90} +58203.6 q^{91} -104869. i q^{92} -3795.28 q^{93} -149604. q^{94} -11596.8 q^{95} +13152.6 q^{96} +(-30179.2 + 87616.0i) q^{97} -133699. q^{98} +4587.89 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.84944			−1.74115			−0.870575	−	0.492035i	$-0.836253\pi$
$2$	−9.84944			−1.74115			−0.870575	+	0.492035i	$0.836253\pi$
$3$	−20.3089			−1.30281			−0.651407	−	0.758728i	$-0.725821\pi$
$3$	−20.3089			−1.30281			−0.651407	+	0.758728i	$0.725821\pi$
$4$	65.0114			2.03161
$5$			53.6529i			0.959772i	0.877331	+	0.479886i	$0.159322\pi$
$5$			53.6529i			0.959772i	−0.877331	+	0.479886i	$0.840678\pi$
$6$	200.031			2.26840
$7$			56.8568i			0.438568i	0.975661	+	0.219284i	$0.0703721\pi$
$7$			56.8568i			0.438568i	−0.975661	+	0.219284i	$0.929628\pi$
$8$	−325.144			−1.79618
$9$	169.450			0.697325
$10$		−	528.451i		−	1.67111i
$11$	27.0752			0.0674668			0.0337334	−	0.999431i	$-0.489260\pi$
$11$	27.0752			0.0674668			0.0337334	+	0.999431i	$0.489260\pi$
$12$	−1320.31			−2.64681
$13$		−	1023.69i		−	1.68000i	−0.542587	−	0.840000i	$-0.682555\pi$
$13$		−	1023.69i		−	1.68000i	0.542587	−	0.840000i	$-0.317445\pi$
$14$		−	560.007i		−	0.763613i
$15$		−	1089.63i		−	1.25041i
$16$	1122.12			1.09582
$17$		−	221.046i		−	0.185507i	−0.995689	−	0.0927536i	$-0.970433\pi$
$17$		−	221.046i		−	0.185507i	0.995689	−	0.0927536i	$-0.0295669\pi$
$18$	−1668.99			−1.21415
$19$			216.145i			0.137360i	0.997639	+	0.0686802i	$0.0218788\pi$
$19$			216.145i			0.137360i	−0.997639	+	0.0686802i	$0.978121\pi$
$20$			3488.05i			1.94988i
$21$		−	1154.70i		−	0.571373i
$22$	−266.676			−0.117470
$23$		−	1613.08i		−	0.635824i	−0.948120	−	0.317912i	$-0.897018\pi$
$23$		−	1613.08i		−	0.635824i	0.948120	−	0.317912i	$-0.102982\pi$
$24$	6603.30			2.34009
$25$	246.365			0.0788368
$26$			10082.7i			2.92513i
$27$	1493.72			0.394330
$28$			3696.34i			0.890998i
$29$			4691.91i			1.03599i	0.855384	+	0.517994i	$0.173321\pi$
$29$			4691.91i			1.03599i	−0.855384	+	0.517994i	$0.826679\pi$
$30$			10732.2i			2.17714i
$31$	186.878			0.0349264			0.0174632	−	0.999848i	$-0.494441\pi$
$31$	186.878			0.0349264			0.0174632	+	0.999848i	$0.494441\pi$
$32$	−647.628			−0.111802
$33$	−549.867			−0.0878967
$34$			2177.18i			0.322996i
$35$	−3050.53			−0.420926
$36$	11016.2			1.41669
$37$		−	13902.2i		−	1.66947i	−0.550651	−	0.834735i	$-0.685621\pi$
$37$		−	13902.2i		−	1.66947i	0.550651	−	0.834735i	$-0.314379\pi$
$38$		−	2128.91i		−	0.239165i
$39$			20789.9i			2.18873i
$40$		−	17444.9i		−	1.72393i
$41$			10059.8i			0.934612i	0.884096	+	0.467306i	$0.154775\pi$
$41$			10059.8i			0.934612i	−0.884096	+	0.467306i	$0.845225\pi$
$42$			11373.1i			0.994846i
$43$	−7968.97			−0.657250			−0.328625	−	0.944460i	$-0.606585\pi$
$43$	−7968.97			−0.657250			−0.328625	+	0.944460i	$0.606585\pi$
$44$	1760.20			0.137066
$45$			9091.48i			0.669273i
$46$			15887.9i			1.10706i
$47$	15189.1			1.00297			0.501484	−	0.865167i	$-0.332788\pi$
$47$	15189.1			1.00297			0.501484	+	0.865167i	$0.332788\pi$
$48$	−22788.9			−1.42765
$49$	13574.3			0.807658
$50$	−2426.56			−0.137267
$51$			4489.20i			0.241681i
$52$		−	66551.4i		−	3.41310i
$53$	−1616.19			−0.0790320			−0.0395160	−	0.999219i	$-0.512582\pi$
$53$	−1616.19			−0.0790320			−0.0395160	+	0.999219i	$0.512582\pi$
$54$	−14712.3			−0.686587
$55$			1452.66i			0.0647528i
$56$		−	18486.6i		−	0.787748i
$57$		−	4389.66i		−	0.178955i
$58$		−	46212.7i		−	1.80381i
$59$			11300.6i			0.422640i	0.977417	+	0.211320i	$0.0677762\pi$
$59$			11300.6i			0.422640i	−0.977417	+	0.211320i	$0.932224\pi$
$60$		−	70838.4i		−	2.54033i
$61$	−12641.6			−0.434988			−0.217494	−	0.976062i	$-0.569788\pi$
$61$	−12641.6			−0.434988			−0.217494	+	0.976062i	$0.569788\pi$
$62$	−1840.64			−0.0608121
$63$			9634.37i			0.305824i
$64$	−29529.0			−0.901153
$65$	54923.8			1.61242
$66$	5415.88			0.153041
$67$			31988.1i			0.870566i	0.900294	+	0.435283i	$0.143352\pi$
$67$			31988.1i			0.870566i	−0.900294	+	0.435283i	$0.856648\pi$
$68$		−	14370.5i		−	0.376878i
$69$			32759.8i			0.828360i
$70$	30046.0			0.732895
$71$			36346.6i			0.855692i	0.903852	+	0.427846i	$0.140727\pi$
$71$			36346.6i			0.855692i	−0.903852	+	0.427846i	$0.859273\pi$
$72$	−55095.6			−1.25252
$73$	−86187.4			−1.89294			−0.946469	−	0.322795i	$-0.895378\pi$
$73$	−86187.4			−1.89294			−0.946469	+	0.322795i	$0.895378\pi$
$74$			136929.i			2.90680i
$75$	−5003.40			−0.102710
$76$			14051.9i			0.279062i
$77$			1539.41i			0.0295888i
$78$		−	204769.i		−	3.81090i
$79$	93058.4			1.67760			0.838799	−	0.544442i	$-0.183258\pi$
$79$	93058.4			1.67760			0.838799	+	0.544442i	$0.183258\pi$
$80$			60204.9i			1.05174i
$81$	−71512.1			−1.21106
$82$		−	99083.8i		−	1.62730i
$83$			47630.2i			0.758904i	0.925211	+	0.379452i	$0.123888\pi$
$83$			47630.2i			0.758904i	−0.925211	+	0.379452i	$0.876112\pi$
$84$		−	75068.4i		−	1.16080i
$85$	11859.8			0.178045
$86$	78489.8			1.14437
$87$		−	95287.3i		−	1.34970i
$88$	−8803.34			−0.121183
$89$	−9609.52			−0.128596			−0.0642979	−	0.997931i	$-0.520481\pi$
$89$	−9609.52			−0.128596			−0.0642979	+	0.997931i	$0.520481\pi$
$90$		−	89546.0i		−	1.16531i
$91$	58203.6			0.736794
$92$		−	104869.i		−	1.29174i
$93$	−3795.28			−0.0455026
$94$	−149604.			−1.74632
$95$	−11596.8			−0.131835
$96$	13152.6			0.145658
$97$	−30179.2	+	87616.0i	−0.325670	+	0.945483i
$97$	−30179.2	+	87616.0i	−0.325670	+	0.945483i
$98$	−133699.			−1.40625
$99$	4587.89			0.0470463
$100$	16016.5			0.160165
$101$	89880.8			0.876725			0.438363	−	0.898798i	$-0.355559\pi$
$101$	89880.8			0.876725			0.438363	+	0.898798i	$0.355559\pi$
$102$		−	44216.1i		−	0.420804i
$103$	82886.9			0.769826			0.384913	−	0.922953i	$-0.374231\pi$
$103$	82886.9			0.769826			0.384913	+	0.922953i	$0.374231\pi$
$104$			332846.i			3.01759i
$105$	61952.8			0.548388
$106$	15918.6			0.137607
$107$			210548.i			1.77784i	0.458065	+	0.888919i	$0.348543\pi$
$107$			210548.i			1.77784i	−0.458065	+	0.888919i	$0.651457\pi$
$108$	97108.8			0.801123
$109$	160830.			1.29658			0.648291	−	0.761393i	$-0.275484\pi$
$109$	160830.			1.29658			0.648291	+	0.761393i	$0.275484\pi$
$110$		−	14307.9i		−	0.112744i
$111$			282338.i			2.17501i
$112$			63800.0i			0.480591i
