LMFDB - Embedded newform 1638.2.x.d.307.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(307,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1638.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.x (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7442857984.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.4
Root			$-3.73923i$ of defining polynomial
Character	$\chi$	$=$	1638.307
Dual form			1638.2.x.d.811.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.80230 - 1.80230i) q^{5} +(1.93693 - 1.80230i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.80230 - 1.80230i) q^{5} +(1.93693 - 1.80230i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.54884 q^{10} +(-0.936931 + 0.936931i) q^{11} +(2.00000 + 3.00000i) q^{13} +(2.64404 + 0.0951965i) q^{14} -1.00000 q^{16} +0.496594 q^{17} +(3.07156 - 3.07156i) q^{19} +(1.80230 + 1.80230i) q^{20} -1.32502 q^{22} +7.37727i q^{23} -1.49659i q^{25} +(-0.707107 + 3.53553i) q^{26} +(1.80230 + 1.93693i) q^{28} -7.25113 q^{29} +(5.73923 - 5.73923i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.351145 + 0.351145i) q^{34} +(0.242641 - 6.73923i) q^{35} +(3.54154 - 3.54154i) q^{37} +4.34384 q^{38} +2.54884i q^{40} +(6.11650 - 6.11650i) q^{41} -6.85574i q^{43} +(-0.936931 - 0.936931i) q^{44} +(-5.21652 + 5.21652i) q^{46} +(5.87386 + 5.87386i) q^{47} +(0.503406 - 6.98188i) q^{49} +(1.05825 - 1.05825i) q^{50} +(-3.00000 + 2.00000i) q^{52} +4.26926 q^{53} +3.37727i q^{55} +(-0.0951965 + 2.64404i) q^{56} +(-5.12732 - 5.12732i) q^{58} +(1.37727 + 1.37727i) q^{59} +0.496594i q^{61} +8.11650 q^{62} -1.00000i q^{64} +(9.01152 + 1.80230i) q^{65} +(9.11650 + 9.11650i) q^{67} +0.496594i q^{68} +(4.93693 - 4.59379i) q^{70} +(-11.3773 - 11.3773i) q^{71} +(3.54154 + 3.54154i) q^{73} +5.00849 q^{74} +(3.07156 + 3.07156i) q^{76} +(-0.126137 + 3.50341i) q^{77} -13.1499 q^{79} +(-1.80230 + 1.80230i) q^{80} +8.65004 q^{82} +(-7.87386 + 7.87386i) q^{83} +(0.895013 - 0.895013i) q^{85} +(4.84774 - 4.84774i) q^{86} -1.32502i q^{88} +(-10.2177 - 10.2177i) q^{89} +(9.28077 + 2.20619i) q^{91} -7.37727 q^{92} +8.30690i q^{94} -11.0718i q^{95} +(9.46034 - 9.46034i) q^{97} +(5.29289 - 4.58097i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^5	$ 8 q + 4 q^{5} + 4 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{16} + 12 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} + 4 q^{28} + 12 q^{29} + 20 q^{31} - 24 q^{34} - 32 q^{35} - 8 q^{37} - 12 q^{38} - 16 q^{41} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 4 q^{49} - 24 q^{50} - 24 q^{52} + 24 q^{53} + 4 q^{56} - 16 q^{58} - 28 q^{59} + 20 q^{65} + 8 q^{67} + 24 q^{70} - 52 q^{71} - 8 q^{73} + 4 q^{74} + 4 q^{76} - 32 q^{77} - 48 q^{79} - 4 q^{80} + 40 q^{82} - 32 q^{83} + 20 q^{85} + 20 q^{86} - 4 q^{89} + 12 q^{91} - 20 q^{92} - 36 q^{97} + 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^5 + 4 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^16 + 12 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 + 4 * q^28 + 12 * q^29 + 20 * q^31 - 24 * q^34 - 32 * q^35 - 8 * q^37 - 12 * q^38 - 16 * q^41 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 4 * q^49 - 24 * q^50 - 24 * q^52 + 24 * q^53 + 4 * q^56 - 16 * q^58 - 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 - 8 * q^73 + 4 * q^74 + 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 40 * q^82 - 32 * q^83 + 20 * q^85 + 20 * q^86 - 4 * q^89 + 12 * q^91 - 20 * q^92 - 36 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	1.80230	−	1.80230i	0.806015	−	0.806015i	−0.178014	−	0.984028i	$-0.556967\pi$
$5$	1.80230	−	1.80230i	0.806015	−	0.806015i	0.984028	+	0.178014i	$0.0569671\pi$
$6$		0			0
$7$	1.93693	−	1.80230i	0.732091	−	0.681207i
$7$	1.93693	−	1.80230i	0.732091	−	0.681207i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	2.54884			0.806015
$11$	−0.936931	+	0.936931i	−0.282495	+	0.282495i	−0.834103	−	0.551608i	$-0.814014\pi$
$11$	−0.936931	+	0.936931i	−0.282495	+	0.282495i	0.551608	+	0.834103i	$0.314014\pi$
$12$		0			0
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$	2.64404	+	0.0951965i	0.706649	+	0.0254423i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.496594			0.120442			0.0602209	−	0.998185i	$-0.480820\pi$
$17$	0.496594			0.120442			0.0602209	+	0.998185i	$0.480820\pi$
$18$		0			0
$19$	3.07156	−	3.07156i	0.704664	−	0.704664i	−0.260744	−	0.965408i	$-0.583968\pi$
$19$	3.07156	−	3.07156i	0.704664	−	0.704664i	0.965408	+	0.260744i	$0.0839678\pi$
$20$	1.80230	+	1.80230i	0.403007	+	0.403007i
$21$		0			0
$22$	−1.32502			−0.282495
$23$			7.37727i			1.53827i	0.639088	+	0.769133i	$0.279312\pi$
$23$			7.37727i			1.53827i	−0.639088	+	0.769133i	$0.720688\pi$
$24$		0			0
$25$		−	1.49659i		−	0.299319i
$26$	−0.707107	+	3.53553i	−0.138675	+	0.693375i
$27$		0			0
$28$	1.80230	+	1.93693i	0.340603	+	0.366046i
$29$	−7.25113			−1.34650			−0.673251	−	0.739414i	$-0.735103\pi$
$29$	−7.25113			−1.34650			−0.673251	+	0.739414i	$0.735103\pi$
$30$		0			0
$31$	5.73923	−	5.73923i	1.03080	−	1.03080i	0.0312865	−	0.999510i	$-0.490040\pi$
$31$	5.73923	−	5.73923i	1.03080	−	1.03080i	0.999510	−	0.0312865i	$-0.00996043\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	0.351145	+	0.351145i	0.0602209	+	0.0602209i
$35$	0.242641	−	6.73923i	0.0410138	−	1.13914i
$36$		0			0
$37$	3.54154	−	3.54154i	0.582225	−	0.582225i	−0.353289	−	0.935514i	$-0.614937\pi$
$37$	3.54154	−	3.54154i	0.582225	−	0.582225i	0.935514	+	0.353289i	$0.114937\pi$
$38$	4.34384			0.704664
$39$		0			0
$40$			2.54884i			0.403007i
$41$	6.11650	−	6.11650i	0.955237	−	0.955237i	−0.0438029	−	0.999040i	$-0.513947\pi$
$41$	6.11650	−	6.11650i	0.955237	−	0.955237i	0.999040	+	0.0438029i	$0.0139473\pi$
$42$		0			0
$43$		−	6.85574i		−	1.04549i	−0.852489	−	0.522745i	$-0.824908\pi$
$43$		−	6.85574i		−	1.04549i	0.852489	−	0.522745i	$-0.175092\pi$
$44$	−0.936931	−	0.936931i	−0.141248	−	0.141248i
$45$		0			0
$46$	−5.21652	+	5.21652i	−0.769133	+	0.769133i
$47$	5.87386	+	5.87386i	0.856791	+	0.856791i	0.990959	−	0.134168i	$-0.0428361\pi$
$47$	5.87386	+	5.87386i	0.856791	+	0.856791i	−0.134168	+	0.990959i	$0.542836\pi$
$48$		0			0
$49$	0.503406	−	6.98188i	0.0719152	−	0.997411i
$50$	1.05825	−	1.05825i	0.149659	−	0.149659i
$51$		0			0
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$	4.26926			0.586427			0.293214	−	0.956047i	$-0.405275\pi$
$53$	4.26926			0.586427			0.293214	+	0.956047i	$0.405275\pi$
$54$		0			0
$55$			3.37727i			0.455391i
$56$	−0.0951965	+	2.64404i	−0.0127212	+	0.353324i
$57$		0			0
$58$	−5.12732	−	5.12732i	−0.673251	−	0.673251i
$59$	1.37727	+	1.37727i	0.179305	+	0.179305i	0.791053	−	0.611748i	$-0.209533\pi$
$59$	1.37727	+	1.37727i	0.179305	+	0.179305i	−0.611748	+	0.791053i	$0.709533\pi$
$60$		0			0
$61$			0.496594i			0.0635823i	0.999495	+	0.0317912i	$0.0101211\pi$
$61$			0.496594i			0.0635823i	−0.999495	+	0.0317912i	$0.989879\pi$
$62$	8.11650			1.03080
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	9.01152	+	1.80230i	1.11774	+	0.223548i
$66$		0			0
$67$	9.11650	+	9.11650i	1.11376	+	1.11376i	0.992638	+	0.121120i	$0.0386487\pi$
