LMFDB - Embedded newform 975.2.i.k.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (of order $3$, 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.2
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	975.451
Dual form			975.2.i.k.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28078 - 2.21837i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-1.28078 - 2.21837i) q^{6} +(-1.78078 - 3.08440i) q^{7} -6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.28078 - 2.21837i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-1.28078 - 2.21837i) q^{6} +(-1.78078 - 3.08440i) q^{7} -6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -4.56155 q^{12} +(-0.500000 + 3.57071i) q^{13} -9.12311 q^{14} +(-3.84233 + 6.65511i) q^{16} +(1.28078 + 2.21837i) q^{17} -2.56155 q^{18} +(0.561553 + 0.972638i) q^{19} -3.56155 q^{21} +(-2.56155 - 4.43674i) q^{22} +(1.00000 - 1.73205i) q^{23} +(-3.28078 + 5.68247i) q^{24} +(7.28078 + 5.68247i) q^{26} -1.00000 q^{27} +(-8.12311 + 14.0696i) q^{28} +(2.84233 - 4.92306i) q^{29} -1.56155 q^{31} +(3.28078 + 5.68247i) q^{32} +(-1.00000 - 1.73205i) q^{33} +6.56155 q^{34} +(-2.28078 + 3.95042i) q^{36} +(1.71922 - 2.97778i) q^{37} +2.87689 q^{38} +(2.84233 + 2.21837i) q^{39} +(-1.28078 + 2.21837i) q^{41} +(-4.56155 + 7.90084i) q^{42} +(0.219224 + 0.379706i) q^{43} -9.12311 q^{44} +(-2.56155 - 4.43674i) q^{46} +8.24621 q^{47} +(3.84233 + 6.65511i) q^{48} +(-2.84233 + 4.92306i) q^{49} +2.56155 q^{51} +(15.2462 - 6.16879i) q^{52} -11.6847 q^{53} +(-1.28078 + 2.21837i) q^{54} +(11.6847 + 20.2384i) q^{56} +1.12311 q^{57} +(-7.28078 - 12.6107i) q^{58} +(5.56155 + 9.63289i) q^{59} +(-6.06155 - 10.4989i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-1.78078 + 3.08440i) q^{63} +1.43845 q^{64} -5.12311 q^{66} +(0.219224 - 0.379706i) q^{67} +(5.84233 - 10.1192i) q^{68} +(-1.00000 - 1.73205i) q^{69} +(-7.00000 - 12.1244i) q^{71} +(3.28078 + 5.68247i) q^{72} +1.87689 q^{73} +(-4.40388 - 7.62775i) q^{74} +(2.56155 - 4.43674i) q^{76} -7.12311 q^{77} +(8.56155 - 3.46410i) q^{78} +9.56155 q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.28078 + 5.68247i) q^{82} +9.12311 q^{83} +(8.12311 + 14.0696i) q^{84} +1.12311 q^{86} +(-2.84233 - 4.92306i) q^{87} +(-6.56155 + 11.3649i) q^{88} +(-6.56155 + 11.3649i) q^{89} +(11.9039 - 4.81645i) q^{91} -9.12311 q^{92} +(-0.780776 + 1.35234i) q^{93} +(10.5616 - 18.2931i) q^{94} +6.56155 q^{96} +(-2.21922 - 3.84381i) q^{97} +(7.28078 + 12.6107i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 2 q^{3} - 5 q^{4} - q^{6} - 3 q^{7} - 18 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + q^2 + 2 * q^3 - 5 * q^4 - q^6 - 3 * q^7 - 18 * q^8 - 2 * q^9	$ 4 q + q^{2} + 2 q^{3} - 5 q^{4} - q^{6} - 3 q^{7} - 18 q^{8} - 2 q^{9} + 4 q^{11} - 10 q^{12} - 2 q^{13} - 20 q^{14} - 3 q^{16} + q^{17} - 2 q^{18} - 6 q^{19} - 6 q^{21} - 2 q^{22} + 4 q^{23} - 9 q^{24} + 25 q^{26} - 4 q^{27} - 16 q^{28} - q^{29} + 2 q^{31} + 9 q^{32} - 4 q^{33} + 18 q^{34} - 5 q^{36} + 11 q^{37} + 28 q^{38} - q^{39} - q^{41} - 10 q^{42} + 5 q^{43} - 20 q^{44} - 2 q^{46} + 3 q^{48} + q^{49} + 2 q^{51} + 28 q^{52} - 22 q^{53} - q^{54} + 22 q^{56} - 12 q^{57} - 25 q^{58} + 14 q^{59} - 16 q^{61} - 8 q^{62} - 3 q^{63} + 14 q^{64} - 4 q^{66} + 5 q^{67} + 11 q^{68} - 4 q^{69} - 28 q^{71} + 9 q^{72} + 24 q^{73} + 3 q^{74} + 2 q^{76} - 12 q^{77} + 26 q^{78} + 30 q^{79} - 2 q^{81} + 9 q^{82} + 20 q^{83} + 16 q^{84} - 12 q^{86} + q^{87} - 18 q^{88} - 18 q^{89} + 27 q^{91} - 20 q^{92} + q^{93} + 34 q^{94} + 18 q^{96} - 13 q^{97} + 25 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q + q^2 + 2 * q^3 - 5 * q^4 - q^6 - 3 * q^7 - 18 * q^8 - 2 * q^9 + 4 * q^11 - 10 * q^12 - 2 * q^13 - 20 * q^14 - 3 * q^16 + q^17 - 2 * q^18 - 6 * q^19 - 6 * q^21 - 2 * q^22 + 4 * q^23 - 9 * q^24 + 25 * q^26 - 4 * q^27 - 16 * q^28 - q^29 + 2 * q^31 + 9 * q^32 - 4 * q^33 + 18 * q^34 - 5 * q^36 + 11 * q^37 + 28 * q^38 - q^39 - q^41 - 10 * q^42 + 5 * q^43 - 20 * q^44 - 2 * q^46 + 3 * q^48 + q^49 + 2 * q^51 + 28 * q^52 - 22 * q^53 - q^54 + 22 * q^56 - 12 * q^57 - 25 * q^58 + 14 * q^59 - 16 * q^61 - 8 * q^62 - 3 * q^63 + 14 * q^64 - 4 * q^66 + 5 * q^67 + 11 * q^68 - 4 * q^69 - 28 * q^71 + 9 * q^72 + 24 * q^73 + 3 * q^74 + 2 * q^76 - 12 * q^77 + 26 * q^78 + 30 * q^79 - 2 * q^81 + 9 * q^82 + 20 * q^83 + 16 * q^84 - 12 * q^86 + q^87 - 18 * q^88 - 18 * q^89 + 27 * q^91 - 20 * q^92 + q^93 + 34 * q^94 + 18 * q^96 - 13 * q^97 + 25 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	1.28078	−	2.21837i	0.905646	−	1.56862i	0.0855975	−	0.996330i	$-0.472720\pi$
$2$	1.28078	−	2.21837i	0.905646	−	1.56862i	0.820048	−	0.572295i	$-0.193947\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.28078	−	3.95042i	−1.14039	−	1.97521i
$5$		0			0
$5$		0			0
$6$	−1.28078	−	2.21837i	−0.522875	−	0.905646i
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	−0.977029	−	0.213107i	$-0.931642\pi$
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	0.303959	−	0.952685i	$-0.401692\pi$
$8$	−6.56155			−2.31986
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−4.56155			−1.31681
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$14$	−9.12311			−2.43825
$15$		0			0
$16$	−3.84233	+	6.65511i	−0.960582	+	1.66378i
$17$	1.28078	+	2.21837i	0.310634	+	0.538034i	0.978500	−	0.206248i	$-0.0661254\pi$
$17$	1.28078	+	2.21837i	0.310634	+	0.538034i	−0.667866	+	0.744282i	$0.732792\pi$
$18$	−2.56155			−0.603764
$19$	0.561553	+	0.972638i	0.128829	+	0.223138i	0.923223	−	0.384264i	$-0.125545\pi$
$19$	0.561553	+	0.972638i	0.128829	+	0.223138i	−0.794394	+	0.607403i	$0.792211\pi$
$20$		0			0
$21$	−3.56155			−0.777195
$22$	−2.56155	−	4.43674i	−0.546125	−	0.945916i
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	−0.742732	−	0.669588i	$-0.766471\pi$
$23$	1.00000	−	1.73205i	0.208514	−	0.361158i	0.951247	+	0.308431i	$0.0998038\pi$
$24$	−3.28078	+	5.68247i	−0.669686	+	1.15993i
$25$		0			0
$26$	7.28078	+	5.68247i	1.42788	+	1.11442i
$27$	−1.00000			−0.192450
$28$	−8.12311	+	14.0696i	−1.53512	+	2.65891i
$29$	2.84233	−	4.92306i	0.527807	−	0.914189i	−0.471667	−	0.881777i	$-0.656348\pi$
$29$	2.84233	−	4.92306i	0.527807	−	0.914189i	0.999475	−	0.0324124i	$-0.0103190\pi$
$30$		0			0
$31$	−1.56155			−0.280463			−0.140232	−	0.990119i	$-0.544785\pi$
$31$	−1.56155			−0.280463			−0.140232	+	0.990119i	$0.544785\pi$
$32$	3.28078	+	5.68247i	0.579965	+	1.00453i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	6.56155			1.12530
$35$		0			0
$36$	−2.28078	+	3.95042i	−0.380129	+	0.658403i
$37$	1.71922	−	2.97778i	0.282639	−	0.489544i	−0.689395	−	0.724385i	$-0.742124\pi$
$37$	1.71922	−	2.97778i	0.282639	−	0.489544i	0.972034	+	0.234841i	$0.0754570\pi$
$38$	2.87689			0.466694
$39$	2.84233	+	2.21837i	0.455137	+	0.355223i
$40$		0			0
$41$	−1.28078	+	2.21837i	−0.200024	+	0.346451i	−0.948536	−	0.316670i	$-0.897435\pi$
$41$	−1.28078	+	2.21837i	−0.200024	+	0.346451i	0.748512	+	0.663121i	$0.230769\pi$
$42$	−4.56155	+	7.90084i	−0.703863	+	1.21913i
$43$	0.219224	+	0.379706i	0.0334313	+	0.0579047i	0.882257	−	0.470768i	$-0.156023\pi$
$43$	0.219224	+	0.379706i	0.0334313	+	0.0579047i	−0.848826	+	0.528673i	$0.822690\pi$
$44$	−9.12311			−1.37536
$45$		0			0
$46$	−2.56155	−	4.43674i	−0.377680	−	0.654162i
$47$	8.24621			1.20283			0.601417	−	0.798935i	$-0.294603\pi$
$47$	8.24621			1.20283			0.601417	+	0.798935i	$0.294603\pi$
$48$	3.84233	+	6.65511i	0.554592	+	0.960582i
$49$	−2.84233	+	4.92306i	−0.406047	+	0.703294i
$50$		0			0
$51$	2.56155			0.358689
$52$	15.2462	−	6.16879i	2.11427	−	0.855457i
$53$	−11.6847			−1.60501			−0.802506	−	0.596645i	$-0.796500\pi$
$53$	−11.6847			−1.60501			−0.802506	+	0.596645i	$0.796500\pi$
$54$	−1.28078	+	2.21837i	−0.174292	+	0.301882i
$55$		0			0
$56$	11.6847	+	20.2384i	1.56143	+	2.70447i
$57$	1.12311			0.148759
$58$	−7.28078	−	12.6107i	−0.956013	−	1.65586i
$59$	5.56155	+	9.63289i	0.724053	+	1.25410i	0.959363	+	0.282175i	$0.0910560\pi$
$59$	5.56155	+	9.63289i	0.724053	+	1.25410i	−0.235310	+	0.971920i	$0.575611\pi$
$60$		0			0
