LMFDB - Embedded newform 75.10.b.e.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(49,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, 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("75.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{4729})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2365x^{2} + 1397124 $ x^4 + 2365*x^2 + 1397124
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.4
Root			$34.8839i$ of defining polynomial
Character	$\chi$	$=$	75.49
Dual form			75.10.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)

$f(q)$	$=$	$q+43.8839i q^{2} -81.0000i q^{3} -1413.79 q^{4} +3554.59 q^{6} -7861.50i q^{7} -39574.2i q^{8} -6561.00 q^{9} +O(q^{10})$	\(q+43.8839i q^{2} -81.0000i q^{3} -1413.79 q^{4} +3554.59 q^{6} -7861.50i q^{7} -39574.2i q^{8} -6561.00 q^{9} -49373.3 q^{11} +114517. i q^{12} -24250.7i q^{13} +344993. q^{14} +1.01281e6 q^{16} +268222. i q^{17} -287922. i q^{18} +168364. q^{19} -636781. q^{21} -2.16669e6i q^{22} +2.12200e6i q^{23} -3.20551e6 q^{24} +1.06422e6 q^{26} +531441. i q^{27} +1.11145e7i q^{28} -389624. q^{29} +90532.2 q^{31} +2.41838e7i q^{32} +3.99924e6i q^{33} -1.17706e7 q^{34} +9.27590e6 q^{36} -3.31991e6i q^{37} +7.38848e6i q^{38} -1.96431e6 q^{39} +2.32694e7 q^{41} -2.79444e7i q^{42} -1.91140e7i q^{43} +6.98036e7 q^{44} -9.31215e7 q^{46} +6.28153e7i q^{47} -8.20372e7i q^{48} -2.14495e7 q^{49} +2.17260e7 q^{51} +3.42855e7i q^{52} +180207. i q^{53} -2.33217e7 q^{54} -3.11112e8 q^{56} -1.36375e7i q^{57} -1.70982e7i q^{58} -3.84564e7 q^{59} -553620. q^{61} +3.97290e6i q^{62} +5.15793e7i q^{63} -5.42724e8 q^{64} -1.75502e8 q^{66} -2.39163e8i q^{67} -3.79211e8i q^{68} +1.71882e8 q^{69} +1.28653e8 q^{71} +2.59646e8i q^{72} +2.39376e8i q^{73} +1.45690e8 q^{74} -2.38033e8 q^{76} +3.88148e8i q^{77} -8.62015e7i q^{78} +5.28027e8 q^{79} +4.30467e7 q^{81} +1.02115e9i q^{82} -2.12210e8i q^{83} +9.00277e8 q^{84} +8.38797e8 q^{86} +3.15595e7i q^{87} +1.95391e9i q^{88} +2.07724e8 q^{89} -1.90647e8 q^{91} -3.00007e9i q^{92} -7.33311e6i q^{93} -2.75658e9 q^{94} +1.95889e9 q^{96} +1.70780e9i q^{97} -9.41288e8i q^{98} +3.23938e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3042 q^{4} + 3078 q^{6} - 26244 q^{9}+O(q^{10}) $ 4 * q - 3042 * q^4 + 3078 * q^6 - 26244 * q^9	$ 4 q - 3042 q^{4} + 3078 q^{6} - 26244 q^{9} + 70976 q^{11} + 490392 q^{14} + 1414530 q^{16} + 806592 q^{19} - 1923264 q^{21} - 8042814 q^{24} - 3815092 q^{26} + 149144 q^{29} - 10054256 q^{31} - 17721764 q^{34} + 19958562 q^{36} - 23275512 q^{39} + 28422664 q^{41} + 121411904 q^{44} - 302983296 q^{46} + 5639900 q^{49} + 62395272 q^{51} - 20194758 q^{54} - 703018680 q^{56} - 375726272 q^{59} + 308160120 q^{61} - 1276602178 q^{64} - 693095616 q^{66} - 36240048 q^{69} - 456541952 q^{71} + 724038452 q^{74} - 526437448 q^{76} + 1864813520 q^{79} + 172186884 q^{81} + 1870206408 q^{84} + 1247853416 q^{86} - 449036328 q^{89} - 1339205056 q^{91} - 3863301632 q^{94} + 4313992446 q^{96} - 465673536 q^{99}+O(q^{100}) $ 4 * q - 3042 * q^4 + 3078 * q^6 - 26244 * q^9 + 70976 * q^11 + 490392 * q^14 + 1414530 * q^16 + 806592 * q^19 - 1923264 * q^21 - 8042814 * q^24 - 3815092 * q^26 + 149144 * q^29 - 10054256 * q^31 - 17721764 * q^34 + 19958562 * q^36 - 23275512 * q^39 + 28422664 * q^41 + 121411904 * q^44 - 302983296 * q^46 + 5639900 * q^49 + 62395272 * q^51 - 20194758 * q^54 - 703018680 * q^56 - 375726272 * q^59 + 308160120 * q^61 - 1276602178 * q^64 - 693095616 * q^66 - 36240048 * q^69 - 456541952 * q^71 + 724038452 * q^74 - 526437448 * q^76 + 1864813520 * q^79 + 172186884 * q^81 + 1870206408 * q^84 + 1247853416 * q^86 - 449036328 * q^89 - 1339205056 * q^91 - 3863301632 * q^94 + 4313992446 * q^96 - 465673536 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$-1$

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 $

$2$	43.8839i	1.93941i	0.244277	+	0.969706i	$0.421449\pi$
$2$	43.8839i	1.93941i	−0.244277	+	0.969706i	$0.578551\pi$
$3$	− 81.0000i	− 0.577350i
$3$	− 81.0000i	− 0.577350i
$4$	−1413.79	−2.76132
$5$	0	0
$5$	0	0
$6$	3554.59	1.11972
$7$	− 7861.50i	− 1.23755i	−0.785567	−	0.618777i	$-0.787629\pi$
$7$	− 7861.50i	− 1.23755i	0.785567	−	0.618777i	$-0.212371\pi$
$8$	− 39574.2i	− 3.41591i
$9$	−6561.00	−0.333333
$10$	0	0
$11$	−49373.3	−1.01678	−0.508388	−	0.861128i	$-0.669758\pi$
$11$	−49373.3	−1.01678	−0.508388	+	0.861128i	$0.669758\pi$
$12$	114517.i	1.59425i
$13$	− 24250.7i	− 0.235494i	−0.993044	−	0.117747i	$-0.962433\pi$
$13$	− 24250.7i	− 0.235494i	0.993044	−	0.117747i	$-0.0375672\pi$
$14$	344993.	2.40013
$15$	0	0
$16$	1.01281e6	3.86355
$17$	268222.i	0.778888i	0.921050	+	0.389444i	$0.127333\pi$
$17$	268222.i	0.778888i	−0.921050	+	0.389444i	$0.872667\pi$
$18$	− 287922.i	− 0.646470i
$19$	168364.	0.296387	0.148193	−	0.988958i	$-0.452654\pi$
$19$	168364.	0.296387	0.148193	+	0.988958i	$0.452654\pi$
$20$	0	0
$21$	−636781.	−0.714502
$22$	− 2.16669e6i	− 1.97195i
$23$	2.12200e6i	1.58114i	0.612373	+	0.790569i	$0.290215\pi$
$23$	2.12200e6i	1.58114i	−0.612373	+	0.790569i	$0.709785\pi$
$24$	−3.20551e6	−1.97218
$25$	0	0
$26$	1.06422e6	0.456720
$27$	531441.i	0.192450i
$28$	1.11145e7i	3.41728i
$29$	−389624.	−0.102295	−0.0511475	−	0.998691i	$-0.516288\pi$
$29$	−389624.	−0.102295	−0.0511475	+	0.998691i	$0.516288\pi$
$30$	0	0
$31$	90532.2	0.0176066	0.00880330	−	0.999961i	$-0.497198\pi$
$31$	90532.2	0.0176066	0.00880330	+	0.999961i	$0.497198\pi$
$32$	2.41838e7i	4.07709i
$33$	3.99924e6i	0.587036i
$34$	−1.17706e7	−1.51058
$35$	0	0
$36$	9.27590e6	0.920438
$37$	− 3.31991e6i	− 0.291218i	−0.989342	−	0.145609i	$-0.953486\pi$
$37$	− 3.31991e6i	− 0.291218i	0.989342	−	0.145609i	$-0.0465142\pi$
$38$	7.38848e6i	0.574816i
$39$	−1.96431e6	−0.135963
$40$	0	0
$41$	2.32694e7	1.28605	0.643024	−	0.765846i	$-0.277679\pi$
$41$	2.32694e7	1.28605	0.643024	+	0.765846i	$0.277679\pi$
$42$	− 2.79444e7i	− 1.38571i
$43$	− 1.91140e7i	− 0.852597i	−0.904583	−	0.426298i	$-0.859817\pi$
$43$	− 1.91140e7i	− 0.852597i	0.904583	−	0.426298i	$-0.140183\pi$
$44$	6.98036e7	2.80764
$45$	0	0
$46$	−9.31215e7	−3.06648
$47$	6.28153e7i	1.87770i	0.344332	+	0.938848i	$0.388105\pi$
$47$	6.28153e7i	1.87770i	−0.344332	+	0.938848i	$0.611895\pi$
