LMFDB - Embedded newform 975.2.i.k.451.1

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			451.1
Root			$-0.780776 + 1.35234i$ of defining polynomial
Character	$\chi$	$=$	975.451
Dual form			975.2.i.k.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 + 1.35234i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(0.780776 + 1.35234i) q^{6} +(0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.780776 + 1.35234i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(0.780776 + 1.35234i) q^{6} +(0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -0.438447 q^{12} +(-0.500000 - 3.57071i) q^{13} -0.876894 q^{14} +(2.34233 - 4.05703i) q^{16} +(-0.780776 - 1.35234i) q^{17} +1.56155 q^{18} +(-3.56155 - 6.16879i) q^{19} +0.561553 q^{21} +(1.56155 + 2.70469i) q^{22} +(1.00000 - 1.73205i) q^{23} +(-1.21922 + 2.11176i) q^{24} +(5.21922 + 2.11176i) q^{26} -1.00000 q^{27} +(0.123106 - 0.213225i) q^{28} +(-3.34233 + 5.78908i) q^{29} +2.56155 q^{31} +(1.21922 + 2.11176i) q^{32} +(-1.00000 - 1.73205i) q^{33} +2.43845 q^{34} +(-0.219224 + 0.379706i) q^{36} +(3.78078 - 6.54850i) q^{37} +11.1231 q^{38} +(-3.34233 - 1.35234i) q^{39} +(0.780776 - 1.35234i) q^{41} +(-0.438447 + 0.759413i) q^{42} +(2.28078 + 3.95042i) q^{43} -0.876894 q^{44} +(1.56155 + 2.70469i) q^{46} -8.24621 q^{47} +(-2.34233 - 4.05703i) q^{48} +(3.34233 - 5.78908i) q^{49} -1.56155 q^{51} +(-1.24621 + 0.972638i) q^{52} +0.684658 q^{53} +(0.780776 - 1.35234i) q^{54} +(-0.684658 - 1.18586i) q^{56} -7.12311 q^{57} +(-5.21922 - 9.03996i) q^{58} +(1.43845 + 2.49146i) q^{59} +(-1.93845 - 3.35749i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(0.280776 - 0.486319i) q^{63} +5.56155 q^{64} +3.12311 q^{66} +(2.28078 - 3.95042i) q^{67} +(-0.342329 + 0.592932i) q^{68} +(-1.00000 - 1.73205i) q^{69} +(-7.00000 - 12.1244i) q^{71} +(1.21922 + 2.11176i) q^{72} +10.1231 q^{73} +(5.90388 + 10.2258i) q^{74} +(-1.56155 + 2.70469i) q^{76} +1.12311 q^{77} +(4.43845 - 3.46410i) q^{78} +5.43845 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.21922 + 2.11176i) q^{82} +0.876894 q^{83} +(-0.123106 - 0.213225i) q^{84} -7.12311 q^{86} +(3.34233 + 5.78908i) q^{87} +(-2.43845 + 4.22351i) q^{88} +(-2.43845 + 4.22351i) q^{89} +(1.59612 - 1.24573i) q^{91} -0.876894 q^{92} +(1.28078 - 2.21837i) q^{93} +(6.43845 - 11.1517i) q^{94} +2.43845 q^{96} +(-4.28078 - 7.41452i) q^{97} +(5.21922 + 9.03996i) 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 $

$2$	−0.780776	+	1.35234i	−0.552092	+	0.956252i	0.446031	+	0.895017i	$0.352837\pi$
$2$	−0.780776	+	1.35234i	−0.552092	+	0.956252i	−0.998123	+	0.0612344i	$0.980496\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.219224	−	0.379706i	−0.109612	−	0.189853i
$5$		0			0
$5$		0			0
$6$	0.780776	+	1.35234i	0.318751	+	0.552092i
$7$	0.280776	+	0.486319i	0.106124	+	0.183811i	0.914197	−	0.405271i	$-0.132823\pi$
$7$	0.280776	+	0.486319i	0.106124	+	0.183811i	−0.808073	+	0.589082i	$0.799489\pi$
$8$	−2.43845			−0.862121
$9$	−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	$0.0691756\pi$
$12$	−0.438447			−0.126569
$13$	−0.500000	−	3.57071i	−0.138675	−	0.990338i
$13$	−0.500000	−	3.57071i	−0.138675	−	0.990338i
$14$	−0.876894			−0.234360
$15$		0			0
$16$	2.34233	−	4.05703i	0.585582	−	1.01426i
$17$	−0.780776	−	1.35234i	−0.189366	−	0.327992i	0.755673	−	0.654949i	$-0.227310\pi$
$17$	−0.780776	−	1.35234i	−0.189366	−	0.327992i	−0.945039	+	0.326957i	$0.893977\pi$
$18$	1.56155			0.368062
$19$	−3.56155	−	6.16879i	−0.817076	−	1.41522i	−0.907827	−	0.419344i	$-0.862260\pi$
$19$	−3.56155	−	6.16879i	−0.817076	−	1.41522i	0.0907512	−	0.995874i	$-0.471073\pi$
$20$		0			0
$21$	0.561553			0.122541
$22$	1.56155	+	2.70469i	0.332924	+	0.576642i
$23$	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	$0.0998038\pi$
$24$	−1.21922	+	2.11176i	−0.248873	+	0.431061i
$25$		0			0
$26$	5.21922	+	2.11176i	1.02357	+	0.414150i
$27$	−1.00000			−0.192450
$28$	0.123106	−	0.213225i	0.0232648	−	0.0402958i
$29$	−3.34233	+	5.78908i	−0.620655	+	1.07501i	0.368709	+	0.929545i	$0.379800\pi$
$29$	−3.34233	+	5.78908i	−0.620655	+	1.07501i	−0.989364	+	0.145461i	$0.953533\pi$
$30$		0			0
$31$	2.56155			0.460068			0.230034	−	0.973183i	$-0.426116\pi$
$31$	2.56155			0.460068			0.230034	+	0.973183i	$0.426116\pi$
$32$	1.21922	+	2.11176i	0.215530	+	0.373309i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	2.43845			0.418190
$35$		0			0
$36$	−0.219224	+	0.379706i	−0.0365373	+	0.0632844i
$37$	3.78078	−	6.54850i	0.621556	−	1.07657i	−0.367640	−	0.929968i	$-0.619834\pi$
$37$	3.78078	−	6.54850i	0.621556	−	1.07657i	0.989196	−	0.146598i	$-0.0468324\pi$
$38$	11.1231			1.80441
$39$	−3.34233	−	1.35234i	−0.535201	−	0.216548i
$40$		0			0
$41$	0.780776	−	1.35234i	0.121937	−	0.211201i	−0.798595	−	0.601869i	$-0.794423\pi$
$41$	0.780776	−	1.35234i	0.121937	−	0.211201i	0.920531	+	0.390669i	$0.127756\pi$
$42$	−0.438447	+	0.759413i	−0.0676539	+	0.117180i
$43$	2.28078	+	3.95042i	0.347815	+	0.602433i	0.985861	−	0.167565i	$-0.0535903\pi$
$43$	2.28078	+	3.95042i	0.347815	+	0.602433i	−0.638046	+	0.769998i	$0.720257\pi$
$44$	−0.876894			−0.132197
$45$		0			0
$46$	1.56155	+	2.70469i	0.230238	+	0.398785i
$47$	−8.24621			−1.20283			−0.601417	−	0.798935i	$-0.705397\pi$
$47$	−8.24621			−1.20283			−0.601417	+	0.798935i	$0.705397\pi$
$48$	−2.34233	−	4.05703i	−0.338086	−	0.585582i
$49$	3.34233	−	5.78908i	0.477476	−	0.827012i
$50$		0			0
$51$	−1.56155			−0.218661
$52$	−1.24621	+	0.972638i	−0.172818	+	0.134881i
$53$	0.684658			0.0940451			0.0470225	−	0.998894i	$-0.485027\pi$
$53$	0.684658			0.0940451			0.0470225	+	0.998894i	$0.485027\pi$
$54$	0.780776	−	1.35234i	0.106250	−	0.184031i
$55$		0			0
$56$	−0.684658	−	1.18586i	−0.0914913	−	0.158468i
$57$	−7.12311			−0.943478
$58$	−5.21922	−	9.03996i	−0.685318	−	1.18700i
$59$	1.43845	+	2.49146i	0.187270	+	0.324361i	0.944339	−	0.328974i	$-0.106703\pi$
$59$	1.43845	+	2.49146i	0.187270	+	0.324361i	−0.757069	+	0.653335i	$0.773369\pi$
$60$		0			0
$61$	−1.93845	−	3.35749i	−0.248193	−	0.429882i	0.714832	−	0.699297i	$-0.246503\pi$
$61$	−1.93845	−	3.35749i	−0.248193	−	0.429882i	−0.963024	+	0.269414i	$0.913170\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	0.280776	−	0.486319i	0.0353745	−	0.0612704i
$64$	5.56155			0.695194
$65$		0			0
$66$	3.12311			0.384428
$67$	2.28078	−	3.95042i	0.278641	−	0.482621i	−0.692406	−	0.721508i	$-0.743449\pi$
$67$	2.28078	−	3.95042i	0.278641	−	0.482621i	0.971047	+	0.238887i	$0.0767826\pi$
$68$	−0.342329	+	0.592932i	−0.0415135	+	0.0719035i
$69$	−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	$-0.478753\pi$
$72$	1.21922	+	2.11176i	0.143687	+	0.248873i
$73$	10.1231			1.18482			0.592410	−	0.805637i	$-0.298177\pi$
$73$	10.1231			1.18482			0.592410	+	0.805637i	$0.298177\pi$
$74$	5.90388	+	10.2258i	0.686312	+	1.18873i
$75$		0			0
$76$	−1.56155	+	2.70469i	−0.179122	+	0.310249i
$77$	1.12311			0.127990
$78$	4.43845	−	3.46410i	0.502555	−	0.392232i
$79$	5.43845			0.611873			0.305937	−	0.952052i	$-0.401030\pi$
$79$	5.43845			0.611873			0.305937	+	0.952052i	$0.401030\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.21922	+	2.11176i	0.134641	+	0.233205i
$83$	0.876894			0.0962517			0.0481258	−	0.998841i	$-0.484675\pi$
$83$	0.876894			0.0962517			0.0481258	+	0.998841i	$0.484675\pi$
$84$	−0.123106	−	0.213225i	−0.0134319	−	0.0232648i
$85$		0			0
$86$	−7.12311			−0.768104
$87$	3.34233	+	5.78908i	0.358335	+	0.620655i
$88$	−2.43845	+	4.22351i	−0.259939	+	0.450228i
$89$	−2.43845	+	4.22351i	−0.258475	+	0.447692i	−0.965834	−	0.259163i	$-0.916553\pi$
