LMFDB - Embedded newform 3.24.a.b.1.1

Newspace parameters

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$10.0561211204$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{530401}) $
Defining polynomial:	$ x^{2} - x - 132600 $ x^2 - x - 132600
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$364.643$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

$f(q)$	$=$	$q-2805.86 q^{2} -177147. q^{3} -515763. q^{4} -1.60439e8 q^{5} +4.97050e8 q^{6} -8.06460e9 q^{7} +2.49844e10 q^{8} +3.13811e10 q^{9} +O(q^{10})$	\(q-2805.86 q^{2} -177147. q^{3} -515763. q^{4} -1.60439e8 q^{5} +4.97050e8 q^{6} -8.06460e9 q^{7} +2.49844e10 q^{8} +3.13811e10 q^{9} +4.50169e11 q^{10} +4.37600e11 q^{11} +9.13659e10 q^{12} +2.40244e12 q^{13} +2.26281e13 q^{14} +2.84212e13 q^{15} -6.57762e13 q^{16} -7.22389e13 q^{17} -8.80508e13 q^{18} -7.65478e14 q^{19} +8.27484e13 q^{20} +1.42862e15 q^{21} -1.22785e15 q^{22} +5.30922e15 q^{23} -4.42591e15 q^{24} +1.38197e16 q^{25} -6.74091e15 q^{26} -5.55906e15 q^{27} +4.15942e15 q^{28} +3.30401e16 q^{29} -7.97460e16 q^{30} -1.91705e17 q^{31} -2.50257e16 q^{32} -7.75196e16 q^{33} +2.02692e17 q^{34} +1.29387e18 q^{35} -1.61852e16 q^{36} -1.19466e18 q^{37} +2.14782e18 q^{38} -4.25585e17 q^{39} -4.00847e18 q^{40} -1.08195e18 q^{41} -4.00851e18 q^{42} +9.41608e18 q^{43} -2.25698e17 q^{44} -5.03474e18 q^{45} -1.48969e19 q^{46} +1.46134e19 q^{47} +1.16521e19 q^{48} +3.76691e19 q^{49} -3.87760e19 q^{50} +1.27969e19 q^{51} -1.23909e18 q^{52} +3.45534e19 q^{53} +1.55979e19 q^{54} -7.02081e19 q^{55} -2.01489e20 q^{56} +1.35602e20 q^{57} -9.27060e19 q^{58} -2.65574e20 q^{59} -1.46586e19 q^{60} +5.20374e20 q^{61} +5.37898e20 q^{62} -2.53076e20 q^{63} +6.21989e20 q^{64} -3.85445e20 q^{65} +2.17509e20 q^{66} -3.34691e20 q^{67} +3.72581e19 q^{68} -9.40513e20 q^{69} -3.63043e21 q^{70} +1.99393e21 q^{71} +7.84037e20 q^{72} +2.19877e20 q^{73} +3.35204e21 q^{74} -2.44811e21 q^{75} +3.94805e20 q^{76} -3.52907e21 q^{77} +1.19413e21 q^{78} -3.54687e20 q^{79} +1.05531e22 q^{80} +9.84771e20 q^{81} +3.03580e21 q^{82} -4.81732e21 q^{83} -7.36829e20 q^{84} +1.15899e22 q^{85} -2.64202e22 q^{86} -5.85296e21 q^{87} +1.09332e22 q^{88} -3.80894e22 q^{89} +1.41268e22 q^{90} -1.93747e22 q^{91} -2.73830e21 q^{92} +3.39600e22 q^{93} -4.10032e22 q^{94} +1.22812e23 q^{95} +4.43322e21 q^{96} +9.60308e22 q^{97} -1.05694e23 q^{98} +1.37324e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9}+O(q^{10}) $ 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9	$ 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9} + 627869790180 q^{10} + 1468972366488 q^{11} + 1144142163252 q^{12} + 10491654264748 q^{13} + 34908555004416 q^{14} + 8292042036540 q^{15} - 50973150676720 q^{16} - 210888011520828 q^{17} - 38975276034378 q^{18} - 907382448537944 q^{19} - 592549041758760 q^{20} + 37548769701888 q^{21} + 385075304370504 q^{22} + 10\!\cdots\!12 q^{23}+ \cdots + 46\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9 + 627869790180 * q^10 + 1468972366488 * q^11 + 1144142163252 * q^12 + 10491654264748 * q^13 + 34908555004416 * q^14 + 8292042036540 * q^15 - 50973150676720 * q^16 - 210888011520828 * q^17 - 38975276034378 * q^18 - 907382448537944 * q^19 - 592549041758760 * q^20 + 37548769701888 * q^21 + 385075304370504 * q^22 + 10116923323892112 * q^23 - 455598880577352 * q^24 + 14810505797591150 * q^25 + 5909481699569604 * q^26 - 11118121133111046 * q^27 - 42508434042586112 * q^28 + 18478753545176892 * q^29 - 111225249721016460 * q^30 - 272793622592745488 * q^31 + 186134219136906336 * q^32 - 260224047806249736 * q^33 - 14135605903588212 * q^34 + 2186169652458823680 * q^35 - 202681351793602044 * q^36 - 478995036787364 * q^37 + 1925903087124629112 * q^38 - 1858565078037313956 * q^39 - 6555203866715785200 * q^40 + 5555714961308771412 * q^41 - 6183945793367281152 * q^42 - 1198322147609320040 * q^43 - 6355093136294718288 * q^44 - 1468910370646951380 * q^45 - 7378368693556745808 * q^46 + 26308565672855777280 * q^47 + 9029740722928917840 * q^48 + 71964232849356271890 * q^49 - 37226516336176411350 * q^50 + 37358178576880117716 * q^51 - 49312907988586886888 * q^52 - 41127501899415224628 * q^53 + 6904353223661959566 * q^54 + 46986672525187689360 * q^55 - 377486892221258373120 * q^56 + 160740078611151165768 * q^57 - 115477922638933597836 * q^58 - 307537061909444286696 * q^59 + 104968285100439057720 * q^60 + 594961179098503751020 * q^61 + 411087431199774869712 * q^62 - 6651651906380353536 * q^63 + 828036632782207954496 * q^64 + 533732415162776445960 * q^65 - 68214934943321672088 * q^66 - 1630225825126993264088 * q^67 + 861243436942941889224 * q^68 - 1792182616057515964464 * q^69 - 2235006928450834744320 * q^70 - 383942598581649272976 * q^71 + 80707974897636174744 * q^72 - 2812202351440561692428 * q^73 + 5219558875357315020756 * q^74 - 2623636670525879449050 * q^75 + 1238138884710050927056 * q^76 + 4569917579124061519872 * q^77 - 1046846954633656639788 * q^78 + 21069388575313284880 * q^79 + 12235121810092022582880 * q^80 + 1969541804367222465762 * q^81 + 13416177399661303790652 * q^82 - 14817262080324402696024 * q^83 + 7530241565342001982464 * q^84 - 4164778183840982876520 * q^85 - 43019621516128896935352 * q^86 - 3273455754267450887124 * q^87 - 12182478384106427357664 * q^88 - 43449805260884456557164 * q^89 + 19703219312328902839620 * q^90 + 44146945026523904417792 * q^91 - 31310234209098260658144 * q^92 + 48324571861437084962736 * q^93 - 22713687421447503614976 * q^94 + 106687644602844474428400 * q^95 - 32973118517445546703392 * q^96 + 107136573045242168450692 * q^97 - 52061241480597067368618 * q^98 + 46097909396733721983192 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2805.86	−0.968770	−0.484385	−	0.874855i	$-0.660957\pi$
$2$	−2805.86	−0.968770	−0.484385	+	0.874855i	$0.660957\pi$
$3$	−177147.	−0.577350
$3$	−177147.	−0.577350
$4$	−515763.	−0.0614838
$5$	−1.60439e8	−1.46945	−0.734724	−	0.678366i	$-0.762688\pi$
$5$	−1.60439e8	−1.46945	−0.734724	+	0.678366i	$0.762688\pi$
$6$	4.97050e8	0.559320
$7$	−8.06460e9	−1.54154	−0.770771	−	0.637112i	$-0.780129\pi$
$7$	−8.06460e9	−1.54154	−0.770771	+	0.637112i	$0.780129\pi$
$8$	2.49844e10	1.02833
$9$	3.13811e10	0.333333
$10$	4.50169e11	1.42356
$11$	4.37600e11	0.462447	0.231223	−	0.972901i	$-0.425727\pi$
$11$	4.37600e11	0.462447	0.231223	+	0.972901i	$0.425727\pi$
$12$	9.13659e10	0.0354977
$13$	2.40244e12	0.371795	0.185898	−	0.982569i	$-0.440481\pi$
$13$	2.40244e12	0.371795	0.185898	+	0.982569i	$0.440481\pi$
$14$	2.26281e13	1.49340
$15$	2.84212e13	0.848386
$16$	−6.57762e13	−0.934736
$17$	−7.22389e13	−0.511221	−0.255610	−	0.966780i	$-0.582276\pi$
$17$	−7.22389e13	−0.511221	−0.255610	+	0.966780i	$0.582276\pi$
$18$	−8.80508e13	−0.322923
$19$	−7.65478e14	−1.50753	−0.753765	−	0.657144i	$-0.771764\pi$
$19$	−7.65478e14	−1.50753	−0.753765	+	0.657144i	$0.771764\pi$
$20$	8.27484e13	0.0903472
$21$	1.42862e15	0.890010