$48$	− 8.20372e7i	− 2.23062i
$49$	−2.14495e7	−0.531539
$50$	0	0
$51$	2.17260e7	0.449691
$52$	3.42855e7i	0.650273i
$53$	180207.i	0.00313711i	0.999999	+	0.00156856i	$0.000499287\pi$
$53$	180207.i	0.00313711i	−0.999999	+	0.00156856i	$0.999501\pi$
$54$	−2.33217e7	−0.373240
$55$	0	0
$56$	−3.11112e8	−4.22738
$57$	− 1.36375e7i	− 0.171119i
$58$	− 1.70982e7i	− 0.198392i
$59$	−3.84564e7	−0.413175	−0.206588	−	0.978428i	$-0.566236\pi$
$59$	−3.84564e7	−0.413175	−0.206588	+	0.978428i	$0.566236\pi$
$60$	0	0
$61$	−553620.	−0.00511950	−0.00255975	−	0.999997i	$-0.500815\pi$
$61$	−553620.	−0.00511950	−0.00255975	+	0.999997i	$0.500815\pi$
$62$	3.97290e6i	0.0341464i
$63$	5.15793e7i	0.412518i
$64$	−5.42724e8	−4.04361
$65$	0	0
$66$	−1.75502e8	−1.13850
$67$	− 2.39163e8i	− 1.44996i	−0.688768	−	0.724982i	$-0.741848\pi$
$67$	− 2.39163e8i	− 1.44996i	0.688768	−	0.724982i	$-0.258152\pi$
$68$	− 3.79211e8i	− 2.15076i
$69$	1.71882e8	0.912871
$70$	0	0
$71$	1.28653e8	0.600838	0.300419	−	0.953807i	$-0.402873\pi$
$71$	1.28653e8	0.600838	0.300419	+	0.953807i	$0.402873\pi$
$72$	2.59646e8i	1.13864i
$73$	2.39376e8i	0.986569i	0.869868	+	0.493284i	$0.164204\pi$
$73$	2.39376e8i	0.986569i	−0.869868	+	0.493284i	$0.835796\pi$
$74$	1.45690e8	0.564792
$75$	0	0
$76$	−2.38033e8	−0.818418
$77$	3.88148e8i	1.25831i
$78$	− 8.62015e7i	− 0.263687i
$79$	5.28027e8	1.52523	0.762613	−	0.646855i	$-0.223916\pi$
$79$	5.28027e8	1.52523	0.762613	+	0.646855i	$0.223916\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	1.02115e9i	2.49418i
$83$	− 2.12210e8i	− 0.490812i	−0.969420	−	0.245406i	$-0.921079\pi$
$83$	− 2.12210e8i	− 0.490812i	0.969420	−	0.245406i	$-0.0789213\pi$
$84$	9.00277e8	1.97297
$85$	0	0
$86$	8.38797e8	1.65354
$87$	3.15595e7i	0.0590601i
$88$	1.95391e9i	3.47322i
$89$	2.07724e8	0.350939	0.175469	−	0.984485i	$-0.443856\pi$
$89$	2.07724e8	0.350939	0.175469	+	0.984485i	$0.443856\pi$
$90$	0	0
$91$	−1.90647e8	−0.291436
$92$	− 3.00007e9i	− 4.36602i
$93$	− 7.33311e6i	− 0.0101652i
$94$	−2.75658e9	−3.64162
$95$	0	0
$96$	1.95889e9	2.35391
$97$	1.70780e9i	1.95868i	0.202214	+	0.979341i	$0.435186\pi$
$97$	1.70780e9i	1.95868i	−0.202214	+	0.979341i	$0.564814\pi$
$98$	− 9.41288e8i	− 1.03087i
$99$	3.23938e8	0.338925
$100$	0	0
$101$	−1.81384e8	−0.173441	−0.0867206	−	0.996233i	$-0.527639\pi$
$101$	−1.81384e8	−0.173441	−0.0867206	+	0.996233i	$0.527639\pi$
$102$	9.53422e8i	0.872136i
$103$	1.70453e9i	1.49223i	0.665816	+	0.746116i	$0.268083\pi$
$103$	1.70453e9i	1.49223i	−0.665816	+	0.746116i	$0.731917\pi$
$104$	−9.59703e8	−0.804427
$105$	0	0
$106$	−7.90818e6	−0.00608415
$107$	1.73298e9i	1.27811i	0.769163	+	0.639053i	$0.220674\pi$
$107$	1.73298e9i	1.27811i	−0.769163	+	0.639053i	$0.779326\pi$
$108$	− 7.51348e8i	− 0.531415i
$109$	1.17238e9	0.795515	0.397757	−	0.917491i	$-0.369789\pi$
$109$	1.17238e9	0.795515	0.397757	+	0.917491i	$0.369789\pi$
$110$	0	0
$111$	−2.68913e8	−0.168135
$112$	− 7.96217e9i	− 4.78135i
$113$	1.22180e9i	0.704935i	0.935824	+	0.352467i	$0.114657\pi$
$113$	1.22180e9i	0.704935i	−0.935824	+	0.352467i	$0.885343\pi$
$114$	5.98467e8	0.331870
$115$	0	0
$116$	5.50848e8	0.282469
$117$	1.59109e8i	0.0784980i
$118$	− 1.68761e9i	− 0.801317i
$119$	2.10863e9	0.963916
$120$	0	0
$121$	7.97750e7	0.0338324
$122$	− 2.42950e7i	− 0.00992881i
$123$	− 1.88482e9i	− 0.742501i
$124$	−1.27994e8	−0.0486174
$125$	0	0
$126$	−2.26350e9	−0.800042
$127$	− 9.50324e8i	− 0.324157i	−0.986778	−	0.162078i	$-0.948180\pi$
$127$	− 9.50324e8i	− 0.324157i	0.986778	−	0.162078i	$-0.0518197\pi$
$128$	− 1.14347e10i	− 3.76513i
$129$	−1.54823e9	−0.492247
$130$	0	0
$131$	−4.03050e9	−1.19574	−0.597872	−	0.801592i	$-0.703987\pi$
$131$	−4.03050e9	−1.19574	−0.597872	+	0.801592i	$0.703987\pi$
$132$	− 5.65410e9i	− 1.62099i
$133$	− 1.32360e9i	− 0.366795i
$134$	1.04954e10	2.81207
$135$	0	0
$136$	1.06147e10	2.66061
$137$	5.51871e9i	1.33843i	0.743070	+	0.669214i	$0.233369\pi$
$137$	5.51871e9i	1.33843i	−0.743070	+	0.669214i	$0.766631\pi$
$138$	7.54284e9i	1.77043i
$139$	3.97776e9	0.903798	0.451899	−	0.892069i	$-0.350747\pi$
$139$	3.97776e9	0.903798	0.451899	+	0.892069i	$0.350747\pi$
$140$	0	0
$141$	5.08804e9	1.08409
$142$	5.64579e9i	1.16527i
$143$	1.19734e9i	0.239445i
$144$	−6.64502e9	−1.28785
$145$	0	0
$146$	−1.05047e10	−1.91336
$147$	1.73741e9i	0.306884i
$148$	4.69367e9i	0.804145i
$149$	2.26538e9	0.376533	0.188266	−	0.982118i	$-0.439713\pi$
$149$	2.26538e9	0.376533	0.188266	+	0.982118i	$0.439713\pi$
$150$	0	0
$151$	−8.49158e9	−1.32921	−0.664603	−	0.747197i	$-0.731399\pi$
$151$	−8.49158e9	−1.32921	−0.664603	+	0.747197i	$0.731399\pi$
$152$	− 6.66288e9i	− 1.01243i
$153$	− 1.75981e9i	− 0.259629i
$154$	−1.70334e10	−2.44039
$155$	0	0
$156$	2.77713e9	0.375435
$157$	7.28379e9i	0.956774i	0.878149	+	0.478387i	$0.158778\pi$
$157$	7.28379e9i	0.956774i	−0.878149	+	0.478387i	$0.841222\pi$
$158$	2.31719e10i	2.95804i
$159$	1.45968e7	0.00181121
$160$	0	0
$161$	1.66821e10	1.95674
$162$	1.88906e9i	0.215490i
$163$	− 1.38419e10i	− 1.53586i	−0.640535	−	0.767929i	$-0.721288\pi$
$163$	− 1.38419e10i	− 1.53586i	0.640535	−	0.767929i	$-0.278712\pi$
$164$	−3.28981e10	−3.55119
$165$	0	0
$166$	9.31262e9	0.951887
$167$	− 6.92038e9i	− 0.688503i	−0.938877	−	0.344252i	$-0.888133\pi$
$167$	− 6.92038e9i	− 0.688503i	0.938877	−	0.344252i	$-0.111867\pi$
$168$	2.52001e10i	2.44068i
$169$	1.00164e10	0.944543
$170$	0	0
$171$	−1.10464e9	−0.0987957
$172$	2.70233e10i	2.35429i
$173$	− 3.26987e9i	− 0.277539i	−0.990325	−	0.138769i	$-0.955685\pi$
$173$	− 3.26987e9i	− 0.277539i	0.990325	−	0.138769i	$-0.0443147\pi$
$174$	−1.38495e9	−0.114542
$175$	0	0
$176$	−5.00056e10	−3.92836
$177$	3.11497e9i	0.238547i
$178$	9.11572e9i	0.680614i
$179$	1.12431e10	0.818556	0.409278	−	0.912410i	$-0.365781\pi$
$179$	1.12431e10	0.818556	0.409278	+	0.912410i	$0.365781\pi$
$180$	0	0
$181$	3.75039e9	0.259731	0.129865	−	0.991532i	$-0.458546\pi$
$181$	3.75039e9	0.259731	0.129865	+	0.991532i	$0.458546\pi$
$182$	− 8.36633e9i	− 0.565215i
$183$	4.48432e7i	0.00295574i
$184$	8.39764e10	5.40103
$185$	0	0
$186$	3.21805e8	0.0197145
$187$	− 1.32430e10i	− 0.791954i
$188$	− 8.88079e10i	− 5.18491i
$189$	4.17792e9	0.238167
$190$	0	0
