LMFDB - Embedded newform 97.6.b.a.96.37

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)

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);

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")

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			96.37
Character	$\chi$	$=$	97.96
Dual form			97.6.b.a.96.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+9.70046 q^{2} +23.5635 q^{3} +62.0990 q^{4} -57.7401i q^{5} +228.576 q^{6} +191.675i q^{7} +291.974 q^{8} +312.237 q^{9} -560.105i q^{10} -661.288 q^{11} +1463.27 q^{12} +473.965i q^{13} +1859.34i q^{14} -1360.56i q^{15} +845.113 q^{16} -1307.89i q^{17} +3028.84 q^{18} -3094.44i q^{19} -3585.60i q^{20} +4516.53i q^{21} -6414.80 q^{22} +1653.86i q^{23} +6879.91 q^{24} -208.916 q^{25} +4597.68i q^{26} +1631.46 q^{27} +11902.8i q^{28} +2925.37i q^{29} -13198.0i q^{30} -460.266 q^{31} -1145.17 q^{32} -15582.2 q^{33} -12687.2i q^{34} +11067.3 q^{35} +19389.6 q^{36} +10302.1i q^{37} -30017.5i q^{38} +11168.3i q^{39} -16858.6i q^{40} -3959.31i q^{41} +43812.4i q^{42} +20160.3 q^{43} -41065.3 q^{44} -18028.6i q^{45} +16043.2i q^{46} -9224.79 q^{47} +19913.8 q^{48} -19932.3 q^{49} -2026.59 q^{50} -30818.5i q^{51} +29432.8i q^{52} +35934.2 q^{53} +15825.9 q^{54} +38182.8i q^{55} +55964.1i q^{56} -72915.6i q^{57} +28377.4i q^{58} -23510.3i q^{59} -84489.1i q^{60} -16811.6 q^{61} -4464.79 q^{62} +59848.0i q^{63} -38152.3 q^{64} +27366.8 q^{65} -151155. q^{66} +46073.4i q^{67} -81218.8i q^{68} +38970.6i q^{69} +107358. q^{70} -5437.01i q^{71} +91165.0 q^{72} -27269.3 q^{73} +99935.2i q^{74} -4922.79 q^{75} -192161. i q^{76} -126752. i q^{77} +108337. i q^{78} +38189.3 q^{79} -48796.9i q^{80} -37430.7 q^{81} -38407.1i q^{82} +32842.4i q^{83} +280472. i q^{84} -75517.8 q^{85} +195565. q^{86} +68931.9i q^{87} -193079. q^{88} +52524.4 q^{89} -174886. i q^{90} -90847.3 q^{91} +102703. i q^{92} -10845.5 q^{93} -89484.7 q^{94} -178673. q^{95} -26984.2 q^{96} +(-92272.9 - 8546.86i) q^{97} -193353. q^{98} -206479. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.70046			1.71482			0.857408	−	0.514638i	$-0.172074\pi$
$2$	9.70046			1.71482			0.857408	+	0.514638i	$0.172074\pi$
$3$	23.5635			1.51160			0.755799	−	0.654804i	$-0.227249\pi$
$3$	23.5635			1.51160			0.755799	+	0.654804i	$0.227249\pi$
$4$	62.0990			1.94059
$5$		−	57.7401i		−	1.03289i	−0.856322	−	0.516443i	$-0.827256\pi$
$5$		−	57.7401i		−	1.03289i	0.856322	−	0.516443i	$-0.172744\pi$
$6$	228.576			2.59211
$7$			191.675i			1.47850i	0.673433	+	0.739249i	$0.264819\pi$
$7$			191.675i			1.47850i	−0.673433	+	0.739249i	$0.735181\pi$
$8$	291.974			1.61294
$9$	312.237			1.28493
$10$		−	560.105i		−	1.77121i
$11$	−661.288			−1.64782			−0.823909	−	0.566723i	$-0.808211\pi$
$11$	−661.288			−1.64782			−0.823909	+	0.566723i	$0.808211\pi$
$12$	1463.27			2.93339
$13$			473.965i			0.777836i	0.921272	+	0.388918i	$0.127151\pi$
$13$			473.965i			0.777836i	−0.921272	+	0.388918i	$0.872849\pi$
$14$			1859.34i			2.53535i
$15$		−	1360.56i		−	1.56131i
$16$	845.113			0.825306
$17$		−	1307.89i		−	1.09761i	−0.835949	−	0.548807i	$-0.815082\pi$
$17$		−	1307.89i		−	1.09761i	0.835949	−	0.548807i	$-0.184918\pi$
$18$	3028.84			2.20341
$19$		−	3094.44i		−	1.96652i	−0.182219	−	0.983258i	$-0.558328\pi$
$19$		−	3094.44i		−	1.96652i	0.182219	−	0.983258i	$-0.441672\pi$
$20$		−	3585.60i		−	2.00441i
$21$			4516.53i			2.23489i
$22$	−6414.80			−2.82570
$23$			1653.86i			0.651896i	0.945388	+	0.325948i	$0.105683\pi$
$23$			1653.86i			0.651896i	−0.945388	+	0.325948i	$0.894317\pi$
$24$	6879.91			2.43812
$25$	−208.916			−0.0668532
$26$			4597.68i			1.33385i
$27$	1631.46			0.430693
$28$			11902.8i			2.86916i
$29$			2925.37i			0.645931i	0.946411	+	0.322965i	$0.104680\pi$
$29$			2925.37i			0.645931i	−0.946411	+	0.322965i	$0.895320\pi$
$30$		−	13198.0i		−	2.67735i
$31$	−460.266			−0.0860210			−0.0430105	−	0.999075i	$-0.513695\pi$
$31$	−460.266			−0.0860210			−0.0430105	+	0.999075i	$0.513695\pi$
$32$	−1145.17			−0.197695
$33$	−15582.2			−2.49084
$34$		−	12687.2i		−	1.88221i
$35$	11067.3			1.52712
$36$	19389.6			2.49352
$37$			10302.1i			1.23715i	0.785726	+	0.618574i	$0.212289\pi$
$37$			10302.1i			1.23715i	−0.785726	+	0.618574i	$0.787711\pi$
$38$		−	30017.5i		−	3.37221i
$39$			11168.3i			1.17578i
$40$		−	16858.6i		−	1.66599i
$41$		−	3959.31i		−	0.367841i	−0.982941	−	0.183920i	$-0.941121\pi$
$41$		−	3959.31i		−	0.367841i	0.982941	−	0.183920i	$-0.0588789\pi$
$42$			43812.4i			3.83243i
$43$	20160.3			1.66275			0.831374	−	0.555713i	$-0.187555\pi$
$43$	20160.3			1.66275			0.831374	+	0.555713i	$0.187555\pi$
$44$	−41065.3			−3.19774
$45$		−	18028.6i		−	1.32718i
$46$			16043.2i			1.11788i
$47$	−9224.79			−0.609133			−0.304566	−	0.952491i	$-0.598512\pi$
$47$	−9224.79			−0.609133			−0.304566	+	0.952491i	$0.598512\pi$
$48$	19913.8			1.24753
$49$	−19932.3			−1.18595
$50$	−2026.59			−0.114641
$51$		−	30818.5i		−	1.65915i
$52$			29432.8i			1.50946i
$53$	35934.2			1.75719			0.878594	−	0.477570i	$-0.158482\pi$
$53$	35934.2			1.75719			0.878594	+	0.477570i	$0.158482\pi$
$54$	15825.9			0.738559
$55$			38182.8i			1.70201i
$56$			55964.1i			2.38473i
$57$		−	72915.6i		−	2.97258i
$58$			28377.4i			1.10765i
$59$		−	23510.3i		−	0.879281i	−0.898174	−	0.439641i	$-0.855106\pi$
$59$		−	23510.3i		−	0.879281i	0.898174	−	0.439641i	$-0.144894\pi$
$60$		−	84489.1i		−	3.02986i
$61$	−16811.6			−0.578475			−0.289237	−	0.957257i	$-0.593402\pi$
$61$	−16811.6			−0.578475			−0.289237	+	0.957257i	$0.593402\pi$
$62$	−4464.79			−0.147510
$63$			59848.0i			1.89976i
$64$	−38152.3			−1.16432
$65$	27366.8			0.803416
$66$	−151155.			−4.27132
$67$			46073.4i			1.25390i	0.779059	+	0.626951i	$0.215697\pi$
$67$			46073.4i			1.25390i	−0.779059	+	0.626951i	$0.784303\pi$
$68$		−	81218.8i		−	2.13002i
$69$			38970.6i			0.985405i
$70$	107358.			2.61873
$71$		−	5437.01i		−	0.128001i	−0.997950	−	0.0640006i	$-0.979614\pi$
$71$		−	5437.01i		−	0.128001i	0.997950	−	0.0640006i	$-0.0203860\pi$
$72$	91165.0			2.07251
$73$	−27269.3			−0.598917			−0.299458	−	0.954109i	$-0.596806\pi$
$73$	−27269.3			−0.598917			−0.299458	+	0.954109i	$0.596806\pi$
$74$			99935.2i			2.12148i
$75$	−4922.79			−0.101055
$76$		−	192161.i		−	3.81621i
$77$		−	126752.i		−	2.43629i
$78$			108337.i			2.01624i
$79$	38189.3			0.688453			0.344227	−	0.938887i	$-0.388141\pi$
$79$	38189.3			0.688453			0.344227	+	0.938887i	$0.388141\pi$