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	−0.934173	−	0.356821i	$-0.883861\pi$
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	0.158071	−	0.987428i	$-0.449473\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	−1.78078	+	3.08440i	−0.224357	+	0.388597i
$64$	1.43845			0.179806
$65$		0			0
$66$	−5.12311			−0.630611
$67$	0.219224	−	0.379706i	0.0267824	−	0.0463885i	−0.852324	−	0.523015i	$-0.824807\pi$
$67$	0.219224	−	0.379706i	0.0267824	−	0.0463885i	0.879106	+	0.476626i	$0.158141\pi$
$68$	5.84233	−	10.1192i	0.708486	−	1.22713i
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$		0			0
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	−0.897447	−	0.441123i	$-0.854580\pi$
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	0.0666994	−	0.997773i	$-0.478753\pi$
$72$	3.28078	+	5.68247i	0.386643	+	0.669686i
$73$	1.87689			0.219674			0.109837	−	0.993950i	$-0.464967\pi$
$73$	1.87689			0.219674			0.109837	+	0.993950i	$0.464967\pi$
$74$	−4.40388	−	7.62775i	−0.511941	−	0.886708i
$75$		0			0
$76$	2.56155	−	4.43674i	0.293830	−	0.508929i
$77$	−7.12311			−0.811753
$78$	8.56155	−	3.46410i	0.969405	−	0.392232i
$79$	9.56155			1.07576			0.537879	−	0.843022i	$-0.319226\pi$
$79$	9.56155			1.07576			0.537879	+	0.843022i	$0.319226\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.28078	+	5.68247i	0.362301	+	0.627524i
$83$	9.12311			1.00139			0.500695	−	0.865624i	$-0.333078\pi$
$83$	9.12311			1.00139			0.500695	+	0.865624i	$0.333078\pi$
$84$	8.12311	+	14.0696i	0.886303	+	1.53512i
$85$		0			0
$86$	1.12311			0.121108
$87$	−2.84233	−	4.92306i	−0.304730	−	0.527807i
$88$	−6.56155	+	11.3649i	−0.699464	+	1.21151i
$89$	−6.56155	+	11.3649i	−0.695523	+	1.20468i	0.274481	+	0.961593i	$0.411494\pi$
$89$	−6.56155	+	11.3649i	−0.695523	+	1.20468i	−0.970004	+	0.243089i	$0.921839\pi$
$90$		0			0
$91$	11.9039	−	4.81645i	1.24787	−	0.504901i
$92$	−9.12311			−0.951150
$93$	−0.780776	+	1.35234i	−0.0809627	+	0.140232i
$94$	10.5616	−	18.2931i	1.08934	−	1.88679i
$95$		0			0
$96$	6.56155			0.669686
$97$	−2.21922	−	3.84381i	−0.225328	−	0.390280i	0.731090	−	0.682281i	$-0.239012\pi$
$97$	−2.21922	−	3.84381i	−0.225328	−	0.390280i	−0.956418	+	0.292002i	$0.905679\pi$
$98$	7.28078	+	12.6107i	0.735469	+	1.27387i
$99$	−2.00000			−0.201008
$100$		0			0
$101$	1.71922	−	2.97778i	0.171069	−	0.296300i	−0.767725	−	0.640780i	$-0.778611\pi$
$101$	1.71922	−	2.97778i	0.171069	−	0.296300i	0.938794	+	0.344479i	$0.111945\pi$
$102$	3.28078	−	5.68247i	0.324845	−	0.562649i
$103$	7.56155			0.745062			0.372531	−	0.928020i	$-0.378490\pi$
$103$	7.56155			0.745062			0.372531	+	0.928020i	$0.378490\pi$
$104$	3.28078	−	23.4294i	0.321707	−	2.29744i
$105$		0			0
$106$	−14.9654	+	25.9209i	−1.45357	+	2.51766i
$107$	4.12311	−	7.14143i	0.398596	−	0.690388i	−0.594957	−	0.803757i	$-0.702831\pi$
$107$	4.12311	−	7.14143i	0.398596	−	0.690388i	0.993553	+	0.113369i	$0.0361644\pi$
$108$	2.28078	+	3.95042i	0.219468	+	0.380129i
$109$	17.8078			1.70567			0.852837	−	0.522177i	$-0.174880\pi$
$109$	17.8078			1.70567			0.852837	+	0.522177i	$0.174880\pi$
$110$		0			0
$111$	−1.71922	−	2.97778i	−0.163181	−	0.282639i
$112$	27.3693			2.58616
$113$	−7.40388	−	12.8239i	−0.696499	−	1.20637i	−0.969673	−	0.244406i	$-0.921407\pi$
$113$	−7.40388	−	12.8239i	−0.696499	−	1.20637i	0.273174	−	0.961965i	$-0.411926\pi$
$114$	1.43845	−	2.49146i	0.134723	−	0.233347i
$115$		0			0
$116$	−25.9309			−2.40762
$117$	3.34233	−	1.35234i	0.308998	−	0.125024i
$118$	28.4924			2.62294
$119$	4.56155	−	7.90084i	0.418157	−	0.724269i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−31.0540			−2.81149
$123$	1.28078	+	2.21837i	0.115484	+	0.200024i
$124$	3.56155	+	6.16879i	0.319837	+	0.553974i
$125$		0			0
$126$	4.56155	+	7.90084i	0.406375	+	0.703863i
$127$	4.78078	−	8.28055i	0.424225	−	0.734780i	−0.572122	−	0.820168i	$-0.693880\pi$
$127$	4.78078	−	8.28055i	0.424225	−	0.734780i	0.996348	+	0.0853884i	$0.0272131\pi$
$128$	−4.71922	+	8.17394i	−0.417124	+	0.722481i
$129$	0.438447			0.0386031
$130$		0			0
$131$	−17.3693			−1.51756			−0.758782	−	0.651345i	$-0.774205\pi$
$131$	−17.3693			−1.51756			−0.758782	+	0.651345i	$0.774205\pi$
$132$	−4.56155	+	7.90084i	−0.397032	+	0.687680i
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	−0.561553	−	0.972638i	−0.0485108	−	0.0840231i
$135$		0			0
$136$	−8.40388	−	14.5560i	−0.720627	−	1.24816i
$137$	−0.719224	−	1.24573i	−0.0614474	−	0.106430i	0.833665	−	0.552270i	$-0.186238\pi$
$137$	−0.719224	−	1.24573i	−0.0614474	−	0.106430i	−0.895113	+	0.445840i	$0.852905\pi$
$138$	−5.12311			−0.436108
$139$	−5.46543	−	9.46641i	−0.463572	−	0.802930i	0.535564	−	0.844495i	$-0.320099\pi$
$139$	−5.46543	−	9.46641i	−0.463572	−	0.802930i	−0.999136	+	0.0415643i	$0.986766\pi$
$140$		0			0
$141$	4.12311	−	7.14143i	0.347228	−	0.601417i
$142$	−35.8617			−3.00945
$143$	5.68466	+	4.43674i	0.475375	+	0.371019i
$144$	7.68466			0.640388
$145$		0			0
$146$	2.40388	−	4.16365i	0.198947	−	0.344586i
$147$	2.84233	+	4.92306i	0.234431	+	0.406047i
$148$	−15.6847			−1.28927
$149$	3.28078	+	5.68247i	0.268772	+	0.465526i	0.968545	−	0.248839i	$-0.0800490\pi$
$149$	3.28078	+	5.68247i	0.268772	+	0.465526i	−0.699773	+	0.714365i	$0.746716\pi$
$150$		0			0
$151$	15.3693			1.25074			0.625369	−	0.780329i	$-0.284949\pi$
$151$	15.3693			1.25074			0.625369	+	0.780329i	$0.284949\pi$
$152$	−3.68466	−	6.38202i	−0.298865	−	0.517650i
$153$	1.28078	−	2.21837i	0.103545	−	0.179345i
$154$	−9.12311	+	15.8017i	−0.735161	+	1.27334i
$155$		0			0
$156$	2.28078	−	16.2880i	0.182608	−	1.30408i
$157$	4.36932			0.348709			0.174355	−	0.984683i	$-0.444216\pi$
$157$	4.36932			0.348709			0.174355	+	0.984683i	$0.444216\pi$
$158$	12.2462	−	21.2111i	0.974256	−	1.68746i
$159$	−5.84233	+	10.1192i	−0.463327	+	0.802506i
$160$		0			0
$161$	−7.12311			−0.561379
$162$	1.28078	+	2.21837i	0.100627	+	0.174292i
$163$	7.90388	+	13.6899i	0.619080	+	1.07228i	0.989654	+	0.143475i	$0.0458276\pi$
$163$	7.90388	+	13.6899i	0.619080	+	1.07228i	−0.370574	+	0.928803i	$0.620839\pi$
$164$	11.6847			0.912419
$165$		0			0
$166$	11.6847	−	20.2384i	0.906905	−	1.57081i
$167$	−3.12311	+	5.40938i	−0.241673	+	0.418590i	−0.961191	−	0.275884i	$-0.911030\pi$
$167$	−3.12311	+	5.40938i	−0.241673	+	0.418590i	0.719518	+	0.694474i	$0.244363\pi$
$168$	23.3693			1.80298
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$		0			0
$171$	0.561553	−	0.972638i	0.0429430	−	0.0743795i
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	1.87689	+	3.25088i	0.142698	+	0.247160i	0.928512	−	0.371303i	$-0.121089\pi$
$173$	1.87689	+	3.25088i	0.142698	+	0.247160i	−0.785814	+	0.618463i	$0.787756\pi$
$174$	−14.5616			−1.10391
$175$		0			0
$176$	7.68466	+	13.3102i	0.579253	+	1.00330i
$177$	11.1231			0.836064
$178$	16.8078	+	29.1119i	1.25980	+	2.18203i
$179$	6.56155	−	11.3649i	0.490433	−	0.849456i	−0.509506	−	0.860467i	$-0.670172\pi$
$179$	6.56155	−	11.3649i	0.490433	−	0.849456i	0.999939	+	0.0110115i	$0.00350513\pi$
$180$		0			0
$181$	9.68466			0.719855			0.359927	−	0.932980i	$-0.382801\pi$
$181$	9.68466			0.719855			0.359927	+	0.932980i	$0.382801\pi$
$182$	4.56155	−	32.5760i	0.338125	−	2.41469i
$183$	−12.1231			−0.896166
$184$	−6.56155	+	11.3649i	−0.483724	+	0.837835i
$185$		0			0
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	5.12311			0.374639
$188$	−18.8078	−	32.5760i	−1.37170	−	2.37585i
$189$	1.78078	+	3.08440i	0.129532	+	0.224357i
$190$		0			0
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	0.881452	−	0.472274i	$-0.156567\pi$
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	−0.849727	+	0.527223i	$0.823233\pi$
$192$	0.719224	−	1.24573i	0.0519055	−	0.0899029i
$193$	9.74621	−	16.8809i	0.701548	−	1.21512i	−0.266375	−	0.963869i	$-0.585826\pi$
$193$	9.74621	−	16.8809i	0.701548	−	1.21512i	0.967923	−	0.251247i	$-0.0808406\pi$
$194$	−11.3693			−0.816269
$195$		0			0
$196$	25.9309			1.85220
$197$	−5.68466	+	9.84612i	−0.405015	+	0.701507i	−0.994323	−	0.106402i	$-0.966067\pi$
$197$	−5.68466	+	9.84612i	−0.405015	+	0.701507i	0.589308	+	0.807908i	$0.299400\pi$
$198$	−2.56155	+	4.43674i	−0.182042	+	0.315305i
