LMFDB - Embedded newform 50.10.b.e.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,10,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	50.b (of order $2$, degree $1$, not 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:	$25.7517918082$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.10.b.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000i q^{2} -204.000i q^{3} -256.000 q^{4} +3264.00 q^{6} -5432.00i q^{7} -4096.00i q^{8} -21933.0 q^{9} +O(q^{10})$	\(q+16.0000i q^{2} -204.000i q^{3} -256.000 q^{4} +3264.00 q^{6} -5432.00i q^{7} -4096.00i q^{8} -21933.0 q^{9} +73932.0 q^{11} +52224.0i q^{12} -114514. i q^{13} +86912.0 q^{14} +65536.0 q^{16} -41682.0i q^{17} -350928. i q^{18} -1.05746e6 q^{19} -1.10813e6 q^{21} +1.18291e6i q^{22} +1.59934e6i q^{23} -835584. q^{24} +1.83222e6 q^{26} +459000. i q^{27} +1.39059e6i q^{28} -2.18451e6 q^{29} -9.61965e6 q^{31} +1.04858e6i q^{32} -1.50821e7i q^{33} +666912. q^{34} +5.61485e6 q^{36} -4.79994e6i q^{37} -1.69194e7i q^{38} -2.33609e7 q^{39} +9.53188e6 q^{41} -1.77300e7i q^{42} -1.34645e7i q^{43} -1.89266e7 q^{44} -2.55894e7 q^{46} -1.14420e7i q^{47} -1.33693e7i q^{48} +1.08470e7 q^{49} -8.50313e6 q^{51} +2.93156e7i q^{52} +5.36158e7i q^{53} -7.34400e6 q^{54} -2.22495e7 q^{56} +2.15722e8i q^{57} -3.49522e7i q^{58} -8.18626e7 q^{59} -1.04691e8 q^{61} -1.53914e8i q^{62} +1.19140e8i q^{63} -1.67772e7 q^{64} +2.41314e8 q^{66} -1.40571e8i q^{67} +1.06706e7i q^{68} +3.26265e8 q^{69} +9.70988e7 q^{71} +8.98376e7i q^{72} +1.71849e8i q^{73} +7.67991e7 q^{74} +2.70710e8 q^{76} -4.01599e8i q^{77} -3.73774e8i q^{78} +1.17380e8 q^{79} -3.38071e8 q^{81} +1.52510e8i q^{82} +3.23638e8i q^{83} +2.83681e8 q^{84} +2.15432e8 q^{86} +4.45640e8i q^{87} -3.02825e8i q^{88} +8.94379e8 q^{89} -6.22040e8 q^{91} -4.09430e8i q^{92} +1.96241e9i q^{93} +1.83071e8 q^{94} +2.13910e8 q^{96} -2.32679e8i q^{97} +1.73552e8i q^{98} -1.62155e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 512 q^{4} + 6528 q^{6} - 43866 q^{9}+O(q^{10}) $ 2 * q - 512 * q^4 + 6528 * q^6 - 43866 * q^9	$ 2 q - 512 q^{4} + 6528 q^{6} - 43866 q^{9} + 147864 q^{11} + 173824 q^{14} + 131072 q^{16} - 2114920 q^{19} - 2216256 q^{21} - 1671168 q^{24} + 3664448 q^{26} - 4369020 q^{29} - 19239296 q^{31} + 1333824 q^{34} + 11229696 q^{36} - 46721712 q^{39} + 19063764 q^{41} - 37853184 q^{44} - 51178752 q^{46} + 21693966 q^{49} - 17006256 q^{51} - 14688000 q^{54} - 44498944 q^{56} - 163725240 q^{59} - 209382596 q^{61} - 33554432 q^{64} + 482628096 q^{66} + 652529088 q^{69} + 194197584 q^{71} + 153598144 q^{74} + 541419520 q^{76} + 234760160 q^{79} - 676142478 q^{81} + 567361536 q^{84} + 430863488 q^{86} + 1788758220 q^{89} - 1244080096 q^{91} + 366142464 q^{94} + 427819008 q^{96} - 3243101112 q^{99}+O(q^{100}) $ 2 * q - 512 * q^4 + 6528 * q^6 - 43866 * q^9 + 147864 * q^11 + 173824 * q^14 + 131072 * q^16 - 2114920 * q^19 - 2216256 * q^21 - 1671168 * q^24 + 3664448 * q^26 - 4369020 * q^29 - 19239296 * q^31 + 1333824 * q^34 + 11229696 * q^36 - 46721712 * q^39 + 19063764 * q^41 - 37853184 * q^44 - 51178752 * q^46 + 21693966 * q^49 - 17006256 * q^51 - 14688000 * q^54 - 44498944 * q^56 - 163725240 * q^59 - 209382596 * q^61 - 33554432 * q^64 + 482628096 * q^66 + 652529088 * q^69 + 194197584 * q^71 + 153598144 * q^74 + 541419520 * q^76 + 234760160 * q^79 - 676142478 * q^81 + 567361536 * q^84 + 430863488 * q^86 + 1788758220 * q^89 - 1244080096 * q^91 + 366142464 * q^94 + 427819008 * q^96 - 3243101112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

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 $

$2$	16.0000i	0.707107i
$2$	16.0000i	0.707107i
$3$	− 204.000i	− 1.45407i	−0.686602	−	0.727034i	$-0.740898\pi$
$3$	− 204.000i	− 1.45407i	0.686602	−	0.727034i	$-0.259102\pi$
$4$	−256.000	−0.500000
$5$	0	0
$5$	0	0
$6$	3264.00	1.02818
$7$	− 5432.00i	− 0.855103i	−0.903991	−	0.427552i	$-0.859376\pi$
$7$	− 5432.00i	− 0.855103i	0.903991	−	0.427552i	$-0.140624\pi$
$8$	− 4096.00i	− 0.353553i
$9$	−21933.0	−1.11431
$10$	0	0
$11$	73932.0	1.52253	0.761264	−	0.648442i	$-0.224579\pi$
$11$	73932.0	1.52253	0.761264	+	0.648442i	$0.224579\pi$
$12$	52224.0i	0.727034i
$13$	− 114514.i	− 1.11202i	−0.831175	−	0.556011i	$-0.812331\pi$
$13$	− 114514.i	− 1.11202i	0.831175	−	0.556011i	$-0.187669\pi$
$14$	86912.0	0.604649
$15$	0	0
$16$	65536.0	0.250000
$17$	− 41682.0i	− 0.121040i	−0.998167	−	0.0605199i	$-0.980724\pi$
$17$	− 41682.0i	− 0.121040i	0.998167	−	0.0605199i	$-0.0192759\pi$
$18$	− 350928.i	− 0.787937i
$19$	−1.05746e6	−1.86154	−0.930771	−	0.365603i	$-0.880863\pi$
$19$	−1.05746e6	−1.86154	−0.930771	+	0.365603i	$0.880863\pi$
$20$	0	0
$21$	−1.10813e6	−1.24338
$22$	1.18291e6i	1.07659i
$23$	1.59934e6i	1.19169i	0.803098	+	0.595847i	$0.203183\pi$
$23$	1.59934e6i	1.19169i	−0.803098	+	0.595847i	$0.796817\pi$
$24$	−835584.	−0.514090
$25$	0	0
$26$	1.83222e6	0.786319
$27$	459000.i	0.166217i
$28$	1.39059e6i	0.427552i
$29$	−2.18451e6	−0.573539	−0.286770	−	0.958000i	$-0.592581\pi$
$29$	−2.18451e6	−0.573539	−0.286770	+	0.958000i	$0.592581\pi$
$30$	0	0
$31$	−9.61965e6	−1.87082	−0.935409	−	0.353567i	$-0.884968\pi$
$31$	−9.61965e6	−1.87082	−0.935409	+	0.353567i	$0.884968\pi$
$32$	1.04858e6i	0.176777i
$33$	− 1.50821e7i	− 2.21386i
$34$	666912.	0.0855881
$35$	0	0
$36$	5.61485e6	0.557156
$37$	− 4.79994e6i	− 0.421045i	−0.977589	−	0.210522i	$-0.932484\pi$
$37$	− 4.79994e6i	− 0.421045i	0.977589	−	0.210522i	$-0.0675165\pi$
$38$	− 1.69194e7i	− 1.31631i
$39$	−2.33609e7	−1.61696
$40$	0	0
$41$	9.53188e6	0.526807	0.263403	−	0.964686i	$-0.415155\pi$
$41$	9.53188e6	0.526807	0.263403	+	0.964686i	$0.415155\pi$
$42$	− 1.77300e7i	− 0.879201i
$43$	− 1.34645e7i	− 0.600595i	−0.953846	−	0.300297i	$-0.902914\pi$
$43$	− 1.34645e7i	− 0.600595i	0.953846	−	0.300297i	$-0.0970859\pi$
$44$	−1.89266e7	−0.761264
$45$	0	0
$46$	−2.55894e7	−0.842654
$47$	− 1.14420e7i	− 0.342027i	−0.985269	−	0.171013i	$-0.945296\pi$
$47$	− 1.14420e7i	− 0.342027i	0.985269	−	0.171013i	$-0.0547041\pi$
$48$	− 1.33693e7i	− 0.363517i
$49$	1.08470e7	0.268798
$50$	0	0
$51$	−8.50313e6	−0.176000
$52$	2.93156e7i	0.556011i
$53$	5.36158e7i	0.933364i	0.884425	+	0.466682i	$0.154551\pi$
