LMFDB - Embedded newform 60.7.k.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(13,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.k (of order $4$, degree $2$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 66x^{10} + 1601x^{8} + 17520x^{6} + 84208x^{4} + 136704x^{2} + 14400 $ x^12 + 66x^10 + 1601x^8 + 17520x^6 + 84208x^4 + 136704*x^2 + 14400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{10}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.4
Root			$-4.93976i$ of defining polynomial
Character	$\chi$	$=$	60.37
Dual form			60.7.k.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.0227 - 11.0227i) q^{3} +(-41.3794 + 117.952i) q^{5} +(-49.0142 - 49.0142i) q^{7} -243.000i q^{9} +O(q^{10})$	\(q+(11.0227 - 11.0227i) q^{3} +(-41.3794 + 117.952i) q^{5} +(-49.0142 - 49.0142i) q^{7} -243.000i q^{9} -2215.70 q^{11} +(-442.309 + 442.309i) q^{13} +(844.041 + 1756.27i) q^{15} +(144.473 + 144.473i) q^{17} +5801.58i q^{19} -1080.54 q^{21} +(-16160.1 + 16160.1i) q^{23} +(-12200.5 - 9761.58i) q^{25} +(-2678.52 - 2678.52i) q^{27} +2136.27i q^{29} -35200.1 q^{31} +(-24423.0 + 24423.0i) q^{33} +(7809.51 - 3753.16i) q^{35} +(20969.4 + 20969.4i) q^{37} +9750.88i q^{39} +25914.6 q^{41} +(71859.9 - 71859.9i) q^{43} +(28662.4 + 10055.2i) q^{45} +(28302.1 + 28302.1i) q^{47} -112844. i q^{49} +3184.96 q^{51} +(-46258.0 + 46258.0i) q^{53} +(91684.2 - 261347. i) q^{55} +(63949.1 + 63949.1i) q^{57} +69042.8i q^{59} +436950. q^{61} +(-11910.4 + 11910.4i) q^{63} +(-33868.9 - 70473.8i) q^{65} +(-351347. - 351347. i) q^{67} +356256. i q^{69} +174026. q^{71} +(-35342.3 + 35342.3i) q^{73} +(-242082. + 26883.4i) q^{75} +(108601. + 108601. i) q^{77} -522263. i q^{79} -59049.0 q^{81} +(-364118. + 364118. i) q^{83} +(-23019.1 + 11062.7i) q^{85} +(23547.5 + 23547.5i) q^{87} +1.28366e6i q^{89} +43358.8 q^{91} +(-388000. + 388000. i) q^{93} +(-684310. - 240066. i) q^{95} +(-630017. - 630017. i) q^{97} +538415. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) $ 12 * q + 312 * q^5 + 120 * q^7	$ 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) $ 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$3$	11.0227	−	11.0227i	0.408248	−	0.408248i
$4$		0			0
$5$	−41.3794	+	117.952i	−0.331035	+	0.943619i
$5$	−41.3794	+	117.952i	−0.331035	+	0.943619i
$6$		0			0
$7$	−49.0142	−	49.0142i	−0.142898	−	0.142898i	0.632039	−	0.774937i	$-0.282218\pi$
$7$	−49.0142	−	49.0142i	−0.142898	−	0.142898i	−0.774937	+	0.632039i	$0.782218\pi$
$8$		0			0
$9$		−	243.000i		−	0.333333i
$10$		0			0
$11$	−2215.70			−1.66469			−0.832343	−	0.554261i	$-0.813001\pi$
$11$	−2215.70			−1.66469			−0.832343	+	0.554261i	$0.813001\pi$
$12$		0			0
$13$	−442.309	+	442.309i	−0.201324	+	0.201324i	−0.800567	−	0.599243i	$-0.795468\pi$
$13$	−442.309	+	442.309i	−0.201324	+	0.201324i	0.599243	+	0.800567i	$0.295468\pi$
$14$		0			0
$15$	844.041	+	1756.27i	0.250086	+	0.520375i
$16$		0			0
$17$	144.473	+	144.473i	0.0294062	+	0.0294062i	0.721657	−	0.692251i	$-0.243381\pi$
$17$	144.473	+	144.473i	0.0294062	+	0.0294062i	−0.692251	+	0.721657i	$0.743381\pi$
$18$		0			0
$19$			5801.58i			0.845835i	0.906168	+	0.422917i	$0.138994\pi$
$19$			5801.58i			0.845835i	−0.906168	+	0.422917i	$0.861006\pi$
$20$		0			0
$21$	−1080.54			−0.116676
$22$		0			0
$23$	−16160.1	+	16160.1i	−1.32819	+	1.32819i	−0.421244	+	0.906947i	$0.638406\pi$
$23$	−16160.1	+	16160.1i	−1.32819	+	1.32819i	−0.906947	+	0.421244i	$0.861594\pi$
$24$		0			0
$25$	−12200.5	−	9761.58i	−0.780832	−	0.624741i
$26$		0			0
$27$	−2678.52	−	2678.52i	−0.136083	−	0.136083i
$28$		0			0
$29$			2136.27i			0.0875917i	0.999041	+	0.0437958i	$0.0139451\pi$
$29$			2136.27i			0.0875917i	−0.999041	+	0.0437958i	$0.986055\pi$
$30$		0			0
$31$	−35200.1			−1.18157			−0.590784	−	0.806830i	$-0.701181\pi$
$31$	−35200.1			−1.18157			−0.590784	+	0.806830i	$0.701181\pi$
$32$		0			0
$33$	−24423.0	+	24423.0i	−0.679605	+	0.679605i
$34$		0			0
$35$	7809.51	−	3753.16i	0.182146	−	0.0875372i
$36$		0			0
$37$	20969.4	+	20969.4i	0.413982	+	0.413982i	0.883123	−	0.469141i	$-0.155436\pi$
$37$	20969.4	+	20969.4i	0.413982	+	0.413982i	−0.469141	+	0.883123i	$0.655436\pi$
$38$		0			0
$39$			9750.88i			0.164380i
$40$		0			0
$41$	25914.6			0.376005			0.188002	−	0.982169i	$-0.439799\pi$
$41$	25914.6			0.376005			0.188002	+	0.982169i	$0.439799\pi$
$42$		0			0
$43$	71859.9	−	71859.9i	0.903819	−	0.903819i	−0.0919452	−	0.995764i	$-0.529308\pi$
$43$	71859.9	−	71859.9i	0.903819	−	0.903819i	0.995764	+	0.0919452i	$0.0293085\pi$
$44$		0			0
$45$	28662.4	+	10055.2i	0.314540	+	0.110345i
$46$		0			0
$47$	28302.1	+	28302.1i	0.272599	+	0.272599i	0.830146	−	0.557547i	$-0.188257\pi$
$47$	28302.1	+	28302.1i	0.272599	+	0.272599i	−0.557547	+	0.830146i	$0.688257\pi$
$48$		0			0
$49$		−	112844.i		−	0.959160i
$50$		0			0
$51$	3184.96			0.0240101
$52$		0			0
$53$	−46258.0	+	46258.0i	−0.310713	+	0.310713i	−0.845186	−	0.534473i	$-0.820510\pi$
$53$	−46258.0	+	46258.0i	−0.310713	+	0.310713i	0.534473	+	0.845186i	$0.320510\pi$
$54$		0			0
$55$	91684.2	−	261347.i	0.551069	−	1.57083i
$56$		0			0
$57$	63949.1	+	63949.1i	0.345311	+	0.345311i
$58$		0			0
$59$			69042.8i			0.336172i	0.985772	+	0.168086i	$0.0537587\pi$
$59$			69042.8i			0.336172i	−0.985772	+	0.168086i	$0.946241\pi$
$60$		0			0
$61$	436950.			1.92505			0.962525	−	0.271194i	$-0.0874184\pi$
$61$	436950.			1.92505			0.962525	+	0.271194i	$0.0874184\pi$
$62$		0			0
$63$	−11910.4	+	11910.4i	−0.0476328	+	0.0476328i
$64$		0			0
$65$	−33868.9	−	70473.8i	−0.123328	−	0.256618i
$66$		0			0
$67$	−351347.	−	351347.i	−1.16818	−	1.16818i	−0.982635	−	0.185549i	$-0.940594\pi$
$67$	−351347.	−	351347.i	−1.16818	−	1.16818i	−0.185549	−	0.982635i	$-0.559406\pi$
$68$		0			0
$69$			356256.i			1.08446i
$70$		0			0
$71$	174026.			0.486226			0.243113	−	0.969998i	$-0.421831\pi$
$71$	174026.			0.486226			0.243113	+	0.969998i	$0.421831\pi$
$72$		0			0
$73$	−35342.3	+	35342.3i	−0.0908502	+	0.0908502i	−0.751071	−	0.660221i	$-0.770463\pi$
$73$	−35342.3	+	35342.3i	−0.0908502	+	0.0908502i	0.660221	+	0.751071i	$0.270463\pi$
$74$		0			0
$75$	−242082.	+	26883.4i	−0.573823	+	0.0637236i
$76$		0			0
$77$	108601.	+	108601.i	0.237881	+	0.237881i
$78$		0			0
$79$		−	522263.i		−	1.05927i	−0.848225	−	0.529637i	$-0.822328\pi$
$79$		−	522263.i		−	1.05927i	0.848225	−	0.529637i	$-0.177672\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−364118.	+	364118.i	−0.636807	+	0.636807i	−0.949766	−	0.312959i	$-0.898680\pi$