$80$		−	48796.9i		−	0.852447i
$81$	−37430.7			−0.633892
$82$		−	38407.1i		−	0.630779i
$83$			32842.4i			0.523287i	0.965165	+	0.261643i	$0.0842644\pi$
$83$			32842.4i			0.523287i	−0.965165	+	0.261643i	$0.915736\pi$
$84$			280472.i			4.33701i
$85$	−75517.8			−1.13371
$86$	195565.			2.85131
$87$			68931.9i			0.976387i
$88$	−193079.			−2.65783
$89$	52524.4			0.702888			0.351444	−	0.936209i	$-0.385691\pi$
$89$	52524.4			0.702888			0.351444	+	0.936209i	$0.385691\pi$
$90$		−	174886.i		−	2.27587i
$91$	−90847.3			−1.15003
$92$			102703.i			1.26506i
$93$	−10845.5			−0.130029
$94$	−89484.7			−1.04455
$95$	−178673.			−2.03119
$96$	−26984.2			−0.298835
$97$	−92272.9	−	8546.86i	−0.995738	−	0.0922311i
$97$	−92272.9	−	8546.86i	−0.995738	−	0.0922311i
$98$	−193353.			−2.03369
$99$	−206479.			−2.11732
$100$	−12973.5			−0.129735
$101$	−21490.7			−0.209627			−0.104814	−	0.994492i	$-0.533425\pi$
$101$	−21490.7			−0.209627			−0.104814	+	0.994492i	$0.533425\pi$
$102$		−	298954.i		−	2.84514i
$103$	67840.6			0.630082			0.315041	−	0.949078i	$-0.397982\pi$
$103$	67840.6			0.630082			0.315041	+	0.949078i	$0.397982\pi$
$104$			138385.i			1.25460i
$105$	260785.			2.30839
$106$	348578.			3.01325
$107$		−	135184.i		−	1.14147i	−0.821133	−	0.570736i	$-0.806658\pi$
$107$		−	135184.i		−	1.14147i	0.821133	−	0.570736i	$-0.193342\pi$
$108$	101312.			0.835799
$109$	47718.9			0.384702			0.192351	−	0.981326i	$-0.438389\pi$
$109$	47718.9			0.384702			0.192351	+	0.981326i	$0.438389\pi$
$110$			370391.i			2.91863i
$111$			242753.i			1.87007i
$112$			161987.i			1.22021i
$113$	69251.3			0.510190			0.255095	−	0.966916i	$-0.417893\pi$
$113$	69251.3			0.510190			0.255095	+	0.966916i	$0.417893\pi$
$114$		−	707315.i		−	5.09743i
$115$	95493.9			0.673334
$116$			181662.i			1.25349i
$117$			147989.i			0.999462i
$118$		−	228061.i		−	1.50781i
$119$	250690.			1.62282
$120$		−	397247.i		−	2.51830i
$121$	276251.			1.71530
$122$	−163080.			−0.991977
$123$		−	93295.1i		−	0.556027i
$124$	−28582.0			−0.166932
$125$		−	168375.i		−	0.963834i
$126$			580554.i			3.25774i
$127$			171478.i			0.943407i	0.881757	+	0.471704i	$0.156361\pi$
$127$			171478.i			0.943407i	−0.881757	+	0.471704i	$0.843639\pi$
$128$	−333449.			−1.79889
$129$	475047.			2.51341
$130$	265471.			1.37771
$131$		−	204901.i		−	1.04320i	−0.853191	−	0.521599i	$-0.825336\pi$
$131$		−	204901.i		−	1.04320i	0.853191	−	0.521599i	$-0.174664\pi$
$132$	−967641.			−4.83370
$133$	593126.			2.90749
$134$			446933.i			2.15021i
$135$		−	94200.8i		−	0.444857i
$136$		−	381870.i		−	1.77039i
$137$		−	62997.3i		−	0.286761i	−0.989668	−	0.143381i	$-0.954203\pi$
$137$		−	62997.3i		−	0.286761i	0.989668	−	0.143381i	$-0.0457973\pi$
$138$			378033.i			1.68979i
$139$			207637.i			0.911523i	0.890102	+	0.455762i	$0.150633\pi$
$139$			207637.i			0.911523i	−0.890102	+	0.455762i	$0.849367\pi$
$140$	687270.			2.96352
$141$	−217368.			−0.920763
$142$		−	52741.5i		−	0.219498i
$143$		−	313428.i		−	1.28173i
$144$	263876.			1.06046
$145$	168911.			0.667173
$146$	−264524.			−1.02703
$147$	−469675.			−1.79269
$148$			639750.i			2.40080i
$149$			335525.i			1.23811i	0.785348	+	0.619055i	$0.212484\pi$
$149$			335525.i			1.23811i	−0.785348	+	0.619055i	$0.787516\pi$
$150$	−47753.4			−0.173291
$151$	−18818.4			−0.0671645			−0.0335823	−	0.999436i	$-0.510692\pi$
$151$	−18818.4			−0.0671645			−0.0335823	+	0.999436i	$0.510692\pi$
$152$		−	903494.i		−	3.17188i
$153$		−	408372.i		−	1.41035i
$154$		−	1.22956e6i		−	4.17779i
$155$			26575.8i			0.0888498i
$156$			693538.i			2.28170i
$157$		−	47153.9i		−	0.152675i	−0.997082	−	0.0763377i	$-0.975677\pi$
$157$		−	47153.9i		−	0.152675i	0.997082	−	0.0763377i	$-0.0243227\pi$
$158$	370454.			1.18057
$159$	846734.			2.65616
$160$			66122.2i			0.204196i
$161$	−317003.			−0.963827
$162$	−363095.			−1.08701
$163$	164631.			0.485337			0.242668	−	0.970109i	$-0.421977\pi$
$163$	164631.			0.485337			0.242668	+	0.970109i	$0.421977\pi$
$164$		−	245869.i		−	0.713829i
$165$			899720.i			2.57275i
$166$			318586.i			0.897340i
$167$	−317807.			−0.881806			−0.440903	−	0.897555i	$-0.645342\pi$
$167$	−317807.			−0.881806			−0.440903	+	0.897555i	$0.645342\pi$
$168$			1.31871e6i			3.60475i
$169$	146650.			0.394971
$170$	−732558.			−1.94410
$171$		−	966197.i		−	2.52683i
$172$	1.25194e6			3.22672
$173$		−	177367.i		−	0.450566i	−0.974293	−	0.225283i	$-0.927669\pi$
$173$		−	177367.i		−	0.450566i	0.974293	−	0.225283i	$-0.0723307\pi$
$174$			668671.i			1.67432i
$175$		−	40044.1i		−	0.0988423i
$176$	−558863.			−1.35995
$177$		−	553984.i		−	1.32912i
$178$	509511.			1.20532
$179$			131293.i			0.306272i	0.988205	+	0.153136i	$0.0489373\pi$
$179$			131293.i			0.306272i	−0.988205	+	0.153136i	$0.951063\pi$
$180$		−	1.11956e6i		−	2.57552i
$181$		−	797784.i		−	1.81004i	−0.425366	−	0.905021i	$-0.639855\pi$
$181$		−	797784.i		−	1.81004i	0.425366	−	0.905021i	$-0.360145\pi$
$182$	−881261.			−1.97209
$183$	−396139.			−0.874421
$184$			482883.i			1.05147i
$185$	594844.			1.27783
$186$	−105206.			−0.222976
$187$			864894.i			1.80867i
$188$	−572850.			−1.18208
$189$			312711.i			0.636778i
$190$	−1.73321e6			−3.48311
$191$	290855.			0.576890			0.288445	−	0.957496i	$-0.406862\pi$
$191$	290855.			0.576890			0.288445	+	0.957496i	$0.406862\pi$
$192$	−899000.			−1.75998
$193$	−582439.			−1.12553			−0.562766	−	0.826617i	$-0.690263\pi$
$193$	−582439.			−1.12553			−0.562766	+	0.826617i	$0.690263\pi$
$194$	−895090.	−	82908.5i	−1.70751	−	0.158159i
$195$	644857.			1.21444
$196$	−1.23778e6			−2.30145
$197$	−397516.			−0.729775			−0.364887	−	0.931052i	$-0.618892\pi$
$197$	−397516.			−0.729775			−0.364887	+	0.931052i	$0.618892\pi$
$198$	−2.00294e6			−3.63082
$199$		−	825010.i		−	1.47682i	−0.674354	−	0.738408i	$-0.735578\pi$
$199$		−	825010.i		−	1.47682i	0.674354	−	0.738408i	$-0.264422\pi$
$200$	−60998.1			−0.107830
$201$			1.08565e6i			1.89539i
$202$	−208470.			−0.359472
$203$	−560721.			−0.955007
$204$		−	1.91380e6i		−	3.21973i
$205$	−228611.			−0.379938
$206$	658085.			1.08047
$207$			516395.i			0.837638i
$208$			400554.i			0.641953i
$209$			2.04631e6i			3.24046i
$210$	2.52973e6			3.95846
$211$			1.13061e6i			1.74826i	0.485688	+	0.874132i	$0.338569\pi$
$211$			1.13061e6i			1.74826i	−0.485688	+	0.874132i	$0.661431\pi$
$212$	2.23148e6			3.40998
$213$		−	128115.i		−	0.193486i
$214$		−	1.31135e6i		−	1.95742i
$215$		−	1.16406e6i		−	1.71743i
$216$	476344.			0.694683
$217$		−	88221.4i		−	0.127182i
