LMFDB - Embedded newform 392.3.g.i.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(99,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.g (of order $2$, degree $1$, 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.15582448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 13x^{4} - 21x^{3} + 20x^{2} - 10x + 2 $ x^6 - 3x^5 + 13x^4 - 21x^3 + 20x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$0.500000 - 2.94141i$ of defining polynomial
Character	$\chi$	$=$	392.99
Dual form			392.3.g.i.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88766 + 0.660851i) q^{2} -1.64878 q^{3} +(3.12655 - 2.49493i) q^{4} -4.56111i q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} -6.28154 q^{9} +O(q^{10})$	\(q+(-1.88766 + 0.660851i) q^{2} -1.64878 q^{3} +(3.12655 - 2.49493i) q^{4} -4.56111i q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} -6.28154 q^{9} +(3.01422 + 8.60985i) q^{10} -12.3797 q^{11} +(-5.15498 + 4.11358i) q^{12} +18.3741i q^{13} +7.52026i q^{15} +(3.55066 - 15.6011i) q^{16} +13.0284 q^{17} +(11.8574 - 4.15116i) q^{18} +3.02524 q^{19} +(-11.3797 - 14.2606i) q^{20} +(23.3686 - 8.18111i) q^{22} -30.3237i q^{23} +(7.01242 - 11.1717i) q^{24} +4.19624 q^{25} +(-12.1426 - 34.6842i) q^{26} +25.1958 q^{27} +22.7701i q^{29} +(-4.96977 - 14.1957i) q^{30} +22.5608i q^{31} +(3.60752 + 31.7960i) q^{32} +20.4113 q^{33} +(-24.5933 + 8.60985i) q^{34} +(-19.6396 + 15.6720i) q^{36} +13.7797i q^{37} +(-5.71063 + 1.99923i) q^{38} -30.2948i q^{39} +(30.9051 + 19.3989i) q^{40} +60.5026 q^{41} +39.0188 q^{43} +(-38.7056 + 30.8864i) q^{44} +28.6508i q^{45} +(20.0395 + 57.2410i) q^{46} +20.3360i q^{47} +(-5.85424 + 25.7226i) q^{48} +(-7.92109 + 2.77309i) q^{50} -21.4810 q^{51} +(45.8422 + 57.4477i) q^{52} -4.76596i q^{53} +(-47.5613 + 16.6507i) q^{54} +56.4650i q^{55} -4.98794 q^{57} +(-15.0476 - 42.9823i) q^{58} -11.7377 q^{59} +(18.7625 + 23.5125i) q^{60} +108.904i q^{61} +(-14.9093 - 42.5872i) q^{62} +(-27.8222 - 57.6361i) q^{64} +83.8066 q^{65} +(-38.5296 + 13.4888i) q^{66} -79.1994 q^{67} +(40.7341 - 32.5050i) q^{68} +49.9970i q^{69} -12.9952i q^{71} +(26.7160 - 42.5623i) q^{72} +98.5819 q^{73} +(-9.10631 - 26.0114i) q^{74} -6.91866 q^{75} +(9.45857 - 7.54776i) q^{76} +(20.0204 + 57.1865i) q^{78} +131.225i q^{79} +(-71.1582 - 16.1950i) q^{80} +14.9915 q^{81} +(-114.209 + 39.9832i) q^{82} -28.3732 q^{83} -59.4242i q^{85} +(-73.6544 + 25.7856i) q^{86} -37.5428i q^{87} +(52.6520 - 83.8817i) q^{88} +157.418 q^{89} +(-18.9339 - 54.0831i) q^{90} +(-75.6555 - 94.8087i) q^{92} -37.1977i q^{93} +(-13.4391 - 38.3876i) q^{94} -13.7985i q^{95} +(-5.94800 - 52.4245i) q^{96} +39.6175 q^{97} +77.7633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9	$ 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9} - 6 q^{10} - 30 q^{11} + 32 q^{12} - 16 q^{16} + 30 q^{17} + 16 q^{18} + 78 q^{19} - 24 q^{20} + 12 q^{22} - 76 q^{24} + 92 q^{25} - 128 q^{26} - 78 q^{27} + 16 q^{30} - 112 q^{32} - 78 q^{33} - 38 q^{34} - 124 q^{36} + 80 q^{38} + 44 q^{40} + 116 q^{41} - 100 q^{43} - 132 q^{44} + 156 q^{46} - 88 q^{48} + 24 q^{50} - 10 q^{51} + 132 q^{52} - 36 q^{54} + 166 q^{57} - 4 q^{58} - 110 q^{59} - 84 q^{60} + 48 q^{62} - 80 q^{64} + 32 q^{65} - 138 q^{66} - 434 q^{67} + 96 q^{68} + 328 q^{72} + 102 q^{73} + 34 q^{74} - 60 q^{75} + 84 q^{76} + 360 q^{78} - 256 q^{80} + 82 q^{81} - 24 q^{82} + 268 q^{83} - 240 q^{86} + 204 q^{88} + 214 q^{89} - 220 q^{90} + 80 q^{92} - 16 q^{94} + 48 q^{96} + 76 q^{97} + 252 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9 - 6 * q^10 - 30 * q^11 + 32 * q^12 - 16 * q^16 + 30 * q^17 + 16 * q^18 + 78 * q^19 - 24 * q^20 + 12 * q^22 - 76 * q^24 + 92 * q^25 - 128 * q^26 - 78 * q^27 + 16 * q^30 - 112 * q^32 - 78 * q^33 - 38 * q^34 - 124 * q^36 + 80 * q^38 + 44 * q^40 + 116 * q^41 - 100 * q^43 - 132 * q^44 + 156 * q^46 - 88 * q^48 + 24 * q^50 - 10 * q^51 + 132 * q^52 - 36 * q^54 + 166 * q^57 - 4 * q^58 - 110 * q^59 - 84 * q^60 + 48 * q^62 - 80 * q^64 + 32 * q^65 - 138 * q^66 - 434 * q^67 + 96 * q^68 + 328 * q^72 + 102 * q^73 + 34 * q^74 - 60 * q^75 + 84 * q^76 + 360 * q^78 - 256 * q^80 + 82 * q^81 - 24 * q^82 + 268 * q^83 - 240 * q^86 + 204 * q^88 + 214 * q^89 - 220 * q^90 + 80 * q^92 - 16 * q^94 + 48 * q^96 + 76 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.88766	+	0.660851i	−0.943832	+	0.330425i
$2$	−1.88766	+	0.660851i	−0.943832	+	0.330425i
$3$	−1.64878			−0.549592			−0.274796	−	0.961503i	$-0.588610\pi$
$3$	−1.64878			−0.549592			−0.274796	+	0.961503i	$0.588610\pi$
$4$	3.12655	−	2.49493i	0.781638	−	0.623732i
$5$		−	4.56111i		−	0.912223i	−0.889923	−	0.456111i	$-0.849242\pi$
$5$		−	4.56111i		−	0.912223i	0.889923	−	0.456111i	$-0.150758\pi$
$6$	3.11234	−	1.08960i	0.518723	−	0.181599i
$7$		0			0
$7$		0			0
$8$	−4.25310	+	6.77577i	−0.531638	+	0.846972i
$9$	−6.28154			−0.697949
$10$	3.01422	+	8.60985i	0.301422	+	0.860985i
$11$	−12.3797			−1.12542			−0.562712	−	0.826653i	$-0.690242\pi$
$11$	−12.3797			−1.12542			−0.562712	+	0.826653i	$0.690242\pi$
$12$	−5.15498	+	4.11358i	−0.429582	+	0.342798i
$13$			18.3741i			1.41340i	0.707516	+	0.706698i	$0.249816\pi$
$13$			18.3741i			1.41340i	−0.707516	+	0.706698i	$0.750184\pi$
$14$		0			0
$15$			7.52026i			0.501350i
$16$	3.55066	−	15.6011i	0.221916	−	0.975066i
$17$	13.0284			0.766378			0.383189	−	0.923670i	$-0.374826\pi$
$17$	13.0284			0.766378			0.383189	+	0.923670i	$0.374826\pi$
$18$	11.8574	−	4.15116i	0.658746	−	0.230620i
$19$	3.02524			0.159223			0.0796115	−	0.996826i	$-0.474632\pi$
$19$	3.02524			0.159223			0.0796115	+	0.996826i	$0.474632\pi$
$20$	−11.3797	−	14.2606i	−0.568983	−	0.713028i
$21$		0			0
$22$	23.3686	−	8.18111i	1.06221	−	0.371869i
$23$		−	30.3237i		−	1.31842i	−0.751958	−	0.659211i	$-0.770890\pi$
$23$		−	30.3237i		−	1.31842i	0.751958	−	0.659211i	$-0.229110\pi$
$24$	7.01242	−	11.1717i	0.292184	−	0.465489i
$25$	4.19624			0.167850
$26$	−12.1426	−	34.6842i	−0.467022	−	1.33401i
$27$	25.1958			0.933179
$28$		0			0
$29$			22.7701i			0.785176i	0.919714	+	0.392588i	$0.128420\pi$
$29$			22.7701i			0.785176i	−0.919714	+	0.392588i	$0.871580\pi$
$30$	−4.96977	−	14.1957i	−0.165659	−	0.473191i
$31$			22.5608i			0.727767i	0.931445	+	0.363883i	$0.118549\pi$
$31$			22.5608i			0.727767i	−0.931445	+	0.363883i	$0.881451\pi$
$32$	3.60752	+	31.7960i	0.112735	+	0.993625i
$33$	20.4113			0.618524
$34$	−24.5933	+	8.60985i	−0.723333	+	0.253231i
$35$		0			0
$36$	−19.6396	+	15.6720i	−0.545543	+	0.435333i
$37$			13.7797i			0.372423i	0.982510	+	0.186212i	$0.0596210\pi$
$37$			13.7797i			0.372423i	−0.982510	+	0.186212i	$0.940379\pi$
$38$	−5.71063	+	1.99923i	−0.150280	+	0.0526114i
$39$		−	30.2948i		−	0.776791i
$40$	30.9051	+	19.3989i	0.772627	+	0.484972i
$41$	60.5026			1.47567			0.737837	−	0.674979i	$-0.235847\pi$
$41$	60.5026			1.47567			0.737837	+	0.674979i	$0.235847\pi$
$42$		0			0
$43$	39.0188			0.907414			0.453707	−	0.891151i	$-0.350101\pi$
$43$	39.0188			0.907414			0.453707	+	0.891151i	$0.350101\pi$
$44$	−38.7056	+	30.8864i	−0.879674	+	0.701963i
$45$			28.6508i			0.636685i
$46$	20.0395	+	57.2410i	0.435640	+	1.24437i
$47$			20.3360i			0.432681i	0.976318	+	0.216341i	$0.0694122\pi$
$47$			20.3360i			0.432681i	−0.976318	+	0.216341i	$0.930588\pi$
$48$	−5.85424	+	25.7226i	−0.121963	+	0.535888i
$49$		0			0
$50$	−7.92109	+	2.77309i	−0.158422	+	0.0554618i
$51$	−21.4810			−0.421195
$52$	45.8422	+	57.4477i	0.881580	+	1.10476i
$53$		−	4.76596i		−	0.0899237i	−0.998989	−	0.0449619i	$-0.985683\pi$
$53$		−	4.76596i		−	0.0899237i	0.998989	−	0.0449619i	$-0.0143166\pi$
$54$	−47.5613	+	16.6507i	−0.880764	+	0.308346i
$55$			56.4650i			1.02664i
