LMFDB - Embedded newform 150.10.c.c.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,10,Mod(49,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("150.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	150.c (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:	$77.2553754246$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.10.c.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} -1296.00 q^{6} +10336.0i q^{7} +4096.00i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} -1296.00 q^{6} +10336.0i q^{7} +4096.00i q^{8} -6561.00 q^{9} +27420.0 q^{11} +20736.0i q^{12} -169762. i q^{13} +165376. q^{14} +65536.0 q^{16} +385086. i q^{17} +104976. i q^{18} +637084. q^{19} +837216. q^{21} -438720. i q^{22} -1.29840e6i q^{23} +331776. q^{24} -2.71619e6 q^{26} +531441. i q^{27} -2.64602e6i q^{28} -7.16297e6 q^{29} -7.03187e6 q^{31} -1.04858e6i q^{32} -2.22102e6i q^{33} +6.16138e6 q^{34} +1.67962e6 q^{36} -1.92604e6i q^{37} -1.01933e7i q^{38} -1.37507e7 q^{39} +8.89607e6 q^{41} -1.33955e7i q^{42} +3.24294e7i q^{43} -7.01952e6 q^{44} -2.07744e7 q^{46} -1.72064e7i q^{47} -5.30842e6i q^{48} -6.64793e7 q^{49} +3.11920e7 q^{51} +4.34591e7i q^{52} -2.06422e7i q^{53} +8.50306e6 q^{54} -4.23363e7 q^{56} -5.16038e7i q^{57} +1.14608e8i q^{58} +6.31934e7 q^{59} -6.37580e7 q^{61} +1.12510e8i q^{62} -6.78145e7i q^{63} -1.67772e7 q^{64} -3.55363e7 q^{66} -1.45262e8i q^{67} -9.85820e7i q^{68} -1.05170e8 q^{69} -3.67657e8 q^{71} -2.68739e7i q^{72} +2.52486e8i q^{73} -3.08166e7 q^{74} -1.63094e8 q^{76} +2.83413e8i q^{77} +2.20012e8i q^{78} +1.85524e8 q^{79} +4.30467e7 q^{81} -1.42337e8i q^{82} -4.67898e8i q^{83} -2.14327e8 q^{84} +5.18871e8 q^{86} +5.80201e8i q^{87} +1.12312e8i q^{88} -5.79096e8 q^{89} +1.75466e9 q^{91} +3.32390e8i q^{92} +5.69582e8i q^{93} -2.75303e8 q^{94} -8.49347e7 q^{96} +1.31452e9i q^{97} +1.06367e9i q^{98} -1.79903e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 512 q^{4} - 2592 q^{6} - 13122 q^{9}+O(q^{10}) $ 2 * q - 512 * q^4 - 2592 * q^6 - 13122 * q^9	$ 2 q - 512 q^{4} - 2592 q^{6} - 13122 q^{9} + 54840 q^{11} + 330752 q^{14} + 131072 q^{16} + 1274168 q^{19} + 1674432 q^{21} + 663552 q^{24} - 5432384 q^{26} - 14325948 q^{29} - 14063744 q^{31} + 12322752 q^{34} + 3359232 q^{36} - 27501444 q^{39} + 17792148 q^{41} - 14039040 q^{44} - 41548800 q^{46} - 132958578 q^{49} + 62383932 q^{51} + 17006112 q^{54} - 84672512 q^{56} + 126386760 q^{59} - 127516100 q^{61} - 33554432 q^{64} - 71072640 q^{66} - 210340800 q^{69} - 735313680 q^{71} - 61633216 q^{74} - 326187008 q^{76} + 371047424 q^{79} + 86093442 q^{81} - 428654592 q^{84} + 1037742208 q^{86} - 1158192756 q^{89} + 3509320064 q^{91} - 550606080 q^{94} - 169869312 q^{96} - 359805240 q^{99}+O(q^{100}) $ 2 * q - 512 * q^4 - 2592 * q^6 - 13122 * q^9 + 54840 * q^11 + 330752 * q^14 + 131072 * q^16 + 1274168 * q^19 + 1674432 * q^21 + 663552 * q^24 - 5432384 * q^26 - 14325948 * q^29 - 14063744 * q^31 + 12322752 * q^34 + 3359232 * q^36 - 27501444 * q^39 + 17792148 * q^41 - 14039040 * q^44 - 41548800 * q^46 - 132958578 * q^49 + 62383932 * q^51 + 17006112 * q^54 - 84672512 * q^56 + 126386760 * q^59 - 127516100 * q^61 - 33554432 * q^64 - 71072640 * q^66 - 210340800 * q^69 - 735313680 * q^71 - 61633216 * q^74 - 326187008 * q^76 + 371047424 * q^79 + 86093442 * q^81 - 428654592 * q^84 + 1037742208 * q^86 - 1158192756 * q^89 + 3509320064 * q^91 - 550606080 * q^94 - 169869312 * q^96 - 359805240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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
$3$	− 81.0000i	− 0.577350i
$3$	− 81.0000i	− 0.577350i
$4$	−256.000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1296.00	−0.408248
$7$	10336.0i	1.62709i	0.581503	+	0.813545i	$0.302465\pi$
$7$	10336.0i	1.62709i	−0.581503	+	0.813545i	$0.697535\pi$
$8$	4096.00i	0.353553i
$9$	−6561.00	−0.333333
$10$	0	0
$11$	27420.0	0.564677	0.282339	−	0.959315i	$-0.408890\pi$
$11$	27420.0	0.564677	0.282339	+	0.959315i	$0.408890\pi$
$12$	20736.0i	0.288675i
$13$	− 169762.i	− 1.64852i	−0.566208	−	0.824262i	$-0.691590\pi$
$13$	− 169762.i	− 1.64852i	0.566208	−	0.824262i	$-0.308410\pi$
$14$	165376.	1.15053
$15$	0	0
$16$	65536.0	0.250000
$17$	385086.i	1.11825i	0.829085	+	0.559123i	$0.188862\pi$
$17$	385086.i	1.11825i	−0.829085	+	0.559123i	$0.811138\pi$
$18$	104976.i	0.235702i
$19$	637084.	1.12152	0.560758	−	0.827980i	$-0.310510\pi$
$19$	637084.	1.12152	0.560758	+	0.827980i	$0.310510\pi$
$20$	0	0
$21$	837216.	0.939400
$22$	− 438720.i	− 0.399287i
$23$	− 1.29840e6i	− 0.967461i	−0.875217	−	0.483730i	$-0.839282\pi$
$23$	− 1.29840e6i	− 0.967461i	0.875217	−	0.483730i	$-0.160718\pi$
$24$	331776.	0.204124
$25$	0	0
$26$	−2.71619e6	−1.16568
$27$	531441.i	0.192450i
$28$	− 2.64602e6i	− 0.813545i
$29$	−7.16297e6	−1.88063	−0.940313	−	0.340311i	$-0.889468\pi$
$29$	−7.16297e6	−1.88063	−0.940313	+	0.340311i	$0.889468\pi$
$30$	0	0
$31$	−7.03187e6	−1.36755	−0.683775	−	0.729693i	$-0.739663\pi$
$31$	−7.03187e6	−1.36755	−0.683775	+	0.729693i	$0.739663\pi$
$32$	− 1.04858e6i	− 0.176777i
$33$	− 2.22102e6i	− 0.326017i
$34$	6.16138e6	0.790720
$35$	0	0
$36$	1.67962e6	0.166667
$37$	− 1.92604e6i	− 0.168950i	−0.996426	−	0.0844748i	$-0.973079\pi$
$37$	− 1.92604e6i	− 0.168950i	0.996426	−	0.0844748i	$-0.0269212\pi$
$38$	− 1.01933e7i	− 0.793032i
$39$	−1.37507e7	−0.951776
$40$	0	0
$41$	8.89607e6	0.491667	0.245833	−	0.969312i	$-0.420938\pi$
$41$	8.89607e6	0.491667	0.245833	+	0.969312i	$0.420938\pi$
$42$	− 1.33955e7i	− 0.664256i
$43$	3.24294e7i	1.44654i	0.690564	+	0.723272i	$0.257363\pi$
$43$	3.24294e7i	1.44654i	−0.690564	+	0.723272i	$0.742637\pi$
$44$	−7.01952e6	−0.282339
$45$	0	0
$46$	−2.07744e7	−0.684098
$47$	− 1.72064e7i	− 0.514340i	−0.966366	−	0.257170i	$-0.917210\pi$
$47$	− 1.72064e7i	− 0.514340i	0.966366	−	0.257170i	$-0.0827901\pi$
$48$	− 5.30842e6i	− 0.144338i
$49$	−6.64793e7	−1.64742
$50$	0	0
$51$	3.11920e7	0.645620
$52$	4.34591e7i	0.824262i
$53$	− 2.06422e7i	− 0.359347i	−0.983726	−	0.179673i	$-0.942496\pi$
$53$	− 2.06422e7i	− 0.359347i	0.983726	−	0.179673i	$-0.0575041\pi$
$54$	8.50306e6	0.136083
