LMFDB - Embedded newform 3.69.b.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,69,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, 69, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 69);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 69 $
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:	$87.8517980619$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	3.2
Dual form			3.69.b.a.2.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79362e10i q^{2} +(1.66655e16 + 6.25230e14i) q^{3} -4.85282e20 q^{4} +1.09211e24i q^{5} +(1.74665e25 - 4.65569e26i) q^{6} +3.32586e27 q^{7} +5.31162e30i q^{8} +(2.77347e32 + 2.08395e31i) q^{9} +O(q^{10})$	\(q-2.79362e10i q^{2} +(1.66655e16 + 6.25230e14i) q^{3} -4.85282e20 q^{4} +1.09211e24i q^{5} +(1.74665e25 - 4.65569e26i) q^{6} +3.32586e27 q^{7} +5.31162e30i q^{8} +(2.77347e32 + 2.08395e31i) q^{9} +3.05093e34 q^{10} -3.05626e35i q^{11} +(-8.08745e36 - 3.03413e35i) q^{12} +7.37092e37 q^{13} -9.29117e37i q^{14} +(-6.82818e38 + 1.82005e40i) q^{15} +5.15635e39 q^{16} +2.71929e41i q^{17} +(5.82176e41 - 7.74800e42i) q^{18} -2.11365e43 q^{19} -5.29979e44i q^{20} +(5.54269e43 + 2.07943e42i) q^{21} -8.53803e45 q^{22} +3.36394e46i q^{23} +(-3.32099e45 + 8.85206e46i) q^{24} -8.53883e47 q^{25} -2.05915e48i q^{26} +(4.60908e48 + 5.20705e47i) q^{27} -1.61398e48 q^{28} +1.39133e48i q^{29} +(5.08451e50 + 1.90753e49i) q^{30} +1.93725e50 q^{31} +1.42366e51i q^{32} +(1.91087e50 - 5.09340e51i) q^{33} +7.59665e51 q^{34} +3.63219e51i q^{35} +(-1.34591e53 - 1.01130e52i) q^{36} +3.10925e53 q^{37} +5.90473e53i q^{38} +(1.22840e54 + 4.60852e52i) q^{39} -5.80085e54 q^{40} +1.55113e54i q^{41} +(5.80912e52 - 1.54842e54i) q^{42} -2.69773e55 q^{43} +1.48315e56i q^{44} +(-2.27589e55 + 3.02892e56i) q^{45} +9.39756e56 q^{46} +2.47346e56i q^{47} +(8.59330e55 + 3.22391e54i) q^{48} -2.91758e57 q^{49} +2.38542e58i q^{50} +(-1.70018e56 + 4.53182e57i) q^{51} -3.57697e58 q^{52} +4.23125e58i q^{53} +(1.45465e58 - 1.28760e59i) q^{54} +3.33777e59 q^{55} +1.76657e58i q^{56} +(-3.52249e59 - 1.32152e58i) q^{57} +3.88686e58 q^{58} -1.31345e59i q^{59} +(3.31359e59 - 8.83235e60i) q^{60} -7.02451e60 q^{61} -5.41195e60i q^{62} +(9.22415e59 + 6.93092e58i) q^{63} +4.12936e61 q^{64} +8.04982e61i q^{65} +(-1.42290e62 - 5.33824e60i) q^{66} +1.58542e62 q^{67} -1.31962e62i q^{68} +(-2.10324e61 + 5.60616e62i) q^{69} +1.01469e62 q^{70} +8.27429e62i q^{71} +(-1.10691e62 + 1.47316e63i) q^{72} +2.43630e63 q^{73} -8.68605e63i q^{74} +(-1.42303e64 - 5.33874e62i) q^{75} +1.02572e64 q^{76} -1.01647e63i q^{77} +(1.28744e63 - 3.43167e64i) q^{78} +3.21579e64 q^{79} +5.63128e63i q^{80} +(7.64868e64 + 1.15595e64i) q^{81} +4.33326e64 q^{82} +1.90418e65i q^{83} +(-2.68977e64 - 1.00911e63i) q^{84} -2.96975e65 q^{85} +7.53642e65i q^{86} +(-8.69905e62 + 2.31872e64i) q^{87} +1.62337e66 q^{88} +7.28951e65i q^{89} +(8.46164e66 + 6.35798e65i) q^{90} +2.45146e65 q^{91} -1.63246e67i q^{92} +(3.22852e66 + 1.21123e65i) q^{93} +6.90989e66 q^{94} -2.30833e67i q^{95} +(-8.90118e65 + 2.37260e67i) q^{96} +1.57021e67 q^{97} +8.15061e67i q^{98} +(6.36910e66 - 8.47644e67i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 18\!\cdots\!78 q^{3}+ \cdots + 84\!\cdots\!78 q^{9}+O(q^{10}) $ 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9	$ 22 q + 18\!\cdots\!78 q^{3}+ \cdots - 11\!\cdots\!00 q^{99}+O(q^{100}) $ 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9 + 2045888067334428934113988216421280 * q^10 - 6488396126470402148347182126675194832 * q^12 - 10813885710533400837304817444785935604 * q^13 + 14557528184647372428101554053003296612160 * q^15 + 373601084063432865853473918269277812744320 * q^16 + 17941511735214427632488941901617371491816160 * q^18 - 79553650357260974891342027178031915087354324 * q^19 - 1298400323255969952377913185067359758477401780 * q^21 + 6768843564804724477092404017437690309759833760 * q^22 - 75879178936902674847903860248712590469230731648 * q^24 - 1290406322757665049559021767067242780449078031050 * q^25 + 2674086297347577939313596696269044232072283756918 * q^27 + 42745403006807704515598614320469990457621586593376 * q^28 + 30776582876805533479749631919828742635540596749600 * q^30 - 464825674673310587378006994001777182420658601801716 * q^31 + 2043086192437245889755473926491971918230943629550400 * q^33 + 13079915711847249768451590870017502856673640042982272 * q^34 - 65327203493646647902060088267317231087935232974706704 * q^36 - 167279080426229420846594751930892532669536008046545844 * q^37 + 1637357069222228057847981309081425400083650534736779020 * q^39 + 6053556854890611145141953130785126755317199579733738240 * q^40 - 12457262572316255979922798677909127605820549100734736160 * q^42 - 18628500859740527128618324584150040016275591666233599764 * q^43 + 367822789535544680671556018223028621483838265619669430400 * q^45 + 1476449543055130371522242587937584327352337186768013053888 * q^46 + 202405740838876412041865477434740772123701917763236585088 * q^48 + 4681199846498689520635057982286342899995310041595285382018 * q^49 + 21407584156868532008405510905089022165080050053906507325184 * q^51 + 24391763772592576034526261030318526583680683849133477696736 * q^52 - 112285817002635953902674086392140195155054790343667891881584 * q^54 + 274409579794012893709322560718339246575325740160175650620800 * q^55 + 101758997342686912720089366682761957082398853447685074732716 * q^57 - 2020457744766163498170953106059196558756720252448185539243040 * q^58 - 13276219488047015535811467987165558930747748946804017101031680 * q^60 + 6331070401548027780910089309848838040805985031947773629039244 * q^61 - 11540105667000326350766773710482957857389205527747058022198004 * q^63 + 74144666416333808948332900789778080404085337330317362556926976 * q^64 - 388082670987835008027383208260911873599566866107012006022495200 * q^66 + 690968797068657030373143885315519666504759571640550029794509356 * q^67 - 1027093066405255275213825064853644794250194801896401414490868864 * q^69 + 4371068227635884746027518083549441915821247332843741516741992000 * q^70 - 8830670280256061265338935058781406802503181323103646058149000960 * q^72 + 8806696028067195590640304057094157167006086961761378058824984556 * q^73 - 35720155285864881642804474725062955577201898766624893474579682250 * q^75 + 50989416920172911215005579159200646780346206610233430042766798432 * q^76 - 79580143447707181310585996419552144412335647108094050067906050720 * q^78 - 3083981169532008720747546215983788345611378750423096573576219764 * q^79 - 88762224122457647598561491684821377170571566383688244793770736938 * q^81 + 416784948027081086888539461807826070456316776812312199920865653440 * q^82 + 990441228134853667871418956670095117692984404086848036534801693920 * q^84 - 866637175758839171101071739839460554945096683648478422830993681920 * q^85 + 3620458445475290511813570050310517312523781688405496711995676422080 * q^87 - 4669471445324986882088763579042561683455173004052019441103363626240 * q^88 + 14582942989396685328395597316366348010236984461538262603110152917920 * q^90 - 6998978018734113734240448628263170029174504049408988631375576481960 * q^91 + 22631183723253759871940463881283634110336753405922973132310746358156 * q^93 - 49667911598354463153752845875961955186127772502753374451274725501568 * q^94 - 5532425547839977216491807518703626514248108709732237368596820947968 * q^96 + 90182295908350258367379728070466489774210357027997619180945877805996 * q^97 - 111427931124550204447734414473904809051459145283833102653529748809600 * 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 $

$2$		−	2.79362e10i		−	1.62610i	−0.582194	−	0.813050i	$-0.697806\pi$
$2$		−	2.79362e10i		−	1.62610i	0.582194	−	0.813050i	$-0.302194\pi$
$3$	1.66655e16	+	6.25230e14i	0.999297	+	0.0374902i
$3$	1.66655e16	+	6.25230e14i	0.999297	+	0.0374902i
$4$	−4.85282e20			−1.64420
$5$			1.09211e24i			1.87622i	0.346332	+	0.938112i	$0.387427\pi$
$5$			1.09211e24i			1.87622i	−0.346332	+	0.938112i	$0.612573\pi$
$6$	1.74665e25	−	4.65569e26i	0.0609627	−	1.62496i
$7$	3.32586e27			0.0614568			0.0307284	−	0.999528i	$-0.490217\pi$
$7$	3.32586e27			0.0614568			0.0307284	+	0.999528i	$0.490217\pi$
$8$			5.31162e30i			1.04753i
$9$	2.77347e32	+	2.08395e31i	0.997189	+	0.0749276i
$10$	3.05093e34			3.05093
$11$		−	3.05626e35i		−	1.19630i	−0.801385	−	0.598149i	$-0.795903\pi$
$11$		−	3.05626e35i		−	1.19630i	0.801385	−	0.598149i	$-0.204097\pi$
$12$	−8.08745e36	−	3.03413e35i	−1.64304	−	0.0616413i
$13$	7.37092e37			0.985026			0.492513	−	0.870305i	$-0.336078\pi$
$13$	7.37092e37			0.985026			0.492513	+	0.870305i	$0.336078\pi$
$14$		−	9.29117e37i		−	0.0999349i
$15$	−6.82818e38	+	1.82005e40i	−0.0703400	+	1.87491i
$16$	5.15635e39			0.0591920
$17$			2.71929e41i			0.397367i	0.980064	+	0.198683i	$0.0636666\pi$
$17$			2.71929e41i			0.397367i	−0.980064	+	0.198683i	$0.936333\pi$
$18$	5.82176e41	−	7.74800e42i	0.121840	−	1.62153i
$19$	−2.11365e43			−0.703737			−0.351869	−	0.936049i	$-0.614454\pi$
