LMFDB - Embedded newform 3.71.b.a.2.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,71,Mod(2,3)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 71, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 71);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 71 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$93.0951693564$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.16
Character	$\chi$	$=$	3.2
Dual form			3.71.b.a.2.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.59410e10i q^{2} +(-2.70537e16 + 4.20862e16i) q^{3} -1.11161e20 q^{4} +4.52111e24i q^{5} +(-1.51262e27 - 9.72336e26i) q^{6} -7.40509e29 q^{7} +3.84364e31i q^{8} +(-1.03935e33 - 2.27718e33i) q^{9} +O(q^{10})$	\(q+3.59410e10i q^{2} +(-2.70537e16 + 4.20862e16i) q^{3} -1.11161e20 q^{4} +4.52111e24i q^{5} +(-1.51262e27 - 9.72336e26i) q^{6} -7.40509e29 q^{7} +3.84364e31i q^{8} +(-1.03935e33 - 2.27718e33i) q^{9} -1.62493e35 q^{10} -3.10104e36i q^{11} +(3.00731e36 - 4.67834e36i) q^{12} +2.12249e37 q^{13} -2.66146e40i q^{14} +(-1.90276e41 - 1.22313e41i) q^{15} -1.51268e42 q^{16} -6.65739e41i q^{17} +(8.18440e43 - 3.73552e43i) q^{18} +3.67374e44 q^{19} -5.02569e44i q^{20} +(2.00335e46 - 3.11653e46i) q^{21} +1.11454e47 q^{22} +5.00537e47i q^{23} +(-1.61764e48 - 1.03985e48i) q^{24} -1.19701e49 q^{25} +7.62843e47i q^{26} +(1.23956e50 + 1.78639e49i) q^{27} +8.23155e49 q^{28} -4.46438e50i q^{29} +(4.39604e51 - 6.83872e51i) q^{30} -1.45568e52 q^{31} -8.98934e51i q^{32} +(1.30511e53 + 8.38946e52i) q^{33} +2.39273e52 q^{34} -3.34792e54i q^{35} +(1.15535e53 + 2.53133e53i) q^{36} +7.83434e54 q^{37} +1.32038e55i q^{38} +(-5.74212e53 + 8.93276e53i) q^{39} -1.73775e56 q^{40} -1.04241e56i q^{41} +(1.12011e57 + 7.20024e56i) q^{42} -1.18190e57 q^{43} +3.44714e56i q^{44} +(1.02954e58 - 4.69901e57i) q^{45} -1.79898e58 q^{46} -1.39113e58i q^{47} +(4.09235e58 - 6.36628e58i) q^{48} +4.04850e59 q^{49} -4.30216e59i q^{50} +(2.80184e58 + 1.80107e58i) q^{51} -2.35937e57 q^{52} -1.97126e59i q^{53} +(-6.42045e59 + 4.45510e60i) q^{54} +1.40201e61 q^{55} -2.84625e61i q^{56} +(-9.93882e60 + 1.54614e61i) q^{57} +1.60454e61 q^{58} +1.24383e61i q^{59} +(2.11513e61 + 1.35964e61i) q^{60} -5.47184e62 q^{61} -5.23186e62i q^{62} +(7.69647e62 + 1.68627e63i) q^{63} -1.46277e63 q^{64} +9.59600e61i q^{65} +(-3.01525e63 + 4.69069e63i) q^{66} -4.78606e63 q^{67} +7.40039e61i q^{68} +(-2.10657e64 - 1.35414e64i) q^{69} +1.20328e65 q^{70} -8.14760e64i q^{71} +(8.75265e64 - 3.99488e64i) q^{72} -2.23896e65 q^{73} +2.81574e65i q^{74} +(3.23835e65 - 5.03776e65i) q^{75} -4.08375e64 q^{76} +2.29635e66i q^{77} +(-3.21052e64 - 2.06377e64i) q^{78} -1.91791e66 q^{79} -6.83897e66i q^{80} +(-4.10530e66 + 4.73356e66i) q^{81} +3.74652e66 q^{82} +1.95479e67i q^{83} +(-2.22694e66 + 3.46435e66i) q^{84} +3.00988e66 q^{85} -4.24788e67i q^{86} +(1.87889e67 + 1.20778e67i) q^{87} +1.19193e68 q^{88} +5.75653e67i q^{89} +(1.68887e68 + 3.70025e68i) q^{90} -1.57172e67 q^{91} -5.56400e67i q^{92} +(3.93816e68 - 6.12641e68i) q^{93} +4.99985e68 q^{94} +1.66094e69i q^{95} +(3.78327e68 + 2.43195e68i) q^{96} +1.88301e69 q^{97} +1.45507e70i q^{98} +(-7.06162e69 + 3.22306e69i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 31\!\cdots\!82 q^{9}+O(q^{10}) $ 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9	$ 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 21\!\cdots\!80 q^{99}+O(q^{100}) $ 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9 - 204904054456738768728763726683461760 * q^10 + 168216518978261501059545818584280696640 * q^12 - 1425273500899614630088058291006011908100 * q^13 - 225789500492205687292660149319768298715840 * q^15 + 7791108876170200924142434286561643963000832 * q^16 - 159240712078782992086911930584730978792685440 * q^18 + 2012529521265601397979311193864856923750823676 * q^19 - 5316334525000974787771605720411010154937122916 * q^21 - 177999664576757911046568099334764110597720653440 * q^22 + 2221044214363105865421794285118261395337437583360 * q^24 - 47913993180689593092577485889381363779493774325690 * q^25 - 327350510975933028532160361074129063579708328041490 * q^27 + 199622305967867855771313967200368144722234985321600 * q^28 + 19529370934845391692884101303550253186745064711003520 * q^30 + 12388430374073163692752061441697409777651574405007404 * q^31 + 91609538538011962010378972773658529100477255901421120 * q^33 + 605761954772905142742127812440233067564260993651653120 * q^34 + 903849673866118209515044215587923561361275075218434112 * q^36 - 2942122339532414491328953596359839081620064777882528420 * q^37 - 83642273913756481299940648535011188445494335818507646004 * q^39 + 272642123044960747425938890972217844718938356564315934720 * q^40 + 1560147154093916143029768098476489647357578674968337342080 * q^42 - 4545359228128189931707988293083620465330530163336481972580 * q^43 - 13684191484560547979485162889557225553655737227535310368640 * q^45 + 34824945738150746982031713560272687284036228683298922087680 * q^46 + 187018310806180504680614747073364302422042767094159794882560 * q^48 + 537429667187009430823177633570141302055322425376808156541794 * q^49 + 93003444735225900297901054333392923286830613776157770499840 * q^51 - 256980181653870794210710907095882776189154704275967737138560 * q^52 + 563860949077651296335542553968680463677661322067851314468800 * q^54 - 3516118540339332578884347645630886351467431915082786354698880 * q^55 + 62619566495727497029128246919971991949893526891401194293093580 * q^57 + 116675137250817318744043251484707490614825810469582794383621760 * q^58 - 289520688194704548710930657842220413516071423272166989563023360 * q^60 - 1004518379975789938184755460502459521248398274882979931600708676 * q^61 + 2259750912371699320668016184778015293200259463243321554460021420 * q^63 - 6990282608978901236062382909358427229318771679854621867713298432 * q^64 + 9802144175872303219237439174047894300074716767326740733265952640 * q^66 - 9530737568144236105810003684427263525901520593033925660073496260 * q^67 + 68660923095126616358914910008665108044130343377859227725343530880 * q^69 - 186825484366209931701114245951001364013348939360625786570907971840 * q^70 + 800859191695150280430684829106757981081528103077118327934086410240 * q^72 - 498564607593670758195755796246723418636521686724391030404386208820 * q^73 + 2109806600351472862056557154002428953234561707550117711339382623630 * q^75 - 5263274864463875706518271175142614969672638525330024503218962553216 * q^76 + 12308167524701892969963937648343555852922730564344320620076689564800 * q^78 - 17307670437682441097149414568687707748355067787533584779481303522964 * q^79 + 13169506853202980530135359556542777642532240836639689883271737852342 * q^81 - 39431820989895068684167150578955043187025954212565254141576902204160 * q^82 + 138763489413867144231869861916118201044140663071190925822310630686336 * q^84 - 61037539079877371876604729964700889725410552523647838067356520814080 * q^85 - 149627312260702067527556548128053547148656320722965526646581032129600 * q^87 + 423107204692289659768926623144292819592688368886126043795359525621760 * q^88 - 954822316211616625813572408526438784570624253142422549351495971955840 * q^90 + 1351237435163715752950727836854267043101210025128484375869461920848568 * q^91 - 1419126662189890378883596636164605113800863195507982624574295260938180 * q^93 + 10138980254856605941232671681032460690110853357766177455228626662453760 * q^94 - 12383253221007478242150050518024370091385337450937902244753056045137920 * q^96 + 5943877415032019678068302054256035030995353737176853716379501144663980 * q^97 - 21983160871333538547745741193506138170867254293489738303957813119108480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$			3.59410e10i			1.04602i	0.852327	+	0.523010i	$0.175191\pi$
$2$			3.59410e10i			1.04602i	−0.852327	+	0.523010i	$0.824809\pi$
$3$	−2.70537e16	+	4.20862e16i	−0.540733	+	0.841194i
$3$	−2.70537e16	+	4.20862e16i	−0.540733	+	0.841194i
$4$	−1.11161e20			−0.0941568
$5$			4.52111e24i			1.55344i	0.629845	+	0.776720i	$0.283118\pi$
$5$			4.52111e24i			1.55344i	−0.629845	+	0.776720i	$0.716882\pi$
$6$	−1.51262e27	−	9.72336e26i	−0.879905	−	0.565617i
$7$	−7.40509e29			−1.95479			−0.977393	−	0.211431i	$-0.932187\pi$
$7$	−7.40509e29			−1.95479			−0.977393	+	0.211431i	$0.932187\pi$
$8$			3.84364e31i			0.947530i
$9$	−1.03935e33	−	2.27718e33i	−0.415215	−	0.909723i
$10$	−1.62493e35			−1.62493
$11$		−	3.10104e36i		−	1.10348i	−0.834017	−	0.551738i	$-0.813965\pi$
$11$		−	3.10104e36i		−	1.10348i	0.834017	−	0.551738i	$-0.186035\pi$
$12$	3.00731e36	−	4.67834e36i	0.0509137	−	0.0792041i
$13$	2.12249e37			0.0218187			0.0109093	−	0.999940i	$-0.496527\pi$
$13$	2.12249e37			0.0218187			0.0109093	+	0.999940i	$0.496527\pi$
$14$		−	2.66146e40i		−	2.04474i
$15$	−1.90276e41	−	1.22313e41i	−1.30675	−	0.839997i
$16$	−1.51268e42			−1.08529
$17$		−	6.65739e41i		−	0.0572257i	−0.999591	−	0.0286129i	$-0.990891\pi$
$17$		−	6.65739e41i		−	0.0572257i	0.999591	−	0.0286129i	$-0.00910900\pi$
$18$	8.18440e43	−	3.73552e43i	0.951588	−	0.434323i
