LMFDB - Embedded newform 4.35.b.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,35,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 35, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 35);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 35 $
Character orbit:	$[\chi]$	$=$	4.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:	$29.2902616171$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 72626617369828 x^{14} - 508386321588656 x^{13} + \cdots + 10\!\cdots\!04 $ x^16 - 8x^15 + 72626617369828x^14 - 508386321588656x^13 + 2070719277905647749353609238x^12 - 12424315667427277473941003264x^11 + 29149279164108071001422670079476973946124x^10 - 145746395820426465446828612470414408396048x^9 + 208496096173568297991996731996084596831140332539876641x^8 - 833984384693398713593064505859129757329019844492402808x^7 + 698875044281632666404075222255491833772167721683562957908849313992x^6 - 2096625132841979053865799383403762221200483615238531437571184911168x^5 + 875349684493967266675808505113830711763013718564229702361030689486070549970192x^4 - 1750699368984440158130214684786333899894027567027597503857227657836248590530944x^3 + 58492108779558800474886843372761385704540074687283929338876917776255190499572053123416832x^2 - 58492108778683450790394972731218418552991821255044754502302019047778482600406279068669952*x + 1002905835814255424301301646724378424153530387112307506080792395282136017819372496998790246522159104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.7
Root			$0.500000 + 4.30163e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.35.b.a.3.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13913.7 - 130331. i) q^{2} -2.06478e8i q^{3} +(-1.67927e10 + 3.62680e9i) q^{4} -9.83896e10 q^{5} +(-2.69106e13 + 2.87289e12i) q^{6} -2.44416e14i q^{7} +(7.06335e14 + 2.13815e15i) q^{8} -2.59561e16 q^{9} +O(q^{10})$	\(q+(-13913.7 - 130331. i) q^{2} -2.06478e8i q^{3} +(-1.67927e10 + 3.62680e9i) q^{4} -9.83896e10 q^{5} +(-2.69106e13 + 2.87289e12i) q^{6} -2.44416e14i q^{7} +(7.06335e14 + 2.13815e15i) q^{8} -2.59561e16 q^{9} +(1.36897e15 + 1.28233e16i) q^{10} +8.27701e17i q^{11} +(7.48855e17 + 3.46732e18i) q^{12} -1.42752e15 q^{13} +(-3.18551e19 + 3.40074e18i) q^{14} +2.03153e19i q^{15} +(2.68841e20 - 1.21807e20i) q^{16} -8.57973e20 q^{17} +(3.61146e20 + 3.38289e21i) q^{18} +6.28457e21i q^{19} +(1.65223e21 - 3.56839e20i) q^{20} -5.04666e22 q^{21} +(1.07875e23 - 1.15164e22i) q^{22} -2.11647e23i q^{23} +(4.41482e23 - 1.45843e23i) q^{24} -5.72396e23 q^{25} +(1.98621e19 + 1.86050e20i) q^{26} +1.91589e24i q^{27} +(8.86447e23 + 4.10440e24i) q^{28} +1.04325e25 q^{29} +(2.64772e24 - 2.82662e23i) q^{30} +4.38466e24i q^{31} +(-1.96159e25 - 3.33436e25i) q^{32} +1.70902e26 q^{33} +(1.19376e25 + 1.11821e26i) q^{34} +2.40480e25i q^{35} +(4.35872e26 - 9.41374e25i) q^{36} -1.02716e26 q^{37} +(8.19077e26 - 8.74420e25i) q^{38} +2.94751e23i q^{39} +(-6.94960e25 - 2.10372e26i) q^{40} -1.40177e27 q^{41} +(7.02179e26 + 6.57738e27i) q^{42} +3.94217e27i q^{43} +(-3.00190e27 - 1.38993e28i) q^{44} +2.55381e27 q^{45} +(-2.75843e28 + 2.94481e27i) q^{46} -3.15393e28i q^{47} +(-2.51506e28 - 5.55097e28i) q^{48} -5.62217e27 q^{49} +(7.96418e27 + 7.46012e28i) q^{50} +1.77153e29i q^{51} +(2.39718e25 - 5.17732e24i) q^{52} -3.97204e29 q^{53} +(2.49700e29 - 2.66572e28i) q^{54} -8.14372e28i q^{55} +(5.22598e29 - 1.72639e29i) q^{56} +1.29763e30 q^{57} +(-1.45155e29 - 1.35968e30i) q^{58} +1.46663e30i q^{59} +(-7.36795e28 - 3.41149e29i) q^{60} +1.24369e30 q^{61} +(5.71459e29 - 6.10070e28i) q^{62} +6.34408e30i q^{63} +(-4.07278e30 + 3.02050e30i) q^{64} +1.40453e26 q^{65} +(-2.37789e30 - 2.22739e31i) q^{66} +1.03158e31i q^{67} +(1.44077e31 - 3.11169e30i) q^{68} -4.37005e31 q^{69} +(3.13421e30 - 3.34598e29i) q^{70} +1.84322e31i q^{71} +(-1.83337e31 - 5.54980e31i) q^{72} -2.03215e30 q^{73} +(1.42917e30 + 1.33872e31i) q^{74} +1.18187e32i q^{75} +(-2.27929e31 - 1.05535e32i) q^{76} +2.02303e32 q^{77} +(3.84153e28 - 4.10109e27i) q^{78} +4.21903e31i q^{79} +(-2.64511e31 + 1.19846e31i) q^{80} -3.72849e31 q^{81} +(1.95039e31 + 1.82695e32i) q^{82} +3.72769e32i q^{83} +(8.47469e32 - 1.83032e32i) q^{84} +8.44156e31 q^{85} +(5.13788e32 - 5.48503e31i) q^{86} -2.15409e33i q^{87} +(-1.76975e33 + 5.84634e32i) q^{88} -1.82401e33 q^{89} +(-3.55330e31 - 3.32841e32i) q^{90} +3.48908e29i q^{91} +(7.67601e32 + 3.55412e33i) q^{92} +9.05337e32 q^{93} +(-4.11056e33 + 4.38830e32i) q^{94} -6.18337e32i q^{95} +(-6.88472e33 + 4.05026e33i) q^{96} +6.65697e33 q^{97} +(7.82254e31 + 7.32745e32i) q^{98} -2.14839e34i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots - 67\!\cdots\!80 q^{9}+O(q^{10}) $ 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9	$ 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots + 16\!\cdots\!32 q^{98}+O(q^{100}) $ 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9 - 45113792455239160 * q^10 + 2389205919902175360 * q^12 - 5233507036411659616 * q^13 - 78584294183795706432 * q^14 + 495182112183820124416 * q^16 - 603670905919309938144 * q^17 - 3049682100893194226508 * q^18 - 33058393758449688290400 * q^20 + 51436061805005728413696 * q^21 + 71660876143050404765280 * q^22 + 216144869785928938234368 * q^24 + 1224730607199300816400560 * q^25 - 2068583291215840445568696 * q^26 + 891252510406495618671360 * q^28 - 4086289565288128397679456 * q^29 + 29601064663371600024444480 * q^30 + 20026414012547463259849728 * q^32 + 73954448514753271238568960 * q^33 + 46288216238217191722231976 * q^34 + 569062048300724903070378384 * q^36 + 950385175701396416644593056 * q^37 - 123498782719680108073563360 * q^38 - 3250024485723791435879459200 * q^40 + 469238845433510127731349792 * q^41 + 2352670327884382399711157760 * q^42 + 7327222247557584897899214720 * q^44 - 24427097188106605438098250080 * q^45 - 19562783684402230406331003072 * q^46 + 10576141603633237485164267520 * q^48 - 5662649722408510114314091760 * q^49 + 20191932196464263485504736220 * q^50 - 299155663662273783907276503904 * q^52 - 287274278887575172234950512736 * q^53 + 6047252470624543429578889536 * q^54 + 957626384837555513184792726528 * q^56 + 2791286265941381406754467578880 * q^57 - 314499391713380785247660833336 * q^58 + 1103184540481814815474103512320 * q^60 - 7360215904797065436447249778528 * q^61 + 6668101684324825273374014288640 * q^62 - 4672502276277215477475812569088 * q^64 + 7390500022468645317433010287680 * q^65 - 12460359580334220374288279205120 * q^66 + 3201090312765007118305938045984 * q^68 - 20909099675706939600670541666304 * q^69 - 13302319794857519494110175324800 * q^70 - 776423968147266229824274003392 * q^72 - 21322365514881309087265291408096 * q^73 + 60200090281780873185690769101576 * q^74 - 104909582027053727863743869884800 * q^76 + 31510097566037837419459121448960 * q^77 + 173718506967281862717403400063040 * q^78 + 360511559214548868760655536888320 * q^80 - 262819454584631237298859074129648 * q^81 - 127799686177535642546403976474264 * q^82 - 481860976739335096182940424300544 * q^84 + 2066519418228326883252673443837760 * q^85 + 680164732953303409567751182232928 * q^86 - 1868588957981221169228370505105920 * q^88 - 2487774705888249186282098457137376 * q^89 + 2710136859758550244207319911170120 * q^90 - 5719642193953545223478177490435840 * q^92 - 4648987096869411453766406983557120 * q^93 - 174301665834847119752293250078592 * q^94 - 1356265248520894619800195113541632 * q^96 + 7119191713926779638291321673063456 * q^97 + 16929214407930779244441537548523732 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−13913.7	−	130331.i	−0.106153	−	0.994350i
$2$	−13913.7	−	130331.i	−0.106153	−	0.994350i
$3$		−	2.06478e8i		−	1.59887i	−0.600753	−	0.799435i	$-0.705133\pi$
$3$		−	2.06478e8i		−	1.59887i	0.600753	−	0.799435i	$-0.294867\pi$
$4$	−1.67927e10	+	3.62680e9i	−0.977463	+	0.211107i
$5$	−9.83896e10			−0.128961			−0.0644806	−	0.997919i	$-0.520539\pi$
$5$	−9.83896e10			−0.128961			−0.0644806	+	0.997919i	$0.520539\pi$
$6$	−2.69106e13	+	2.87289e12i	−1.58984	+	0.169726i
$7$		−	2.44416e14i		−	1.05066i	−0.850898	−	0.525331i	$-0.823942\pi$
$7$		−	2.44416e14i		−	1.05066i	0.850898	−	0.525331i	$-0.176058\pi$
$8$	7.06335e14	+	2.13815e15i	0.313676	+	0.949530i
$9$	−2.59561e16			−1.55638
$10$	1.36897e15	+	1.28233e16i	0.0136897	+	0.128233i
$11$			8.27701e17i			1.63756i	0.574106	+	0.818781i	$0.305350\pi$
$11$			8.27701e17i			1.63756i	−0.574106	+	0.818781i	$0.694650\pi$
$12$	7.48855e17	+	3.46732e18i	0.337533	+	1.56284i
$13$	−1.42752e15			−0.000165023			−8.25115e−5	−	1.00000i	$-0.500026\pi$
$13$	−1.42752e15			−0.000165023			−8.25115e−5		1.00000i	$0.500026\pi$
$14$	−3.18551e19	+	3.40074e18i	−1.04472	+	0.111531i
$15$			2.03153e19i			0.206192i
$16$	2.68841e20	−	1.21807e20i	0.910867	−	0.412699i
$17$	−8.57973e20			−1.03715			−0.518575	−	0.855032i	$-0.673537\pi$
$17$	−8.57973e20			−1.03715			−0.518575	+	0.855032i	$0.673537\pi$
$18$	3.61146e20	+	3.38289e21i	0.165215	+	1.54759i
$19$			6.28457e21i			1.14674i	0.819297	+	0.573370i	$0.194364\pi$
$19$			6.28457e21i			1.14674i	−0.819297	+	0.573370i	$0.805636\pi$
$20$	1.65223e21	−	3.56839e20i	0.126055	−	0.0272247i
$21$	−5.04666e22			−1.67987
$22$	1.07875e23	−	1.15164e22i	1.62831	−	0.173833i
$23$		−	2.11647e23i		−	1.50051i	−0.661148	−	0.750256i	$-0.729930\pi$