$53$	5.36158e7i	0.933364i	−0.884425	+	0.466682i	$0.845449\pi$
$54$	−7.34400e6	−0.117533
$55$	0	0
$56$	−2.22495e7	−0.302325
$57$	2.15722e8i	2.70681i
$58$	− 3.49522e7i	− 0.405553i
$59$	−8.18626e7	−0.879532	−0.439766	−	0.898112i	$-0.644939\pi$
$59$	−8.18626e7	−0.879532	−0.439766	+	0.898112i	$0.644939\pi$
$60$	0	0
$61$	−1.04691e8	−0.968114	−0.484057	−	0.875037i	$-0.660837\pi$
$61$	−1.04691e8	−0.968114	−0.484057	+	0.875037i	$0.660837\pi$
$62$	− 1.53914e8i	− 1.32287i
$63$	1.19140e8i	0.952852i
$64$	−1.67772e7	−0.125000
$65$	0	0
$66$	2.41314e8	1.56543
$67$	− 1.40571e8i	− 0.852235i	−0.904668	−	0.426118i	$-0.859881\pi$
$67$	− 1.40571e8i	− 0.852235i	0.904668	−	0.426118i	$-0.140119\pi$
$68$	1.06706e7i	0.0605199i
$69$	3.26265e8	1.73280
$70$	0	0
$71$	9.70988e7	0.453473	0.226736	−	0.973956i	$-0.427194\pi$
$71$	9.70988e7	0.453473	0.226736	+	0.973956i	$0.427194\pi$
$72$	8.98376e7i	0.393969i
$73$	1.71849e8i	0.708262i	0.935196	+	0.354131i	$0.115223\pi$
$73$	1.71849e8i	0.708262i	−0.935196	+	0.354131i	$0.884777\pi$
$74$	7.67991e7	0.297724
$75$	0	0
$76$	2.70710e8	0.930771
$77$	− 4.01599e8i	− 1.30192i
$78$	− 3.73774e8i	− 1.14336i
$79$	1.17380e8	0.339057	0.169528	−	0.985525i	$-0.445776\pi$
$79$	1.17380e8	0.339057	0.169528	+	0.985525i	$0.445776\pi$
$80$	0	0
$81$	−3.38071e8	−0.872621
$82$	1.52510e8i	0.372509i
$83$	3.23638e8i	0.748527i	0.927322	+	0.374264i	$0.122104\pi$
$83$	3.23638e8i	0.748527i	−0.927322	+	0.374264i	$0.877896\pi$
$84$	2.83681e8	0.621689
$85$	0	0
$86$	2.15432e8	0.424685
$87$	4.45640e8i	0.833965i
$88$	− 3.02825e8i	− 0.538295i
$89$	8.94379e8	1.51101	0.755504	−	0.655144i	$-0.227392\pi$
$89$	8.94379e8	1.51101	0.755504	+	0.655144i	$0.227392\pi$
$90$	0	0
$91$	−6.22040e8	−0.950894
$92$	− 4.09430e8i	− 0.595847i
$93$	1.96241e9i	2.72030i
$94$	1.83071e8	0.241849
$95$	0	0
$96$	2.13910e8	0.257045
$97$	− 2.32679e8i	− 0.266860i	−0.991058	−	0.133430i	$-0.957401\pi$
$97$	− 2.32679e8i	− 0.266860i	0.991058	−	0.133430i	$-0.0425991\pi$
$98$	1.73552e8i	0.190069i
$99$	−1.62155e9	−1.69657
$100$	0	0
$101$	6.51288e8	0.622769	0.311384	−	0.950284i	$-0.399207\pi$
$101$	6.51288e8	0.622769	0.311384	+	0.950284i	$0.399207\pi$
$102$	− 1.36050e8i	− 0.124451i
$103$	− 1.71129e9i	− 1.49815i	−0.662484	−	0.749076i	$-0.730498\pi$
$103$	− 1.71129e9i	− 1.49815i	0.662484	−	0.749076i	$-0.269502\pi$
$104$	−4.69049e8	−0.393159
$105$	0	0
$106$	−8.57852e8	−0.659988
$107$	1.31553e9i	0.970228i	0.874451	+	0.485114i	$0.161222\pi$
$107$	1.31553e9i	0.970228i	−0.874451	+	0.485114i	$0.838778\pi$
$108$	− 1.17504e8i	− 0.0831086i
$109$	−3.10670e8	−0.210805	−0.105402	−	0.994430i	$-0.533613\pi$
$109$	−3.10670e8	−0.210805	−0.105402	+	0.994430i	$0.533613\pi$
$110$	0	0
$111$	−9.79188e8	−0.612227
$112$	− 3.55992e8i	− 0.213776i
$113$	− 2.74850e9i	− 1.58578i	−0.609366	−	0.792889i	$-0.708576\pi$
$113$	− 2.74850e9i	− 1.58578i	0.609366	−	0.792889i	$-0.291424\pi$
$114$	−3.45155e9	−1.91400
$115$	0	0
$116$	5.59235e8	0.286770
$117$	2.51164e9i	1.23914i
$118$	− 1.30980e9i	− 0.621923i
$119$	−2.26417e8	−0.103502
$120$	0	0
$121$	3.10799e9	1.31809
$122$	− 1.67506e9i	− 0.684560i
$123$	− 1.94450e9i	− 0.766012i
$124$	2.46263e9	0.935409
$125$	0	0
$126$	−1.90624e9	−0.673768
$127$	− 2.64323e9i	− 0.901608i	−0.892623	−	0.450804i	$-0.851137\pi$
$127$	− 2.64323e9i	− 0.901608i	0.892623	−	0.450804i	$-0.148863\pi$
$128$	− 2.68435e8i	− 0.0883883i
$129$	−2.74675e9	−0.873305
$130$	0	0
$131$	−2.63724e9	−0.782401	−0.391201	−	0.920305i	$-0.627940\pi$
$131$	−2.63724e9	−0.782401	−0.391201	+	0.920305i	$0.627940\pi$
$132$	3.86102e9i	1.10693i
$133$	5.74412e9i	1.59181i
$134$	2.24914e9	0.602621
$135$	0	0
$136$	−1.70729e8	−0.0427941
$137$	− 5.16539e9i	− 1.25274i	−0.779526	−	0.626370i	$-0.784540\pi$
$137$	− 5.16539e9i	− 1.25274i	0.779526	−	0.626370i	$-0.215460\pi$
$138$	5.22023e9i	1.22528i
$139$	−2.76751e9	−0.628815	−0.314407	−	0.949288i	$-0.601806\pi$
$139$	−2.76751e9	−0.628815	−0.314407	+	0.949288i	$0.601806\pi$
$140$	0	0
$141$	−2.33416e9	−0.497330
$142$	1.55358e9i	0.320654i
$143$	− 8.46625e9i	− 1.69309i
$144$	−1.43740e9	−0.278578
$145$	0	0
$146$	−2.74958e9	−0.500817
$147$	− 2.21278e9i	− 0.390851i
$148$	1.22879e9i	0.210522i
$149$	6.04151e9	1.00417	0.502085	−	0.864818i	$-0.332566\pi$
$149$	6.04151e9	1.00417	0.502085	+	0.864818i	$0.332566\pi$
$150$	0	0
$151$	4.07206e8	0.0637408	0.0318704	−	0.999492i	$-0.489854\pi$
$151$	4.07206e8	0.0637408	0.0318704	+	0.999492i	$0.489854\pi$
$152$	4.33136e9i	0.658154i
$153$	9.14211e8i	0.134876i
$154$	6.42558e9	0.920596
$155$	0	0
$156$	5.98038e9	0.808478
$157$	− 1.80938e8i	− 0.0237674i	−0.999929	−	0.0118837i	$-0.996217\pi$
$157$	− 1.80938e8i	− 0.0237674i	0.999929	−	0.0118837i	$-0.00378279\pi$
$158$	1.87808e9i	0.239749i
$159$	1.09376e10	1.35717
$160$	0	0
$161$	8.68759e9	1.01902
$162$	− 5.40914e9i	− 0.617036i
$163$	5.88002e9i	0.652432i	0.945295	+	0.326216i	$0.105774\pi$
$163$	5.88002e9i	0.652432i	−0.945295	+	0.326216i	$0.894226\pi$
$164$	−2.44016e9	−0.263403
$165$	0	0
$166$	−5.17820e9	−0.529289
$167$	− 1.36197e9i	− 0.135501i	−0.997702	−	0.0677507i	$-0.978418\pi$
$167$	− 1.36197e9i	− 0.135501i	0.997702	−	0.0677507i	$-0.0215823\pi$
$168$	4.53889e9i	0.439600i
$169$	−2.50896e9	−0.236594
$170$	0	0
$171$	2.31933e10	2.07434
$172$	3.44691e9i	0.300297i
$173$	− 1.41778e10i	− 1.20338i	−0.798731	−	0.601688i	$-0.794495\pi$
$173$	− 1.41778e10i	− 1.20338i	0.798731	−	0.601688i	$-0.205505\pi$
$174$	−7.13024e9	−0.589702
$175$	0	0
$176$	4.84521e9	0.380632
$177$	1.67000e10i	1.27890i
$178$	1.43101e10i	1.06844i
$179$	−2.66456e9	−0.193993	−0.0969967	−	0.995285i	$-0.530924\pi$
$179$	−2.66456e9	−0.193993	−0.0969967	+	0.995285i	$0.530924\pi$
$180$	0	0
$181$	−4.05446e9	−0.280789	−0.140394	−	0.990096i	$-0.544837\pi$
$181$	−4.05446e9	−0.280789	−0.140394	+	0.990096i	$0.544837\pi$
$182$	− 9.95264e9i	− 0.672384i
$183$	2.13570e10i	1.40770i
$184$	6.55088e9	0.421327
$185$	0	0
$186$	−3.13985e10	−1.92354
$187$	− 3.08163e9i	− 0.184287i
$188$	2.92914e9i	0.171013i
$189$	2.49329e9	0.142133
$190$	0	0
$191$	−1.01385e10	−0.551216	−0.275608	−	0.961270i	$-0.588879\pi$
$191$	−1.01385e10	−0.551216	−0.275608	+	0.961270i	$0.588879\pi$
$192$	3.42255e9i	0.181758i
