LMFDB - Embedded newform 2.46.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,46,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 46, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 46);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 46 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

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:	yes
Analytic conductor:	$25.6511452149$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 200169772272162 $ x^2 - x - 200169772272162
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.41481e7$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.19430e6 q^{2} +8.42595e10 q^{3} +1.75922e13 q^{4} +9.15156e15 q^{5} +3.53410e17 q^{6} +2.40505e18 q^{7} +7.37870e19 q^{8} +4.14534e21 q^{9} +O(q^{10})$	\(q+4.19430e6 q^{2} +8.42595e10 q^{3} +1.75922e13 q^{4} +9.15156e15 q^{5} +3.53410e17 q^{6} +2.40505e18 q^{7} +7.37870e19 q^{8} +4.14534e21 q^{9} +3.83844e22 q^{10} -2.26758e22 q^{11} +1.48231e24 q^{12} -1.41709e25 q^{13} +1.00875e25 q^{14} +7.71106e26 q^{15} +3.09485e26 q^{16} -8.28250e27 q^{17} +1.73868e28 q^{18} -8.92967e28 q^{19} +1.60996e29 q^{20} +2.02648e29 q^{21} -9.51092e28 q^{22} +5.64660e28 q^{23} +6.21725e30 q^{24} +5.53294e31 q^{25} -5.94372e31 q^{26} +1.00356e32 q^{27} +4.23100e31 q^{28} +9.80921e32 q^{29} +3.23425e33 q^{30} +3.29486e33 q^{31} +1.29807e33 q^{32} -1.91065e33 q^{33} -3.47393e34 q^{34} +2.20099e34 q^{35} +7.29256e34 q^{36} -7.74992e34 q^{37} -3.74538e35 q^{38} -1.19403e36 q^{39} +6.75266e35 q^{40} +5.05178e35 q^{41} +8.49967e35 q^{42} -5.76861e36 q^{43} -3.98917e35 q^{44} +3.79364e37 q^{45} +2.36836e35 q^{46} +2.26489e37 q^{47} +2.60770e37 q^{48} -1.01223e38 q^{49} +2.32068e38 q^{50} -6.97879e38 q^{51} -2.49298e38 q^{52} +4.94854e38 q^{53} +4.20922e38 q^{54} -2.07519e38 q^{55} +1.77461e38 q^{56} -7.52409e39 q^{57} +4.11428e39 q^{58} +6.55445e39 q^{59} +1.35654e40 q^{60} -9.04607e38 q^{61} +1.38196e40 q^{62} +9.96975e39 q^{63} +5.44452e39 q^{64} -1.29686e41 q^{65} -8.01385e39 q^{66} +5.14474e40 q^{67} -1.45707e41 q^{68} +4.75780e39 q^{69} +9.23164e40 q^{70} -3.63418e41 q^{71} +3.05872e41 q^{72} +1.16814e41 q^{73} -3.25055e41 q^{74} +4.66202e42 q^{75} -1.57092e42 q^{76} -5.45364e40 q^{77} -5.00814e42 q^{78} +6.51808e41 q^{79} +2.83227e42 q^{80} -3.79074e42 q^{81} +2.11887e42 q^{82} +7.53712e42 q^{83} +3.56502e42 q^{84} -7.57978e43 q^{85} -2.41953e43 q^{86} +8.26519e43 q^{87} -1.67318e42 q^{88} +8.95725e42 q^{89} +1.59117e44 q^{90} -3.40818e43 q^{91} +9.93361e41 q^{92} +2.77623e44 q^{93} +9.49964e43 q^{94} -8.17205e44 q^{95} +1.09375e44 q^{96} -3.53206e44 q^{97} -4.24559e44 q^{98} -9.39990e43 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8388608 q^{2} + 59861217192 q^{3} + 35184372088832 q^{4} + 43\!\cdots\!00 q^{5}+ \cdots + 17\!\cdots\!46 q^{9}+O(q^{10}) $ 2 * q + 8388608 * q^2 + 59861217192 * q^3 + 35184372088832 * q^4 + 4397113991405100 * q^5 + 251076142713274368 * q^6 + 7902493193471299024 * q^7 + 147573952589676412928 * q^8 + 1786304036785022132346 * q^9	$ 2 q + 8388608 q^{2} + 59861217192 q^{3} + 35184372088832 q^{4} + 43\!\cdots\!00 q^{5}+ \cdots - 60\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 8388608 * q^2 + 59861217192 * q^3 + 35184372088832 * q^4 + 4397113991405100 * q^5 + 251076142713274368 * q^6 + 7902493193471299024 * q^7 + 147573952589676412928 * q^8 + 1786304036785022132346 * q^9 + 18442832802606376550400 * q^10 + 193382581450547160321144 * q^11 + 1053089669686857534799872 * q^12 - 2312522953149074458311428 * q^13 + 33145458811349443381559296 * q^14 + 887105821761177992792895600 * q^15 + 618970019642690137449562112 * q^16 - 6570195850083651340869113436 * q^17 + 7492302166703565469787357184 * q^18 - 90017706781963544559646145720 * q^19 + 77354847395303135590848921600 * q^20 + 68520038925423887971291504704 * q^21 + 811105334908355756723615563776 * q^22 + 6994240792574843290864127840112 * q^23 + 4416978213926265305641242329088 * q^24 + 49512459978770470802589886478750 * q^25 - 9699424272484975596793455706112 * q^26 + 229991950494949775668061619638160 * q^27 + 139022130474278215773047681449984 * q^28 + 2213533364393458041951352752067740 * q^29 + 3720791496636195899883213186662400 * q^30 + 9650213165135522593230027496907584 * q^31 + 2596148429267413814265248164610048 * q^32 - 7182093662425694531112429563503776 * q^33 - 27557398734789259153612685961068544 * q^34 - 4127376326123989419154702521376800 * q^35 + 31424992947013431464190991386279936 * q^36 - 191012116158864196077428143000334996 * q^37 - 377561627626416822800702067577978880 * q^38 - 1483358494573103280616285570941860688 * q^39 + 324449745849509522821239995262566400 * q^40 - 1859015758492235069891763906253181676 * q^41 + 287393873345061115013539843346006016 * q^42 - 804011321867909724415330269683219528 * q^43 + 3402022350627456183848887653607931904 * q^44 + 49152292604663223059510333785715634300 * q^45 + 29335972133259835514244574856293122048 * q^46 + 36113177408029567180393469011774996704 * q^47 + 18526149390583790276512285265863114752 * q^48 - 178007647936693771635782071066946504526 * q^49 + 207670308938796900769185971217367040000 * q^50 - 739656360671997562398082418319435614256 * q^51 - 40682334023780823085533178441968386048 * q^52 - 666709323646290352590173897241305644788 * q^53 + 964656157928769823883653523494813040640 * q^54 - 1234757427854121513410799121046863930800 * q^55 + 583101077936787017529756982496393691136 * q^56 - 7506503344295441602576163948903964954720 * q^57 + 9284231844408938639188726653408730152960 * q^58 - 146711135631672307609725431066231780520 * q^59 + 15606130657507183007663760601670850969600 * q^60 + 16810546706420180245915601401744048614364 * q^61 + 40475927679380582954875077250389467201536 * q^62 - 2998939361959904611357533830735407560048 * q^63 + 10889035741470030830827987437816582766592 * q^64 - 186066269875585688065791914119720830029400 * q^65 - 30123884176686740274622987767922141691904 * q^66 - 82849230292769990365217317623577369391576 * q^67 - 115584107742921528825034303177253638373376 * q^68 - 164511673341122762782732560374725517322048 * q^69 - 17311471034167153316718245404220797747200 * q^70 + 110021245082064036014734112205046755165264 * q^71 + 131805973617630223643982131935439480684544 * q^72 + 1370836674469116973463675637713005724981332 * q^73 - 801162882853588733064341169898877075062784 * q^74 + 4803946793204919951439280730048232066935000 * q^75 - 1583608244999990585540275884850587128299520 * q^76 + 1133232767290964910783519570187778061966528 * q^77 - 6221656467221945382302009035343730051121152 * q^78 + 3371318639385645567529086614760361521517600 * q^79 + 1360840866815581189607218197089763301785600 * q^80 + 15703043630901782235731006317467167823282 * q^81 - 7797277231907015522587304919053344916373504 * q^82 - 9535514832176774675296631302412724036501048 * q^83 + 1205417272546683214945750219105526416932864 * q^84 - 83938909157693870911847863922509210121293800 * q^85 - 3372267903355861228754117411453406399168512 * q^86 + 52578297788213642356327012703383395390657840 * q^87 + 14269115953326141981742124881078363216674816 * q^88 + 67091763129503006680067356236410639491425780 * q^89 + 206159657480909375131396431038762227807027200 * q^90 + 31109166335206640196214146530166173423725664 * q^91 + 123043985262420261136738077298049666978414592 * q^92 + 122563730951297540335159337178889500300996864 * q^93 + 151469644455208045742993048649963915775574016 * q^94 - 813776794885228423572147822920801774025474000 * q^95 + 77704302493523153891936584139750725656772608 * q^96 - 829992687576057861045815591338653044052747836 * q^97 - 746618189771466433147047283804377991719419904 * q^98 - 603689043964735474143738491805547270151997288 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.19430e6	0.707107