$55$	0	0
$56$	−4.23363e7	−0.575263
$57$	− 5.16038e7i	− 0.647508i
$58$	1.14608e8i	1.32980i
$59$	6.31934e7	0.678950	0.339475	−	0.940615i	$-0.389751\pi$
$59$	6.31934e7	0.678950	0.339475	+	0.940615i	$0.389751\pi$
$60$	0	0
$61$	−6.37580e7	−0.589591	−0.294795	−	0.955560i	$-0.595252\pi$
$61$	−6.37580e7	−0.589591	−0.294795	+	0.955560i	$0.595252\pi$
$62$	1.12510e8i	0.967004i
$63$	− 6.78145e7i	− 0.542363i
$64$	−1.67772e7	−0.125000
$65$	0	0
$66$	−3.55363e7	−0.230529
$67$	− 1.45262e8i	− 0.880674i	−0.897833	−	0.440337i	$-0.854859\pi$
$67$	− 1.45262e8i	− 0.880674i	0.897833	−	0.440337i	$-0.145141\pi$
$68$	− 9.85820e7i	− 0.559123i
$69$	−1.05170e8	−0.558564
$70$	0	0
$71$	−3.67657e8	−1.71704	−0.858519	−	0.512781i	$-0.828615\pi$
$71$	−3.67657e8	−1.71704	−0.858519	+	0.512781i	$0.828615\pi$
$72$	− 2.68739e7i	− 0.117851i
$73$	2.52486e8i	1.04060i	0.853983	+	0.520301i	$0.174180\pi$
$73$	2.52486e8i	1.04060i	−0.853983	+	0.520301i	$0.825820\pi$
$74$	−3.08166e7	−0.119465
$75$	0	0
$76$	−1.63094e8	−0.560758
$77$	2.83413e8i	0.918780i
$78$	2.20012e8i	0.673007i
$79$	1.85524e8	0.535892	0.267946	−	0.963434i	$-0.413655\pi$
$79$	1.85524e8	0.535892	0.267946	+	0.963434i	$0.413655\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	− 1.42337e8i	− 0.347661i
$83$	− 4.67898e8i	− 1.08218i	−0.840965	−	0.541090i	$-0.818012\pi$
$83$	− 4.67898e8i	− 1.08218i	0.840965	−	0.541090i	$-0.181988\pi$
$84$	−2.14327e8	−0.469700
$85$	0	0
$86$	5.18871e8	1.02286
$87$	5.80201e8i	1.08578i
$88$	1.12312e8i	0.199644i
$89$	−5.79096e8	−0.978354	−0.489177	−	0.872185i	$-0.662703\pi$
$89$	−5.79096e8	−0.978354	−0.489177	+	0.872185i	$0.662703\pi$
$90$	0	0
$91$	1.75466e9	2.68230
$92$	3.32390e8i	0.483730i
$93$	5.69582e8i	0.789556i
$94$	−2.75303e8	−0.363694
$95$	0	0
$96$	−8.49347e7	−0.102062
$97$	1.31452e9i	1.50763i	0.657090	+	0.753813i	$0.271787\pi$
$97$	1.31452e9i	1.50763i	−0.657090	+	0.753813i	$0.728213\pi$
$98$	1.06367e9i	1.16490i
$99$	−1.79903e8	−0.188226
$100$	0	0
$101$	−4.40286e8	−0.421006	−0.210503	−	0.977593i	$-0.567510\pi$
$101$	−4.40286e8	−0.421006	−0.210503	+	0.977593i	$0.567510\pi$
$102$	− 4.99071e8i	− 0.456522i
$103$	− 5.91306e8i	− 0.517660i	−0.965923	−	0.258830i	$-0.916663\pi$
$103$	− 5.91306e8i	− 0.517660i	0.965923	−	0.258830i	$-0.0833369\pi$
$104$	6.95345e8	0.582841
$105$	0	0
$106$	−3.30274e8	−0.254096
$107$	9.15121e8i	0.674918i	0.941340	+	0.337459i	$0.109568\pi$
$107$	9.15121e8i	0.674918i	−0.941340	+	0.337459i	$0.890432\pi$
$108$	− 1.36049e8i	− 0.0962250i
$109$	−2.37000e9	−1.60816	−0.804079	−	0.594523i	$-0.797341\pi$
$109$	−2.37000e9	−1.60816	−0.804079	+	0.594523i	$0.797341\pi$
$110$	0	0
$111$	−1.56009e8	−0.0975431
$112$	6.77380e8i	0.406772i
$113$	2.26842e8i	0.130879i	0.997857	+	0.0654394i	$0.0208449\pi$
$113$	2.26842e8i	0.130879i	−0.997857	+	0.0654394i	$0.979155\pi$
$114$	−8.25661e8	−0.457857
$115$	0	0
$116$	1.83372e9	0.940313
$117$	1.11381e9i	0.549508i
$118$	− 1.01109e9i	− 0.480090i
$119$	−3.98025e9	−1.81949
$120$	0	0
$121$	−1.60609e9	−0.681139
$122$	1.02013e9i	0.416904i
$123$	− 7.20582e8i	− 0.283864i
$124$	1.80016e9	0.683775
$125$	0	0
$126$	−1.08503e9	−0.383509
$127$	4.44062e9i	1.51470i	0.653009	+	0.757350i	$0.273506\pi$
$127$	4.44062e9i	1.51470i	−0.653009	+	0.757350i	$0.726494\pi$
$128$	2.68435e8i	0.0883883i
$129$	2.62678e9	0.835162
$130$	0	0
$131$	2.56985e9	0.762407	0.381204	−	0.924491i	$-0.375510\pi$
$131$	2.56985e9	0.762407	0.381204	+	0.924491i	$0.375510\pi$
$132$	5.68581e8i	0.163008i
$133$	6.58490e9i	1.82481i
$134$	−2.32419e9	−0.622731
$135$	0	0
$136$	−1.57731e9	−0.395360
$137$	3.05072e9i	0.739878i	0.929056	+	0.369939i	$0.120621\pi$
$137$	3.05072e9i	0.739878i	−0.929056	+	0.369939i	$0.879379\pi$
$138$	1.68273e9i	0.394964i
$139$	−2.21959e9	−0.504321	−0.252160	−	0.967685i	$-0.581141\pi$
$139$	−2.21959e9	−0.504321	−0.252160	+	0.967685i	$0.581141\pi$
$140$	0	0
$141$	−1.39372e9	−0.296955
$142$	5.88251e9i	1.21413i
$143$	− 4.65487e9i	− 0.930884i
$144$	−4.29982e8	−0.0833333
$145$	0	0
$146$	4.03978e9	0.735817
$147$	5.38482e9i	0.951138i
$148$	4.93066e8i	0.0844748i
$149$	−2.77268e9	−0.460853	−0.230426	−	0.973090i	$-0.574012\pi$
$149$	−2.77268e9	−0.460853	−0.230426	+	0.973090i	$0.574012\pi$
$150$	0	0
$151$	−2.53999e9	−0.397591	−0.198795	−	0.980041i	$-0.563703\pi$
$151$	−2.53999e9	−0.397591	−0.198795	+	0.980041i	$0.563703\pi$
$152$	2.60950e9i	0.396516i
$153$	− 2.52655e9i	− 0.372749i
$154$	4.53461e9	0.649676
$155$	0	0
$156$	3.52018e9	0.475888
$157$	− 9.52972e9i	− 1.25179i	−0.779907	−	0.625895i	$-0.784734\pi$
$157$	− 9.52972e9i	− 1.25179i	0.779907	−	0.625895i	$-0.215266\pi$
$158$	− 2.96838e9i	− 0.378933i
$159$	−1.67201e9	−0.207469
$160$	0	0
$161$	1.34203e10	1.57414
$162$	− 6.88748e8i	− 0.0785674i
$163$	3.29763e9i	0.365896i	0.983123	+	0.182948i	$0.0585640\pi$
$163$	3.29763e9i	0.365896i	−0.983123	+	0.182948i	$0.941436\pi$
$164$	−2.27739e9	−0.245833
$165$	0	0
$166$	−7.48636e9	−0.765217
$167$	− 1.07574e10i	− 1.07025i	−0.844774	−	0.535123i	$-0.820265\pi$
$167$	− 1.07574e10i	− 1.07025i	0.844774	−	0.535123i	$-0.179735\pi$
$168$	3.42924e9i	0.332128i
$169$	−1.82146e10	−1.71763
$170$	0	0
$171$	−4.17991e9	−0.373839
$172$	− 8.30194e9i	− 0.723272i
$173$	8.56587e9i	0.727049i	0.931585	+	0.363525i	$0.118427\pi$
$173$	8.56587e9i	0.727049i	−0.931585	+	0.363525i	$0.881573\pi$
$174$	9.28321e9	0.767762
$175$	0	0
$176$	1.79700e9	0.141169
$177$	− 5.11866e9i	− 0.391992i
$178$	9.26554e9i	0.691800i
$179$	6.25110e9	0.455112	0.227556	−	0.973765i	$-0.426927\pi$
$179$	6.25110e9	0.455112	0.227556	+	0.973765i	$0.426927\pi$
$180$	0	0
$181$	−2.24946e10	−1.55785	−0.778925	−	0.627117i	$-0.784235\pi$
$181$	−2.24946e10	−1.55785	−0.778925	+	0.627117i	$0.784235\pi$
$182$	− 2.80746e10i	− 1.89667i
$183$	5.16440e9i	0.340400i
$184$	5.31825e9	0.342049
$185$	0	0
$186$	9.11331e9	0.558300
$187$	1.05591e10i	0.631449i
$188$	4.40485e9i	0.257170i
$189$	−5.49297e9	−0.313133
$190$	0	0
$191$	−2.69014e10	−1.46260	−0.731300	−	0.682056i	$-0.761086\pi$
$191$	−2.69014e10	−1.46260	−0.731300	+	0.682056i	$0.761086\pi$
$192$	1.35895e9i	0.0721688i
$193$	− 1.35021e10i	− 0.700476i	−0.936661	−	0.350238i	$-0.886101\pi$