$193$	− 7.57686e9i	− 0.393080i	−0.980496	−	0.196540i	$-0.937029\pi$
$193$	− 7.57686e9i	− 0.393080i	0.980496	−	0.196540i	$-0.0629706\pi$
$194$	3.72286e9	0.188699
$195$	0	0
$196$	−2.77683e9	−0.134399
$197$	2.20768e8i	0.0104433i	0.999986	+	0.00522166i	$0.00166211\pi$
$197$	2.20768e8i	0.0104433i	−0.999986	+	0.00522166i	$0.998338\pi$
$198$	− 2.59448e10i	− 1.19966i
$199$	2.99296e10	1.35289	0.676445	−	0.736493i	$-0.263519\pi$
$199$	2.99296e10	1.35289	0.676445	+	0.736493i	$0.263519\pi$
$200$	0	0
$201$	−2.86765e10	−1.23921
$202$	1.04206e10i	0.440364i
$203$	1.18663e10i	0.490435i
$204$	2.17680e9	0.0880001
$205$	0	0
$206$	2.73806e10	1.05935
$207$	− 3.50782e10i	− 1.32792i
$208$	− 7.50479e9i	− 0.278006i
$209$	−7.81801e10	−2.83425
$210$	0	0
$211$	2.92533e10	1.01602	0.508012	−	0.861350i	$-0.330381\pi$
$211$	2.92533e10	1.01602	0.508012	+	0.861350i	$0.330381\pi$
$212$	− 1.37256e10i	− 0.466682i
$213$	− 1.98082e10i	− 0.659380i
$214$	−2.10485e10	−0.686055
$215$	0	0
$216$	1.88006e9	0.0587666
$217$	5.22539e10i	1.59974i
$218$	− 4.97072e9i	− 0.149061i
$219$	3.50572e10	1.02986
$220$	0	0
$221$	−4.77317e9	−0.134599
$222$	− 1.56670e10i	− 0.432910i
$223$	− 5.18482e10i	− 1.40398i	−0.712186	−	0.701991i	$-0.752295\pi$
$223$	− 5.18482e10i	− 1.40398i	0.712186	−	0.701991i	$-0.247705\pi$
$224$	5.69586e9	0.151162
$225$	0	0
$226$	4.39760e10	1.12131
$227$	− 4.56273e10i	− 1.14053i	−0.821460	−	0.570267i	$-0.806840\pi$
$227$	− 4.56273e10i	− 1.14053i	0.821460	−	0.570267i	$-0.193160\pi$
$228$	− 5.52248e10i	− 1.35340i
$229$	−6.21495e10	−1.49341	−0.746703	−	0.665158i	$-0.768364\pi$
$229$	−6.21495e10	−1.49341	−0.746703	+	0.665158i	$0.768364\pi$
$230$	0	0
$231$	−8.19261e10	−1.89308
$232$	8.94775e9i	0.202777i
$233$	− 3.72165e9i	− 0.0827245i	−0.999144	−	0.0413623i	$-0.986830\pi$
$233$	− 3.72165e9i	− 0.0827245i	0.999144	−	0.0413623i	$-0.0131698\pi$
$234$	−4.01862e10	−0.876204
$235$	0	0
$236$	2.09568e10	0.439766
$237$	− 2.39455e10i	− 0.493011i
$238$	− 3.62267e9i	− 0.0731867i
$239$	−3.62221e9	−0.0718098	−0.0359049	−	0.999355i	$-0.511431\pi$
$239$	−3.62221e9	−0.0718098	−0.0359049	+	0.999355i	$0.511431\pi$
$240$	0	0
$241$	−3.36556e10	−0.642660	−0.321330	−	0.946967i	$-0.604130\pi$
$241$	−3.36556e10	−0.642660	−0.321330	+	0.946967i	$0.604130\pi$
$242$	4.97279e10i	0.932032i
$243$	7.80010e10i	1.43507i
$244$	2.68010e10	0.484057
$245$	0	0
$246$	3.11121e10	0.541653
$247$	1.21094e11i	2.07008i
$248$	3.94021e10i	0.661434i
$249$	6.60221e10	1.08841
$250$	0	0
$251$	−5.88110e10	−0.935248	−0.467624	−	0.883928i	$-0.654890\pi$
$251$	−5.88110e10	−0.935248	−0.467624	+	0.883928i	$0.654890\pi$
$252$	− 3.04999e10i	− 0.476426i
$253$	1.18242e11i	1.81439i
$254$	4.22917e10	0.637533
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	7.52072e10i	1.07538i	0.843144	+	0.537688i	$0.180702\pi$
$257$	7.52072e10i	1.07538i	−0.843144	+	0.537688i	$0.819298\pi$
$258$	− 4.39481e10i	− 0.617520i
$259$	−2.60733e10	−0.360037
$260$	0	0
$261$	4.79129e10	0.639101
$262$	− 4.21959e10i	− 0.553241i
$263$	− 1.16316e10i	− 0.149913i	−0.997187	−	0.0749565i	$-0.976118\pi$
$263$	− 1.16316e10i	− 0.149913i	0.997187	−	0.0749565i	$-0.0238818\pi$
$264$	−6.17764e10	−0.782717
$265$	0	0
$266$	−9.19060e10	−1.12558
$267$	− 1.82453e11i	− 2.19711i
$268$	3.59862e10i	0.426118i
$269$	−2.83871e10	−0.330549	−0.165275	−	0.986248i	$-0.552851\pi$
$269$	−2.83871e10	−0.330549	−0.165275	+	0.986248i	$0.552851\pi$
$270$	0	0
$271$	1.47987e11	1.66672	0.833361	−	0.552729i	$-0.186414\pi$
$271$	1.47987e11	1.66672	0.833361	+	0.552729i	$0.186414\pi$
$272$	− 2.73167e9i	− 0.0302600i
$273$	1.26896e11i	1.38266i
$274$	8.26463e10	0.885820
$275$	0	0
$276$	−8.35237e10	−0.866401
$277$	7.58857e10i	0.774464i	0.921982	+	0.387232i	$0.126569\pi$
$277$	7.58857e10i	0.774464i	−0.921982	+	0.387232i	$0.873431\pi$
$278$	− 4.42802e10i	− 0.444639i
$279$	2.10988e11	2.08467
$280$	0	0
$281$	1.72151e11	1.64714	0.823570	−	0.567215i	$-0.191979\pi$
$281$	1.72151e11	1.64714	0.823570	+	0.567215i	$0.191979\pi$
$282$	− 3.73465e10i	− 0.351665i
$283$	− 1.49932e11i	− 1.38949i	−0.719256	−	0.694745i	$-0.755517\pi$
$283$	− 1.49932e11i	− 1.38949i	0.719256	−	0.694745i	$-0.244483\pi$
$284$	−2.48573e10	−0.226736
$285$	0	0
$286$	1.35460e11	1.19719
$287$	− 5.17772e10i	− 0.450474i
$288$	− 2.29984e10i	− 0.196984i
$289$	1.16850e11	0.985349
$290$	0	0
$291$	−4.74664e10	−0.388032
$292$	− 4.39933e10i	− 0.354131i
$293$	9.51745e9i	0.0754426i	0.999288	+	0.0377213i	$0.0120099\pi$
$293$	9.51745e9i	0.0754426i	−0.999288	+	0.0377213i	$0.987990\pi$
$294$	3.54046e10	0.276373
$295$	0	0
$296$	−1.96606e10	−0.148862
$297$	3.39348e10i	0.253070i
$298$	9.66642e10i	0.710056i
$299$	1.83146e11	1.32519
$300$	0	0
$301$	−7.31391e10	−0.513571
$302$	6.51529e9i	0.0450716i
$303$	− 1.32863e11i	− 0.905547i
$304$	−6.93017e10	−0.465385
$305$	0	0
$306$	−1.46274e10	−0.0953718
$307$	− 9.05900e10i	− 0.582046i	−0.956716	−	0.291023i	$-0.906004\pi$
$307$	− 9.05900e10i	− 0.582046i	0.956716	−	0.291023i	$-0.0939957\pi$
$308$	1.02809e11i	0.650959i
$309$	−3.49103e11	−2.17841
$310$	0	0
$311$	−2.81285e11	−1.70500	−0.852501	−	0.522726i	$-0.824915\pi$
$311$	−2.81285e11	−1.70500	−0.852501	+	0.522726i	$0.824915\pi$
$312$	9.56861e10i	0.571680i
$313$	− 9.11248e10i	− 0.536645i	−0.963329	−	0.268323i	$-0.913531\pi$
$313$	− 9.11248e10i	− 0.536645i	0.963329	−	0.268323i	$-0.0864693\pi$
$314$	2.89501e9	0.0168061
$315$	0	0
$316$	−3.00493e10	−0.169528
$317$	− 1.03167e11i	− 0.573819i	−0.957958	−	0.286909i	$-0.907372\pi$
$317$	− 1.03167e11i	− 0.573819i	0.957958	−	0.286909i	$-0.0926279\pi$
$318$	1.75002e11i	0.959667i
$319$	−1.61505e11	−0.873230
$320$	0	0
$321$	2.68368e11	1.41078
$322$	1.39001e11i	0.720556i
$323$	4.40770e10i	0.225321i
$324$	8.65462e10	0.436310
$325$	0	0
$326$	−9.40804e10	−0.461339
$327$	6.33767e10i	0.306524i
$328$	− 3.90426e10i	− 0.186254i
$329$	−6.21527e10	−0.292468
$330$	0	0
$331$	2.51080e11	1.14970	0.574851	−	0.818258i	$-0.305060\pi$
$331$	2.51080e11	1.14970	0.574851	+	0.818258i	$0.305060\pi$
$332$	− 8.28512e10i	− 0.374264i
$333$	1.05277e11i	0.469175i
$334$	2.17916e10	0.0958140
$335$	0	0
$336$	−7.26223e10	−0.310844
$337$	4.04967e11i	1.71035i	0.518339	+	0.855175i	$0.326550\pi$
$337$	4.04967e11i	1.71035i	−0.518339	+	0.855175i	$0.673450\pi$