$19$	3.67374e44			0.643772			0.321886	−	0.946778i	$-0.395683\pi$
$19$	3.67374e44			0.643772			0.321886	+	0.946778i	$0.395683\pi$
$20$		−	5.02569e44i		−	0.146267i
$21$	2.00335e46	−	3.11653e46i	1.05702	−	1.64435i
$22$	1.11454e47			1.15426
$23$			5.00537e47i			1.09386i	0.837178	+	0.546930i	$0.184204\pi$
$23$			5.00537e47i			1.09386i	−0.837178	+	0.546930i	$0.815796\pi$
$24$	−1.61764e48	−	1.03985e48i	−0.797056	−	0.512361i
$25$	−1.19701e49			−1.41318
$26$			7.62843e47i			0.0228227i
$27$	1.23956e50	+	1.78639e49i	0.989775	+	0.142641i
$28$	8.23155e49			0.184056
$29$		−	4.46438e50i		−	0.292301i	−0.989262	−	0.146151i	$-0.953312\pi$
$29$		−	4.46438e50i		−	0.292301i	0.989262	−	0.146151i	$-0.0466884\pi$
$30$	4.39604e51	−	6.83872e51i	0.878653	−	1.36688i
$31$	−1.45568e52			−0.923436			−0.461718	−	0.887027i	$-0.652767\pi$
$31$	−1.45568e52			−0.923436			−0.461718	+	0.887027i	$0.652767\pi$
$32$		−	8.98934e51i		−	0.187706i
$33$	1.30511e53	+	8.38946e52i	0.928238	+	0.596687i
$34$	2.39273e52			0.0598592
$35$		−	3.34792e54i		−	3.03664i
$36$	1.15535e53	+	2.53133e53i	0.0390953	+	0.0856566i
$37$	7.83434e54			1.01611			0.508056	−	0.861324i	$-0.330364\pi$
$37$	7.83434e54			1.01611			0.508056	+	0.861324i	$0.330364\pi$
$38$			1.32038e55i			0.673398i
$39$	−5.74212e53	+	8.93276e53i	−0.0117981	+	0.0183537i
$40$	−1.73775e56			−1.47193
$41$		−	1.04241e56i		−	0.372051i	−0.982545	−	0.186026i	$-0.940439\pi$
$41$		−	1.04241e56i		−	0.372051i	0.982545	−	0.186026i	$-0.0595608\pi$
$42$	1.12011e57	+	7.20024e56i	1.72003	+	1.10566i
$43$	−1.18190e57			−0.796501			−0.398251	−	0.917277i	$-0.630383\pi$
$43$	−1.18190e57			−0.796501			−0.398251	+	0.917277i	$0.630383\pi$
$44$			3.44714e56i			0.103900i
$45$	1.02954e58	−	4.69901e57i	1.41320	−	0.645012i
$46$	−1.79898e58			−1.14420
$47$		−	1.39113e58i		−	0.416814i	−0.978042	−	0.208407i	$-0.933172\pi$
$47$		−	1.39113e58i		−	0.416814i	0.978042	−	0.208407i	$-0.0668278\pi$
$48$	4.09235e58	−	6.36628e58i	0.586853	−	0.912941i
$49$	4.04850e59			2.82119
$50$		−	4.30216e59i		−	1.47821i
$51$	2.80184e58	+	1.80107e58i	0.0481380	+	0.0309439i
$52$	−2.35937e57			−0.00205437
$53$		−	1.97126e59i		−	0.0881229i	−0.999029	−	0.0440615i	$-0.985970\pi$
$53$		−	1.97126e59i		−	0.0881229i	0.999029	−	0.0440615i	$-0.0140297\pi$
$54$	−6.42045e59	+	4.45510e60i	−0.149205	+	1.03532i
$55$	1.40201e61			1.71419
$56$		−	2.84625e61i		−	1.85222i
$57$	−9.93882e60	+	1.54614e61i	−0.348109	+	0.541537i
$58$	1.60454e61			0.305753
$59$			1.24383e61i			0.130299i	0.997876	+	0.0651493i	$0.0207524\pi$
$59$			1.24383e61i			0.130299i	−0.997876	+	0.0651493i	$0.979248\pi$
$60$	2.11513e61	+	1.35964e61i	0.123039	+	0.0790914i
$61$	−5.47184e62			−1.78480			−0.892399	−	0.451248i	$-0.850979\pi$
$61$	−5.47184e62			−1.78480			−0.892399	+	0.451248i	$0.850979\pi$
$62$		−	5.23186e62i		−	0.965932i
$63$	7.69647e62	+	1.68627e63i	0.811657	+	1.77831i
$64$	−1.46277e63			−0.888947
$65$			9.59600e61i			0.0338940i
$66$	−3.01525e63	+	4.69069e63i	−0.624146	+	0.970955i
$67$	−4.78606e63			−0.585275			−0.292638	−	0.956223i	$-0.594533\pi$
$67$	−4.78606e63			−0.585275			−0.292638	+	0.956223i	$0.594533\pi$
$68$			7.40039e61i			0.00538819i
$69$	−2.10657e64	−	1.35414e64i	−0.920149	−	0.591486i
$70$	1.20328e65			3.17639
$71$		−	8.14760e64i		−	1.30914i	−0.756000	−	0.654572i	$-0.772849\pi$
$71$		−	8.14760e64i		−	1.30914i	0.756000	−	0.654572i	$-0.227151\pi$
$72$	8.75265e64	−	3.99488e64i	0.861990	−	0.393429i
$73$	−2.23896e65			−1.36065			−0.680326	−	0.732910i	$-0.738162\pi$
$73$	−2.23896e65			−1.36065			−0.680326	+	0.732910i	$0.738162\pi$
$74$			2.81574e65i			1.06287i
$75$	3.23835e65	−	5.03776e65i	0.764153	−	1.18876i
$76$	−4.08375e64			−0.0606155
$77$			2.29635e66i			2.15706i
$78$	−3.21052e64	−	2.06377e64i	−0.0191984	−	0.0123410i
$79$	−1.91791e66			−0.734312			−0.367156	−	0.930159i	$-0.619669\pi$
$79$	−1.91791e66			−0.734312			−0.367156	+	0.930159i	$0.619669\pi$
$80$		−	6.83897e66i		−	1.68594i
$81$	−4.10530e66	+	4.73356e66i	−0.655193	+	0.755462i
$82$	3.74652e66			0.389173
$83$			1.95479e67i			1.32851i	0.747505	+	0.664257i	$0.231252\pi$
$83$			1.95479e67i			1.32851i	−0.747505	+	0.664257i	$0.768748\pi$
$84$	−2.22694e66	+	3.46435e66i	−0.0995253	+	0.154827i
$85$	3.00988e66			0.0888968
$86$		−	4.24788e67i		−	0.833156i
$87$	1.87889e67	+	1.20778e67i	0.245882	+	0.158057i
$88$	1.19193e68			1.04558
$89$			5.75653e67i			0.340024i	0.985442	+	0.170012i	$0.0543807\pi$
$89$			5.75653e67i			0.340024i	−0.985442	+	0.170012i	$0.945619\pi$
$90$	1.68887e68	+	3.70025e68i	0.674695	+	1.47824i
$91$	−1.57172e67			−0.0426508
$92$		−	5.56400e67i		−	0.102994i
$93$	3.93816e68	−	6.12641e68i	0.499333	−	0.776789i
$94$	4.99985e68			0.435995
$95$			1.66094e69i			1.00006i
$96$	3.78327e68	+	2.43195e68i	0.157897	+	0.101499i
$97$	1.88301e69			0.546818			0.273409	−	0.961898i	$-0.411849\pi$
$97$	1.88301e69			0.546818			0.273409	+	0.961898i	$0.411849\pi$
$98$			1.45507e70i			2.95102i
$99$	−7.06162e69	+	3.22306e69i	−1.00386	+	0.458180i
$100$	1.33060e69			0.133060
$101$			1.30149e70i			0.918740i	0.888245	+	0.459370i	$0.151925\pi$
$101$			1.30149e70i			0.918740i	−0.888245	+	0.459370i	$0.848075\pi$
$102$	−6.47322e68	+	1.00701e69i	−0.0323679	+	0.0503532i
$103$	4.39362e70			1.56142			0.780710	−	0.624893i	$-0.214858\pi$
$103$	4.39362e70			1.56142			0.780710	+	0.624893i	$0.214858\pi$
$104$			8.15808e68i			0.0206738i
$105$	1.40901e71	+	9.05738e70i	2.55441	+	1.64201i
$106$	7.08490e69			0.0921783
$107$		−	1.08435e71i		−	1.01564i	−0.861464	−	0.507818i	$-0.830452\pi$
$107$		−	1.08435e71i		−	1.01564i	0.861464	−	0.507818i	$-0.169548\pi$
$108$	−1.37790e70	−	1.98576e69i	−0.0931940	−	0.0134306i
$109$	−3.66250e70			−0.179411			−0.0897056	−	0.995968i	$-0.528593\pi$
$109$	−3.66250e70			−0.179411			−0.0897056	+	0.995968i	$0.528593\pi$
$110$			5.03897e71i			1.79307i
$111$	−2.11948e71	+	3.29718e71i	−0.549446	+	0.854748i
$112$	1.12015e72			2.12151
$113$			5.32278e71i			0.738572i	0.929316	+	0.369286i	$0.120398\pi$
$113$			5.32278e71i			0.738572i	−0.929316	+	0.369286i	$0.879602\pi$
$114$	−5.55697e71	−	3.57211e71i	−0.566458	−	0.364129i
$115$	−2.26298e72			−1.69925
$116$			4.96263e70i			0.0275221i
$117$	−2.20601e70	−	4.83329e70i	−0.00905944	−	0.0198489i
$118$	−4.47044e71			−0.136295
$119$			4.92986e71i			0.111864i
$120$	4.70126e72	−	7.31354e72i	0.795922	−	1.23818i
$121$	−1.71897e72			−0.217661
$122$		−	1.96663e73i		−	1.86693i
$123$	4.38711e72	+	2.82010e72i	0.312967	+	0.201181i
$124$	1.61814e72			0.0869478
$125$		−	1.58228e73i		−	0.641849i
$126$	−6.06062e73	+	2.76619e73i	−1.86015	+	0.849009i
$127$	−1.88173e73			−0.437953			−0.218976	−	0.975730i	$-0.570272\pi$
$127$	−1.88173e73			−0.437953			−0.218976	+	0.975730i	$0.570272\pi$
$128$		−	6.31860e73i		−	1.11756i
$129$	3.19749e73	−	4.97419e73i	0.430695	−	0.670012i
$130$	−3.44889e72			−0.0354538
$131$		−	9.05888e73i		−	0.712162i	−0.934455	−	0.356081i	$-0.884113\pi$
$131$		−	9.05888e73i		−	0.712162i	0.934455	−	0.356081i	$-0.115887\pi$
$132$	−1.45077e73	−	9.32578e72i	−0.0873999	−	0.0561821i
$133$	−2.72044e74			−1.25844
$134$		−	1.72016e74i		−	0.612209i
$135$	−8.07645e73	+	5.60419e74i	−0.221584	+	1.53756i
$136$	2.55886e73			0.0542231
$137$			6.98683e74i			1.14567i	0.819670	+	0.572836i	$0.194157\pi$
$137$			6.98683e74i			1.14567i	−0.819670	+	0.572836i	$0.805843\pi$
$138$	4.86690e74	−	7.57122e74i	0.618706	−	0.962494i
$139$	4.99052e74			0.492751			0.246376	−	0.969174i	$-0.420760\pi$
$139$	4.99052e74			0.492751			0.246376	+	0.969174i	$0.420760\pi$
$140$			3.72157e74i			0.285921i
$141$	5.85474e74	+	3.76352e74i	0.350621	+	0.225385i
$142$	2.92832e75			1.36939
$143$		−	6.58192e73i		−	0.0240764i
$144$	1.57220e75	+	3.44463e75i	0.450629	+	0.987315i
$145$	2.01839e75			0.454073
$146$		−	8.04705e75i		−	1.42327i
$147$	−1.09527e76	+	1.70386e76i	−1.52551	+	2.37317i
$148$	−8.70870e74			−0.0956739
$149$			1.53822e74i			0.0133505i	0.999978	+	0.00667526i	$0.00212482\pi$
$149$			1.53822e74i			0.0133505i	−0.999978	+	0.00667526i	$0.997875\pi$
$150$	1.81062e76	+	1.16390e76i	1.24346	+	0.799319i
$151$	2.24915e75			0.122413			0.0612063	−	0.998125i	$-0.480505\pi$
$151$	2.24915e75			0.122413			0.0612063	+	0.998125i	$0.480505\pi$
$152$			1.41205e76i			0.609993i
$153$	−1.51601e75	+	6.91934e74i	−0.0520596	+	0.0237610i
$154$	−8.25330e76			−2.25633
$155$		−	6.58129e76i		−	1.43450i
$156$	6.38298e73	−	9.92972e73i	0.00111087	−	0.00172813i
$157$	1.22164e77			1.70002			0.850011	−	0.526765i	$-0.176595\pi$
$157$	1.22164e77			1.70002			0.850011	+	0.526765i	$0.176595\pi$
$158$		−	6.89316e76i		−	0.768105i
$159$	8.29630e75	+	5.33300e75i	0.0741285	+	0.0476510i
$160$	4.06418e76			0.291590
$161$		−	3.70652e77i		−	2.13826i
$162$	−1.70129e77	−	1.47548e77i	−0.790228	−	0.685344i
$163$	−3.87023e76			−0.144934			−0.0724670	−	0.997371i	$-0.523087\pi$
$163$	−3.87023e76			−0.144934			−0.0724670	+	0.997371i	$0.523087\pi$
$164$			1.15875e76i			0.0350312i
$165$	−3.79297e77	+	5.90055e77i	−0.926917	+	1.44196i
$166$	−7.02569e77			−1.38965
$167$		−	4.05162e77i		−	0.649460i	−0.945807	−	0.324730i	$-0.894727\pi$