$199$	11.5885	+	20.0719i	0.821490	+	1.42286i	0.904573	+	0.426320i	$0.140190\pi$
$199$	11.5885	+	20.0719i	0.821490	+	1.42286i	−0.0830828	+	0.996543i	$0.526477\pi$
$200$		0			0
$201$	−0.219224	−	0.379706i	−0.0154628	−	0.0267824i
$202$	−4.40388	−	7.62775i	−0.309856	−	0.536686i
$203$	−20.2462			−1.42101
$204$	−5.84233	−	10.1192i	−0.409045	−	0.708486i
$205$		0			0
$206$	9.68466	−	16.7743i	0.674762	−	1.16872i
$207$	−2.00000			−0.139010
$208$	−21.8423	−	17.0474i	−1.51449	−	1.18203i
$209$	2.24621			0.155374
$210$		0			0
$211$	−3.65767	+	6.33527i	−0.251804	+	0.436138i	−0.964023	−	0.265820i	$-0.914357\pi$
$211$	−3.65767	+	6.33527i	−0.251804	+	0.436138i	0.712218	+	0.701958i	$0.247691\pi$
$212$	26.6501	+	46.1593i	1.83034	+	3.17023i
$213$	−14.0000			−0.959264
$214$	−10.5616	−	18.2931i	−0.721973	−	1.25049i
$215$		0			0
$216$	6.56155			0.446457
$217$	2.78078	+	4.81645i	0.188771	+	0.326962i
$218$	22.8078	−	39.5042i	1.54474	−	2.67556i
$219$	0.938447	−	1.62544i	0.0634144	−	0.109837i
$220$		0			0
$221$	−8.56155	+	3.46410i	−0.575912	+	0.233021i
$222$	−8.80776			−0.591138
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$	11.6847	−	20.2384i	0.780714	−	1.35224i
$225$		0			0
$226$	−37.9309			−2.52312
$227$	−0.561553	−	0.972638i	−0.0372716	−	0.0645563i	0.846788	−	0.531931i	$-0.178533\pi$
$227$	−0.561553	−	0.972638i	−0.0372716	−	0.0645563i	−0.884059	+	0.467374i	$0.845200\pi$
$228$	−2.56155	−	4.43674i	−0.169643	−	0.293830i
$229$	0.246211			0.0162701			0.00813505	−	0.999967i	$-0.497411\pi$
$229$	0.246211			0.0162701			0.00813505	+	0.999967i	$0.497411\pi$
$230$		0			0
$231$	−3.56155	+	6.16879i	−0.234333	+	0.405877i
$232$	−18.6501	+	32.3029i	−1.22444	+	2.12079i
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$	1.28078	−	9.14657i	0.0837270	−	0.597930i
$235$		0			0
$236$	25.3693	−	43.9409i	1.65140	−	2.86031i
$237$	4.78078	−	8.28055i	0.310545	−	0.537879i
$238$	−11.6847	−	20.2384i	−0.757404	−	1.31186i
$239$	−0.630683			−0.0407955			−0.0203977	−	0.999792i	$-0.506493\pi$
$239$	−0.630683			−0.0407955			−0.0203977	+	0.999792i	$0.506493\pi$
$240$		0			0
$241$	−1.40388	−	2.43160i	−0.0904320	−	0.156633i	0.817261	−	0.576268i	$-0.195491\pi$
$241$	−1.40388	−	2.43160i	−0.0904320	−	0.156633i	−0.907693	+	0.419635i	$0.862158\pi$
$242$	17.9309			1.15264
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−27.6501	+	47.8914i	−1.77012	+	3.06593i
$245$		0			0
$246$	6.56155			0.418349
$247$	−3.75379	+	1.51883i	−0.238848	+	0.0966406i
$248$	10.2462			0.650635
$249$	4.56155	−	7.90084i	0.289077	−	0.500695i
$250$		0			0
$251$	15.3693	+	26.6204i	0.970103	+	1.68027i	0.695231	+	0.718786i	$0.255302\pi$
$251$	15.3693	+	26.6204i	0.970103	+	1.68027i	0.274871	+	0.961481i	$0.411365\pi$
$252$	16.2462			1.02342
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	−12.2462	−	21.2111i	−0.768396	−	1.33090i
$255$		0			0
$256$	13.5270	+	23.4294i	0.845437	+	1.46434i
$257$	−8.08854	+	14.0098i	−0.504549	+	0.873905i	0.495437	+	0.868644i	$0.335008\pi$
$257$	−8.08854	+	14.0098i	−0.504549	+	0.873905i	−0.999986	+	0.00526106i	$0.998325\pi$
$258$	0.561553	−	0.972638i	0.0349608	−	0.0605538i
$259$	−12.2462			−0.760943
$260$		0			0
$261$	−5.68466			−0.351872
$262$	−22.2462	+	38.5316i	−1.37438	+	2.38049i
$263$	−7.68466	+	13.3102i	−0.473856	+	0.820743i	−0.999552	−	0.0299295i	$-0.990472\pi$
$263$	−7.68466	+	13.3102i	−0.473856	+	0.820743i	0.525696	+	0.850673i	$0.323805\pi$
$264$	6.56155	+	11.3649i	0.403836	+	0.699464i
$265$		0			0
$266$	−5.12311	−	8.87348i	−0.314118	−	0.544068i
$267$	6.56155	+	11.3649i	0.401561	+	0.695523i
$268$	−2.00000			−0.122169
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	0.810087	−	0.586310i	$-0.199420\pi$
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	−0.912803	+	0.408401i	$0.866086\pi$
$270$		0			0
$271$	0.534565	−	0.925894i	0.0324725	−	0.0562441i	−0.849332	−	0.527858i	$-0.822995\pi$
$271$	0.534565	−	0.925894i	0.0324725	−	0.0562441i	0.881805	+	0.471614i	$0.156329\pi$
$272$	−19.6847			−1.19356
$273$	1.78078	−	12.7173i	0.107777	−	0.769685i
$274$	−3.68466			−0.222598
$275$		0			0
$276$	−4.56155	+	7.90084i	−0.274573	+	0.475575i
$277$	8.84233	+	15.3154i	0.531284	+	0.920211i	0.999333	+	0.0365086i	$0.0116236\pi$
$277$	8.84233	+	15.3154i	0.531284	+	0.920211i	−0.468049	+	0.883702i	$0.655043\pi$
$278$	−28.0000			−1.67933
$279$	0.780776	+	1.35234i	0.0467439	+	0.0809627i
$280$		0			0
$281$	−2.80776			−0.167497			−0.0837486	−	0.996487i	$-0.526689\pi$
$281$	−2.80776			−0.167497			−0.0837486	+	0.996487i	$0.526689\pi$
$282$	−10.5616	−	18.2931i	−0.628931	−	1.08934i
$283$	−0.657671	+	1.13912i	−0.0390945	+	0.0677136i	−0.884911	−	0.465761i	$-0.845781\pi$
$283$	−0.657671	+	1.13912i	−0.0390945	+	0.0677136i	0.845816	+	0.533475i	$0.179114\pi$
$284$	−31.9309	+	55.3059i	−1.89475	+	3.28180i
$285$		0			0
$286$	17.1231	−	6.92820i	1.01251	−	0.409673i
$287$	9.12311			0.538520
$288$	3.28078	−	5.68247i	0.193322	−	0.334843i
$289$	5.21922	−	9.03996i	0.307013	−	0.531762i
$290$		0			0
$291$	−4.43845			−0.260186
$292$	−4.28078	−	7.41452i	−0.250513	−	0.433902i
$293$	12.2808	+	21.2709i	0.717451	+	1.24266i	0.962007	+	0.273026i	$0.0880244\pi$
$293$	12.2808	+	21.2709i	0.717451	+	1.24266i	−0.244556	+	0.969635i	$0.578642\pi$
$294$	14.5616			0.849247
$295$		0			0
$296$	−11.2808	+	19.5389i	−0.655682	+	1.13567i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	16.8078			0.973648
$299$	5.68466	+	4.43674i	0.328752	+	0.256583i
$300$		0			0
$301$	0.780776	−	1.35234i	0.0450032	−	0.0779478i
$302$	19.6847	−	34.0948i	1.13272	−	1.96194i
$303$	−1.71922	−	2.97778i	−0.0987668	−	0.171069i
$304$	−8.63068			−0.495004
$305$		0			0
$306$	−3.28078	−	5.68247i	−0.187550	−	0.324845i
$307$	−10.1922			−0.581702			−0.290851	−	0.956768i	$-0.593938\pi$
$307$	−10.1922			−0.581702			−0.290851	+	0.956768i	$0.593938\pi$
$308$	16.2462	+	28.1393i	0.925714	+	1.60338i
$309$	3.78078	−	6.54850i	0.215081	−	0.372531i
$310$		0			0
$311$	−10.8769			−0.616772			−0.308386	−	0.951261i	$-0.599789\pi$
$311$	−10.8769			−0.616772			−0.308386	+	0.951261i	$0.599789\pi$
$312$	−18.6501	−	14.5560i	−1.05585	−	0.824068i
$313$	1.31534			0.0743475			0.0371738	−	0.999309i	$-0.488165\pi$
$313$	1.31534			0.0743475			0.0371738	+	0.999309i	$0.488165\pi$
$314$	5.59612	−	9.69276i	0.315807	−	0.546994i
$315$		0			0
$316$	−21.8078	−	37.7722i	−1.22678	−	2.12485i
$317$	23.0540			1.29484			0.647420	−	0.762133i	$-0.275848\pi$
$317$	23.0540			1.29484			0.647420	+	0.762133i	$0.275848\pi$
$318$	14.9654	+	25.9209i	0.839220	+	1.45357i
$319$	−5.68466	−	9.84612i	−0.318280	−	0.551277i
$320$		0			0
$321$	−4.12311	−	7.14143i	−0.230129	−	0.398596i
$322$	−9.12311	+	15.8017i	−0.508411	+	0.880593i
$323$	−1.43845	+	2.49146i	−0.0800373	+	0.138629i
$324$	4.56155			0.253420
$325$		0			0
$326$	40.4924			2.24267
$327$	8.90388	−	15.4220i	0.492386	−	0.852837i
$328$	8.40388	−	14.5560i	0.464027	−	0.803718i
$329$	−14.6847	−	25.4346i	−0.809591	−	1.40225i
$330$		0			0
$331$	11.9039	+	20.6181i	0.654297	+	1.13327i	0.982070	+	0.188518i	$0.0603685\pi$
$331$	11.9039	+	20.6181i	0.654297	+	1.13327i	−0.327773	+	0.944756i	$0.606298\pi$
$332$	−20.8078	−	36.0401i	−1.14197	−	1.97796i
$333$	−3.43845			−0.188426
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$		0			0
$336$	13.6847	−	23.7025i	0.746559	−	1.29308i
$337$	−2.12311			−0.115653			−0.0578265	−	0.998327i	$-0.518417\pi$
$337$	−2.12311			−0.115653			−0.0578265	+	0.998327i	$0.518417\pi$
$338$	−23.9309	+	23.1563i	−1.30167	+	1.25954i
$339$	−14.8078			−0.804247
$340$		0			0
$341$	−1.56155	+	2.70469i	−0.0845628	+	0.146467i
$342$	−1.43845	−	2.49146i	−0.0777823	−	0.134723i
$343$	−4.68466			−0.252948
$344$	−1.43845	−	2.49146i	−0.0775559	−	0.134331i
$345$		0			0
$346$	9.61553			0.516934
$347$	−6.80776	−	11.7914i	−0.365460	−	0.632995i	0.623390	−	0.781911i	$-0.285755\pi$
$347$	−6.80776	−	11.7914i	−0.365460	−	0.632995i	−0.988850	+	0.148916i	$0.952422\pi$
$348$	−12.9654	+	22.4568i	−0.695020	+	1.20381i
$349$	6.90388	−	11.9579i	0.369556	−	0.640090i	−0.619940	−	0.784649i	$-0.712843\pi$
$349$	6.90388	−	11.9579i	0.369556	−	0.640090i	0.989496	+	0.144559i	$0.0461763\pi$
$350$		0			0