$338$	− 4.01433e10i	− 0.167297i
$339$	−5.60694e11	−2.30583
$340$	0	0
$341$	−7.11200e11	−2.84837
$342$	3.71092e11i	1.46678i
$343$	− 2.78122e11i	− 1.08495i
$344$	−5.51505e10	−0.212342
$345$	0	0
$346$	2.26845e11	0.850916
$347$	− 4.20848e11i	− 1.55827i	−0.626857	−	0.779134i	$-0.715659\pi$
$347$	− 4.20848e11i	− 1.55827i	0.626857	−	0.779134i	$-0.284341\pi$
$348$	− 1.14084e11i	− 0.416982i
$349$	3.99383e11	1.44104	0.720518	−	0.693436i	$-0.243904\pi$
$349$	3.99383e11	1.44104	0.720518	+	0.693436i	$0.243904\pi$
$350$	0	0
$351$	5.25619e10	0.184837
$352$	7.75233e10i	0.269148i
$353$	− 7.88806e10i	− 0.270386i	−0.990819	−	0.135193i	$-0.956835\pi$
$353$	− 7.88806e10i	− 0.270386i	0.990819	−	0.135193i	$-0.0431654\pi$
$354$	−2.67200e11	−0.904318
$355$	0	0
$356$	−2.28961e11	−0.755504
$357$	4.61890e10i	0.150498i
$358$	− 4.26330e10i	− 0.137174i
$359$	−1.39842e11	−0.444337	−0.222168	−	0.975008i	$-0.571314\pi$
$359$	−1.39842e11	−0.444337	−0.222168	+	0.975008i	$0.571314\pi$
$360$	0	0
$361$	7.95534e11	2.46534
$362$	− 6.48714e10i	− 0.198547i
$363$	− 6.34031e11i	− 1.91660i
$364$	1.59242e11	0.475447
$365$	0	0
$366$	−3.41712e11	−0.995396
$367$	− 5.08662e11i	− 1.46363i	−0.681502	−	0.731816i	$-0.738673\pi$
$367$	− 5.08662e11i	− 1.46363i	0.681502	−	0.731816i	$-0.261327\pi$
$368$	1.04814e11i	0.297923i
$369$	−2.09063e11	−0.587027
$370$	0	0
$371$	2.91241e11	0.798123
$372$	− 5.02376e11i	− 1.36015i
$373$	− 2.96761e11i	− 0.793810i	−0.917860	−	0.396905i	$-0.870084\pi$
$373$	− 2.96761e11i	− 0.793810i	0.917860	−	0.396905i	$-0.129916\pi$
$374$	4.93061e10	0.130310
$375$	0	0
$376$	−4.68662e10	−0.120925
$377$	2.50157e11i	0.637788i
$378$	3.98926e10i	0.100503i
$379$	4.53918e11	1.13006	0.565030	−	0.825071i	$-0.308865\pi$
$379$	4.53918e11	1.13006	0.565030	+	0.825071i	$0.308865\pi$
$380$	0	0
$381$	−5.39219e11	−1.31100
$382$	− 1.62215e11i	− 0.389768i
$383$	2.67567e11i	0.635387i	0.948193	+	0.317694i	$0.102908\pi$
$383$	2.67567e11i	0.635387i	−0.948193	+	0.317694i	$0.897092\pi$
$384$	−5.47608e10	−0.128523
$385$	0	0
$386$	1.21230e11	0.277950
$387$	2.95317e11i	0.669250i
$388$	5.95657e10i	0.133430i
$389$	−3.34750e11	−0.741221	−0.370610	−	0.928788i	$-0.620852\pi$
$389$	−3.34750e11	−0.741221	−0.370610	+	0.928788i	$0.620852\pi$
$390$	0	0
$391$	6.66635e10	0.144242
$392$	− 4.44292e10i	− 0.0950346i
$393$	5.37998e11i	1.13766i
$394$	−3.53229e9	−0.00738454
$395$	0	0
$396$	4.15117e11	0.848286
$397$	4.55573e11i	0.920451i	0.887802	+	0.460226i	$0.152231\pi$
$397$	4.55573e11i	0.920451i	−0.887802	+	0.460226i	$0.847769\pi$
$398$	4.78874e11i	0.956638i
$399$	1.17180e12	2.31460
$400$	0	0
$401$	2.18973e11	0.422904	0.211452	−	0.977388i	$-0.432181\pi$
$401$	2.18973e11	0.422904	0.211452	+	0.977388i	$0.432181\pi$
$402$	− 4.58824e11i	− 0.876252i
$403$	1.10158e12i	2.08039i
$404$	−1.66730e11	−0.311384
$405$	0	0
$406$	−1.89860e11	−0.346790
$407$	− 3.54869e11i	− 0.641053i
$408$	3.48288e10i	0.0622254i
$409$	3.63048e11	0.641519	0.320760	−	0.947161i	$-0.396062\pi$
$409$	3.63048e11	0.641519	0.320760	+	0.947161i	$0.396062\pi$
$410$	0	0
$411$	−1.05374e12	−1.82157
$412$	4.38090e11i	0.749076i
$413$	4.44678e11i	0.752091i
$414$	5.61252e11	0.938980
$415$	0	0
$416$	1.20077e11	0.196580
$417$	5.64572e11i	0.914339i
$418$	− 1.25088e12i	− 2.00412i
$419$	1.14340e12	1.81232	0.906158	−	0.422939i	$-0.139001\pi$
$419$	1.14340e12	1.81232	0.906158	+	0.422939i	$0.139001\pi$
$420$	0	0
$421$	6.58288e11	1.02128	0.510642	−	0.859793i	$-0.329408\pi$
$421$	6.58288e11	1.02128	0.510642	+	0.859793i	$0.329408\pi$
$422$	4.68053e11i	0.718437i
$423$	2.50956e11i	0.381124i
$424$	2.19610e11	0.329994
$425$	0	0
$426$	3.16930e11	0.466252
$427$	5.68683e11i	0.827837i
$428$	− 3.36776e11i	− 0.485114i
$429$	−1.72711e12	−2.46186
$430$	0	0
$431$	−1.27825e11	−0.178430	−0.0892152	−	0.996012i	$-0.528436\pi$
$431$	−1.27825e11	−0.178430	−0.0892152	+	0.996012i	$0.528436\pi$
$432$	3.00810e10i	0.0415543i
$433$	− 5.76786e10i	− 0.0788531i	−0.999222	−	0.0394266i	$-0.987447\pi$
$433$	− 5.76786e10i	− 0.0788531i	0.999222	−	0.0394266i	$-0.0125531\pi$
$434$	−8.36063e11	−1.13119
$435$	0	0
$436$	7.95315e10	0.105402
$437$	− 1.69123e12i	− 2.21839i
$438$	5.60915e11i	0.728221i
$439$	−4.11418e11	−0.528681	−0.264340	−	0.964429i	$-0.585154\pi$
$439$	−4.11418e11	−0.528681	−0.264340	+	0.964429i	$0.585154\pi$
$440$	0	0
$441$	−2.37907e11	−0.299525
$442$	− 7.63708e10i	− 0.0951759i
$443$	1.17254e11i	0.144647i	0.997381	+	0.0723237i	$0.0230415\pi$
$443$	1.17254e11i	0.144647i	−0.997381	+	0.0723237i	$0.976959\pi$
$444$	2.50672e11	0.306114
$445$	0	0
$446$	8.29571e11	0.992766
$447$	− 1.23247e12i	− 1.46013i
$448$	9.11338e10i	0.106888i
$449$	−9.15676e10	−0.106325	−0.0531623	−	0.998586i	$-0.516930\pi$
$449$	−9.15676e10	−0.106325	−0.0531623	+	0.998586i	$0.516930\pi$
$450$	0	0
$451$	7.04711e11	0.802078
$452$	7.03615e11i	0.792889i
$453$	− 8.30700e10i	− 0.0926834i
$454$	7.30036e11	0.806479
$455$	0	0
$456$	8.83597e11	0.957001
$457$	1.55029e12i	1.66261i	0.555816	+	0.831305i	$0.312406\pi$
$457$	1.55029e12i	1.66261i	−0.555816	+	0.831305i	$0.687594\pi$
$458$	− 9.94392e11i	− 1.05600i
$459$	1.91320e10	0.0201189
$460$	0	0
$461$	−1.61825e12	−1.66875	−0.834374	−	0.551198i	$-0.814171\pi$
$461$	−1.61825e12	−1.66875	−0.834374	+	0.551198i	$0.814171\pi$
$462$	− 1.31082e12i	− 1.33861i
$463$	9.04370e11i	0.914601i	0.889312	+	0.457301i	$0.151184\pi$
$463$	9.04370e11i	0.914601i	−0.889312	+	0.457301i	$0.848816\pi$
$464$	−1.43164e11	−0.143385
$465$	0	0
$466$	5.95465e10	0.0584951
$467$	1.28255e12i	1.24781i	0.781502	+	0.623903i	$0.214454\pi$
$467$	1.28255e12i	1.24781i	−0.781502	+	0.623903i	$0.785546\pi$
$468$	− 6.42979e11i	− 0.619570i
$469$	−7.63582e11	−0.728749
$470$	0	0
$471$	−3.69113e10	−0.0345594
$472$	3.35309e11i	0.310961i
$473$	− 9.95456e11i	− 0.914423i
$474$	3.83129e11	0.348612
$475$	0	0
$476$	5.79627e10	0.0517508
$477$	− 1.17595e12i	− 1.04006i
$478$	− 5.79554e10i	− 0.0507772i
$479$	5.31423e11	0.461244	0.230622	−	0.973043i	$-0.425924\pi$
$479$	5.31423e11	0.461244	0.230622	+	0.973043i	$0.425924\pi$
$480$	0	0
$481$	−5.49661e11	−0.468211
$482$	− 5.38490e11i	− 0.454429i
$483$	− 1.77227e12i	− 1.48172i
$484$	−7.95646e11	−0.659046
$485$	0	0
