LMFDB - Embedded newform 97.6.b.a.96.12

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			96.12
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.09653 q^{2} -8.23001 q^{3} -6.02536 q^{4} +103.917i q^{5} +41.9445 q^{6} +183.907i q^{7} +193.797 q^{8} -175.267 q^{9} -529.617i q^{10} +653.553 q^{11} +49.5888 q^{12} +414.613i q^{13} -937.288i q^{14} -855.240i q^{15} -794.884 q^{16} +1634.87i q^{17} +893.254 q^{18} +1001.37i q^{19} -626.138i q^{20} -1513.56i q^{21} -3330.86 q^{22} +3936.24i q^{23} -1594.96 q^{24} -7673.78 q^{25} -2113.09i q^{26} +3442.34 q^{27} -1108.11i q^{28} -4383.54i q^{29} +4358.76i q^{30} +5539.70 q^{31} -2150.37 q^{32} -5378.75 q^{33} -8332.18i q^{34} -19111.1 q^{35} +1056.05 q^{36} +3639.87i q^{37} -5103.54i q^{38} -3412.27i q^{39} +20138.9i q^{40} -5093.92i q^{41} +7713.89i q^{42} -16828.7 q^{43} -3937.90 q^{44} -18213.2i q^{45} -20061.2i q^{46} +20108.8 q^{47} +6541.90 q^{48} -17014.8 q^{49} +39109.7 q^{50} -13455.0i q^{51} -2498.19i q^{52} +573.904 q^{53} -17544.0 q^{54} +67915.4i q^{55} +35640.7i q^{56} -8241.32i q^{57} +22340.9i q^{58} -11533.9i q^{59} +5153.13i q^{60} +52634.5 q^{61} -28233.3 q^{62} -32232.8i q^{63} +36395.7 q^{64} -43085.4 q^{65} +27413.0 q^{66} -19934.1i q^{67} -9850.69i q^{68} -32395.3i q^{69} +97400.3 q^{70} -15299.8i q^{71} -33966.3 q^{72} +26799.4 q^{73} -18550.7i q^{74} +63155.3 q^{75} -6033.64i q^{76} +120193. i q^{77} +17390.7i q^{78} +39795.1 q^{79} -82602.1i q^{80} +14259.4 q^{81} +25961.3i q^{82} -62355.3i q^{83} +9119.72i q^{84} -169891. q^{85} +85768.2 q^{86} +36076.6i q^{87} +126657. q^{88} -64176.5 q^{89} +92824.4i q^{90} -76250.3 q^{91} -23717.3i q^{92} -45591.8 q^{93} -102485. q^{94} -104060. q^{95} +17697.6 q^{96} +(91325.1 - 15718.4i) q^{97} +86716.4 q^{98} -114546. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.09653			−0.900948			−0.450474	−	0.892790i	$-0.648745\pi$
$2$	−5.09653			−0.900948			−0.450474	+	0.892790i	$0.648745\pi$
$3$	−8.23001			−0.527955			−0.263978	−	0.964529i	$-0.585035\pi$
$3$	−8.23001			−0.527955			−0.263978	+	0.964529i	$0.585035\pi$
$4$	−6.02536			−0.188292
$5$			103.917i			1.85893i	0.368914	+	0.929464i	$0.379730\pi$
$5$			103.917i			1.85893i	−0.368914	+	0.929464i	$0.620270\pi$
$6$	41.9445			0.475660
$7$			183.907i			1.41858i	0.704918	+	0.709289i	$0.250984\pi$
$7$			183.907i			1.41858i	−0.704918	+	0.709289i	$0.749016\pi$
$8$	193.797			1.07059
$9$	−175.267			−0.721263
$10$		−	529.617i		−	1.67480i
$11$	653.553			1.62854			0.814272	−	0.580484i	$-0.197137\pi$
$11$	653.553			1.62854			0.814272	+	0.580484i	$0.197137\pi$
$12$	49.5888			0.0994100
$13$			414.613i			0.680432i	0.940347	+	0.340216i	$0.110500\pi$
$13$			414.613i			0.680432i	−0.940347	+	0.340216i	$0.889500\pi$
$14$		−	937.288i		−	1.27807i
$15$		−	855.240i		−	0.981431i
$16$	−794.884			−0.776253
$17$			1634.87i			1.37202i	0.727590	+	0.686012i	$0.240640\pi$
$17$			1634.87i			1.37202i	−0.727590	+	0.686012i	$0.759360\pi$
$18$	893.254			0.649821
$19$			1001.37i			0.636374i	0.948028	+	0.318187i	$0.103074\pi$
$19$			1001.37i			0.636374i	−0.948028	+	0.318187i	$0.896926\pi$
$20$		−	626.138i		−	0.350022i
$21$		−	1513.56i		−	0.748946i
$22$	−3330.86			−1.46723
$23$			3936.24i			1.55154i	0.631017	+	0.775769i	$0.282638\pi$
$23$			3936.24i			1.55154i	−0.631017	+	0.775769i	$0.717362\pi$
$24$	−1594.96			−0.565224
$25$	−7673.78			−2.45561
$26$		−	2113.09i		−	0.613034i
$27$	3442.34			0.908750
$28$		−	1108.11i		−	0.267108i
$29$		−	4383.54i		−	0.967899i	−0.875096	−	0.483950i	$-0.839202\pi$
$29$		−	4383.54i		−	0.967899i	0.875096	−	0.483950i	$-0.160798\pi$
$30$			4358.76i			0.884218i
$31$	5539.70			1.03534			0.517669	−	0.855581i	$-0.326800\pi$
$31$	5539.70			1.03534			0.517669	+	0.855581i	$0.326800\pi$
$32$	−2150.37			−0.371226
$33$	−5378.75			−0.859798
$34$		−	8332.18i		−	1.23612i
$35$	−19111.1			−2.63703
$36$	1056.05			0.135808
$37$			3639.87i			0.437101i	0.975826	+	0.218551i	$0.0701328\pi$
$37$			3639.87i			0.437101i	−0.975826	+	0.218551i	$0.929867\pi$
$38$		−	5103.54i		−	0.573340i
$39$		−	3412.27i		−	0.359238i
$40$			20138.9i			1.99015i
$41$		−	5093.92i		−	0.473252i	−0.971601	−	0.236626i	$-0.923958\pi$
$41$		−	5093.92i		−	0.473252i	0.971601	−	0.236626i	$-0.0760416\pi$
$42$			7713.89i			0.674761i
$43$	−16828.7			−1.38797			−0.693985	−	0.719989i	$-0.744147\pi$
$43$	−16828.7			−1.38797			−0.693985	+	0.719989i	$0.744147\pi$
$44$	−3937.90			−0.306643
$45$		−	18213.2i		−	1.34078i
$46$		−	20061.2i		−	1.39786i
$47$	20108.8			1.32783			0.663914	−	0.747809i	$-0.268894\pi$
$47$	20108.8			1.32783			0.663914	+	0.747809i	$0.268894\pi$
$48$	6541.90			0.409827
$49$	−17014.8			−1.01236
$50$	39109.7			2.21238
$51$		−	13455.0i		−	0.724367i
$52$		−	2498.19i		−	0.128120i
$53$	573.904			0.0280640			0.0140320	−	0.999902i	$-0.495533\pi$
$53$	573.904			0.0280640			0.0140320	+	0.999902i	$0.495533\pi$
$54$	−17544.0			−0.818737
$55$			67915.4i			3.02734i
$56$			35640.7i			1.51872i
$57$		−	8241.32i		−	0.335977i
$58$			22340.9i			0.872027i
$59$		−	11533.9i		−	0.431366i	−0.976463	−	0.215683i	$-0.930802\pi$
$59$		−	11533.9i		−	0.431366i	0.976463	−	0.215683i	$-0.0691977\pi$
$60$			5153.13i			0.184796i
$61$	52634.5			1.81111			0.905557	−	0.424224i	$-0.139453\pi$
$61$	52634.5			1.81111			0.905557	+	0.424224i	$0.139453\pi$
$62$	−28233.3			−0.932786
$63$		−	32232.8i		−	1.02317i
$64$	36395.7			1.11071
$65$	−43085.4			−1.26487
$66$	27413.0			0.774634
$67$		−	19934.1i		−	0.542513i	−0.962507	−	0.271256i	$-0.912561\pi$
$67$		−	19934.1i		−	0.542513i	0.962507	−	0.271256i	$-0.0874391\pi$
$68$		−	9850.69i		−	0.258342i
$69$		−	32395.3i		−	0.819143i
$70$	97400.3			2.37583
$71$		−	15299.8i		−	0.360197i	−0.983649	−	0.180098i	$-0.942358\pi$
$71$		−	15299.8i		−	0.360197i	0.983649	−	0.180098i	$-0.0576416\pi$
$72$	−33966.3			−0.772177
$73$	26799.4			0.588596			0.294298	−	0.955714i	$-0.404914\pi$
$73$	26799.4			0.588596			0.294298	+	0.955714i	$0.404914\pi$
$74$		−	18550.7i		−	0.393805i
$75$	63155.3			1.29645
$76$		−	6033.64i		−	0.119824i
$77$			120193.i			2.31022i
$78$			17390.7i			0.323655i
$79$	39795.1			0.717400			0.358700	−	0.933453i	$-0.383220\pi$
$79$	39795.1			0.717400			0.358700	+	0.933453i	$0.383220\pi$
$80$		−	82602.1i		−	1.44300i
$81$	14259.4			0.241484
$82$			25961.3i			0.426376i
$83$		−	62355.3i		−	0.993524i	−0.867887	−	0.496762i	$-0.834522\pi$