$23$		−	2.11647e23i		−	1.50051i	0.661148	−	0.750256i	$-0.270070\pi$
$24$	4.41482e23	−	1.45843e23i	1.51817	−	0.501526i
$25$	−5.72396e23			−0.983369
$26$	1.98621e19	+	1.86050e20i	1.75178e−5	+	0.000164091i
$27$			1.91589e24i			0.889582i
$28$	8.86447e23	+	4.10440e24i	0.221802	+	1.02698i
$29$	1.04325e25			1.43755			0.718775	−	0.695243i	$-0.244703\pi$
$29$	1.04325e25			1.43755			0.718775	+	0.695243i	$0.244703\pi$
$30$	2.64772e24	−	2.82662e23i	0.205027	−	0.0218880i
$31$			4.38466e24i			0.194441i	0.995263	+	0.0972203i	$0.0309951\pi$
$31$			4.38466e24i			0.194441i	−0.995263	+	0.0972203i	$0.969005\pi$
$32$	−1.96159e25	−	3.33436e25i	−0.507059	−	0.861911i
$33$	1.70902e26			2.61825
$34$	1.19376e25	+	1.11821e26i	0.110097	+	1.03129i
$35$			2.40480e25i			0.135495i
$36$	4.35872e26	−	9.41374e25i	1.52131	−	0.328564i
$37$	−1.02716e26			−0.225014			−0.112507	−	0.993651i	$-0.535888\pi$
$37$	−1.02716e26			−0.225014			−0.112507	+	0.993651i	$0.535888\pi$
$38$	8.19077e26	−	8.74420e25i	1.14026	−	0.121730i
$39$			2.94751e23i			0.000263850i
$40$	−6.94960e25	−	2.10372e26i	−0.0404520	−	0.122453i
$41$	−1.40177e27			−0.536231			−0.268116	−	0.963387i	$-0.586401\pi$
$41$	−1.40177e27			−0.536231			−0.268116	+	0.963387i	$0.586401\pi$
$42$	7.02179e26	+	6.57738e27i	0.178324	+	1.67038i
$43$			3.94217e27i			0.671075i	0.942027	+	0.335538i	$0.108918\pi$
$43$			3.94217e27i			0.671075i	−0.942027	+	0.335538i	$0.891082\pi$
$44$	−3.00190e27	−	1.38993e28i	−0.345701	−	1.60066i
$45$	2.55381e27			0.200713
$46$	−2.75843e28	+	2.94481e27i	−1.49203	+	0.159284i
$47$		−	3.15393e28i		−	1.18355i	−0.806102	−	0.591777i	$-0.798427\pi$
$47$		−	3.15393e28i		−	1.18355i	0.806102	−	0.591777i	$-0.201573\pi$
$48$	−2.51506e28	−	5.55097e28i	−0.659852	−	1.45636i
$49$	−5.62217e27			−0.103889
$50$	7.96418e27	+	7.46012e28i	0.104388	+	0.977813i
$51$			1.77153e29i			1.65827i
$52$	2.39718e25	−	5.17732e24i	0.000161304	−	3.48376e-5i
$53$	−3.97204e29			−1.93341			−0.966704	−	0.255896i	$-0.917630\pi$
$53$	−3.97204e29			−1.93341			−0.966704	+	0.255896i	$0.917630\pi$
$54$	2.49700e29	−	2.66572e28i	0.884556	−	0.0944323i
$55$		−	8.14372e28i		−	0.211182i
$56$	5.22598e29	−	1.72639e29i	0.997635	−	0.329567i
$57$	1.29763e30			1.83349
$58$	−1.45155e29	−	1.35968e30i	−0.152601	−	1.42943i
$59$			1.46663e30i			1.15302i	0.817091	+	0.576509i	$0.195585\pi$
$59$			1.46663e30i			1.15302i	−0.817091	+	0.576509i	$0.804415\pi$
$60$	−7.36795e28	−	3.41149e29i	−0.0435287	−	0.201545i
$61$	1.24369e30			0.554761			0.277380	−	0.960760i	$-0.410534\pi$
$61$	1.24369e30			0.554761			0.277380	+	0.960760i	$0.410534\pi$
$62$	5.71459e29	−	6.10070e28i	0.193342	−	0.0206406i
$63$			6.34408e30i			1.63523i
$64$	−4.07278e30	+	3.02050e30i	−0.803215	+	0.595689i
$65$	1.40453e26			2.12816e−5
$66$	−2.37789e30	−	2.22739e31i	−0.277936	−	2.60345i
$67$			1.03158e31i			0.933752i	0.884323	+	0.466876i	$0.154621\pi$
$67$			1.03158e31i			0.933752i	−0.884323	+	0.466876i	$0.845379\pi$
$68$	1.44077e31	−	3.11169e30i	1.01378	−	0.218950i
$69$	−4.37005e31			−2.39912
$70$	3.13421e30	−	3.34598e29i	0.134729	−	0.0143832i
$71$			1.84322e31i			0.622566i	0.950317	+	0.311283i	$0.100759\pi$
$71$			1.84322e31i			0.622566i	−0.950317	+	0.311283i	$0.899241\pi$
$72$	−1.83337e31	−	5.54980e31i	−0.488199	−	1.47783i
$73$	−2.03215e30			−0.0428023			−0.0214011	−	0.999771i	$-0.506813\pi$
$73$	−2.03215e30			−0.0428023			−0.0214011	+	0.999771i	$0.506813\pi$
$74$	1.42917e30	+	1.33872e31i	0.0238860	+	0.223743i
$75$			1.18187e32i			1.57228i
$76$	−2.27929e31	−	1.05535e32i	−0.242085	−	1.12089i
$77$	2.02303e32			1.72052
$78$	3.84153e28	−	4.10109e27i	0.000262359	−	2.80086e-5i
$79$			4.21903e31i			0.232034i	0.993247	+	0.116017i	$0.0370128\pi$
$79$			4.21903e31i			0.232034i	−0.993247	+	0.116017i	$0.962987\pi$
$80$	−2.64511e31	+	1.19846e31i	−0.117467	+	0.0532222i
$81$	−3.72849e31			−0.134057
$82$	1.95039e31	+	1.82695e32i	0.0569228	+	0.533201i
$83$			3.72769e32i			0.885345i	0.896683	+	0.442672i	$0.145970\pi$
$83$			3.72769e32i			0.885345i	−0.896683	+	0.442672i	$0.854030\pi$
$84$	8.47469e32	−	1.83032e32i	1.64201	−	0.354633i
$85$	8.44156e31			0.133752
$86$	5.13788e32	−	5.48503e31i	0.667284	−	0.0712370i
$87$		−	2.15409e33i		−	2.29845i
$88$	−1.76975e33	+	5.84634e32i	−1.55491	+	0.513663i
$89$	−1.82401e33			−1.32251			−0.661254	−	0.750162i	$-0.729975\pi$
$89$	−1.82401e33			−1.32251			−0.661254	+	0.750162i	$0.729975\pi$
$90$	−3.55330e31	−	3.32841e32i	−0.0213064	−	0.199579i
$91$			3.48908e29i			0.000173383i
$92$	7.67601e32	+	3.55412e33i	0.316769	+	1.46669i
$93$	9.05337e32			0.310885
$94$	−4.11056e33	+	4.38830e32i	−1.17687	+	0.125638i
$95$		−	6.18337e32i		−	0.147885i
$96$	−6.88472e33	+	4.05026e33i	−1.37808	+	0.810721i
$97$	6.65697e33			1.11727			0.558634	−	0.829414i	$-0.311326\pi$
$97$	6.65697e33			1.11727			0.558634	+	0.829414i	$0.311326\pi$
$98$	7.82254e31	+	7.32745e32i	0.0110282	+	0.103302i
$99$		−	2.14839e34i		−	2.54867i
$100$	9.61207e33	−	2.07596e33i	0.961207	−	0.207596i
$101$	−7.54884e33			−0.637407			−0.318704	−	0.947854i	$-0.603247\pi$
$101$	−7.54884e33			−0.637407			−0.318704	+	0.947854i	$0.603247\pi$
$102$	2.30886e34	−	2.46486e33i	1.64890	−	0.176031i
$103$			1.40342e34i			0.849091i	0.905407	+	0.424545i	$0.139566\pi$
$103$			1.40342e34i			0.849091i	−0.905407	+	0.424545i	$0.860434\pi$
$104$	−1.00831e30	−	3.05225e30i	−5.17637e−5	−	0.000156694i
$105$	4.96538e33			0.216638
$106$	5.52659e33	+	5.17681e34i	0.205238	+	1.92248i
$107$			2.29083e34i			0.725218i	0.931941	+	0.362609i	$0.118114\pi$
$107$			2.29083e34i			0.725218i	−0.931941	+	0.362609i	$0.881886\pi$
$108$	−6.94854e33	−	3.21729e34i	−0.187797	−	0.869534i
$109$	4.41619e33			0.102046			0.0510231	−	0.998697i	$-0.483752\pi$
$109$	4.41619e33			0.102046			0.0510231	+	0.998697i	$0.483752\pi$
$110$	−1.06138e34	+	1.13310e33i	−0.209989	+	0.0224177i
$111$			2.12087e34i			0.359768i
$112$	−2.97716e34	−	6.57089e34i	−0.433607	−	0.957013i
$113$	1.20061e34			0.150337			0.0751687	−	0.997171i	$-0.476050\pi$
$113$	1.20061e34			0.150337			0.0751687	+	0.997171i	$0.476050\pi$
$114$	−1.80549e34	−	1.69122e35i	−0.194631	−	1.82313i
$115$			2.08239e34i			0.193508i
$116$	−1.75190e35	+	3.78366e34i	−1.40515	+	0.303477i
$117$	3.70527e31			0.000256839
$118$	1.91148e35	−	2.04063e34i	1.14650	−	0.122397i
$119$			2.09702e35i			1.08969i
$120$	−4.34372e34	+	1.43494e34i	−0.195786	+	0.0646774i
$121$	−4.29612e35			−1.68161
$122$	−1.73044e34	−	1.62092e35i	−0.0588898	−	0.551626i
$123$			2.89436e35i			0.857363i
$124$	−1.59023e34	−	7.36302e34i	−0.0410479	−	0.190059i
$125$	1.13588e35			0.255778
$126$	8.26832e35	−	8.82699e34i	1.62599	−	0.173585i
$127$		−	3.55898e35i		−	0.611875i	−0.952052	−	0.305937i	$-0.901030\pi$
$127$		−	3.55898e35i		−	0.611875i	0.952052	−	0.305937i	$-0.0989698\pi$
$128$	4.50334e35	+	4.88785e35i	0.677587	+	0.735442i
$129$	8.13971e35			1.07296
$130$	−1.95423e30	−	1.83054e31i	−2.25911e−6	−	2.11613e-5i
$131$		−	3.20125e35i		−	0.324868i	−0.986719	−	0.162434i	$-0.948066\pi$
$131$		−	3.20125e35i		−	0.324868i	0.986719	−	0.162434i	$-0.0519345\pi$
$132$	−2.86991e36	+	6.19828e35i	−2.55924	+	0.552731i
$133$	1.53605e36			1.20483
$134$	1.34447e36	−	1.43532e35i	0.928476	−	0.0991210i
$135$		−	1.88503e35i		−	0.114722i
$136$	−6.06016e35	−	1.83448e36i	−0.325329	−	0.984806i
$137$	−2.92181e35			−0.138485			−0.0692425	−	0.997600i	$-0.522058\pi$
$137$	−2.92181e35			−0.138485			−0.0692425	+	0.997600i	$0.522058\pi$
$138$	6.08038e35	+	5.69555e36i	0.254675	+	2.38557i
$139$		−	5.04371e36i		−	1.86852i	−0.356589	−	0.934261i	$-0.616060\pi$
$139$		−	5.04371e36i		−	1.86852i	0.356589	−	0.934261i	$-0.383940\pi$
$140$	−8.72171e34	−	4.03830e35i	−0.0286039	−	0.132441i
$141$	−6.51217e36			−1.89235
$142$	2.40229e36	−	2.56461e35i	0.619048	−	0.0660875i
$143$		−	1.18156e33i		−	0.000270235i
$144$	−6.97805e36	+	3.16164e36i	−1.41766	+	0.642318i
$145$	−1.02645e36			−0.185388
$146$	2.82748e34	+	2.64853e35i	0.00454361	+	0.0425604i
$147$			1.16086e36i			0.166105i
$148$	1.72488e36	−	3.72531e35i	0.219943	−	0.0475021i
$149$	−2.86716e35			−0.0326051			−0.0163026	−	0.999867i	$-0.505189\pi$
$149$	−2.86716e35			−0.0326051			−0.0163026	+	0.999867i	$0.505189\pi$
$150$	1.54035e37	−	1.64443e36i	1.56339	−	0.166903i
$151$		−	3.70248e36i		−	0.335648i	−0.985817	−	0.167824i	$-0.946326\pi$
$151$		−	3.70248e36i		−	0.335648i	0.985817	−	0.167824i	$-0.0536741\pi$
$152$	−1.34374e37	+	4.43901e36i	−1.08886	+	0.359704i
$153$	2.22696e37			1.61420
$154$	−2.81480e36	−	2.63665e37i	−0.182640	−	1.71080i
$155$		−	4.31405e35i		−	0.0250753i
$156$	−1.06900e33	−	4.94966e33i	−5.57007e−5	−	0.000257904i
$157$	2.32526e37			1.08687			0.543434	−	0.839452i	$-0.317124\pi$
$157$	2.32526e37			1.08687			0.543434	+	0.839452i	$0.317124\pi$
$158$	5.49873e36	−	5.87026e35i	0.230723	−	0.0246313i
$159$			8.20139e37i			3.09127i
$160$	1.93000e36	+	3.28066e36i	0.0653910	+	0.111153i
$161$	−5.17299e37			−1.57653
$162$	5.18773e35	+	4.85940e36i	0.0142306	+	0.133299i
$163$		−	4.09425e37i		−	1.01154i	−0.862667	−	0.505772i	$-0.831208\pi$
$163$		−	4.09425e37i		−	1.01154i	0.862667	−	0.505772i	$-0.168792\pi$
$164$	2.35395e37	−	5.08395e36i	0.524146	−	0.113202i
$165$	−1.68150e37			−0.337652
$166$	4.85835e37	−	5.18662e36i	0.880342	−	0.0939824i
$167$			6.36262e37i			1.04101i	0.853858	+	0.520506i	$0.174257\pi$