$83$	−364118.	+	364118.i	−0.636807	+	0.636807i	0.312959	+	0.949766i	$0.398680\pi$
$84$		0			0
$85$	−23019.1	+	11062.7i	−0.0374827	+	0.0180137i
$86$		0			0
$87$	23547.5	+	23547.5i	0.0357592	+	0.0357592i
$88$		0			0
$89$			1.28366e6i			1.82087i	0.413655	+	0.910434i	$0.364252\pi$
$89$			1.28366e6i			1.82087i	−0.413655	+	0.910434i	$0.635748\pi$
$90$		0			0
$91$	43358.8			0.0575378
$92$		0			0
$93$	−388000.	+	388000.i	−0.482373	+	0.482373i
$94$		0			0
$95$	−684310.	−	240066.i	−0.798145	−	0.280001i
$96$		0			0
$97$	−630017.	−	630017.i	−0.690299	−	0.690299i	0.271998	−	0.962298i	$-0.412315\pi$
$97$	−630017.	−	630017.i	−0.690299	−	0.690299i	−0.962298	+	0.271998i	$0.912315\pi$
$98$		0			0
$99$			538415.i			0.554895i
$100$		0			0
$101$	826496.			0.802189			0.401094	−	0.916037i	$-0.368630\pi$
$101$	826496.			0.802189			0.401094	+	0.916037i	$0.368630\pi$
$102$		0			0
$103$	−209170.	+	209170.i	−0.191420	+	0.191420i	−0.796309	−	0.604890i	$-0.793217\pi$
$103$	−209170.	+	209170.i	−0.191420	+	0.191420i	0.604890	+	0.796309i	$0.293217\pi$
$104$		0			0
$105$	44711.9	−	127452.i	0.0386239	−	0.110098i
$106$		0			0
$107$	−1.37628e6	−	1.37628e6i	−1.12345	−	1.12345i	−0.991218	−	0.132235i	$-0.957785\pi$
$107$	−1.37628e6	−	1.37628e6i	−1.12345	−	1.12345i	−0.132235	−	0.991218i	$-0.542215\pi$
$108$		0			0
$109$			1.60378e6i			1.23841i	0.785229	+	0.619205i	$0.212545\pi$
$109$			1.60378e6i			1.23841i	−0.785229	+	0.619205i	$0.787455\pi$
$110$		0			0
$111$	462280.			0.338015
$112$		0			0
$113$	−1.45030e6	+	1.45030e6i	−1.00513	+	1.00513i	−0.00514691	+	0.999987i	$0.501638\pi$
$113$	−1.45030e6	+	1.45030e6i	−1.00513	+	1.00513i	−0.999987	+	0.00514691i	$0.998362\pi$
$114$		0			0
$115$	−1.23743e6	−	2.57482e6i	−0.813628	−	1.69298i
$116$		0			0
$117$	107481.	+	107481.i	0.0671080	+	0.0671080i
$118$		0			0
$119$		−	14162.4i		−	0.00840420i
$120$		0			0
$121$	3.13775e6			1.77118
$122$		0			0
$123$	285649.	−	285649.i	0.153503	−	0.153503i
$124$		0			0
$125$	1.65625e6	−	1.03515e6i	0.848000	−	0.529996i
$126$		0			0
$127$	1.07777e6	+	1.07777e6i	0.526158	+	0.526158i	0.919425	−	0.393266i	$-0.128655\pi$
$127$	1.07777e6	+	1.07777e6i	0.526158	+	0.526158i	−0.393266	+	0.919425i	$0.628655\pi$
$128$		0			0
$129$		−	1.58418e6i		−	0.737965i
$130$		0			0
$131$	3.23504e6			1.43902			0.719508	−	0.694485i	$-0.244368\pi$
$131$	3.23504e6			1.43902			0.719508	+	0.694485i	$0.244368\pi$
$132$		0			0
$133$	284360.	−	284360.i	0.120868	−	0.120868i
$134$		0			0
$135$	426773.	−	205102.i	0.173458	−	0.0833621i
$136$		0			0
$137$	208697.	+	208697.i	0.0811623	+	0.0811623i	0.746522	−	0.665360i	$-0.231722\pi$
$137$	208697.	+	208697.i	0.0811623	+	0.0811623i	−0.665360	+	0.746522i	$0.731722\pi$
$138$		0			0
$139$			2.42037e6i			0.901234i	0.892717	+	0.450617i	$0.148796\pi$
$139$			2.42037e6i			0.901234i	−0.892717	+	0.450617i	$0.851204\pi$
$140$		0			0
$141$	623930.			0.222576
$142$		0			0
$143$	980023.	−	980023.i	0.335141	−	0.335141i
$144$		0			0
$145$	−251978.	−	88397.6i	−0.0826531	−	0.0289959i
$146$		0			0
$147$	−1.24385e6	−	1.24385e6i	−0.391575	−	0.391575i
$148$		0			0
$149$		−	3.94738e6i		−	1.19330i	−0.802501	−	0.596651i	$-0.796498\pi$
$149$		−	3.94738e6i		−	1.19330i	0.802501	−	0.596651i	$-0.203502\pi$
$150$		0			0
$151$	−2.24338e6			−0.651586			−0.325793	−	0.945441i	$-0.605631\pi$
$151$	−2.24338e6			−0.651586			−0.325793	+	0.945441i	$0.605631\pi$
$152$		0			0
$153$	35106.8	−	35106.8i	0.00980206	−	0.00980206i
$154$		0			0
$155$	1.45656e6	−	4.15193e6i	0.391140	−	1.11495i
$156$		0			0
$157$	1.14471e6	+	1.14471e6i	0.295799	+	0.295799i	0.839366	−	0.543567i	$-0.182927\pi$
$157$	1.14471e6	+	1.14471e6i	0.295799	+	0.295799i	−0.543567	+	0.839366i	$0.682927\pi$
$158$		0			0
$159$			1.01978e6i			0.253696i
$160$		0			0
$161$	1.58415e6			0.379593
$162$		0			0
$163$	−4.77293e6	+	4.77293e6i	−1.10210	+	1.10210i	−0.107947	+	0.994157i	$0.534428\pi$
$163$	−4.77293e6	+	4.77293e6i	−1.10210	+	1.10210i	−0.994157	+	0.107947i	$0.965572\pi$
$164$		0			0
$165$	−1.87014e6	−	3.89135e6i	−0.416315	−	0.866261i
$166$		0			0
$167$	−800805.	−	800805.i	−0.171940	−	0.171940i	0.615891	−	0.787831i	$-0.288796\pi$
$167$	−800805.	−	800805.i	−0.171940	−	0.171940i	−0.787831	+	0.615891i	$0.788796\pi$
$168$		0			0
$169$			4.43553e6i			0.918937i
$170$		0			0
$171$	1.40978e6			0.281945
$172$		0			0
$173$	−4.48711e6	+	4.48711e6i	−0.866619	+	0.866619i	−0.992096	−	0.125478i	$-0.959954\pi$
$173$	−4.48711e6	+	4.48711e6i	−0.866619	+	0.866619i	0.125478	+	0.992096i	$0.459954\pi$
$174$		0			0
$175$	119541.	+	1.07645e6i	0.0223051	+	0.200854i
$176$		0			0
$177$	761038.	+	761038.i	0.137242	+	0.137242i
$178$		0			0
$179$			4.57201e6i			0.797164i	0.917133	+	0.398582i	$0.130498\pi$
$179$			4.57201e6i			0.797164i	−0.917133	+	0.398582i	$0.869502\pi$
$180$		0			0
$181$	2.24285e6			0.378238			0.189119	−	0.981954i	$-0.439437\pi$
$181$	2.24285e6			0.378238			0.189119	+	0.981954i	$0.439437\pi$
$182$		0			0
$183$	4.81637e6	−	4.81637e6i	0.785898	−	0.785898i
$184$		0			0
$185$	−3.34110e6	+	1.60569e6i	−0.527684	+	0.253599i
$186$		0			0
$187$	−320108.	−	320108.i	−0.0489521	−	0.0489521i
$188$		0			0
$189$			262571.i			0.0388920i
$190$		0			0
$191$	−2.31292e6			−0.331940			−0.165970	−	0.986131i	$-0.553076\pi$
$191$	−2.31292e6			−0.331940			−0.165970	+	0.986131i	$0.553076\pi$
$192$		0			0
$193$	−5.84140e6	+	5.84140e6i	−0.812540	+	0.812540i	−0.985014	−	0.172474i	$-0.944824\pi$
$193$	−5.84140e6	+	5.84140e6i	−0.812540	+	0.812540i	0.172474	+	0.985014i	$0.444824\pi$
$194$		0			0
$195$	−1.15014e6	−	403485.i	−0.155112	−	0.0544156i
$196$		0			0
$197$	−7.02698e6	−	7.02698e6i	−0.919115	−	0.919115i	0.0778500	−	0.996965i	$-0.475194\pi$
$197$	−7.02698e6	−	7.02698e6i	−0.919115	−	0.919115i	−0.996965	+	0.0778500i	$0.975194\pi$
$198$		0			0
$199$			6.46608e6i			0.820506i	0.911972	+	0.410253i	$0.134560\pi$
$199$			6.46608e6i			0.820506i	−0.911972	+	0.410253i	$0.865440\pi$
$200$		0			0
$201$	−7.74558e6			−0.953819
$202$		0			0
$203$	104708.	−	104708.i	0.0125167	−	0.0125167i
$204$		0			0
$205$	−1.07233e6	+	3.05669e6i	−0.124471	+	0.354805i
$206$		0			0
$207$	3.92691e6	+	3.92691e6i	0.442730	+	0.442730i
$208$		0			0
$209$		−	1.28545e7i		−	1.40805i
$210$		0			0
$211$	−7.87679e6			−0.838498			−0.419249	−	0.907871i	$-0.637707\pi$
$211$	−7.87679e6			−0.838498			−0.419249	+	0.907871i	$0.637707\pi$
$212$		0			0
$213$	1.91823e6	−	1.91823e6i	0.198501	−	0.198501i
$214$		0			0