$19$	−2.11365e43			−0.703737			−0.351869	+	0.936049i	$0.614454\pi$
$20$		−	5.29979e44i		−	3.08489i
$21$	5.54269e43	+	2.07943e42i	0.0614136	+	0.00230403i
$22$	−8.53803e45			−1.94530
$23$			3.36394e46i			1.69084i	0.534105	+	0.845418i	$0.320649\pi$
$23$			3.36394e46i			1.69084i	−0.534105	+	0.845418i	$0.679351\pi$
$24$	−3.32099e45	+	8.85206e46i	−0.0392722	+	1.04680i
$25$	−8.53883e47			−2.52022
$26$		−	2.05915e48i		−	1.60175i
$27$	4.60908e48	+	5.20705e47i	0.993679	+	0.112260i
$28$	−1.61398e48			−0.101047
$29$			1.39133e48i			0.0264180i	0.999913	+	0.0132090i	$0.00420468\pi$
$29$			1.39133e48i			0.0264180i	−0.999913	+	0.0132090i	$0.995795\pi$
$30$	5.08451e50	+	1.90753e49i	3.04878	+	0.114380i
$31$	1.93725e50			0.380968			0.190484	−	0.981690i	$-0.438994\pi$
$31$	1.93725e50			0.380968			0.190484	+	0.981690i	$0.438994\pi$
$32$			1.42366e51i			0.951280i
$33$	1.91087e50	−	5.09340e51i	0.0448494	−	1.19546i
$34$	7.59665e51			0.646158
$35$			3.63219e51i			0.115307i
$36$	−1.34591e53	−	1.01130e52i	−1.63958	−	0.123196i
$37$	3.10925e53			1.49210			0.746048	−	0.665892i	$-0.231949\pi$
$37$	3.10925e53			1.49210			0.746048	+	0.665892i	$0.231949\pi$
$38$			5.90473e53i			1.14435i
$39$	1.22840e54	+	4.60852e52i	0.984333	+	0.0369288i
$40$	−5.80085e54			−1.96541
$41$			1.55113e54i			0.226985i	0.993539	+	0.113493i	$0.0362038\pi$
$41$			1.55113e54i			0.226985i	−0.993539	+	0.113493i	$0.963796\pi$
$42$	5.80912e52	−	1.54842e54i	0.00374658	−	0.0998647i
$43$	−2.69773e55			−0.781755			−0.390877	−	0.920443i	$-0.627828\pi$
$43$	−2.69773e55			−0.781755			−0.390877	+	0.920443i	$0.627828\pi$
$44$			1.48315e56i			1.96695i
$45$	−2.27589e55	+	3.02892e56i	−0.140581	+	1.87095i
$46$	9.39756e56			2.74947
$47$			2.47346e56i			0.348319i	0.984717	+	0.174160i	$0.0557208\pi$
$47$			2.47346e56i			0.348319i	−0.984717	+	0.174160i	$0.944279\pi$
$48$	8.59330e55	+	3.22391e54i	0.0591504	+	0.00221912i
$49$	−2.91758e57			−0.996223
$50$			2.38542e58i			4.09812i
$51$	−1.70018e56	+	4.53182e57i	−0.0148974	+	0.397088i
$52$	−3.57697e58			−1.61958
$53$			4.23125e58i			1.00251i	0.865300	+	0.501255i	$0.167128\pi$
$53$			4.23125e58i			1.00251i	−0.865300	+	0.501255i	$0.832872\pi$
$54$	1.45465e58	−	1.28760e59i	0.182545	−	1.61582i
$55$	3.33777e59			2.24452
$56$			1.76657e58i			0.0643780i
$57$	−3.52249e59	−	1.32152e58i	−0.703243	−	0.0263832i
$58$	3.88686e58			0.0429583
$59$		−	1.31345e59i		−	0.0811793i	−0.999176	−	0.0405897i	$-0.987076\pi$
$59$		−	1.31345e59i		−	0.0811793i	0.999176	−	0.0405897i	$-0.0129236\pi$
$60$	3.31359e59	−	8.83235e60i	0.115653	−	3.08272i
$61$	−7.02451e60			−1.39766			−0.698830	−	0.715288i	$-0.746296\pi$
$61$	−7.02451e60			−1.39766			−0.698830	+	0.715288i	$0.746296\pi$
$62$		−	5.41195e60i		−	0.619492i
$63$	9.22415e59	+	6.93092e58i	0.0612841	+	0.00460481i
$64$	4.12936e61			1.60607
$65$			8.04982e61i			1.84813i
$66$	−1.42290e62	−	5.33824e60i	−1.94393	−	0.0729296i
$67$	1.58542e62			1.29898			0.649489	−	0.760371i	$-0.274983\pi$
$67$	1.58542e62			1.29898			0.649489	+	0.760371i	$0.274983\pi$
$68$		−	1.31962e62i		−	0.653350i
$69$	−2.10324e61	+	5.60616e62i	−0.0633898	+	1.68965i
$70$	1.01469e62			0.187500
$71$			8.27429e62i			0.943945i	0.881613	+	0.471972i	$0.156458\pi$
$71$			8.27429e62i			0.943945i	−0.881613	+	0.471972i	$0.843542\pi$
$72$	−1.10691e62	+	1.47316e63i	−0.0784891	+	1.04459i
$73$	2.43630e63			1.08082			0.540411	−	0.841401i	$-0.318269\pi$
$73$	2.43630e63			1.08082			0.540411	+	0.841401i	$0.318269\pi$
$74$		−	8.68605e63i		−	2.42630i
$75$	−1.42303e64	−	5.33874e62i	−2.51845	−	0.0944834i
$76$	1.02572e64			1.15708
$77$		−	1.01647e63i		−	0.0735207i
$78$	1.28744e63	−	3.43167e64i	0.0600499	−	1.60062i
$79$	3.21579e64			0.972673			0.486336	−	0.873772i	$-0.338333\pi$
$79$	3.21579e64			0.972673			0.486336	+	0.873772i	$0.338333\pi$
$80$			5.63128e63i			0.111057i
$81$	7.64868e64	+	1.15595e64i	0.988772	+	0.149434i
$82$	4.33326e64			0.369100
$83$			1.90418e65i			1.07412i	0.843543	+	0.537061i	$0.180466\pi$
$83$			1.90418e65i			1.07412i	−0.843543	+	0.537061i	$0.819534\pi$
$84$	−2.68977e64	−	1.00911e63i	−0.100976	−	0.00378828i
$85$	−2.96975e65			−0.745549
$86$			7.53642e65i			1.27121i
$87$	−8.69905e62	+	2.31872e64i	−0.000990415	+	0.0263994i
$88$	1.62337e66			1.25316
$89$			7.28951e65i			0.383211i	0.981472	+	0.191606i	$0.0613694\pi$
$89$			7.28951e65i			0.383211i	−0.981472	+	0.191606i	$0.938631\pi$
$90$	8.46164e66	+	6.35798e65i	3.04235	+	0.228599i
$91$	2.45146e65			0.0605366
$92$		−	1.63246e67i		−	2.78007i
$93$	3.22852e66	+	1.21123e65i	0.380701	+	0.0142826i
$94$	6.90989e66			0.566401
$95$		−	2.30833e67i		−	1.32037i
$96$	−8.90118e65	+	2.37260e67i	−0.0356636	+	0.950611i
$97$	1.57021e67			0.442301			0.221151	−	0.975240i	$-0.429019\pi$
$97$	1.57021e67			0.442301			0.221151	+	0.975240i	$0.429019\pi$
$98$			8.15061e67i			1.61996i
$99$	6.36910e66	−	8.47644e67i	0.0896358	−	1.19294i
$100$	4.14374e68			4.14374
$101$			1.26316e68i			0.900603i	0.892877	+	0.450301i	$0.148683\pi$
$101$			1.26316e68i			0.900603i	−0.892877	+	0.450301i	$0.851317\pi$
$102$	1.26602e68	+	4.74965e66i	0.645704	+	0.0242246i
$103$	−1.99737e68			−0.731128			−0.365564	−	0.930786i	$-0.619124\pi$
$103$	−1.99737e68			−0.731128			−0.365564	+	0.930786i	$0.619124\pi$
$104$			3.91515e68i			1.03185i
$105$	−2.27095e66	+	6.05321e67i	−0.00432287	+	0.115226i
$106$	1.18205e69			1.63018
$107$		−	1.18939e68i		−	0.119199i	−0.998222	−	0.0595997i	$-0.981018\pi$
$107$		−	1.18939e68i		−	0.119199i	0.998222	−	0.0595997i	$-0.0189824\pi$
$108$	−2.23670e69	−	2.52689e68i	−1.63381	−	0.184577i
$109$	−2.01543e68			−0.107613			−0.0538067	−	0.998551i	$-0.517135\pi$
$109$	−2.01543e68			−0.107613			−0.0538067	+	0.998551i	$0.517135\pi$
$110$		−	9.32444e69i		−	3.64982i
$111$	5.18171e69	+	1.94400e68i	1.49105	+	0.0559390i
$112$	1.71493e67			0.00363775
$113$			9.02780e69i			1.41552i	0.706455	+	0.707758i	$0.250293\pi$
$113$			9.02780e69i			1.41552i	−0.706455	+	0.707758i	$0.749707\pi$
$114$	−3.69182e68	+	9.84050e69i	−0.0429018	+	1.14354i
$115$	−3.67378e70			−3.17239
$116$		−	6.75190e68i		−	0.0434364i
$117$	2.04430e70	+	1.53606e69i	0.982257	+	0.0738056i
$118$	−3.66928e69			−0.132006
$119$			9.04396e68i			0.0244209i
$120$	−9.66739e70	−	3.62687e69i	−1.96402	−	0.0736834i
$121$	−2.81392e70			−0.431130
$122$			1.96238e71i			2.27273i
$123$	−9.69814e68	+	2.58503e70i	−0.00850971	+	0.226825i
$124$	−9.40114e70			−0.626388
$125$		−	5.62511e71i		−	2.85227i
$126$	1.93623e69	−	2.57687e70i	0.00748789	−	0.0996540i
$127$	−2.78443e71			−0.823020			−0.411510	−	0.911405i	$-0.634999\pi$
$127$	−2.78443e71			−0.823020			−0.411510	+	0.911405i	$0.634999\pi$
$128$		−	7.33394e71i		−	1.66035i
$129$	−4.49589e71	−	1.68670e70i	−0.781205	−	0.0293081i
$130$	2.24881e72			3.00524
$131$			1.12008e72i			1.15352i	0.816913	+	0.576761i	$0.195684\pi$
$131$			1.12008e72i			1.15352i	−0.816913	+	0.576761i	$0.804316\pi$
$132$	−9.27310e70	+	2.47174e72i	−0.0737414	+	1.96557i
$133$	−7.02970e70			−0.0432495
$134$		−	4.42907e72i		−	2.11227i
$135$	−5.68666e71	+	5.03360e72i	−0.210624	+	1.86436i
$136$	−1.44438e72			−0.416255
$137$		−	7.36748e69i		−	0.00165508i	−1.00000		0.000827541i	$-0.999737\pi$
$137$		−	7.36748e69i		−	0.00165508i	1.00000		0.000827541i	$-0.000263415\pi$
$138$	1.56615e73	+	5.87564e71i	2.74754	+	0.103078i
$139$	−2.06710e71			−0.0283699			−0.0141849	−	0.999899i	$-0.504515\pi$
$139$	−2.06710e71			−0.0283699			−0.0141849	+	0.999899i	$0.504515\pi$
$140$		−	1.76264e72i		−	0.189587i
$141$	−1.54648e71	+	4.12213e72i	−0.0130585	+	0.348074i
$142$	2.31152e73			1.53495
$143$		−	2.25275e73i		−	1.17838i
$144$	1.43010e72	+	1.07456e71i	0.0590256	+	0.00443512i
$145$	−1.51949e72			−0.0495661
$146$		−	6.80610e73i		−	1.75752i
$147$	−4.86229e73	−	1.82416e72i	−0.995523	−	0.0373486i
$148$	−1.50886e74			−2.45330
$149$		−	8.86241e73i		−	1.14609i	−0.819524	−	0.573045i	$-0.805762\pi$
$149$		−	8.86241e73i		−	1.14609i	0.819524	−	0.573045i	$-0.194238\pi$
$150$	−1.49144e73	+	3.97542e74i	−0.153639	+	4.09524i
$151$	1.69596e74			1.39380			0.696899	−	0.717169i	$-0.254563\pi$
$151$	1.69596e74			1.39380			0.696899	+	0.717169i	$0.254563\pi$
$152$		−	1.12269e74i		−	0.737188i
$153$	−5.66686e72	+	7.54185e73i	−0.0297738	+	0.396250i
$154$	−2.83963e73			−0.119552
$155$			2.11569e74i			0.714782i
$156$	−5.96119e74	−	2.23643e73i	−1.61844	−	0.0607183i
$157$	5.89266e73			0.128743			0.0643715	−	0.997926i	$-0.479496\pi$
$157$	5.89266e73			0.128743			0.0643715	+	0.997926i	$0.479496\pi$
$158$		−	8.98369e74i		−	1.58166i
$159$	−2.64550e73	+	7.05156e74i	−0.0375843	+	1.00181i
$160$	−1.55479e75			−1.78481
$161$			1.11880e74i			0.103913i
$162$	3.22929e74	−	2.13675e75i	0.242995	−	1.60784i
$163$	−1.24711e75			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$163$	−1.24711e75			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$164$		−	7.52736e74i		−	0.373209i
$165$	5.56254e75	+	2.08687e74i	2.24295	+	0.0841476i
$166$	5.31956e75			1.74663
$167$			3.46986e74i			0.0928863i	0.998921	+	0.0464431i	$0.0147886\pi$
$167$			3.46986e74i			0.0928863i	−0.998921	+	0.0464431i	$0.985211\pi$