$167$			6.36262e37i			1.04101i	−0.853858	+	0.520506i	$0.825743\pi$
$168$	−3.56463e37	−	1.07905e38i	−0.526934	−	1.59509i
$169$	−7.48297e37			−1.00000
$170$	−1.17454e36	−	1.10020e37i	−0.0141983	−	0.132996i
$171$		−	1.63123e38i		−	1.78476i
$172$	−1.42974e37	−	6.61996e37i	−0.141669	−	0.655951i
$173$	1.13894e37			0.102263			0.0511313	−	0.998692i	$-0.483717\pi$
$173$	1.13894e37			0.102263			0.0511313	+	0.998692i	$0.483717\pi$
$174$	−2.80745e38	+	2.99714e37i	−2.28547	+	0.243989i
$175$			1.39903e38i			1.03319i
$176$	1.00820e38	+	2.22520e38i	0.675821	+	1.49160i
$177$	3.02827e38			1.84352
$178$	2.53789e37	+	2.37726e38i	0.140389	+	1.31503i
$179$		−	2.60205e37i		−	0.130862i	−0.997857	−	0.0654310i	$-0.979158\pi$
$179$		−	2.60205e37i		−	0.130862i	0.997857	−	0.0654310i	$-0.0208422\pi$
$180$	−4.28853e37	+	9.26214e36i	−0.196189	+	0.0423720i
$181$	−1.58463e38			−0.659767			−0.329884	−	0.944022i	$-0.607010\pi$
$181$	−1.58463e38			−0.659767			−0.329884	+	0.944022i	$0.607010\pi$
$182$	4.54737e34	−	4.85462e33i	0.000172404	−	1.84052e-5i
$183$		−	2.56795e38i		−	0.886990i
$184$	4.52534e38	−	1.49494e38i	1.42478	−	0.470674i
$185$	1.01062e37			0.0290181
$186$	−1.25966e37	−	1.17994e38i	−0.0330015	−	0.309129i
$187$		−	7.10145e38i		−	1.69840i
$188$	1.14387e38	+	5.29629e38i	0.249857	+	1.15688i
$189$	4.68273e38			0.934650
$190$	−8.05887e37	+	8.60338e36i	−0.147049	+	0.0156985i
$191$			2.66106e38i			0.444107i	0.975035	+	0.222053i	$0.0712759\pi$
$191$			2.66106e38i			0.444107i	−0.975035	+	0.222053i	$0.928724\pi$
$192$	6.23668e38	+	8.40941e38i	0.952429	+	1.28424i
$193$	−8.43744e38			−1.17960			−0.589802	−	0.807548i	$-0.700794\pi$
$193$	−8.43744e38			−1.17960			−0.589802	+	0.807548i	$0.700794\pi$
$194$	−9.26234e37	−	8.67612e38i	−0.118602	−	1.11095i
$195$		−	2.90005e34i		−	3.40264e-5i
$196$	9.44113e37	−	2.03905e37i	0.101548	−	0.0219318i
$197$	−8.22429e38			−0.811283			−0.405642	−	0.914032i	$-0.632952\pi$
$197$	−8.22429e38			−0.811283			−0.405642	+	0.914032i	$0.632952\pi$
$198$	−2.80002e39	+	2.98921e38i	−2.53427	+	0.270551i
$199$			1.78954e39i			1.48676i	0.668871	+	0.743379i	$0.266778\pi$
$199$			1.78954e39i			1.48676i	−0.668871	+	0.743379i	$0.733222\pi$
$200$	−4.04303e38	−	1.22387e39i	−0.308459	−	0.933739i
$201$	2.12999e39			1.49295
$202$	1.05033e38	+	9.83851e38i	0.0676630	+	0.633806i
$203$		−	2.54987e39i		−	1.51038i
$204$	−6.42497e38	−	2.97487e39i	−0.350073	−	1.62090i
$205$	1.37920e38			0.0691530
$206$	1.82909e39	−	1.95268e38i	0.844293	−	0.0901339i
$207$			5.49353e39i			2.33537i
$208$	−3.83775e35	+	1.73882e35i	−0.000150314	+	6.81049e-5i
$209$	−5.20175e39			−1.87786
$210$	−6.90871e37	−	6.47145e38i	−0.0229969	−	0.215414i
$211$			1.00395e38i			0.0308256i	0.999881	+	0.0154128i	$0.00490625\pi$
$211$			1.00395e38i			0.0308256i	−0.999881	+	0.0154128i	$0.995094\pi$
$212$	6.67012e39	−	1.44058e39i	1.88984	−	0.408157i
$213$	3.80585e39			0.995401
$214$	2.98567e39	−	3.18740e38i	0.721120	−	0.0769844i
$215$		−	3.87868e38i		−	0.0865427i
$216$	−4.09646e39	+	1.35326e39i	−0.844685	+	0.279040i
$217$	1.07168e39			0.204291
$218$	−6.14457e37	−	5.75568e38i	−0.0108326	−	0.101470i
$219$			4.19594e38i			0.0684352i
$220$	2.95356e38	+	1.36755e39i	0.0445821	+	0.206423i
$221$	1.22477e36			0.000171154
$222$	2.76416e39	−	2.95092e38i	0.357735	−	0.0381906i
$223$			1.29976e39i			0.155840i	0.996960	+	0.0779202i	$0.0248279\pi$
$223$			1.29976e39i			0.155840i	−0.996960	+	0.0779202i	$0.975172\pi$
$224$	−8.14970e39	+	4.79444e39i	−0.905577	+	0.532747i
$225$	1.48572e40			1.53050
$226$	−1.67049e38	−	1.56477e39i	−0.0159588	−	0.149488i
$227$			1.62272e39i			0.143815i	0.997411	+	0.0719075i	$0.0229086\pi$
$227$			1.62272e39i			0.143815i	−0.997411	+	0.0719075i	$0.977091\pi$
$228$	−2.17906e40	+	4.70623e39i	−1.79216	+	0.387062i
$229$	−2.14104e40			−1.63464			−0.817318	−	0.576187i	$-0.804540\pi$
$229$	−2.14104e40			−1.63464			−0.817318	+	0.576187i	$0.804540\pi$
$230$	2.71400e39	−	2.89738e38i	0.192414	−	0.0205415i
$231$		−	4.17712e40i		−	2.75089i
$232$	7.36884e39	+	2.23063e40i	0.450924	+	1.36500i
$233$	−3.49857e39			−0.198994			−0.0994971	−	0.995038i	$-0.531723\pi$
$233$	−3.49857e39			−0.198994			−0.0994971	+	0.995038i	$0.531723\pi$
$234$	−5.15543e35	−	4.82914e36i	−2.72643e−5	−	0.000255388i
$235$			3.10314e39i			0.152633i
$236$	−5.31916e39	−	2.46286e40i	−0.243410	−	1.12703i
$237$	8.71138e39			0.370993
$238$	2.73308e40	−	2.91774e39i	1.08354	−	0.115675i
$239$		−	1.53723e40i		−	0.567513i	−0.958896	−	0.283756i	$-0.908419\pi$
$239$		−	1.53723e40i		−	0.567513i	0.958896	−	0.283756i	$-0.0915807\pi$
$240$	2.47455e39	+	5.46158e39i	0.0850953	+	0.187814i
$241$	−3.46295e40			−1.10958			−0.554788	−	0.831992i	$-0.687201\pi$
$241$	−3.46295e40			−1.10958			−0.554788	+	0.831992i	$0.687201\pi$
$242$	5.97752e39	+	5.59920e40i	0.178509	+	1.67211i
$243$			3.96501e40i			1.10392i
$244$	−2.08849e40	+	4.51062e39i	−0.542258	+	0.117114i
$245$	5.53163e38			0.0133977
$246$	3.77225e40	−	4.02713e39i	0.852519	−	0.0910121i
$247$		−	8.97134e36i		−	0.000189238i
$248$	−9.37507e39	+	3.09704e39i	−0.184627	+	0.0609913i
$249$	7.69687e40			1.41555
$250$	−1.58044e39	−	1.48041e40i	−0.0271517	−	0.254332i
$251$			5.70369e40i			0.915594i	0.889057	+	0.457797i	$0.151361\pi$
$251$			5.70369e40i			0.915594i	−0.889057	+	0.457797i	$0.848639\pi$
$252$	−2.30087e40	−	1.06534e41i	−0.345209	−	1.59838i
$253$	1.75181e41			2.45718
$254$	−4.63847e40	+	4.95188e39i	−0.608418	+	0.0649526i
$255$		−	1.74300e40i		−	0.213852i
$256$	5.74382e40	−	6.54935e40i	0.659359	−	0.751829i
$257$	−1.52030e41			−1.63330			−0.816648	−	0.577136i	$-0.804170\pi$
$257$	−1.52030e41			−1.63330			−0.816648	+	0.577136i	$0.804170\pi$
$258$	−1.13254e40	−	1.06086e41i	−0.113899	−	1.06690i
$259$			2.51055e40i			0.236414i
$260$	−2.35858e36	+	5.09394e35i	−2.08019e−5	+	4.49269e-6i
$261$	−2.70787e41			−2.23738
$262$	−4.17223e40	+	4.45414e39i	−0.323033	+	0.0344859i
$263$			6.08574e40i			0.441637i	0.975315	+	0.220819i	$0.0708729\pi$
$263$			6.08574e40i			0.441637i	−0.975315	+	0.220819i	$0.929127\pi$
$264$	1.20714e41	+	3.65415e41i	0.821281	+	2.48611i
$265$	3.90807e40			0.249335
$266$	−2.13722e40	−	2.00196e41i	−0.127897	−	1.19803i
$267$			3.76619e41i			2.11452i
$268$	−3.74133e40	−	1.73230e41i	−0.197122	−	0.912708i
$269$	−1.13170e41			−0.559684			−0.279842	−	0.960046i	$-0.590282\pi$
$269$	−1.13170e41			−0.559684			−0.279842	+	0.960046i	$0.590282\pi$
$270$	−2.45679e40	+	2.62279e39i	−0.114073	+	0.0121781i
$271$		−	3.43302e41i		−	1.49692i	−0.663179	−	0.748460i	$-0.730793\pi$
$271$		−	3.43302e41i		−	1.49692i	0.663179	−	0.748460i	$-0.269207\pi$
$272$	−2.30658e41	+	1.04507e41i	−0.944706	+	0.428031i
$273$	7.20419e37			0.000277217
$274$	4.06533e39	+	3.80804e40i	0.0147007	+	0.137702i
$275$		−	4.73773e41i		−	1.61033i
$276$	7.33849e41	−	1.58493e41i	2.34505	−	0.506472i
$277$	4.79456e41			1.44076			0.720382	−	0.693577i	$-0.243966\pi$
$277$	4.79456e41			1.44076			0.720382	+	0.693577i	$0.243966\pi$
$278$	−6.57354e41	+	7.01769e40i	−1.85797	+	0.198350i
$279$		−	1.13809e41i		−	0.302624i
$280$	−5.14182e40	+	1.69859e40i	−0.128656	+	0.0425013i
$281$	5.60865e41			1.32084			0.660421	−	0.750895i	$-0.270378\pi$
$281$	5.60865e41			1.32084			0.660421	+	0.750895i	$0.270378\pi$
$282$	9.06088e40	+	8.48741e41i	0.200879	+	1.88166i
$283$			2.26767e41i			0.473380i	0.971585	+	0.236690i	$0.0760626\pi$
$283$			2.26767e41i			0.473380i	−0.971585	+	0.236690i	$0.923937\pi$
$284$	−6.68498e40	−	3.09526e41i	−0.131428	−	0.608535i
$285$	−1.27673e41			−0.236448
$286$	−1.53994e38	+	1.64399e37i	−0.000268709	+	2.86864e-5i
$287$			3.42616e41i			0.563397i
$288$	5.09152e41	+	8.65468e41i	0.789178	+	1.34146i
$289$	5.17905e40			0.0756809
$290$	1.42818e40	+	1.33779e41i	0.0196796	+	0.184341i
$291$		−	1.37452e42i		−	1.78636i
$292$	3.41252e40	−	7.37019e39i	0.0418376	−	0.00903587i
$293$	−9.89944e41			−1.14515			−0.572574	−	0.819853i	$-0.694055\pi$
$293$	−9.89944e41			−1.14515			−0.572574	+	0.819853i	$0.694055\pi$
$294$	1.51296e41	−	1.61518e40i	0.165167	−	0.0176326i
$295$		−	1.44301e41i		−	0.148694i
$296$	−7.25521e40	−	2.19623e41i	−0.0705815	−	0.213658i
$297$	−1.58578e42			−1.45675
$298$	3.98930e39	+	3.73681e40i	0.00346115	+	0.0324209i
$299$			3.02130e38i			0.000247619i
$300$	−4.28641e41	−	1.98468e42i	−0.331920	−	1.53684i
$301$	9.63528e41			0.705073
$302$	−4.82549e41	+	5.15154e40i	−0.333752	+	0.0356302i
$303$			1.55867e42i			1.01913i
$304$	7.65507e41	+	1.68955e42i	0.473258	+	1.04453i
$305$	−1.22366e41			−0.0715426
$306$	−3.09854e41	−	2.90243e42i	−0.171353	−	1.60508i
$307$			1.41594e42i			0.740787i	0.928875	+	0.370394i	$0.120777\pi$
$307$			1.41594e42i			0.740787i	−0.928875	+	0.370394i	$0.879223\pi$
$308$	−3.39722e42	+	7.33713e41i	−1.68175	+	0.363215i
$309$	2.89775e42			1.35758
$310$	−5.62256e40	+	6.00246e39i	−0.0249336	+	0.00266183i
$311$			4.84373e41i			0.203354i	0.994817	+	0.101677i	$0.0324209\pi$
$311$			4.84373e41i			0.203354i	−0.994817	+	0.101677i	$0.967579\pi$
$312$	−6.30223e38	+	2.08193e38i	−0.000250534	+	8.27634e-5i
$313$	4.36229e41			0.164233			0.0821166	−	0.996623i	$-0.473832\pi$
$313$	4.36229e41			0.164233			0.0821166	+	0.996623i	$0.473832\pi$
$314$	−3.23530e41	−	3.03054e42i	−0.115375	−	1.08073i
$315$		−	6.24191e41i		−	0.210881i
$316$	−1.53016e41	−	7.08489e41i	−0.0489842	−	0.226805i
$317$	−4.70429e42			−1.42721			−0.713603	−	0.700551i	$-0.752938\pi$