$56$		0			0
$57$	−4.98794			−0.0875077
$58$	−15.0476	−	42.9823i	−0.259442	−	0.741074i
$59$	−11.7377			−0.198944			−0.0994718	−	0.995040i	$-0.531715\pi$
$59$	−11.7377			−0.198944			−0.0994718	+	0.995040i	$0.531715\pi$
$60$	18.7625	+	23.5125i	0.312708	+	0.391875i
$61$			108.904i			1.78531i	0.450738	+	0.892656i	$0.351161\pi$
$61$			108.904i			1.78531i	−0.450738	+	0.892656i	$0.648839\pi$
$62$	−14.9093	−	42.5872i	−0.240473	−	0.686890i
$63$		0			0
$64$	−27.8222	−	57.6361i	−0.434722	−	0.900565i
$65$	83.8066			1.28933
$66$	−38.5296	+	13.4888i	−0.583783	+	0.204376i
$67$	−79.1994			−1.18208			−0.591041	−	0.806642i	$-0.701283\pi$
$67$	−79.1994			−1.18208			−0.591041	+	0.806642i	$0.701283\pi$
$68$	40.7341	−	32.5050i	0.599031	−	0.478015i
$69$			49.9970i			0.724595i
$70$		0			0
$71$		−	12.9952i		−	0.183031i	−0.995804	−	0.0915157i	$-0.970829\pi$
$71$		−	12.9952i		−	0.183031i	0.995804	−	0.0915157i	$-0.0291712\pi$
$72$	26.7160	−	42.5623i	0.371056	−	0.591143i
$73$	98.5819			1.35044			0.675218	−	0.737618i	$-0.264049\pi$
$73$	98.5819			1.35044			0.675218	+	0.737618i	$0.264049\pi$
$74$	−9.10631	−	26.0114i	−0.123058	−	0.351505i
$75$	−6.91866			−0.0922488
$76$	9.45857	−	7.54776i	0.124455	−	0.0993126i
$77$		0			0
$78$	20.0204	+	57.1865i	0.256671	+	0.733160i
$79$			131.225i			1.66107i	0.556966	+	0.830535i	$0.311965\pi$
$79$			131.225i			1.66107i	−0.556966	+	0.830535i	$0.688035\pi$
$80$	−71.1582	−	16.1950i	−0.889477	−	0.202437i
$81$	14.9915			0.185081
$82$	−114.209	+	39.9832i	−1.39279	+	0.487600i
$83$	−28.3732			−0.341846			−0.170923	−	0.985284i	$-0.554675\pi$
$83$	−28.3732			−0.341846			−0.170923	+	0.985284i	$0.554675\pi$
$84$		0			0
$85$		−	59.4242i		−	0.699108i
$86$	−73.6544	+	25.7856i	−0.856447	+	0.299833i
$87$		−	37.5428i		−	0.431526i
$88$	52.6520	−	83.8817i	0.598318	−	0.953202i
$89$	157.418			1.76874			0.884371	−	0.466785i	$-0.154588\pi$
$89$	157.418			1.76874			0.884371	+	0.466785i	$0.154588\pi$
$90$	−18.9339	−	54.0831i	−0.210377	−	0.600923i
$91$		0			0
$92$	−75.6555	−	94.8087i	−0.822343	−	1.03053i
$93$		−	37.1977i		−	0.399975i
$94$	−13.4391	−	38.3876i	−0.142969	−	0.408379i
$95$		−	13.7985i		−	0.145247i
$96$	−5.94800	−	52.4245i	−0.0619583	−	0.546088i
$97$	39.6175			0.408428			0.204214	−	0.978926i	$-0.434536\pi$
$97$	39.6175			0.408428			0.204214	+	0.978926i	$0.434536\pi$
$98$		0			0
$99$	77.7633			0.785488
$100$	13.1198	−	10.4693i	0.131198	−	0.104693i
$101$			43.6183i			0.431864i	0.976408	+	0.215932i	$0.0692790\pi$
$101$			43.6183i			0.431864i	−0.976408	+	0.215932i	$0.930721\pi$
$102$	40.5489	−	14.1957i	0.397538	−	0.139174i
$103$		−	62.9020i		−	0.610699i	−0.952240	−	0.305350i	$-0.901227\pi$
$103$		−	62.9020i		−	0.610699i	0.952240	−	0.305350i	$-0.0987734\pi$
$104$	−124.499	−	78.1471i	−1.19711	−	0.751415i
$105$		0			0
$106$	3.14959	+	8.99653i	0.0297131	+	0.0848729i
$107$	44.2267			0.413334			0.206667	−	0.978411i	$-0.433738\pi$
$107$	44.2267			0.413334			0.206667	+	0.978411i	$0.433738\pi$
$108$	78.7761	−	62.8618i	0.729408	−	0.582054i
$109$		−	8.81520i		−	0.0808734i	−0.999182	−	0.0404367i	$-0.987125\pi$
$109$		−	8.81520i		−	0.0808734i	0.999182	−	0.0404367i	$-0.0128749\pi$
$110$	−37.3150	−	106.587i	−0.339227	−	0.968973i
$111$		−	22.7196i		−	0.204681i
$112$		0			0
$113$	−121.408			−1.07440			−0.537202	−	0.843454i	$-0.680519\pi$
$113$	−121.408			−1.07440			−0.537202	+	0.843454i	$0.680519\pi$
$114$	9.41556	−	3.29629i	0.0825926	−	0.0289148i
$115$	−138.310			−1.20269
$116$	56.8098	+	71.1919i	0.489740	+	0.613723i
$117$		−	115.418i		−	0.986477i
$118$	22.1568	−	7.75685i	0.187769	−	0.0657360i
$119$		0			0
$120$	−50.9556	−	31.9844i	−0.424630	−	0.266537i
$121$	32.2559			0.266578
$122$	−71.9694	−	205.574i	−0.589913	−	1.68504i
$123$	−99.7553			−0.811018
$124$	56.2875	+	70.5374i	0.453932	+	0.568850i
$125$		−	133.167i		−	1.06534i
$126$		0			0
$127$			222.845i			1.75468i	0.479868	+	0.877341i	$0.340685\pi$
$127$			222.845i			1.75468i	−0.479868	+	0.877341i	$0.659315\pi$
$128$	90.6079	+	90.4113i	0.707874	+	0.706339i
$129$	−64.3333			−0.498708
$130$	−158.199	+	55.3836i	−1.21691	+	0.426028i
$131$	−237.054			−1.80957			−0.904785	−	0.425869i	$-0.859968\pi$
$131$	−237.054			−1.80957			−0.904785	+	0.425869i	$0.859968\pi$
$132$	63.8169	−	50.9247i	0.483462	−	0.385793i
$133$		0			0
$134$	149.502	−	52.3390i	1.11569	−	0.390590i
$135$		−	114.921i		−	0.851267i
$136$	−55.4113	+	88.2777i	−0.407436	+	0.649101i
$137$	−9.66276			−0.0705311			−0.0352656	−	0.999378i	$-0.511228\pi$
$137$	−9.66276			−0.0705311			−0.0352656	+	0.999378i	$0.511228\pi$
$138$	−33.0406	−	94.3776i	−0.239424	−	0.683896i
$139$	63.0621			0.453684			0.226842	−	0.973932i	$-0.427160\pi$
$139$	63.0621			0.453684			0.226842	+	0.973932i	$0.427160\pi$
$140$		0			0
$141$		−	33.5296i		−	0.237798i
$142$	8.58791	+	24.5306i	0.0604782	+	0.172751i
$143$		−	227.466i		−	1.59067i
$144$	−22.3036	+	97.9986i	−0.154886	+	0.680546i
$145$	103.857			0.716255
$146$	−186.089	+	65.1479i	−1.27459	+	0.446219i
$147$		0			0
$148$	34.3793	+	43.0829i	0.232293	+	0.291100i
$149$			269.912i			1.81149i	0.423820	+	0.905746i	$0.360689\pi$
$149$			269.912i			1.81149i	−0.423820	+	0.905746i	$0.639311\pi$
$150$	13.0601	−	4.57220i	0.0870674	−	0.0304813i
$151$		−	108.178i		−	0.716408i	−0.933643	−	0.358204i	$-0.883389\pi$
$151$		−	108.178i		−	0.716408i	0.933643	−	0.358204i	$-0.116611\pi$
$152$	−12.8667	+	20.4983i	−0.0846491	+	0.134857i
$153$	−81.8386			−0.534893
$154$		0			0
$155$	102.902			0.663885
$156$	−75.5835	−	94.7184i	−0.484510	−	0.607169i
$157$		−	118.432i		−	0.754343i	−0.926144	−	0.377171i	$-0.876897\pi$
$157$		−	118.432i		−	0.754343i	0.926144	−	0.377171i	$-0.123103\pi$
$158$	−86.7199	−	247.708i	−0.548860	−	1.56777i
$159$			7.85800i			0.0494214i
$160$	145.025	−	16.4543i	0.906407	−	0.102839i
$161$		0			0
$162$	−28.2990	+	9.90717i	−0.174685	+	0.0611554i
$163$	−82.0284			−0.503242			−0.251621	−	0.967826i	$-0.580964\pi$
$163$	−82.0284			−0.503242			−0.251621	+	0.967826i	$0.580964\pi$
$164$	189.165	−	150.950i	1.15344	−	0.920425i
$165$		−	93.0982i		−	0.564231i
$166$	53.5591	−	18.7505i	0.322645	−	0.112955i
$167$		−	131.596i		−	0.788002i	−0.919110	−	0.394001i	$-0.871091\pi$
$167$		−	131.596i		−	0.788002i	0.919110	−	0.394001i	$-0.128909\pi$
$168$		0			0
$169$	−168.609			−0.997687
$170$	39.2705	+	112.173i	0.231003	+	0.659840i
$171$	−19.0031			−0.111130
$172$	121.994	−	97.3492i	0.709269	−	0.565983i
$173$			110.114i			0.636494i	0.948008	+	0.318247i	$0.103094\pi$
$173$			110.114i			0.636494i	−0.948008	+	0.318247i	$0.896906\pi$
$174$	24.8102	+	70.8682i	0.142587	+	0.407289i
$175$		0			0
$176$	−43.9559	+	193.136i	−0.249749	+	1.09736i
$177$	19.3528			0.109338
$178$	−297.152	+	104.030i	−1.66940	+	0.584437i
$179$	153.853			0.859512			0.429756	−	0.902945i	$-0.358600\pi$
$179$	153.853			0.859512			0.429756	+	0.902945i	$0.358600\pi$
$180$	71.4817	+	89.5782i	0.397121	+	0.497657i
$181$			227.511i			1.25697i	0.777823	+	0.628484i	$0.216324\pi$
$181$			227.511i			1.25697i	−0.777823	+	0.628484i	$0.783676\pi$
$182$		0			0
$183$		−	179.558i		−	0.981194i
$184$	205.467	+	128.970i	1.11667	+	0.700924i
$185$	62.8506			0.339733
$186$	24.5821	+	70.2167i	0.132162	+	0.377509i
$187$	−161.288			−0.862500
$188$	50.7370	+	63.5817i	0.269877	+	0.338200i
$189$		0			0
$190$	9.11872	+	26.0469i	0.0479933	+	0.137089i
$191$		−	121.546i		−	0.636364i	−0.948030	−	0.318182i	$-0.896928\pi$
$191$		−	121.546i		−	0.636364i	0.948030	−	0.318182i	$-0.103072\pi$
$192$	45.8726	+	95.0291i	0.238920	+	0.494943i
$193$	85.4552			0.442773			0.221386	−	0.975186i	$-0.428942\pi$
$193$	85.4552			0.442773			0.221386	+	0.975186i	$0.428942\pi$
$194$	−74.7846	+	26.1813i	−0.385487	+	0.134955i