$215$	5.50253e6	+	1.14496e7i	0.553665	+	1.15206i
$216$		0			0
$217$	1.72530e6	+	1.72530e6i	0.168844	+	0.168844i
$218$		0			0
$219$			779135.i			0.0741789i
$220$		0			0
$221$	−127803.			−0.0118403
$222$		0			0
$223$	1.06814e7	−	1.06814e7i	0.963195	−	0.963195i	−0.0361514	−	0.999346i	$-0.511510\pi$
$223$	1.06814e7	−	1.06814e7i	0.963195	−	0.963195i	0.999346	+	0.0361514i	$0.0115099\pi$
$224$		0			0
$225$	−2.37206e6	+	2.96472e6i	−0.208247	+	0.260277i
$226$		0			0
$227$	7.71265e6	+	7.71265e6i	0.659366	+	0.659366i	0.955230	−	0.295864i	$-0.0956077\pi$
$227$	7.71265e6	+	7.71265e6i	0.659366	+	0.659366i	−0.295864	+	0.955230i	$0.595608\pi$
$228$		0			0
$229$		−	1.26947e7i		−	1.05710i	−0.848901	−	0.528551i	$-0.822735\pi$
$229$		−	1.26947e7i		−	1.05710i	0.848901	−	0.528551i	$-0.177265\pi$
$230$		0			0
$231$	2.39414e6			0.194229
$232$		0			0
$233$	1.57409e6	−	1.57409e6i	0.124441	−	0.124441i	−0.642144	−	0.766584i	$-0.721955\pi$
$233$	1.57409e6	−	1.57409e6i	0.124441	−	0.124441i	0.766584	+	0.642144i	$0.221955\pi$
$234$		0			0
$235$	−4.50941e6	+	2.16717e6i	−0.347469	+	0.166990i
$236$		0			0
$237$	−5.75675e6	−	5.75675e6i	−0.432446	−	0.432446i
$238$		0			0
$239$		−	3.78639e6i		−	0.277352i	−0.990338	−	0.138676i	$-0.955715\pi$
$239$		−	3.78639e6i		−	0.277352i	0.990338	−	0.138676i	$-0.0442847\pi$
$240$		0			0
$241$	3.28254e6			0.234509			0.117254	−	0.993102i	$-0.462591\pi$
$241$	3.28254e6			0.234509			0.117254	+	0.993102i	$0.462591\pi$
$242$		0			0
$243$	−650880.	+	650880.i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	1.33102e7	+	4.66942e6i	0.905081	+	0.317515i
$246$		0			0
$247$	−2.56609e6	−	2.56609e6i	−0.170287	−	0.170287i
$248$		0			0
$249$			8.02713e6i			0.519951i
$250$		0			0
$251$	2.07767e7			1.31388			0.656938	−	0.753945i	$-0.271851\pi$
$251$	2.07767e7			1.31388			0.656938	+	0.753945i	$0.271851\pi$
$252$		0			0
$253$	3.58059e7	−	3.58059e7i	2.21102	−	2.21102i
$254$		0			0
$255$	−131792.	+	375673.i	−0.00794817	+	0.0226563i
$256$		0			0
$257$	−1.14588e7	−	1.14588e7i	−0.675054	−	0.675054i	0.283823	−	0.958877i	$-0.408397\pi$
$257$	−1.14588e7	−	1.14588e7i	−0.675054	−	0.675054i	−0.958877	+	0.283823i	$0.908397\pi$
$258$		0			0
$259$		−	2.05560e6i		−	0.118315i
$260$		0			0
$261$	519114.			0.0291972
$262$		0			0
$263$	−1.48866e7	+	1.48866e7i	−0.818332	+	0.818332i	−0.985866	−	0.167534i	$-0.946420\pi$
$263$	−1.48866e7	+	1.48866e7i	−0.818332	+	0.818332i	0.167534	+	0.985866i	$0.446420\pi$
$264$		0			0
$265$	−3.54212e6	−	7.37037e6i	−0.190338	−	0.396052i
$266$		0			0
$267$	1.41494e7	+	1.41494e7i	0.743366	+	0.743366i
$268$		0			0
$269$		−	1.86327e7i		−	0.957235i	−0.878024	−	0.478617i	$-0.841138\pi$
$269$		−	1.86327e7i		−	0.957235i	0.878024	−	0.478617i	$-0.158862\pi$
$270$		0			0
$271$	−2.81546e7			−1.41463			−0.707314	−	0.706900i	$-0.750093\pi$
$271$	−2.81546e7			−1.41463			−0.707314	+	0.706900i	$0.750093\pi$
$272$		0			0
$273$	477931.	−	477931.i	0.0234897	−	0.0234897i
$274$		0			0
$275$	2.70326e7	+	2.16287e7i	1.29984	+	1.04000i
$276$		0			0
$277$	2.59589e7	+	2.59589e7i	1.22137	+	1.22137i	0.967146	+	0.254222i	$0.0818193\pi$
$277$	2.59589e7	+	2.59589e7i	1.22137	+	1.22137i	0.254222	+	0.967146i	$0.418181\pi$
$278$		0			0
$279$			8.55362e6i			0.393856i
$280$		0			0
$281$	−3.74030e7			−1.68573			−0.842864	−	0.538126i	$-0.819132\pi$
$281$	−3.74030e7			−1.68573			−0.842864	+	0.538126i	$0.819132\pi$
$282$		0			0
$283$	2.07057e7	−	2.07057e7i	0.913545	−	0.913545i	−0.0830040	−	0.996549i	$-0.526451\pi$
$283$	2.07057e7	−	2.07057e7i	0.913545	−	0.913545i	0.996549	+	0.0830040i	$0.0264514\pi$
$284$		0			0
$285$	−1.01891e7	+	4.89677e6i	−0.440151	+	0.211532i
$286$		0			0
$287$	−1.27018e6	−	1.27018e6i	−0.0537305	−	0.0537305i
$288$		0			0
$289$		−	2.40958e7i		−	0.998271i
$290$		0			0
$291$	−1.38890e7			−0.563627
$292$		0			0
$293$	−1.73111e7	+	1.73111e7i	−0.688211	+	0.688211i	−0.961836	−	0.273626i	$-0.911777\pi$
$293$	−1.73111e7	+	1.73111e7i	−0.688211	+	0.688211i	0.273626	+	0.961836i	$0.411777\pi$
$294$		0			0
$295$	−8.14375e6	−	2.85695e6i	−0.317219	−	0.111285i
$296$		0			0
$297$	5.93478e6	+	5.93478e6i	0.226535	+	0.226535i
$298$		0			0
$299$		−	1.42955e7i		−	0.534794i
$300$		0			0
$301$	−7.04431e6			−0.258309
$302$		0			0
$303$	9.11022e6	−	9.11022e6i	0.327492	−	0.327492i
$304$		0			0
$305$	−1.80807e7	+	5.15392e7i	−0.637259	+	1.81651i
$306$		0			0
$307$	−2.74278e7	−	2.74278e7i	−0.947929	−	0.947929i	0.0507806	−	0.998710i	$-0.483829\pi$
$307$	−2.74278e7	−	2.74278e7i	−0.947929	−	0.947929i	−0.998710	+	0.0507806i	$0.983829\pi$
$308$		0			0
$309$			4.61123e6i			0.156294i
$310$		0			0
$311$	−4.34214e7			−1.44352			−0.721760	−	0.692143i	$-0.756667\pi$
$311$	−4.34214e7			−1.44352			−0.721760	+	0.692143i	$0.756667\pi$
$312$		0			0
$313$	−2.15286e7	+	2.15286e7i	−0.702073	+	0.702073i	−0.964855	−	0.262782i	$-0.915360\pi$
$313$	−2.15286e7	+	2.15286e7i	−0.702073	+	0.702073i	0.262782	+	0.964855i	$0.415360\pi$
$314$		0			0
$315$	−912018.	−	1.89771e6i	−0.0291791	−	0.0607153i
$316$		0			0
$317$	2.02040e7	+	2.02040e7i	0.634250	+	0.634250i	0.949131	−	0.314881i	$-0.101965\pi$
$317$	2.02040e7	+	2.02040e7i	0.634250	+	0.634250i	−0.314881	+	0.949131i	$0.601965\pi$
$318$		0			0
$319$		−	4.73334e6i		−	0.145813i
$320$		0			0
$321$	−3.03406e7			−0.917296
$322$		0			0
$323$	−838170.	+	838170.i	−0.0248728	+	0.0248728i
$324$		0			0
$325$	9.71402e6	−	1.07875e6i	0.282976	−	0.0314247i
$326$		0			0
$327$	1.76780e7	+	1.76780e7i	0.505579	+	0.505579i
$328$		0			0
$329$		−	2.77440e6i		−	0.0779080i
$330$		0			0
$331$	−3.25341e7			−0.897128			−0.448564	−	0.893751i	$-0.648064\pi$
$331$	−3.25341e7			−0.897128			−0.448564	+	0.893751i	$0.648064\pi$
$332$		0			0
$333$	5.09557e6	−	5.09557e6i	0.137994	−	0.137994i
$334$		0			0
$335$	5.59806e7	−	2.69036e7i	1.48903	−	0.715611i
$336$		0			0
$337$	3.68444e7	+	3.68444e7i	0.962680	+	0.962680i	0.999328	−	0.0366481i	$-0.0116681\pi$
$337$	3.68444e7	+	3.68444e7i	0.962680	+	0.962680i	−0.0366481	+	0.999328i	$0.511668\pi$
$338$		0			0
$339$			3.19726e7i			0.820688i
$340$		0			0
$341$	7.79928e7			1.96694
$342$		0			0
$343$	−1.12974e7	+	1.12974e7i	−0.279961	+	0.279961i
$344$		0			0
$345$	−4.20212e7	−	1.47417e7i	−1.02332	−	0.358995i
$346$		0			0
$347$	−4.51503e7	−	4.51503e7i	−1.08062	−	1.08062i	−0.996452	−	0.0841664i	$-0.973177\pi$
$347$	−4.51503e7	−	4.51503e7i	−1.08062	−	1.08062i	−0.0841664	−	0.996452i	$-0.526823\pi$
$348$		0			0
$349$			9.12648e6i			0.214698i	0.994221	+	0.107349i	$0.0342361\pi$