$317$	−4.70429e42			−1.42721			−0.713603	+	0.700551i	$0.752938\pi$
$318$	1.06890e43	−	1.14112e42i	3.07380	−	0.328149i
$319$			8.63500e42i			2.35408i
$320$	4.00720e41	−	2.97186e41i	0.103584	−	0.0768208i
$321$	4.73006e42			1.15953
$322$	7.19757e41	+	6.74203e42i	0.167354	+	1.56762i
$323$		−	5.39199e42i		−	1.18934i
$324$	6.26114e41	−	1.35225e41i	0.131035	−	0.0283003i
$325$	8.17105e38			0.000162278
$326$	−5.33609e42	+	5.69663e41i	−1.00583	+	0.107379i
$327$		−	9.11846e41i		−	0.163159i
$328$	−9.90121e41	−	2.99720e42i	−0.168203	−	0.509168i
$329$	−7.70870e42			−1.24351
$330$	2.33960e41	+	2.19152e42i	0.0358430	+	0.335745i
$331$		−	8.87142e42i		−	1.29097i	−0.763772	−	0.645486i	$-0.776655\pi$
$331$		−	8.87142e42i		−	1.29097i	0.763772	−	0.645486i	$-0.223345\pi$
$332$	−1.35196e42	−	6.25980e42i	−0.186903	−	0.865392i
$333$	2.66611e42			0.350208
$334$	8.29249e42	−	8.85279e41i	1.03513	−	0.110507i
$335$		−	1.01497e42i		−	0.120418i
$336$	−1.35675e43	+	6.14720e42i	−1.53014	+	0.693281i
$337$	6.71505e42			0.720014			0.360007	−	0.932950i	$-0.382774\pi$
$337$	6.71505e42			0.720014			0.360007	+	0.932950i	$0.382774\pi$
$338$	1.04116e42	+	9.75266e42i	0.106153	+	0.994350i
$339$		−	2.47899e42i		−	0.240370i
$340$	−1.41756e42	+	3.06158e41i	−0.130738	+	0.0282361i
$341$	−3.62919e42			−0.318409
$342$	−2.12600e43	+	2.26965e42i	−1.77468	+	0.189459i
$343$		−	1.18529e43i		−	0.941509i
$344$	−8.42895e42	+	2.78449e42i	−0.637206	+	0.210500i
$345$	4.29968e42			0.309393
$346$	−1.58469e41	−	1.48440e42i	−0.0108555	−	0.101685i
$347$			9.22894e42i			0.601936i	0.953634	+	0.300968i	$0.0973098\pi$
$347$			9.22894e42i			0.601936i	−0.953634	+	0.300968i	$0.902690\pi$
$348$	7.81243e42	+	3.61729e43i	0.485220	+	2.24665i
$349$	−4.70367e42			−0.278230			−0.139115	−	0.990276i	$-0.544426\pi$
$349$	−4.70367e42			−0.278230			−0.139115	+	0.990276i	$0.544426\pi$
$350$	1.82337e43	−	1.94657e42i	1.02735	−	0.109676i
$351$		−	2.73496e39i		−	0.000146802i
$352$	2.75985e43	−	1.62361e43i	1.41143	−	0.830341i
$353$	−2.63667e43			−1.28495			−0.642475	−	0.766306i	$-0.722092\pi$
$353$	−2.63667e43			−1.28495			−0.642475	+	0.766306i	$0.722092\pi$
$354$	−4.21346e42	−	3.94678e43i	−0.195696	−	1.83311i
$355$		−	1.81354e42i		−	0.0802868i
$356$	3.06301e43	−	6.61533e42i	1.29270	−	0.279191i
$357$	4.32989e43			1.74228
$358$	−3.39128e42	+	3.62042e41i	−0.130123	+	0.0138915i
$359$		−	4.48664e43i		−	1.64178i	−0.571084	−	0.820892i	$-0.693477\pi$
$359$		−	4.48664e43i		−	1.64178i	0.571084	−	0.820892i	$-0.306523\pi$
$360$	1.80384e42	+	5.46043e42i	0.0629588	+	0.190583i
$361$	−9.46122e42			−0.315010
$362$	2.20481e42	+	2.06526e43i	0.0700366	+	0.656039i
$363$			8.87056e43i			2.68868i
$364$	−1.26542e39	−	5.85910e39i	−3.66025e−5	−	0.000169476i
$365$	1.99942e41			0.00551983
$366$	−3.34685e43	+	3.57298e42i	−0.881978	+	0.0941570i
$367$			6.13662e42i			0.154385i	0.997016	+	0.0771926i	$0.0245957\pi$
$367$			6.13662e42i			0.154385i	−0.997016	+	0.0771926i	$0.975404\pi$
$368$	−2.57802e43	−	5.68993e43i	−0.619260	−	1.36677i
$369$	3.63845e43			0.834581
$370$	−1.40615e41	−	1.31716e42i	−0.00308037	−	0.0288541i
$371$			9.70829e43i			2.03136i
$372$	−1.52030e43	+	3.28347e42i	−0.303879	+	0.0656301i
$373$	−3.99570e43			−0.763031			−0.381516	−	0.924362i	$-0.624598\pi$
$373$	−3.99570e43			−0.763031			−0.381516	+	0.924362i	$0.624598\pi$
$374$	−9.25542e43	+	9.88078e42i	−1.68880	+	0.180291i
$375$		−	2.34535e43i		−	0.408955i
$376$	6.74358e43	−	2.22773e43i	1.12382	−	0.371252i
$377$	−1.48926e40			−0.000237229
$378$	−6.51544e42	−	6.10307e43i	−0.0992163	−	0.929369i
$379$		−	9.47081e43i		−	1.37886i	−0.724352	−	0.689431i	$-0.757861\pi$
$379$		−	9.47081e43i		−	1.37886i	0.724352	−	0.689431i	$-0.242139\pi$
$380$	2.24258e42	+	1.03835e43i	0.0312196	+	0.144552i
$381$	−7.34852e43			−0.978308
$382$	3.46820e43	−	3.70253e42i	0.441597	−	0.0471435i
$383$		−	5.73540e42i		−	0.0698529i	−0.999390	−	0.0349264i	$-0.988880\pi$
$383$		−	5.73540e42i		−	0.0698529i	0.999390	−	0.0349264i	$-0.0111197\pi$
$384$	1.00924e44	−	9.29842e43i	1.17588	−	1.08337i
$385$	−1.99045e43			−0.221881
$386$	1.17396e43	+	1.09966e44i	0.125219	+	1.17294i
$387$		−	1.02323e44i		−	1.04445i
$388$	−1.11788e44	+	2.41435e43i	−1.09209	+	0.235863i
$389$	−1.03776e42			−0.00970403			−0.00485201	−	0.999988i	$-0.501544\pi$
$389$	−1.03776e42			−0.00970403			−0.00485201	+	0.999988i	$0.501544\pi$
$390$	−3.77967e39	+	4.03505e38i	−3.38342e−5	+	3.61202e-6i
$391$			1.81587e44i			1.55626i
$392$	−3.97113e42	−	1.20210e43i	−0.0325875	−	0.0986459i
$393$	−6.60988e43			−0.519422
$394$	1.14431e43	+	1.07188e44i	0.0861205	+	0.806699i
$395$		−	4.15109e42i		−	0.0299234i
$396$	7.79176e43	+	3.60772e44i	0.538044	+	2.49123i
$397$	2.59664e44			1.71780			0.858901	−	0.512142i	$-0.171148\pi$
$397$	2.59664e44			1.71780			0.858901	+	0.512142i	$0.171148\pi$
$398$	2.33234e44	−	2.48993e43i	1.47836	−	0.157824i
$399$		−	3.17161e44i		−	1.92637i
$400$	−1.53883e44	+	6.97220e43i	−0.895719	+	0.405836i
$401$	1.72736e44			0.963670			0.481835	−	0.876262i	$-0.339970\pi$
$401$	1.72736e44			0.963670			0.481835	+	0.876262i	$0.339970\pi$
$402$	−2.96361e43	−	2.77604e44i	−0.158482	−	1.48451i
$403$		−	6.25918e39i		−	3.20872e-5i
$404$	1.26765e44	−	2.73781e43i	0.623042	−	0.134561i
$405$	3.66845e42			0.0172881
$406$	−3.32328e44	+	3.54783e43i	−1.50184	+	0.160332i
$407$		−	8.50183e43i		−	0.368475i
$408$	−3.78779e44	+	1.25129e44i	−1.57458	+	0.520158i
$409$	−4.01194e43			−0.159977			−0.0799886	−	0.996796i	$-0.525488\pi$
$409$	−4.01194e43			−0.159977			−0.0799886	+	0.996796i	$0.525488\pi$
$410$	−1.91898e42	−	1.79753e43i	−0.00734083	−	0.0687623i
$411$			6.03290e43i			0.221419i
$412$	−5.08991e43	−	2.35671e44i	−0.179249	−	0.829954i
$413$	3.58467e44			1.21143
$414$	7.15979e44	−	7.64356e43i	2.32217	−	0.247908i
$415$		−	3.66766e43i		−	0.114175i
$416$	2.80020e40	+	4.75985e40i	8.36764e−5	+	0.000142235i
$417$	−1.04142e45			−2.98752
$418$	7.23758e43	+	6.77951e44i	0.199341	+	1.86725i
$419$		−	1.45130e44i		−	0.383812i	−0.981413	−	0.191906i	$-0.938533\pi$
$419$		−	1.45130e44i		−	0.383812i	0.981413	−	0.191906i	$-0.0614668\pi$
$420$	−8.33821e43	+	1.80084e43i	−0.211756	+	0.0457339i
$421$	−6.25352e44			−1.52521			−0.762604	−	0.646865i	$-0.776080\pi$
$421$	−6.25352e44			−1.52521			−0.762604	+	0.646865i	$0.776080\pi$
$422$	1.30847e43	−	1.39688e42i	0.0306515	−	0.00327225i
$423$			8.18636e44i			1.84206i
$424$	−2.80559e44	−	8.49282e44i	−0.606463	−	1.83583i
$425$	4.91100e44			1.01990
$426$	−5.29536e43	−	4.96021e44i	−0.105665	−	0.989777i
$427$		−	3.03978e44i		−	0.582865i
$428$	−8.30838e43	−	3.84692e44i	−0.153099	−	0.708874i
$429$	−2.43966e41			−0.000432071
$430$	−5.05514e43	+	5.39670e42i	−0.0860537	+	0.00918681i
$431$			7.56338e44i			1.23766i	0.785524	+	0.618831i	$0.212394\pi$
$431$			7.56338e44i			1.23766i	−0.785524	+	0.618831i	$0.787606\pi$
$432$	2.33369e44	+	5.15068e44i	0.367130	+	0.810292i
$433$	3.09504e44			0.468136			0.234068	−	0.972220i	$-0.424796\pi$
$433$	3.09504e44			0.468136			0.234068	+	0.972220i	$0.424796\pi$
$434$	−1.49111e43	−	1.39674e44i	−0.0216862	−	0.203137i
$435$			2.11940e44i			0.296411i
$436$	−7.41596e43	+	1.60166e43i	−0.0997464	+	0.0215427i
$437$	1.33011e45			1.72069
$438$	5.46863e43	−	5.83813e42i	0.0680485	−	0.00726464i
$439$			4.62150e44i			0.553206i	0.960984	+	0.276603i	$0.0892086\pi$
$439$			4.62150e44i			0.553206i	−0.960984	+	0.276603i	$0.910791\pi$
$440$	1.74125e44	−	5.75219e43i	0.200524	−	0.0662427i
$441$	1.45929e44			0.161691
$442$	−1.70412e40	−	1.59626e41i	−1.81686e−5	−	0.000170187i
$443$		−	5.29565e44i		−	0.543320i	−0.962393	−	0.271660i	$-0.912427\pi$
$443$		−	5.29565e44i		−	0.543320i	0.962393	−	0.271660i	$-0.0875727\pi$
$444$	−7.69195e43	−	3.56150e44i	−0.0759497	−	0.351660i
$445$	1.79464e44			0.170552
$446$	1.69399e44	−	1.80845e43i	0.154960	−	0.0165430i
$447$			5.92006e43i			0.0521313i
$448$	7.38259e44	+	9.95453e44i	0.625867	+	0.843907i
$449$	−6.12633e44			−0.500049			−0.250024	−	0.968240i	$-0.580439\pi$
$449$	−6.12633e44			−0.500049			−0.250024	+	0.968240i	$0.580439\pi$
$450$	−2.06719e44	−	1.93635e45i	−0.162468	−	1.52185i
$451$		−	1.16025e45i		−	0.878112i
$452$	−2.01614e44	+	4.35436e43i	−0.146949	+	0.0317373i
$453$	−7.64481e44			−0.536658
$454$	2.11491e44	−	2.25781e43i	0.143002	−	0.0152665i
$455$		−	3.43289e40i		−	2.23597e-5i
$456$	9.16559e44	+	2.77452e45i	0.575120	+	1.74095i
$457$	−1.65297e45			−0.999284			−0.499642	−	0.866232i	$-0.666535\pi$
$457$	−1.65297e45			−0.999284			−0.499642	+	0.866232i	$0.666535\pi$
$458$	2.97898e44	+	2.79044e45i	0.173522	+	1.62540i
$459$		−	1.64378e45i		−	0.922631i
$460$	−7.55240e43	−	3.49689e44i	−0.0408509	−	0.189147i
$461$	−8.94739e44			−0.466424			−0.233212	−	0.972426i	$-0.574924\pi$
$461$	−8.94739e44			−0.466424			−0.233212	+	0.972426i	$0.574924\pi$
$462$	−5.44410e45	+	5.81194e44i	−2.73535	+	0.292017i
$463$		−	9.20323e44i		−	0.445721i	−0.974850	−	0.222861i	$-0.928461\pi$
$463$		−	9.20323e44i		−	0.445721i	0.974850	−	0.222861i	$-0.0715395\pi$
$464$	2.80468e45	−	1.27076e45i	1.30942	−	0.593275i
$465$	−8.90757e43			−0.0400921
$466$	4.86783e43	+	4.55974e44i	0.0211239	+	0.197870i
$467$			3.06817e45i			1.28379i	0.766794	+	0.641893i	$0.221851\pi$
$467$			3.06817e45i			1.28379i	−0.766794	+	0.641893i	$0.778149\pi$
$468$	−6.22215e41	+	1.34383e41i	−0.000251050	+	5.42206e-5i