$195$	−138.178			−0.708606
$196$		0			0
$197$		−	214.100i		−	1.08680i	−0.839474	−	0.543400i	$-0.817137\pi$
$197$		−	214.100i		−	1.08680i	0.839474	−	0.543400i	$-0.182863\pi$
$198$	−146.791	+	51.3899i	−0.741368	+	0.259545i
$199$			248.223i			1.24735i	0.781682	+	0.623677i	$0.214362\pi$
$199$			248.223i			1.24735i	−0.781682	+	0.623677i	$0.785638\pi$
$200$	−17.8470	+	28.4328i	−0.0892352	+	0.142164i
$201$	130.582			0.649662
$202$	−28.8252	−	82.3366i	−0.142699	−	0.407607i
$203$		0			0
$204$	−67.1614	+	53.5935i	−0.329222	+	0.262713i
$205$		−	275.959i		−	1.34614i
$206$	41.5689	+	118.738i	0.201791	+	0.576398i
$207$			190.480i			0.920191i
$208$	286.656	+	65.2403i	1.37815	+	0.313655i
$209$	−37.4514			−0.179193
$210$		0			0
$211$	191.753			0.908783			0.454392	−	0.890802i	$-0.349857\pi$
$211$	191.753			0.908783			0.454392	+	0.890802i	$0.349857\pi$
$212$	−11.8907	−	14.9010i	−0.0560883	−	0.0702878i
$213$			21.4262i			0.100593i
$214$	−83.4852	+	29.2273i	−0.390118	+	0.136576i
$215$		−	177.969i		−	0.827764i
$216$	−107.161	+	170.721i	−0.496113	+	0.790376i
$217$		0			0
$218$	5.82553	+	16.6401i	0.0267226	+	0.0763309i
$219$	−162.539			−0.742189
$220$	140.876	+	176.541i	0.640347	+	0.802458i
$221$			239.386i			1.08320i
$222$	15.0143	+	42.8870i	0.0676318	+	0.193184i
$223$			41.2269i			0.184874i	0.995719	+	0.0924370i	$0.0294657\pi$
$223$			41.2269i			0.184874i	−0.995719	+	0.0924370i	$0.970534\pi$
$224$		0			0
$225$	−26.3588			−0.117150
$226$	229.177	−	80.2324i	1.01406	−	0.355011i
$227$	−70.4437			−0.310325			−0.155162	−	0.987889i	$-0.549590\pi$
$227$	−70.4437			−0.310325			−0.155162	+	0.987889i	$0.549590\pi$
$228$	−15.5951	+	12.4446i	−0.0683994	+	0.0545814i
$229$			94.5190i			0.412747i	0.978473	+	0.206373i	$0.0661661\pi$
$229$			94.5190i			0.412747i	−0.978473	+	0.206373i	$0.933834\pi$
$230$	261.083	−	91.4022i	1.13514	−	0.397401i
$231$		0			0
$232$	−154.285	−	96.8436i	−0.665022	−	0.417429i
$233$	−136.287			−0.584922			−0.292461	−	0.956277i	$-0.594474\pi$
$233$	−136.287			−0.584922			−0.292461	+	0.956277i	$0.594474\pi$
$234$	76.2740	+	217.870i	0.325957	+	0.931069i
$235$	92.7550			0.394702
$236$	−36.6984	+	29.2847i	−0.155502	+	0.124088i
$237$		−	216.360i		−	0.912911i
$238$		0			0
$239$		−	173.230i		−	0.724813i	−0.932020	−	0.362406i	$-0.881955\pi$
$239$		−	173.230i		−	0.724813i	0.932020	−	0.362406i	$-0.118045\pi$
$240$	117.324	+	26.7018i	0.488850	+	0.111258i
$241$	328.923			1.36483			0.682413	−	0.730967i	$-0.260931\pi$
$241$	328.923			1.36483			0.682413	+	0.730967i	$0.260931\pi$
$242$	−60.8883	+	21.3163i	−0.251605	+	0.0880840i
$243$	−251.480			−1.03490
$244$	271.708	+	340.494i	1.11356	+	1.39547i
$245$		0			0
$246$	188.304	−	65.9234i	0.765465	−	0.267981i
$247$			55.5862i			0.225045i
$248$	−152.867	−	95.9533i	−0.616398	−	0.386908i
$249$	46.7811			0.187876
$250$	88.0038	+	251.375i	0.352015	+	1.00550i
$251$	−160.255			−0.638466			−0.319233	−	0.947676i	$-0.603425\pi$
$251$	−160.255			−0.638466			−0.319233	+	0.947676i	$0.603425\pi$
$252$		0			0
$253$			375.397i			1.48378i
$254$	−147.267	−	420.656i	−0.579792	−	1.65612i
$255$			97.9772i			0.384224i
$256$	−230.786	−	110.788i	−0.901507	−	0.432765i
$257$	−145.442			−0.565921			−0.282960	−	0.959132i	$-0.591316\pi$
$257$	−145.442			−0.565921			−0.282960	+	0.959132i	$0.591316\pi$
$258$	121.440	−	42.5147i	0.470696	−	0.164786i
$259$		0			0
$260$	262.026	−	209.091i	1.00779	−	0.804198i
$261$		−	143.031i		−	0.548012i
$262$	447.478	−	156.657i	1.70793	−	0.597928i
$263$			202.785i			0.771045i	0.922698	+	0.385523i	$0.125979\pi$
$263$			202.785i			0.771045i	−0.922698	+	0.385523i	$0.874021\pi$
$264$	−86.8113	+	138.302i	−0.328831	+	0.523872i
$265$	−21.7381			−0.0820305
$266$		0			0
$267$	−259.547			−0.972087
$268$	−247.621	+	197.597i	−0.923960	+	0.737302i
$269$			221.312i			0.822720i	0.911473	+	0.411360i	$0.134946\pi$
$269$			221.312i			0.822720i	−0.911473	+	0.411360i	$0.865054\pi$
$270$	75.9457	+	216.932i	0.281280	+	0.803453i
$271$		−	117.376i		−	0.433122i	−0.976269	−	0.216561i	$-0.930516\pi$
$271$		−	117.376i		−	0.433122i	0.976269	−	0.216561i	$-0.0694840\pi$
$272$	46.2595	−	203.257i	0.170072	−	0.747269i
$273$		0			0
$274$	18.2401	−	6.38565i	0.0665695	−	0.0233053i
$275$	−51.9480			−0.188902
$276$	124.739	+	156.318i	0.451953	+	0.566371i
$277$			255.509i			0.922416i	0.887292	+	0.461208i	$0.152584\pi$
$277$			255.509i			0.922416i	−0.887292	+	0.461208i	$0.847416\pi$
$278$	−119.040	+	41.6746i	−0.428202	+	0.149909i
$279$		−	141.716i		−	0.507944i
$280$		0			0
$281$	−278.004			−0.989336			−0.494668	−	0.869082i	$-0.664710\pi$
$281$	−278.004			−0.989336			−0.494668	+	0.869082i	$0.664710\pi$
$282$	22.1580	+	63.2926i	0.0785746	+	0.224442i
$283$	−56.6896			−0.200317			−0.100158	−	0.994972i	$-0.531935\pi$
$283$	−56.6896			−0.200317			−0.100158	+	0.994972i	$0.531935\pi$
$284$	−32.4222	−	40.6303i	−0.114163	−	0.143064i
$285$			22.7506i			0.0798266i
$286$	150.321	+	429.379i	0.525597	+	1.50132i
$287$		0			0
$288$	−22.6608	−	199.728i	−0.0786833	−	0.693499i
$289$	−119.260			−0.412664
$290$	−196.047	+	68.6340i	−0.676025	+	0.236669i
$291$	−65.3204			−0.224469
$292$	308.221	−	245.955i	1.05555	−	0.842311i
$293$		−	287.871i		−	0.982493i	−0.871020	−	0.491247i	$-0.836541\pi$
$293$		−	287.871i		−	0.982493i	0.871020	−	0.491247i	$-0.163459\pi$
$294$		0			0
$295$			53.5369i			0.181481i
$296$	−93.3679	−	58.6064i	−0.315432	−	0.197994i
$297$	−311.916			−1.05022
$298$	−178.372	−	509.504i	−0.598563	−	1.70975i
$299$	557.172			1.86345
$300$	−21.6315	+	17.2616i	−0.0721052	+	0.0575385i
$301$		0			0
$302$	71.4893	+	204.203i	0.236720	+	0.676169i
$303$		−	71.9168i		−	0.237349i
$304$	10.7416	−	47.1969i	0.0353342	−	0.155253i
$305$	496.724			1.62860
$306$	154.484	−	54.0831i	0.504849	−	0.176742i
$307$	−53.6483			−0.174750			−0.0873750	−	0.996175i	$-0.527848\pi$
$307$	−53.6483			−0.174750			−0.0873750	+	0.996175i	$0.527848\pi$
$308$		0			0
$309$			103.711i			0.335636i
$310$	−194.245	+	68.0030i	−0.626596	+	0.219365i
$311$			105.108i			0.337968i	0.985619	+	0.168984i	$0.0540487\pi$
$311$			105.108i			0.337968i	−0.985619	+	0.168984i	$0.945951\pi$
$312$	205.271	+	128.847i	0.657920	+	0.412972i
$313$	−210.490			−0.672492			−0.336246	−	0.941774i	$-0.609157\pi$
$313$	−210.490			−0.672492			−0.336246	+	0.941774i	$0.609157\pi$
$314$	78.2657	+	223.559i	0.249254	+	0.711973i
$315$		0			0
$316$	327.396	+	410.280i	1.03606	+	1.29836i
$317$			62.8880i			0.198385i	0.995068	+	0.0991925i	$0.0316259\pi$
$317$			62.8880i			0.198385i	−0.995068	+	0.0991925i	$0.968374\pi$
$318$	−5.19296	−	14.8333i	−0.0163301	−	0.0466455i
$319$		−	281.886i		−	0.883655i
$320$	−262.885	+	126.900i	−0.821516	+	0.396563i
$321$	−72.9199			−0.227165
$322$		0			0
$323$	39.4141			0.122025
$324$	46.8718	−	37.4028i	0.144666	−	0.115441i
$325$			77.1023i			0.237238i
$326$	154.842	−	54.2085i	0.474976	−	0.166284i
$327$			14.5343i			0.0444474i
$328$	−257.324	+	409.952i	−0.784524	+	1.24985i
$329$		0			0
$330$	61.5240	+	175.738i	0.186436	+	0.532540i
$331$	196.579			0.593893			0.296947	−	0.954894i	$-0.404032\pi$
$331$	196.579			0.593893			0.296947	+	0.954894i	$0.404032\pi$
$332$	−88.7104	+	70.7892i	−0.267200	+	0.213220i
$333$		−	86.5575i		−	0.259932i
$334$	86.9656	+	248.410i	0.260376	+	0.743742i
$335$			361.238i			1.07832i
$336$		0			0
$337$	591.516			1.75524			0.877620	−	0.479358i	$-0.159130\pi$
$337$	591.516			1.75524			0.877620	+	0.479358i	$0.159130\pi$
$338$	318.277	−	111.425i	0.941649	−	0.329661i
$339$	200.174			0.590484
$340$	−148.259	−	185.793i	−0.436056	−	0.546449i
$341$		−	279.295i		−	0.819046i
$342$	35.8716	−	12.5582i	0.104888	−	0.0367200i
$343$		0			0