$83$		−	62355.3i		−	0.993524i	0.867887	−	0.496762i	$-0.165478\pi$
$84$			9119.72i			0.141021i
$85$	−169891.			−2.55049
$86$	85768.2			1.25049
$87$			36076.6i			0.511008i
$88$	126657.			1.74350
$89$	−64176.5			−0.858818			−0.429409	−	0.903110i	$-0.641278\pi$
$89$	−64176.5			−0.858818			−0.429409	+	0.903110i	$0.641278\pi$
$90$			92824.4i			1.20797i
$91$	−76250.3			−0.965246
$92$		−	23717.3i		−	0.292143i
$93$	−45591.8			−0.546612
$94$	−102485.			−1.19630
$95$	−104060.			−1.18297
$96$	17697.6			0.195991
$97$	91325.1	−	15718.4i	0.985509	−	0.169621i
$97$	91325.1	−	15718.4i	0.985509	−	0.169621i
$98$	86716.4			0.912087
$99$	−114546.			−1.17461
$100$	46237.3			0.462373
$101$	−19572.5			−0.190916			−0.0954580	−	0.995433i	$-0.530432\pi$
$101$	−19572.5			−0.190916			−0.0954580	+	0.995433i	$0.530432\pi$
$102$			68573.9i			0.652617i
$103$	−5267.33			−0.0489212			−0.0244606	−	0.999701i	$-0.507787\pi$
$103$	−5267.33			−0.0489212			−0.0244606	+	0.999701i	$0.507787\pi$
$104$			80351.0i			0.728463i
$105$	157285.			1.39224
$106$	−2924.92			−0.0252842
$107$			174347.i			1.47216i	0.676896	+	0.736079i	$0.263325\pi$
$107$			174347.i			1.47216i	−0.676896	+	0.736079i	$0.736675\pi$
$108$	−20741.3			−0.171111
$109$	74882.0			0.603686			0.301843	−	0.953358i	$-0.402398\pi$
$109$	74882.0			0.603686			0.301843	+	0.953358i	$0.402398\pi$
$110$		−	346133.i		−	2.72748i
$111$		−	29956.2i		−	0.230770i
$112$		−	146185.i		−	1.10118i
$113$	−7617.02			−0.0561163			−0.0280581	−	0.999606i	$-0.508932\pi$
$113$	−7617.02			−0.0561163			−0.0280581	+	0.999606i	$0.508932\pi$
$114$			42002.2i			0.302698i
$115$	−409043.			−2.88420
$116$			26412.4i			0.182248i
$117$		−	72668.0i		−	0.490770i
$118$			58782.8i			0.388638i
$119$	−300665.			−1.94632
$120$		−	165743.i		−	1.05071i
$121$	266081.			1.65215
$122$	−268253.			−1.63172
$123$			41923.0i			0.249856i
$124$	−33378.7			−0.194946
$125$		−	472697.i		−	2.70587i
$126$			164276.i			0.921821i
$127$		−	32623.4i		−	0.179482i	−0.995965	−	0.0897408i	$-0.971396\pi$
$127$		−	32623.4i		−	0.179482i	0.995965	−	0.0897408i	$-0.0286039\pi$
$128$	−116680.			−0.629465
$129$	138501.			0.732787
$130$	219586.			1.13959
$131$			56873.8i			0.289557i	0.989464	+	0.144778i	$0.0462470\pi$
$131$			56873.8i			0.289557i	−0.989464	+	0.144778i	$0.953753\pi$
$132$	32408.9			0.161894
$133$	−184160.			−0.902746
$134$			101595.i			0.488776i
$135$			357718.i			1.68930i
$136$			316834.i			1.46887i
$137$			3708.92i			0.0168829i	0.999964	+	0.00844144i	$0.00268703\pi$
$137$			3708.92i			0.0168829i	−0.999964	+	0.00844144i	$0.997313\pi$
$138$			165104.i			0.738005i
$139$		−	304737.i		−	1.33779i	−0.743357	−	0.668894i	$-0.766768\pi$
$139$		−	304737.i		−	1.33779i	0.743357	−	0.668894i	$-0.233232\pi$
$140$	115151.			0.496534
$141$	−165496.			−0.701034
$142$			77975.9i			0.324519i
$143$			270972.i			1.10811i
$144$	139317.			0.559883
$145$	455525.			1.79925
$146$	−136584.			−0.530294
$147$	140032.			0.534483
$148$		−	21931.5i		−	0.0823028i
$149$		−	826.445i		−	0.00304964i	−0.999999	−	0.00152482i	$-0.999515\pi$
$149$		−	826.445i		−	0.00304964i	0.999999	−	0.00152482i	$-0.000485365\pi$
$150$	−321873.			−1.16804
$151$	335639.			1.19793			0.598963	−	0.800777i	$-0.295580\pi$
$151$	335639.			1.19793			0.598963	+	0.800777i	$0.295580\pi$
$152$			194064.i			0.681296i
$153$		−	286539.i		−	0.989590i
$154$		−	612568.i		−	2.08138i
$155$			575670.i			1.92462i
$156$			20560.2i			0.0676418i
$157$			37150.5i			0.120286i	0.998190	+	0.0601431i	$0.0191557\pi$
$157$			37150.5i			0.120286i	−0.998190	+	0.0601431i	$0.980844\pi$
$158$	−202817.			−0.646340
$159$	−4723.24			−0.0148165
$160$		−	223460.i		−	0.690082i
$161$	−723903.			−2.20098
$162$	−72673.3			−0.217564
$163$	−85345.8			−0.251601			−0.125801	−	0.992056i	$-0.540150\pi$
$163$	−85345.8			−0.251601			−0.125801	+	0.992056i	$0.540150\pi$
$164$			30692.7i			0.0891098i
$165$		−	558945.i		−	1.59830i
$166$			317796.i			0.895113i
$167$	162822.			0.451775			0.225888	−	0.974153i	$-0.427472\pi$
$167$	162822.			0.451775			0.225888	+	0.974153i	$0.427472\pi$
$168$		−	293323.i		−	0.801814i
$169$	199389.			0.537012
$170$	865857.			2.29786
$171$		−	175508.i		−	0.458993i
$172$	101399.			0.261344
$173$			327607.i			0.832220i	0.909314	+	0.416110i	$0.136607\pi$
$173$			327607.i			0.832220i	−0.909314	+	0.416110i	$0.863393\pi$
$174$		−	183865.i		−	0.460391i
$175$		−	1.41126e6i		−	3.48347i
$176$	−519499.			−1.26416
$177$			94924.0i			0.227742i
$178$	327078.			0.773751
$179$		−	215099.i		−	0.501771i	−0.968017	−	0.250886i	$-0.919278\pi$
$179$		−	215099.i		−	0.501771i	0.968017	−	0.250886i	$-0.0807218\pi$
$180$			109741.i			0.252458i
$181$			122529.i			0.277997i	0.990293	+	0.138999i	$0.0443884\pi$
$181$			122529.i			0.277997i	−0.990293	+	0.138999i	$0.955612\pi$
$182$	388612.			0.869636
$183$	−433182.			−0.956188
$184$			762834.i			1.66106i
$185$	−378245.			−0.812539
$186$	232360.			0.492469
$187$			1.06848e6i			2.23440i
$188$	−121163.			−0.250020
$189$			633071.i			1.28913i
$190$	530345.			1.06580
$191$	−273366.			−0.542202			−0.271101	−	0.962551i	$-0.587388\pi$
$191$	−273366.			−0.542202			−0.271101	+	0.962551i	$0.587388\pi$
$192$	−299537.			−0.586405
$193$	323806.			0.625736			0.312868	−	0.949797i	$-0.398710\pi$
$193$	323806.			0.625736			0.312868	+	0.949797i	$0.398710\pi$
$194$	−465441.	+	80109.5i	−0.887893	+	0.152820i
$195$	354594.			0.667797
$196$	102520.			0.190620
$197$	635410.			1.16651			0.583255	−	0.812289i	$-0.301779\pi$
$197$	635410.			1.16651			0.583255	+	0.812289i	$0.301779\pi$
$198$	583789.			1.05826
$199$			969033.i			1.73463i	0.497763	+	0.867313i	$0.334155\pi$
$199$			969033.i			1.73463i	−0.497763	+	0.867313i	$0.665845\pi$
$200$	−1.48716e6			−2.62895
$201$			164058.i			0.286423i
$202$	99751.7			0.172005
$203$	806164.			1.37304
$204$			81071.3i			0.136393i
$205$	529346.			0.879741
$206$	26845.1			0.0440755
$207$		−	689893.i		−	1.11907i
$208$		−	329569.i		−	0.528188i
$209$			654452.i			1.03636i
$210$	−801606.			−1.25433
$211$		−	578763.i		−	0.894942i	−0.894299	−	0.447471i	$-0.852325\pi$
$211$		−	578763.i		−	0.894942i	0.894299	−	0.447471i	$-0.147675\pi$
$212$	−3457.98			−0.00528424
$213$			125918.i			0.190168i
$214$		−	888564.i		−	1.32634i
$215$		−	1.74879e6i		−	2.58014i
$216$	667117.			0.972899
$217$			1.01879e6i			1.46871i
$218$	−381639.			−0.543890
$219$	−220559.			−0.310752
$220$		−	409215.i		−	0.570026i
$221$	−677840.			−0.933569