$218$	462895.			0.659693
$219$	−642558.			−0.905321
$220$			2.37111e6i			3.30290i
$221$	619896.			0.853764
$222$			2.35482e6i			3.20682i
$223$			241698.i			0.325470i	0.986670	+	0.162735i	$0.0520316\pi$
$223$			241698.i			0.325470i	−0.986670	+	0.162735i	$0.947968\pi$
$224$		−	219501.i		−	0.292291i
$225$	−65231.4			−0.0859014
$226$	671769.			0.874881
$227$	1.18467e6			1.52592			0.762960	−	0.646445i	$-0.223745\pi$
$227$	1.18467e6			1.52592			0.762960	+	0.646445i	$0.223745\pi$
$228$		−	4.52798e6i		−	5.76856i
$229$	−878967.			−1.10760			−0.553801	−	0.832649i	$-0.686823\pi$
$229$	−878967.			−1.10760			−0.553801	+	0.832649i	$0.686823\pi$
$230$	926334.			1.15464
$231$		−	2.98673e6i		−	3.68269i
$232$			854131.i			1.04185i
$233$		−	1.11250e6i		−	1.34249i	−0.741236	−	0.671244i	$-0.765760\pi$
$233$		−	1.11250e6i		−	1.34249i	0.741236	−	0.671244i	$-0.234240\pi$
$234$			1.43557e6i			1.71389i
$235$			532640.i			0.629165i
$236$		−	1.45996e6i		−	1.70633i
$237$	899873.			1.04066
$238$	2.43181e6			2.78284
$239$			517616.i			0.586155i	0.956089	+	0.293078i	$0.0946794\pi$
$239$			517616.i			0.586155i	−0.956089	+	0.293078i	$0.905321\pi$
$240$		−	1.14982e6i		−	1.28856i
$241$	−1.14130e6			−1.26578			−0.632888	−	0.774244i	$-0.718131\pi$
$241$	−1.14130e6			−1.26578			−0.632888	+	0.774244i	$0.718131\pi$
$242$	2.67976e6			2.94143
$243$	−1.27844e6			−1.38888
$244$	−1.04398e6			−1.12258
$245$			1.15089e6i			1.22496i
$246$		−	905006.i		−	0.953484i
$247$	1.46666e6			1.52963
$248$	−134385.			−0.138747
$249$			773881.i			0.790999i
$250$		−	1.63331e6i		−	1.65280i
$251$			611595.i			0.612745i	0.951912	+	0.306372i	$0.0991153\pi$
$251$			611595.i			0.612745i	−0.951912	+	0.306372i	$0.900885\pi$
$252$			3.71650e6i			3.68666i
$253$		−	1.09368e6i		−	1.07421i
$254$			1.66342e6i			1.61777i
$255$	−1.77946e6			−1.71371
$256$	−2.01374e6			−1.92045
$257$		−	777179.i		−	0.733986i	−0.930224	−	0.366993i	$-0.880387\pi$
$257$		−	777179.i		−	0.733986i	0.930224	−	0.366993i	$-0.119613\pi$
$258$	4.60818e6			4.31003
$259$	−1.97466e6			−1.82912
$260$	1.69945e6			1.55910
$261$			913409.i			0.829973i
$262$		−	1.98764e6i		−	1.78889i
$263$			1.63239e6i			1.45524i	0.685982	+	0.727619i	$0.259373\pi$
$263$			1.63239e6i			1.45524i	−0.685982	+	0.727619i	$0.740627\pi$
$264$	−4.54960e6			−4.01757
$265$		−	2.07484e6i		−	1.81497i
$266$	5.75360e6			4.98581
$267$	1.23766e6			1.06248
$268$			2.86111e6i			2.43331i
$269$	−1.64501e6			−1.38608			−0.693040	−	0.720899i	$-0.743729\pi$
$269$	−1.64501e6			−1.38608			−0.693040	+	0.720899i	$0.743729\pi$
$270$		−	913791.i		−	0.762847i
$271$			1.32613e6i			1.09689i	0.836187	+	0.548445i	$0.184780\pi$
$271$			1.32613e6i			1.09689i	−0.836187	+	0.548445i	$0.815220\pi$
$272$		−	1.10532e6i		−	0.905868i
$273$	−2.14068e6			−1.73838
$274$		−	611103.i		−	0.491742i
$275$	138154.			0.110162
$276$			2.42003e6i			1.91227i
$277$		−	1.34949e6i		−	1.05674i	−0.849013	−	0.528372i	$-0.822803\pi$
$277$		−	1.34949e6i		−	1.05674i	0.849013	−	0.528372i	$-0.177197\pi$
$278$			2.01418e6i			1.56309i
$279$	−143712.			−0.110531
$280$	3.23137e6			2.46315
$281$		−	1.78038e6i		−	1.34508i	−0.740063	−	0.672538i	$-0.765204\pi$
$281$		−	1.78038e6i		−	1.34508i	0.740063	−	0.672538i	$-0.234796\pi$
$282$	−2.10857e6			−1.57894
$283$	−346444.			−0.257139			−0.128569	−	0.991701i	$-0.541038\pi$
$283$	−346444.			−0.257139			−0.128569	+	0.991701i	$0.541038\pi$
$284$		−	337632.i		−	0.248398i
$285$	−4.21015e6			−3.07034
$286$		−	3.04039e6i		−	2.19793i
$287$	758901.			0.543852
$288$	−357564.			−0.254023
$289$	−290726.			−0.204757
$290$	1.63852e6			1.14408
$291$	−2.17427e6	−	201394.i	−1.50515	−	0.139416i
$292$	−1.69339e6			−1.16225
$293$	1.51300e6			1.02961			0.514803	−	0.857309i	$-0.327865\pi$
$293$	1.51300e6			1.02961			0.514803	+	0.857309i	$0.327865\pi$
$294$	−4.55606e6			−3.07412
$295$	−1.35749e6			−0.908197
$296$			3.00794e6i			1.99545i
$297$	−1.07887e6			−0.709703
$298$			3.25475e6i			2.12313i
$299$	−783871.			−0.507069
$300$	−305700.			−0.196107
$301$			3.86423e6i			2.45837i
$302$	−182547.			−0.115175
$303$	−506396.			−0.316872
$304$		−	2.61515e6i		−	1.62298i
$305$			970703.i			0.597498i
$306$		−	3.96140e6i		−	2.41850i
$307$	2.58820e6			1.56730			0.783649	−	0.621204i	$-0.213356\pi$
$307$	2.58820e6			1.56730			0.783649	+	0.621204i	$0.213356\pi$
$308$		−	7.87120e6i		−	4.72785i
$309$	1.59856e6			0.952430
$310$			257797.i			0.152361i
$311$		−	1.68515e6i		−	0.987955i	−0.869475	−	0.493977i	$-0.835543\pi$
$311$		−	1.68515e6i		−	0.987955i	0.869475	−	0.493977i	$-0.164457\pi$
$312$			3.26084e6i			1.89646i
$313$	−1.23809e6			−0.714320			−0.357160	−	0.934043i	$-0.616255\pi$
$313$	−1.23809e6			−0.714320			−0.357160	+	0.934043i	$0.616255\pi$
$314$		−	457415.i		−	0.261810i
$315$	3.45563e6			1.96223
$316$	2.37152e6			1.33601
$317$		−	1.37569e6i		−	0.768906i	−0.923145	−	0.384453i	$-0.874390\pi$
$317$		−	1.37569e6i		−	0.768906i	0.923145	−	0.384453i	$-0.125610\pi$
$318$	8.21371e6			4.55482
$319$		−	1.93451e6i		−	1.06438i
$320$			2.20292e6i			1.20261i
$321$		−	3.18540e6i		−	1.72545i
$322$	−3.07508e6			−1.65279
$323$	−4.04719e6			−2.15848
$324$	−2.32441e6			−1.23013
$325$		−	99019.1i		−	0.0520009i
$326$	1.59700e6			0.832263
$327$	1.12442e6			0.581514
$328$		−	1.15601e6i		−	0.593306i
$329$		−	1.76816e6i		−	0.900601i
$330$			8.72770e6i			4.41179i
$331$			3.41063e6i			1.71106i	0.517756	+	0.855528i	$0.326768\pi$
$331$			3.41063e6i			1.71106i	−0.517756	+	0.855528i	$0.673232\pi$
$332$			2.03948e6i			1.01549i
$333$			3.21670e6i			1.58964i
$334$	−3.08288e6			−1.51213
$335$	2.66028e6			1.29514
$336$			3.81698e6i			1.84447i
$337$			2.17425e6i			1.04288i	0.853287	+	0.521441i	$0.174605\pi$
$337$			2.17425e6i			1.04288i	−0.853287	+	0.521441i	$0.825395\pi$
$338$	1.42257e6			0.677302
$339$	1.63180e6			0.771201
$340$	−4.68958e6			−2.20007
$341$	304368.			0.141747
$342$		−	9.37256e6i		−	4.33304i
$343$		−	599049.i		−	0.274933i
$344$	5.88629e6			2.68192
$345$	2.25017e6			1.01781
$346$		−	1.72055e6i		−	0.772638i
$347$		−	1.49404e6i		−	0.666099i	−0.942909	−	0.333050i	$-0.891922\pi$
$347$		−	1.49404e6i		−	0.666099i	0.942909	−	0.333050i	$-0.108078\pi$
$348$			4.28060e6i			1.89477i
$349$			2.63957e6i			1.16003i	0.814605	+	0.580016i	$0.196954\pi$
$349$			2.63957e6i			1.16003i	−0.814605	+	0.580016i	$0.803046\pi$
$350$		−	388446.i		−	0.169496i
$351$			773257.i			0.335009i
$352$	757287.			0.325765