$469$	2.52135e45			0.981057
$470$	4.04436e44	−	4.31763e43i	0.151770	−	0.0162025i
$471$		−	4.80115e45i		−	1.73776i
$472$	−3.13587e45	+	1.03593e45i	−1.09482	+	0.361673i
$473$	−3.26294e45			−1.09893
$474$	−1.21208e44	−	1.13537e45i	−0.0393822	−	0.368896i
$475$		−	3.59727e45i		−	1.12767i
$476$	−7.60547e44	−	3.52146e45i	−0.230042	−	1.06514i
$477$	1.03099e46			3.00912
$478$	−2.00350e45	+	2.13887e44i	−0.564306	+	0.0602435i
$479$		−	5.42853e44i		−	0.147563i	−0.997274	−	0.0737816i	$-0.976493\pi$
$479$		−	5.42853e44i		−	0.147563i	0.997274	−	0.0737816i	$-0.0235068\pi$
$480$	6.77385e44	−	3.98503e44i	0.177719	−	0.104552i
$481$	1.46629e41			3.71325e−5
$482$	4.81827e44	+	4.51332e45i	0.117785	+	1.10331i
$483$			1.06811e46i			2.52066i
$484$	7.21434e45	−	1.55812e45i	1.64371	−	0.355000i
$485$	−6.54977e44			−0.144084
$486$	5.16766e45	−	5.51682e44i	1.09768	−	0.117185i
$487$			1.60864e45i			0.329963i	0.986297	+	0.164982i	$0.0527565\pi$
$487$			1.60864e45i			0.329963i	−0.986297	+	0.164982i	$0.947244\pi$
$488$	8.78463e44	+	2.65920e45i	0.174015	+	0.526762i
$489$	−8.45372e45			−1.61733
$490$	−7.69657e42	−	7.20945e43i	−0.00142221	−	0.0133220i
$491$			6.31846e45i			1.12778i	0.825849	+	0.563892i	$0.190697\pi$
$491$			6.31846e45i			1.12778i	−0.825849	+	0.563892i	$0.809303\pi$
$492$	−1.04972e45	−	4.86040e45i	−0.180996	−	0.838041i
$493$	−8.95080e45			−1.49095
$494$	−1.16925e42	+	1.24825e41i	−0.000188169	+	2.00883e-5i
$495$			2.11379e45i			0.328680i
$496$	5.34084e44	+	1.17877e45i	0.0802455	+	0.177110i
$497$	4.50512e45			0.654106
$498$	−1.07092e45	−	1.00314e46i	−0.150266	−	1.40755i
$499$		−	5.83237e45i		−	0.790926i	−0.918482	−	0.395463i	$-0.870584\pi$
$499$		−	5.83237e45i		−	0.790926i	0.918482	−	0.395463i	$-0.129416\pi$
$500$	−1.90745e45	+	4.11961e44i	−0.250013	+	0.0539965i
$501$	1.31374e46			1.66444
$502$	7.43370e45	−	7.93598e44i	0.910421	−	0.0971935i
$503$		−	1.04404e46i		−	1.23612i	−0.786130	−	0.618061i	$-0.787919\pi$
$503$		−	1.04404e46i		−	1.23612i	0.786130	−	0.618061i	$-0.212081\pi$
$504$	−1.35646e46	+	4.48104e45i	−1.55270	+	0.512932i
$505$	7.42727e44			0.0822008
$506$	−2.43742e45	−	2.28315e46i	−0.260838	−	2.44330i
$507$			1.54507e46i			1.59887i
$508$	1.29077e45	+	5.97649e45i	0.129171	+	0.598085i
$509$	−1.28854e46			−1.24708			−0.623542	−	0.781790i	$-0.714307\pi$
$509$	−1.28854e46			−1.24708			−0.623542	+	0.781790i	$0.714307\pi$
$510$	−2.27167e45	+	2.42516e44i	−0.212644	+	0.0227012i
$511$			4.96689e44i			0.0449707i
$512$	−9.33504e45	−	6.57475e45i	−0.817574	−	0.575824i
$513$	−1.20405e46			−1.02012
$514$	2.11530e45	+	1.98142e46i	0.173380	+	1.62407i
$515$		−	1.38082e45i		−	0.109500i
$516$	−1.36688e46	+	2.95211e45i	−1.04878	+	0.226510i
$517$	2.61051e46			1.93814
$518$	3.27203e45	−	3.49311e44i	0.235078	−	0.0250961i
$519$		−	2.35166e45i		−	0.163505i
$520$	9.92067e40	+	3.00310e41i	6.67551e−6	+	2.02075e-5i
$521$	−1.86900e46			−1.21722			−0.608609	−	0.793470i	$-0.708272\pi$
$521$	−1.86900e46			−1.21722			−0.608609	+	0.793470i	$0.708272\pi$
$522$	3.76766e45	+	3.52920e46i	0.237505	+	2.22473i
$523$		−	8.20885e45i		−	0.500903i	−0.968129	−	0.250451i	$-0.919421\pi$
$523$		−	8.20885e45i		−	0.500903i	0.968129	−	0.250451i	$-0.0805790\pi$
$524$	1.16103e45	+	5.37575e45i	0.0685821	+	0.317547i
$525$	2.88869e46			1.65193
$526$	7.93163e45	−	8.46754e44i	0.439142	−	0.0468813i
$527$		−	3.76192e45i		−	0.201664i
$528$	4.59455e46	−	2.08171e46i	2.38488	−	1.08055i
$529$	−2.48994e46			−1.25153
$530$	−5.43759e44	−	5.09345e45i	−0.0264677	−	0.247926i
$531$		−	3.80679e46i		−	1.79454i
$532$	−2.57944e46	+	5.57094e45i	−1.17768	+	0.254349i
$533$	2.00106e42			8.84905e−5
$534$	4.90853e46	−	5.24018e45i	2.10257	−	0.224463i
$535$		−	2.25394e45i		−	0.0935250i
$536$	−2.20568e46	+	7.28641e45i	−0.886626	+	0.292895i
$537$	−5.37266e45			−0.209231
$538$	1.57462e45	+	1.47496e46i	0.0594124	+	0.556521i
$539$		−	4.65347e45i		−	0.170125i
$540$	6.83664e44	+	3.16548e45i	0.0242186	+	0.112136i
$541$	4.82532e46			1.65643			0.828214	−	0.560411i	$-0.189357\pi$
$541$	4.82532e46			1.65643			0.828214	+	0.560411i	$0.189357\pi$
$542$	−4.47431e46	+	4.77662e45i	−1.48846	+	0.158903i
$543$			3.27191e46i			1.05488i
$544$	1.68299e46	+	2.86079e46i	0.525897	+	0.893932i
$545$	−4.34507e44			−0.0131600
$546$	−1.00237e42	−	9.38932e42i	−2.94276e−5	−	0.000275651i
$547$		−	3.25185e46i		−	0.925434i	−0.886506	−	0.462717i	$-0.846875\pi$
$547$		−	3.25185e46i		−	0.925434i	0.886506	−	0.462717i	$-0.153125\pi$
$548$	4.90651e45	−	1.05968e45i	0.135364	−	0.0292352i
$549$	−3.22814e46			−0.863420
$550$	−6.17475e46	+	6.59196e45i	−1.60123	+	0.170942i
$551$			6.55638e46i			1.64849i
$552$	−3.08672e46	−	9.34384e46i	−0.752546	−	2.27804i
$553$	1.03120e46			0.243790
$554$	−6.67104e45	−	6.24882e46i	−0.152942	−	1.43262i
$555$		−	2.08671e45i		−	0.0463961i
$556$	1.82925e46	+	8.46974e46i	0.394459	+	1.82641i
$557$	5.25316e46			1.09871			0.549354	−	0.835590i	$-0.314874\pi$
$557$	5.25316e46			1.09871			0.549354	+	0.835590i	$0.314874\pi$
$558$	−1.48328e46	+	1.58350e45i	−0.300914	+	0.0321246i
$559$		−	5.62751e42i		−	0.000110743i
$560$	2.92922e45	+	6.46507e45i	0.0559185	+	0.123418i
$561$	−1.46629e47			−2.71552
$562$	−7.80374e45	−	7.30983e46i	−0.140212	−	1.31338i
$563$			2.34251e46i			0.408355i	0.978934	+	0.204178i	$0.0654520\pi$
$563$			2.34251e46i			0.408355i	−0.978934	+	0.204178i	$0.934548\pi$
$564$	1.09357e47	−	2.36183e46i	1.84970	−	0.399489i
$565$	−1.18127e45			−0.0193877
$566$	2.95548e46	−	3.15517e45i	0.470705	−	0.0502509i
$567$			9.11303e45i			0.140848i
$568$	−3.94108e46	+	1.30193e46i	−0.591145	+	0.195284i
$569$	−6.54998e46			−0.953523			−0.476762	−	0.879033i	$-0.658189\pi$
$569$	−6.54998e46			−0.953523			−0.476762	+	0.879033i	$0.658189\pi$
$570$	1.77641e45	+	1.66398e46i	0.0250998	+	0.235112i
$571$		−	2.57697e46i		−	0.353423i	−0.984263	−	0.176712i	$-0.943454\pi$
$571$		−	2.57697e46i		−	0.353423i	0.984263	−	0.176712i	$-0.0565460\pi$
$572$	4.28527e42	+	1.98415e43i	5.70487e−5	+	0.000264145i
$573$	5.49451e46			0.710068
$574$	4.46536e46	−	4.76707e45i	0.560214	−	0.0598066i
$575$			1.21146e47i			1.47556i
$576$	1.05713e47	−	7.84004e46i	1.25011	−	0.927120i
$577$	1.28742e47			1.47819			0.739095	−	0.673601i	$-0.235253\pi$
$577$	1.28742e47			1.47819			0.739095	+	0.673601i	$0.235253\pi$
$578$	−7.20600e44	−	6.74993e45i	−0.00803380	−	0.0752533i
$579$			1.74215e47i			1.88603i
$580$	1.72368e46	−	3.72273e45i	0.181210	−	0.0391368i
$581$	9.11107e46			0.930197
$582$	−1.79143e47	+	1.91247e46i	−1.77627	+	0.189629i
$583$		−	3.28766e47i		−	3.16608i
$584$	−1.43538e45	−	4.34504e45i	−0.0134260	−	0.0406420i
$585$	−3.64560e42			−3.31222e−5
$586$	1.37738e46	+	1.29021e47i	0.121561	+	1.13868i
$587$		−	9.45338e46i		−	0.810475i	−0.914211	−	0.405237i	$-0.867189\pi$
$587$		−	9.45338e46i		−	0.810475i	0.914211	−	0.405237i	$-0.132811\pi$
$588$	−4.21019e45	−	1.94939e46i	−0.0350660	−	0.162362i
$589$	−2.75557e46			−0.222973
$590$	−1.88069e46	+	2.00777e45i	−0.147854	+	0.0157844i
$591$			1.69814e47i			1.29714i
$592$	−2.76143e46	+	1.25116e46i	−0.204958	+	0.0928632i
$593$	−1.51004e47			−1.08908			−0.544538	−	0.838736i	$-0.683295\pi$
$593$	−1.51004e47			−1.08908			−0.544538	+	0.838736i	$0.683295\pi$
$594$	2.20642e46	+	2.06677e47i	0.154639	+	1.44852i
$595$		−	2.06325e46i		−	0.140528i
$596$	4.81473e45	−	1.03986e45i	0.0318703	−	0.00688318i
$597$	3.69502e47			2.37713
$598$	3.93770e43	−	4.20376e42i	0.000246220	−	2.62856e-5i
$599$			5.03057e46i			0.305746i	0.988246	+	0.152873i	$0.0488526\pi$
$599$			5.03057e46i			0.305746i	−0.988246	+	0.152873i	$0.951147\pi$
$600$	−2.52702e47	+	8.34798e46i	−1.49293	+	0.493185i
$601$	−2.70134e47			−1.55136			−0.775681	−	0.631126i	$-0.782593\pi$
$601$	−2.70134e47			−1.55136			−0.775681	+	0.631126i	$0.782593\pi$
$602$	−1.34063e46	−	1.25578e47i	−0.0748459	−	0.701089i
$603$		−	2.67758e47i		−	1.45327i
$604$	1.34281e46	+	6.21746e46i	0.0708578	+	0.328084i
$605$	4.22694e46			0.216863
$606$	2.03144e47	−	2.16870e46i	1.01337	−	0.108184i
$607$		−	3.84708e47i		−	1.86605i	−0.359811	−	0.933025i	$-0.617159\pi$
$607$		−	3.84708e47i		−	1.86605i	0.359811	−	0.933025i	$-0.382841\pi$
$608$	2.09550e47	−	1.23278e47i	0.988387	−	0.581464i
$609$	−5.26493e47			−2.41490
$610$	1.70257e45	+	1.59482e46i	0.00759449	+	0.0711384i
$611$			4.50229e43i			0.000195314i
$612$	−3.73966e47	+	8.07673e46i	−1.57782	+	0.340770i
$613$	−2.58221e47			−1.05965			−0.529825	−	0.848107i	$-0.677743\pi$
$613$	−2.58221e47			−1.05965			−0.529825	+	0.848107i	$0.677743\pi$
$614$	1.84542e47	−	1.97011e46i	0.736602	−	0.0786372i
$615$		−	2.84774e46i		−	0.110567i
$616$	1.42894e47	+	4.32555e47i	0.539686	+	1.63369i
$617$	3.30657e47			1.21487			0.607436	−	0.794369i	$-0.292198\pi$
$617$	3.30657e47			1.21487			0.607436	+	0.794369i	$0.292198\pi$
$618$	−4.03186e46	−	3.77668e47i	−0.144112	−	1.34991i
$619$			5.99556e46i			0.208492i	0.994552	+	0.104246i	$0.0332429\pi$
$619$			5.99556e46i			0.208492i	−0.994552	+	0.104246i	$0.966757\pi$
$620$	1.56462e45	+	7.24444e45i	0.00529358	+	0.0245102i
$621$	4.05492e47			1.33483
$622$	6.31290e46	−	6.73944e45i	0.202205	−	0.0215868i
$623$			4.45818e47i			1.38951i
$624$	3.59029e43	+	7.92411e43i	0.000108891	+	0.000240332i
$625$	3.22002e47			0.950384
$626$	−6.06958e45	−	5.68544e46i	−0.0174339	−	0.163305i
$627$			1.07405e48i			3.00245i
$628$	−3.90473e47	+	8.43323e46i	−1.06237	+	0.229446i