$67$	9.11650	+	9.11650i	1.11376	+	1.11376i	0.121120	+	0.992638i	$0.461351\pi$
$68$			0.496594i			0.0602209i
$69$		0			0
$70$	4.93693	−	4.59379i	0.590076	−	0.549062i
$71$	−11.3773	−	11.3773i	−1.35023	−	1.35023i	−0.885396	−	0.464837i	$-0.846113\pi$
$71$	−11.3773	−	11.3773i	−1.35023	−	1.35023i	−0.464837	−	0.885396i	$-0.653887\pi$
$72$		0			0
$73$	3.54154	+	3.54154i	0.414506	+	0.414506i	0.883305	−	0.468799i	$-0.155313\pi$
$73$	3.54154	+	3.54154i	0.414506	+	0.414506i	−0.468799	+	0.883305i	$0.655313\pi$
$74$	5.00849			0.582225
$75$		0			0
$76$	3.07156	+	3.07156i	0.352332	+	0.352332i
$77$	−0.126137	+	3.50341i	−0.0143747	+	0.399250i
$78$		0			0
$79$	−13.1499			−1.47948			−0.739741	−	0.672891i	$-0.765052\pi$
$79$	−13.1499			−1.47948			−0.739741	+	0.672891i	$0.765052\pi$
$80$	−1.80230	+	1.80230i	−0.201504	+	0.201504i
$81$		0			0
$82$	8.65004			0.955237
$83$	−7.87386	+	7.87386i	−0.864269	+	0.864269i	−0.991831	−	0.127562i	$-0.959285\pi$
$83$	−7.87386	+	7.87386i	−0.864269	+	0.864269i	0.127562	+	0.991831i	$0.459285\pi$
$84$		0			0
$85$	0.895013	−	0.895013i	0.0970778	−	0.0970778i
$86$	4.84774	−	4.84774i	0.522745	−	0.522745i
$87$		0			0
$88$		−	1.32502i		−	0.141248i
$89$	−10.2177	−	10.2177i	−1.08307	−	1.08307i	−0.996221	−	0.0868533i	$-0.972319\pi$
$89$	−10.2177	−	10.2177i	−1.08307	−	1.08307i	−0.0868533	−	0.996221i	$-0.527681\pi$
$90$		0			0
$91$	9.28077	+	2.20619i	0.972889	+	0.231271i
$92$	−7.37727			−0.769133
$93$		0			0
$94$			8.30690i			0.856791i
$95$		−	11.0718i		−	1.13594i
$96$		0			0
$97$	9.46034	−	9.46034i	0.960552	−	0.960552i	−0.0386985	−	0.999251i	$-0.512321\pi$
$97$	9.46034	−	9.46034i	0.960552	−	0.960552i	0.999251	+	0.0386985i	$0.0123212\pi$
$98$	5.29289	−	4.58097i	0.534663	−	0.462748i
$99$		0			0
$100$	1.49659			0.149659
$101$	4.66465			0.464150			0.232075	−	0.972698i	$-0.425449\pi$
$101$	4.66465			0.464150			0.232075	+	0.972698i	$0.425449\pi$
$102$		0			0
$103$	−18.5865			−1.83138			−0.915690	−	0.401885i	$-0.868355\pi$
$103$	−18.5865			−1.83138			−0.915690	+	0.401885i	$0.868355\pi$
$104$	−3.53553	−	0.707107i	−0.346688	−	0.0693375i
$105$		0			0
$106$	3.01882	+	3.01882i	0.293214	+	0.293214i
$107$	−6.95694			−0.672553			−0.336276	−	0.941763i	$-0.609168\pi$
$107$	−6.95694			−0.672553			−0.336276	+	0.941763i	$0.609168\pi$
$108$		0			0
$109$	2.94374	+	2.94374i	0.281959	+	0.281959i	0.833890	−	0.551931i	$-0.186109\pi$
$109$	2.94374	+	2.94374i	0.281959	+	0.281959i	−0.551931	+	0.833890i	$0.686109\pi$
$110$	−2.38809	+	2.38809i	−0.227695	+	0.227695i
$111$		0			0
$112$	−1.93693	+	1.80230i	−0.183023	+	0.170302i
$113$	2.93996			0.276568			0.138284	−	0.990393i	$-0.455841\pi$
$113$	2.93996			0.276568			0.138284	+	0.990393i	$0.455841\pi$
$114$		0			0
$115$	13.2961	+	13.2961i	1.23987	+	1.23987i
$116$		−	7.25113i		−	0.673251i
$117$		0			0
$118$			1.94775i			0.179305i
$119$	0.961868	−	0.895013i	0.0881743	−	0.0820457i
$120$		0			0
$121$			9.24432i			0.840393i
$122$	−0.351145	+	0.351145i	−0.0317912	+	0.0317912i
$123$		0			0
$124$	5.73923	+	5.73923i	0.515398	+	0.515398i
$125$	6.31420	+	6.31420i	0.564759	+	0.564759i
$126$		0			0
$127$			19.8376i			1.76030i	0.474692	+	0.880152i	$0.342559\pi$
$127$			19.8376i			1.76030i	−0.474692	+	0.880152i	$0.657441\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	5.09768	+	7.64653i	0.447096	+	0.670645i
$131$			5.10801i			0.446289i	0.974785	+	0.223145i	$0.0716322\pi$
$131$			5.10801i			0.446289i	−0.974785	+	0.223145i	$0.928368\pi$
$132$		0			0
$133$	0.413518	−	11.4853i	0.0358566	−	0.995900i
$134$			12.8927i			1.11376i
$135$		0			0
$136$	−0.351145	+	0.351145i	−0.0301104	+	0.0301104i
$137$	−3.80230	+	3.80230i	−0.324853	+	0.324853i	−0.850625	−	0.525773i	$-0.823776\pi$
$137$	−3.80230	+	3.80230i	−0.324853	+	0.324853i	0.525773	+	0.850625i	$0.323776\pi$
$138$		0			0
$139$			2.93996i			0.249364i	0.992197	+	0.124682i	$0.0397910\pi$
$139$			2.93996i			0.249364i	−0.992197	+	0.124682i	$0.960209\pi$
$140$	6.73923	+	0.242641i	0.569569	+	0.0205069i
$141$		0			0
$142$		−	16.0899i		−	1.35023i
$143$	−4.68466	−	0.936931i	−0.391751	−	0.0783501i
$144$		0			0
$145$	−13.0687	+	13.0687i	−1.08530	+	1.08530i
$146$			5.00849i			0.414506i
$147$		0			0
$148$	3.54154	+	3.54154i	0.291113	+	0.291113i
$149$	1.74605	+	1.74605i	0.143042	+	0.143042i	0.775001	−	0.631960i	$-0.217749\pi$
$149$	1.74605	+	1.74605i	0.143042	+	0.143042i	−0.631960	+	0.775001i	$0.717749\pi$
$150$		0			0
$151$	−6.55003	+	6.55003i	−0.533034	+	0.533034i	−0.921474	−	0.388440i	$-0.873014\pi$
$151$	−6.55003	+	6.55003i	−0.533034	+	0.533034i	0.388440	+	0.921474i	$0.373014\pi$
$152$			4.34384i			0.352332i
$153$		0			0
$154$	−2.56647	+	2.38809i	−0.206812	+	0.192438i
$155$		−	20.6877i		−	1.66167i
$156$		0			0
$157$		−	1.70581i		−	0.136138i	−0.997681	−	0.0680691i	$-0.978316\pi$
$157$		−	1.70581i		−	0.136138i	0.997681	−	0.0680691i	$-0.0216838\pi$
$158$	−9.29841	−	9.29841i	−0.739741	−	0.739741i
$159$		0			0
$160$	−2.54884			−0.201504
$161$	13.2961	+	14.2893i	1.04788	+	1.12615i
$162$		0			0
$163$	−4.23583	+	4.23583i	−0.331776	+	0.331776i	−0.853261	−	0.521485i	$-0.825378\pi$
$163$	−4.23583	+	4.23583i	−0.331776	+	0.331776i	0.521485	+	0.853261i	$0.325378\pi$
$164$	6.11650	+	6.11650i	0.477619	+	0.477619i
$165$		0			0
$166$	−11.1353			−0.864269
$167$	−8.02001	−	8.02001i	−0.620607	−	0.620607i	0.325080	−	0.945687i	$-0.394609\pi$
$167$	−8.02001	−	8.02001i	−0.620607	−	0.620607i	−0.945687	+	0.325080i	$0.894609\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	1.26574			0.0970778
$171$		0			0
$172$	6.85574			0.522745
$173$	−4.21603			−0.320538			−0.160269	−	0.987073i	$-0.551236\pi$
$173$	−4.21603			−0.320538			−0.160269	+	0.987073i	$0.551236\pi$
$174$		0			0
$175$	−2.69732	−	2.89880i	−0.203898	−	0.219129i
$176$	0.936931	−	0.936931i	0.0706239	−	0.0706239i
$177$		0			0
$178$		−	14.4500i		−	1.08307i
$179$		−	5.33535i		−	0.398783i	−0.979920	−	0.199391i	$-0.936103\pi$
$179$		−	5.33535i		−	0.398783i	0.979920	−	0.199391i	$-0.0638965\pi$
$180$		0			0
$181$	1.79760			0.133615			0.0668073	−	0.997766i	$-0.478719\pi$
$181$	1.79760			0.133615			0.0668073	+	0.997766i	$0.478719\pi$
$182$	5.00249	+	8.12251i	0.370809	+	0.602080i
$183$		0			0
$184$	−5.21652	−	5.21652i	−0.384567	−	0.384567i
$185$		−	12.7659i		−	0.938564i
$186$		0			0
$187$	−0.465274	+	0.465274i	−0.0340242	+	0.0340242i
$188$	−5.87386	+	5.87386i	−0.428395	+	0.428395i
$189$		0			0
$190$	7.82892	−	7.82892i	0.567969	−	0.567969i
$191$	18.7889			1.35952			0.679758	−	0.733437i	$-0.262085\pi$
$191$	18.7889			1.35952			0.679758	+	0.733437i	$0.262085\pi$
$192$		0			0
$193$	1.37046	−	1.37046i	0.0986476	−	0.0986476i	−0.656061	−	0.754708i	$-0.727778\pi$
$193$	1.37046	−	1.37046i	0.0986476	−	0.0986476i	0.754708	+	0.656061i	$0.227778\pi$
$194$	13.3789			0.960552
$195$		0			0
$196$	6.98188	+	0.503406i	0.498705	+	0.0359576i
$197$	2.86537	+	2.86537i	0.204149	+	0.204149i	0.801775	−	0.597626i	$-0.203889\pi$
$197$	2.86537	+	2.86537i	0.204149	+	0.204149i	−0.597626	+	0.801775i	$0.703889\pi$
$198$		0			0
$199$	−14.0650			−0.997038			−0.498519	−	0.866879i	$-0.666123\pi$