$191$	1.72426e10	0.937460	0.468730	−	0.883342i	$-0.344712\pi$
$191$	1.72426e10	0.937460	0.468730	+	0.883342i	$0.344712\pi$
$192$	4.39606e10i	2.33458i
$193$	6.01060e9i	0.311824i	0.987771	+	0.155912i	$0.0498317\pi$
$193$	6.01060e9i	0.311824i	−0.987771	+	0.155912i	$0.950168\pi$
$194$	−7.49448e10	−3.79869
$195$	0	0
$196$	3.03252e10	1.46775
$197$	− 1.19077e10i	− 0.563289i	−0.959519	−	0.281645i	$-0.909120\pi$
$197$	− 1.19077e10i	− 0.563289i	0.959519	−	0.281645i	$-0.0908799\pi$
$198$	1.42157e10i	0.657315i
$199$	6.10946e9	0.276162	0.138081	−	0.990421i	$-0.455907\pi$
$199$	6.10946e9	0.276162	0.138081	+	0.990421i	$0.455907\pi$
$200$	0	0
$201$	−1.93722e10	−0.837137
$202$	− 7.95982e9i	− 0.336374i
$203$	3.06303e9i	0.126596i
$204$	−3.07161e10	−1.24174
$205$	0	0
$206$	−7.48012e10	−2.89405
$207$	− 1.39224e10i	− 0.527046i
$208$	− 2.45613e10i	− 0.909842i
$209$	−8.31271e9	−0.301359
$210$	0	0
$211$	−3.67892e10	−1.27776	−0.638881	−	0.769306i	$-0.720602\pi$
$211$	−3.67892e10	−1.27776	−0.638881	+	0.769306i	$0.720602\pi$
$212$	− 2.54775e8i	− 0.00866256i
$213$	− 1.04209e10i	− 0.346894i
$214$	−7.60499e10	−2.47877
$215$	0	0
$216$	2.10313e10	0.657393
$217$	− 7.11719e8i	− 0.0217891i
$218$	5.14485e10i	1.54283i
$219$	1.93894e10	0.569596
$220$	0	0
$221$	6.50459e9	0.183423
$222$	− 1.18009e10i	− 0.326083i
$223$	5.01307e9i	0.135747i	0.997694	+	0.0678737i	$0.0216215\pi$
$223$	5.01307e9i	0.135747i	−0.997694	+	0.0678737i	$0.978379\pi$
$224$	1.90121e11	5.04562
$225$	0	0
$226$	−5.36175e10	−1.36716
$227$	− 2.73858e10i	− 0.684555i	−0.939599	−	0.342278i	$-0.888802\pi$
$227$	− 2.73858e10i	− 0.684555i	0.939599	−	0.342278i	$-0.111198\pi$
$228$	1.92806e10i	0.472514i
$229$	−5.36868e10	−1.29005	−0.645027	−	0.764159i	$-0.723154\pi$
$229$	−5.36868e10	−1.29005	−0.645027	+	0.764159i	$0.723154\pi$
$230$	0	0
$231$	3.14400e10	0.726488
$232$	1.54191e10i	0.349431i
$233$	− 7.25874e10i	− 1.61347i	−0.590916	−	0.806733i	$-0.701234\pi$
$233$	− 7.25874e10i	− 1.61347i	0.590916	−	0.806733i	$-0.298766\pi$
$234$	−6.98232e9	−0.152240
$235$	0	0
$236$	5.43694e10	1.14091
$237$	− 4.27702e10i	− 0.880590i
$238$	9.25348e10i	1.86943i
$239$	−1.73313e10	−0.343589	−0.171795	−	0.985133i	$-0.554957\pi$
$239$	−1.73313e10	−0.343589	−0.171795	+	0.985133i	$0.554957\pi$
$240$	0	0
$241$	4.06448e10	0.776119	0.388059	−	0.921634i	$-0.373146\pi$
$241$	4.06448e10	0.776119	0.388059	+	0.921634i	$0.373146\pi$
$242$	3.50084e9i	0.0656149i
$243$	− 3.48678e9i	− 0.0641500i
$244$	7.82704e8	0.0141365
$245$	0	0
$246$	8.27132e10	1.44001
$247$	− 4.08296e9i	− 0.0697973i
$248$	− 3.58274e9i	− 0.0601426i
$249$	−1.71890e10	−0.283371
$250$	0	0
$251$	1.00920e11	1.60490	0.802448	−	0.596723i	$-0.203531\pi$
$251$	1.00920e11	1.60490	0.802448	+	0.596723i	$0.203531\pi$
$252$	− 7.29224e10i	− 1.13909i
$253$	− 1.04770e11i	− 1.60766i
$254$	4.17039e10	0.628673
$255$	0	0
$256$	2.23924e11	3.25852
$257$	5.03660e10i	0.720176i	0.932918	+	0.360088i	$0.117253\pi$
$257$	5.03660e10i	0.720176i	−0.932918	+	0.360088i	$0.882747\pi$
$258$	− 6.79425e10i	− 0.954669i
$259$	−2.60995e10	−0.360398
$260$	0	0
$261$	2.55632e9	0.0340984
$262$	− 1.76874e11i	− 2.31904i
$263$	5.58677e10i	0.720046i	0.932943	+	0.360023i	$0.117231\pi$
$263$	5.58677e10i	0.720046i	−0.932943	+	0.360023i	$0.882769\pi$
$264$	1.58267e11	2.00526
$265$	0	0
$266$	5.80845e10	0.711366
$267$	− 1.68256e10i	− 0.202614i
$268$	3.38127e11i	4.00381i
$269$	1.05175e11	1.22469	0.612345	−	0.790590i	$-0.290226\pi$
$269$	1.05175e11	1.22469	0.612345	+	0.790590i	$0.290226\pi$
$270$	0	0
$271$	−5.44180e10	−0.612887	−0.306444	−	0.951889i	$-0.599139\pi$
$271$	−5.44180e10	−0.612887	−0.306444	+	0.951889i	$0.599139\pi$
$272$	2.71657e11i	3.00927i
$273$	1.54424e10i	0.168261i
$274$	−2.42182e11	−2.59576
$275$	0	0
$276$	−2.43005e11	−2.52072
$277$	1.64528e11i	1.67912i	0.543268	+	0.839560i	$0.317187\pi$
$277$	1.64528e11i	1.67912i	−0.543268	+	0.839560i	$0.682813\pi$
$278$	1.74559e11i	1.75284i
$279$	−5.93982e8	−0.00586887
$280$	0	0
$281$	−6.74255e10	−0.645128	−0.322564	−	0.946548i	$-0.604545\pi$
$281$	−6.74255e10	−0.645128	−0.322564	+	0.946548i	$0.604545\pi$
$282$	2.23283e11i	2.10249i
$283$	− 1.41917e11i	− 1.31521i	−0.753364	−	0.657603i	$-0.771570\pi$
$283$	− 1.41917e11i	− 1.31521i	0.753364	−	0.657603i	$-0.228430\pi$
$284$	−1.81889e11	−1.65910
$285$	0	0
$286$	−5.25438e10	−0.464381
$287$	− 1.82932e11i	− 1.59155i
$288$	− 1.58670e11i	− 1.35903i
$289$	4.66446e10	0.393333
$290$	0	0
$291$	1.38332e11	1.13085
$292$	− 3.38428e11i	− 2.72423i
$293$	− 2.79097e10i	− 0.221233i	−0.993863	−	0.110617i	$-0.964717\pi$
$293$	− 2.79097e10i	− 0.221233i	0.993863	−	0.110617i	$-0.0352826\pi$
$294$	−7.62443e10	−0.595175
$295$	0	0
$296$	−1.31383e11	−0.994776
$297$	− 2.62390e10i	− 0.195679i
$298$	9.94136e10i	0.730252i
$299$	5.14600e10	0.372349
$300$	0	0
$301$	−1.50265e11	−1.05513
$302$	− 3.72643e11i	− 2.57788i
$303$	1.46921e10i	0.100136i
$304$	1.70520e11	1.14510
$305$	0	0
$306$	7.72272e10	0.503528
$307$	1.59767e11i	1.02651i	0.858235	+	0.513257i	$0.171561\pi$
$307$	1.59767e11i	1.02651i	−0.858235	+	0.513257i	$0.828439\pi$
$308$	− 5.48761e11i	− 3.47460i
$309$	1.38067e11	0.861540
$310$	0	0
$311$	−7.84292e10	−0.475396	−0.237698	−	0.971339i	$-0.576393\pi$
$311$	−7.84292e10	−0.475396	−0.237698	+	0.971339i	$0.576393\pi$
$312$	7.77359e10i	0.464436i
$313$	1.26229e11i	0.743378i	0.928357	+	0.371689i	$0.121221\pi$
$313$	1.26229e11i	0.743378i	−0.928357	+	0.371689i	$0.878779\pi$
$314$	−3.19641e11	−1.85558
$315$	0	0
$316$	−7.46521e11	−4.21163
$317$	− 9.59499e10i	− 0.533676i	−0.963741	−	0.266838i	$-0.914021\pi$
$317$	− 9.59499e10i	− 0.533676i	0.963741	−	0.266838i	$-0.0859789\pi$
$318$	6.40563e8i	0.00351269i
$319$	1.92370e10	0.104011
$320$	0	0
$321$	1.40372e11	0.737915
$322$	7.32074e11i	3.79493i
$323$	4.51591e10i	0.230852i
$324$	−6.08592e10	−0.306813
$325$	0	0
$326$	6.07435e11	2.97866
$327$	− 9.49626e10i	− 0.459291i
$328$	− 9.20867e11i	− 4.39303i
$329$	4.93822e11	2.32375
$330$	0	0
$331$	7.73728e10	0.354293	0.177146	−	0.984185i	$-0.443313\pi$
$331$	7.73728e10	0.354293	0.177146	+	0.984185i	$0.443313\pi$
$332$	3.00022e11i	1.35529i
$333$	2.17819e10i	0.0970727i
$334$	3.03693e11	1.33529
$335$	0	0
$336$	−6.44936e11	−2.76051