$344$	−165.951	+	264.383i	−0.482416	+	0.768554i
$345$	228.042			0.660992
$346$	−72.7686	−	207.857i	−0.210314	−	0.600744i
$347$	247.540			0.713371			0.356685	−	0.934225i	$-0.383907\pi$
$347$	247.540			0.713371			0.356685	+	0.934225i	$0.383907\pi$
$348$	−93.6666	−	117.380i	−0.269157	−	0.337297i
$349$			288.749i			0.827362i	0.910422	+	0.413681i	$0.135757\pi$
$349$			288.749i			0.827362i	−0.910422	+	0.413681i	$0.864243\pi$
$350$		0			0
$351$			462.952i			1.31895i
$352$	−44.6599	−	393.624i	−0.126875	−	1.11825i
$353$	1.26966			0.00359677			0.00179839	−	0.999998i	$-0.499428\pi$
$353$	1.26966			0.00359677			0.00179839	+	0.999998i	$0.499428\pi$
$354$	−36.5316	+	12.7893i	−0.103197	+	0.0361280i
$355$	−59.2727			−0.166965
$356$	492.176	−	392.747i	1.38252	−	1.10322i
$357$		0			0
$358$	−290.422	+	101.674i	−0.811235	+	0.284005i
$359$		−	17.4021i		−	0.0484738i	−0.999706	−	0.0242369i	$-0.992284\pi$
$359$		−	17.4021i		−	0.0484738i	0.999706	−	0.0242369i	$-0.00771560\pi$
$360$	−194.131	−	121.855i	−0.539254	−	0.338486i
$361$	−351.848			−0.974648
$362$	−150.351	−	429.465i	−0.415334	−	1.18637i
$363$	−53.1828			−0.146509
$364$		0			0
$365$		−	449.643i		−	1.23190i
$366$	118.661	+	338.946i	0.324211	+	0.926082i
$367$		−	530.032i		−	1.44423i	−0.691773	−	0.722115i	$-0.743170\pi$
$367$		−	530.032i		−	1.44423i	0.691773	−	0.722115i	$-0.256830\pi$
$368$	−473.082	−	107.669i	−1.28555	−	0.292579i
$369$	−380.049			−1.02994
$370$	−118.641	+	41.5349i	−0.320651	+	0.112256i
$371$		0			0
$372$	−92.8055	−	116.300i	−0.249477	−	0.312636i
$373$		−	118.613i		−	0.317998i	−0.987279	−	0.158999i	$-0.949173\pi$
$373$		−	118.613i		−	0.317998i	0.987279	−	0.158999i	$-0.0508267\pi$
$374$	304.457	−	106.587i	0.814055	−	0.284992i
$375$			219.563i			0.585502i
$376$	−137.792	−	86.4913i	−0.366469	−	0.230030i
$377$	−418.381			−1.10976
$378$		0			0
$379$	−345.947			−0.912790			−0.456395	−	0.889777i	$-0.650860\pi$
$379$	−345.947			−0.912790			−0.456395	+	0.889777i	$0.650860\pi$
$380$	−34.4262	−	43.1416i	−0.0905952	−	0.113531i
$381$		−	367.421i		−	0.964359i
$382$	80.3235	+	229.437i	0.210271	+	0.600621i
$383$			404.873i			1.05711i	0.848899	+	0.528555i	$0.177266\pi$
$383$			404.873i			1.05711i	−0.848899	+	0.528555i	$0.822734\pi$
$384$	−149.392	−	149.068i	−0.389042	−	0.388198i
$385$		0			0
$386$	−161.311	+	56.4731i	−0.417903	+	0.146303i
$387$	−245.098			−0.633328
$388$	123.866	−	98.8429i	0.319243	−	0.254750i
$389$		−	134.397i		−	0.345493i	−0.984966	−	0.172747i	$-0.944736\pi$
$389$		−	134.397i		−	0.345493i	0.984966	−	0.172747i	$-0.0552642\pi$
$390$	260.834	−	91.3152i	0.668805	−	0.234142i
$391$		−	395.070i		−	1.01041i
$392$		0			0
$393$	390.848			0.994525
$394$	141.488	+	404.148i	0.359107	+	1.02576i
$395$	598.530			1.51527
$396$	243.131	−	194.014i	0.613967	−	0.489934i
$397$		−	612.481i		−	1.54277i	−0.636367	−	0.771386i	$-0.719564\pi$
$397$		−	612.481i		−	1.54277i	0.636367	−	0.771386i	$-0.280436\pi$
$398$	−164.039	−	468.563i	−0.412158	−	1.17729i
$399$		0			0
$400$	14.8994	−	65.4657i	0.0372485	−	0.163664i
$401$	−126.247			−0.314830			−0.157415	−	0.987533i	$-0.550316\pi$
$401$	−126.247			−0.314830			−0.157415	+	0.987533i	$0.550316\pi$
$402$	−246.495	+	86.2953i	−0.613172	+	0.214665i
$403$	−414.535			−1.02862
$404$	108.824	+	136.375i	0.269368	+	0.337561i
$405$		−	68.3781i		−	0.168835i
$406$		0			0
$407$		−	170.588i		−	0.419134i
$408$	91.3608	−	145.550i	0.223924	−	0.356741i
$409$	−342.519			−0.837455			−0.418727	−	0.908112i	$-0.637524\pi$
$409$	−342.519			−0.837455			−0.418727	+	0.908112i	$0.637524\pi$
$410$	182.368	+	520.918i	0.444800	+	1.27053i
$411$	15.9317			0.0387634
$412$	−156.936	−	196.667i	−0.380913	−	0.477346i
$413$		0			0
$414$	−125.879	−	359.561i	−0.304055	−	0.868506i
$415$			129.414i			0.311840i
$416$	−584.224	+	66.2851i	−1.40439	+	0.159339i
$417$	−103.975			−0.249341
$418$	70.6957	−	24.7498i	0.169128	−	0.0592101i
$419$	376.392			0.898311			0.449155	−	0.893454i	$-0.351725\pi$
$419$	376.392			0.898311			0.449155	+	0.893454i	$0.351725\pi$
$420$		0			0
$421$		−	111.135i		−	0.263978i	−0.991251	−	0.131989i	$-0.957864\pi$
$421$		−	111.135i		−	0.263978i	0.991251	−	0.131989i	$-0.0421363\pi$
$422$	−361.966	+	126.720i	−0.857739	+	0.300285i
$423$		−	127.742i		−	0.301989i
$424$	32.2930	+	20.2701i	0.0761629	+	0.0478069i
$425$	54.6704			0.128636
$426$	−14.1595	−	40.4455i	−0.0332384	−	0.0949425i
$427$		0			0
$428$	138.277	−	110.342i	0.323077	−	0.257810i
$429$			375.040i			0.874219i
$430$	117.611	+	335.946i	0.273514	+	0.781270i
$431$			41.2784i			0.0957734i	0.998853	+	0.0478867i	$0.0152486\pi$
$431$			41.2784i			0.0957734i	−0.998853	+	0.0478867i	$0.984751\pi$
$432$	89.4618	−	393.082i	0.207087	−	0.909911i
$433$	675.176			1.55930			0.779649	−	0.626217i	$-0.215397\pi$
$433$	675.176			1.55930			0.779649	+	0.626217i	$0.215397\pi$
$434$		0			0
$435$	−171.237			−0.393648
$436$	−21.9933	−	27.5612i	−0.0504433	−	0.0632137i
$437$		−	91.7365i		−	0.209923i
$438$	306.820	−	107.414i	0.700502	−	0.245238i
$439$			530.256i			1.20787i	0.797032	+	0.603936i	$0.206402\pi$
$439$			530.256i			1.20787i	−0.797032	+	0.603936i	$0.793598\pi$
$440$	−382.594	−	240.152i	−0.869532	−	0.545799i
$441$		0			0
$442$	−158.199	−	451.881i	−0.357915	−	1.02235i
$443$	332.033			0.749510			0.374755	−	0.927124i	$-0.377727\pi$
$443$	332.033			0.749510			0.374755	+	0.927124i	$0.377727\pi$
$444$	−56.6838	−	71.0340i	−0.127666	−	0.159986i
$445$		−	718.002i		−	1.61349i
$446$	−27.2448	−	77.8225i	−0.0610871	−	0.174490i
$447$		−	445.025i		−	0.995582i
$448$		0			0
$449$	−19.4200			−0.0432517			−0.0216259	−	0.999766i	$-0.506884\pi$
$449$	−19.4200			−0.0432517			−0.0216259	+	0.999766i	$0.506884\pi$
$450$	49.7566	−	17.4193i	0.110570	−	0.0387095i
$451$	−749.002			−1.66076
$452$	−379.587	+	302.904i	−0.839795	+	0.670141i
$453$			178.361i			0.393732i
$454$	132.974	−	46.5528i	0.292894	−	0.102539i
$455$		0			0
$456$	21.2142	−	33.7972i	0.0465224	−	0.0741166i
$457$	−177.959			−0.389408			−0.194704	−	0.980862i	$-0.562375\pi$
$457$	−177.959			−0.389408			−0.194704	+	0.980862i	$0.562375\pi$
$458$	−62.4629	−	178.420i	−0.136382	−	0.389563i
$459$	328.262			0.715168
$460$	−432.433	+	345.073i	−0.940072	+	0.750160i
$461$			299.341i			0.649329i	0.945829	+	0.324664i	$0.105251\pi$
$461$			299.341i			0.649329i	−0.945829	+	0.324664i	$0.894749\pi$
$462$		0			0
$463$		−	505.213i		−	1.09117i	−0.838055	−	0.545586i	$-0.816307\pi$
$463$		−	505.213i		−	1.09117i	0.838055	−	0.545586i	$-0.183693\pi$
$464$	355.238	+	80.8488i	0.765598	+	0.174243i
$465$	−169.663			−0.364866
$466$	257.264	−	90.0652i	0.552068	−	0.193273i
$467$	650.324			1.39256			0.696278	−	0.717772i	$-0.254838\pi$
$467$	650.324			1.39256			0.696278	+	0.717772i	$0.254838\pi$
$468$	−287.959	−	360.860i	−0.615298	−	0.771068i
$469$		0			0
$470$	−175.090	+	61.2972i	−0.372532	+	0.130420i
$471$			195.268i			0.414581i
$472$	49.9215	−	79.5318i	0.105766	−	0.168500i
$473$	−483.039			−1.02122
$474$	142.982	+	408.415i	0.301649	+	0.861635i
$475$	12.6946			0.0267255
$476$		0			0
$477$			29.9375i			0.0627621i
$478$	114.479	+	327.000i	0.239497	+	0.684101i
$479$			660.951i			1.37986i	0.723878	+	0.689928i	$0.242358\pi$
$479$			660.951i			1.37986i	−0.723878	+	0.689928i	$0.757642\pi$
$480$	−239.114	+	27.1295i	−0.498154	+	0.0565198i
$481$	−253.190			−0.526382
$482$	−620.896	+	217.369i	−1.28817	+	0.450973i
$483$		0			0
$484$	100.850	−	80.4762i	0.208367	−	0.166273i
$485$		−	180.700i		−	0.372577i
$486$	474.710	−	166.191i	0.976770	−	0.341957i
$487$		−	386.100i		−	0.792813i	−0.918075	−	0.396407i	$-0.870257\pi$
$487$		−	386.100i		−	0.792813i	0.918075	−	0.396407i	$-0.129743\pi$
$488$	−737.909	−	463.180i	−1.51211	−	0.949140i