$222$			152673.i			0.207912i
$223$			246336.i			0.331715i	0.986150	+	0.165858i	$0.0530392\pi$
$223$			246336.i			0.331715i	−0.986150	+	0.165858i	$0.946961\pi$
$224$		−	395468.i		−	0.526613i
$225$	1.34496e6			1.77114
$226$	38820.4			0.0505579
$227$	16425.2			0.0211566			0.0105783	−	0.999944i	$-0.496633\pi$
$227$	16425.2			0.0211566			0.0105783	+	0.999944i	$0.496633\pi$
$228$			49656.9i			0.0632620i
$229$	818791.			1.03177			0.515887	−	0.856657i	$-0.327463\pi$
$229$	818791.			1.03177			0.515887	+	0.856657i	$0.327463\pi$
$230$	2.08470e6			2.59851
$231$		−	989190.i		−	1.21969i
$232$		−	849519.i		−	1.03622i
$233$			105442.i			0.127240i	0.997974	+	0.0636200i	$0.0202646\pi$
$233$			105442.i			0.127240i	−0.997974	+	0.0636200i	$0.979735\pi$
$234$			370355.i			0.442159i
$235$			2.08965e6i			2.46834i
$236$			69495.8i			0.0812229i
$237$	−327514.			−0.378755
$238$	1.53235e6			1.75354
$239$		−	268662.i		−	0.304236i	−0.988362	−	0.152118i	$-0.951391\pi$
$239$		−	268662.i		−	0.304236i	0.988362	−	0.152118i	$-0.0486094\pi$
$240$			679816.i			0.761839i
$241$	−1.57482e6			−1.74658			−0.873290	−	0.487201i	$-0.838018\pi$
$241$	−1.57482e6			−1.74658			−0.873290	+	0.487201i	$0.838018\pi$
$242$	−1.35609e6			−1.48851
$243$	−953844.			−1.03624
$244$	−317142.			−0.341019
$245$		−	1.76813e6i		−	1.88191i
$246$		−	213662.i		−	0.225107i
$247$	−415183.			−0.433009
$248$	1.07358e6			1.10842
$249$			513185.i			0.524536i
$250$			2.40911e6i			2.43785i
$251$		−	1.11475e6i		−	1.11685i	−0.829556	−	0.558423i	$-0.811406\pi$
$251$		−	1.11475e6i		−	1.11685i	0.829556	−	0.558423i	$-0.188594\pi$
$252$			194214.i			0.192655i
$253$			2.57255e6i			2.52675i
$254$			166266.i			0.161704i
$255$	1.39821e6			1.34655
$256$	−569999.			−0.543593
$257$		−	1.55726e6i		−	1.47072i	−0.677678	−	0.735359i	$-0.737014\pi$
$257$		−	1.55726e6i		−	1.47072i	0.677678	−	0.735359i	$-0.262986\pi$
$258$	−705873.			−0.660203
$259$	−669398.			−0.620062
$260$	259605.			0.238166
$261$			768290.i			0.698110i
$262$		−	289859.i		−	0.260876i
$263$		−	1.31158e6i		−	1.16925i	−0.811304	−	0.584624i	$-0.801242\pi$
$263$		−	1.31158e6i		−	1.16925i	0.811304	−	0.584624i	$-0.198758\pi$
$264$	−1.04239e6			−0.920492
$265$			59638.5i			0.0521690i
$266$	938576.			0.813328
$267$	528174.			0.453418
$268$			120110.i			0.102151i
$269$	−1.83671e6			−1.54760			−0.773800	−	0.633430i	$-0.781647\pi$
$269$	−1.83671e6			−1.54760			−0.773800	+	0.633430i	$0.781647\pi$
$270$		−	1.82312e6i		−	1.52197i
$271$			302515.i			0.250221i	0.992143	+	0.125110i	$0.0399285\pi$
$271$			302515.i			0.250221i	−0.992143	+	0.125110i	$0.960072\pi$
$272$		−	1.29953e6i		−	1.06504i
$273$	627540.			0.509607
$274$		−	18902.6i		−	0.0152106i
$275$	−5.01523e6			−3.99907
$276$			195194.i			0.154238i
$277$		−	949331.i		−	0.743393i	−0.928354	−	0.371696i	$-0.878776\pi$
$277$		−	949331.i		−	0.743393i	0.928354	−	0.371696i	$-0.121224\pi$
$278$			1.55310e6i			1.20528i
$279$	−970926.			−0.746751
$280$	−3.70368e6			−2.82318
$281$			1.36364e6i			1.03023i	0.857122	+	0.515114i	$0.172250\pi$
$281$			1.36364e6i			1.03023i	−0.857122	+	0.515114i	$0.827750\pi$
$282$	843454.			0.631595
$283$	−101300.			−0.0751874			−0.0375937	−	0.999293i	$-0.511969\pi$
$283$	−101300.			−0.0751874			−0.0375937	+	0.999293i	$0.511969\pi$
$284$			92186.8i			0.0678224i
$285$	856415.			0.624557
$286$		−	1.38102e6i		−	0.998352i
$287$	936808.			0.671345
$288$	376889.			0.267751
$289$	−1.25295e6			−0.882449
$290$	−2.32160e6			−1.62103
$291$	−751606.	+	129363.i	−0.520305	+	0.0895524i
$292$	−161476.			−0.110828
$293$	2.54883e6			1.73449			0.867244	−	0.497883i	$-0.165889\pi$
$293$	2.54883e6			1.73449			0.867244	+	0.497883i	$0.165889\pi$
$294$	−713677.			−0.481541
$295$	1.19857e6			0.801878
$296$			705398.i			0.467956i
$297$	2.24975e6			1.47994
$298$			4212.00i			0.00274757i
$299$	−1.63202e6			−1.05572
$300$	−380533.			−0.244112
$301$		−	3.09492e6i		−	1.96894i
$302$	−1.71059e6			−1.07927
$303$	161082.			0.100795
$304$		−	795976.i		−	0.493988i
$305$			5.46963e6i			3.36673i
$306$			1.46036e6i			0.891569i
$307$	2.06219e6			1.24877			0.624384	−	0.781117i	$-0.285350\pi$
$307$	2.06219e6			1.24877			0.624384	+	0.781117i	$0.285350\pi$
$308$		−	724207.i		−	0.434996i
$309$	43350.2			0.0258282
$310$		−	2.93392e6i		−	1.73398i
$311$		−	1.12967e6i		−	0.662291i	−0.943580	−	0.331146i	$-0.892565\pi$
$311$		−	1.12967e6i		−	0.662291i	0.943580	−	0.331146i	$-0.107435\pi$
$312$		−	661289.i		−	0.384596i
$313$	−803462.			−0.463558			−0.231779	−	0.972768i	$-0.574455\pi$
$313$	−803462.			−0.463558			−0.231779	+	0.972768i	$0.574455\pi$
$314$		−	189339.i		−	0.108372i
$315$	3.34954e6			1.90199
$316$	−239780.			−0.135081
$317$		−	2.38973e6i		−	1.33567i	−0.744307	−	0.667837i	$-0.767220\pi$
$317$		−	2.38973e6i		−	1.33567i	0.744307	−	0.667837i	$-0.232780\pi$
$318$	24072.1			0.0133489
$319$		−	2.86488e6i		−	1.57627i
$320$			3.78214e6i			2.06473i
$321$		−	1.43488e6i		−	0.777234i
$322$	3.68939e6			1.98297
$323$	−1.63712e6			−0.873120
$324$	−85917.8			−0.0454695
$325$		−	3.18165e6i		−	1.67088i
$326$	434968.			0.226680
$327$	−616280.			−0.318719
$328$		−	987189.i		−	0.506659i
$329$			3.69815e6i			1.88363i
$330$			2.84868e6i			1.43999i
$331$			3.92148e6i			1.96735i	0.179968	+	0.983673i	$0.442401\pi$
$331$			3.92148e6i			1.96735i	−0.179968	+	0.983673i	$0.557599\pi$
$332$			375713.i			0.187073i
$333$		−	637949.i		−	0.315265i
$334$	−829829.			−0.407026
$335$	2.07150e6			1.00849
$336$			1.20310e6i			0.581372i
$337$			2.07463e6i			0.995096i	0.867436	+	0.497548i	$0.165766\pi$
$337$			2.07463e6i			0.995096i	−0.867436	+	0.497548i	$0.834234\pi$
$338$	−1.01619e6			−0.483820
$339$	62688.1			0.0296269
$340$	1.02366e6			0.480238
$341$	3.62049e6			1.68609
$342$			894481.i			0.413529i
$343$		−	38214.0i		−	0.0175383i
$344$	−3.26137e6			−1.48595
$345$	3.36643e6			1.52273
$346$		−	1.66966e6i		−	0.749787i
$347$		−	2.52555e6i		−	1.12598i	−0.826462	−	0.562992i	$-0.809650\pi$
$347$		−	2.52555e6i		−	1.12598i	0.826462	−	0.562992i	$-0.190350\pi$
$348$		−	217374.i		−	0.0962189i
$349$		−	2.38874e6i		−	1.04980i	−0.851165	−	0.524899i	$-0.824103\pi$
$349$		−	2.38874e6i		−	1.04980i	0.851165	−	0.524899i	$-0.175897\pi$
$350$			7.19254e6i			3.13843i
$351$			1.42724e6i			0.618343i
$352$	−1.40538e6			−0.604557
$353$	3.78796e6			1.61796			0.808981	−	0.587835i	$-0.200020\pi$
$353$	3.78796e6			1.61796			0.808981	+	0.587835i	$0.200020\pi$