$113$	−150009.			−1.10515			−0.552574	−	0.833464i	$-0.686354\pi$
$113$	−150009.			−1.10515			−0.552574	+	0.833464i	$0.686354\pi$
$114$			43235.7i			0.311588i
$115$	86546.5			0.610246
$116$			305028.i			2.10472i
$117$		−	173464.i		−	1.17151i
$118$		−	111304.i		−	0.735880i
$119$	12568.0			0.0813575
$120$			354286.i			2.24596i
$121$	−160318.			−0.995448
$122$	124512.			0.757379
$123$		−	204304.i		−	1.21763i
$124$	12149.2			0.0709567
$125$			180884.i			1.03544i
$126$		−	94893.1i		−	0.532486i
$127$			45050.3i			0.247850i	0.992292	+	0.123925i	$0.0395482\pi$
$127$			45050.3i			0.247850i	−0.992292	+	0.123925i	$0.960452\pi$
$128$	311568.			1.68085
$129$	161841.			0.856275
$130$	−540969.			−2.80746
$131$			132471.i			0.674437i	0.941426	+	0.337218i	$0.109486\pi$
$131$			132471.i			0.674437i	−0.941426	+	0.337218i	$0.890514\pi$
$132$	−35747.6			−0.178572
$133$	−12289.3			−0.0602419
$134$		−	315065.i		−	1.51579i
$135$			80142.4i			0.378467i
$136$			71871.8i			0.333205i
$137$		−	179400.i		−	0.816622i	−0.912843	−	0.408311i	$-0.866118\pi$
$137$		−	179400.i		−	0.816622i	0.912843	−	0.408311i	$-0.133882\pi$
$138$		−	322666.i		−	1.44230i
$139$		−	296979.i		−	1.30373i	−0.758334	−	0.651866i	$-0.773986\pi$
$139$		−	296979.i		−	1.30373i	0.758334	−	0.651866i	$-0.226014\pi$
$140$	−198319.			−0.855155
$141$	−308473.			−1.30668
$142$		−	357993.i		−	1.48989i
$143$		−	27716.6i		−	0.113344i
$144$	190143.			0.764141
$145$	−251735.			−0.994312
$146$	848897.			3.29589
$147$	−275679.			−1.05223
$148$		−	903801.i		−	3.39171i
$149$		−	322988.i		−	1.19185i	−0.803041	−	0.595924i	$-0.796786\pi$
$149$		−	322988.i		−	1.19185i	0.803041	−	0.595924i	$-0.203214\pi$
$150$	49280.6			0.178833
$151$	171009.			0.610348			0.305174	−	0.952297i	$-0.401285\pi$
$151$	171009.			0.610348			0.305174	+	0.952297i	$0.401285\pi$
$152$		−	70278.3i		−	0.246724i
$153$		−	37456.3i		−	0.129359i
$154$		−	15162.3i		−	0.0515185i
$155$			10026.5i			0.0335214i
$156$			1.35158e6i			4.44663i
$157$			209963.i			0.679818i	0.940458	+	0.339909i	$0.110396\pi$
$157$			209963.i			0.679818i	−0.940458	+	0.339909i	$0.889604\pi$
$158$	−916573.			−2.92095
$159$	32823.0			0.102964
$160$		−	34747.1i		−	0.107305i
$161$	91714.6			0.278852
$162$	704353.			2.10864
$163$	55510.4			0.163646			0.0818230	−	0.996647i	$-0.473926\pi$
$163$	55510.4			0.163646			0.0818230	+	0.996647i	$0.473926\pi$
$164$			654004.i			1.89876i
$165$		−	29502.0i		−	0.0843609i
$166$		−	469131.i		−	1.32137i
$167$	339558.			0.942155			0.471078	−	0.882092i	$-0.343865\pi$
$167$	339558.			0.942155			0.471078	+	0.882092i	$0.343865\pi$
$168$			375442.i			1.02629i
$169$	−676644.			−1.82240
$170$	−116812.			−0.310003
$171$			36625.8i			0.0957848i
$172$	−518074.			−1.33527
$173$		−	658685.i		−	1.67326i	−0.547772	−	0.836628i	$-0.684524\pi$
$173$		−	658685.i		−	1.67326i	0.547772	−	0.836628i	$-0.315476\pi$
$174$			938527.i			2.35003i
$175$			14007.5i			0.0345753i
$176$	30381.6			0.0739314
$177$		−	229502.i		−	0.550622i
$178$	94648.4			0.223905
$179$			424590.i			0.990460i	0.868762	+	0.495230i	$0.164916\pi$
$179$			424590.i			0.990460i	−0.868762	+	0.495230i	$0.835084\pi$
$180$			591050.i			1.35970i
$181$		−	401114.i		−	0.910062i	−0.890475	−	0.455031i	$-0.849628\pi$
$181$		−	401114.i		−	0.910062i	0.890475	−	0.455031i	$-0.150372\pi$
$182$	−573272.			−1.28287
$183$	256736.			0.566708
$184$			524483.i			1.14206i
$185$	745893.			1.60231
$186$	37381.3			0.0792269
$187$		−	5984.87i		−	0.0125156i
$188$	987464.			2.03764
$189$			84928.0i			0.172940i
$190$	114222.			0.229544
$191$	−336542.			−0.667507			−0.333753	−	0.942660i	$-0.608315\pi$
$191$	−336542.			−0.667507			−0.333753	+	0.942660i	$0.608315\pi$
$192$	599700.			1.17404
$193$	702926.			1.35837			0.679183	−	0.733969i	$-0.262334\pi$
$193$	702926.			1.35837			0.679183	+	0.733969i	$0.262334\pi$
$194$	297248.	−	862968.i	0.567041	−	1.64623i
$195$	−1.11544e6			−2.10068
$196$	882485.			1.64084
$197$	317036.			0.582026			0.291013	−	0.956719i	$-0.406008\pi$
$197$	317036.			0.582026			0.291013	+	0.956719i	$0.406008\pi$
$198$	−45188.2			−0.0819147
$199$			644760.i			1.15416i	0.816688	+	0.577079i	$0.195808\pi$
$199$			644760.i			1.15416i	−0.816688	+	0.577079i	$0.804192\pi$
$200$	−80104.1			−0.141605
$201$		−	649642.i		−	1.13419i
$202$	−885275.			−1.52651
$203$	−266767.			−0.454351
$204$			291849.i			0.491002i
$205$	−539740.			−0.897015
$206$	−816389.			−1.34038
$207$		−	273336.i		−	0.443375i
$208$		−	1.14870e6i		−	1.84097i
$209$			5852.18i			0.00926727i
$210$	−610200.			−0.954826
$211$			432926.i			0.669433i	0.942319	+	0.334717i	$0.108641\pi$
$211$			432926.i			0.669433i	−0.942319	+	0.334717i	$0.891359\pi$
$212$	−105071.			−0.160562
$213$		−	738157.i		−	1.11481i
$214$		−	2.07378e6i		−	3.09548i
$215$		−	427558.i		−	0.630811i
$216$	−485673.			−0.708288
$217$			10625.3i			0.0153176i
$218$	−1.58408e6			−2.25754
$219$	1.75037e6			2.46615
$220$			94439.7i			0.131552i
$221$	−226282.			−0.311652
$222$		−	2.78087e6i		−	3.78702i
$223$			1.39579e6i			1.87956i	0.341777	+	0.939781i	$0.388971\pi$
$223$			1.39579e6i			1.87956i	−0.341777	+	0.939781i	$0.611029\pi$
$224$		−	36822.0i		−	0.0490329i
$225$	41746.5			0.0549749
$226$	1.47750e6			1.92423
$227$	−886828.			−1.14229			−0.571143	−	0.820851i	$-0.693500\pi$
$227$	−886828.			−1.14229			−0.571143	+	0.820851i	$0.693500\pi$
$228$		−	285378.i		−	0.363566i
$229$	312844.			0.394220			0.197110	−	0.980381i	$-0.436844\pi$
$229$	312844.			0.394220			0.197110	+	0.980381i	$0.436844\pi$
$230$	−852434.			−1.06253
$231$		−	31263.6i		−	0.0385487i
$232$		−	1.52554e6i		−	1.86082i
$233$			1.26963e6i			1.53211i	0.642778	+	0.766053i	$0.277782\pi$
$233$			1.26963e6i			1.53211i	−0.642778	+	0.766053i	$0.722218\pi$
$234$			1.70852e6i			2.03977i
$235$			814939.i			0.962621i
$236$			734667.i			0.858638i
$237$	−1.88991e6			−2.18560
$238$	−123787.			−0.141656
$239$			540790.i			0.612398i	0.951967	+	0.306199i	$0.0990573\pi$
$239$			540790.i			0.612398i	−0.951967	+	0.306199i	$0.900943\pi$
$240$		−	1.22269e6i		−	1.37022i
$241$	1.40246e6			1.55542			0.777710	−	0.628623i	$-0.216381\pi$
$241$	1.40246e6			1.55542			0.777710	+	0.628623i	$0.216381\pi$