$168$	−1.10451e73	+	2.94407e74i	−0.00241354	+	0.0643328i
$169$	−1.66441e74			−0.0297244
$170$			8.29635e75i			1.21234i
$171$	−5.86214e75	−	4.40474e74i	−0.701759	−	0.0527294i
$172$	1.30916e76			1.28536
$173$			1.34170e76i			1.08165i	0.841134	+	0.540826i	$0.181888\pi$
$173$			1.34170e76i			1.08165i	−0.841134	+	0.540826i	$0.818112\pi$
$174$	6.47762e74	+	2.43018e73i	0.0429281	+	0.00161051i
$175$	−2.83989e75			−0.154885
$176$		−	1.57592e75i		−	0.0708113i
$177$	8.21209e73	−	2.18893e75i	0.00304343	−	0.0811222i
$178$	2.03641e76			0.623139
$179$			2.93375e75i			0.0742027i	0.999312	+	0.0371013i	$0.0118124\pi$
$179$			2.93375e75i			0.0742027i	−0.999312	+	0.0371013i	$0.988188\pi$
$180$	1.10445e76	−	1.46988e77i	0.231143	−	3.07621i
$181$	2.24303e76			0.388833			0.194417	−	0.980919i	$-0.437719\pi$
$181$	2.24303e76			0.388833			0.194417	+	0.980919i	$0.437719\pi$
$182$		−	6.84845e75i		−	0.0984385i
$183$	−1.17067e77	−	4.39194e75i	−1.39668	−	0.0523985i
$184$	−1.78680e77			−1.77121
$185$			3.39563e77i			2.79951i
$186$	3.38371e75	−	9.01925e76i	0.0232249	−	0.619057i
$187$	8.31086e76			0.475369
$188$		−	1.20032e77i		−	0.572706i
$189$	1.53291e76	+	1.73179e75i	0.0610684	+	0.00689913i
$190$	−6.44859e77			−2.14705
$191$			4.14478e77i			1.15443i	0.816593	+	0.577214i	$0.195860\pi$
$191$			4.14478e77i			1.15443i	−0.816593	+	0.577214i	$0.804140\pi$
$192$	6.88177e77	+	2.58180e76i	1.60494	+	0.0602118i
$193$	−5.91832e77			−1.15678			−0.578389	−	0.815761i	$-0.696318\pi$
$193$	−5.91832e77			−1.15678			−0.578389	+	0.815761i	$0.696318\pi$
$194$		−	4.38656e77i		−	0.719226i
$195$	−5.03299e76	+	1.34154e78i	−0.0692867	+	1.84683i
$196$	1.41585e78			1.63799
$197$		−	8.55640e77i		−	0.832606i	−0.909226	−	0.416303i	$-0.863326\pi$
$197$		−	8.55640e77i		−	0.832606i	0.909226	−	0.416303i	$-0.136674\pi$
$198$	−2.36799e78	−	1.77928e77i	−1.93983	−	0.145757i
$199$	1.51348e78			1.04465			0.522325	−	0.852746i	$-0.325065\pi$
$199$	1.51348e78			1.04465			0.522325	+	0.852746i	$0.325065\pi$
$200$		−	4.53550e78i		−	2.64001i
$201$	2.64218e78	+	9.91255e76i	1.29807	+	0.0486989i
$202$	3.52880e78			1.46447
$203$			4.62738e75i			0.00162357i
$204$	8.25067e76	−	2.19921e78i	0.0244942	−	0.652891i
$205$	−1.69400e78			−0.425875
$206$			5.57989e78i			1.18889i
$207$	−7.01028e77	+	9.32977e78i	−0.126690	+	1.68608i
$208$	3.80070e77			0.0583057
$209$			6.45987e78i			0.841880i
$210$	1.69104e78	+	6.34418e76i	0.187369	+	0.00702942i
$211$	1.90241e78			0.179350			0.0896748	−	0.995971i	$-0.471417\pi$
$211$	1.90241e78			0.179350			0.0896748	+	0.995971i	$0.471417\pi$
$212$		−	2.05335e79i		−	1.64833i
$213$	−5.17333e77	+	1.37895e79i	−0.0353887	+	0.943281i
$214$	−3.32269e78			−0.193830
$215$		−	2.94621e79i		−	1.46675i
$216$	−2.76579e78	+	2.44817e79i	−0.117596	+	1.04091i
$217$	6.44303e77			0.0234131
$218$			5.63034e78i			0.174990i
$219$	4.06021e79	+	1.52325e78i	1.08006	+	0.0405202i
$220$	−1.61976e80			−3.69045
$221$			2.00436e79i			0.391417i
$222$	5.43078e78	−	1.44757e80i	0.0909623	−	2.42459i
$223$	−4.64965e79			−0.668429			−0.334214	−	0.942497i	$-0.608471\pi$
$223$	−4.64965e79			−0.668429			−0.334214	+	0.942497i	$0.608471\pi$
$224$			4.73490e78i			0.0584627i
$225$	−2.36821e80	−	1.77945e79i	−2.51313	−	0.188834i
$226$	2.52202e80			2.30177
$227$		−	2.51122e79i		−	0.197245i	−0.995125	−	0.0986224i	$-0.968556\pi$
$227$		−	2.51122e79i		−	0.197245i	0.995125	−	0.0986224i	$-0.0314436\pi$
$228$	1.70940e80	+	6.41309e78i	1.15627	+	0.0433793i
$229$	2.45669e80			1.43200			0.716001	−	0.698099i	$-0.245970\pi$
$229$	2.45669e80			1.43200			0.716001	+	0.698099i	$0.245970\pi$
$230$			1.02631e81i			5.15862i
$231$	6.35528e77	−	1.69399e79i	0.00275630	−	0.0734690i
$232$	−7.39024e78			−0.0276737
$233$		−	5.26460e80i		−	1.70319i	−0.524198	−	0.851596i	$-0.675635\pi$
$233$		−	5.26460e80i		−	1.70319i	0.524198	−	0.851596i	$-0.324365\pi$
$234$	4.29117e79	−	5.71099e80i	0.120015	−	1.59725i
$235$	−2.70128e80			−0.653525
$236$			6.37394e79i			0.133475i
$237$	5.35926e80	+	2.01061e79i	0.971989	+	0.0364657i
$238$	2.52654e79			0.0397108
$239$		−	7.83965e80i		−	1.06848i	−0.845332	−	0.534242i	$-0.820597\pi$
$239$		−	7.83965e80i		−	1.06848i	0.845332	−	0.534242i	$-0.179403\pi$
$240$	−3.52085e78	+	9.38479e79i	−0.00416356	+	0.110979i
$241$	−9.36225e80			−0.961171			−0.480586	−	0.876948i	$-0.659576\pi$
$241$	−9.36225e80			−0.961171			−0.480586	+	0.876948i	$0.659576\pi$
$242$			7.86100e80i			0.701061i
$243$	1.26746e81	+	2.40467e80i	0.982474	+	0.186398i
$244$	3.40887e81			2.29803
$245$		−	3.18631e81i		−	1.86914i
$246$	7.22158e80	+	2.70929e79i	0.368841	+	0.0138376i
$247$	−1.55795e81			−0.693199
$248$			1.02900e81i			0.399077i
$249$	−1.19055e80	+	3.17341e81i	−0.0402690	+	1.07337i
$250$	−1.57144e82			−4.63807
$251$			3.20771e81i			0.826588i	0.910598	+	0.413294i	$0.135622\pi$
$251$			3.20771e81i			0.826588i	−0.910598	+	0.413294i	$0.864378\pi$
$252$	−4.47631e80	−	3.36345e79i	−0.100763	−	0.00757123i
$253$	1.02811e82			2.02275
$254$			7.77865e81i			1.33831i
$255$	−4.94922e81	−	1.85678e80i	−0.745025	−	0.0279508i
$256$	−8.30051e81			−1.09382
$257$		−	1.00605e82i		−	1.16117i	−0.814201	−	0.580583i	$-0.802825\pi$
$257$		−	1.00605e82i		−	1.16117i	0.814201	−	0.580583i	$-0.197175\pi$
$258$	−4.71200e80	+	1.25598e82i	−0.0476579	+	1.27032i
$259$	1.03409e81			0.0916995
$260$		−	3.90643e82i		−	3.03869i
$261$	−2.89947e79	+	3.85882e80i	−0.00197944	+	0.0263437i
$262$	3.12908e82			1.87574
$263$		−	7.89555e81i		−	0.415803i	−0.978150	−	0.207901i	$-0.933337\pi$
$263$		−	7.89555e81i		−	0.415803i	0.978150	−	0.207901i	$-0.0666633\pi$
$264$	2.70542e82	+	1.01498e81i	1.25228	+	0.0469812i
$265$	−4.62097e82			−1.88093
$266$			1.96383e81i			0.0703280i
$267$	−4.55762e80	+	1.21483e82i	−0.0143666	+	0.382942i
$268$	−7.69377e82			−2.13578
$269$			2.97989e82i			0.728825i	0.931238	+	0.364413i	$0.118730\pi$
$269$			2.97989e82i			0.728825i	−0.931238	+	0.364413i	$0.881270\pi$
$270$	1.40620e83	+	1.58863e82i	3.03164	+	0.342496i
$271$	7.08505e82			1.34706			0.673531	−	0.739159i	$-0.264777\pi$
$271$	7.08505e82			1.34706			0.673531	+	0.739159i	$0.264777\pi$
$272$			1.40216e81i			0.0235209i
$273$	4.08547e81	+	1.53273e80i	0.0604940	+	0.00226953i
$274$	−2.05819e80			−0.00269133
$275$			2.60969e83i			3.01493i
$276$	1.02066e82	−	2.72057e83i	0.104225	−	2.77812i
$277$	−5.64197e82			−0.509470			−0.254735	−	0.967011i	$-0.581988\pi$
$277$	−5.64197e82			−0.509470			−0.254735	+	0.967011i	$0.581988\pi$
$278$			5.77467e81i			0.0461322i
$279$	5.37291e82	+	4.03714e81i	0.379897	+	0.0285451i
$280$	−1.92928e82			−0.120788
$281$			1.03114e83i			0.571876i	0.958248	+	0.285938i	$0.0923052\pi$
$281$			1.03114e83i			0.571876i	−0.958248	+	0.285938i	$0.907695\pi$
$282$	1.15157e83	+	4.32028e81i	0.566003	+	0.0212345i
$283$	−3.18171e83			−1.38651			−0.693253	−	0.720694i	$-0.743823\pi$
$283$	−3.18171e83			−1.38651			−0.693253	+	0.720694i	$0.743823\pi$
$284$		−	4.01536e83i		−	1.55203i
$285$	1.44324e82	−	3.84694e83i	0.0495009	−	1.31944i
$286$	−6.29331e83			−1.91617
$287$			5.15884e81i			0.0139498i
$288$	−2.96685e82	+	3.94848e83i	−0.0712771	+	0.948606i
$289$	3.94357e83			0.842100
$290$			4.24486e82i			0.0805993i
$291$	2.61682e83	+	9.81742e81i	0.441991	+	0.0165820i
$292$	−1.18229e84			−1.77709
$293$		−	4.75812e83i		−	0.636703i	−0.947973	−	0.318351i	$-0.896871\pi$
$293$		−	4.75812e83i		−	0.636703i	0.947973	−	0.318351i	$-0.103129\pi$
$294$	−5.09601e82	+	1.35834e84i	−0.0607325	+	1.61882i
$295$	1.43443e83			0.152311
$296$			1.65151e84i			1.56302i
$297$	1.59141e83	−	1.40866e84i	0.134296	−	1.18874i
$298$	−2.47582e84			−1.86366
$299$			2.47953e84i			1.66552i
$300$	6.90573e84	+	2.59079e83i	4.14083	+	0.155350i
$301$	−8.97226e82			−0.0480442
$302$		−	4.73787e84i		−	2.26645i
$303$	−7.89769e82	+	2.10512e84i	−0.0337637	+	0.899969i
$304$	−1.08987e83			−0.0416556
$305$		−	7.67151e84i		−	2.62232i
$306$	2.10690e84	+	1.58310e83i	0.644342	+	0.0484151i
$307$	−2.61657e84			−0.716188			−0.358094	−	0.933686i	$-0.616573\pi$
$307$	−2.61657e84			−0.716188			−0.358094	+	0.933686i	$0.616573\pi$
$308$			4.93274e83i			0.120883i
$309$	−3.32871e84	−	1.24882e83i	−0.730614	−	0.0274101i
$310$	5.91042e84			1.16231
$311$			3.26180e84i			0.574916i	0.957793	+	0.287458i	$0.0928102\pi$
$311$			3.26180e84i			0.574916i	−0.957793	+	0.287458i	$0.907190\pi$
$312$	−2.44787e83	+	6.52478e84i	−0.0386841	+	1.03112i
$313$	4.37145e84			0.619610			0.309805	−	0.950800i	$-0.399736\pi$
$313$	4.37145e84			0.619610			0.309805	+	0.950800i	$0.399736\pi$
$314$		−	1.64618e84i		−	0.209349i
$315$	−7.56930e82	+	1.00738e84i	−0.00863967	+	0.114983i
$316$	−1.56057e85			−1.59927
$317$		−	1.77098e85i		−	1.63004i	−0.579430	−	0.815022i	$-0.696725\pi$
$317$		−	1.77098e85i		−	1.63004i	0.579430	−	0.815022i	$-0.303275\pi$
$318$	1.96994e85	+	7.39052e83i	1.62903	+	0.0611157i
$319$	4.25229e83			0.0316038
$320$			4.50970e85i			3.01334i
$321$	7.43640e82	−	1.98217e84i	0.00446881	−	0.119116i
$322$	3.12549e84			0.168974
$323$		−	5.74762e84i		−	0.279642i
$324$	−3.71177e85	−	5.60963e84i	−1.62574	−	0.245699i