$167$		−	4.05162e77i		−	0.649460i	0.945807	−	0.324730i	$-0.105273\pi$
$168$	1.19788e78	+	7.70016e77i	1.55807	+	1.00156i
$169$	−9.45862e77			−0.999524
$170$			1.08178e77i			0.0929878i
$171$	−3.81829e77	−	8.36576e77i	−0.267304	−	0.585654i
$172$	1.31381e77			0.0749960
$173$		−	1.78714e78i		−	0.832810i	−0.909179	−	0.416405i	$-0.863290\pi$
$173$		−	1.78714e78i		−	0.832810i	0.909179	−	0.416405i	$-0.136710\pi$
$174$	−4.34088e77	+	6.75290e77i	−0.165331	+	0.257198i
$175$	8.86396e78			2.76246
$176$			4.69087e78i			1.19759i
$177$	−5.23480e77	−	3.36502e77i	−0.109606	−	0.0704568i
$178$	−2.06895e78			−0.355672
$179$			1.31236e79i			1.85437i	0.374601	+	0.927186i	$0.377780\pi$
$179$			1.31236e79i			1.85437i	−0.374601	+	0.927186i	$0.622220\pi$
$180$	−1.14444e78	+	5.22345e77i	−0.133062	+	0.0607323i
$181$	6.67267e78			0.639071			0.319536	−	0.947574i	$-0.396473\pi$
$181$	6.67267e78			0.639071			0.319536	+	0.947574i	$0.396473\pi$
$182$		−	5.64892e77i		−	0.0446136i
$183$	1.48034e79	−	2.30289e79i	0.965099	−	1.50136i
$184$	−1.92388e79			−1.03646
$185$			3.54199e79i			1.57847i
$186$	2.20189e79	+	1.41541e79i	0.812537	+	0.522312i
$187$	−2.06448e78			−0.0631473
$188$			1.54639e78i			0.0392458i
$189$	−9.17907e79	−	1.32284e79i	−1.93480	−	0.278832i
$190$	−5.96956e79			−1.04608
$191$		−	1.17782e80i		−	1.71756i	−0.512348	−	0.858778i	$-0.671224\pi$
$191$		−	1.17782e80i		−	1.71756i	0.512348	−	0.858778i	$-0.328776\pi$
$192$	3.95733e79	−	6.15623e79i	0.480683	−	0.747777i
$193$	1.13375e80			1.14819			0.574094	−	0.818790i	$-0.305355\pi$
$193$	1.13375e80			1.14819			0.574094	+	0.818790i	$0.305355\pi$
$194$			6.76773e79i			0.571982i
$195$	−4.03860e78	−	2.59608e78i	−0.0285114	−	0.0183276i
$196$	−4.50035e79			−0.265634
$197$			8.67794e79i			0.428646i	0.976763	+	0.214323i	$0.0687545\pi$
$197$			8.67794e79i			0.428646i	−0.976763	+	0.214323i	$0.931246\pi$
$198$	−1.15840e80	−	2.53801e80i	−0.479266	−	1.05006i
$199$	9.39266e78			0.0325785			0.0162893	−	0.999867i	$-0.494815\pi$
$199$	9.39266e78			0.0325785			0.0162893	+	0.999867i	$0.494815\pi$
$200$		−	4.60087e80i		−	1.33903i
$201$	1.29481e80	−	2.01427e80i	0.316478	−	0.492330i
$202$	−4.67768e80			−0.961020
$203$			3.30591e80i			0.571387i
$204$	−3.11455e78	−	2.00208e78i	−0.00453251	−	0.00291357i
$205$	4.71284e80			0.577960
$206$			1.57911e81i			1.63328i
$207$	1.13981e81	−	5.20232e80i	0.995110	−	0.454187i
$208$	−3.21064e79			−0.0236796
$209$		−	1.13924e81i		−	0.710388i
$210$	−3.25531e81	+	5.06413e81i	−1.71758	+	2.67196i
$211$	−1.30082e81			−0.581210			−0.290605	−	0.956843i	$-0.593857\pi$
$211$	−1.30082e81			−0.581210			−0.290605	+	0.956843i	$0.593857\pi$
$212$			2.19127e79i			0.00829737i
$213$	3.42902e81	+	2.20423e81i	1.10124	+	0.707898i
$214$	3.89727e81			1.06238
$215$		−	5.34352e81i		−	1.23732i
$216$	−6.86623e80	+	4.76442e81i	−0.135156	+	0.937841i
$217$	1.07795e82			1.80512
$218$		−	1.31634e81i		−	0.187668i
$219$	6.05723e81	−	9.42295e81i	0.735749	−	1.14457i
$220$	−1.55849e81			−0.161402
$221$		−	1.41302e79i		−	0.00124859i
$222$	−1.18504e82	−	7.61761e81i	−0.894083	−	0.574731i
$223$	−3.01451e82			−1.94333			−0.971664	−	0.236366i	$-0.924044\pi$
$223$	−3.01451e82			−1.94333			−0.971664	+	0.236366i	$0.924044\pi$
$224$			6.65669e81i			0.366925i
$225$	1.24411e82	+	2.72580e82i	0.586773	+	1.28560i
$226$	−1.91306e82			−0.772560
$227$		−	2.33908e81i		−	0.0809357i	−0.999181	−	0.0404678i	$-0.987115\pi$
$227$		−	2.33908e81i		−	0.0809357i	0.999181	−	0.0404678i	$-0.0128848\pi$
$228$	1.10481e81	−	1.71870e81i	0.0327768	−	0.0509894i
$229$	1.50099e82			0.382064			0.191032	−	0.981584i	$-0.438817\pi$
$229$	1.50099e82			0.382064			0.191032	+	0.981584i	$0.438817\pi$
$230$		−	8.13337e82i		−	1.77745i
$231$	−9.66447e82	−	6.21248e82i	−1.81451	−	1.16639i
$232$	1.71594e82			0.276964
$233$			5.29580e82i			0.735316i	0.929961	+	0.367658i	$0.119840\pi$
$233$			5.29580e82i			0.735316i	−0.929961	+	0.367658i	$0.880160\pi$
$234$	1.73713e81	−	7.92859e80i	0.0207624	−	0.00947635i
$235$	6.28944e82			0.647496
$236$		−	1.38265e81i		−	0.0122685i
$237$	5.18867e82	−	8.07178e82i	0.397067	−	0.617699i
$238$	−1.77184e82			−0.117012
$239$		−	7.59041e82i		−	0.432852i	−0.976299	−	0.216426i	$-0.930560\pi$
$239$		−	7.59041e82i		−	0.432852i	0.976299	−	0.216426i	$-0.0694399\pi$
$240$	2.87826e83	+	1.85020e83i	1.41820	+	0.911641i
$241$	−4.65753e82			−0.198408			−0.0992040	−	0.995067i	$-0.531630\pi$
$241$	−4.65753e82			−0.198408			−0.0992040	+	0.995067i	$0.531630\pi$
$242$		−	6.17816e82i		−	0.227678i
$243$	−8.81543e82	−	3.00837e83i	−0.281206	−	0.959648i
$244$	6.08253e82			0.168051
$245$			1.83037e84i			4.38255i
$246$	−1.01357e83	+	1.57677e83i	−0.210439	+	0.327370i
$247$	7.79747e81			0.0140462
$248$		−	5.59511e83i		−	0.874983i
$249$	−8.22696e83	−	5.28842e83i	−1.11754	−	0.718371i
$250$	5.68686e83			0.671386
$251$			9.96266e83i			1.02281i	0.859340	+	0.511405i	$0.170875\pi$
$251$			9.96266e83i			1.02281i	−0.859340	+	0.511405i	$0.829125\pi$
$252$	−8.55545e82	−	1.87447e83i	−0.0764230	−	0.167440i
$253$	1.55218e84			1.20705
$254$		−	6.76312e83i		−	0.458107i
$255$	−8.14283e82	+	1.26674e83i	−0.0480695	+	0.0747795i
$256$	5.44034e83			0.280045
$257$		−	2.84222e84i		−	1.27643i	−0.769856	−	0.638217i	$-0.779672\pi$
$257$		−	2.84222e84i		−	1.27643i	0.769856	−	0.638217i	$-0.220328\pi$
$258$	1.78777e84	+	1.14921e84i	0.700846	+	0.450515i
$259$	−5.80140e84			−1.98628
$260$		−	1.06670e82i		−	0.00319135i
$261$	−1.01662e84	+	4.64004e83i	−0.265913	+	0.121368i
$262$	3.25585e84			0.744936
$263$		−	7.57922e84i		−	1.51766i	−0.651291	−	0.758828i	$-0.725772\pi$
$263$		−	7.57922e84i		−	1.51766i	0.651291	−	0.758828i	$-0.274228\pi$
$264$	−3.22461e84	+	5.01637e84i	−0.565378	+	0.879533i
$265$	8.91229e83			0.136894
$266$		−	9.77751e84i		−	1.31635i
$267$	−2.42271e84	−	1.55735e84i	−0.286027	−	0.183863i
$268$	5.32022e83			0.0551076
$269$			1.91045e84i			0.173702i	0.996221	+	0.0868510i	$0.0276804\pi$
$269$			1.91045e84i			0.173702i	−0.996221	+	0.0868510i	$0.972320\pi$
$270$	−2.01420e85	−	2.90275e84i	−1.60831	−	0.231781i
$271$	1.77914e85			1.24820			0.624100	−	0.781345i	$-0.285466\pi$
$271$	1.77914e85			1.24820			0.624100	+	0.781345i	$0.285466\pi$
$272$			1.00705e84i			0.0621066i
$273$	4.25209e83	−	6.61479e83i	0.0230627	−	0.0358776i
$274$	−2.51114e85			−1.19840
$275$			3.71197e85i			1.55941i
$276$	2.34168e84	+	1.50527e84i	0.0866382	+	0.0556925i
$277$	4.80070e84			0.156500			0.0782498	−	0.996934i	$-0.475067\pi$
$277$	4.80070e84			0.156500			0.0782498	+	0.996934i	$0.475067\pi$
$278$			1.79364e85i			0.515428i
$279$	1.51296e85	+	3.31485e85i	0.383425	+	0.840071i
$280$	1.28682e86			2.87731
$281$		−	6.61386e85i		−	1.30537i	−0.757629	−	0.652685i	$-0.773643\pi$
$281$		−	6.61386e85i		−	1.30537i	0.757629	−	0.652685i	$-0.226357\pi$
$282$	−1.35264e85	+	2.10425e85i	−0.235757	+	0.366757i
$283$	1.05548e85			0.162527			0.0812633	−	0.996693i	$-0.474105\pi$
$283$	1.05548e85			0.162527			0.0812633	+	0.996693i	$0.474105\pi$
$284$			9.05693e84i			0.123265i
$285$	−6.99026e85	−	4.49345e85i	−0.841246	−	0.540767i
$286$	2.36561e84			0.0251844
$287$			7.71913e85i			0.727281i
$288$	−2.04703e85	+	9.34305e84i	−0.170761	+	0.0779384i
$289$	1.34896e86			0.996725
$290$			7.25430e85i			0.474969i
$291$	−5.09425e85	+	7.92490e85i	−0.295683	+	0.459980i
$292$	2.48885e85			0.128115
$293$			7.28463e84i			0.0332691i	0.999862	+	0.0166345i	$0.00529518\pi$
$293$			7.28463e84i			0.0332691i	−0.999862	+	0.0166345i	$0.994705\pi$
$294$	−6.12385e86	−	3.93651e86i	−2.48238	−	1.59571i
$295$	−5.62348e85			−0.202411
$296$			3.01123e86i			0.962797i
$297$	5.53966e85	−	3.84393e86i	0.157401	−	1.09219i
$298$	−5.52849e84			−0.0139649
$299$			1.06238e85i			0.0238666i
$300$	−3.59978e85	+	5.60001e85i	−0.0719501	+	0.111930i
$301$	8.75211e86			1.55699
$302$			8.08368e85i			0.128046i
$303$	−5.47748e86	−	3.52101e86i	−0.772838	−	0.496793i
$304$	−5.55717e86			−0.698680
$305$		−	2.47388e87i		−	2.77258i
$306$	−2.48688e85	−	5.44867e85i	−0.0248545	−	0.0544553i
$307$	1.16936e87			1.04257			0.521285	−	0.853383i	$-0.325453\pi$
$307$	1.16936e87			1.04257			0.521285	+	0.853383i	$0.325453\pi$
$308$		−	2.55264e86i		−	0.203102i
$309$	−1.18864e87	+	1.84911e87i	−0.844312	+	1.31346i
$310$	2.36538e87			1.50052
$311$			1.08138e87i			0.612865i	0.951892	+	0.306432i	$0.0991354\pi$
$311$			1.08138e87i			0.612865i	−0.951892	+	0.306432i	$0.900865\pi$
$312$	−3.43343e85	−	2.20706e85i	−0.0173907	−	0.0111790i
$313$	1.96393e87			0.889351			0.444675	−	0.895692i	$-0.353319\pi$
$313$	1.96393e87			0.889351			0.444675	+	0.895692i	$0.353319\pi$
$314$			4.39068e87i			1.77826i
$315$	−7.62382e87	+	3.47966e87i	−2.76251	+	1.26086i
$316$	2.13197e86			0.0691405
$317$			3.17733e86i			0.0922545i	0.998936	+	0.0461273i	$0.0146880\pi$
$317$			3.17733e86i			0.0922545i	−0.998936	+	0.0461273i	$0.985312\pi$
$318$	−1.91673e86	+	2.98177e86i	−0.0498439	+	0.0775398i
$319$	−1.38442e87			−0.322548
$320$		−	6.61332e87i		−	1.38093i
$321$	4.56363e87	+	2.93358e87i	0.854348	+	0.549189i
$322$	1.33216e88			2.23666
$323$		−	2.44575e86i		−	0.0368403i
$324$	4.56348e86	−	5.26186e86i	0.0616908	−	0.0711318i
$325$	−2.54064e86			−0.0308337