$349$			9.12648e6i			0.214698i	−0.994221	+	0.107349i	$0.965764\pi$
$350$		0			0
$351$	2.36946e6			0.0547935
$352$		0			0
$353$	−3.91869e7	+	3.91869e7i	−0.890876	+	0.890876i	−0.994606	−	0.103730i	$-0.966922\pi$
$353$	−3.91869e7	+	3.91869e7i	−0.890876	+	0.890876i	0.103730	+	0.994606i	$0.466922\pi$
$354$		0			0
$355$	−7.20107e6	+	2.05267e7i	−0.160958	+	0.458812i
$356$		0			0
$357$	−156108.	−	156108.i	−0.00343100	−	0.00343100i
$358$		0			0
$359$		−	2.75365e7i		−	0.595148i	−0.954699	−	0.297574i	$-0.903823\pi$
$359$		−	2.75365e7i		−	0.595148i	0.954699	−	0.297574i	$-0.0961774\pi$
$360$		0			0
$361$	1.33875e7			0.284563
$362$		0			0
$363$	3.45865e7	−	3.45865e7i	0.723081	−	0.723081i
$364$		0			0
$365$	−2.70626e6	−	5.63115e6i	−0.0556534	−	0.115803i
$366$		0			0
$367$	−2.78347e7	−	2.78347e7i	−0.563103	−	0.563103i	0.367085	−	0.930188i	$-0.380356\pi$
$367$	−2.78347e7	−	2.78347e7i	−0.563103	−	0.563103i	−0.930188	+	0.367085i	$0.880356\pi$
$368$		0			0
$369$		−	6.29725e6i		−	0.125335i
$370$		0			0
$371$	4.53460e6			0.0888009
$372$		0			0
$373$	4.74882e7	−	4.74882e7i	0.915080	−	0.915080i	−0.0815866	−	0.996666i	$-0.525999\pi$
$373$	4.74882e7	−	4.74882e7i	0.915080	−	0.915080i	0.996666	+	0.0815866i	$0.0259987\pi$
$374$		0			0
$375$	6.84622e6	−	2.96665e7i	0.129825	−	0.562565i
$376$		0			0
$377$	−944893.	−	944893.i	−0.0176343	−	0.0176343i
$378$		0			0
$379$			3.44948e7i			0.633630i	0.948487	+	0.316815i	$0.102613\pi$
$379$			3.44948e7i			0.633630i	−0.948487	+	0.316815i	$0.897387\pi$
$380$		0			0
$381$	2.37600e7			0.429606
$382$		0			0
$383$	−1.37191e7	+	1.37191e7i	−0.244192	+	0.244192i	−0.818582	−	0.574390i	$-0.805239\pi$
$383$	−1.37191e7	+	1.37191e7i	−0.244192	+	0.244192i	0.574390	+	0.818582i	$0.305239\pi$
$384$		0			0
$385$	−1.73035e7	+	8.31587e6i	−0.303216	+	0.145722i
$386$		0			0
$387$	−1.74620e7	−	1.74620e7i	−0.301273	−	0.301273i
$388$		0			0
$389$		−	9.06282e7i		−	1.53962i	−0.638271	−	0.769811i	$-0.720350\pi$
$389$		−	9.06282e7i		−	1.53962i	0.638271	−	0.769811i	$-0.279650\pi$
$390$		0			0
$391$	−4.66938e6			−0.0781141
$392$		0			0
$393$	3.56589e7	−	3.56589e7i	0.587475	−	0.587475i
$394$		0			0
$395$	6.16021e7	+	2.16109e7i	0.999550	+	0.350656i
$396$		0			0
$397$	7.73386e7	+	7.73386e7i	1.23602	+	1.23602i	0.961614	+	0.274404i	$0.0884807\pi$
$397$	7.73386e7	+	7.73386e7i	1.23602	+	1.23602i	0.274404	+	0.961614i	$0.411519\pi$
$398$		0			0
$399$		−	6.26882e6i		−	0.0986887i
$400$		0			0
$401$	4.19852e7			0.651123			0.325561	−	0.945521i	$-0.394447\pi$
$401$	4.19852e7			0.651123			0.325561	+	0.945521i	$0.394447\pi$
$402$		0			0
$403$	1.55693e7	−	1.55693e7i	0.237878	−	0.237878i
$404$		0			0
$405$	2.44341e6	−	6.96497e6i	0.0367817	−	0.104847i
$406$		0			0
$407$	−4.64619e7	−	4.64619e7i	−0.689150	−	0.689150i
$408$		0			0
$409$			1.19743e8i			1.75018i	0.483964	+	0.875088i	$0.339197\pi$
$409$			1.19743e8i			1.75018i	−0.483964	+	0.875088i	$0.660803\pi$
$410$		0			0
$411$	4.60081e6			0.0662688
$412$		0			0
$413$	3.38407e6	−	3.38407e6i	0.0480385	−	0.0480385i
$414$		0			0
$415$	−2.78816e7	−	5.80155e7i	−0.390098	−	0.811708i
$416$		0			0
$417$	2.66790e7	+	2.66790e7i	0.367927	+	0.367927i
$418$		0			0
$419$		−	2.91956e7i		−	0.396895i	−0.980111	−	0.198448i	$-0.936410\pi$
$419$		−	2.91956e7i		−	0.396895i	0.980111	−	0.198448i	$-0.0635900\pi$
$420$		0			0
$421$	9.92290e7			1.32982			0.664909	−	0.746924i	$-0.268470\pi$
$421$	9.92290e7			1.32982			0.664909	+	0.746924i	$0.268470\pi$
$422$		0			0
$423$	6.87740e6	−	6.87740e6i	0.0908664	−	0.0908664i
$424$		0			0
$425$	−352356.	−	3.17292e6i	−0.00459002	−	0.0413326i
$426$		0			0
$427$	−2.14167e7	−	2.14167e7i	−0.275087	−	0.275087i
$428$		0			0
$429$		−	2.16050e7i		−	0.273642i
$430$		0			0
$431$	1.53767e8			1.92058			0.960288	−	0.279010i	$-0.0900063\pi$
$431$	1.53767e8			1.92058			0.960288	+	0.279010i	$0.0900063\pi$
$432$		0			0
$433$	−5.49822e7	+	5.49822e7i	−0.677265	+	0.677265i	−0.959381	−	0.282115i	$-0.908964\pi$
$433$	−5.49822e7	+	5.49822e7i	−0.677265	+	0.677265i	0.282115	+	0.959381i	$0.408964\pi$
$434$		0			0
$435$	−3.75186e6	+	1.80310e6i	−0.0455805	+	0.0219055i
$436$		0			0
$437$	−9.37542e7	−	9.37542e7i	−1.12343	−	1.12343i
$438$		0			0
$439$			1.55682e8i			1.84012i	0.391780	+	0.920059i	$0.371860\pi$
$439$			1.55682e8i			1.84012i	−0.391780	+	0.920059i	$0.628140\pi$
$440$		0			0
$441$	−2.74211e7			−0.319720
$442$		0			0
$443$	−6.64753e7	+	6.64753e7i	−0.764626	+	0.764626i	−0.977155	−	0.212529i	$-0.931830\pi$
$443$	−6.64753e7	+	6.64753e7i	−0.764626	+	0.764626i	0.212529	+	0.977155i	$0.431830\pi$
$444$		0			0
$445$	−1.51410e8	−	5.31168e7i	−1.71820	−	0.602771i
$446$		0			0
$447$	−4.35108e7	−	4.35108e7i	−0.487163	−	0.487163i
$448$		0			0
$449$			5.74059e6i			0.0634187i	0.999497	+	0.0317094i	$0.0100951\pi$
$449$			5.74059e6i			0.0634187i	−0.999497	+	0.0317094i	$0.989905\pi$
$450$		0			0
$451$	−5.74190e7			−0.625930
$452$		0			0
$453$	−2.47281e7	+	2.47281e7i	−0.266009	+	0.266009i
$454$		0			0
$455$	−1.79416e6	+	5.11427e6i	−0.0190470	+	0.0542937i
$456$		0			0
$457$	−2.09831e7	−	2.09831e7i	−0.219847	−	0.219847i	0.588587	−	0.808434i	$-0.299684\pi$
$457$	−2.09831e7	−	2.09831e7i	−0.219847	−	0.219847i	−0.808434	+	0.588587i	$0.799684\pi$
$458$		0			0
$459$		−	773945.i		−	0.00800335i
$460$		0			0
$461$	6.08153e7			0.620740			0.310370	−	0.950616i	$-0.399547\pi$
$461$	6.08153e7			0.620740			0.310370	+	0.950616i	$0.399547\pi$
$462$		0			0
$463$	−6.28810e7	+	6.28810e7i	−0.633543	+	0.633543i	−0.948955	−	0.315412i	$-0.897857\pi$
$463$	−6.28810e7	+	6.28810e7i	−0.633543	+	0.633543i	0.315412	+	0.948955i	$0.397857\pi$
$464$		0			0
$465$	−2.97103e7	−	6.18207e7i	−0.295494	−	0.614859i
$466$		0			0
$467$	−1.10364e7	−	1.10364e7i	−0.108362	−	0.108362i	0.650847	−	0.759209i	$-0.274414\pi$
$467$	−1.10364e7	−	1.10364e7i	−0.108362	−	0.108362i	−0.759209	+	0.650847i	$0.774414\pi$
$468$		0			0
$469$			3.44419e7i			0.333863i
$470$		0			0
$471$	2.52356e7			0.241519
$472$		0			0
$473$	−1.59220e8	+	1.59220e8i	−1.50457	+	1.50457i
$474$		0			0
$475$	5.66326e7	−	7.07822e7i	0.528428	−	0.660455i
$476$		0			0
$477$	1.12407e7	+	1.12407e7i	0.103571	+	0.103571i
$478$		0			0
$479$			7.85058e7i			0.714324i	0.934042	+	0.357162i	$0.116256\pi$
$479$			7.85058e7i			0.714324i	−0.934042	+	0.357162i	$0.883744\pi$
$480$		0			0
$481$	−1.85499e7			−0.166689
$482$		0			0
$483$	1.74616e7	−	1.74616e7i	0.154968	−	0.154968i
$484$		0			0