$89$	−2.43845	+	4.22351i	−0.258475	+	0.447692i	0.707359	+	0.706855i	$0.249887\pi$
$90$		0			0
$91$	1.59612	−	1.24573i	0.167319	−	0.130588i
$92$	−0.876894			−0.0914226
$93$	1.28078	−	2.21837i	0.132810	−	0.230034i
$94$	6.43845	−	11.1517i	0.664075	−	1.15021i
$95$		0			0
$96$	2.43845			0.248873
$97$	−4.28078	−	7.41452i	−0.434647	−	0.752831i	0.562620	−	0.826716i	$-0.309794\pi$
$97$	−4.28078	−	7.41452i	−0.434647	−	0.752831i	−0.997267	+	0.0738851i	$0.976460\pi$
$98$	5.21922	+	9.03996i	0.527221	+	0.913174i
$99$	−2.00000			−0.201008
$100$		0			0
$101$	3.78078	−	6.54850i	0.376201	−	0.651600i	−0.614305	−	0.789069i	$-0.710563\pi$
$101$	3.78078	−	6.54850i	0.376201	−	0.651600i	0.990506	+	0.137469i	$0.0438968\pi$
$102$	1.21922	−	2.11176i	0.120721	−	0.209095i
$103$	3.43845			0.338800			0.169400	−	0.985547i	$-0.445817\pi$
$103$	3.43845			0.338800			0.169400	+	0.985547i	$0.445817\pi$
$104$	1.21922	+	8.70700i	0.119555	+	0.853791i
$105$		0			0
$106$	−0.534565	+	0.925894i	−0.0519216	+	0.0899308i
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	−0.993553	−	0.113369i	$-0.963836\pi$
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	0.594957	+	0.803757i	$0.297169\pi$
$108$	0.219224	+	0.379706i	0.0210948	+	0.0365373i
$109$	−2.80776			−0.268935			−0.134468	−	0.990918i	$-0.542932\pi$
$109$	−2.80776			−0.268935			−0.134468	+	0.990918i	$0.542932\pi$
$110$		0			0
$111$	−3.78078	−	6.54850i	−0.358855	−	0.621556i
$112$	2.63068			0.248576
$113$	2.90388	+	5.02967i	0.273174	+	0.473152i	0.969673	−	0.244406i	$-0.0785931\pi$
$113$	2.90388	+	5.02967i	0.273174	+	0.473152i	−0.696499	+	0.717558i	$0.745260\pi$
$114$	5.56155	−	9.63289i	0.520887	−	0.902203i
$115$		0			0
$116$	2.93087			0.272124
$117$	−2.84233	+	2.21837i	−0.262773	+	0.205088i
$118$	−4.49242			−0.413561
$119$	0.438447	−	0.759413i	0.0401924	−	0.0696153i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	6.05398			0.548101
$123$	−0.780776	−	1.35234i	−0.0704002	−	0.121937i
$124$	−0.561553	−	0.972638i	−0.0504289	−	0.0873455i
$125$		0			0
$126$	0.438447	+	0.759413i	0.0390600	+	0.0676539i
$127$	2.71922	−	4.70983i	0.241292	−	0.417930i	−0.719791	−	0.694191i	$-0.755762\pi$
$127$	2.71922	−	4.70983i	0.241292	−	0.417930i	0.961083	+	0.276261i	$0.0890955\pi$
$128$	−6.78078	+	11.7446i	−0.599342	+	1.03809i
$129$	4.56155			0.401622
$130$		0			0
$131$	7.36932			0.643860			0.321930	−	0.946763i	$-0.395668\pi$
$131$	7.36932			0.643860			0.321930	+	0.946763i	$0.395668\pi$
$132$	−0.438447	+	0.759413i	−0.0381619	+	0.0660984i
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	3.56155	+	6.16879i	0.307671	+	0.532902i
$135$		0			0
$136$	1.90388	+	3.29762i	0.163257	+	0.282769i
$137$	−2.78078	−	4.81645i	−0.237578	−	0.411497i	0.722441	−	0.691433i	$-0.243020\pi$
$137$	−2.78078	−	4.81645i	−0.237578	−	0.411497i	−0.960019	+	0.279936i	$0.909687\pi$
$138$	3.12311			0.265856
$139$	8.96543	+	15.5286i	0.760438	+	1.31712i	0.942625	+	0.333854i	$0.108349\pi$
$139$	8.96543	+	15.5286i	0.760438	+	1.31712i	−0.182187	+	0.983264i	$0.558318\pi$
$140$		0			0
$141$	−4.12311	+	7.14143i	−0.347228	+	0.601417i
$142$	21.8617			1.83460
$143$	−6.68466	−	2.70469i	−0.558999	−	0.226177i
$144$	−4.68466			−0.390388
$145$		0			0
$146$	−7.90388	+	13.6899i	−0.654130	+	1.13299i
$147$	−3.34233	−	5.78908i	−0.275671	−	0.477476i
$148$	−3.31534			−0.272519
$149$	1.21922	+	2.11176i	0.0998827	+	0.173002i	0.911636	−	0.410999i	$-0.134820\pi$
$149$	1.21922	+	2.11176i	0.0998827	+	0.173002i	−0.811753	+	0.584001i	$0.801487\pi$
$150$		0			0
$151$	−9.36932			−0.762464			−0.381232	−	0.924479i	$-0.624500\pi$
$151$	−9.36932			−0.762464			−0.381232	+	0.924479i	$0.624500\pi$
$152$	8.68466	+	15.0423i	0.704419	+	1.22009i
$153$	−0.780776	+	1.35234i	−0.0631220	+	0.109331i
$154$	−0.876894	+	1.51883i	−0.0706622	+	0.122390i
$155$		0			0
$156$	0.219224	+	1.56557i	0.0175519	+	0.125346i
$157$	−20.3693			−1.62565			−0.812824	−	0.582509i	$-0.802071\pi$
$157$	−20.3693			−1.62565			−0.812824	+	0.582509i	$0.802071\pi$
$158$	−4.24621	+	7.35465i	−0.337810	+	0.585105i
$159$	0.342329	−	0.592932i	0.0271485	−	0.0470225i
$160$		0			0
$161$	1.12311			0.0885131
$162$	−0.780776	−	1.35234i	−0.0613436	−	0.106250i
$163$	−2.40388	−	4.16365i	−0.188287	−	0.326122i	0.756393	−	0.654118i	$-0.226960\pi$
$163$	−2.40388	−	4.16365i	−0.188287	−	0.326122i	−0.944679	+	0.327996i	$0.893627\pi$
$164$	−0.684658			−0.0534628
$165$		0			0
$166$	−0.684658	+	1.18586i	−0.0531398	+	0.0920408i
$167$	5.12311	−	8.87348i	0.396438	−	0.686650i	−0.596846	−	0.802356i	$-0.703580\pi$
$167$	5.12311	−	8.87348i	0.396438	−	0.686650i	0.993284	+	0.115706i	$0.0369129\pi$
$168$	−1.36932			−0.105645
$169$	−12.5000	+	3.57071i	−0.961538	+	0.274670i
$170$		0			0
$171$	−3.56155	+	6.16879i	−0.272359	+	0.471739i
$172$	1.00000	−	1.73205i	0.0762493	−	0.132068i
$173$	10.1231	+	17.5337i	0.769645	+	1.33307i	0.937755	+	0.347297i	$0.112900\pi$
$173$	10.1231	+	17.5337i	0.769645	+	1.33307i	−0.168110	+	0.985768i	$0.553766\pi$
$174$	−10.4384			−0.791337
$175$		0			0
$176$	−4.68466	−	8.11407i	−0.353119	−	0.611621i
$177$	2.87689			0.216241
$178$	−3.80776	−	6.59524i	−0.285404	−	0.494334i
$179$	2.43845	−	4.22351i	0.182258	−	0.315680i	−0.760391	−	0.649466i	$-0.774993\pi$
$179$	2.43845	−	4.22351i	0.182258	−	0.315680i	0.942649	+	0.333785i	$0.108326\pi$
$180$		0			0
$181$	−2.68466			−0.199549			−0.0997745	−	0.995010i	$-0.531812\pi$
$181$	−2.68466			−0.199549			−0.0997745	+	0.995010i	$0.531812\pi$
$182$	0.438447	+	3.13114i	0.0324999	+	0.232095i
$183$	−3.87689			−0.286588
$184$	−2.43845	+	4.22351i	−0.179765	+	0.311362i
$185$		0			0
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−3.12311			−0.228384
$188$	1.80776	+	3.13114i	0.131845	+	0.228362i
$189$	−0.280776	−	0.486319i	−0.0204235	−	0.0353745i
$190$		0			0
$191$	4.56155	+	7.90084i	0.330062	+	0.571685i	0.982524	−	0.186137i	$-0.0595969\pi$
$191$	4.56155	+	7.90084i	0.330062	+	0.571685i	−0.652461	+	0.757822i	$0.726264\pi$
$192$	2.78078	−	4.81645i	0.200685	−	0.347597i
$193$	−6.74621	+	11.6848i	−0.485603	+	0.841089i	−0.999863	−	0.0165453i	$-0.994733\pi$
$193$	−6.74621	+	11.6848i	−0.485603	+	0.841089i	0.514260	+	0.857634i	$0.328067\pi$
$194$	13.3693			0.959861
$195$		0			0
$196$	−2.93087			−0.209348
$197$	6.68466	−	11.5782i	0.476262	−	0.824910i	−0.523368	−	0.852107i	$-0.675325\pi$
$197$	6.68466	−	11.5782i	0.476262	−	0.824910i	0.999630	+	0.0271965i	$0.00865798\pi$
$198$	1.56155	−	2.70469i	0.110975	−	0.192214i
$199$	−11.0885	−	19.2059i	−0.786046	−	1.36147i	−0.928372	−	0.371651i	$-0.878792\pi$
$199$	−11.0885	−	19.2059i	−0.786046	−	1.36147i	0.142327	−	0.989820i	$-0.454542\pi$
$200$		0			0
$201$	−2.28078	−	3.95042i	−0.160874	−	0.278641i
$202$	5.90388	+	10.2258i	0.415396	+	0.719486i
$203$	−3.75379			−0.263464
$204$	0.342329	+	0.592932i	0.0239678	+	0.0415135i
$205$		0			0
$206$	−2.68466	+	4.64996i	−0.187049	+	0.323978i
$207$	−2.00000			−0.139010
$208$	−15.6577	−	6.33527i	−1.08566	−	0.439272i
$209$	−14.2462			−0.985431
$210$		0			0
$211$	−9.84233	+	17.0474i	−0.677574	+	1.17359i	0.298136	+	0.954524i	$0.403635\pi$
$211$	−9.84233	+	17.0474i	−0.677574	+	1.17359i	−0.975709	+	0.219069i	$0.929698\pi$
$212$	−0.150093	−	0.259969i	−0.0103084	−	0.0178548i
$213$	−14.0000			−0.959264
$214$	−6.43845	−	11.1517i	−0.440123	−	0.762316i
$215$		0			0
$216$	2.43845			0.165915
$217$	0.719224	+	1.24573i	0.0488241	+	0.0845658i
$218$	2.19224	−	3.79706i	0.148477	−	0.257170i
$219$	5.06155	−	8.76687i	0.342028	−	0.592410i
$220$		0			0
$221$	−4.43845	+	3.46410i	−0.298562	+	0.233021i
$222$	11.8078			0.792485
$223$	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	$0.0803503\pi$