$326$		−	1.39100e87i		−	0.151604i
$327$	9.90841e86	−	1.54141e87i	0.0970136	−	0.150920i
$328$	4.00664e87			0.352530
$329$			1.03014e88i			0.814782i
$330$	−2.12071e88	−	1.36323e88i	−1.50832	−	0.969574i
$331$	−8.76038e87			−0.560458			−0.280229	−	0.959933i	$-0.590410\pi$
$331$	−8.76038e87			−0.560458			−0.280229	+	0.959933i	$0.590410\pi$
$332$		−	2.17295e87i		−	0.125089i
$333$	−8.14260e87	−	1.78402e88i	−0.421905	−	0.924381i
$334$	1.45619e88			0.679348
$335$		−	2.16383e88i		−	0.909190i
$336$	−3.03042e88	+	4.71429e88i	−1.14717	+	1.78460i
$337$	3.87239e88			1.32109			0.660546	−	0.750786i	$-0.270325\pi$
$337$	3.87239e88			1.32109			0.660546	+	0.750786i	$0.270325\pi$
$338$		−	3.39952e88i		−	1.04552i
$339$	−2.24016e88	−	1.44001e88i	−0.621282	−	0.399370i
$340$	−3.34580e86			−0.00837024
$341$			4.51412e88i			1.01899i
$342$	3.00673e88	−	1.37233e88i	0.612606	−	0.279605i
$343$	−1.93530e89			−3.56003
$344$		−	4.54281e88i		−	0.754708i
$345$	6.12221e88	−	9.52404e88i	0.918839	−	1.42940i
$346$	6.42317e88			0.871136
$347$			7.66494e88i			0.939674i	0.882753	+	0.469837i	$0.155687\pi$
$347$			7.66494e88i			0.939674i	−0.882753	+	0.469837i	$0.844313\pi$
$348$	−2.08858e87	−	1.34258e87i	−0.0231515	−	0.0148821i
$349$	1.78384e89			1.78840			0.894201	−	0.447666i	$-0.147745\pi$
$349$	1.78384e89			1.78840			0.894201	+	0.447666i	$0.147745\pi$
$350$			3.18579e89i			2.88959i
$351$	2.63096e87	+	3.79159e86i	0.0215956	+	0.00311223i
$352$	−2.78763e88			−0.207129
$353$		−	1.76715e89i		−	1.18894i	−0.804118	−	0.594469i	$-0.797362\pi$
$353$		−	1.76715e89i		−	1.18894i	0.804118	−	0.594469i	$-0.202638\pi$
$354$	1.20942e88	−	1.88144e88i	0.0736992	−	0.114650i
$355$	3.68362e89			2.03368
$356$		−	6.39899e87i		−	0.0320156i
$357$	−2.07479e88	−	1.33371e88i	−0.0940994	−	0.0604886i
$358$	−4.71675e89			−1.93971
$359$			1.32623e89i			0.494666i	0.968931	+	0.247333i	$0.0795542\pi$
$359$			1.32623e89i			0.494666i	−0.968931	+	0.247333i	$0.920446\pi$
$360$	1.80613e89	+	3.95717e89i	0.611168	+	1.33905i
$361$	−1.90687e89			−0.585558
$362$			2.39822e89i			0.668481i
$363$	4.65046e88	−	7.23452e88i	0.117697	−	0.183095i
$364$	1.74714e87			0.00401586
$365$		−	1.01226e90i		−	2.11369i
$366$	8.27681e89	+	5.32047e89i	1.57045	+	1.00951i
$367$	−4.64116e89			−0.800413			−0.400207	−	0.916425i	$-0.631062\pi$
$367$	−4.64116e89			−0.800413			−0.400207	+	0.916425i	$0.631062\pi$
$368$		−	7.57150e89i		−	1.18716i
$369$	−2.37375e89	+	1.08343e89i	−0.338464	+	0.154481i
$370$	−1.27302e90			−1.65111
$371$			1.45974e89i			0.172261i
$372$	−4.37768e88	+	6.81016e88i	−0.0470155	+	0.0731400i
$373$	−6.77190e89			−0.662066			−0.331033	−	0.943619i	$-0.607397\pi$
$373$	−6.77190e89			−0.662066			−0.331033	+	0.943619i	$0.607397\pi$
$374$		−	7.41994e88i		−	0.0660533i
$375$	6.65922e89	+	4.28065e89i	0.539919	+	0.347069i
$376$	5.34699e89			0.394943
$377$		−	9.47559e87i		−	0.00637762i
$378$	4.75440e89	−	3.29904e90i	0.291664	−	2.02384i
$379$	−5.48447e89			−0.306734			−0.153367	−	0.988169i	$-0.549012\pi$
$379$	−5.48447e89			−0.306734			−0.153367	+	0.988169i	$0.549012\pi$
$380$		−	1.84631e89i		−	0.0941626i
$381$	5.09078e89	−	7.91950e89i	0.236816	−	0.368403i
$382$	4.23320e90			1.79660
$383$		−	3.94644e90i		−	1.52844i	−0.644956	−	0.764220i	$-0.723124\pi$
$383$		−	3.94644e90i		−	1.52844i	0.644956	−	0.764220i	$-0.276876\pi$
$384$	2.65926e90	+	1.70942e90i	0.940087	+	0.604303i
$385$	−1.03820e91			−3.35087
$386$			4.07482e90i			1.20103i
$387$	1.22841e90	+	2.69141e90i	0.330719	+	0.724596i
$388$	−2.09317e89			−0.0514866
$389$			2.50415e90i			0.562892i	0.959577	+	0.281446i	$0.0908140\pi$
$389$			2.50415e90i			0.562892i	−0.959577	+	0.281446i	$0.909186\pi$
$390$	9.33054e88	−	1.45151e89i	0.0191710	−	0.0298235i
$391$	3.33227e89			0.0625970
$392$			1.55610e91i			2.67316i
$393$	3.81254e90	+	2.45076e90i	0.599067	+	0.385090i
$394$	−3.11893e90			−0.448372
$395$		−	8.67109e90i		−	1.14071i
$396$	7.84975e89	−	3.58278e89i	0.0945201	−	0.0431408i
$397$	−1.28063e90			−0.141175			−0.0705874	−	0.997506i	$-0.522487\pi$
$397$	−1.28063e90			−0.141175			−0.0705874	+	0.997506i	$0.522487\pi$
$398$			3.37581e89i			0.0340777i
$399$	7.35979e90	−	1.14493e91i	0.680478	−	1.05859i
$400$	1.81069e91			1.53371
$401$			9.43039e90i			0.731942i	0.930626	+	0.365971i	$0.119263\pi$
$401$			9.43039e90i			0.731942i	−0.930626	+	0.365971i	$0.880737\pi$
$402$	7.23949e90	+	4.65366e90i	0.514987	+	0.331042i
$403$	−3.08967e89			−0.0201481
$404$		−	1.44674e90i		−	0.0865055i
$405$	−2.14010e91	−	1.85605e91i	−1.17357	−	1.01780i
$406$	−1.18818e91			−0.597681
$407$		−	2.42946e91i		−	1.12126i
$408$	−6.92266e89	+	1.07693e90i	−0.0293202	+	0.0456121i
$409$	2.38883e91			0.928688			0.464344	−	0.885655i	$-0.346290\pi$
$409$	2.38883e91			0.928688			0.464344	+	0.885655i	$0.346290\pi$
$410$			1.69384e91i			0.604557i
$411$	−2.94050e91	−	1.89020e91i	−0.963733	−	0.619503i
$412$	−4.88398e90			−0.147018
$413$		−	9.21066e90i		−	0.254706i
$414$	1.86976e91	+	4.09659e91i	0.475089	+	1.04090i
$415$	−8.83780e91			−2.06377
$416$		−	1.90798e89i		−	0.00409550i
$417$	−1.35012e91	+	2.10032e91i	−0.266447	+	0.414500i
$418$	4.09454e91			0.743079
$419$		−	8.86601e91i		−	1.47992i	−0.672652	−	0.739959i	$-0.734845\pi$
$419$		−	8.86601e91i		−	1.47992i	0.672652	−	0.739959i	$-0.265155\pi$
$420$	−1.56627e91	−	1.00682e91i	−0.240515	−	0.154607i
$421$	−3.87699e91			−0.547800			−0.273900	−	0.961758i	$-0.588314\pi$
$421$	−3.87699e91			−0.547800			−0.273900	+	0.961758i	$0.588314\pi$
$422$		−	4.67529e91i		−	0.607957i
$423$	−3.16785e91	+	1.44587e91i	−0.379185	+	0.173067i
$424$	7.57682e90			0.0834991
$425$			7.96895e90i			0.0808702i
$426$	−7.92221e91	+	1.23242e92i	−0.740475	+	1.15192i
$427$	4.05195e92			3.48890
$428$			1.20537e91i			0.0956291i
$429$	2.77008e90	+	1.78065e90i	0.0202529	+	0.0130189i
$430$	1.92051e92			1.29426
$431$		−	2.18570e92i		−	1.35795i	−0.734159	−	0.678977i	$-0.762423\pi$
$431$		−	2.18570e92i		−	1.35795i	0.734159	−	0.678977i	$-0.237577\pi$
$432$	−1.87505e92	−	2.70223e91i	−1.07419	−	0.154807i
$433$	−4.76221e91			−0.251613			−0.125806	−	0.992055i	$-0.540152\pi$
$433$	−4.76221e91			−0.251613			−0.125806	+	0.992055i	$0.540152\pi$
$434$			3.87424e92i			1.88819i
$435$	−5.46050e91	+	8.49466e91i	−0.245532	+	0.381963i
$436$	4.07126e90			0.0168928
$437$			1.83884e92i			0.704196i
$438$	3.38670e92	+	2.17703e92i	1.19724	+	0.769608i
$439$	−1.20661e92			−0.393831			−0.196916	−	0.980420i	$-0.563093\pi$
$439$	−1.20661e92			−0.393831			−0.196916	+	0.980420i	$0.563093\pi$
$440$			5.38883e92i			1.62424i
$441$	−4.20781e92	−	9.21917e92i	−1.17140	−	2.56650i
$442$	5.07854e89			0.00130605
$443$			5.68726e92i			1.35136i	0.737193	+	0.675682i	$0.236151\pi$
$443$			5.68726e92i			1.35136i	−0.737193	+	0.675682i	$0.763849\pi$
$444$	2.35603e91	−	3.66517e91i	0.0517340	−	0.0804803i
$445$	−2.60259e92			−0.528208
$446$		−	1.08344e93i		−	2.03276i
$447$	−6.47377e90	−	4.16145e90i	−0.0112304	−	0.00721906i
$448$	1.08319e93			1.73770
$449$		−	8.09292e92i		−	1.20084i	−0.799687	−	0.600418i	$-0.795001\pi$
$449$		−	8.09292e92i		−	1.20084i	0.799687	−	0.600418i	$-0.204999\pi$
$450$	−9.79680e92	+	4.47145e92i	−1.34476	+	0.613776i
$451$	−3.23255e92			−0.410550
$452$		−	5.91683e91i		−	0.0695415i
$453$	−6.08480e91	+	9.46585e91i	−0.0661926	+	0.102973i
$454$	8.40688e91			0.0846603
$455$		−	7.10593e91i		−	0.0662555i
$456$	−5.94279e92	−	3.82012e92i	−0.513123	−	0.329843i
$457$	3.71819e92			0.297348			0.148674	−	0.988886i	$-0.452500\pi$
$457$	3.71819e92			0.297348			0.148674	+	0.988886i	$0.452500\pi$
$458$			5.39471e92i			0.399647i
$459$	1.18927e91	−	8.25224e91i	0.00816273	−	0.0566406i
$460$	2.51555e92			0.159996
$461$		−	6.27656e92i		−	0.369989i	−0.982740	−	0.184995i	$-0.940773\pi$
$461$		−	6.27656e92i		−	0.369989i	0.982740	−	0.184995i	$-0.0592268\pi$
$462$	2.23282e93	−	3.47350e93i	1.22007	−	1.89801i
$463$	−3.47563e93			−1.76076			−0.880378	−	0.474272i	$-0.842711\pi$
$463$	−3.47563e93			−1.76076			−0.880378	+	0.474272i	$0.842711\pi$
$464$			6.75315e92i			0.317232i
$465$	2.76982e93	+	1.78048e93i	1.20670	+	0.775684i
$466$	−1.90336e93			−0.769155
$467$		−	9.47096e92i		−	0.355061i	−0.984115	−	0.177531i	$-0.943189\pi$
$467$		−	9.47096e92i		−	0.355061i	0.984115	−	0.177531i	$-0.0568109\pi$
$468$	2.45221e90	+	5.37271e90i	0.000853008	+	0.00186891i
$469$	3.54412e93			1.14409
$470$			2.26049e93i			0.677293i
$471$	−3.30498e93	+	5.14141e93i	−0.919258	+	1.43005i
$472$	−4.78082e92			−0.123462
$473$			3.66513e93i			0.878921i
$474$	2.90107e93	+	1.86486e93i	0.646125	+	0.415340i
$475$	−4.39750e93			−0.909765
$476$		−	5.48006e91i		−	0.0105328i
$477$	−4.48892e92	+	2.04883e92i	−0.0801675	+	0.0365900i
$478$	2.72807e93			0.452771
$479$		−	7.30323e93i		−	1.12661i	−0.826251	−	0.563303i	$-0.809531\pi$
$479$		−	7.30323e93i		−	1.12661i	0.826251	−	0.563303i	$-0.190469\pi$
$480$	−1.09951e93	+	1.71046e93i	−0.157673	+	0.245284i
$481$	1.66283e92			0.0221702
$482$		−	1.67396e93i		−	0.207539i
$483$	1.55994e94	+	1.00275e94i	1.79869	+	1.15623i
$484$	1.91082e92			0.0204943
$485$			8.51331e93i			0.849450i
$486$	1.08124e94	−	3.16835e93i	1.00381	−	0.294147i