$354$		−	483783.i		−	0.205184i
$355$	1.58991e6			0.669580
$356$	386687.			0.161709
$357$	2.47447e6			1.02757
$358$			1.09626e6i			0.452070i
$359$		−	901848.i		−	0.369315i	−0.982803	−	0.184658i	$-0.940882\pi$
$359$		−	901848.i		−	0.369315i	0.982803	−	0.184658i	$-0.0591176\pi$
$360$		−	3.52968e6i		−	1.43542i
$361$	1.47335e6			0.595028
$362$		−	624471.i		−	0.250461i
$363$	−2.18985e6			−0.872264
$364$	459435.			0.181749
$365$			2.78491e6i			1.09416i
$366$	2.20773e6			0.861475
$367$			91865.0i			0.0356029i	0.999842	+	0.0178014i	$0.00566667\pi$
$367$			91865.0i			0.0356029i	−0.999842	+	0.0178014i	$0.994333\pi$
$368$		−	3.12886e6i		−	1.20439i
$369$			892796.i			0.341339i
$370$	1.92774e6			0.732055
$371$			105545.i			0.0398110i
$372$	274707.			0.102923
$373$			3.04251e6i			1.13230i	0.824304	+	0.566148i	$0.191567\pi$
$373$			3.04251e6i			1.13230i	−0.824304	+	0.566148i	$0.808433\pi$
$374$		−	5.44553e6i		−	2.01308i
$375$			3.89030e6i			1.42858i
$376$	3.89704e6			1.42156
$377$	1.81747e6			0.658589
$378$		−	3.22647e6i		−	1.16144i
$379$	790110.			0.282546			0.141273	−	0.989971i	$-0.454880\pi$
$379$	790110.			0.282546			0.141273	+	0.989971i	$0.454880\pi$
$380$	626999.			0.222745
$381$			268491.i			0.0947583i
$382$	1.39322e6			0.488496
$383$		−	2.67566e6i		−	0.932039i	−0.884774	−	0.466020i	$-0.845688\pi$
$383$		−	2.67566e6i		−	0.932039i	0.884774	−	0.466020i	$-0.154312\pi$
$384$	960278.			0.332329
$385$	−1.24901e7			−4.29452
$386$	−1.65029e6			−0.563756
$387$	2.94952e6			1.00109
$388$	−550267.	+	94709.3i	−0.185564	+	0.0319384i
$389$	1.95611e6			0.655418			0.327709	−	0.944779i	$-0.393723\pi$
$389$	1.95611e6			0.655418			0.327709	+	0.944779i	$0.393723\pi$
$390$	−1.80720e6			−0.601650
$391$	−6.43526e6			−2.12875
$392$	−3.29742e6			−1.08383
$393$		−	468072.i		−	0.152873i
$394$	−3.23839e6			−1.05097
$395$			4.13539e6i			1.33359i
$396$	690183.			0.221170
$397$	−102543.			−0.0326535			−0.0163268	−	0.999867i	$-0.505197\pi$
$397$	−102543.			−0.0326535			−0.0163268	+	0.999867i	$0.505197\pi$
$398$		−	4.93871e6i		−	1.56281i
$399$	1.51564e6			0.476610
$400$	6.09976e6			1.90618
$401$			1.58111e6i			0.491024i	0.969394	+	0.245512i	$0.0789560\pi$
$401$			1.58111e6i			0.491024i	−0.969394	+	0.245512i	$0.921044\pi$
$402$		−	836127.i		−	0.258052i
$403$			2.29683e6i			0.704477i
$404$	117931.			0.0359480
$405$			1.48179e6i			0.448900i
$406$	−4.10864e6			−1.23704
$407$			2.37885e6i			0.711838i
$408$		−	2.60755e6i		−	0.775500i
$409$		−	6.57325e6i		−	1.94300i	−0.237046	−	0.971498i	$-0.576179\pi$
$409$		−	6.57325e6i		−	1.94300i	0.237046	−	0.971498i	$-0.423821\pi$
$410$	−2.69783e6			−0.792601
$411$		−	30524.5i		−	0.00891341i
$412$	31737.5			0.00921150
$413$	2.12116e6			0.611926
$414$			3.51606e6i			1.00822i
$415$	6.47979e6			1.84689
$416$		−	891571.i		−	0.252594i
$417$			2.50799e6i			0.706293i
$418$		−	3.33543e6i		−	0.933709i
$419$	−1.52855e6			−0.425347			−0.212673	−	0.977123i	$-0.568217\pi$
$419$	−1.52855e6			−0.425347			−0.212673	+	0.977123i	$0.568217\pi$
$420$	−947696.			−0.262148
$421$	2.83766e6			0.780288			0.390144	−	0.920754i	$-0.372425\pi$
$421$	2.83766e6			0.780288			0.390144	+	0.920754i	$0.372425\pi$
$422$			2.94968e6i			0.806296i
$423$	−3.52441e6			−0.957713
$424$	111221.			0.0300451
$425$		−	1.25457e7i		−	3.36915i
$426$		−	641743.i		−	0.171331i
$427$			9.67985e6i			2.56921i
$428$		−	1.05050e6i		−	0.277196i
$429$		−	2.23010e6i		−	0.585034i
$430$			8.91279e6i			2.32457i
$431$	−2.18381e6			−0.566267			−0.283133	−	0.959081i	$-0.591374\pi$
$431$	−2.18381e6			−0.566267			−0.283133	+	0.959081i	$0.591374\pi$
$432$	−2.73626e6			−0.705420
$433$		−	1.55032e6i		−	0.397375i	−0.980063	−	0.198688i	$-0.936332\pi$
$433$		−	1.55032e6i		−	0.397375i	0.980063	−	0.198688i	$-0.0636679\pi$
$434$		−	5.19229e6i		−	1.32323i
$435$	−3.74898e6			−0.949926
$436$	−451191.			−0.113670
$437$	−3.94165e6			−0.987359
$438$	1.12409e6			0.279972
$439$			4.87834e6i			1.20812i	0.796938	+	0.604061i	$0.206452\pi$
$439$			4.87834e6i			1.20812i	−0.796938	+	0.604061i	$0.793548\pi$
$440$			1.31618e7i			3.24104i
$441$	2.98213e6			0.730180
$442$	3.45463e6			0.841097
$443$			1.98458e6i			0.480463i	0.970716	+	0.240232i	$0.0772234\pi$
$443$			1.98458e6i			0.480463i	−0.970716	+	0.240232i	$0.922777\pi$
$444$			180497.i			0.0434522i
$445$		−	6.66904e6i		−	1.59648i
$446$		−	1.25546e6i		−	0.298858i
$447$			6801.65i			0.00161007i
$448$			6.69342e6i			1.57563i
$449$	−3.14402e6			−0.735987			−0.367993	−	0.929828i	$-0.619955\pi$
$449$	−3.14402e6			−0.735987			−0.367993	+	0.929828i	$0.619955\pi$
$450$	−6.85463e6			−1.59571
$451$		−	3.32915e6i		−	0.770712i
$452$	45895.3			0.0105663
$453$	−2.76231e6			−0.632452
$454$	−83711.5			−0.0190610
$455$		−	7.92371e6i		−	1.79432i
$456$		−	1.59715e6i		−	0.359694i
$457$		−	5.02168e6i		−	1.12476i	−0.826880	−	0.562378i	$-0.809886\pi$
$457$		−	5.02168e6i		−	1.12476i	0.826880	−	0.562378i	$-0.190114\pi$
$458$	−4.17300e6			−0.929574
$459$			5.62779e6i			1.24683i
$460$	2.46463e6			0.543072
$461$	5.23018e6			1.14621			0.573105	−	0.819482i	$-0.305739\pi$
$461$	5.23018e6			1.14621			0.573105	+	0.819482i	$0.305739\pi$
$462$			5.04144e6i			1.09888i
$463$	−8.95082e6			−1.94048			−0.970242	−	0.242135i	$-0.922152\pi$
$463$	−8.95082e6			−1.94048			−0.970242	+	0.242135i	$0.922152\pi$
$464$			3.48440e6i			0.751335i
$465$		−	4.73777e6i		−	1.01611i
$466$		−	537388.i		−	0.114637i
$467$	−859468.			−0.182363			−0.0911817	−	0.995834i	$-0.529064\pi$
$467$	−859468.			−0.182363			−0.0911817	+	0.995834i	$0.529064\pi$
$468$			437851.i			0.0924084i
$469$	3.66602e6			0.769597
$470$		−	1.06500e7i		−	2.22384i
$471$		−	305749.i		−	0.0635058i
$472$		−	2.23524e6i		−	0.461816i
$473$	−1.09985e7			−2.26037
$474$	1.66918e6			0.341239
$475$		−	7.68433e6i		−	1.56269i
$476$	1.81161e6			0.366478
$477$	−100586.			−0.0202415
$478$			1.36924e6i			0.274101i
$479$	−6.15460e6			−1.22564			−0.612818	−	0.790224i	$-0.709964\pi$
$479$	−6.15460e6			−1.22564			−0.612818	+	0.790224i	$0.709964\pi$
$480$			1.83908e6i			0.364332i
$481$	−1.50914e6			−0.297417
$482$	8.02612e6			1.57358
$483$	5.95773e6			1.16202
$484$	−1.60323e6			−0.311088
$485$	1.63342e6	+	9.49025e6i	0.315313	+	1.83199i
$486$	4.86129e6			0.933601
$487$	−2.37736e6			−0.454226			−0.227113	−	0.973868i	$-0.572929\pi$
$487$	−2.37736e6			−0.454226			−0.227113	+	0.973868i	$0.572929\pi$
$488$	1.02004e7			1.93896