$193$	− 1.35021e10i	− 0.700476i	0.936661	−	0.350238i	$-0.113899\pi$
$194$	2.10323e10	1.06605
$195$	0	0
$196$	1.70187e10	0.823709
$197$	2.11455e10i	1.00028i	0.865945	+	0.500138i	$0.166718\pi$
$197$	2.11455e10i	1.00028i	−0.865945	+	0.500138i	$0.833282\pi$
$198$	2.87844e9i	0.133096i
$199$	−5.66505e9	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$199$	−5.66505e9	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$200$	0	0
$201$	−1.17662e10	−0.508458
$202$	7.04458e9i	0.297697i
$203$	− 7.40365e10i	− 3.05995i
$204$	−7.98514e9	−0.322810
$205$	0	0
$206$	−9.46089e9	−0.366041
$207$	8.51880e9i	0.322487i
$208$	− 1.11255e10i	− 0.412131i
$209$	1.74688e10	0.633295
$210$	0	0
$211$	−2.18540e10	−0.759031	−0.379516	−	0.925185i	$-0.623909\pi$
$211$	−2.18540e10	−0.759031	−0.379516	+	0.925185i	$0.623909\pi$
$212$	5.28439e9i	0.179673i
$213$	2.97802e10i	0.991333i
$214$	1.46419e10	0.477239
$215$	0	0
$216$	−2.17678e9	−0.0680414
$217$	− 7.26814e10i	− 2.22513i
$218$	3.79200e10i	1.13714i
$219$	2.04514e10	0.600792
$220$	0	0
$221$	6.53730e10	1.84346
$222$	2.49615e9i	0.0689734i
$223$	− 3.41926e10i	− 0.925891i	−0.886387	−	0.462945i	$-0.846793\pi$
$223$	− 3.41926e10i	− 0.925891i	0.886387	−	0.462945i	$-0.153207\pi$
$224$	1.08381e10	0.287631
$225$	0	0
$226$	3.62946e9	0.0925453
$227$	2.23784e10i	0.559388i	0.960089	+	0.279694i	$0.0902330\pi$
$227$	2.23784e10i	0.559388i	−0.960089	+	0.279694i	$0.909767\pi$
$228$	1.32106e10i	0.323754i
$229$	2.76787e9	0.0665099	0.0332550	−	0.999447i	$-0.489413\pi$
$229$	2.76787e9	0.0665099	0.0332550	+	0.999447i	$0.489413\pi$
$230$	0	0
$231$	2.29565e10	0.530458
$232$	− 2.93395e10i	− 0.664902i
$233$	− 6.55570e10i	− 1.45719i	−0.684942	−	0.728597i	$-0.740173\pi$
$233$	− 6.55570e10i	− 1.45719i	0.684942	−	0.728597i	$-0.259827\pi$
$234$	1.78209e10	0.388561
$235$	0	0
$236$	−1.61775e10	−0.339475
$237$	− 1.50274e10i	− 0.309398i
$238$	6.36840e10i	1.28657i
$239$	−2.70069e10	−0.535406	−0.267703	−	0.963501i	$-0.586265\pi$
$239$	−2.70069e10	−0.535406	−0.267703	+	0.963501i	$0.586265\pi$
$240$	0	0
$241$	−1.73578e10	−0.331450	−0.165725	−	0.986172i	$-0.552996\pi$
$241$	−1.73578e10	−0.331450	−0.165725	+	0.986172i	$0.552996\pi$
$242$	2.56975e10i	0.481638i
$243$	− 3.48678e9i	− 0.0641500i
$244$	1.63221e10	0.294795
$245$	0	0
$246$	−1.15293e10	−0.200722
$247$	− 1.08153e11i	− 1.84885i
$248$	− 2.88025e10i	− 0.483502i
$249$	−3.78997e10	−0.624797
$250$	0	0
$251$	−2.23811e10	−0.355918	−0.177959	−	0.984038i	$-0.556949\pi$
$251$	−2.23811e10	−0.355918	−0.177959	+	0.984038i	$0.556949\pi$
$252$	1.73605e10i	0.271182i
$253$	− 3.56021e10i	− 0.546303i
$254$	7.10499e10	1.07105
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	− 1.29994e11i	− 1.85876i	−0.369125	−	0.929380i	$-0.620343\pi$
$257$	− 1.29994e11i	− 1.85876i	0.369125	−	0.929380i	$-0.379657\pi$
$258$	− 4.20286e10i	− 0.590549i
$259$	1.99075e10	0.274896
$260$	0	0
$261$	4.69963e10	0.626875
$262$	− 4.11176e10i	− 0.539103i
$263$	7.50129e10i	0.966796i	0.875401	+	0.483398i	$0.160598\pi$
$263$	7.50129e10i	0.966796i	−0.875401	+	0.483398i	$0.839402\pi$
$264$	9.09730e9	0.115264
$265$	0	0
$266$	1.05358e11	1.29033
$267$	4.69068e10i	0.564853i
$268$	3.71871e10i	0.440337i
$269$	3.22655e10	0.375710	0.187855	−	0.982197i	$-0.439846\pi$
$269$	3.22655e10	0.375710	0.187855	+	0.982197i	$0.439846\pi$
$270$	0	0
$271$	−3.88817e10	−0.437909	−0.218954	−	0.975735i	$-0.570265\pi$
$271$	−3.88817e10	−0.437909	−0.218954	+	0.975735i	$0.570265\pi$
$272$	2.52370e10i	0.279562i
$273$	− 1.42127e11i	− 1.54862i
$274$	4.88115e10	0.523172
$275$	0	0
$276$	2.69236e10	0.279282
$277$	1.39247e11i	1.42110i	0.703645	+	0.710552i	$0.251555\pi$
$277$	1.39247e11i	1.42110i	−0.703645	+	0.710552i	$0.748445\pi$
$278$	3.55135e10i	0.356608i
$279$	4.61361e10	0.455850
$280$	0	0
$281$	1.21771e11	1.16511	0.582553	−	0.812793i	$-0.302054\pi$
$281$	1.21771e11	1.16511	0.582553	+	0.812793i	$0.302054\pi$
$282$	2.22995e10i	0.209979i
$283$	1.12442e11i	1.04205i	0.853541	+	0.521025i	$0.174450\pi$
$283$	1.12442e11i	1.04205i	−0.853541	+	0.521025i	$0.825550\pi$
$284$	9.41202e10	0.858519
$285$	0	0
$286$	−7.44780e10	−0.658235
$287$	9.19498e10i	0.799986i
$288$	6.87971e9i	0.0589256i
$289$	−2.97034e10	−0.250475
$290$	0	0
$291$	1.06476e11	0.870428
$292$	− 6.46365e10i	− 0.520301i
$293$	− 5.73383e10i	− 0.454507i	−0.973836	−	0.227253i	$-0.927025\pi$
$293$	− 5.73383e10i	− 0.454507i	0.973836	−	0.227253i	$-0.0729745\pi$
$294$	8.61572e10	0.672556
$295$	0	0
$296$	7.88905e9	0.0597327
$297$	1.45721e10i	0.108672i
$298$	4.43629e10i	0.325872i
$299$	−2.20419e11	−1.59488
$300$	0	0
$301$	−3.35191e11	−2.35365
$302$	4.06399e10i	0.281139i
$303$	3.56632e10i	0.243068i
$304$	4.17519e10	0.280379
$305$	0	0
$306$	−4.04248e10	−0.263573
$307$	1.59602e11i	1.02545i	0.858552	+	0.512727i	$0.171365\pi$
$307$	1.59602e11i	1.02545i	−0.858552	+	0.512727i	$0.828635\pi$
$308$	− 7.25538e10i	− 0.459390i
$309$	−4.78958e10	−0.298871
$310$	0	0
$311$	−1.22091e11	−0.740051	−0.370025	−	0.929022i	$-0.620651\pi$
$311$	−1.22091e11	−0.740051	−0.370025	+	0.929022i	$0.620651\pi$
$312$	− 5.63230e10i	− 0.336504i
$313$	− 1.28323e11i	− 0.755707i	−0.925865	−	0.377854i	$-0.876662\pi$
$313$	− 1.28323e11i	− 0.755707i	0.925865	−	0.377854i	$-0.123338\pi$
$314$	−1.52476e11	−0.885150
$315$	0	0
$316$	−4.74941e10	−0.267946
$317$	− 1.25978e11i	− 0.700694i	−0.936620	−	0.350347i	$-0.886064\pi$
$317$	− 1.25978e11i	− 0.700694i	0.936620	−	0.350347i	$-0.113936\pi$
$318$	2.67522e10i	0.146703i
$319$	−1.96409e11	−1.06195
$320$	0	0
$321$	7.41248e10	0.389664
$322$	− 2.14724e11i	− 1.11309i
$323$	2.45332e11i	1.25413i
$324$	−1.10200e10	−0.0555556
$325$	0	0
$326$	5.27621e10	0.258728
$327$	1.91970e11i	0.928470i
$328$	3.64383e10i	0.173831i
$329$	1.77846e11	0.836878
$330$	0	0
$331$	−2.67273e11	−1.22385	−0.611926	−	0.790915i	$-0.709605\pi$
$331$	−2.67273e11	−1.22385	−0.611926	+	0.790915i	$0.709605\pi$
$332$	1.19782e11i	0.541090i
$333$	1.26367e10i	0.0563165i
$334$	−1.72119e11	−0.756779
$335$	0	0
$336$	5.48678e10	0.234850
$337$	− 3.93835e11i	− 1.66333i	−0.555275	−	0.831667i	$-0.687387\pi$
$337$	− 3.93835e11i	− 1.66333i	0.555275	−	0.831667i	$-0.312613\pi$