$224$	−0.684658	+	1.18586i	−0.0457457	+	0.0792338i
$225$		0			0
$226$	−9.06913			−0.603270
$227$	3.56155	+	6.16879i	0.236389	+	0.409437i	0.959675	−	0.281111i	$-0.0907028\pi$
$227$	3.56155	+	6.16879i	0.236389	+	0.409437i	−0.723287	+	0.690548i	$0.757370\pi$
$228$	1.56155	+	2.70469i	0.103416	+	0.179122i
$229$	−16.2462			−1.07358			−0.536790	−	0.843716i	$-0.680363\pi$
$229$	−16.2462			−1.07358			−0.536790	+	0.843716i	$0.680363\pi$
$230$		0			0
$231$	0.561553	−	0.972638i	0.0369475	−	0.0639949i
$232$	8.15009	−	14.1164i	0.535080	−	0.926785i
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$	−0.780776	−	5.57586i	−0.0510410	−	0.364505i
$235$		0			0
$236$	0.630683	−	1.09238i	0.0410540	−	0.0711076i
$237$	2.71922	−	4.70983i	0.176633	−	0.305937i
$238$	0.684658	+	1.18586i	0.0443798	+	0.0768681i
$239$	−25.3693			−1.64100			−0.820502	−	0.571643i	$-0.806306\pi$
$239$	−25.3693			−1.64100			−0.820502	+	0.571643i	$0.806306\pi$
$240$		0			0
$241$	8.90388	+	15.4220i	0.573549	+	0.993417i	0.996198	+	0.0871229i	$0.0277673\pi$
$241$	8.90388	+	15.4220i	0.573549	+	0.993417i	−0.422648	+	0.906294i	$0.638899\pi$
$242$	−10.9309			−0.702663
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.849907	+	1.47208i	−0.0544097	+	0.0942404i
$245$		0			0
$246$	2.43845			0.155470
$247$	−20.2462	+	15.8017i	−1.28824	+	1.00544i
$248$	−6.24621			−0.396635
$249$	0.438447	−	0.759413i	0.0277855	−	0.0481258i
$250$		0			0
$251$	−9.36932	−	16.2281i	−0.591386	−	1.02431i	−0.994046	−	0.108961i	$-0.965248\pi$
$251$	−9.36932	−	16.2281i	−0.591386	−	1.02431i	0.402660	−	0.915350i	$-0.368086\pi$
$252$	−0.246211			−0.0155099
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	4.24621	+	7.35465i	0.266431	+	0.461472i
$255$		0			0
$256$	−5.02699	−	8.70700i	−0.314187	−	0.544187i
$257$	14.5885	−	25.2681i	0.910008	−	1.57618i	0.0959583	−	0.995385i	$-0.469408\pi$
$257$	14.5885	−	25.2681i	0.910008	−	1.57618i	0.814050	−	0.580795i	$-0.197258\pi$
$258$	−3.56155	+	6.16879i	−0.221733	+	0.384052i
$259$	4.24621			0.263847
$260$		0			0
$261$	6.68466			0.413770
$262$	−5.75379	+	9.96585i	−0.355470	+	0.615693i
$263$	4.68466	−	8.11407i	0.288868	−	0.500335i	−0.684672	−	0.728852i	$-0.740054\pi$
$263$	4.68466	−	8.11407i	0.288868	−	0.500335i	0.973540	+	0.228517i	$0.0733877\pi$
$264$	2.43845	+	4.22351i	0.150076	+	0.259939i
$265$		0			0
$266$	3.12311	+	5.40938i	0.191490	+	0.331670i
$267$	2.43845	+	4.22351i	0.149231	+	0.258475i
$268$	−2.00000			−0.122169
$269$	10.6847	+	18.5064i	0.651455	+	1.12835i	0.982770	+	0.184833i	$0.0591745\pi$
$269$	10.6847	+	18.5064i	0.651455	+	1.12835i	−0.331315	+	0.943520i	$0.607492\pi$
$270$		0			0
$271$	14.9654	−	25.9209i	0.909085	−	1.57458i	0.0937481	−	0.995596i	$-0.470115\pi$
$271$	14.9654	−	25.9209i	0.909085	−	1.57458i	0.815337	−	0.578986i	$-0.196551\pi$
$272$	−7.31534			−0.443558
$273$	−0.280776	−	2.00514i	−0.0169934	−	0.121357i
$274$	8.68466			0.524659
$275$		0			0
$276$	−0.438447	+	0.759413i	−0.0263914	+	0.0457113i
$277$	2.65767	+	4.60322i	0.159684	+	0.276581i	0.934755	−	0.355294i	$-0.115619\pi$
$277$	2.65767	+	4.60322i	0.159684	+	0.276581i	−0.775071	+	0.631874i	$0.782286\pi$
$278$	−28.0000			−1.67933
$279$	−1.28078	−	2.21837i	−0.0766781	−	0.132810i
$280$		0			0
$281$	17.8078			1.06232			0.531161	−	0.847271i	$-0.321756\pi$
$281$	17.8078			1.06232			0.531161	+	0.847271i	$0.321756\pi$
$282$	−6.43845	−	11.1517i	−0.383404	−	0.664075i
$283$	−6.84233	+	11.8513i	−0.406734	+	0.704484i	−0.994522	−	0.104531i	$-0.966666\pi$
$283$	−6.84233	+	11.8513i	−0.406734	+	0.704484i	0.587787	+	0.809015i	$0.299999\pi$
$284$	−3.06913	+	5.31589i	−0.182119	+	0.315440i
$285$		0			0
$286$	8.87689	−	6.92820i	0.524902	−	0.409673i
$287$	0.876894			0.0517614
$288$	1.21922	−	2.11176i	0.0718434	−	0.124436i
$289$	7.28078	−	12.6107i	0.428281	−	0.741804i
$290$		0			0
$291$	−8.56155			−0.501887
$292$	−2.21922	−	3.84381i	−0.129870	−	0.224942i
$293$	10.2192	+	17.7002i	0.597013	+	1.03406i	0.993259	+	0.115913i	$0.0369794\pi$
$293$	10.2192	+	17.7002i	0.597013	+	1.03406i	−0.396246	+	0.918144i	$0.629687\pi$
$294$	10.4384			0.608783
$295$		0			0
$296$	−9.21922	+	15.9682i	−0.535856	+	0.928131i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	−3.80776			−0.220578
$299$	−6.68466	−	2.70469i	−0.386584	−	0.156416i
$300$		0			0
$301$	−1.28078	+	2.21837i	−0.0738227	+	0.127865i
$302$	7.31534	−	12.6705i	0.420951	−	0.729108i
$303$	−3.78078	−	6.54850i	−0.217200	−	0.376201i
$304$	−33.3693			−1.91386
$305$		0			0
$306$	−1.21922	−	2.11176i	−0.0696984	−	0.120721i
$307$	−30.8078			−1.75829			−0.879146	−	0.476553i	$-0.841886\pi$
$307$	−30.8078			−1.75829			−0.879146	+	0.476553i	$0.841886\pi$
$308$	−0.246211	−	0.426450i	−0.0140292	−	0.0242993i
$309$	1.71922	−	2.97778i	0.0978032	−	0.169400i
$310$		0			0
$311$	−19.1231			−1.08437			−0.542186	−	0.840259i	$-0.682403\pi$
$311$	−19.1231			−1.08437			−0.542186	+	0.840259i	$0.682403\pi$
$312$	8.15009	+	3.29762i	0.461408	+	0.186691i
$313$	13.6847			0.773503			0.386751	−	0.922184i	$-0.373597\pi$
$313$	13.6847			0.773503			0.386751	+	0.922184i	$0.373597\pi$
$314$	15.9039	−	27.5463i	0.897508	−	1.55453i
$315$		0			0
$316$	−1.19224	−	2.06501i	−0.0670685	−	0.116166i
$317$	−14.0540			−0.789350			−0.394675	−	0.918821i	$-0.629143\pi$
$317$	−14.0540			−0.789350			−0.394675	+	0.918821i	$0.629143\pi$
$318$	0.534565	+	0.925894i	0.0299769	+	0.0519216i
$319$	6.68466	+	11.5782i	0.374269	+	0.648253i
$320$		0			0
$321$	4.12311	+	7.14143i	0.230129	+	0.398596i
$322$	−0.876894	+	1.51883i	−0.0488674	+	0.0846408i
$323$	−5.56155	+	9.63289i	−0.309453	+	0.535988i
$324$	0.438447			0.0243582
$325$		0			0
$326$	7.50758			0.415806
$327$	−1.40388	+	2.43160i	−0.0776349	+	0.134468i
$328$	−1.90388	+	3.29762i	−0.105124	+	0.182081i
$329$	−2.31534	−	4.01029i	−0.127649	−	0.221094i
$330$		0			0
$331$	1.59612	+	2.76456i	0.0877306	+	0.151954i	0.906552	−	0.422095i	$-0.138705\pi$
$331$	1.59612	+	2.76456i	0.0877306	+	0.151954i	−0.818821	+	0.574049i	$0.805372\pi$
$332$	−0.192236	−	0.332962i	−0.0105503	−	0.0182737i
$333$	−7.56155			−0.414371
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$		0			0
$336$	1.31534	−	2.27824i	0.0717578	−	0.124288i
$337$	6.12311			0.333547			0.166773	−	0.985995i	$-0.446665\pi$
$337$	6.12311			0.333547			0.166773	+	0.985995i	$0.446665\pi$
$338$	4.93087	−	19.6922i	0.268204	−	1.07112i
$339$	5.80776			0.315434
$340$		0			0
$341$	2.56155	−	4.43674i	0.138716	−	0.240263i
$342$	−5.56155	−	9.63289i	−0.300734	−	0.520887i
$343$	7.68466			0.414933
$344$	−5.56155	−	9.63289i	−0.299859	−	0.519371i
$345$		0			0
$346$	−31.6155			−1.69966
$347$	13.8078	+	23.9157i	0.741240	+	1.28386i	0.951931	+	0.306312i	$0.0990951\pi$
$347$	13.8078	+	23.9157i	0.741240	+	1.28386i	−0.210692	+	0.977553i	$0.567572\pi$
$348$	1.46543	−	2.53821i	0.0785556	−	0.136062i
$349$	−3.40388	+	5.89570i	−0.182206	+	0.315589i	−0.942631	−	0.333836i	$-0.891657\pi$
$349$	−3.40388	+	5.89570i	−0.182206	+	0.315589i	0.760426	+	0.649425i	$0.224990\pi$
$350$		0			0
$351$	0.500000	+	3.57071i	0.0266880	+	0.190591i
$352$	4.87689			0.259939
$353$	2.65767	−	4.60322i	0.141454	−	0.245005i	−0.786591	−	0.617475i	$-0.788156\pi$
$353$	2.65767	−	4.60322i	0.141454	−	0.245005i	0.928044	+	0.372470i	$0.121489\pi$
$354$	−2.24621	+	3.89055i	−0.119385	+	0.206781i
$355$		0			0
$356$	2.13826			0.113328
$357$	−0.438447	−	0.759413i	−0.0232051	−	0.0401924i
$358$	3.80776	+	6.59524i	0.201247	+	0.348569i
$359$	−9.36932			−0.494494			−0.247247	−	0.968953i	$-0.579526\pi$
$359$	−9.36932			−0.494494			−0.247247	+	0.968953i	$0.579526\pi$
$360$		0			0