$353$	1.31513e6			0.561733			0.280867	−	0.959747i	$-0.409378\pi$
$353$	1.31513e6			0.561733			0.280867	+	0.959747i	$0.409378\pi$
$354$		−	5.37390e6i		−	2.27919i
$355$	−313933.			−0.132211
$356$	3.26171e6			1.36402
$357$	5.90714e6			2.45305
$358$			1.27360e6i			0.525200i
$359$			533264.i			0.218377i	0.994021	+	0.109188i	$0.0348252\pi$
$359$			533264.i			0.218377i	−0.994021	+	0.109188i	$0.965175\pi$
$360$		−	5.26387e6i		−	2.14067i
$361$	−7.09943e6			−2.86718
$362$		−	7.73887e6i		−	3.10389i
$363$	6.50943e6			2.59285
$364$	−5.64153e6			−2.23174
$365$			1.57453e6i			0.618612i
$366$	−3.84274e6			−1.49947
$367$			99446.9i			0.0385413i	0.999814	+	0.0192706i	$0.00613441\pi$
$367$			99446.9i			0.0385413i	−0.999814	+	0.0192706i	$0.993866\pi$
$368$			1.39770e6i			0.538014i
$369$		−	1.23624e6i		−	0.472648i
$370$	5.77026e6			2.19125
$371$			6.88769e6i			2.59800i
$372$	−673491.			−0.252333
$373$		−	3.54276e6i		−	1.31847i	−0.751938	−	0.659234i	$-0.770881\pi$
$373$		−	3.54276e6i		−	1.31847i	0.751938	−	0.659234i	$-0.229119\pi$
$374$			8.38987e6i			3.10153i
$375$		−	3.96750e6i		−	1.45693i
$376$	−2.69340e6			−0.982496
$377$	−1.38652e6			−0.502428
$378$			3.03344e6i			1.09196i
$379$	−1.97849e6			−0.707514			−0.353757	−	0.935337i	$-0.615096\pi$
$379$	−1.97849e6			−0.707514			−0.353757	+	0.935337i	$0.615096\pi$
$380$	−1.10954e7			−3.94170
$381$			4.04062e6i			1.42605i
$382$	2.82143e6			0.989260
$383$			295922.i			0.103082i	0.998671	+	0.0515408i	$0.0164132\pi$
$383$			295922.i			0.103082i	−0.998671	+	0.0515408i	$0.983587\pi$
$384$	−7.85723e6			−2.71920
$385$	−7.31870e6			−2.51641
$386$	−5.64993e6			−1.93008
$387$	6.29480e6			2.13651
$388$	−5.73005e6	−	530751.i	−1.93232	−	0.178983i
$389$	239087.			0.0801090			0.0400545	−	0.999197i	$-0.487247\pi$
$389$	239087.			0.0801090			0.0400545	+	0.999197i	$0.487247\pi$
$390$	6.25541e6			2.08254
$391$	2.16307e6			0.715531
$392$	−5.81972e6			−1.91288
$393$		−	4.82819e6i		−	1.57689i
$394$	−3.85609e6			−1.25143
$395$		−	2.20506e6i		−	0.711093i
$396$	−1.28221e7			−4.10886
$397$	−5.04030e6			−1.60502			−0.802509	−	0.596640i	$-0.796502\pi$
$397$	−5.04030e6			−1.60502			−0.802509	+	0.596640i	$0.796502\pi$
$398$		−	8.00298e6i		−	2.53247i
$399$	1.39761e7			4.39495
$400$	−176558.			−0.0551744
$401$		−	66388.0i		−	0.0206172i	−0.999947	−	0.0103086i	$-0.996719\pi$
$401$		−	66388.0i		−	0.0206172i	0.999947	−	0.0103086i	$-0.00328138\pi$
$402$			1.05313e7i			3.25025i
$403$		−	218150.i		−	0.0669102i
$404$	−1.33455e6			−0.406801
$405$			2.16125e6i			0.654738i
$406$	−5.43925e6			−1.63766
$407$		−	6.81266e6i		−	2.03859i
$408$		−	8.99819e6i		−	2.67611i
$409$		−	3.41121e6i		−	1.00832i	−0.863609	−	0.504162i	$-0.831801\pi$
$409$		−	3.41121e6i		−	1.00832i	0.863609	−	0.504162i	$-0.168199\pi$
$410$	−2.21763e6			−0.651523
$411$		−	1.48443e6i		−	0.433467i
$412$	4.21283e6			1.22273
$413$	4.50634e6			1.30002
$414$			5.00927e6i			1.43640i
$415$	1.89632e6			0.540495
$416$		−	542771.i		−	0.153774i
$417$			4.89265e6i			1.37786i
$418$			1.98502e7i			5.55679i
$419$	2.39154e6			0.665491			0.332745	−	0.943017i	$-0.392025\pi$
$419$	2.39154e6			0.665491			0.332745	+	0.943017i	$0.392025\pi$
$420$	1.61945e7			4.47964
$421$	−4.07829e6			−1.12143			−0.560715	−	0.828009i	$-0.689474\pi$
$421$	−4.07829e6			−1.12143			−0.560715	+	0.828009i	$0.689474\pi$
$422$			1.09674e7i			2.99795i
$423$	−2.88032e6			−0.782690
$424$	1.04918e7			2.83424
$425$			273240.i			0.0733791i
$426$		−	1.24277e6i		−	0.331793i
$427$		−	3.22236e6i		−	0.855273i
$428$		−	8.39478e6i		−	2.21513i
$429$		−	7.38544e6i		−	1.93746i
$430$		−	1.12919e7i		−	2.94507i
$431$	949783.			0.246281			0.123141	−	0.992389i	$-0.460703\pi$
$431$	949783.			0.246281			0.123141	+	0.992389i	$0.460703\pi$
$432$	1.37877e6			0.355453
$433$			708127.i			0.181506i	0.995873	+	0.0907531i	$0.0289274\pi$
$433$			708127.i			0.181506i	−0.995873	+	0.0907531i	$0.971073\pi$
$434$		−	855789.i		−	0.218093i
$435$	3.98013e6			1.00850
$436$	2.96329e6			0.746549
$437$	5.11776e6			1.28196
$438$	−6.23311e6			−1.55246
$439$		−	685572.i		−	0.169782i	−0.996390	−	0.0848910i	$-0.972946\pi$
$439$		−	685572.i		−	0.169782i	0.996390	−	0.0848910i	$-0.0270542\pi$
$440$			1.11484e7i			2.74524i
$441$	−6.22361e6			−1.52386
$442$	6.01328e6			1.46405
$443$			3.48228e6i			0.843053i	0.906816	+	0.421527i	$0.138506\pi$
$443$			3.48228e6i			0.843053i	−0.906816	+	0.421527i	$0.861494\pi$
$444$			1.50747e7i			3.62904i
$445$		−	3.03276e6i		−	0.726003i
$446$			2.34458e6i			0.558121i
$447$			7.90613e6i			1.87152i
$448$		−	7.31285e6i		−	1.72144i
$449$	−5.72250e6			−1.33958			−0.669792	−	0.742548i	$-0.733617\pi$
$449$	−5.72250e6			−1.33958			−0.669792	+	0.742548i	$0.733617\pi$
$450$	−632775.			−0.147305
$451$			2.61825e6i			0.606135i
$452$	4.30043e6			0.990070
$453$	−443426.			−0.101526
$454$	1.14918e7			2.61667
$455$			5.24553e6i			1.18785i
$456$		−	2.12894e7i		−	4.79460i
$457$			2.42337e6i			0.542788i	0.962468	+	0.271394i	$0.0874846\pi$
$457$			2.42337e6i			0.542788i	−0.962468	+	0.271394i	$0.912515\pi$
$458$	−8.52638e6			−1.89933
$459$		−	2.13378e6i		−	0.472735i
$460$	5.93007e6			1.30667
$461$	2.99163e6			0.655625			0.327813	−	0.944743i	$-0.393689\pi$
$461$	2.99163e6			0.655625			0.327813	+	0.944743i	$0.393689\pi$
$462$		−	2.89726e7i		−	6.31514i
$463$	736176.			0.159599			0.0797993	−	0.996811i	$-0.474572\pi$
$463$	736176.			0.159599			0.0797993	+	0.996811i	$0.474572\pi$
$464$			2.47227e6i			0.533091i
$465$			626217.i			0.134305i
$466$		−	1.07918e7i		−	2.30212i
$467$	2.80630e6			0.595445			0.297722	−	0.954653i	$-0.403773\pi$
$467$	2.80630e6			0.595445			0.297722	+	0.954653i	$0.403773\pi$
$468$			9.18999e6i			1.93955i
$469$	−8.83113e6			−1.85389
$470$			5.16686e6i			1.07890i
$471$		−	1.11111e6i		−	0.230784i
$472$		−	6.86439e6i		−	1.41823i
$473$	−1.33318e7			−2.73991
$474$	8.72918e6			1.78455
$475$			646478.i			0.131468i
$476$	1.55676e7			3.14923
$477$	1.12200e7			2.25786
$478$			5.02111e6i			1.00515i
$479$	−3.19140e6			−0.635540			−0.317770	−	0.948168i	$-0.602934\pi$
$479$	−3.19140e6			−0.635540			−0.317770	+	0.948168i	$0.602934\pi$
$480$			1.55807e6i			0.308662i
$481$	−4.88284e6			−0.962299
$482$	−1.10711e7			−2.17057
$483$	−7.46970e6			−1.45692
$484$	1.71549e7			3.32870
$485$	−493496.	+	5.32785e6i	−0.0952642	+	1.02848i
$486$	−1.24015e7			−2.38168
$487$	−1.31903e6			−0.252018			−0.126009	−	0.992029i	$-0.540217\pi$
$487$	−1.31903e6			−0.252018			−0.126009	+	0.992029i	$0.540217\pi$