$22$	−1.22785e15	−0.448005
$23$	5.30922e15	1.16188	0.580940	−	0.813947i	$-0.302685\pi$
$23$	5.30922e15	1.16188	0.580940	+	0.813947i	$0.302685\pi$
$24$	−4.42591e15	−0.593709
$25$	1.38197e16	1.15928
$26$	−6.74091e15	−0.360184
$27$	−5.55906e15	−0.192450
$28$	4.15942e15	0.0947798
$29$	3.30401e16	0.502881	0.251440	−	0.967873i	$-0.419096\pi$
$29$	3.30401e16	0.502881	0.251440	+	0.967873i	$0.419096\pi$
$30$	−7.97460e16	−0.821892
$31$	−1.91705e17	−1.35511	−0.677555	−	0.735472i	$-0.736961\pi$
$31$	−1.91705e17	−1.35511	−0.677555	+	0.735472i	$0.736961\pi$
$32$	−2.50257e16	−0.122789
$33$	−7.75196e16	−0.266994
$34$	2.02692e17	0.495255
$35$	1.29387e18	2.26522
$36$	−1.61852e16	−0.0204946
$37$	−1.19466e18	−1.10388	−0.551941	−	0.833883i	$-0.686113\pi$
$37$	−1.19466e18	−1.10388	−0.551941	+	0.833883i	$0.686113\pi$
$38$	2.14782e18	1.46045
$39$	−4.25585e17	−0.214656
$40$	−4.00847e18	−1.51108
$41$	−1.08195e18	−0.307039	−0.153519	−	0.988146i	$-0.549061\pi$
$41$	−1.08195e18	−0.307039	−0.153519	+	0.988146i	$0.549061\pi$
$42$	−4.00851e18	−0.862215
$43$	9.41608e18	1.54519	0.772597	−	0.634897i	$-0.218957\pi$
$43$	9.41608e18	1.54519	0.772597	+	0.634897i	$0.218957\pi$
$44$	−2.25698e17	−0.0284330
$45$	−5.03474e18	−0.489816
$46$	−1.48969e19	−1.12559
$47$	1.46134e19	0.862237	0.431119	−	0.902295i	$-0.358119\pi$
$47$	1.46134e19	0.862237	0.431119	+	0.902295i	$0.358119\pi$
$48$	1.16521e19	0.539670
$49$	3.76691e19	1.37635
$50$	−3.87760e19	−1.12307
$51$	1.27969e19	0.295153
$52$	−1.23909e18	−0.0228594
$53$	3.45534e19	0.512058	0.256029	−	0.966669i	$-0.417586\pi$
$53$	3.45534e19	0.512058	0.256029	+	0.966669i	$0.417586\pi$
$54$	1.55979e19	0.186440
$55$	−7.02081e19	−0.679542
$56$	−2.01489e20	−1.58522
$57$	1.35602e20	0.870373
$58$	−9.27060e19	−0.487176
$59$	−2.65574e20	−1.14654	−0.573268	−	0.819368i	$-0.694325\pi$
$59$	−2.65574e20	−1.14654	−0.573268	+	0.819368i	$0.694325\pi$
$60$	−1.46586e19	−0.0521620
$61$	5.20374e20	1.53117	0.765584	−	0.643336i	$-0.222450\pi$
$61$	5.20374e20	1.53117	0.765584	+	0.643336i	$0.222450\pi$
$62$	5.37898e20	1.31279
$63$	−2.53076e20	−0.513847
$64$	6.21989e20	1.05369
$65$	−3.85445e20	−0.546334
$66$	2.17509e20	0.258656
$67$	−3.34691e20	−0.334799	−0.167399	−	0.985889i	$-0.553537\pi$
$67$	−3.34691e20	−0.334799	−0.167399	+	0.985889i	$0.553537\pi$
$68$	3.72581e19	0.0314318
$69$	−9.40513e20	−0.670811
$70$	−3.63043e21	−2.19448
$71$	1.99393e21	1.02386	0.511928	−	0.859028i	$-0.328931\pi$
$71$	1.99393e21	1.02386	0.511928	+	0.859028i	$0.328931\pi$
$72$	7.84037e20	0.342778
$73$	2.19877e20	0.0820290	0.0410145	−	0.999159i	$-0.486941\pi$
$73$	2.19877e20	0.0820290	0.0410145	+	0.999159i	$0.486941\pi$
$74$	3.35204e21	1.06941
$75$	−2.44811e21	−0.669309
$76$	3.94805e20	0.0926886
$77$	−3.52907e21	−0.712881
$78$	1.19413e21	0.207953
$79$	−3.54687e20	−0.0533498	−0.0266749	−	0.999644i	$-0.508492\pi$
$79$	−3.54687e20	−0.0533498	−0.0266749	+	0.999644i	$0.508492\pi$
$80$	1.05531e22	1.37355
$81$	9.84771e20	0.111111
$82$	3.03580e21	0.297450
$83$	−4.81732e21	−0.410589	−0.205295	−	0.978700i	$-0.565815\pi$
$83$	−4.81732e21	−0.410589	−0.205295	+	0.978700i	$0.565815\pi$
$84$	−7.36829e20	−0.0547211
$85$	1.15899e22	0.751212
$86$	−2.64202e22	−1.49694
$87$	−5.85296e21	−0.290338
$88$	1.09332e22	0.475550
$89$	−3.80894e22	−1.45485	−0.727426	−	0.686186i	$-0.759284\pi$
$89$	−3.80894e22	−1.45485	−0.727426	+	0.686186i	$0.759284\pi$
$90$	1.41268e22	0.474519
$91$	−1.93747e22	−0.573138
$92$	−2.73830e21	−0.0714367
$93$	3.39600e22	0.782373
$94$	−4.10032e22	−0.835310
$95$	1.22812e23	2.21524
$96$	4.43322e21	0.0708925
$97$	9.60308e22	1.36312	0.681562	−	0.731760i	$-0.261301\pi$
$97$	9.60308e22	1.36312	0.681562	+	0.731760i	$0.261301\pi$
$98$	−1.05694e23	−1.33337
$99$	1.37324e22	0.154149
$100$	−7.12768e21	−0.0712768
$101$	1.42212e22	0.126835	0.0634176	−	0.997987i	$-0.479800\pi$
$101$	1.42212e22	0.126835	0.0634176	+	0.997987i	$0.479800\pi$
$102$	−3.59063e22	−0.285936
$103$	−8.52949e22	−0.607149	−0.303574	−	0.952808i	$-0.598180\pi$
$103$	−8.52949e22	−0.607149	−0.303574	+	0.952808i	$0.598180\pi$
$104$	6.00236e22	0.382330
$105$	−2.29206e23	−1.30782
$106$	−9.69521e22	−0.496066
$107$	6.63340e21	0.0304665	0.0152333	−	0.999884i	$-0.495151\pi$
$107$	6.63340e21	0.0304665	0.0152333	+	0.999884i	$0.495151\pi$
$108$	2.86716e21	0.0118326
$109$	−6.22821e22	−0.231184	−0.115592	−	0.993297i	$-0.536877\pi$
$109$	−6.22821e22	−0.231184	−0.115592	+	0.993297i	$0.536877\pi$
$110$	1.96994e23	0.658320
$111$	2.11630e23	0.637327
$112$	5.30459e23	1.44094
$113$	2.16525e23	0.531015	0.265508	−	0.964109i	$-0.414460\pi$
$113$	2.16525e23	0.531015	0.265508	+	0.964109i	$0.414460\pi$
$114$	−3.80480e23	−0.843192
$115$	−8.51805e23	−1.70732
$116$	−1.70409e22	−0.0309190
$117$	7.53911e22	0.123932
$118$	7.45164e23	1.11073
$119$	5.82578e23	0.788068
$120$	7.10088e23	0.872425
$121$	−7.03936e23	−0.786143
$122$	−1.46010e24	−1.48335
$123$	1.91664e23	0.177269
$124$	9.88745e22	0.0833173
$125$	−3.04632e23	−0.234051
$126$	7.10095e23	0.497800
$127$	−3.88241e23	−0.248518	−0.124259	−	0.992250i	$-0.539655\pi$
$127$	−3.88241e23	−0.248518	−0.124259	+	0.992250i	$0.539655\pi$
$128$	−1.53528e24	−0.897995
$129$	−1.66803e24	−0.892118
$130$	1.08150e24	0.529272
$131$	−2.29586e24	−1.02879	−0.514394	−	0.857554i	$-0.671983\pi$
$131$	−2.29586e24	−1.02879	−0.514394	+	0.857554i	$0.671983\pi$
$132$	3.99817e22	0.0164158
$133$	6.17327e24	2.32392
$134$	9.39095e23	0.324343
$135$	8.91889e23	0.282795
$136$	−1.80485e24	−0.525706
$137$	5.74414e24	1.53794	0.768968	−	0.639287i	$-0.220770\pi$
$137$	5.74414e24	1.53794	0.768968	+	0.639287i	$0.220770\pi$
$138$	2.63895e24	0.649862
$139$	−3.37226e24	−0.764278	−0.382139	−	0.924105i	$-0.624812\pi$
$139$	−3.37226e24	−0.764278	−0.382139	+	0.924105i	$0.624812\pi$
$140$	−6.67333e23	−0.139274
$141$	−2.58873e24	−0.497813
$142$	−5.59469e24	−0.991882
$143$	1.05131e24	0.171936
$144$	−2.06413e24	−0.311579
$145$	−5.30092e24	−0.738957
$146$	−6.16945e23	−0.0794673
$147$	−6.67296e24	−0.794638
$148$	6.16159e23	0.0678708
$149$	1.40559e25	1.43290	0.716451	−	0.697637i	$-0.245765\pi$
$149$	1.40559e25	1.43290	0.716451	+	0.697637i	$0.245765\pi$
$150$	6.86906e24	0.648407
$151$	−5.05826e24	−0.442350	−0.221175	−	0.975234i	$-0.570989\pi$
$151$	−5.05826e24	−0.442350	−0.221175	+	0.975234i	$0.570989\pi$
$152$	−1.91250e25	−1.55024
$153$	−2.26693e24	−0.170407
$154$	9.90208e24	0.690619
$155$	3.07570e25	1.99126
$156$	2.19501e23	0.0131979
$157$	9.65397e24	0.539337	0.269668	−	0.962953i	$-0.413086\pi$
$157$	9.65397e24	0.539337	0.269668	+	0.962953i	$0.413086\pi$
$158$	9.95200e23	0.0516838
$159$	−6.12104e24	−0.295637
$160$	4.01509e24	0.180433
$161$	−4.28168e25	−1.79109
$162$	−2.76313e24	−0.107641
$163$	1.70611e25	0.619225	0.309613	−	0.950863i	$-0.399801\pi$
$163$	1.70611e25	0.619225	0.309613	+	0.950863i	$0.399801\pi$
$164$	5.58031e23	0.0188779
$165$	1.24371e25	0.392334
$166$	1.35167e25	0.397767
$167$	−4.07224e25	−1.11839	−0.559195	−	0.829036i	$-0.688890\pi$