$199$	−14.0650			−0.997038			−0.498519	+	0.866879i	$0.666123\pi$
$200$	1.05825	+	1.05825i	0.0748297	+	0.0748297i
$201$		0			0
$202$	3.29841	+	3.29841i	0.232075	+	0.232075i
$203$	−14.0449	+	13.0687i	−0.985762	+	0.917246i
$204$		0			0
$205$		−	22.0476i		−	1.53987i
$206$	−13.1426	−	13.1426i	−0.915690	−	0.915690i
$207$		0			0
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$			5.75568i			0.398129i
$210$		0			0
$211$	−14.8557			−1.02271			−0.511356	−	0.859369i	$-0.670856\pi$
$211$	−14.8557			−1.02271			−0.511356	+	0.859369i	$0.670856\pi$
$212$			4.26926i			0.293214i
$213$		0			0
$214$	−4.91930	−	4.91930i	−0.336276	−	0.336276i
$215$	−12.3561	−	12.3561i	−0.842680	−	0.842680i
$216$		0			0
$217$	0.772662	−	21.4603i	0.0524517	−	1.45682i
$218$			4.16308i			0.281959i
$219$		0			0
$220$	−3.37727			−0.227695
$221$	0.993188	+	1.48978i	0.0668090	+	0.100214i
$222$		0			0
$223$	6.24945	−	6.24945i	0.418494	−	0.418494i	−0.466190	−	0.884685i	$-0.654374\pi$
$223$	6.24945	−	6.24945i	0.418494	−	0.418494i	0.884685	+	0.466190i	$0.154374\pi$
$224$	−2.64404	−	0.0951965i	−0.176662	−	0.00636058i
$225$		0			0
$226$	2.07886	+	2.07886i	0.138284	+	0.138284i
$227$	5.50341	−	5.50341i	0.365274	−	0.365274i	−0.500476	−	0.865750i	$-0.666842\pi$
$227$	5.50341	−	5.50341i	0.365274	−	0.365274i	0.865750	+	0.500476i	$0.166842\pi$
$228$		0			0
$229$	−2.50341	−	2.50341i	−0.165430	−	0.165430i	0.619537	−	0.784967i	$-0.287320\pi$
$229$	−2.50341	−	2.50341i	−0.165430	−	0.165430i	−0.784967	+	0.619537i	$0.787320\pi$
$230$			18.8035i			1.23987i
$231$		0			0
$232$	5.12732	−	5.12732i	0.336625	−	0.336625i
$233$			16.5615i			1.08498i	0.840061	+	0.542491i	$0.182519\pi$
$233$			16.5615i			1.08498i	−0.840061	+	0.542491i	$0.817481\pi$
$234$		0			0
$235$	21.1730			1.38117
$236$	−1.37727	+	1.37727i	−0.0896526	+	0.0896526i
$237$		0			0
$238$	1.31301	+	0.0472740i	0.0851100	+	0.00306432i
$239$	2.41238	+	2.41238i	0.156044	+	0.156044i	0.780811	−	0.624767i	$-0.214806\pi$
$239$	2.41238	+	2.41238i	0.156044	+	0.156044i	−0.624767	+	0.780811i	$0.714806\pi$
$240$		0			0
$241$	−8.37727	−	8.37727i	−0.539627	−	0.539627i	0.383792	−	0.923419i	$-0.374618\pi$
$241$	−8.37727	−	8.37727i	−0.539627	−	0.539627i	−0.923419	+	0.383792i	$0.874618\pi$
$242$	−6.53672	+	6.53672i	−0.420196	+	0.420196i
$243$		0			0
$244$	−0.496594			−0.0317912
$245$	−11.6762	−	13.4907i	−0.745963	−	0.861892i
$246$		0			0
$247$	15.3578	+	3.07156i	0.977193	+	0.195439i
$248$			8.11650i			0.515398i
$249$		0			0
$250$			8.92963i			0.564759i
$251$	−26.8727			−1.69619			−0.848096	−	0.529843i	$-0.822251\pi$
$251$	−26.8727			−1.69619			−0.848096	+	0.529843i	$0.822251\pi$
$252$		0			0
$253$	−6.91199	−	6.91199i	−0.434553	−	0.434553i
$254$	−14.0273	+	14.0273i	−0.880152	+	0.880152i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−7.98302			−0.497967			−0.248984	−	0.968508i	$-0.580096\pi$
$257$	−7.98302			−0.497967			−0.248984	+	0.968508i	$0.580096\pi$
$258$		0			0
$259$	0.476791	−	13.2426i	0.0296263	−	0.822858i
$260$	−1.80230	+	9.01152i	−0.111774	+	0.558871i
$261$		0			0
$262$	−3.61191	+	3.61191i	−0.223145	+	0.223145i
$263$	2.47166			0.152409			0.0762044	−	0.997092i	$-0.475720\pi$
$263$	2.47166			0.152409			0.0762044	+	0.997092i	$0.475720\pi$
$264$		0			0
$265$	7.69449	−	7.69449i	0.472669	−	0.472669i
$266$	8.41372	−	7.82892i	0.515878	−	0.480022i
$267$		0			0
$268$	−9.11650	+	9.11650i	−0.556879	+	0.556879i
$269$		−	5.83761i		−	0.355926i	−0.984037	−	0.177963i	$-0.943049\pi$
$269$		−	5.83761i		−	0.355926i	0.984037	−	0.177963i	$-0.0569507\pi$
$270$		0			0
$271$	−8.57799	−	8.57799i	−0.521076	−	0.521076i	0.396820	−	0.917896i	$-0.370114\pi$
$271$	−8.57799	−	8.57799i	−0.521076	−	0.521076i	−0.917896	+	0.396820i	$0.870114\pi$
$272$	−0.496594			−0.0301104
$273$		0			0
$274$	−5.37727			−0.324853
$275$	1.40221	+	1.40221i	0.0845562	+	0.0845562i
$276$		0			0
$277$		−	2.66465i		−	0.160103i	−0.996791	−	0.0800516i	$-0.974491\pi$
$277$		−	2.66465i		−	0.160103i	0.996791	−	0.0800516i	$-0.0255085\pi$
$278$	−2.07886	+	2.07886i	−0.124682	+	0.124682i
$279$		0			0
$280$	4.59379	+	4.93693i	0.274531	+	0.295038i
$281$	8.09952	−	8.09952i	0.483177	−	0.483177i	−0.422968	−	0.906145i	$-0.639012\pi$
$281$	8.09952	−	8.09952i	0.483177	−	0.483177i	0.906145	+	0.422968i	$0.139012\pi$
$282$		0			0
$283$	−30.2730			−1.79954			−0.899772	−	0.436360i	$-0.856267\pi$
$283$	−30.2730			−1.79954			−0.899772	+	0.436360i	$0.856267\pi$
$284$	11.3773	−	11.3773i	0.675117	−	0.675117i
$285$		0			0
$286$	−2.65004	−	3.97506i	−0.156700	−	0.235050i
$287$	0.823453	−	22.8710i	0.0486069	−	1.35003i
$288$		0			0
$289$	−16.7534			−0.985494
$290$	−18.4820			−1.08530
$291$		0			0
$292$	−3.54154	+	3.54154i	−0.207253	+	0.207253i
$293$	17.9235	+	17.9235i	1.04710	+	1.04710i	0.998834	+	0.0482683i	$0.0153702\pi$
$293$	17.9235	+	17.9235i	1.04710	+	1.04710i	0.0482683	+	0.998834i	$0.484630\pi$
$294$		0			0
$295$	4.96451			0.289045
$296$			5.00849i			0.291113i
$297$		0			0
$298$			2.46928i			0.143042i
$299$	−22.1318	+	14.7545i	−1.27992	+	0.853277i
$300$		0			0
$301$	−12.3561	−	13.2791i	−0.712195	−	0.765394i
$302$	−9.26314			−0.533034
$303$		0			0
$304$	−3.07156	+	3.07156i	−0.176166	+	0.176166i
$305$	0.895013	+	0.895013i	0.0512483	+	0.0512483i
$306$		0			0
$307$	−5.09157	−	5.09157i	−0.290591	−	0.290591i	0.546723	−	0.837314i	$-0.315875\pi$
$307$	−5.09157	−	5.09157i	−0.290591	−	0.290591i	−0.837314	+	0.546723i	$0.815875\pi$
$308$	−3.50341	−	0.126137i	−0.199625	−	0.00718734i
$309$		0			0
$310$	14.6284	−	14.6284i	0.830837	−	0.830837i
$311$	14.0729			0.798001			0.399001	−	0.916951i	$-0.369357\pi$
$311$	14.0729			0.798001			0.399001	+	0.916951i	$0.369357\pi$
$312$		0			0
$313$			28.3059i			1.59994i	0.600037	+	0.799972i	$0.295153\pi$
$313$			28.3059i			1.59994i	−0.600037	+	0.799972i	$0.704847\pi$
$314$	1.20619	−	1.20619i	0.0680691	−	0.0680691i
$315$		0			0
$316$		−	13.1499i		−	0.739741i
$317$	−20.5119	−	20.5119i	−1.15206	−	1.15206i	−0.986138	−	0.165924i	$-0.946939\pi$
$317$	−20.5119	−	20.5119i	−1.15206	−	1.15206i	−0.165924	−	0.986138i	$-0.553061\pi$
$318$		0			0
$319$	6.79381	−	6.79381i	0.380380	−	0.380380i
$320$	−1.80230	−	1.80230i	−0.100752	−	0.100752i
$321$		0			0
$322$	−0.702290	+	19.5058i	−0.0391371	+	1.08701i
$323$	1.52532	−	1.52532i	0.0848709	−	0.0848709i
$324$		0			0
$325$	4.48978	−	2.99319i	0.249048	−	0.166032i
$326$	−5.99037			−0.331776
$327$		0			0
$328$			8.65004i			0.477619i
$329$	21.9638	+	0.790787i	1.21090	+	0.0435975i
$330$		0			0
$331$	−9.65502	−	9.65502i	−0.530688	−	0.530688i	0.390089	−	0.920777i	$-0.372444\pi$
$331$	−9.65502	−	9.65502i	−0.530688	−	0.530688i	−0.920777	+	0.390089i	$0.872444\pi$
$332$	−7.87386	−	7.87386i	−0.432134	−	0.432134i
$333$		0			0
$334$		−	11.3420i		−	0.620607i
$335$	32.8614			1.79541
$336$		0			0
$337$		−	7.25113i		−	0.394994i	−0.980303	−	0.197497i	$-0.936719\pi$
$337$		−	7.25113i		−	0.394994i	0.980303	−	0.197497i	$-0.0632813\pi$
$338$	−12.0208	+	4.94975i	−0.653846	+	0.269231i
$339$		0			0
$340$	0.895013	+	0.895013i	0.0485389	+	0.0485389i
$341$			10.7545i			0.582391i
$342$		0			0
$343$	−11.6084	−	14.4307i	−0.626794	−	0.779185i