$629$	8.81277e46			0.233374
$630$	−8.13517e46	+	8.68484e45i	−0.209690	+	0.0223858i
$631$		−	6.07308e47i		−	1.52374i	−0.647732	−	0.761869i	$-0.724282\pi$
$631$		−	6.07308e47i		−	1.52374i	0.647732	−	0.761869i	$-0.275718\pi$
$632$	−9.02093e46	+	2.98005e46i	−0.220324	+	0.0727835i
$633$	2.07295e46			0.0492862
$634$	6.54543e46	+	6.13116e47i	0.151503	+	1.41914i
$635$			3.50167e46i			0.0789081i
$636$	−2.97448e47	−	1.37723e48i	−0.652589	−	3.02160i
$637$	8.02574e42			1.71441e−5
$638$	1.12541e48	−	1.20145e47i	2.34078	−	0.249893i
$639$		−	4.78427e47i		−	0.968950i
$640$	−4.43082e46	−	4.80914e46i	−0.0873825	−	0.0948435i
$641$	2.41109e47			0.463048			0.231524	−	0.972829i	$-0.425629\pi$
$641$	2.41109e47			0.463048			0.231524	+	0.972829i	$0.425629\pi$
$642$	−6.58129e46	−	6.16476e47i	−0.123088	−	1.15298i
$643$			5.40041e47i			0.983648i	0.870695	+	0.491824i	$0.163670\pi$
$643$			5.40041e47i			0.983648i	−0.870695	+	0.491824i	$0.836330\pi$
$644$	8.68684e47	−	1.87614e47i	1.54100	−	0.332817i
$645$	−8.00863e46			−0.138370
$646$	−7.02746e47	+	7.50228e46i	−1.18262	+	0.126253i
$647$			4.36128e47i			0.714893i	0.933934	+	0.357446i	$0.116352\pi$
$647$			4.36128e47i			0.714893i	−0.933934	+	0.357446i	$0.883648\pi$
$648$	−2.63356e46	−	7.97209e46i	−0.0420503	−	0.127291i
$649$	−1.21393e48			−1.88814
$650$	−1.13690e43	−	1.06494e44i	−1.72264e−5	−	0.000161362i
$651$		−	2.21279e47i		−	0.326635i
$652$	1.48490e47	+	6.87534e47i	0.213544	+	0.988746i
$653$	−1.00735e48			−1.41142			−0.705708	−	0.708503i	$-0.749371\pi$
$653$	−1.00735e48			−1.41142			−0.705708	+	0.708503i	$0.749371\pi$
$654$	−1.18842e47	+	1.26872e46i	−0.162237	+	0.0173198i
$655$			3.14969e46i			0.0418954i
$656$	−3.76853e47	+	1.70746e47i	−0.488435	+	0.221302i
$657$	5.27466e46			0.0666167
$658$	1.07257e47	+	1.00469e48i	0.132003	+	1.23649i
$659$			3.61108e47i			0.433097i	0.976272	+	0.216549i	$0.0694800\pi$
$659$			3.61108e47i			0.433097i	−0.976272	+	0.216549i	$0.930520\pi$
$660$	2.82369e47	−	6.09846e46i	0.330043	−	0.0712809i
$661$	8.55205e47			0.974194			0.487097	−	0.873348i	$-0.338056\pi$
$661$	8.55205e47			0.974194			0.487097	+	0.873348i	$0.338056\pi$
$662$	−1.15622e48	+	1.23435e47i	−1.28368	+	0.137041i
$663$		−	2.52888e44i		−	0.000273652i
$664$	−7.97037e47	+	2.63300e47i	−0.840662	+	0.277711i
$665$	−1.51131e47			−0.155377
$666$	−3.70956e46	−	3.47478e47i	−0.0371758	−	0.348229i
$667$		−	2.20801e48i		−	2.15706i
$668$	−2.30759e47	−	1.06845e48i	−0.219765	−	1.01755i
$669$	2.68372e47			0.249168
$670$	−1.32282e47	+	1.41220e46i	−0.119737	+	0.0127828i
$671$			1.02941e48i			0.908455i
$672$	9.89947e47	+	1.68274e48i	0.851793	+	1.44790i
$673$	7.02961e47			0.589760			0.294880	−	0.955534i	$-0.404720\pi$
$673$	7.02961e47			0.589760			0.294880	+	0.955534i	$0.404720\pi$
$674$	−9.34315e46	−	8.75182e47i	−0.0764320	−	0.715946i
$675$		−	1.09665e48i		−	0.874788i
$676$	1.25659e48	−	2.71392e47i	0.977463	−	0.211107i
$677$	2.16196e48			1.63999			0.819995	−	0.572371i	$-0.193976\pi$
$677$	2.16196e48			1.63999			0.819995	+	0.572371i	$0.193976\pi$
$678$	−3.23090e47	+	3.44921e46i	−0.239012	+	0.0255161i
$679$		−	1.62707e48i		−	1.17387i
$680$	5.96256e46	+	1.80493e47i	0.0419548	+	0.127002i
$681$	3.35056e47			0.229941
$682$	5.04956e46	+	4.72997e47i	0.0338002	+	0.316610i
$683$		−	1.85000e48i		−	1.20787i	−0.797034	−	0.603935i	$-0.793599\pi$
$683$		−	1.85000e48i		−	1.20787i	0.797034	−	0.603935i	$-0.206401\pi$
$684$	5.91613e47	+	2.73927e48i	0.376777	+	1.74454i
$685$	2.87476e46			0.0178592
$686$	−1.54480e48	+	1.64918e47i	−0.936189	+	0.0999445i
$687$			4.42077e48i			2.61357i
$688$	4.80185e47	+	1.05981e48i	0.276952	+	0.611261i
$689$	5.67015e44			0.000319057
$690$	−5.98246e46	−	5.60383e47i	−0.0328432	−	0.307645i
$691$		−	1.23154e48i		−	0.659663i	−0.944040	−	0.329832i	$-0.893008\pi$
$691$		−	1.23154e48i		−	0.659663i	0.944040	−	0.329832i	$-0.106992\pi$
$692$	−1.91259e47	+	4.13070e46i	−0.0999579	+	0.0215884i
$693$	−5.25100e48			−2.67779
$694$	1.20282e48	−	1.28409e47i	0.598535	−	0.0638976i
$695$			4.96248e47i			0.240967i
$696$	4.60576e48	−	1.52151e48i	2.18245	−	0.720969i
$697$	1.20268e48			0.556152
$698$	6.54456e46	+	6.13036e47i	0.0295351	+	0.276658i
$699$			7.22379e47i			0.318166i
$700$	−5.07399e47	−	2.34934e48i	−0.218114	−	1.00990i
$701$	−1.29352e48			−0.542707			−0.271354	−	0.962480i	$-0.587471\pi$
$701$	−1.29352e48			−0.542707			−0.271354	+	0.962480i	$0.587471\pi$
$702$	−3.56452e44	+	3.80536e43i	−0.000145972	+	1.55835e-5i
$703$		−	6.45528e47i		−	0.258032i
$704$	−2.50007e48	−	3.37105e48i	−0.975478	−	1.31531i
$705$	6.40730e47			0.244040
$706$	3.66860e47	+	3.43641e48i	0.136402	+	1.27769i
$707$			1.84506e48i			0.669699i
$708$	−5.08527e48	+	1.09829e48i	−1.80198	+	0.389181i
$709$	2.28154e48			0.789299			0.394650	−	0.918832i	$-0.370866\pi$
$709$	2.28154e48			0.789299			0.394650	+	0.918832i	$0.370866\pi$
$710$	−2.36361e47	+	2.52331e46i	−0.0798332	+	0.00852272i
$711$		−	1.09510e48i		−	0.361134i
$712$	−1.28836e48	−	3.90002e48i	−0.414838	−	1.25576i
$713$	9.28001e47			0.291760
$714$	−6.02450e47	−	5.64321e48i	−0.184949	−	1.73243i
$715$			1.16253e44i			3.48499e-5i
$716$	9.43709e46	+	4.36953e47i	0.0276259	+	0.127913i
$717$	−3.17405e48			−0.907379
$718$	−5.84750e48	+	6.24260e47i	−1.63251	+	0.174281i
$719$			4.96265e48i			1.35308i	0.736408	+	0.676538i	$0.236521\pi$
$719$			4.96265e48i			1.35308i	−0.736408	+	0.676538i	$0.763479\pi$
$720$	6.86567e47	−	3.11072e47i	0.182823	−	0.0828341i
$721$	3.43017e48			0.892107
$722$	1.31641e47	+	1.23309e48i	0.0334394	+	0.313230i
$723$			7.15024e48i			1.77407i
$724$	2.66101e48	−	5.74711e47i	0.644898	−	0.139282i
$725$	−5.97153e48			−1.41364
$726$	1.15611e49	−	1.23423e48i	2.67348	−	0.285412i
$727$		−	5.83611e48i		−	1.31837i	−0.751980	−	0.659186i	$-0.770901\pi$
$727$		−	5.83611e48i		−	1.31837i	0.751980	−	0.659186i	$-0.229099\pi$
$728$	−7.46018e44	+	2.46446e44i	−0.000164633	+	5.43861e-5i
$729$	7.56508e48			1.63097
$730$	−2.78195e45	−	2.60587e46i	−0.000585949	−	0.00548864i
$731$		−	3.38227e48i		−	0.696006i
$732$	9.31344e47	+	4.31228e48i	0.187250	+	0.866999i
$733$	1.58029e48			0.310434			0.155217	−	0.987880i	$-0.450392\pi$
$733$	1.58029e48			0.310434			0.155217	+	0.987880i	$0.450392\pi$
$734$	7.99794e47	−	8.53834e46i	0.153513	−	0.0163885i
$735$		−	1.14216e47i		−	0.0214211i
$736$	−7.05707e48	+	4.15165e48i	−1.29331	+	0.760848i
$737$	−8.53840e48			−1.52908
$738$	−5.06245e47	−	4.74204e48i	−0.0885936	−	0.829865i
$739$			5.27868e48i			0.902754i	0.892333	+	0.451377i	$0.149067\pi$
$739$			5.27868e48i			0.902754i	−0.892333	+	0.451377i	$0.850933\pi$
$740$	−1.69710e47	+	3.66532e46i	−0.0283641	+	0.00612593i
$741$	−1.85239e45			−0.000302567
$742$	1.26530e49	−	1.35079e48i	2.01988	−	0.215636i
$743$		−	5.35628e48i		−	0.835705i	−0.908515	−	0.417853i	$-0.862783\pi$
$743$		−	5.35628e48i		−	0.835705i	0.908515	−	0.417853i	$-0.137217\pi$
$744$	6.39471e47	+	1.93575e48i	0.0975171	+	0.295195i
$745$	2.82099e46			0.00420479
$746$	5.55951e47	+	5.20765e48i	0.0809984	+	0.758720i
$747$		−	9.67562e48i		−	1.37793i
$748$	2.57555e48	+	1.19252e49i	0.358544	+	1.66012i
$749$	5.59915e48			0.761959
$750$	−3.05672e48	+	3.26326e47i	−0.406644	+	0.0434120i
$751$			1.28099e49i			1.66597i	0.553296	+	0.832984i	$0.313370\pi$
$751$			1.28099e49i			1.66597i	−0.553296	+	0.832984i	$0.686630\pi$
$752$	−3.84172e48	−	8.47904e48i	−0.488452	−	1.07806i
$753$	1.17769e49			1.46391
$754$	2.07212e44	+	1.94097e45i	2.51826e−5	+	0.000235888i
$755$			3.64285e47i			0.0432856i
$756$	−7.86357e48	+	1.69833e48i	−0.913585	+	0.197311i
$757$	−1.42894e49			−1.62325			−0.811624	−	0.584181i	$-0.801416\pi$
$757$	−1.42894e49			−1.62325			−0.811624	+	0.584181i	$0.801416\pi$
$758$	−1.23434e49	+	1.31774e48i	−1.37107	+	0.146371i
$759$		−	3.61710e49i		−	3.92871i
$760$	1.32210e48	−	4.36753e47i	0.140421	−	0.0463879i
$761$	8.09903e48			0.841189			0.420595	−	0.907249i	$-0.361821\pi$
$761$	8.09903e48			0.841189			0.420595	+	0.907249i	$0.361821\pi$
$762$	1.02246e48	+	9.57743e48i	0.103851	+	0.972780i
$763$		−	1.07939e48i		−	0.107216i
$764$	−9.65112e47	−	4.46863e48i	−0.0937542	−	0.434098i
$765$	−2.19110e48			−0.208169
$766$	−7.47502e47	+	7.98009e46i	−0.0694582	+	0.00741513i
$767$		−	2.09364e45i		−	0.000190274i
$768$	−1.35230e49	−	1.18597e49i	−1.20208	−	1.05423i
$769$	3.72506e48			0.323881			0.161940	−	0.986801i	$-0.448225\pi$
$769$	3.72506e48			0.323881			0.161940	+	0.986801i	$0.448225\pi$
$770$	2.76947e47	+	2.59419e48i	0.0235534	+	0.220627i
$771$			3.13908e49i			2.61143i
$772$	1.41687e49	−	3.06009e48i	1.15302	−	0.249023i
$773$	−1.84833e49			−1.47139			−0.735695	−	0.677313i	$-0.763144\pi$
$773$	−1.84833e49			−1.47139			−0.735695	+	0.677313i	$0.763144\pi$
$774$	−1.33359e49	+	1.42370e48i	−1.03855	+	0.110872i
$775$		−	2.50976e48i		−	0.191207i
$776$	4.70205e48	+	1.42336e49i	0.350460	+	1.06088i
$777$	5.18373e48			0.377994
$778$	1.44391e46	+	1.35252e47i	0.00103012	+	0.00964920i
$779$		−	8.80954e48i		−	0.614917i
$780$	1.05179e44	+	4.86995e44i	7.18323e−6	+	3.32596e-5i
$781$	−1.52563e49			−1.01949
$782$	2.36665e49	−	2.52656e48i	1.54746	−	0.165202i
$783$			1.99875e49i			1.27882i
$784$	−1.51147e48	+	6.84821e47i	−0.0946293	+	0.0428750i
$785$	−2.28781e48			−0.140164
$786$	9.19682e47	+	8.61475e48i	0.0551384	+	0.516487i
$787$		−	3.82522e47i		−	0.0224433i	−0.999937	−	0.0112216i	$-0.996428\pi$