$351$	0.500000	−	3.57071i	0.0266880	−	0.190591i
$352$	13.1231			0.699464
$353$	8.84233	−	15.3154i	0.470630	−	0.815155i	−0.528806	−	0.848743i	$-0.677360\pi$
$353$	8.84233	−	15.3154i	0.470630	−	0.815155i	0.999436	+	0.0335881i	$0.0106934\pi$
$354$	14.2462	−	24.6752i	0.757178	−	1.31147i
$355$		0			0
$356$	59.8617			3.17267
$357$	−4.56155	−	7.90084i	−0.241423	−	0.418157i
$358$	−16.8078	−	29.1119i	−0.888318	−	1.53861i
$359$	15.3693			0.811162			0.405581	−	0.914059i	$-0.367069\pi$
$359$	15.3693			0.811162			0.405581	+	0.914059i	$0.367069\pi$
$360$		0			0
$361$	8.86932	−	15.3621i	0.466806	−	0.808532i
$362$	12.4039	−	21.4842i	0.651934	−	1.12918i
$363$	7.00000			0.367405
$364$	−46.1771	−	36.0401i	−2.42034	−	1.88901i
$365$		0			0
$366$	−15.5270	+	26.8935i	−0.811609	+	1.40575i
$367$	10.0270	−	17.3673i	0.523404	−	0.906563i	−0.476224	−	0.879324i	$-0.657995\pi$
$367$	10.0270	−	17.3673i	0.523404	−	0.906563i	0.999629	−	0.0272394i	$-0.00867165\pi$
$368$	7.68466	+	13.3102i	0.400591	+	0.693843i
$369$	2.56155			0.133349
$370$		0			0
$371$	20.8078	+	36.0401i	1.08029	+	1.87111i
$372$	7.12311			0.369316
$373$	1.81534	+	3.14426i	0.0939948	+	0.162804i	0.909189	−	0.416384i	$-0.136703\pi$
$373$	1.81534	+	3.14426i	0.0939948	+	0.162804i	−0.815194	+	0.579188i	$0.803370\pi$
$374$	6.56155	−	11.3649i	0.339290	−	0.587667i
$375$		0			0
$376$	−54.1080			−2.79040
$377$	16.1577	+	12.6107i	0.832162	+	0.649483i
$378$	9.12311			0.469242
$379$	−5.65767	+	9.79937i	−0.290615	+	0.503360i	−0.973955	−	0.226740i	$-0.927193\pi$
$379$	−5.65767	+	9.79937i	−0.290615	+	0.503360i	0.683340	+	0.730100i	$0.260527\pi$
$380$		0			0
$381$	−4.78078	−	8.28055i	−0.244927	−	0.424225i
$382$	2.24621			0.114926
$383$	13.3693	+	23.1563i	0.683140	+	1.18323i	0.974017	+	0.226473i	$0.0727195\pi$
$383$	13.3693	+	23.1563i	0.683140	+	1.18323i	−0.290877	+	0.956760i	$0.593947\pi$
$384$	4.71922	+	8.17394i	0.240827	+	0.417124i
$385$		0			0
$386$	−24.9654	−	43.2414i	−1.27071	−	2.20093i
$387$	0.219224	−	0.379706i	0.0111438	−	0.0193016i
$388$	−10.1231	+	17.5337i	−0.513923	+	0.890140i
$389$	−3.05398			−0.154843			−0.0774213	−	0.996998i	$-0.524669\pi$
$389$	−3.05398			−0.154843			−0.0774213	+	0.996998i	$0.524669\pi$
$390$		0			0
$391$	5.12311			0.259087
$392$	18.6501	−	32.3029i	0.941972	−	1.63154i
$393$	−8.68466	+	15.0423i	−0.438083	+	0.758782i
$394$	14.5616	+	25.2213i	0.733600	+	1.27063i
$395$		0			0
$396$	4.56155	+	7.90084i	0.229227	+	0.397032i
$397$	−6.02699	−	10.4390i	−0.302486	−	0.523921i	0.674213	−	0.738537i	$-0.264483\pi$
$397$	−6.02699	−	10.4390i	−0.302486	−	0.523921i	−0.976698	+	0.214617i	$0.931150\pi$
$398$	59.3693			2.97591
$399$	−2.00000	−	3.46410i	−0.100125	−	0.173422i
$400$		0			0
$401$	−9.28078	+	16.0748i	−0.463460	+	0.802736i	−0.999131	−	0.0416909i	$-0.986726\pi$
$401$	−9.28078	+	16.0748i	−0.463460	+	0.802736i	0.535671	+	0.844427i	$0.320059\pi$
$402$	−1.12311			−0.0560154
$403$	0.780776	−	5.57586i	0.0388932	−	0.277753i
$404$	−15.6847			−0.780341
$405$		0			0
$406$	−25.9309	+	44.9136i	−1.28693	+	2.22902i
$407$	−3.43845	−	5.95557i	−0.170437	−	0.295206i
$408$	−16.8078			−0.832108
$409$	9.18466	+	15.9083i	0.454152	+	0.786615i	0.998639	−	0.0521548i	$-0.0166089\pi$
$409$	9.18466	+	15.9083i	0.454152	+	0.786615i	−0.544487	+	0.838769i	$0.683276\pi$
$410$		0			0
$411$	−1.43845			−0.0709534
$412$	−17.2462	−	29.8713i	−0.849660	−	1.47165i
$413$	19.8078	−	34.3081i	0.974676	−	1.68819i
$414$	−2.56155	+	4.43674i	−0.125893	+	0.218054i
$415$		0			0
$416$	−21.9309	+	8.87348i	−1.07525	+	0.435058i
$417$	−10.9309			−0.535287
$418$	2.87689	−	4.98293i	0.140714	−	0.243723i
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	−0.563521	−	0.826102i	$-0.690554\pi$
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	0.997186	+	0.0749725i	$0.0238869\pi$
$420$		0			0
$421$	14.7538			0.719056			0.359528	−	0.933134i	$-0.382938\pi$
$421$	14.7538			0.719056			0.359528	+	0.933134i	$0.382938\pi$
$422$	9.36932	+	16.2281i	0.456091	+	0.789973i
$423$	−4.12311	−	7.14143i	−0.200472	−	0.347228i
$424$	76.6695			3.72340
$425$		0			0
$426$	−17.9309	+	31.0572i	−0.868753	+	1.50473i
$427$	−21.5885	+	37.3924i	−1.04474	+	1.80955i
$428$	−37.6155			−1.81822
$429$	6.68466	−	2.70469i	0.322738	−	0.130584i
$430$		0			0
$431$	1.43845	−	2.49146i	0.0692876	−	0.120010i	−0.829300	−	0.558803i	$-0.811261\pi$
$431$	1.43845	−	2.49146i	0.0692876	−	0.120010i	0.898588	+	0.438794i	$0.144594\pi$
$432$	3.84233	−	6.65511i	0.184864	−	0.320194i
$433$	12.6231	+	21.8639i	0.606628	+	1.05071i	0.991792	+	0.127862i	$0.0408115\pi$
$433$	12.6231	+	21.8639i	0.606628	+	1.05071i	−0.385164	+	0.922848i	$0.625855\pi$
$434$	14.2462			0.683840
$435$		0			0
$436$	−40.6155	−	70.3482i	−1.94513	−	3.36907i
$437$	2.24621			0.107451
$438$	−2.40388	−	4.16365i	−0.114862	−	0.198947i
$439$	0.657671	−	1.13912i	0.0313889	−	0.0543672i	−0.849904	−	0.526937i	$-0.823340\pi$
$439$	0.657671	−	1.13912i	0.0313889	−	0.0543672i	0.881293	+	0.472570i	$0.156674\pi$
$440$		0			0
$441$	5.68466			0.270698
$442$	−3.28078	+	23.4294i	−0.156051	+	1.11442i
$443$	−14.7386			−0.700254			−0.350127	−	0.936702i	$-0.613862\pi$
$443$	−14.7386			−0.700254			−0.350127	+	0.936702i	$0.613862\pi$
$444$	−7.84233	+	13.5833i	−0.372180	+	0.644635i
$445$		0			0
$446$	−10.2462	−	17.7470i	−0.485172	−	0.840343i
$447$	6.56155			0.310351
$448$	−2.56155	−	4.43674i	−0.121022	−	0.209616i
$449$	−4.12311	−	7.14143i	−0.194581	−	0.337025i	0.752182	−	0.658956i	$-0.229002\pi$
$449$	−4.12311	−	7.14143i	−0.194581	−	0.337025i	−0.946763	+	0.321931i	$0.895668\pi$
$450$		0			0
$451$	2.56155	+	4.43674i	0.120619	+	0.208918i
$452$	−33.7732	+	58.4969i	−1.58856	+	2.75146i
$453$	7.68466	−	13.3102i	0.361057	−	0.625369i
$454$	−2.87689			−0.135019
$455$		0			0
$456$	−7.36932			−0.345100
$457$	−14.3078	+	24.7818i	−0.669289	+	1.15924i	0.308814	+	0.951122i	$0.400068\pi$
$457$	−14.3078	+	24.7818i	−0.669289	+	1.15924i	−0.978103	+	0.208120i	$0.933265\pi$
$458$	0.315342	−	0.546188i	0.0147349	−	0.0255217i
$459$	−1.28078	−	2.21837i	−0.0597815	−	0.103545i
$460$		0			0
$461$	18.4039	+	31.8765i	0.857154	+	1.48463i	0.874632	+	0.484787i	$0.161103\pi$
$461$	18.4039	+	31.8765i	0.857154	+	1.48463i	−0.0174778	+	0.999847i	$0.505564\pi$
$462$	9.12311	+	15.8017i	0.424445	+	0.735161i
$463$	26.6847			1.24014			0.620071	−	0.784546i	$-0.287104\pi$
$463$	26.6847			1.24014			0.620071	+	0.784546i	$0.287104\pi$
$464$	21.8423	+	37.8320i	1.01400	+	1.75631i
$465$		0			0
$466$	−33.3002	+	57.6776i	−1.54260	+	2.67186i
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$	−12.9654	−	10.1192i	−0.599327	−	0.467761i
$469$	−1.56155			−0.0721058
$470$		0			0
$471$	2.18466	−	3.78394i	0.100664	−	0.174355i
$472$	−36.4924	−	63.2067i	−1.67970	−	2.90933i
$473$	0.876894			0.0403196
$474$	−12.2462	−	21.2111i	−0.562487	−	0.974256i
$475$		0			0
$476$	−41.6155			−1.90744
$477$	5.84233	+	10.1192i	0.267502	+	0.463327i
$478$	−0.807764	+	1.39909i	−0.0369463	+	0.0639928i
$479$	3.12311	−	5.40938i	0.142698	−	0.247161i	−0.785814	−	0.618463i	$-0.787755\pi$
$479$	3.12311	−	5.40938i	0.142698	−	0.247161i	0.928512	+	0.371303i	$0.121089\pi$
$480$		0			0
$481$	9.77320	+	7.62775i	0.445620	+	0.347795i
$482$	−7.19224			−0.327597
$483$	−3.56155	+	6.16879i	−0.162056	+	0.280690i
$484$	15.9654	−	27.6529i	0.725702	−	1.25695i
$485$		0			0
$486$	2.56155			0.116194
$487$	−0.561553	−	0.972638i	−0.0254464	−	0.0440744i	0.853022	−	0.521875i	$-0.174767\pi$
$487$	−0.561553	−	0.972638i	−0.0254464	−	0.0440744i	−0.878468	+	0.477801i	$0.841434\pi$
$488$	39.7732	+	68.8892i	1.80045	+	3.11847i
$489$	15.8078			0.714852
$490$		0			0
$491$	9.87689	−	17.1073i	0.445738	−	0.772041i	−0.552365	−	0.833602i	$-0.686275\pi$
$491$	9.87689	−	17.1073i	0.445738	−	0.772041i	0.998103	+	0.0615613i	$0.0196080\pi$
$492$	5.84233	−	10.1192i	0.263393	−	0.456209i
$493$	14.5616			0.655819
$494$	−1.43845	+	10.2726i	−0.0647188	+	0.462185i
$495$		0			0
$496$	6.00000	−	10.3923i	0.269408	−	0.466628i
$497$	−24.9309	+	43.1815i	−1.11830	+	1.93696i
$498$	−11.6847	−	20.2384i	−0.523602	−	0.906905i
$499$	−28.4924			−1.27550			−0.637748	−	0.770245i	$-0.720134\pi$