$487$	1.63822e94			1.41533			0.707667	−	0.706546i	$-0.249748\pi$
$487$	1.63822e94			1.41533			0.707667	+	0.706546i	$0.249748\pi$
$488$		−	2.10318e94i		−	1.69115i
$489$	1.04704e93	−	1.62883e93i	0.0783707	−	0.121918i
$490$	−6.57853e94			−4.58423
$491$		−	1.73916e94i		−	1.12846i	−0.825617	−	0.564231i	$-0.809173\pi$
$491$		−	1.73916e94i		−	1.12846i	0.825617	−	0.564231i	$-0.190827\pi$
$492$	−4.87674e92	−	3.13485e92i	−0.0294680	−	0.0189425i
$493$	−2.97211e92			−0.0167272
$494$			2.80248e92i			0.0146926i
$495$	−1.45718e94	−	3.19263e94i	−0.711756	−	1.55944i
$496$	2.20197e94			1.00220
$497$			6.03337e94i			2.55910i
$498$	1.90071e94	−	2.95685e94i	0.751430	−	1.16897i
$499$	2.59080e93			0.0954806			0.0477403	−	0.998860i	$-0.484798\pi$
$499$	2.59080e93			0.0954806			0.0477403	+	0.998860i	$0.484798\pi$
$500$			1.75887e93i			0.0604344i
$501$	1.70518e94	+	1.09611e94i	0.546322	+	0.351185i
$502$	−3.58068e94			−1.06988
$503$		−	2.24971e94i		−	0.626969i	−0.949593	−	0.313485i	$-0.898504\pi$
$503$		−	2.24971e94i		−	0.626969i	0.949593	−	0.313485i	$-0.101496\pi$
$504$	−6.48142e94	+	2.95824e94i	−1.68501	+	0.769069i
$505$	−5.88417e94			−1.42721
$506$			5.57870e94i			1.26260i
$507$	2.55891e94	−	3.98078e94i	0.540476	−	0.840794i
$508$	2.09174e93			0.0412362
$509$		−	5.51952e94i		−	1.01573i	−0.861436	−	0.507866i	$-0.830435\pi$
$509$		−	5.51952e94i		−	1.01573i	0.861436	−	0.507866i	$-0.169565\pi$
$510$	−4.55280e93	−	2.92661e93i	−0.0782208	−	0.0502816i
$511$	1.65797e95			2.65978
$512$		−	5.50437e94i		−	0.824630i
$513$	4.55382e94	+	6.56272e93i	0.637189	+	0.0918282i
$514$	1.02152e95			1.33518
$515$			1.98640e95i			2.42557i
$516$	−3.55435e93	+	5.52935e93i	−0.0405528	+	0.0630862i
$517$	−4.31394e94			−0.459944
$518$		−	2.08508e95i		−	2.07769i
$519$	7.52142e94	+	4.83489e94i	0.700555	+	0.450328i
$520$	−3.68835e93			−0.0321156
$521$			1.56070e95i			1.27057i	0.772278	+	0.635284i	$0.219117\pi$
$521$			1.56070e95i			1.27057i	−0.772278	+	0.635284i	$0.780883\pi$
$522$	−1.66768e94	−	3.65382e94i	−0.126953	−	0.278151i
$523$	−1.96925e95			−1.40198			−0.700989	−	0.713172i	$-0.747258\pi$
$523$	−1.96925e95			−1.40198			−0.700989	+	0.713172i	$0.747258\pi$
$524$			1.00699e94i			0.0670549i
$525$	−2.39803e95	+	3.73051e95i	−1.49375	+	2.32377i
$526$	2.72404e95			1.58750
$527$			9.69103e93i			0.0528443i
$528$	−1.97421e95	−	1.26905e95i	−1.00741	−	0.647579i
$529$	−4.11507e94			−0.196530
$530$			3.20316e94i			0.143194i
$531$	2.83242e94	−	1.29277e94i	0.118536	−	0.0541020i
$532$	3.02406e94			0.118490
$533$		−	2.21250e93i		−	0.00811766i
$534$	5.59728e94	−	8.70743e94i	0.192324	−	0.299189i
$535$	4.90248e95			1.57773
$536$		−	1.83959e95i		−	0.554566i
$537$	−5.52323e95	−	3.55042e95i	−1.55989	−	1.00272i
$538$	−6.86633e94			−0.181696
$539$		−	1.25546e96i		−	3.11311i
$540$	8.97784e93	−	6.22966e94i	0.0208637	−	0.144771i
$541$	−4.33587e94			−0.0944435			−0.0472217	−	0.998884i	$-0.515037\pi$
$541$	−4.33587e94			−0.0944435			−0.0472217	+	0.998884i	$0.515037\pi$
$542$			6.39439e95i			1.30564i
$543$	−1.80520e95	+	2.80828e95i	−0.345567	+	0.537583i
$544$	−5.98455e93			−0.0107416
$545$		−	1.65585e95i		−	0.278705i
$546$	2.37742e94	+	1.52824e94i	0.0375287	+	0.0241240i
$547$	4.33489e95			0.641833			0.320917	−	0.947107i	$-0.396009\pi$
$547$	4.33489e95			0.641833			0.320917	+	0.947107i	$0.396009\pi$
$548$		−	7.76661e94i		−	0.107873i
$549$	5.68714e95	+	1.24604e96i	0.741075	+	1.62367i
$550$	−1.33412e96			−1.63117
$551$		−	1.64009e95i		−	0.188175i
$552$	5.20482e95	−	8.09690e95i	0.560451	−	0.871868i
$553$	1.42023e96			1.43542
$554$			1.72542e95i			0.163702i
$555$	−1.49069e96	−	9.58239e95i	−1.32780	−	0.853532i
$556$	−5.54750e94			−0.0463959
$557$			6.19497e94i			0.0486528i	0.999704	+	0.0243264i	$0.00774409\pi$
$557$			6.19497e94i			0.0486528i	−0.999704	+	0.0243264i	$0.992256\pi$
$558$	−1.19139e96	+	5.43772e95i	−0.878731	+	0.401070i
$559$	−2.50858e94			−0.0173786
$560$			5.06432e96i			3.29564i
$561$	5.58519e94	−	8.68863e94i	0.0341458	−	0.0531191i
$562$	2.37708e96			1.36544
$563$		−	3.12789e95i		−	0.168833i	−0.996431	−	0.0844165i	$-0.973097\pi$
$563$		−	3.12789e95i		−	0.168833i	0.996431	−	0.0844165i	$-0.0269026\pi$
$564$	−6.50816e94	−	4.18355e94i	−0.0330134	−	0.0212215i
$565$	−2.40648e96			−1.14733
$566$			3.79349e95i			0.170006i
$567$	3.04001e96	−	3.50525e96i	1.28076	−	1.47677i
$568$	3.13164e96			1.24045
$569$			2.21817e96i			0.826163i	0.910694	+	0.413082i	$0.135548\pi$
$569$			2.21817e96i			0.826163i	−0.910694	+	0.413082i	$0.864452\pi$
$570$	1.61499e96	−	2.51237e96i	0.565652	−	0.879960i
$571$	−4.18837e96			−1.37969			−0.689845	−	0.723957i	$-0.742321\pi$
$571$	−4.18837e96			−1.37969			−0.689845	+	0.723957i	$0.742321\pi$
$572$			7.31651e93i			0.00226695i
$573$	4.95700e96	+	3.18644e96i	1.44480	+	0.928740i
$574$	−2.77433e96			−0.760750
$575$		−	5.99147e96i		−	1.54582i
$576$	1.52032e96	+	3.33098e96i	0.369104	+	0.808696i
$577$	−3.18991e96			−0.728828			−0.364414	−	0.931237i	$-0.618731\pi$
$577$	−3.18991e96			−0.728828			−0.364414	+	0.931237i	$0.618731\pi$
$578$			4.84830e96i			1.04259i
$579$	−3.06722e96	+	4.77154e96i	−0.620863	+	0.965848i
$580$	−2.24366e95			−0.0427540
$581$		−	1.44754e97i		−	2.59696i
$582$	−2.84828e96	−	1.83092e96i	−0.481148	−	0.309290i
$583$	−6.11296e95			−0.0972416
$584$		−	8.60576e96i		−	1.28926i
$585$	2.18518e95	−	9.97359e94i	0.0308342	−	0.0140733i
$586$	−2.61816e95			−0.0348001
$587$			3.70887e96i			0.464418i	0.972666	+	0.232209i	$0.0745953\pi$
$587$			3.70887e96i			0.464418i	−0.972666	+	0.232209i	$0.925405\pi$
$588$	1.21751e96	−	1.89403e96i	0.143637	−	0.223450i
$589$	−5.34779e96			−0.594482
$590$		−	2.02113e96i		−	0.211726i
$591$	−3.65222e96	−	2.34770e96i	−0.360574	−	0.231783i
$592$	−1.18508e97			−1.10278
$593$			1.15949e97i			1.01707i	0.861041	+	0.508536i	$0.169813\pi$
$593$			1.15949e97i			1.01707i	−0.861041	+	0.508536i	$0.830187\pi$
$594$	1.38154e97	+	1.99101e96i	1.14246	+	0.164644i
$595$	−2.22884e96			−0.173774
$596$		−	1.70989e94i		−	0.00125704i
$597$	−2.54106e95	+	3.95302e95i	−0.0176163	+	0.0274048i
$598$	−3.81831e95			−0.0249649
$599$		−	1.67806e97i		−	1.03483i	−0.855734	−	0.517416i	$-0.826894\pi$
$599$		−	1.67806e97i		−	1.03483i	0.855734	−	0.517416i	$-0.173106\pi$
$600$	1.93633e97	+	1.24471e97i	1.12638	+	0.724057i
$601$	−1.51568e97			−0.831768			−0.415884	−	0.909418i	$-0.636528\pi$
$601$	−1.51568e97			−0.831768			−0.415884	+	0.909418i	$0.636528\pi$
$602$			3.14559e97i			1.62864i
$603$	4.97438e96	+	1.08987e97i	0.243015	+	0.532438i
$604$	−2.50018e95			−0.0115260
$605$		−	7.77167e96i		−	0.338124i
$606$	1.26549e97	−	1.96866e97i	0.519655	−	0.808404i
$607$	1.96911e97			0.763247			0.381624	−	0.924318i	$-0.375365\pi$
$607$	1.96911e97			0.763247			0.381624	+	0.924318i	$0.375365\pi$
$608$		−	3.30245e96i		−	0.120840i
$609$	−1.39133e97	−	8.94372e96i	−0.480647	−	0.308968i
$610$	8.89135e97			2.90017
$611$		−	2.95265e95i		−	0.00909432i
$612$	1.68520e95	−	7.69159e94i	0.00490176	−	0.00223726i
$613$	−6.20571e96			−0.170480			−0.0852402	−	0.996360i	$-0.527166\pi$
$613$	−6.20571e96			−0.170480			−0.0852402	+	0.996360i	$0.527166\pi$
$614$			4.20279e97i			1.09055i
$615$	−1.27500e97	+	1.98346e97i	−0.312522	+	0.486177i
$616$	−8.82633e97			−2.04388
$617$			1.33029e97i			0.291049i	0.989355	+	0.145524i	$0.0464869\pi$
$617$			1.33029e97i			0.291049i	−0.989355	+	0.145524i	$0.953513\pi$
$618$	−6.64588e97	−	4.27208e97i	−1.37390	−	0.883167i
$619$	6.10661e97			1.19297			0.596483	−	0.802626i	$-0.296564\pi$
$619$	6.10661e97			1.19297			0.596483	+	0.802626i	$0.296564\pi$
$620$			7.31581e96i			0.135068i
$621$	−8.94153e96	+	6.20446e97i	−0.156029	+	1.08267i
$622$	−3.88658e97			−0.641069
$623$		−	4.26276e97i		−	0.664675i
$624$	8.68597e95	−	1.35124e96i	0.0128043	−	0.0199191i
$625$	−2.98541e97			−0.416105
$626$			7.05854e97i			0.930278i
$627$	4.79463e97	+	3.08207e97i	0.597574	+	0.384130i
$628$	−1.35798e97			−0.160069
$629$		−	5.21562e96i		−	0.0581478i
$630$	−1.25062e98	−	2.74007e98i	−1.31888	−	2.88963i
$631$	1.44093e98			1.43753			0.718763	−	0.695255i	$-0.244709\pi$
$631$	1.44093e98			1.43753			0.718763	+	0.695255i	$0.244709\pi$
$632$		−	7.37176e97i		−	0.695783i
$633$	3.51922e97	−	5.47468e97i	0.314279	−	0.488910i
$634$	−1.14196e97			−0.0965000
$635$		−	8.50751e97i		−	0.680334i
$636$	−9.22222e95	−	5.92820e95i	−0.00697970	−	0.00448666i
$637$	8.59291e96			0.0615545
$638$		−	4.97574e97i		−	0.337391i
$639$	−1.85535e98	+	8.46819e97i	−1.19096	+	0.543577i
$640$	2.85671e98			1.73607
$641$		−	1.62308e96i		−	0.00933919i	−0.999989	−	0.00466959i	$-0.998514\pi$
$641$		−	1.62308e96i		−	0.00933919i	0.999989	−	0.00466959i	$-0.00148638\pi$
$642$	−1.05436e98	+	1.64021e98i	−0.574462	+	0.893664i
$643$	−1.09911e98			−0.567099			−0.283550	−	0.958958i	$-0.591512\pi$
$643$	−1.09911e98			−0.567099			−0.283550	+	0.958958i	$0.591512\pi$
$644$			4.12020e97i			0.201332i
$645$	2.24889e98	+	1.44562e98i	1.04082	+	0.669059i
$646$	8.79025e96			0.0385357
$647$		−	1.94829e98i		−	0.809101i	−0.914516	−	0.404550i	$-0.867428\pi$
$647$		−	1.94829e98i		−	0.809101i	0.914516	−	0.404550i	$-0.132572\pi$