$242$	1.57904e6			1.73323
$243$	1.08935e6			1.18346
$244$	−821847.			−0.883724
$245$			728301.i			0.775168i
$246$			2.01228e6i			2.12007i
$247$	221265.			0.230765
$248$	−60762.2			−0.0627342
$249$		−	967315.i		−	0.988711i
$250$		−	1.78160e6i		−	1.80285i
$251$			161412.i			0.161715i	0.996726	+	0.0808576i	$0.0257659\pi$
$251$			161412.i			0.161715i	−0.996726	+	0.0808576i	$0.974234\pi$
$252$			626344.i			0.621315i
$253$		−	43674.5i		−	0.0428970i
$254$		−	443721.i		−	0.431544i
$255$	−240859.			−0.231959
$256$	−2.12384e6			−2.02545
$257$		−	1.03503e6i		−	0.977505i	−0.872422	−	0.488753i	$-0.837452\pi$
$257$		−	1.03503e6i		−	0.977505i	0.872422	−	0.488753i	$-0.162548\pi$
$258$	−1.59404e6			−1.49090
$259$	790433.			0.732177
$260$	3.57068e6			3.27580
$261$			795044.i			0.722420i
$262$		−	1.30476e6i		−	1.17430i
$263$			1.00345e6i			0.894552i	0.894396	+	0.447276i	$0.147606\pi$
$263$			1.00345e6i			0.894552i	−0.894396	+	0.447276i	$0.852394\pi$
$264$	178786.			0.157879
$265$		−	86713.4i		−	0.0758527i
$266$	121043.			0.104890
$267$	195158.			0.167536
$268$			2.07959e6i			1.76865i
$269$	−467877.			−0.394231			−0.197116	−	0.980380i	$-0.563157\pi$
$269$	−467877.			−0.394231			−0.197116	+	0.980380i	$0.563157\pi$
$270$		−	789357.i		−	0.658968i
$271$		−	181352.i		−	0.150002i	−0.997183	−	0.0750012i	$-0.976104\pi$
$271$		−	181352.i		−	0.150002i	0.997183	−	0.0750012i	$-0.0238961\pi$
$272$		−	248040.i		−	0.203282i
$273$	−1.18205e6			−0.959906
$274$			1.76699e6i			1.42186i
$275$	6670.39			0.00531887
$276$			2.12976e6i			1.68290i
$277$		−	463196.i		−	0.362715i	−0.983417	−	0.181357i	$-0.941951\pi$
$277$		−	463196.i		−	0.362715i	0.983417	−	0.181357i	$-0.0580491\pi$
$278$			2.92508e6i			2.27000i
$279$	31666.4			0.0243550
$280$	991861.			0.756059
$281$			1.38758e6i			1.04832i	0.851621	+	0.524158i	$0.175620\pi$
$281$			1.38758e6i			1.04832i	−0.851621	+	0.524158i	$0.824380\pi$
$282$	3.03829e6			2.27513
$283$	312588.			0.232010			0.116005	−	0.993249i	$-0.462991\pi$
$283$	312588.			0.232010			0.116005	+	0.993249i	$0.462991\pi$
$284$			2.36294e6i			1.73843i
$285$	235518.			0.171756
$286$			272993.i			0.197349i
$287$	−571970.			−0.409891
$288$	−109740.			−0.0779625
$289$	1.37100e6			0.965587
$290$	2.47944e6			1.73125
$291$	612905.	−	1.77938e6i	0.424288	−	1.23179i
$292$	−5.60316e6			−3.84570
$293$	2.32564e6			1.58261			0.791305	−	0.611421i	$-0.209402\pi$
$293$	2.32564e6			1.58261			0.791305	+	0.611421i	$0.209402\pi$
$294$	2.71528e6			1.83209
$295$	−606309.			−0.405638
$296$			4.52021e6i			2.99867i
$297$	40442.8			0.0266042
$298$			3.18125e6i			2.07519i
$299$	−1.65129e6			−1.06818
$300$	−325278.			−0.208666
$301$		−	453090.i		−	0.288249i
$302$	−1.68435e6			−1.06271
$303$	−1.82538e6			−1.14221
$304$			242540.i			0.150522i
$305$		−	678258.i		−	0.417489i
$306$			368923.i			0.225233i
$307$	1.47323e6			0.892124			0.446062	−	0.895002i	$-0.352826\pi$
$307$	1.47323e6			0.892124			0.446062	+	0.895002i	$0.352826\pi$
$308$			100079.i			0.0601128i
$309$	−1.68334e6			−1.00294
$310$		−	98755.8i		−	0.0583658i
$311$			2.49814e6i			1.46459i	0.680988	+	0.732294i	$0.261550\pi$
$311$			2.49814e6i			1.46459i	−0.680988	+	0.732294i	$0.738450\pi$
$312$		−	6.75972e6i		−	3.93135i
$313$	−634039.			−0.365810			−0.182905	−	0.983131i	$-0.558550\pi$
$313$	−634039.			−0.365810			−0.182905	+	0.983131i	$0.558550\pi$
$314$		−	2.06801e6i		−	1.18367i
$315$	−516912.			−0.293522
$316$	6.04986e6			3.40822
$317$		−	1.27336e6i		−	0.711707i	−0.934542	−	0.355854i	$-0.884190\pi$
$317$		−	1.27336e6i		−	0.711707i	0.934542	−	0.355854i	$-0.115810\pi$
$318$	−323288.			−0.179276
$319$			127034.i			0.0698948i
$320$		−	1.58432e6i		−	0.864902i
$321$		−	4.27599e6i		−	2.31619i
$322$	−903337.			−0.485523
$323$	47778.1			0.0254813
$324$	−4.64910e6			−2.46040
$325$		−	252201.i		−	0.132446i
$326$	−546746.			−0.284932
$327$	−3.26627e6			−1.68920
$328$		−	3.27089e6i		−	1.67873i
$329$			863602.i			0.439870i
$330$			290578.i			0.146885i
$331$		−	3.20956e6i		−	1.61018i	−0.593149	−	0.805092i	$-0.702116\pi$
$331$		−	3.20956e6i		−	1.61018i	0.593149	−	0.805092i	$-0.297884\pi$
$332$			3.09651e6i			1.54179i
$333$		−	2.35572e6i		−	1.16416i
$334$	−3.34445e6			−1.64043
$335$	−1.71626e6			−0.835545
$336$		−	1.29570e6i		−	0.626120i
$337$			2.89131e6i			1.38682i	0.720543	+	0.693410i	$0.243892\pi$
$337$			2.89131e6i			1.38682i	−0.720543	+	0.693410i	$0.756108\pi$
$338$	6.66456e6			3.17307
$339$	3.04650e6			1.43980
$340$	771021.			0.361717
$341$	5059.76			0.00235637
$342$		−	360743.i		−	0.166776i
$343$			1.72738e6i			0.792781i
$344$	2.59106e6			1.18054
$345$	−1.75766e6			−0.795037
$346$			6.48767e6i			2.91339i
$347$		−	3.62569e6i		−	1.61647i	−0.588860	−	0.808235i	$-0.700423\pi$
$347$		−	3.62569e6i		−	1.61647i	0.588860	−	0.808235i	$-0.299577\pi$
$348$		−	6.19476e6i		−	2.74206i
$349$			1.35725e6i			0.596481i	0.954491	+	0.298241i	$0.0963998\pi$
$349$			1.35725e6i			0.596481i	−0.954491	+	0.298241i	$0.903600\pi$
$350$		−	137966.i		−	0.0602008i
$351$		−	1.52910e6i		−	0.662474i
$352$	−17534.7			−0.00754294
$353$	−2.73892e6			−1.16988			−0.584942	−	0.811075i	$-0.698883\pi$
$353$	−2.73892e6			−1.16988			−0.584942	+	0.811075i	$0.698883\pi$
$354$			2.26046e6i			0.958715i
$355$	−1.95010e6			−0.821269
$356$	−624729.			−0.261256
$357$	−255241.			−0.105994
$358$		−	4.18197e6i		−	1.72454i
$359$		−	1.00251e6i		−	0.410537i	−0.978706	−	0.205268i	$-0.934193\pi$
$359$		−	1.00251e6i		−	0.410537i	0.978706	−	0.205268i	$-0.0658067\pi$
$360$		−	2.95604e6i		−	1.20214i
$361$	2.42938e6			0.981132
$362$			3.95075e6i			1.58456i
$363$	3.25587e6			1.29688
$364$	3.78390e6			1.49688
$365$		−	4.62420e6i		−	1.81679i
$366$	−2.52871e6			−0.986724
$367$		−	295514.i		−	0.114528i	−0.998359	−	0.0572642i	$-0.981762\pi$
$367$		−	295514.i		−	0.114528i	0.998359	−	0.0572642i	$-0.0182377\pi$
$368$		−	1.81007e6i		−	0.696747i
$369$			1.70464e6i			0.651728i
$370$	−7.34663e6			−2.78987
$371$		−	91891.4i		−	0.0346609i
$372$	−246736.			−0.0924433
$373$			1.39611e6i			0.519572i	0.965666	+	0.259786i	$0.0836521\pi$
$373$			1.39611e6i			0.519572i	−0.965666	+	0.259786i	$0.916348\pi$
$374$			58947.6i			0.0217915i