$485$	1.00382e8	−	4.82423e7i	0.879892	−	0.422866i
$486$		0			0
$487$	4.26865e7	+	4.26865e7i	0.369576	+	0.369576i	0.867322	−	0.497747i	$-0.165839\pi$
$487$	4.26865e7	+	4.26865e7i	0.369576	+	0.369576i	−0.497747	+	0.867322i	$0.665839\pi$
$488$		0			0
$489$			1.05221e8i			0.899864i
$490$		0			0
$491$	−1.07781e8			−0.910541			−0.455271	−	0.890353i	$-0.650457\pi$
$491$	−1.07781e8			−0.910541			−0.455271	+	0.890353i	$0.650457\pi$
$492$		0			0
$493$	−308633.	+	308633.i	−0.00257574	+	0.00257574i
$494$		0			0
$495$	−6.35072e7	−	2.22793e7i	−0.523610	−	0.183690i
$496$		0			0
$497$	−8.52972e6	−	8.52972e6i	−0.0694809	−	0.0694809i
$498$		0			0
$499$			1.60362e7i			0.129063i	0.997916	+	0.0645314i	$0.0205553\pi$
$499$			1.60362e7i			0.129063i	−0.997916	+	0.0645314i	$0.979445\pi$
$500$		0			0
$501$	−1.76541e7			−0.140389
$502$		0			0
$503$	−6.58572e6	+	6.58572e6i	−0.0517487	+	0.0517487i	−0.732508	−	0.680759i	$-0.761650\pi$
$503$	−6.58572e6	+	6.58572e6i	−0.0517487	+	0.0517487i	0.680759	+	0.732508i	$0.261650\pi$
$504$		0			0
$505$	−3.41999e7	+	9.74871e7i	−0.265552	+	0.756960i
$506$		0			0
$507$	4.88916e7	+	4.88916e7i	0.375155	+	0.375155i
$508$		0			0
$509$		−	1.18727e8i		−	0.900322i	−0.892948	−	0.450161i	$-0.851367\pi$
$509$		−	1.18727e8i		−	0.900322i	0.892948	−	0.450161i	$-0.148633\pi$
$510$		0			0
$511$	3.46455e6			0.0259647
$512$		0			0
$513$	1.55396e7	−	1.55396e7i	0.115104	−	0.115104i
$514$		0			0
$515$	−1.60167e7	−	3.33274e7i	−0.117261	−	0.243994i
$516$		0			0
$517$	−6.27088e7	−	6.27088e7i	−0.453792	−	0.453792i
$518$		0			0
$519$			9.89201e7i			0.707591i
$520$		0			0
$521$	8.45567e7			0.597909			0.298954	−	0.954267i	$-0.403362\pi$
$521$	8.45567e7			0.597909			0.298954	+	0.954267i	$0.403362\pi$
$522$		0			0
$523$	8.30053e7	−	8.30053e7i	0.580231	−	0.580231i	−0.354736	−	0.934967i	$-0.615429\pi$
$523$	8.30053e7	−	8.30053e7i	0.580231	−	0.580231i	0.934967	+	0.354736i	$0.115429\pi$
$524$		0			0
$525$	1.31831e7	+	1.05478e7i	0.0911044	+	0.0728924i
$526$		0			0
$527$	−5.08545e6	−	5.08545e6i	−0.0347454	−	0.0347454i
$528$		0			0
$529$		−	3.74262e8i		−	2.52818i
$530$		0			0
$531$	1.67774e7			0.112057
$532$		0			0
$533$	−1.14623e7	+	1.14623e7i	−0.0756988	+	0.0756988i
$534$		0			0
$535$	2.19285e8	−	1.05386e8i	1.43201	−	0.688209i
$536$		0			0
$537$	5.03959e7	+	5.03959e7i	0.325441	+	0.325441i
$538$		0			0
$539$			2.50029e8i			1.59670i
$540$		0			0
$541$	2.02711e8			1.28022			0.640111	−	0.768282i	$-0.278888\pi$
$541$	2.02711e8			1.28022			0.640111	+	0.768282i	$0.278888\pi$
$542$		0			0
$543$	2.47223e7	−	2.47223e7i	0.154415	−	0.154415i
$544$		0			0
$545$	−1.89169e8	−	6.63633e7i	−1.16859	−	0.409957i
$546$		0			0
$547$	−1.08515e7	−	1.08515e7i	−0.0663022	−	0.0663022i	0.673178	−	0.739480i	$-0.264929\pi$
$547$	−1.08515e7	−	1.08515e7i	−0.0663022	−	0.0663022i	−0.739480	+	0.673178i	$0.764929\pi$
$548$		0			0
$549$		−	1.06179e8i		−	0.641683i
$550$		0			0
$551$	−1.23938e7			−0.0740881
$552$		0			0
$553$	−2.55983e7	+	2.55983e7i	−0.151368	+	0.151368i
$554$		0			0
$555$	−1.91288e7	+	5.45270e7i	−0.111895	+	0.318957i
$556$		0			0
$557$	2.01939e8	+	2.01939e8i	1.16857	+	1.16857i	0.982544	+	0.186028i	$0.0595614\pi$
$557$	2.01939e8	+	2.01939e8i	1.16857	+	1.16857i	0.186028	+	0.982544i	$0.440439\pi$
$558$		0			0
$559$			6.35686e7i			0.363921i
$560$		0			0
$561$	−7.05690e6			−0.0399692
$562$		0			0
$563$	−1.75434e7	+	1.75434e7i	−0.0983082	+	0.0983082i	−0.754550	−	0.656242i	$-0.772145\pi$
$563$	−1.75434e7	+	1.75434e7i	−0.0983082	+	0.0983082i	0.656242	+	0.754550i	$0.272145\pi$
$564$		0			0
$565$	−1.11054e8	−	2.31079e8i	−0.615728	−	1.28120i
$566$		0			0
$567$	2.89424e6	+	2.89424e6i	0.0158776	+	0.0158776i
$568$		0			0
$569$		−	5.97338e7i		−	0.324253i	−0.986770	−	0.162126i	$-0.948165\pi$
$569$		−	5.97338e7i		−	0.324253i	0.986770	−	0.162126i	$-0.0518352\pi$
$570$		0			0
$571$	2.12108e8			1.13933			0.569664	−	0.821878i	$-0.307073\pi$
$571$	2.12108e8			1.13933			0.569664	+	0.821878i	$0.307073\pi$
$572$		0			0
$573$	−2.54946e7	+	2.54946e7i	−0.135514	+	0.135514i
$574$		0			0
$575$	3.54909e8	−	3.94131e7i	1.86687	−	0.207318i
$576$		0			0
$577$	−1.37392e8	−	1.37392e8i	−0.715209	−	0.715209i	0.252411	−	0.967620i	$-0.418777\pi$
$577$	−1.37392e8	−	1.37392e8i	−0.715209	−	0.715209i	−0.967620	+	0.252411i	$0.918777\pi$
$578$		0			0
$579$			1.28776e8i			0.663436i
$580$		0			0
$581$	3.56939e7			0.181997
$582$		0			0
$583$	1.02494e8	−	1.02494e8i	0.517240	−	0.517240i
$584$		0			0
$585$	−1.71251e7	+	8.23014e6i	−0.0855394	+	0.0411093i
$586$		0			0
$587$	−1.33344e8	−	1.33344e8i	−0.659262	−	0.659262i	0.295943	−	0.955206i	$-0.404366\pi$
$587$	−1.33344e8	−	1.33344e8i	−0.659262	−	0.659262i	−0.955206	+	0.295943i	$0.904366\pi$
$588$		0			0
$589$		−	2.04216e8i		−	0.999411i
$590$		0			0
$591$	−1.54913e8			−0.750454
$592$		0			0
$593$	1.46313e8	−	1.46313e8i	0.701648	−	0.701648i	−0.263117	−	0.964764i	$-0.584750\pi$
$593$	1.46313e8	−	1.46313e8i	0.701648	−	0.701648i	0.964764	+	0.263117i	$0.0847504\pi$
$594$		0			0
$595$	1.67049e6	+	586031.i	0.00793036	+	0.00278208i
$596$		0			0
$597$	7.12736e7	+	7.12736e7i	0.334970	+	0.334970i
$598$		0			0
$599$		−	1.05020e8i		−	0.488641i	−0.969694	−	0.244321i	$-0.921435\pi$
$599$		−	1.05020e8i		−	0.488641i	0.969694	−	0.244321i	$-0.0785650\pi$
$600$		0			0
$601$	−2.58385e8			−1.19026			−0.595132	−	0.803628i	$-0.702900\pi$
$601$	−2.58385e8			−1.19026			−0.595132	+	0.803628i	$0.702900\pi$
$602$		0			0
$603$	−8.53772e7	+	8.53772e7i	−0.389395	+	0.389395i
$604$		0			0
$605$	−1.29838e8	+	3.70105e8i	−0.586323	+	1.67132i
$606$		0			0
$607$	1.21552e8	+	1.21552e8i	0.543498	+	0.543498i	0.924552	−	0.381055i	$-0.124439\pi$
$607$	1.21552e8	+	1.21552e8i	0.543498	+	0.543498i	−0.381055	+	0.924552i	$0.624439\pi$
$608$		0			0
$609$		−	2.30832e6i		−	0.0102199i
$610$		0			0
$611$	−2.50365e7			−0.109761
$612$		0			0
$613$	9.23690e7	−	9.23690e7i	0.401000	−	0.401000i	−0.477585	−	0.878585i	$-0.658488\pi$
$613$	9.23690e7	−	9.23690e7i	0.401000	−	0.401000i	0.878585	+	0.477585i	$0.158488\pi$
$614$		0			0
$615$	2.18730e7	+	4.55130e7i	0.0940336	+	0.195664i
$616$		0			0
$617$	−5.83859e7	−	5.83859e7i	−0.248572	−	0.248572i	0.571812	−	0.820384i	$-0.306241\pi$
$617$	−5.83859e7	−	5.83859e7i	−0.248572	−	0.248572i	−0.820384	+	0.571812i	$0.806241\pi$
$618$		0			0
$619$			1.24199e8i			0.523658i	0.965114	+	0.261829i	$0.0843256\pi$
$619$			1.24199e8i			0.523658i	−0.965114	+	0.261829i	$0.915674\pi$
$620$		0			0