$338$	2.91434e11i	1.21455i
$339$	1.83742e10	0.0755630
$340$	0	0
$341$	−1.92814e11	−0.772225
$342$	6.68785e10i	0.264344i
$343$	− 2.70035e11i	− 1.05341i
$344$	−1.32831e11	−0.511430
$345$	0	0
$346$	1.37054e11	0.514101
$347$	2.50368e11i	0.927035i	0.886088	+	0.463518i	$0.153413\pi$
$347$	2.50368e11i	0.927035i	−0.886088	+	0.463518i	$0.846587\pi$
$348$	− 1.48531e11i	− 0.542890i
$349$	−1.69543e11	−0.611739	−0.305869	−	0.952073i	$-0.598947\pi$
$349$	−1.69543e11	−0.611739	−0.305869	+	0.952073i	$0.598947\pi$
$350$	0	0
$351$	9.02185e10	0.317259
$352$	− 2.87520e10i	− 0.0998218i
$353$	4.12724e11i	1.41473i	0.706848	+	0.707365i	$0.250116\pi$
$353$	4.12724e11i	1.41473i	−0.706848	+	0.707365i	$0.749884\pi$
$354$	−8.18986e10	−0.277180
$355$	0	0
$356$	1.48249e11	0.489177
$357$	3.22400e11i	1.05048i
$358$	− 1.00018e11i	− 0.321813i
$359$	−3.52888e11	−1.12127	−0.560637	−	0.828062i	$-0.689444\pi$
$359$	−3.52888e11	−1.12127	−0.560637	+	0.828062i	$0.689444\pi$
$360$	0	0
$361$	8.31883e10	0.257798
$362$	3.59914e11i	1.10157i
$363$	1.30093e11i	0.393256i
$364$	−4.49193e11	−1.34115
$365$	0	0
$366$	8.26304e10	0.240699
$367$	− 5.62062e11i	− 1.61729i	−0.588299	−	0.808644i	$-0.700202\pi$
$367$	− 5.62062e11i	− 1.61729i	0.588299	−	0.808644i	$-0.299798\pi$
$368$	− 8.50919e10i	− 0.241865i
$369$	−5.83671e10	−0.163889
$370$	0	0
$371$	2.13357e11	0.584689
$372$	− 1.45813e11i	− 0.394778i
$373$	− 1.89328e10i	− 0.0506436i	−0.999679	−	0.0253218i	$-0.991939\pi$
$373$	− 1.89328e10i	− 0.0506436i	0.999679	−	0.0253218i	$-0.00806103\pi$
$374$	1.68945e11	0.446502
$375$	0	0
$376$	7.04776e10	0.181847
$377$	1.21600e12i	3.10026i
$378$	8.78876e10i	0.221419i
$379$	−7.10525e11	−1.76890	−0.884449	−	0.466637i	$-0.845465\pi$
$379$	−7.10525e11	−1.76890	−0.884449	+	0.466637i	$0.845465\pi$
$380$	0	0
$381$	3.59690e11	0.874512
$382$	4.30423e11i	1.03421i
$383$	− 6.37883e11i	− 1.51477i	−0.652969	−	0.757385i	$-0.726477\pi$
$383$	− 6.37883e11i	− 1.51477i	0.652969	−	0.757385i	$-0.273523\pi$
$384$	2.17433e10	0.0510310
$385$	0	0
$386$	−2.16034e11	−0.495311
$387$	− 2.12770e11i	− 0.482181i
$388$	− 3.36516e11i	− 0.753813i
$389$	8.56047e11	1.89550	0.947751	−	0.319010i	$-0.103350\pi$
$389$	8.56047e11	1.89550	0.947751	+	0.319010i	$0.103350\pi$
$390$	0	0
$391$	4.99996e11	1.08186
$392$	− 2.72299e11i	− 0.582450i
$393$	− 2.08158e11i	− 0.440176i
$394$	3.38328e11	0.707303
$395$	0	0
$396$	4.60551e10	0.0941129
$397$	4.22739e11i	0.854113i	0.904225	+	0.427057i	$0.140450\pi$
$397$	4.22739e11i	0.854113i	−0.904225	+	0.427057i	$0.859550\pi$
$398$	9.06408e10i	0.181071i
$399$	5.33377e11	1.05355
$400$	0	0
$401$	−8.96364e10	−0.173115	−0.0865575	−	0.996247i	$-0.527587\pi$
$401$	−8.96364e10	−0.173115	−0.0865575	+	0.996247i	$0.527587\pi$
$402$	1.88260e11i	0.359534i
$403$	1.19374e12i	2.25444i
$404$	1.12713e11	0.210503
$405$	0	0
$406$	−1.18458e12	−2.16371
$407$	− 5.28120e10i	− 0.0954020i
$408$	1.27762e11i	0.228261i
$409$	−5.75119e10	−0.101626	−0.0508128	−	0.998708i	$-0.516181\pi$
$409$	−5.75119e10	−0.101626	−0.0508128	+	0.998708i	$0.516181\pi$
$410$	0	0
$411$	2.47108e11	0.427169
$412$	1.51374e11i	0.258830i
$413$	6.53167e11i	1.10471i
$414$	1.36301e11	0.228033
$415$	0	0
$416$	−1.78008e11	−0.291421
$417$	1.79787e11i	0.291170i
$418$	− 2.79501e11i	− 0.447807i
$419$	6.82070e11	1.08110	0.540550	−	0.841312i	$-0.318216\pi$
$419$	6.82070e11	1.08110	0.540550	+	0.841312i	$0.318216\pi$
$420$	0	0
$421$	−1.18903e12	−1.84469	−0.922343	−	0.386373i	$-0.873728\pi$
$421$	−1.18903e12	−1.84469	−0.922343	+	0.386373i	$0.873728\pi$
$422$	3.49664e11i	0.536716i
$423$	1.12891e11i	0.171447i
$424$	8.45503e10	0.127048
$425$	0	0
$426$	4.76483e11	0.700978
$427$	− 6.59003e11i	− 0.959317i
$428$	− 2.34271e11i	− 0.337459i
$429$	−3.77045e11	−0.537446
$430$	0	0
$431$	1.08626e12	1.51631	0.758155	−	0.652074i	$-0.226101\pi$
$431$	1.08626e12	1.51631	0.758155	+	0.652074i	$0.226101\pi$
$432$	3.48285e10i	0.0481125i
$433$	2.75569e11i	0.376734i	0.982099	+	0.188367i	$0.0603195\pi$
$433$	2.75569e11i	0.376734i	−0.982099	+	0.188367i	$0.939681\pi$
$434$	−1.16290e12	−1.57340
$435$	0	0
$436$	6.06719e11	0.804079
$437$	− 8.27190e11i	− 1.08502i
$438$	− 3.27222e11i	− 0.424824i
$439$	1.31894e11	0.169487	0.0847434	−	0.996403i	$-0.472993\pi$
$439$	1.31894e11	0.169487	0.0847434	+	0.996403i	$0.472993\pi$
$440$	0	0
$441$	4.36171e11	0.549140
$442$	− 1.04597e12i	− 1.30352i
$443$	− 1.17850e12i	− 1.45382i	−0.686730	−	0.726912i	$-0.740955\pi$
$443$	− 1.17850e12i	− 1.45382i	0.686730	−	0.726912i	$-0.259045\pi$
$444$	3.99383e10	0.0487715
$445$	0	0
$446$	−5.47081e11	−0.654704
$447$	2.24587e11i	0.266073i
$448$	− 1.73409e11i	− 0.203386i
$449$	1.32158e11	0.153457	0.0767283	−	0.997052i	$-0.475553\pi$
$449$	1.32158e11	0.153457	0.0767283	+	0.997052i	$0.475553\pi$
$450$	0	0
$451$	2.43930e11	0.277633
$452$	− 5.80714e10i	− 0.0654394i
$453$	2.05740e11i	0.229549i
$454$	3.58055e11	0.395547
$455$	0	0
$456$	2.11369e11	0.228929
$457$	7.17700e10i	0.0769697i	0.999259	+	0.0384849i	$0.0122531\pi$
$457$	7.17700e10i	0.0769697i	−0.999259	+	0.0384849i	$0.987747\pi$
$458$	− 4.42860e10i	− 0.0470296i
$459$	−2.04650e11	−0.215207
$460$	0	0
$461$	1.64460e12	1.69592	0.847961	−	0.530059i	$-0.177830\pi$
$461$	1.64460e12	1.69592	0.847961	+	0.530059i	$0.177830\pi$
$462$	− 3.67303e11i	− 0.375090i
$463$	1.22023e12i	1.23404i	0.786949	+	0.617018i	$0.211659\pi$
$463$	1.22023e12i	1.23404i	−0.786949	+	0.617018i	$0.788341\pi$
$464$	−4.69433e11	−0.470156
$465$	0	0
$466$	−1.04891e12	−1.03039
$467$	5.18912e11i	0.504856i	0.967616	+	0.252428i	$0.0812291\pi$
$467$	5.18912e11i	0.504856i	−0.967616	+	0.252428i	$0.918771\pi$
$468$	− 2.85135e11i	− 0.274754i
$469$	1.50143e12	1.43294
$470$	0	0
$471$	−7.71907e11	−0.722722
$472$	2.58840e11i	0.240045i
$473$	8.89215e11i	0.816830i
$474$	−2.40439e11	−0.218777
$475$	0	0
$476$	1.01894e12	0.909743
$477$	1.35433e11i	0.119782i
$478$	4.32110e11i	0.378589i
$479$	1.51788e12	1.31743	0.658717	−	0.752391i	$-0.271100\pi$
$479$	1.51788e12	1.31743	0.658717	+	0.752391i	$0.271100\pi$
$480$	0	0
$481$	−3.26968e11	−0.278518
$482$	2.77725e11i	0.234371i
$483$	− 1.08704e12i	− 0.908833i
$484$	4.11159e11	0.340570