$489$	702397.			0.132834
$490$			9.01133e6i			1.69550i
$491$	−3.64867e6			−0.683015			−0.341508	−	0.939879i	$-0.610938\pi$
$491$	−3.64867e6			−0.683015			−0.341508	+	0.939879i	$0.610938\pi$
$492$		−	252601.i		−	0.0470460i
$493$	7.16653e6			1.32798
$494$	2.11599e6			0.390119
$495$		−	1.19033e7i		−	2.18351i
$496$	−4.40342e6			−0.803684
$497$	2.81374e6			0.510967
$498$		−	2.61546e6i		−	0.472580i
$499$		−	8.50543e6i		−	1.52913i	−0.644545	−	0.764566i	$-0.722953\pi$
$499$		−	8.50543e6i		−	1.52913i	0.644545	−	0.764566i	$-0.277047\pi$
$500$			2.84817e6i			0.509496i
$501$	−1.34003e6			−0.238517
$502$			5.68136e6i			1.00622i
$503$	−1.12322e6			−0.197945			−0.0989725	−	0.995090i	$-0.531556\pi$
$503$	−1.12322e6			−0.197945			−0.0989725	+	0.995090i	$0.531556\pi$
$504$		−	6.24664e6i		−	1.09539i
$505$		−	2.03392e6i		−	0.354899i
$506$		−	1.31111e7i		−	2.27647i
$507$	−1.64097e6			−0.283519
$508$			196568.i			0.0337951i
$509$	−9.38185e6			−1.60507			−0.802535	−	0.596605i	$-0.796516\pi$
$509$	−9.38185e6			−1.60507			−0.802535	+	0.596605i	$0.796516\pi$
$510$	−7.12601e6			−1.21317
$511$			4.92859e6i			0.834969i
$512$	6.63878e6			1.11921
$513$			3.44707e6i			0.578305i
$514$			7.93664e6i			1.32504i
$515$		−	547366.i		−	0.0909410i
$516$	−834516.			−0.137978
$517$	1.31422e7			2.16243
$518$	3.41161e6			0.558644
$519$		−	2.69621e6i		−	0.439375i
$520$	−8.34985e6			−1.35416
$521$	5.51387e6			0.889944			0.444972	−	0.895545i	$-0.353214\pi$
$521$	5.51387e6			0.889944			0.444972	+	0.895545i	$0.353214\pi$
$522$		−	3.91561e6i		−	0.628961i
$523$			1.16040e7i			1.85504i	0.373768	+	0.927522i	$0.378066\pi$
$523$			1.16040e7i			1.85504i	−0.373768	+	0.927522i	$0.621934\pi$
$524$		−	342685.i		−	0.0545214i
$525$			1.16147e7i			1.83912i
$526$			6.68453e6i			1.05343i
$527$			9.05670e6i			1.42051i
$528$	4.27548e6			0.667422
$529$	−9.05767e6			−1.40727
$530$		−	303950.i		−	0.0470015i
$531$			2.02151e6i			0.311128i
$532$	1.10963e6			0.169980
$533$	2.11201e6			0.322016
$534$	−2.69185e6			−0.408506
$535$	−1.81176e7			−2.73663
$536$		−	3.86318e6i		−	0.580809i
$537$			1.77027e6i			0.264913i
$538$	9.36083e6			1.39431
$539$	−1.11201e7			−1.64868
$540$		−	2.15538e6i		−	0.318083i
$541$			1.46464e6i			0.215148i	0.994197	+	0.107574i	$0.0343082\pi$
$541$			1.46464e6i			0.215148i	−0.994197	+	0.107574i	$0.965692\pi$
$542$		−	1.54178e6i		−	0.225436i
$543$		−	1.00841e6i		−	0.146770i
$544$		−	3.51558e6i		−	0.509331i
$545$			7.78153e6i			1.12221i
$546$	−3.19828e6			−0.459129
$547$	−4.07050e6			−0.581673			−0.290837	−	0.956773i	$-0.593934\pi$
$547$	−4.07050e6			−0.581673			−0.290837	+	0.956773i	$0.593934\pi$
$548$		−	22347.6i		−	0.00317892i
$549$	−9.22509e6			−1.30629
$550$	2.55603e7			3.60295
$551$	4.38957e6			0.615946
$552$		−	6.27813e6i		−	0.876966i
$553$			7.31859e6i			1.01769i
$554$			4.83830e6i			0.669758i
$555$	3.11296e6			0.428984
$556$			1.83615e6i			0.251896i
$557$	7.02584e6			0.959534			0.479767	−	0.877396i	$-0.340721\pi$
$557$	7.02584e6			0.959534			0.479767	+	0.877396i	$0.340721\pi$
$558$	4.94836e6			0.672784
$559$		−	6.97741e6i		−	0.944419i
$560$	1.51911e7			2.04701
$561$		−	8.79357e6i		−	1.17966i
$562$		−	6.94982e6i		−	0.928182i
$563$			8.38208e6i			1.11450i	0.830344	+	0.557251i	$0.188144\pi$
$563$			8.38208e6i			1.11450i	−0.830344	+	0.557251i	$0.811856\pi$
$564$	997172.			0.131999
$565$		−	791539.i		−	0.104316i
$566$	516280.			0.0677399
$567$			2.62240e6i			0.342563i
$568$		−	2.96506e6i		−	0.385623i
$569$			2.47779e6i			0.320836i	0.987049	+	0.160418i	$0.0512843\pi$
$569$			2.47779e6i			0.320836i	−0.987049	+	0.160418i	$0.948716\pi$
$570$	−4.36475e6			−0.562694
$571$	7.06328e6			0.906601			0.453300	−	0.891358i	$-0.350247\pi$
$571$	7.06328e6			0.906601			0.453300	+	0.891358i	$0.350247\pi$
$572$		−	1.63270e6i		−	0.208649i
$573$	2.24981e6			0.286259
$574$	−4.77447e6			−0.604847
$575$		−	3.02059e7i		−	3.80997i
$576$	−6.37896e6			−0.801113
$577$		−	3.35619e6i		−	0.419669i	−0.977737	−	0.209834i	$-0.932708\pi$
$577$		−	3.35619e6i		−	0.419669i	0.977737	−	0.209834i	$-0.0672925\pi$
$578$	6.38570e6			0.795040
$579$	−2.66492e6			−0.330361
$580$	−2.74470e6			−0.338786
$581$	1.14676e7			1.40939
$582$	3.83059e6	−	659302.i	0.468768	−	0.0806821i
$583$	375077.			0.0457035
$584$	5.19365e6			0.630145
$585$	7.55145e6			0.912306
$586$	−1.29902e7			−1.56268
$587$			5.64914e6i			0.676686i	0.941023	+	0.338343i	$0.109866\pi$
$587$			5.64914e6i			0.676686i	−0.941023	+	0.338343i	$0.890134\pi$
$588$	−843743.			−0.100639
$589$			5.54732e6i			0.658862i
$590$	−6.10855e6			−0.722450
$591$	−5.22943e6			−0.615865
$592$		−	2.89327e6i		−	0.339301i
$593$	8.90285e6			1.03966			0.519831	−	0.854269i	$-0.325995\pi$
$593$	8.90285e6			1.03966			0.519831	+	0.854269i	$0.325995\pi$
$594$	−1.14659e7			−1.33335
$595$		−	3.12442e7i		−	3.61807i
$596$			4979.63i			0.000574224i
$597$		−	7.97515e6i		−	0.915805i
$598$	8.31763e6			0.951145
$599$			5.40387e6i			0.615372i	0.951488	+	0.307686i	$0.0995546\pi$
$599$			5.40387e6i			0.615372i	−0.951488	+	0.307686i	$0.900445\pi$
$600$	1.22393e7			1.38797
$601$			1.89110e6i			0.213564i	0.994282	+	0.106782i	$0.0340547\pi$
$601$			1.89110e6i			0.213564i	−0.994282	+	0.106782i	$0.965945\pi$
$602$			1.57734e7i			1.77392i
$603$			3.49379e6i			0.391294i
$604$	−2.02235e6			−0.225560
$605$			2.76504e7i			3.07124i
$606$	−820958.			−0.0908112
$607$	−1.14035e6			−0.125622			−0.0628112	−	0.998025i	$-0.520007\pi$
$607$	−1.14035e6			−0.125622			−0.0628112	+	0.998025i	$0.520007\pi$
$608$		−	2.15333e6i		−	0.236239i
$609$	−6.63474e6			−0.724904
$610$		−	2.78761e7i		−	3.03325i
$611$			8.33738e6i			0.903497i
$612$			1.72650e6i			0.186332i
$613$	−9.29895e6			−0.999500			−0.499750	−	0.866170i	$-0.666575\pi$
$613$	−9.29895e6			−0.999500			−0.499750	+	0.866170i	$0.666575\pi$
$614$	−1.05100e7			−1.12508
$615$	−4.35652e6			−0.464464
$616$			2.32931e7i			2.47329i
$617$	−9.59474e6			−1.01466			−0.507330	−	0.861752i	$-0.669367\pi$
$617$	−9.59474e6			−1.01466			−0.507330	+	0.861752i	$0.669367\pi$
$618$	−220935.			−0.0232699
$619$			7.44317e6i			0.780785i	0.920649	+	0.390393i	$0.127661\pi$
$619$			7.44317e6i			0.780785i	−0.920649	+	0.390393i	$0.872339\pi$
$620$		−	3.46862e6i		−	0.362391i
$621$			1.35499e7i			1.40996i
$622$			5.75738e6i			0.596690i
$623$		−	1.18025e7i		−	1.21830i
$624$			2.71236e6i			0.278859i
$625$	2.51407e7			2.57441