$361$	−15.8693	+	27.4865i	−0.835227	+	1.44666i
$362$	2.09612	−	3.63058i	0.110170	−	0.190819i
$363$	7.00000			0.367405
$364$	−0.822919	−	0.332962i	−0.0431327	−	0.0174520i
$365$		0			0
$366$	3.02699	−	5.24290i	0.158223	−	0.274051i
$367$	−8.52699	+	14.7692i	−0.445105	+	0.770945i	−0.998060	−	0.0622668i	$-0.980167\pi$
$367$	−8.52699	+	14.7692i	−0.445105	+	0.770945i	0.552954	+	0.833212i	$0.313500\pi$
$368$	−4.68466	−	8.11407i	−0.244205	−	0.422975i
$369$	−1.56155			−0.0812912
$370$		0			0
$371$	0.192236	+	0.332962i	0.00998039	+	0.0172865i
$372$	−1.12311			−0.0582303
$373$	14.1847	+	24.5685i	0.734454	+	1.27211i	0.954963	+	0.296726i	$0.0958949\pi$
$373$	14.1847	+	24.5685i	0.734454	+	1.27211i	−0.220509	+	0.975385i	$0.570772\pi$
$374$	2.43845	−	4.22351i	0.126089	−	0.218393i
$375$		0			0
$376$	20.1080			1.03699
$377$	22.3423	+	9.03996i	1.15069	+	0.465582i
$378$	0.876894			0.0451026
$379$	−11.8423	+	20.5115i	−0.608300	+	1.05361i	0.383221	+	0.923657i	$0.374815\pi$
$379$	−11.8423	+	20.5115i	−0.608300	+	1.05361i	−0.991521	+	0.129949i	$0.958519\pi$
$380$		0			0
$381$	−2.71922	−	4.70983i	−0.139310	−	0.241292i
$382$	−14.2462			−0.728900
$383$	−11.3693	−	19.6922i	−0.580945	−	1.00623i	−0.995368	−	0.0961417i	$-0.969350\pi$
$383$	−11.3693	−	19.6922i	−0.580945	−	1.00623i	0.414423	−	0.910085i	$-0.363984\pi$
$384$	6.78078	+	11.7446i	0.346030	+	0.599342i
$385$		0			0
$386$	−10.5346	−	18.2464i	−0.536195	−	0.928717i
$387$	2.28078	−	3.95042i	0.115938	−	0.200811i
$388$	−1.87689	+	3.25088i	−0.0952849	+	0.165038i
$389$	34.0540			1.72661			0.863303	−	0.504687i	$-0.168392\pi$
$389$	34.0540			1.72661			0.863303	+	0.504687i	$0.168392\pi$
$390$		0			0
$391$	−3.12311			−0.157942
$392$	−8.15009	+	14.1164i	−0.411642	+	0.712985i
$393$	3.68466	−	6.38202i	0.185866	−	0.321930i
$394$	10.4384	+	18.0799i	0.525881	+	0.910853i
$395$		0			0
$396$	0.438447	+	0.759413i	0.0220328	+	0.0381619i
$397$	12.5270	+	21.6974i	0.628711	+	1.08896i	0.987811	+	0.155661i	$0.0497507\pi$
$397$	12.5270	+	21.6974i	0.628711	+	1.08896i	−0.359099	+	0.933299i	$0.616916\pi$
$398$	34.6307			1.73588
$399$	−2.00000	−	3.46410i	−0.100125	−	0.173422i
$400$		0			0
$401$	−7.21922	+	12.5041i	−0.360511	+	0.624423i	−0.988045	−	0.154166i	$-0.950731\pi$
$401$	−7.21922	+	12.5041i	−0.360511	+	0.624423i	0.627534	+	0.778589i	$0.284064\pi$
$402$	7.12311			0.355268
$403$	−1.28078	−	9.14657i	−0.0638000	−	0.455623i
$404$	−3.31534			−0.164944
$405$		0			0
$406$	2.93087	−	5.07642i	0.145457	−	0.251938i
$407$	−7.56155	−	13.0970i	−0.374812	−	0.649194i
$408$	3.80776			0.188512
$409$	−3.18466	−	5.51599i	−0.157471	−	0.272748i	0.776485	−	0.630136i	$-0.217001\pi$
$409$	−3.18466	−	5.51599i	−0.157471	−	0.272748i	−0.933956	+	0.357388i	$0.883667\pi$
$410$		0			0
$411$	−5.56155			−0.274331
$412$	−0.753789	−	1.30560i	−0.0371365	−	0.0643223i
$413$	−0.807764	+	1.39909i	−0.0397475	+	0.0688446i
$414$	1.56155	−	2.70469i	0.0767461	−	0.132928i
$415$		0			0
$416$	6.93087	−	5.40938i	0.339814	−	0.265217i
$417$	17.9309			0.878078
$418$	11.1231	−	19.2658i	0.544049	−	0.942320i
$419$	17.1231	−	29.6581i	0.836518	−	1.44889i	−0.0562697	−	0.998416i	$-0.517921\pi$
$419$	17.1231	−	29.6581i	0.836518	−	1.44889i	0.892788	−	0.450477i	$-0.148746\pi$
$420$		0			0
$421$	31.2462			1.52285			0.761424	−	0.648255i	$-0.224501\pi$
$421$	31.2462			1.52285			0.761424	+	0.648255i	$0.224501\pi$
$422$	−15.3693	−	26.6204i	−0.748167	−	1.29586i
$423$	4.12311	+	7.14143i	0.200472	+	0.347228i
$424$	−1.66950			−0.0810783
$425$		0			0
$426$	10.9309	−	18.9328i	0.529602	−	0.917298i
$427$	1.08854	−	1.88541i	0.0526782	−	0.0912413i
$428$	3.61553			0.174763
$429$	−5.68466	+	4.43674i	−0.274458	+	0.214208i
$430$		0			0
$431$	5.56155	−	9.63289i	0.267891	−	0.464000i	−0.700426	−	0.713725i	$-0.747007\pi$
$431$	5.56155	−	9.63289i	0.267891	−	0.464000i	0.968317	+	0.249725i	$0.0803401\pi$
$432$	−2.34233	+	4.05703i	−0.112695	+	0.195194i
$433$	4.37689	+	7.58100i	0.210340	+	0.364320i	0.951821	−	0.306654i	$-0.0992095\pi$
$433$	4.37689	+	7.58100i	0.210340	+	0.364320i	−0.741481	+	0.670974i	$0.765876\pi$
$434$	−2.24621			−0.107822
$435$		0			0
$436$	0.615528	+	1.06613i	0.0294785	+	0.0510582i
$437$	−14.2462			−0.681489
$438$	7.90388	+	13.6899i	0.377662	+	0.654130i
$439$	6.84233	−	11.8513i	0.326567	−	0.565630i	−0.655262	−	0.755402i	$-0.727442\pi$
$439$	6.84233	−	11.8513i	0.326567	−	0.565630i	0.981828	+	0.189772i	$0.0607749\pi$
$440$		0			0
$441$	−6.68466			−0.318317
$442$	−1.21922	−	8.70700i	−0.0579926	−	0.414150i
$443$	34.7386			1.65048			0.825241	−	0.564781i	$-0.191039\pi$
$443$	34.7386			1.65048			0.825241	+	0.564781i	$0.191039\pi$
$444$	−1.65767	+	2.87117i	−0.0786696	+	0.136260i
$445$		0			0
$446$	6.24621	+	10.8188i	0.295767	+	0.512283i
$447$	2.43845			0.115335
$448$	1.56155	+	2.70469i	0.0737764	+	0.127785i
$449$	4.12311	+	7.14143i	0.194581	+	0.337025i	0.946763	−	0.321931i	$-0.104332\pi$
$449$	4.12311	+	7.14143i	0.194581	+	0.337025i	−0.752182	+	0.658956i	$0.770998\pi$
$450$		0			0
$451$	−1.56155	−	2.70469i	−0.0735307	−	0.127359i
$452$	1.27320	−	2.20525i	0.0598862	−	0.103726i
$453$	−4.68466	+	8.11407i	−0.220104	+	0.381232i
$454$	−11.1231			−0.522033
$455$		0			0
$456$	17.3693			0.813393
$457$	6.30776	−	10.9254i	0.295065	−	0.511067i	−0.679935	−	0.733272i	$-0.737992\pi$
$457$	6.30776	−	10.9254i	0.295065	−	0.511067i	0.975000	+	0.222205i	$0.0713254\pi$
$458$	12.6847	−	21.9705i	0.592715	−	1.02661i
$459$	0.780776	+	1.35234i	0.0364435	+	0.0631220i
$460$		0			0
$461$	8.09612	+	14.0229i	0.377074	+	0.653111i	0.990635	−	0.136536i	$-0.0435970\pi$
$461$	8.09612	+	14.0229i	0.377074	+	0.653111i	−0.613561	+	0.789647i	$0.710264\pi$
$462$	0.876894	+	1.51883i	0.0407968	+	0.0706622i
$463$	14.3153			0.665290			0.332645	−	0.943052i	$-0.392059\pi$
$463$	14.3153			0.665290			0.332645	+	0.943052i	$0.392059\pi$
$464$	15.6577	+	27.1199i	0.726889	+	1.25901i
$465$		0			0
$466$	20.3002	−	35.1610i	0.940388	−	1.62880i
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$	1.46543	+	0.592932i	0.0677397	+	0.0274083i
$469$	2.56155			0.118282
$470$		0			0
$471$	−10.1847	+	17.6403i	−0.469284	+	0.812824i
$472$	−3.50758	−	6.07530i	−0.161449	−	0.279638i
$473$	9.12311			0.419481
$474$	4.24621	+	7.35465i	0.195035	+	0.337810i
$475$		0			0
$476$	−0.384472			−0.0176222
$477$	−0.342329	−	0.592932i	−0.0156742	−	0.0271485i
$478$	19.8078	−	34.3081i	0.905986	−	1.56921i
$479$	−5.12311	+	8.87348i	−0.234081	+	0.405440i	−0.959005	−	0.283389i	$-0.908541\pi$
$479$	−5.12311	+	8.87348i	−0.234081	+	0.405440i	0.724924	+	0.688828i	$0.241875\pi$
$480$		0			0
$481$	−25.2732	−	10.2258i	−1.15236	−	0.466257i
$482$	−27.8078			−1.26661
$483$	0.561553	−	0.972638i	0.0255515	−	0.0442566i
$484$	1.53457	−	2.65794i	0.0697530	−	0.120816i
$485$		0			0
$486$	−1.56155			−0.0708335
$487$	3.56155	+	6.16879i	0.161389	+	0.279535i	0.935367	−	0.353678i	$-0.115069\pi$
$487$	3.56155	+	6.16879i	0.161389	+	0.279535i	−0.773978	+	0.633213i	$0.781736\pi$
$488$	4.72680	+	8.18706i	0.213972	+	0.370611i
$489$	−4.80776			−0.217415
$490$		0			0
$491$	18.1231	−	31.3901i	0.817884	−	1.41662i	−0.0893539	−	0.996000i	$-0.528480\pi$
$491$	18.1231	−	31.3901i	0.817884	−	1.41662i	0.907238	−	0.420617i	$-0.138186\pi$
$492$	−0.342329	+	0.592932i	−0.0154334	+	0.0267314i
$493$	10.4384			0.470124
$494$	−5.56155	−	39.7174i	−0.250226	−	1.78697i
$495$		0			0
$496$	6.00000	−	10.3923i	0.269408	−	0.466628i
$497$	3.93087	−	6.80847i	0.176324	−	0.305401i
$498$	0.684658	+	1.18586i	0.0306803	+	0.0531398i
$499$	4.49242			0.201108			0.100554	−	0.994932i	$-0.467938\pi$
$499$	4.49242			0.201108			0.100554	+	0.994932i	$0.467938\pi$