$325$	−6.29390e85			−2.48248
$326$			3.48395e85i			1.23787i
$327$	−3.35880e84	−	1.26011e83i	−0.107538	−	0.00403445i
$328$	−8.23901e84			−0.237774
$329$			8.22637e83i			0.0214066i
$330$	5.82992e84	−	1.55396e86i	0.136832	−	3.64725i
$331$	4.13132e84			0.0874857			0.0437428	−	0.999043i	$-0.486072\pi$
$331$	4.13132e84			0.0874857			0.0437428	+	0.999043i	$0.486072\pi$
$332$		−	9.24066e85i		−	1.76607i
$333$	8.62340e85	+	6.47952e84i	1.48790	+	0.111799i
$334$	9.69345e84			0.151042
$335$			1.73145e86i			2.43718i
$336$	2.85801e83	+	1.07223e82i	0.00363520	+	0.000136380i
$337$	8.86151e85			1.01881			0.509403	−	0.860528i	$-0.329866\pi$
$337$	8.86151e85			1.01881			0.509403	+	0.860528i	$0.329866\pi$
$338$			4.64974e84i			0.0483349i
$339$	−5.64445e84	+	1.50452e86i	−0.0530679	+	1.41452i
$340$	1.44117e86			1.22583
$341$		−	5.92076e85i		−	0.455752i
$342$	−1.23052e85	+	1.63766e86i	−0.0857432	+	1.14113i
$343$	−1.94437e85			−0.122682
$344$		−	1.43293e86i		−	0.818913i
$345$	−6.12252e86	−	2.29696e85i	−3.17016	−	0.118933i
$346$	3.74819e86			1.75887
$347$		−	2.18023e85i		−	0.0927471i	−0.998924	−	0.0463735i	$-0.985234\pi$
$347$		−	2.18023e85i		−	0.0927471i	0.998924	−	0.0463735i	$-0.0147665\pi$
$348$	4.22149e83	−	1.12523e85i	0.00162844	−	0.0434059i
$349$	3.03922e86			1.06340			0.531701	−	0.846932i	$-0.321553\pi$
$349$	3.03922e86			1.06340			0.531701	+	0.846932i	$0.321553\pi$
$350$			7.93357e85i			0.251858i
$351$	3.39731e86	+	3.83808e85i	0.978799	+	0.110579i
$352$	4.35109e86			1.13801
$353$		−	2.14532e86i		−	0.509510i	−0.967006	−	0.254755i	$-0.918005\pi$
$353$		−	2.14532e86i		−	0.509510i	0.967006	−	0.254755i	$-0.0819949\pi$
$354$	−6.11502e85	−	2.29414e84i	−0.131913	−	0.00494891i
$355$	−9.03640e86			−1.77105
$356$		−	3.53747e86i		−	0.630075i
$357$	−5.65456e83	+	1.50722e85i	−0.000915544	+	0.0244037i
$358$	8.19577e85			0.120661
$359$		−	9.47379e86i		−	1.26856i	−0.773102	−	0.634282i	$-0.781296\pi$
$359$		−	9.47379e86i		−	1.26856i	0.773102	−	0.634282i	$-0.218704\pi$
$360$	−1.60885e87	−	1.20887e86i	−1.95988	−	0.147263i
$361$	−4.55328e86			−0.504754
$362$		−	6.26616e86i		−	0.632281i
$363$	−4.68952e86	−	1.75935e85i	−0.430827	−	0.0161631i
$364$	−1.18965e86			−0.0995342
$365$			2.66070e87i			2.02786i
$366$	−1.22694e86	+	3.27039e87i	−0.0852052	+	2.27114i
$367$	−2.70405e87			−1.71147			−0.855735	−	0.517414i	$-0.826895\pi$
$367$	−2.70405e87			−1.71147			−0.855735	+	0.517414i	$0.826895\pi$
$368$			1.73457e86i			0.100084i
$369$	−3.23248e85	+	4.30201e86i	−0.0170074	+	0.226347i
$370$	9.48609e87			4.55228
$371$			1.40725e86i			0.0616111i
$372$	−1.56674e87	−	5.87788e85i	−0.625948	−	0.0234834i
$373$	−1.56266e87			−0.569854			−0.284927	−	0.958549i	$-0.591969\pi$
$373$	−1.56266e87			−0.569854			−0.284927	+	0.958549i	$0.591969\pi$
$374$		−	2.32174e87i		−	0.772998i
$375$	3.51699e86	−	9.37450e87i	0.106932	−	2.85026i
$376$	−1.31381e87			−0.364875
$377$			1.02554e86i			0.0260224i
$378$	4.83796e85	−	4.28237e86i	0.0112187	−	0.0993032i
$379$	3.50859e87			0.743702			0.371851	−	0.928292i	$-0.378723\pi$
$379$	3.50859e87			0.743702			0.371851	+	0.928292i	$0.378723\pi$
$380$			1.12019e88i			2.17095i
$381$	−4.64039e87	−	1.74091e86i	−0.822442	−	0.0308552i
$382$	1.15789e88			1.87721
$383$		−	7.43660e87i		−	1.10310i	−0.834141	−	0.551551i	$-0.814036\pi$
$383$		−	7.43660e87i		−	1.10310i	0.834141	−	0.551551i	$-0.185964\pi$
$384$	4.58540e86	−	1.22224e88i	0.0622466	−	1.65918i
$385$	1.11009e87			0.137941
$386$			1.65335e88i			1.88103i
$387$	−7.48205e87	−	5.62193e86i	−0.779557	−	0.0585750i
$388$	−7.61994e87			−0.727232
$389$		−	5.12010e87i		−	0.447705i	−0.974623	−	0.223853i	$-0.928137\pi$
$389$		−	5.12010e87i		−	0.447705i	0.974623	−	0.223853i	$-0.0718635\pi$
$390$	3.74775e88	+	1.40603e87i	3.00313	+	0.112667i
$391$	−9.14751e87			−0.671883
$392$		−	1.54971e88i		−	1.04358i
$393$	−7.00309e86	+	1.86667e88i	−0.0432457	+	1.15271i
$394$	−2.39033e88			−1.35390
$395$			3.51199e88i			1.82495i
$396$	−3.09081e87	+	4.11347e88i	−0.147379	+	1.96142i
$397$	−3.82502e88			−1.67401			−0.837003	−	0.547199i	$-0.815694\pi$
$397$	−3.82502e88			−1.67401			−0.837003	+	0.547199i	$0.815694\pi$
$398$		−	4.22807e88i		−	1.69871i
$399$	−1.17153e87	−	4.39518e85i	−0.0432191	−	0.00162143i
$400$	−4.40292e87			−0.149177
$401$			8.59382e87i			0.267472i	0.991017	+	0.133736i	$0.0426973\pi$
$401$			8.59382e87i			0.267472i	−0.991017	+	0.133736i	$0.957303\pi$
$402$	2.76919e87	−	7.38124e88i	0.0791893	−	2.11078i
$403$	1.42793e88			0.375264
$404$		−	6.12991e88i		−	1.48077i
$405$	−1.26242e88	+	8.35317e88i	−0.280372	+	1.85516i
$406$	1.29271e86			0.00264008
$407$		−	9.50269e88i		−	1.78499i
$408$	−2.40713e88	−	9.03071e86i	−0.415962	−	0.0156055i
$409$	−8.64823e88			−1.37510			−0.687551	−	0.726137i	$-0.741314\pi$
$409$	−8.64823e88			−1.37510			−0.687551	+	0.726137i	$0.741314\pi$
$410$			4.73239e88i			0.692515i
$411$	4.60637e84	−	1.22782e86i	6.20493e−5	−	0.00165392i
$412$	9.69289e88			1.20212
$413$		−	4.36835e86i		−	0.00498902i
$414$	2.60638e89	+	1.95840e88i	2.74174	+	0.206011i
$415$	−2.07957e89			−2.01529
$416$			1.04937e89i			0.937035i
$417$	−3.44491e87	−	1.29241e86i	−0.0283499	−	0.00106359i
$418$	1.80464e89			1.36898
$419$			2.04263e89i			1.42861i	0.699836	+	0.714303i	$0.253256\pi$
$419$			2.04263e89i			1.42861i	−0.699836	+	0.714303i	$0.746744\pi$
$420$	1.10205e87	−	2.93751e88i	0.00710766	−	0.189454i
$421$	2.54434e89			1.51351			0.756753	−	0.653701i	$-0.226785\pi$
$421$	2.54434e89			1.51351			0.756753	+	0.653701i	$0.226785\pi$
$422$		−	5.31460e88i		−	0.291640i
$423$	−5.15456e87	+	6.86005e88i	−0.0260987	+	0.347340i
$424$	−2.24748e89			−1.05016
$425$		−	2.32195e89i		−	1.00145i
$426$	3.85225e89	+	1.44523e88i	1.53387	+	0.0575455i
$427$	−2.33625e88			−0.0858958
$428$			5.77188e88i			0.195988i
$429$	1.40849e88	−	3.75431e89i	0.0441778	−	1.17756i
$430$	−8.23057e89			−2.38508
$431$			1.30776e89i			0.350187i	0.984552	+	0.175094i	$0.0560228\pi$
$431$			1.30776e89i			0.350187i	−0.984552	+	0.175094i	$0.943977\pi$
$432$	2.37660e88	+	2.68494e87i	0.0588179	+	0.00664488i
$433$	−3.47828e89			−0.795748			−0.397874	−	0.917440i	$-0.630252\pi$
$433$	−3.47828e89			−0.795748			−0.397874	+	0.917440i	$0.630252\pi$
$434$		−	1.79994e88i		−	0.0380720i
$435$	−2.53229e88	−	9.50028e86i	−0.0495312	−	0.00185824i
$436$	9.78051e88			0.176938
$437$		−	7.11019e89i		−	1.18991i
$438$	4.25538e88	−	1.13427e90i	0.0658898	−	1.75629i
$439$	1.25664e90			1.80060			0.900302	−	0.435265i	$-0.143345\pi$
$439$	1.25664e90			1.80060			0.900302	+	0.435265i	$0.143345\pi$
$440$			1.77289e90i			2.35121i
$441$	−8.09182e89	−	6.08010e88i	−0.993423	−	0.0746446i
$442$	5.59943e89			0.636482
$443$			1.27977e90i			1.34711i	0.739135	+	0.673557i	$0.235234\pi$
$443$			1.27977e90i			1.34711i	−0.739135	+	0.673557i	$0.764766\pi$
$444$	−2.51459e90	−	9.43387e88i	−2.45158	−	0.0919748i
$445$	−7.96092e89			−0.718990
$446$			1.29894e90i			1.08693i
$447$	5.54105e88	−	1.47696e90i	0.0429671	−	1.14528i
$448$	1.37337e89			0.0987039
$449$		−	1.30947e90i		−	0.872407i	−0.899848	−	0.436203i	$-0.856323\pi$
$449$		−	1.30947e90i		−	0.872407i	0.899848	−	0.436203i	$-0.143677\pi$
$450$	−4.97110e89	+	6.61589e90i	−0.307063	+	4.08660i
$451$	4.74066e89			0.271542
$452$		−	4.38103e90i		−	2.32739i
$453$	2.82640e90	+	1.06037e89i	1.39282	+	0.0522537i
$454$	−7.01539e89			−0.320740
$455$			2.67726e89i			0.113580i
$456$	7.01940e88	−	1.87101e90i	0.0276373	−	0.736669i
$457$	−2.83153e90			−1.03483			−0.517416	−	0.855734i	$-0.673106\pi$
$457$	−2.83153e90			−1.03483			−0.517416	+	0.855734i	$0.673106\pi$
$458$		−	6.86305e90i		−	2.32858i
$459$	−1.41595e89	+	1.25334e90i	−0.0446083	+	0.394855i
$460$	1.78282e91			5.21604
$461$		−	2.54751e90i		−	0.692283i	−0.938182	−	0.346142i	$-0.887492\pi$
$461$		−	2.54751e90i		−	0.692283i	0.938182	−	0.346142i	$-0.112508\pi$
$462$	−4.73237e89	−	1.77542e88i	−0.119468	−	0.00448203i
$463$	3.99190e90			0.936324			0.468162	−	0.883643i	$-0.344916\pi$
$463$	3.99190e90			0.936324			0.468162	+	0.883643i	$0.344916\pi$
$464$			7.17421e87i			0.00156373i
$465$	−1.32279e89	+	3.52589e90i	−0.0267973	+	0.714280i
$466$	−1.47073e91			−2.76956
$467$			6.07654e90i			1.06385i	0.846790	+	0.531927i	$0.178532\pi$
$467$			6.07654e90i			1.06385i	−0.846790	+	0.531927i	$0.821468\pi$
$468$	−9.92061e90	−	7.45423e89i	−1.61503	−	0.121351i
$469$	5.27289e89			0.0798311
$470$			7.54634e90i			1.06270i
$471$	9.82039e89	+	3.68427e88i	0.128652	+	0.00482659i
$472$	6.97655e89			0.0850379
$473$			8.24497e90i			0.935212i
$474$	5.61688e89	−	1.49717e91i	0.0592968	−	1.58055i
$475$	1.80481e91			1.77357
$476$		−	4.38887e89i		−	0.0401528i
$477$	−8.81770e89	+	1.17352e91i	−0.0751157	+	0.999692i
$478$	−2.19010e91			−1.73746
$479$		−	1.48803e91i		−	1.09952i	−0.835323	−	0.549760i	$-0.814719\pi$
$479$		−	1.48803e91i		−	1.09952i	0.835323	−	0.549760i	$-0.185281\pi$
$480$	−2.59113e91	−	9.72104e89i	−1.78356	−	0.0669130i
$481$	2.29180e91			1.46975
$482$			2.61545e91i			1.56296i
$483$	−6.99506e88	+	1.86453e90i	−0.00389573	+	0.103840i