$375$		−	3.67354e6i		−	1.34898i
$376$	−4.93864e6			−1.80151
$377$	4.80305e6			1.74046
$378$		−	836493.i		−	0.301115i
$379$	2.76544e6			0.988932			0.494466	−	0.869197i	$-0.335364\pi$
$379$	2.76544e6			0.988932			0.494466	+	0.869197i	$0.335364\pi$
$380$	−753925.			−0.267836
$381$		−	914921.i		−	0.322902i
$382$	3.31475e6			1.16223
$383$		−	2.19818e6i		−	0.765713i	−0.923808	−	0.382857i	$-0.874940\pi$
$383$		−	2.19818e6i		−	0.765713i	0.923808	−	0.382857i	$-0.125060\pi$
$384$	−6.32759e6			−2.18983
$385$	−82593.8			−0.0283985
$386$	−6.92343e6			−2.36512
$387$	−1.35034e6			−0.458317
$388$	−1.96199e6	+	5.69604e6i	−0.661634	+	1.92085i
$389$	−3.82768e6			−1.28251			−0.641256	−	0.767327i	$-0.721586\pi$
$389$	−3.82768e6			−1.28251			−0.641256	+	0.767327i	$0.721586\pi$
$390$	1.09865e7			3.65760
$391$	−356566.			−0.117950
$392$	−4.41360e6			−1.45070
$393$		−	2.69033e6i		−	0.878666i
$394$	−3.12262e6			−1.01340
$395$			4.99285e6i			1.61011i
$396$	298265.			0.0955795
$397$	1.39213e6			0.443305			0.221653	−	0.975126i	$-0.428855\pi$
$397$	1.39213e6			0.443305			0.221653	+	0.975126i	$0.428855\pi$
$398$		−	6.35052e6i		−	2.00956i
$399$	249582.			0.0784840
$400$	276451.			0.0863908
$401$		−	4.42318e6i		−	1.37364i	−0.726827	−	0.686821i	$-0.759006\pi$
$401$		−	4.42318e6i		−	1.37364i	0.726827	−	0.686821i	$-0.240994\pi$
$402$			6.39861e6i			1.97479i
$403$		−	191305.i		−	0.0586763i
$404$	5.84328e6			1.78116
$405$		−	3.83683e6i		−	1.16234i
$406$	2.62750e6			0.791094
$407$		−	376405.i		−	0.112634i
$408$		−	1.45963e6i		−	0.434104i
$409$			4.36639e6i			1.29067i	0.763901	+	0.645333i	$0.223282\pi$
$409$			4.36639e6i			1.29067i	−0.763901	+	0.645333i	$0.776718\pi$
$410$	5.31613e6			1.56184
$411$			3.64341e6i			1.06391i
$412$	5.38859e6			1.56398
$413$	−642514.			−0.185356
$414$			2.69221e6i			0.771984i
$415$	−2.55550e6			−0.728376
$416$			662969.i			0.187828i
$417$			6.03130e6i			1.69852i
$418$		−	57640.7i		−	0.0161357i
$419$	1.29627e6			0.360713			0.180357	−	0.983601i	$-0.442275\pi$
$419$	1.29627e6			0.360713			0.180357	+	0.983601i	$0.442275\pi$
$420$	4.02764e6			1.11411
$421$	−5.08746e6			−1.39893			−0.699465	−	0.714667i	$-0.746578\pi$
$421$	−5.08746e6			−1.39893			−0.699465	+	0.714667i	$0.746578\pi$
$422$		−	4.26407e6i		−	1.16558i
$423$	2.57379e6			0.699394
$424$	525494.			0.141956
$425$		−	54458.1i		−	0.0146248i
$426$			7.27043e6i			1.94105i
$427$		−	718760.i		−	0.190772i
$428$			1.36880e7i			3.61187i
$429$			562892.i			0.147666i
$430$			4.21121e6i			1.09834i
$431$	−1.80275e6			−0.467458			−0.233729	−	0.972302i	$-0.575093\pi$
$431$	−1.80275e6			−0.467458			−0.233729	+	0.972302i	$0.575093\pi$
$432$	1.67613e6			0.432114
$433$			4.64188e6i			1.18980i	0.803799	+	0.594901i	$0.202809\pi$
$433$			4.64188e6i			1.18980i	−0.803799	+	0.594901i	$0.797191\pi$
$434$		−	104653.i		−	0.0266702i
$435$	5.11244e6			1.29540
$436$	1.04558e7			2.63414
$437$	348660.			0.0873370
$438$	−1.72401e7			−4.29393
$439$			3.60581e6i			0.892979i	0.894789	+	0.446490i	$0.147326\pi$
$439$			3.60581e6i			0.892979i	−0.894789	+	0.446490i	$0.852674\pi$
$440$		−	472325.i		−	0.116308i
$441$	2.30017e6			0.563200
$442$	2.22875e6			0.542633
$443$		−	5.70113e6i		−	1.38023i	−0.723699	−	0.690116i	$-0.757560\pi$
$443$		−	5.70113e6i		−	1.38023i	0.723699	−	0.690116i	$-0.242440\pi$
$444$			1.83552e7i			4.41877i
$445$		−	515579.i		−	0.123423i
$446$		−	1.37477e7i		−	3.27260i
$447$			6.55952e6i			1.55276i
$448$		−	1.67892e6i		−	0.395217i
$449$	783588.			0.183431			0.0917154	−	0.995785i	$-0.470765\pi$
$449$	783588.			0.183431			0.0917154	+	0.995785i	$0.470765\pi$
$450$	−411180.			−0.0957196
$451$			272372.i			0.0630553i
$452$	−9.75227e6			−2.24522
$453$	−3.47301e6			−0.795170
$454$	8.73476e6			1.98889
$455$			3.12279e6i			0.707155i
$456$			1.42727e6i			0.321436i
$457$		−	3.01387e6i		−	0.675046i	−0.941317	−	0.337523i	$-0.890411\pi$
$457$		−	3.01387e6i		−	0.675046i	0.941317	−	0.337523i	$-0.109589\pi$
$458$	−3.08134e6			−0.686397
$459$		−	330181.i		−	0.0731510i
$460$	5.62651e6			1.23978
$461$	219342.			0.0480694			0.0240347	−	0.999711i	$-0.492349\pi$
$461$	219342.			0.0480694			0.0240347	+	0.999711i	$0.492349\pi$
$462$			307929.i			0.0671191i
$463$	6.70534e6			1.45368			0.726840	−	0.686807i	$-0.240988\pi$
$463$	6.70534e6			1.45368			0.726840	+	0.686807i	$0.240988\pi$
$464$			5.26487e6i			1.13525i
$465$		−	203628.i		−	0.0436721i
$466$		−	1.25052e7i		−	2.66763i
$467$	−4.94032e6			−1.04824			−0.524122	−	0.851643i	$-0.675607\pi$
$467$	−4.94032e6			−1.04824			−0.524122	+	0.851643i	$0.675607\pi$
$468$		−	1.12771e7i		−	2.38004i
$469$	−1.81874e6			−0.381803
$470$		−	8.02669e6i		−	1.67607i
$471$		−	4.26410e6i		−	0.885677i
$472$		−	3.67431e6i		−	0.759139i
$473$	−215761.			−0.0443426
$474$	1.86145e7			3.80546
$475$			53250.6i			0.0108291i
$476$	817061.			0.165286
$477$	−273863.			−0.0551110
$478$		−	5.32648e6i		−	1.06628i
$479$	4.45638e6			0.887449			0.443724	−	0.896163i	$-0.353657\pi$
$479$	4.45638e6			0.887449			0.443724	+	0.896163i	$0.353657\pi$
$480$			705674.i			0.139798i
$481$	−1.42315e7			−2.80471
$482$	−1.38134e7			−2.70822
$483$	−1.86262e6			−0.363292
$484$	−1.04225e7			−2.02236
$485$	−4.70085e6	−	1.61920e6i	−0.907449	−	0.312569i
$486$	−1.07295e7			−2.06058
$487$	3.85763e6			0.737053			0.368526	−	0.929617i	$-0.379862\pi$
$487$	3.85763e6			0.737053			0.368526	+	0.929617i	$0.379862\pi$
$488$	4.11033e6			0.781317
$489$	−1.12735e6			−0.213200
$490$		−	7.17336e6i		−	1.34968i
$491$	−613010.			−0.114753			−0.0573765	−	0.998353i	$-0.518274\pi$
$491$	−613010.			−0.114753			−0.0573765	+	0.998353i	$0.518274\pi$
$492$		−	1.32821e7i		−	2.47374i
$493$	1.03713e6			0.192183
$494$	−2.17934e6			−0.401797
$495$			246154.i			0.0451537i
$496$	209699.			0.0382730
$497$	−2.06655e6			−0.375279
$498$			9.52751e6i			1.72150i
$499$			7.76214e6i			1.39550i	0.716341	+	0.697750i	$0.245815\pi$
$499$			7.76214e6i			1.39550i	−0.716341	+	0.697750i	$0.754185\pi$
$500$			1.17595e7i			2.10360i
$501$	−6.89603e6			−1.22745
$502$		−	1.58982e6i		−	0.281571i
$503$	2.37672e6			0.418849			0.209425	−	0.977825i	$-0.432841\pi$
$503$	2.37672e6			0.418849			0.209425	+	0.977825i	$0.432841\pi$