$337$	1.73809e11i	0.734071i	0.930207	+	0.367035i	$0.119627\pi$
$337$	1.73809e11i	0.734071i	−0.930207	+	0.367035i	$0.880373\pi$
$338$	4.39558e11i	1.83186i
$339$	9.89662e10	0.406994
$340$	0	0
$341$	−4.46987e9	−0.0179020
$342$	− 4.84758e10i	− 0.191605i
$343$	− 1.48614e11i	− 0.579746i
$344$	−7.56421e11	−2.91240
$345$	0	0
$346$	1.43495e11	0.538262
$347$	4.11335e11i	1.52305i	0.648138	+	0.761523i	$0.275548\pi$
$347$	4.11335e11i	1.52305i	−0.648138	+	0.761523i	$0.724452\pi$
$348$	− 4.46187e10i	− 0.163084i
$349$	−2.97923e11	−1.07495	−0.537477	−	0.843278i	$-0.680623\pi$
$349$	−2.97923e11	−1.07495	−0.537477	+	0.843278i	$0.680623\pi$
$350$	0	0
$351$	1.28878e10	0.0453208
$352$	− 1.19404e12i	− 4.14549i
$353$	− 5.69499e9i	− 0.0195212i	−0.999952	−	0.00976061i	$-0.996893\pi$
$353$	− 5.69499e9i	− 0.0195212i	0.999952	−	0.00976061i	$-0.00310695\pi$
$354$	−1.36697e11	−0.462640
$355$	0	0
$356$	−2.93678e11	−0.969052
$357$	− 1.70799e11i	− 0.556517i
$358$	4.93392e11i	1.58752i
$359$	−6.19565e11	−1.96862	−0.984310	−	0.176446i	$-0.943540\pi$
$359$	−6.19565e11	−1.96862	−0.984310	+	0.176446i	$0.943540\pi$
$360$	0	0
$361$	−2.94341e11	−0.912155
$362$	1.64582e11i	0.503724i
$363$	− 6.46178e9i	− 0.0195331i
$364$	2.69536e11	0.804748
$365$	0	0
$366$	−1.96789e9	−0.00573240
$367$	− 4.06833e9i	− 0.0117063i	−0.999983	−	0.00585314i	$-0.998137\pi$
$367$	− 4.06833e9i	− 0.0117063i	0.999983	−	0.00585314i	$-0.00186312\pi$
$368$	2.14917e12i	6.10880i
$369$	−1.52670e11	−0.428683
$370$	0	0
$371$	1.41670e9	0.00388235
$372$	1.03675e10i	0.0280693i
$373$	6.75397e11i	1.80663i	0.428978	+	0.903315i	$0.358874\pi$
$373$	6.75397e11i	1.80663i	−0.428978	+	0.903315i	$0.641126\pi$
$374$	5.81155e11	1.53592
$375$	0	0
$376$	2.48586e12	6.41405
$377$	9.44867e9i	0.0240899i
$378$	1.83343e11i	0.461904i
$379$	3.67146e11	0.914033	0.457017	−	0.889458i	$-0.348918\pi$
$379$	3.67146e11	0.914033	0.457017	+	0.889458i	$0.348918\pi$
$380$	0	0
$381$	−7.69763e10	−0.187152
$382$	7.56672e11i	1.81812i
$383$	− 2.22057e11i	− 0.527314i	−0.964616	−	0.263657i	$-0.915071\pi$
$383$	− 2.22057e11i	− 0.527314i	0.964616	−	0.263657i	$-0.0849287\pi$
$384$	−9.26210e11	−2.17380
$385$	0	0
$386$	−2.63768e11	−0.604756
$387$	1.25407e11i	0.284199i
$388$	− 2.41448e12i	− 5.40854i
$389$	7.23043e11	1.60100	0.800499	−	0.599334i	$-0.204568\pi$
$389$	7.23043e11	1.60100	0.800499	+	0.599334i	$0.204568\pi$
$390$	0	0
$391$	−5.69168e11	−1.23153
$392$	8.48847e11i	1.81569i
$393$	3.26470e11i	0.690363i
$394$	5.22558e11	1.09245
$395$	0	0
$396$	−4.57982e11	−0.935879
$397$	6.06161e11i	1.22470i	0.790585	+	0.612352i	$0.209776\pi$
$397$	6.06161e11i	1.22470i	−0.790585	+	0.612352i	$0.790224\pi$
$398$	2.68107e11i	0.535592i
$399$	−1.07211e11	−0.211769
$400$	0	0
$401$	6.72510e11	1.29882	0.649411	−	0.760438i	$-0.275016\pi$
$401$	6.72510e11	1.29882	0.649411	+	0.760438i	$0.275016\pi$
$402$	− 8.50126e11i	− 1.62355i
$403$	− 2.19547e9i	− 0.00414625i
$404$	2.56439e11	0.478926
$405$	0	0
$406$	−1.34417e11	−0.245521
$407$	1.63915e11i	0.296103i
$408$	− 8.59789e11i	− 1.53611i
$409$	3.02482e10	0.0534497	0.0267248	−	0.999643i	$-0.491492\pi$
$409$	3.02482e10	0.0534497	0.0267248	+	0.999643i	$0.491492\pi$
$410$	0	0
$411$	4.47015e11	0.772742
$412$	− 2.40985e12i	− 4.12052i
$413$	3.02325e11i	0.511326i
$414$	6.10970e11	1.02216
$415$	0	0
$416$	5.86476e11	0.960130
$417$	− 3.22198e11i	− 0.521808i
$418$	− 3.64794e11i	− 0.584459i
$419$	1.61938e11	0.256676	0.128338	−	0.991731i	$-0.459036\pi$
$419$	1.61938e11	0.256676	0.128338	+	0.991731i	$0.459036\pi$
$420$	0	0
$421$	−8.06547e11	−1.25130	−0.625648	−	0.780105i	$-0.715165\pi$
$421$	−8.06547e11	−1.25130	−0.625648	+	0.780105i	$0.715165\pi$
$422$	− 1.61445e12i	− 2.47810i
$423$	− 4.12131e11i	− 0.625899i
$424$	7.13154e9	0.0107161
$425$	0	0
$426$	4.57309e11	0.672770
$427$	4.35228e9i	0.00633565i
$428$	− 2.45008e12i	− 3.52925i
$429$	9.69844e10	0.138243
$430$	0	0
$431$	8.54653e11	1.19300	0.596502	−	0.802611i	$-0.296557\pi$
$431$	8.54653e11	1.19300	0.596502	+	0.802611i	$0.296557\pi$
$432$	5.38246e11i	0.743540i
$433$	− 8.21884e11i	− 1.12361i	−0.827270	−	0.561804i	$-0.810107\pi$
$433$	− 8.21884e11i	− 1.12361i	0.827270	−	0.561804i	$-0.189893\pi$
$434$	3.12330e10	0.0422580
$435$	0	0
$436$	−1.65750e12	−2.19667
$437$	3.57269e11i	0.468629i
$438$	8.50883e11i	1.10468i
$439$	−9.97807e11	−1.28220	−0.641100	−	0.767457i	$-0.721522\pi$
$439$	−9.97807e11	−1.28220	−0.641100	+	0.767457i	$0.721522\pi$
$440$	0	0
$441$	1.40730e11	0.177180
$442$	2.85447e11i	0.355733i
$443$	2.22586e11i	0.274588i	0.990530	+	0.137294i	$0.0438405\pi$
$443$	2.22586e11i	0.274588i	−0.990530	+	0.137294i	$0.956160\pi$
$444$	3.80187e11	0.464273
$445$	0	0
$446$	−2.19993e11	−0.263270
$447$	− 1.83496e11i	− 0.217391i
$448$	4.26662e12i	5.00418i
$449$	−1.28886e12	−1.49657	−0.748287	−	0.663375i	$-0.769123\pi$
$449$	−1.28886e12	−1.49657	−0.748287	+	0.663375i	$0.769123\pi$
$450$	0	0
$451$	−1.14889e12	−1.30762
$452$	− 1.72738e12i	− 1.94655i
$453$	6.87818e11i	0.767417i
$454$	1.20179e12	1.32763
$455$	0	0
$456$	−5.39694e11	−0.584528
$457$	8.77644e11i	0.941230i	0.882339	+	0.470615i	$0.155968\pi$
$457$	8.77644e11i	0.941230i	−0.882339	+	0.470615i	$0.844032\pi$
$458$	− 2.35599e12i	− 2.50195i
$459$	−1.42544e11	−0.149897
$460$	0	0
$461$	−3.31142e11	−0.341476	−0.170738	−	0.985316i	$-0.554615\pi$
$461$	−3.31142e11	−0.341476	−0.170738	+	0.985316i	$0.554615\pi$
$462$	1.37971e12i	1.40896i
$463$	1.05840e12i	1.07037i	0.844735	+	0.535186i	$0.179758\pi$
$463$	1.05840e12i	1.07037i	−0.844735	+	0.535186i	$0.820242\pi$
$464$	−3.94613e11	−0.395222
$465$	0	0
$466$	3.18542e12	3.12917
$467$	− 1.49420e12i	− 1.45373i	−0.686782	−	0.726864i	$-0.740977\pi$
$467$	− 1.49420e12i	− 1.45373i	0.686782	−	0.726864i	$-0.259023\pi$
$468$	− 2.24947e11i	− 0.216758i
$469$	−1.88018e12	−1.79441
$470$	0	0
$471$	5.89987e11	0.552394
$472$	1.52188e12i	1.41137i
$473$	9.43722e11i	0.866900i
$474$	1.87692e12	1.70783
$475$	0	0
$476$	−2.98117e12	−2.66168
$477$	− 1.18234e9i	− 0.00104570i
$478$	− 7.60563e11i	− 0.666361i
$479$	−1.04497e12	−0.906970	−0.453485	−	0.891264i	$-0.649819\pi$
$479$	−1.04497e12	−0.906970	−0.453485	+	0.891264i	$0.649819\pi$
$480$	0	0
$481$	−8.05102e10	−0.0685801