$484$	1.36554e91			0.708864
$485$			1.71483e91i			0.829857i
$486$	6.71772e90	−	3.54080e91i	0.303102	−	1.59760i
$487$	−1.16838e91			−0.491587			−0.245794	−	0.969322i	$-0.579049\pi$
$487$	−1.16838e91			−0.491587			−0.245794	+	0.969322i	$0.579049\pi$
$488$		−	3.73115e91i		−	1.46409i
$489$	−2.07837e91	−	7.79732e89i	−0.760714	−	0.0285394i
$490$	−8.90134e91			−3.03940
$491$		−	6.06098e91i		−	1.93096i	−0.260485	−	0.965478i	$-0.583882\pi$
$491$		−	6.06098e91i		−	1.93096i	0.260485	−	0.965478i	$-0.416118\pi$
$492$	4.70633e89	−	1.25447e91i	0.0139917	−	0.372946i
$493$	−3.78344e89			−0.0104976
$494$			4.35233e91i			1.12721i
$495$	9.25718e91	+	6.95574e90i	2.23821	+	0.168177i
$496$	9.98916e89			0.0225503
$497$			2.75191e90i			0.0580119i
$498$	8.86530e91	+	3.32595e90i	1.74540	+	0.0654815i
$499$	3.84830e91			0.707702			0.353851	−	0.935302i	$-0.384872\pi$
$499$	3.84830e91			0.707702			0.353851	+	0.935302i	$0.384872\pi$
$500$			2.72976e92i			4.68970i
$501$	−2.16946e89	+	5.78267e90i	−0.00348232	+	0.0928210i
$502$	8.96112e91			1.34411
$503$		−	4.10295e91i		−	0.575155i	−0.957757	−	0.287578i	$-0.907150\pi$
$503$		−	4.10295e91i		−	0.575155i	0.957757	−	0.287578i	$-0.0928499\pi$
$504$	−3.68144e89	+	4.89952e90i	−0.00482369	+	0.0641970i
$505$	−1.37951e92			−1.68973
$506$		−	2.87214e92i		−	3.28919i
$507$	−2.77382e90	−	1.04064e89i	−0.0297035	−	0.00111437i
$508$	1.35124e92			1.35321
$509$		−	2.32882e91i		−	0.218138i	−0.994034	−	0.109069i	$-0.965213\pi$
$509$		−	2.32882e91i		−	0.218138i	0.994034	−	0.109069i	$-0.0347870\pi$
$510$	−5.18713e90	+	1.38262e92i	−0.0454507	+	1.21149i
$511$	8.10279e90			0.0664239
$512$			1.54246e91i			0.118314i
$513$	−9.74198e91	−	1.10059e91i	−0.699289	−	0.0790014i
$514$	−2.81053e92			−1.88817
$515$		−	2.18134e92i		−	1.37176i
$516$	2.18177e92	+	8.18526e90i	1.28446	+	0.0481884i
$517$	7.55954e91			0.416694
$518$		−	2.88886e91i		−	0.149113i
$519$	−8.38871e90	+	2.23600e92i	−0.0405513	+	1.08089i
$520$	−4.27576e92			−1.93597
$521$		−	1.99012e91i		−	0.0844106i	−0.999109	−	0.0422053i	$-0.986562\pi$
$521$		−	1.99012e91i		−	0.0844106i	0.999109	−	0.0422053i	$-0.0134384\pi$
$522$	1.07801e91	+	8.10002e89i	0.0428375	+	0.00321876i
$523$	3.22181e92			1.19962			0.599808	−	0.800144i	$-0.295243\pi$
$523$	3.22181e92			1.19962			0.599808	+	0.800144i	$0.295243\pi$
$524$		−	5.43556e92i		−	1.89662i
$525$	−4.73281e91	−	1.77559e90i	−0.154776	−	0.00580665i
$526$	−2.20572e92			−0.676136
$527$			5.26795e91i			0.151384i
$528$	9.85311e89	−	2.62634e91i	0.00265473	−	0.0707615i
$529$	−7.35793e92			−1.85893
$530$			1.29092e93i			3.05858i
$531$	2.73717e90	−	3.64281e91i	0.00608257	−	0.0809511i
$532$	3.41139e91			0.0711108
$533$			1.14333e92i			0.223586i
$534$	3.39377e92	+	1.27323e91i	0.622701	+	0.0233616i
$535$	1.29894e92			0.223645
$536$			8.42117e92i			1.36072i
$537$	−1.83427e90	+	4.88922e91i	−0.00278187	+	0.0741505i
$538$	8.32469e92			1.18514
$539$			8.91691e92i			1.19178i
$540$	2.75963e92	−	2.44272e93i	0.346309	−	3.06539i
$541$	−1.49985e92			−0.176742			−0.0883712	−	0.996088i	$-0.528166\pi$
$541$	−1.49985e92			−0.176742			−0.0883712	+	0.996088i	$0.528166\pi$
$542$		−	1.97929e93i		−	2.19046i
$543$	3.73811e92	+	1.40241e91i	0.388560	+	0.0145774i
$544$	−3.87135e92			−0.378007
$545$		−	2.20106e92i		−	0.201907i
$546$	4.28186e90	−	1.14132e92i	0.00369047	−	0.0983693i
$547$	−2.40672e92			−0.194920			−0.0974599	−	0.995239i	$-0.531072\pi$
$547$	−2.40672e92			−0.194920			−0.0974599	+	0.995239i	$0.531072\pi$
$548$			3.57530e90i			0.00272129i
$549$	−1.94822e93	−	1.46387e92i	−1.39373	−	0.104723i
$550$	7.29048e93			4.90258
$551$		−	2.94079e91i		−	0.0185913i
$552$	−2.97778e93	−	1.11716e92i	−1.76996	−	0.0664028i
$553$	1.06953e92			0.0597774
$554$			1.57615e93i			0.828449i
$555$	−2.12305e92	+	5.65897e93i	−0.104954	+	2.79754i
$556$	1.00312e92			0.0466457
$557$		−	3.08215e93i		−	1.34827i	−0.738609	−	0.674134i	$-0.764517\pi$
$557$		−	3.08215e93i		−	1.34827i	0.738609	−	0.674134i	$-0.235483\pi$
$558$	1.12782e92	−	1.50098e93i	0.0464171	−	0.617751i
$559$	−1.98847e93			−0.770049
$560$			1.87288e91i			0.00682524i
$561$	1.38504e93	+	5.19620e91i	0.475035	+	0.0178217i
$562$	2.88061e93			0.929928
$563$			1.37661e93i			0.418337i	0.977880	+	0.209168i	$0.0670756\pi$
$563$			1.37661e93i			0.418337i	−0.977880	+	0.209168i	$0.932924\pi$
$564$	7.50479e91	−	2.00040e93i	0.0214708	−	0.572303i
$565$	−9.85931e93			−2.65583
$566$			8.88849e93i			2.25460i
$567$	2.54384e92	+	3.84453e91i	0.0607668	+	0.00918374i
$568$	−4.39498e93			−0.988813
$569$		−	8.65426e93i		−	1.83406i	−0.398822	−	0.917028i	$-0.630581\pi$
$569$		−	8.65426e93i		−	1.83406i	0.398822	−	0.917028i	$-0.369419\pi$
$570$	−1.07469e94	−	4.03186e92i	−2.14554	−	0.0804933i
$571$	5.17582e93			0.973535			0.486767	−	0.873532i	$-0.338176\pi$
$571$	5.17582e93			0.973535			0.486767	+	0.873532i	$0.338176\pi$
$572$			1.09322e94i			1.93750i
$573$	−2.59144e92	+	6.90746e93i	−0.0432797	+	1.15362i
$574$	1.44118e92			0.0226837
$575$		−	2.87241e94i		−	4.26128i
$576$	1.14526e94	+	8.60538e92i	1.60155	+	0.120339i
$577$	8.18955e93			1.07965			0.539824	−	0.841778i	$-0.318491\pi$
$577$	8.18955e93			1.07965			0.539824	+	0.841778i	$0.318491\pi$
$578$		−	1.10168e94i		−	1.36934i
$579$	−9.86315e93	−	3.70031e92i	−1.15596	−	0.0433678i
$580$	7.37379e92			0.0814965
$581$			6.33305e92i			0.0660122i
$582$	2.74261e92	−	7.31041e93i	0.0269639	−	0.718721i
$583$	1.29318e94			1.19930
$584$			1.29407e94i			1.13220i
$585$	−1.67754e93	+	2.23259e94i	−0.138476	+	1.84293i
$586$	−1.32924e94			−1.03534
$587$			1.33314e94i			0.979894i	0.871752	+	0.489947i	$0.162984\pi$
$587$			1.33314e94i			0.979894i	−0.871752	+	0.489947i	$0.837016\pi$
$588$	2.35958e94	+	8.85233e92i	1.63684	+	0.0614085i
$589$	−4.09468e93			−0.268102
$590$		−	4.00724e93i		−	0.247672i
$591$	5.34972e92	−	1.42596e94i	0.0312145	−	0.832020i
$592$	1.60324e93			0.0883202
$593$			1.60925e94i			0.837073i	0.908200	+	0.418536i	$0.137457\pi$
$593$			1.60925e94i			0.837073i	−0.908200	+	0.418536i	$0.862543\pi$
$594$	−3.93525e94	−	4.44580e93i	−1.93300	−	0.218379i
$595$	−9.87696e92			−0.0458191
$596$			4.30077e94i			1.88440i
$597$	2.52228e94	+	9.46271e92i	1.04392	+	0.0391641i
$598$	6.92686e94			2.70830
$599$		−	3.45065e92i		−	0.0127464i	−0.999980	−	0.00637322i	$-0.997971\pi$
$599$		−	3.45065e92i		−	0.0127464i	0.999980	−	0.00637322i	$-0.00202867\pi$
$600$	2.83573e93	−	7.55862e94i	0.0989744	−	2.63815i
$601$	9.42431e93			0.310826			0.155413	−	0.987850i	$-0.450329\pi$
$601$	9.42431e93			0.310826			0.155413	+	0.987850i	$0.450329\pi$
$602$			2.50651e93i			0.0781246i
$603$	4.39712e94	+	3.30394e93i	1.29533	+	0.0973294i
$604$	−8.23019e94			−2.29168
$605$		−	3.07310e94i		−	0.808897i
$606$	5.88090e94	+	2.20631e93i	1.46344	+	0.0549032i
$607$	−4.34165e94			−1.02150			−0.510751	−	0.859729i	$-0.670632\pi$
$607$	−4.34165e94			−1.02150			−0.510751	+	0.859729i	$0.670632\pi$
$608$		−	3.00913e94i		−	0.669451i
$609$	−2.89318e90	+	7.71174e91i	−6.08678e−5	+	0.00162242i
$610$	−2.14313e95			−4.26416
$611$			1.82316e94i			0.343103i
$612$	2.75002e93	−	3.65992e94i	0.0489540	−	0.651514i
$613$	4.62367e94			0.778629			0.389314	−	0.921105i	$-0.372712\pi$
$613$	4.62367e94			0.778629			0.389314	+	0.921105i	$0.372712\pi$
$614$			7.30969e94i			1.16459i
$615$	−2.82313e94	−	1.05914e93i	−0.425575	−	0.0159661i
$616$	5.39910e93			0.0770153
$617$		−	2.43093e94i		−	0.328154i	−0.986448	−	0.164077i	$-0.947535\pi$
$617$		−	2.43093e94i		−	0.328154i	0.986448	−	0.164077i	$-0.0524645\pi$
$618$	−3.48872e93	+	9.29915e94i	−0.0445716	+	1.18805i
$619$	−1.25455e95			−1.51707			−0.758535	−	0.651633i	$-0.774084\pi$
$619$	−1.25455e95			−1.51707			−0.758535	+	0.651633i	$0.774084\pi$
$620$		−	1.02670e95i		−	1.17524i
$621$	−1.75162e94	+	1.55047e95i	−0.189813	+	1.68015i
$622$	9.11223e94			0.934871
$623$			2.42439e93i			0.0235509i
$624$	6.33405e93	+	2.37632e92i	0.0582647	+	0.00218589i
$625$	3.25015e95			2.83128
$626$		−	1.22122e95i		−	1.00755i
$627$	−4.03891e93	+	1.07657e95i	−0.0315622	+	0.841288i
$628$	−2.85960e94			−0.211679
$629$			8.45494e94i			0.592910i
$630$	2.81422e94	+	2.11457e93i	0.186973	+	0.0140490i
$631$	1.67111e95			1.05198			0.525990	−	0.850491i	$-0.323695\pi$
$631$	1.67111e95			1.05198			0.525990	+	0.850491i	$0.323695\pi$
$632$			1.70811e95i			1.01891i
$633$	3.17045e94	+	1.18944e93i	0.179224	+	0.00672385i
$634$	−4.94745e95			−2.65061
$635$		−	3.04090e95i		−	1.54417i
$636$	1.28381e94	−	3.42200e95i	0.0617960	−	1.64717i
$637$	−2.15053e95			−0.981305
$638$		−	1.18793e94i		−	0.0513909i
$639$	−1.72432e94	+	2.29484e95i	−0.0707275	+	0.941291i
$640$	8.00945e95			3.11518
$641$		−	4.33364e95i		−	1.59838i	−0.601080	−	0.799189i	$-0.705263\pi$
$641$		−	4.33364e95i		−	1.59838i	0.601080	−	0.799189i	$-0.294737\pi$
$642$	−5.53741e94	−	2.07745e93i	−0.193694	−	0.00726673i
$643$	2.94631e95			0.977474			0.488737	−	0.872431i	$-0.337458\pi$
$643$	2.94631e95			0.977474			0.488737	+	0.872431i	$0.337458\pi$
$644$		−	5.42932e94i		−	0.170854i
$645$	1.84206e94	−	4.90999e95i	0.0549886	−	1.46572i
$646$	−1.60567e95			−0.454726