$2$	4.19430e6	0.707107
$3$	8.42595e10	1.55021	0.775105	−	0.631833i	$-0.217697\pi$
$3$	8.42595e10	1.55021	0.775105	+	0.631833i	$0.217697\pi$
$4$	1.75922e13	0.500000
$5$	9.15156e15	1.71660	0.858302	−	0.513145i	$-0.171520\pi$
$5$	9.15156e15	1.71660	0.858302	+	0.513145i	$0.171520\pi$
$6$	3.53410e17	1.09616
$7$	2.40505e18	0.232497	0.116249	−	0.993220i	$-0.462913\pi$
$7$	2.40505e18	0.232497	0.116249	+	0.993220i	$0.462913\pi$
$8$	7.37870e19	0.353553
$9$	4.14534e21	1.40315
$10$	3.83844e22	1.21382
$11$	−2.26758e22	−0.0839899	−0.0419950	−	0.999118i	$-0.513371\pi$
$11$	−2.26758e22	−0.0839899	−0.0419950	+	0.999118i	$0.513371\pi$
$12$	1.48231e24	0.775105
$13$	−1.41709e25	−1.22369	−0.611847	−	0.790976i	$-0.709573\pi$
$13$	−1.41709e25	−1.22369	−0.611847	+	0.790976i	$0.709573\pi$
$14$	1.00875e25	0.164400
$15$	7.71106e26	2.66110
$16$	3.09485e26	0.250000
$17$	−8.28250e27	−1.71025	−0.855127	−	0.518418i	$-0.826521\pi$
$17$	−8.28250e27	−1.71025	−0.855127	+	0.518418i	$0.826521\pi$
$18$	1.73868e28	0.992177
$19$	−8.92967e28	−1.50966	−0.754831	−	0.655920i	$-0.772281\pi$
$19$	−8.92967e28	−1.50966	−0.754831	+	0.655920i	$0.772281\pi$
$20$	1.60996e29	0.858302
$21$	2.02648e29	0.360419
$22$	−9.51092e28	−0.0593898
$23$	5.64660e28	0.0129691	0.00648456	−	0.999979i	$-0.497936\pi$
$23$	5.64660e28	0.0129691	0.00648456	+	0.999979i	$0.497936\pi$
$24$	6.21725e30	0.548082
$25$	5.53294e31	1.94673
$26$	−5.94372e31	−0.865282
$27$	1.00356e32	0.624966
$28$	4.23100e31	0.116249
$29$	9.80921e32	1.22371	0.611856	−	0.790969i	$-0.290423\pi$
$29$	9.80921e32	1.22371	0.611856	+	0.790969i	$0.290423\pi$
$30$	3.23425e33	1.88168
$31$	3.29486e33	0.916640	0.458320	−	0.888787i	$-0.348451\pi$
$31$	3.29486e33	0.916640	0.458320	+	0.888787i	$0.348451\pi$
$32$	1.29807e33	0.176777
$33$	−1.91065e33	−0.130202
$34$	−3.47393e34	−1.20933
$35$	2.20099e34	0.399106
$36$	7.29256e34	0.701575
$37$	−7.74992e34	−0.402493	−0.201247	−	0.979541i	$-0.564499\pi$
$37$	−7.74992e34	−0.402493	−0.201247	+	0.979541i	$0.564499\pi$
$38$	−3.74538e35	−1.06749
$39$	−1.19403e36	−1.89698
$40$	6.75266e35	0.606911
$41$	5.05178e35	0.260500	0.130250	−	0.991481i	$-0.458422\pi$
$41$	5.05178e35	0.260500	0.130250	+	0.991481i	$0.458422\pi$
$42$	8.49967e35	0.254855
$43$	−5.76861e36	−1.01866	−0.509332	−	0.860570i	$-0.670108\pi$
$43$	−5.76861e36	−1.01866	−0.509332	+	0.860570i	$0.670108\pi$
$44$	−3.98917e35	−0.0419950
$45$	3.79364e37	2.40865
$46$	2.36836e35	0.00917056
$47$	2.26489e37	0.540562	0.270281	−	0.962781i	$-0.412883\pi$
$47$	2.26489e37	0.540562	0.270281	+	0.962781i	$0.412883\pi$
$48$	2.60770e37	0.387552
$49$	−1.01223e38	−0.945945
$50$	2.32068e38	1.37655
$51$	−6.97879e38	−2.65125
$52$	−2.49298e38	−0.611847
$53$	4.94854e38	0.791170	0.395585	−	0.918429i	$-0.370542\pi$
$53$	4.94854e38	0.791170	0.395585	+	0.918429i	$0.370542\pi$
$54$	4.20922e38	0.441918
$55$	−2.07519e38	−0.144177
$56$	1.77461e38	0.0822002
$57$	−7.52409e39	−2.34029
$58$	4.11428e39	0.865295
$59$	6.55445e39	0.938353	0.469176	−	0.883104i	$-0.344551\pi$
$59$	6.55445e39	0.938353	0.469176	+	0.883104i	$0.344551\pi$
$60$	1.35654e40	1.33055
$61$	−9.04607e38	−0.0611700	−0.0305850	−	0.999532i	$-0.509737\pi$
$61$	−9.04607e38	−0.0611700	−0.0305850	+	0.999532i	$0.509737\pi$
$62$	1.38196e40	0.648163
$63$	9.96975e39	0.326228
$64$	5.44452e39	0.125000
$65$	−1.29686e41	−2.10060
$66$	−8.01385e39	−0.0920667
$67$	5.14474e40	0.421386	0.210693	−	0.977552i	$-0.432428\pi$
$67$	5.14474e40	0.421386	0.210693	+	0.977552i	$0.432428\pi$
$68$	−1.45707e41	−0.855127
$69$	4.75780e39	0.0201049
$70$	9.23164e40	0.282210
$71$	−3.63418e41	−0.807408	−0.403704	−	0.914890i	$-0.632277\pi$
$71$	−3.63418e41	−0.807408	−0.403704	+	0.914890i	$0.632277\pi$
$72$	3.05872e41	0.496088
$73$	1.16814e41	0.138909	0.0694547	−	0.997585i	$-0.477874\pi$
$73$	1.16814e41	0.138909	0.0694547	+	0.997585i	$0.477874\pi$
$74$	−3.25055e41	−0.284606
$75$	4.66202e42	3.01784
$76$	−1.57092e42	−0.754831
$77$	−5.45364e40	−0.0195274
$78$	−5.00814e42	−1.34137
$79$	6.51808e41	0.131072	0.0655360	−	0.997850i	$-0.479124\pi$
$79$	6.51808e41	0.131072	0.0655360	+	0.997850i	$0.479124\pi$
$80$	2.83227e42	0.429151
$81$	−3.79074e42	−0.434321
$82$	2.11887e42	0.184201
$83$	7.53712e42	0.498825	0.249413	−	0.968397i	$-0.419762\pi$
$83$	7.53712e42	0.498825	0.249413	+	0.968397i	$0.419762\pi$
$84$	3.56502e42	0.180210
$85$	−7.57978e43	−2.93583
$86$	−2.41953e43	−0.720304
$87$	8.26519e43	1.89701
$88$	−1.67318e42	−0.0296949
$89$	8.95725e42	0.123282	0.0616410	−	0.998098i	$-0.480367\pi$
$89$	8.95725e42	0.123282	0.0616410	+	0.998098i	$0.480367\pi$
$90$	1.59117e44	1.70317
$91$	−3.40818e43	−0.284505
$92$	9.93361e41	0.00648456
$93$	2.77623e44	1.42098
$94$	9.49964e43	0.382235
$95$	−8.17205e44	−2.59149
$96$	1.09375e44	0.274041
$97$	−3.53206e44	−0.700913	−0.350457	−	0.936579i	$-0.613974\pi$
$97$	−3.53206e44	−0.700913	−0.350457	+	0.936579i	$0.613974\pi$
$98$	−4.24559e44	−0.668884
$99$	−9.39990e43	−0.117850
$100$	9.73365e44	0.973365
$101$	2.10202e45	1.68037	0.840185	−	0.542299i	$-0.182446\pi$
$101$	2.10202e45	1.68037	0.840185	+	0.542299i	$0.182446\pi$
$102$	−2.92712e45	−1.87472
$103$	−1.21899e45	−0.626847	−0.313424	−	0.949613i	$-0.601476\pi$
$103$	−1.21899e45	−0.626847	−0.313424	+	0.949613i	$0.601476\pi$
$104$	−1.04563e45	−0.432641
$105$	1.85455e45	0.618698
$106$	2.07557e45	0.559442
$107$	7.34757e45	1.60328	0.801639	−	0.597809i	$-0.203962\pi$
$107$	7.34757e45	1.60328	0.801639	+	0.597809i	$0.203962\pi$
$108$	1.76547e45	0.312483
$109$	−3.31318e45	−0.476594	−0.238297	−	0.971192i	$-0.576589\pi$
$109$	−3.31318e45	−0.476594	−0.238297	+	0.971192i	$0.576589\pi$
$110$	−8.70398e44	−0.101949
$111$	−6.53004e45	−0.623949
$112$	7.44326e44	0.0581243
$113$	1.55110e46	0.991685	0.495843	−	0.868412i	$-0.334859\pi$
$113$	1.55110e46	0.991685	0.495843	+	0.868412i	$0.334859\pi$
$114$	−3.15583e46	−1.65484
$115$	5.16752e44	0.0222629
$116$	1.72565e46	0.611856
$117$	−5.87433e46	−1.71703
$118$	2.74914e46	0.663516
$119$	−1.99198e46	−0.397630
$120$	5.68976e46	0.940840
$121$	−7.23763e46	−0.992946
$122$	−3.79420e45	−0.0432538
$123$	4.25660e46	0.403830
$124$	5.79638e46	0.458320
$125$	2.46247e47	1.62516
$126$	4.18162e46	0.230678
$127$	2.31561e47	1.06926	0.534628	−	0.845088i	$-0.320452\pi$
$127$	2.31561e47	1.06926	0.534628	+	0.845088i	$0.320452\pi$
$128$	2.28360e46	0.0883883
$129$	−4.86060e47	−1.57914
$130$	−5.43943e47	−1.48535
$131$	−2.30986e47	−0.530861	−0.265431	−	0.964130i	$-0.585514\pi$
$131$	−2.30986e47	−0.530861	−0.265431	+	0.964130i	$0.585514\pi$
$132$	−3.36125e46	−0.0651010
$133$	−2.14763e47	−0.350992
$134$	2.15786e47	0.297965
$135$	9.18410e47	1.07282
$136$	−6.11141e47	−0.604666
$137$	9.92834e47	0.833036	0.416518	−	0.909128i	$-0.363250\pi$
$137$	9.92834e47	0.833036	0.416518	+	0.909128i	$0.363250\pi$
$138$	1.99556e46	0.0142163
$139$	−2.03965e48	−1.23516	−0.617579	−	0.786509i	$-0.711886\pi$
$139$	−2.03965e48	−1.23516	−0.617579	+	0.786509i	$0.711886\pi$
$140$	3.87203e47	0.199553
$141$	1.90838e48	0.837984
$142$	−1.52428e48	−0.570924