$167$	−4.07224e25	−1.11839	−0.559195	+	0.829036i	$0.688890\pi$
$168$	3.56932e25	0.915228
$169$	−3.59822e25	−0.861768
$170$	−3.25197e25	−0.727752
$171$	−2.40215e25	−0.502510
$172$	−4.85647e24	−0.0950043
$173$	8.85089e25	1.61978	0.809891	−	0.586580i	$-0.199526\pi$
$173$	8.85089e25	1.61978	0.809891	+	0.586580i	$0.199526\pi$
$174$	1.64226e25	0.281271
$175$	−1.11450e26	−1.78708
$176$	−2.87837e25	−0.432266
$177$	4.70457e25	0.661953
$178$	1.06873e26	1.40942
$179$	−5.75965e25	−0.712174	−0.356087	−	0.934453i	$-0.615889\pi$
$179$	−5.75965e25	−0.712174	−0.356087	+	0.934453i	$0.615889\pi$
$180$	2.59673e24	0.0301157
$181$	5.86096e25	0.637771	0.318886	−	0.947793i	$-0.396691\pi$
$181$	5.86096e25	0.637771	0.318886	+	0.947793i	$0.396691\pi$
$182$	5.43627e25	0.555240
$183$	−9.21827e25	−0.884020
$184$	1.32648e26	1.19480
$185$	1.91669e26	1.62210
$186$	−9.52870e25	−0.757940
$187$	−3.16118e25	−0.236412
$188$	−7.53707e24	−0.0530136
$189$	4.48316e25	0.296670
$190$	−3.44594e26	−2.14606
$191$	−4.89385e25	−0.286924	−0.143462	−	0.989656i	$-0.545823\pi$
$191$	−4.89385e25	−0.286924	−0.143462	+	0.989656i	$0.545823\pi$
$192$	−1.10184e26	−0.608349
$193$	−4.30761e25	−0.224041	−0.112021	−	0.993706i	$-0.535732\pi$
$193$	−4.30761e25	−0.224041	−0.112021	+	0.993706i	$0.535732\pi$
$194$	−2.69449e26	−1.32055
$195$	6.82803e25	0.315426
$196$	−1.94283e25	−0.0846233
$197$	2.77750e26	1.14102	0.570509	−	0.821291i	$-0.306746\pi$
$197$	2.77750e26	1.14102	0.570509	+	0.821291i	$0.306746\pi$
$198$	−3.85311e25	−0.149335
$199$	2.40263e26	0.878774	0.439387	−	0.898298i	$-0.355196\pi$
$199$	2.40263e26	0.878774	0.439387	+	0.898298i	$0.355196\pi$
$200$	3.45276e26	1.19213
$201$	5.92895e25	0.193296
$202$	−3.99026e25	−0.122874
$203$	−2.66456e26	−0.775212
$204$	−6.60017e24	−0.0181471
$205$	1.73587e26	0.451178
$206$	2.39326e26	0.588188
$207$	1.66609e26	0.387293
$208$	−1.58023e26	−0.347531
$209$	−3.34973e26	−0.697153
$210$	6.43120e26	1.26698
$211$	−3.16141e26	−0.589703	−0.294851	−	0.955543i	$-0.595270\pi$
$211$	−3.16141e26	−0.589703	−0.294851	+	0.955543i	$0.595270\pi$
$212$	−1.78214e25	−0.0314832
$213$	−3.53219e26	−0.591124
$214$	−1.86124e25	−0.0295151
$215$	−1.51070e27	−2.27058
$216$	−1.38890e26	−0.197903
$217$	1.54603e27	2.08896
$218$	1.74755e26	0.223965
$219$	−3.89506e25	−0.0473595
$220$	3.62107e25	0.0417808
$221$	−1.73550e26	−0.190069
$222$	−5.93803e26	−0.617423
$223$	−4.77095e26	−0.471084	−0.235542	−	0.971864i	$-0.575687\pi$
$223$	−4.77095e26	−0.471084	−0.235542	+	0.971864i	$0.575687\pi$
$224$	2.01822e26	0.189285
$225$	4.33676e26	0.386426
$226$	−6.07540e26	−0.514432
$227$	−4.56159e26	−0.367129	−0.183565	−	0.983008i	$-0.558764\pi$
$227$	−4.56159e26	−0.367129	−0.183565	+	0.983008i	$0.558764\pi$
$228$	−6.99385e25	−0.0535138
$229$	1.36743e26	0.0994942	0.0497471	−	0.998762i	$-0.484158\pi$
$229$	1.36743e26	0.0994942	0.0497471	+	0.998762i	$0.484158\pi$
$230$	2.39005e27	1.65400
$231$	6.25165e26	0.411582
$232$	8.25488e26	0.517129
$233$	1.01159e27	0.603130	0.301565	−	0.953446i	$-0.402491\pi$
$233$	1.01159e27	0.603130	0.301565	+	0.953446i	$0.402491\pi$
$234$	−2.11537e26	−0.120061
$235$	−2.34456e27	−1.26701
$236$	1.36973e26	0.0704934
$237$	6.28317e25	0.0308015
$238$	−1.63463e27	−0.763457
$239$	2.91639e27	1.29799	0.648993	−	0.760794i	$-0.275190\pi$
$239$	2.91639e27	1.29799	0.648993	+	0.760794i	$0.275190\pi$
$240$	−1.86944e27	−0.793017
$241$	1.34542e27	0.544079	0.272039	−	0.962286i	$-0.412302\pi$
$241$	1.34542e27	0.544079	0.272039	+	0.962286i	$0.412302\pi$
$242$	1.97515e27	0.761592
$243$	−1.74449e26	−0.0641500
$244$	−2.68390e26	−0.0941419
$245$	−6.04358e27	−2.02248
$246$	−5.37783e26	−0.171733
$247$	−1.83901e27	−0.560493
$248$	−4.78964e27	−1.39351
$249$	8.53374e26	0.237054
$250$	8.54753e26	0.226741
$251$	3.42333e27	0.867363	0.433681	−	0.901066i	$-0.357214\pi$
$251$	3.42333e27	0.867363	0.433681	+	0.901066i	$0.357214\pi$
$252$	1.30527e26	0.0315933
$253$	2.32332e27	0.537307
$254$	1.08935e27	0.240757
$255$	−2.05312e27	−0.433713
$256$	−9.09835e26	−0.183740
$257$	3.47997e27	0.671962	0.335981	−	0.941869i	$-0.390932\pi$
$257$	3.47997e27	0.671962	0.335981	+	0.941869i	$0.390932\pi$
$258$	4.68026e27	0.864258
$259$	9.63442e27	1.70168
$260$	1.98798e26	0.0335907
$261$	1.03683e27	0.167627
$262$	6.44187e27	0.996660
$263$	−7.94565e27	−1.17663	−0.588313	−	0.808634i	$-0.700208\pi$
$263$	−7.94565e27	−1.17663	−0.588313	+	0.808634i	$0.700208\pi$
$264$	−1.93678e27	−0.274559
$265$	−5.54371e27	−0.752442
$266$	−1.73213e28	−2.25135
$267$	6.74742e27	0.839959
$268$	1.72621e26	0.0205847
$269$	8.25439e27	0.943048	0.471524	−	0.881853i	$-0.343704\pi$
$269$	8.25439e27	0.943048	0.471524	+	0.881853i	$0.343704\pi$
$270$	−2.50251e27	−0.273964
$271$	−1.26880e28	−1.33120	−0.665602	−	0.746307i	$-0.731825\pi$
$271$	−1.26880e28	−1.33120	−0.665602	+	0.746307i	$0.731825\pi$
$272$	4.75160e27	0.477856
$273$	3.43217e27	0.330902
$274$	−1.61172e28	−1.48991
$275$	6.04749e27	0.536104
$276$	4.85082e26	0.0412440
$277$	−9.00378e27	−0.734358	−0.367179	−	0.930150i	$-0.619676\pi$
$277$	−9.00378e27	−0.734358	−0.367179	+	0.930150i	$0.619676\pi$
$278$	9.46209e27	0.740410
$279$	−6.01592e27	−0.451703
$280$	3.23267e28	2.32940
$281$	−1.44072e28	−0.996454	−0.498227	−	0.867047i	$-0.666015\pi$
$281$	−1.44072e28	−0.996454	−0.498227	+	0.867047i	$0.666015\pi$
$282$	7.26360e27	0.482267
$283$	1.15566e28	0.736692	0.368346	−	0.929689i	$-0.379924\pi$
$283$	1.15566e28	0.736692	0.368346	+	0.929689i	$0.379924\pi$
$284$	−1.02840e27	−0.0629505
$285$	−2.17558e28	−1.27897
$286$	−2.94982e27	−0.166566
$287$	8.72551e27	0.473313
$288$	−7.85332e26	−0.0409298
$289$	−1.47491e28	−0.738653
$290$	1.48736e28	0.715880
$291$	−1.70116e28	−0.787000
$292$	−1.13405e26	−0.00504345
$293$	4.02839e28	1.72248	0.861238	−	0.508201i	$-0.169689\pi$
$293$	4.02839e28	1.72248	0.861238	+	0.508201i	$0.169689\pi$
$294$	1.87234e28	0.769822
$295$	4.26084e28	1.68478
$296$	−2.98478e28	−1.13516
$297$	−2.43265e27	−0.0889979
$298$	−3.94389e28	−1.38815
$299$	1.27551e28	0.431981
$300$	1.26265e27	0.0411517
$301$	−7.59369e28	−2.38198
$302$	1.41928e28	0.428536
$303$	−2.51924e27	−0.0732283
$304$	5.03502e28	1.40914
$305$	−8.34882e28	−2.24997
$306$	6.36069e27	0.165085
$307$	3.90618e28	0.976475	0.488237	−	0.872711i	$-0.337640\pi$
$307$	3.90618e28	0.976475	0.488237	+	0.872711i	$0.337640\pi$
$308$	1.82017e27	0.0438306
$309$	1.51097e28	0.350537
$310$	−8.62997e28	−1.92908
$311$	9.65010e27	0.207868	0.103934	−	0.994584i	$-0.466857\pi$
$311$	9.65010e27	0.207868	0.103934	+	0.994584i	$0.466857\pi$
$312$	−1.06330e28	−0.220738
$313$	5.80452e28	1.16147	0.580733	−	0.814094i	$-0.302766\pi$
$313$	5.80452e28	1.16147	0.580733	+	0.814094i	$0.302766\pi$
$314$	−2.70877e28	−0.522494
$315$	4.06032e28	0.755072
$316$	1.82934e26	0.00328015
$317$	8.81588e28	1.52435	0.762174	−	0.647373i	$-0.224132\pi$
$317$	8.81588e28	1.52435	0.762174	+	0.647373i	$0.224132\pi$
$318$	1.71748e28	0.286404
$319$	1.44584e28	0.232556
$320$	−9.97912e28	−1.54834