$621$	8.65702e7			0.361488
$622$		0			0
$623$	6.29173e7	−	6.29173e7i	0.260199	−	0.260199i
$624$		0			0
$625$	5.35636e7	+	2.38192e8i	0.219396	+	0.975636i
$626$		0			0
$627$	−1.41692e8	−	1.41692e8i	−0.574834	−	0.574834i
$628$		0			0
$629$			6.05902e6i			0.0243473i
$630$		0			0
$631$	−2.71587e8			−1.08099			−0.540495	−	0.841347i	$-0.681763\pi$
$631$	−2.71587e8			−1.08099			−0.540495	+	0.841347i	$0.681763\pi$
$632$		0			0
$633$	−8.68235e7	+	8.68235e7i	−0.342315	+	0.342315i
$634$		0			0
$635$	−1.71723e8	+	8.25283e7i	−0.670669	+	0.322316i
$636$		0			0
$637$	4.99120e7	+	4.99120e7i	0.193102	+	0.193102i
$638$		0			0
$639$		−	4.22882e7i		−	0.162075i
$640$		0			0
$641$	−8.79390e6			−0.0333893			−0.0166947	−	0.999861i	$-0.505314\pi$
$641$	−8.79390e6			−0.0333893			−0.0166947	+	0.999861i	$0.505314\pi$
$642$		0			0
$643$	2.73138e8	−	2.73138e8i	1.02742	−	1.02742i	0.0278106	−	0.999613i	$-0.491146\pi$
$643$	2.73138e8	−	2.73138e8i	1.02742	−	1.02742i	0.999613	−	0.0278106i	$-0.00885354\pi$
$644$		0			0
$645$	1.86858e8	+	6.55524e7i	0.696357	+	0.244292i
$646$		0			0
$647$	2.67434e8	+	2.67434e8i	0.987424	+	0.987424i	0.999922	−	0.0124977i	$-0.00397824\pi$
$647$	2.67434e8	+	2.67434e8i	0.987424	+	0.987424i	−0.0124977	+	0.999922i	$0.503978\pi$
$648$		0			0
$649$		−	1.52978e8i		−	0.559622i
$650$		0			0
$651$	3.80350e7			0.137861
$652$		0			0
$653$	−1.69114e8	+	1.69114e8i	−0.607351	+	0.607351i	−0.942253	−	0.334902i	$-0.891297\pi$
$653$	−1.69114e8	+	1.69114e8i	−0.607351	+	0.607351i	0.334902	+	0.942253i	$0.391297\pi$
$654$		0			0
$655$	−1.33864e8	+	3.81580e8i	−0.476364	+	1.35788i
$656$		0			0
$657$	8.58818e6	+	8.58818e6i	0.0302834	+	0.0302834i
$658$		0			0
$659$			1.82211e8i			0.636675i	0.947977	+	0.318338i	$0.103125\pi$
$659$			1.82211e8i			0.636675i	−0.947977	+	0.318338i	$0.896875\pi$
$660$		0			0
$661$	−4.68167e8			−1.62105			−0.810526	−	0.585703i	$-0.800818\pi$
$661$	−4.68167e8			−1.62105			−0.810526	+	0.585703i	$0.800818\pi$
$662$		0			0
$663$	−1.40873e6	+	1.40873e6i	−0.00483380	+	0.00483380i
$664$		0			0
$665$	2.17743e7	+	4.53075e7i	0.0740420	+	0.154065i
$666$		0			0
$667$	−3.45224e7	−	3.45224e7i	−0.116339	−	0.116339i
$668$		0			0
$669$		−	2.35476e8i		−	0.786445i
$670$		0			0
$671$	−9.68148e8			−3.20460
$672$		0			0
$673$	−1.81041e8	+	1.81041e8i	−0.593927	+	0.593927i	−0.938690	−	0.344763i	$-0.887959\pi$
$673$	−1.81041e8	+	1.81041e8i	−0.593927	+	0.593927i	0.344763	+	0.938690i	$0.387959\pi$
$674$		0			0
$675$	6.53267e6	+	5.88258e7i	0.0212412	+	0.191274i
$676$		0			0
$677$	−1.71267e8	−	1.71267e8i	−0.551961	−	0.551961i	0.375046	−	0.927006i	$-0.377627\pi$
$677$	−1.71267e8	−	1.71267e8i	−0.551961	−	0.551961i	−0.927006	+	0.375046i	$0.877627\pi$
$678$		0			0
$679$			6.17596e7i			0.197285i
$680$		0			0
$681$	1.70029e8			0.538370
$682$		0			0
$683$	1.15548e8	−	1.15548e8i	0.362660	−	0.362660i	−0.502131	−	0.864792i	$-0.667451\pi$
$683$	1.15548e8	−	1.15548e8i	0.362660	−	0.362660i	0.864792	+	0.502131i	$0.167451\pi$
$684$		0			0
$685$	−3.32520e7	+	1.59805e7i	−0.103454	+	0.0497187i
$686$		0			0
$687$	−1.39930e8	−	1.39930e8i	−0.431560	−	0.431560i
$688$		0			0
$689$		−	4.09207e7i		−	0.125108i
$690$		0			0
$691$	3.38296e8			1.02533			0.512663	−	0.858590i	$-0.328659\pi$
$691$	3.38296e8			1.02533			0.512663	+	0.858590i	$0.328659\pi$
$692$		0			0
$693$	2.63899e7	−	2.63899e7i	0.0792937	−	0.0792937i
$694$		0			0
$695$	−2.85489e8	−	1.00153e8i	−0.850421	−	0.298340i
$696$		0			0
$697$	3.74395e6	+	3.74395e6i	0.0110569	+	0.0110569i
$698$		0			0
$699$		−	3.47015e7i		−	0.101605i
$700$		0			0
$701$	3.02164e8			0.877181			0.438590	−	0.898687i	$-0.355478\pi$
$701$	3.02164e8			0.877181			0.438590	+	0.898687i	$0.355478\pi$
$702$		0			0
$703$	−1.21656e8	+	1.21656e8i	−0.350161	+	0.350161i
$704$		0			0
$705$	−2.58178e7	+	7.35940e7i	−0.0736805	+	0.210027i
$706$		0			0
$707$	−4.05100e7	−	4.05100e7i	−0.114632	−	0.114632i
$708$		0			0
$709$			4.70327e8i			1.31966i	0.751416	+	0.659829i	$0.229371\pi$
$709$			4.70327e8i			1.31966i	−0.751416	+	0.659829i	$0.770629\pi$
$710$		0			0
$711$	−1.26910e8			−0.353091
$712$		0			0
$713$	5.68837e8	−	5.68837e8i	1.56935	−	1.56935i
$714$		0			0
$715$	7.50432e7	+	1.56149e8i	0.205302	+	0.427189i
$716$		0			0
$717$	−4.17362e7	−	4.17362e7i	−0.113229	−	0.113229i
$718$		0			0
$719$		−	4.59221e8i		−	1.23548i	−0.786383	−	0.617739i	$-0.788049\pi$
$719$		−	4.59221e8i		−	1.23548i	0.786383	−	0.617739i	$-0.211951\pi$
$720$		0			0
$721$	2.05046e7			0.0547072
$722$		0			0
$723$	3.61825e7	−	3.61825e7i	0.0957377	−	0.0957377i
$724$		0			0
$725$	2.08534e7	−	2.60636e7i	0.0547221	−	0.0683944i
$726$		0			0
$727$	7.87331e7	+	7.87331e7i	0.204906	+	0.204906i	0.802098	−	0.597192i	$-0.203717\pi$
$727$	7.87331e7	+	7.87331e7i	0.204906	+	0.204906i	−0.597192	+	0.802098i	$0.703717\pi$
$728$		0			0
$729$			1.43489e7i			0.0370370i
$730$		0			0
$731$	2.07636e7			0.0531557
$732$		0			0
$733$	−4.56706e8	+	4.56706e8i	−1.15964	+	1.15964i	−0.175093	+	0.984552i	$0.556022\pi$
$733$	−4.56706e8	+	4.56706e8i	−1.15964	+	1.15964i	−0.984552	+	0.175093i	$0.943978\pi$
$734$		0			0
$735$	1.98184e8	−	9.52451e7i	0.499123	−	0.239873i
$736$		0			0
$737$	7.78478e8	+	7.78478e8i	1.94466	+	1.94466i
$738$		0			0
$739$		−	4.49586e8i		−	1.11399i	−0.830517	−	0.556993i	$-0.811955\pi$
$739$		−	4.49586e8i		−	1.11399i	0.830517	−	0.556993i	$-0.188045\pi$
$740$		0			0
$741$	−5.65705e7			−0.139039
$742$		0			0
$743$	3.80478e8	−	3.80478e8i	0.927604	−	0.927604i	−0.0699467	−	0.997551i	$-0.522283\pi$
$743$	3.80478e8	−	3.80478e8i	0.927604	−	0.927604i	0.997551	+	0.0699467i	$0.0222829\pi$
$744$		0			0
$745$	4.65603e8	+	1.63340e8i	1.12602	+	0.395025i
$746$		0			0
$747$	8.84807e7	+	8.84807e7i	0.212269	+	0.212269i
$748$		0			0
$749$			1.34914e8i			0.321080i
$750$		0			0
$751$	7.14309e7			0.168642			0.0843212	−	0.996439i	$-0.473128\pi$
$751$	7.14309e7			0.168642			0.0843212	+	0.996439i	$0.473128\pi$
$752$		0			0
$753$	2.29015e8	−	2.29015e8i	0.536388	−	0.536388i
$754$		0			0
$755$	9.28296e7	−	2.64612e8i	0.215698	−	0.614848i
$756$		0			0
$757$	2.92805e8	+	2.92805e8i	0.674979	+	0.674979i	0.958860	−	0.283881i	$-0.0916219\pi$
$757$	2.92805e8	+	2.92805e8i	0.674979	+	0.674979i	−0.283881	+	0.958860i	$0.591622\pi$
$758$		0			0
$759$		−	7.89356e8i		−	1.80529i
$760$		0			0
$761$	−2.78300e8			−0.631479			−0.315740	−	0.948846i	$-0.602253\pi$
$761$	−2.78300e8			−0.631479			−0.315740	+	0.948846i	$0.602253\pi$
$762$		0			0