$500$		0			0
$501$	−5.12311	−	8.87348i	−0.228883	−	0.396438i
$502$	29.2614			1.30600
$503$	−14.1231	−	24.4619i	−0.629718	−	1.09070i	−0.987608	−	0.156940i	$-0.949837\pi$
$503$	−14.1231	−	24.4619i	−0.629718	−	1.09070i	0.357890	−	0.933764i	$-0.383496\pi$
$504$	−0.684658	+	1.18586i	−0.0304971	+	0.0528225i
$505$		0			0
$506$	6.24621			0.277678
$507$	−3.15767	+	12.6107i	−0.140237	+	0.560060i
$508$	−2.38447			−0.105794
$509$	6.90388	−	11.9579i	0.306009	−	0.530023i	−0.671476	−	0.741026i	$-0.734340\pi$
$509$	6.90388	−	11.9579i	0.306009	−	0.530023i	0.977486	+	0.211003i	$0.0676728\pi$
$510$		0			0
$511$	2.84233	+	4.92306i	0.125737	+	0.217783i
$512$	−11.4233			−0.504843
$513$	3.56155	+	6.16879i	0.157246	+	0.272359i
$514$	22.7808	+	39.4575i	1.00482	+	1.74039i
$515$		0			0
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	−8.24621	+	14.2829i	−0.362668	+	0.628159i
$518$	−3.31534	+	5.74234i	−0.145668	+	0.252304i
$519$	20.2462			0.888710
$520$		0			0
$521$	−9.06913			−0.397326			−0.198663	−	0.980068i	$-0.563660\pi$
$521$	−9.06913			−0.397326			−0.198663	+	0.980068i	$0.563660\pi$
$522$	−5.21922	+	9.03996i	−0.228439	+	0.395668i
$523$	16.9309	−	29.3251i	0.740335	−	1.28230i	−0.212007	−	0.977268i	$-0.568000\pi$
$523$	16.9309	−	29.3251i	0.740335	−	1.28230i	0.952343	−	0.305030i	$-0.0986666\pi$
$524$	−1.61553	−	2.79818i	−0.0705747	−	0.122239i
$525$		0			0
$526$	7.31534	+	12.6705i	0.318964	+	0.552462i
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$	−9.36932			−0.407747
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	1.43845	−	2.49146i	0.0624233	−	0.108120i
$532$	−1.75379			−0.0760364
$533$	−5.21922	−	2.11176i	−0.226070	−	0.0914704i
$534$	−7.61553			−0.329556
$535$		0			0
$536$	−5.56155	+	9.63289i	−0.240222	+	0.416078i
$537$	−2.43845	−	4.22351i	−0.105227	−	0.182258i
$538$	−33.3693			−1.43865
$539$	−6.68466	−	11.5782i	−0.287929	−	0.498707i
$540$		0			0
$541$	19.7386			0.848630			0.424315	−	0.905515i	$-0.360515\pi$
$541$	19.7386			0.848630			0.424315	+	0.905515i	$0.360515\pi$
$542$	23.3693	+	40.4768i	1.00380	+	1.73863i
$543$	−1.34233	+	2.32498i	−0.0576049	+	0.0997745i
$544$	1.90388	−	3.29762i	0.0816283	−	0.141384i
$545$		0			0
$546$	2.93087	+	1.18586i	0.125430	+	0.0507503i
$547$	−3.93087			−0.168072			−0.0840359	−	0.996463i	$-0.526781\pi$
$547$	−3.93087			−0.168072			−0.0840359	+	0.996463i	$0.526781\pi$
$548$	−1.21922	+	2.11176i	−0.0520827	+	0.0902098i
$549$	−1.93845	+	3.35749i	−0.0827309	+	0.143294i
$550$		0			0
$551$	47.6155			2.02849
$552$	2.43845	+	4.22351i	0.103787	+	0.179765i
$553$	1.52699	+	2.64482i	0.0649341	+	0.112469i
$554$	−8.30019			−0.352641
$555$		0			0
$556$	3.93087	−	6.80847i	0.166706	−	0.288743i
$557$	−21.4654	+	37.1792i	−0.909520	+	1.57533i	−0.0947869	+	0.995498i	$0.530217\pi$
$557$	−21.4654	+	37.1792i	−0.909520	+	1.57533i	−0.814733	+	0.579837i	$0.803116\pi$
$558$	4.00000			0.169334
$559$	12.9654	−	10.1192i	0.548379	−	0.427997i
$560$		0			0
$561$	−1.56155	+	2.70469i	−0.0659288	+	0.114192i
$562$	−13.9039	+	24.0822i	−0.586500	+	1.01585i
$563$	−11.6847	−	20.2384i	−0.492450	−	0.852948i	0.507513	−	0.861644i	$-0.330565\pi$
$563$	−11.6847	−	20.2384i	−0.492450	−	0.852948i	−0.999962	+	0.00869657i	$0.997232\pi$
$564$	3.61553			0.152241
$565$		0			0
$566$	−10.6847	−	18.5064i	−0.449110	−	0.777881i
$567$	−0.561553			−0.0235830
$568$	17.0691	+	29.5646i	0.716205	+	1.24050i
$569$	4.36932	−	7.56788i	0.183171	−	0.317262i	−0.759787	−	0.650171i	$-0.774697\pi$
$569$	4.36932	−	7.56788i	0.183171	−	0.317262i	0.942959	+	0.332910i	$0.108030\pi$
$570$		0			0
$571$	−5.36932			−0.224699			−0.112349	−	0.993669i	$-0.535838\pi$
$571$	−5.36932			−0.224699			−0.112349	+	0.993669i	$0.535838\pi$
$572$	0.438447	+	3.13114i	0.0183324	+	0.130920i
$573$	9.12311			0.381123
$574$	−0.684658	+	1.18586i	−0.0285771	+	0.0494970i
$575$		0			0
$576$	−2.78078	−	4.81645i	−0.115866	−	0.200685i
$577$	17.3153			0.720847			0.360424	−	0.932789i	$-0.382632\pi$
$577$	17.3153			0.720847			0.360424	+	0.932789i	$0.382632\pi$
$578$	11.3693	+	19.6922i	0.472901	+	0.819089i
$579$	6.74621	+	11.6848i	0.280363	+	0.485603i
$580$		0			0
$581$	0.246211	+	0.426450i	0.0102146	+	0.0176921i
$582$	6.68466	−	11.5782i	0.277088	−	0.479931i
$583$	0.684658	−	1.18586i	0.0283557	−	0.0491134i
$584$	−24.6847			−1.02146
$585$		0			0
$586$	−31.9157			−1.31843
$587$	19.6847	−	34.0948i	0.812473	−	1.40724i	−0.0986556	−	0.995122i	$-0.531454\pi$
$587$	19.6847	−	34.0948i	0.812473	−	1.40724i	0.911128	−	0.412123i	$-0.135212\pi$
$588$	−1.46543	+	2.53821i	−0.0604335	+	0.104674i
$589$	−9.12311	−	15.8017i	−0.375911	−	0.651097i
$590$		0			0
$591$	−6.68466	−	11.5782i	−0.274970	−	0.476262i
$592$	−17.7116	−	30.6775i	−0.727944	−	1.26084i
$593$	17.4233			0.715489			0.357744	−	0.933820i	$-0.383546\pi$
$593$	17.4233			0.715489			0.357744	+	0.933820i	$0.383546\pi$
$594$	−1.56155	−	2.70469i	−0.0640713	−	0.110975i
$595$		0			0
$596$	0.534565	−	0.925894i	0.0218966	−	0.0379261i
$597$	−22.1771			−0.907648
$598$	8.87689	−	6.92820i	0.363003	−	0.283315i
$599$	−41.6155			−1.70036			−0.850182	−	0.526489i	$-0.823508\pi$
$599$	−41.6155			−1.70036			−0.850182	+	0.526489i	$0.823508\pi$
$600$		0			0
$601$	3.53457	−	6.12205i	0.144178	−	0.249723i	−0.784888	−	0.619638i	$-0.787280\pi$
$601$	3.53457	−	6.12205i	0.144178	−	0.249723i	0.929066	+	0.369914i	$0.120613\pi$
$602$	−2.00000	−	3.46410i	−0.0815139	−	0.141186i
$603$	−4.56155			−0.185761
$604$	2.05398	+	3.55759i	0.0835751	+	0.144756i
$605$		0			0
$606$	11.8078			0.479658
$607$	−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	$0.938600\pi$
$608$	8.68466	−	15.0423i	0.352209	−	0.610045i
$609$	−1.87689	+	3.25088i	−0.0760556	+	0.131732i
$610$		0			0
$611$	4.12311	+	29.4449i	0.166803	+	1.19121i
$612$	0.684658			0.0276757
$613$	−17.4309	+	30.1912i	−0.704026	+	1.21941i	0.263016	+	0.964792i	$0.415283\pi$
$613$	−17.4309	+	30.1912i	−0.704026	+	1.21941i	−0.967042	+	0.254618i	$0.918050\pi$
$614$	24.0540	−	41.6627i	0.970739	−	1.68137i
$615$		0			0
$616$	−2.73863			−0.110343
$617$	4.90388	+	8.49377i	0.197423	+	0.341946i	0.947692	−	0.319186i	$-0.103409\pi$
$617$	4.90388	+	8.49377i	0.197423	+	0.341946i	−0.750269	+	0.661132i	$0.770076\pi$
$618$	2.68466	+	4.64996i	0.107993	+	0.187049i
$619$	29.3002			1.17767			0.588837	−	0.808252i	$-0.299586\pi$
$619$	29.3002			1.17767			0.588837	+	0.808252i	$0.299586\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$	14.9309	−	25.8610i	0.598673	−	1.03693i
$623$	−2.73863			−0.109721
$624$	−13.3153	+	10.3923i	−0.533040	+	0.416025i
$625$		0			0
$626$	−10.6847	+	18.5064i	−0.427045	+	0.739663i
$627$	−7.12311	+	12.3376i	−0.284469	+	0.492716i
$628$	4.46543	+	7.73436i	0.178190	+	0.308635i
$629$	−11.8078			−0.470806
$630$		0			0
$631$	9.28078	+	16.0748i	0.369462	+	0.639927i	0.989481	−	0.144660i	$-0.0462087\pi$
$631$	9.28078	+	16.0748i	0.369462	+	0.639927i	−0.620020	+	0.784586i	$0.712875\pi$
$632$	−13.2614			−0.527509
$633$	9.84233	+	17.0474i	0.391197	+	0.677574i
$634$	10.9730	−	19.0058i	0.435794	−	0.754817i
$635$		0			0
$636$	−0.300187			−0.0119032
$637$	−22.3423	−	9.03996i	−0.885235	−	0.358176i
$638$	−20.8769			−0.826524
$639$	−7.00000	+	12.1244i	−0.276916	+	0.479632i
$640$		0			0
$641$	9.58854	+	16.6078i	0.378725	+	0.655970i	0.990877	−	0.134770i	$-0.0430294\pi$
$641$	9.58854	+	16.6078i	0.378725	+	0.655970i	−0.612152	+	0.790740i	$0.709696\pi$
$642$	−12.8769			−0.508210
$643$	−15.7732	−	27.3200i	−0.622034	−	1.07739i	−0.989106	−	0.147202i	$-0.952973\pi$
$643$	−15.7732	−	27.3200i	−0.622034	−	1.07739i	0.367072	−	0.930192i	$-0.380360\pi$