$485$	0	0
$486$	−5.57886e10	−0.0453609
$487$	− 2.11955e12i	− 1.70751i	−0.520677	−	0.853754i	$-0.674320\pi$
$487$	− 2.11955e12i	− 1.70751i	0.520677	−	0.853754i	$-0.325680\pi$
$488$	− 2.61153e11i	− 0.208452i
$489$	2.67108e11	0.211250
$490$	0	0
$491$	−6.34518e11	−0.492694	−0.246347	−	0.969182i	$-0.579230\pi$
$491$	−6.34518e11	−0.492694	−0.246347	+	0.969182i	$0.579230\pi$
$492$	1.84469e11i	0.141932i
$493$	− 2.75836e12i	− 2.10300i
$494$	−1.73044e12	−1.30733
$495$	0	0
$496$	−4.60841e11	−0.341888
$497$	− 3.80010e12i	− 2.79377i
$498$	6.06395e11i	0.441798i
$499$	−3.71937e11	−0.268545	−0.134273	−	0.990944i	$-0.542870\pi$
$499$	−3.71937e11	−0.268545	−0.134273	+	0.990944i	$0.542870\pi$
$500$	0	0
$501$	−8.71351e11	−0.617907
$502$	3.58098e11i	0.251672i
$503$	− 1.30603e12i	− 0.909696i	−0.890569	−	0.454848i	$-0.849694\pi$
$503$	− 1.30603e12i	− 0.909696i	0.890569	−	0.454848i	$-0.150306\pi$
$504$	2.77768e11	0.191754
$505$	0	0
$506$	−5.69634e11	−0.386295
$507$	1.47539e12i	0.991676i
$508$	− 1.13680e12i	− 0.757350i
$509$	2.46188e12	1.62569	0.812844	−	0.582481i	$-0.197918\pi$
$509$	2.46188e12	1.62569	0.812844	+	0.582481i	$0.197918\pi$
$510$	0	0
$511$	−2.60970e12	−1.69315
$512$	− 6.87195e10i	− 0.0441942i
$513$	3.38573e11i	0.215836i
$514$	−2.07990e12	−1.31434
$515$	0	0
$516$	−6.72457e11	−0.417581
$517$	− 4.71801e11i	− 0.290436i
$518$	− 3.18520e11i	− 0.194381i
$519$	6.93835e11	0.419762
$520$	0	0
$521$	−3.38151e11	−0.201067	−0.100533	−	0.994934i	$-0.532055\pi$
$521$	−3.38151e11	−0.201067	−0.100533	+	0.994934i	$0.532055\pi$
$522$	− 7.51940e11i	− 0.443268i
$523$	1.35866e12i	0.794061i	0.917805	+	0.397030i	$0.129959\pi$
$523$	1.35866e12i	0.794061i	−0.917805	+	0.397030i	$0.870041\pi$
$524$	−6.57882e11	−0.381204
$525$	0	0
$526$	1.20021e12	0.683628
$527$	− 2.70788e12i	− 1.52926i
$528$	− 1.45557e11i	− 0.0815042i
$529$	1.15310e11	0.0640202
$530$	0	0
$531$	−4.14612e11	−0.226317
$532$	− 1.68573e12i	− 0.912403i
$533$	− 1.51022e12i	− 0.810525i
$534$	7.50509e11	0.399411
$535$	0	0
$536$	5.94993e11	0.311365
$537$	− 5.06339e11i	− 0.262759i
$538$	− 5.16248e11i	− 0.265667i
$539$	−1.82286e12	−0.930260
$540$	0	0
$541$	2.72399e12	1.36716	0.683578	−	0.729877i	$-0.260423\pi$
$541$	2.72399e12	1.36716	0.683578	+	0.729877i	$0.260423\pi$
$542$	6.22107e11i	0.309648i
$543$	1.82207e12i	0.899425i
$544$	4.03792e11	0.197680
$545$	0	0
$546$	−2.27404e12	−1.09504
$547$	2.29514e12i	1.09614i	0.836433	+	0.548070i	$0.184637\pi$
$547$	2.29514e12i	1.09614i	−0.836433	+	0.548070i	$0.815363\pi$
$548$	− 7.80984e11i	− 0.369939i
$549$	4.18317e11	0.196530
$550$	0	0
$551$	−4.56342e12	−2.10915
$552$	− 4.30778e11i	− 0.197482i
$553$	1.91757e12i	0.871944i
$554$	2.22795e12	1.00487
$555$	0	0
$556$	5.68216e11	0.252160
$557$	3.66541e11i	0.161352i	0.996740	+	0.0806760i	$0.0257079\pi$
$557$	3.66541e11i	0.161352i	−0.996740	+	0.0806760i	$0.974292\pi$
$558$	− 7.38178e11i	− 0.322335i
$559$	5.50529e12	2.38466
$560$	0	0
$561$	8.55284e11	0.364567
$562$	− 1.94834e12i	− 0.823855i
$563$	2.20274e12i	0.924006i	0.886878	+	0.462003i	$0.152869\pi$
$563$	2.20274e12i	0.924006i	−0.886878	+	0.462003i	$0.847131\pi$
$564$	3.56793e11	0.148477
$565$	0	0
$566$	1.79907e12	0.736841
$567$	4.44931e11i	0.180788i
$568$	− 1.50592e12i	− 0.607065i
$569$	−2.30440e12	−0.921620	−0.460810	−	0.887499i	$-0.652441\pi$
$569$	−2.30440e12	−0.921620	−0.460810	+	0.887499i	$0.652441\pi$
$570$	0	0
$571$	1.91693e12	0.754647	0.377323	−	0.926082i	$-0.376845\pi$
$571$	1.91693e12	0.754647	0.377323	+	0.926082i	$0.376845\pi$
$572$	1.19165e12i	0.465442i
$573$	2.17902e12i	0.844432i
$574$	1.47120e12	0.565675
$575$	0	0
$576$	1.10075e11	0.0416667
$577$	4.61602e12i	1.73371i	0.498559	+	0.866856i	$0.333863\pi$
$577$	4.61602e12i	1.73371i	−0.498559	+	0.866856i	$0.666137\pi$
$578$	4.75254e11i	0.177113i
$579$	−1.09367e12	−0.404420
$580$	0	0
$581$	4.83619e12	1.76080
$582$	− 1.70361e12i	− 0.615485i
$583$	− 5.66008e11i	− 0.202915i
$584$	−1.03418e12	−0.367908
$585$	0	0
$586$	−9.17412e11	−0.321385
$587$	− 3.31976e11i	− 0.115408i	−0.998334	−	0.0577039i	$-0.981622\pi$
$587$	− 3.31976e11i	− 0.115408i	0.998334	−	0.0577039i	$-0.0183779\pi$
$588$	− 1.37851e12i	− 0.475569i
$589$	−4.47989e12	−1.53373
$590$	0	0
$591$	1.71279e12	0.577510
$592$	− 1.26225e11i	− 0.0422374i
$593$	2.45977e12i	0.816861i	0.912789	+	0.408431i	$0.133924\pi$
$593$	2.45977e12i	0.816861i	−0.912789	+	0.408431i	$0.866076\pi$
$594$	2.33154e11	0.0768429
$595$	0	0
$596$	7.09807e11	0.230426
$597$	4.58869e11i	0.147844i
$598$	3.52670e12i	1.12775i
$599$	1.26724e12	0.402198	0.201099	−	0.979571i	$-0.435549\pi$
$599$	1.26724e12	0.402198	0.201099	+	0.979571i	$0.435549\pi$
$600$	0	0
$601$	2.25368e12	0.704624	0.352312	−	0.935883i	$-0.385396\pi$
$601$	2.25368e12	0.704624	0.352312	+	0.935883i	$0.385396\pi$
$602$	5.36305e12i	1.66429i
$603$	9.53064e11i	0.293558i
$604$	6.50239e11	0.198795
$605$	0	0
$606$	5.70611e11	0.171875
$607$	− 1.54071e12i	− 0.460652i	−0.973114	−	0.230326i	$-0.926021\pi$
$607$	− 1.54071e12i	− 0.460652i	0.973114	−	0.230326i	$-0.0739792\pi$
$608$	− 6.68031e11i	− 0.198258i
$609$	−5.99696e12	−1.76666
$610$	0	0
$611$	−2.92100e12	−0.847903
$612$	6.46797e11i	0.186374i
$613$	− 6.24615e11i	− 0.178665i	−0.996002	−	0.0893327i	$-0.971527\pi$
$613$	− 6.24615e11i	− 0.178665i	0.996002	−	0.0893327i	$-0.0284734\pi$
$614$	2.55363e12	0.725105
$615$	0	0
$616$	−1.16086e12	−0.324838
$617$	− 1.83847e11i	− 0.0510709i	−0.999674	−	0.0255355i	$-0.991871\pi$
$617$	− 1.83847e11i	− 0.0510709i	0.999674	−	0.0255355i	$-0.00812907\pi$
$618$	7.66332e11i	0.211334i
$619$	−3.53823e12	−0.968675	−0.484337	−	0.874881i	$-0.660939\pi$
$619$	−3.53823e12	−0.968675	−0.484337	+	0.874881i	$0.660939\pi$
$620$	0	0
$621$	6.90023e11	0.186188
$622$	1.95345e12i	0.523295i
$623$	− 5.98554e12i	− 1.59187i
$624$	−9.01167e11	−0.237944
$625$	0	0
$626$	−2.05316e12	−0.534366
$627$	− 1.41498e12i	− 0.365633i
$628$	2.43961e12i	0.625895i
$629$	7.41690e11	0.188927
$630$	0	0
$631$	−8.92700e11	−0.224168	−0.112084	−	0.993699i	$-0.535753\pi$
$631$	−8.92700e11	−0.224168	−0.112084	+	0.993699i	$0.535753\pi$
$632$	7.59905e11i	0.189467i
$633$	1.77017e12i	0.438227i