$486$	−1.24802e12	−1.01475
$487$	1.10916e12i	0.893539i	0.894649	+	0.446770i	$0.147426\pi$
$487$	1.10916e12i	0.893539i	−0.894649	+	0.446770i	$0.852574\pi$
$488$	4.28816e11i	0.342280i
$489$	1.19953e12	0.948679
$490$	0	0
$491$	−9.04143e11	−0.702054	−0.351027	−	0.936365i	$-0.614168\pi$
$491$	−9.04143e11	−0.702054	−0.351027	+	0.936365i	$0.614168\pi$
$492$	4.97793e11i	0.383006i
$493$	9.10547e10i	0.0694211i
$494$	−1.93750e12	−1.46376
$495$	0	0
$496$	−6.30433e11	−0.467705
$497$	− 5.27441e11i	− 0.387766i
$498$	1.05635e12i	0.769621i
$499$	−1.01146e12	−0.730290	−0.365145	−	0.930951i	$-0.618981\pi$
$499$	−1.01146e12	−0.730290	−0.365145	+	0.930951i	$0.618981\pi$
$500$	0	0
$501$	−2.77842e11	−0.197028
$502$	− 9.40975e11i	− 0.661320i
$503$	1.26417e11i	0.0880538i	0.999030	+	0.0440269i	$0.0140187\pi$
$503$	1.26417e11i	0.0880538i	−0.999030	+	0.0440269i	$0.985981\pi$
$504$	4.87998e11	0.336884
$505$	0	0
$506$	−1.89187e12	−1.28297
$507$	5.11827e11i	0.344023i
$508$	6.76666e11i	0.450804i
$509$	4.08226e11	0.269569	0.134785	−	0.990875i	$-0.456966\pi$
$509$	4.08226e11	0.269569	0.134785	+	0.990875i	$0.456966\pi$
$510$	0	0
$511$	9.33483e11	0.605637
$512$	6.87195e10i	0.0441942i
$513$	− 4.85374e11i	− 0.309420i
$514$	−1.20332e12	−0.760406
$515$	0	0
$516$	7.03169e11	0.436653
$517$	− 8.45926e11i	− 0.520745i
$518$	− 4.17173e11i	− 0.254584i
$519$	−2.89227e12	−1.74979
$520$	0	0
$521$	2.96958e12	1.76573	0.882867	−	0.469624i	$-0.155610\pi$
$521$	2.96958e12	1.76573	0.882867	+	0.469624i	$0.155610\pi$
$522$	7.66606e11i	0.451913i
$523$	− 4.01653e11i	− 0.234743i	−0.993088	−	0.117372i	$-0.962553\pi$
$523$	− 4.01653e11i	− 0.234743i	0.993088	−	0.117372i	$-0.0374469\pi$
$524$	6.75134e11	0.391201
$525$	0	0
$526$	1.86106e11	0.106004
$527$	4.00966e11i	0.226444i
$528$	− 9.88422e11i	− 0.553465i
$529$	−7.56723e11	−0.420133
$530$	0	0
$531$	1.79549e12	0.980073
$532$	− 1.47050e12i	− 0.795905i
$533$	− 1.09153e12i	− 0.585821i
$534$	2.91925e12	1.55359
$535$	0	0
$536$	−5.75779e11	−0.301311
$537$	5.43571e11i	0.282080i
$538$	− 4.54194e11i	− 0.233734i
$539$	8.01939e11	0.409253
$540$	0	0
$541$	−6.35088e11	−0.318747	−0.159374	−	0.987218i	$-0.550947\pi$
$541$	−6.35088e11	−0.318747	−0.159374	+	0.987218i	$0.550947\pi$
$542$	2.36780e12i	1.17855i
$543$	8.27110e11i	0.408285i
$544$	4.37067e10	0.0213970
$545$	0	0
$546$	−2.03034e12	−0.977691
$547$	− 2.74387e12i	− 1.31045i	−0.755434	−	0.655224i	$-0.772574\pi$
$547$	− 2.74387e12i	− 1.31045i	0.755434	−	0.655224i	$-0.227426\pi$
$548$	1.32234e12i	0.626370i
$549$	2.29619e12	1.07878
$550$	0	0
$551$	2.31003e12	1.06767
$552$	− 1.33638e12i	− 0.612638i
$553$	− 6.37609e11i	− 0.289929i
$554$	−1.21417e12	−0.547629
$555$	0	0
$556$	7.08483e11	0.314407
$557$	1.31358e12i	0.578238i	0.957293	+	0.289119i	$0.0933624\pi$
$557$	1.31358e12i	0.578238i	−0.957293	+	0.289119i	$0.906638\pi$
$558$	3.37580e12i	1.47409i
$559$	−1.54187e12	−0.667875
$560$	0	0
$561$	−6.28653e11	−0.267965
$562$	2.75441e12i	1.16470i
$563$	− 3.11100e12i	− 1.30500i	−0.757787	−	0.652502i	$-0.773719\pi$
$563$	− 3.11100e12i	− 1.30500i	0.757787	−	0.652502i	$-0.226281\pi$
$564$	5.97545e11	0.248665
$565$	0	0
$566$	2.39891e12	0.982518
$567$	1.83640e12i	0.746181i
$568$	− 3.97717e11i	− 0.160327i
$569$	1.45889e12	0.583470	0.291735	−	0.956499i	$-0.405767\pi$
$569$	1.45889e12	0.583470	0.291735	+	0.956499i	$0.405767\pi$
$570$	0	0
$571$	−3.94710e12	−1.55387	−0.776936	−	0.629579i	$-0.783227\pi$
$571$	−3.94710e12	−1.55387	−0.776936	+	0.629579i	$0.783227\pi$
$572$	2.16736e12i	0.846543i
$573$	2.06824e12i	0.801505i
$574$	8.28435e11	0.318533
$575$	0	0
$576$	3.67975e11	0.139289
$577$	5.27904e11i	0.198273i	0.995074	+	0.0991365i	$0.0316080\pi$
$577$	5.27904e11i	0.198273i	−0.995074	+	0.0991365i	$0.968392\pi$
$578$	1.86961e12i	0.696747i
$579$	−1.54568e12	−0.571565
$580$	0	0
$581$	1.75800e12	0.640068
$582$	− 7.59463e11i	− 0.274380i
$583$	3.96392e12i	1.42107i
$584$	7.03893e11	0.250408
$585$	0	0
$586$	−1.52279e11	−0.0533460
$587$	− 4.56943e12i	− 1.58851i	−0.607584	−	0.794255i	$-0.707861\pi$
$587$	− 4.56943e12i	− 1.58851i	0.607584	−	0.794255i	$-0.292139\pi$
$588$	5.66473e11i	0.195425i
$589$	1.01724e13	3.48261
$590$	0	0
$591$	4.50367e10	0.0151853
$592$	− 3.14569e11i	− 0.105261i
$593$	3.19168e12i	1.05992i	0.848022	+	0.529960i	$0.177793\pi$
$593$	3.19168e12i	1.05992i	−0.848022	+	0.529960i	$0.822207\pi$
$594$	−5.42957e11	−0.178948
$595$	0	0
$596$	−1.54663e12	−0.502085
$597$	− 6.10565e12i	− 1.96719i
$598$	2.93034e12i	0.937050i
$599$	−2.72611e12	−0.865211	−0.432605	−	0.901583i	$-0.642406\pi$
$599$	−2.72611e12	−0.865211	−0.432605	+	0.901583i	$0.642406\pi$
$600$	0	0
$601$	1.16094e11	0.0362974	0.0181487	−	0.999835i	$-0.494223\pi$
$601$	1.16094e11	0.0362974	0.0181487	+	0.999835i	$0.494223\pi$
$602$	− 1.17023e12i	− 0.363149i
$603$	3.08315e12i	0.949656i
$604$	−1.04245e11	−0.0318704
$605$	0	0
$606$	2.12580e12	0.640319
$607$	3.81951e12i	1.14198i	0.820957	+	0.570990i	$0.193441\pi$
$607$	3.81951e12i	1.14198i	−0.820957	+	0.570990i	$0.806559\pi$
$608$	− 1.10883e12i	− 0.329077i
$609$	2.42072e12	0.713126
$610$	0	0
$611$	−1.31026e12	−0.380341
$612$	− 2.34038e11i	− 0.0674381i
$613$	− 3.74021e12i	− 1.06985i	−0.844899	−	0.534926i	$-0.820340\pi$
$613$	− 3.74021e12i	− 1.06985i	0.844899	−	0.534926i	$-0.179660\pi$
$614$	1.44944e12	0.411569
$615$	0	0
$616$	−1.64495e12	−0.460298
$617$	− 6.24435e12i	− 1.73462i	−0.497769	−	0.867310i	$-0.665847\pi$
$617$	− 6.24435e12i	− 1.73462i	0.497769	−	0.867310i	$-0.334153\pi$
$618$	− 5.58565e12i	− 1.54037i
$619$	−4.46634e12	−1.22277	−0.611383	−	0.791335i	$-0.709387\pi$
$619$	−4.46634e12	−1.22277	−0.611383	+	0.791335i	$0.709387\pi$
$620$	0	0
$621$	−7.34095e11	−0.198080
$622$	− 4.50056e12i	− 1.20562i
$623$	− 4.85827e12i	− 1.29207i
$624$	−1.53098e12	−0.404239
$625$	0	0
$626$	1.45800e12	0.379465
$627$	1.59487e13i	4.12119i
$628$	4.63201e10i	0.0118837i
$629$	−2.00071e11	−0.0509632
$630$	0	0
$631$	−3.08003e12	−0.773434	−0.386717	−	0.922198i	$-0.626391\pi$
$631$	−3.08003e12	−0.773434	−0.386717	+	0.922198i	$0.626391\pi$
$632$	− 4.80789e11i	− 0.119875i
$633$	− 5.96767e12i	− 1.47737i
$634$	1.65067e12	0.405751
$635$	0	0
$636$	−2.80003e12	−0.678587
$637$	− 1.24213e12i	− 0.298910i