$143$	3.21337e47	0.102778
$144$	1.28292e48	0.350787
$145$	8.97696e48	2.10063
$146$	4.89955e47	0.0982238
$147$	−8.52897e48	−1.46641
$148$	−1.36338e48	−0.201247
$149$	−6.52261e48	−0.827428	−0.413714	−	0.910407i	$-0.635769\pi$
$149$	−6.52261e48	−0.827428	−0.413714	+	0.910407i	$0.635769\pi$
$150$	1.95539e49	2.13393
$151$	−1.08241e49	−1.01721	−0.508607	−	0.860999i	$-0.669839\pi$
$151$	−1.08241e49	−1.01721	−0.508607	+	0.860999i	$0.669839\pi$
$152$	−6.58894e48	−0.533746
$153$	−3.43338e49	−2.39974
$154$	−2.28742e47	−0.0138080
$155$	3.01531e49	1.57351
$156$	−2.10057e49	−0.948491
$157$	1.45314e49	0.568285	0.284142	−	0.958782i	$-0.408291\pi$
$157$	1.45314e49	0.568285	0.284142	+	0.958782i	$0.408291\pi$
$158$	2.73388e48	0.0926819
$159$	4.16961e49	1.22648
$160$	1.18794e49	0.303456
$161$	1.35803e47	0.00301529
$162$	−1.58995e49	−0.307111
$163$	8.24708e48	0.138701	0.0693504	−	0.997592i	$-0.477907\pi$
$163$	8.24708e48	0.138701	0.0693504	+	0.997592i	$0.477907\pi$
$164$	8.88719e48	0.130250
$165$	−1.74854e49	−0.223505
$166$	3.16130e49	0.352723
$167$	1.00649e50	0.981041	0.490520	−	0.871430i	$-0.336807\pi$
$167$	1.00649e50	0.981041	0.490520	+	0.871430i	$0.336807\pi$
$168$	1.49528e49	0.127428
$169$	6.67083e49	0.497427
$170$	−3.17919e50	−2.07595
$171$	−3.70166e50	−2.11828
$172$	−1.01482e50	−0.509332
$173$	−3.40672e49	−0.150072	−0.0750360	−	0.997181i	$-0.523907\pi$
$173$	−3.40672e49	−0.150072	−0.0750360	+	0.997181i	$0.523907\pi$
$174$	3.46667e50	1.34139
$175$	1.33070e50	0.452609
$176$	−7.01782e48	−0.0209975
$177$	5.52275e50	1.45464
$178$	3.75694e49	0.0871735
$179$	−8.12350e50	−1.66169	−0.830845	−	0.556504i	$-0.812142\pi$
$179$	−8.12350e50	−1.66169	−0.830845	+	0.556504i	$0.812142\pi$
$180$	6.67384e50	1.20433
$181$	1.82409e50	0.290588	0.145294	−	0.989389i	$-0.453587\pi$
$181$	1.82409e50	0.290588	0.145294	+	0.989389i	$0.453587\pi$
$182$	−1.42949e50	−0.201176
$183$	−7.62217e49	−0.0948264
$184$	4.16646e48	0.00458528
$185$	−7.09239e50	−0.690921
$186$	1.16444e51	1.00479
$187$	1.87812e50	0.143644
$188$	3.98444e50	0.270281
$189$	2.41360e50	0.145303
$190$	−3.42760e51	−1.83246
$191$	3.10542e51	1.47526	0.737632	−	0.675203i	$-0.235944\pi$
$191$	3.10542e51	1.47526	0.737632	+	0.675203i	$0.235944\pi$
$192$	4.58752e50	0.193776
$193$	1.19600e50	0.0449461	0.0224731	−	0.999747i	$-0.492846\pi$
$193$	1.19600e50	0.0449461	0.0224731	+	0.999747i	$0.492846\pi$
$194$	−1.48145e51	−0.495620
$195$	−1.09273e52	−3.25637
$196$	−1.78073e51	−0.472973
$197$	2.88056e51	0.682317	0.341159	−	0.940006i	$-0.389181\pi$
$197$	2.88056e51	0.682317	0.341159	+	0.940006i	$0.389181\pi$
$198$	−3.94260e50	−0.0833328
$199$	9.35977e51	1.76633	0.883163	−	0.469066i	$-0.155409\pi$
$199$	9.35977e51	1.76633	0.883163	+	0.469066i	$0.155409\pi$
$200$	4.08259e51	0.688273
$201$	4.33493e51	0.653237
$202$	8.81649e51	1.18820
$203$	2.35916e51	0.284510
$204$	−1.22772e52	−1.32563
$205$	4.62317e51	0.447176
$206$	−5.11280e51	−0.443248
$207$	2.34071e50	0.0181976
$208$	−4.38569e51	−0.305923
$209$	2.02487e51	0.126796
$210$	7.77853e51	0.437485
$211$	−1.91731e52	−0.969030	−0.484515	−	0.874783i	$-0.661004\pi$
$211$	−1.91731e52	−0.969030	−0.484515	+	0.874783i	$0.661004\pi$
$212$	8.70556e51	0.395585
$213$	−3.06214e52	−1.25165
$214$	3.08179e52	1.13369
$215$	−5.27918e52	−1.74864
$216$	7.40493e51	0.220959
$217$	7.92430e51	0.213116
$218$	−1.38965e52	−0.337003
$219$	9.84271e51	0.215339
$220$	−3.65071e51	−0.0720887
$221$	1.17371e53	2.09283
$222$	−2.73890e52	−0.441198
$223$	−1.15767e53	−1.68549	−0.842745	−	0.538313i	$-0.819062\pi$
$223$	−1.15767e53	−1.68549	−0.842745	+	0.538313i	$0.819062\pi$
$224$	3.12193e51	0.0411001
$225$	2.29359e53	2.73155
$226$	6.50577e52	0.701227
$227$	−1.10597e53	−1.07935	−0.539675	−	0.841874i	$-0.681453\pi$
$227$	−1.10597e53	−1.07935	−0.539675	+	0.841874i	$0.681453\pi$
$228$	−1.32365e53	−1.17015
$229$	1.24444e53	0.996954	0.498477	−	0.866903i	$-0.333893\pi$
$229$	1.24444e53	0.996954	0.498477	+	0.866903i	$0.333893\pi$
$230$	2.16742e51	0.0157422
$231$	−4.59521e51	−0.0302716
$232$	7.23792e52	0.432647
$233$	−2.96954e53	−1.61132	−0.805660	−	0.592379i	$-0.798189\pi$
$233$	−2.96954e53	−1.61132	−0.805660	+	0.592379i	$0.798189\pi$
$234$	−2.46387e53	−1.21412
$235$	2.07273e53	0.927931
$236$	1.15307e53	0.469176
$237$	5.49210e52	0.203189
$238$	−8.35498e52	−0.281167
$239$	−4.48675e53	−1.37398	−0.686988	−	0.726669i	$-0.741068\pi$
$239$	−4.48675e53	−1.37398	−0.686988	+	0.726669i	$0.741068\pi$
$240$	2.38646e53	0.665274
$241$	6.98803e53	1.77407	0.887037	−	0.461699i	$-0.152760\pi$
$241$	6.98803e53	1.77407	0.887037	+	0.461699i	$0.152760\pi$
$242$	−3.03568e53	−0.702119
$243$	−6.15887e53	−1.29825
$244$	−1.59140e52	−0.0305850
$245$	−9.26345e53	−1.62381
$246$	1.78535e53	0.285551
$247$	1.26542e54	1.84736
$248$	2.43118e53	0.324081
$249$	6.35074e53	0.773284
$250$	1.03284e54	1.14916
$251$	1.09514e54	1.11381	0.556906	−	0.830576i	$-0.311988\pi$
$251$	1.09514e54	1.11381	0.556906	+	0.830576i	$0.311988\pi$
$252$	1.75390e53	0.163114
$253$	−1.28041e51	−0.00108928
$254$	9.71237e53	0.756078
$255$	−6.38668e54	−4.55115
$256$	9.57810e52	0.0625000
$257$	1.38122e54	0.825595	0.412797	−	0.910823i	$-0.364552\pi$
$257$	1.38122e54	0.825595	0.412797	+	0.910823i	$0.364552\pi$
$258$	−2.03868e54	−1.11662
$259$	−1.86389e53	−0.0935785
$260$	−2.28146e54	−1.05030
$261$	4.06625e54	1.71705
$262$	−9.68824e53	−0.375376
$263$	−1.51797e54	−0.539831	−0.269916	−	0.962884i	$-0.586996\pi$
$263$	−1.51797e54	−0.539831	−0.269916	+	0.962884i	$0.586996\pi$
$264$	−1.40981e53	−0.0460333
$265$	4.52869e54	1.35813
$266$	−9.00781e53	−0.248189
$267$	7.54733e53	0.191113
$268$	9.05072e53	0.210693
$269$	−2.86241e54	−0.612782	−0.306391	−	0.951906i	$-0.599121\pi$
$269$	−2.86241e54	−0.612782	−0.306391	+	0.951906i	$0.599121\pi$
$270$	3.85209e54	0.758598
$271$	4.33618e54	0.785776	0.392888	−	0.919586i	$-0.371476\pi$
$271$	4.33618e54	0.785776	0.392888	+	0.919586i	$0.371476\pi$
$272$	−2.56331e54	−0.427564
$273$	−2.87171e54	−0.441043
$274$	4.16425e54	0.589045
$275$	−1.25464e54	−0.163506
$276$	8.37000e52	0.0100524
$277$	2.02502e53	0.0224199	0.0112100	−	0.999937i	$-0.496432\pi$
$277$	2.02502e53	0.0224199	0.0112100	+	0.999937i	$0.496432\pi$
$278$	−8.55491e54	−0.873389
$279$	1.36583e55	1.28618
$280$	1.62405e54	0.141105
$281$	−4.10598e52	−0.00329249	−0.00164624	−	0.999999i	$-0.500524\pi$
$281$	−4.10598e52	−0.00329249	−0.00164624	+	0.999999i	$0.500524\pi$
$282$	8.00435e54	0.592544
$283$	−1.78570e54	−0.122071	−0.0610355	−	0.998136i	$-0.519440\pi$
$283$	−1.78570e54	−0.122071	−0.0610355	+	0.998136i	$0.519440\pi$
$284$	−6.39331e54	−0.403704
$285$	−6.88572e55	−4.01735
$286$	1.34779e54	0.0726750
$287$	1.21498e54	0.0605656
$288$	5.38096e54	0.248044
$289$	4.51467e55	1.92497
$290$	3.76521e55	1.48537
$291$	−2.97610e55	−1.08656
$292$	2.05502e54	0.0694547
$293$	−4.76796e54	−0.149214	−0.0746072	−	0.997213i	$-0.523770\pi$
$293$	−4.76796e54	−0.149214	−0.0746072	+	0.997213i	$0.523770\pi$
$294$	−3.57731e55	−1.03691
$295$	5.99835e55	1.61078
$296$	−5.71843e54	−0.142303
$297$	−2.27564e54	−0.0524909
$298$	−2.73578e55	−0.585080
$299$	−8.00176e53	−0.0158702
$300$	8.20152e55	1.50892
$301$	−1.38738e55	−0.236837
$302$	−4.53998e55	−0.719279
$303$	1.77115e56	2.60493
$304$	−2.76360e55	−0.377415
$305$	−8.27857e54	−0.105005
$306$	−1.44006e56	−1.69687
$307$	−3.49688e55	−0.382884	−0.191442	−	0.981504i	$-0.561316\pi$
$307$	−3.49688e55	−0.382884	−0.191442	+	0.981504i	$0.561316\pi$