$482$	1.78365e12i	1.50521i
$483$	− 1.35125e12i	− 1.12973i
$484$	−1.12785e11	−0.0934219
$485$	0	0
$486$	1.53014e11	0.124413
$487$	− 2.30343e12i	− 1.85564i	−0.373027	−	0.927820i	$-0.621680\pi$
$487$	− 2.30343e12i	− 1.85564i	0.373027	−	0.927820i	$-0.378320\pi$
$488$	2.19091e10i	0.0174878i
$489$	−1.12119e12	−0.886728
$490$	0	0
$491$	−5.37950e11	−0.417711	−0.208855	−	0.977947i	$-0.566974\pi$
$491$	−5.37950e11	−0.417711	−0.208855	+	0.977947i	$0.566974\pi$
$492$	2.66475e12i	2.05028i
$493$	− 1.04506e11i	− 0.0796764i
$494$	1.79176e11	0.135366
$495$	0	0
$496$	9.16915e10	0.0680239
$497$	− 1.01141e12i	− 0.743570i
$498$	− 7.54322e11i	− 0.549572i
$499$	1.01572e12	0.733364	0.366682	−	0.930346i	$-0.380494\pi$
$499$	1.01572e12	0.733364	0.366682	+	0.930346i	$0.380494\pi$
$500$	0	0
$501$	−5.60551e11	−0.397508
$502$	4.42877e12i	3.11255i
$503$	1.07349e12i	0.747723i	0.927485	+	0.373861i	$0.121966\pi$
$503$	1.07349e12i	0.747723i	−0.927485	+	0.373861i	$0.878034\pi$
$504$	2.04121e12	1.40913
$505$	0	0
$506$	4.59772e12	3.11792
$507$	− 8.11329e11i	− 0.545332i
$508$	1.34356e12i	0.895099i
$509$	1.48831e12	0.982799	0.491400	−	0.870934i	$-0.336485\pi$
$509$	1.48831e12	0.982799	0.491400	+	0.870934i	$0.336485\pi$
$510$	0	0
$511$	1.88185e12	1.22093
$512$	3.97208e12i	2.55449i
$513$	8.94758e10i	0.0570397i
$514$	−2.21026e12	−1.39672
$515$	0	0
$516$	2.18888e12	1.35925
$517$	− 3.10140e12i	− 1.90919i
$518$	− 1.14534e12i	− 0.698960i
$519$	−2.64860e11	−0.160237
$520$	0	0
$521$	−9.98544e11	−0.593742	−0.296871	−	0.954918i	$-0.595943\pi$
$521$	−9.98544e11	−0.593742	−0.296871	+	0.954918i	$0.595943\pi$
$522$	1.12181e11i	0.0661307i
$523$	1.59973e12i	0.934954i	0.884005	+	0.467477i	$0.154837\pi$
$523$	1.59973e12i	0.934954i	−0.884005	+	0.467477i	$0.845163\pi$
$524$	5.69829e12	3.30182
$525$	0	0
$526$	−2.45169e12	−1.39646
$527$	2.42828e10i	0.0137136i
$528$	4.05045e12i	2.26804i
$529$	−2.70173e12	−1.50000
$530$	0	0
$531$	2.52312e11	0.137725
$532$	1.87129e12i	1.01284i
$533$	− 5.64300e11i	− 0.302857i
$534$	7.38373e11	0.392953
$535$	0	0
$536$	−9.46467e12	−4.95295
$537$	− 9.10693e11i	− 0.472593i
$538$	4.61548e12i	2.37518i
$539$	1.05903e12	0.540456
$540$	0	0
$541$	5.11810e11	0.256875	0.128437	−	0.991718i	$-0.459004\pi$
$541$	5.11810e11	0.256875	0.128437	+	0.991718i	$0.459004\pi$
$542$	− 2.38807e12i	− 1.18864i
$543$	− 3.03782e11i	− 0.149956i
$544$	−6.48665e12	−3.17560
$545$	0	0
$546$	−6.77673e11	−0.326327
$547$	1.40910e12i	0.672977i	0.941688	+	0.336489i	$0.109239\pi$
$547$	1.40910e12i	0.672977i	−0.941688	+	0.336489i	$0.890761\pi$
$548$	− 7.80231e12i	− 3.69582i
$549$	3.63230e9	0.00170650
$550$	0	0
$551$	−6.55988e10	−0.0303189
$552$	− 6.80208e12i	− 3.11829i
$553$	− 4.15108e12i	− 1.88755i
$554$	−7.22013e12	−3.25650
$555$	0	0
$556$	−5.62372e12	−2.49567
$557$	2.36835e12i	1.04255i	0.853388	+	0.521276i	$0.174544\pi$
$557$	2.36835e12i	1.04255i	−0.853388	+	0.521276i	$0.825456\pi$
$558$	− 2.60662e10i	− 0.0113821i
$559$	−4.63529e11	−0.200781
$560$	0	0
$561$	−1.07269e12	−0.457235
$562$	− 2.95889e12i	− 1.25117i
$563$	2.36245e12i	0.991005i	0.868607	+	0.495502i	$0.165016\pi$
$563$	2.36245e12i	0.991005i	−0.868607	+	0.495502i	$0.834984\pi$
$564$	−7.19344e12	−2.99351
$565$	0	0
$566$	6.22784e12	2.55073
$567$	− 3.38412e11i	− 0.137506i
$568$	− 5.09134e12i	− 2.05241i
$569$	−2.25679e11	−0.0902582	−0.0451291	−	0.998981i	$-0.514370\pi$
$569$	−2.25679e11	−0.0902582	−0.0451291	+	0.998981i	$0.514370\pi$
$570$	0	0
$571$	−9.15389e11	−0.360366	−0.180183	−	0.983633i	$-0.557669\pi$
$571$	−9.15389e11	−0.360366	−0.180183	+	0.983633i	$0.557669\pi$
$572$	− 1.69279e12i	− 0.661182i
$573$	− 1.39665e12i	− 0.541243i
$574$	8.02777e12	3.08668
$575$	0	0
$576$	3.56081e12	1.34787
$577$	2.22404e12i	0.835318i	0.908604	+	0.417659i	$0.137149\pi$
$577$	2.22404e12i	0.835318i	−0.908604	+	0.417659i	$0.862851\pi$
$578$	2.04694e12i	0.762835i
$579$	4.86859e11	0.180032
$580$	0	0
$581$	−1.66829e12	−0.607407
$582$	6.07053e12i	2.19318i
$583$	− 8.89741e9i	− 0.00318974i
$584$	9.47310e12	3.37003
$585$	0	0
$586$	1.22478e12	0.429062
$587$	5.60186e12i	1.94742i	0.227783	+	0.973712i	$0.426852\pi$
$587$	5.60186e12i	1.94742i	−0.227783	+	0.973712i	$0.573148\pi$
$588$	− 2.45634e12i	− 0.847404i
$589$	1.52424e10	0.00521837
$590$	0	0
$591$	−9.64527e11	−0.325215
$592$	− 3.36242e12i	− 1.12513i
$593$	− 2.78326e12i	− 0.924289i	−0.886805	−	0.462145i	$-0.847080\pi$
$593$	− 2.78326e12i	− 0.924289i	0.886805	−	0.462145i	$-0.152920\pi$
$594$	1.15147e12	0.379501
$595$	0	0
$596$	−3.20278e12	−1.03973
$597$	− 4.94867e11i	− 0.159442i
$598$	2.25826e12i	0.722137i
$599$	1.36720e12	0.433922	0.216961	−	0.976180i	$-0.430386\pi$
$599$	1.36720e12	0.433922	0.216961	+	0.976180i	$0.430386\pi$
$600$	0	0
$601$	4.74171e12	1.48252	0.741259	−	0.671219i	$-0.234229\pi$
$601$	4.74171e12	1.48252	0.741259	+	0.671219i	$0.234229\pi$
$602$	− 6.59420e12i	− 2.04634i
$603$	1.56915e12i	0.483321i
$604$	1.20053e13	3.67036
$605$	0	0
$606$	−6.44746e11	−0.194206
$607$	− 5.74836e12i	− 1.71868i	−0.511406	−	0.859339i	$-0.670875\pi$
$607$	− 5.74836e12i	− 1.71868i	0.511406	−	0.859339i	$-0.329125\pi$
$608$	4.07170e12i	1.20840i
$609$	2.48105e11	0.0730900
$610$	0	0
$611$	1.52332e12	0.442186
$612$	2.48800e12i	0.716918i
$613$	− 2.99054e12i	− 0.855416i	−0.903917	−	0.427708i	$-0.859321\pi$
$613$	− 2.99054e12i	− 0.855416i	0.903917	−	0.427708i	$-0.140679\pi$
$614$	−7.01120e12	−1.99083
$615$	0	0
$616$	1.53606e13	4.29829
$617$	6.27174e12i	1.74223i	0.491081	+	0.871114i	$0.336602\pi$
$617$	6.27174e12i	1.74223i	−0.491081	+	0.871114i	$0.663398\pi$
$618$	6.05890e12i	1.67088i
$619$	2.67240e12	0.731632	0.365816	−	0.930687i	$-0.380790\pi$
$619$	2.67240e12	0.731632	0.365816	+	0.930687i	$0.380790\pi$
$620$	0	0
$621$	−1.12772e12	−0.304290
$622$	− 3.44177e12i	− 0.921989i
$623$	− 1.63302e12i	− 0.434305i
$624$	−1.98946e12	−0.525297
$625$	0	0
$626$	−5.53942e12	−1.44172
$627$	6.73329e11i	0.173990i
$628$	− 1.02978e13i	− 2.64195i
$629$	8.90474e11	0.226826
$630$	0	0
$631$	2.73608e12	0.687064	0.343532	−	0.939141i	$-0.388377\pi$
$631$	2.73608e12	0.687064	0.343532	+	0.939141i	$0.388377\pi$
$632$	− 2.08962e13i	− 5.21004i
$633$	2.97993e12i	0.737716i
$634$	4.21065e12	1.03502