$647$			3.04069e94i			0.0817009i	0.999165	+	0.0408505i	$0.0130067\pi$
$647$			3.04069e94i			0.0817009i	−0.999165	+	0.0408505i	$0.986993\pi$
$648$	−6.13998e94	+	4.06269e95i	−0.156537	+	1.03577i
$649$	−4.01425e94			−0.0971147
$650$			1.75827e96i			4.03676i
$651$	1.07376e94	+	4.02838e92i	0.0233967	+	0.000877761i
$652$	6.05201e95			1.25165
$653$		−	5.95688e95i		−	1.16942i	−0.811242	−	0.584710i	$-0.801208\pi$
$653$		−	5.95688e95i		−	1.16942i	0.811242	−	0.584710i	$-0.198792\pi$
$654$	−3.52026e93	+	9.38321e94i	−0.00656041	+	0.174867i
$655$	−1.22325e96			−2.16427
$656$			7.99817e93i			0.0134357i
$657$	6.75700e95	+	5.07713e94i	1.07778	+	0.0809834i
$658$	2.29813e94			0.0348092
$659$			2.88720e95i			0.415311i	0.978202	+	0.207655i	$0.0665833\pi$
$659$			2.88720e95i			0.415311i	−0.978202	+	0.207655i	$0.933417\pi$
$660$	−2.69940e96	−	1.01272e95i	−3.68785	−	0.138355i
$661$	2.97483e95			0.386023			0.193011	−	0.981197i	$-0.438175\pi$
$661$	2.97483e95			0.386023			0.193011	+	0.981197i	$0.438175\pi$
$662$		−	1.15413e95i		−	0.142260i
$663$	−1.25319e94	+	3.34036e95i	−0.0146743	+	0.391141i
$664$	−1.01143e96			−1.12518
$665$		−	7.67718e94i		−	0.0811457i
$666$	1.81013e95	−	2.40905e96i	0.181797	−	2.41948i
$667$	−4.68036e94			−0.0446685
$668$		−	1.68386e95i		−	0.152724i
$669$	−7.74886e95	−	2.90710e94i	−0.667959	−	0.0250595i
$670$	4.83701e96			3.96309
$671$			2.14687e96i			1.67202i
$672$	−2.96041e93	+	7.89093e94i	−0.00219177	+	0.0584216i
$673$	−5.55556e95			−0.391035			−0.195518	−	0.980700i	$-0.562639\pi$
$673$	−5.55556e95			−0.391035			−0.195518	+	0.980700i	$0.562639\pi$
$674$		−	2.47557e96i		−	1.65668i
$675$	−3.93561e96	−	4.44621e95i	−2.50429	−	0.282919i
$676$	8.07710e94			0.0488729
$677$			1.97863e96i			1.13854i	0.822149	+	0.569272i	$0.192775\pi$
$677$			1.97863e96i			1.13854i	−0.822149	+	0.569272i	$0.807225\pi$
$678$	4.20306e96	+	1.57684e95i	2.30015	+	0.0862937i
$679$	5.22229e94			0.0271824
$680$		−	1.57742e96i		−	0.780987i
$681$	1.57009e94	−	4.18506e95i	0.00739474	−	0.197106i
$682$	−1.65403e96			−0.741098
$683$		−	1.97130e96i		−	0.840326i	−0.907449	−	0.420163i	$-0.861973\pi$
$683$		−	1.97130e96i		−	0.840326i	0.907449	−	0.420163i	$-0.138027\pi$
$684$	2.84479e96	+	2.13754e95i	1.15383	+	0.0866976i
$685$	8.04607e93			0.00310531
$686$			5.43183e95i			0.199492i
$687$	4.09419e96	+	1.53600e95i	1.43100	+	0.0536860i
$688$	−1.39104e95			−0.0462736
$689$			3.11882e96i			0.987498i
$690$	−6.41682e95	+	1.71040e97i	−0.193398	+	5.15499i
$691$	−2.27338e95			−0.0652256			−0.0326128	−	0.999468i	$-0.510383\pi$
$691$	−2.27338e95			−0.0652256			−0.0326128	+	0.999468i	$0.510383\pi$
$692$		−	6.51103e96i		−	1.77845i
$693$	2.11827e94	−	2.81914e95i	0.00550873	−	0.0733141i
$694$	−6.09073e95			−0.150816
$695$		−	2.25749e95i		−	0.0532282i
$696$	−1.23162e95	−	4.62060e93i	−0.0276542	−	0.00103749i
$697$	−4.21797e95			−0.0901963
$698$		−	8.49042e96i		−	1.72920i
$699$	3.29159e95	−	8.77369e96i	0.0638530	−	1.70200i
$700$	1.37815e96			0.254661
$701$			8.29799e96i			1.46070i	0.683074	+	0.730349i	$0.260642\pi$
$701$			8.29799e96i			1.46070i	−0.683074	+	0.730349i	$0.739358\pi$
$702$	1.07221e96	−	9.49079e96i	0.179812	−	1.59162i
$703$	−6.57187e96			−1.05004
$704$		−	1.26204e97i		−	1.92134i
$705$	−4.50180e96	−	1.68892e95i	−0.653065	−	0.0245008i
$706$	−5.99321e96			−0.828514
$707$			4.20110e95i			0.0553482i
$708$	−3.98518e94	+	1.06225e96i	−0.00500400	+	0.133381i
$709$	−1.06132e97			−1.27021			−0.635106	−	0.772425i	$-0.719043\pi$
$709$	−1.06132e97			−1.27021			−0.635106	+	0.772425i	$0.719043\pi$
$710$			2.52442e97i			2.87991i
$711$	8.91889e96	+	6.70155e95i	0.969939	+	0.0728801i
$712$	−3.87191e96			−0.401426
$713$			6.51680e96i			0.644155i
$714$	4.21059e95	+	1.57967e94i	0.0396829	+	0.00148877i
$715$	2.46024e97			2.21091
$716$		−	1.42369e96i		−	0.122004i
$717$	4.90159e95	−	1.30651e97i	0.0400576	−	1.06773i
$718$	−2.64662e97			−2.06281
$719$		−	3.51594e96i		−	0.261372i	−0.991424	−	0.130686i	$-0.958282\pi$
$719$		−	3.51594e96i		−	0.261372i	0.991424	−	0.130686i	$-0.0417179\pi$
$720$	−1.17353e95	+	1.56182e96i	−0.00832127	+	0.110745i
$721$	−6.64297e95			−0.0449328
$722$			1.27201e97i			0.820779i
$723$	−1.56026e97	−	5.85356e95i	−0.960496	−	0.0360345i
$724$	−1.08850e97			−0.639319
$725$		−	1.18804e96i		−	0.0665791i
$726$	−4.91494e95	+	1.31007e97i	−0.0262829	+	0.700568i
$727$	−7.43344e96			−0.379332			−0.189666	−	0.981849i	$-0.560741\pi$
$727$	−7.43344e96			−0.379332			−0.189666	+	0.981849i	$0.560741\pi$
$728$			1.30212e96i			0.0634140i
$729$	2.09725e97	+	4.79994e96i	0.974796	+	0.223100i
$730$	7.43298e97			3.29751
$731$		−	7.33590e96i		−	0.310644i
$732$	5.68103e97	+	2.13133e96i	2.29642	+	0.0861536i
$733$	−3.75152e97			−1.44768			−0.723840	−	0.689968i	$-0.757625\pi$
$733$	−3.75152e97			−1.44768			−0.723840	+	0.689968i	$0.757625\pi$
$734$			7.55409e97i			2.78302i
$735$	1.99218e96	−	5.31013e97i	0.0700743	−	1.86782i
$736$	−4.78912e97			−1.60846
$737$		−	4.84547e97i		−	1.55397i
$738$	1.20182e97	+	9.03031e95i	0.368063	+	0.0276558i
$739$	5.23635e97			1.53150			0.765751	−	0.643137i	$-0.222367\pi$
$739$	5.23635e97			1.53150			0.765751	+	0.643137i	$0.222367\pi$
$740$		−	1.64784e98i		−	4.60295i
$741$	−2.59640e97	−	9.74080e95i	−0.692712	−	0.0259882i
$742$	3.93132e96			0.100186
$743$			5.19396e97i			1.26438i	0.774812	+	0.632191i	$0.217844\pi$
$743$			5.19396e97i			1.26438i	−0.774812	+	0.632191i	$0.782156\pi$
$744$	−6.43359e95	+	1.71487e97i	−0.0149614	+	0.398796i
$745$	9.67870e97			2.15032
$746$			4.36547e97i			0.926639i
$747$	−3.96823e96	+	5.28119e97i	−0.0804815	+	1.07110i
$748$	−4.03311e97			−0.781602
$749$		−	3.95573e95i		−	0.00732562i
$750$	−2.61888e98	−	9.82512e96i	−4.63481	−	0.173882i
$751$	2.52671e96			0.0427364			0.0213682	−	0.999772i	$-0.493198\pi$
$751$	2.52671e96			0.0427364			0.0213682	+	0.999772i	$0.493198\pi$
$752$			1.27540e96i			0.0206177i
$753$	−2.00556e96	+	5.34580e97i	−0.0309889	+	0.826007i
$754$	2.86497e96			0.0423150
$755$			1.85217e98i			2.61508i
$756$	−7.43895e96	−	8.40407e95i	−0.100409	−	0.0113435i
$757$	−1.34280e97			−0.173281			−0.0866405	−	0.996240i	$-0.527613\pi$
$757$	−1.34280e97			−0.173281			−0.0866405	+	0.996240i	$0.527613\pi$
$758$		−	9.80165e97i		−	1.20933i
$759$	1.71339e98	+	6.42805e96i	2.02132	+	0.0758331i
$760$	1.22610e98			1.38313
$761$		−	8.84164e97i		−	0.953794i	−0.878959	−	0.476897i	$-0.841761\pi$
$761$		−	8.84164e97i		−	0.953794i	0.878959	−	0.476897i	$-0.158239\pi$
$762$	−4.86345e96	+	1.29635e98i	−0.0501736	+	1.33737i
$763$	−6.70303e95			−0.00661358
$764$		−	2.01139e98i		−	1.89811i
$765$	−8.23650e97	−	6.18881e96i	−0.743454	−	0.0558622i
$766$	−2.07750e98			−1.79375
$767$		−	9.68134e96i		−	0.0799637i
$768$	−1.38332e98	−	5.18973e96i	−1.09305	−	0.0410075i
$769$	−3.71032e97			−0.280489			−0.140245	−	0.990117i	$-0.544789\pi$
$769$	−3.71032e97			−0.280489			−0.140245	+	0.990117i	$0.544789\pi$
$770$		−	3.10118e97i		−	0.224306i
$771$	6.29015e96	−	1.67663e98i	0.0435323	−	1.16035i
$772$	2.87205e98			1.90197
$773$			4.90112e97i			0.310594i	0.987868	+	0.155297i	$0.0496334\pi$
$773$			4.90112e97i			0.310594i	−0.987868	+	0.155297i	$0.950367\pi$
$774$	−1.57055e97	+	2.09020e98i	−0.0952488	+	1.26764i
$775$	−1.65419e98			−0.960123
$776$			8.34035e97i			0.463325i
$777$	1.72336e97	+	6.46546e95i	0.0916351	+	0.00343783i
$778$	−1.43036e98			−0.728013
$779$		−	3.27855e97i		−	0.159738i
$780$	2.44242e97	−	6.51025e98i	0.113921	−	3.03656i
$781$	2.52884e98			1.12924
$782$			2.55547e98i			1.09255i
$783$	−7.24475e95	+	6.41277e96i	−0.00296568	+	0.0262510i
$784$	−1.50441e97			−0.0589685
$785$			6.43541e97i			0.241551i
$786$	5.21476e98	+	1.95640e97i	1.87442	+	0.0703218i
$787$	2.09654e98			0.721708			0.360854	−	0.932622i	$-0.382485\pi$
$787$	2.09654e98			0.721708			0.360854	+	0.932622i	$0.382485\pi$
$788$			4.15227e98i			1.36897i
$789$	4.93654e96	−	1.31583e98i	0.0155885	−	0.415510i
$790$	9.81115e98			2.96755
$791$			3.00252e97i			0.0869931i
$792$	4.50236e98	+	3.38302e97i	1.24964	+	0.0938964i
$793$	−5.17771e98			−1.37673
$794$			1.06857e99i			2.72210i
$795$	−7.70106e98	−	2.88917e97i	−1.87961	−	0.0705165i
$796$	−7.34463e98			−1.71761
$797$			1.39156e98i			0.311830i	0.987770	+	0.155915i	$0.0498326\pi$
$797$			1.39156e98i			0.311830i	−0.987770	+	0.155915i	$0.950167\pi$
$798$	−1.22785e96	+	3.27281e97i	−0.00263661	+	0.0702785i
$799$	−6.72604e97			−0.138410
$800$		−	1.21564e99i		−	2.39743i
$801$	−1.51910e97	+	2.02172e98i	−0.0287131	+	0.382134i
$802$	2.40078e98			0.434935
$803$		−	7.44598e98i		−	1.29299i
$804$	−1.28220e99	−	4.81038e97i	−2.13428	−	0.0800707i
$805$	−1.22185e98			−0.194965
$806$		−	3.98910e98i		−	0.610216i
$807$	−1.86312e97	+	4.96613e98i	−0.0273238	+	0.728313i
$808$	−6.70945e98			−0.943410
$809$		−	9.84308e98i		−	1.32703i	−0.748162	−	0.663516i	$-0.769064\pi$
$809$		−	9.84308e98i		−	1.32703i	0.748162	−	0.663516i	$-0.230936\pi$
$810$	2.33356e99	+	3.52673e98i	3.01667	+	0.455912i
$811$	−5.55686e98			−0.688843			−0.344422	−	0.938815i	$-0.611925\pi$