$489$	135.246			0.276578
$490$		0			0
$491$	−898.359			−1.82965			−0.914826	−	0.403848i	$-0.867672\pi$
$491$	−898.359			−1.82965			−0.914826	+	0.403848i	$0.867672\pi$
$492$	−311.890	+	248.882i	−0.633923	+	0.505858i
$493$			296.659i			0.601742i
$494$	−36.7342	−	104.928i	−0.0743607	−	0.212405i
$495$		−	354.687i		−	0.716540i
$496$	351.972	+	80.1055i	0.709620	+	0.161503i
$497$		0			0
$498$	−88.3070	+	30.9153i	−0.177323	+	0.0620790i
$499$	791.176			1.58552			0.792761	−	0.609532i	$-0.208643\pi$
$499$	791.176			1.58552			0.792761	+	0.609532i	$0.208643\pi$
$500$	−332.243	−	416.355i	−0.664486	−	0.832709i
$501$			216.973i			0.433080i
$502$	302.508	−	105.905i	0.602605	−	0.210966i
$503$			798.990i			1.58845i	0.607624	+	0.794225i	$0.292123\pi$
$503$			798.990i			1.58845i	−0.607624	+	0.794225i	$0.707877\pi$
$504$		0			0
$505$	198.948			0.393956
$506$	−248.082	−	708.624i	−0.490280	−	1.40044i
$507$	277.999			0.548321
$508$	555.981	+	696.735i	1.09445	+	1.37153i
$509$			551.106i			1.08272i	0.840790	+	0.541362i	$0.182091\pi$
$509$			551.106i			1.08272i	−0.840790	+	0.541362i	$0.817909\pi$
$510$	−64.7483	−	184.948i	−0.126957	−	0.362643i
$511$		0			0
$512$	508.860	+	56.6155i	0.993868	+	0.110577i
$513$	76.2234			0.148584
$514$	274.545	−	96.1152i	0.534134	−	0.186995i
$515$	−286.903			−0.557094
$516$	−201.141	+	160.507i	−0.389809	+	0.311060i
$517$		−	251.753i		−	0.486950i
$518$		0			0
$519$		−	181.553i		−	0.349812i
$520$	−356.438	+	567.854i	−0.685458	+	1.09203i
$521$	−142.783			−0.274055			−0.137028	−	0.990567i	$-0.543755\pi$
$521$	−142.783			−0.274055			−0.137028	+	0.990567i	$0.543755\pi$
$522$	94.5223	+	269.995i	0.181077	+	0.517232i
$523$	832.511			1.59180			0.795900	−	0.605429i	$-0.206998\pi$
$523$	832.511			1.59180			0.795900	+	0.605429i	$0.206998\pi$
$524$	−741.160	+	591.432i	−1.41443	+	1.12869i
$525$		0			0
$526$	−134.011	−	382.790i	−0.254773	−	0.727737i
$527$			293.931i			0.557745i
$528$	72.4735	−	318.437i	0.137260	−	0.603101i
$529$	−390.528			−0.738238
$530$	41.0342	−	14.3656i	0.0774230	−	0.0271050i
$531$	73.7306			0.138852
$532$		0			0
$533$			1111.68i			2.08571i
$534$	489.938	−	171.522i	0.917486	−	0.321202i
$535$		−	201.723i		−	0.377052i
$536$	336.843	−	536.637i	0.628439	−	1.00119i
$537$	−253.669			−0.472381
$538$	−146.254	−	417.762i	−0.271848	−	0.776510i
$539$		0			0
$540$	−286.720	−	359.307i	−0.530963	−	0.665383i
$541$			616.465i			1.13949i	0.821821	+	0.569746i	$0.192958\pi$
$541$			616.465i			1.13949i	−0.821821	+	0.569746i	$0.807042\pi$
$542$	77.5681	+	221.567i	0.143115	+	0.408794i
$543$		−	375.115i		−	0.690819i
$544$	47.0004	+	414.252i	0.0863977	+	0.761493i
$545$	−40.2071			−0.0737746
$546$		0			0
$547$	577.704			1.05613			0.528065	−	0.849204i	$-0.322918\pi$
$547$	577.704			1.05613			0.528065	+	0.849204i	$0.322918\pi$
$548$	−30.2111	+	24.1079i	−0.0551298	+	0.0439925i
$549$		−	684.085i		−	1.24606i
$550$	98.0604	−	34.3299i	0.178292	−	0.0624180i
$551$			68.8850i			0.125018i
$552$	−338.768	−	212.643i	−0.613711	−	0.385222i
$553$		0			0
$554$	−168.853	−	482.316i	−0.304790	−	0.870606i
$555$	−103.627			−0.186715
$556$	197.167	−	157.335i	0.354617	−	0.282977i
$557$			514.710i			0.924075i	0.886860	+	0.462038i	$0.152881\pi$
$557$			514.710i			0.924075i	−0.886860	+	0.462038i	$0.847119\pi$
$558$	93.6533	+	267.513i	0.167838	+	0.479414i
$559$			716.937i			1.28253i
$560$		0			0
$561$	265.927			0.474023
$562$	524.777	−	183.719i	0.933767	−	0.326902i
$563$	608.719			1.08121			0.540603	−	0.841278i	$-0.318196\pi$
$563$	608.719			1.08121			0.540603	+	0.841278i	$0.318196\pi$
$564$	−83.6539	−	104.832i	−0.148322	−	0.185872i
$565$			553.754i			0.980096i
$566$	107.011	−	37.4634i	0.189065	−	0.0661897i
$567$		0			0
$568$	88.0527	+	55.2701i	0.155022	+	0.0973064i
$569$	186.374			0.327547			0.163774	−	0.986498i	$-0.447633\pi$
$569$	186.374			0.327547			0.163774	+	0.986498i	$0.447633\pi$
$570$	−15.0347	−	42.9454i	−0.0263767	−	0.0753429i
$571$	183.776			0.321849			0.160924	−	0.986967i	$-0.448552\pi$
$571$	183.776			0.321849			0.160924	+	0.986967i	$0.448552\pi$
$572$	−567.510	−	711.183i	−0.992151	−	1.24333i
$573$			200.401i			0.349741i
$574$		0			0
$575$		−	127.246i		−	0.221297i
$576$	174.766	+	362.044i	0.303414	+	0.628548i
$577$	−134.456			−0.233026			−0.116513	−	0.993189i	$-0.537172\pi$
$577$	−134.456			−0.233026			−0.116513	+	0.993189i	$0.537172\pi$
$578$	225.123	−	78.8130i	0.389486	−	0.136355i
$579$	−140.896			−0.243345
$580$	324.714	−	259.116i	0.559852	−	0.446752i
$581$		0			0
$582$	123.303	−	43.1670i	0.211861	−	0.0741702i
$583$			59.0009i			0.101202i
$584$	−419.279	+	667.968i	−0.717944	+	1.14378i
$585$	−526.434			−0.899887
$586$	190.240	+	543.403i	0.324641	+	0.927309i
$587$	921.405			1.56968			0.784842	−	0.619696i	$-0.212744\pi$
$587$	921.405			1.56968			0.784842	+	0.619696i	$0.212744\pi$
$588$		0			0
$589$			68.2517i			0.115877i
$590$	−35.3799	−	101.060i	−0.0599659	−	0.171287i
$591$			353.002i			0.597297i
$592$	214.977	+	48.9269i	0.363137	+	0.0826467i
$593$	−96.3746			−0.162520			−0.0812602	−	0.996693i	$-0.525894\pi$
$593$	−96.3746			−0.162520			−0.0812602	+	0.996693i	$0.525894\pi$
$594$	588.792	−	206.130i	0.991233	−	0.347020i
$595$		0			0
$596$	673.412	+	843.895i	1.12989	+	1.41593i
$597$		−	409.265i		−	0.685536i
$598$	−1051.75	+	368.208i	−1.75879	+	0.615732i
$599$			167.098i			0.278961i	0.990225	+	0.139481i	$0.0445433\pi$
$599$			167.098i			0.278961i	−0.990225	+	0.139481i	$0.955457\pi$
$600$	29.4258	−	46.8793i	0.0490430	−	0.0781321i
$601$	−88.4635			−0.147194			−0.0735969	−	0.997288i	$-0.523448\pi$
$601$	−88.4635			−0.147194			−0.0735969	+	0.997288i	$0.523448\pi$
$602$		0			0
$603$	497.494			0.825032
$604$	−269.896	−	338.223i	−0.446847	−	0.559972i
$605$		−	147.123i		−	0.243178i
$606$	47.5263	+	135.755i	0.0784262	+	0.224018i
$607$		−	55.5692i		−	0.0915472i	−0.998952	−	0.0457736i	$-0.985425\pi$
$607$		−	55.5692i		−	0.0915472i	0.998952	−	0.0457736i	$-0.0145753\pi$
$608$	10.9136	+	96.1905i	0.0179500	+	0.158208i
$609$		0			0
$610$	−937.648	+	328.260i	−1.53713	+	0.538132i
$611$	−373.657			−0.611550
$612$	−255.873	+	204.181i	−0.418092	+	0.333630i
$613$		−	869.117i		−	1.41781i	−0.705304	−	0.708905i	$-0.749190\pi$
$613$		−	869.117i		−	1.41781i	0.705304	−	0.708905i	$-0.250810\pi$
$614$	101.270	−	35.4535i	0.164935	−	0.0577419i
$615$			454.995i			0.739829i
$616$		0			0
$617$	−249.359			−0.404147			−0.202074	−	0.979370i	$-0.564768\pi$
$617$	−249.359			−0.404147			−0.202074	+	0.979370i	$0.564768\pi$
$618$	−68.5378	−	195.772i	−0.110903	−	0.316784i
$619$	497.673			0.803995			0.401998	−	0.915641i	$-0.368316\pi$
$619$	497.673			0.803995			0.401998	+	0.915641i	$0.368316\pi$
$620$	321.729	−	256.734i	0.518918	−	0.414087i
$621$		−	764.031i		−	1.23032i
$622$	−69.4608	−	198.409i	−0.111673	−	0.318985i
$623$		0			0
$624$	−472.631	−	107.567i	−0.757422	−	0.172382i
$625$	−502.486			−0.803977
$626$	397.334	−	139.102i	0.634719	−	0.222208i
$627$	61.7490			0.0984833
$628$	−295.479	−	370.283i	−0.470508	−	0.589623i
$629$			179.527i			0.285417i
$630$		0			0
$631$			172.763i			0.273792i	0.990585	+	0.136896i	$0.0437126\pi$
$631$			172.763i			0.273792i	−0.990585	+	0.136896i	$0.956287\pi$
$632$	−889.148	−	558.112i	−1.40688	−	0.883088i
$633$	−316.158			−0.499460
$634$	−41.5596	−	118.711i	−0.0655514	−	0.187242i
$635$	1016.42			1.60066
$636$	19.6051	+	24.5684i	0.0308257	+	0.0386296i
$637$		0			0
$638$	186.285	+	532.106i	0.291982	+	0.834022i
$639$			81.6300i			0.127746i
$640$	412.376	−	413.273i	0.644338	−	0.645739i
$641$	−427.898			−0.667547			−0.333774	−	0.942653i	$-0.608322\pi$
$641$	−427.898			−0.667547			−0.333774	+	0.942653i	$0.608322\pi$