$344$	4.84774	+	4.84774i	0.261373	+	0.261373i
$345$		0			0
$346$	−2.98118	−	2.98118i	−0.160269	−	0.160269i
$347$	−29.7647			−1.59785			−0.798927	−	0.601429i	$-0.794598\pi$
$347$	−29.7647			−1.59785			−0.798927	+	0.601429i	$0.794598\pi$
$348$		0			0
$349$	13.1431	+	13.1431i	0.703535	+	0.703535i	0.965168	−	0.261633i	$-0.0842608\pi$
$349$	13.1431	+	13.1431i	0.703535	+	0.703535i	−0.261633	+	0.965168i	$0.584261\pi$
$350$	0.142470	−	3.95705i	0.00761536	−	0.211513i
$351$		0			0
$352$	1.32502			0.0706239
$353$	13.5531	−	13.5531i	0.721356	−	0.721356i	−0.247525	−	0.968881i	$-0.579617\pi$
$353$	13.5531	−	13.5531i	0.721356	−	0.721356i	0.968881	+	0.247525i	$0.0796173\pi$
$354$		0			0
$355$	−41.0106			−2.17662
$356$	10.2177	−	10.2177i	0.541537	−	0.541537i
$357$		0			0
$358$	3.77266	−	3.77266i	0.199391	−	0.199391i
$359$	4.04192	−	4.04192i	0.213324	−	0.213324i	−0.592354	−	0.805678i	$-0.701801\pi$
$359$	4.04192	−	4.04192i	0.213324	−	0.213324i	0.805678	+	0.592354i	$0.201801\pi$
$360$		0			0
$361$			0.131045i			0.00689710i
$362$	1.27109	+	1.27109i	0.0668073	+	0.0668073i
$363$		0			0
$364$	−2.20619	+	9.28077i	−0.115636	+	0.486445i
$365$	12.7659			0.668195
$366$		0			0
$367$		−	4.26926i		−	0.222853i	−0.993773	−	0.111427i	$-0.964458\pi$
$367$		−	4.26926i		−	0.222853i	0.993773	−	0.111427i	$-0.0355420\pi$
$368$		−	7.37727i		−	0.384567i
$369$		0			0
$370$	9.02682	−	9.02682i	0.469282	−	0.469282i
$371$	8.26926	−	7.69449i	0.429318	−	0.399478i
$372$		0			0
$373$	9.67146			0.500769			0.250385	−	0.968146i	$-0.419443\pi$
$373$	9.67146			0.500769			0.250385	+	0.968146i	$0.419443\pi$
$374$	−0.657997			−0.0340242
$375$		0			0
$376$	−8.30690			−0.428395
$377$	−14.5023	−	21.7534i	−0.746905	−	1.12036i
$378$		0			0
$379$	−0.746047	−	0.746047i	−0.0383218	−	0.0383218i	0.687686	−	0.726008i	$-0.258627\pi$
$379$	−0.746047	−	0.746047i	−0.0383218	−	0.0383218i	−0.726008	+	0.687686i	$0.758627\pi$
$380$	11.0718			0.567969
$381$		0			0
$382$	13.2857	+	13.2857i	0.679758	+	0.679758i
$383$	−18.1461	+	18.1461i	−0.927225	+	0.927225i	−0.997526	−	0.0703012i	$-0.977604\pi$
$383$	−18.1461	+	18.1461i	−0.927225	+	0.927225i	0.0703012	+	0.997526i	$0.477604\pi$
$384$		0			0
$385$	6.08686	+	6.54154i	0.310215	+	0.333388i
$386$	1.93812			0.0986476
$387$		0			0
$388$	9.46034	+	9.46034i	0.480276	+	0.480276i
$389$			6.73756i			0.341608i	0.985305	+	0.170804i	$0.0546364\pi$
$389$			6.73756i			0.341608i	−0.985305	+	0.170804i	$0.945364\pi$
$390$		0			0
$391$			3.66351i			0.185271i
$392$	4.58097	+	5.29289i	0.231374	+	0.267331i
$393$		0			0
$394$			4.05225i			0.204149i
$395$	−23.7002	+	23.7002i	−1.19248	+	1.19248i
$396$		0			0
$397$	−21.7715	−	21.7715i	−1.09268	−	1.09268i	−0.995241	−	0.0974398i	$-0.968935\pi$
$397$	−21.7715	−	21.7715i	−1.09268	−	1.09268i	−0.0974398	−	0.995241i	$-0.531065\pi$
$398$	−9.94542	−	9.94542i	−0.498519	−	0.498519i
$399$		0			0
$400$			1.49659i			0.0748297i
$401$	−16.5119	+	16.5119i	−0.824565	+	0.824565i	−0.986759	−	0.162194i	$-0.948143\pi$
$401$	−16.5119	+	16.5119i	−0.824565	+	0.824565i	0.162194	+	0.986759i	$0.448143\pi$
$402$		0			0
$403$	28.6962	+	5.73923i	1.42946	+	0.285892i
$404$			4.66465i			0.232075i
$405$		0			0
$406$	−19.1723	−	0.690282i	−0.951504	−	0.0342581i
$407$			6.63636i			0.328952i
$408$		0			0
$409$	4.00379	−	4.00379i	0.197975	−	0.197975i	−0.601157	−	0.799131i	$-0.705293\pi$
$409$	4.00379	−	4.00379i	0.197975	−	0.197975i	0.799131	+	0.601157i	$0.205293\pi$
$410$	15.5900	−	15.5900i	0.769935	−	0.769935i
$411$		0			0
$412$		−	18.5865i		−	0.915690i
$413$	5.14993	+	0.185419i	0.253412	+	0.00912388i
$414$		0			0
$415$			28.3822i			1.39323i
$416$	0.707107	−	3.53553i	0.0346688	−	0.173344i
$417$		0			0
$418$	−4.06988	+	4.06988i	−0.199064	+	0.199064i
$419$			15.1782i			0.741505i	0.928732	+	0.370752i	$0.120900\pi$
$419$			15.1782i			0.741505i	−0.928732	+	0.370752i	$0.879100\pi$
$420$		0			0
$421$	11.0650	+	11.0650i	0.539273	+	0.539273i	0.923315	−	0.384043i	$-0.125468\pi$
$421$	11.0650	+	11.0650i	0.539273	+	0.539273i	−0.384043	+	0.923315i	$0.625468\pi$
$422$	−10.5046	−	10.5046i	−0.511356	−	0.511356i
$423$		0			0
$424$	−3.01882	+	3.01882i	−0.146607	+	0.146607i
$425$		−	0.743199i		−	0.0360505i
$426$		0			0
$427$	0.895013	+	0.961868i	0.0433127	+	0.0465481i
$428$		−	6.95694i		−	0.336276i
$429$		0			0
$430$		−	17.4742i		−	0.842680i
$431$	−9.60461	−	9.60461i	−0.462638	−	0.462638i	0.436881	−	0.899519i	$-0.356083\pi$
$431$	−9.60461	−	9.60461i	−0.462638	−	0.462638i	−0.899519	+	0.436881i	$0.856083\pi$
$432$		0			0
$433$	−6.52489			−0.313566			−0.156783	−	0.987633i	$-0.550112\pi$
$433$	−6.52489			−0.313566			−0.156783	+	0.987633i	$0.550112\pi$
$434$	15.7211	−	14.6284i	0.754637	−	0.702186i
$435$		0			0
$436$	−2.94374	+	2.94374i	−0.140980	+	0.140980i
$437$	22.6597	+	22.6597i	1.08396	+	1.08396i
$438$		0			0
$439$	1.61592			0.0771236			0.0385618	−	0.999256i	$-0.487722\pi$
$439$	1.61592			0.0771236			0.0385618	+	0.999256i	$0.487722\pi$
$440$	−2.38809	−	2.38809i	−0.113848	−	0.113848i
$441$		0			0
$442$	−0.351145	+	1.75572i	−0.0167023	+	0.0835113i
$443$	19.0408			0.904655			0.452327	−	0.891852i	$-0.350594\pi$
$443$	19.0408			0.904655			0.452327	+	0.891852i	$0.350594\pi$
$444$		0			0
$445$	−36.8308			−1.74595
$446$	8.83806			0.418494
$447$		0			0
$448$	−1.80230	−	1.93693i	−0.0851508	−	0.0915114i
$449$	10.3408	−	10.3408i	0.488013	−	0.488013i	−0.419666	−	0.907679i	$-0.637853\pi$
$449$	10.3408	−	10.3408i	0.488013	−	0.488013i	0.907679	+	0.419666i	$0.137853\pi$
$450$		0			0
$451$			11.4615i			0.539700i
$452$			2.93996i			0.138284i
$453$		0			0
$454$	7.78299			0.365274
$455$	20.7030	−	12.7505i	0.970571	−	0.597755i
$456$		0			0
$457$	20.0718	+	20.0718i	0.938917	+	0.938917i	0.998239	−	0.0593215i	$-0.0188937\pi$
$457$	20.0718	+	20.0718i	0.938917	+	0.938917i	−0.0593215	+	0.998239i	$0.518894\pi$
$458$		−	3.54035i		−	0.165430i
$459$		0			0
$460$	−13.2961	+	13.2961i	−0.619933	+	0.619933i
$461$	13.4069	−	13.4069i	0.624422	−	0.624422i	−0.322237	−	0.946659i	$-0.604435\pi$
$461$	13.4069	−	13.4069i	0.624422	−	0.624422i	0.946659	+	0.322237i	$0.104435\pi$
$462$		0			0
$463$	−17.7592	+	17.7592i	−0.825342	+	0.825342i	−0.986868	−	0.161526i	$-0.948358\pi$
$463$	−17.7592	+	17.7592i	−0.825342	+	0.825342i	0.161526	+	0.986868i	$0.448358\pi$
$464$	7.25113			0.336625
$465$		0			0
$466$	−11.7108	+	11.7108i	−0.542491	+	0.542491i
$467$	−39.5072			−1.82817			−0.914087	−	0.405518i	$-0.867091\pi$
$467$	−39.5072			−1.82817			−0.914087	+	0.405518i	$0.867091\pi$
$468$		0			0
$469$	34.0887	+	1.22734i	1.57407	+	0.0566732i
$470$	14.9715	+	14.9715i	0.690586	+	0.690586i
$471$		0			0
$472$	−1.94775			−0.0896526
$473$	6.42336	+	6.42336i	0.295346	+	0.295346i
$474$		0			0
$475$	−4.59688	−	4.59688i	−0.210919	−	0.210919i
$476$	0.895013	+	0.961868i	0.0410228	+	0.0440872i
$477$		0			0
$478$			3.41161i			0.156044i
$479$	−20.1768	−	20.1768i	−0.921899	−	0.921899i	0.0752644	−	0.997164i	$-0.476020\pi$
$479$	−20.1768	−	20.1768i	−0.921899	−	0.921899i	−0.997164	+	0.0752644i	$0.976020\pi$
$480$		0			0
$481$	17.7077	+	3.54154i	0.807401	+	0.161480i