$308$	−9.59414e53	−0.00976371
$309$	−1.02711e56	−0.971745
$310$	1.26471e56	1.11264
$311$	−2.01431e56	−1.64823	−0.824114	−	0.566424i	$-0.808327\pi$
$311$	−2.01431e56	−1.64823	−0.824114	+	0.566424i	$0.808327\pi$
$312$	−8.81042e55	−0.670684
$313$	3.35361e55	0.237556	0.118778	−	0.992921i	$-0.462102\pi$
$313$	3.35361e55	0.237556	0.118778	+	0.992921i	$0.462102\pi$
$314$	6.09492e55	0.401838
$315$	9.12388e55	0.560005
$316$	1.14667e55	0.0655360
$317$	−3.07131e56	−1.63489	−0.817447	−	0.576003i	$-0.804612\pi$
$317$	−3.07131e56	−1.63489	−0.817447	+	0.576003i	$0.804612\pi$
$318$	1.74886e56	0.867252
$319$	−2.22432e55	−0.102779
$320$	4.98258e55	0.214576
$321$	6.19102e56	2.48542
$322$	5.69601e53	0.00213213
$323$	7.39600e56	2.58191
$324$	−6.66873e55	−0.217160
$325$	−7.84069e56	−2.38220
$326$	3.45908e55	0.0980763
$327$	−2.79167e56	−0.738821
$328$	3.72756e55	0.0921007
$329$	5.44717e55	0.125679
$330$	−7.33392e55	−0.158042
$331$	−7.13132e56	−1.43562	−0.717811	−	0.696238i	$-0.754856\pi$
$331$	−7.13132e56	−1.43562	−0.717811	+	0.696238i	$0.754856\pi$
$332$	1.32594e56	0.249413
$333$	−3.21261e56	−0.564758
$334$	4.22151e56	0.693700
$335$	4.70824e56	0.723353
$336$	6.27165e55	0.0901049
$337$	−2.95209e56	−0.396695	−0.198347	−	0.980132i	$-0.563557\pi$
$337$	−2.95209e56	−0.396695	−0.198347	+	0.980132i	$0.563557\pi$
$338$	2.79795e56	0.351734
$339$	1.30695e57	1.53732
$340$	−1.33345e57	−1.46792
$341$	−7.47136e55	−0.0769885
$342$	−1.55259e57	−1.49785
$343$	−5.00802e56	−0.452427
$344$	−4.25648e56	−0.360152
$345$	4.35413e55	0.0345121
$346$	−1.42888e56	−0.106117
$347$	9.98119e56	0.694655	0.347327	−	0.937744i	$-0.387089\pi$
$347$	9.98119e56	0.694655	0.347327	+	0.937744i	$0.387089\pi$
$348$	1.45403e57	0.948505
$349$	2.34101e57	1.43163	0.715815	−	0.698290i	$-0.246055\pi$
$349$	2.34101e57	1.43163	0.715815	+	0.698290i	$0.246055\pi$
$350$	5.58135e56	0.320043
$351$	−1.42213e57	−0.764768
$352$	−2.94349e55	−0.0148475
$353$	3.60871e57	1.70774	0.853868	−	0.520490i	$-0.174251\pi$
$353$	3.60871e57	1.70774	0.853868	+	0.520490i	$0.174251\pi$
$354$	2.31641e57	1.02859
$355$	−3.32584e57	−1.38600
$356$	1.57578e56	0.0616410
$357$	−1.67843e57	−0.616409
$358$	−3.40724e57	−1.17499
$359$	−3.97739e57	−1.28817	−0.644085	−	0.764954i	$-0.722762\pi$
$359$	−3.97739e57	−1.28817	−0.644085	+	0.764954i	$0.722762\pi$
$360$	2.79921e57	0.851587
$361$	4.47516e57	1.27908
$362$	7.65078e56	0.205477
$363$	−6.09839e57	−1.53927
$364$	−5.99573e56	−0.142253
$365$	1.06903e57	0.238452
$366$	−3.19697e56	−0.0670524
$367$	−5.81690e57	−1.14737	−0.573687	−	0.819074i	$-0.694487\pi$
$367$	−5.81690e57	−1.14737	−0.573687	+	0.819074i	$0.694487\pi$
$368$	1.74754e55	0.00324228
$369$	2.09414e57	0.365521
$370$	−2.97476e57	−0.488555
$371$	1.19015e57	0.183945
$372$	4.88400e57	0.710492
$373$	−4.48758e57	−0.614559	−0.307280	−	0.951619i	$-0.599419\pi$
$373$	−4.48758e57	−0.614559	−0.307280	+	0.951619i	$0.599419\pi$
$374$	7.87742e56	0.101572
$375$	2.07487e58	2.51934
$376$	1.67119e57	0.191118
$377$	−1.39006e58	−1.49745
$378$	1.01234e57	0.102745
$379$	5.66691e57	0.541956	0.270978	−	0.962586i	$-0.412653\pi$
$379$	5.66691e57	0.541956	0.270978	+	0.962586i	$0.412653\pi$
$380$	−1.43764e58	−1.29575
$381$	1.95112e58	1.65757
$382$	1.30251e58	1.04317
$383$	2.00511e57	0.151414	0.0757071	−	0.997130i	$-0.475879\pi$
$383$	2.00511e57	0.151414	0.0757071	+	0.997130i	$0.475879\pi$
$384$	1.92415e57	0.137020
$385$	−4.99093e56	−0.0335209
$386$	5.01640e56	0.0317817
$387$	−2.39129e58	−1.42934
$388$	−6.21367e57	−0.350457
$389$	8.19212e57	0.436044	0.218022	−	0.975944i	$-0.430040\pi$
$389$	8.19212e57	0.436044	0.218022	+	0.975944i	$0.430040\pi$
$390$	−4.58323e58	−2.30260
$391$	−4.67680e56	−0.0221805
$392$	−7.46891e57	−0.334442
$393$	−1.94627e58	−0.822946
$394$	1.20819e58	0.482471
$395$	5.96506e57	0.224999
$396$	−1.65365e57	−0.0589252
$397$	4.87869e58	1.64254	0.821272	−	0.570536i	$-0.193265\pi$
$397$	4.87869e58	1.64254	0.821272	+	0.570536i	$0.193265\pi$
$398$	3.92577e58	1.24898
$399$	−1.80958e58	−0.544111
$400$	1.71236e58	0.486682
$401$	−3.28101e58	−0.881575	−0.440787	−	0.897612i	$-0.645301\pi$
$401$	−3.28101e58	−0.881575	−0.440787	+	0.897612i	$0.645301\pi$
$402$	1.81820e58	0.461908
$403$	−4.66912e58	−1.12169
$404$	3.69791e58	0.840185
$405$	−3.46912e58	−0.745557
$406$	9.89504e57	0.201179
$407$	1.75736e57	0.0338054
$408$	−5.14944e58	−0.937360
$409$	6.00632e58	1.03475	0.517374	−	0.855760i	$-0.326910\pi$
$409$	6.00632e58	1.03475	0.517374	+	0.855760i	$0.326910\pi$
$410$	1.93910e58	0.316201
$411$	8.36556e58	1.29138
$412$	−2.14447e58	−0.313424
$413$	1.57638e58	0.218164
$414$	9.81765e56	0.0128677
$415$	6.89764e58	0.856285
$416$	−1.83949e58	−0.216321
$417$	−1.71860e59	−1.91475
$418$	8.49294e57	0.0896585
$419$	−1.92350e58	−0.192432	−0.0962158	−	0.995361i	$-0.530674\pi$
$419$	−1.92350e58	−0.192432	−0.0962158	+	0.995361i	$0.530674\pi$
$420$	3.26255e58	0.309349
$421$	8.35122e58	0.750590	0.375295	−	0.926906i	$-0.377541\pi$
$421$	8.35122e58	0.750590	0.375295	+	0.926906i	$0.377541\pi$
$422$	−8.04179e58	−0.685208
$423$	9.38875e58	0.758489
$424$	3.65138e58	0.279721
$425$	−4.58266e59	−3.32940
$426$	−1.28435e59	−0.885052
$427$	−2.17562e57	−0.0142219
$428$	1.29260e59	0.801639
$429$	2.70757e58	0.159327
$430$	−2.21425e59	−1.23648
$431$	1.25796e59	0.666697	0.333349	−	0.942804i	$-0.391821\pi$
$431$	1.25796e59	0.666697	0.333349	+	0.942804i	$0.391821\pi$
$432$	3.10585e58	0.156242
$433$	3.89848e59	1.86173	0.930867	−	0.365358i	$-0.119054\pi$
$433$	3.89848e59	1.86173	0.930867	+	0.365358i	$0.119054\pi$
$434$	3.32369e58	0.150696
$435$	7.56394e59	3.25641
$436$	−5.82861e58	−0.238297
$437$	−5.04223e57	−0.0195790
$438$	4.12833e58	0.152267
$439$	−5.55747e59	−1.94727	−0.973634	−	0.228117i	$-0.926743\pi$
$439$	−5.55747e59	−1.94727	−0.973634	+	0.228117i	$0.926743\pi$
$440$	−1.53122e58	−0.0509744
$441$	−4.19603e59	−1.32730
$442$	4.92288e59	1.47985
$443$	1.32192e59	0.377678	0.188839	−	0.982008i	$-0.439528\pi$
$443$	1.32192e59	0.377678	0.188839	+	0.982008i	$0.439528\pi$
$444$	−1.14878e59	−0.311974
$445$	8.19728e58	0.211626
$446$	−4.85563e59	−1.19182
$447$	−5.49592e59	−1.28269
$448$	1.30943e58	0.0290622
$449$	2.37087e59	0.500455	0.250227	−	0.968187i	$-0.419495\pi$
$449$	2.37087e59	0.500455	0.250227	+	0.968187i	$0.419495\pi$
$450$	9.62003e59	1.93150
$451$	−1.14553e58	−0.0218794
$452$	2.72872e59	0.495843
$453$	−9.12037e59	−1.57690
$454$	−4.63878e59	−0.763215
$455$	−3.11901e59	−0.488383
$456$	−5.55180e59	−0.827418
$457$	−9.26977e56	−0.00131509	−0.000657544	−	1.00000i	$-0.500209\pi$
$457$	−9.26977e56	−0.00131509	−0.000657544		1.00000i	$0.500209\pi$
$458$	5.21955e59	0.704953
$459$	−8.31195e59	−1.06885
$460$	9.09080e57	0.0111314
$461$	3.50613e59	0.408843	0.204422	−	0.978883i	$-0.434469\pi$
$461$	3.50613e59	0.408843	0.204422	+	0.978883i	$0.434469\pi$
$462$	−1.92737e58	−0.0214053
$463$	1.56971e60	1.66053	0.830264	−	0.557370i	$-0.188189\pi$
$463$	1.56971e60	1.66053	0.830264	+	0.557370i	$0.188189\pi$
$464$	3.03580e59	0.305928
$465$	2.54069e60	2.43927
$466$	−1.24552e60	−1.13937
$467$	−5.15126e59	−0.449039	−0.224519	−	0.974470i	$-0.572081\pi$
$467$	−5.15126e59	−0.449039	−0.224519	+	0.974470i	$0.572081\pi$
$468$	−1.03342e60	−0.858513
$469$	1.23733e59	0.0979711
$470$	8.69366e59	0.656146
$471$	1.22441e60	0.880961
$472$	4.83633e59	0.331758
$473$	1.30808e59	0.0855575
$474$	2.30355e59	0.143676
$475$	−4.94073e60	−2.93890
$476$	−3.50433e59	−0.198815