$499$	−28.4924			−1.27550			−0.637748	+	0.770245i	$0.720134\pi$
$500$		0			0
$501$	3.12311	+	5.40938i	0.139530	+	0.241673i
$502$	78.7386			3.51428
$503$	−5.87689	−	10.1791i	−0.262038	−	0.453863i	0.704746	−	0.709460i	$-0.251061\pi$
$503$	−5.87689	−	10.1791i	−0.262038	−	0.453863i	−0.966783	+	0.255597i	$0.917728\pi$
$504$	11.6847	−	20.2384i	0.520476	−	0.901491i
$505$		0			0
$506$	−10.2462			−0.455500
$507$	−9.34233	+	9.03996i	−0.414907	+	0.401479i
$508$	−43.6155			−1.93513
$509$	−3.40388	+	5.89570i	−0.150874	+	0.261322i	−0.931549	−	0.363615i	$-0.881542\pi$
$509$	−3.40388	+	5.89570i	−0.150874	+	0.261322i	0.780675	+	0.624938i	$0.214876\pi$
$510$		0			0
$511$	−3.34233	−	5.78908i	−0.147856	−	0.256094i
$512$	50.4233			2.22842
$513$	−0.561553	−	0.972638i	−0.0247932	−	0.0429430i
$514$	20.7192	+	35.8867i	0.913886	+	1.58290i
$515$		0			0
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	8.24621	−	14.2829i	0.362668	−	0.628159i
$518$	−15.6847	+	27.1666i	−0.689144	+	1.19363i
$519$	3.75379			0.164773
$520$		0			0
$521$	−37.9309			−1.66178			−0.830891	−	0.556436i	$-0.812169\pi$
$521$	−37.9309			−1.66178			−0.830891	+	0.556436i	$0.812169\pi$
$522$	−7.28078	+	12.6107i	−0.318671	+	0.551954i
$523$	−11.9309	+	20.6649i	−0.521701	+	0.903612i	0.477981	+	0.878370i	$0.341369\pi$
$523$	−11.9309	+	20.6649i	−0.521701	+	0.903612i	−0.999681	+	0.0252415i	$0.991965\pi$
$524$	39.6155	+	68.6161i	1.73061	+	2.99751i
$525$		0			0
$526$	19.6847	+	34.0948i	0.858292	+	1.48661i
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$	15.3693			0.668864
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	5.56155	−	9.63289i	0.241351	−	0.418032i
$532$	−18.2462			−0.791074
$533$	−7.28078	−	5.68247i	−0.315365	−	0.246135i
$534$	33.6155			1.45469
$535$		0			0
$536$	−1.43845	+	2.49146i	−0.0621315	+	0.107615i
$537$	−6.56155	−	11.3649i	−0.283152	−	0.490433i
$538$	−8.63068			−0.372095
$539$	5.68466	+	9.84612i	0.244856	+	0.424102i
$540$		0			0
$541$	−29.7386			−1.27856			−0.639282	−	0.768972i	$-0.720768\pi$
$541$	−29.7386			−1.27856			−0.639282	+	0.768972i	$0.720768\pi$
$542$	−1.36932	−	2.37173i	−0.0588172	−	0.101874i
$543$	4.84233	−	8.38716i	0.207804	−	0.359927i
$544$	−8.40388	+	14.5560i	−0.360313	+	0.624081i
$545$		0			0
$546$	−25.9309	−	20.2384i	−1.10974	−	0.866125i
$547$	24.9309			1.06597			0.532984	−	0.846126i	$-0.321071\pi$
$547$	24.9309			1.06597			0.532984	+	0.846126i	$0.321071\pi$
$548$	−3.28078	+	5.68247i	−0.140148	+	0.242743i
$549$	−6.06155	+	10.4989i	−0.258701	+	0.448083i
$550$		0			0
$551$	6.38447			0.271988
$552$	6.56155	+	11.3649i	0.279278	+	0.483724i
$553$	−17.0270	−	29.4916i	−0.724061	−	1.25411i
$554$	45.3002			1.92462
$555$		0			0
$556$	−24.9309	+	43.1815i	−1.05730	+	1.83130i
$557$	−7.03457	+	12.1842i	−0.298064	+	0.516262i	−0.975693	−	0.219142i	$-0.929674\pi$
$557$	−7.03457	+	12.1842i	−0.298064	+	0.516262i	0.677629	+	0.735404i	$0.263008\pi$
$558$	4.00000			0.169334
$559$	−1.46543	+	0.592932i	−0.0619813	+	0.0250783i
$560$		0			0
$561$	2.56155	−	4.43674i	0.108149	−	0.187319i
$562$	−3.59612	+	6.22866i	−0.151693	+	0.262740i
$563$	0.684658	+	1.18586i	0.0288549	+	0.0499782i	0.880092	−	0.474803i	$-0.157481\pi$
$563$	0.684658	+	1.18586i	0.0288549	+	0.0499782i	−0.851237	+	0.524781i	$0.824147\pi$
$564$	−37.6155			−1.58390
$565$		0			0
$566$	1.68466	+	2.91791i	0.0708115	+	0.122649i
$567$	3.56155			0.149571
$568$	45.9309	+	79.5546i	1.92722	+	3.33804i
$569$	−20.3693	+	35.2807i	−0.853926	+	1.47904i	0.0237115	+	0.999719i	$0.492452\pi$
$569$	−20.3693	+	35.2807i	−0.853926	+	1.47904i	−0.877638	+	0.479325i	$0.840882\pi$
$570$		0			0
$571$	19.3693			0.810581			0.405290	−	0.914188i	$-0.367170\pi$
$571$	19.3693			0.810581			0.405290	+	0.914188i	$0.367170\pi$
$572$	4.56155	−	32.5760i	0.190728	−	1.36207i
$573$	0.876894			0.0366328
$574$	11.6847	−	20.2384i	0.487708	−	0.844735i
$575$		0			0
$576$	−0.719224	−	1.24573i	−0.0299676	−	0.0519055i
$577$	29.6847			1.23579			0.617894	−	0.786261i	$-0.287986\pi$
$577$	29.6847			1.23579			0.617894	+	0.786261i	$0.287986\pi$
$578$	−13.3693	−	23.1563i	−0.556090	−	0.963177i
$579$	−9.74621	−	16.8809i	−0.405039	−	0.701548i
$580$		0			0
$581$	−16.2462	−	28.1393i	−0.674006	−	1.16741i
$582$	−5.68466	+	9.84612i	−0.235637	+	0.408135i
$583$	−11.6847	+	20.2384i	−0.483929	+	0.838190i
$584$	−12.3153			−0.509612
$585$		0			0
$586$	62.9157			2.59902
$587$	7.31534	−	12.6705i	0.301936	−	0.522969i	−0.674638	−	0.738149i	$-0.735700\pi$
$587$	7.31534	−	12.6705i	0.301936	−	0.522969i	0.976575	+	0.215179i	$0.0690336\pi$
$588$	12.9654	−	22.4568i	0.534686	−	0.926102i
$589$	−0.876894	−	1.51883i	−0.0361318	−	0.0625821i
$590$		0			0
$591$	5.68466	+	9.84612i	0.233836	+	0.405015i
$592$	13.2116	+	22.8832i	0.542995	+	0.940495i
$593$	−44.4233			−1.82425			−0.912123	−	0.409917i	$-0.865558\pi$
$593$	−44.4233			−1.82425			−0.912123	+	0.409917i	$0.865558\pi$
$594$	2.56155	+	4.43674i	0.105102	+	0.182042i
$595$		0			0
$596$	14.9654	−	25.9209i	0.613008	−	1.06176i
$597$	23.1771			0.948575
$598$	17.1231	−	6.92820i	0.700216	−	0.283315i
$599$	−0.384472			−0.0157091			−0.00785455	−	0.999969i	$-0.502500\pi$
$599$	−0.384472			−0.0157091			−0.00785455	+	0.999969i	$0.502500\pi$
$600$		0			0
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	−0.222846	−	0.974854i	$-0.571535\pi$
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	0.955671	−	0.294437i	$-0.0951321\pi$
$602$	−2.00000	−	3.46410i	−0.0815139	−	0.141186i
$603$	−0.438447			−0.0178549
$604$	−35.0540	−	60.7153i	−1.42633	−	2.47047i
$605$		0			0
$606$	−8.80776			−0.357791
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$	−3.68466	+	6.38202i	−0.149433	+	0.258825i
$609$	−10.1231	+	17.5337i	−0.410209	+	0.710503i
$610$		0			0
$611$	−4.12311	+	29.4449i	−0.166803	+	1.19121i
$612$	−11.6847			−0.472324
$613$	11.4309	−	19.7988i	0.461688	−	0.799668i	−0.537357	−	0.843355i	$-0.680577\pi$
$613$	11.4309	−	19.7988i	0.461688	−	0.799668i	0.999045	+	0.0436871i	$0.0139105\pi$
$614$	−13.0540	+	22.6101i	−0.526816	+	0.912471i
$615$		0			0
$616$	46.7386			1.88315
$617$	−5.40388	−	9.35980i	−0.217552	−	0.376811i	0.736507	−	0.676430i	$-0.236474\pi$
$617$	−5.40388	−	9.35980i	−0.217552	−	0.376811i	−0.954059	+	0.299619i	$0.903141\pi$
$618$	−9.68466	−	16.7743i	−0.389574	−	0.674762i
$619$	−24.3002			−0.976707			−0.488353	−	0.872646i	$-0.662402\pi$
$619$	−24.3002			−0.976707			−0.488353	+	0.872646i	$0.662402\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$	−13.9309	+	24.1290i	−0.558577	+	0.967484i
$623$	46.7386			1.87254
$624$	−25.6847	+	10.3923i	−1.02821	+	0.416025i
$625$		0			0
$626$	1.68466	−	2.91791i	0.0673325	−	0.116623i
$627$	1.12311	−	1.94528i	0.0448525	−	0.0776868i
$628$	−9.96543	−	17.2606i	−0.397664	−	0.688774i
$629$	8.80776			0.351189
$630$		0			0
$631$	7.21922	+	12.5041i	0.287393	+	0.497779i	0.973187	−	0.230017i	$-0.0738782\pi$
$631$	7.21922	+	12.5041i	0.287393	+	0.497779i	−0.685794	+	0.727796i	$0.740545\pi$
$632$	−62.7386			−2.49561
$633$	3.65767	+	6.33527i	0.145379	+	0.251804i
$634$	29.5270	−	51.1422i	1.17267	−	2.03112i
$635$		0			0
$636$	53.3002			2.11349
$637$	−16.1577	−	12.6107i	−0.640190	−	0.499653i
$638$	−29.1231			−1.15299
$639$	−7.00000	+	12.1244i	−0.276916	+	0.479632i
$640$		0			0
$641$	−13.0885	−	22.6700i	−0.516966	−	0.895412i	−0.999806	−	0.0197030i	$-0.993728\pi$
$641$	−13.0885	−	22.6700i	−0.516966	−	0.895412i	0.482840	−	0.875709i	$-0.339605\pi$
$642$	−21.1231			−0.833662
$643$	19.2732	+	33.3822i	0.760061	+	1.31646i	0.942819	+	0.333306i	$0.108164\pi$
$643$	19.2732	+	33.3822i	0.760061	+	1.31646i	−0.182758	+	0.983158i	$0.558502\pi$
$644$	16.2462	+	28.1393i	0.640190	+	1.10884i
$645$		0			0
$646$	3.68466	+	6.38202i	0.144971	+	0.251097i
$647$	−23.8078	+	41.2363i	−0.935980	+	1.62116i	−0.163102	+	0.986609i	$0.552150\pi$
$647$	−23.8078	+	41.2363i	−0.935980	+	1.62116i	−0.772877	+	0.634555i	$0.781183\pi$
$648$	3.28078	−	5.68247i	0.128881	−	0.223229i
$649$	22.2462			0.873240
$650$		0			0
$651$	5.56155			0.217974
$652$	36.0540	−	62.4473i	1.41198	−	2.44563i
$653$	7.43845	−	12.8838i	0.291089	−	0.504181i	−0.682979	−	0.730438i	$-0.739316\pi$