$626$	4.09487e6			0.417642
$627$		−	5.38615e6i		−	0.547154i
$628$		−	223845.i		−	0.0226490i
$629$	−5.95073e6			−0.599713
$630$	−1.70711e7			−1.71360
$631$	3.24194e6			0.324139			0.162069	−	0.986779i	$-0.448183\pi$
$631$	3.24194e6			0.324139			0.162069	+	0.986779i	$0.448183\pi$
$632$	7.71218e6			0.768041
$633$			4.76323e6i			0.472489i
$634$			1.21793e7i			1.20337i
$635$	3.39013e6			0.333643
$636$	28459.2			0.00278985
$637$		−	7.05455e6i		−	0.688844i
$638$			1.46009e7i			1.42013i
$639$			2.68155e6i			0.259797i
$640$		−	1.21251e7i		−	1.17013i
$641$			1.03152e7i			0.991591i	0.868439	+	0.495795i	$0.165123\pi$
$641$			1.03152e7i			0.991591i	−0.868439	+	0.495795i	$0.834877\pi$
$642$			7.31289e6i			0.700247i
$643$	5.41281e6			0.516292			0.258146	−	0.966106i	$-0.416888\pi$
$643$	5.41281e6			0.516292			0.258146	+	0.966106i	$0.416888\pi$
$644$	4.36178e6			0.414428
$645$			1.43926e7i			1.36220i
$646$	8.34363e6			0.786636
$647$	−1.58343e7			−1.48710			−0.743549	−	0.668682i	$-0.766859\pi$
$647$	−1.58343e7			−1.48710			−0.743549	+	0.668682i	$0.766859\pi$
$648$	2.76343e6			0.258530
$649$		−	7.53801e6i		−	0.702498i
$650$			1.62154e7i			1.50537i
$651$		−	8.38465e6i		−	0.775412i
$652$	514239.			0.0473747
$653$		−	8.78106e6i		−	0.805868i	−0.915229	−	0.402934i	$-0.867990\pi$
$653$		−	8.78106e6i		−	0.805868i	0.915229	−	0.402934i	$-0.132010\pi$
$654$	3.14089e6			0.287150
$655$	−5.91017e6			−0.538265
$656$			4.04907e6i			0.367364i
$657$	−4.69704e6			−0.424532
$658$		−	1.88478e7i		−	1.69705i
$659$		−	1.94354e7i		−	1.74333i	−0.490103	−	0.871665i	$-0.663041\pi$
$659$		−	1.94354e7i		−	1.74333i	0.490103	−	0.871665i	$-0.336959\pi$
$660$			3.36784e6i			0.300948i
$661$	−9.98175e6			−0.888593			−0.444297	−	0.895880i	$-0.646546\pi$
$661$	−9.98175e6			−0.888593			−0.444297	+	0.895880i	$0.646546\pi$
$662$		−	1.99860e7i		−	1.77248i
$663$	5.57863e6			0.492883
$664$		−	1.20843e7i		−	1.06366i
$665$		−	1.91374e7i		−	1.67814i
$666$			3.25133e6i			0.284037i
$667$	1.72547e7			1.50173
$668$	−981062.			−0.0850659
$669$		−	2.02735e6i		−	0.175131i
$670$	−1.05575e7			−0.908599
$671$	3.43995e7			2.94948
$672$			3.25471e6i			0.278028i
$673$	1.94779e7			1.65769			0.828847	−	0.559476i	$-0.188998\pi$
$673$	1.94779e7			1.65769			0.828847	+	0.559476i	$0.188998\pi$
$674$		−	1.05734e7i		−	0.896530i
$675$	−2.64158e7			−2.23154
$676$	−1.20139e6			−0.101115
$677$	2.29141e6			0.192146			0.0960730	−	0.995374i	$-0.469372\pi$
$677$	2.29141e6			0.192146			0.0960730	+	0.995374i	$0.469372\pi$
$678$	−319492.			−0.0266923
$679$	2.89073e6	+	1.67953e7i	0.240621	+	1.39802i
$680$	−3.29245e7			−2.73053
$681$	−135180.			−0.0111697
$682$	−1.84519e7			−1.51908
$683$	−1.07216e7			−0.879446			−0.439723	−	0.898133i	$-0.644923\pi$
$683$	−1.07216e7			−0.879446			−0.439723	+	0.898133i	$0.644923\pi$
$684$			1.05750e6i			0.0864250i
$685$	−385421.			−0.0313840
$686$			194759.i			0.0158011i
$687$	−6.73866e6			−0.544730
$688$	1.33769e7			1.07742
$689$			237948.i			0.0190957i
$690$	−1.71571e7			−1.37190
$691$	1.46529e7			1.16742			0.583712	−	0.811961i	$-0.301600\pi$
$691$	1.46529e7			1.16742			0.583712	+	0.811961i	$0.301600\pi$
$692$		−	1.97395e6i		−	0.156701i
$693$		−	2.10659e7i		−	1.66627i
$694$			1.28716e7i			1.01445i
$695$	3.16674e7			2.48685
$696$			6.99155e6i			0.547080i
$697$	8.32791e6			0.649313
$698$			1.21743e7i			0.945813i
$699$		−	867788.i		−	0.0671771i
$700$			8.50336e6i			0.655912i
$701$	7.11200e6			0.546634			0.273317	−	0.961924i	$-0.411879\pi$
$701$	7.11200e6			0.546634			0.273317	+	0.961924i	$0.411879\pi$
$702$		−	7.27397e6i		−	0.557095i
$703$	−3.64488e6			−0.278160
$704$	2.37865e7			1.80884
$705$		−	1.71979e7i		−	1.30317i
$706$	−1.93054e7			−1.45770
$707$		−	3.59952e6i		−	0.270829i
$708$		−	571951.i		−	0.0428821i
$709$			3.49062e6i			0.260788i	0.991462	+	0.130394i	$0.0416242\pi$
$709$			3.49062e6i			0.260788i	−0.991462	+	0.130394i	$0.958376\pi$
$710$	−8.10304e6			−0.603257
$711$	−6.97476e6			−0.517434
$712$	−1.24372e7			−0.919442
$713$			2.18056e7i			1.60637i
$714$	−1.26112e7			−0.925789
$715$	−2.81586e7			−2.05990
$716$			1.29605e6i			0.0944798i
$717$			2.21109e6i			0.160623i
$718$			4.59630e6i			0.332734i
$719$		−	1.16177e7i		−	0.838105i	−0.907962	−	0.419052i	$-0.862362\pi$
$719$		−	1.16177e7i		−	0.838105i	0.907962	−	0.419052i	$-0.137638\pi$
$720$			1.44774e7i			1.04078i
$721$		−	968698.i		−	0.0693985i
$722$	−7.50897e6			−0.536089
$723$	1.29608e7			0.922116
$724$		−	738279.i		−	0.0523448i
$725$			3.36383e7i			2.37678i
$726$	1.11606e7			0.785865
$727$	1.84210e6			0.129264			0.0646320	−	0.997909i	$-0.479413\pi$
$727$	1.84210e6			0.129264			0.0646320	+	0.997909i	$0.479413\pi$
$728$	−1.47771e7			−1.03338
$729$	4.38512e6			0.305606
$730$		−	1.41934e7i		−	0.985778i
$731$		−	2.75128e7i		−	1.90433i
$732$	2.61008e6			0.180043
$733$	−5.53722e6			−0.380655			−0.190328	−	0.981721i	$-0.560955\pi$
$733$	−5.53722e6			−0.380655			−0.190328	+	0.981721i	$0.560955\pi$
$734$		−	468193.i		−	0.0320763i
$735$			1.45517e7i			0.993564i
$736$		−	8.46438e6i		−	0.575971i
$737$		−	1.30280e7i		−	0.883506i
$738$		−	4.55016e6i		−	0.307529i
$739$			6.90538e6i			0.465132i	0.972581	+	0.232566i	$0.0747122\pi$
$739$			6.90538e6i			0.465132i	−0.972581	+	0.232566i	$0.925288\pi$
$740$	2.27906e6			0.152995
$741$	3.41696e6			0.228610
$742$		−	537914.i		−	0.0358676i
$743$	−1.91134e7			−1.27018			−0.635090	−	0.772438i	$-0.719037\pi$
$743$	−1.91134e7			−1.27018			−0.635090	+	0.772438i	$0.719037\pi$
$744$	−8.83557e6			−0.585197
$745$	85881.8			0.00566906
$746$		−	1.55063e7i		−	1.02014i
$747$			1.09288e7i			0.716592i
$748$		−	6.43796e6i		−	0.420721i
$749$	−3.20636e7			−2.08837
$750$		−	1.98270e7i		−	1.28708i
$751$	−5.39082e6			−0.348783			−0.174391	−	0.984676i	$-0.555796\pi$
$751$	−5.39082e6			−0.348783			−0.174391	+	0.984676i	$0.555796\pi$
$752$	−1.59842e7			−1.03073
$753$			9.17441e6i			0.589645i
$754$	−9.26281e6			−0.593355
$755$			3.48787e7i			2.22686i
$756$		−	3.81448e6i		−	0.242734i
$757$		−	2.69483e6i		−	0.170920i	−0.996342	−	0.0854598i	$-0.972764\pi$
$757$		−	2.69483e6i		−	0.170920i	0.996342	−	0.0854598i	$-0.0272359\pi$
$758$	−4.02682e6			−0.254560
$759$		−	2.11721e7i		−	1.33401i
$760$	−2.01666e7			−1.26648
$761$		−	2.97077e6i		−	0.185955i	−0.995668	−	0.0929773i	$-0.970362\pi$
$761$		−	2.97077e6i		−	0.185955i	0.995668	−	0.0929773i	$-0.0296384\pi$
$762$		−	1.36837e6i		−	0.0853723i