$477$	2.05134e60	1.11013
$478$	−1.88188e60	−0.971548
$479$	−1.24707e59	−0.0614247	−0.0307124	−	0.999528i	$-0.509778\pi$
$479$	−1.24707e59	−0.0614247	−0.0307124	+	0.999528i	$0.509778\pi$
$480$	1.00095e60	0.470420
$481$	1.09824e60	0.492528
$482$	2.93099e60	1.25446
$483$	1.14427e58	0.00467433
$484$	−1.27326e60	−0.496473
$485$	−3.23239e60	−1.20319
$486$	−2.58322e60	−0.918005
$487$	1.00331e60	0.340435	0.170217	−	0.985407i	$-0.445553\pi$
$487$	1.00331e60	0.340435	0.170217	+	0.985407i	$0.445553\pi$
$488$	−6.67482e58	−0.0216269
$489$	6.94894e59	0.215015
$490$	−3.88537e60	−1.14821
$491$	5.26113e60	1.48507	0.742533	−	0.669809i	$-0.233624\pi$
$491$	5.26113e60	1.48507	0.742533	+	0.669809i	$0.233624\pi$
$492$	7.48830e59	0.201915
$493$	−8.12448e60	−2.09286
$494$	5.30754e60	1.30628
$495$	−8.60237e59	−0.202303
$496$	1.01971e60	0.229160
$497$	−8.74037e59	−0.187720
$498$	2.66369e60	0.546794
$499$	−5.83222e60	−1.14438	−0.572192	−	0.820120i	$-0.693907\pi$
$499$	−5.83222e60	−1.14438	−0.572192	+	0.820120i	$0.693907\pi$
$500$	4.33203e60	0.812580
$501$	8.48059e60	1.52082
$502$	4.59336e60	0.787584
$503$	−7.84309e60	−1.28590	−0.642950	−	0.765908i	$-0.722290\pi$
$503$	−7.84309e60	−1.28590	−0.642950	+	0.765908i	$0.722290\pi$
$504$	7.35638e59	0.115339
$505$	1.92367e61	2.88453
$506$	−5.37044e57	−0.000770235 0
$507$	5.62080e60	0.771115
$508$	4.07366e60	0.534628
$509$	−9.69762e60	−1.21763	−0.608814	−	0.793313i	$-0.708355\pi$
$509$	−9.69762e60	−1.21763	−0.608814	+	0.793313i	$0.708355\pi$
$510$	−2.67877e61	−3.21815
$511$	2.80944e59	0.0322961
$512$	4.01735e59	0.0441942
$513$	−8.96142e60	−0.943488
$514$	5.79325e60	0.583784
$515$	−1.11556e61	−1.07605
$516$	−8.55086e60	−0.789571
$517$	−5.13582e59	−0.0454018
$518$	−7.81773e59	−0.0661700
$519$	−2.87049e60	−0.232643
$520$	−9.56915e60	−0.742674
$521$	1.82321e61	1.35516	0.677578	−	0.735451i	$-0.263030\pi$
$521$	1.82321e61	1.35516	0.677578	+	0.735451i	$0.263030\pi$
$522$	1.70551e61	1.21414
$523$	2.09855e61	1.43097	0.715485	−	0.698628i	$-0.246206\pi$
$523$	2.09855e61	1.43097	0.715485	+	0.698628i	$0.246206\pi$
$524$	−4.06354e60	−0.265431
$525$	1.12124e61	0.701639
$526$	−6.36681e60	−0.381718
$527$	−2.72897e61	−1.56769
$528$	−5.91318e59	−0.0325505
$529$	−1.89531e61	−0.999832
$530$	1.89947e61	0.960340
$531$	2.71705e61	1.31665
$532$	−3.77815e60	−0.175496
$533$	−7.15884e60	−0.318772
$534$	3.16558e60	0.135137
$535$	6.72417e61	2.75219
$536$	3.79615e60	0.148983
$537$	−6.84481e61	−2.57597
$538$	−1.20058e61	−0.433302
$539$	2.29530e60	0.0794498
$540$	1.61568e61	0.536410
$541$	−1.80933e61	−0.576208	−0.288104	−	0.957599i	$-0.593025\pi$
$541$	−1.80933e61	−0.576208	−0.288104	+	0.957599i	$0.593025\pi$
$542$	1.81873e61	0.555627
$543$	1.53697e61	0.450472
$544$	−1.07513e61	−0.302333
$545$	−3.03208e61	−0.818123
$546$	−1.20448e61	−0.311865
$547$	4.13809e61	1.02822	0.514109	−	0.857725i	$-0.328123\pi$
$547$	4.13809e61	1.02822	0.514109	+	0.857725i	$0.328123\pi$
$548$	1.74661e61	0.416518
$549$	−3.74991e60	−0.0858307
$550$	−5.26233e60	−0.115616
$551$	−8.75930e61	−1.84739
$552$	3.51063e59	0.00710814
$553$	1.56763e60	0.0304739
$554$	8.49355e59	0.0158533
$555$	−5.97601e61	−1.07107
$556$	−3.58819e61	−0.617579
$557$	−3.44196e61	−0.568937	−0.284468	−	0.958685i	$-0.591817\pi$
$557$	−3.44196e61	−0.568937	−0.284468	+	0.958685i	$0.591817\pi$
$558$	5.72872e61	0.909469
$559$	8.17466e61	1.24653
$560$	6.81175e60	0.0997764
$561$	1.58250e61	0.222679
$562$	−1.72217e59	−0.00232814
$563$	4.54036e61	0.589728	0.294864	−	0.955539i	$-0.404726\pi$
$563$	4.54036e61	0.589728	0.294864	+	0.955539i	$0.404726\pi$
$564$	3.35727e61	0.418992
$565$	1.41950e62	1.70233
$566$	−7.48975e60	−0.0863173
$567$	−9.11690e60	−0.100978
$568$	−2.68155e61	−0.285462
$569$	5.98392e61	0.612293	0.306147	−	0.951984i	$-0.400960\pi$
$569$	5.98392e61	0.612293	0.306147	+	0.951984i	$0.400960\pi$
$570$	−2.88808e62	−2.84070
$571$	−1.08957e62	−1.03025	−0.515126	−	0.857115i	$-0.672255\pi$
$571$	−1.08957e62	−1.03025	−0.515126	+	0.857115i	$0.672255\pi$
$572$	5.65302e60	0.0513890
$573$	2.61661e62	2.28697
$574$	5.09599e60	0.0428263
$575$	3.12423e60	0.0252474
$576$	2.25694e61	0.175394
$577$	−1.18087e62	−0.882566	−0.441283	−	0.897368i	$-0.645476\pi$
$577$	−1.18087e62	−0.882566	−0.441283	+	0.897368i	$0.645476\pi$
$578$	1.89359e62	1.36116
$579$	1.00774e61	0.0696759
$580$	1.57924e62	1.05031
$581$	1.81271e61	0.115975
$582$	−1.24826e62	−0.768316
$583$	−1.12212e61	−0.0664503
$584$	8.61937e60	0.0491119
$585$	−5.37593e62	−2.94745
$586$	−1.99983e61	−0.105511
$587$	−1.98103e62	−1.00585	−0.502926	−	0.864329i	$-0.667743\pi$
$587$	−1.98103e62	−1.00585	−0.502926	+	0.864329i	$0.667743\pi$
$588$	−1.50043e62	−0.733207
$589$	−2.94220e62	−1.38382
$590$	2.51589e62	1.13899
$591$	2.42714e62	1.05773
$592$	−2.39848e61	−0.100623
$593$	2.96894e62	1.19914	0.599572	−	0.800321i	$-0.295338\pi$
$593$	2.96894e62	1.19914	0.599572	+	0.800321i	$0.295338\pi$
$594$	−9.54473e60	−0.0371167
$595$	−1.82297e62	−0.682573
$596$	−1.14747e62	−0.413714
$597$	7.88649e62	2.73818
$598$	−3.35618e60	−0.0112220
$599$	−2.63817e62	−0.849571	−0.424785	−	0.905294i	$-0.639650\pi$
$599$	−2.63817e62	−0.849571	−0.424785	+	0.905294i	$0.639650\pi$
$600$	3.43997e62	1.06697
$601$	4.88309e62	1.45888	0.729440	−	0.684045i	$-0.239781\pi$
$601$	4.88309e62	1.45888	0.729440	+	0.684045i	$0.239781\pi$
$602$	−5.81909e61	−0.167469
$603$	2.13267e62	0.591268
$604$	−1.90420e62	−0.508607
$605$	−6.62356e62	−1.70449
$606$	7.42873e62	1.84196
$607$	−2.99644e62	−0.715913	−0.357957	−	0.933738i	$-0.616526\pi$
$607$	−2.99644e62	−0.715913	−0.357957	+	0.933738i	$0.616526\pi$
$608$	−1.15914e62	−0.266873
$609$	1.98782e62	0.441049
$610$	−3.47228e61	−0.0742496
$611$	−3.20956e62	−0.661482
$612$	−6.04007e62	−1.19987
$613$	−5.28240e62	−1.01151	−0.505756	−	0.862677i	$-0.668786\pi$
$613$	−5.28240e62	−1.01151	−0.505756	+	0.862677i	$0.668786\pi$
$614$	−1.46670e62	−0.270740
$615$	3.89546e62	0.693216
$616$	−4.02407e60	−0.00690399
$617$	5.87091e62	0.971157	0.485578	−	0.874193i	$-0.338609\pi$
$617$	5.87091e62	0.971157	0.485578	+	0.874193i	$0.338609\pi$
$618$	−4.30802e62	−0.687127
$619$	−9.91111e61	−0.152434	−0.0762172	−	0.997091i	$-0.524284\pi$
$619$	−9.91111e61	−0.152434	−0.0762172	+	0.997091i	$0.524284\pi$
$620$	5.30459e62	0.786754
$621$	5.66668e60	0.00810527
$622$	−8.44862e62	−1.16547
$623$	2.15426e61	0.0286627
$624$	−3.69536e62	−0.474245
$625$	6.80992e62	0.843027
$626$	1.40661e62	0.167977
$627$	1.70615e62	0.196561
$628$	2.55640e62	0.284142
$629$	6.41887e62	0.688366
$630$	3.82683e62	0.395983
$631$	−1.71119e63	−1.70858	−0.854292	−	0.519793i	$-0.826009\pi$
$631$	−1.71119e63	−1.70858	−0.854292	+	0.519793i	$0.826009\pi$
$632$	4.80949e61	0.0463410
$633$	−1.61552e63	−1.50220
$634$	−1.28820e63	−1.15605
$635$	2.11914e63	1.83549
$636$	7.33526e62	0.613240
$637$	1.43442e63	1.15755
$638$	−9.32946e61	−0.0726760
$639$	−1.50649e63	−1.13291
$640$	2.08985e62	0.151728
$641$	1.93392e63	1.35560	0.677801	−	0.735245i	$-0.262933\pi$
$641$	1.93392e63	1.35560	0.677801	+	0.735245i	$0.262933\pi$
$642$	2.59670e63	1.75745
$643$	7.02129e62	0.458849	0.229425	−	0.973326i	$-0.426316\pi$
$643$	7.02129e62	0.458849	0.229425	+	0.973326i	$0.426316\pi$
$644$	2.38908e60	0.00150764
$645$	−4.44821e63	−2.71076
$646$	3.10211e63	1.82568
$647$	7.19051e62	0.408708	0.204354	−	0.978897i	$-0.434491\pi$
$647$	7.19051e62	0.408708	0.204354	+	0.978897i	$0.434491\pi$
$648$	−2.79707e62	−0.153556