$638$	− 2.58408e12i	− 0.617467i
$639$	−2.12967e12	−0.505310
$640$	0	0
$641$	7.87684e12	1.84285	0.921427	−	0.388552i	$-0.127025\pi$
$641$	7.87684e12	1.84285	0.921427	+	0.388552i	$0.127025\pi$
$642$	4.29389e12i	0.997570i
$643$	− 2.80833e12i	− 0.647886i	−0.946077	−	0.323943i	$-0.894991\pi$
$643$	− 2.80833e12i	− 0.647886i	0.946077	−	0.323943i	$-0.105009\pi$
$644$	−2.22402e12	−0.509510
$645$	0	0
$646$	−7.05233e11	−0.159326
$647$	− 2.03365e12i	− 0.456254i	−0.973631	−	0.228127i	$-0.926740\pi$
$647$	− 2.03365e12i	− 0.456254i	0.973631	−	0.228127i	$-0.0732602\pi$
$648$	1.38474e12i	0.308518i
$649$	−6.05227e12	−1.33911
$650$	0	0
$651$	1.06598e13	2.32613
$652$	− 1.50529e12i	− 0.326216i
$653$	5.29056e12i	1.13865i	0.822111	+	0.569327i	$0.192796\pi$
$653$	5.29056e12i	1.13865i	−0.822111	+	0.569327i	$0.807204\pi$
$654$	−1.01403e12	−0.216745
$655$	0	0
$656$	6.24681e11	0.131702
$657$	− 3.76916e12i	− 0.789225i
$658$	− 9.94443e11i	− 0.206806i
$659$	5.06766e12	1.04670	0.523351	−	0.852117i	$-0.324682\pi$
$659$	5.06766e12	1.04670	0.523351	+	0.852117i	$0.324682\pi$
$660$	0	0
$661$	−6.05804e12	−1.23431	−0.617157	−	0.786840i	$-0.711716\pi$
$661$	−6.05804e12	−1.23431	−0.617157	+	0.786840i	$0.711716\pi$
$662$	4.01728e12i	0.812963i
$663$	9.73727e11i	0.195716i
$664$	1.32562e12	0.264644
$665$	0	0
$666$	−1.68443e12	−0.331757
$667$	− 3.49377e12i	− 0.683483i
$668$	3.48665e11i	0.0677507i
$669$	−1.05770e13	−2.04149
$670$	0	0
$671$	−7.74004e12	−1.47398
$672$	− 1.16196e12i	− 0.219800i
$673$	5.03218e12i	0.945559i	0.881181	+	0.472779i	$0.156749\pi$
$673$	5.03218e12i	0.945559i	−0.881181	+	0.472779i	$0.843251\pi$
$674$	−6.47947e12	−1.20940
$675$	0	0
$676$	6.42293e11	0.118297
$677$	8.61276e12i	1.57577i	0.615821	+	0.787886i	$0.288824\pi$
$677$	8.61276e12i	1.57577i	−0.615821	+	0.787886i	$0.711176\pi$
$678$	− 8.97110e12i	− 1.63047i
$679$	−1.26391e12	−0.228193
$680$	0	0
$681$	−9.30796e12	−1.65841
$682$	− 1.13792e13i	− 2.01410i
$683$	− 3.37706e11i	− 0.0593807i	−0.999559	−	0.0296903i	$-0.990548\pi$
$683$	− 3.37706e11i	− 0.0593807i	0.999559	−	0.0296903i	$-0.00945212\pi$
$684$	−5.93748e12	−1.03717
$685$	0	0
$686$	4.44995e12	0.767178
$687$	1.26785e13i	2.17151i
$688$	− 8.82408e11i	− 0.150149i
$689$	6.13976e12	1.03792
$690$	0	0
$691$	1.74896e11	0.0291830	0.0145915	−	0.999894i	$-0.495355\pi$
$691$	1.74896e11	0.0291830	0.0145915	+	0.999894i	$0.495355\pi$
$692$	3.62952e12i	0.601688i
$693$	8.80826e12i	1.45074i
$694$	6.73356e12	1.10186
$695$	0	0
$696$	1.82534e12	0.294851
$697$	− 3.97308e11i	− 0.0637646i
$698$	6.39012e12i	1.01897i
$699$	−7.59217e11	−0.120287
$700$	0	0
$701$	−5.36577e12	−0.839269	−0.419634	−	0.907693i	$-0.637842\pi$
$701$	−5.36577e12	−0.839269	−0.419634	+	0.907693i	$0.637842\pi$
$702$	8.40991e11i	0.130700i
$703$	5.07575e12i	0.783792i
$704$	−1.24037e12	−0.190316
$705$	0	0
$706$	1.26209e12	0.191192
$707$	− 3.53779e12i	− 0.532531i
$708$	− 4.27519e12i	− 0.639449i
$709$	−5.45452e12	−0.810679	−0.405339	−	0.914166i	$-0.632847\pi$
$709$	−5.45452e12	−0.810679	−0.405339	+	0.914166i	$0.632847\pi$
$710$	0	0
$711$	−2.57450e12	−0.377815
$712$	− 3.66338e12i	− 0.534222i
$713$	− 1.53850e13i	− 2.22944i
$714$	−7.39024e11	−0.106418
$715$	0	0
$716$	6.82128e11	0.0969967
$717$	7.38932e11i	0.104416i
$718$	− 2.23747e12i	− 0.314194i
$719$	6.60953e12	0.922339	0.461169	−	0.887312i	$-0.347430\pi$
$719$	6.60953e12	0.922339	0.461169	+	0.887312i	$0.347430\pi$
$720$	0	0
$721$	−9.29572e12	−1.28107
$722$	1.27285e13i	1.74326i
$723$	6.86575e12i	0.934471i
$724$	1.03794e12	0.140394
$725$	0	0
$726$	1.01445e13	1.35524
$727$	− 1.12652e13i	− 1.49566i	−0.663888	−	0.747832i	$-0.731095\pi$
$727$	− 1.12652e13i	− 1.49566i	0.663888	−	0.747832i	$-0.268905\pi$
$728$	2.54788e12i	0.336192i
$729$	9.25795e12	1.21406
$730$	0	0
$731$	−5.61227e11	−0.0726959
$732$	− 5.46740e12i	− 0.703851i
$733$	− 1.55010e13i	− 1.98332i	−0.128890	−	0.991659i	$-0.541141\pi$
$733$	− 1.55010e13i	− 1.98332i	0.128890	−	0.991659i	$-0.458859\pi$
$734$	8.13859e12	1.03494
$735$	0	0
$736$	−1.67703e12	−0.210664
$737$	− 1.03927e13i	− 1.29755i
$738$	− 3.34500e12i	− 0.415091i
$739$	−8.86702e12	−1.09365	−0.546824	−	0.837247i	$-0.684163\pi$
$739$	−8.86702e12	−1.09365	−0.546824	+	0.837247i	$0.684163\pi$
$740$	0	0
$741$	2.47032e13	3.01003
$742$	4.65985e12i	0.564358i
$743$	1.04586e13i	1.25900i	0.777001	+	0.629500i	$0.216740\pi$
$743$	1.04586e13i	1.25900i	−0.777001	+	0.629500i	$0.783260\pi$
$744$	8.03802e12	0.961770
$745$	0	0
$746$	4.74817e12	0.561309
$747$	− 7.09834e12i	− 0.834093i
$748$	7.88898e11i	0.0921433i
$749$	7.14596e12	0.829645
$750$	0	0
$751$	3.37332e11	0.0386971	0.0193485	−	0.999813i	$-0.493841\pi$
$751$	3.37332e11	0.0386971	0.0193485	+	0.999813i	$0.493841\pi$
$752$	− 7.49860e11i	− 0.0855066i
$753$	1.19974e13i	1.35991i
$754$	−4.00251e12	−0.450984
$755$	0	0
$756$	−6.38282e11	−0.0710664
$757$	− 1.61864e12i	− 0.179151i	−0.995980	−	0.0895756i	$-0.971449\pi$
$757$	− 1.61864e12i	− 0.179151i	0.995980	−	0.0895756i	$-0.0285511\pi$
$758$	7.26269e12i	0.799073i
$759$	2.41214e13	2.63824
$760$	0	0
$761$	−3.16676e12	−0.342282	−0.171141	−	0.985247i	$-0.554745\pi$
$761$	−3.16676e12	−0.342282	−0.171141	+	0.985247i	$0.554745\pi$
$762$	− 8.62750e12i	− 0.927016i
$763$	1.68756e12i	0.180260i
$764$	2.59544e12	0.275608
$765$	0	0
$766$	−4.28108e12	−0.449287
$767$	9.37442e12i	0.978059i
$768$	− 8.76173e11i	− 0.0908792i
$769$	−9.41136e12	−0.970474	−0.485237	−	0.874383i	$-0.661267\pi$
$769$	−9.41136e12	−0.970474	−0.485237	+	0.874383i	$0.661267\pi$
$770$	0	0
$771$	1.53423e13	1.56367
$772$	1.93967e12i	0.196540i
$773$	− 3.00421e12i	− 0.302638i	−0.988485	−	0.151319i	$-0.951648\pi$
$773$	− 3.00421e12i	− 0.302638i	0.988485	−	0.151319i	$-0.0483520\pi$
$774$	−4.72506e12	−0.473231
$775$	0	0
$776$	−9.53051e11	−0.0943493
$777$	5.31895e12i	0.523518i
$778$	− 5.35600e12i	− 0.524122i
$779$	−1.00796e13	−0.980673
$780$	0	0
$781$	7.17871e12	0.690425
$782$	1.06662e12i	0.101995i
$783$	− 1.00269e12i	− 0.0953320i
$784$	7.10868e11	0.0671996
$785$	0	0
$786$	−8.60796e12	−0.804450
$787$	− 4.78765e12i	− 0.444873i	−0.974947	−	0.222436i	$-0.928599\pi$
$787$	− 4.78765e12i	− 0.444873i	0.974947	−	0.222436i	$-0.0714010\pi$
$788$	− 5.65167e10i	− 0.00522166i