$504$		−	3.13256e6i		−	0.549316i
$505$			4.82237e6i			0.841457i
$506$			430169.i			0.0746901i
$507$	1.37419e7			2.37425
$508$			2.92879e6i			0.503533i
$509$	1.13070e7			1.93443			0.967213	−	0.253967i	$-0.0817356\pi$
$509$	1.13070e7			1.93443			0.967213	+	0.253967i	$0.0817356\pi$
$510$	2.37232e6			0.403876
$511$		−	4.90033e6i		−	0.830182i
$512$	1.09485e7			1.84577
$513$			322860.i			0.0541653i
$514$			1.01944e7i			1.70198i
$515$			4.44712e6i			0.738858i
$516$	1.05215e7			1.73961
$517$	411248.			0.0676671
$518$	−7.78532e6			−1.27483
$519$			1.33771e7i			2.17994i
$520$	−1.78581e7			−2.89620
$521$	7.15599e6			1.15498			0.577492	−	0.816397i	$-0.304032\pi$
$521$	7.15599e6			1.15498			0.577492	+	0.816397i	$0.304032\pi$
$522$		−	7.83073e6i		−	1.25784i
$523$			6.14699e6i			0.982671i	0.870970	+	0.491336i	$0.163491\pi$
$523$			6.14699e6i			0.982671i	−0.870970	+	0.491336i	$0.836509\pi$
$524$			8.61210e6i			1.37019i
$525$		−	284477.i		−	0.0450452i
$526$		−	9.88340e6i		−	1.55755i
$527$		−	41308.6i		−	0.00647910i
$528$	−617015.			−0.0963188
$529$	3.83431e6			0.595728
$530$			854078.i			0.132071i
$531$			1.91488e6i			0.294717i
$532$	−798946.			−0.122388
$533$	1.02981e7			1.57015
$534$	−1.92220e6			−0.291706
$535$	−1.12965e7			−1.70632
$536$		−	1.04007e7i		−	1.56370i
$537$		−	8.62294e6i		−	1.29039i
$538$	4.60832e6			0.686416
$539$	367527.			0.0544901
$540$			5.21017e6i			0.768895i
$541$		−	6.71070e6i		−	0.985768i	−0.870095	−	0.492884i	$-0.835943\pi$
$541$		−	6.71070e6i		−	0.985768i	0.870095	−	0.492884i	$-0.164057\pi$
$542$			1.78621e6i			0.261177i
$543$			8.14617e6i			1.18564i
$544$			143156.i			0.0207401i
$545$			8.62897e6i			1.24442i
$546$	1.16425e7			1.67134
$547$	1.05907e7			1.51341			0.756706	−	0.653755i	$-0.226807\pi$
$547$	1.05907e7			1.51341			0.756706	+	0.653755i	$0.226807\pi$
$548$		−	1.16630e7i		−	1.65905i
$549$	−2.14212e6			−0.303328
$550$	−65699.6			−0.00926096
$551$	−1.01413e6			−0.142304
$552$		−	1.06517e7i		−	1.48789i
$553$			5.29100e6i			0.735741i
$554$			4.56222e6i			0.631541i
$555$	−1.51482e7			−2.08752
$556$		−	1.93070e7i		−	2.64867i
$557$	6.72290e6			0.918160			0.459080	−	0.888395i	$-0.348179\pi$
$557$	6.72290e6			0.918160			0.459080	+	0.888395i	$0.348179\pi$
$558$	−311897.			−0.0424058
$559$			8.15773e6i			1.10418i
$560$	−3.42305e6			−0.461258
$561$			121546.i			0.0163055i
$562$		−	1.36669e7i		−	1.82528i
$563$			1.27501e7i			1.69529i	0.530564	+	0.847645i	$0.321980\pi$
$563$			1.27501e7i			1.69529i	−0.530564	+	0.847645i	$0.678020\pi$
$564$	−2.00543e7			−2.65466
$565$		−	8.04840e6i		−	1.06069i
$566$	−3.07882e6			−0.403964
$567$		−	4.06594e6i		−	0.531134i
$568$		−	1.18179e7i		−	1.53698i
$569$			7.64909e6i			0.990443i	0.868767	+	0.495221i	$0.164913\pi$
$569$			7.64909e6i			0.990443i	−0.868767	+	0.495221i	$0.835087\pi$
$570$	−2.31972e6			−0.299053
$571$	1.31819e7			1.69195			0.845977	−	0.533219i	$-0.179018\pi$
$571$	1.31819e7			1.69195			0.845977	+	0.533219i	$0.179018\pi$
$572$		−	1.80189e6i		−	0.230271i
$573$	6.83478e6			0.869637
$574$	5.63358e6			0.713682
$575$		−	397407.i		−	0.0501263i
$576$	−5.00369e6			−0.628397
$577$			8.48401e6i			1.06087i	0.847726	+	0.530434i	$0.177971\pi$
$577$			8.48401e6i			1.06087i	−0.847726	+	0.530434i	$0.822029\pi$
$578$	−1.35035e7			−1.68123
$579$	−1.42756e7			−1.76970
$580$	−1.63656e7			−2.02005
$581$	−2.70810e6			−0.332831
$582$	−6.03677e6	+	1.75259e7i	−0.738749	+	2.14473i
$583$	−43758.7			−0.00533204
$584$	2.80233e7			3.40006
$585$	9.30684e6			1.12438
$586$	−2.29063e7			−2.75556
$587$			1.07814e7i			1.29145i	0.763568	+	0.645727i	$0.223446\pi$
$587$			1.07814e7i			1.29145i	−0.763568	+	0.645727i	$0.776554\pi$
$588$	−1.79223e7			−2.13771
$589$			40392.7i			0.00479750i
$590$	5.97180e6			0.706278
$591$	−6.43863e6			−0.758272
$592$		−	1.55999e7i		−	1.82944i
$593$	2.74665e6			0.320750			0.160375	−	0.987056i	$-0.448730\pi$
$593$	2.74665e6			0.320750			0.160375	+	0.987056i	$0.448730\pi$
$594$	−398338.			−0.0463219
$595$			674308.i			0.0780847i
$596$		−	2.09979e7i		−	2.42136i
$597$		−	1.30943e7i		−	1.50365i
$598$	1.62643e7			1.85987
$599$			3.05676e6i			0.348092i	0.984738	+	0.174046i	$0.0556842\pi$
$599$			3.05676e6i			0.348092i	−0.984738	+	0.174046i	$0.944316\pi$
$600$	1.62682e6			0.184485
$601$		−	5.16646e6i		−	0.583454i	−0.956502	−	0.291727i	$-0.905770\pi$
$601$		−	5.16646e6i		−	0.583454i	0.956502	−	0.291727i	$-0.0942300\pi$
$602$			4.46268e6i			0.501885i
$603$			5.42038e6i			0.607067i
$604$	1.11176e7			1.23999
$605$		−	8.60152e6i		−	0.955404i
$606$	1.79789e7			1.98876
$607$	−1.03671e7			−1.14206			−0.571028	−	0.820931i	$-0.693455\pi$
$607$	−1.03671e7			−1.14206			−0.571028	+	0.820931i	$0.693455\pi$
$608$		−	139982.i		−	0.0153572i
$609$	5.41773e6			0.591935
$610$			6.68046e6i			0.726912i
$611$		−	1.55489e7i		−	1.68499i
$612$		−	2.43508e6i		−	0.262806i
$613$	8.49591e6			0.913185			0.456592	−	0.889676i	$-0.349070\pi$
$613$	8.49591e6			0.913185			0.456592	+	0.889676i	$0.349070\pi$
$614$	−1.45105e7			−1.55332
$615$	1.09615e7			1.16864
$616$		−	500529.i		−	0.0531469i
$617$	−3.62235e6			−0.383070			−0.191535	−	0.981486i	$-0.561347\pi$
$617$	−3.62235e6			−0.383070			−0.191535	+	0.981486i	$0.561347\pi$
$618$	1.65799e7			1.74627
$619$			3.27287e6i			0.343323i	0.985156	+	0.171661i	$0.0549135\pi$
$619$			3.27287e6i			0.343323i	−0.985156	+	0.171661i	$0.945087\pi$
$620$			651840.i			0.0681022i
$621$		−	2.40949e6i		−	0.250724i
$622$		−	2.46053e7i		−	2.55007i
$623$		−	546366.i		−	0.0563980i
$624$			2.33288e7i			2.39845i
$625$	−8.93504e6			−0.914948
$626$	6.24493e6			0.636930
$627$		−	118851.i		−	0.0120735i
$628$			1.36500e7i			1.38112i
$629$	−3.07303e6			−0.309699
$630$	5.09129e6			0.511066
$631$	−3.30474e6			−0.330418			−0.165209	−	0.986259i	$-0.552830\pi$
$631$	−3.30474e6			−0.330418			−0.165209	+	0.986259i	$0.552830\pi$
$632$	−3.02574e7			−3.01327
$633$		−	8.79223e6i		−	0.872147i
$634$			1.25418e7i			1.23919i
$635$	−2.41708e6			−0.237880
$636$	2.13387e6			0.209182
$637$		−	1.38959e7i		−	1.35687i
$638$		−	1.25122e6i		−	0.121697i
$639$			6.15892e6i			0.596695i
$640$			1.67165e7i			1.61323i
$641$		−	1.03519e7i		−	0.995119i	−0.867430	−	0.497560i	$-0.834230\pi$