$787$		−	3.82522e47i		−	0.0224433i	0.999937	−	0.0112216i	$-0.00357203\pi$
$788$	1.38108e49	−	2.98278e48i	0.792999	−	0.171268i
$789$	1.25657e49			0.706120
$790$	−5.41017e47	+	5.77572e46i	−0.0297544	+	0.00317648i
$791$		−	2.93447e48i		−	0.157954i
$792$	4.59358e49	−	1.51748e49i	2.42004	−	0.799457i
$793$	−1.77539e45			−9.15482e−5
$794$	−3.61290e48	−	3.38424e49i	−0.182351	−	1.70810i
$795$		−	8.06932e48i		−	0.398654i
$796$	−6.49031e48	−	3.00513e49i	−0.313865	−	1.45325i
$797$	1.48526e48			0.0703090			0.0351545	−	0.999382i	$-0.488808\pi$
$797$	1.48526e48			0.0703090			0.0351545	+	0.999382i	$0.488808\pi$
$798$	−4.13360e49	+	4.41290e48i	−1.91549	+	0.204491i
$799$			2.70598e49i			1.22752i
$800$	1.12281e49	+	1.90857e49i	0.498626	+	0.847577i
$801$	4.73442e49			2.05833
$802$	−2.40340e48	−	2.25129e49i	−0.102297	−	0.958225i
$803$		−	1.68201e48i		−	0.0700914i
$804$	−3.57682e49	+	7.72504e48i	−1.45930	+	0.315172i
$805$	5.08969e48			0.203311
$806$	−8.15767e44	+	8.70886e43i	−3.19059e−5	+	3.40617e-6i
$807$			2.33671e49i			0.894861i
$808$	−5.33201e48	−	1.61406e49i	−0.199939	−	0.605237i
$809$	2.53140e49			0.929470			0.464735	−	0.885450i	$-0.346150\pi$
$809$	2.53140e49			0.929470			0.464735	+	0.885450i	$0.346150\pi$
$810$	−5.10419e46	−	4.78114e47i	−0.00183519	−	0.0171904i
$811$			8.28010e48i			0.291529i	0.989319	+	0.145764i	$0.0465641\pi$
$811$			8.28010e48i			0.291529i	−0.989319	+	0.145764i	$0.953436\pi$
$812$	9.24786e48	+	4.28192e49i	0.318852	+	1.47634i
$813$	−7.08845e49			−2.39338
$814$	−1.10806e49	+	1.18292e48i	−0.366393	+	0.0391149i
$815$			4.02831e48i			0.130450i
$816$	2.15785e49	+	4.76258e49i	0.684366	+	1.51046i
$817$	−2.47748e49			−0.769548
$818$	5.58211e47	+	5.22882e48i	0.0169821	+	0.159073i
$819$		−	9.05628e45i		−	0.000269851i
$820$	−2.31604e48	+	5.00207e47i	−0.0675945	+	0.0145987i
$821$	4.68995e49			1.34071			0.670354	−	0.742041i	$-0.266142\pi$
$821$	4.68995e49			1.34071			0.670354	+	0.742041i	$0.266142\pi$
$822$	7.86277e48	−	8.39403e47i	0.220168	−	0.0235044i
$823$		−	9.64741e48i		−	0.264614i	−0.991209	−	0.132307i	$-0.957761\pi$
$823$		−	9.64741e48i		−	0.264614i	0.991209	−	0.132307i	$-0.0422385\pi$
$824$	−3.00072e49	+	9.91282e48i	−0.806237	+	0.266339i
$825$	−9.78238e49			−2.57470
$826$	−4.98762e48	−	4.67195e49i	−0.128598	−	1.20459i
$827$		−	4.84407e49i		−	1.22354i	−0.791037	−	0.611768i	$-0.790459\pi$
$827$		−	4.84407e49i		−	1.22354i	0.791037	−	0.611768i	$-0.209541\pi$
$828$	−1.99239e49	−	9.22511e49i	−0.493014	−	2.28274i
$829$	1.73752e49			0.421213			0.210606	−	0.977571i	$-0.432456\pi$
$829$	1.73752e49			0.421213			0.210606	+	0.977571i	$0.432456\pi$
$830$	−4.78011e48	+	5.10309e47i	−0.113530	+	0.0121201i
$831$		−	9.89973e49i		−	2.30359i
$832$	5.81397e45	−	4.31182e45i	0.000132549	−	9.83024e-5i
$833$	4.82367e48			0.107749
$834$	1.44900e49	+	1.35729e50i	0.317136	+	2.97064i
$835$		−	6.26016e48i		−	0.134250i
$836$	8.73513e49	−	1.88657e49i	1.83554	−	0.396429i
$837$	−8.40052e48			−0.172971
$838$	−1.89150e49	+	2.01930e48i	−0.381643	+	0.0407430i
$839$			5.78499e49i			1.14380i	0.820324	+	0.571899i	$0.193793\pi$
$839$			5.78499e49i			1.14380i	−0.820324	+	0.571899i	$0.806207\pi$
$840$	3.50722e48	+	1.06167e49i	0.0679541	+	0.205704i
$841$	5.61710e49			1.06655
$842$	8.70100e48	+	8.15031e49i	0.161906	+	1.51659i
$843$		−	1.15806e50i		−	2.11185i
$844$	−3.64114e47	−	1.68591e48i	−0.00650752	−	0.0301309i
$845$	7.36246e48			0.128961
$846$	1.06694e50	−	1.13903e49i	1.83165	−	0.195541i
$847$			1.05004e50i			1.76680i
$848$	−1.06785e50	+	4.83823e49i	−1.76108	+	0.797916i
$849$	4.68224e49			0.756872
$850$	−6.83304e48	−	6.40058e49i	−0.108266	−	1.01414i
$851$			2.17396e49i			0.337636i
$852$	−6.39104e49	+	1.38030e49i	−0.972967	+	0.210136i
$853$	−3.57759e49			−0.533896			−0.266948	−	0.963711i	$-0.586015\pi$
$853$	−3.57759e49			−0.533896			−0.266948	+	0.963711i	$0.586015\pi$
$854$	−3.96179e49	+	4.22947e48i	−0.579572	+	0.0618732i
$855$			1.60496e49i			0.230165i
$856$	−4.89814e49	+	1.61809e49i	−0.688616	+	0.227483i
$857$	9.83494e49			1.35550			0.677748	−	0.735295i	$-0.262956\pi$
$857$	9.83494e49			1.35550			0.677748	+	0.735295i	$0.262956\pi$
$858$	3.39448e45	+	3.17964e46i	4.58658e−5	+	0.000429630i
$859$			5.91395e49i			0.783419i	0.920089	+	0.391709i	$0.128116\pi$
$859$			5.91395e49i			0.783419i	−0.920089	+	0.391709i	$0.871884\pi$
$860$	1.40672e48	+	6.51335e48i	0.0182698	+	0.0845922i
$861$	7.07426e49			0.900799
$862$	9.85746e49	−	1.05235e49i	1.23067	−	0.131382i
$863$		−	9.08630e49i		−	1.11225i	−0.831098	−	0.556127i	$-0.812287\pi$
$863$		−	9.08630e49i		−	1.11225i	0.831098	−	0.556127i	$-0.187713\pi$
$864$	6.38826e49	−	3.75819e49i	0.766741	−	0.451071i
$865$	−1.12060e48			−0.0131879
$866$	−4.30636e48	−	4.03381e49i	−0.0496943	−	0.465491i
$867$		−	1.06936e49i		−	0.121004i
$868$	−1.79964e49	+	3.88677e48i	−0.199687	+	0.0431274i
$869$	−3.49210e49			−0.379971
$870$	2.76224e49	−	2.94887e48i	0.294736	−	0.0314651i
$871$		−	1.47260e46i		−	0.000154091i
$872$	3.11931e48	+	9.44248e48i	0.0320094	+	0.0968959i
$873$	−1.72789e50			−1.73890
$874$	−1.85068e49	−	1.73355e50i	−0.182658	−	1.71097i
$875$		−	2.77627e49i		−	0.268736i
$876$	−1.52178e48	−	7.04611e48i	−0.0144472	−	0.0668929i
$877$	−8.02895e49			−0.747593			−0.373797	−	0.927511i	$-0.621944\pi$
$877$	−8.02895e49			−0.747593			−0.373797	+	0.927511i	$0.621944\pi$
$878$	6.02327e49	−	6.43024e48i	0.550080	−	0.0587247i
$879$			2.04402e50i			1.83094i
$880$	−9.91964e48	−	2.18936e49i	−0.0871547	−	0.192359i
$881$	−1.23832e50			−1.06719			−0.533595	−	0.845740i	$-0.679159\pi$
$881$	−1.23832e50			−1.06719			−0.533595	+	0.845740i	$0.679159\pi$
$882$	−2.03042e48	−	1.90192e49i	−0.0171641	−	0.160778i
$883$			1.63234e50i			1.35356i	0.736183	+	0.676782i	$0.236626\pi$
$883$			1.63234e50i			1.35356i	−0.736183	+	0.676782i	$0.763374\pi$
$884$	−2.05672e46	+	4.44199e45i	−0.000167296	+	3.61318e-5i
$885$	−2.97950e49			−0.237743
$886$	−6.90190e49	+	7.36824e48i	−0.540250	+	0.0576754i
$887$		−	8.69859e49i		−	0.667955i	−0.942581	−	0.333978i	$-0.891609\pi$
$887$		−	8.69859e49i		−	0.667955i	0.942581	−	0.333978i	$-0.108391\pi$
$888$	−4.53473e49	+	1.49804e49i	−0.341611	+	0.112851i
$889$	−8.69872e49			−0.642873
$890$	−2.49702e48	−	2.33898e49i	−0.0181047	−	0.169588i
$891$		−	3.08608e49i		−	0.219526i
$892$	−4.71396e48	−	2.18264e49i	−0.0328991	−	0.152328i
$893$	1.98211e50			1.35723
$894$	7.71570e48	−	8.23703e47i	0.0518367	−	0.00553392i
$895$			2.56014e48i			0.0168761i
$896$	1.19467e50	−	1.10069e50i	0.772701	−	0.711915i
$897$	6.23833e46			0.000395910
$898$	8.52402e48	+	7.98453e49i	0.0530819	+	0.497223i
$899$			4.57430e49i			0.279518i
$900$	−2.49491e50	+	5.38839e49i	−1.49601	+	0.323099i
$901$	3.40790e50			2.00524
$902$	−1.51217e50	+	1.61434e49i	−0.873150	+	0.0932146i
$903$		−	1.98948e50i		−	1.12732i
$904$	8.48030e48	+	2.56708e49i	0.0471572	+	0.142750i
$905$	1.55911e49			0.0850844
$906$	1.06368e49	+	9.96359e49i	0.0569681	+	0.533625i
$907$			3.67748e50i			1.93298i	0.256709	+	0.966489i	$0.417362\pi$
$907$			3.67748e50i			1.93298i	−0.256709	+	0.966489i	$0.582638\pi$
$908$	−5.88528e48	−	2.72498e49i	−0.0303604	−	0.140574i
$909$	1.95938e50			0.992049
$910$	−4.47413e45	+	4.77644e44i	−2.22334e−5	+	2.37356e-6i
$911$		−	2.34408e50i		−	1.14330i	−0.820498	−	0.571649i	$-0.806304\pi$
$911$		−	2.34408e50i		−	1.14330i	0.820498	−	0.571649i	$-0.193696\pi$
$912$	3.48855e50	−	1.58061e50i	1.67006	−	0.756678i
$913$	−3.08541e50			−1.44981
$914$	2.29990e49	+	2.15434e50i	0.106077	+	0.993638i
$915$			2.52660e49i			0.114387i
$916$	3.59537e50	−	7.76510e49i	1.59780	−	0.345084i
$917$	−7.82436e49			−0.341326
$918$	−2.14236e50	+	2.28711e49i	−0.917418	+	0.0979405i
$919$		−	3.55594e50i		−	1.49483i	−0.664360	−	0.747413i	$-0.731296\pi$
$919$		−	3.55594e50i		−	1.49483i	0.664360	−	0.747413i	$-0.268704\pi$
$920$	−4.45246e49	+	1.47086e49i	−0.183741	+	0.0606987i
$921$	2.92362e50			1.18442
$922$	1.24492e49	+	1.16613e50i	0.0495125	+	0.463788i
$923$		−	2.63123e46i		−	0.000102738i
$924$	1.51496e50	+	7.01451e50i	0.580734	+	2.68889i
$925$	5.87944e49			0.221272
$926$	−1.19947e50	+	1.28051e49i	−0.443203	+	0.0473149i
$927$		−	3.64272e50i		−	1.32151i
$928$	−2.04643e50	−	3.47857e50i	−0.728922	−	1.23904i
$929$	−4.92212e50			−1.72141			−0.860707	−	0.509101i	$-0.829978\pi$
$929$	−4.92212e50			−1.72141			−0.860707	+	0.509101i	$0.829978\pi$
$930$	1.23938e48	+	1.16094e49i	0.00425592	+	0.0398656i
$931$		−	3.53329e49i		−	0.119134i
$932$	5.87505e49	−	1.26886e49i	0.194509	−	0.0420091i
$933$	1.00012e50			0.325137
$934$	3.99879e50	−	4.26898e49i	1.27653	−	0.136278i
$935$			6.98709e49i			0.219027i
$936$	2.61716e46	+	7.92244e46i	8.05641e−5	+	0.000243876i
$937$	1.06210e50			0.321066			0.160533	−	0.987030i	$-0.448679\pi$
$937$	1.06210e50			0.321066			0.160533	+	0.987030i	$0.448679\pi$
$938$	−3.50814e49	−	3.28611e50i	−0.104143	−	0.975514i
$939$		−	9.00718e49i		−	0.262587i
$940$	−1.12544e49	−	5.21100e49i	−0.0322219	−	0.149193i
$941$	−5.70086e50			−1.60294			−0.801469	−	0.598036i	$-0.795948\pi$
$941$	−5.70086e50			−1.60294			−0.801469	+	0.598036i	$0.795948\pi$
$942$	−6.25740e50	+	6.68020e49i	−1.72794	+	0.184469i
$943$			2.96681e50i			0.804621i
$944$	1.78646e50	+	3.94289e50i	0.475849	+	1.05025i
$945$	−4.60732e49			−0.120534
$946$	4.53997e49	+	4.25263e50i	0.116655	+	1.09272i