$635$	0	0
$636$	−2.06368e10	−0.00500133
$637$	5.20167e11i	0.125174i
$638$	8.44195e11i	0.201720i
$639$	−8.44093e11	−0.200279
$640$	0	0
$641$	−2.58542e12	−0.604882	−0.302441	−	0.953168i	$-0.597802\pi$
$641$	−2.58542e12	−0.604882	−0.302441	+	0.953168i	$0.597802\pi$
$642$	6.16004e12i	1.43112i
$643$	4.53865e12i	1.04707i	0.852003	+	0.523537i	$0.175388\pi$
$643$	4.53865e12i	1.04707i	−0.852003	+	0.523537i	$0.824612\pi$
$644$	−2.35850e13	−5.40319
$645$	0	0
$646$	−1.98176e12	−0.447717
$647$	2.68597e12i	0.602604i	0.953529	+	0.301302i	$0.0974213\pi$
$647$	2.68597e12i	0.602604i	−0.953529	+	0.301302i	$0.902579\pi$
$648$	− 1.70354e12i	− 0.379546i
$649$	1.89872e12	0.420106
$650$	0	0
$651$	−5.76492e10	−0.0125799
$652$	1.95696e13i	4.24099i
$653$	6.39120e12i	1.37554i	0.725929	+	0.687770i	$0.241410\pi$
$653$	6.39120e12i	1.37554i	−0.725929	+	0.687770i	$0.758590\pi$
$654$	4.16732e12	0.890753
$655$	0	0
$656$	2.35674e13	4.96871
$657$	− 1.57054e12i	− 0.328856i
$658$	2.16708e13i	4.50670i
$659$	4.23105e12	0.873904	0.436952	−	0.899485i	$-0.356058\pi$
$659$	4.23105e12	0.873904	0.436952	+	0.899485i	$0.356058\pi$
$660$	0	0
$661$	−3.77872e12	−0.769907	−0.384953	−	0.922936i	$-0.625782\pi$
$661$	−3.77872e12	−0.769907	−0.384953	+	0.922936i	$0.625782\pi$
$662$	3.39542e12i	0.687120i
$663$	− 5.26872e11i	− 0.105900i
$664$	−8.39806e12	−1.67657
$665$	0	0
$666$	−9.55875e11	−0.188264
$667$	− 8.26782e11i	− 0.161743i
$668$	9.78399e12i	1.90117i
$669$	4.06058e11	0.0783738
$670$	0	0
$671$	2.73340e10	0.00520538
$672$	− 1.53998e13i	− 2.91309i
$673$	− 2.75736e12i	− 0.518114i	−0.965862	−	0.259057i	$-0.916588\pi$
$673$	− 2.75736e12i	− 0.518114i	0.965862	−	0.259057i	$-0.0834118\pi$
$674$	−7.62742e12	−1.42367
$675$	0	0
$676$	−1.41611e13	−2.60818
$677$	− 2.40567e12i	− 0.440136i	−0.975485	−	0.220068i	$-0.929372\pi$
$677$	− 2.40567e12i	− 0.440136i	0.975485	−	0.220068i	$-0.0706279\pi$
$678$	4.34302e12i	0.789329i
$679$	1.34259e13	2.42397
$680$	0	0
$681$	−2.21825e12	−0.395228
$682$	− 1.96155e11i	− 0.0347193i
$683$	7.88192e11i	0.138592i	0.997596	+	0.0692961i	$0.0220753\pi$
$683$	7.88192e11i	0.138592i	−0.997596	+	0.0692961i	$0.977925\pi$
$684$	1.56173e12	0.272806
$685$	0	0
$686$	6.52178e12	1.12436
$687$	4.34863e12i	0.744813i
$688$	− 1.93588e13i	− 3.29405i
$689$	4.37015e9	0.000738771 0
$690$	0	0
$691$	3.54288e12	0.591161	0.295580	−	0.955318i	$-0.404487\pi$
$691$	3.54288e12	0.591161	0.295580	+	0.955318i	$0.404487\pi$
$692$	4.62293e12i	0.766372i
$693$	− 2.54664e12i	− 0.419438i
$694$	−1.80510e13	−2.95381
$695$	0	0
$696$	1.24894e12	0.201744
$697$	6.24137e12i	1.00169i
$698$	− 1.30740e13i	− 2.08478i
$699$	−5.87958e12	−0.931535
$700$	0	0
$701$	−3.66998e12	−0.574027	−0.287014	−	0.957926i	$-0.592663\pi$
$701$	−3.66998e12	−0.574027	−0.287014	+	0.957926i	$0.592663\pi$
$702$	5.65568e11i	0.0878957i
$703$	− 5.58955e11i	− 0.0863133i
$704$	2.67961e13	4.11144
$705$	0	0
$706$	2.49918e11	0.0378597
$707$	1.42595e12i	0.214643i
$708$	− 4.40392e12i	− 0.658703i
$709$	−6.68373e12	−0.993369	−0.496685	−	0.867931i	$-0.665449\pi$
$709$	−6.68373e12	−0.993369	−0.496685	+	0.867931i	$0.665449\pi$
$710$	0	0
$711$	−3.46438e12	−0.508409
$712$	− 8.22050e12i	− 1.19878i
$713$	1.92109e11i	0.0278385i
$714$	7.49532e12	1.07932
$715$	0	0
$716$	−1.58954e13	−2.26029
$717$	1.40383e12i	0.198371i
$718$	− 2.71889e13i	− 3.81796i
$719$	1.23056e13	1.71721	0.858604	−	0.512640i	$-0.171332\pi$
$719$	1.23056e13	1.71721	0.858604	+	0.512640i	$0.171332\pi$
$720$	0	0
$721$	1.34001e13	1.84672
$722$	− 1.29168e13i	− 1.76904i
$723$	− 3.29223e12i	− 0.448092i
$724$	−5.30228e12	−0.717198
$725$	0	0
$726$	2.83568e11	0.0378828
$727$	− 1.07672e13i	− 1.42954i	−0.699360	−	0.714770i	$-0.746531\pi$
$727$	− 1.07672e13i	− 1.42954i	0.699360	−	0.714770i	$-0.253469\pi$
$728$	7.54470e12i	0.995522i
$729$	−2.82430e11	−0.0370370
$730$	0	0
$731$	5.12681e12	0.664078
$732$	− 6.33990e10i	− 0.00816174i
$733$	1.06410e13i	1.36149i	0.732521	+	0.680744i	$0.238343\pi$
$733$	1.06410e13i	1.36149i	−0.732521	+	0.680744i	$0.761657\pi$
$734$	1.78534e11	0.0227033
$735$	0	0
$736$	−5.13181e13	−6.44644
$737$	1.18083e13i	1.47429i
$738$	− 6.69977e12i	− 0.831393i
$739$	4.24704e12	0.523825	0.261912	−	0.965092i	$-0.415647\pi$
$739$	4.24704e12	0.523825	0.261912	+	0.965092i	$0.415647\pi$
$740$	0	0
$741$	−3.30720e11	−0.0402975
$742$	6.21701e10i	0.00752947i
$743$	− 1.10732e13i	− 1.33298i	−0.745516	−	0.666488i	$-0.767797\pi$
$743$	− 1.10732e13i	− 1.33298i	0.745516	−	0.666488i	$-0.232203\pi$
$744$	−2.90202e11	−0.0347234
$745$	0	0
$746$	−2.96390e13	−3.50380
$747$	1.39231e12i	0.163604i
$748$	1.87229e13i	2.18684i
$749$	1.36238e13	1.58172
$750$	0	0
$751$	1.45365e13	1.66755	0.833777	−	0.552102i	$-0.186174\pi$
$751$	1.45365e13	1.66755	0.833777	+	0.552102i	$0.186174\pi$
$752$	6.36197e13i	7.25456i
$753$	− 8.17454e12i	− 0.926587i
$754$	−4.14644e11	−0.0467202
$755$	0	0
$756$	−5.90672e12	−0.657655
$757$	− 5.75556e12i	− 0.637025i	−0.947919	−	0.318512i	$-0.896817\pi$
$757$	− 5.75556e12i	− 0.637025i	0.947919	−	0.318512i	$-0.103183\pi$
$758$	1.61118e13i	1.77269i
$759$	−8.48638e12	−0.928184
$760$	0	0
$761$	−1.44303e13	−1.55971	−0.779854	−	0.625961i	$-0.784707\pi$
$761$	−1.44303e13	−1.55971	−0.779854	+	0.625961i	$0.784707\pi$
$762$	− 3.37802e12i	− 0.362965i
$763$	− 9.21664e12i	− 0.984492i
$764$	−2.43775e13	−2.58862
$765$	0	0
$766$	9.74471e12	1.02268
$767$	9.32595e11i	0.0973003i
$768$	− 1.81378e13i	− 1.88131i
$769$	−2.65690e12	−0.273973	−0.136986	−	0.990573i	$-0.543742\pi$
$769$	−2.65690e12	−0.273973	−0.136986	+	0.990573i	$0.543742\pi$
$770$	0	0
$771$	4.07965e12	0.415794
$772$	− 8.49775e12i	− 0.861046i
$773$	4.35569e12i	0.438783i	0.975637	+	0.219391i	$0.0704072\pi$
$773$	4.35569e12i	0.438783i	−0.975637	+	0.219391i	$0.929593\pi$
$774$	−5.50334e12	−0.551179
$775$	0	0
$776$	6.75848e13	6.69069
$777$	2.11406e12i	0.208076i
$778$	3.17299e13i	3.10499i
$779$	3.91774e12	0.381168
$780$	0	0
$781$	−6.35203e12	−0.610918
$782$	− 2.49773e13i	− 2.38844i
$783$	− 2.07062e11i	− 0.0196867i
$784$	−2.17242e13	−2.05363
$785$	0	0
$786$	−1.43268e13	−1.33890
$787$	− 2.02013e13i	− 1.87713i	−0.345106	−	0.938564i	$-0.612157\pi$
$787$	− 2.02013e13i	− 1.87713i	0.345106	−	0.938564i	$-0.387843\pi$