$653$	7.43845	−	12.8838i	0.291089	−	0.504181i	0.974068	+	0.226258i	$0.0726491\pi$
$654$	−22.8078	−	39.5042i	−0.891854	−	1.54474i
$655$		0			0
$656$	−9.84233	−	17.0474i	−0.384278	−	0.665590i
$657$	−0.938447	−	1.62544i	−0.0366123	−	0.0634144i
$658$	−75.2311			−2.93281
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	0.693280	−	0.720668i	$-0.256165\pi$
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	−0.970757	+	0.240064i	$0.922831\pi$
$660$		0			0
$661$	−15.1847	+	26.3006i	−0.590615	+	1.02297i	0.403535	+	0.914964i	$0.367781\pi$
$661$	−15.1847	+	26.3006i	−0.590615	+	1.02297i	−0.994150	+	0.108011i	$0.965552\pi$
$662$	60.9848			2.37024
$663$	−1.28078	+	9.14657i	−0.0497412	+	0.355223i
$664$	−59.8617			−2.32309
$665$		0			0
$666$	−4.40388	+	7.62775i	−0.170647	+	0.295569i
$667$	−5.68466	−	9.84612i	−0.220111	−	0.381243i
$668$	28.4924			1.10240
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$		0			0
$671$	−24.2462			−0.936015
$672$	−11.6847	−	20.2384i	−0.450745	−	0.780714i
$673$	−3.37689	+	5.84895i	−0.130170	+	0.225461i	−0.923742	−	0.383016i	$-0.874886\pi$
$673$	−3.37689	+	5.84895i	−0.130170	+	0.225461i	0.793572	+	0.608476i	$0.208219\pi$
$674$	−2.71922	+	4.70983i	−0.104741	+	0.181416i
$675$		0			0
$676$	14.4039	+	57.5243i	0.553995	+	2.21247i
$677$	−25.6155			−0.984485			−0.492242	−	0.870458i	$-0.663823\pi$
$677$	−25.6155			−0.984485			−0.492242	+	0.870458i	$0.663823\pi$
$678$	−18.9654	+	32.8491i	−0.728363	+	1.26156i
$679$	−7.90388	+	13.6899i	−0.303323	+	0.525371i
$680$		0			0
$681$	−1.12311			−0.0430375
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	18.0540	+	31.2704i	0.690816	+	1.19653i	0.971571	+	0.236749i	$0.0760819\pi$
$683$	18.0540	+	31.2704i	0.690816	+	1.19653i	−0.280755	+	0.959780i	$0.590585\pi$
$684$	−5.12311			−0.195887
$685$		0			0
$686$	−6.00000	+	10.3923i	−0.229081	+	0.396780i
$687$	0.123106	−	0.213225i	0.00469677	−	0.00813505i
$688$	−3.36932			−0.128454
$689$	5.84233	−	41.7226i	0.222575	−	1.58950i
$690$		0			0
$691$	−1.15009	+	1.99202i	−0.0437516	+	0.0757800i	−0.887072	−	0.461631i	$-0.847264\pi$
$691$	−1.15009	+	1.99202i	−0.0437516	+	0.0757800i	0.843320	+	0.537411i	$0.180598\pi$
$692$	8.56155	−	14.8290i	0.325461	−	0.563716i
$693$	3.56155	+	6.16879i	0.135292	+	0.234333i
$694$	−34.8769			−1.32391
$695$		0			0
$696$	18.6501	+	32.3029i	0.706930	+	1.22444i
$697$	−6.56155			−0.248537
$698$	−17.6847	−	30.6307i	−0.669374	−	1.15939i
$699$	−13.0000	+	22.5167i	−0.491705	+	0.851658i
$700$		0			0
$701$	19.3693			0.731569			0.365785	−	0.930700i	$-0.380801\pi$
$701$	19.3693			0.731569			0.365785	+	0.930700i	$0.380801\pi$
$702$	−7.28078	−	5.68247i	−0.274795	−	0.214471i
$703$	3.86174			0.145648
$704$	1.43845	−	2.49146i	0.0542135	−	0.0939006i
$705$		0			0
$706$	−22.6501	−	39.2311i	−0.852448	−	1.47648i
$707$	−12.2462			−0.460566
$708$	−25.3693	−	43.9409i	−0.953437	−	1.65140i
$709$	−12.7462	−	22.0771i	−0.478694	−	0.829122i	0.521008	−	0.853552i	$-0.325556\pi$
$709$	−12.7462	−	22.0771i	−0.478694	−	0.829122i	−0.999702	+	0.0244297i	$0.992223\pi$
$710$		0			0
$711$	−4.78078	−	8.28055i	−0.179293	−	0.310545i
$712$	43.0540	−	74.5717i	1.61352	−	2.79469i
$713$	−1.56155	+	2.70469i	−0.0584806	+	0.101291i
$714$	−23.3693			−0.874575
$715$		0			0
$716$	−59.8617			−2.23714
$717$	−0.315342	+	0.546188i	−0.0117766	+	0.0203977i
$718$	19.6847	−	34.0948i	0.734625	−	1.27241i
$719$	−0.684658	−	1.18586i	−0.0255335	−	0.0442252i	0.852976	−	0.521950i	$-0.174795\pi$
$719$	−0.684658	−	1.18586i	−0.0255335	−	0.0442252i	−0.878510	+	0.477724i	$0.841462\pi$
$720$		0			0
$721$	−13.4654	−	23.3228i	−0.501479	−	0.868587i
$722$	−22.7192	−	39.3508i	−0.845522	−	1.46449i
$723$	−2.80776			−0.104422
$724$	−22.0885	−	38.2585i	−0.820914	−	1.42187i
$725$		0			0
$726$	8.96543	−	15.5286i	0.332738	−	0.576320i
$727$	−39.6695			−1.47126			−0.735630	−	0.677383i	$-0.763114\pi$
$727$	−39.6695			−1.47126			−0.735630	+	0.677383i	$0.763114\pi$
$728$	−78.1080	+	31.6034i	−2.89487	+	1.17130i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.561553	+	0.972638i	−0.0207698	+	0.0359743i
$732$	27.6501	+	47.8914i	1.02198	+	1.77012i
$733$	−53.4924			−1.97579			−0.987894	−	0.155131i	$-0.950420\pi$
$733$	−53.4924			−1.97579			−0.987894	+	0.155131i	$0.950420\pi$
$734$	−25.6847	−	44.4871i	−0.948038	−	1.64205i
$735$		0			0
$736$	13.1231			0.483724
$737$	−0.438447	−	0.759413i	−0.0161504	−	0.0279733i
$738$	3.28078	−	5.68247i	0.120767	−	0.209175i
$739$	3.12311	−	5.40938i	0.114885	−	0.198987i	−0.802849	−	0.596183i	$-0.796683\pi$
$739$	3.12311	−	5.40938i	0.114885	−	0.198987i	0.917734	+	0.397196i	$0.130017\pi$
$740$		0			0
$741$	−0.561553	+	4.01029i	−0.0206292	+	0.147322i
$742$	106.600			3.91342
$743$	−18.6847	+	32.3628i	−0.685474	+	1.18728i	0.287814	+	0.957686i	$0.407071\pi$
$743$	−18.6847	+	32.3628i	−0.685474	+	1.18728i	−0.973288	+	0.229589i	$0.926262\pi$
$744$	5.12311	−	8.87348i	0.187822	−	0.325318i
$745$		0			0
$746$	9.30019			0.340504
$747$	−4.56155	−	7.90084i	−0.166898	−	0.289077i
$748$	−11.6847	−	20.2384i	−0.427233	−	0.739990i
$749$	−29.3693			−1.07313
$750$		0			0
$751$	15.0540	−	26.0743i	0.549327	−	0.951463i	−0.448993	−	0.893535i	$-0.648217\pi$
$751$	15.0540	−	26.0743i	0.549327	−	0.951463i	0.998321	−	0.0579278i	$-0.0184493\pi$
$752$	−31.6847	+	54.8794i	−1.15542	+	2.00125i
$753$	30.7386			1.12018
$754$	48.6695	−	19.6922i	1.77244	−	0.717149i
$755$		0			0
$756$	8.12311	−	14.0696i	0.295434	−	0.511708i
$757$	15.0000	−	25.9808i	0.545184	−	0.944287i	−0.453411	−	0.891302i	$-0.649793\pi$
$757$	15.0000	−	25.9808i	0.545184	−	0.944287i	0.998595	−	0.0529853i	$-0.0168737\pi$
$758$	14.4924	+	25.1016i	0.526388	+	0.911732i
$759$	−4.00000			−0.145191
$760$		0			0
$761$	7.68466	+	13.3102i	0.278569	+	0.482495i	0.971029	−	0.238961i	$-0.0768067\pi$
$761$	7.68466	+	13.3102i	0.278569	+	0.482495i	−0.692461	+	0.721456i	$0.743473\pi$
$762$	−24.4924			−0.887267
$763$	−31.7116	−	54.9262i	−1.14804	−	1.98846i
$764$	2.00000	−	3.46410i	0.0723575	−	0.125327i
$765$		0			0
$766$	68.4924			2.47473
$767$	−37.1771	+	15.0423i	−1.34239	+	0.543145i
$768$	27.0540			0.976226
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	−0.656873	−	0.754002i	$-0.728121\pi$
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	0.981421	+	0.191867i	$0.0614544\pi$
$770$		0			0
$771$	8.08854	+	14.0098i	0.291302	+	0.504549i
$772$	−88.9157			−3.20015
$773$	−3.87689	−	6.71498i	−0.139442	−	0.241521i	0.787843	−	0.615876i	$-0.211198\pi$
$773$	−3.87689	−	6.71498i	−0.139442	−	0.241521i	−0.927286	+	0.374355i	$0.877864\pi$
$774$	−0.561553	−	0.972638i	−0.0201846	−	0.0349608i
$775$		0			0
$776$	14.5616	+	25.2213i	0.522729	+	0.905394i
$777$	−6.12311	+	10.6055i	−0.219665	+	0.380471i
$778$	−3.91146	+	6.77485i	−0.140233	+	0.242890i
$779$	−2.87689			−0.103075
$780$		0			0
$781$	−28.0000			−1.00192
$782$	6.56155	−	11.3649i	0.234641	−	0.406410i
$783$	−2.84233	+	4.92306i	−0.101577	+	0.175936i
$784$	−21.8423	−	37.8320i	−0.780083	−	1.35114i
$785$		0			0
$786$	22.2462	+	38.5316i	0.793496	+	1.37438i
$787$	−0.588540	−	1.01938i	−0.0209792	−	0.0363370i	0.855345	−	0.518058i	$-0.173345\pi$
$787$	−0.588540	−	1.01938i	−0.0209792	−	0.0363370i	−0.876324	+	0.481721i	$0.840012\pi$
$788$	51.8617			1.84750
$789$	7.68466	+	13.3102i	0.273581	+	0.473856i
$790$		0			0
$791$	−26.3693	+	45.6730i	−0.937585	+	1.62394i
$792$	13.1231			0.466309
$793$	40.5194	−	16.3946i	1.43889	−	0.582190i
$794$	−30.8769			−1.09578
$795$		0			0
$796$	52.8617	−	91.5592i	1.87363	−	3.24523i
$797$	−20.8078	−	36.0401i	−0.737049	−	1.27661i	−0.953819	−	0.300383i	$-0.902885\pi$
$797$	−20.8078	−	36.0401i	−0.737049	−	1.27661i	0.216770	−	0.976223i	$-0.430448\pi$
$798$	−10.2462			−0.362712
$799$	10.5616	+	18.2931i	0.373641	+	0.647165i
$800$		0			0
$801$	13.1231			0.463682
$802$	23.7732	+	41.1764i	0.839461	+	1.45399i
$803$	1.87689	−	3.25088i	0.0662342	−	0.114721i
$804$	−1.00000	+	1.73205i	−0.0352673	+	0.0610847i
$805$		0			0
$806$	−11.3693	−	8.87348i	−0.400467	−	0.312555i
$807$	−3.36932			−0.118606
$808$	−11.2808	+	19.5389i	−0.396856	+	0.687375i
$809$	−18.6501	+	32.3029i	−0.655702	+	1.13571i	0.326015	+	0.945365i	$0.394294\pi$