$763$	7.86078e7	−	7.86078e7i	0.176967	−	0.176967i
$764$		0			0
$765$	2.68823e6	+	5.59363e6i	0.00600458	+	0.0124942i
$766$		0			0
$767$	−3.05382e7	−	3.05382e7i	−0.0676796	−	0.0676796i
$768$		0			0
$769$		−	3.57076e8i		−	0.785202i	−0.919709	−	0.392601i	$-0.871575\pi$
$769$		−	3.57076e8i		−	0.785202i	0.919709	−	0.392601i	$-0.128425\pi$
$770$		0			0
$771$	−2.52613e8			−0.551179
$772$		0			0
$773$	5.06169e8	−	5.06169e8i	1.09587	−	1.09587i	0.100977	−	0.994889i	$-0.467803\pi$
$773$	5.06169e8	−	5.06169e8i	1.09587	−	1.09587i	0.994889	−	0.100977i	$-0.0321968\pi$
$774$		0			0
$775$	4.29459e8	+	3.43609e8i	0.922606	+	0.738174i
$776$		0			0
$777$	−2.26583e7	−	2.26583e7i	−0.0483018	−	0.0483018i
$778$		0			0
$779$			1.50346e8i			0.318038i
$780$		0			0
$781$	−3.85588e8			−0.809413
$782$		0			0
$783$	5.72205e6	−	5.72205e6i	0.0119197	−	0.0119197i
$784$		0			0
$785$	−1.82389e8	+	8.76539e7i	−0.377041	+	0.181202i
$786$		0			0
$787$	−4.66599e8	−	4.66599e8i	−0.957238	−	0.957238i	0.0418842	−	0.999122i	$-0.486664\pi$
$787$	−4.66599e8	−	4.66599e8i	−0.957238	−	0.957238i	−0.999122	+	0.0418842i	$0.986664\pi$
$788$		0			0
$789$			3.28182e8i			0.668165i
$790$		0			0
$791$	1.42171e8			0.287264
$792$		0			0
$793$	−1.93267e8	+	1.93267e8i	−0.387559	+	0.387559i
$794$		0			0
$795$	−1.20285e8	−	4.21977e7i	−0.239392	−	0.0839823i
$796$		0			0
$797$	−4.43105e8	−	4.43105e8i	−0.875250	−	0.875250i	0.117789	−	0.993039i	$-0.462419\pi$
$797$	−4.43105e8	−	4.43105e8i	−0.875250	−	0.875250i	−0.993039	+	0.117789i	$0.962419\pi$
$798$		0			0
$799$			8.17774e6i			0.0160322i
$800$		0			0
$801$	3.11928e8			0.606956
$802$		0			0
$803$	7.83078e7	−	7.83078e7i	0.151237	−	0.151237i
$804$		0			0
$805$	−6.55510e7	+	1.86854e8i	−0.125659	+	0.358191i
$806$		0			0
$807$	−2.05382e8	−	2.05382e8i	−0.390789	−	0.390789i
$808$		0			0
$809$			2.55036e8i			0.481676i	0.970565	+	0.240838i	$0.0774223\pi$
$809$			2.55036e8i			0.481676i	−0.970565	+	0.240838i	$0.922578\pi$
$810$		0			0
$811$	−1.98583e7			−0.0372288			−0.0186144	−	0.999827i	$-0.505925\pi$
$811$	−1.98583e7			−0.0372288			−0.0186144	+	0.999827i	$0.505925\pi$
$812$		0			0
$813$	−3.10340e8	+	3.10340e8i	−0.577519	+	0.577519i
$814$		0			0
$815$	−3.65477e8	−	7.60479e8i	−0.675130	−	1.40480i
$816$		0			0
$817$	4.16901e8	+	4.16901e8i	0.764481	+	0.764481i
$818$		0			0
$819$		−	1.05362e7i		−	0.0191793i
$820$		0			0
$821$	−2.22302e8			−0.401712			−0.200856	−	0.979621i	$-0.564372\pi$
$821$	−2.22302e8			−0.401712			−0.200856	+	0.979621i	$0.564372\pi$
$822$		0			0
$823$	−2.77753e8	+	2.77753e8i	−0.498263	+	0.498263i	−0.910897	−	0.412634i	$-0.864609\pi$
$823$	−2.77753e8	+	2.77753e8i	−0.498263	+	0.498263i	0.412634	+	0.910897i	$0.364609\pi$
$824$		0			0
$825$	5.36379e8	−	5.95655e7i	0.955235	−	0.106080i
$826$		0			0
$827$	6.42324e8	+	6.42324e8i	1.13563	+	1.13563i	0.989224	+	0.146408i	$0.0467712\pi$
$827$	6.42324e8	+	6.42324e8i	1.13563	+	1.13563i	0.146408	+	0.989224i	$0.453229\pi$
$828$		0			0
$829$		−	1.96694e8i		−	0.345246i	−0.984988	−	0.172623i	$-0.944776\pi$
$829$		−	1.96694e8i		−	0.345246i	0.984988	−	0.172623i	$-0.0552242\pi$
$830$		0			0
$831$	5.72274e8			0.997243
$832$		0			0
$833$	1.63029e7	−	1.63029e7i	0.0282052	−	0.0282052i
$834$		0			0
$835$	1.27594e8	−	6.13200e7i	0.219164	−	0.105328i
$836$		0			0
$837$	9.42841e7	+	9.42841e7i	0.160791	+	0.160791i
$838$		0			0
$839$			3.86057e8i			0.653681i	0.945080	+	0.326840i	$0.105984\pi$
$839$			3.86057e8i			0.653681i	−0.945080	+	0.326840i	$0.894016\pi$
$840$		0			0
$841$	5.90260e8			0.992328
$842$		0			0
$843$	−4.12282e8	+	4.12282e8i	−0.688196	+	0.688196i
$844$		0			0
$845$	−5.23182e8	−	1.83540e8i	−0.867126	−	0.304200i
$846$		0			0
$847$	−1.53794e8	−	1.53794e8i	−0.253099	−	0.253099i
$848$		0			0
$849$		−	4.56465e8i		−	0.745907i
$850$		0			0
$851$	−6.77737e8			−1.09969
$852$		0			0
$853$	−3.66611e8	+	3.66611e8i	−0.590689	+	0.590689i	−0.937817	−	0.347129i	$-0.887157\pi$
$853$	−3.66611e8	+	3.66611e8i	−0.590689	+	0.590689i	0.347129	+	0.937817i	$0.387157\pi$
$854$		0			0
$855$	−5.83360e7	+	1.66287e8i	−0.0933336	+	0.266048i
$856$		0			0
$857$	−1.98083e8	−	1.98083e8i	−0.314706	−	0.314706i	0.532024	−	0.846729i	$-0.321432\pi$
$857$	−1.98083e8	−	1.98083e8i	−0.314706	−	0.314706i	−0.846729	+	0.532024i	$0.821432\pi$
$858$		0			0
$859$			4.38378e8i			0.691623i	0.938304	+	0.345812i	$0.112396\pi$
$859$			4.38378e8i			0.691623i	−0.938304	+	0.345812i	$0.887604\pi$
$860$		0			0
$861$	−2.80017e7			−0.0438708
$862$		0			0
$863$	−5.32113e8	+	5.32113e8i	−0.827888	+	0.827888i	−0.987224	−	0.159337i	$-0.949064\pi$
$863$	−5.32113e8	+	5.32113e8i	−0.827888	+	0.827888i	0.159337	+	0.987224i	$0.449064\pi$
$864$		0			0
$865$	−3.43591e8	−	7.14938e8i	−0.530876	−	1.10464i
$866$		0			0
$867$	−2.65601e8	−	2.65601e8i	−0.407542	−	0.407542i
$868$		0			0
$869$			1.15718e9i			1.76336i
$870$		0			0
$871$	3.10807e8			0.470367
$872$		0			0
$873$	−1.53094e8	+	1.53094e8i	−0.230100	+	0.230100i
$874$		0			0
$875$	−1.31917e8	−	3.04428e7i	−0.196913	−	0.0454423i
$876$		0			0
$877$	−2.92552e8	−	2.92552e8i	−0.433715	−	0.433715i	0.456175	−	0.889890i	$-0.349219\pi$
$877$	−2.92552e8	−	2.92552e8i	−0.433715	−	0.433715i	−0.889890	+	0.456175i	$0.849219\pi$
$878$		0			0
$879$			3.81630e8i			0.561922i
$880$		0			0
$881$	5.14917e8			0.753026			0.376513	−	0.926411i	$-0.377123\pi$
$881$	5.14917e8			0.753026			0.376513	+	0.926411i	$0.377123\pi$
$882$		0			0
$883$	−3.80892e6	+	3.80892e6i	−0.00553248	+	0.00553248i	−0.709868	−	0.704335i	$-0.751245\pi$
$883$	−3.80892e6	+	3.80892e6i	−0.00553248	+	0.00553248i	0.704335	+	0.709868i	$0.251245\pi$
$884$		0			0
$885$	−1.21257e8	+	5.82749e7i	−0.174936	+	0.0840721i
$886$		0			0
$887$	7.01926e7	+	7.01926e7i	0.100582	+	0.100582i	0.755607	−	0.655025i	$-0.227342\pi$
$887$	7.01926e7	+	7.01926e7i	0.100582	+	0.100582i	−0.655025	+	0.755607i	$0.727342\pi$
$888$		0			0
$889$		−	1.05652e8i		−	0.150374i
$890$		0			0
$891$	1.30835e8			0.184965
$892$		0			0
$893$	−1.64197e8	+	1.64197e8i	−0.230574	+	0.230574i
$894$		0			0
$895$	−5.39279e8	−	1.89187e8i	−0.752219	−	0.263889i
$896$		0			0
$897$	−1.57575e8	−	1.57575e8i	−0.218329	−	0.218329i
$898$		0			0
$899$		−	7.51970e7i		−	0.103496i
$900$		0			0
$901$	−1.33660e7			−0.0182738
$902$		0			0
$903$	−7.76473e7	+	7.76473e7i	−0.105454	+	0.105454i
$904$		0			0
$905$	−9.28078e7	+	2.64550e8i	−0.125210	+	0.356912i
$906$		0			0
$907$	−5.94748e8	−	5.94748e8i	−0.797096	−	0.797096i	0.185540	−	0.982637i	$-0.440596\pi$