$642$	137.648	−	48.1892i	0.214406	−	0.0750611i
$643$	15.9463			0.0247998			0.0123999	−	0.999923i	$-0.496053\pi$
$643$	15.9463			0.0247998			0.0123999	+	0.999923i	$0.496053\pi$
$644$		0			0
$645$			293.431i			0.454932i
$646$	−74.4006	+	26.0469i	−0.115171	+	0.0403202i
$647$			520.204i			0.804025i	0.915634	+	0.402012i	$0.131689\pi$
$647$			520.204i			0.804025i	−0.915634	+	0.402012i	$0.868311\pi$
$648$	−63.7606	+	101.579i	−0.0983960	+	0.156758i
$649$	145.308			0.223896
$650$	−50.9531	−	145.543i	−0.0783894	−	0.223913i
$651$		0			0
$652$	−256.466	+	204.655i	−0.393353	+	0.313888i
$653$		−	424.568i		−	0.650181i	−0.945683	−	0.325091i	$-0.894605\pi$
$653$		−	424.568i		−	0.650181i	0.945683	−	0.325091i	$-0.105395\pi$
$654$	−9.60500	−	27.4359i	−0.0146865	−	0.0419509i
$655$			1081.23i			1.65073i
$656$	214.824	−	943.904i	0.327476	−	1.43888i
$657$	−619.246			−0.942535
$658$		0			0
$659$	304.044			0.461372			0.230686	−	0.973028i	$-0.425903\pi$
$659$	304.044			0.461372			0.230686	+	0.973028i	$0.425903\pi$
$660$	−232.273	−	291.076i	−0.351929	−	0.441025i
$661$			179.108i			0.270966i	0.990780	+	0.135483i	$0.0432586\pi$
$661$			179.108i			0.270966i	−0.990780	+	0.135483i	$0.956741\pi$
$662$	−371.075	+	129.909i	−0.560536	+	0.196237i
$663$		−	394.694i		−	0.595316i
$664$	120.674	−	192.251i	0.181738	−	0.289534i
$665$		0			0
$666$	57.2016	+	163.391i	0.0858883	+	0.245333i
$667$	690.474			1.03519
$668$	−328.324	−	411.443i	−0.491502	−	0.615933i
$669$		−	67.9739i		−	0.101605i
$670$	−238.724	−	681.895i	−0.356305	−	1.01775i
$671$		−	1348.20i		−	2.00923i
$672$		0			0
$673$	544.352			0.808844			0.404422	−	0.914573i	$-0.367473\pi$
$673$	544.352			0.808844			0.404422	+	0.914573i	$0.367473\pi$
$674$	−1116.58	+	390.904i	−1.65665	+	0.579976i
$675$	105.728			0.156634
$676$	−527.165	+	420.668i	−0.779830	+	0.622289i
$677$			544.344i			0.804053i	0.915628	+	0.402027i	$0.131694\pi$
$677$			544.344i			0.804053i	−0.915628	+	0.402027i	$0.868306\pi$
$678$	−377.861	+	132.285i	−0.557318	+	0.195111i
$679$		0			0
$680$	402.645	+	252.737i	0.592125	+	0.371672i
$681$	116.146			0.170552
$682$	184.572	+	527.214i	0.270634	+	0.773042i
$683$	886.988			1.29866			0.649332	−	0.760505i	$-0.275049\pi$
$683$	886.988			1.29866			0.649332	+	0.760505i	$0.275049\pi$
$684$	−59.4143	+	47.4115i	−0.0868631	+	0.0693151i
$685$			44.0730i			0.0643401i
$686$		0			0
$687$		−	155.841i		−	0.226842i
$688$	138.542	−	608.734i	0.201370	−	0.884788i
$689$	87.5704			0.127098
$690$	−430.467	+	150.702i	−0.623865	+	0.218408i
$691$	−1178.48			−1.70548			−0.852738	−	0.522340i	$-0.825059\pi$
$691$	−1178.48			−1.70548			−0.852738	+	0.522340i	$0.825059\pi$
$692$	274.725	+	344.276i	0.397002	+	0.497508i
$693$		0			0
$694$	−467.272	+	163.587i	−0.673302	+	0.235716i
$695$		−	287.633i		−	0.413861i
$696$	254.382	+	159.673i	0.365491	+	0.229416i
$697$	788.254			1.13092
$698$	−190.820	−	545.062i	−0.273381	−	0.780890i
$699$	224.706			0.321468
$700$		0			0
$701$		−	901.601i		−	1.28616i	−0.765797	−	0.643082i	$-0.777655\pi$
$701$		−	901.601i		−	1.28616i	0.765797	−	0.643082i	$-0.222345\pi$
$702$	−305.942	−	873.898i	−0.435815	−	1.24487i
$703$			41.6868i			0.0592984i
$704$	344.429	+	713.516i	0.489246	+	1.01352i
$705$	−152.932			−0.216925
$706$	−2.39669	+	0.839056i	−0.00339475	+	0.00118846i
$707$		0			0
$708$	60.5075	−	48.2839i	0.0854626	−	0.0681975i
$709$		−	332.802i		−	0.469397i	−0.972068	−	0.234698i	$-0.924590\pi$
$709$		−	332.802i		−	0.469397i	0.972068	−	0.234698i	$-0.0754102\pi$
$710$	111.887	−	39.1704i	0.157587	−	0.0551696i
$711$		−	824.292i		−	1.15934i
$712$	−669.515	+	1066.63i	−0.940330	+	1.49807i
$713$	684.126			0.959504
$714$		0			0
$715$	−1037.50			−1.45104
$716$	481.028	−	383.852i	0.671827	−	0.536105i
$717$			285.618i			0.398351i
$718$	11.5002	+	32.8493i	0.0160170	+	0.0457512i
$719$			1184.95i			1.64805i	0.566551	+	0.824027i	$0.308277\pi$
$719$			1184.95i			1.64805i	−0.566551	+	0.824027i	$0.691723\pi$
$720$	446.983	+	101.729i	0.620809	+	0.141291i
$721$		0			0
$722$	664.171	−	232.519i	0.919904	−	0.322049i
$723$	−542.320			−0.750097
$724$	567.624	+	711.325i	0.784011	+	0.982494i
$725$			95.5488i			0.131791i
$726$	100.391	−	35.1459i	0.138280	−	0.0484103i
$727$			19.9398i			0.0274275i	0.999906	+	0.0137138i	$0.00436536\pi$
$727$			19.9398i			0.0274275i	−0.999906	+	0.0137138i	$0.995635\pi$
$728$		0			0
$729$	279.711			0.383691
$730$	297.147	+	848.775i	0.407051	+	1.16271i
$731$	508.354			0.695423
$732$	−447.986	−	561.399i	−0.612002	−	0.766938i
$733$		−	1037.30i		−	1.41514i	−0.706644	−	0.707569i	$-0.749792\pi$
$733$		−	1037.30i		−	1.41514i	0.706644	−	0.707569i	$-0.250208\pi$
$734$	350.272	+	1000.52i	0.477210	+	1.36311i
$735$		0			0
$736$	964.173	−	109.393i	1.31002	−	0.148632i
$737$	980.462			1.33034
$738$	717.406	−	251.156i	0.972094	−	0.340320i
$739$	−419.971			−0.568297			−0.284148	−	0.958780i	$-0.591711\pi$
$739$	−419.971			−0.568297			−0.284148	+	0.958780i	$0.591711\pi$
$740$	196.506	−	156.808i	0.265548	−	0.211903i
$741$		−	91.6491i		−	0.123683i
$742$		0			0
$743$			1241.67i			1.67116i	0.549370	+	0.835579i	$0.314868\pi$
$743$			1241.67i			1.67116i	−0.549370	+	0.835579i	$0.685132\pi$
$744$	252.043	+	158.206i	0.338767	+	0.212642i
$745$	1231.10			1.65249
$746$	78.3857	+	223.902i	0.105075	+	0.300137i
$747$	178.227			0.238591
$748$	−504.274	+	402.401i	−0.674163	+	0.537969i
$749$		0			0
$750$	−145.099	−	414.462i	−0.193465	−	0.552615i
$751$		−	647.797i		−	0.862579i	−0.902214	−	0.431289i	$-0.858059\pi$
$751$		−	647.797i		−	0.862579i	0.902214	−	0.431289i	$-0.141941\pi$
$752$	317.263	+	72.2063i	0.421893	+	0.0960190i
$753$	264.225			0.350896
$754$	789.763	−	276.487i	1.04743	−	0.366694i
$755$	−493.411			−0.653524
$756$		0			0
$757$			105.310i			0.139116i	0.997578	+	0.0695578i	$0.0221588\pi$
$757$			105.310i			0.139116i	−0.997578	+	0.0695578i	$0.977841\pi$
$758$	653.032	−	228.620i	0.861520	−	0.301609i
$759$		−	618.946i		−	0.815476i
$760$	93.4952	+	58.6863i	0.123020	+	0.0772188i
$761$	421.884			0.554381			0.277190	−	0.960815i	$-0.410597\pi$
$761$	421.884			0.554381			0.277190	+	0.960815i	$0.410597\pi$
$762$	242.810	+	693.567i	0.318649	+	0.910193i
$763$		0			0
$764$	−303.247	−	380.018i	−0.396921	−	0.497406i
$765$			373.275i			0.487941i
$766$	−267.561	−	764.264i	−0.349296	−	0.997733i
$767$		−	215.670i		−	0.281186i
$768$	380.514	+	182.665i	0.495461	+	0.237844i
$769$	189.767			0.246772			0.123386	−	0.992359i	$-0.460625\pi$
$769$	189.767			0.246772			0.123386	+	0.992359i	$0.460625\pi$
$770$		0			0
$771$	239.801			0.311025
$772$	267.180	−	213.205i	0.346088	−	0.276172i
$773$			842.788i			1.09028i	0.838345	+	0.545141i	$0.183524\pi$
$773$			842.788i			1.09028i	−0.838345	+	0.545141i	$0.816476\pi$
$774$	462.663	−	161.973i	0.597756	−	0.209268i
$775$			94.6704i			0.122155i
$776$	−168.497	+	268.439i	−0.217136	+	0.345927i
$777$		0			0
$778$	88.8164	+	253.696i	0.114160	+	0.326088i
$779$	183.035			0.234961
$780$	−432.021	+	344.745i	−0.553874	+	0.441981i
$781$			160.876i			0.205988i
$782$	261.083	+	745.760i	0.333865	+	0.953658i
$783$			573.712i			0.732710i
$784$		0			0
$785$	−540.181			−0.688128
$786$	−737.790	+	258.292i	−0.938665	+	0.328616i
$787$	−1494.20			−1.89860			−0.949298	−	0.314376i	$-0.898205\pi$
$787$	−1494.20			−1.89860			−0.949298	+	0.314376i	$0.898205\pi$
$788$	−534.164	−	669.394i	−0.677873	−	0.849485i
$789$		−	334.347i		−	0.423760i
$790$	−1129.82	+	395.539i	−1.43016	+	0.500682i
$791$		0			0
$792$	−330.735	+	526.906i	−0.417595	+	0.665286i
$793$	−2001.02			−2.52335
$794$	404.758	+	1156.16i	0.509771	+	1.45612i
$795$	35.8412			0.0450833
$796$	619.300	+	776.084i	0.778015	+	0.974979i
$797$			292.040i			0.366424i	0.983073	+	0.183212i	$0.0586494\pi$