$809$	−18.6501	+	32.3029i	−0.655702	+	1.13571i	−0.981717	+	0.190345i	$0.939039\pi$
$810$		0			0
$811$	−1.56155			−0.0548335			−0.0274168	−	0.999624i	$-0.508728\pi$
$811$	−1.56155			−0.0548335			−0.0274168	+	0.999624i	$0.508728\pi$
$812$	46.1771	+	79.9811i	1.62050	+	2.80678i
$813$	−0.534565	−	0.925894i	−0.0187480	−	0.0324725i
$814$	−17.6155			−0.617424
$815$		0			0
$816$	−9.84233	+	17.0474i	−0.344550	+	0.596779i
$817$	−0.246211	+	0.426450i	−0.00861384	+	0.0149196i
$818$	47.0540			1.64520
$819$	−10.1231	−	7.90084i	−0.353730	−	0.276078i
$820$		0			0
$821$	13.2462	−	22.9431i	0.462296	−	0.800720i	−0.536779	−	0.843723i	$-0.680359\pi$
$821$	13.2462	−	22.9431i	0.462296	−	0.800720i	0.999075	+	0.0430028i	$0.0136924\pi$
$822$	−1.84233	+	3.19101i	−0.0642586	+	0.111299i
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$	−49.6155			−1.72844
$825$		0			0
$826$	−50.7386	−	87.8819i	−1.76542	−	3.05780i
$827$	−34.7386			−1.20798			−0.603990	−	0.796992i	$-0.706423\pi$
$827$	−34.7386			−1.20798			−0.603990	+	0.796992i	$0.706423\pi$
$828$	4.56155	+	7.90084i	0.158525	+	0.274573i
$829$	9.74621	−	16.8809i	0.338500	−	0.586299i	−0.645651	−	0.763633i	$-0.723414\pi$
$829$	9.74621	−	16.8809i	0.338500	−	0.586299i	0.984151	+	0.177334i	$0.0567472\pi$
$830$		0			0
$831$	17.6847			0.613474
$832$	−0.719224	+	5.13628i	−0.0249346	+	0.178069i
$833$	−14.5616			−0.504528
$834$	−14.0000	+	24.2487i	−0.484780	+	0.839664i
$835$		0			0
$836$	−5.12311	−	8.87348i	−0.177186	−	0.306896i
$837$	1.56155			0.0539752
$838$	−22.7386	−	39.3845i	−0.785493	−	1.36051i
$839$	9.80776	+	16.9875i	0.338602	+	0.586475i	0.984170	−	0.177227i	$-0.0567128\pi$
$839$	9.80776	+	16.9875i	0.338602	+	0.586475i	−0.645568	+	0.763703i	$0.723379\pi$
$840$		0			0
$841$	−1.65767	−	2.87117i	−0.0571611	−	0.0990059i
$842$	18.8963	−	32.7294i	0.651210	−	1.12793i
$843$	−1.40388	+	2.43160i	−0.0483523	+	0.0837486i
$844$	33.3693			1.14862
$845$		0			0
$846$	−21.1231			−0.726227
$847$	12.4654	−	21.5908i	0.428317	−	0.741868i
$848$	44.8963	−	77.7627i	1.54175	−	2.67038i
$849$	0.657671	+	1.13912i	0.0225712	+	0.0390945i
$850$		0			0
$851$	−3.43845	−	5.95557i	−0.117868	−	0.204154i
$852$	31.9309	+	55.3059i	1.09393	+	1.89475i
$853$	6.12311			0.209651			0.104826	−	0.994491i	$-0.466572\pi$
$853$	6.12311			0.209651			0.104826	+	0.994491i	$0.466572\pi$
$854$	55.3002	+	95.7827i	1.89233	+	3.27762i
$855$		0			0
$856$	−27.0540	+	46.8589i	−0.924686	+	1.60160i
$857$	−31.4384			−1.07392			−0.536958	−	0.843609i	$-0.680427\pi$
$857$	−31.4384			−1.07392			−0.536958	+	0.843609i	$0.680427\pi$
$858$	2.56155	−	18.2931i	0.0874500	−	0.624518i
$859$	20.4384			0.697351			0.348675	−	0.937244i	$-0.386632\pi$
$859$	20.4384			0.697351			0.348675	+	0.937244i	$0.386632\pi$
$860$		0			0
$861$	4.56155	−	7.90084i	0.155457	−	0.269260i
$862$	−3.68466	−	6.38202i	−0.125500	−	0.217372i
$863$	2.49242			0.0848430			0.0424215	−	0.999100i	$-0.486493\pi$
$863$	2.49242			0.0848430			0.0424215	+	0.999100i	$0.486493\pi$
$864$	−3.28078	−	5.68247i	−0.111614	−	0.193322i
$865$		0			0
$866$	64.6695			2.19756
$867$	−5.21922	−	9.03996i	−0.177254	−	0.307013i
$868$	12.6847	−	21.9705i	0.430545	−	0.745726i
$869$	9.56155	−	16.5611i	0.324353	−	0.561797i
$870$		0			0
$871$	1.24621	+	0.972638i	0.0422263	+	0.0329566i
$872$	−116.847			−3.95692
$873$	−2.21922	+	3.84381i	−0.0751093	+	0.130093i
$874$	2.87689	−	4.98293i	0.0973124	−	0.168550i
$875$		0			0
$876$	−8.56155			−0.289268
$877$	9.71922	+	16.8342i	0.328195	+	0.568450i	0.982154	−	0.188080i	$-0.0602264\pi$
$877$	9.71922	+	16.8342i	0.328195	+	0.568450i	−0.653959	+	0.756530i	$0.726893\pi$
$878$	−1.68466	−	2.91791i	−0.0568545	−	0.0984748i
$879$	24.5616			0.828441
$880$		0			0
$881$	18.9654	−	32.8491i	0.638962	−	1.10671i	−0.346699	−	0.937976i	$-0.612698\pi$
$881$	18.9654	−	32.8491i	0.638962	−	1.10671i	0.985661	−	0.168738i	$-0.0539691\pi$
$882$	7.28078	−	12.6107i	0.245156	−	0.424624i
$883$	11.8078			0.397363			0.198681	−	0.980064i	$-0.436334\pi$
$883$	11.8078			0.397363			0.198681	+	0.980064i	$0.436334\pi$
$884$	33.2116	+	25.9209i	1.11703	+	0.871814i
$885$		0			0
$886$	−18.8769	+	32.6957i	−0.634182	+	1.09843i
$887$	24.6847	−	42.7551i	0.828830	−	1.43558i	−0.0701272	−	0.997538i	$-0.522341\pi$
$887$	24.6847	−	42.7551i	0.828830	−	1.43558i	0.898957	−	0.438037i	$-0.144326\pi$
$888$	11.2808	+	19.5389i	0.378558	+	0.655682i
$889$	−34.0540			−1.14213
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	−36.4924			−1.22186
$893$	4.63068	+	8.02058i	0.154960	+	0.268398i
$894$	8.40388	−	14.5560i	0.281068	−	0.486824i
$895$		0			0
$896$	33.6155			1.12302
$897$	6.68466	−	2.70469i	0.223194	−	0.0903069i
$898$	−21.1231			−0.704887
$899$	−4.43845	+	7.68762i	−0.148031	+	0.256396i
$900$		0			0
$901$	−14.9654	−	25.9209i	−0.498571	−	0.863550i
$902$	13.1231			0.436952
$903$	−0.780776	−	1.35234i	−0.0259826	−	0.0450032i
$904$	48.5810	+	84.1447i	1.61578	+	2.79861i
$905$		0			0
$906$	−19.6847	−	34.0948i	−0.653979	−	1.13272i
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$	−2.56155	+	4.43674i	−0.0850081	+	0.147238i
$909$	−3.43845			−0.114046
$910$		0			0
$911$	−10.7386			−0.355787			−0.177893	−	0.984050i	$-0.556928\pi$
$911$	−10.7386			−0.355787			−0.177893	+	0.984050i	$0.556928\pi$
$912$	−4.31534	+	7.47439i	−0.142895	+	0.247502i
$913$	9.12311	−	15.8017i	0.301931	−	0.522959i
$914$	36.6501	+	63.4798i	1.21228	+	2.09973i
$915$		0			0
$916$	−0.561553	−	0.972638i	−0.0185542	−	0.0321369i
$917$	30.9309	+	53.5738i	1.02143	+	1.76916i
$918$	−6.56155			−0.216564
$919$	−22.2462	−	38.5316i	−0.733835	−	1.27104i	−0.955233	−	0.295856i	$-0.904395\pi$
$919$	−22.2462	−	38.5316i	−0.733835	−	1.27104i	0.221398	−	0.975184i	$-0.428938\pi$
$920$		0			0
$921$	−5.09612	+	8.82674i	−0.167923	+	0.290851i
$922$	94.2850			3.10511
$923$	46.7926	−	18.9328i	1.54020	−	0.623181i
$924$	32.4924			1.06892
$925$		0			0
$926$	34.1771	−	59.1964i	1.12313	−	1.94532i
$927$	−3.78078	−	6.54850i	−0.124177	−	0.215081i
$928$	37.3002			1.22444
$929$	−6.40388	−	11.0918i	−0.210105	−	0.363912i	0.741643	−	0.670795i	$-0.234047\pi$
$929$	−6.40388	−	11.0918i	−0.210105	−	0.363912i	−0.951747	+	0.306884i	$0.900714\pi$
$930$		0			0
$931$	−6.38447			−0.209243
$932$	59.3002	+	102.711i	1.94244	+	3.36441i
$933$	−5.43845	+	9.41967i	−0.178047	+	0.308386i
$934$	33.3002	−	57.6776i	1.08962	−	1.88727i
$935$		0			0
$936$	−21.9309	+	8.87348i	−0.716833	+	0.290039i
$937$	3.43845			0.112329			0.0561646	−	0.998422i	$-0.482113\pi$
$937$	3.43845			0.112329			0.0561646	+	0.998422i	$0.482113\pi$
$938$	−2.00000	+	3.46410i	−0.0653023	+	0.113107i
$939$	0.657671	−	1.13912i	0.0214623	−	0.0371738i
$940$		0			0
$941$	−2.49242			−0.0812507			−0.0406253	−	0.999174i	$-0.512935\pi$
$941$	−2.49242			−0.0812507			−0.0406253	+	0.999174i	$0.512935\pi$
$942$	−5.59612	−	9.69276i	−0.182331	−	0.315807i
$943$	2.56155	+	4.43674i	0.0834156	+	0.144480i
$944$	−85.4773			−2.78205
$945$		0			0
$946$	1.12311	−	1.94528i	0.0365153	−	0.0632464i
$947$	5.36932	−	9.29993i	0.174479	−	0.302207i	−0.765502	−	0.643434i	$-0.777509\pi$
$947$	5.36932	−	9.29993i	0.174479	−	0.302207i	0.939981	+	0.341227i	$0.110842\pi$
$948$	−43.6155			−1.41657
$949$	−0.938447	+	6.70185i	−0.0304633	+	0.217551i
$950$		0			0
$951$	11.5270	−	19.9653i	0.373788	−	0.647420i
$952$	−29.9309	+	51.8418i	−0.970065	+	1.68020i
$953$	−17.4924	−	30.2978i	−0.566635	−	0.981441i	−0.996896	−	0.0787360i	$-0.974912\pi$
$953$	−17.4924	−	30.2978i	−0.566635	−	0.981441i	0.430260	−	0.902705i	$-0.358422\pi$
$954$	29.9309			0.969048
$955$		0			0
$956$	1.43845	+	2.49146i	0.0465227	+	0.0805797i
$957$	−11.3693			−0.367518
$958$	−8.00000	−	13.8564i	−0.258468	−	0.447680i
$959$	−2.56155	+	4.43674i	−0.0827169	+	0.143270i
$960$		0			0
$961$	−28.5616			−0.921340
$962$	29.4384	−	11.9111i	0.949134	−	0.384030i
$963$	−8.24621			−0.265730
$964$	−6.40388	+	11.0918i	−0.206255	+	0.357244i
$965$		0			0
$966$	9.12311	+	15.8017i	0.293531	+	0.508411i
$967$	9.12311			0.293379			0.146690	−	0.989183i	$-0.453138\pi$
$967$	9.12311			0.293379			0.146690	+	0.989183i	$0.453138\pi$