$488$	−4.90854e6			−0.933046
$489$	3.87928e6			0.733634
$490$			1.11642e7i			2.10057i
$491$	−959814.			−0.179673			−0.0898366	−	0.995957i	$-0.528634\pi$
$491$	−959814.			−0.179673			−0.0898366	+	0.995957i	$0.528634\pi$
$492$		−	5.79353e6i		−	1.07902i
$493$	3.82607e6			0.708983
$494$	1.42272e7			2.62303
$495$			1.19221e7i			2.18695i
$496$	−388977.			−0.0709936
$497$	1.04214e6			0.189249
$498$			7.50700e6i			1.35642i
$499$		−	3.37705e6i		−	0.607135i	−0.952810	−	0.303568i	$-0.901822\pi$
$499$		−	3.37705e6i		−	0.607135i	0.952810	−	0.303568i	$-0.0981778\pi$
$500$		−	1.04559e7i		−	1.87041i
$501$	−7.48864e6			−1.33293
$502$			5.93276e6i			1.05074i
$503$	992609.			0.174928			0.0874638	−	0.996168i	$-0.472124\pi$
$503$	992609.			0.174928			0.0874638	+	0.996168i	$0.472124\pi$
$504$			1.74741e7i			3.06420i
$505$			1.24088e6i			0.216521i
$506$		−	1.06092e7i		−	1.84207i
$507$	3.45558e6			0.597036
$508$			1.06486e7i			1.83077i
$509$	−3.89296e6			−0.666017			−0.333009	−	0.942924i	$-0.608064\pi$
$509$	−3.89296e6			−0.666017			−0.333009	+	0.942924i	$0.608064\pi$
$510$	−1.72616e7			−2.93870
$511$		−	5.22684e6i		−	0.885497i
$512$	−8.86383e6			−1.49433
$513$		−	5.04845e6i		−	0.846964i
$514$		−	7.53899e6i		−	1.25865i
$515$		−	3.91712e6i		−	0.650802i
$516$	2.94999e7			4.87750
$517$	6.10025e6			1.00374
$518$	−1.91551e7			−3.13660
$519$		−	4.17939e6i		−	0.681075i
$520$	7.99039e6			1.29586
$521$	−1.14595e7			−1.84957			−0.924784	−	0.380492i	$-0.875755\pi$
$521$	−1.14595e7			−1.84957			−0.924784	+	0.380492i	$0.875755\pi$
$522$			8.86049e6i			1.42325i
$523$		−	4.90469e6i		−	0.784075i	−0.919949	−	0.392037i	$-0.871770\pi$
$523$		−	4.90469e6i		−	0.784075i	0.919949	−	0.392037i	$-0.128230\pi$
$524$		−	1.27242e7i		−	2.02442i
$525$		−	943577.i		−	0.149410i
$526$			1.58349e7i			2.49546i
$527$			601978.i			0.0944178i
$528$	−1.31688e7			−2.05570
$529$	3.70110e6			0.575031
$530$		−	2.01269e7i		−	3.11235i
$531$		−	7.34078e6i		−	1.12981i
$532$	3.68325e7			5.64225
$533$	1.87658e6			0.286120
$534$	1.20058e7			1.82196
$535$	−7.80553e6			−1.17901
$536$			1.34522e7i			2.02247i
$537$			3.09371e6i			0.462960i
$538$	−1.59574e7			−2.37687
$539$	1.31810e7			1.95424
$540$		−	5.84977e6i		−	0.863285i
$541$			4.21250e6i			0.618795i	0.950933	+	0.309397i	$0.100127\pi$
$541$			4.21250e6i			0.618795i	−0.950933	+	0.309397i	$0.899873\pi$
$542$			1.28641e7i			1.88096i
$543$		−	1.87986e7i		−	2.73606i
$544$			1.49776e6i			0.216993i
$545$		−	2.75529e6i		−	0.397353i
$546$	−2.07656e7			−2.98100
$547$	9.69218e6			1.38501			0.692506	−	0.721413i	$-0.256507\pi$
$547$	9.69218e6			1.38501			0.692506	+	0.721413i	$0.256507\pi$
$548$		−	3.91206e6i		−	0.556486i
$549$	−5.24920e6			−0.743297
$550$	1.34016e6			0.188907
$551$	9.05237e6			1.27023
$552$			1.13784e7i			1.58940i
$553$			7.31994e6i			1.01788i
$554$		−	1.30907e7i		−	1.81212i
$555$	1.40166e7			1.93157
$556$			1.28940e7i			1.76890i
$557$	9.66293e6			1.31969			0.659843	−	0.751403i	$-0.270623\pi$
$557$	9.66293e6			1.31969			0.659843	+	0.751403i	$0.270623\pi$
$558$	−1.39407e6			−0.189539
$559$			9.55530e6i			1.29335i
$560$	9.35315e6			1.26034
$561$			2.03799e7i			2.73398i
$562$		−	1.72705e7i		−	2.30656i
$563$			3.87178e6i			0.514801i	0.966305	+	0.257400i	$0.0828659\pi$
$563$			3.87178e6i			0.514801i	−0.966305	+	0.257400i	$0.917134\pi$
$564$	−1.34983e7			−1.78683
$565$		−	3.99857e6i		−	0.526968i
$566$	−3.36067e6			−0.440945
$567$		−	7.17453e6i		−	0.937207i
$568$		−	1.58746e6i		−	0.206458i
$569$			9.94208e6i			1.28735i	0.765299	+	0.643675i	$0.222591\pi$
$569$			9.94208e6i			1.28735i	−0.765299	+	0.643675i	$0.777409\pi$
$570$	−4.08404e7			−5.26506
$571$	−4.17403e6			−0.535754			−0.267877	−	0.963453i	$-0.586322\pi$
$571$	−4.17403e6			−0.535754			−0.267877	+	0.963453i	$0.586322\pi$
$572$		−	1.94635e7i		−	2.48732i
$573$	6.85355e6			0.872025
$574$	7.36169e6			0.932606
$575$		−	345518.i		−	0.0435814i
$576$	−1.19126e7			−1.49606
$577$		−	3.12854e6i		−	0.391203i	−0.980683	−	0.195601i	$-0.937334\pi$
$577$		−	3.12854e6i		−	0.391203i	0.980683	−	0.195601i	$-0.0626659\pi$
$578$	−2.82018e6			−0.351121
$579$	−1.37243e7			−1.70135
$580$	1.04892e7			1.29471
$581$	−6.29507e6			−0.773678
$582$	−2.10914e7	−	1.95361e6i	−2.58106	−	0.239073i
$583$	−2.37629e7			−2.89552
$584$	−7.96191e6			−0.966018
$585$	8.54492e6			1.03233
$586$	1.46768e7			1.76558
$587$			8.96319e6i			1.07366i	0.843690	+	0.536831i	$0.180379\pi$
$587$			8.96319e6i			1.07366i	−0.843690	+	0.536831i	$0.819621\pi$
$588$	−2.91663e7			−3.47887
$589$			1.42426e6i			0.169162i
$590$	−1.31682e7			−1.55739
$591$	−9.36685e6			−1.10313
$592$			8.70645e6i			1.02103i
$593$	3.75344e6			0.438322			0.219161	−	0.975689i	$-0.429668\pi$
$593$	3.75344e6			0.438322			0.219161	+	0.975689i	$0.429668\pi$
$594$	−1.04655e7			−1.21701
$595$		−	1.44749e7i		−	1.67619i
$596$			2.08357e7i			2.40267i
$597$		−	1.94401e7i		−	2.23235i
$598$	−7.60391e6			−0.869529
$599$		−	8.77495e6i		−	0.999258i	−0.866240	−	0.499629i	$-0.833470\pi$
$599$		−	8.77495e6i		−	0.999258i	0.866240	−	0.499629i	$-0.166530\pi$
$600$	−1.43733e6			−0.162996
$601$			8.88683e6i			1.00360i	0.864984	+	0.501800i	$0.167329\pi$
$601$			8.88683e6i			1.00360i	−0.864984	+	0.501800i	$0.832671\pi$
$602$			3.74848e7i			4.21565i
$603$			1.43858e7i			1.61117i
$604$	−1.16860e6			−0.130339
$605$		−	1.59508e7i		−	1.77171i
$606$	−4.91228e6			−0.543377
$607$	1.63838e7			1.80486			0.902431	−	0.430834i	$-0.141781\pi$
$607$	1.63838e7			1.80486			0.902431	+	0.430834i	$0.141781\pi$
$608$			3.54365e6i			0.388770i
$609$	−1.32125e7			−1.44359
$610$			9.41627e6i			1.02460i
$611$		−	4.37223e6i		−	0.473806i
$612$		−	2.53595e7i		−	2.73692i
$613$	3.47067e6			0.373045			0.186523	−	0.982451i	$-0.440278\pi$
$613$	3.47067e6			0.373045			0.186523	+	0.982451i	$0.440278\pi$
$614$	2.51067e7			2.68763
$615$	−5.38687e6			−0.574313
$616$		−	3.70084e7i		−	3.92960i
$617$	1.34349e7			1.42077			0.710384	−	0.703815i	$-0.248521\pi$
$617$	1.34349e7			1.42077			0.710384	+	0.703815i	$0.248521\pi$
$618$	1.55068e7			1.63324
$619$		−	7.89404e6i		−	0.828081i	−0.910258	−	0.414041i	$-0.864117\pi$
$619$		−	7.89404e6i		−	0.828081i	0.910258	−	0.414041i	$-0.135883\pi$
$620$			1.65033e6i			0.172421i
$621$			2.69821e6i			0.280767i
$622$		−	1.63467e7i		−	1.69416i
$623$			1.00676e7i			1.03922i
$624$			9.43845e6i			0.970374i
$625$	−1.03748e7			−1.06238
$626$	−1.20101e7			−1.22493