$789$	−2.37285e12	−0.217983
$790$	0	0
$791$	−1.49298e13	−1.35600
$792$	6.64187e12i	0.599829i
$793$	1.19886e13i	1.07656i
$794$	−7.28917e12	−0.650857
$795$	0	0
$796$	−7.66199e12	−0.676445
$797$	8.82657e12i	0.774871i	0.921897	+	0.387436i	$0.126639\pi$
$797$	8.82657e12i	0.774871i	−0.921897	+	0.387436i	$0.873361\pi$
$798$	1.87488e13i	1.63667i
$799$	−4.76923e11	−0.0413988
$800$	0	0
$801$	−1.96164e13	−1.68373
$802$	3.50358e12i	0.299038i
$803$	1.27051e13i	1.07835i
$804$	7.34118e12	0.619604
$805$	0	0
$806$	−1.76253e13	−1.47106
$807$	5.79097e12i	0.480641i
$808$	− 2.66767e12i	− 0.220182i
$809$	4.75875e12	0.390593	0.195296	−	0.980744i	$-0.437433\pi$
$809$	4.75875e12	0.390593	0.195296	+	0.980744i	$0.437433\pi$
$810$	0	0
$811$	1.32270e13	1.07366	0.536831	−	0.843690i	$-0.319621\pi$
$811$	1.32270e13	1.07366	0.536831	+	0.843690i	$0.319621\pi$
$812$	− 3.03776e12i	− 0.245218i
$813$	− 3.01894e13i	− 2.42353i
$814$	5.67791e12	0.453293
$815$	0	0
$816$	−5.57261e11	−0.0440000
$817$	1.42382e13i	1.11803i
$818$	5.80877e12i	0.453623i
$819$	1.36432e13	1.05959
$820$	0	0
$821$	1.96204e13	1.50717	0.753587	−	0.657348i	$-0.228322\pi$
$821$	1.96204e13	1.50717	0.753587	+	0.657348i	$0.228322\pi$
$822$	− 1.68598e13i	− 1.28804i
$823$	1.44369e12i	0.109692i	0.998495	+	0.0548461i	$0.0174668\pi$
$823$	1.44369e12i	0.109692i	−0.998495	+	0.0548461i	$0.982533\pi$
$824$	−7.00944e12	−0.529677
$825$	0	0
$826$	−7.11484e12	−0.531808
$827$	6.15968e12i	0.457913i	0.973437	+	0.228957i	$0.0735314\pi$
$827$	6.15968e12i	0.457913i	−0.973437	+	0.228957i	$0.926469\pi$
$828$	8.98003e12i	0.663959i
$829$	7.89482e12	0.580560	0.290280	−	0.956942i	$-0.406252\pi$
$829$	7.89482e12	0.580560	0.290280	+	0.956942i	$0.406252\pi$
$830$	0	0
$831$	1.54807e13	1.12612
$832$	1.92123e12i	0.139003i
$833$	− 4.52124e11i	− 0.0325353i
$834$	−9.03315e12	−0.646535
$835$	0	0
$836$	2.00141e13	1.41712
$837$	− 4.41542e12i	− 0.310962i
$838$	1.82944e13i	1.28150i
$839$	−1.39455e13	−0.971642	−0.485821	−	0.874058i	$-0.661479\pi$
$839$	−1.39455e13	−0.971642	−0.485821	+	0.874058i	$0.661479\pi$
$840$	0	0
$841$	−9.73506e12	−0.671053
$842$	1.05326e13i	0.722157i
$843$	− 3.51188e13i	− 2.39505i
$844$	−7.48884e12	−0.508012
$845$	0	0
$846$	−4.01530e12	−0.269495
$847$	− 1.68826e13i	− 1.12711i
$848$	3.51376e12i	0.233341i
$849$	−3.05861e13	−2.02041
$850$	0	0
$851$	7.67672e12	0.501756
$852$	5.07089e12i	0.329690i
$853$	2.06868e12i	0.133789i	0.997760	+	0.0668947i	$0.0213092\pi$
$853$	2.06868e12i	0.133789i	−0.997760	+	0.0668947i	$0.978691\pi$
$854$	−9.09893e12	−0.585369
$855$	0	0
$856$	5.38841e12	0.343027
$857$	− 1.27749e13i	− 0.808989i	−0.914540	−	0.404494i	$-0.867447\pi$
$857$	− 1.27749e13i	− 0.808989i	0.914540	−	0.404494i	$-0.132553\pi$
$858$	− 2.76338e13i	− 1.74080i
$859$	−2.44751e13	−1.53376	−0.766878	−	0.641793i	$-0.778191\pi$
$859$	−2.44751e13	−1.53376	−0.766878	+	0.641793i	$0.778191\pi$
$860$	0	0
$861$	−1.05625e13	−0.655020
$862$	− 2.04520e12i	− 0.126169i
$863$	− 3.04987e13i	− 1.87169i	−0.352417	−	0.935843i	$-0.614640\pi$
$863$	− 3.04987e13i	− 1.87169i	0.352417	−	0.935843i	$-0.385360\pi$
$864$	−4.81296e11	−0.0293833
$865$	0	0
$866$	9.22857e11	0.0557576
$867$	− 2.38375e13i	− 1.43276i
$868$	− 1.33770e13i	− 0.799871i
$869$	8.67814e12	0.516224
$870$	0	0
$871$	−1.60974e13	−0.947704
$872$	1.27250e12i	0.0745307i
$873$	5.10334e12i	0.297365i
$874$	2.70597e13	1.56864
$875$	0	0
$876$	−8.97464e12	−0.514930
$877$	3.32305e13i	1.89688i	0.316960	+	0.948439i	$0.397338\pi$
$877$	3.32305e13i	1.89688i	−0.316960	+	0.948439i	$0.602662\pi$
$878$	− 6.58270e12i	− 0.373834i
$879$	1.94156e12	0.109699
$880$	0	0
$881$	1.65219e13	0.923995	0.461998	−	0.886881i	$-0.347133\pi$
$881$	1.65219e13	0.923995	0.461998	+	0.886881i	$0.347133\pi$
$882$	− 3.80651e12i	− 0.211796i
$883$	− 2.19061e13i	− 1.21267i	−0.795211	−	0.606333i	$-0.792640\pi$
$883$	− 2.19061e13i	− 1.21267i	0.795211	−	0.606333i	$-0.207360\pi$
$884$	1.22193e12	0.0672995
$885$	0	0
$886$	−1.87606e12	−0.102281
$887$	− 1.63192e13i	− 0.885203i	−0.896718	−	0.442601i	$-0.854056\pi$
$887$	− 1.63192e13i	− 0.885203i	0.896718	−	0.442601i	$-0.145944\pi$
$888$	4.01075e12i	0.216455i
$889$	−1.43580e13	−0.770968
$890$	0	0
$891$	−2.49943e13	−1.32859
$892$	1.32731e13i	0.701991i
$893$	1.20994e13i	0.636697i
$894$	1.97195e13	1.03247
$895$	0	0
$896$	−1.45814e12	−0.0755812
$897$	− 3.73619e13i	− 1.92691i
$898$	− 1.46508e12i	− 0.0751828i
$899$	2.10142e13	1.07299
$900$	0	0
$901$	2.23481e12	0.112974
$902$	1.12754e13i	0.567155i
$903$	1.49204e13i	0.746766i
$904$	−1.12578e13	−0.560657
$905$	0	0
$906$	1.32912e12	0.0655371
$907$	1.98103e12i	0.0971980i	0.998818	+	0.0485990i	$0.0154756\pi$
$907$	1.98103e12i	0.0971980i	−0.998818	+	0.0485990i	$0.984524\pi$
$908$	1.16806e13i	0.570267i
$909$	−1.42847e13	−0.693958
$910$	0	0
$911$	−1.60376e12	−0.0771446	−0.0385723	−	0.999256i	$-0.512281\pi$
$911$	−1.60376e12	−0.0771446	−0.0385723	+	0.999256i	$0.512281\pi$
$912$	1.41375e13i	0.676702i
$913$	2.39272e13i	1.13965i
$914$	−2.48047e13	−1.17564
$915$	0	0
$916$	1.59103e13	0.746703
$917$	1.43255e13i	0.669034i
$918$	3.06113e11i	0.0142262i
$919$	2.81428e13	1.30151	0.650755	−	0.759288i	$-0.274452\pi$
$919$	2.81428e13	1.30151	0.650755	+	0.759288i	$0.274452\pi$
$920$	0	0
$921$	−1.84804e13	−0.846335
$922$	− 2.58920e13i	− 1.17998i
$923$	− 1.11192e13i	− 0.504272i
$924$	2.09731e13	0.946539
$925$	0	0
$926$	−1.44699e13	−0.646721
$927$	3.75337e13i	1.66941i
$928$	− 2.29062e12i	− 0.101388i
$929$	5.39418e12	0.237605	0.118802	−	0.992918i	$-0.462095\pi$
$929$	5.39418e12	0.237605	0.118802	+	0.992918i	$0.462095\pi$
$930$	0	0
$931$	−1.14703e13	−0.500379
$932$	9.52743e11i	0.0413623i
$933$	5.73821e13i	2.47919i
$934$	−2.05208e13	−0.882333
$935$	0	0
$936$	1.02877e13	0.438102
$937$	1.25051e13i	0.529978i	0.964251	+	0.264989i	$0.0853683\pi$
$937$	1.25051e13i	0.529978i	−0.964251	+	0.264989i	$0.914632\pi$
$938$	− 1.22173e13i	− 0.515303i
$939$	−1.85895e13	−0.780318
$940$	0	0
$941$	9.23095e12	0.383789	0.191895	−	0.981416i	$-0.438537\pi$
$941$	9.23095e12	0.383789	0.191895	+	0.981416i	$0.438537\pi$
$942$	− 5.90582e11i	− 0.0244372i
$943$	1.52447e13i	0.627792i
$944$	−5.36495e12	−0.219883
$945$	0	0
$946$	1.59273e13	0.646595