$634$	−2.01565e12	−0.495465
$635$	0	0
$636$	4.28036e11	0.103734
$637$	1.12857e13i	2.71581i
$638$	3.14254e12i	0.750910i
$639$	2.41220e12	0.572346
$640$	0	0
$641$	2.07063e12	0.484442	0.242221	−	0.970221i	$-0.422124\pi$
$641$	2.07063e12	0.484442	0.242221	+	0.970221i	$0.422124\pi$
$642$	− 1.18600e12i	− 0.275534i
$643$	1.78129e12i	0.410946i	0.978663	+	0.205473i	$0.0658732\pi$
$643$	1.78129e12i	0.410946i	−0.978663	+	0.205473i	$0.934127\pi$
$644$	−3.43559e12	−0.787072
$645$	0	0
$646$	3.92531e12	0.886805
$647$	− 5.92399e12i	− 1.32906i	−0.747261	−	0.664531i	$-0.768631\pi$
$647$	− 5.92399e12i	− 1.32906i	0.747261	−	0.664531i	$-0.231369\pi$
$648$	1.76319e11i	0.0392837i
$649$	1.73276e12	0.383387
$650$	0	0
$651$	−5.88720e12	−1.28468
$652$	− 8.44194e11i	− 0.182948i
$653$	− 8.11273e12i	− 1.74605i	−0.487671	−	0.873027i	$-0.662153\pi$
$653$	− 8.11273e12i	− 1.74605i	0.487671	−	0.873027i	$-0.337847\pi$
$654$	3.07152e12	0.656528
$655$	0	0
$656$	5.83013e11	0.122917
$657$	− 1.65656e12i	− 0.346867i
$658$	− 2.84553e12i	− 0.591762i
$659$	3.93328e12	0.812401	0.406200	−	0.913784i	$-0.366853\pi$
$659$	3.93328e12	0.812401	0.406200	+	0.913784i	$0.366853\pi$
$660$	0	0
$661$	−2.15528e11	−0.0439134	−0.0219567	−	0.999759i	$-0.506990\pi$
$661$	−2.15528e11	−0.0439134	−0.0219567	+	0.999759i	$0.506990\pi$
$662$	4.27636e12i	0.865394i
$663$	− 5.29521e12i	− 1.06432i
$664$	1.91651e12	0.382608
$665$	0	0
$666$	2.02188e11	0.0398218
$667$	9.30041e12i	1.81943i
$668$	2.75390e12i	0.535123i
$669$	−2.76960e12	−0.534563
$670$	0	0
$671$	−1.74825e12	−0.332929
$672$	− 8.77885e11i	− 0.166064i
$673$	− 5.04401e12i	− 0.947782i	−0.880584	−	0.473891i	$-0.842849\pi$
$673$	− 5.04401e12i	− 0.947782i	0.880584	−	0.473891i	$-0.157151\pi$
$674$	−6.30135e12	−1.17615
$675$	0	0
$676$	4.66295e12	0.858816
$677$	7.45393e12i	1.36376i	0.731466	+	0.681878i	$0.238836\pi$
$677$	7.45393e12i	1.36376i	−0.731466	+	0.681878i	$0.761164\pi$
$678$	− 2.93987e11i	− 0.0534311i
$679$	−1.35868e13	−2.45304
$680$	0	0
$681$	1.81265e12	0.322963
$682$	3.08502e12i	0.546045i
$683$	2.99014e12i	0.525773i	0.964827	+	0.262886i	$0.0846744\pi$
$683$	2.99014e12i	0.525773i	−0.964827	+	0.262886i	$0.915326\pi$
$684$	1.07006e12	0.186919
$685$	0	0
$686$	−4.32056e12	−0.744872
$687$	− 2.24198e11i	− 0.0383995i
$688$	2.12530e12i	0.361636i
$689$	−3.50425e12	−0.592392
$690$	0	0
$691$	6.56691e12	1.09575	0.547873	−	0.836562i	$-0.315438\pi$
$691$	6.56691e12	1.09575	0.547873	+	0.836562i	$0.315438\pi$
$692$	− 2.19286e12i	− 0.363525i
$693$	− 1.85947e12i	− 0.306260i
$694$	4.00589e12	0.655513
$695$	0	0
$696$	−2.37650e12	−0.383881
$697$	3.42575e12i	0.549805i
$698$	2.71269e12i	0.432565i
$699$	−5.31012e12	−0.841312
$700$	0	0
$701$	−6.97167e12	−1.09045	−0.545225	−	0.838290i	$-0.683556\pi$
$701$	−6.97167e12	−1.09045	−0.545225	+	0.838290i	$0.683556\pi$
$702$	− 1.44350e12i	− 0.224336i
$703$	− 1.22705e12i	− 0.189480i
$704$	−4.60031e11	−0.0705847
$705$	0	0
$706$	6.60359e12	1.00037
$707$	− 4.55080e12i	− 0.685015i
$708$	1.31038e12i	0.195996i
$709$	7.35853e12	1.09366	0.546831	−	0.837243i	$-0.315834\pi$
$709$	7.35853e12	1.09366	0.546831	+	0.837243i	$0.315834\pi$
$710$	0	0
$711$	−1.21722e12	−0.178631
$712$	− 2.37198e12i	− 0.345900i
$713$	9.13018e12i	1.32305i
$714$	5.15840e12	0.742802
$715$	0	0
$716$	−1.60028e12	−0.227556
$717$	2.18756e12i	0.309117i
$718$	5.64620e12i	0.792860i
$719$	−2.14069e12	−0.298727	−0.149364	−	0.988782i	$-0.547722\pi$
$719$	−2.14069e12	−0.298727	−0.149364	+	0.988782i	$0.547722\pi$
$720$	0	0
$721$	6.11174e12	0.842279
$722$	− 1.33101e12i	− 0.182291i
$723$	1.40598e12i	0.191363i
$724$	5.75863e12	0.778925
$725$	0	0
$726$	2.08149e12	0.278074
$727$	− 6.36038e12i	− 0.844458i	−0.906489	−	0.422229i	$-0.861248\pi$
$727$	− 6.36038e12i	− 0.844458i	0.906489	−	0.422229i	$-0.138752\pi$
$728$	7.18709e12i	0.948335i
$729$	−2.82430e11	−0.0370370
$730$	0	0
$731$	−1.24881e13	−1.61759
$732$	− 1.32209e12i	− 0.170200i
$733$	1.99432e12i	0.255169i	0.991828	+	0.127584i	$0.0407224\pi$
$733$	1.99432e12i	0.255169i	−0.991828	+	0.127584i	$0.959278\pi$
$734$	−8.99300e12	−1.14359
$735$	0	0
$736$	−1.36147e12	−0.171024
$737$	− 3.98308e12i	− 0.497297i
$738$	9.33874e11i	0.115887i
$739$	−1.14331e13	−1.41015	−0.705074	−	0.709134i	$-0.749086\pi$
$739$	−1.14331e13	−1.41015	−0.705074	+	0.709134i	$0.749086\pi$
$740$	0	0
$741$	−8.76036e12	−1.06743
$742$	− 3.41372e12i	− 0.413438i
$743$	7.54874e12i	0.908709i	0.890821	+	0.454354i	$0.150130\pi$
$743$	7.54874e12i	0.908709i	−0.890821	+	0.454354i	$0.849870\pi$
$744$	−2.33301e12	−0.279150
$745$	0	0
$746$	−3.02924e11	−0.0358104
$747$	3.06988e12i	0.360727i
$748$	− 2.70312e12i	− 0.315724i
$749$	−9.45869e12	−1.09815
$750$	0	0
$751$	1.26303e13	1.44889	0.724445	−	0.689333i	$-0.242096\pi$
$751$	1.26303e13	1.44889	0.724445	+	0.689333i	$0.242096\pi$
$752$	− 1.12764e12i	− 0.128585i
$753$	1.81287e12i	0.205489i
$754$	1.94560e13	2.19221
$755$	0	0
$756$	1.40620e12	0.156567
$757$	− 2.57624e12i	− 0.285138i	−0.989785	−	0.142569i	$-0.954464\pi$
$757$	− 2.57624e12i	− 0.285138i	0.989785	−	0.142569i	$-0.0455363\pi$
$758$	1.13684e13i	1.25080i
$759$	−2.88377e12	−0.315408
$760$	0	0
$761$	6.30666e12	0.681660	0.340830	−	0.940125i	$-0.389292\pi$
$761$	6.30666e12	0.681660	0.340830	+	0.940125i	$0.389292\pi$
$762$	− 5.75504e12i	− 0.618374i
$763$	− 2.44963e13i	− 2.61662i
$764$	6.88677e12	0.731300
$765$	0	0
$766$	−1.02061e13	−1.07110
$767$	− 1.07278e13i	− 1.11927i
$768$	− 3.47892e11i	− 0.0360844i
$769$	7.10661e12	0.732814	0.366407	−	0.930455i	$-0.380588\pi$
$769$	7.10661e12	0.732814	0.366407	+	0.930455i	$0.380588\pi$
$770$	0	0
$771$	−1.05295e13	−1.07316
$772$	3.45654e12i	0.350238i
$773$	− 7.86838e12i	− 0.792643i	−0.918112	−	0.396322i	$-0.870287\pi$
$773$	− 7.86838e12i	− 0.792643i	0.918112	−	0.396322i	$-0.129713\pi$
$774$	−3.40431e12	−0.340954
$775$	0	0
$776$	−5.38426e12	−0.533026
$777$	− 1.61251e12i	− 0.158711i
$778$	− 1.36968e13i	− 1.34032i
$779$	5.66755e12	0.551412
$780$	0	0
$781$	−1.00812e13	−0.969573
$782$	− 7.99993e12i	− 0.764990i
$783$	− 3.80670e12i	− 0.361927i
$784$	−4.35679e12	−0.411855
$785$	0	0
$786$	−3.33053e12	−0.311251