$644$	−0.246211	−	0.426450i	−0.00970208	−	0.0168045i
$645$		0			0
$646$	−8.68466	−	15.0423i	−0.341693	−	0.591830i
$647$	−3.19224	+	5.52911i	−0.125500	+	0.217372i	−0.921928	−	0.387361i	$-0.873387\pi$
$647$	−3.19224	+	5.52911i	−0.125500	+	0.217372i	0.796428	+	0.604733i	$0.206720\pi$
$648$	1.21922	−	2.11176i	0.0478956	−	0.0829577i
$649$	5.75379			0.225856
$650$		0			0
$651$	1.43845			0.0563772
$652$	−1.05398	+	1.82554i	−0.0412769	+	0.0714936i
$653$	11.5616	−	20.0252i	0.452439	−	0.783647i	−0.546098	−	0.837721i	$-0.683888\pi$
$653$	11.5616	−	20.0252i	0.452439	−	0.783647i	0.998537	+	0.0540745i	$0.0172209\pi$
$654$	−2.19224	−	3.79706i	−0.0857232	−	0.148477i
$655$		0			0
$656$	−3.65767	−	6.33527i	−0.142808	−	0.247351i
$657$	−5.06155	−	8.76687i	−0.197470	−	0.342028i
$658$	7.23106			0.281896
$659$	1.12311	+	1.94528i	0.0437500	+	0.0757772i	0.887071	−	0.461633i	$-0.152736\pi$
$659$	1.12311	+	1.94528i	0.0437500	+	0.0757772i	−0.843321	+	0.537410i	$0.819403\pi$
$660$		0			0
$661$	−2.81534	+	4.87631i	−0.109504	+	0.189667i	−0.915569	−	0.402160i	$-0.868260\pi$
$661$	−2.81534	+	4.87631i	−0.109504	+	0.189667i	0.806065	+	0.591827i	$0.201593\pi$
$662$	−4.98485			−0.193742
$663$	0.780776	+	5.57586i	0.0303228	+	0.216548i
$664$	−2.13826			−0.0829806
$665$		0			0
$666$	5.90388	−	10.2258i	0.228771	−	0.396243i
$667$	6.68466	+	11.5782i	0.258831	+	0.448308i
$668$	−4.49242			−0.173817
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$		0			0
$671$	−7.75379			−0.299332
$672$	0.684658	+	1.18586i	0.0264113	+	0.0457457i
$673$	−11.6231	+	20.1318i	−0.448038	+	0.776024i	−0.998258	−	0.0589952i	$-0.981210\pi$
$673$	−11.6231	+	20.1318i	−0.448038	+	0.776024i	0.550220	+	0.835019i	$0.314544\pi$
$674$	−4.78078	+	8.28055i	−0.184149	+	0.318955i
$675$		0			0
$676$	4.09612	+	3.96355i	0.157543	+	0.152444i
$677$	15.6155			0.600153			0.300077	−	0.953915i	$-0.402988\pi$
$677$	15.6155			0.600153			0.300077	+	0.953915i	$0.402988\pi$
$678$	−4.53457	+	7.85410i	−0.174149	+	0.301635i
$679$	2.40388	−	4.16365i	0.0922525	−	0.159786i
$680$		0			0
$681$	7.12311			0.272958
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	−19.0540	−	33.0025i	−0.729080	−	1.26280i	−0.957272	−	0.289188i	$-0.906615\pi$
$683$	−19.0540	−	33.0025i	−0.729080	−	1.26280i	0.228192	−	0.973616i	$-0.426719\pi$
$684$	3.12311			0.119415
$685$		0			0
$686$	−6.00000	+	10.3923i	−0.229081	+	0.396780i
$687$	−8.12311	+	14.0696i	−0.309916	+	0.536790i
$688$	21.3693			0.814698
$689$	−0.342329	−	2.44472i	−0.0130417	−	0.0931364i
$690$		0			0
$691$	25.6501	−	44.4273i	0.975776	−	1.69009i	0.298424	−	0.954433i	$-0.403539\pi$
$691$	25.6501	−	44.4273i	0.975776	−	1.69009i	0.677352	−	0.735659i	$-0.263128\pi$
$692$	4.43845	−	7.68762i	0.168724	−	0.292239i
$693$	−0.561553	−	0.972638i	−0.0213316	−	0.0369475i
$694$	−43.1231			−1.63693
$695$		0			0
$696$	−8.15009	−	14.1164i	−0.308928	−	0.535080i
$697$	−2.43845			−0.0923628
$698$	−5.31534	−	9.20644i	−0.201189	−	0.348469i
$699$	−13.0000	+	22.5167i	−0.491705	+	0.851658i
$700$		0			0
$701$	−5.36932			−0.202796			−0.101398	−	0.994846i	$-0.532332\pi$
$701$	−5.36932			−0.202796			−0.101398	+	0.994846i	$0.532332\pi$
$702$	−5.21922	−	2.11176i	−0.196987	−	0.0797031i
$703$	−53.8617			−2.03143
$704$	5.56155	−	9.63289i	0.209609	−	0.363053i
$705$		0			0
$706$	4.15009	+	7.18817i	0.156191	+	0.270530i
$707$	4.24621			0.159695
$708$	−0.630683	−	1.09238i	−0.0237025	−	0.0410540i
$709$	3.74621	+	6.48863i	0.140692	+	0.243686i	0.927757	−	0.373184i	$-0.121734\pi$
$709$	3.74621	+	6.48863i	0.140692	+	0.243686i	−0.787065	+	0.616869i	$0.788401\pi$
$710$		0			0
$711$	−2.71922	−	4.70983i	−0.101979	−	0.176633i
$712$	5.94602	−	10.2988i	0.222837	−	0.385964i
$713$	2.56155	−	4.43674i	0.0959309	−	0.166157i
$714$	1.36932			0.0512454
$715$		0			0
$716$	−2.13826			−0.0799106
$717$	−12.6847	+	21.9705i	−0.473717	+	0.820502i
$718$	7.31534	−	12.6705i	0.273006	−	0.472860i
$719$	11.6847	+	20.2384i	0.435764	+	0.754766i	0.997358	−	0.0726475i	$-0.0231448\pi$
$719$	11.6847	+	20.2384i	0.435764	+	0.754766i	−0.561593	+	0.827413i	$0.689811\pi$
$720$		0			0
$721$	0.965435	+	1.67218i	0.0359547	+	0.0622753i
$722$	−24.7808	−	42.9216i	−0.922245	−	1.59738i
$723$	17.8078			0.662278
$724$	0.588540	+	1.01938i	0.0218729	+	0.0378850i
$725$		0			0
$726$	−5.46543	+	9.46641i	−0.202841	+	0.351331i
$727$	38.6695			1.43417			0.717086	−	0.696984i	$-0.245475\pi$
$727$	38.6695			1.43417			0.717086	+	0.696984i	$0.245475\pi$
$728$	−3.89205	+	3.03765i	−0.144249	+	0.112583i
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.56155	−	6.16879i	0.131729	−	0.228161i
$732$	0.849907	+	1.47208i	0.0314135	+	0.0544097i
$733$	−20.5076			−0.757465			−0.378732	−	0.925506i	$-0.623640\pi$
$733$	−20.5076			−0.757465			−0.378732	+	0.925506i	$0.623640\pi$
$734$	−13.3153	−	23.0628i	−0.491478	−	0.851265i
$735$		0			0
$736$	4.87689			0.179765
$737$	−4.56155	−	7.90084i	−0.168027	−	0.291031i
$738$	1.21922	−	2.11176i	0.0448802	−	0.0777349i
$739$	−5.12311	+	8.87348i	−0.188456	+	0.326416i	−0.944736	−	0.327833i	$-0.893682\pi$
$739$	−5.12311	+	8.87348i	−0.188456	+	0.326416i	0.756279	+	0.654249i	$0.227015\pi$
$740$		0			0
$741$	3.56155	+	25.4346i	0.130837	+	0.934362i
$742$	−0.600373			−0.0220404
$743$	−6.31534	+	10.9385i	−0.231687	+	0.401294i	−0.958305	−	0.285748i	$-0.907758\pi$
$743$	−6.31534	+	10.9385i	−0.231687	+	0.401294i	0.726617	+	0.687042i	$0.241091\pi$
$744$	−3.12311	+	5.40938i	−0.114499	+	0.198317i
$745$		0			0
$746$	−44.3002			−1.62195
$747$	−0.438447	−	0.759413i	−0.0160419	−	0.0277855i
$748$	0.684658	+	1.18586i	0.0250336	+	0.0433595i
$749$	−4.63068			−0.169201
$750$		0			0
$751$	−22.0540	+	38.1986i	−0.804761	+	1.39389i	0.111691	+	0.993743i	$0.464373\pi$
$751$	−22.0540	+	38.1986i	−0.804761	+	1.39389i	−0.916452	+	0.400144i	$0.868960\pi$
$752$	−19.3153	+	33.4552i	−0.704358	+	1.21998i
$753$	−18.7386			−0.682874
$754$	−29.6695	+	23.1563i	−1.08050	+	0.843304i
$755$		0			0
$756$	−0.123106	+	0.213225i	−0.00447731	+	0.00775493i
$757$	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	$-0.0168737\pi$
$758$	−18.4924	−	32.0298i	−0.671675	−	1.16338i
$759$	−4.00000			−0.145191
$760$		0			0
$761$	−4.68466	−	8.11407i	−0.169819	−	0.294135i	0.768537	−	0.639805i	$-0.220985\pi$
$761$	−4.68466	−	8.11407i	−0.169819	−	0.294135i	−0.938356	+	0.345670i	$0.887652\pi$
$762$	8.49242			0.307648
$763$	−0.788354	−	1.36547i	−0.0285403	−	0.0494333i
$764$	2.00000	−	3.46410i	0.0723575	−	0.125327i
$765$		0			0
$766$	35.5076			1.28294
$767$	8.17708	−	6.38202i	0.295257	−	0.230441i
$768$	−10.0540			−0.362792
$769$	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
$771$	−14.5885	−	25.2681i	−0.525393	−	0.910008i
$772$	5.91571			0.212911
$773$	−12.1231	−	20.9978i	−0.436038	−	0.755240i	0.561342	−	0.827584i	$-0.310285\pi$
$773$	−12.1231	−	20.9978i	−0.436038	−	0.755240i	−0.997380	+	0.0723444i	$0.976952\pi$
$774$	3.56155	+	6.16879i	0.128017	+	0.221733i
$775$		0			0
$776$	10.4384	+	18.0799i	0.374718	+	0.649031i
$777$	2.12311	−	3.67733i	0.0761660	−	0.131923i
$778$	−26.5885	+	46.0527i	−0.953245	+	1.65107i
$779$	−11.1231			−0.398527
$780$		0			0
$781$	−28.0000			−1.00192
$782$	2.43845	−	4.22351i	0.0871987	−	0.151033i
$783$	3.34233	−	5.78908i	0.119445	−	0.206885i
$784$	−15.6577	−	27.1199i	−0.559203	−	0.968567i
$785$		0			0
$786$	5.75379	+	9.96585i	0.205231	+	0.355470i
$787$	22.0885	+	38.2585i	0.787371	+	1.36377i	0.927572	+	0.373644i	$0.121892\pi$
$787$	22.0885	+	38.2585i	0.787371	+	1.36377i	−0.140201	+	0.990123i	$0.544775\pi$
$788$	−5.86174			−0.208816
$789$	−4.68466	−	8.11407i	−0.166778	−	0.288868i
$790$		0			0