$947$		−	4.92884e50i		−	1.24393i	−0.783046	−	0.621964i	$-0.786335\pi$
$947$		−	4.92884e50i		−	1.24393i	0.783046	−	0.621964i	$-0.213665\pi$
$948$	−1.46288e50	+	3.15944e49i	−0.362632	+	0.0783193i
$949$	2.90093e45			7.06336e−6
$950$	−4.68837e50	+	5.00514e49i	−1.12130	+	0.119706i
$951$			9.71333e50i			2.28191i
$952$	−4.48375e50	+	1.48120e50i	−1.03470	+	0.341810i
$953$	−5.46419e50			−1.23864			−0.619322	−	0.785137i	$-0.712593\pi$
$953$	−5.46419e50			−1.23864			−0.619322	+	0.785137i	$0.712593\pi$
$954$	−1.43449e50	−	1.34370e51i	−0.319429	−	2.99212i
$955$		−	2.61821e49i		−	0.0572725i
$956$	5.57524e49	+	2.58143e50i	0.119806	+	0.554723i
$957$	1.78294e51			3.76386
$958$	−7.07507e49	+	7.55311e48i	−0.146729	+	0.0156644i
$959$			7.14137e49i			0.145501i
$960$	−6.13624e49	−	8.27399e49i	−0.122826	−	0.165617i
$961$	4.89283e50			0.962193
$962$	−2.04016e45	−	1.91104e46i	−3.94174e−6	−	3.69227e-5i
$963$		−	5.94609e50i		−	1.12872i
$964$	5.81523e50	−	1.25594e50i	1.08457	−	0.234240i
$965$	8.30156e49			0.152123
$966$	1.39208e51	−	1.48614e50i	2.50642	−	0.267577i
$967$			4.63299e50i			0.819618i	0.912171	+	0.409809i	$0.134405\pi$
$967$			4.63299e50i			0.819618i	−0.912171	+	0.409809i	$0.865595\pi$
$968$	−3.03450e50	−	9.18576e50i	−0.527480	−	1.59674i
$969$	−1.11333e51			−1.90160
$970$	9.11318e48	+	8.53640e49i	0.0152950	+	0.143270i
$971$			1.06097e51i			1.74975i	0.484347	+	0.874876i	$0.339057\pi$
$971$			1.06097e51i			1.74975i	−0.484347	+	0.874876i	$0.660943\pi$
$972$	−1.43803e50	−	6.65832e50i	−0.233046	−	1.07904i
$973$	−1.23276e51			−1.96318
$974$	2.09656e50	−	2.23822e49i	0.328099	−	0.0350268i
$975$		−	1.68714e47i		−	0.000259462i
$976$	3.34355e50	−	1.51491e50i	0.505313	−	0.228949i
$977$	8.99382e50			1.33579			0.667893	−	0.744258i	$-0.267197\pi$
$977$	8.99382e50			1.33579			0.667893	+	0.744258i	$0.267197\pi$
$978$	1.17623e50	+	1.10179e51i	0.171685	+	1.60819i
$979$		−	1.50974e51i		−	2.16569i
$980$	−9.28909e48	+	2.00621e48i	−0.0130957	+	0.00282835i
$981$	−1.14627e50			−0.158823
$982$	8.23494e50	−	8.79135e49i	1.12141	−	0.119718i
$983$			1.13523e51i			1.51941i	0.650268	+	0.759705i	$0.274657\pi$
$983$			1.13523e51i			1.51941i	−0.650268	+	0.759705i	$0.725343\pi$
$984$	−6.18857e50	+	2.04438e50i	−0.814092	+	0.268934i
$985$	8.09184e49			0.104624
$986$	1.24539e50	+	1.16657e51i	0.158270	+	1.48253i
$987$			1.59168e51i			1.98822i
$988$	3.25372e46	+	1.50653e47i	3.99496e−5	+	0.000184973i
$989$	8.34348e50			1.00696
$990$	2.75493e50	−	2.94107e49i	0.326823	−	0.0348905i
$991$		−	2.99413e50i		−	0.349155i	−0.984643	−	0.174577i	$-0.944144\pi$
$991$		−	2.99413e50i		−	0.349155i	0.984643	−	0.174577i	$-0.0558559\pi$
$992$	1.46200e50	−	8.60090e49i	0.167591	−	0.0985929i
$993$	−1.83175e51			−2.06410
$994$	−6.26831e49	−	5.87159e50i	−0.0694356	−	0.650410i
$995$		−	1.76073e50i		−	0.191734i
$996$	−1.29251e51	+	2.79150e50i	−1.38365	+	0.298833i
$997$	1.56974e51			1.65200			0.826002	−	0.563667i	$-0.190610\pi$
$997$	1.56974e51			1.65200			0.826002	+	0.563667i	$0.190610\pi$
$998$	−7.60141e50	+	8.11502e49i	−0.786457	+	0.0839596i
$999$		−	1.96793e50i		−	0.200169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.35.b.a.3.7	✓	16
4.3	odd	2	inner	4.35.b.a.3.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.35.b.a.3.7	✓	16	1.1	even	1	trivial
4.35.b.a.3.8	yes	16	4.3	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-13913.7 - 130331. i) q^{2} -2.06478e8i q^{3} +(-1.67927e10 + 3.62680e9i) q^{4} -9.83896e10 q^{5} +(-2.69106e13 + 2.87289e12i) q^{6} -2.44416e14i q^{7} +(7.06335e14 + 2.13815e15i) q^{8} -2.59561e16 q^{9} +O(q^{10})\)	\(q+(-13913.7 - 130331. i) q^{2} -2.06478e8i q^{3} +(-1.67927e10 + 3.62680e9i) q^{4} -9.83896e10 q^{5} +(-2.69106e13 + 2.87289e12i) q^{6} -2.44416e14i q^{7} +(7.06335e14 + 2.13815e15i) q^{8} -2.59561e16 q^{9} +(1.36897e15 + 1.28233e16i) q^{10} +8.27701e17i q^{11} +(7.48855e17 + 3.46732e18i) q^{12} -1.42752e15 q^{13} +(-3.18551e19 + 3.40074e18i) q^{14} +2.03153e19i q^{15} +(2.68841e20 - 1.21807e20i) q^{16} -8.57973e20 q^{17} +(3.61146e20 + 3.38289e21i) q^{18} +6.28457e21i q^{19} +(1.65223e21 - 3.56839e20i) q^{20} -5.04666e22 q^{21} +(1.07875e23 - 1.15164e22i) q^{22} -2.11647e23i q^{23} +(4.41482e23 - 1.45843e23i) q^{24} -5.72396e23 q^{25} +(1.98621e19 + 1.86050e20i) q^{26} +1.91589e24i q^{27} +(8.86447e23 + 4.10440e24i) q^{28} +1.04325e25 q^{29} +(2.64772e24 - 2.82662e23i) q^{30} +4.38466e24i q^{31} +(-1.96159e25 - 3.33436e25i) q^{32} +1.70902e26 q^{33} +(1.19376e25 + 1.11821e26i) q^{34} +2.40480e25i q^{35} +(4.35872e26 - 9.41374e25i) q^{36} -1.02716e26 q^{37} +(8.19077e26 - 8.74420e25i) q^{38} +2.94751e23i q^{39} +(-6.94960e25 - 2.10372e26i) q^{40} -1.40177e27 q^{41} +(7.02179e26 + 6.57738e27i) q^{42} +3.94217e27i q^{43} +(-3.00190e27 - 1.38993e28i) q^{44} +2.55381e27 q^{45} +(-2.75843e28 + 2.94481e27i) q^{46} -3.15393e28i q^{47} +(-2.51506e28 - 5.55097e28i) q^{48} -5.62217e27 q^{49} +(7.96418e27 + 7.46012e28i) q^{50} +1.77153e29i q^{51} +(2.39718e25 - 5.17732e24i) q^{52} -3.97204e29 q^{53} +(2.49700e29 - 2.66572e28i) q^{54} -8.14372e28i q^{55} +(5.22598e29 - 1.72639e29i) q^{56} +1.29763e30 q^{57} +(-1.45155e29 - 1.35968e30i) q^{58} +1.46663e30i q^{59} +(-7.36795e28 - 3.41149e29i) q^{60} +1.24369e30 q^{61} +(5.71459e29 - 6.10070e28i) q^{62} +6.34408e30i q^{63} +(-4.07278e30 + 3.02050e30i) q^{64} +1.40453e26 q^{65} +(-2.37789e30 - 2.22739e31i) q^{66} +1.03158e31i q^{67} +(1.44077e31 - 3.11169e30i) q^{68} -4.37005e31 q^{69} +(3.13421e30 - 3.34598e29i) q^{70} +1.84322e31i q^{71} +(-1.83337e31 - 5.54980e31i) q^{72} -2.03215e30 q^{73} +(1.42917e30 + 1.33872e31i) q^{74} +1.18187e32i q^{75} +(-2.27929e31 - 1.05535e32i) q^{76} +2.02303e32 q^{77} +(3.84153e28 - 4.10109e27i) q^{78} +4.21903e31i q^{79} +(-2.64511e31 + 1.19846e31i) q^{80} -3.72849e31 q^{81} +(1.95039e31 + 1.82695e32i) q^{82} +3.72769e32i q^{83} +(8.47469e32 - 1.83032e32i) q^{84} +8.44156e31 q^{85} +(5.13788e32 - 5.48503e31i) q^{86} -2.15409e33i q^{87} +(-1.76975e33 + 5.84634e32i) q^{88} -1.82401e33 q^{89} +(-3.55330e31 - 3.32841e32i) q^{90} +3.48908e29i q^{91} +(7.67601e32 + 3.55412e33i) q^{92} +9.05337e32 q^{93} +(-4.11056e33 + 4.38830e32i) q^{94} -6.18337e32i q^{95} +(-6.88472e33 + 4.05026e33i) q^{96} +6.65697e33 q^{97} +(7.82254e31 + 7.32745e32i) q^{98} -2.14839e34i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots - 67\!\cdots\!80 q^{9}+O(q^{10}) \) 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9	\( 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots + 16\!\cdots\!32 q^{98}+O(q^{100}) \) 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9 - 45113792455239160 * q^10 + 2389205919902175360 * q^12 - 5233507036411659616 * q^13 - 78584294183795706432 * q^14 + 495182112183820124416 * q^16 - 603670905919309938144 * q^17 - 3049682100893194226508 * q^18 - 33058393758449688290400 * q^20 + 51436061805005728413696 * q^21 + 71660876143050404765280 * q^22 + 216144869785928938234368 * q^24 + 1224730607199300816400560 * q^25 - 2068583291215840445568696 * q^26 + 891252510406495618671360 * q^28 - 4086289565288128397679456 * q^29 + 29601064663371600024444480 * q^30 + 20026414012547463259849728 * q^32 + 73954448514753271238568960 * q^33 + 46288216238217191722231976 * q^34 + 569062048300724903070378384 * q^36 + 950385175701396416644593056 * q^37 - 123498782719680108073563360 * q^38 - 3250024485723791435879459200 * q^40 + 469238845433510127731349792 * q^41 + 2352670327884382399711157760 * q^42 + 7327222247557584897899214720 * q^44 - 24427097188106605438098250080 * q^45 - 19562783684402230406331003072 * q^46 + 10576141603633237485164267520 * q^48 - 5662649722408510114314091760 * q^49 + 20191932196464263485504736220 * q^50 - 299155663662273783907276503904 * q^52 - 287274278887575172234950512736 * q^53 + 6047252470624543429578889536 * q^54 + 957626384837555513184792726528 * q^56 + 2791286265941381406754467578880 * q^57 - 314499391713380785247660833336 * q^58 + 1103184540481814815474103512320 * q^60 - 7360215904797065436447249778528 * q^61 + 6668101684324825273374014288640 * q^62 - 4672502276277215477475812569088 * q^64 + 7390500022468645317433010287680 * q^65 - 12460359580334220374288279205120 * q^66 + 3201090312765007118305938045984 * q^68 - 20909099675706939600670541666304 * q^69 - 13302319794857519494110175324800 * q^70 - 776423968147266229824274003392 * q^72 - 21322365514881309087265291408096 * q^73 + 60200090281780873185690769101576 * q^74 - 104909582027053727863743869884800 * q^76 + 31510097566037837419459121448960 * q^77 + 173718506967281862717403400063040 * q^78 + 360511559214548868760655536888320 * q^80 - 262819454584631237298859074129648 * q^81 - 127799686177535642546403976474264 * q^82 - 481860976739335096182940424300544 * q^84 + 2066519418228326883252673443837760 * q^85 + 680164732953303409567751182232928 * q^86 - 1868588957981221169228370505105920 * q^88 - 2487774705888249186282098457137376 * q^89 + 2710136859758550244207319911170120 * q^90 - 5719642193953545223478177490435840 * q^92 - 4648987096869411453766406983557120 * q^93 - 174301665834847119752293250078592 * q^94 - 1356265248520894619800195113541632 * q^96 + 7119191713926779638291321673063456 * q^97 + 16929214407930779244441537548523732 * q^98

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