$788$	1.68351e13i	1.55542i
$789$	4.52529e12	0.415719
$790$	0	0
$791$	9.60521e12	0.872394
$792$	− 1.28196e13i	− 1.15774i
$793$	1.34257e10i	0.00120561i
$794$	−2.66007e13	−2.37520
$795$	0	0
$796$	−8.63752e12	−0.762571
$797$	− 2.07284e12i	− 0.181971i	−0.995852	−	0.0909857i	$-0.970998\pi$
$797$	− 2.07284e12i	− 0.181971i	0.995852	−	0.0909857i	$-0.0290017\pi$
$798$	− 4.70485e12i	− 0.410707i
$799$	−1.68485e13	−1.46251
$800$	0	0
$801$	−1.36288e12	−0.116980
$802$	2.95124e13i	2.51895i
$803$	− 1.18188e13i	− 1.00312i
$804$	2.73883e13	2.31160
$805$	0	0
$806$	9.63458e10	0.00804128
$807$	− 8.51916e12i	− 0.707075i
$808$	7.17812e12i	0.592460i
$809$	−1.41673e13	−1.16284	−0.581418	−	0.813605i	$-0.697502\pi$
$809$	−1.41673e13	−1.16284	−0.581418	+	0.813605i	$0.697502\pi$
$810$	0	0
$811$	2.04580e12	0.166062	0.0830310	−	0.996547i	$-0.473540\pi$
$811$	2.04580e12	0.166062	0.0830310	+	0.996547i	$0.473540\pi$
$812$	− 4.33049e12i	− 0.349570i
$813$	4.40786e12i	0.353851i
$814$	−7.19322e12	−0.574266
$815$	0	0
$816$	2.20042e13	1.73740
$817$	− 3.21812e12i	− 0.252699i
$818$	1.32741e12i	0.103661i
$819$	1.25084e12	0.0971455
$820$	0	0
$821$	−1.27265e13	−0.977607	−0.488804	−	0.872394i	$-0.662567\pi$
$821$	−1.27265e13	−0.977607	−0.488804	+	0.872394i	$0.662567\pi$
$822$	1.96168e13i	1.49866i
$823$	− 6.94698e12i	− 0.527833i	−0.964546	−	0.263917i	$-0.914986\pi$
$823$	− 6.94698e12i	− 0.527833i	0.964546	−	0.263917i	$-0.0850143\pi$
$824$	6.74552e13	5.09733
$825$	0	0
$826$	−1.32672e13	−0.991672
$827$	5.09129e11i	0.0378489i	0.999821	+	0.0189244i	$0.00602419\pi$
$827$	5.09129e11i	0.0378489i	−0.999821	+	0.0189244i	$0.993976\pi$
$828$	1.96834e13i	1.45534i
$829$	1.87663e13	1.38001	0.690006	−	0.723804i	$-0.257608\pi$
$829$	1.87663e13	1.38001	0.690006	+	0.723804i	$0.257608\pi$
$830$	0	0
$831$	1.33268e13	0.969440
$832$	1.31615e13i	0.952245i
$833$	− 5.75324e12i	− 0.414009i
$834$	1.41393e13	1.01200
$835$	0	0
$836$	1.17525e13	0.832147
$837$	4.81125e10i	0.00338839i
$838$	7.10645e12i	0.497800i
$839$	−6.68721e12	−0.465925	−0.232962	−	0.972486i	$-0.574842\pi$
$839$	−6.68721e12	−0.465925	−0.232962	+	0.972486i	$0.574842\pi$
$840$	0	0
$841$	−1.43553e13	−0.989536
$842$	− 3.53944e13i	− 2.42678i
$843$	5.46147e12i	0.372465i
$844$	5.20124e13	3.52830
$845$	0	0
$846$	1.80859e13	1.21387
$847$	− 6.27151e11i	− 0.0418694i
$848$	1.82515e11i	0.0121204i
$849$	−1.14952e13	−0.759335
$850$	0	0
$851$	7.04484e12	0.460456
$852$	1.47330e13i	0.957884i
$853$	− 9.37029e12i	− 0.606014i	−0.952988	−	0.303007i	$-0.902009\pi$
$853$	− 9.37029e12i	− 0.606014i	0.952988	−	0.303007i	$-0.0979905\pi$
$854$	−1.90995e11	−0.0122874
$855$	0	0
$856$	6.85813e13	4.36590
$857$	8.81996e12i	0.558538i	0.960213	+	0.279269i	$0.0900921\pi$
$857$	8.81996e12i	0.558538i	−0.960213	+	0.279269i	$0.909908\pi$
$858$	4.25605e12i	0.268111i
$859$	−1.98932e13	−1.24663	−0.623313	−	0.781973i	$-0.714214\pi$
$859$	−1.98932e13	−1.24663	−0.623313	+	0.781973i	$0.714214\pi$
$860$	0	0
$861$	−1.48175e13	−0.918884
$862$	3.75055e13i	2.31373i
$863$	1.20953e13i	0.742278i	0.928577	+	0.371139i	$0.121033\pi$
$863$	1.20953e13i	0.742278i	−0.928577	+	0.371139i	$0.878967\pi$
$864$	−1.28523e13	−0.784636
$865$	0	0
$866$	3.60674e13	2.17914
$867$	− 3.77821e12i	− 0.227091i
$868$	1.00622e12i	0.0601666i
$869$	−2.60704e13	−1.55081
$870$	0	0
$871$	−5.79987e12	−0.341458
$872$	− 4.63959e13i	− 2.71741i
$873$	− 1.12049e13i	− 0.652894i
$874$	−1.56783e13	−0.908864
$875$	0	0
$876$	−2.74127e13	−1.57283
$877$	− 2.52693e13i	− 1.44243i	−0.692710	−	0.721216i	$-0.743584\pi$
$877$	− 2.52693e13i	− 1.44243i	0.692710	−	0.721216i	$-0.256416\pi$
$878$	− 4.37876e13i	− 2.48671i
$879$	−2.26068e12	−0.127729
$880$	0	0
$881$	4.23113e12	0.236628	0.118314	−	0.992976i	$-0.462251\pi$
$881$	4.23113e12	0.236628	0.118314	+	0.992976i	$0.462251\pi$
$882$	6.17579e12i	0.343624i
$883$	− 5.41348e12i	− 0.299677i	−0.988710	−	0.149839i	$-0.952125\pi$
$883$	− 5.41348e12i	− 0.299677i	0.988710	−	0.149839i	$-0.0478754\pi$
$884$	−9.19615e12	−0.506490
$885$	0	0
$886$	−9.76794e12	−0.532539
$887$	− 6.28957e12i	− 0.341165i	−0.985343	−	0.170583i	$-0.945435\pi$
$887$	− 6.28957e12i	− 0.341165i	0.985343	−	0.170583i	$-0.0545650\pi$
$888$	1.06420e13i	0.574334i
$889$	−7.47097e12	−0.401161
$890$	0	0
$891$	−2.12536e12	−0.112975
$892$	− 7.08744e12i	− 0.374841i
$893$	1.05759e13i	0.556525i
$894$	8.05250e12	0.421611
$895$	0	0
$896$	−8.98938e13	−4.65955
$897$	− 4.16826e12i	− 0.214976i
$898$	− 5.65603e13i	− 2.90247i
$899$	−3.52735e10	−0.00180107
$900$	0	0
$901$	−4.83356e10	−0.00244346
$902$	− 5.04176e13i	− 2.53602i
$903$	1.21714e13i	0.609182i
$904$	4.83519e13	2.40800
$905$	0	0
$906$	−3.01841e13	−1.48834
$907$	− 1.27094e13i	− 0.623580i	−0.950151	−	0.311790i	$-0.899072\pi$
$907$	− 1.27094e13i	− 0.623580i	0.950151	−	0.311790i	$-0.100928\pi$
$908$	3.87178e13i	1.89027i
$909$	1.19006e12	0.0578138
$910$	0	0
$911$	9.10912e12	0.438171	0.219086	−	0.975706i	$-0.429693\pi$
$911$	9.10912e12	0.438171	0.219086	+	0.975706i	$0.429693\pi$
$912$	− 1.38122e13i	− 0.661127i
$913$	1.04775e13i	0.499046i
$914$	−3.85144e13	−1.82543
$915$	0	0
$916$	7.59021e13	3.56225
$917$	3.16858e13i	1.47980i
$918$	− 6.25540e12i	− 0.290712i
$919$	6.78526e12	0.313795	0.156898	−	0.987615i	$-0.449851\pi$
$919$	6.78526e12	0.313795	0.156898	+	0.987615i	$0.449851\pi$
$920$	0	0
$921$	1.29411e13	0.592658
$922$	− 1.45318e13i	− 0.662263i
$923$	− 3.11993e12i	− 0.141494i
$924$	−4.44496e13	−2.00606
$925$	0	0
$926$	−4.64466e13	−2.07589
$927$	− 1.11834e13i	− 0.497410i
$928$	− 9.42261e12i	− 0.417066i
$929$	−3.16131e12	−0.139250	−0.0696252	−	0.997573i	$-0.522180\pi$
$929$	−3.16131e12	−0.139250	−0.0696252	+	0.997573i	$0.522180\pi$
$930$	0	0
$931$	−3.61134e12	−0.157541
$932$	1.02624e14i	4.45529i
$933$	6.35276e12i	0.274470i
$934$	6.55713e13	2.81938
$935$	0	0
$936$	6.29661e12	0.268142
$937$	3.75670e13i	1.59213i	0.605211	+	0.796065i	$0.293089\pi$
$937$	3.75670e13i	1.59213i	−0.605211	+	0.796065i	$0.706911\pi$
$938$	− 8.25094e13i	− 3.48009i
$939$	1.02246e13	0.429190
$940$	0	0
$941$	−3.13713e13	−1.30431	−0.652153	−	0.758087i	$-0.726134\pi$
$941$	−3.13713e13	−1.30431	−0.652153	+	0.758087i	$0.726134\pi$