$787$	− 6.06449e12i	− 0.563518i	−0.959485	−	0.281759i	$-0.909082\pi$
$787$	− 6.06449e12i	− 0.563518i	0.959485	−	0.281759i	$-0.0909178\pi$
$788$	− 5.41325e12i	− 0.500138i
$789$	6.07604e12	0.558180
$790$	0	0
$791$	−2.34463e12	−0.212952
$792$	− 7.36881e11i	− 0.0665479i
$793$	1.08237e13i	0.971955i
$794$	6.76383e12	0.603949
$795$	0	0
$796$	1.45025e12	0.128037
$797$	4.14199e12i	0.363619i	0.983334	+	0.181809i	$0.0581954\pi$
$797$	4.14199e12i	0.363619i	−0.983334	+	0.181809i	$0.941805\pi$
$798$	− 8.53403e12i	− 0.744974i
$799$	6.62596e12	0.575159
$800$	0	0
$801$	3.79945e12	0.326118
$802$	1.43418e12i	0.122411i
$803$	6.92317e12i	0.587605i
$804$	3.01215e12	0.254229
$805$	0	0
$806$	1.90999e13	1.59413
$807$	− 2.61350e12i	− 0.216916i
$808$	− 1.80341e12i	− 0.148848i
$809$	1.73515e13	1.42419	0.712097	−	0.702081i	$-0.247745\pi$
$809$	1.73515e13	1.42419	0.712097	+	0.702081i	$0.247745\pi$
$810$	0	0
$811$	−7.02987e11	−0.0570628	−0.0285314	−	0.999593i	$-0.509083\pi$
$811$	−7.02987e11	−0.0570628	−0.0285314	+	0.999593i	$0.509083\pi$
$812$	1.89533e13i	1.52997i
$813$	3.14942e12i	0.252827i
$814$	−8.44991e11	−0.0674594
$815$	0	0
$816$	2.04420e12	0.161405
$817$	2.06603e13i	1.62232i
$818$	9.20190e11i	0.0718601i
$819$	−1.15123e13	−0.894099
$820$	0	0
$821$	−1.14184e13	−0.877122	−0.438561	−	0.898701i	$-0.644512\pi$
$821$	−1.14184e13	−0.877122	−0.438561	+	0.898701i	$0.644512\pi$
$822$	− 3.95373e12i	− 0.302054i
$823$	2.20408e13i	1.67467i	0.546691	+	0.837335i	$0.315887\pi$
$823$	2.20408e13i	1.67467i	−0.546691	+	0.837335i	$0.684113\pi$
$824$	2.42199e12	0.183020
$825$	0	0
$826$	1.04507e13	0.781149
$827$	− 2.61998e13i	− 1.94771i	−0.227180	−	0.973853i	$-0.572951\pi$
$827$	− 2.61998e13i	− 1.94771i	0.227180	−	0.973853i	$-0.427049\pi$
$828$	− 2.18081e12i	− 0.161243i
$829$	2.45093e13	1.80234	0.901169	−	0.433468i	$-0.142710\pi$
$829$	2.45093e13	1.80234	0.901169	+	0.433468i	$0.142710\pi$
$830$	0	0
$831$	1.12790e13	0.820475
$832$	2.84813e12i	0.206066i
$833$	− 2.56002e13i	− 1.84222i
$834$	2.87659e12	0.205888
$835$	0	0
$836$	−4.47202e12	−0.316647
$837$	− 3.73703e12i	− 0.263185i
$838$	− 1.09131e13i	− 0.764454i
$839$	−1.14689e12	−0.0799087	−0.0399543	−	0.999202i	$-0.512721\pi$
$839$	−1.14689e12	−0.0799087	−0.0399543	+	0.999202i	$0.512721\pi$
$840$	0	0
$841$	3.68011e13	2.53675
$842$	1.90244e13i	1.30439i
$843$	− 9.86345e12i	− 0.672674i
$844$	5.59462e12	0.379516
$845$	0	0
$846$	1.80626e12	0.121231
$847$	− 1.66006e13i	− 1.10827i
$848$	− 1.35280e12i	− 0.0898367i
$849$	9.10778e12	0.601628
$850$	0	0
$851$	−2.50077e12	−0.163452
$852$	− 7.62373e12i	− 0.495666i
$853$	2.17660e12i	0.140769i	0.997520	+	0.0703847i	$0.0224227\pi$
$853$	2.17660e12i	0.140769i	−0.997520	+	0.0703847i	$0.977577\pi$
$854$	−1.05441e13	−0.678339
$855$	0	0
$856$	−3.74833e12	−0.238620
$857$	− 2.79690e13i	− 1.77119i	−0.464463	−	0.885593i	$-0.653753\pi$
$857$	− 2.79690e13i	− 1.77119i	0.464463	−	0.885593i	$-0.346247\pi$
$858$	6.03272e12i	0.380032i
$859$	−8.22473e12	−0.515409	−0.257705	−	0.966224i	$-0.582966\pi$
$859$	−8.22473e12	−0.515409	−0.257705	+	0.966224i	$0.582966\pi$
$860$	0	0
$861$	7.44794e12	0.461872
$862$	− 1.73802e13i	− 1.07219i
$863$	− 2.67759e13i	− 1.64322i	−0.570050	−	0.821610i	$-0.693076\pi$
$863$	− 2.67759e13i	− 1.64322i	0.570050	−	0.821610i	$-0.306924\pi$
$864$	5.57256e11	0.0340207
$865$	0	0
$866$	4.40911e12	0.266391
$867$	2.40597e12i	0.144612i
$868$	1.86064e13i	1.11256i
$869$	5.08706e12	0.302606
$870$	0	0
$871$	−2.46600e13	−1.45181
$872$	− 9.70751e12i	− 0.568570i
$873$	− 8.62455e12i	− 0.502542i
$874$	−1.32350e13	−0.767227
$875$	0	0
$876$	−5.23555e12	−0.300396
$877$	1.39444e13i	0.795982i	0.917389	+	0.397991i	$0.130292\pi$
$877$	1.39444e13i	0.795982i	−0.917389	+	0.397991i	$0.869708\pi$
$878$	− 2.11031e12i	− 0.119845i
$879$	−4.64440e12	−0.262409
$880$	0	0
$881$	−1.26780e13	−0.709020	−0.354510	−	0.935052i	$-0.615352\pi$
$881$	−1.26780e13	−0.709020	−0.354510	+	0.935052i	$0.615352\pi$
$882$	− 6.97873e12i	− 0.388300i
$883$	1.29515e13i	0.716964i	0.933537	+	0.358482i	$0.116706\pi$
$883$	1.29515e13i	0.716964i	−0.933537	+	0.358482i	$0.883294\pi$
$884$	−1.67355e13	−0.921728
$885$	0	0
$886$	−1.88560e13	−1.02801
$887$	1.51647e13i	0.822578i	0.911505	+	0.411289i	$0.134921\pi$
$887$	1.51647e13i	0.822578i	−0.911505	+	0.411289i	$0.865079\pi$
$888$	− 6.39013e11i	− 0.0344867i
$889$	−4.58982e13	−2.46455
$890$	0	0
$891$	1.18034e12	0.0627419
$892$	8.75330e12i	0.462945i
$893$	− 1.09619e13i	− 0.576841i
$894$	3.59340e12	0.188142
$895$	0	0
$896$	−2.77455e12	−0.143816
$897$	1.78539e13i	0.920806i
$898$	− 2.11453e12i	− 0.108510i
$899$	5.03691e13	2.57185
$900$	0	0
$901$	7.94900e12	0.401838
$902$	− 3.90289e12i	− 0.196316i
$903$	2.71504e13i	1.35888i
$904$	−9.29143e11	−0.0462727
$905$	0	0
$906$	3.29183e12	0.162316
$907$	− 1.69425e13i	− 0.831275i	−0.909530	−	0.415637i	$-0.863559\pi$
$907$	− 1.69425e13i	− 0.831275i	0.909530	−	0.415637i	$-0.136441\pi$
$908$	− 5.72887e12i	− 0.279694i
$909$	2.88872e12	0.140335
$910$	0	0
$911$	−5.05250e11	−0.0243038	−0.0121519	−	0.999926i	$-0.503868\pi$
$911$	−5.05250e11	−0.0243038	−0.0121519	+	0.999926i	$0.503868\pi$
$912$	− 3.38191e12i	− 0.161877i
$913$	− 1.28298e13i	− 0.611082i
$914$	1.14832e12	0.0544258
$915$	0	0
$916$	−7.08576e11	−0.0332550
$917$	2.65620e13i	1.24050i
$918$	3.27441e12i	0.152174i
$919$	8.02347e12	0.371059	0.185529	−	0.982639i	$-0.440600\pi$
$919$	8.02347e12	0.371059	0.185529	+	0.982639i	$0.440600\pi$
$920$	0	0
$921$	1.29278e13	0.592046
$922$	− 2.63136e13i	− 1.19920i
$923$	6.24142e13i	2.83058i
$924$	−5.87685e12	−0.265229
$925$	0	0
$926$	1.95237e13	0.872595
$927$	3.87956e12i	0.172553i
$928$	7.51092e12i	0.332451i
$929$	9.53417e11	0.0419964	0.0209982	−	0.999780i	$-0.493316\pi$
$929$	9.53417e11	0.0419964	0.0209982	+	0.999780i	$0.493316\pi$
$930$	0	0
$931$	−4.23529e13	−1.84761
$932$	1.67826e13i	0.728597i
$933$	9.88936e12i	0.427268i
$934$	8.30258e12	0.356987
$935$	0	0
$936$	−4.56216e12	−0.194280
$937$	− 1.30100e13i	− 0.551377i	−0.961247	−	0.275688i	$-0.911094\pi$
$937$	− 1.30100e13i	− 0.551377i	0.961247	−	0.275688i	$-0.0889057\pi$
$938$	− 2.40228e13i	− 1.01324i
$939$	−1.03941e13	−0.436308
$940$	0	0