$321$	−1.17509e27	−0.0175898
$322$	1.20138e29	1.73515
$323$	5.52972e28	0.770681
$324$	−5.07908e26	−0.00683153
$325$	3.32009e28	0.431014
$326$	−4.78709e28	−0.599887
$327$	1.10331e28	0.133474
$328$	−2.70319e28	−0.315739
$329$	−1.17852e29	−1.32918
$330$	−3.48969e28	−0.380081
$331$	−1.57171e29	−1.65329	−0.826646	−	0.562723i	$-0.809754\pi$
$331$	−1.57171e29	−1.65329	−0.826646	+	0.562723i	$0.809754\pi$
$332$	2.48460e27	0.0252446
$333$	−3.74896e28	−0.367961
$334$	1.14261e29	1.08346
$335$	5.36974e28	0.491969
$336$	−9.39692e28	−0.831924
$337$	−7.23440e28	−0.618954	−0.309477	−	0.950907i	$-0.600154\pi$
$337$	−7.23440e28	−0.618954	−0.309477	+	0.950907i	$0.600154\pi$
$338$	1.00961e29	0.834856
$339$	−3.83568e28	−0.306582
$340$	−5.97765e27	−0.0461873
$341$	−8.38903e28	−0.626667
$342$	6.74009e28	0.486817
$343$	−8.30679e28	−0.580164
$344$	2.35255e29	1.58898
$345$	1.50895e29	0.985722
$346$	−2.48343e29	−1.56920
$347$	2.40365e28	0.146921	0.0734603	−	0.997298i	$-0.476596\pi$
$347$	2.40365e28	0.146921	0.0734603	+	0.997298i	$0.476596\pi$
$348$	3.01874e27	0.0178511
$349$	2.63663e29	1.50854	0.754269	−	0.656566i	$-0.227992\pi$
$349$	2.63663e29	1.50854	0.754269	+	0.656566i	$0.227992\pi$
$350$	3.12713e29	1.73127
$351$	−1.33553e28	−0.0715521
$352$	−1.09512e28	−0.0567836
$353$	−5.21932e28	−0.261942	−0.130971	−	0.991386i	$-0.541809\pi$
$353$	−5.21932e28	−0.261942	−0.130971	+	0.991386i	$0.541809\pi$
$354$	−1.32004e29	−0.641281
$355$	−3.19904e29	−1.50450
$356$	1.96451e28	0.0894498
$357$	−1.03202e29	−0.454991
$358$	1.61608e29	0.689933
$359$	−1.93870e29	−0.801538	−0.400769	−	0.916179i	$-0.631257\pi$
$359$	−1.93870e29	−0.801538	−0.400769	+	0.916179i	$0.631257\pi$
$360$	−1.25790e29	−0.503695
$361$	3.28126e29	1.27265
$362$	−1.64450e29	−0.617854
$363$	1.24700e29	0.453880
$364$	9.99277e27	0.0352387
$365$	−3.52768e28	−0.120537
$366$	2.58652e29	0.856412
$367$	5.00067e29	1.60460	0.802302	−	0.596918i	$-0.203608\pi$
$367$	5.00067e29	1.60460	0.802302	+	0.596918i	$0.203608\pi$
$368$	−3.49221e29	−1.08605
$369$	−3.39528e28	−0.102346
$370$	−5.37796e29	−1.57144
$371$	−2.78660e29	−0.789359
$372$	−1.75153e28	−0.0481032
$373$	−5.08622e29	−1.35439	−0.677195	−	0.735804i	$-0.736805\pi$
$373$	−5.08622e29	−1.35439	−0.677195	+	0.735804i	$0.736805\pi$
$374$	8.86981e28	0.229029
$375$	5.39646e28	0.135129
$376$	3.65108e29	0.886668
$377$	7.93770e28	0.186969
$378$	−1.25791e29	−0.287405
$379$	3.25520e29	0.721483	0.360742	−	0.932666i	$-0.382524\pi$
$379$	3.25520e29	0.721483	0.360742	+	0.932666i	$0.382524\pi$
$380$	−6.33420e28	−0.136201
$381$	6.87757e28	0.143482
$382$	1.37314e29	0.277963
$383$	−3.64395e29	−0.715792	−0.357896	−	0.933761i	$-0.616506\pi$
$383$	−3.64395e29	−0.715792	−0.357896	+	0.933761i	$0.616506\pi$
$384$	2.71971e29	0.518458
$385$	5.66200e29	1.04754
$386$	1.20866e29	0.217044
$387$	2.95487e29	0.515065
$388$	−4.95291e28	−0.0838100
$389$	3.87947e29	0.637312	0.318656	−	0.947870i	$-0.396768\pi$
$389$	3.87947e29	0.637312	0.318656	+	0.947870i	$0.396768\pi$
$390$	−1.91585e29	−0.305576
$391$	−3.83532e29	−0.593977
$392$	9.41139e29	1.41535
$393$	4.06705e29	0.593971
$394$	−7.79327e29	−1.10538
$395$	5.69055e28	0.0783948
$396$	−7.08265e27	−0.00947766
$397$	−1.90170e29	−0.247202	−0.123601	−	0.992332i	$-0.539444\pi$
$397$	−1.90170e29	−0.247202	−0.123601	+	0.992332i	$0.539444\pi$
$398$	−6.74145e29	−0.851330
$399$	−1.09358e30	−1.34172
$400$	−9.09005e29	−1.08362
$401$	3.60649e29	0.417757	0.208879	−	0.977942i	$-0.433019\pi$
$401$	3.60649e29	0.417757	0.208879	+	0.977942i	$0.433019\pi$
$402$	−1.66358e29	−0.187259
$403$	−4.60561e29	−0.503824
$404$	−7.33476e27	−0.00779830
$405$	−1.57995e29	−0.163272
$406$	7.47637e29	0.751002
$407$	−5.22782e29	−0.510487
$408$	3.19723e29	0.303516
$409$	1.06335e30	0.981432	0.490716	−	0.871320i	$-0.336735\pi$
$409$	1.06335e30	0.981432	0.490716	+	0.871320i	$0.336735\pi$
$410$	−4.87060e29	−0.437088
$411$	−1.01756e30	−0.887928
$412$	4.39920e28	0.0373298
$413$	2.14175e30	1.76744
$414$	−4.67482e29	−0.375198
$415$	7.72885e29	0.603339
$416$	−6.01227e28	−0.0456526
$417$	5.97386e29	0.441256
$418$	9.39888e29	0.675381
$419$	1.01398e29	0.0708874	0.0354437	−	0.999372i	$-0.488716\pi$
$419$	1.01398e29	0.0708874	0.0354437	+	0.999372i	$0.488716\pi$
$420$	1.18216e29	0.0804099
$421$	−1.31228e30	−0.868523	−0.434262	−	0.900787i	$-0.642991\pi$
$421$	−1.31228e30	−0.868523	−0.434262	+	0.900787i	$0.642991\pi$
$422$	8.87048e29	0.571287
$423$	4.58585e29	0.287412
$424$	8.63297e29	0.526566
$425$	−9.98317e29	−0.592647
$426$	9.91082e29	0.572663
$427$	−4.19661e30	−2.36036
$428$	−3.42126e27	−0.00187320
$429$	−1.86236e29	−0.0992671
$430$	4.23882e30	2.19967
$431$	2.07677e30	1.04930	0.524649	−	0.851319i	$-0.324197\pi$
$431$	2.07677e30	1.04930	0.524649	+	0.851319i	$0.324197\pi$
$432$	3.65654e29	0.179890
$433$	−3.77508e30	−1.80849	−0.904243	−	0.427019i	$-0.859564\pi$
$433$	−3.77508e30	−1.80849	−0.904243	+	0.427019i	$0.859564\pi$
$434$	−4.33793e30	−2.02372
$435$	9.39042e29	0.426637
$436$	3.21228e28	0.0142141
$437$	−4.06409e30	−1.75157
$438$	1.09290e29	0.0458805
$439$	1.39779e30	0.571609	0.285805	−	0.958288i	$-0.407739\pi$
$439$	1.39779e30	0.571609	0.285805	+	0.958288i	$0.407739\pi$
$440$	−1.75411e30	−0.698796
$441$	1.18209e30	0.458784
$442$	4.86956e29	0.184134
$443$	4.24438e30	1.56376	0.781882	−	0.623426i	$-0.214260\pi$
$443$	4.24438e30	1.56376	0.781882	+	0.623426i	$0.214260\pi$
$444$	−1.09151e29	−0.0391852
$445$	6.11101e30	2.13783
$446$	1.33866e30	0.456373
$447$	−2.48996e30	−0.827287
$448$	−5.01610e30	−1.62431
$449$	−3.75377e30	−1.18477	−0.592386	−	0.805654i	$-0.701814\pi$
$449$	−3.75377e30	−1.18477	−0.592386	+	0.805654i	$0.701814\pi$
$450$	−1.21683e30	−0.374358
$451$	−4.73462e29	−0.141989
$452$	−1.11676e29	−0.0326488
$453$	8.96055e29	0.255391
$454$	1.27992e30	0.355664
$455$	3.10846e30	0.842197
$456$	3.38794e30	0.895034
$457$	−4.50794e29	−0.116129	−0.0580646	−	0.998313i	$-0.518493\pi$
$457$	−4.50794e29	−0.116129	−0.0580646	+	0.998313i	$0.518493\pi$
$458$	−3.83682e29	−0.0963870
$459$	4.01580e29	0.0983845
$460$	4.39330e29	0.104972
$461$	3.64054e30	0.848410	0.424205	−	0.905566i	$-0.360554\pi$
$461$	3.64054e30	0.848410	0.424205	+	0.905566i	$0.360554\pi$
$462$	−1.75412e30	−0.398729
$463$	7.58411e30	1.68160	0.840801	−	0.541345i	$-0.182085\pi$
$463$	7.58411e30	1.68160	0.840801	+	0.541345i	$0.182085\pi$
$464$	−2.17325e30	−0.470061
$465$	−5.44850e30	−1.14966
$466$	−2.83837e30	−0.584294
$467$	−4.97036e29	−0.0998259	−0.0499130	−	0.998754i	$-0.515894\pi$
$467$	−4.97036e29	−0.0998259	−0.0499130	+	0.998754i	$0.515894\pi$
$468$	−3.88840e28	−0.00761979
$469$	2.69915e30	0.516106
$470$	6.57851e30	1.22744
$471$	−1.71017e30	−0.311386
$472$	−6.63522e30	−1.17902
$473$	4.12048e30	0.714570
$474$	−1.76297e29	−0.0298396
$475$	−1.05786e31	−1.74765
$476$	−3.00472e29	−0.0484534
$477$	1.08432e30	0.170686
$478$	−8.18299e30	−1.25745
$479$	6.87924e29	0.103201	0.0516003	−	0.998668i	$-0.483568\pi$
$479$	6.87924e29	0.103201	0.0516003	+	0.998668i	$0.483568\pi$