$942$	2.58909e13i	1.07132i
$943$	4.93776e13i	2.03342i
$944$	−3.89488e13	−1.59632
$945$	0	0
$946$	−4.14142e13	−1.68127
$947$	− 1.78574e13i	− 0.721513i	−0.932660	−	0.360757i	$-0.882519\pi$
$947$	− 1.78574e13i	− 0.721513i	0.932660	−	0.360757i	$-0.117481\pi$
$948$	6.04682e13i	2.43159i
$949$	5.80504e12	0.232331
$950$	0	0
$951$	−7.77194e12	−0.308118
$952$	− 8.34473e13i	− 3.29265i
$953$	− 8.76602e12i	− 0.344258i	−0.985074	−	0.172129i	$-0.944935\pi$
$953$	− 8.76602e12i	− 0.344258i	0.985074	−	0.172129i	$-0.0550647\pi$
$954$	5.18856e10	0.00202805
$955$	0	0
$956$	2.45028e13	0.948758
$957$	− 1.55820e12i	− 0.0600509i
$958$	− 4.58572e13i	− 1.75899i
$959$	4.33853e13	1.65638
$960$	0	0
$961$	−2.64314e13	−0.999690
$962$	− 3.53310e12i	− 0.133005i
$963$	− 1.13701e13i	− 0.426035i
$964$	−5.74633e13	−2.14311
$965$	0	0
$966$	5.92980e13	2.19100
$967$	2.92145e13i	1.07443i	0.843444	+	0.537217i	$0.180524\pi$
$967$	2.92145e13i	1.07443i	−0.843444	+	0.537217i	$0.819476\pi$
$968$	− 3.15703e12i	− 0.115569i
$969$	3.65789e12	0.133283
$970$	0	0
$971$	1.10119e13	0.397536	0.198768	−	0.980047i	$-0.436306\pi$
$971$	1.10119e13	0.397536	0.198768	+	0.980047i	$0.436306\pi$
$972$	4.92959e12i	0.177138i
$973$	− 3.12711e13i	− 1.11850i
$974$	1.01083e14	3.59885
$975$	0	0
$976$	−5.60709e11	−0.0197794
$977$	8.77989e12i	0.308293i	0.988048	+	0.154146i	$0.0492627\pi$
$977$	8.77989e12i	0.308293i	−0.988048	+	0.154146i	$0.950737\pi$
$978$	− 4.92022e13i	− 1.71973i
$979$	−1.02560e13	−0.356826
$980$	0	0
$981$	−7.69197e12	−0.265172
$982$	− 2.36073e13i	− 0.810113i
$983$	5.68473e13i	1.94186i	0.239355	+	0.970932i	$0.423064\pi$
$983$	5.68473e13i	1.94186i	−0.239355	+	0.970932i	$0.576936\pi$
$984$	−7.45902e13	−2.53632
$985$	0	0
$986$	4.58612e12	0.154525
$987$	− 3.99996e13i	− 1.34162i
$988$	5.77246e12i	0.192732i
$989$	4.05599e13	1.34807
$990$	0	0
$991$	4.32479e13	1.42440	0.712202	−	0.701974i	$-0.247698\pi$
$991$	4.32479e13	1.42440	0.712202	+	0.701974i	$0.247698\pi$
$992$	2.18942e12i	0.0717837i
$993$	− 6.26720e12i	− 0.204551i
$994$	4.43844e13	1.44209
$995$	0	0
$996$	2.43018e13	0.782476
$997$	5.30139e13i	1.69927i	0.527374	+	0.849633i	$0.323177\pi$
$997$	5.30139e13i	1.69927i	−0.527374	+	0.849633i	$0.676823\pi$
$998$	4.45735e13i	1.42229i
$999$	1.76434e12	0.0560450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.b.e.49.4		4
3.2	odd	2		225.10.b.g.199.1		4
5.2	odd	4		75.10.a.g.1.1		2
5.3	odd	4		15.10.a.c.1.2	✓	2
5.4	even	2	inner	75.10.b.e.49.1		4
15.2	even	4		225.10.a.j.1.2		2
15.8	even	4		45.10.a.e.1.1		2
15.14	odd	2		225.10.b.g.199.4		4
20.3	even	4		240.10.a.m.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.c.1.2	✓	2	5.3	odd	4
45.10.a.e.1.1		2	15.8	even	4
75.10.a.g.1.1		2	5.2	odd	4
75.10.b.e.49.1		4	5.4	even	2	inner
75.10.b.e.49.4		4	1.1	even	1	trivial
225.10.a.j.1.2		2	15.2	even	4
225.10.b.g.199.1		4	3.2	odd	2
225.10.b.g.199.4		4	15.14	odd	2
240.10.a.m.1.2		2	20.3	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+43.8839i q^{2} -81.0000i q^{3} -1413.79 q^{4} +3554.59 q^{6} -7861.50i q^{7} -39574.2i q^{8} -6561.00 q^{9} +O(q^{10})\)	\(q+43.8839i q^{2} -81.0000i q^{3} -1413.79 q^{4} +3554.59 q^{6} -7861.50i q^{7} -39574.2i q^{8} -6561.00 q^{9} -49373.3 q^{11} +114517. i q^{12} -24250.7i q^{13} +344993. q^{14} +1.01281e6 q^{16} +268222. i q^{17} -287922. i q^{18} +168364. q^{19} -636781. q^{21} -2.16669e6i q^{22} +2.12200e6i q^{23} -3.20551e6 q^{24} +1.06422e6 q^{26} +531441. i q^{27} +1.11145e7i q^{28} -389624. q^{29} +90532.2 q^{31} +2.41838e7i q^{32} +3.99924e6i q^{33} -1.17706e7 q^{34} +9.27590e6 q^{36} -3.31991e6i q^{37} +7.38848e6i q^{38} -1.96431e6 q^{39} +2.32694e7 q^{41} -2.79444e7i q^{42} -1.91140e7i q^{43} +6.98036e7 q^{44} -9.31215e7 q^{46} +6.28153e7i q^{47} -8.20372e7i q^{48} -2.14495e7 q^{49} +2.17260e7 q^{51} +3.42855e7i q^{52} +180207. i q^{53} -2.33217e7 q^{54} -3.11112e8 q^{56} -1.36375e7i q^{57} -1.70982e7i q^{58} -3.84564e7 q^{59} -553620. q^{61} +3.97290e6i q^{62} +5.15793e7i q^{63} -5.42724e8 q^{64} -1.75502e8 q^{66} -2.39163e8i q^{67} -3.79211e8i q^{68} +1.71882e8 q^{69} +1.28653e8 q^{71} +2.59646e8i q^{72} +2.39376e8i q^{73} +1.45690e8 q^{74} -2.38033e8 q^{76} +3.88148e8i q^{77} -8.62015e7i q^{78} +5.28027e8 q^{79} +4.30467e7 q^{81} +1.02115e9i q^{82} -2.12210e8i q^{83} +9.00277e8 q^{84} +8.38797e8 q^{86} +3.15595e7i q^{87} +1.95391e9i q^{88} +2.07724e8 q^{89} -1.90647e8 q^{91} -3.00007e9i q^{92} -7.33311e6i q^{93} -2.75658e9 q^{94} +1.95889e9 q^{96} +1.70780e9i q^{97} -9.41288e8i q^{98} +3.23938e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3042 q^{4} + 3078 q^{6} - 26244 q^{9}+O(q^{10}) \) 4 * q - 3042 * q^4 + 3078 * q^6 - 26244 * q^9	\( 4 q - 3042 q^{4} + 3078 q^{6} - 26244 q^{9} + 70976 q^{11} + 490392 q^{14} + 1414530 q^{16} + 806592 q^{19} - 1923264 q^{21} - 8042814 q^{24} - 3815092 q^{26} + 149144 q^{29} - 10054256 q^{31} - 17721764 q^{34} + 19958562 q^{36} - 23275512 q^{39} + 28422664 q^{41} + 121411904 q^{44} - 302983296 q^{46} + 5639900 q^{49} + 62395272 q^{51} - 20194758 q^{54} - 703018680 q^{56} - 375726272 q^{59} + 308160120 q^{61} - 1276602178 q^{64} - 693095616 q^{66} - 36240048 q^{69} - 456541952 q^{71} + 724038452 q^{74} - 526437448 q^{76} + 1864813520 q^{79} + 172186884 q^{81} + 1870206408 q^{84} + 1247853416 q^{86} - 449036328 q^{89} - 1339205056 q^{91} - 3863301632 q^{94} + 4313992446 q^{96} - 465673536 q^{99}+O(q^{100}) \) 4 * q - 3042 * q^4 + 3078 * q^6 - 26244 * q^9 + 70976 * q^11 + 490392 * q^14 + 1414530 * q^16 + 806592 * q^19 - 1923264 * q^21 - 8042814 * q^24 - 3815092 * q^26 + 149144 * q^29 - 10054256 * q^31 - 17721764 * q^34 + 19958562 * q^36 - 23275512 * q^39 + 28422664 * q^41 + 121411904 * q^44 - 302983296 * q^46 + 5639900 * q^49 + 62395272 * q^51 - 20194758 * q^54 - 703018680 * q^56 - 375726272 * q^59 + 308160120 * q^61 - 1276602178 * q^64 - 693095616 * q^66 - 36240048 * q^69 - 456541952 * q^71 + 724038452 * q^74 - 526437448 * q^76 + 1864813520 * q^79 + 172186884 * q^81 + 1870206408 * q^84 + 1247853416 * q^86 - 449036328 * q^89 - 1339205056 * q^91 - 3863301632 * q^94 + 4313992446 * q^96 - 465673536 * q^99

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