$797$			292.040i			0.366424i	−0.983073	+	0.183212i	$0.941351\pi$
$798$		0			0
$799$			264.947i			0.331598i
$800$	15.1380	+	133.424i	0.0189225	+	0.166780i
$801$	−988.827			−1.23449
$802$	238.311	−	83.4303i	0.297146	−	0.104028i
$803$	−1220.41			−1.51981
$804$	408.272	−	325.793i	0.507801	−	0.405215i
$805$		0			0
$806$	782.502	−	273.946i	0.970847	−	0.339883i
$807$		−	364.893i		−	0.452160i
$808$	−295.548	−	185.513i	−0.365777	−	0.229595i
$809$	156.906			0.193951			0.0969754	−	0.995287i	$-0.469083\pi$
$809$	156.906			0.193951			0.0969754	+	0.995287i	$0.469083\pi$
$810$	45.1877	+	129.075i	0.0557873	+	0.159352i
$811$	−1183.00			−1.45869			−0.729347	−	0.684144i	$-0.760176\pi$
$811$	−1183.00			−1.45869			−0.729347	+	0.684144i	$0.760176\pi$
$812$		0			0
$813$			193.527i			0.238040i
$814$	112.733	+	322.012i	0.138493	+	0.395592i
$815$			374.141i			0.459068i
$816$	−76.2716	+	335.126i	−0.0934700	+	0.410693i
$817$	118.041			0.144481
$818$	646.561	−	226.354i	0.790417	−	0.276716i
$819$		0			0
$820$	−688.499	−	862.801i	−0.839633	−	1.05220i
$821$			185.415i			0.225840i	0.993604	+	0.112920i	$0.0360204\pi$
$821$			185.415i			0.225840i	−0.993604	+	0.112920i	$0.963980\pi$
$822$	−30.0738	+	10.5285i	−0.0365861	+	0.0128084i
$823$			652.316i			0.792608i	0.918119	+	0.396304i	$0.129707\pi$
$823$			652.316i			0.792608i	−0.918119	+	0.396304i	$0.870293\pi$
$824$	426.210	+	267.529i	0.517245	+	0.324671i
$825$	85.6506			0.103819
$826$		0			0
$827$	−829.430			−1.00294			−0.501469	−	0.865176i	$-0.667207\pi$
$827$	−829.430			−1.00294			−0.501469	+	0.865176i	$0.667207\pi$
$828$	475.233	+	595.544i	0.573953	+	0.719256i
$829$			755.129i			0.910892i	0.890263	+	0.455446i	$0.150520\pi$
$829$			755.129i			0.910892i	−0.890263	+	0.455446i	$0.849480\pi$
$830$	−85.5230	−	244.289i	−0.103040	−	0.294324i
$831$		−	421.277i		−	0.506952i
$832$	1059.01	−	511.209i	1.27285	−	0.614434i
$833$		0			0
$834$	196.270	−	68.7122i	0.235336	−	0.0823887i
$835$	−600.226			−0.718834
$836$	−117.094	+	93.4386i	−0.140064	+	0.111769i
$837$			568.437i			0.679137i
$838$	−710.502	+	248.739i	−0.847855	+	0.296825i
$839$		−	88.6147i		−	0.105619i	−0.998605	−	0.0528097i	$-0.983182\pi$
$839$		−	88.6147i		−	0.105619i	0.998605	−	0.0528097i	$-0.0168177\pi$
$840$		0			0
$841$	322.522			0.383499
$842$	73.4435	+	209.785i	0.0872250	+	0.249151i
$843$	458.366			0.543731
$844$	599.527	−	478.411i	0.710340	−	0.566838i
$845$			769.045i			0.910113i
$846$	84.4181	+	241.133i	0.0997850	+	0.285027i
$847$		0			0
$848$	−74.3540	−	16.9223i	−0.0876816	−	0.0199555i
$849$	93.4685			0.110092
$850$	−103.199	+	36.1290i	−0.121411	+	0.0425047i
$851$	417.851			0.491011
$852$	53.4569	+	66.9902i	0.0627429	+	0.0786270i
$853$		−	367.466i		−	0.430792i	−0.976527	−	0.215396i	$-0.930896\pi$
$853$		−	367.466i		−	0.430792i	0.976527	−	0.215396i	$-0.0691042\pi$
$854$		0			0
$855$			86.6755i			0.101375i
$856$	−188.101	+	299.670i	−0.219744	+	0.350082i
$857$	165.340			0.192928			0.0964642	−	0.995336i	$-0.469247\pi$
$857$	165.340			0.192928			0.0964642	+	0.995336i	$0.469247\pi$
$858$	−247.845	−	707.949i	−0.288864	−	0.825116i
$859$	650.972			0.757825			0.378913	−	0.925432i	$-0.376298\pi$
$859$	650.972			0.757825			0.378913	+	0.925432i	$0.376298\pi$
$860$	−444.021	−	556.430i	−0.516303	−	0.647012i
$861$		0			0
$862$	−27.2788	−	77.9197i	−0.0316460	−	0.0903941i
$863$			136.736i			0.158442i	0.996857	+	0.0792212i	$0.0252433\pi$
$863$			136.736i			0.158442i	−0.996857	+	0.0792212i	$0.974757\pi$
$864$	90.8945	+	801.127i	0.105202	+	0.927230i
$865$	502.240			0.580625
$866$	−1274.51	+	446.191i	−1.47172	+	0.515232i
$867$	196.633			0.226797
$868$		0			0
$869$		−	1624.51i		−	1.86941i
$870$	323.238	−	113.162i	0.371538	−	0.130071i
$871$		−	1455.22i		−	1.67075i
$872$	59.7298	+	37.4920i	0.0684975	+	0.0429954i
$873$	−248.859			−0.285062
$874$	60.6241	+	173.168i	0.0693640	+	0.198132i
$875$		0			0
$876$	−508.188	+	405.524i	−0.580123	+	0.462927i
$877$			176.502i			0.201256i	0.994924	+	0.100628i	$0.0320852\pi$
$877$			176.502i			0.201256i	−0.994924	+	0.100628i	$0.967915\pi$
$878$	−350.420	−	1000.95i	−0.399112	−	1.14003i
$879$			474.634i			0.539971i
$880$	880.914	+	200.488i	1.00104	+	0.227827i
$881$	−734.879			−0.834142			−0.417071	−	0.908874i	$-0.636943\pi$
$881$	−734.879			−0.834142			−0.417071	+	0.908874i	$0.636943\pi$
$882$		0			0
$883$	872.637			0.988264			0.494132	−	0.869387i	$-0.335486\pi$
$883$	872.637			0.988264			0.494132	+	0.869387i	$0.335486\pi$
$884$	597.252	+	748.454i	0.675624	+	0.846667i
$885$		−	88.2703i		−	0.0997405i
$886$	−626.766	+	219.424i	−0.707411	+	0.247657i
$887$		−	24.0981i		−	0.0271681i	−0.999908	−	0.0135840i	$-0.995676\pi$
$887$		−	24.0981i		−	0.0271681i	0.999908	−	0.0135840i	$-0.00432407\pi$
$888$	153.943	+	96.6288i	0.173359	+	0.108816i
$889$		0			0
$890$	474.492	+	1355.35i	0.533137	+	1.52286i
$891$	−185.590			−0.208294
$892$	102.858	+	128.898i	0.115312	+	0.144505i
$893$			61.5213i			0.0688929i
$894$	294.095	+	840.058i	0.328966	+	0.939662i
$895$		−	701.740i		−	0.784067i
$896$		0			0
$897$	−918.652			−1.02414
$898$	36.6585	−	12.8337i	0.0408224	−	0.0142915i
$899$	−513.711			−0.571425
$900$	−82.4123	+	65.7634i	−0.0915692	+	0.0730705i
$901$		−	62.0930i		−	0.0689156i
$902$	1413.86	−	494.978i	1.56748	−	0.548756i
$903$		0			0
$904$	516.360	−	822.631i	0.571194	−	0.909990i
$905$	1037.70			1.14663
$906$	−117.870	−	336.685i	−0.130099	−	0.371617i
$907$	−1413.31			−1.55822			−0.779110	−	0.626887i	$-0.784329\pi$
$907$	−1413.31			−1.55822			−0.779110	+	0.626887i	$0.784329\pi$
$908$	−220.246	+	175.752i	−0.242562	+	0.193560i
$909$		−	273.990i		−	0.301419i
$910$		0			0
$911$		−	1778.28i		−	1.95201i	−0.217746	−	0.976005i	$-0.569871\pi$
$911$		−	1778.28i		−	1.95201i	0.217746	−	0.976005i	$-0.430129\pi$
$912$	−17.7105	+	77.8171i	−0.0194194	+	0.0853258i
$913$	351.251			0.384722
$914$	335.927	−	117.605i	0.367535	−	0.128670i
$915$	−818.987			−0.895067
$916$	235.818	+	295.518i	0.257443	+	0.322618i
$917$		0			0
$918$	−619.649	+	216.932i	−0.674999	+	0.236310i
$919$			893.841i			0.972624i	0.873785	+	0.486312i	$0.161658\pi$
$919$			893.841i			0.972624i	−0.873785	+	0.486312i	$0.838342\pi$
$920$	588.247	−	937.157i	0.639398	−	1.01865i
$921$	88.4540			0.0960413
$922$	−197.820	−	565.055i	−0.214555	−	0.612858i
$923$	238.776			0.258696
$924$		0			0
$925$			57.8228i			0.0625111i
$926$	333.870	+	953.672i	0.360551	+	1.02988i
$927$			395.122i			0.426237i
$928$	−723.998	+	82.1436i	−0.780170	+	0.0885169i
$929$	729.460			0.785210			0.392605	−	0.919707i	$-0.371574\pi$
$929$	729.460			0.785210			0.392605	+	0.919707i	$0.371574\pi$
$930$	320.266	−	112.122i	0.344372	−	0.120561i
$931$		0			0
$932$	−426.108	+	340.026i	−0.457197	+	0.364835i
$933$		−	173.300i		−	0.185745i
$934$	−1227.59	+	429.767i	−1.31434	+	0.460136i
$935$			735.651i			0.786792i
$936$	782.045	+	490.884i	0.835518	+	0.524449i
$937$	−637.240			−0.680085			−0.340042	−	0.940410i	$-0.610441\pi$
$937$	−637.240			−0.680085			−0.340042	+	0.940410i	$0.610441\pi$
$938$		0			0
$939$	347.051			0.369596
$940$	290.003	−	231.417i	0.308514	−	0.246188i
$941$		−	1753.57i		−	1.86352i	−0.363072	−	0.931761i	$-0.618272\pi$
$941$		−	1753.57i		−	1.86352i	0.363072	−	0.931761i	$-0.381728\pi$
$942$	−129.043	−	368.599i	−0.136988	−	0.391295i
$943$		−	1834.66i		−	1.94556i
$944$	−41.6764	+	183.120i	−0.0441488	+	0.193983i
$945$		0			0
$946$	911.816	−	319.217i	0.963865	−	0.337439i
$947$	−873.993			−0.922907			−0.461453	−	0.887164i	$-0.652672\pi$
$947$	−873.993			−0.922907			−0.461453	+	0.887164i	$0.652672\pi$
$948$	−539.803	−	676.461i	−0.569412	−	0.713566i
$949$			1811.36i			1.90870i