$480$	−7.11261e29	−0.104173
$481$	−2.87009e30	−0.410418
$482$	−3.77506e30	−0.527087
$483$	7.58486e30	1.03408
$484$	3.63064e29	0.0483350
$485$	−1.54071e31	−2.00304
$486$	4.89480e29	0.0621467
$487$	1.42477e30	0.176670	0.0883349	−	0.996091i	$-0.471845\pi$
$487$	1.42477e30	0.176670	0.0883349	+	0.996091i	$0.471845\pi$
$488$	1.30012e31	1.57455
$489$	−3.02232e30	−0.357510
$490$	1.69574e31	1.95932
$491$	1.42373e31	1.60690	0.803452	−	0.595369i	$-0.202994\pi$
$491$	1.42373e31	1.60690	0.803452	+	0.595369i	$0.202994\pi$
$492$	−9.88534e28	−0.0108992
$493$	−2.38678e30	−0.257083
$494$	5.16001e30	0.542989
$495$	−2.20320e30	−0.226514
$496$	1.26096e31	1.26667
$497$	−1.60803e31	−1.57832
$498$	−2.39445e30	−0.229651
$499$	1.65690e31	1.55289	0.776445	−	0.630185i	$-0.217021\pi$
$499$	1.65690e31	1.55289	0.776445	+	0.630185i	$0.217021\pi$
$500$	1.57118e29	0.0143903
$501$	7.21385e30	0.645703
$502$	−9.60538e30	−0.840276
$503$	−2.06539e31	−1.76592	−0.882960	−	0.469448i	$-0.844453\pi$
$503$	−2.06539e31	−1.76592	−0.882960	+	0.469448i	$0.844453\pi$
$504$	−6.32295e30	−0.528407
$505$	−2.28163e30	−0.186378
$506$	−6.51890e30	−0.520527
$507$	6.37414e30	0.497542
$508$	2.00240e29	0.0152798
$509$	−2.07213e31	−1.54583	−0.772916	−	0.634508i	$-0.781203\pi$
$509$	−2.07213e31	−1.54583	−0.772916	+	0.634508i	$0.781203\pi$
$510$	5.76076e30	0.420168
$511$	−1.77322e30	−0.126451
$512$	1.54318e31	1.07600
$513$	4.25534e30	0.290124
$514$	−9.76431e30	−0.650977
$515$	1.36846e31	0.892174
$516$	8.60308e29	0.0548508
$517$	6.39484e30	0.398739
$518$	−2.70328e31	−1.64854
$519$	−1.56791e31	−0.935182
$520$	−9.63010e30	−0.561814
$521$	2.06129e31	1.17626	0.588131	−	0.808765i	$-0.299864\pi$
$521$	2.06129e31	1.17626	0.588131	+	0.808765i	$0.299864\pi$
$522$	−2.90921e30	−0.162392
$523$	−2.36613e31	−1.29202	−0.646009	−	0.763329i	$-0.723563\pi$
$523$	−2.36613e31	−1.29202	−0.646009	+	0.763329i	$0.723563\pi$
$524$	1.18412e30	0.0632538
$525$	1.97431e31	1.03177
$526$	2.22944e31	1.13988
$527$	1.38486e31	0.692760
$528$	5.09894e30	0.249569
$529$	7.30739e30	0.349963
$530$	1.55549e31	0.728944
$531$	−8.33401e30	−0.382179
$532$	−3.18395e30	−0.142883
$533$	−2.59932e30	−0.114156
$534$	−1.89323e31	−0.813728
$535$	−1.06425e30	−0.0447690
$536$	−8.36205e30	−0.344285
$537$	1.02030e31	0.411174
$538$	−2.31607e31	−0.913597
$539$	1.64840e31	0.636490
$540$	−4.60003e29	−0.0173873
$541$	1.35546e31	0.501553	0.250776	−	0.968045i	$-0.419314\pi$
$541$	1.35546e31	0.501553	0.250776	+	0.968045i	$0.419314\pi$
$542$	3.56006e31	1.28963
$543$	−1.03825e31	−0.368218
$544$	1.80783e30	0.0627725
$545$	9.99246e30	0.339713
$546$	−9.63020e30	−0.320568
$547$	−5.86214e30	−0.191074	−0.0955371	−	0.995426i	$-0.530457\pi$
$547$	−5.86214e30	−0.191074	−0.0955371	+	0.995426i	$0.530457\pi$
$548$	−2.96262e30	−0.0945581
$549$	1.63299e31	0.510389
$550$	−1.69684e31	−0.519362
$551$	−2.52915e31	−0.758108
$552$	−2.34982e31	−0.689818
$553$	2.86041e30	0.0822410
$554$	2.52633e31	0.711424
$555$	−3.39536e31	−0.936519
$556$	1.73929e30	0.0469907
$557$	−3.63450e31	−0.961857	−0.480928	−	0.876760i	$-0.659700\pi$
$557$	−3.63450e31	−0.961857	−0.480928	+	0.876760i	$0.659700\pi$
$558$	1.68798e31	0.437597
$559$	2.26216e31	0.574496
$560$	−8.51062e31	−2.11738
$561$	5.59993e30	0.136493
$562$	4.04246e31	0.965336
$563$	5.87315e31	1.37412	0.687060	−	0.726601i	$-0.258901\pi$
$563$	5.87315e31	1.37412	0.687060	+	0.726601i	$0.258901\pi$
$564$	1.33517e30	0.0306074
$565$	−3.47391e31	−0.780299
$566$	−3.24262e31	−0.713686
$567$	−7.94179e30	−0.171282
$568$	4.98172e31	1.05287
$569$	−3.38209e31	−0.700477	−0.350238	−	0.936661i	$-0.613899\pi$
$569$	−3.38209e31	−0.700477	−0.350238	+	0.936661i	$0.613899\pi$
$570$	6.10438e31	1.23903
$571$	−7.49909e31	−1.49174	−0.745871	−	0.666091i	$-0.767966\pi$
$571$	−7.49909e31	−1.49174	−0.745871	+	0.666091i	$0.767966\pi$
$572$	−5.42226e29	−0.0105712
$573$	8.66930e30	0.165656
$574$	−2.44825e31	−0.458532
$575$	7.33717e31	1.34694
$576$	1.95187e31	0.351230
$577$	6.33342e31	1.11716	0.558581	−	0.829450i	$-0.311346\pi$
$577$	6.33342e31	1.11716	0.558581	+	0.829450i	$0.311346\pi$
$578$	4.13839e31	0.715586
$579$	7.63081e30	0.129350
$580$	2.73402e30	0.0454338
$581$	3.88498e31	0.632940
$582$	4.77321e31	0.762423
$583$	1.51206e31	0.236799
$584$	5.49350e30	0.0843532
$585$	−1.20957e31	−0.182111
$586$	−1.13031e32	−1.66868
$587$	−8.61217e31	−1.24674	−0.623368	−	0.781929i	$-0.714236\pi$
$587$	−8.61217e31	−1.24674	−0.623368	+	0.781929i	$0.714236\pi$
$588$	3.44167e30	0.0488573
$589$	1.46746e32	2.04287
$590$	−1.19553e32	−1.63216
$591$	−4.92026e31	−0.658767
$592$	7.85799e31	1.03184
$593$	−1.31209e32	−1.68980	−0.844901	−	0.534923i	$-0.820341\pi$
$593$	−1.31209e32	−1.68980	−0.844901	+	0.534923i	$0.820341\pi$
$594$	6.82567e30	0.0862186
$595$	−9.34681e31	−1.15803
$596$	−7.24952e30	−0.0881002
$597$	−4.25619e31	−0.507361
$598$	−3.57890e31	−0.418491
$599$	−2.38949e30	−0.0274092	−0.0137046	−	0.999906i	$-0.504362\pi$
$599$	−2.38949e30	−0.0274092	−0.0137046	+	0.999906i	$0.504362\pi$
$600$	−6.11647e31	−0.688274
$601$	−4.19607e31	−0.463219	−0.231610	−	0.972809i	$-0.574399\pi$
$601$	−4.19607e31	−0.463219	−0.231610	+	0.972809i	$0.574399\pi$
$602$	2.13068e32	2.30759
$603$	−1.05030e31	−0.111600
$604$	2.60886e30	0.0271973
$605$	1.12939e32	1.15520
$606$	7.06863e30	0.0709414
$607$	−1.86893e32	−1.84045	−0.920225	−	0.391390i	$-0.871994\pi$
$607$	−1.86893e32	−1.84045	−0.920225	+	0.391390i	$0.871994\pi$
$608$	1.91566e31	0.185109
$609$	4.72018e31	0.447569
$610$	2.34256e32	2.17971
$611$	3.51079e31	0.320576
$612$	1.16920e30	0.0104773
$613$	1.22268e32	1.07527	0.537637	−	0.843176i	$-0.319317\pi$
$613$	1.22268e32	1.07527	0.537637	+	0.843176i	$0.319317\pi$
$614$	−1.09602e32	−0.945980
$615$	−3.07504e31	−0.260488
$616$	−8.81718e31	−0.733080
$617$	4.63661e31	0.378374	0.189187	−	0.981941i	$-0.439415\pi$
$617$	4.63661e31	0.378374	0.189187	+	0.981941i	$0.439415\pi$
$618$	−4.23958e31	−0.339590
$619$	2.85976e31	0.224847	0.112424	−	0.993660i	$-0.464139\pi$
$619$	2.85976e31	0.224847	0.112424	+	0.993660i	$0.464139\pi$
$620$	−1.58633e31	−0.122430
$621$	−2.95143e31	−0.223604
$622$	−2.70768e31	−0.201376
$623$	3.07176e32	2.24272
$624$	2.79934e31	0.200647
$625$	−1.15869e32	−0.815353
$626$	−1.62867e32	−1.12519
$627$	5.93395e31	0.402501
$628$	−4.97916e30	−0.0331605
$629$	8.63006e31	0.564328
$630$	−1.13927e32	−0.731492
$631$	−8.23803e31	−0.519381	−0.259690	−	0.965692i	$-0.583620\pi$
$631$	−8.23803e31	−0.519381	−0.259690	+	0.965692i	$0.583620\pi$
$632$	−8.86163e30	−0.0548615
$633$	5.60035e31	0.340465
$634$	−2.47361e32	−1.47674
$635$	6.22889e31	0.365185
$636$	3.15701e30	0.0181768
$637$	9.04977e31	0.511722
$638$	−4.05682e31	−0.225293
$639$	6.25716e31	0.341285
$640$	2.46319e32	1.31956
$641$	−2.94822e32	−1.55129	−0.775645	−	0.631169i	$-0.782575\pi$
$641$	−2.94822e32	−1.55129	−0.775645	+	0.631169i	$0.782575\pi$
$642$	3.29713e30	0.0170405
$643$	3.36821e31	0.170991	0.0854953	−	0.996339i	$-0.472753\pi$