$907$	−5.94748e8	−	5.94748e8i	−0.797096	−	0.797096i	−0.982637	+	0.185540i	$0.940596\pi$
$908$		0			0
$909$		−	2.00838e8i		−	0.267396i
$910$		0			0
$911$	5.60705e7			0.0741616			0.0370808	−	0.999312i	$-0.488194\pi$
$911$	5.60705e7			0.0741616			0.0370808	+	0.999312i	$0.488194\pi$
$912$		0			0
$913$	8.06775e8	−	8.06775e8i	1.06008	−	1.06008i
$914$		0			0
$915$	3.68803e8	+	7.67400e8i	0.481428	+	1.00175i
$916$		0			0
$917$	−1.58563e8	−	1.58563e8i	−0.205633	−	0.205633i
$918$		0			0
$919$			6.82031e8i			0.878734i	0.898308	+	0.439367i	$0.144797\pi$
$919$			6.82031e8i			0.878734i	−0.898308	+	0.439367i	$0.855203\pi$
$920$		0			0
$921$	−6.04657e8			−0.773981
$922$		0			0
$923$	−7.69730e7	+	7.69730e7i	−0.0978889	+	0.0978889i
$924$		0			0
$925$	−5.11426e7	−	4.60532e8i	−0.0646186	−	0.581882i
$926$		0			0
$927$	5.08282e7	+	5.08282e7i	0.0638066	+	0.0638066i
$928$		0			0
$929$			3.29168e8i			0.410554i	0.978704	+	0.205277i	$0.0658095\pi$
$929$			3.29168e8i			0.410554i	−0.978704	+	0.205277i	$0.934191\pi$
$930$		0			0
$931$	6.54675e8			0.811291
$932$		0			0
$933$	−4.78622e8	+	4.78622e8i	−0.589315	+	0.589315i
$934$		0			0
$935$	5.10033e7	−	2.45116e7i	0.0623969	−	0.0299872i
$936$		0			0
$937$	−7.28137e8	−	7.28137e8i	−0.885105	−	0.885105i	0.108943	−	0.994048i	$-0.465253\pi$
$937$	−7.28137e8	−	7.28137e8i	−0.885105	−	0.885105i	−0.994048	+	0.108943i	$0.965253\pi$
$938$		0			0
$939$			4.74606e8i			0.573241i
$940$		0			0
$941$	6.56517e7			0.0787910			0.0393955	−	0.999224i	$-0.487457\pi$
$941$	6.56517e7			0.0787910			0.0393955	+	0.999224i	$0.487457\pi$
$942$		0			0
$943$	−4.18783e8	+	4.18783e8i	−0.499406	+	0.499406i
$944$		0			0
$945$	−3.09708e7	−	1.08650e7i	−0.0366992	−	0.0128746i
$946$		0			0
$947$	6.42479e8	+	6.42479e8i	0.756500	+	0.756500i	0.975684	−	0.219184i	$-0.0703394\pi$
$947$	6.42479e8	+	6.42479e8i	0.756500	+	0.756500i	−0.219184	+	0.975684i	$0.570339\pi$
$948$		0			0
$949$		−	3.12644e7i		−	0.0365807i
$950$		0			0
$951$	4.45406e8			0.517863
$952$		0			0
$953$	1.10683e9	−	1.10683e9i	1.27879	−	1.27879i	0.337450	−	0.941344i	$-0.390436\pi$
$953$	1.10683e9	−	1.10683e9i	1.27879	−	1.27879i	0.941344	−	0.337450i	$-0.109564\pi$
$954$		0			0
$955$	9.57070e7	−	2.72814e8i	0.109884	−	0.313225i
$956$		0			0
$957$	−5.21742e7	−	5.21742e7i	−0.0595278	−	0.0595278i
$958$		0			0
$959$		−	2.04582e7i		−	0.0231959i
$960$		0			0
$961$	3.51543e8			0.396103
$962$		0			0
$963$	−3.34436e8	+	3.34436e8i	−0.374485	+	0.374485i
$964$		0			0
$965$	−4.47293e8	−	9.30719e8i	−0.497749	−	1.03571i
$966$		0			0
$967$	6.35883e8	+	6.35883e8i	0.703231	+	0.703231i	0.965103	−	0.261872i	$-0.0843398\pi$
$967$	6.35883e8	+	6.35883e8i	0.703231	+	0.703231i	−0.261872	+	0.965103i	$0.584340\pi$
$968$		0			0
$969$			1.84778e7i			0.0203085i
$970$		0			0
$971$	1.42207e9			1.55333			0.776663	−	0.629917i	$-0.216911\pi$
$971$	1.42207e9			1.55333			0.776663	+	0.629917i	$0.216911\pi$
$972$		0			0
$973$	1.18633e8	−	1.18633e8i	0.128785	−	0.128785i
$974$		0			0
$975$	9.51840e7	−	1.18966e8i	0.102695	−	0.128353i
$976$		0			0
$977$	−3.92668e8	−	3.92668e8i	−0.421058	−	0.421058i	0.464510	−	0.885568i	$-0.346231\pi$
$977$	−3.92668e8	−	3.92668e8i	−0.421058	−	0.421058i	−0.885568	+	0.464510i	$0.846231\pi$
$978$		0			0
$979$		−	2.84419e9i		−	3.03117i
$980$		0			0
$981$	3.89718e8			0.412804
$982$		0			0
$983$	−2.32929e8	+	2.32929e8i	−0.245224	+	0.245224i	−0.819007	−	0.573783i	$-0.805475\pi$
$983$	−2.32929e8	+	2.32929e8i	−0.245224	+	0.245224i	0.573783	+	0.819007i	$0.305475\pi$
$984$		0			0
$985$	1.11962e9	−	5.38076e8i	1.17155	−	0.563035i
$986$		0			0
$987$	−3.05814e7	−	3.05814e7i	−0.0318058	−	0.0318058i
$988$		0			0
$989$			2.32253e9i			2.40089i
$990$		0			0
$991$	1.50016e9			1.54141			0.770704	−	0.637193i	$-0.219905\pi$
$991$	1.50016e9			1.54141			0.770704	+	0.637193i	$0.219905\pi$
$992$		0			0
$993$	−3.58613e8	+	3.58613e8i	−0.366251	+	0.366251i
$994$		0			0
$995$	−7.62689e8	−	2.67562e8i	−0.774244	−	0.271616i
$996$		0			0
$997$	−1.05541e9	−	1.05541e9i	−1.06496	−	1.06496i	−0.997738	−	0.0672268i	$-0.978585\pi$
$997$	−1.05541e9	−	1.05541e9i	−1.06496	−	1.06496i	−0.0672268	−	0.997738i	$-0.521415\pi$
$998$		0			0
$999$		−	1.12334e8i		−	0.112672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.k.a.37.4	yes	12
3.2	odd	2		180.7.l.b.37.5		12
4.3	odd	2		240.7.bg.d.97.1		12
5.2	odd	4		300.7.k.d.193.2		12
5.3	odd	4	inner	60.7.k.a.13.4	✓	12
5.4	even	2		300.7.k.d.157.2		12
15.8	even	4		180.7.l.b.73.5		12
20.3	even	4		240.7.bg.d.193.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.k.a.13.4	✓	12	5.3	odd	4	inner
60.7.k.a.37.4	yes	12	1.1	even	1	trivial
180.7.l.b.37.5		12	3.2	odd	2
180.7.l.b.73.5		12	15.8	even	4
240.7.bg.d.97.1		12	4.3	odd	2
240.7.bg.d.193.1		12	20.3	even	4
300.7.k.d.157.2		12	5.4	even	2
300.7.k.d.193.2		12	5.2	odd	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(11.0227 - 11.0227i) q^{3} +(-41.3794 + 117.952i) q^{5} +(-49.0142 - 49.0142i) q^{7} -243.000i q^{9} +O(q^{10})\)	\(q+(11.0227 - 11.0227i) q^{3} +(-41.3794 + 117.952i) q^{5} +(-49.0142 - 49.0142i) q^{7} -243.000i q^{9} -2215.70 q^{11} +(-442.309 + 442.309i) q^{13} +(844.041 + 1756.27i) q^{15} +(144.473 + 144.473i) q^{17} +5801.58i q^{19} -1080.54 q^{21} +(-16160.1 + 16160.1i) q^{23} +(-12200.5 - 9761.58i) q^{25} +(-2678.52 - 2678.52i) q^{27} +2136.27i q^{29} -35200.1 q^{31} +(-24423.0 + 24423.0i) q^{33} +(7809.51 - 3753.16i) q^{35} +(20969.4 + 20969.4i) q^{37} +9750.88i q^{39} +25914.6 q^{41} +(71859.9 - 71859.9i) q^{43} +(28662.4 + 10055.2i) q^{45} +(28302.1 + 28302.1i) q^{47} -112844. i q^{49} +3184.96 q^{51} +(-46258.0 + 46258.0i) q^{53} +(91684.2 - 261347. i) q^{55} +(63949.1 + 63949.1i) q^{57} +69042.8i q^{59} +436950. q^{61} +(-11910.4 + 11910.4i) q^{63} +(-33868.9 - 70473.8i) q^{65} +(-351347. - 351347. i) q^{67} +356256. i q^{69} +174026. q^{71} +(-35342.3 + 35342.3i) q^{73} +(-242082. + 26883.4i) q^{75} +(108601. + 108601. i) q^{77} -522263. i q^{79} -59049.0 q^{81} +(-364118. + 364118. i) q^{83} +(-23019.1 + 11062.7i) q^{85} +(23547.5 + 23547.5i) q^{87} +1.28366e6i q^{89} +43358.8 q^{91} +(-388000. + 388000. i) q^{93} +(-684310. - 240066. i) q^{95} +(-630017. - 630017. i) q^{97} +538415. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) \) 12 * q + 312 * q^5 + 120 * q^7	\( 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) \) 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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