$763$			1.37713e7i			0.856376i
$764$	1.64713e6			0.102093
$765$	2.97763e7			1.83958
$766$			1.36366e7i			0.839719i
$767$	4.78210e6			0.293515
$768$	4.69110e6			0.286993
$769$			2.75967e7i			1.68283i	0.540387	+	0.841417i	$0.318278\pi$
$769$			2.75967e7i			1.68283i	−0.540387	+	0.841417i	$0.681722\pi$
$770$	6.36563e7			3.86914
$771$			1.28163e7i			0.776473i
$772$	−1.95105e6			−0.117821
$773$	1.63083e7			0.981658			0.490829	−	0.871256i	$-0.336694\pi$
$773$	1.63083e7			0.981658			0.490829	+	0.871256i	$0.336694\pi$
$774$	−1.50323e7			−0.901932
$775$	−4.25105e7			−2.54239
$776$	1.76986e7	−	3.04619e6i	1.05508	−	0.181595i
$777$	5.50915e6			0.327365
$778$	−9.96935e6			−0.590497
$779$	5.10092e6			0.301165
$780$	−2.13655e6			−0.125741
$781$		−	9.99924e6i		−	0.586596i
$782$	3.27975e7			1.91789
$783$		−	1.50896e7i		−	0.879578i
$784$	1.35248e7			0.785850
$785$	−3.86058e6			−0.223603
$786$			2.38554e6i			0.137731i
$787$	−2.18607e7			−1.25814			−0.629068	−	0.777350i	$-0.716563\pi$
$787$	−2.18607e7			−1.25814			−0.629068	+	0.777350i	$0.716563\pi$
$788$	−3.82857e6			−0.219645
$789$			1.07943e7i			0.617311i
$790$		−	2.10762e7i		−	1.20150i
$791$		−	1.40082e6i		−	0.0796053i
$792$	−2.21988e7			−1.25752
$793$			2.18230e7i			1.23234i
$794$	522614.			0.0294191
$795$		−	490826.i		−	0.0275429i
$796$		−	5.83877e6i		−	0.326617i
$797$		−	1.85218e6i		−	0.103285i	−0.998666	−	0.0516425i	$-0.983554\pi$
$797$		−	1.85218e6i		−	0.103285i	0.998666	−	0.0516425i	$-0.0164456\pi$
$798$	−7.72449e6			−0.429401
$799$			3.28753e7i			1.82181i
$800$	1.65015e7			0.911586
$801$	1.12480e7			0.619434
$802$		−	8.05820e6i		−	0.442387i
$803$	1.75148e7			0.958554
$804$		−	988508.i		−	0.0539312i
$805$		−	7.52260e7i		−	4.09146i
$806$		−	1.17059e7i		−	0.634697i
$807$	1.51161e7			0.817064
$808$	−3.79310e6			−0.204393
$809$	−2.07339e7			−1.11381			−0.556904	−	0.830577i	$-0.688011\pi$
$809$	−2.07339e7			−1.11381			−0.556904	+	0.830577i	$0.688011\pi$
$810$		−	7.55200e6i		−	0.404436i
$811$	5.39538e6			0.288052			0.144026	−	0.989574i	$-0.453995\pi$
$811$	5.39538e6			0.288052			0.144026	+	0.989574i	$0.453995\pi$
$812$	−4.85743e6			−0.258533
$813$		−	2.48970e6i		−	0.132105i
$814$		−	1.21239e7i		−	0.641329i
$815$		−	8.86890e6i		−	0.467709i
$816$			1.06952e7i			0.562293i
$817$		−	1.68519e7i		−	0.883269i
$818$			3.35008e7i			1.75054i
$819$	1.33641e7			0.696196
$820$	−3.18950e6			−0.165649
$821$		−	1.79050e7i		−	0.927077i	−0.886077	−	0.463539i	$-0.846580\pi$
$821$		−	1.79050e7i		−	0.927077i	0.886077	−	0.463539i	$-0.153420\pi$
$822$			155569.i			0.00803052i
$823$	1.53587e7			0.790412			0.395206	−	0.918592i	$-0.370673\pi$
$823$	1.53587e7			0.790412			0.395206	+	0.918592i	$0.370673\pi$
$824$	−1.02079e6			−0.0523746
$825$	4.12754e7			2.11133
$826$	−1.08106e7			−0.551314
$827$		−	4.54148e6i		−	0.230905i	−0.993313	−	0.115453i	$-0.963168\pi$
$827$		−	4.54148e6i		−	0.230905i	0.993313	−	0.115453i	$-0.0368318\pi$
$828$			4.15686e6i			0.210712i
$829$	1.33785e7			0.676118			0.338059	−	0.941125i	$-0.390230\pi$
$829$	1.33785e7			0.676118			0.338059	+	0.941125i	$0.390230\pi$
$830$	−3.30244e7			−1.66395
$831$			7.81300e6i			0.392478i
$832$			1.50901e7i			0.755762i
$833$		−	2.78170e7i		−	1.38899i
$834$		−	1.27820e7i		−	0.636333i
$835$			1.69200e7i			0.839817i
$836$		−	3.94331e6i		−	0.195139i
$837$	1.90695e7			0.940863
$838$	7.79028e6			0.383215
$839$			3.29949e7i			1.61823i	0.587647	+	0.809117i	$0.300054\pi$
$839$			3.29949e7i			1.61823i	−0.587647	+	0.809117i	$0.699946\pi$
$840$	3.04813e7			1.49051
$841$	1.29572e6			0.0631714
$842$	−1.44622e7			−0.702999
$843$		−	1.12228e7i		−	0.543914i
$844$			3.48726e6i			0.168511i
$845$			2.07199e7i			0.998267i
$846$	1.79623e7			0.862850
$847$			4.89342e7i			2.34371i
$848$	−456187.			−0.0217848
$849$	833703.			0.0396956
$850$			6.39393e7i			3.03543i
$851$	−1.43274e7			−0.678179
$852$		−	758699.i		−	0.0358072i
$853$		−	1.95159e7i		−	0.918367i	−0.888341	−	0.459184i	$-0.848142\pi$
$853$		−	1.95159e7i		−	0.918367i	0.888341	−	0.459184i	$-0.151858\pi$
$854$		−	4.93337e7i		−	2.31472i
$855$	1.82383e7			0.853235
$856$			3.37880e7i			1.57608i
$857$	−5.31594e6			−0.247245			−0.123623	−	0.992329i	$-0.539451\pi$
$857$	−5.31594e6			−0.247245			−0.123623	+	0.992329i	$0.539451\pi$
$858$			1.13658e7i			0.527086i
$859$		−	5.84386e6i		−	0.270220i	−0.990831	−	0.135110i	$-0.956861\pi$
$859$		−	5.84386e6i		−	0.270220i	0.990831	−	0.135110i	$-0.0431387\pi$
$860$			1.05371e7i			0.485820i
$861$	−7.70994e6			−0.354440
$862$	1.11298e7			0.510177
$863$			8.08672e6i			0.369611i	0.982775	+	0.184806i	$0.0591656\pi$
$863$			8.08672e6i			0.369611i	−0.982775	+	0.184806i	$0.940834\pi$
$864$	−7.40231e6			−0.337352
$865$	−3.40440e7			−1.54704
$866$			7.90124e6i			0.358015i
$867$	1.03118e7			0.465894
$868$		−	6.13858e6i		−	0.276547i
$869$	2.60082e7			1.16832
$870$	1.91068e7			0.855834
$871$	8.26495e6			0.369143
$872$	1.45119e7			0.646300
$873$	−1.60063e7	+	2.75492e6i	−0.710811	+	0.122342i
$874$	2.00888e7			0.889559
$875$	8.69322e7			3.83849
$876$	1.32895e6			0.0585123
$877$	−2.90626e7			−1.27596			−0.637978	−	0.770054i	$-0.720229\pi$
$877$	−2.90626e7			−1.27596			−0.637978	+	0.770054i	$0.720229\pi$
$878$		−	2.48626e7i		−	1.08846i
$879$	−2.09769e7			−0.915732
$880$		−	5.39849e7i		−	2.34999i
$881$	2.21453e7			0.961263			0.480631	−	0.876923i	$-0.340408\pi$
$881$	2.21453e7			0.961263			0.480631	+	0.876923i	$0.340408\pi$
$882$	−1.51985e7			−0.657855
$883$			3.27712e7i			1.41446i	0.706983	+	0.707231i	$0.250056\pi$
$883$			3.27712e7i			1.41446i	−0.706983	+	0.707231i	$0.749944\pi$
$884$	4.08423e6			0.175784
$885$	−9.86424e6			−0.423356
$886$		−	1.01145e7i		−	0.432872i
$887$		−	2.27438e7i		−	0.970633i	−0.874339	−	0.485316i	$-0.838704\pi$
$887$		−	2.27438e7i		−	0.970633i	0.874339	−	0.485316i	$-0.161296\pi$
$888$		−	5.80543e6i		−	0.247060i
$889$	5.99968e6			0.254609
$890$			3.39890e7i			1.43835i
$891$	9.31925e6			0.393266
$892$		−	1.48426e6i		−	0.0624594i
$893$			2.01365e7i			0.844995i
$894$		−	34664.8i		−	0.00145059i
$895$	2.23525e7			0.932757
$896$		−	2.14583e7i		−	0.892945i
$897$	1.34315e7			0.557371
$898$	1.60236e7			0.663086
$899$		−	2.42835e7i		−	1.00210i
$900$	−8.10387e6			−0.333493
$901$			938260.i			0.0385045i
$902$			1.69671e7i			0.694371i
$903$			2.54712e7i			1.03951i
$904$	−1.47616e6			−0.0600775
$905$	−1.27328e7			−0.516777
$906$	1.40782e7			0.569806