$627$			4.82182e7i			4.89827i
$628$		−	2.92821e6i		−	0.296281i
$629$	1.34740e7			1.35791
$630$	3.35212e7			3.36487
$631$	7.12267e6			0.712146			0.356073	−	0.934458i	$-0.384115\pi$
$631$	7.12267e6			0.712146			0.356073	+	0.934458i	$0.384115\pi$
$632$	1.11503e7			1.11043
$633$			2.66411e7i			2.64267i
$634$		−	1.33449e7i		−	1.31853i
$635$	9.90116e6			0.974432
$636$	5.25813e7			5.15452
$637$		−	9.44724e6i		−	0.922478i
$638$		−	1.87657e7i		−	1.82521i
$639$		−	1.69763e6i		−	0.164472i
$640$			1.92534e7i			1.85805i
$641$		−	2.03585e7i		−	1.95704i	−0.206149	−	0.978521i	$-0.566093\pi$
$641$		−	2.03585e7i		−	1.95704i	0.206149	−	0.978521i	$-0.433907\pi$
$642$		−	3.08999e7i		−	2.95882i
$643$	401967.			0.0383409			0.0191705	−	0.999816i	$-0.493897\pi$
$643$	401967.			0.0383409			0.0191705	+	0.999816i	$0.493897\pi$
$644$	−1.96856e7			−1.87040
$645$		−	2.74293e7i		−	2.59606i
$646$	−3.92596e7			−3.70139
$647$	−9.83652e6			−0.923806			−0.461903	−	0.886930i	$-0.652833\pi$
$647$	−9.83652e6			−0.923806			−0.461903	+	0.886930i	$0.652833\pi$
$648$	−1.09288e7			−1.02243
$649$			1.55471e7i			1.44890i
$650$		−	960531.i		−	0.0891719i
$651$		−	2.07880e6i		−	0.192248i
$652$	1.02234e7			0.941841
$653$			1.05010e6i			0.0963714i	0.998838	+	0.0481857i	$0.0153439\pi$
$653$			1.05010e6i			0.0963714i	−0.998838	+	0.0481857i	$0.984656\pi$
$654$	1.09074e7			0.997189
$655$	−1.18310e7			−1.07750
$656$		−	3.34607e6i		−	0.303581i
$657$	−8.51447e6			−0.769563
$658$		−	1.71520e7i		−	1.54436i
$659$			1.57505e7i			1.41280i	0.707811	+	0.706402i	$0.249683\pi$
$659$			1.57505e7i			1.41280i	−0.707811	+	0.706402i	$0.750317\pi$
$660$			5.58717e7i			4.99266i
$661$	2.03566e7			1.81218			0.906090	−	0.423085i	$-0.139053\pi$
$661$	2.03566e7			1.81218			0.906090	+	0.423085i	$0.139053\pi$
$662$			3.30847e7i			2.93415i
$663$	1.46069e7			1.29055
$664$			9.58912e6i			0.844031i
$665$		−	3.42472e7i		−	3.00310i
$666$			3.12035e7i			2.72595i
$667$	−4.83815e6			−0.421080
$668$	−1.97355e7			−1.71123
$669$			5.69525e6i			0.491980i
$670$	2.58060e7			2.22092
$671$	1.11173e7			0.953221
$672$		−	5.17219e6i		−	0.441826i
$673$	−1.21197e7			−1.03147			−0.515734	−	0.856749i	$-0.672481\pi$
$673$	−1.21197e7			−1.03147			−0.515734	+	0.856749i	$0.672481\pi$
$674$			2.10913e7i			1.78835i
$675$	−340839.			−0.0287932
$676$	9.10680e6			0.766477
$677$	−6.84814e6			−0.574250			−0.287125	−	0.957893i	$-0.592699\pi$
$677$	−6.84814e6			−0.574250			−0.287125	+	0.957893i	$0.592699\pi$
$678$	1.58292e7			1.32247
$679$	1.63822e6	−	1.76864e7i	0.136363	−	1.47220i
$680$	−2.20492e7			−1.82861
$681$	2.79149e7			2.30658
$682$	2.95251e6			0.243070
$683$	−8.95904e6			−0.734868			−0.367434	−	0.930050i	$-0.619764\pi$
$683$	−8.95904e6			−0.734868			−0.367434	+	0.930050i	$0.619764\pi$
$684$		−	5.99998e7i		−	4.90354i
$685$	−3.63747e6			−0.296192
$686$		−	5.81105e6i		−	0.471460i
$687$	−2.07115e7			−1.67425
$688$	1.70378e7			1.37228
$689$			1.70316e7i			1.36680i
$690$	2.18277e7			1.74536
$691$	−1.08420e7			−0.863806			−0.431903	−	0.901920i	$-0.642158\pi$
$691$	−1.08420e7			−0.863806			−0.431903	+	0.901920i	$0.642158\pi$
$692$		−	1.10143e7i		−	0.874366i
$693$		−	3.95768e7i		−	3.13046i
$694$		−	1.44929e7i		−	1.14224i
$695$	1.19890e7			0.941500
$696$			2.01263e7i			1.57486i
$697$	−5.17835e6			−0.403747
$698$			2.56051e7i			1.98924i
$699$		−	2.62144e7i		−	2.02930i
$700$		−	2.48669e6i		−	0.191813i
$701$	−2.11068e7			−1.62229			−0.811144	−	0.584846i	$-0.801155\pi$
$701$	−2.11068e7			−1.62229			−0.811144	+	0.584846i	$0.801155\pi$
$702$			7.50095e6i			0.574478i
$703$	3.18792e7			2.43287
$704$	2.52297e7			1.91858
$705$			1.25508e7i			0.951043i
$706$	1.27573e7			0.963269
$707$		−	4.11924e6i		−	0.309933i
$708$		−	3.44018e7i		−	2.57928i
$709$			2.58722e7i			1.93294i	0.256780	+	0.966470i	$0.417338\pi$
$709$			2.58722e7i			1.93294i	−0.256780	+	0.966470i	$0.582662\pi$
$710$	−3.04530e6			−0.226717
$711$	1.19241e7			0.884611
$712$	1.53357e7			1.13372
$713$		−	761214.i		−	0.0560767i
$714$	5.73019e7			4.20653
$715$	−1.80973e7			−1.32388
$716$			8.15313e6i			0.594349i
$717$			1.21968e7i			0.886030i
$718$			5.17291e6i			0.374476i
$719$			1.98306e7i			1.43059i	0.698824	+	0.715293i	$0.253707\pi$
$719$			1.98306e7i			1.43059i	−0.698824	+	0.715293i	$0.746293\pi$
$720$		−	1.52362e7i		−	1.09533i
$721$			1.30034e7i			0.931574i
$722$	−6.88678e7			−4.91669
$723$	−2.68929e7			−1.91334
$724$		−	4.95415e7i		−	3.51256i
$725$		−	611158.i		−	0.0431826i
$726$	6.31445e7			4.44625
$727$	6.28783e6			0.441230			0.220615	−	0.975361i	$-0.429194\pi$
$727$	6.28783e6			0.441230			0.220615	+	0.975361i	$0.429194\pi$
$728$	−2.65250e7			−1.85493
$729$	−2.10289e7			−1.46554
$730$			1.52737e7i			1.06081i
$731$		−	2.63676e7i		−	1.82506i
$732$	−2.45998e7			−1.69689
$733$	−2.49951e7			−1.71828			−0.859142	−	0.511738i	$-0.829002\pi$
$733$	−2.49951e7			−1.71828			−0.859142	+	0.511738i	$0.829002\pi$
$734$			964680.i			0.0660912i
$735$			2.71191e7i			1.85164i
$736$		−	1.89395e6i		−	0.128876i
$737$		−	3.04678e7i		−	2.06620i
$738$		−	1.19921e7i		−	0.810504i
$739$			2.42965e6i			0.163656i	0.996646	+	0.0818280i	$0.0260758\pi$
$739$			2.42965e6i			0.163656i	−0.996646	+	0.0818280i	$0.973924\pi$
$740$	3.69392e7			2.47975
$741$	3.45595e7			2.31218
$742$			6.68138e7i			4.45509i
$743$	7.20809e6			0.479014			0.239507	−	0.970895i	$-0.423014\pi$
$743$	7.20809e6			0.479014			0.239507	+	0.970895i	$0.423014\pi$
$744$	−3.16659e6			−0.209729
$745$	1.93732e7			1.27883
$746$		−	3.43664e7i		−	2.26093i
$747$			1.02546e7i			0.672385i
$748$			5.37090e7i			3.50989i
$749$	2.59114e7			1.68766
$750$		−	3.84865e7i		−	2.49836i
$751$	5.54053e6			0.358469			0.179234	−	0.983806i	$-0.442638\pi$
$751$	5.54053e6			0.358469			0.179234	+	0.983806i	$0.442638\pi$
$752$	−7.79599e6			−0.502721
$753$			1.44113e7i			0.926223i
$754$	−1.34499e7			−0.861572
$755$			1.08657e6i			0.0693733i
$756$			1.94190e7i			1.23573i
$757$		−	632395.i		−	0.0401096i	−0.999799	−	0.0200548i	$-0.993616\pi$
$757$		−	632395.i		−	0.0401096i	0.999799	−	0.0200548i	$-0.00638407\pi$
$758$	−1.91922e7			−1.21326
$759$		−	2.57708e7i		−	1.62377i
$760$	−5.21678e7			−3.27619
$761$			1.50102e7i			0.939558i	0.882784	+	0.469779i	$0.155666\pi$
$761$			1.50102e7i			0.939558i	−0.882784	+	0.469779i	$0.844334\pi$
$762$			3.91959e7i			2.44542i
$763$			9.14652e6i			0.568781i
$764$	1.80618e7			1.11951
$765$	−2.35795e7			−1.45673
$766$			2.87058e6i			0.176766i