$648$	−1.81941e98	−	1.57793e98i	−0.715823	−	0.620814i
$649$	3.85716e97			0.143782
$650$		−	9.13130e96i		−	0.0322526i
$651$	−2.91624e98	+	4.53667e98i	−0.976088	+	1.51846i
$652$	4.30217e96			0.0136465
$653$			4.28286e98i			1.28758i	0.765204	+	0.643788i	$0.222638\pi$
$653$			4.28286e98i			1.28758i	−0.765204	+	0.643788i	$0.777362\pi$
$654$	5.53996e97	+	3.56118e97i	0.157865	+	0.101478i
$655$	4.09562e98			1.10630
$656$			1.57683e98i			0.403784i
$657$	2.32706e98	+	5.09852e98i	0.564963	+	1.23782i
$658$	−3.70243e98			−0.852277
$659$			7.10313e97i			0.155046i	0.996991	+	0.0775230i	$0.0247011\pi$
$659$			7.10313e97i			0.155046i	−0.996991	+	0.0775230i	$0.975299\pi$
$660$	4.21629e97	−	6.55909e97i	0.0872755	−	0.135771i
$661$	3.75375e98			0.736909			0.368454	−	0.929646i	$-0.379887\pi$
$661$	3.75375e98			0.736909			0.368454	+	0.929646i	$0.379887\pi$
$662$		−	3.14856e98i		−	0.586250i
$663$	5.94688e95	+	3.82275e95i	0.00105031	+	0.000675154i
$664$	−7.51349e98			−1.25881
$665$		−	1.22994e99i		−	1.95491i
$666$	6.41193e98	−	2.92653e98i	0.966921	−	0.441321i
$667$	2.23458e98			0.319737
$668$			4.50381e97i			0.0611511i
$669$	8.15536e98	−	1.26869e99i	1.05082	−	1.63472i
$670$	7.77701e98			0.951031
$671$			1.69684e99i			1.96948i
$672$	−2.80155e98	−	1.80088e98i	−0.308655	−	0.198409i
$673$	−6.53329e98			−0.683289			−0.341645	−	0.939829i	$-0.610984\pi$
$673$	−6.53329e98			−0.683289			−0.341645	+	0.939829i	$0.610984\pi$
$674$			1.39177e99i			1.38189i
$675$	−1.48377e99	−	2.13832e98i	−1.39873	−	0.201577i
$676$	1.05143e98			0.0941119
$677$		−	1.60241e99i		−	1.36198i	−0.732293	−	0.680990i	$-0.761550\pi$
$677$		−	1.60241e99i		−	1.36198i	0.732293	−	0.680990i	$-0.238450\pi$
$678$	5.17553e98	−	8.05134e98i	0.417749	−	0.649873i
$679$	−1.39439e99			−1.06891
$680$			1.15689e98i			0.0842324i
$681$	9.84431e97	+	6.32808e97i	0.0680826	+	0.0437646i
$682$	−1.62242e99			−1.06588
$683$			3.10840e99i			1.94005i	0.243009	+	0.970024i	$0.421866\pi$
$683$			3.10840e99i			1.94005i	−0.243009	+	0.970024i	$0.578134\pi$
$684$	4.24444e97	+	9.29943e97i	0.0251685	+	0.0551433i
$685$	−3.15882e99			−1.77974
$686$		−	6.95565e99i		−	3.72386i
$687$	−4.06074e98	+	6.31711e98i	−0.206595	+	0.321390i
$688$	1.78784e99			0.864436
$689$		−	4.18398e96i		−	0.00192272i
$690$	3.42303e99	+	2.20038e99i	1.49518	+	0.961124i
$691$	4.42153e98			0.183586			0.0917932	−	0.995778i	$-0.470740\pi$
$691$	4.42153e98			0.183586			0.0917932	+	0.995778i	$0.470740\pi$
$692$			1.98660e98i			0.0784147i
$693$	5.22920e99	−	2.38671e99i	1.96233	−	0.895645i
$694$	−2.75485e99			−0.982917
$695$			2.25627e99i			0.765460i
$696$	−4.64227e98	+	7.22176e98i	−0.149764	+	0.232981i
$697$	−6.93972e97			−0.0212909
$698$			6.41128e99i			1.87070i
$699$	−2.22880e99	−	1.43271e99i	−0.618544	−	0.397610i
$700$	−9.85324e98			−0.260104
$701$		−	2.10653e99i		−	0.528976i	−0.964389	−	0.264488i	$-0.914797\pi$
$701$		−	2.10653e99i		−	0.528976i	0.964389	−	0.264488i	$-0.0852030\pi$
$702$	−1.36273e97	+	9.45590e97i	−0.00325546	+	0.0225894i
$703$	2.87813e99			0.654145
$704$			4.53610e99i			0.980933i
$705$	−1.70153e99	+	2.64699e99i	−0.350122	+	0.544670i
$706$	6.35132e99			1.24365
$707$		−	9.63765e99i		−	1.79594i
$708$	5.81904e97	+	3.74058e97i	0.0103202	+	0.00663398i
$709$	6.64479e99			1.12166			0.560832	−	0.827930i	$-0.310481\pi$
$709$	6.64479e99			1.12166			0.560832	+	0.827930i	$0.310481\pi$
$710$			1.32393e100i			2.12727i
$711$	1.99338e99	+	4.36743e99i	0.304898	+	0.668021i
$712$	−2.21260e99			−0.322183
$713$		−	7.28622e99i		−	1.01011i
$714$	4.79348e98	−	7.45700e98i	0.0632723	−	0.0984298i
$715$	2.97576e98			0.0374012
$716$		−	1.45883e99i		−	0.174602i
$717$	3.19452e99	+	2.05349e99i	0.364112	+	0.234057i
$718$	−4.76659e99			−0.517430
$719$		−	1.61591e100i		−	1.67073i	−0.549699	−	0.835363i	$-0.685258\pi$
$719$		−	1.61591e100i		−	1.67073i	0.549699	−	0.835363i	$-0.314742\pi$
$720$	−1.55736e100	+	7.10807e99i	−1.53373	+	0.700026i
$721$	−3.25352e100			−3.05224
$722$		−	6.85348e99i		−	0.612505i
$723$	1.26003e99	−	1.96018e99i	0.107286	−	0.166900i
$724$	−7.41738e98			−0.0601729
$725$			5.34390e99i			0.413074i
$726$	2.60015e99	+	1.67142e99i	0.191521	+	0.123113i
$727$	1.88749e100			1.32489			0.662445	−	0.749110i	$-0.269519\pi$
$727$	1.88749e100			1.32489			0.662445	+	0.749110i	$0.269519\pi$
$728$		−	6.04113e98i		−	0.0404129i
$729$	1.50460e100	+	4.42868e99i	0.959307	+	0.282365i
$730$	3.63816e100			2.21096
$731$			7.86839e98i			0.0455804i
$732$	−1.64555e99	+	2.55991e99i	−0.0908706	+	0.141363i
$733$	−1.01253e100			−0.533050			−0.266525	−	0.963828i	$-0.585876\pi$
$733$	−1.01253e100			−0.533050			−0.266525	+	0.963828i	$0.585876\pi$
$734$		−	1.66808e100i		−	0.837248i
$735$	−7.70335e100	−	4.95184e100i	−3.68657	−	2.36979i
$736$	4.49949e99			0.205324
$737$			1.48418e100i			0.645838i
$738$	−3.89393e99	−	8.53149e99i	−0.161591	−	0.354040i
$739$	4.17266e100			1.65142			0.825710	−	0.564095i	$-0.190775\pi$
$739$	4.17266e100			1.65142			0.825710	+	0.564095i	$0.190775\pi$
$740$		−	3.93730e99i		−	0.148624i
$741$	−2.10950e98	+	3.28166e98i	−0.00759527	+	0.0118156i
$742$	−5.24644e99			−0.180189
$743$			3.73669e100i			1.22427i	0.790752	+	0.612137i	$0.209690\pi$
$743$			3.73669e100i			1.22427i	−0.790752	+	0.612137i	$0.790310\pi$
$744$	2.35477e100	+	1.51368e100i	0.736031	+	0.473132i
$745$	−6.95444e98			−0.0207392
$746$		−	2.43389e100i		−	0.692534i
$747$	4.45140e100	−	2.03170e100i	1.20858	−	0.551619i
$748$	2.29489e98			0.00594574
$749$			8.02974e100i			1.98535i
$750$	−1.53851e100	+	2.39339e100i	−0.363041	+	0.564766i
$751$	−1.28558e100			−0.289536			−0.144768	−	0.989466i	$-0.546244\pi$
$751$	−1.28558e100			−0.289536			−0.144768	+	0.989466i	$0.546244\pi$
$752$			2.10433e100i			0.452364i
$753$	−4.19291e100	−	2.69527e100i	−0.860382	−	0.553068i
$754$	3.40562e98			0.00667112
$755$			1.01687e100i			0.190161i
$756$	1.02035e100	+	1.47047e99i	0.182174	+	0.0262540i
$757$	4.96066e100			0.845636			0.422818	−	0.906215i	$-0.361041\pi$
$757$	4.96066e100			0.845636			0.422818	+	0.906215i	$0.361041\pi$
$758$		−	1.97117e100i		−	0.320850i
$759$	−4.19924e100	+	6.53256e100i	−0.652692	+	1.01536i
$760$	−6.38404e100			−0.947588
$761$			6.63804e100i			0.940972i	0.882407	+	0.470486i	$0.155921\pi$
$761$			6.63804e100i			0.940972i	−0.882407	+	0.470486i	$0.844079\pi$
$762$	2.84634e100	+	1.82968e100i	0.385357	+	0.247714i
$763$	2.71211e100			0.350711
$764$			1.30927e100i			0.161720i
$765$	−3.12831e99	−	6.85402e99i	−0.0369113	−	0.0808715i
$766$	1.41839e101			1.59878
$767$			2.64001e98i			0.00284294i
$768$	−1.47181e100	+	2.28963e100i	−0.151429	+	0.235572i
$769$	−1.27094e101			−1.24940			−0.624702	−	0.780863i	$-0.714780\pi$
$769$	−1.27094e101			−1.24940			−0.624702	+	0.780863i	$0.714780\pi$
$770$		−	3.73140e101i		−	3.50507i
$771$	1.19618e101	+	7.68926e100i	1.07373	+	0.690210i
$772$	−1.26029e100			−0.108110
$773$		−	1.70558e101i		−	1.39827i	−0.714991	−	0.699134i	$-0.753569\pi$
$773$		−	1.70558e101i		−	1.39827i	0.714991	−	0.699134i	$-0.246431\pi$
$774$	−9.67318e100	+	4.41502e100i	−0.757941	+	0.345939i
$775$	1.74246e101			1.30498
$776$			7.23762e100i			0.518126i
$777$	1.56949e101	−	2.44159e101i	1.07405	−	1.67085i
$778$	−9.00017e100			−0.588796
$779$		−	3.82954e100i		−	0.239516i
$780$	4.48933e98	+	2.88581e98i	0.00268454	+	0.00172567i
$781$	−2.52660e101			−1.44461
$782$			1.19765e100i			0.0654776i
$783$	7.97511e99	−	5.53387e100i	0.0416941	−	0.289312i
$784$	−6.12407e101			−3.06181
$785$			5.52316e101i			2.64088i
$786$	−8.80828e100	+	1.37026e101i	−0.402811	+	0.626636i
$787$	−9.99960e100			−0.437388			−0.218694	−	0.975793i	$-0.570180\pi$
$787$	−9.99960e100			−0.437388			−0.218694	+	0.975793i	$0.570180\pi$
$788$		−	9.64646e99i		−	0.0403599i
$789$	3.18981e101	+	2.05046e101i	1.27664	+	0.820647i
$790$	3.11647e101			1.19321
$791$		−	3.94157e101i		−	1.44375i
$792$	−1.23883e101	−	2.71423e101i	−0.434140	−	0.951186i
$793$	−1.16139e100			−0.0389419
$794$		−	4.60272e100i		−	0.147671i
$795$	−2.41111e100	+	3.75085e100i	−0.0740230	+	0.115154i
$796$	−1.04409e99			−0.00306749
$797$		−	2.74470e101i		−	0.771710i	−0.922559	−	0.385855i	$-0.873907\pi$
$797$		−	2.74470e101i		−	0.771710i	0.922559	−	0.385855i	$-0.126093\pi$
$798$	4.11499e101	+	2.64518e101i	1.10730	+	0.711793i
$799$	−9.26128e99			−0.0238525
$800$			1.07603e101i			0.265262i
$801$	1.31086e101	−	5.98303e100i	0.309328	−	0.141183i
$802$	−3.38937e101			−0.765626
$803$			6.94311e101i			1.50145i
$804$	−1.43932e100	+	2.23908e100i	−0.0297985	+	0.0463562i
$805$	1.67576e102			3.32166
$806$		−	1.11046e100i		−	0.0210753i
$807$	−8.04035e100	−	5.16847e100i	−0.146117	−	0.0939265i
$808$	−5.00245e101			−0.870533
$809$			4.15744e101i			0.692832i	0.938081	+	0.346416i	$0.112601\pi$
$809$			4.15744e101i			0.692832i	−0.938081	+	0.346416i	$0.887399\pi$
$810$	6.67082e101	−	7.69171e101i	1.06464	−	1.22757i
$811$	−1.06024e102			−1.62060			−0.810300	−	0.586015i	$-0.800696\pi$
$811$	−1.06024e102			−1.62060			−0.810300	+	0.586015i	$0.800696\pi$
$812$		−	3.67487e100i		−	0.0537999i
$813$	−4.81323e101	+	7.48772e101i	−0.674943	+	1.04998i
$814$	8.73171e101			1.17286