$649$	−1.48627e62	−0.0788122
$650$	−3.28862e63	−1.68447
$651$	6.67697e62	0.330375
$652$	1.45084e62	0.0693504
$653$	−2.19682e63	−1.01449	−0.507245	−	0.861802i	$-0.669336\pi$
$653$	−2.19682e63	−1.01449	−0.507245	+	0.861802i	$0.669336\pi$
$654$	−1.17091e63	−0.522425
$655$	−2.11388e63	−0.911278
$656$	1.56345e62	0.0651250
$657$	4.84235e62	0.194911
$658$	2.28471e62	0.0888686
$659$	−1.02768e63	−0.386309	−0.193154	−	0.981168i	$-0.561872\pi$
$659$	−1.02768e63	−0.386309	−0.193154	+	0.981168i	$0.561872\pi$
$660$	−3.07607e62	−0.111753
$661$	−2.49132e62	−0.0874775	−0.0437388	−	0.999043i	$-0.513927\pi$
$661$	−2.49132e62	−0.0874775	−0.0437388	+	0.999043i	$0.513927\pi$
$662$	−2.99109e63	−1.01514
$663$	9.88959e63	3.24432
$664$	5.56141e62	0.176361
$665$	−1.96542e63	−0.602515
$666$	−1.34747e63	−0.399344
$667$	5.53887e61	0.0158705
$668$	1.77063e63	0.490520
$669$	−9.75448e63	−2.61286
$670$	1.97478e63	0.511488
$671$	2.05127e61	0.00513767
$672$	2.63052e62	0.0637138
$673$	7.84230e63	1.83698	0.918490	−	0.395445i	$-0.129410\pi$
$673$	7.84230e63	1.83698	0.918490	+	0.395445i	$0.129410\pi$
$674$	−1.23820e63	−0.280506
$675$	5.55261e63	1.21664
$676$	1.17354e63	0.248713
$677$	5.70570e63	1.16967	0.584836	−	0.811152i	$-0.301159\pi$
$677$	5.70570e63	1.16967	0.584836	+	0.811152i	$0.301159\pi$
$678$	5.48173e63	1.08705
$679$	−8.49478e62	−0.162960
$680$	−5.59289e63	−1.03797
$681$	−9.31886e63	−1.67322
$682$	−3.13371e62	−0.0544391
$683$	2.08383e63	0.350265	0.175133	−	0.984545i	$-0.443965\pi$
$683$	2.08383e63	0.350265	0.175133	+	0.984545i	$0.443965\pi$
$684$	−6.51202e63	−1.05914
$685$	9.08598e63	1.42999
$686$	−2.10052e63	−0.319914
$687$	1.04856e64	1.54549
$688$	−1.78530e63	−0.254666
$689$	−7.01254e63	−0.968150
$690$	1.82625e62	0.0244037
$691$	−1.38146e64	−1.78683	−0.893416	−	0.449231i	$-0.851698\pi$
$691$	−1.38146e64	−1.78683	−0.893416	+	0.449231i	$0.851698\pi$
$692$	−5.99317e62	−0.0750360
$693$	−2.26072e62	−0.0273999
$694$	4.18641e63	0.491195
$695$	−1.86660e64	−2.12028
$696$	6.09863e63	0.670694
$697$	−4.18414e63	−0.445522
$698$	9.81890e63	1.01232
$699$	−2.50212e64	−2.49788
$700$	2.34099e63	0.226305
$701$	1.60948e64	1.50671	0.753357	−	0.657612i	$-0.228433\pi$
$701$	1.60948e64	1.50671	0.753357	+	0.657612i	$0.228433\pi$
$702$	−5.96485e63	−0.540772
$703$	6.92042e63	0.607628
$704$	−1.23459e62	−0.0104987
$705$	1.74647e64	1.43849
$706$	1.51360e64	1.20755
$707$	5.05545e63	0.390682
$708$	9.71572e63	0.727322
$709$	7.68985e63	0.557670	0.278835	−	0.960339i	$-0.410052\pi$
$709$	7.68985e63	0.557670	0.278835	+	0.960339i	$0.410052\pi$
$710$	−1.39496e64	−0.980050
$711$	2.70197e63	0.183914
$712$	6.60928e62	0.0435868
$713$	1.86048e62	0.0118880
$714$	−7.03986e63	−0.435867
$715$	2.94074e63	0.176429
$716$	−1.42910e64	−0.830845
$717$	−3.78051e64	−2.12995
$718$	−1.66824e64	−0.910874
$719$	−2.29028e62	−0.0121196	−0.00605981	−	0.999982i	$-0.501929\pi$
$719$	−2.29028e62	−0.0121196	−0.00605981	+	0.999982i	$0.501929\pi$
$720$	1.17407e64	0.602163
$721$	−2.93172e63	−0.145740
$722$	1.87702e64	0.904444
$723$	5.88808e64	2.75018
$724$	3.20897e63	0.145294
$725$	5.42738e64	2.38224
$726$	−2.55785e64	−1.08843
$727$	−3.85052e64	−1.58853	−0.794265	−	0.607571i	$-0.792144\pi$
$727$	−3.85052e64	−1.58853	−0.794265	+	0.607571i	$0.792144\pi$
$728$	−2.51479e63	−0.100588
$729$	−4.06953e64	−1.57825
$730$	4.48385e63	0.168611
$731$	4.77785e64	1.74218
$732$	−1.34091e63	−0.0474132
$733$	−2.40241e64	−0.823774	−0.411887	−	0.911235i	$-0.635130\pi$
$733$	−2.40241e64	−0.823774	−0.411887	+	0.911235i	$0.635130\pi$
$734$	−2.43978e64	−0.811316
$735$	−7.80534e64	−2.51725
$736$	7.32971e61	0.00229264
$737$	−1.16661e63	−0.0353922
$738$	8.78345e63	0.258462
$739$	−4.02781e64	−1.14966	−0.574829	−	0.818274i	$-0.694931\pi$
$739$	−4.02781e64	−1.14966	−0.574829	+	0.818274i	$0.694931\pi$
$740$	−1.24771e64	−0.345461
$741$	1.06623e65	2.86380
$742$	4.99184e63	0.130069
$743$	−4.67691e63	−0.118225	−0.0591127	−	0.998251i	$-0.518827\pi$
$743$	−4.67691e63	−0.118225	−0.0591127	+	0.998251i	$0.518827\pi$
$744$	2.04850e64	0.502394
$745$	−5.96921e64	−1.42037
$746$	−1.88223e64	−0.434559
$747$	3.12439e64	0.699926
$748$	3.30403e63	0.0718221
$749$	1.76713e64	0.372758
$750$	8.70262e64	1.78144
$751$	2.23260e64	0.443519	0.221759	−	0.975101i	$-0.428820\pi$
$751$	2.23260e64	0.443519	0.221759	+	0.975101i	$0.428820\pi$
$752$	7.00950e63	0.135140
$753$	9.22761e64	1.72664
$754$	−5.83032e64	−1.05886
$755$	−9.90579e64	−1.74615
$756$	4.24605e63	0.0726515
$757$	7.40291e64	1.22955	0.614774	−	0.788703i	$-0.289247\pi$
$757$	7.40291e64	1.22955	0.614774	+	0.788703i	$0.289247\pi$
$758$	2.37687e64	0.383221
$759$	−1.07887e62	−0.00168861
$760$	−6.02991e64	−0.916230
$761$	5.17577e64	0.763520	0.381760	−	0.924262i	$-0.375318\pi$
$761$	5.17577e64	0.763520	0.381760	+	0.924262i	$0.375318\pi$
$762$	8.18359e64	1.17208
$763$	−7.96835e63	−0.110807
$764$	5.46312e64	0.737632
$765$	−3.14208e65	−4.11941
$766$	8.41005e63	0.107066
$767$	−9.28827e64	−1.14826
$768$	8.07045e63	0.0968881
$769$	−6.96026e64	−0.811489	−0.405744	−	0.913987i	$-0.632988\pi$
$769$	−6.96026e64	−0.811489	−0.405744	+	0.913987i	$0.632988\pi$
$770$	−2.09335e63	−0.0237028
$771$	1.16381e65	1.27984
$772$	2.10403e63	0.0224731
$773$	2.77811e64	0.288211	0.144105	−	0.989562i	$-0.453970\pi$
$773$	2.77811e64	0.288211	0.144105	+	0.989562i	$0.453970\pi$
$774$	−1.00298e65	−1.01069
$775$	1.82303e65	1.78445
$776$	−2.60620e64	−0.247810
$777$	−1.57051e64	−0.145066
$778$	3.43602e64	0.308329
$779$	−4.51108e64	−0.393267
$780$	−1.92235e65	−1.62818
$781$	8.24078e63	0.0678141
$782$	−1.96159e63	−0.0156840
$783$	9.84409e64	0.764779
$784$	−3.13269e64	−0.236486
$785$	1.32985e65	0.975520
$786$	−8.16326e64	−0.581911
$787$	1.45459e65	1.00765	0.503823	−	0.863807i	$-0.331926\pi$
$787$	1.45459e65	1.00765	0.503823	+	0.863807i	$0.331926\pi$
$788$	5.06753e64	0.341159
$789$	−1.27903e65	−0.836851
$790$	2.50193e64	0.159098
$791$	3.73046e64	0.230564
$792$	−6.93590e63	−0.0416664
$793$	1.28191e64	0.0748534
$794$	2.04627e65	1.16145
$795$	3.81585e65	2.10538
$796$	1.64659e65	0.883163
$797$	−3.38183e65	−1.76335	−0.881677	−	0.471854i	$-0.843585\pi$
$797$	−3.38183e65	−1.76335	−0.881677	+	0.471854i	$0.843585\pi$
$798$	−7.58993e64	−0.384745
$799$	−1.87590e65	−0.924499
$800$	7.18217e64	0.344136
$801$	3.71309e64	0.172983
$802$	−1.37616e65	−0.623368
$803$	−2.64886e63	−0.0116670
$804$	7.62609e64	0.326619
$805$	1.24281e63	0.00517605
$806$	−1.95837e65	−0.793152
$807$	−2.41185e65	−0.949940
$808$	1.55101e65	0.594101
$809$	−3.80533e65	−1.41759	−0.708795	−	0.705415i	$-0.750761\pi$
$809$	−3.80533e65	−1.41759	−0.708795	+	0.705415i	$0.750761\pi$
$810$	−1.45505e65	−0.527188
$811$	−1.46170e65	−0.515096	−0.257548	−	0.966265i	$-0.582915\pi$
$811$	−1.46170e65	−0.515096	−0.257548	+	0.966265i	$0.582915\pi$
$812$	4.15028e64	0.142255
$813$	3.65365e65	1.21812
$814$	7.37088e63	0.0239040
$815$	7.54737e64	0.238094
$816$	−2.15983e65	−0.662813
$817$	5.15118e65	1.53784
$818$	2.51923e65	0.731677
$819$	−1.41281e65	−0.399204
$820$	8.13317e64	0.223588
$821$	−5.74746e65	−1.53729	−0.768644	−	0.639677i	$-0.779068\pi$
$821$	−5.74746e65	−1.53729	−0.768644	+	0.639677i	$0.779068\pi$
$822$	3.50877e65	0.913144
$823$	−1.26608e65	−0.320601	−0.160301	−	0.987068i	$-0.551246\pi$
$823$	−1.26608e65	−0.320601	−0.160301	+	0.987068i	$0.551246\pi$
$824$	−8.99454e64	−0.221624
$825$	−1.05715e65	−0.253468
$826$	6.61181e64	0.154266
$827$	−2.28500e65	−0.518815	−0.259408	−	0.965768i	$-0.583527\pi$