$643$	3.36821e31	0.170991	0.0854953	+	0.996339i	$0.472753\pi$
$644$	2.20833e31	0.110123
$645$	2.67617e32	1.31092
$646$	−1.55156e32	−0.746613
$647$	−1.54155e32	−0.728715	−0.364357	−	0.931259i	$-0.618711\pi$
$647$	−1.54155e32	−0.728715	−0.364357	+	0.931259i	$0.618711\pi$
$648$	2.46039e31	0.114259
$649$	−1.16215e32	−0.530212
$650$	−9.31571e31	−0.417554
$651$	−2.73874e32	−1.20606
$652$	−8.79946e30	−0.0380723
$653$	−4.51453e32	−1.91916	−0.959580	−	0.281434i	$-0.909190\pi$
$653$	−4.51453e32	−1.91916	−0.959580	+	0.281434i	$0.909190\pi$
$654$	−3.09573e31	−0.129306
$655$	3.68345e32	1.51175
$656$	7.11666e31	0.287000
$657$	6.89998e30	0.0273430
$658$	3.30675e32	1.28767
$659$	5.01392e32	1.91865	0.959323	−	0.282311i	$-0.0911010\pi$
$659$	5.01392e32	1.91865	0.959323	+	0.282311i	$0.0911010\pi$
$660$	−6.41462e30	−0.0241221
$661$	2.97857e32	1.10076	0.550378	−	0.834915i	$-0.314483\pi$
$661$	2.97857e32	1.10076	0.550378	+	0.834915i	$0.314483\pi$
$662$	4.40999e32	1.60166
$663$	3.07438e31	0.109737
$664$	−1.20358e32	−0.422223
$665$	−9.90432e32	−3.41488
$666$	1.05190e32	0.356470
$667$	1.75417e32	0.584286
$668$	2.10031e31	0.0687629
$669$	8.45159e31	0.271981
$670$	−1.50667e32	−0.476605
$671$	2.27716e32	0.708084
$672$	−3.57522e31	−0.109284
$673$	−1.11603e31	−0.0335354	−0.0167677	−	0.999859i	$-0.505338\pi$
$673$	−1.11603e31	−0.0335354	−0.0167677	+	0.999859i	$0.505338\pi$
$674$	2.02987e32	0.599625
$675$	−7.68244e31	−0.223103
$676$	1.85583e31	0.0529847
$677$	1.78822e32	0.501939	0.250970	−	0.967995i	$-0.419251\pi$
$677$	1.78822e32	0.501939	0.250970	+	0.967995i	$0.419251\pi$
$678$	1.07624e32	0.297007
$679$	−7.74450e32	−2.10131
$680$	2.89567e32	0.772497
$681$	8.08072e31	0.211962
$682$	2.35384e32	0.607096
$683$	−4.63491e32	−1.17545	−0.587724	−	0.809062i	$-0.699976\pi$
$683$	−4.63491e32	−1.17545	−0.587724	+	0.809062i	$0.699976\pi$
$684$	1.23894e31	0.0308962
$685$	−9.21583e32	−2.25992
$686$	2.33077e32	0.562046
$687$	−2.42236e31	−0.0574430
$688$	−6.19354e32	−1.44435
$689$	8.30126e31	0.190381
$690$	−4.23389e32	−0.954939
$691$	7.28816e32	1.61667	0.808333	−	0.588726i	$-0.200370\pi$
$691$	7.28816e32	1.61667	0.808333	+	0.588726i	$0.200370\pi$
$692$	−4.56496e31	−0.0995903
$693$	−1.10746e32	−0.237627
$694$	−6.74431e31	−0.142332
$695$	5.41042e32	1.12307
$696$	−1.46233e32	−0.298565
$697$	7.81589e31	0.156965
$698$	−7.39800e32	−1.46143
$699$	−1.79200e32	−0.348217
$700$	5.74819e31	0.109876
$701$	8.88871e32	1.67140	0.835702	−	0.549183i	$-0.185061\pi$
$701$	8.88871e32	1.67140	0.835702	+	0.549183i	$0.185061\pi$
$702$	3.74731e31	0.0693175
$703$	9.14482e32	1.66414
$704$	2.72183e32	0.487276
$705$	4.15332e32	0.731510
$706$	1.46447e32	0.253762
$707$	−1.14688e32	−0.195522
$708$	−2.42644e31	−0.0406994
$709$	2.94549e32	0.486101	0.243050	−	0.970014i	$-0.421852\pi$
$709$	2.94549e32	0.486101	0.243050	+	0.970014i	$0.421852\pi$
$710$	8.97605e32	1.45752
$711$	−1.11304e31	−0.0177833
$712$	−9.51641e32	−1.49607
$713$	−1.01781e33	−1.57447
$714$	2.89570e32	0.440782
$715$	−1.68671e32	−0.252650
$716$	2.97061e31	0.0437871
$717$	−5.16630e32	−0.749393
$718$	5.43972e32	0.776507
$719$	−1.42330e32	−0.199947	−0.0999734	−	0.994990i	$-0.531876\pi$
$719$	−1.42330e32	−0.199947	−0.0999734	+	0.994990i	$0.531876\pi$
$720$	3.31166e32	0.457849
$721$	6.87870e32	0.935945
$722$	−9.20676e32	−1.23290
$723$	−2.38337e32	−0.314124
$724$	−3.02287e31	−0.0392126
$725$	4.56604e32	0.582978
$726$	−3.49891e32	−0.439705
$727$	−1.10613e33	−1.36824	−0.684118	−	0.729371i	$-0.739813\pi$
$727$	−1.10613e33	−1.36824	−0.684118	+	0.729371i	$0.739813\pi$
$728$	−4.84066e32	−0.589378
$729$	3.09032e31	0.0370370
$730$	9.89819e31	0.116773
$731$	−6.80207e32	−0.789935
$732$	4.75445e31	0.0543529
$733$	1.11000e33	1.24918	0.624592	−	0.780951i	$-0.285265\pi$
$733$	1.11000e33	1.24918	0.624592	+	0.780951i	$0.285265\pi$
$734$	−1.40312e33	−1.55449
$735$	1.07060e33	1.16768
$736$	−1.32867e32	−0.142667
$737$	−1.46461e32	−0.154827
$738$	9.52667e31	0.0991501
$739$	7.82934e31	0.0802259	0.0401129	−	0.999195i	$-0.487228\pi$
$739$	7.82934e31	0.0802259	0.0401129	+	0.999195i	$0.487228\pi$
$740$	−9.88558e31	−0.0997327
$741$	3.25776e32	0.323601
$742$	7.81880e32	0.764707
$743$	1.22041e33	1.17526	0.587631	−	0.809129i	$-0.300061\pi$
$743$	1.22041e33	1.17526	0.587631	+	0.809129i	$0.300061\pi$
$744$	8.48471e32	0.804541
$745$	−2.25511e33	−2.10558
$746$	1.42712e33	1.31209
$747$	−1.51173e32	−0.136863
$748$	1.63042e31	0.0145355
$749$	−5.34957e31	−0.0469654
$750$	−1.51417e32	−0.130909
$751$	−1.43927e33	−1.22542	−0.612708	−	0.790309i	$-0.709920\pi$
$751$	−1.43927e33	−1.22542	−0.612708	+	0.790309i	$0.709920\pi$
$752$	−9.61216e32	−0.805964
$753$	−6.06432e32	−0.500772
$754$	−2.22721e32	−0.181130
$755$	8.11541e32	0.650011
$756$	−2.31225e31	−0.0182404
$757$	7.52652e32	0.584778	0.292389	−	0.956299i	$-0.405550\pi$
$757$	7.52652e32	0.584778	0.292389	+	0.956299i	$0.405550\pi$
$758$	−9.13362e32	−0.698951
$759$	−4.11569e32	−0.310215
$760$	3.06839e33	2.27800
$761$	2.01529e33	1.47372	0.736859	−	0.676046i	$-0.236308\pi$
$761$	2.01529e33	1.47372	0.736859	+	0.676046i	$0.236308\pi$
$762$	−1.92975e32	−0.139001
$763$	5.02280e32	0.356380
$764$	2.52406e31	0.0176412
$765$	3.63704e32	0.250404
$766$	1.02244e33	0.693438
$767$	−6.38027e32	−0.426277
$768$	1.61175e32	0.106082
$769$	−2.69734e32	−0.174897	−0.0874487	−	0.996169i	$-0.527871\pi$
$769$	−2.69734e32	−0.174897	−0.0874487	+	0.996169i	$0.527871\pi$
$770$	−1.58868e33	−1.01483
$771$	−6.16467e32	−0.387958
$772$	2.22171e31	0.0137749
$773$	−3.48915e31	−0.0213135	−0.0106568	−	0.999943i	$-0.503392\pi$
$773$	−3.48915e31	−0.0213135	−0.0106568	+	0.999943i	$0.503392\pi$
$774$	−8.29094e32	−0.498979
$775$	−2.64930e33	−1.57095
$776$	2.39927e33	1.40175
$777$	−1.70671e33	−0.982466
$778$	−1.08853e33	−0.617409
$779$	8.28210e32	0.462870
$780$	−3.52165e31	−0.0193936
$781$	8.72545e32	0.473479
$782$	1.07614e33	0.575427
$783$	−1.83672e32	−0.0967794
$784$	−2.47773e33	−1.28653
$785$	−1.54887e33	−0.792528
$786$	−1.14116e33	−0.575422
$787$	−7.64381e32	−0.379840	−0.189920	−	0.981800i	$-0.560823\pi$
$787$	−7.64381e32	−0.379840	−0.189920	+	0.981800i	$0.560823\pi$
$788$	−1.43253e32	−0.0701541
$789$	1.40755e33	0.679325
$790$	−1.59669e32	−0.0759466
$791$	−1.74619e33	−0.818582
$792$	3.43095e32	0.158517
$793$	1.25017e33	0.569281
$794$	5.33591e32	0.239482
$795$	9.82052e32	0.434423
$796$	−1.23919e32	−0.0540303
$797$	3.28083e33	1.40998	0.704990	−	0.709218i	$-0.250952\pi$
$797$	3.28083e33	1.40998	0.704990	+	0.709218i	$0.250952\pi$
$798$	3.06842e33	1.29982
$799$	−1.05566e33	−0.440794
$800$	−3.45847e32	−0.142347
$801$	−1.19529e33	−0.484951
$802$	−1.01193e33	−0.404711
$803$	9.62184e31	0.0379341
$804$	−3.05793e31	−0.0118846
$805$	6.86947e33	2.63191
$806$	1.29227e33	0.488090
$807$	−1.46224e33	−0.544469
$808$	3.55308e32	0.130429
$809$	−1.06623e33	−0.385870	−0.192935	−	0.981212i	$-0.561801\pi$
$809$	−1.06623e33	−0.385870	−0.192935	+	0.981212i	$0.561801\pi$