$811$	−5.55686e98			−0.688843			−0.344422	+	0.938815i	$0.611925\pi$
$812$		−	2.24558e96i		−	0.00266947i
$813$	1.18076e99	+	4.42979e97i	1.34611	+	0.0505016i
$814$	−2.65469e99			−2.90258
$815$		−	1.36198e99i		−	1.42827i
$816$	−8.76673e95	+	2.33676e97i	−0.000881804	+	0.0235044i
$817$	5.70205e98			0.550150
$818$			2.41598e99i			2.23605i
$819$	6.79904e97	+	5.10872e96i	0.0603664	+	0.00453586i
$820$	8.22067e98			0.700223
$821$			1.66907e98i			0.136398i	0.997672	+	0.0681990i	$0.0217253\pi$
$821$			1.66907e98i			0.136398i	−0.997672	+	0.0681990i	$0.978275\pi$
$822$	−3.43007e96	−	1.28684e95i	−0.00268944	−	0.000100898i
$823$	−1.49452e99			−1.12436			−0.562182	−	0.827014i	$-0.690038\pi$
$823$	−1.49452e99			−1.12436			−0.562182	+	0.827014i	$0.690038\pi$
$824$		−	1.06093e99i		−	0.765880i
$825$	−1.63166e98	+	4.34917e99i	−0.113030	+	3.01281i
$826$	−1.22035e97			−0.00811265
$827$		−	5.38542e98i		−	0.343583i	−0.985133	−	0.171792i	$-0.945044\pi$
$827$		−	5.38542e98i		−	0.343583i	0.985133	−	0.171792i	$-0.0549556\pi$
$828$	3.40196e98	−	4.52757e99i	0.208304	−	2.77226i
$829$	−1.10030e99			−0.646629			−0.323314	−	0.946292i	$-0.604797\pi$
$829$	−1.10030e99			−0.646629			−0.323314	+	0.946292i	$0.604797\pi$
$830$			5.80953e99i			3.27707i
$831$	−9.40260e98	−	3.52753e97i	−0.509112	−	0.0191001i
$832$	3.04372e99			1.58202
$833$		−	7.93375e98i		−	0.395866i
$834$	−3.61050e96	+	9.62376e97i	−0.00172950	+	0.0460998i
$835$	−3.78945e98			−0.174275
$836$		−	3.13486e99i		−	1.38422i
$837$	8.92895e98	+	1.00874e98i	0.378560	+	0.0427674i
$838$	5.70632e99			2.32306
$839$			2.85586e98i			0.111643i	0.998441	+	0.0558213i	$0.0177777\pi$
$839$			2.85586e98i			0.111643i	−0.998441	+	0.0558213i	$0.982222\pi$
$840$	−3.21523e98	−	1.20624e97i	−0.120703	−	0.00452835i
$841$	2.77179e99			0.999302
$842$		−	7.10792e99i		−	2.46111i
$843$	−6.44699e97	+	1.71844e99i	−0.0214397	+	0.571474i
$844$	−9.23205e98			−0.294887
$845$		−	1.81772e98i		−	0.0557697i
$846$	1.91644e99	+	1.43999e98i	0.564809	+	0.0424391i
$847$	−9.35868e97			−0.0264959
$848$			2.18178e98i			0.0593406i
$849$	−5.30247e99	−	1.98930e98i	−1.38553	−	0.0519804i
$850$	−6.48665e99			−1.62846
$851$			1.04593e100i			2.52289i
$852$	2.51053e98	−	6.69178e99i	0.0581860	−	1.55094i
$853$	7.68144e99			1.71071			0.855354	−	0.518044i	$-0.173340\pi$
$853$	7.68144e99			1.71071			0.855354	+	0.518044i	$0.173340\pi$
$854$			6.52659e98i			0.139675i
$855$	4.81045e98	−	6.40208e99i	0.0989321	−	1.31666i
$856$	6.31756e98			0.124865
$857$		−	7.92060e99i		−	1.50456i	−0.658842	−	0.752281i	$-0.728953\pi$
$857$		−	7.92060e99i		−	1.50456i	0.658842	−	0.752281i	$-0.271047\pi$
$858$	−1.04881e100	−	3.93477e98i	−1.91482	−	0.0718376i
$859$	−2.93182e99			−0.514481			−0.257241	−	0.966347i	$-0.582813\pi$
$859$	−2.93182e99			−0.514481			−0.257241	+	0.966347i	$0.582813\pi$
$860$			1.42974e100i			2.41163i
$861$	−3.22546e96	+	8.59744e97i	−0.000522980	+	0.0139400i
$862$	3.65338e99			0.569439
$863$			9.00076e99i			1.34869i	0.738416	+	0.674345i	$0.235574\pi$
$863$			9.00076e99i			1.34869i	−0.738416	+	0.674345i	$0.764426\pi$
$864$	−7.41310e98	+	6.56178e99i	−0.106790	+	0.945267i
$865$	−1.46528e100			−2.02942
$866$			9.71697e99i			1.29397i
$867$	6.57215e99	+	2.46564e98i	0.841508	+	0.0315705i
$868$	−3.12669e98			−0.0384958
$869$		−	9.82831e99i		−	1.16361i
$870$	−2.65402e97	+	7.07425e98i	−0.00302168	+	0.0805427i
$871$	1.16860e100			1.27953
$872$		−	1.07052e99i		−	0.112729i
$873$	4.35492e99	+	3.27224e98i	0.441058	+	0.0331406i
$874$	−1.98632e100			−1.93490
$875$		−	1.87083e99i		−	0.175291i
$876$	−1.97035e100	−	7.39206e98i	−1.77584	−	0.0666233i
$877$	1.50267e100			1.30280			0.651400	−	0.758734i	$-0.274182\pi$
$877$	1.50267e100			1.30280			0.651400	+	0.758734i	$0.274182\pi$
$878$		−	3.51058e100i		−	2.92796i
$879$	2.97492e98	−	7.92963e99i	0.0238701	−	0.636255i
$880$	1.72107e99			0.132858
$881$		−	1.69541e100i		−	1.25919i	−0.776922	−	0.629597i	$-0.783220\pi$
$881$		−	1.69541e100i		−	1.25919i	0.776922	−	0.629597i	$-0.216780\pi$
$882$	−1.69855e99	+	2.26054e100i	−0.121380	+	1.61540i
$883$	1.42620e100			0.980655			0.490327	−	0.871538i	$-0.336877\pi$
$883$	1.42620e100			0.980655			0.490327	+	0.871538i	$0.336877\pi$
$884$		−	9.72682e99i		−	0.643567i
$885$	2.39054e99	+	8.96848e97i	0.152204	+	0.00571015i
$886$	3.57518e100			2.19054
$887$			4.32206e99i			0.254852i	0.991848	+	0.127426i	$0.0406715\pi$
$887$			4.32206e99i			0.254852i	−0.991848	+	0.127426i	$0.959328\pi$
$888$	−1.03258e99	+	2.75232e100i	−0.0585979	+	1.56192i
$889$	−9.26063e98			−0.0505802
$890$			2.22398e100i			1.16915i
$891$	3.53290e99	−	2.33764e100i	0.178768	−	1.18287i
$892$	2.25639e100			1.09903
$893$		−	5.22802e99i		−	0.245125i
$894$	−4.12607e100	−	1.54796e99i	−1.86235	−	0.0698688i
$895$	−3.20396e99			−0.139221
$896$		−	2.43916e99i		−	0.102040i
$897$	−1.55028e99	+	4.13225e100i	−0.0624405	+	1.66435i
$898$	−3.65815e100			−1.41862
$899$			2.69537e98i			0.0100644i
$900$	1.14925e101	+	8.63535e99i	4.13209	+	0.310481i
$901$	−1.15060e100			−0.398364
$902$		−	1.32436e100i		−	0.441554i
$903$	−1.49527e99	−	5.60973e97i	−0.0480104	−	0.00180118i
$904$	−4.79522e100			−1.48280
$905$			2.44963e100i			0.729538i
$906$	2.96226e99	−	7.89587e100i	0.0849697	−	2.26486i
$907$	−3.39886e100			−0.939044			−0.469522	−	0.882921i	$-0.655574\pi$
$907$	−3.39886e100			−0.939044			−0.469522	+	0.882921i	$0.655574\pi$
$908$			1.21865e100i			0.324310i
$909$	−2.63237e99	+	3.50334e100i	−0.0674800	+	0.898071i
$910$	7.47923e99			0.184693
$911$			6.46266e100i			1.53740i	0.639610	+	0.768700i	$0.279096\pi$
$911$			6.46266e100i			1.53740i	−0.639610	+	0.768700i	$0.720904\pi$
$912$	−1.81632e99	−	6.81421e97i	−0.0416264	−	0.00156168i
$913$	5.81969e100			1.28497
$914$			7.91020e100i			1.68274i
$915$	4.79646e99	−	1.27849e101i	0.0983113	−	2.62048i
$916$	−1.19219e101			−2.35450
$917$			3.72523e99i			0.0708918i
$918$	3.50135e100	+	3.95561e99i	0.642074	+	0.0725375i
$919$	9.41784e100			1.66427			0.832135	−	0.554573i	$-0.187118\pi$
$919$	9.41784e100			1.66427			0.832135	+	0.554573i	$0.187118\pi$
$920$		−	1.95137e101i		−	3.32318i
$921$	−4.36063e100	−	1.63596e99i	−0.715685	−	0.0268500i
$922$	−7.11676e100			−1.12572
$923$			6.09891e100i			0.929810i
$924$	−3.08410e98	+	8.22064e99i	−0.00453191	+	0.120798i
$925$	−2.65494e101			−3.76041
$926$		−	1.11518e101i		−	1.52256i
$927$	−5.53964e100	−	4.16242e99i	−0.729073	−	0.0547817i
$928$	−1.98079e99			−0.0251309
$929$		−	4.78407e100i		−	0.585144i	−0.956243	−	0.292572i	$-0.905489\pi$
$929$		−	4.78407e100i		−	0.585144i	0.956243	−	0.292572i	$-0.0945112\pi$
$930$	9.84998e100	+	3.69537e99i	1.16149	+	0.0435751i
$931$	6.16675e100			0.701080
$932$			2.55481e101i			2.80039i
$933$	−2.03938e99	+	5.43594e100i	−0.0215537	+	0.574512i
$934$	1.69755e101			1.72993
$935$			9.07634e100i			0.891900i
$936$	−8.15898e99	+	1.08585e101i	−0.0773138	+	1.02895i
$937$	7.29674e100			0.666780			0.333390	−	0.942789i	$-0.391807\pi$
$937$	7.29674e100			0.666780			0.333390	+	0.942789i	$0.391807\pi$
$938$		−	1.47304e100i		−	0.129813i
$939$	7.28523e100	+	2.73316e99i	0.619174	+	0.0232293i
$940$	1.31088e101			1.07452
$941$			5.51551e100i			0.436053i	0.975943	+	0.218026i	$0.0699619\pi$
$941$			5.51551e100i			0.436053i	−0.975943	+	0.218026i	$0.930038\pi$
$942$	1.02924e99	−	2.74344e100i	0.00784852	−	0.209202i
$943$	−5.21791e100			−0.383795
$944$		−	6.77261e98i		−	0.00480517i
$945$	−1.89130e99	+	1.67410e100i	−0.0129443	+	0.114578i
$946$	2.30333e101			1.52075
$947$		−	1.01839e101i		−	0.648658i	−0.945944	−	0.324329i	$-0.894862\pi$
$947$		−	1.01839e101i		−	0.648658i	0.945944	−	0.324329i	$-0.105138\pi$
$948$	−2.60075e101	−	9.75713e99i	−1.59814	−	0.0599568i
$949$	1.79578e101			1.06464
$950$		−	5.04195e101i		−	2.88400i
$951$	1.10727e100	−	2.95142e101i	0.0611106	−	1.62890i
$952$	−4.80381e99			−0.0255817
$953$			1.71486e101i			0.881192i	0.897706	+	0.440596i	$0.145233\pi$
$953$			1.71486e101i			0.881192i	−0.897706	+	0.440596i	$0.854767\pi$
$954$	3.27837e101	+	2.46333e100i	1.62560	+	0.122146i
$955$	−4.52654e101			−2.16597
$956$			3.80444e101i			1.75680i
$957$	7.08663e99	+	2.65866e98i	0.0315816	+	0.00118483i
$958$	−4.15698e101			−1.78793
$959$		−	2.45032e97i		−	0.000101716i
$960$	−2.81960e100	+	7.51563e101i	−0.112971	+	3.01123i
$961$	−2.21051e101			−0.854863
$962$		−	6.40242e101i		−	2.38997i
$963$	2.47862e99	−	3.29872e100i	0.00893133	−	0.118864i
$964$	4.54333e101			1.58036
$965$		−	6.46343e101i		−	2.17037i
$966$	5.20878e100	+	1.95415e99i	0.168855	+	0.00633485i
$967$	4.87350e101			1.52525			0.762625	−	0.646841i	$-0.223910\pi$
$967$	4.87350e101			1.52525			0.762625	+	0.646841i	$0.223910\pi$
$968$		−	1.49464e101i		−	0.451623i
$969$	3.59359e99	−	9.57867e100i	0.0104838	−	0.279445i
$970$	4.79059e101			1.34943
$971$			5.38961e101i			1.46590i	0.680284	+	0.732949i	$0.261857\pi$
$971$			5.38961e101i			1.46590i	−0.680284	+	0.732949i	$0.738143\pi$
$972$	−6.15076e101	−	1.16694e101i	−1.61538	−	0.306476i
$973$	−6.87486e98			−0.00174352
$974$			3.26402e101i			0.799370i
$975$	−1.04891e102	−	3.93514e100i	−2.48073	−	0.0930686i