$827$	−2.28500e65	−0.518815	−0.259408	+	0.965768i	$0.583527\pi$
$828$	4.11782e63	0.00909881
$829$	−2.23622e65	−0.480880	−0.240440	−	0.970664i	$-0.577292\pi$
$829$	−2.23622e65	−0.480880	−0.240440	+	0.970664i	$0.577292\pi$
$830$	2.89308e65	0.605485
$831$	1.70627e64	0.0347556
$832$	−7.71539e64	−0.152962
$833$	8.38377e65	1.61781
$834$	−7.20832e65	−1.35394
$835$	9.21092e65	1.68406
$836$	3.56220e64	0.0633982
$837$	3.30658e65	0.572869
$838$	−8.06773e64	−0.136070
$839$	−4.34958e65	−0.714172	−0.357086	−	0.934071i	$-0.616230\pi$
$839$	−4.34958e65	−0.714172	−0.357086	+	0.934071i	$0.616230\pi$
$840$	1.36841e65	0.218743
$841$	3.19652e65	0.497470
$842$	3.50275e65	0.530747
$843$	−3.45967e63	−0.00510405
$844$	−3.37297e65	−0.484515
$845$	6.10485e65	0.853885
$846$	3.93793e65	0.536333
$847$	−1.74068e65	−0.230857
$848$	1.53150e65	0.197793
$849$	−1.50462e65	−0.189236
$850$	−1.92211e66	−2.35424
$851$	−4.37607e63	−0.00521998
$852$	−5.38697e65	−0.625826
$853$	1.06033e66	1.19975	0.599873	−	0.800096i	$-0.295218\pi$
$853$	1.06033e66	1.19975	0.599873	+	0.800096i	$0.295218\pi$
$854$	−9.12523e63	−0.0100564
$855$	−3.38759e66	−3.63625
$856$	5.42155e65	0.566844
$857$	−1.04110e66	−1.06029	−0.530143	−	0.847909i	$-0.677862\pi$
$857$	−1.04110e66	−1.06029	−0.530143	+	0.847909i	$0.677862\pi$
$858$	1.13564e65	0.112661
$859$	1.12789e66	1.08999	0.544993	−	0.838441i	$-0.316532\pi$
$859$	1.12789e66	1.08999	0.544993	+	0.838441i	$0.316532\pi$
$860$	−9.28723e65	−0.874322
$861$	1.02373e65	0.0938893
$862$	5.27627e65	0.471426
$863$	−9.28485e65	−0.808225	−0.404112	−	0.914709i	$-0.632420\pi$
$863$	−9.28485e65	−0.808225	−0.404112	+	0.914709i	$0.632420\pi$
$864$	1.30269e65	0.110479
$865$	−3.11769e65	−0.257614
$866$	1.63514e66	1.31644
$867$	3.80403e66	2.98411
$868$	1.39406e65	0.106558
$869$	−1.47803e64	−0.0110087
$870$	3.17255e66	2.30263
$871$	−7.29057e65	−0.515648
$872$	−2.44469e65	−0.168501
$873$	−1.46416e66	−0.983486
$874$	−2.11486e64	−0.0138444
$875$	5.92237e65	0.377845
$876$	1.73155e65	0.107669
$877$	−1.96909e65	−0.119337	−0.0596683	−	0.998218i	$-0.519004\pi$
$877$	−1.96909e65	−0.119337	−0.0596683	+	0.998218i	$0.519004\pi$
$878$	−2.33097e66	−1.37693
$879$	−4.01745e65	−0.231314
$880$	−6.42240e64	−0.0360444
$881$	−1.06116e66	−0.580530	−0.290265	−	0.956946i	$-0.593743\pi$
$881$	−1.06116e66	−0.580530	−0.290265	+	0.956946i	$0.593743\pi$
$882$	−1.75994e66	−0.938545
$883$	−3.15617e66	−1.64076	−0.820380	−	0.571819i	$-0.806238\pi$
$883$	−3.15617e66	−1.64076	−0.820380	+	0.571819i	$0.806238\pi$
$884$	2.06481e66	1.04641
$885$	5.05418e66	2.49705
$886$	5.54454e65	0.267059
$887$	3.30858e66	1.55368	0.776838	−	0.629701i	$-0.216823\pi$
$887$	3.30858e66	1.55368	0.776838	+	0.629701i	$0.216823\pi$
$888$	−4.81832e65	−0.220599
$889$	5.56915e65	0.248599
$890$	3.43819e65	0.149642
$891$	8.59579e64	0.0364786
$892$	−2.03660e66	−0.842745
$893$	−2.02247e66	−0.816066
$894$	−2.30515e66	−0.906997
$895$	−7.43427e66	−2.85246
$896$	5.49216e64	0.0205500
$897$	−6.74224e64	−0.0246022
$898$	9.94414e65	0.353875
$899$	3.23200e66	1.12170
$900$	4.03493e66	1.36578
$901$	−4.09863e66	−1.35310
$902$	−4.80471e64	−0.0154711
$903$	−1.16900e66	−0.367146
$904$	1.14451e66	0.350614
$905$	1.66933e66	0.498825
$906$	−3.82536e66	−1.11503
$907$	1.48081e66	0.421051	0.210525	−	0.977588i	$-0.432483\pi$
$907$	1.48081e66	0.421051	0.210525	+	0.977588i	$0.432483\pi$
$908$	−1.94565e66	−0.539675
$909$	8.71358e66	2.35781
$910$	−1.30821e66	−0.345339
$911$	1.79478e66	0.462218	0.231109	−	0.972928i	$-0.425765\pi$
$911$	1.79478e66	0.462218	0.231109	+	0.972928i	$0.425765\pi$
$912$	−2.32859e66	−0.585073
$913$	−1.70910e65	−0.0418963
$914$	−3.88802e63	−0.000929907 0
$915$	−6.97548e65	−0.162779
$916$	2.18924e66	0.498477
$917$	−5.55532e65	−0.123424
$918$	−3.48628e66	−0.755792
$919$	8.33355e66	1.76291	0.881457	−	0.472264i	$-0.156563\pi$
$919$	8.33355e66	1.76291	0.881457	+	0.472264i	$0.156563\pi$
$920$	3.81296e64	0.00787111
$921$	−2.94646e66	−0.593551
$922$	1.47058e66	0.289096
$923$	5.14996e66	0.988020
$924$	−8.08397e64	−0.0151358
$925$	−4.28798e66	−0.783545
$926$	6.58383e66	1.17417
$927$	−5.05312e66	−0.879561
$928$	1.27331e66	0.216324
$929$	−8.96135e66	−1.48600	−0.743002	−	0.669290i	$-0.766599\pi$
$929$	−8.96135e66	−1.48600	−0.743002	+	0.669290i	$0.766599\pi$
$930$	1.06564e67	1.72482
$931$	9.03885e66	1.42806
$932$	−5.22408e66	−0.805660
$933$	−1.69725e67	−2.55510
$934$	−2.16059e66	−0.317518
$935$	1.71878e66	0.246580
$936$	−4.33449e66	−0.607060
$937$	−6.33708e66	−0.866460	−0.433230	−	0.901283i	$-0.642626\pi$
$937$	−6.33708e66	−0.866460	−0.433230	+	0.901283i	$0.642626\pi$
$938$	5.18976e65	0.0692761
$939$	2.82574e66	0.368261
$940$	3.64638e66	0.463965
$941$	4.46198e66	0.554321	0.277161	−	0.960824i	$-0.410607\pi$
$941$	4.46198e66	0.554321	0.277161	+	0.960824i	$0.410607\pi$
$942$	5.13555e66	0.622933
$943$	2.85254e64	0.00337846
$944$	2.02851e66	0.234588
$945$	2.20882e66	0.249428
$946$	5.48648e65	0.0604983
$947$	−8.10439e66	−0.872661	−0.436331	−	0.899786i	$-0.643722\pi$
$947$	−8.10439e66	−0.872661	−0.436331	+	0.899786i	$0.643722\pi$
$948$	9.66180e65	0.101595
$949$	−1.65537e66	−0.169983
$950$	−2.07229e67	−2.07812
$951$	−2.58787e67	−2.53443
$952$	−1.46982e66	−0.140583
$953$	1.39812e67	1.30603	0.653016	−	0.757344i	$-0.273504\pi$
$953$	1.39812e67	1.30603	0.653016	+	0.757344i	$0.273504\pi$
$954$	8.60394e66	0.784981
$955$	2.84195e67	2.53244
$956$	−7.89318e66	−0.686988
$957$	−1.87420e66	−0.159330
$958$	−5.23061e65	−0.0434338
$959$	2.38781e66	0.193679
$960$	4.19830e66	0.332637
$961$	−2.06430e66	−0.159771
$962$	4.60633e66	0.348270
$963$	3.04582e67	2.24964
$964$	1.22935e67	0.887037
$965$	1.09453e66	0.0771547
$966$	4.79943e64	0.00330525
$967$	−1.86670e67	−1.25597	−0.627986	−	0.778225i	$-0.716120\pi$
$967$	−1.86670e67	−1.25597	−0.627986	+	0.778225i	$0.716120\pi$
$968$	−5.34043e66	−0.351059
$969$	6.23183e67	4.00249
$970$	−1.35576e67	−0.850784
$971$	−1.16192e67	−0.712430	−0.356215	−	0.934404i	$-0.615933\pi$
$971$	−1.16192e67	−0.712430	−0.356215	+	0.934404i	$0.615933\pi$
$972$	−1.08348e67	−0.649127
$973$	−4.90545e66	−0.287171
$974$	4.20819e66	0.240724
$975$	−6.60652e67	−3.69291
$976$	−2.79962e65	−0.0152925
$977$	−7.37562e65	−0.0393705	−0.0196853	−	0.999806i	$-0.506266\pi$
$977$	−7.37562e65	−0.0393705	−0.0196853	+	0.999806i	$0.506266\pi$
$978$	2.91460e66	0.152039
$979$	−2.03113e65	−0.0103544
$980$	−1.62964e67	−0.811907
$981$	−1.37343e67	−0.668733
$982$	2.20668e67	1.05010
$983$	−2.68134e67	−1.24709	−0.623545	−	0.781787i	$-0.714308\pi$
$983$	−2.68134e67	−1.24709	−0.623545	+	0.781787i	$0.714308\pi$
$984$	3.14082e66	0.142775
$985$	2.63616e67	1.17127
$986$	−3.40765e67	−1.47987
$987$	4.58976e66	0.194829
$988$	2.22615e67	0.923682
$989$	−3.25730e65	−0.0132112
$990$	−3.60810e66	−0.143049
$991$	3.78750e67	1.46790	0.733948	−	0.679206i	$-0.237676\pi$
$991$	3.78750e67	1.46790	0.733948	+	0.679206i	$0.237676\pi$
$992$	4.27697e66	0.162041
$993$	−6.00881e67	−2.22552
$994$	−3.66598e66	−0.132738
$995$	8.56565e67	3.03208
$996$	1.11723e67	0.386642
$997$	−1.31201e67	−0.443910	−0.221955	−	0.975057i	$-0.571244\pi$
$997$	−1.31201e67	−0.443910	−0.221955	+	0.975057i	$0.571244\pi$
$998$	−2.44621e67	−0.809202
$999$	−7.77747e66	−0.251545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.46.a.b.1.2	✓	2
3.2	odd	2		18.46.a.b.1.1		2
4.3	odd	2		16.46.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.46.a.b.1.2	✓	2	1.1	even	1	trivial