$968$	−22.9654	−	39.7773i	−0.738137	−	1.27849i
$969$	1.43845	+	2.49146i	0.0462096	+	0.0800373i
$970$		0			0
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	−0.881043	−	0.473035i	$-0.843158\pi$
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	0.0308612	−	0.999524i	$-0.490175\pi$
$972$	2.28078	−	3.95042i	0.0731559	−	0.126710i
$973$	−19.4654	+	33.7151i	−0.624033	+	1.08086i
$974$	−2.87689			−0.0921816
$975$		0			0
$976$	93.1619			2.98204
$977$	7.91146	−	13.7030i	0.253110	−	0.438399i	−0.711270	−	0.702918i	$-0.751880\pi$
$977$	7.91146	−	13.7030i	0.253110	−	0.438399i	0.964380	+	0.264519i	$0.0852132\pi$
$978$	20.2462	−	35.0675i	0.647402	−	1.12133i
$979$	13.1231	+	22.7299i	0.419416	+	0.726450i
$980$		0			0
$981$	−8.90388	−	15.4220i	−0.284279	−	0.492386i
$982$	−25.3002	−	43.8212i	−0.807361	−	1.39839i
$983$	27.6155			0.880799			0.440399	−	0.897802i	$-0.354837\pi$
$983$	27.6155			0.880799			0.440399	+	0.897802i	$0.354837\pi$
$984$	−8.40388	−	14.5560i	−0.267906	−	0.464027i
$985$		0			0
$986$	18.6501	−	32.3029i	0.593940	−	1.02873i
$987$	−29.3693			−0.934836
$988$	14.5616	+	11.3649i	0.463265	+	0.361567i
$989$	0.876894			0.0278836
$990$		0			0
$991$	−20.1771	+	34.9477i	−0.640946	+	1.11015i	0.344276	+	0.938869i	$0.388124\pi$
$991$	−20.1771	+	34.9477i	−0.640946	+	1.11015i	−0.985222	+	0.171283i	$0.945209\pi$
$992$	−5.12311	−	8.87348i	−0.162659	−	0.281733i
$993$	23.8078			0.755517
$994$	63.8617	+	110.612i	2.02557	+	3.50839i
$995$		0			0
$996$	−41.6155			−1.31864
$997$	10.3078	+	17.8536i	0.326450	+	0.565428i	0.981805	−	0.189893i	$-0.0608141\pi$
$997$	10.3078	+	17.8536i	0.326450	+	0.565428i	−0.655355	+	0.755321i	$0.727481\pi$
$998$	−36.4924	+	63.2067i	−1.15515	+	2.00077i
$999$	−1.71922	+	2.97778i	−0.0543938	+	0.0942129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.k.451.2		4
5.2	odd	4		975.2.bb.i.724.4		8
5.3	odd	4		975.2.bb.i.724.1		8
5.4	even	2		39.2.e.b.22.1	yes	4
13.3	even	3	inner	975.2.i.k.601.2		4
15.14	odd	2		117.2.g.c.100.2		4
20.19	odd	2		624.2.q.h.529.2		4
60.59	even	2		1872.2.t.r.1153.1		4
65.3	odd	12		975.2.bb.i.874.4		8
65.4	even	6		507.2.a.d.1.1		2
65.9	even	6		507.2.a.g.1.2		2
65.19	odd	12		507.2.b.d.337.1		4
65.24	odd	12		507.2.j.g.361.4		8
65.29	even	6		39.2.e.b.16.1	✓	4
65.34	odd	4		507.2.j.g.316.1		8
65.42	odd	12		975.2.bb.i.874.1		8
65.44	odd	4		507.2.j.g.316.4		8
65.49	even	6		507.2.e.g.484.2		4
65.54	odd	12		507.2.j.g.361.1		8
65.59	odd	12		507.2.b.d.337.4		4
65.64	even	2		507.2.e.g.22.2		4
195.29	odd	6		117.2.g.c.55.2		4
195.59	even	12		1521.2.b.h.1351.1		4
195.74	odd	6		1521.2.a.g.1.1		2
195.134	odd	6		1521.2.a.m.1.2		2
195.149	even	12		1521.2.b.h.1351.4		4
260.139	odd	6		8112.2.a.bk.1.2		2
260.159	odd	6		624.2.q.h.289.2		4
260.199	odd	6		8112.2.a.bo.1.1		2
780.419	even	6		1872.2.t.r.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.1	✓	4	65.29	even	6
39.2.e.b.22.1	yes	4	5.4	even	2
117.2.g.c.55.2		4	195.29	odd	6
117.2.g.c.100.2		4	15.14	odd	2
507.2.a.d.1.1		2	65.4	even	6
507.2.a.g.1.2		2	65.9	even	6
507.2.b.d.337.1		4	65.19	odd	12
507.2.b.d.337.4		4	65.59	odd	12
507.2.e.g.22.2		4	65.64	even	2
507.2.e.g.484.2		4	65.49	even	6
507.2.j.g.316.1		8	65.34	odd	4
507.2.j.g.316.4		8	65.44	odd	4
507.2.j.g.361.1		8	65.54	odd	12
507.2.j.g.361.4		8	65.24	odd	12
624.2.q.h.289.2		4	260.159	odd	6
624.2.q.h.529.2		4	20.19	odd	2
975.2.i.k.451.2		4	1.1	even	1	trivial
975.2.i.k.601.2		4	13.3	even	3	inner
975.2.bb.i.724.1		8	5.3	odd	4
975.2.bb.i.724.4		8	5.2	odd	4
975.2.bb.i.874.1		8	65.42	odd	12
975.2.bb.i.874.4		8	65.3	odd	12
1521.2.a.g.1.1		2	195.74	odd	6
1521.2.a.m.1.2		2	195.134	odd	6
1521.2.b.h.1351.1		4	195.59	even	12
1521.2.b.h.1351.4		4	195.149	even	12
1872.2.t.r.289.1		4	780.419	even	6
1872.2.t.r.1153.1		4	60.59	even	2
8112.2.a.bk.1.2		2	260.139	odd	6
8112.2.a.bo.1.1		2	260.199	odd	6

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28078 - 2.21837i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-1.28078 - 2.21837i) q^{6} +(-1.78078 - 3.08440i) q^{7} -6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.28078 - 2.21837i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +(-1.28078 - 2.21837i) q^{6} +(-1.78078 - 3.08440i) q^{7} -6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -4.56155 q^{12} +(-0.500000 + 3.57071i) q^{13} -9.12311 q^{14} +(-3.84233 + 6.65511i) q^{16} +(1.28078 + 2.21837i) q^{17} -2.56155 q^{18} +(0.561553 + 0.972638i) q^{19} -3.56155 q^{21} +(-2.56155 - 4.43674i) q^{22} +(1.00000 - 1.73205i) q^{23} +(-3.28078 + 5.68247i) q^{24} +(7.28078 + 5.68247i) q^{26} -1.00000 q^{27} +(-8.12311 + 14.0696i) q^{28} +(2.84233 - 4.92306i) q^{29} -1.56155 q^{31} +(3.28078 + 5.68247i) q^{32} +(-1.00000 - 1.73205i) q^{33} +6.56155 q^{34} +(-2.28078 + 3.95042i) q^{36} +(1.71922 - 2.97778i) q^{37} +2.87689 q^{38} +(2.84233 + 2.21837i) q^{39} +(-1.28078 + 2.21837i) q^{41} +(-4.56155 + 7.90084i) q^{42} +(0.219224 + 0.379706i) q^{43} -9.12311 q^{44} +(-2.56155 - 4.43674i) q^{46} +8.24621 q^{47} +(3.84233 + 6.65511i) q^{48} +(-2.84233 + 4.92306i) q^{49} +2.56155 q^{51} +(15.2462 - 6.16879i) q^{52} -11.6847 q^{53} +(-1.28078 + 2.21837i) q^{54} +(11.6847 + 20.2384i) q^{56} +1.12311 q^{57} +(-7.28078 - 12.6107i) q^{58} +(5.56155 + 9.63289i) q^{59} +(-6.06155 - 10.4989i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-1.78078 + 3.08440i) q^{63} +1.43845 q^{64} -5.12311 q^{66} +(0.219224 - 0.379706i) q^{67} +(5.84233 - 10.1192i) q^{68} +(-1.00000 - 1.73205i) q^{69} +(-7.00000 - 12.1244i) q^{71} +(3.28078 + 5.68247i) q^{72} +1.87689 q^{73} +(-4.40388 - 7.62775i) q^{74} +(2.56155 - 4.43674i) q^{76} -7.12311 q^{77} +(8.56155 - 3.46410i) q^{78} +9.56155 q^{79} +(-0.500000 + 0.866025i) q^{81} +(3.28078 + 5.68247i) q^{82} +9.12311 q^{83} +(8.12311 + 14.0696i) q^{84} +1.12311 q^{86} +(-2.84233 - 4.92306i) q^{87} +(-6.56155 + 11.3649i) q^{88} +(-6.56155 + 11.3649i) q^{89} +(11.9039 - 4.81645i) q^{91} -9.12311 q^{92} +(-0.780776 + 1.35234i) q^{93} +(10.5616 - 18.2931i) q^{94} +6.56155 q^{96} +(-2.21922 - 3.84381i) q^{97} +(7.28078 + 12.6107i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 2 q^{3} - 5 q^{4} - q^{6} - 3 q^{7} - 18 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + q^2 + 2 * q^3 - 5 * q^4 - q^6 - 3 * q^7 - 18 * q^8 - 2 * q^9	\( 4 q + q^{2} + 2 q^{3} - 5 q^{4} - q^{6} - 3 q^{7} - 18 q^{8} - 2 q^{9} + 4 q^{11} - 10 q^{12} - 2 q^{13} - 20 q^{14} - 3 q^{16} + q^{17} - 2 q^{18} - 6 q^{19} - 6 q^{21} - 2 q^{22} + 4 q^{23} - 9 q^{24} + 25 q^{26} - 4 q^{27} - 16 q^{28} - q^{29} + 2 q^{31} + 9 q^{32} - 4 q^{33} + 18 q^{34} - 5 q^{36} + 11 q^{37} + 28 q^{38} - q^{39} - q^{41} - 10 q^{42} + 5 q^{43} - 20 q^{44} - 2 q^{46} + 3 q^{48} + q^{49} + 2 q^{51} + 28 q^{52} - 22 q^{53} - q^{54} + 22 q^{56} - 12 q^{57} - 25 q^{58} + 14 q^{59} - 16 q^{61} - 8 q^{62} - 3 q^{63} + 14 q^{64} - 4 q^{66} + 5 q^{67} + 11 q^{68} - 4 q^{69} - 28 q^{71} + 9 q^{72} + 24 q^{73} + 3 q^{74} + 2 q^{76} - 12 q^{77} + 26 q^{78} + 30 q^{79} - 2 q^{81} + 9 q^{82} + 20 q^{83} + 16 q^{84} - 12 q^{86} + q^{87} - 18 q^{88} - 18 q^{89} + 27 q^{91} - 20 q^{92} + q^{93} + 34 q^{94} + 18 q^{96} - 13 q^{97} + 25 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - 5 * q^4 - q^6 - 3 * q^7 - 18 * q^8 - 2 * q^9 + 4 * q^11 - 10 * q^12 - 2 * q^13 - 20 * q^14 - 3 * q^16 + q^17 - 2 * q^18 - 6 * q^19 - 6 * q^21 - 2 * q^22 + 4 * q^23 - 9 * q^24 + 25 * q^26 - 4 * q^27 - 16 * q^28 - q^29 + 2 * q^31 + 9 * q^32 - 4 * q^33 + 18 * q^34 - 5 * q^36 + 11 * q^37 + 28 * q^38 - q^39 - q^41 - 10 * q^42 + 5 * q^43 - 20 * q^44 - 2 * q^46 + 3 * q^48 + q^49 + 2 * q^51 + 28 * q^52 - 22 * q^53 - q^54 + 22 * q^56 - 12 * q^57 - 25 * q^58 + 14 * q^59 - 16 * q^61 - 8 * q^62 - 3 * q^63 + 14 * q^64 - 4 * q^66 + 5 * q^67 + 11 * q^68 - 4 * q^69 - 28 * q^71 + 9 * q^72 + 24 * q^73 + 3 * q^74 + 2 * q^76 - 12 * q^77 + 26 * q^78 + 30 * q^79 - 2 * q^81 + 9 * q^82 + 20 * q^83 + 16 * q^84 - 12 * q^86 + q^87 - 18 * q^88 - 18 * q^89 + 27 * q^91 - 20 * q^92 + q^93 + 34 * q^94 + 18 * q^96 - 13 * q^97 + 25 * q^98 - 8 * q^99

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