$815$		−	1.74977e101i		−	0.225147i
$816$	−4.23828e100	−	2.72443e100i	−0.0522437	−	0.0335831i
$817$	−4.34201e101			−0.512765
$818$			8.58569e101i			0.971425i
$819$	1.63357e100	+	3.57909e100i	0.0177093	+	0.0388004i
$820$	−5.23883e100			−0.0544188
$821$			2.97259e101i			0.295886i	0.988996	+	0.147943i	$0.0472653\pi$
$821$			2.97259e101i			0.295886i	−0.988996	+	0.147943i	$0.952735\pi$
$822$	6.79355e101	−	1.05684e102i	0.648013	−	1.00808i
$823$	−9.30798e101			−0.850866			−0.425433	−	0.904990i	$-0.639878\pi$
$823$	−9.30798e101			−0.850866			−0.425433	+	0.904990i	$0.639878\pi$
$824$			1.68875e102i			1.47949i
$825$	−1.56223e102	−	1.00423e102i	−1.31177	−	0.843225i
$826$	3.31040e101			0.266427
$827$		−	9.86318e101i		−	0.760894i	−0.924803	−	0.380447i	$-0.875770\pi$
$827$		−	9.86318e101i		−	0.760894i	0.924803	−	0.380447i	$-0.124230\pi$
$828$	−1.26702e101	+	5.78294e100i	−0.0936963	+	0.0427648i
$829$	−1.05456e102			−0.747588			−0.373794	−	0.927512i	$-0.621943\pi$
$829$	−1.05456e102			−0.747588			−0.373794	+	0.927512i	$0.621943\pi$
$830$		−	3.17639e102i		−	2.15874i
$831$	−1.29877e101	+	2.02044e101i	−0.0846245	+	0.131647i
$832$	−3.10471e100			−0.0193956
$833$		−	2.69525e101i		−	0.161445i
$834$	−7.54876e101	−	4.85247e101i	−0.433575	−	0.278709i
$835$	1.83178e102			1.00890
$836$			1.26639e101i			0.0668878i
$837$	−1.80441e102	−	2.60041e101i	−0.913994	−	0.131720i
$838$	3.18653e102			1.54802
$839$		−	3.11398e102i		−	1.45093i	−0.688258	−	0.725466i	$-0.741624\pi$
$839$		−	3.11398e102i		−	1.45093i	0.688258	−	0.725466i	$-0.258376\pi$
$840$	−3.48133e102	+	5.41574e102i	−1.55586	+	2.42038i
$841$	2.13340e102			0.914560
$842$		−	1.39343e102i		−	0.573009i
$843$	2.78352e102	+	1.78929e102i	1.09807	+	0.705857i
$844$	1.44601e101			0.0547248
$845$		−	4.27635e102i		−	1.55270i
$846$	−5.19658e101	−	1.13855e102i	−0.181032	−	0.396635i
$847$	1.27292e102			0.425481
$848$			2.98188e101i			0.0956390i
$849$	−2.85546e101	+	4.44212e101i	−0.0878836	+	0.136716i
$850$	−2.86412e101			−0.0845918
$851$			3.92137e102i			1.11149i
$852$	−3.81172e101	−	2.45024e101i	−0.103690	−	0.0666533i
$853$	−6.43080e102			−1.67899			−0.839497	−	0.543364i	$-0.817150\pi$
$853$	−6.43080e102			−1.67899			−0.839497	+	0.543364i	$0.817150\pi$
$854$			1.45631e103i			3.64945i
$855$	3.78225e102	−	1.72629e102i	0.909779	−	0.415241i
$856$	4.16786e102			0.962346
$857$		−	4.68342e102i		−	1.03809i	−0.854747	−	0.519044i	$-0.826288\pi$
$857$		−	4.68342e102i		−	1.03809i	0.854747	−	0.519044i	$-0.173712\pi$
$858$	−6.39984e100	+	9.95594e100i	−0.0136180	+	0.0211849i
$859$	−4.80220e102			−0.981023			−0.490512	−	0.871435i	$-0.663190\pi$
$859$	−4.80220e102			−0.981023			−0.490512	+	0.871435i	$0.663190\pi$
$860$			5.93989e101i			0.116502i
$861$	−3.24869e102	−	2.08831e102i	−0.611784	−	0.393265i
$862$	7.85560e102			1.42045
$863$		−	1.42856e102i		−	0.248039i	−0.992280	−	0.124019i	$-0.960421\pi$
$863$		−	1.42856e102i		−	0.248039i	0.992280	−	0.124019i	$-0.0395785\pi$
$864$	1.60584e101	−	1.11428e102i	0.0267746	−	0.185787i
$865$	8.07987e102			1.29372
$866$		−	1.71159e102i		−	0.263192i
$867$	−3.64945e102	+	5.67728e102i	−0.538962	+	0.838439i
$868$	−1.19825e102			−0.169964
$869$			5.94752e102i			0.810297i
$870$	−3.05306e102	−	1.96256e102i	−0.399541	−	0.256832i
$871$	−1.01584e101			−0.0127699
$872$		−	1.40773e102i		−	0.169997i
$873$	−1.95711e102	−	4.28796e102i	−0.227047	−	0.497453i
$874$	−6.60897e102			−0.736603
$875$			1.17169e103i			1.25468i
$876$	−6.73325e101	+	1.04746e102i	−0.0692758	+	0.107769i
$877$	1.29124e103			1.27650			0.638251	−	0.769828i	$-0.279658\pi$
$877$	1.29124e103			1.27650			0.638251	+	0.769828i	$0.279658\pi$
$878$		−	4.33669e102i		−	0.411955i
$879$	−3.06583e101	−	1.97076e101i	−0.0279857	−	0.0179897i
$880$	−2.12079e103			−1.86039
$881$		−	9.73174e102i		−	0.820415i	−0.911992	−	0.410208i	$-0.865456\pi$
$881$		−	9.73174e102i		−	0.820415i	0.911992	−	0.410208i	$-0.134544\pi$
$882$	3.31346e103	−	1.51233e103i	2.68461	−	1.22531i
$883$	−5.47304e102			−0.426191			−0.213095	−	0.977031i	$-0.568354\pi$
$883$	−5.47304e102			−0.426191			−0.213095	+	0.977031i	$0.568354\pi$
$884$			1.57073e99i			0.000117563i
$885$	1.52136e102	−	2.36671e102i	0.109450	−	0.170267i
$886$	−2.04405e103			−1.41355
$887$		−	2.75200e103i		−	1.82945i	−0.404073	−	0.914727i	$-0.632406\pi$
$887$		−	2.75200e103i		−	1.82945i	0.404073	−	0.914727i	$-0.367594\pi$
$888$	−1.26732e103	−	8.14651e102i	−0.809899	−	0.520616i
$889$	1.39344e103			0.856104
$890$		−	9.35395e102i		−	0.552516i
$891$	1.46790e103	+	1.27307e103i	0.833635	+	0.722990i
$892$	3.35095e102			0.182978
$893$		−	5.11064e102i		−	0.268333i
$894$	1.49566e101	−	2.32674e101i	0.00755128	−	0.0117472i
$895$	−5.93332e103			−2.88066
$896$			4.67898e103i			2.18459i
$897$	−4.47117e101	−	2.87414e101i	−0.0200764	−	0.0129054i
$898$	2.90867e103			1.25610
$899$			6.49871e102i			0.269922i
$900$	−1.38296e102	−	3.03002e102i	−0.0552487	−	0.121048i
$901$	−1.31235e101			−0.00504290
$902$		−	1.16181e103i		−	0.429443i
$903$	−2.36777e103	+	3.68344e103i	−0.841916	+	1.30973i
$904$	−2.04588e103			−0.699819
$905$			3.01679e103i			0.992760i
$906$	−3.40212e102	−	2.18694e102i	−0.107712	−	0.0692387i
$907$	1.09066e103			0.332227			0.166114	−	0.986107i	$-0.446878\pi$
$907$	1.09066e103			0.332227			0.166114	+	0.986107i	$0.446878\pi$
$908$			2.60014e101i			0.00762064i
$909$	2.96372e103	−	1.35270e103i	0.835799	−	0.381475i
$910$	2.55394e102			0.0693046
$911$		−	5.02111e103i		−	1.31116i	−0.755125	−	0.655581i	$-0.772424\pi$
$911$		−	5.02111e103i		−	1.31116i	0.755125	−	0.655581i	$-0.227576\pi$
$912$	1.50342e103	−	2.33880e103i	0.377800	−	0.587726i
$913$	6.06187e103			1.46598
$914$			1.33635e103i			0.311031i
$915$	1.04116e104	+	6.69276e103i	2.33228	+	1.49922i
$916$	−1.66851e102			−0.0359739
$917$			6.70818e103i			1.39212i
$918$	2.96593e102	+	4.27434e101i	0.0592472	+	0.00853838i
$919$	−4.22374e103			−0.812184			−0.406092	−	0.913832i	$-0.633109\pi$
$919$	−4.22374e103			−0.812184			−0.406092	+	0.913832i	$0.633109\pi$
$920$		−	8.69808e103i		−	1.61009i
$921$	−3.16355e103	+	4.92140e103i	−0.563752	+	0.877003i
$922$	2.25585e103			0.387016
$923$		−	1.72932e102i		−	0.0285638i
$924$	1.07431e103	+	6.90583e102i	0.170848	+	0.109824i
$925$	−9.37777e103			−1.43595
$926$		−	1.24918e104i		−	1.84179i
$927$	−4.56650e103	−	1.00051e104i	−0.648325	−	1.42046i
$928$	−4.01318e102			−0.0548668
$929$			9.60850e103i			1.26504i	0.774542	+	0.632522i	$0.217980\pi$
$929$			9.60850e103i			1.26504i	−0.774542	+	0.632522i	$0.782020\pi$
$930$	−6.39923e103	+	9.95499e103i	−0.811380	+	1.26223i
$931$	1.48731e104			1.81620
$932$		−	5.88684e102i		−	0.0692350i
$933$	−4.55112e103	−	2.92554e103i	−0.515538	−	0.331396i
$934$	3.40396e103			0.371401
$935$		−	9.33374e102i		−	0.0980956i
$936$	1.85774e102	−	8.47908e101i	0.0188075	−	0.00858409i
$937$	−9.18988e103			−0.896240			−0.448120	−	0.893973i	$-0.647906\pi$
$937$	−9.18988e103			−0.896240			−0.448120	+	0.893973i	$0.647906\pi$
$938$			1.27379e104i			1.19674i
$939$	−5.31315e103	+	8.26542e103i	−0.480902	+	0.748117i
$940$	−6.99138e102			−0.0609661
$941$		−	4.47332e103i		−	0.375832i	−0.982185	−	0.187916i	$-0.939827\pi$
$941$		−	4.47332e103i		−	0.375832i	0.982185	−	0.187916i	$-0.0601732\pi$
$942$	−1.84787e104	−	1.18784e104i	−1.49586	−	0.961562i
$943$	5.21764e103			0.406972
$944$		−	1.88151e103i		−	0.141412i
$945$	5.98069e103	−	4.14996e104i	0.433150	−	3.00559i
$946$	−1.31728e104			−0.919368
$947$			1.11178e104i			0.747774i	0.927474	+	0.373887i	$0.121975\pi$
$947$			1.11178e104i			0.747774i	−0.927474	+	0.373887i	$0.878025\pi$
$948$	−5.76776e102	+	8.97264e102i	−0.0373865	+	0.0581605i
$949$	−4.75217e102			−0.0296876
$950$		−	1.58050e104i		−	0.951632i
$951$	−1.33722e103	−	8.59585e102i	−0.0776039	−	0.0498851i
$952$	−1.89486e103			−0.105995
$953$			3.08066e104i			1.66109i	0.556954	+	0.830543i	$0.311970\pi$
$953$			3.08066e104i			1.66109i	−0.556954	+	0.830543i	$0.688030\pi$
$954$	−7.36368e102	−	1.61336e103i	−0.0382738	−	0.0838567i
$955$	5.32505e104			2.66812
$956$			8.43756e102i			0.0407559i
$957$	3.74537e103	−	5.82651e103i	0.174412	−	0.271325i
$958$	2.62485e104			1.17845
$959$		−	5.17382e104i		−	2.23954i
$960$	2.78330e104	+	1.78915e104i	1.16163	+	0.746713i
$961$	−3.65948e103			−0.147266
$962$			5.97637e102i			0.0231905i
$963$	−2.46927e104	+	1.12702e104i	−0.923948	+	0.421708i
$964$	5.17734e102			0.0186814
$965$			5.12582e104i			1.78364i
$966$	−3.60399e104	+	5.60656e104i	−1.20944	+	1.88147i
$967$	−1.72980e104			−0.559847			−0.279923	−	0.960022i	$-0.590309\pi$
$967$	−1.72980e104			−0.559847			−0.279923	+	0.960022i	$0.590309\pi$
$968$		−	6.60711e103i		−	0.206241i
$969$	1.02932e103	+	6.61666e102i	0.0309899	+	0.0199208i
$970$	−3.05977e104			−0.888541
$971$		−	1.94004e104i		−	0.543422i	−0.962379	−	0.271711i	$-0.912410\pi$
$971$		−	1.94004e104i		−	0.543422i	0.962379	−	0.271711i	$-0.0875895\pi$
$972$	9.79930e102	+	3.34413e103i	0.0264774	+	0.0903573i
$973$	−3.69553e104			−0.963223
$974$			5.88793e104i			1.48047i
$975$	6.87337e102	−	1.06926e103i	0.0166728	−	0.0259371i
$976$	8.27711e104			1.93703