$810$	4.43313e32	0.158173
$811$	6.88669e32	0.242254	0.121127	−	0.992637i	$-0.461349\pi$
$811$	6.88669e32	0.242254	0.121127	+	0.992637i	$0.461349\pi$
$812$	1.37428e32	0.0476629
$813$	2.24763e33	0.768571
$814$	1.46685e33	0.494545
$815$	−2.73726e33	−0.909919
$816$	−8.41731e32	−0.275890
$817$	−7.20780e33	−2.32943
$818$	−2.98362e33	−0.950782
$819$	−6.07999e32	−0.191046
$820$	−8.95297e31	−0.0277401
$821$	1.55564e33	0.475293	0.237647	−	0.971352i	$-0.423624\pi$
$821$	1.55564e33	0.475293	0.237647	+	0.971352i	$0.423624\pi$
$822$	2.85512e33	0.860199
$823$	5.22482e33	1.55229	0.776146	−	0.630554i	$-0.217172\pi$
$823$	5.22482e33	1.55229	0.776146	+	0.630554i	$0.217172\pi$
$824$	−2.13104e33	−0.624352
$825$	−1.07130e33	−0.309520
$826$	−6.00945e33	−1.71224
$827$	−3.58810e33	−1.00821	−0.504105	−	0.863642i	$-0.668178\pi$
$827$	−3.58810e33	−1.00821	−0.504105	+	0.863642i	$0.668178\pi$
$828$	−8.59308e31	−0.0238122
$829$	8.83624e32	0.241485	0.120743	−	0.992684i	$-0.461472\pi$
$829$	8.83624e32	0.241485	0.120743	+	0.992684i	$0.461472\pi$
$830$	−2.16861e33	−0.584497
$831$	1.59499e33	0.423982
$832$	1.49429e33	0.391757
$833$	−2.72117e33	−0.703620
$834$	−1.67618e33	−0.427476
$835$	6.53345e33	1.64342
$836$	1.72767e32	0.0428636
$837$	1.06570e33	0.260791
$838$	−2.84509e32	−0.0686736
$839$	4.70731e32	0.112075	0.0560377	−	0.998429i	$-0.482153\pi$
$839$	4.70731e32	0.112075	0.0560377	+	0.998429i	$0.482153\pi$
$840$	−5.72658e33	−1.34488
$841$	−3.22507e33	−0.747111
$842$	3.68206e33	0.841400
$843$	2.55220e33	0.575303
$844$	1.63054e32	0.0362571
$845$	5.77294e33	1.26632
$846$	−1.28672e33	−0.278437
$847$	5.67696e33	1.21187
$848$	−2.27279e33	−0.478639
$849$	−2.04722e33	−0.425329
$850$	2.80114e33	0.574139
$851$	−6.34269e33	−1.28258
$852$	1.82177e32	0.0363445
$853$	−3.75623e33	−0.739329	−0.369665	−	0.929165i	$-0.620527\pi$
$853$	−3.75623e33	−0.739329	−0.369665	+	0.929165i	$0.620527\pi$
$854$	1.17751e34	2.28665
$855$	3.85398e33	0.738413
$856$	1.65732e32	0.0313297
$857$	8.04748e33	1.50100	0.750499	−	0.660871i	$-0.229813\pi$
$857$	8.04748e33	1.50100	0.750499	+	0.660871i	$0.229813\pi$
$858$	5.22553e32	0.0961670
$859$	−4.64719e33	−0.843858	−0.421929	−	0.906629i	$-0.638647\pi$
$859$	−4.64719e33	−0.843858	−0.421929	+	0.906629i	$0.638647\pi$
$860$	7.79165e32	0.139604
$861$	−1.54570e33	−0.273268
$862$	−5.82711e33	−1.01653
$863$	−8.37927e33	−1.44239	−0.721194	−	0.692733i	$-0.756406\pi$
$863$	−8.37927e33	−1.44239	−0.721194	+	0.692733i	$0.756406\pi$
$864$	1.39119e32	0.0236308
$865$	−1.42003e34	−2.38019
$866$	1.05923e34	1.75201
$867$	2.61276e33	0.426462
$868$	−7.97384e32	−0.128437
$869$	−1.55211e32	−0.0246715
$870$	−2.63482e33	−0.413313
$871$	−8.04075e32	−0.124477
$872$	−1.55608e33	−0.237735
$873$	3.01355e33	0.454375
$874$	1.14033e34	1.69687
$875$	2.45673e33	0.360799
$876$	2.00893e31	0.00291184
$877$	7.40167e33	1.05885	0.529425	−	0.848357i	$-0.322408\pi$
$877$	7.40167e33	1.05885	0.529425	+	0.848357i	$0.322408\pi$
$878$	−3.92200e33	−0.553758
$879$	−7.13616e33	−0.994472
$880$	4.61802e33	0.635192
$881$	8.68785e32	0.117948	0.0589738	−	0.998260i	$-0.481217\pi$
$881$	8.68785e32	0.117948	0.0589738	+	0.998260i	$0.481217\pi$
$882$	−3.31679e33	−0.444457
$883$	−7.76396e33	−1.02692	−0.513459	−	0.858114i	$-0.671636\pi$
$883$	−7.76396e33	−1.02692	−0.513459	+	0.858114i	$0.671636\pi$
$884$	8.95105e31	0.0116862
$885$	−7.54796e33	−0.972706
$886$	−1.19091e34	−1.51493
$887$	3.55847e33	0.446829	0.223415	−	0.974723i	$-0.428280\pi$
$887$	3.55847e33	0.446829	0.223415	+	0.974723i	$0.428280\pi$
$888$	5.28744e33	0.655385
$889$	3.13101e33	0.383102
$890$	−1.71466e34	−2.07107
$891$	4.30936e32	0.0513830
$892$	2.46068e32	0.0289640
$893$	−1.11863e34	−1.29985
$894$	6.98648e33	0.801451
$895$	9.24071e33	1.04650
$896$	1.23815e34	1.38430
$897$	−2.25953e33	−0.249405
$898$	1.05326e34	1.14777
$899$	−6.33397e33	−0.681459
$900$	−2.23674e32	−0.0237589
$901$	−2.49610e33	−0.261774
$902$	1.32847e33	0.137555
$903$	1.34520e34	1.37524
$904$	5.40976e33	0.546061
$905$	−9.40325e33	−0.937172
$906$	−2.51420e33	−0.247415
$907$	1.11723e34	1.08557	0.542786	−	0.839871i	$-0.317370\pi$
$907$	1.11723e34	1.08557	0.542786	+	0.839871i	$0.317370\pi$
$908$	2.35270e32	0.0225725
$909$	4.46275e32	0.0422784
$910$	−8.72189e33	−0.815896
$911$	1.42411e34	1.31548	0.657738	−	0.753247i	$-0.271513\pi$
$911$	1.42411e34	1.31548	0.657738	+	0.753247i	$0.271513\pi$
$912$	−8.91939e33	−0.813569
$913$	−2.10806e33	−0.189876
$914$	1.26486e33	0.112503
$915$	1.47897e34	1.29902
$916$	−7.05271e31	−0.00611727
$917$	1.85152e34	1.58592
$918$	−1.12678e33	−0.0953120
$919$	2.28691e34	1.91038	0.955191	−	0.295991i	$-0.0956499\pi$
$919$	2.28691e34	1.91038	0.955191	+	0.295991i	$0.0956499\pi$
$920$	−2.12819e34	−1.75570
$921$	−6.91968e33	−0.563768
$922$	−1.02149e34	−0.821914
$923$	4.79030e33	0.380665
$924$	−3.22437e32	−0.0253056
$925$	−1.65097e34	−1.27971
$926$	−2.12799e34	−1.62909
$927$	−2.67664e33	−0.202383
$928$	−8.26852e32	−0.0617484
$929$	−1.64699e34	−1.21482	−0.607409	−	0.794389i	$-0.707791\pi$
$929$	−1.64699e34	−1.21482	−0.607409	+	0.794389i	$0.707791\pi$
$930$	1.52877e34	1.11375
$931$	−2.88348e34	−2.07489
$932$	−5.21740e32	−0.0370827
$933$	−1.70949e33	−0.120013
$934$	1.39461e33	0.0967084
$935$	5.07175e33	0.347396
$936$	1.88360e33	0.127443
$937$	1.12309e34	0.750602	0.375301	−	0.926903i	$-0.377539\pi$
$937$	1.12309e34	0.750602	0.375301	+	0.926903i	$0.377539\pi$
$938$	−7.57343e33	−0.499988
$939$	−1.02825e34	−0.670573
$940$	1.20924e33	0.0779007
$941$	1.59102e34	1.01250	0.506251	−	0.862386i	$-0.331031\pi$
$941$	1.59102e34	1.01250	0.506251	+	0.862386i	$0.331031\pi$
$942$	4.79850e33	0.301662
$943$	−5.74432e33	−0.356742
$944$	1.74685e34	1.07171
$945$	−7.19273e33	−0.435941
$946$	−1.15615e34	−0.692254
$947$	1.27050e34	0.751537	0.375768	−	0.926714i	$-0.377379\pi$
$947$	1.27050e34	0.751537	0.375768	+	0.926714i	$0.377379\pi$
$948$	−3.24062e31	−0.00189379
$949$	5.28242e32	0.0304980
$950$	2.96822e34	1.69307
$951$	−1.56171e34	−0.880082
$952$	1.45554e34	0.810398
$953$	1.87378e34	1.03074	0.515372	−	0.856966i	$-0.327654\pi$
$953$	1.87378e34	1.03074	0.515372	+	0.856966i	$0.327654\pi$
$954$	−3.04246e33	−0.165355
$955$	7.85163e33	0.421620
$956$	−1.50417e33	−0.0798051
$957$	−2.56126e33	−0.134266
$958$	−1.93022e33	−0.0999777
$959$	−4.63242e34	−2.37079
$960$	1.76777e34	0.893937
$961$	1.67376e34	0.836324
$962$	8.05306e33	0.397601
$963$	2.08163e32	0.0101555
$964$	−6.93918e32	−0.0334520
$965$	6.91108e33	0.329217
$966$	−2.12821e34	−1.00179
$967$	−1.43720e34	−0.668520	−0.334260	−	0.942481i	$-0.608486\pi$
$967$	−1.43720e34	−0.668520	−0.334260	+	0.942481i	$0.608486\pi$
$968$	−1.75874e34	−0.808418
$969$	−9.79574e33	−0.444953
$970$	4.32300e34	1.94049
$971$	2.53347e34	1.12381	0.561907	−	0.827201i	$-0.310068\pi$
$971$	2.53347e34	1.12381	0.561907	+	0.827201i	$0.310068\pi$
$972$	8.99745e31	0.00394418
$973$	2.71960e34	1.17817
$974$	−3.99771e33	−0.171153
$975$	−5.88145e33	−0.248846
$976$	−3.42282e34	−1.43124