$482$		−	11.8472i		−	0.539627i
$483$		0			0
$484$	−9.24432			−0.420196
$485$		−	34.1008i		−	1.54844i
$486$		0			0
$487$	−14.5837	−	14.5837i	−0.660849	−	0.660849i	0.294731	−	0.955580i	$-0.404770\pi$
$487$	−14.5837	−	14.5837i	−0.660849	−	0.660849i	−0.955580	+	0.294731i	$0.904770\pi$
$488$	−0.351145	−	0.351145i	−0.0158956	−	0.0158956i
$489$		0			0
$490$	1.28310	−	17.7957i	0.0579647	−	0.803928i
$491$			10.3591i			0.467502i	0.972297	+	0.233751i	$0.0751000\pi$
$491$			10.3591i			0.467502i	−0.972297	+	0.233751i	$0.924900\pi$
$492$		0			0
$493$	−3.60087			−0.162175
$494$	8.68768	+	13.0315i	0.390877	+	0.586316i
$495$		0			0
$496$	−5.73923	+	5.73923i	−0.257699	+	0.257699i
$497$	−42.5423	−	1.53170i	−1.90828	−	0.0687061i
$498$		0			0
$499$	30.2834	+	30.2834i	1.35567	+	1.35567i	0.879178	+	0.476494i	$0.158093\pi$
$499$	30.2834	+	30.2834i	1.35567	+	1.35567i	0.476494	+	0.879178i	$0.341907\pi$
$500$	−6.31420	+	6.31420i	−0.282380	+	0.282380i
$501$		0			0
$502$	−19.0019	−	19.0019i	−0.848096	−	0.848096i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$		0			0
$505$	8.40711	−	8.40711i	0.374112	−	0.374112i
$506$		−	9.77504i		−	0.434553i
$507$		0			0
$508$	−19.8376			−0.880152
$509$	27.9685	−	27.9685i	1.23968	−	1.23968i	0.279548	−	0.960132i	$-0.409815\pi$
$509$	27.9685	−	27.9685i	1.23968	−	1.23968i	0.960132	−	0.279548i	$-0.0901847\pi$
$510$		0			0
$511$	13.2426	+	0.476791i	0.585820	+	0.0210920i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−5.64485	−	5.64485i	−0.248984	−	0.248984i
$515$	−33.4985	+	33.4985i	−1.47612	+	1.47612i
$516$		0			0
$517$	−11.0068			−0.484079
$518$	9.70110	−	9.02682i	0.426242	−	0.396616i
$519$		0			0
$520$	−7.64653	+	5.09768i	−0.335322	+	0.223548i
$521$		−	18.7160i		−	0.819962i	−0.912094	−	0.409981i	$-0.865535\pi$
$521$		−	18.7160i		−	0.819962i	0.912094	−	0.409981i	$-0.134465\pi$
$522$		0			0
$523$			5.69449i			0.249003i	0.992219	+	0.124501i	$0.0397331\pi$
$523$			5.69449i			0.249003i	−0.992219	+	0.124501i	$0.960267\pi$
$524$	−5.10801			−0.223145
$525$		0			0
$526$	1.74773	+	1.74773i	0.0762044	+	0.0762044i
$527$	2.85007	−	2.85007i	0.124151	−	0.124151i
$528$		0			0
$529$	−31.4241			−1.36626
$530$	10.8817			0.472669
$531$		0			0
$532$	11.4853	+	0.413518i	0.497950	+	0.0179283i
$533$	30.5825	+	6.11650i	1.32468	+	0.264935i
$534$		0			0
$535$	−12.5385	+	12.5385i	−0.542087	+	0.542087i
$536$	−12.8927			−0.556879
$537$		0			0
$538$	4.12782	−	4.12782i	0.177963	−	0.177963i
$539$	6.06988	+	7.01319i	0.261448	+	0.302080i
$540$		0			0
$541$	6.48149	−	6.48149i	0.278661	−	0.278661i	−0.553913	−	0.832574i	$-0.686866\pi$
$541$	6.48149	−	6.48149i	0.278661	−	0.278661i	0.832574	+	0.553913i	$0.186866\pi$
$542$		−	12.1311i		−	0.521076i
$543$		0			0
$544$	−0.351145	−	0.351145i	−0.0150552	−	0.0150552i
$545$	10.6110			0.454527
$546$		0			0
$547$	39.5294			1.69016			0.845078	−	0.534643i	$-0.179554\pi$
$547$	39.5294			1.69016			0.845078	+	0.534643i	$0.179554\pi$
$548$	−3.80230	−	3.80230i	−0.162426	−	0.162426i
$549$		0			0
$550$			1.98302i			0.0845562i
$551$	−22.2723	+	22.2723i	−0.948831	+	0.948831i
$552$		0			0
$553$	−25.4705	+	23.7002i	−1.08312	+	1.00783i
$554$	1.88419	−	1.88419i	0.0800516	−	0.0800516i
$555$		0			0
$556$	−2.93996			−0.124682
$557$	0.806090	−	0.806090i	0.0341551	−	0.0341551i	−0.689823	−	0.723978i	$-0.742312\pi$
$557$	0.806090	−	0.806090i	0.0341551	−	0.0341551i	0.723978	+	0.689823i	$0.242312\pi$
$558$		0			0
$559$	20.5672	−	13.7115i	0.869900	−	0.579934i
$560$	−0.242641	+	6.73923i	−0.0102534	+	0.284785i
$561$		0			0
$562$	11.4545			0.483177
$563$	44.4350			1.87271			0.936357	−	0.351050i	$-0.114175\pi$
$563$	44.4350			1.87271			0.936357	+	0.351050i	$0.114175\pi$
$564$		0			0
$565$	5.29869	−	5.29869i	0.222918	−	0.222918i
$566$	−21.4063	−	21.4063i	−0.899772	−	0.899772i
$567$		0			0
$568$	16.0899			0.675117
$569$		−	5.40826i		−	0.226726i	−0.993554	−	0.113363i	$-0.963838\pi$
$569$		−	5.40826i		−	0.226726i	0.993554	−	0.113363i	$-0.0361623\pi$
$570$		0			0
$571$			2.46830i			0.103295i	0.998665	+	0.0516476i	$0.0164472\pi$
$571$			2.46830i			0.103295i	−0.998665	+	0.0516476i	$0.983553\pi$
$572$	0.936931	−	4.68466i	0.0391751	−	0.195875i
$573$		0			0
$574$	16.7545	−	15.5900i	0.699321	−	0.650714i
$575$	11.0408			0.460432
$576$		0			0
$577$	27.0650	−	27.0650i	1.12673	−	1.12673i	0.136023	−	0.990706i	$-0.456568\pi$
$577$	27.0650	−	27.0650i	1.12673	−	1.12673i	0.990706	−	0.136023i	$-0.0434321\pi$
$578$	−11.8464	−	11.8464i	−0.492747	−	0.492747i
$579$		0			0
$580$	−13.0687	−	13.0687i	−0.542650	−	0.542650i
$581$	−1.06004	+	29.4422i	−0.0439780	+	1.22147i
$582$		0			0
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	−5.00849			−0.207253
$585$		0			0
$586$			25.3477i			1.04710i
$587$	10.6533	−	10.6533i	0.439710	−	0.439710i	−0.452204	−	0.891914i	$-0.649362\pi$
$587$	10.6533	−	10.6533i	0.439710	−	0.439710i	0.891914	+	0.452204i	$0.149362\pi$
$588$		0			0
$589$		−	35.2568i		−	1.45273i
$590$	3.51044	+	3.51044i	0.144523	+	0.144523i
$591$		0			0
$592$	−3.54154	+	3.54154i	−0.145556	+	0.145556i
$593$	−11.4938	−	11.4938i	−0.471993	−	0.471993i	0.430566	−	0.902559i	$-0.358314\pi$
$593$	−11.4938	−	11.4938i	−0.471993	−	0.471993i	−0.902559	+	0.430566i	$0.858314\pi$
$594$		0			0
$595$	0.120494	−	3.34666i	0.00493977	−	0.137200i
$596$	−1.74605	+	1.74605i	−0.0715209	+	0.0715209i
$597$		0			0
$598$	−26.0826	−	5.21652i	−1.06660	−	0.213319i
$599$	30.3149			1.23863			0.619317	−	0.785141i	$-0.287409\pi$
$599$	30.3149			1.23863			0.619317	+	0.785141i	$0.287409\pi$
$600$		0			0
$601$			11.9638i			0.488012i	0.969774	+	0.244006i	$0.0784616\pi$
$601$			11.9638i			0.488012i	−0.969774	+	0.244006i	$0.921538\pi$
$602$	0.652642	−	18.1268i	0.0265997	−	0.738795i
$603$		0			0
$604$	−6.55003	−	6.55003i	−0.266517	−	0.266517i
$605$	16.6611	+	16.6611i	0.677369	+	0.677369i
$606$		0			0
$607$			41.6103i			1.68891i	0.535627	+	0.844454i	$0.320075\pi$
$607$			41.6103i			1.68891i	−0.535627	+	0.844454i	$0.679925\pi$
$608$	−4.34384			−0.176166
$609$		0			0
$610$			1.26574i			0.0512483i
$611$	−5.87386	+	29.3693i	−0.237631	+	1.18816i
$612$		0			0
$613$	−27.9736	−	27.9736i	−1.12984	−	1.12984i	−0.990202	−	0.139640i	$-0.955405\pi$
$613$	−27.9736	−	27.9736i	−1.12984	−	1.12984i	−0.139640	−	0.990202i	$-0.544595\pi$
$614$		−	7.20056i		−	0.290591i
$615$		0			0
$616$	−2.38809	−	2.56647i	−0.0962189	−	0.103406i
$617$	−15.7830	−	15.7830i	−0.635401	−	0.635401i	0.314016	−	0.949418i	$-0.398325\pi$
$617$	−15.7830	−	15.7830i	−0.635401	−	0.635401i	−0.949418	+	0.314016i	$0.898325\pi$
$618$		0			0
$619$	−0.473765	−	0.473765i	−0.0190422	−	0.0190422i	0.697522	−	0.716564i	$-0.254286\pi$
$619$	−0.473765	−	0.473765i	−0.0190422	−	0.0190422i	−0.716564	+	0.697522i	$0.754286\pi$
$620$	20.6877			0.830837
$621$		0			0
$622$	9.95105	+	9.95105i	0.399001	+	0.399001i
$623$	−38.2064	−	1.37559i	−1.53071	−	0.0551119i
$624$		0			0
$625$	30.2432			1.20973
$626$	−20.0153	+	20.0153i	−0.799972	+	0.799972i
$627$		0			0
$628$	1.70581			0.0680691
$629$	1.75871	−	1.75871i	0.0701242	−	0.0701242i
$630$		0			0
$631$	−30.2978	+	30.2978i	−1.20613	+	1.20613i	−0.233866	+	0.972269i	$0.575138\pi$