$791$	−1.63068	+	2.82443i	−0.0579804	+	0.100425i
$792$	4.87689			0.173293
$793$	−11.0194	+	8.60039i	−0.391311	+	0.305409i
$794$	−39.1231			−1.38843
$795$		0			0
$796$	−4.86174	+	8.42078i	−0.172320	+	0.298467i
$797$	−0.192236	−	0.332962i	−0.00680935	−	0.0117941i	0.862601	−	0.505885i	$-0.168834\pi$
$797$	−0.192236	−	0.332962i	−0.00680935	−	0.0117941i	−0.869410	+	0.494091i	$0.835501\pi$
$798$	6.24621			0.221113
$799$	6.43845	+	11.1517i	0.227776	+	0.394519i
$800$		0			0
$801$	4.87689			0.172317
$802$	−11.2732	−	19.5258i	−0.398070	−	0.689478i
$803$	10.1231	−	17.5337i	0.357237	−	0.618752i
$804$	−1.00000	+	1.73205i	−0.0352673	+	0.0610847i
$805$		0			0
$806$	13.3693	+	5.40938i	0.470914	+	0.190537i
$807$	21.3693			0.752236
$808$	−9.21922	+	15.9682i	−0.324331	+	0.561758i
$809$	8.15009	−	14.1164i	0.286542	−	0.496305i	−0.686440	−	0.727187i	$-0.740828\pi$
$809$	8.15009	−	14.1164i	0.286542	−	0.496305i	0.972982	+	0.230881i	$0.0741609\pi$
$810$		0			0
$811$	2.56155			0.0899483			0.0449741	−	0.998988i	$-0.485679\pi$
$811$	2.56155			0.0899483			0.0449741	+	0.998988i	$0.485679\pi$
$812$	0.822919	+	1.42534i	0.0288788	+	0.0500195i
$813$	−14.9654	−	25.9209i	−0.524861	−	0.909085i
$814$	23.6155			0.827724
$815$		0			0
$816$	−3.65767	+	6.33527i	−0.128044	+	0.221779i
$817$	16.2462	−	28.1393i	0.568383	−	0.984468i
$818$	9.94602			0.347755
$819$	−1.87689	−	0.759413i	−0.0655840	−	0.0265360i
$820$		0			0
$821$	−3.24621	+	5.62260i	−0.113294	+	0.196230i	−0.917096	−	0.398666i	$-0.869473\pi$
$821$	−3.24621	+	5.62260i	−0.113294	+	0.196230i	0.803803	+	0.594896i	$0.202807\pi$
$822$	4.34233	−	7.52113i	0.151456	−	0.262330i
$823$	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	$0.788806\pi$
$824$	−8.38447			−0.292087
$825$		0			0
$826$	−1.26137	−	2.18475i	−0.0438885	−	0.0760172i
$827$	14.7386			0.512513			0.256256	−	0.966609i	$-0.417511\pi$
$827$	14.7386			0.512513			0.256256	+	0.966609i	$0.417511\pi$
$828$	0.438447	+	0.759413i	0.0152371	+	0.0263914i
$829$	−6.74621	+	11.6848i	−0.234306	+	0.405829i	−0.959071	−	0.283167i	$-0.908615\pi$
$829$	−6.74621	+	11.6848i	−0.234306	+	0.405829i	0.724765	+	0.688996i	$0.241948\pi$
$830$		0			0
$831$	5.31534			0.184387
$832$	−2.78078	−	19.8587i	−0.0964061	−	0.688477i
$833$	−10.4384			−0.361671
$834$	−14.0000	+	24.2487i	−0.484780	+	0.839664i
$835$		0			0
$836$	3.12311	+	5.40938i	0.108015	+	0.187087i
$837$	−2.56155			−0.0885402
$838$	26.7386	+	46.3127i	0.923671	+	1.59984i
$839$	−10.8078	−	18.7196i	−0.373125	−	0.646272i	0.616919	−	0.787027i	$-0.288381\pi$
$839$	−10.8078	−	18.7196i	−0.373125	−	0.646272i	−0.990045	+	0.140754i	$0.955047\pi$
$840$		0			0
$841$	−7.84233	−	13.5833i	−0.270425	−	0.468390i
$842$	−24.3963	+	42.2556i	−0.840752	+	1.45623i
$843$	8.90388	−	15.4220i	0.306666	−	0.531161i
$844$	8.63068			0.297080
$845$		0			0
$846$	−12.8769			−0.442717
$847$	−1.96543	+	3.40423i	−0.0675331	+	0.116971i
$848$	1.60370	−	2.77768i	0.0550711	−	0.0953860i
$849$	6.84233	+	11.8513i	0.234828	+	0.406734i
$850$		0			0
$851$	−7.56155	−	13.0970i	−0.259207	−	0.448959i
$852$	3.06913	+	5.31589i	0.105147	+	0.182119i
$853$	−2.12311			−0.0726938			−0.0363469	−	0.999339i	$-0.511572\pi$
$853$	−2.12311			−0.0726938			−0.0363469	+	0.999339i	$0.511572\pi$
$854$	1.69981	+	2.94416i	0.0581664	+	0.100747i
$855$		0			0
$856$	10.0540	−	17.4140i	0.343638	−	0.595198i
$857$	−35.5616			−1.21476			−0.607380	−	0.794412i	$-0.707779\pi$
$857$	−35.5616			−1.21476			−0.607380	+	0.794412i	$0.707779\pi$
$858$	−1.56155	−	11.1517i	−0.0533105	−	0.380713i
$859$	24.5616			0.838029			0.419015	−	0.907979i	$-0.362376\pi$
$859$	24.5616			0.838029			0.419015	+	0.907979i	$0.362376\pi$
$860$		0			0
$861$	0.438447	−	0.759413i	0.0149422	−	0.0258807i
$862$	8.68466	+	15.0423i	0.295801	+	0.512342i
$863$	−30.4924			−1.03797			−0.518987	−	0.854782i	$-0.673691\pi$
$863$	−30.4924			−1.03797			−0.518987	+	0.854782i	$0.673691\pi$
$864$	−1.21922	−	2.11176i	−0.0414788	−	0.0718434i
$865$		0			0
$866$	−13.6695			−0.464509
$867$	−7.28078	−	12.6107i	−0.247268	−	0.428281i
$868$	0.315342	−	0.546188i	0.0107034	−	0.0185388i
$869$	5.43845	−	9.41967i	0.184487	−	0.319540i
$870$		0			0
$871$	−15.2462	−	6.16879i	−0.516598	−	0.209021i
$872$	6.84658			0.231855
$873$	−4.28078	+	7.41452i	−0.144882	+	0.250944i
$874$	11.1231	−	19.2658i	0.376245	−	0.651675i
$875$		0			0
$876$	−4.43845			−0.149961
$877$	11.7808	+	20.4049i	0.397809	+	0.689025i	0.993455	−	0.114222i	$-0.0364375\pi$
$877$	11.7808	+	20.4049i	0.397809	+	0.689025i	−0.595647	+	0.803247i	$0.703104\pi$
$878$	10.6847	+	18.5064i	0.360590	+	0.624560i
$879$	20.4384			0.689372
$880$		0			0
$881$	4.53457	−	7.85410i	0.152773	−	0.264611i	−0.779473	−	0.626436i	$-0.784513\pi$
$881$	4.53457	−	7.85410i	0.152773	−	0.264611i	0.932246	+	0.361825i	$0.117846\pi$
$882$	5.21922	−	9.03996i	0.175740	−	0.304391i
$883$	−8.80776			−0.296405			−0.148202	−	0.988957i	$-0.547349\pi$
$883$	−8.80776			−0.296405			−0.148202	+	0.988957i	$0.547349\pi$
$884$	2.28835	+	0.925894i	0.0769657	+	0.0311412i
$885$		0			0
$886$	−27.1231	+	46.9786i	−0.911219	+	1.57828i
$887$	12.3153	−	21.3308i	0.413509	−	0.716218i	−0.581762	−	0.813359i	$-0.697636\pi$
$887$	12.3153	−	21.3308i	0.413509	−	0.716218i	0.995271	+	0.0971410i	$0.0309698\pi$
$888$	9.21922	+	15.9682i	0.309377	+	0.535856i
$889$	3.05398			0.102427
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	−3.50758			−0.117442
$893$	29.3693	+	50.8691i	0.982807	+	1.70227i
$894$	−1.90388	+	3.29762i	−0.0636753	+	0.110289i
$895$		0			0
$896$	−7.61553			−0.254417
$897$	−5.68466	+	4.43674i	−0.189805	+	0.148138i
$898$	−12.8769			−0.429708
$899$	−8.56155	+	14.8290i	−0.285544	+	0.494576i
$900$		0			0
$901$	−0.534565	−	0.925894i	−0.0178089	−	0.0308460i
$902$	4.87689			0.162383
$903$	1.28078	+	2.21837i	0.0426216	+	0.0738227i
$904$	−7.08096	−	12.2646i	−0.235509	−	0.407914i
$905$		0			0
$906$	−7.31534	−	12.6705i	−0.243036	−	0.420951i
$907$	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	$0.0127705\pi$
$908$	1.56155	−	2.70469i	0.0518220	−	0.0897583i
$909$	−7.56155			−0.250801
$910$		0			0
$911$	38.7386			1.28347			0.641734	−	0.766927i	$-0.278215\pi$
$911$	38.7386			1.28347			0.641734	+	0.766927i	$0.278215\pi$
$912$	−16.6847	+	28.8987i	−0.552484	+	0.956931i
$913$	0.876894	−	1.51883i	0.0290210	−	0.0502658i
$914$	9.84991	+	17.0605i	0.325806	+	0.564312i
$915$		0			0
$916$	3.56155	+	6.16879i	0.117677	+	0.203823i
$917$	2.06913	+	3.58384i	0.0683287	+	0.118349i
$918$	−2.43845			−0.0804807
$919$	−5.75379	−	9.96585i	−0.189800	−	0.328743i	0.755383	−	0.655283i	$-0.227451\pi$
$919$	−5.75379	−	9.96585i	−0.189800	−	0.328743i	−0.945183	+	0.326540i	$0.894117\pi$
$920$		0			0
$921$	−15.4039	+	26.6803i	−0.507575	+	0.879146i
$922$	−25.2850			−0.832718
$923$	−39.7926	+	31.0572i	−1.30979	+	1.02226i
$924$	−0.492423			−0.0161995
$925$		0			0
$926$	−11.1771	+	19.3593i	−0.367302	+	0.636185i
$927$	−1.71922	−	2.97778i	−0.0564667	−	0.0978032i
$928$	−16.3002			−0.535080
$929$	3.90388	+	6.76172i	0.128082	+	0.221845i	0.922934	−	0.384959i	$-0.125785\pi$
$929$	3.90388	+	6.76172i	0.128082	+	0.221845i	−0.794851	+	0.606804i	$0.792451\pi$
$930$		0			0
$931$	−47.6155			−1.56054
$932$	5.69981	+	9.87237i	0.186704	+	0.323380i
$933$	−9.56155	+	16.5611i	−0.313031	+	0.542186i
$934$	−20.3002	+	35.1610i	−0.664242	+	1.15050i
$935$		0			0
$936$	6.93087	−	5.40938i	0.226543	−	0.176811i
$937$	7.56155			0.247025			0.123513	−	0.992343i	$-0.460584\pi$
$937$	7.56155			0.247025			0.123513	+	0.992343i	$0.460584\pi$
$938$	−2.00000	+	3.46410i	−0.0653023	+	0.113107i
$939$	6.84233	−	11.8513i	0.223291	−	0.386751i