$641$		−	1.03519e7i		−	0.995119i	0.867430	−	0.497560i	$-0.165770\pi$
$642$			4.21161e7i			4.03284i
$643$	936990.			0.0893733			0.0446866	−	0.999001i	$-0.485771\pi$
$643$	936990.			0.0893733			0.0446866	+	0.999001i	$0.485771\pi$
$644$	5.96249e6			0.566517
$645$			8.68322e6i			0.821829i
$646$	−470587.			−0.0443669
$647$	−166064.			−0.0155961			−0.00779804	−	0.999970i	$-0.502482\pi$
$647$	−166064.			−0.0155961			−0.00779804	+	0.999970i	$0.502482\pi$
$648$	2.32517e7			2.17529
$649$			305966.i			0.0285142i
$650$			2.48404e6i			0.230608i
$651$		−	215787.i		−	0.0199560i
$652$	3.60881e6			0.332464
$653$		−	2.72073e6i		−	0.249690i	−0.992176	−	0.124845i	$-0.960157\pi$
$653$		−	2.72073e6i		−	0.249690i	0.992176	−	0.124845i	$-0.0398434\pi$
$654$	3.21709e7			2.94116
$655$	−7.10743e6			−0.647306
$656$			1.12883e7i			1.02417i
$657$	−1.46044e7			−1.31999
$658$		−	8.50600e6i		−	0.765880i
$659$		−	9.12292e6i		−	0.818315i	−0.912464	−	0.409157i	$-0.865823\pi$
$659$		−	9.12292e6i		−	0.818315i	0.912464	−	0.409157i	$-0.134177\pi$
$660$		−	1.91796e6i		−	0.171388i
$661$	−1.72620e7			−1.53669			−0.768347	−	0.640034i	$-0.778920\pi$
$661$	−1.72620e7			−1.53669			−0.768347	+	0.640034i	$0.778920\pi$
$662$			3.16124e7i			2.80357i
$663$	4.59554e6			0.406025
$664$		−	1.54867e7i		−	1.36313i
$665$		−	659358.i		−	0.0578185i
$666$			2.32026e7i			2.02698i
$667$	7.56843e6			0.658705
$668$	2.20751e7			1.91409
$669$		−	2.83468e7i		−	2.44872i
$670$	1.69042e7			1.45481
$671$	−342274.			−0.0293472
$672$			747813.i			0.0638807i
$673$	−1.87435e7			−1.59519			−0.797595	−	0.603194i	$-0.793895\pi$
$673$	−1.87435e7			−1.59519			−0.797595	+	0.603194i	$0.793895\pi$
$674$		−	2.84778e7i		−	2.41466i
$675$	368000.			0.0310877
$676$	−4.39895e7			−3.70240
$677$	−5.90068e6			−0.494801			−0.247401	−	0.968913i	$-0.579576\pi$
$677$	−5.90068e6			−0.494801			−0.247401	+	0.968913i	$0.579576\pi$
$678$	−3.00064e7			−2.50691
$679$	−4.98156e6	−	1.71589e6i	−0.414659	−	0.142829i
$680$	−3.85613e6			−0.319801
$681$	1.80105e7			1.48819
$682$	−49835.8			−0.00410280
$683$	−2.08087e7			−1.70684			−0.853420	−	0.521224i	$-0.825476\pi$
$683$	−2.08087e7			−1.70684			−0.853420	+	0.521224i	$0.825476\pi$
$684$			2.38109e6i			0.194597i
$685$	9.62533e6			0.783771
$686$		−	1.70137e7i		−	1.38035i
$687$	−6.35350e6			−0.513596
$688$	−8.94212e6			−0.720227
$689$			1.65448e6i			0.132774i
$690$	1.73120e7			1.38428
$691$	7.74942e6			0.617411			0.308705	−	0.951158i	$-0.400104\pi$
$691$	7.74942e6			0.617411			0.308705	+	0.951158i	$0.400104\pi$
$692$		−	4.28220e7i		−	3.39940i
$693$			260853.i			0.0206330i
$694$			3.57110e7i			2.81452i
$695$	1.59338e7			1.25129
$696$			3.09821e7i			2.42431i
$697$	2.22369e6			0.173377
$698$		−	1.33682e7i		−	1.03856i
$699$		−	2.57848e7i		−	1.99605i
$700$			910649.i			0.0702434i
$701$	−2.04705e7			−1.57338			−0.786690	−	0.617349i	$-0.788207\pi$
$701$	−2.04705e7			−1.57338			−0.786690	+	0.617349i	$0.788207\pi$
$702$			1.50608e7i			1.15347i
$703$	3.00489e6			0.229319
$704$	−799504.			−0.0607980
$705$		−	1.65505e7i		−	1.25412i
$706$	2.69768e7			2.03694
$707$			5.11033e6i			0.384504i
$708$		−	1.49202e7i		−	1.11865i
$709$			86165.3i			0.00643749i	0.999995	+	0.00321875i	$0.00102456\pi$
$709$			86165.3i			0.00643749i	−0.999995	+	0.00321875i	$0.998975\pi$
$710$	1.92074e7			1.42995
$711$	1.57687e7			1.16983
$712$	3.12448e6			0.230981
$713$		−	301449.i		−	0.0222070i
$714$	2.51398e6			0.184551
$715$	1.48707e6			0.108785
$716$			2.76032e7i			2.01223i
$717$		−	1.09828e7i		−	0.797841i
$718$			9.87414e6i			0.714806i
$719$			1.72158e7i			1.24195i	0.783830	+	0.620976i	$0.213264\pi$
$719$			1.72158e7i			1.24195i	−0.783830	+	0.620976i	$0.786736\pi$
$720$			1.02017e7i			0.733401i
$721$			4.71268e6i			0.337621i
$722$	−2.39280e7			−1.70830
$723$	−2.84824e7			−2.02642
$724$		−	2.60770e7i		−	1.84889i
$725$			1.15592e6i			0.0816740i
$726$	−3.20685e7			−2.25807
$727$	1.35156e6			0.0948418			0.0474209	−	0.998875i	$-0.484900\pi$
$727$	1.35156e6			0.0948418			0.0474209	+	0.998875i	$0.484900\pi$
$728$	−1.89245e7			−1.32342
$729$	−4.74613e6			−0.330766
$730$			4.55458e7i			3.16330i
$731$			1.76151e6i			0.121925i
$732$	1.66908e7			1.15133
$733$	1.33666e7			0.918888			0.459444	−	0.888207i	$-0.348049\pi$
$733$	1.33666e7			0.918888			0.459444	+	0.888207i	$0.348049\pi$
$734$			2.91065e6i			0.199411i
$735$		−	1.47910e7i		−	1.00990i
$736$			1.04468e6i			0.0710865i
$737$			866085.i			0.0587343i
$738$		−	1.67897e7i		−	1.13476i
$739$		−	1.42800e7i		−	0.961874i	−0.876755	−	0.480937i	$-0.840297\pi$
$739$		−	1.42800e7i		−	0.961874i	0.876755	−	0.480937i	$-0.159703\pi$
$740$	4.84915e7			3.25527
$741$	−4.49364e6			−0.300644
$742$			905078.i			0.0603499i
$743$	2.03063e7			1.34946			0.674728	−	0.738066i	$-0.264261\pi$
$743$	2.03063e7			1.34946			0.674728	+	0.738066i	$0.264261\pi$
$744$	1.23401e6			0.0817309
$745$	1.73292e7			1.14390
$746$		−	1.37509e7i		−	0.904654i
$747$			8.07093e6i			0.529203i
$748$		−	389085.i		−	0.0254267i
$749$	−1.19711e7			−0.779703
$750$			3.61823e7i			2.34878i
$751$	2.71822e7			1.75867			0.879334	−	0.476205i	$-0.157988\pi$
$751$	2.71822e7			1.75867			0.879334	+	0.476205i	$0.157988\pi$
$752$	1.70439e7			1.09907
$753$		−	3.27809e6i		−	0.210685i
$754$	−4.73073e7			−3.03040
$755$			9.17515e6i			0.585795i
$756$			5.52129e6i			0.351347i
$757$			1.84541e6i			0.117045i	0.998286	+	0.0585224i	$0.0186389\pi$
$757$			1.84541e6i			0.117045i	−0.998286	+	0.0585224i	$0.981361\pi$
$758$	−2.72380e7			−1.72188
$759$			886980.i			0.0558868i
$760$	3.77063e6			0.236799
$761$			1.13627e7i			0.711247i	0.934629	+	0.355624i	$0.115731\pi$
$761$			1.13627e7i			0.711247i	−0.934629	+	0.355624i	$0.884269\pi$
$762$			9.01146e6i			0.562222i
$763$			9.14425e6i			0.568639i
$764$	−2.18791e7			−1.35611
$765$	2.00964e6			0.124155
$766$			2.16508e7i			1.33322i
$767$	1.15683e7			0.710035
$768$	4.31328e7			2.63879
$769$			4.61827e6i			0.281620i	0.990037	+	0.140810i	$0.0449707\pi$
$769$			4.61827e6i			0.281620i	−0.990037	+	0.140810i	$0.955029\pi$
$770$	813502.			0.0494461
$771$			2.10202e7i			1.27351i
$772$	4.56982e7			2.75966