$631$	−30.2978	+	30.2978i	−1.20613	+	1.20613i	−0.972269	+	0.233866i	$0.924862\pi$
$632$	9.29841	−	9.29841i	0.369871	−	0.369871i
$633$		0			0
$634$		−	29.0082i		−	1.15206i
$635$	35.7534	+	35.7534i	1.41883	+	1.41883i
$636$		0			0
$637$	21.9524	−	12.4535i	0.869787	−	0.493427i
$638$	9.60790			0.380380
$639$		0			0
$640$		−	2.54884i		−	0.100752i
$641$		−	5.40556i		−	0.213507i	−0.994286	−	0.106753i	$-0.965954\pi$
$641$		−	5.40556i		−	0.213507i	0.994286	−	0.106753i	$-0.0340456\pi$
$642$		0			0
$643$	9.08518	−	9.08518i	0.358285	−	0.358285i	−0.504896	−	0.863180i	$-0.668469\pi$
$643$	9.08518	−	9.08518i	0.358285	−	0.358285i	0.863180	+	0.504896i	$0.168469\pi$
$644$	−14.2893	+	13.2961i	−0.563076	+	0.523939i
$645$		0			0
$646$	2.15712			0.0848709
$647$	−15.0468			−0.591552			−0.295776	−	0.955257i	$-0.595578\pi$
$647$	−15.0468			−0.591552			−0.295776	+	0.955257i	$0.595578\pi$
$648$		0			0
$649$	−2.58081			−0.101306
$650$	5.29126	+	1.05825i	0.207540	+	0.0415080i
$651$		0			0
$652$	−4.23583	−	4.23583i	−0.165888	−	0.165888i
$653$	−6.17411			−0.241611			−0.120806	−	0.992676i	$-0.538548\pi$
$653$	−6.17411			−0.241611			−0.120806	+	0.992676i	$0.538548\pi$
$654$		0			0
$655$	9.20619	+	9.20619i	0.359716	+	0.359716i
$656$	−6.11650	+	6.11650i	−0.238809	+	0.238809i
$657$		0			0
$658$	14.9715	+	16.0899i	0.583652	+	0.627249i
$659$	−2.70131			−0.105228			−0.0526140	−	0.998615i	$-0.516755\pi$
$659$	−2.70131			−0.105228			−0.0526140	+	0.998615i	$0.516755\pi$
$660$		0			0
$661$	15.1148	+	15.1148i	0.587899	+	0.587899i	0.937062	−	0.349163i	$-0.113534\pi$
$661$	15.1148	+	15.1148i	0.587899	+	0.587899i	−0.349163	+	0.937062i	$0.613534\pi$
$662$		−	13.6543i		−	0.530688i
$663$		0			0
$664$		−	11.1353i		−	0.432134i
$665$	−19.9547	−	21.4452i	−0.773809	−	0.831611i
$666$		0			0
$667$		−	53.4935i		−	2.07128i
$668$	8.02001	−	8.02001i	0.310303	−	0.310303i
$669$		0			0
$670$	23.2365	+	23.2365i	0.897705	+	0.897705i
$671$	−0.465274	−	0.465274i	−0.0179617	−	0.0179617i
$672$		0			0
$673$			18.7262i			0.721844i	0.932596	+	0.360922i	$0.117538\pi$
$673$			18.7262i			0.721844i	−0.932596	+	0.360922i	$0.882462\pi$
$674$	5.12732	−	5.12732i	0.197497	−	0.197497i
$675$		0			0
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	25.6884i		−	0.987287i	−0.869664	−	0.493644i	$-0.835665\pi$
$677$		−	25.6884i		−	0.987287i	0.869664	−	0.493644i	$-0.164335\pi$
$678$		0			0
$679$	1.27363	−	35.3744i	0.0488774	−	1.35755i
$680$			1.26574i			0.0485389i
$681$		0			0
$682$	−7.60461	+	7.60461i	−0.291195	+	0.291195i
$683$	−10.6677	+	10.6677i	−0.408187	+	0.408187i	−0.881106	−	0.472919i	$-0.843200\pi$
$683$	−10.6677	+	10.6677i	−0.408187	+	0.408187i	0.472919	+	0.881106i	$0.343200\pi$
$684$		0			0
$685$			13.7058i			0.523672i
$686$	1.99567	−	18.4124i	0.0761952	−	0.702990i
$687$		0			0
$688$			6.85574i			0.261373i
$689$	8.53851	+	12.8078i	0.325291	+	0.487937i
$690$		0			0
$691$	−18.7630	+	18.7630i	−0.713779	+	0.713779i	−0.967324	−	0.253544i	$-0.918404\pi$
$691$	−18.7630	+	18.7630i	−0.713779	+	0.713779i	0.253544	+	0.967324i	$0.418404\pi$
$692$		−	4.21603i		−	0.160269i
$693$		0			0
$694$	−21.0468	−	21.0468i	−0.798927	−	0.798927i
$695$	5.29869	+	5.29869i	0.200991	+	0.200991i
$696$		0			0
$697$	3.03742	−	3.03742i	0.115050	−	0.115050i
$698$			18.5872i			0.703535i
$699$		0			0
$700$	2.89880	−	2.69732i	0.109564	−	0.101949i
$701$			30.4354i			1.14953i	0.818319	+	0.574765i	$0.194906\pi$
$701$			30.4354i			1.14953i	−0.818319	+	0.574765i	$0.805094\pi$
$702$		0			0
$703$		−	21.7561i		−	0.820546i
$704$	0.936931	+	0.936931i	0.0353119	+	0.0353119i
$705$		0			0
$706$	19.1669			0.721356
$707$	9.03511	−	8.40711i	0.339800	−	0.316182i
$708$		0			0
$709$	−31.7070	+	31.7070i	−1.19078	+	1.19078i	−0.213932	+	0.976849i	$0.568627\pi$
$709$	−31.7070	+	31.7070i	−1.19078	+	1.19078i	−0.976849	+	0.213932i	$0.931373\pi$
$710$	−28.9989	−	28.9989i	−1.08831	−	1.08831i
$711$		0			0
$712$	14.4500			0.541537
$713$	42.3399	+	42.3399i	1.58564	+	1.58564i
$714$		0			0
$715$	−10.1318	+	6.75454i	−0.378908	+	0.252605i
$716$	5.33535			0.199391
$717$		0			0
$718$	5.71614			0.213324
$719$	0.575169			0.0214502			0.0107251	−	0.999942i	$-0.496586\pi$
$719$	0.575169			0.0214502			0.0107251	+	0.999942i	$0.496586\pi$
$720$		0			0
$721$	−36.0007	+	33.4985i	−1.34074	+	1.24755i
$722$	−0.0926627	+	0.0926627i	−0.00344855	+	0.00344855i
$723$		0			0
$724$			1.79760i			0.0668073i
$725$			10.8520i			0.403033i
$726$		0			0
$727$	32.1850			1.19368			0.596838	−	0.802361i	$-0.296423\pi$
$727$	32.1850			1.19368			0.596838	+	0.802361i	$0.296423\pi$
$728$	−8.12251	+	5.00249i	−0.301040	+	0.185404i
$729$		0			0
$730$	9.02682	+	9.02682i	0.334098	+	0.334098i
$731$		−	3.40452i		−	0.125921i
$732$		0			0
$733$	−31.3478	+	31.3478i	−1.15786	+	1.15786i	−0.172923	+	0.984935i	$0.555321\pi$
$733$	−31.3478	+	31.3478i	−1.15786	+	1.15786i	−0.984935	+	0.172923i	$0.944679\pi$
$734$	3.01882	−	3.01882i	0.111427	−	0.111427i
$735$		0			0
$736$	5.21652	−	5.21652i	0.192283	−	0.192283i
$737$	−17.0831			−0.629263
$738$		0			0
$739$	18.7211	−	18.7211i	0.688667	−	0.688667i	−0.273270	−	0.961937i	$-0.588105\pi$
$739$	18.7211	−	18.7211i	0.688667	−	0.688667i	0.961937	+	0.273270i	$0.0881053\pi$
$740$	12.7659			0.469282
$741$		0			0
$742$	11.2881	+	0.406418i	0.414398	+	0.0149201i
$743$	−20.3172	−	20.3172i	−0.745367	−	0.745367i	0.228239	−	0.973605i	$-0.426703\pi$
$743$	−20.3172	−	20.3172i	−0.745367	−	0.745367i	−0.973605	+	0.228239i	$0.926703\pi$
$744$		0			0
$745$	6.29381			0.230587
$746$	6.83876	+	6.83876i	0.250385	+	0.250385i
$747$		0			0
$748$	−0.465274	−	0.465274i	−0.0170121	−	0.0170121i
$749$	−13.4751	+	12.5385i	−0.492370	+	0.458147i
$750$		0			0
$751$		−	37.6220i		−	1.37285i	−0.727202	−	0.686423i	$-0.759180\pi$
$751$		−	37.6220i		−	1.37285i	0.727202	−	0.686423i	$-0.240820\pi$
$752$	−5.87386	−	5.87386i	−0.214198	−	0.214198i
$753$		0			0
$754$	5.12732	−	25.6366i	0.186726	−	0.933631i
$755$			23.6103i			0.859266i
$756$		0			0
$757$	18.5249			0.673299			0.336649	−	0.941630i	$-0.390706\pi$
$757$	18.5249			0.673299			0.336649	+	0.941630i	$0.390706\pi$
$758$		−	1.05507i		−	0.0383218i
$759$		0			0
$760$	7.82892	+	7.82892i	0.283985	+	0.283985i
$761$	−20.0153	−	20.0153i	−0.725554	−	0.725554i	0.244177	−	0.969731i	$-0.421482\pi$
$761$	−20.0153	−	20.0153i	−0.725554	−	0.725554i	−0.969731	+	0.244177i	$0.921482\pi$
$762$		0			0
$763$	11.0073	+	0.396311i	0.398493	+	0.0143474i
$764$			18.7889i			0.679758i
$765$		0			0
$766$	−25.6625			−0.927225
$767$	−1.37727	+	6.88634i	−0.0497303	+	0.248651i
$768$		0			0
$769$	22.3493	−	22.3493i	0.805937	−	0.805937i	−0.178079	−	0.984016i	$-0.556988\pi$
$769$	22.3493	−	22.3493i	0.805937	−	0.805937i	0.984016	+	0.178079i	$0.0569884\pi$
$770$	−0.321504	+	8.92963i	−0.0115862	+	0.321801i
$771$		0			0
$772$	1.37046	+	1.37046i	0.0493238	+	0.0493238i
$773$	−27.6399	+	27.6399i	−0.994139	+	0.994139i	−0.999983	−	0.00584422i	$-0.998140\pi$
$773$	−27.6399	+	27.6399i	−0.994139	+	0.994139i	0.00584422	+	0.999983i	$0.498140\pi$
$774$		0			0
$775$	−8.58930	−	8.58930i	−0.308537	−	0.308537i