$977$			1.97759e104i			0.446505i	0.974761	+	0.223252i	$0.0716674\pi$
$977$			1.97759e104i			0.446505i	−0.974761	+	0.223252i	$0.928333\pi$
$978$	5.85419e103	+	3.76316e103i	0.127528	+	0.0819772i
$979$	1.78512e104			0.375209
$980$		−	2.03465e104i		−	0.412646i
$981$	3.80661e103	+	8.34016e103i	0.0744943	+	0.163215i
$982$	6.25070e104			1.18039
$983$		−	9.32252e104i		−	1.69887i	−0.527693	−	0.849435i	$-0.676943\pi$
$983$		−	9.32252e104i		−	1.69887i	0.527693	−	0.849435i	$-0.323057\pi$
$984$	−1.08395e104	+	1.68624e104i	−0.190625	+	0.296546i
$985$	−3.92339e104			−0.665876
$986$		−	1.06820e103i		−	0.0174969i
$987$	−4.33549e104	−	2.78692e104i	−0.685390	−	0.440579i
$988$	−8.66772e101			−0.00132255
$989$		−	5.91587e104i		−	0.871261i
$990$	1.14746e105	−	5.23724e104i	1.63120	−	0.744511i
$991$	−9.27845e104			−1.27320			−0.636602	−	0.771193i	$-0.719660\pi$
$991$	−9.27845e104			−1.27320			−0.636602	+	0.771193i	$0.719660\pi$
$992$			1.30856e104i			0.173335i
$993$	2.37001e104	−	3.68691e104i	0.303058	−	0.471454i
$994$	−2.16845e105			−2.67686
$995$			4.24653e103i			0.0506088i
$996$	9.14514e103	+	5.87865e103i	0.105224	+	0.0676395i
$997$	3.73377e104			0.414779			0.207389	−	0.978258i	$-0.433503\pi$
$997$	3.73377e104			0.414779			0.207389	+	0.978258i	$0.433503\pi$
$998$			9.31159e103i			0.0998745i
$999$	9.71114e104	+	1.39952e104i	1.00572	+	0.144939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.71.b.a.2.16	yes	22
3.2	odd	2	inner	3.71.b.a.2.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.71.b.a.2.7	✓	22	3.2	odd	2	inner
3.71.b.a.2.16	yes	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 71 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.59410e10i q^{2} +(-2.70537e16 + 4.20862e16i) q^{3} -1.11161e20 q^{4} +4.52111e24i q^{5} +(-1.51262e27 - 9.72336e26i) q^{6} -7.40509e29 q^{7} +3.84364e31i q^{8} +(-1.03935e33 - 2.27718e33i) q^{9} +O(q^{10})\)	\(q+3.59410e10i q^{2} +(-2.70537e16 + 4.20862e16i) q^{3} -1.11161e20 q^{4} +4.52111e24i q^{5} +(-1.51262e27 - 9.72336e26i) q^{6} -7.40509e29 q^{7} +3.84364e31i q^{8} +(-1.03935e33 - 2.27718e33i) q^{9} -1.62493e35 q^{10} -3.10104e36i q^{11} +(3.00731e36 - 4.67834e36i) q^{12} +2.12249e37 q^{13} -2.66146e40i q^{14} +(-1.90276e41 - 1.22313e41i) q^{15} -1.51268e42 q^{16} -6.65739e41i q^{17} +(8.18440e43 - 3.73552e43i) q^{18} +3.67374e44 q^{19} -5.02569e44i q^{20} +(2.00335e46 - 3.11653e46i) q^{21} +1.11454e47 q^{22} +5.00537e47i q^{23} +(-1.61764e48 - 1.03985e48i) q^{24} -1.19701e49 q^{25} +7.62843e47i q^{26} +(1.23956e50 + 1.78639e49i) q^{27} +8.23155e49 q^{28} -4.46438e50i q^{29} +(4.39604e51 - 6.83872e51i) q^{30} -1.45568e52 q^{31} -8.98934e51i q^{32} +(1.30511e53 + 8.38946e52i) q^{33} +2.39273e52 q^{34} -3.34792e54i q^{35} +(1.15535e53 + 2.53133e53i) q^{36} +7.83434e54 q^{37} +1.32038e55i q^{38} +(-5.74212e53 + 8.93276e53i) q^{39} -1.73775e56 q^{40} -1.04241e56i q^{41} +(1.12011e57 + 7.20024e56i) q^{42} -1.18190e57 q^{43} +3.44714e56i q^{44} +(1.02954e58 - 4.69901e57i) q^{45} -1.79898e58 q^{46} -1.39113e58i q^{47} +(4.09235e58 - 6.36628e58i) q^{48} +4.04850e59 q^{49} -4.30216e59i q^{50} +(2.80184e58 + 1.80107e58i) q^{51} -2.35937e57 q^{52} -1.97126e59i q^{53} +(-6.42045e59 + 4.45510e60i) q^{54} +1.40201e61 q^{55} -2.84625e61i q^{56} +(-9.93882e60 + 1.54614e61i) q^{57} +1.60454e61 q^{58} +1.24383e61i q^{59} +(2.11513e61 + 1.35964e61i) q^{60} -5.47184e62 q^{61} -5.23186e62i q^{62} +(7.69647e62 + 1.68627e63i) q^{63} -1.46277e63 q^{64} +9.59600e61i q^{65} +(-3.01525e63 + 4.69069e63i) q^{66} -4.78606e63 q^{67} +7.40039e61i q^{68} +(-2.10657e64 - 1.35414e64i) q^{69} +1.20328e65 q^{70} -8.14760e64i q^{71} +(8.75265e64 - 3.99488e64i) q^{72} -2.23896e65 q^{73} +2.81574e65i q^{74} +(3.23835e65 - 5.03776e65i) q^{75} -4.08375e64 q^{76} +2.29635e66i q^{77} +(-3.21052e64 - 2.06377e64i) q^{78} -1.91791e66 q^{79} -6.83897e66i q^{80} +(-4.10530e66 + 4.73356e66i) q^{81} +3.74652e66 q^{82} +1.95479e67i q^{83} +(-2.22694e66 + 3.46435e66i) q^{84} +3.00988e66 q^{85} -4.24788e67i q^{86} +(1.87889e67 + 1.20778e67i) q^{87} +1.19193e68 q^{88} +5.75653e67i q^{89} +(1.68887e68 + 3.70025e68i) q^{90} -1.57172e67 q^{91} -5.56400e67i q^{92} +(3.93816e68 - 6.12641e68i) q^{93} +4.99985e68 q^{94} +1.66094e69i q^{95} +(3.78327e68 + 2.43195e68i) q^{96} +1.88301e69 q^{97} +1.45507e70i q^{98} +(-7.06162e69 + 3.22306e69i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 31\!\cdots\!82 q^{9}+O(q^{10}) \) 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9	\( 22 q - 57\!\cdots\!10 q^{3}+ \cdots - 21\!\cdots\!80 q^{99}+O(q^{100}) \) 22 * q - 57760946614928610 * q^3 - 12924724784889679105472 * q^4 - 2542746418602623176312578240 * q^6 + 3460300354929279082139211020 * q^7 - 3187627653443587997840864868739482 * q^9 - 204904054456738768728763726683461760 * q^10 + 168216518978261501059545818584280696640 * q^12 - 1425273500899614630088058291006011908100 * q^13 - 225789500492205687292660149319768298715840 * q^15 + 7791108876170200924142434286561643963000832 * q^16 - 159240712078782992086911930584730978792685440 * q^18 + 2012529521265601397979311193864856923750823676 * q^19 - 5316334525000974787771605720411010154937122916 * q^21 - 177999664576757911046568099334764110597720653440 * q^22 + 2221044214363105865421794285118261395337437583360 * q^24 - 47913993180689593092577485889381363779493774325690 * q^25 - 327350510975933028532160361074129063579708328041490 * q^27 + 199622305967867855771313967200368144722234985321600 * q^28 + 19529370934845391692884101303550253186745064711003520 * q^30 + 12388430374073163692752061441697409777651574405007404 * q^31 + 91609538538011962010378972773658529100477255901421120 * q^33 + 605761954772905142742127812440233067564260993651653120 * q^34 + 903849673866118209515044215587923561361275075218434112 * q^36 - 2942122339532414491328953596359839081620064777882528420 * q^37 - 83642273913756481299940648535011188445494335818507646004 * q^39 + 272642123044960747425938890972217844718938356564315934720 * q^40 + 1560147154093916143029768098476489647357578674968337342080 * q^42 - 4545359228128189931707988293083620465330530163336481972580 * q^43 - 13684191484560547979485162889557225553655737227535310368640 * q^45 + 34824945738150746982031713560272687284036228683298922087680 * q^46 + 187018310806180504680614747073364302422042767094159794882560 * q^48 + 537429667187009430823177633570141302055322425376808156541794 * q^49 + 93003444735225900297901054333392923286830613776157770499840 * q^51 - 256980181653870794210710907095882776189154704275967737138560 * q^52 + 563860949077651296335542553968680463677661322067851314468800 * q^54 - 3516118540339332578884347645630886351467431915082786354698880 * q^55 + 62619566495727497029128246919971991949893526891401194293093580 * q^57 + 116675137250817318744043251484707490614825810469582794383621760 * q^58 - 289520688194704548710930657842220413516071423272166989563023360 * q^60 - 1004518379975789938184755460502459521248398274882979931600708676 * q^61 + 2259750912371699320668016184778015293200259463243321554460021420 * q^63 - 6990282608978901236062382909358427229318771679854621867713298432 * q^64 + 9802144175872303219237439174047894300074716767326740733265952640 * q^66 - 9530737568144236105810003684427263525901520593033925660073496260 * q^67 + 68660923095126616358914910008665108044130343377859227725343530880 * q^69 - 186825484366209931701114245951001364013348939360625786570907971840 * q^70 + 800859191695150280430684829106757981081528103077118327934086410240 * q^72 - 498564607593670758195755796246723418636521686724391030404386208820 * q^73 + 2109806600351472862056557154002428953234561707550117711339382623630 * q^75 - 5263274864463875706518271175142614969672638525330024503218962553216 * q^76 + 12308167524701892969963937648343555852922730564344320620076689564800 * q^78 - 17307670437682441097149414568687707748355067787533584779481303522964 * q^79 + 13169506853202980530135359556542777642532240836639689883271737852342 * q^81 - 39431820989895068684167150578955043187025954212565254141576902204160 * q^82 + 138763489413867144231869861916118201044140663071190925822310630686336 * q^84 - 61037539079877371876604729964700889725410552523647838067356520814080 * q^85 - 149627312260702067527556548128053547148656320722965526646581032129600 * q^87 + 423107204692289659768926623144292819592688368886126043795359525621760 * q^88 - 954822316211616625813572408526438784570624253142422549351495971955840 * q^90 + 1351237435163715752950727836854267043101210025128484375869461920848568 * q^91 - 1419126662189890378883596636164605113800863195507982624574295260938180 * q^93 + 10138980254856605941232671681032460690110853357766177455228626662453760 * q^94 - 12383253221007478242150050518024370091385337450937902244753056045137920 * q^96 + 5943877415032019678068302054256035030995353737176853716379501144663980 * q^97 - 21983160871333538547745741193506138170867254293489738303957813119108480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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