$941$	3.64039e13	1.51354	0.756771	−	0.653680i	$-0.226776\pi$
$941$	3.64039e13	1.51354	0.756771	+	0.653680i	$0.226776\pi$
$942$	1.23505e13i	0.511041i
$943$	− 1.15507e13i	− 0.475668i
$944$	4.14144e12	0.169737
$945$	0	0
$946$	1.42274e13	0.577586
$947$	− 9.30409e12i	− 0.375923i	−0.982176	−	0.187962i	$-0.939812\pi$
$947$	− 9.30409e12i	− 0.375923i	0.982176	−	0.187962i	$-0.0601881\pi$
$948$	3.84702e12i	0.154699i
$949$	4.28626e13	1.71546
$950$	0	0
$951$	−1.02042e13	−0.404546
$952$	− 1.63031e13i	− 0.643286i
$953$	− 9.85076e11i	− 0.0386858i	−0.999813	−	0.0193429i	$-0.993843\pi$
$953$	− 9.85076e11i	− 0.0386858i	0.999813	−	0.0193429i	$-0.00615742\pi$
$954$	2.16693e12	0.0846988
$955$	0	0
$956$	6.91376e12	0.267703
$957$	1.59091e13i	0.613115i
$958$	− 2.42861e13i	− 0.931566i
$959$	−3.15322e13	−1.20385
$960$	0	0
$961$	2.30076e13	0.870194
$962$	5.23149e12i	0.196942i
$963$	− 6.00411e12i	− 0.224973i
$964$	4.44360e12	0.165725
$965$	0	0
$966$	−1.73927e13	−0.642642
$967$	4.74300e13i	1.74435i	0.489194	+	0.872175i	$0.337291\pi$
$967$	4.74300e13i	1.74435i	−0.489194	+	0.872175i	$0.662709\pi$
$968$	− 6.57855e12i	− 0.240819i
$969$	1.98719e13	0.724073
$970$	0	0
$971$	7.49831e12	0.270693	0.135346	−	0.990798i	$-0.456785\pi$
$971$	7.49831e12	0.270693	0.135346	+	0.990798i	$0.456785\pi$
$972$	8.92617e11i	0.0320750i
$973$	− 2.29417e13i	− 0.820574i
$974$	−3.39127e13	−1.20739
$975$	0	0
$976$	−4.17845e12	−0.147398
$977$	2.38786e12i	0.0838462i	0.999121	+	0.0419231i	$0.0133485\pi$
$977$	2.38786e12i	0.0838462i	−0.999121	+	0.0419231i	$0.986652\pi$
$978$	− 4.27373e12i	− 0.149377i
$979$	−1.58788e13	−0.552454
$980$	0	0
$981$	1.55496e13	0.536053
$982$	1.01523e13i	0.348387i
$983$	− 1.59099e13i	− 0.543472i	−0.962372	−	0.271736i	$-0.912402\pi$
$983$	− 1.59099e13i	− 0.543472i	0.962372	−	0.271736i	$-0.0875977\pi$
$984$	2.95150e12	0.100361
$985$	0	0
$986$	−4.41338e13	−1.48705
$987$	− 1.44055e13i	− 0.483172i
$988$	2.76871e13i	0.924423i
$989$	4.21064e13	1.39947
$990$	0	0
$991$	−5.42340e13	−1.78624	−0.893121	−	0.449816i	$-0.851489\pi$
$991$	−5.42340e13	−1.78624	−0.893121	+	0.449816i	$0.851489\pi$
$992$	7.37345e12i	0.241751i
$993$	2.16491e13i	0.706591i
$994$	−6.08016e13	−1.97550
$995$	0	0
$996$	9.70233e12	0.312398
$997$	− 3.98284e12i	− 0.127663i	−0.997961	−	0.0638314i	$-0.979668\pi$
$997$	− 3.98284e12i	− 0.127663i	0.997961	−	0.0638314i	$-0.0203320\pi$
$998$	5.95100e12i	0.189890i
$999$	1.02358e12	0.0325144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.10.c.c.49.1		2
5.2	odd	4		30.10.a.e.1.1	✓	1
5.3	odd	4		150.10.a.e.1.1		1
5.4	even	2	inner	150.10.c.c.49.2		2
15.2	even	4		90.10.a.a.1.1		1
20.7	even	4		240.10.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.10.a.e.1.1	✓	1	5.2	odd	4
90.10.a.a.1.1		1	15.2	even	4
150.10.a.e.1.1		1	5.3	odd	4
150.10.c.c.49.1		2	1.1	even	1	trivial
150.10.c.c.49.2		2	5.4	even	2	inner
240.10.a.j.1.1		1	20.7	even	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} -1296.00 q^{6} +10336.0i q^{7} +4096.00i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q-16.0000i q^{2} -81.0000i q^{3} -256.000 q^{4} -1296.00 q^{6} +10336.0i q^{7} +4096.00i q^{8} -6561.00 q^{9} +27420.0 q^{11} +20736.0i q^{12} -169762. i q^{13} +165376. q^{14} +65536.0 q^{16} +385086. i q^{17} +104976. i q^{18} +637084. q^{19} +837216. q^{21} -438720. i q^{22} -1.29840e6i q^{23} +331776. q^{24} -2.71619e6 q^{26} +531441. i q^{27} -2.64602e6i q^{28} -7.16297e6 q^{29} -7.03187e6 q^{31} -1.04858e6i q^{32} -2.22102e6i q^{33} +6.16138e6 q^{34} +1.67962e6 q^{36} -1.92604e6i q^{37} -1.01933e7i q^{38} -1.37507e7 q^{39} +8.89607e6 q^{41} -1.33955e7i q^{42} +3.24294e7i q^{43} -7.01952e6 q^{44} -2.07744e7 q^{46} -1.72064e7i q^{47} -5.30842e6i q^{48} -6.64793e7 q^{49} +3.11920e7 q^{51} +4.34591e7i q^{52} -2.06422e7i q^{53} +8.50306e6 q^{54} -4.23363e7 q^{56} -5.16038e7i q^{57} +1.14608e8i q^{58} +6.31934e7 q^{59} -6.37580e7 q^{61} +1.12510e8i q^{62} -6.78145e7i q^{63} -1.67772e7 q^{64} -3.55363e7 q^{66} -1.45262e8i q^{67} -9.85820e7i q^{68} -1.05170e8 q^{69} -3.67657e8 q^{71} -2.68739e7i q^{72} +2.52486e8i q^{73} -3.08166e7 q^{74} -1.63094e8 q^{76} +2.83413e8i q^{77} +2.20012e8i q^{78} +1.85524e8 q^{79} +4.30467e7 q^{81} -1.42337e8i q^{82} -4.67898e8i q^{83} -2.14327e8 q^{84} +5.18871e8 q^{86} +5.80201e8i q^{87} +1.12312e8i q^{88} -5.79096e8 q^{89} +1.75466e9 q^{91} +3.32390e8i q^{92} +5.69582e8i q^{93} -2.75303e8 q^{94} -8.49347e7 q^{96} +1.31452e9i q^{97} +1.06367e9i q^{98} -1.79903e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 512 q^{4} - 2592 q^{6} - 13122 q^{9}+O(q^{10}) \) 2 * q - 512 * q^4 - 2592 * q^6 - 13122 * q^9	\( 2 q - 512 q^{4} - 2592 q^{6} - 13122 q^{9} + 54840 q^{11} + 330752 q^{14} + 131072 q^{16} + 1274168 q^{19} + 1674432 q^{21} + 663552 q^{24} - 5432384 q^{26} - 14325948 q^{29} - 14063744 q^{31} + 12322752 q^{34} + 3359232 q^{36} - 27501444 q^{39} + 17792148 q^{41} - 14039040 q^{44} - 41548800 q^{46} - 132958578 q^{49} + 62383932 q^{51} + 17006112 q^{54} - 84672512 q^{56} + 126386760 q^{59} - 127516100 q^{61} - 33554432 q^{64} - 71072640 q^{66} - 210340800 q^{69} - 735313680 q^{71} - 61633216 q^{74} - 326187008 q^{76} + 371047424 q^{79} + 86093442 q^{81} - 428654592 q^{84} + 1037742208 q^{86} - 1158192756 q^{89} + 3509320064 q^{91} - 550606080 q^{94} - 169869312 q^{96} - 359805240 q^{99}+O(q^{100}) \) 2 * q - 512 * q^4 - 2592 * q^6 - 13122 * q^9 + 54840 * q^11 + 330752 * q^14 + 131072 * q^16 + 1274168 * q^19 + 1674432 * q^21 + 663552 * q^24 - 5432384 * q^26 - 14325948 * q^29 - 14063744 * q^31 + 12322752 * q^34 + 3359232 * q^36 - 27501444 * q^39 + 17792148 * q^41 - 14039040 * q^44 - 41548800 * q^46 - 132958578 * q^49 + 62383932 * q^51 + 17006112 * q^54 - 84672512 * q^56 + 126386760 * q^59 - 127516100 * q^61 - 33554432 * q^64 - 71072640 * q^66 - 210340800 * q^69 - 735313680 * q^71 - 61633216 * q^74 - 326187008 * q^76 + 371047424 * q^79 + 86093442 * q^81 - 428654592 * q^84 + 1037742208 * q^86 - 1158192756 * q^89 + 3509320064 * q^91 - 550606080 * q^94 - 169869312 * q^96 - 359805240 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more