$776$			13.3789i			0.480276i
$777$		0			0
$778$	−4.76417	+	4.76417i	−0.170804	+	0.170804i
$779$		−	37.5744i		−	1.34624i
$780$		0			0
$781$	21.3194			0.762870
$782$	−2.59049	+	2.59049i	−0.0926357	+	0.0926357i
$783$		0			0
$784$	−0.503406	+	6.98188i	−0.0179788	+	0.249353i
$785$	−3.07438	−	3.07438i	−0.109729	−	0.109729i
$786$		0			0
$787$	29.7592	+	29.7592i	1.06080	+	1.06080i	0.998028	+	0.0627747i	$0.0199949\pi$
$787$	29.7592	+	29.7592i	1.06080	+	1.06080i	0.0627747	+	0.998028i	$0.480005\pi$
$788$	−2.86537	+	2.86537i	−0.102075	+	0.102075i
$789$		0			0
$790$	−33.5171			−1.19248
$791$	5.69449	−	5.29869i	0.202473	−	0.188400i
$792$		0			0
$793$	−1.48978	+	0.993188i	−0.0529037	+	0.0352691i
$794$		−	30.7896i		−	1.09268i
$795$		0			0
$796$		−	14.0650i		−	0.498519i
$797$	19.9732			0.707486			0.353743	−	0.935343i	$-0.384909\pi$
$797$	19.9732			0.707486			0.353743	+	0.935343i	$0.384909\pi$
$798$		0			0
$799$	2.91692	+	2.91692i	0.103193	+	0.103193i
$800$	−1.05825	+	1.05825i	−0.0374148	+	0.0374148i
$801$		0			0
$802$	−23.3513			−0.824565
$803$	−6.63636			−0.234192
$804$		0			0
$805$	49.7171	+	1.79003i	1.75230	+	0.0630901i
$806$	16.2330	+	24.3495i	0.571783	+	0.857675i
$807$		0			0
$808$	−3.29841	+	3.29841i	−0.116037	+	0.116037i
$809$	−1.89084			−0.0664785			−0.0332393	−	0.999447i	$-0.510582\pi$
$809$	−1.89084			−0.0664785			−0.0332393	+	0.999447i	$0.510582\pi$
$810$		0			0
$811$	−7.61007	+	7.61007i	−0.267226	+	0.267226i	−0.827981	−	0.560756i	$-0.810511\pi$
$811$	−7.61007	+	7.61007i	−0.267226	+	0.267226i	0.560756	+	0.827981i	$0.310511\pi$
$812$	−13.0687	−	14.0449i	−0.458623	−	0.492881i
$813$		0			0
$814$	−4.69261	+	4.69261i	−0.164476	+	0.164476i
$815$			15.2685i			0.534832i
$816$		0			0
$817$	−21.0578	−	21.0578i	−0.736719	−	0.736719i
$818$	5.66221			0.197975
$819$		0			0
$820$	22.0476			0.769935
$821$	−32.0304	−	32.0304i	−1.11787	−	1.11787i	−0.992054	−	0.125814i	$-0.959846\pi$
$821$	−32.0304	−	32.0304i	−1.11787	−	1.11787i	−0.125814	−	0.992054i	$-0.540154\pi$
$822$		0			0
$823$		−	54.2791i		−	1.89205i	−0.324094	−	0.946025i	$-0.605060\pi$
$823$		−	54.2791i		−	1.89205i	0.324094	−	0.946025i	$-0.394940\pi$
$824$	13.1426	−	13.1426i	0.457845	−	0.457845i
$825$		0			0
$826$	3.51044	+	3.77266i	0.122144	+	0.131268i
$827$	−27.2462	+	27.2462i	−0.947443	+	0.947443i	−0.998686	−	0.0512430i	$-0.983682\pi$
$827$	−27.2462	+	27.2462i	−0.947443	+	0.947443i	0.0512430	+	0.998686i	$0.483682\pi$
$828$		0			0
$829$	41.4649			1.44013			0.720067	−	0.693904i	$-0.244111\pi$
$829$	41.4649			1.44013			0.720067	+	0.693904i	$0.244111\pi$
$830$	−20.0692	+	20.0692i	−0.696613	+	0.696613i
$831$		0			0
$832$	3.00000	−	2.00000i	0.104006	−	0.0693375i
$833$	0.249988	−	3.46716i	0.00866158	−	0.120130i
$834$		0			0
$835$	−28.9090			−1.00044
$836$	−5.75568			−0.199064
$837$		0			0
$838$	−10.7326	+	10.7326i	−0.370752	+	0.370752i
$839$	−0.0702127	−	0.0702127i	−0.00242401	−	0.00242401i	0.705894	−	0.708318i	$-0.250546\pi$
$839$	−0.0702127	−	0.0702127i	−0.00242401	−	0.00242401i	−0.708318	+	0.705894i	$0.750546\pi$
$840$		0			0
$841$	23.5789			0.813066
$842$			15.6482i			0.539273i
$843$		0			0
$844$		−	14.8557i		−	0.511356i
$845$	12.6161	+	30.6392i	0.434008	+	1.05402i
$846$		0			0
$847$	16.6611	+	17.9056i	0.572481	+	0.615244i
$848$	−4.26926			−0.146607
$849$		0			0
$850$	0.525521	−	0.525521i	0.0180252	−	0.0180252i
$851$	26.1269	+	26.1269i	0.895618	+	0.895618i
$852$		0			0
$853$	27.4773	+	27.4773i	0.940806	+	0.940806i	0.998343	−	0.0575376i	$-0.0183249\pi$
$853$	27.4773	+	27.4773i	0.940806	+	0.940806i	−0.0575376	+	0.998343i	$0.518325\pi$
$854$	−0.0472740	+	1.31301i	−0.00161768	+	0.0449304i
$855$		0			0
$856$	4.91930	−	4.91930i	0.168138	−	0.168138i
$857$	50.2104			1.71515			0.857577	−	0.514356i	$-0.171969\pi$
$857$	50.2104			1.71515			0.857577	+	0.514356i	$0.171969\pi$
$858$		0			0
$859$			41.3127i			1.40957i	0.709420	+	0.704786i	$0.248957\pi$
$859$			41.3127i			1.40957i	−0.709420	+	0.704786i	$0.751043\pi$
$860$	12.3561	−	12.3561i	0.421340	−	0.421340i
$861$		0			0
$862$		−	13.5830i		−	0.462638i
$863$	12.8421	+	12.8421i	0.437151	+	0.437151i	0.891052	−	0.453901i	$-0.149968\pi$
$863$	12.8421	+	12.8421i	0.437151	+	0.437151i	−0.453901	+	0.891052i	$0.649968\pi$
$864$		0			0
$865$	−7.59856	+	7.59856i	−0.258359	+	0.258359i
$866$	−4.61379	−	4.61379i	−0.156783	−	0.156783i
$867$		0			0
$868$	21.4603	+	0.772662i	0.728412	+	0.0262259i
$869$	12.3206	−	12.3206i	0.417947	−	0.417947i
$870$		0			0
$871$	−9.11650	+	45.5825i	−0.308901	+	1.54450i
$872$	−4.16308			−0.140980
$873$		0			0
$874$			32.0457i			1.08396i
$875$	23.6103	+	0.850069i	0.798173	+	0.0287376i
$876$		0			0
$877$	12.9294	+	12.9294i	0.436595	+	0.436595i	0.890864	−	0.454269i	$-0.150100\pi$
$877$	12.9294	+	12.9294i	0.436595	+	0.436595i	−0.454269	+	0.890864i	$0.650100\pi$
$878$	1.14263	+	1.14263i	0.0385618	+	0.0385618i
$879$		0			0
$880$		−	3.37727i		−	0.113848i
$881$	−42.1888			−1.42138			−0.710688	−	0.703507i	$-0.751616\pi$
$881$	−42.1888			−1.42138			−0.710688	+	0.703507i	$0.751616\pi$
$882$		0			0
$883$		−	15.6635i		−	0.527119i	−0.964643	−	0.263559i	$-0.915103\pi$
$883$		−	15.6635i		−	0.527119i	0.964643	−	0.263559i	$-0.0848965\pi$
$884$	−1.48978	+	0.993188i	−0.0501068	+	0.0334045i
$885$		0			0
$886$	13.4639	+	13.4639i	0.452327	+	0.452327i
$887$			25.2662i			0.848356i	0.905579	+	0.424178i	$0.139437\pi$
$887$			25.2662i			0.848356i	−0.905579	+	0.424178i	$0.860563\pi$
$888$		0			0
$889$	35.7534	+	38.4241i	1.19913	+	1.28870i
$890$	−26.0433	−	26.0433i	−0.872974	−	0.872974i
$891$		0			0
$892$	6.24945	+	6.24945i	0.209247	+	0.209247i
$893$	36.0838			1.20750
$894$		0			0
$895$	−9.61592	−	9.61592i	−0.321425	−	0.321425i
$896$	0.0951965	−	2.64404i	0.00318029	−	0.0883311i
$897$		0			0
$898$	14.6241			0.488013
$899$	−41.6159	+	41.6159i	−1.38797	+	1.38797i
$900$		0			0
$901$	2.12009			0.0706303
$902$	−8.10450	+	8.10450i	−0.269850	+	0.269850i
$903$		0			0
$904$	−2.07886	+	2.07886i	−0.0691420	+	0.0691420i
$905$	3.23982	−	3.23982i	0.107695	−	0.107695i
$906$		0			0
$907$		−	8.71829i		−	0.289486i	−0.989469	−	0.144743i	$-0.953764\pi$
$907$		−	8.71829i		−	0.289486i	0.989469	−	0.144743i	$-0.0462355\pi$
$908$	5.50341	+	5.50341i	0.182637	+	0.182637i
$909$		0			0
$910$	23.6552	+	5.62322i	0.784163	+	0.186408i
$911$	53.1847			1.76209			0.881044	−	0.473035i	$-0.156842\pi$
$911$	53.1847			1.76209			0.881044	+	0.473035i	$0.156842\pi$
$912$		0			0
$913$		−	14.7545i		−	0.488304i
$914$			28.3858i			0.938917i
$915$		0			0
$916$	2.50341	−	2.50341i	0.0827149	−	0.0827149i
$917$	9.20619	+	9.89387i	0.304015	+	0.326724i
$918$		0			0
$919$	−37.9468			−1.25175			−0.625874	−	0.779924i	$-0.715258\pi$
$919$	−37.9468			−1.25175			−0.625874	+	0.779924i	$0.715258\pi$
$920$	−18.8035			−0.619933
$921$		0			0
$922$	18.9602			0.624422
$923$	11.3773	−	56.8863i	0.374487	−	1.87244i
$924$		0			0
$925$	−5.30024	−	5.30024i	−0.174271	−	0.174271i
$926$	−25.1154			−0.825342
$927$		0			0
$928$	5.12732	+	5.12732i	0.168313	+	0.168313i
$929$	−3.27439	+	3.27439i	−0.107429	+	0.107429i	−0.758778	−	0.651349i	$-0.774203\pi$