$977$	−7.40861e32	−0.0306161	−0.0153080	−	0.999883i	$-0.504873\pi$
$977$	−7.40861e32	−0.0306161	−0.0153080	+	0.999883i	$0.504873\pi$
$978$	8.48019e33	0.346345
$979$	−1.66679e34	−0.672792
$980$	3.11705e33	0.124350
$981$	−1.95448e33	−0.0770614
$982$	−3.99478e34	−1.55672
$983$	−3.84141e34	−1.47953	−0.739767	−	0.672863i	$-0.765065\pi$
$983$	−3.84141e34	−1.47953	−0.739767	+	0.672863i	$0.765065\pi$
$984$	4.78862e33	0.182292
$985$	−4.45619e34	−1.67667
$986$	6.69697e33	0.249054
$987$	2.08770e34	0.767400
$988$	9.48496e32	0.0344612
$989$	4.99921e34	1.79533
$990$	6.18188e33	0.219440
$991$	6.00940e33	0.210855	0.105427	−	0.994427i	$-0.466379\pi$
$991$	6.00940e33	0.210855	0.105427	+	0.994427i	$0.466379\pi$
$992$	4.79756e33	0.166393
$993$	2.78423e34	0.954528
$994$	4.51189e34	1.52903
$995$	−3.85476e34	−1.29131
$996$	−4.40139e32	−0.0145749
$997$	−1.73502e34	−0.567950	−0.283975	−	0.958832i	$-0.591653\pi$
$997$	−1.73502e34	−0.567950	−0.283975	+	0.958832i	$0.591653\pi$
$998$	−4.64904e34	−1.50439
$999$	6.64116e33	0.212442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.24.a.b.1.1	✓	2
3.2	odd	2		9.24.a.c.1.2		2
4.3	odd	2		48.24.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.24.a.b.1.1	✓	2	1.1	even	1	trivial
9.24.a.c.1.2		2	3.2	odd	2
48.24.a.g.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-2805.86 q^{2} -177147. q^{3} -515763. q^{4} -1.60439e8 q^{5} +4.97050e8 q^{6} -8.06460e9 q^{7} +2.49844e10 q^{8} +3.13811e10 q^{9} +O(q^{10})\)	\(q-2805.86 q^{2} -177147. q^{3} -515763. q^{4} -1.60439e8 q^{5} +4.97050e8 q^{6} -8.06460e9 q^{7} +2.49844e10 q^{8} +3.13811e10 q^{9} +4.50169e11 q^{10} +4.37600e11 q^{11} +9.13659e10 q^{12} +2.40244e12 q^{13} +2.26281e13 q^{14} +2.84212e13 q^{15} -6.57762e13 q^{16} -7.22389e13 q^{17} -8.80508e13 q^{18} -7.65478e14 q^{19} +8.27484e13 q^{20} +1.42862e15 q^{21} -1.22785e15 q^{22} +5.30922e15 q^{23} -4.42591e15 q^{24} +1.38197e16 q^{25} -6.74091e15 q^{26} -5.55906e15 q^{27} +4.15942e15 q^{28} +3.30401e16 q^{29} -7.97460e16 q^{30} -1.91705e17 q^{31} -2.50257e16 q^{32} -7.75196e16 q^{33} +2.02692e17 q^{34} +1.29387e18 q^{35} -1.61852e16 q^{36} -1.19466e18 q^{37} +2.14782e18 q^{38} -4.25585e17 q^{39} -4.00847e18 q^{40} -1.08195e18 q^{41} -4.00851e18 q^{42} +9.41608e18 q^{43} -2.25698e17 q^{44} -5.03474e18 q^{45} -1.48969e19 q^{46} +1.46134e19 q^{47} +1.16521e19 q^{48} +3.76691e19 q^{49} -3.87760e19 q^{50} +1.27969e19 q^{51} -1.23909e18 q^{52} +3.45534e19 q^{53} +1.55979e19 q^{54} -7.02081e19 q^{55} -2.01489e20 q^{56} +1.35602e20 q^{57} -9.27060e19 q^{58} -2.65574e20 q^{59} -1.46586e19 q^{60} +5.20374e20 q^{61} +5.37898e20 q^{62} -2.53076e20 q^{63} +6.21989e20 q^{64} -3.85445e20 q^{65} +2.17509e20 q^{66} -3.34691e20 q^{67} +3.72581e19 q^{68} -9.40513e20 q^{69} -3.63043e21 q^{70} +1.99393e21 q^{71} +7.84037e20 q^{72} +2.19877e20 q^{73} +3.35204e21 q^{74} -2.44811e21 q^{75} +3.94805e20 q^{76} -3.52907e21 q^{77} +1.19413e21 q^{78} -3.54687e20 q^{79} +1.05531e22 q^{80} +9.84771e20 q^{81} +3.03580e21 q^{82} -4.81732e21 q^{83} -7.36829e20 q^{84} +1.15899e22 q^{85} -2.64202e22 q^{86} -5.85296e21 q^{87} +1.09332e22 q^{88} -3.80894e22 q^{89} +1.41268e22 q^{90} -1.93747e22 q^{91} -2.73830e21 q^{92} +3.39600e22 q^{93} -4.10032e22 q^{94} +1.22812e23 q^{95} +4.43322e21 q^{96} +9.60308e22 q^{97} -1.05694e23 q^{98} +1.37324e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9}+O(q^{10}) \) 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9	\( 2 q - 1242 q^{2} - 354294 q^{3} - 6458716 q^{4} - 46808820 q^{5} + 220016574 q^{6} - 211963904 q^{7} + 2571869016 q^{8} + 62762119218 q^{9} + 627869790180 q^{10} + 1468972366488 q^{11} + 1144142163252 q^{12} + 10491654264748 q^{13} + 34908555004416 q^{14} + 8292042036540 q^{15} - 50973150676720 q^{16} - 210888011520828 q^{17} - 38975276034378 q^{18} - 907382448537944 q^{19} - 592549041758760 q^{20} + 37548769701888 q^{21} + 385075304370504 q^{22} + 10\!\cdots\!12 q^{23}+ \cdots + 46\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q - 1242 * q^2 - 354294 * q^3 - 6458716 * q^4 - 46808820 * q^5 + 220016574 * q^6 - 211963904 * q^7 + 2571869016 * q^8 + 62762119218 * q^9 + 627869790180 * q^10 + 1468972366488 * q^11 + 1144142163252 * q^12 + 10491654264748 * q^13 + 34908555004416 * q^14 + 8292042036540 * q^15 - 50973150676720 * q^16 - 210888011520828 * q^17 - 38975276034378 * q^18 - 907382448537944 * q^19 - 592549041758760 * q^20 + 37548769701888 * q^21 + 385075304370504 * q^22 + 10116923323892112 * q^23 - 455598880577352 * q^24 + 14810505797591150 * q^25 + 5909481699569604 * q^26 - 11118121133111046 * q^27 - 42508434042586112 * q^28 + 18478753545176892 * q^29 - 111225249721016460 * q^30 - 272793622592745488 * q^31 + 186134219136906336 * q^32 - 260224047806249736 * q^33 - 14135605903588212 * q^34 + 2186169652458823680 * q^35 - 202681351793602044 * q^36 - 478995036787364 * q^37 + 1925903087124629112 * q^38 - 1858565078037313956 * q^39 - 6555203866715785200 * q^40 + 5555714961308771412 * q^41 - 6183945793367281152 * q^42 - 1198322147609320040 * q^43 - 6355093136294718288 * q^44 - 1468910370646951380 * q^45 - 7378368693556745808 * q^46 + 26308565672855777280 * q^47 + 9029740722928917840 * q^48 + 71964232849356271890 * q^49 - 37226516336176411350 * q^50 + 37358178576880117716 * q^51 - 49312907988586886888 * q^52 - 41127501899415224628 * q^53 + 6904353223661959566 * q^54 + 46986672525187689360 * q^55 - 377486892221258373120 * q^56 + 160740078611151165768 * q^57 - 115477922638933597836 * q^58 - 307537061909444286696 * q^59 + 104968285100439057720 * q^60 + 594961179098503751020 * q^61 + 411087431199774869712 * q^62 - 6651651906380353536 * q^63 + 828036632782207954496 * q^64 + 533732415162776445960 * q^65 - 68214934943321672088 * q^66 - 1630225825126993264088 * q^67 + 861243436942941889224 * q^68 - 1792182616057515964464 * q^69 - 2235006928450834744320 * q^70 - 383942598581649272976 * q^71 + 80707974897636174744 * q^72 - 2812202351440561692428 * q^73 + 5219558875357315020756 * q^74 - 2623636670525879449050 * q^75 + 1238138884710050927056 * q^76 + 4569917579124061519872 * q^77 - 1046846954633656639788 * q^78 + 21069388575313284880 * q^79 + 12235121810092022582880 * q^80 + 1969541804367222465762 * q^81 + 13416177399661303790652 * q^82 - 14817262080324402696024 * q^83 + 7530241565342001982464 * q^84 - 4164778183840982876520 * q^85 - 43019621516128896935352 * q^86 - 3273455754267450887124 * q^87 - 12182478384106427357664 * q^88 - 43449805260884456557164 * q^89 + 19703219312328902839620 * q^90 + 44146945026523904417792 * q^91 - 31310234209098260658144 * q^92 + 48324571861437084962736 * q^93 - 22713687421447503614976 * q^94 + 106687644602844474428400 * q^95 - 32973118517445546703392 * q^96 + 107136573045242168450692 * q^97 - 52061241480597067368618 * q^98 + 46097909396733721983192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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