$773$	−1.89047e7			−1.13795			−0.568973	−	0.822356i	$-0.692659\pi$
$773$	−1.89047e7			−1.13795			−0.568973	+	0.822356i	$0.692659\pi$
$774$	1.33001e7			0.797999
$775$	46040.2			0.00275349
$776$	9.81257e6	−	2.84878e7i	0.584963	−	1.69826i
$777$	−1.60528e7			−0.953890
$778$	3.77005e7			2.23305
$779$	−2.17439e6			−0.128379
$780$	−7.25163e7			−4.26775
$781$			984091.i			0.0577308i
$782$	3.51197e6			0.205369
$783$			7.00839e6i			0.408521i
$784$	1.52320e7			0.885046
$785$	−1.12651e7			−0.652471
$786$			2.64982e7i			1.52989i
$787$	−1.33403e7			−0.767767			−0.383883	−	0.923382i	$-0.625413\pi$
$787$	−1.33403e7			−0.767767			−0.383883	+	0.923382i	$0.625413\pi$
$788$	2.06109e7			1.18245
$789$		−	2.03789e7i		−	1.16544i
$790$		−	4.91768e7i		−	2.80345i
$791$		−	8.52901e6i		−	0.484682i
$792$	−1.49172e6			−0.0845037
$793$			1.29410e7i			0.730779i
$794$	−1.37117e7			−0.771862
$795$			1.76105e6i			0.0988220i
$796$			4.19167e7i			2.34480i
$797$			5.94191e6i			0.331345i	0.986181	+	0.165673i	$0.0529795\pi$
$797$			5.94191e6i			0.331345i	−0.986181	+	0.165673i	$0.947021\pi$
$798$	−2.45824e6			−0.136652
$799$		−	3.35749e6i		−	0.186058i
$800$	−159553.			−0.00881414
$801$	−1.62833e6			−0.0896730
$802$			4.35658e7i			2.39172i
$803$	−2.33354e6			−0.127710
$804$		−	4.22342e7i		−	2.30422i
$805$			4.92075e6i			0.267634i
$806$			1.88424e6i			0.102164i
$807$	9.50205e6			0.513610
$808$	−2.92242e7			−1.57476
$809$	2.73919e7			1.47147			0.735733	−	0.677272i	$-0.236838\pi$
$809$	2.73919e7			1.47147			0.735733	+	0.677272i	$0.236838\pi$
$810$			3.77906e7i			2.02382i
$811$	1.72840e7			0.922769			0.461384	−	0.887200i	$-0.347353\pi$
$811$	1.72840e7			0.922769			0.461384	+	0.887200i	$0.347353\pi$
$812$	−1.73429e7			−0.923063
$813$			3.68304e6i			0.195425i
$814$			3.70737e6i			0.196113i
$815$			2.97829e6i			0.157063i
$816$			5.03741e6i			0.264839i
$817$		−	1.72245e6i		−	0.0902802i
$818$		−	4.30065e7i		−	2.24725i
$819$	9.86259e6			0.513785
$820$	−3.50892e7			−1.82238
$821$		−	9.87853e6i		−	0.511487i	−0.966745	−	0.255743i	$-0.917680\pi$
$821$		−	9.87853e6i		−	0.511487i	0.966745	−	0.255743i	$-0.0823202\pi$
$822$		−	3.58855e7i		−	1.85242i
$823$	−1.81822e6			−0.0935723			−0.0467862	−	0.998905i	$-0.514898\pi$
$823$	−1.81822e6			−0.0935723			−0.0467862	+	0.998905i	$0.514898\pi$
$824$	−2.69501e7			−1.38275
$825$	−135468.			−0.00692950
$826$	6.32841e6			0.322734
$827$		−	2.22552e6i		−	0.113153i	−0.998398	−	0.0565766i	$-0.981981\pi$
$827$		−	2.22552e6i		−	0.113153i	0.998398	−	0.0565766i	$-0.0180185\pi$
$828$		−	1.77700e7i		−	0.900764i
$829$	−2.63047e7			−1.32937			−0.664687	−	0.747122i	$-0.731435\pi$
$829$	−2.63047e7			−1.32937			−0.664687	+	0.747122i	$0.731435\pi$
$830$	2.51702e7			1.26821
$831$			9.40698e6i			0.472550i
$832$			3.02285e7i			1.51394i
$833$		−	3.00055e6i		−	0.149826i
$834$		−	5.94050e7i		−	2.95738i
$835$			1.82183e7i			0.904255i
$836$			380458.i			0.0188274i
$837$	279143.			0.0137725
$838$	−1.27676e7			−0.628056
$839$		−	1.33272e7i		−	0.653633i	−0.945088	−	0.326816i	$-0.894024\pi$
$839$		−	1.33272e7i		−	0.653633i	0.945088	−	0.326816i	$-0.105976\pi$
$840$	−2.01436e7			−0.985004
$841$	−1.50286e6			−0.0732705
$842$	5.01086e7			2.43575
$843$		−	2.81802e7i		−	1.36576i
$844$			2.81451e7i			1.36002i
$845$		−	3.63039e7i		−	1.74909i
$846$	−2.53504e7			−1.21775
$847$		−	9.11516e6i		−	0.436572i
$848$	−1.81356e6			−0.0866047
$849$	−6.34831e6			−0.302266
$850$			536381.i			0.0254640i
$851$	−2.24254e7			−1.06149
$852$		−	4.79886e7i		−	2.26485i
$853$			1.04169e7i			0.490191i	0.969499	+	0.245095i	$0.0788193\pi$
$853$			1.04169e7i			0.490191i	−0.969499	+	0.245095i	$0.921181\pi$
$854$			7.07938e6i			0.332162i
$855$	−1.96508e6			−0.0919316
$856$		−	6.84584e7i		−	3.19332i
$857$	1.28667e7			0.598435			0.299217	−	0.954185i	$-0.403274\pi$
$857$	1.28667e7			0.598435			0.299217	+	0.954185i	$0.403274\pi$
$858$		−	5.54417e6i		−	0.257110i
$859$		−	3.71311e7i		−	1.71694i	−0.512863	−	0.858470i	$-0.671415\pi$
$859$		−	3.71311e7i		−	1.71694i	0.512863	−	0.858470i	$-0.328585\pi$
$860$		−	2.77962e7i		−	1.28156i
$861$	1.16161e7			0.534012
$862$	1.77561e7			0.813915
$863$			9.95845e6i			0.455161i	0.973759	+	0.227580i	$0.0730814\pi$
$863$			9.95845e6i			0.455161i	−0.973759	+	0.227580i	$0.926919\pi$
$864$	−967374.			−0.0440869
$865$	3.53404e7			1.60594
$866$		−	4.57199e7i		−	2.07162i
$867$	−2.78434e7			−1.25798
$868$			690764.i			0.0311193i
$869$	2.51958e6			0.113182
$870$	−5.03547e7			−2.25549
$871$	3.27459e7			1.46255
$872$	−5.22927e7			−2.32890
$873$	−5.11386e6	+	1.48465e7i	−0.227098	+	0.659309i
$874$	−3.43410e6			−0.152067
$875$	−1.02845e7			−0.454110
$876$	1.13794e8			5.01024
$877$	−1.68443e7			−0.739525			−0.369763	−	0.929126i	$-0.620561\pi$
$877$	−1.68443e7			−0.739525			−0.369763	+	0.929126i	$0.620561\pi$
$878$		−	3.55152e7i		−	1.55481i
$879$	−4.72312e7			−2.06185
$880$			1.63006e6i			0.0709573i
$881$	−3.08869e7			−1.34071			−0.670354	−	0.742042i	$-0.733858\pi$
$881$	−3.08869e7			−1.34071			−0.670354	+	0.742042i	$0.733858\pi$
$882$	−2.26553e7			−0.980616
$883$		−	9.80289e6i		−	0.423109i	−0.977366	−	0.211555i	$-0.932147\pi$
$883$		−	9.80289e6i		−	0.423109i	0.977366	−	0.211555i	$-0.0678526\pi$
$884$	−1.47109e7			−0.633154
$885$	1.23134e7			0.528471
$886$			5.61530e7i			2.40319i
$887$			922105.i			0.0393524i	0.999806	+	0.0196762i	$0.00626353\pi$
$887$			922105.i			0.0393524i	−0.999806	+	0.0196762i	$0.993736\pi$
$888$		−	9.18003e7i		−	3.90672i
$889$	−2.56142e6			−0.108699
$890$			5.07816e6i			0.214898i
$891$	−1.93620e6			−0.0817066
$892$			9.07420e7i			3.81853i
$893$			3.28305e6i			0.137768i
$894$		−	6.46076e7i		−	2.70358i
$895$	−2.27805e7			−0.950616
$896$			1.77148e7i			0.737166i
$897$	3.35359e7			1.39164
$898$	−7.71790e6			−0.319381
$899$			876814.i			0.0361833i
$900$	2.71400e6			0.111687
$901$			357253.i			0.0146610i
$902$		−	2.68271e6i		−	0.109789i
$903$			9.20173e6i			0.375535i
$904$	4.87744e7			1.98505
$905$	2.15209e7			0.873453
$906$	3.42072e7			1.38451
$907$		−	3.90070e7i		−	1.57443i	−0.616676	−	0.787217i	$-0.711521\pi$
$907$		−	3.90070e7i		−	1.57443i	0.616676	−	0.787217i	$-0.288479\pi$
$908$	−5.76539e7			−2.32067