$929$	−3.27439	+	3.27439i	−0.107429	+	0.107429i	0.651349	+	0.758778i	$0.274203\pi$
$930$		0			0
$931$	−19.8990	−	22.9915i	−0.652163	−	0.753516i
$932$	−16.5615			−0.542491
$933$		0			0
$934$	−27.9358	−	27.9358i	−0.914087	−	0.914087i
$935$			1.67713i			0.0548481i
$936$		0			0
$937$		−	50.1699i		−	1.63898i	−0.573094	−	0.819490i	$-0.694257\pi$
$937$		−	50.1699i		−	1.63898i	0.573094	−	0.819490i	$-0.305743\pi$
$938$	23.2365	+	24.9722i	0.758699	+	0.815373i
$939$		0			0
$940$			21.1730i			0.690586i
$941$	−4.98020	+	4.98020i	−0.162350	+	0.162350i	−0.783607	−	0.621257i	$-0.786622\pi$
$941$	−4.98020	+	4.98020i	−0.162350	+	0.162350i	0.621257	+	0.783607i	$0.286622\pi$
$942$		0			0
$943$	45.1231	+	45.1231i	1.46941	+	1.46941i
$944$	−1.37727	−	1.37727i	−0.0448263	−	0.0448263i
$945$		0			0
$946$			9.08400i			0.295346i
$947$	−4.66768	+	4.66768i	−0.151679	+	0.151679i	−0.778868	−	0.627188i	$-0.784206\pi$
$947$	−4.66768	+	4.66768i	−0.151679	+	0.151679i	0.627188	+	0.778868i	$0.284206\pi$
$948$		0			0
$949$	−3.54154	+	17.7077i	−0.114963	+	0.574816i
$950$		−	6.50097i		−	0.210919i
$951$		0			0
$952$	−0.0472740	+	1.31301i	−0.00153216	+	0.0425550i
$953$		−	16.3818i		−	0.530658i	−0.964158	−	0.265329i	$-0.914520\pi$
$953$		−	16.3818i		−	0.530658i	0.964158	−	0.265329i	$-0.0854805\pi$
$954$		0			0
$955$	33.8633	−	33.8633i	1.09579	−	1.09579i
$956$	−2.41238	+	2.41238i	−0.0780218	+	0.0780218i
$957$		0			0
$958$		−	28.5342i		−	0.921899i
$959$	−0.511897	+	14.2177i	−0.0165300	+	0.459114i
$960$		0			0
$961$		−	34.8776i		−	1.12508i
$962$	10.0170	+	15.0255i	0.322960	+	0.484441i
$963$		0			0
$964$	8.37727	−	8.37727i	0.269814	−	0.269814i
$965$		−	4.93996i		−	0.159023i
$966$		0			0
$967$	−37.7762	−	37.7762i	−1.21480	−	1.21480i	−0.969429	−	0.245373i	$-0.921090\pi$
$967$	−37.7762	−	37.7762i	−1.21480	−	1.21480i	−0.245373	−	0.969429i	$-0.578910\pi$
$968$	−6.53672	−	6.53672i	−0.210098	−	0.210098i
$969$		0			0
$970$	24.1129	−	24.1129i	0.774219	−	0.774219i
$971$		−	23.3617i		−	0.749714i	−0.927083	−	0.374857i	$-0.877692\pi$
$971$		−	23.3617i		−	0.749714i	0.927083	−	0.374857i	$-0.122308\pi$
$972$		0			0
$973$	5.29869	+	5.69449i	0.169868	+	0.182557i
$974$		−	20.6244i		−	0.660849i
$975$		0			0
$976$		−	0.496594i		−	0.0158956i
$977$	29.3537	+	29.3537i	0.939107	+	0.939107i	0.998250	−	0.0591422i	$-0.0188365\pi$
$977$	29.3537	+	29.3537i	0.939107	+	0.939107i	−0.0591422	+	0.998250i	$0.518837\pi$
$978$		0			0
$979$	19.1466			0.611927
$980$	13.4907	−	11.6762i	0.430946	−	0.372981i
$981$		0			0
$982$	−7.32502	+	7.32502i	−0.233751	+	0.233751i
$983$	19.8845	+	19.8845i	0.634216	+	0.634216i	0.949123	−	0.314907i	$-0.101973\pi$
$983$	19.8845	+	19.8845i	0.634216	+	0.634216i	−0.314907	+	0.949123i	$0.601973\pi$
$984$		0			0
$985$	10.3285			0.329095
$986$	−2.54620	−	2.54620i	−0.0810875	−	0.0810875i
$987$		0			0
$988$	−3.07156	+	15.3578i	−0.0977193	+	0.488597i
$989$	50.5766			1.60824
$990$		0			0
$991$	17.8399			0.566703			0.283352	−	0.959016i	$-0.408554\pi$
$991$	17.8399			0.566703			0.283352	+	0.959016i	$0.408554\pi$
$992$	−8.11650			−0.257699
$993$		0			0
$994$	−28.9989	−	31.1650i	−0.919788	−	0.988494i
$995$	−25.3493	+	25.3493i	−0.803627	+	0.803627i
$996$		0			0
$997$			24.4660i			0.774846i	0.921902	+	0.387423i	$0.126635\pi$
$997$			24.4660i			0.774846i	−0.921902	+	0.387423i	$0.873365\pi$
$998$			42.8272i			1.35567i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.x.d.307.4		8
3.2	odd	2		546.2.o.a.307.1	yes	8
7.6	odd	2		1638.2.x.b.307.3		8
13.5	odd	4		1638.2.x.b.811.3		8
21.20	even	2		546.2.o.d.307.2	yes	8
39.5	even	4		546.2.o.d.265.2	yes	8
91.83	even	4	inner	1638.2.x.d.811.4		8
273.83	odd	4		546.2.o.a.265.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.1	✓	8	273.83	odd	4
546.2.o.a.307.1	yes	8	3.2	odd	2
546.2.o.d.265.2	yes	8	39.5	even	4
546.2.o.d.307.2	yes	8	21.20	even	2
1638.2.x.b.307.3		8	7.6	odd	2
1638.2.x.b.811.3		8	13.5	odd	4
1638.2.x.d.307.4		8	1.1	even	1	trivial
1638.2.x.d.811.4		8	91.83	even	4	inner

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.80230 - 1.80230i) q^{5} +(1.93693 - 1.80230i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(1.80230 - 1.80230i) q^{5} +(1.93693 - 1.80230i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.54884 q^{10} +(-0.936931 + 0.936931i) q^{11} +(2.00000 + 3.00000i) q^{13} +(2.64404 + 0.0951965i) q^{14} -1.00000 q^{16} +0.496594 q^{17} +(3.07156 - 3.07156i) q^{19} +(1.80230 + 1.80230i) q^{20} -1.32502 q^{22} +7.37727i q^{23} -1.49659i q^{25} +(-0.707107 + 3.53553i) q^{26} +(1.80230 + 1.93693i) q^{28} -7.25113 q^{29} +(5.73923 - 5.73923i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.351145 + 0.351145i) q^{34} +(0.242641 - 6.73923i) q^{35} +(3.54154 - 3.54154i) q^{37} +4.34384 q^{38} +2.54884i q^{40} +(6.11650 - 6.11650i) q^{41} -6.85574i q^{43} +(-0.936931 - 0.936931i) q^{44} +(-5.21652 + 5.21652i) q^{46} +(5.87386 + 5.87386i) q^{47} +(0.503406 - 6.98188i) q^{49} +(1.05825 - 1.05825i) q^{50} +(-3.00000 + 2.00000i) q^{52} +4.26926 q^{53} +3.37727i q^{55} +(-0.0951965 + 2.64404i) q^{56} +(-5.12732 - 5.12732i) q^{58} +(1.37727 + 1.37727i) q^{59} +0.496594i q^{61} +8.11650 q^{62} -1.00000i q^{64} +(9.01152 + 1.80230i) q^{65} +(9.11650 + 9.11650i) q^{67} +0.496594i q^{68} +(4.93693 - 4.59379i) q^{70} +(-11.3773 - 11.3773i) q^{71} +(3.54154 + 3.54154i) q^{73} +5.00849 q^{74} +(3.07156 + 3.07156i) q^{76} +(-0.126137 + 3.50341i) q^{77} -13.1499 q^{79} +(-1.80230 + 1.80230i) q^{80} +8.65004 q^{82} +(-7.87386 + 7.87386i) q^{83} +(0.895013 - 0.895013i) q^{85} +(4.84774 - 4.84774i) q^{86} -1.32502i q^{88} +(-10.2177 - 10.2177i) q^{89} +(9.28077 + 2.20619i) q^{91} -7.37727 q^{92} +8.30690i q^{94} -11.0718i q^{95} +(9.46034 - 9.46034i) q^{97} +(5.29289 - 4.58097i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^5	\( 8 q + 4 q^{5} + 4 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{16} + 12 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} + 4 q^{28} + 12 q^{29} + 20 q^{31} - 24 q^{34} - 32 q^{35} - 8 q^{37} - 12 q^{38} - 16 q^{41} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 4 q^{49} - 24 q^{50} - 24 q^{52} + 24 q^{53} + 4 q^{56} - 16 q^{58} - 28 q^{59} + 20 q^{65} + 8 q^{67} + 24 q^{70} - 52 q^{71} - 8 q^{73} + 4 q^{74} + 4 q^{76} - 32 q^{77} - 48 q^{79} - 4 q^{80} + 40 q^{82} - 32 q^{83} + 20 q^{85} + 20 q^{86} - 4 q^{89} + 12 q^{91} - 20 q^{92} - 36 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^5 + 4 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^16 + 12 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 + 4 * q^28 + 12 * q^29 + 20 * q^31 - 24 * q^34 - 32 * q^35 - 8 * q^37 - 12 * q^38 - 16 * q^41 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 4 * q^49 - 24 * q^50 - 24 * q^52 + 24 * q^53 + 4 * q^56 - 16 * q^58 - 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 - 8 * q^73 + 4 * q^74 + 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 40 * q^82 - 32 * q^83 + 20 * q^85 + 20 * q^86 - 4 * q^89 + 12 * q^91 - 20 * q^92 - 36 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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