$767$	1.11431e7			0.683937
$768$	−4.74507e7			−2.90295
$769$		−	671338.i		−	0.0409379i	−0.999790	−	0.0204689i	$-0.993484\pi$
$769$		−	671338.i		−	0.0409379i	0.999790	−	0.0204689i	$-0.00651592\pi$
$770$	−7.09947e7			−4.31518
$771$		−	1.83130e7i		−	1.10949i
$772$	−3.61689e7			−2.18420
$773$	1.97585e7			1.18934			0.594669	−	0.803971i	$-0.297283\pi$
$773$	1.97585e7			1.18934			0.594669	+	0.803971i	$0.297283\pi$
$774$	6.10625e7			3.66372
$775$	96157.0			0.00575078
$776$	−2.69413e7	−	2.49546e6i	−1.60607	−	0.148763i
$777$	−4.65298e7			−2.76489
$778$	2.31925e6			0.137372
$779$	−1.22518e7			−0.723365
$780$	4.00449e7			2.35674
$781$			3.59543e6i			0.210923i
$782$	2.09828e7			1.22700
$783$			4.77263e6i			0.278198i
$784$	−1.68451e7			−0.978775
$785$	−2.72267e6			−0.157696
$786$		−	4.68356e7i		−	2.70408i
$787$	−9.54969e6			−0.549607			−0.274804	−	0.961500i	$-0.588613\pi$
$787$	−9.54969e6			−0.549607			−0.274804	+	0.961500i	$0.588613\pi$
$788$	−2.46853e7			−1.41619
$789$			3.84647e7i			2.19973i
$790$		−	2.13901e7i		−	1.21939i
$791$			1.32737e7i			0.754314i
$792$	−6.02863e7			−3.41512
$793$		−	7.96811e6i		−	0.449959i
$794$	−4.88932e7			−2.75231
$795$		−	4.88905e7i		−	2.74351i
$796$		−	5.12323e7i		−	2.86590i
$797$			1.13269e7i			0.631634i	0.948820	+	0.315817i	$0.102279\pi$
$797$			1.13269e7i			0.631634i	−0.948820	+	0.315817i	$0.897721\pi$
$798$	1.35575e8			7.53653
$799$			1.20650e7i			0.668593i
$800$	239245.			0.0132165
$801$	1.64000e7			0.903158
$802$		−	643994.i		−	0.0353546i
$803$	1.80328e7			0.986905
$804$			6.74177e7i			3.67819i
$805$			1.83038e7i			0.995523i
$806$		−	2.11616e6i		−	0.114739i
$807$	−3.87622e7			−2.09519
$808$	−6.27473e6			−0.338117
$809$	3.64994e7			1.96072			0.980358	−	0.197228i	$-0.0631938\pi$
$809$	3.64994e7			1.96072			0.980358	+	0.197228i	$0.0631938\pi$
$810$			2.09651e7i			1.12275i
$811$	−253235.			−0.0135198			−0.00675992	−	0.999977i	$-0.502152\pi$
$811$	−253235.			−0.0135198			−0.00675992	+	0.999977i	$0.502152\pi$
$812$	−3.48202e7			−1.85328
$813$			3.12482e7i			1.65806i
$814$		−	6.60860e7i		−	3.49581i
$815$		−	9.50582e6i		−	0.501298i
$816$		−	2.60451e7i		−	1.36931i
$817$		−	6.23849e7i		−	3.26982i
$818$		−	3.30903e7i		−	1.72909i
$819$	−2.83659e7			−1.47770
$820$	−1.41965e7			−0.737304
$821$			4.70020e6i			0.243365i	0.992569	+	0.121683i	$0.0388290\pi$
$821$			4.70020e6i			0.243365i	−0.992569	+	0.121683i	$0.961171\pi$
$822$		−	1.43997e7i		−	0.743316i
$823$	−2.81815e6			−0.145032			−0.0725161	−	0.997367i	$-0.523103\pi$
$823$	−2.81815e6			−0.145032			−0.0725161	+	0.997367i	$0.523103\pi$
$824$	1.98077e7			1.01629
$825$	3.25539e6			0.166520
$826$	4.37135e7			2.22929
$827$			1.21172e7i			0.616082i	0.951373	+	0.308041i	$0.0996734\pi$
$827$			1.21172e7i			0.616082i	−0.951373	+	0.308041i	$0.900327\pi$
$828$			3.20676e7i			1.62551i
$829$	−5.73952e6			−0.290061			−0.145030	−	0.989427i	$-0.546328\pi$
$829$	−5.73952e6			−0.290061			−0.145030	+	0.989427i	$0.546328\pi$
$830$	1.83952e7			0.926850
$831$		−	3.17986e7i		−	1.59737i
$832$		−	1.80829e7i		−	0.905647i
$833$			2.60694e7i			1.30172i
$834$			4.74609e7i			2.36277i
$835$			1.83502e7i			0.910805i
$836$			1.27074e8i			6.28841i
$837$	−750906.			−0.0370486
$838$	2.31990e7			1.14119
$839$		−	1.82913e7i		−	0.897096i	−0.893759	−	0.448548i	$-0.851941\pi$
$839$		−	1.82913e7i		−	0.897096i	0.893759	−	0.448548i	$-0.148059\pi$
$840$	7.61423e7			3.72330
$841$	1.19534e7			0.582773
$842$	−3.95613e7			−1.92305
$843$		−	4.19519e7i		−	2.03321i
$844$			7.02098e7i			3.39267i
$845$		−	8.46757e6i		−	0.407960i
$846$	−2.79404e7			−1.34217
$847$			5.29504e7i			2.53607i
$848$	3.03685e7			1.45022
$849$	−8.16343e6			−0.388690
$850$			2.65056e6i			0.125832i
$851$	−1.70382e7			−0.806492
$852$		−	7.95579e6i		−	0.375478i
$853$		−	1.92665e7i		−	0.906631i	−0.891350	−	0.453316i	$-0.850241\pi$
$853$		−	1.92665e7i		−	0.906631i	0.891350	−	0.453316i	$-0.149759\pi$
$854$		−	3.12584e7i		−	1.46664i
$855$	−5.57883e7			−2.60992
$856$		−	3.94701e7i		−	1.84113i
$857$	3.12095e7			1.45156			0.725780	−	0.687927i	$-0.241479\pi$
$857$	3.12095e7			1.45156			0.725780	+	0.687927i	$0.241479\pi$
$858$		−	7.16422e7i		−	3.32239i
$859$			5.53964e6i			0.256153i	0.991764	+	0.128076i	$0.0408803\pi$
$859$			5.53964e6i			0.256153i	−0.991764	+	0.128076i	$0.959120\pi$
$860$		−	7.22869e7i		−	3.33283i
$861$	1.78823e7			0.822085
$862$	9.21333e6			0.422327
$863$		−	1.56403e7i		−	0.714854i	−0.933941	−	0.357427i	$-0.883654\pi$
$863$		−	1.56403e7i		−	0.714854i	0.933941	−	0.357427i	$-0.116346\pi$
$864$	−1.86830e6			−0.0851457
$865$	−1.02412e7			−0.465384
$866$			6.86916e6i			0.311250i
$867$	−6.85052e6			−0.309511
$868$		−	5.47846e6i		−	0.246808i
$869$	−2.52542e7			−1.13444
$870$	3.86091e7			1.72939
$871$	−2.18372e7			−0.975330
$872$	1.39327e7			0.620502
$873$	−2.88110e7	−	2.66865e6i	−1.27945	−	0.118510i
$874$	4.96446e7			2.19833
$875$	3.22733e7			1.42503
$876$	−3.99022e7			−1.75686
$877$	9.61848e6			0.422287			0.211143	−	0.977455i	$-0.432281\pi$
$877$	9.61848e6			0.422287			0.211143	+	0.977455i	$0.432281\pi$
$878$		−	6.65036e6i		−	0.291145i
$879$	3.56516e7			1.55635
$880$			3.22688e7i			1.40468i
$881$	−3.13390e7			−1.36033			−0.680166	−	0.733058i	$-0.738092\pi$
$881$	−3.13390e7			−1.36033			−0.680166	+	0.733058i	$0.738092\pi$
$882$	−6.03719e7			−2.61314
$883$		−	2.20929e7i		−	0.953566i	−0.879021	−	0.476783i	$-0.841803\pi$
$883$		−	2.20929e7i		−	0.953566i	0.879021	−	0.476783i	$-0.158197\pi$
$884$	3.84949e7			1.65681
$885$	−3.19871e7			−1.37283
$886$			3.37798e7i			1.44568i
$887$			3.97008e7i			1.69430i	0.531355	+	0.847149i	$0.321683\pi$
$887$			3.97008e7i			1.69430i	−0.531355	+	0.847149i	$0.678317\pi$
$888$			7.08776e7i			3.01631i
$889$	−3.28681e7			−1.39483
$890$		−	2.94192e7i		−	1.24496i
$891$	2.47525e7			1.04454
$892$			1.50092e7i			0.631605i
$893$			2.85455e7i			1.19787i
$894$			7.66931e7i			3.20932i
$895$	7.58084e6			0.316344
$896$		−	6.39140e7i		−	2.65966i
$897$	−1.84707e7			−0.766483
$898$	−5.55109e7			−2.29714
$899$		−	1.34645e6i		−	0.0555636i
$900$	−4.05080e6			−0.166700
$901$		−	4.69981e7i		−	1.92871i
$902$			2.53982e7i			1.03941i
$903$			9.10547e7i			3.71606i
$904$	2.02195e7			0.822906
$905$	−4.60641e7			−1.86957
$906$	−4.30144e6			−0.174098
$907$			2.47665e7i			0.999646i	0.866128	+	0.499823i	$0.166602\pi$
$907$			2.47665e7i			0.999646i	−0.866128	+	0.499823i	$0.833398\pi$
$908$	7.35666e7			2.96119
$909$	−6.71020e6			−0.269355