$909$	1.52303e7			0.611362
$910$		−	3.07577e7i		−	1.23126i
$911$		−	2.44321e7i		−	0.975361i	−0.873022	−	0.487680i	$-0.837843\pi$
$911$		−	2.44321e7i		−	0.975361i	0.873022	−	0.487680i	$-0.162157\pi$
$912$		−	4.92572e6i		−	0.196102i
$913$			1.28960e6i			0.0512009i
$914$			2.96849e7i			1.17536i
$915$			1.37746e7i			0.543911i
$916$	2.03384e7			0.800900
$917$	−7.53185e6			−0.295786
$918$			3.25210e6i			0.127367i
$919$			2.39860e7i			0.936847i	0.883504	+	0.468424i	$0.155178\pi$
$919$			2.39860e7i			0.936847i	−0.883504	+	0.468424i	$0.844822\pi$
$920$	−2.81401e7			−1.09611
$921$	−2.99197e7			−1.16227
$922$	−2.16039e6			−0.0836962
$923$	3.72075e7			1.43756
$924$		−	2.03249e6i		−	0.0783158i
$925$		−	3.42501e6i		−	0.131616i
$926$	−6.60439e7			−2.53107
$927$	1.40452e7			0.536819
$928$		−	3.03861e6i		−	0.115826i
$929$			3.25331e6i			0.123676i	0.998086	+	0.0618380i	$0.0196962\pi$
$929$			3.25331e6i			0.123676i	−0.998086	+	0.0618380i	$0.980304\pi$
$930$			2.00562e6i			0.0760398i
$931$			2.93402e6i			0.110940i
$932$			8.25407e7i			3.11264i
$933$		−	5.07344e7i		−	1.90809i
$934$	4.86593e7			1.82515
$935$	321106.			0.0120121
$936$			5.64007e7i			2.10424i
$937$	1.13762e7			0.423299			0.211650	−	0.977346i	$-0.432116\pi$
$937$	1.13762e7			0.423299			0.211650	+	0.977346i	$0.432116\pi$
$938$	1.79136e7			0.664776
$939$	1.28766e7			0.476582
$940$			5.29803e7i			1.95567i
$941$			4.69557e7i			1.72868i	0.502910	+	0.864339i	$0.332263\pi$
$941$			4.69557e7i			1.72868i	−0.502910	+	0.864339i	$0.667737\pi$
$942$			4.19990e7i			1.54210i
$943$	1.62273e7			0.594249
$944$			1.26806e7i			0.463137i
$945$	−4.55664e6			−0.165983
$946$	2.12513e6			0.0772071
$947$		−	3.07280e7i		−	1.11342i	−0.830706	−	0.556711i	$-0.812063\pi$
$947$		−	3.07280e7i		−	1.11342i	0.830706	−	0.556711i	$-0.187937\pi$
$948$	−1.22866e8			−4.44027
$949$			8.82289e7i			3.18013i
$950$		−	524489.i		−	0.0188550i
$951$			2.58604e7i			0.927222i
$952$	−4.08640e6			−0.146133
$953$			3.03422e7i			1.08222i	0.840952	+	0.541110i	$0.181996\pi$
$953$			3.03422e7i			1.08222i	−0.840952	+	0.541110i	$0.818004\pi$
$954$	2.69740e6			0.0959565
$955$		−	1.80564e7i		−	0.640654i
$956$			3.51575e7i			1.24415i
$957$		−	2.57993e6i		−	0.0910599i
$958$	−4.38928e7			−1.54518
$959$	1.02001e7			0.358144
$960$			3.21757e7i			1.12681i
$961$	−2.85942e7			−0.998780
$962$	1.40172e8			4.88342
$963$			3.56774e7i			1.23973i
$964$	9.11759e7			3.16000
$965$			3.77140e7i			1.30372i
$966$	1.83457e7			0.632547
$967$	−5.33380e7			−1.83430			−0.917150	−	0.398541i	$-0.869517\pi$
$967$	−5.33380e7			−1.83430			−0.917150	+	0.398541i	$0.869517\pi$
$968$	5.21264e7			1.78801
$969$	−970318.			−0.0331975
$970$	4.63007e7	+	1.59482e7i	1.58001	+	0.544231i
$971$	−6.34870e6			−0.216091			−0.108045	−	0.994146i	$-0.534459\pi$
$971$	−6.34870e6			−0.216091			−0.108045	+	0.994146i	$0.534459\pi$
$972$	7.08205e7			2.40433
$973$	1.68853e7			0.571776
$974$	−3.79955e7			−1.28332
$975$			5.12191e6i			0.172552i
$976$	−1.41853e7			−0.476667
$977$			3.73779e7i			1.25279i	0.779505	+	0.626396i	$0.215470\pi$
$977$			3.73779e7i			1.25279i	−0.779505	+	0.626396i	$0.784530\pi$
$978$	1.11038e7			0.371214
$979$	−260180.			−0.00867595
$980$			4.73479e7i			1.57484i
$981$	2.72526e7			0.904138
$982$	6.03780e6			0.199802
$983$			8.13412e6i			0.268489i	0.990948	+	0.134245i	$0.0428608\pi$
$983$			8.13412e6i			0.268489i	−0.990948	+	0.134245i	$0.957139\pi$
$984$			6.64281e7i			2.18708i
$985$			1.70099e7i			0.558613i
$986$	−1.02151e7			−0.334620
$987$		−	1.75388e7i		−	0.573069i
$988$	1.43848e7			0.468824
$989$			1.28546e7i			0.417895i
$990$		−	2.42448e6i		−	0.0786194i
$991$			5.78746e7i			1.87199i	0.352011	+	0.935996i	$0.385498\pi$
$991$			5.78746e7i			1.87199i	−0.352011	+	0.935996i	$0.614502\pi$
$992$	−121027.			−0.00390485
$993$			6.51825e7i			2.09777i
$994$	2.03543e7			0.653417
$995$	−3.45932e7			−1.10773
$996$		−	6.28865e7i		−	2.00867i
$997$	−5.67003e7			−1.80654			−0.903270	−	0.429072i	$-0.858841\pi$
$997$	−5.67003e7			−1.80654			−0.903270	+	0.429072i	$0.858841\pi$
$998$		−	7.64527e7i		−	2.42978i
$999$		−	2.07660e7i		−	0.658322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.4	yes	40
97.96	even	2	inner	97.6.b.a.96.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.3	✓	40	97.96	even	2	inner
97.6.b.a.96.4	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-9.84944 q^{2} -20.3089 q^{3} +65.0114 q^{4} +53.6529i q^{5} +200.031 q^{6} +56.8568i q^{7} -325.144 q^{8} +169.450 q^{9} -528.451i q^{10} +27.0752 q^{11} -1320.31 q^{12} -1023.69i q^{13} -560.007i q^{14} -1089.63i q^{15} +1122.12 q^{16} -221.046i q^{17} -1668.99 q^{18} +216.145i q^{19} +3488.05i q^{20} -1154.70i q^{21} -266.676 q^{22} -1613.08i q^{23} +6603.30 q^{24} +246.365 q^{25} +10082.7i q^{26} +1493.72 q^{27} +3696.34i q^{28} +4691.91i q^{29} +10732.2i q^{30} +186.878 q^{31} -647.628 q^{32} -549.867 q^{33} +2177.18i q^{34} -3050.53 q^{35} +11016.2 q^{36} -13902.2i q^{37} -2128.91i q^{38} +20789.9i q^{39} -17444.9i q^{40} +10059.8i q^{41} +11373.1i q^{42} -7968.97 q^{43} +1760.20 q^{44} +9091.48i q^{45} +15887.9i q^{46} +15189.1 q^{47} -22788.9 q^{48} +13574.3 q^{49} -2426.56 q^{50} +4489.20i q^{51} -66551.4i q^{52} -1616.19 q^{53} -14712.3 q^{54} +1452.66i q^{55} -18486.6i q^{56} -4389.66i q^{57} -46212.7i q^{58} +11300.6i q^{59} -70838.4i q^{60} -12641.6 q^{61} -1840.64 q^{62} +9634.37i q^{63} -29529.0 q^{64} +54923.8 q^{65} +5415.88 q^{66} +31988.1i q^{67} -14370.5i q^{68} +32759.8i q^{69} +30046.0 q^{70} +36346.6i q^{71} -55095.6 q^{72} -86187.4 q^{73} +136929. i q^{74} -5003.40 q^{75} +14051.9i q^{76} +1539.41i q^{77} -204769. i q^{78} +93058.4 q^{79} +60204.9i q^{80} -71512.1 q^{81} -99083.8i q^{82} +47630.2i q^{83} -75068.4i q^{84} +11859.8 q^{85} +78489.8 q^{86} -95287.3i q^{87} -8803.34 q^{88} -9609.52 q^{89} -89546.0i q^{90} +58203.6 q^{91} -104869. i q^{92} -3795.28 q^{93} -149604. q^{94} -11596.8 q^{95} +13152.6 q^{96} +(-30179.2 + 87616.0i) q^{97} -133699. q^{98} +4587.89 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 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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