$947$	− 4.13417e13i	− 1.67037i	−0.549967	−	0.835186i	$-0.685360\pi$
$947$	− 4.13417e13i	− 1.67037i	0.549967	−	0.835186i	$-0.314640\pi$
$948$	6.13006e12i	0.246506i
$949$	1.96791e13	0.787603
$950$	0	0
$951$	−2.10461e13	−0.834371
$952$	9.27402e11i	0.0365933i
$953$	1.05715e13i	0.415162i	0.978218	+	0.207581i	$0.0665591\pi$
$953$	1.05715e13i	0.415162i	−0.978218	+	0.207581i	$0.933441\pi$
$954$	1.88153e13	0.735433
$955$	0	0
$956$	9.27287e11	0.0359049
$957$	3.29471e13i	1.26973i
$958$	8.50277e12i	0.326149i
$959$	−2.80584e13	−1.07122
$960$	0	0
$961$	6.60980e13	2.49996
$962$	− 8.79457e12i	− 0.331075i
$963$	− 2.88535e13i	− 1.08114i
$964$	8.61585e12	0.321330
$965$	0	0
$966$	2.83563e13	1.04774
$967$	4.28128e13i	1.57454i	0.616607	+	0.787271i	$0.288507\pi$
$967$	4.28128e13i	1.57454i	−0.616607	+	0.787271i	$0.711493\pi$
$968$	− 1.27303e13i	− 0.466016i
$969$	8.99172e12	0.327632
$970$	0	0
$971$	5.22930e12	0.188780	0.0943902	−	0.995535i	$-0.469910\pi$
$971$	5.22930e12	0.188780	0.0943902	+	0.995535i	$0.469910\pi$
$972$	− 1.99683e13i	− 0.717533i
$973$	1.50331e13i	0.537702i
$974$	−1.77466e13	−0.631828
$975$	0	0
$976$	−6.86105e12	−0.242028
$977$	− 3.56421e12i	− 0.125152i	−0.998040	−	0.0625760i	$-0.980068\pi$
$977$	− 3.56421e12i	− 0.125152i	0.998040	−	0.0625760i	$-0.0199316\pi$
$978$	1.91924e13i	0.670818i
$979$	6.61232e13	2.30055
$980$	0	0
$981$	6.81393e12	0.234902
$982$	− 1.44663e13i	− 0.496427i
$983$	1.92286e13i	0.656837i	0.944532	+	0.328418i	$0.106516\pi$
$983$	1.92286e13i	0.656837i	−0.944532	+	0.328418i	$0.893484\pi$
$984$	−7.96469e12	−0.270826
$985$	0	0
$986$	−1.45688e12	−0.0490881
$987$	1.26791e13i	0.425268i
$988$	− 3.10001e13i	− 1.03504i
$989$	2.15342e13	0.715725
$990$	0	0
$991$	−3.28794e13	−1.08291	−0.541454	−	0.840730i	$-0.682126\pi$
$991$	−3.28794e13	−1.08291	−0.541454	+	0.840730i	$0.682126\pi$
$992$	− 1.00869e13i	− 0.330717i
$993$	− 5.12203e13i	− 1.67175i
$994$	8.43905e12	0.274192
$995$	0	0
$996$	−1.69017e13	−0.544205
$997$	− 1.66280e13i	− 0.532982i	−0.963837	−	0.266491i	$-0.914136\pi$
$997$	− 1.66280e13i	− 0.532982i	0.963837	−	0.266491i	$-0.0858643\pi$
$998$	− 1.61833e13i	− 0.516393i
$999$	2.20317e12	0.0699848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.10.b.e.49.2		2
4.3	odd	2		400.10.c.b.49.2		2
5.2	odd	4		10.10.a.a.1.1	✓	1
5.3	odd	4		50.10.a.f.1.1		1
5.4	even	2	inner	50.10.b.e.49.1		2
15.2	even	4		90.10.a.g.1.1		1
20.3	even	4		400.10.a.a.1.1		1
20.7	even	4		80.10.a.e.1.1		1
20.19	odd	2		400.10.c.b.49.1		2
40.27	even	4		320.10.a.a.1.1		1
40.37	odd	4		320.10.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.10.a.a.1.1	✓	1	5.2	odd	4
50.10.a.f.1.1		1	5.3	odd	4
50.10.b.e.49.1		2	5.4	even	2	inner
50.10.b.e.49.2		2	1.1	even	1	trivial
80.10.a.e.1.1		1	20.7	even	4
90.10.a.g.1.1		1	15.2	even	4
320.10.a.a.1.1		1	40.27	even	4
320.10.a.j.1.1		1	40.37	odd	4
400.10.a.a.1.1		1	20.3	even	4
400.10.c.b.49.1		2	20.19	odd	2
400.10.c.b.49.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+16.0000i q^{2} -204.000i q^{3} -256.000 q^{4} +3264.00 q^{6} -5432.00i q^{7} -4096.00i q^{8} -21933.0 q^{9} +O(q^{10})\)	\(q+16.0000i q^{2} -204.000i q^{3} -256.000 q^{4} +3264.00 q^{6} -5432.00i q^{7} -4096.00i q^{8} -21933.0 q^{9} +73932.0 q^{11} +52224.0i q^{12} -114514. i q^{13} +86912.0 q^{14} +65536.0 q^{16} -41682.0i q^{17} -350928. i q^{18} -1.05746e6 q^{19} -1.10813e6 q^{21} +1.18291e6i q^{22} +1.59934e6i q^{23} -835584. q^{24} +1.83222e6 q^{26} +459000. i q^{27} +1.39059e6i q^{28} -2.18451e6 q^{29} -9.61965e6 q^{31} +1.04858e6i q^{32} -1.50821e7i q^{33} +666912. q^{34} +5.61485e6 q^{36} -4.79994e6i q^{37} -1.69194e7i q^{38} -2.33609e7 q^{39} +9.53188e6 q^{41} -1.77300e7i q^{42} -1.34645e7i q^{43} -1.89266e7 q^{44} -2.55894e7 q^{46} -1.14420e7i q^{47} -1.33693e7i q^{48} +1.08470e7 q^{49} -8.50313e6 q^{51} +2.93156e7i q^{52} +5.36158e7i q^{53} -7.34400e6 q^{54} -2.22495e7 q^{56} +2.15722e8i q^{57} -3.49522e7i q^{58} -8.18626e7 q^{59} -1.04691e8 q^{61} -1.53914e8i q^{62} +1.19140e8i q^{63} -1.67772e7 q^{64} +2.41314e8 q^{66} -1.40571e8i q^{67} +1.06706e7i q^{68} +3.26265e8 q^{69} +9.70988e7 q^{71} +8.98376e7i q^{72} +1.71849e8i q^{73} +7.67991e7 q^{74} +2.70710e8 q^{76} -4.01599e8i q^{77} -3.73774e8i q^{78} +1.17380e8 q^{79} -3.38071e8 q^{81} +1.52510e8i q^{82} +3.23638e8i q^{83} +2.83681e8 q^{84} +2.15432e8 q^{86} +4.45640e8i q^{87} -3.02825e8i q^{88} +8.94379e8 q^{89} -6.22040e8 q^{91} -4.09430e8i q^{92} +1.96241e9i q^{93} +1.83071e8 q^{94} +2.13910e8 q^{96} -2.32679e8i q^{97} +1.73552e8i q^{98} -1.62155e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 512 q^{4} + 6528 q^{6} - 43866 q^{9}+O(q^{10}) \) 2 * q - 512 * q^4 + 6528 * q^6 - 43866 * q^9	\( 2 q - 512 q^{4} + 6528 q^{6} - 43866 q^{9} + 147864 q^{11} + 173824 q^{14} + 131072 q^{16} - 2114920 q^{19} - 2216256 q^{21} - 1671168 q^{24} + 3664448 q^{26} - 4369020 q^{29} - 19239296 q^{31} + 1333824 q^{34} + 11229696 q^{36} - 46721712 q^{39} + 19063764 q^{41} - 37853184 q^{44} - 51178752 q^{46} + 21693966 q^{49} - 17006256 q^{51} - 14688000 q^{54} - 44498944 q^{56} - 163725240 q^{59} - 209382596 q^{61} - 33554432 q^{64} + 482628096 q^{66} + 652529088 q^{69} + 194197584 q^{71} + 153598144 q^{74} + 541419520 q^{76} + 234760160 q^{79} - 676142478 q^{81} + 567361536 q^{84} + 430863488 q^{86} + 1788758220 q^{89} - 1244080096 q^{91} + 366142464 q^{94} + 427819008 q^{96} - 3243101112 q^{99}+O(q^{100}) \) 2 * q - 512 * q^4 + 6528 * q^6 - 43866 * q^9 + 147864 * q^11 + 173824 * q^14 + 131072 * q^16 - 2114920 * q^19 - 2216256 * q^21 - 1671168 * q^24 + 3664448 * q^26 - 4369020 * q^29 - 19239296 * q^31 + 1333824 * q^34 + 11229696 * q^36 - 46721712 * q^39 + 19063764 * q^41 - 37853184 * q^44 - 51178752 * q^46 + 21693966 * q^49 - 17006256 * q^51 - 14688000 * q^54 - 44498944 * q^56 - 163725240 * q^59 - 209382596 * q^61 - 33554432 * q^64 + 482628096 * q^66 + 652529088 * q^69 + 194197584 * q^71 + 153598144 * q^74 + 541419520 * q^76 + 234760160 * q^79 - 676142478 * q^81 + 567361536 * q^84 + 430863488 * q^86 + 1788758220 * q^89 - 1244080096 * q^91 + 366142464 * q^94 + 427819008 * q^96 - 3243101112 * q^99

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