16.46.a.a.1.1		2	4.3	odd	2
18.46.a.b.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 46 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+4.19430e6 q^{2} +8.42595e10 q^{3} +1.75922e13 q^{4} +9.15156e15 q^{5} +3.53410e17 q^{6} +2.40505e18 q^{7} +7.37870e19 q^{8} +4.14534e21 q^{9} +O(q^{10})\)	\(q+4.19430e6 q^{2} +8.42595e10 q^{3} +1.75922e13 q^{4} +9.15156e15 q^{5} +3.53410e17 q^{6} +2.40505e18 q^{7} +7.37870e19 q^{8} +4.14534e21 q^{9} +3.83844e22 q^{10} -2.26758e22 q^{11} +1.48231e24 q^{12} -1.41709e25 q^{13} +1.00875e25 q^{14} +7.71106e26 q^{15} +3.09485e26 q^{16} -8.28250e27 q^{17} +1.73868e28 q^{18} -8.92967e28 q^{19} +1.60996e29 q^{20} +2.02648e29 q^{21} -9.51092e28 q^{22} +5.64660e28 q^{23} +6.21725e30 q^{24} +5.53294e31 q^{25} -5.94372e31 q^{26} +1.00356e32 q^{27} +4.23100e31 q^{28} +9.80921e32 q^{29} +3.23425e33 q^{30} +3.29486e33 q^{31} +1.29807e33 q^{32} -1.91065e33 q^{33} -3.47393e34 q^{34} +2.20099e34 q^{35} +7.29256e34 q^{36} -7.74992e34 q^{37} -3.74538e35 q^{38} -1.19403e36 q^{39} +6.75266e35 q^{40} +5.05178e35 q^{41} +8.49967e35 q^{42} -5.76861e36 q^{43} -3.98917e35 q^{44} +3.79364e37 q^{45} +2.36836e35 q^{46} +2.26489e37 q^{47} +2.60770e37 q^{48} -1.01223e38 q^{49} +2.32068e38 q^{50} -6.97879e38 q^{51} -2.49298e38 q^{52} +4.94854e38 q^{53} +4.20922e38 q^{54} -2.07519e38 q^{55} +1.77461e38 q^{56} -7.52409e39 q^{57} +4.11428e39 q^{58} +6.55445e39 q^{59} +1.35654e40 q^{60} -9.04607e38 q^{61} +1.38196e40 q^{62} +9.96975e39 q^{63} +5.44452e39 q^{64} -1.29686e41 q^{65} -8.01385e39 q^{66} +5.14474e40 q^{67} -1.45707e41 q^{68} +4.75780e39 q^{69} +9.23164e40 q^{70} -3.63418e41 q^{71} +3.05872e41 q^{72} +1.16814e41 q^{73} -3.25055e41 q^{74} +4.66202e42 q^{75} -1.57092e42 q^{76} -5.45364e40 q^{77} -5.00814e42 q^{78} +6.51808e41 q^{79} +2.83227e42 q^{80} -3.79074e42 q^{81} +2.11887e42 q^{82} +7.53712e42 q^{83} +3.56502e42 q^{84} -7.57978e43 q^{85} -2.41953e43 q^{86} +8.26519e43 q^{87} -1.67318e42 q^{88} +8.95725e42 q^{89} +1.59117e44 q^{90} -3.40818e43 q^{91} +9.93361e41 q^{92} +2.77623e44 q^{93} +9.49964e43 q^{94} -8.17205e44 q^{95} +1.09375e44 q^{96} -3.53206e44 q^{97} -4.24559e44 q^{98} -9.39990e43 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8388608 q^{2} + 59861217192 q^{3} + 35184372088832 q^{4} + 43\!\cdots\!00 q^{5}+ \cdots + 17\!\cdots\!46 q^{9}+O(q^{10}) \) 2 * q + 8388608 * q^2 + 59861217192 * q^3 + 35184372088832 * q^4 + 4397113991405100 * q^5 + 251076142713274368 * q^6 + 7902493193471299024 * q^7 + 147573952589676412928 * q^8 + 1786304036785022132346 * q^9	\( 2 q + 8388608 q^{2} + 59861217192 q^{3} + 35184372088832 q^{4} + 43\!\cdots\!00 q^{5}+ \cdots - 60\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 8388608 * q^2 + 59861217192 * q^3 + 35184372088832 * q^4 + 4397113991405100 * q^5 + 251076142713274368 * q^6 + 7902493193471299024 * q^7 + 147573952589676412928 * q^8 + 1786304036785022132346 * q^9 + 18442832802606376550400 * q^10 + 193382581450547160321144 * q^11 + 1053089669686857534799872 * q^12 - 2312522953149074458311428 * q^13 + 33145458811349443381559296 * q^14 + 887105821761177992792895600 * q^15 + 618970019642690137449562112 * q^16 - 6570195850083651340869113436 * q^17 + 7492302166703565469787357184 * q^18 - 90017706781963544559646145720 * q^19 + 77354847395303135590848921600 * q^20 + 68520038925423887971291504704 * q^21 + 811105334908355756723615563776 * q^22 + 6994240792574843290864127840112 * q^23 + 4416978213926265305641242329088 * q^24 + 49512459978770470802589886478750 * q^25 - 9699424272484975596793455706112 * q^26 + 229991950494949775668061619638160 * q^27 + 139022130474278215773047681449984 * q^28 + 2213533364393458041951352752067740 * q^29 + 3720791496636195899883213186662400 * q^30 + 9650213165135522593230027496907584 * q^31 + 2596148429267413814265248164610048 * q^32 - 7182093662425694531112429563503776 * q^33 - 27557398734789259153612685961068544 * q^34 - 4127376326123989419154702521376800 * q^35 + 31424992947013431464190991386279936 * q^36 - 191012116158864196077428143000334996 * q^37 - 377561627626416822800702067577978880 * q^38 - 1483358494573103280616285570941860688 * q^39 + 324449745849509522821239995262566400 * q^40 - 1859015758492235069891763906253181676 * q^41 + 287393873345061115013539843346006016 * q^42 - 804011321867909724415330269683219528 * q^43 + 3402022350627456183848887653607931904 * q^44 + 49152292604663223059510333785715634300 * q^45 + 29335972133259835514244574856293122048 * q^46 + 36113177408029567180393469011774996704 * q^47 + 18526149390583790276512285265863114752 * q^48 - 178007647936693771635782071066946504526 * q^49 + 207670308938796900769185971217367040000 * q^50 - 739656360671997562398082418319435614256 * q^51 - 40682334023780823085533178441968386048 * q^52 - 666709323646290352590173897241305644788 * q^53 + 964656157928769823883653523494813040640 * q^54 - 1234757427854121513410799121046863930800 * q^55 + 583101077936787017529756982496393691136 * q^56 - 7506503344295441602576163948903964954720 * q^57 + 9284231844408938639188726653408730152960 * q^58 - 146711135631672307609725431066231780520 * q^59 + 15606130657507183007663760601670850969600 * q^60 + 16810546706420180245915601401744048614364 * q^61 + 40475927679380582954875077250389467201536 * q^62 - 2998939361959904611357533830735407560048 * q^63 + 10889035741470030830827987437816582766592 * q^64 - 186066269875585688065791914119720830029400 * q^65 - 30123884176686740274622987767922141691904 * q^66 - 82849230292769990365217317623577369391576 * q^67 - 115584107742921528825034303177253638373376 * q^68 - 164511673341122762782732560374725517322048 * q^69 - 17311471034167153316718245404220797747200 * q^70 + 110021245082064036014734112205046755165264 * q^71 + 131805973617630223643982131935439480684544 * q^72 + 1370836674469116973463675637713005724981332 * q^73 - 801162882853588733064341169898877075062784 * q^74 + 4803946793204919951439280730048232066935000 * q^75 - 1583608244999990585540275884850587128299520 * q^76 + 1133232767290964910783519570187778061966528 * q^77 - 6221656467221945382302009035343730051121152 * q^78 + 3371318639385645567529086614760361521517600 * q^79 + 1360840866815581189607218197089763301785600 * q^80 + 15703043630901782235731006317467167823282 * q^81 - 7797277231907015522587304919053344916373504 * q^82 - 9535514832176774675296631302412724036501048 * q^83 + 1205417272546683214945750219105526416932864 * q^84 - 83938909157693870911847863922509210121293800 * q^85 - 3372267903355861228754117411453406399168512 * q^86 + 52578297788213642356327012703383395390657840 * q^87 + 14269115953326141981742124881078363216674816 * q^88 + 67091763129503006680067356236410639491425780 * q^89 + 206159657480909375131396431038762227807027200 * q^90 + 31109166335206640196214146530166173423725664 * q^91 + 123043985262420261136738077298049666978414592 * q^92 + 122563730951297540335159337178889500300996864 * q^93 + 151469644455208045742993048649963915775574016 * q^94 - 813776794885228423572147822920801774025474000 * q^95 + 77704302493523153891936584139750725656772608 * q^96 - 829992687576057861045815591338653044052747836 * q^97 - 746618189771466433147047283804377991719419904 * q^98 - 603689043964735474143738491805547270151997288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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