$976$	−3.62208e100			−0.0827303
$977$		−	3.24453e101i		−	0.715710i	−0.933777	−	0.357855i	$-0.883508\pi$
$977$		−	3.24453e101i		−	0.715710i	0.933777	−	0.357855i	$-0.116492\pi$
$978$	−2.17827e100	+	5.80617e101i	−0.0464078	+	1.23700i
$979$	2.22787e101			0.458435
$980$			1.54626e102i			3.07324i
$981$	−5.58972e100	−	4.20005e99i	−0.107311	−	0.00806322i
$982$	−1.69321e102			−3.13993
$983$			3.48011e101i			0.623410i	0.950179	+	0.311705i	$0.100900\pi$
$983$			3.48011e101i			0.623410i	−0.950179	+	0.311705i	$0.899100\pi$
$984$	−1.37307e101	−	5.15128e99i	−0.237607	−	0.00891419i
$985$	9.34450e101			1.56215
$986$			1.05695e100i			0.0170702i
$987$	−5.14337e98	+	1.37096e100i	−0.000802537	+	0.0213915i
$988$	7.56047e101			1.13976
$989$		−	9.07499e101i		−	1.32182i
$990$	1.94317e101	−	2.58610e102i	0.273472	−	3.63956i
$991$	−9.90075e101			−1.34637			−0.673184	−	0.739475i	$-0.735074\pi$
$991$	−9.90075e101			−1.34637			−0.673184	+	0.739475i	$0.735074\pi$
$992$			2.75800e101i			0.362408i
$993$	6.88503e100	+	2.58303e99i	0.0874242	+	0.00327985i
$994$	7.68778e100			0.0943331
$995$			1.65288e102i			1.96000i
$996$	5.77754e100	−	1.54000e102i	0.0662103	−	1.76483i
$997$	5.30218e101			0.587245			0.293622	−	0.955921i	$-0.405139\pi$
$997$	5.30218e101			0.587245			0.293622	+	0.955921i	$0.405139\pi$
$998$		−	1.07507e102i		−	1.15079i
$999$	1.43308e102	+	1.61900e101i	1.48266	+	0.167502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.69.b.a.2.3	✓	22
3.2	odd	2	inner	3.69.b.a.2.20	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.69.b.a.2.3	✓	22	1.1	even	1	trivial
3.69.b.a.2.20	yes	22	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 69 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.79362e10i q^{2} +(1.66655e16 + 6.25230e14i) q^{3} -4.85282e20 q^{4} +1.09211e24i q^{5} +(1.74665e25 - 4.65569e26i) q^{6} +3.32586e27 q^{7} +5.31162e30i q^{8} +(2.77347e32 + 2.08395e31i) q^{9} +O(q^{10})\)	\(q-2.79362e10i q^{2} +(1.66655e16 + 6.25230e14i) q^{3} -4.85282e20 q^{4} +1.09211e24i q^{5} +(1.74665e25 - 4.65569e26i) q^{6} +3.32586e27 q^{7} +5.31162e30i q^{8} +(2.77347e32 + 2.08395e31i) q^{9} +3.05093e34 q^{10} -3.05626e35i q^{11} +(-8.08745e36 - 3.03413e35i) q^{12} +7.37092e37 q^{13} -9.29117e37i q^{14} +(-6.82818e38 + 1.82005e40i) q^{15} +5.15635e39 q^{16} +2.71929e41i q^{17} +(5.82176e41 - 7.74800e42i) q^{18} -2.11365e43 q^{19} -5.29979e44i q^{20} +(5.54269e43 + 2.07943e42i) q^{21} -8.53803e45 q^{22} +3.36394e46i q^{23} +(-3.32099e45 + 8.85206e46i) q^{24} -8.53883e47 q^{25} -2.05915e48i q^{26} +(4.60908e48 + 5.20705e47i) q^{27} -1.61398e48 q^{28} +1.39133e48i q^{29} +(5.08451e50 + 1.90753e49i) q^{30} +1.93725e50 q^{31} +1.42366e51i q^{32} +(1.91087e50 - 5.09340e51i) q^{33} +7.59665e51 q^{34} +3.63219e51i q^{35} +(-1.34591e53 - 1.01130e52i) q^{36} +3.10925e53 q^{37} +5.90473e53i q^{38} +(1.22840e54 + 4.60852e52i) q^{39} -5.80085e54 q^{40} +1.55113e54i q^{41} +(5.80912e52 - 1.54842e54i) q^{42} -2.69773e55 q^{43} +1.48315e56i q^{44} +(-2.27589e55 + 3.02892e56i) q^{45} +9.39756e56 q^{46} +2.47346e56i q^{47} +(8.59330e55 + 3.22391e54i) q^{48} -2.91758e57 q^{49} +2.38542e58i q^{50} +(-1.70018e56 + 4.53182e57i) q^{51} -3.57697e58 q^{52} +4.23125e58i q^{53} +(1.45465e58 - 1.28760e59i) q^{54} +3.33777e59 q^{55} +1.76657e58i q^{56} +(-3.52249e59 - 1.32152e58i) q^{57} +3.88686e58 q^{58} -1.31345e59i q^{59} +(3.31359e59 - 8.83235e60i) q^{60} -7.02451e60 q^{61} -5.41195e60i q^{62} +(9.22415e59 + 6.93092e58i) q^{63} +4.12936e61 q^{64} +8.04982e61i q^{65} +(-1.42290e62 - 5.33824e60i) q^{66} +1.58542e62 q^{67} -1.31962e62i q^{68} +(-2.10324e61 + 5.60616e62i) q^{69} +1.01469e62 q^{70} +8.27429e62i q^{71} +(-1.10691e62 + 1.47316e63i) q^{72} +2.43630e63 q^{73} -8.68605e63i q^{74} +(-1.42303e64 - 5.33874e62i) q^{75} +1.02572e64 q^{76} -1.01647e63i q^{77} +(1.28744e63 - 3.43167e64i) q^{78} +3.21579e64 q^{79} +5.63128e63i q^{80} +(7.64868e64 + 1.15595e64i) q^{81} +4.33326e64 q^{82} +1.90418e65i q^{83} +(-2.68977e64 - 1.00911e63i) q^{84} -2.96975e65 q^{85} +7.53642e65i q^{86} +(-8.69905e62 + 2.31872e64i) q^{87} +1.62337e66 q^{88} +7.28951e65i q^{89} +(8.46164e66 + 6.35798e65i) q^{90} +2.45146e65 q^{91} -1.63246e67i q^{92} +(3.22852e66 + 1.21123e65i) q^{93} +6.90989e66 q^{94} -2.30833e67i q^{95} +(-8.90118e65 + 2.37260e67i) q^{96} +1.57021e67 q^{97} +8.15061e67i q^{98} +(6.36910e66 - 8.47644e67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 18\!\cdots\!78 q^{3}+ \cdots + 84\!\cdots\!78 q^{9}+O(q^{10}) \) 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9	\( 22 q + 18\!\cdots\!78 q^{3}+ \cdots - 11\!\cdots\!00 q^{99}+O(q^{100}) \) 22 * q + 18789723640115478 * q^3 - 2943217790812903705616 * q^4 + 606827522425378326847120944 * q^6 - 3605688981734492610233621044 * q^7 + 84409856735558666343023488765878 * q^9 + 2045888067334428934113988216421280 * q^10 - 6488396126470402148347182126675194832 * q^12 - 10813885710533400837304817444785935604 * q^13 + 14557528184647372428101554053003296612160 * q^15 + 373601084063432865853473918269277812744320 * q^16 + 17941511735214427632488941901617371491816160 * q^18 - 79553650357260974891342027178031915087354324 * q^19 - 1298400323255969952377913185067359758477401780 * q^21 + 6768843564804724477092404017437690309759833760 * q^22 - 75879178936902674847903860248712590469230731648 * q^24 - 1290406322757665049559021767067242780449078031050 * q^25 + 2674086297347577939313596696269044232072283756918 * q^27 + 42745403006807704515598614320469990457621586593376 * q^28 + 30776582876805533479749631919828742635540596749600 * q^30 - 464825674673310587378006994001777182420658601801716 * q^31 + 2043086192437245889755473926491971918230943629550400 * q^33 + 13079915711847249768451590870017502856673640042982272 * q^34 - 65327203493646647902060088267317231087935232974706704 * q^36 - 167279080426229420846594751930892532669536008046545844 * q^37 + 1637357069222228057847981309081425400083650534736779020 * q^39 + 6053556854890611145141953130785126755317199579733738240 * q^40 - 12457262572316255979922798677909127605820549100734736160 * q^42 - 18628500859740527128618324584150040016275591666233599764 * q^43 + 367822789535544680671556018223028621483838265619669430400 * q^45 + 1476449543055130371522242587937584327352337186768013053888 * q^46 + 202405740838876412041865477434740772123701917763236585088 * q^48 + 4681199846498689520635057982286342899995310041595285382018 * q^49 + 21407584156868532008405510905089022165080050053906507325184 * q^51 + 24391763772592576034526261030318526583680683849133477696736 * q^52 - 112285817002635953902674086392140195155054790343667891881584 * q^54 + 274409579794012893709322560718339246575325740160175650620800 * q^55 + 101758997342686912720089366682761957082398853447685074732716 * q^57 - 2020457744766163498170953106059196558756720252448185539243040 * q^58 - 13276219488047015535811467987165558930747748946804017101031680 * q^60 + 6331070401548027780910089309848838040805985031947773629039244 * q^61 - 11540105667000326350766773710482957857389205527747058022198004 * q^63 + 74144666416333808948332900789778080404085337330317362556926976 * q^64 - 388082670987835008027383208260911873599566866107012006022495200 * q^66 + 690968797068657030373143885315519666504759571640550029794509356 * q^67 - 1027093066405255275213825064853644794250194801896401414490868864 * q^69 + 4371068227635884746027518083549441915821247332843741516741992000 * q^70 - 8830670280256061265338935058781406802503181323103646058149000960 * q^72 + 8806696028067195590640304057094157167006086961761378058824984556 * q^73 - 35720155285864881642804474725062955577201898766624893474579682250 * q^75 + 50989416920172911215005579159200646780346206610233430042766798432 * q^76 - 79580143447707181310585996419552144412335647108094050067906050720 * q^78 - 3083981169532008720747546215983788345611378750423096573576219764 * q^79 - 88762224122457647598561491684821377170571566383688244793770736938 * q^81 + 416784948027081086888539461807826070456316776812312199920865653440 * q^82 + 990441228134853667871418956670095117692984404086848036534801693920 * q^84 - 866637175758839171101071739839460554945096683648478422830993681920 * q^85 + 3620458445475290511813570050310517312523781688405496711995676422080 * q^87 - 4669471445324986882088763579042561683455173004052019441103363626240 * q^88 + 14582942989396685328395597316366348010236984461538262603110152917920 * q^90 - 6998978018734113734240448628263170029174504049408988631375576481960 * q^91 + 22631183723253759871940463881283634110336753405922973132310746358156 * q^93 - 49667911598354463153752845875961955186127772502753374451274725501568 * q^94 - 5532425547839977216491807518703626514248108709732237368596820947968 * q^96 + 90182295908350258367379728070466489774210357027997619180945877805996 * q^97 - 111427931124550204447734414473904809051459145283833102653529748809600 * q^99

Introduction

L-functions

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