$940$		0			0
$941$	30.4924			0.994025			0.497012	−	0.867744i	$-0.334430\pi$
$941$	30.4924			0.994025			0.497012	+	0.867744i	$0.334430\pi$
$942$	−15.9039	−	27.5463i	−0.518176	−	0.897508i
$943$	−1.56155	−	2.70469i	−0.0508512	−	0.0880768i
$944$	13.4773			0.438648
$945$		0			0
$946$	−7.12311	+	12.3376i	−0.231592	+	0.401129i
$947$	−19.3693	+	33.5486i	−0.629418	+	1.09018i	0.358250	+	0.933626i	$0.383373\pi$
$947$	−19.3693	+	33.5486i	−0.629418	+	1.09018i	−0.987669	+	0.156559i	$0.949960\pi$
$948$	−2.38447			−0.0774440
$949$	−5.06155	−	36.1467i	−0.164305	−	1.17337i
$950$		0			0
$951$	−7.02699	+	12.1711i	−0.227866	+	0.394675i
$952$	−1.06913	+	1.85179i	−0.0346507	+	0.0600168i
$953$	15.4924	+	26.8337i	0.501849	+	0.869228i	0.999998	+	0.00213612i	$0.000679948\pi$
$953$	15.4924	+	26.8337i	0.501849	+	0.869228i	−0.498149	+	0.867091i	$0.665987\pi$
$954$	1.06913			0.0346144
$955$		0			0
$956$	5.56155	+	9.63289i	0.179873	+	0.311550i
$957$	13.3693			0.432169
$958$	−8.00000	−	13.8564i	−0.258468	−	0.447680i
$959$	1.56155	−	2.70469i	0.0504252	−	0.0873390i
$960$		0			0
$961$	−24.4384			−0.788337
$962$	33.5616	−	26.1940i	1.08207	−	0.844528i
$963$	8.24621			0.265730
$964$	3.90388	−	6.76172i	0.125736	−	0.217780i
$965$		0			0
$966$	0.876894	+	1.51883i	0.0282136	+	0.0488674i
$967$	0.876894			0.0281990			0.0140995	−	0.999901i	$-0.495512\pi$
$967$	0.876894			0.0281990			0.0140995	+	0.999901i	$0.495512\pi$
$968$	−8.53457	−	14.7823i	−0.274311	−	0.475121i
$969$	5.56155	+	9.63289i	0.178663	+	0.309453i
$970$		0			0
$971$	6.49242	+	11.2452i	0.208352	+	0.360876i	0.951195	−	0.308589i	$-0.0998568\pi$
$971$	6.49242	+	11.2452i	0.208352	+	0.360876i	−0.742844	+	0.669465i	$0.766523\pi$
$972$	0.219224	−	0.379706i	0.00703160	−	0.0121791i
$973$	−5.03457	+	8.72012i	−0.161401	+	0.279554i
$974$	−11.1231			−0.356407
$975$		0			0
$976$	−18.1619			−0.581349
$977$	30.5885	−	52.9809i	0.978614	−	1.69501i	0.311162	−	0.950357i	$-0.399282\pi$
$977$	30.5885	−	52.9809i	0.978614	−	1.69501i	0.667453	−	0.744652i	$-0.267385\pi$
$978$	3.75379	−	6.50175i	0.120033	−	0.207903i
$979$	4.87689	+	8.44703i	0.155866	+	0.269968i
$980$		0			0
$981$	1.40388	+	2.43160i	0.0448225	+	0.0776349i
$982$	28.3002	+	49.0174i	0.903095	+	1.56421i
$983$	−13.6155			−0.434268			−0.217134	−	0.976142i	$-0.569671\pi$
$983$	−13.6155			−0.434268			−0.217134	+	0.976142i	$0.569671\pi$
$984$	1.90388	+	3.29762i	0.0606935	+	0.105124i
$985$		0			0
$986$	−8.15009	+	14.1164i	−0.259552	+	0.449557i
$987$	−4.63068			−0.147396
$988$	10.4384	+	4.22351i	0.332091	+	0.134368i
$989$	9.12311			0.290098
$990$		0			0
$991$	25.1771	−	43.6080i	0.799776	−	1.38525i	−0.119985	−	0.992776i	$-0.538285\pi$
$991$	25.1771	−	43.6080i	0.799776	−	1.38525i	0.919762	−	0.392478i	$-0.128382\pi$
$992$	3.12311	+	5.40938i	0.0991587	+	0.171748i
$993$	3.19224			0.101303
$994$	6.13826	+	10.6318i	0.194694	+	0.337220i
$995$		0			0
$996$	−0.384472			−0.0121825
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	0.655355	−	0.755321i	$-0.272519\pi$
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	−0.981805	+	0.189893i	$0.939186\pi$
$998$	−3.50758	+	6.07530i	−0.111030	+	0.192310i
$999$	−3.78078	+	6.54850i	−0.119618	+	0.207185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.i.k.451.1		4
5.2	odd	4		975.2.bb.i.724.2		8
5.3	odd	4		975.2.bb.i.724.3		8
5.4	even	2		39.2.e.b.22.2	yes	4
13.3	even	3	inner	975.2.i.k.601.1		4
15.14	odd	2		117.2.g.c.100.1		4
20.19	odd	2		624.2.q.h.529.1		4
60.59	even	2		1872.2.t.r.1153.2		4
65.3	odd	12		975.2.bb.i.874.2		8
65.4	even	6		507.2.a.d.1.2		2
65.9	even	6		507.2.a.g.1.1		2
65.19	odd	12		507.2.b.d.337.3		4
65.24	odd	12		507.2.j.g.361.2		8
65.29	even	6		39.2.e.b.16.2	✓	4
65.34	odd	4		507.2.j.g.316.3		8
65.42	odd	12		975.2.bb.i.874.3		8
65.44	odd	4		507.2.j.g.316.2		8
65.49	even	6		507.2.e.g.484.1		4
65.54	odd	12		507.2.j.g.361.3		8
65.59	odd	12		507.2.b.d.337.2		4
65.64	even	2		507.2.e.g.22.1		4
195.29	odd	6		117.2.g.c.55.1		4
195.59	even	12		1521.2.b.h.1351.3		4
195.74	odd	6		1521.2.a.g.1.2		2
195.134	odd	6		1521.2.a.m.1.1		2
195.149	even	12		1521.2.b.h.1351.2		4
260.139	odd	6		8112.2.a.bk.1.1		2
260.159	odd	6		624.2.q.h.289.1		4
260.199	odd	6		8112.2.a.bo.1.2		2
780.419	even	6		1872.2.t.r.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.2	✓	4	65.29	even	6
39.2.e.b.22.2	yes	4	5.4	even	2
117.2.g.c.55.1		4	195.29	odd	6
117.2.g.c.100.1		4	15.14	odd	2
507.2.a.d.1.2		2	65.4	even	6
507.2.a.g.1.1		2	65.9	even	6
507.2.b.d.337.2		4	65.59	odd	12
507.2.b.d.337.3		4	65.19	odd	12
507.2.e.g.22.1		4	65.64	even	2
507.2.e.g.484.1		4	65.49	even	6
507.2.j.g.316.2		8	65.44	odd	4
507.2.j.g.316.3		8	65.34	odd	4
507.2.j.g.361.2		8	65.24	odd	12
507.2.j.g.361.3		8	65.54	odd	12
624.2.q.h.289.1		4	260.159	odd	6
624.2.q.h.529.1		4	20.19	odd	2
975.2.i.k.451.1		4	1.1	even	1	trivial
975.2.i.k.601.1		4	13.3	even	3	inner
975.2.bb.i.724.2		8	5.2	odd	4
975.2.bb.i.724.3		8	5.3	odd	4
975.2.bb.i.874.2		8	65.3	odd	12
975.2.bb.i.874.3		8	65.42	odd	12
1521.2.a.g.1.2		2	195.74	odd	6
1521.2.a.m.1.1		2	195.134	odd	6
1521.2.b.h.1351.2		4	195.149	even	12
1521.2.b.h.1351.3		4	195.59	even	12
1872.2.t.r.289.2		4	780.419	even	6
1872.2.t.r.1153.2		4	60.59	even	2
8112.2.a.bk.1.1		2	260.139	odd	6
8112.2.a.bo.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.780776 + 1.35234i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(0.780776 + 1.35234i) q^{6} +(0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.780776 + 1.35234i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(0.780776 + 1.35234i) q^{6} +(0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -0.438447 q^{12} +(-0.500000 - 3.57071i) q^{13} -0.876894 q^{14} +(2.34233 - 4.05703i) q^{16} +(-0.780776 - 1.35234i) q^{17} +1.56155 q^{18} +(-3.56155 - 6.16879i) q^{19} +0.561553 q^{21} +(1.56155 + 2.70469i) q^{22} +(1.00000 - 1.73205i) q^{23} +(-1.21922 + 2.11176i) q^{24} +(5.21922 + 2.11176i) q^{26} -1.00000 q^{27} +(0.123106 - 0.213225i) q^{28} +(-3.34233 + 5.78908i) q^{29} +2.56155 q^{31} +(1.21922 + 2.11176i) q^{32} +(-1.00000 - 1.73205i) q^{33} +2.43845 q^{34} +(-0.219224 + 0.379706i) q^{36} +(3.78078 - 6.54850i) q^{37} +11.1231 q^{38} +(-3.34233 - 1.35234i) q^{39} +(0.780776 - 1.35234i) q^{41} +(-0.438447 + 0.759413i) q^{42} +(2.28078 + 3.95042i) q^{43} -0.876894 q^{44} +(1.56155 + 2.70469i) q^{46} -8.24621 q^{47} +(-2.34233 - 4.05703i) q^{48} +(3.34233 - 5.78908i) q^{49} -1.56155 q^{51} +(-1.24621 + 0.972638i) q^{52} +0.684658 q^{53} +(0.780776 - 1.35234i) q^{54} +(-0.684658 - 1.18586i) q^{56} -7.12311 q^{57} +(-5.21922 - 9.03996i) q^{58} +(1.43845 + 2.49146i) q^{59} +(-1.93845 - 3.35749i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(0.280776 - 0.486319i) q^{63} +5.56155 q^{64} +3.12311 q^{66} +(2.28078 - 3.95042i) q^{67} +(-0.342329 + 0.592932i) q^{68} +(-1.00000 - 1.73205i) q^{69} +(-7.00000 - 12.1244i) q^{71} +(1.21922 + 2.11176i) q^{72} +10.1231 q^{73} +(5.90388 + 10.2258i) q^{74} +(-1.56155 + 2.70469i) q^{76} +1.12311 q^{77} +(4.43845 - 3.46410i) q^{78} +5.43845 q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.21922 + 2.11176i) q^{82} +0.876894 q^{83} +(-0.123106 - 0.213225i) q^{84} -7.12311 q^{86} +(3.34233 + 5.78908i) q^{87} +(-2.43845 + 4.22351i) q^{88} +(-2.43845 + 4.22351i) q^{89} +(1.59612 - 1.24573i) q^{91} -0.876894 q^{92} +(1.28078 - 2.21837i) q^{93} +(6.43845 - 11.1517i) q^{94} +2.43845 q^{96} +(-4.28078 - 7.41452i) q^{97} +(5.21922 + 9.03996i) 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

Introduction

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