$910$			5.08841e7i			2.03694i
$911$			1.94358e7i			0.775903i	0.921680	+	0.387951i	$0.126817\pi$
$911$			1.94358e7i			0.775903i	−0.921680	+	0.387951i	$0.873183\pi$
$912$		−	6.16220e7i		−	2.45329i
$913$		−	2.17183e7i		−	0.862281i
$914$			2.35079e7i			0.930781i
$915$			2.28731e7i			0.903177i
$916$	−5.45829e7			−2.14940
$917$	3.92745e7			1.54236
$918$		−	2.06986e7i		−	0.810653i
$919$		−	3.41588e7i		−	1.33418i	−0.744977	−	0.667090i	$-0.767540\pi$
$919$		−	3.41588e7i		−	1.33418i	0.744977	−	0.667090i	$-0.232460\pi$
$920$	2.78817e7			1.08605
$921$	6.09869e7			2.36912
$922$	2.90202e7			1.12428
$923$	2.57695e6			0.0995640
$924$		−	1.85473e8i		−	7.14661i
$925$		−	2.15228e6i		−	0.0827074i
$926$	7.14124e6			0.273682
$927$	2.11824e7			0.809608
$928$		−	3.35005e6i		−	0.127697i
$929$		−	3.53563e7i		−	1.34409i	−0.740511	−	0.672044i	$-0.765417\pi$
$929$		−	3.53563e7i		−	1.34409i	0.740511	−	0.672044i	$-0.234583\pi$
$930$			6.07460e6i			0.230309i
$931$			6.16793e7i			2.33220i
$932$		−	6.90851e7i		−	2.60522i
$933$		−	3.97079e7i		−	1.49339i
$934$	2.72224e7			1.02108
$935$	4.99390e7			1.86815
$936$			4.32090e7i			1.61207i
$937$	3.40217e7			1.26592			0.632962	−	0.774183i	$-0.281839\pi$
$937$	3.40217e7			1.26592			0.632962	+	0.774183i	$0.281839\pi$
$938$	−8.56660e7			−3.17908
$939$	−2.91738e7			−1.07976
$940$			3.30764e7i			1.22095i
$941$			2.01303e7i			0.741098i	0.928813	+	0.370549i	$0.120831\pi$
$941$			2.01303e7i			0.741098i	−0.928813	+	0.370549i	$0.879169\pi$
$942$		−	1.07783e7i		−	0.395751i
$943$	6.54814e6			0.239794
$944$		−	1.98689e7i		−	0.725676i
$945$	1.80559e7			0.657719
$946$	−1.29325e8			−4.69843
$947$			4.07602e6i			0.147694i	0.997270	+	0.0738468i	$0.0235276\pi$
$947$			4.07602e6i			0.147694i	−0.997270	+	0.0738468i	$0.976472\pi$
$948$	5.58812e7			2.01950
$949$		−	1.29247e7i		−	0.465859i
$950$			6.27114e6i			0.225443i
$951$		−	3.24161e7i		−	1.16228i
$952$	7.31950e7			2.61751
$953$		−	1.86597e7i		−	0.665539i	−0.943008	−	0.332769i	$-0.892017\pi$
$953$		−	1.86597e7i		−	0.665539i	0.943008	−	0.332769i	$-0.107983\pi$
$954$	1.08839e8			3.87181
$955$		−	1.67940e7i		−	0.595862i
$956$			3.21434e7i			1.13749i
$957$		−	4.55838e7i		−	1.60891i
$958$	−3.09581e7			−1.08983
$959$	1.20750e7			0.423976
$960$			5.19084e7i			1.81785i
$961$	−2.84173e7			−0.992600
$962$	−4.73658e7			−1.65016
$963$		−	4.22094e7i		−	1.46671i
$964$	−7.08734e7			−2.45635
$965$			3.36301e7i			1.16255i
$966$	−7.24595e7			−2.49835
$967$	−3.36773e6			−0.115817			−0.0579084	−	0.998322i	$-0.518443\pi$
$967$	−3.36773e6			−0.115817			−0.0579084	+	0.998322i	$0.518443\pi$
$968$	8.06580e7			2.76668
$969$	−9.53658e7			−3.26275
$970$	−4.78714e6	+	5.16826e7i	−0.163361	+	1.76366i
$971$	4.48103e6			0.152521			0.0762606	−	0.997088i	$-0.475702\pi$
$971$	4.48103e6			0.152521			0.0762606	+	0.997088i	$0.475702\pi$
$972$	−7.93899e7			−2.69525
$973$	−3.97988e7			−1.34768
$974$	−1.27952e7			−0.432165
$975$		−	2.33323e6i		−	0.0786044i
$976$	−1.42077e7			−0.477419
$977$		−	4.64168e7i		−	1.55575i	−0.628421	−	0.777873i	$-0.716299\pi$
$977$		−	4.64168e7i		−	1.55575i	0.628421	−	0.777873i	$-0.283701\pi$
$978$	3.76308e7			1.25805
$979$	−3.47337e7			−1.15823
$980$			7.14694e7i			2.37714i
$981$	1.48996e7			0.494313
$982$	−9.31064e6			−0.308107
$983$		−	2.72607e7i		−	0.899815i	−0.893075	−	0.449907i	$-0.851457\pi$
$983$		−	2.72607e7i		−	0.899815i	0.893075	−	0.449907i	$-0.148543\pi$
$984$		−	2.72397e7i		−	0.896840i
$985$			2.29526e7i			0.753774i
$986$	3.71147e7			1.21577
$987$		−	4.16640e7i		−	1.36135i
$988$	9.10778e7			2.96838
$989$			3.33423e7i			1.08394i
$990$			1.15650e8i			3.75022i
$991$		−	2.17415e7i		−	0.703243i	−0.936142	−	0.351622i	$-0.885630\pi$
$991$		−	2.17415e7i		−	0.703243i	0.936142	−	0.351622i	$-0.114370\pi$
$992$	527082.			0.0170059
$993$			8.03662e7i			2.58643i
$994$	1.01092e7			0.324528
$995$	−4.76361e7			−1.52538
$996$			4.80572e7i			1.53501i
$997$	1.21628e7			0.387520			0.193760	−	0.981049i	$-0.437932\pi$
$997$	1.21628e7			0.387520			0.193760	+	0.981049i	$0.437932\pi$
$998$		−	3.27589e7i		−	1.04113i
$999$			1.68075e7i			0.532831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.b.a.96.37	✓	40
97.96	even	2	inner	97.6.b.a.96.38	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.b.a.96.37	✓	40	1.1	even	1	trivial
97.6.b.a.96.38	yes	40	97.96	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+9.70046 q^{2} +23.5635 q^{3} +62.0990 q^{4} -57.7401i q^{5} +228.576 q^{6} +191.675i q^{7} +291.974 q^{8} +312.237 q^{9} -560.105i q^{10} -661.288 q^{11} +1463.27 q^{12} +473.965i q^{13} +1859.34i q^{14} -1360.56i q^{15} +845.113 q^{16} -1307.89i q^{17} +3028.84 q^{18} -3094.44i q^{19} -3585.60i q^{20} +4516.53i q^{21} -6414.80 q^{22} +1653.86i q^{23} +6879.91 q^{24} -208.916 q^{25} +4597.68i q^{26} +1631.46 q^{27} +11902.8i q^{28} +2925.37i q^{29} -13198.0i q^{30} -460.266 q^{31} -1145.17 q^{32} -15582.2 q^{33} -12687.2i q^{34} +11067.3 q^{35} +19389.6 q^{36} +10302.1i q^{37} -30017.5i q^{38} +11168.3i q^{39} -16858.6i q^{40} -3959.31i q^{41} +43812.4i q^{42} +20160.3 q^{43} -41065.3 q^{44} -18028.6i q^{45} +16043.2i q^{46} -9224.79 q^{47} +19913.8 q^{48} -19932.3 q^{49} -2026.59 q^{50} -30818.5i q^{51} +29432.8i q^{52} +35934.2 q^{53} +15825.9 q^{54} +38182.8i q^{55} +55964.1i q^{56} -72915.6i q^{57} +28377.4i q^{58} -23510.3i q^{59} -84489.1i q^{60} -16811.6 q^{61} -4464.79 q^{62} +59848.0i q^{63} -38152.3 q^{64} +27366.8 q^{65} -151155. q^{66} +46073.4i q^{67} -81218.8i q^{68} +38970.6i q^{69} +107358. q^{70} -5437.01i q^{71} +91165.0 q^{72} -27269.3 q^{73} +99935.2i q^{74} -4922.79 q^{75} -192161. i q^{76} -126752. i q^{77} +108337. i q^{78} +38189.3 q^{79} -48796.9i q^{80} -37430.7 q^{81} -38407.1i q^{82} +32842.4i q^{83} +280472. i q^{84} -75517.8 q^{85} +195565. q^{86} +68931.9i q^{87} -193079. q^{88} +52524.4 q^{89} -174886. i q^{90} -90847.3 q^{91} +102703. i q^{92} -10845.5 q^{93} -89484.7 q^{94} -178673. q^{95} -26984.2 q^{96} +(-92272.9 - 8546.86i) q^{97} -193353. q^{98} -206479. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 40 q^{3} + 638 q^{4} - 130 q^{6} + 180 q^{8} + 3300 q^{9} + 382 q^{11} + 2586 q^{12} + 10174 q^{16} + 4738 q^{18} + 1996 q^{22} - 3102 q^{24} - 25178 q^{25} + 3046 q^{27} + 14796 q^{31}+ \cdots - 562238 q^{99}+O(q^{100}) \) 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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