$907$			4.46116e6i			0.180065i	0.995939	+	0.0900325i	$0.0286971\pi$
$907$			4.46116e6i			0.180065i	−0.995939	+	0.0900325i	$0.971303\pi$
$908$	−98967.7			−0.00398363
$909$	3.43041e6			0.137701
$910$			4.03835e7i			1.61659i
$911$			3.26294e7i			1.30260i	0.758818	+	0.651302i	$0.225777\pi$
$911$			3.26294e7i			1.30260i	−0.758818	+	0.651302i	$0.774223\pi$
$912$			6.55089e6i			0.260803i
$913$		−	4.07525e7i		−	1.61800i
$914$			2.55932e7i			1.01335i
$915$		−	4.50151e7i		−	1.77748i
$916$	−4.93351e6			−0.194275
$917$	−1.04595e7			−0.410759
$918$		−	2.86822e7i		−	1.12333i
$919$			7.65662e6i			0.299053i	0.988758	+	0.149527i	$0.0477749\pi$
$919$			7.65662e6i			0.299053i	−0.988758	+	0.149527i	$0.952225\pi$
$920$	−7.92716e7			−3.08779
$921$	−1.69718e7			−0.659294
$922$	−2.66558e7			−1.03268
$923$	6.34350e6			0.245089
$924$			5.96023e6i			0.229659i
$925$		−	2.79316e7i		−	1.07335i
$926$	4.56181e7			1.74828
$927$	923188.			0.0352851
$928$			9.42623e6i			0.359309i
$929$		−	4.85091e7i		−	1.84410i	−0.387074	−	0.922049i	$-0.626514\pi$
$929$		−	4.85091e7i		−	1.84410i	0.387074	−	0.922049i	$-0.373486\pi$
$930$			2.41462e7i			0.915464i
$931$		−	1.70382e7i		−	0.644242i
$932$		−	635326.i		−	0.0239583i
$933$			9.29716e6i			0.349660i
$934$	4.38031e6			0.164300
$935$	−1.11033e8			−4.15359
$936$		−	1.40829e7i		−	0.525414i
$937$	−2.54091e7			−0.945454			−0.472727	−	0.881209i	$-0.656730\pi$
$937$	−2.54091e7			−0.945454			−0.472727	+	0.881209i	$0.656730\pi$
$938$	−1.86840e7			−0.693367
$939$	6.61250e6			0.244738
$940$		−	1.25909e7i		−	0.464769i
$941$		−	9.25927e6i		−	0.340881i	−0.985368	−	0.170440i	$-0.945481\pi$
$941$		−	9.25927e6i		−	0.340881i	0.985368	−	0.170440i	$-0.0545191\pi$
$942$			1.55826e6i			0.0572154i
$943$	2.00509e7			0.734269
$944$			9.16810e6i			0.334849i
$945$	−6.57869e7			−2.39640
$946$	5.60541e7			2.03648
$947$		−	4.85770e7i		−	1.76017i	−0.474812	−	0.880087i	$-0.657484\pi$
$947$		−	4.85770e7i		−	1.76017i	0.474812	−	0.880087i	$-0.342516\pi$
$948$	1.97339e6			0.0713168
$949$			1.11114e7i			0.400499i
$950$			3.91634e7i			1.40790i
$951$			1.96675e7i			0.705177i
$952$	−5.82680e7			−2.08371
$953$			2.31081e6i			0.0824200i	0.999151	+	0.0412100i	$0.0131213\pi$
$953$			2.31081e6i			0.0824200i	−0.999151	+	0.0412100i	$0.986879\pi$
$954$	512642.			0.0182366
$955$		−	2.84075e7i		−	1.00791i
$956$			1.61878e6i			0.0572854i
$957$			2.35780e7i			0.832198i
$958$	3.13671e7			1.10423
$959$	−682097.			−0.0239497
$960$		−	3.11270e7i		−	1.09008i
$961$	2.05913e6			0.0719242
$962$	7.69137e6			0.267958
$963$		−	3.05572e7i		−	1.06181i
$964$	9.48886e6			0.328868
$965$			3.36490e7i			1.16320i
$966$	−3.03638e7			−1.04692
$967$	−2.50588e7			−0.861775			−0.430888	−	0.902406i	$-0.641799\pi$
$967$	−2.50588e7			−0.861775			−0.430888	+	0.902406i	$0.641799\pi$
$968$	5.15659e7			1.76878
$969$	1.34735e7			0.460969
$970$	−8.32476e6	−	4.83673e7i	−0.284081	−	1.65053i
$971$	−2.18812e7			−0.744773			−0.372386	−	0.928078i	$-0.621460\pi$
$971$	−2.18812e7			−0.744773			−0.372386	+	0.928078i	$0.621460\pi$
$972$	5.74725e6			0.195117
$973$	5.60432e7			1.89776
$974$	1.21163e7			0.409234
$975$			2.61850e7i			0.882148i
$976$	−4.18383e7			−1.40588
$977$			1.36900e7i			0.458845i	0.973327	+	0.229423i	$0.0736838\pi$
$977$			1.36900e7i			0.458845i	−0.973327	+	0.229423i	$0.926316\pi$
$978$	−3.57979e6			−0.119677
$979$	−4.19428e7			−1.39862
$980$			1.06536e7i			0.354349i
$981$	−1.31243e7			−0.435417
$982$	1.85955e7			0.615361
$983$		−	1.70915e7i		−	0.564152i	−0.959392	−	0.282076i	$-0.908977\pi$
$983$		−	1.70915e7i		−	0.564152i	0.959392	−	0.282076i	$-0.0910230\pi$
$984$			8.12457e6i			0.267493i
$985$			6.60300e7i			2.16846i
$986$	−3.65245e7			−1.19644
$987$		−	3.04358e7i		−	0.994471i
$988$	2.50163e6			0.0815324
$989$		−	6.62420e7i		−	2.15349i
$990$			6.06657e7i			1.96723i
$991$			1.56307e7i			0.505584i	0.967521	+	0.252792i	$0.0813488\pi$
$991$			1.56307e7i			0.505584i	−0.967521	+	0.252792i	$0.918651\pi$
$992$	−1.19124e7			−0.384344
$993$		−	3.22739e7i		−	1.03867i
$994$	−1.43403e7			−0.460355
$995$	−1.00699e8			−3.22454
$996$		−	3.09212e6i		−	0.0987662i
$997$	−8.66923e6			−0.276212			−0.138106	−	0.990417i	$-0.544101\pi$
$997$	−8.66923e6			−0.276212			−0.138106	+	0.990417i	$0.544101\pi$
$998$			4.33482e7i			1.37767i
$999$			1.25297e7i			0.397216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.12	yes	40
97.96	even	2	inner	97.6.b.a.96.11	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.11	✓	40	97.96	even	2	inner
97.6.b.a.96.12	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)

\(f(q)\)	\(=\)	\(q-5.09653 q^{2} -8.23001 q^{3} -6.02536 q^{4} +103.917i q^{5} +41.9445 q^{6} +183.907i q^{7} +193.797 q^{8} -175.267 q^{9} -529.617i q^{10} +653.553 q^{11} +49.5888 q^{12} +414.613i q^{13} -937.288i q^{14} -855.240i q^{15} -794.884 q^{16} +1634.87i q^{17} +893.254 q^{18} +1001.37i q^{19} -626.138i q^{20} -1513.56i q^{21} -3330.86 q^{22} +3936.24i q^{23} -1594.96 q^{24} -7673.78 q^{25} -2113.09i q^{26} +3442.34 q^{27} -1108.11i q^{28} -4383.54i q^{29} +4358.76i q^{30} +5539.70 q^{31} -2150.37 q^{32} -5378.75 q^{33} -8332.18i q^{34} -19111.1 q^{35} +1056.05 q^{36} +3639.87i q^{37} -5103.54i q^{38} -3412.27i q^{39} +20138.9i q^{40} -5093.92i q^{41} +7713.89i q^{42} -16828.7 q^{43} -3937.90 q^{44} -18213.2i q^{45} -20061.2i q^{46} +20108.8 q^{47} +6541.90 q^{48} -17014.8 q^{49} +39109.7 q^{50} -13455.0i q^{51} -2498.19i q^{52} +573.904 q^{53} -17544.0 q^{54} +67915.4i q^{55} +35640.7i q^{56} -8241.32i q^{57} +22340.9i q^{58} -11533.9i q^{59} +5153.13i q^{60} +52634.5 q^{61} -28233.3 q^{62} -32232.8i q^{63} +36395.7 q^{64} -43085.4 q^{65} +27413.0 q^{66} -19934.1i q^{67} -9850.69i q^{68} -32395.3i q^{69} +97400.3 q^{70} -15299.8i q^{71} -33966.3 q^{72} +26799.4 q^{73} -18550.7i q^{74} +63155.3 q^{75} -6033.64i q^{76} +120193. i q^{77} +17390.7i q^{78} +39795.1 q^{79} -82602.1i q^{80} +14259.4 q^{81} +25961.3i q^{82} -62355.3i q^{83} +9119.72i q^{84} -169891. q^{85} +85768.2 q^{86} +36076.6i q^{87} +126657. q^{88} -64176.5 q^{89} +92824.4i q^{90} -76250.3 q^{91} -23717.3i q^{92} -45591.8 q^{93} -102485. q^{94} -104060. q^{95} +17697.6 q^{96} +(91325.1 - 15718.4i) q^{97} +86716.4 q^{98} -114546. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 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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