$950$	−23.9632	+	8.38925i	−0.0252244	+	0.00883079i
$951$		−	103.688i		−	0.109031i
$952$		0			0
$953$	−880.208			−0.923618			−0.461809	−	0.886979i	$-0.652800\pi$
$953$	−880.208			−0.923618			−0.461809	+	0.886979i	$0.652800\pi$
$954$	−19.7843	−	56.5120i	−0.0207382	−	0.0592369i
$955$	−554.383			−0.580506
$956$	−432.197	−	541.613i	−0.452089	−	0.566541i
$957$			464.767i			0.485650i
$958$	−436.790	−	1247.65i	−0.455939	−	1.30235i
$959$		0			0
$960$	433.439	−	209.230i	0.451498	−	0.217948i
$961$	452.012			0.470356
$962$	477.937	−	167.321i	0.496816	−	0.173930i
$963$	−277.812			−0.288486
$964$	1028.39	−	820.640i	1.06680	−	0.851286i
$965$		−	389.771i		−	0.403908i
$966$		0			0
$967$		−	259.016i		−	0.267855i	−0.990991	−	0.133928i	$-0.957241\pi$
$967$		−	259.016i		−	0.267855i	0.990991	−	0.133928i	$-0.0427590\pi$
$968$	−137.188	+	218.559i	−0.141723	+	0.225784i
$969$	−64.9851			−0.0670640
$970$	119.416	+	341.101i	0.123109	+	0.351650i
$971$	432.650			0.445572			0.222786	−	0.974867i	$-0.428485\pi$
$971$	432.650			0.445572			0.222786	+	0.974867i	$0.428485\pi$
$972$	−786.266	+	627.425i	−0.808916	+	0.645499i
$973$		0			0
$974$	255.155	+	728.827i	0.261966	+	0.748283i
$975$		−	127.124i		−	0.130384i
$976$	1699.02	+	386.681i	1.74080	+	0.396190i
$977$	815.509			0.834708			0.417354	−	0.908744i	$-0.362958\pi$
$977$	815.509			0.834708			0.417354	+	0.908744i	$0.362958\pi$
$978$	−255.300	+	89.3777i	−0.261043	+	0.0913883i
$979$	−1948.78			−1.99058
$980$		0			0
$981$			55.3730i			0.0564455i
$982$	1695.80	−	593.681i	1.72688	−	0.604564i
$983$			139.412i			0.141823i	0.997483	+	0.0709116i	$0.0225908\pi$
$983$			139.412i			0.141823i	−0.997483	+	0.0709116i	$0.977409\pi$
$984$	424.270	−	675.919i	0.431168	−	0.686910i
$985$	−976.533			−0.991404
$986$	−196.047	−	559.992i	−0.198831	−	0.567943i
$987$		0			0
$988$	138.684	+	173.793i	0.140368	+	0.175904i
$989$		−	1183.20i		−	1.19636i
$990$	234.395	+	669.530i	0.236763	+	0.676293i
$991$		−	1548.78i		−	1.56285i	−0.624002	−	0.781423i	$-0.714494\pi$
$991$		−	1548.78i		−	1.56285i	0.624002	−	0.781423i	$-0.285506\pi$
$992$	−717.342	+	81.3885i	−0.723127	+	0.0820448i
$993$	−324.114			−0.326399
$994$		0			0
$995$	1132.18			1.13786
$996$	146.264	−	116.716i	0.146851	−	0.117184i
$997$		−	1282.50i		−	1.28636i	−0.765717	−	0.643178i	$-0.777616\pi$
$997$		−	1282.50i		−	1.28636i	0.765717	−	0.643178i	$-0.222384\pi$
$998$	−1493.47	+	522.849i	−1.49647	+	0.523897i
$999$			347.190i			0.347538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.g.i.99.2		6
4.3	odd	2		1568.3.g.l.687.3		6
7.2	even	3		392.3.k.l.67.5		12
7.3	odd	6		56.3.k.d.51.4	yes	12
7.4	even	3		392.3.k.l.275.4		12
7.5	odd	6		56.3.k.d.11.5	yes	12
7.6	odd	2		392.3.g.j.99.2		6
8.3	odd	2	inner	392.3.g.i.99.1		6
8.5	even	2		1568.3.g.l.687.4		6
28.3	even	6		224.3.o.d.79.3		12
28.19	even	6		224.3.o.d.207.4		12
28.27	even	2		1568.3.g.j.687.4		6
56.3	even	6		56.3.k.d.51.5	yes	12
56.5	odd	6		224.3.o.d.207.3		12
56.11	odd	6		392.3.k.l.275.5		12
56.13	odd	2		1568.3.g.j.687.3		6
56.19	even	6		56.3.k.d.11.4	✓	12
56.27	even	2		392.3.g.j.99.1		6
56.45	odd	6		224.3.o.d.79.4		12
56.51	odd	6		392.3.k.l.67.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.4	✓	12	56.19	even	6
56.3.k.d.11.5	yes	12	7.5	odd	6
56.3.k.d.51.4	yes	12	7.3	odd	6
56.3.k.d.51.5	yes	12	56.3	even	6
224.3.o.d.79.3		12	28.3	even	6
224.3.o.d.79.4		12	56.45	odd	6
224.3.o.d.207.3		12	56.5	odd	6
224.3.o.d.207.4		12	28.19	even	6
392.3.g.i.99.1		6	8.3	odd	2	inner
392.3.g.i.99.2		6	1.1	even	1	trivial
392.3.g.j.99.1		6	56.27	even	2
392.3.g.j.99.2		6	7.6	odd	2
392.3.k.l.67.4		12	56.51	odd	6
392.3.k.l.67.5		12	7.2	even	3
392.3.k.l.275.4		12	7.4	even	3
392.3.k.l.275.5		12	56.11	odd	6
1568.3.g.j.687.3		6	56.13	odd	2
1568.3.g.j.687.4		6	28.27	even	2
1568.3.g.l.687.3		6	4.3	odd	2
1568.3.g.l.687.4		6	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88766 + 0.660851i) q^{2} -1.64878 q^{3} +(3.12655 - 2.49493i) q^{4} -4.56111i q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} -6.28154 q^{9} +O(q^{10})\)	\(q+(-1.88766 + 0.660851i) q^{2} -1.64878 q^{3} +(3.12655 - 2.49493i) q^{4} -4.56111i q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} -6.28154 q^{9} +(3.01422 + 8.60985i) q^{10} -12.3797 q^{11} +(-5.15498 + 4.11358i) q^{12} +18.3741i q^{13} +7.52026i q^{15} +(3.55066 - 15.6011i) q^{16} +13.0284 q^{17} +(11.8574 - 4.15116i) q^{18} +3.02524 q^{19} +(-11.3797 - 14.2606i) q^{20} +(23.3686 - 8.18111i) q^{22} -30.3237i q^{23} +(7.01242 - 11.1717i) q^{24} +4.19624 q^{25} +(-12.1426 - 34.6842i) q^{26} +25.1958 q^{27} +22.7701i q^{29} +(-4.96977 - 14.1957i) q^{30} +22.5608i q^{31} +(3.60752 + 31.7960i) q^{32} +20.4113 q^{33} +(-24.5933 + 8.60985i) q^{34} +(-19.6396 + 15.6720i) q^{36} +13.7797i q^{37} +(-5.71063 + 1.99923i) q^{38} -30.2948i q^{39} +(30.9051 + 19.3989i) q^{40} +60.5026 q^{41} +39.0188 q^{43} +(-38.7056 + 30.8864i) q^{44} +28.6508i q^{45} +(20.0395 + 57.2410i) q^{46} +20.3360i q^{47} +(-5.85424 + 25.7226i) q^{48} +(-7.92109 + 2.77309i) q^{50} -21.4810 q^{51} +(45.8422 + 57.4477i) q^{52} -4.76596i q^{53} +(-47.5613 + 16.6507i) q^{54} +56.4650i q^{55} -4.98794 q^{57} +(-15.0476 - 42.9823i) q^{58} -11.7377 q^{59} +(18.7625 + 23.5125i) q^{60} +108.904i q^{61} +(-14.9093 - 42.5872i) q^{62} +(-27.8222 - 57.6361i) q^{64} +83.8066 q^{65} +(-38.5296 + 13.4888i) q^{66} -79.1994 q^{67} +(40.7341 - 32.5050i) q^{68} +49.9970i q^{69} -12.9952i q^{71} +(26.7160 - 42.5623i) q^{72} +98.5819 q^{73} +(-9.10631 - 26.0114i) q^{74} -6.91866 q^{75} +(9.45857 - 7.54776i) q^{76} +(20.0204 + 57.1865i) q^{78} +131.225i q^{79} +(-71.1582 - 16.1950i) q^{80} +14.9915 q^{81} +(-114.209 + 39.9832i) q^{82} -28.3732 q^{83} -59.4242i q^{85} +(-73.6544 + 25.7856i) q^{86} -37.5428i q^{87} +(52.6520 - 83.8817i) q^{88} +157.418 q^{89} +(-18.9339 - 54.0831i) q^{90} +(-75.6555 - 94.8087i) q^{92} -37.1977i q^{93} +(-13.4391 - 38.3876i) q^{94} -13.7985i q^{95} +(-5.94800 - 52.4245i) q^{96} +39.6175 q^{97} +77.7633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 28 q^{6} + 4 q^{8} + 40 q^{9} - 6 q^{10} - 30 q^{11} + 32 q^{12} - 16 q^{16} + 30 q^{17} + 16 q^{18} + 78 q^{19} - 24 q^{20} + 12 q^{22} - 76 q^{24} + 92 q^{25} - 128 q^{26} - 78 q^{27} + 16 q^{30} - 112 q^{32} - 78 q^{33} - 38 q^{34} - 124 q^{36} + 80 q^{38} + 44 q^{40} + 116 q^{41} - 100 q^{43} - 132 q^{44} + 156 q^{46} - 88 q^{48} + 24 q^{50} - 10 q^{51} + 132 q^{52} - 36 q^{54} + 166 q^{57} - 4 q^{58} - 110 q^{59} - 84 q^{60} + 48 q^{62} - 80 q^{64} + 32 q^{65} - 138 q^{66} - 434 q^{67} + 96 q^{68} + 328 q^{72} + 102 q^{73} + 34 q^{74} - 60 q^{75} + 84 q^{76} + 360 q^{78} - 256 q^{80} + 82 q^{81} - 24 q^{82} + 268 q^{83} - 240 q^{86} + 204 q^{88} + 214 q^{89} - 220 q^{90} + 80 q^{92} - 16 q^{94} + 48 q^{96} + 76 q^{97} + 252 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 28 * q^6 + 4 * q^8 + 40 * q^9 - 6 * q^10 - 30 * q^11 + 32 * q^12 - 16 * q^16 + 30 * q^17 + 16 * q^18 + 78 * q^19 - 24 * q^20 + 12 * q^22 - 76 * q^24 + 92 * q^25 - 128 * q^26 - 78 * q^27 + 16 * q^30 - 112 * q^32 - 78 * q^33 - 38 * q^34 - 124 * q^36 + 80 * q^38 + 44 * q^40 + 116 * q^41 - 100 * q^43 - 132 * q^44 + 156 * q^46 - 88 * q^48 + 24 * q^50 - 10 * q^51 + 132 * q^52 - 36 * q^54 + 166 * q^57 - 4 * q^58 - 110 * q^59 - 84 * q^60 + 48 * q^62 - 80 * q^64 + 32 * q^65 - 138 * q^66 - 434 * q^67 + 96 * q^68 + 328 * q^72 + 102 * q^73 + 34 * q^74 - 60 * q^75 + 84 * q^76 + 360 * q^78 - 256 * q^80 + 82 * q^81 - 24 * q^82 + 268 * q^83 - 240 * q^86 + 204 * q^88 + 214 * q^89 - 220 * q^90 + 80 * q^92 - 16 * q^94 + 48 * q^96 + 76 * q^97 + 252 * q^99

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