LMFDB - Embedded newform 850.2.h.m.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(251,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("850.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.h (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.17572153600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 80x^{4} - 98x^{3} + 93x^{2} - 50x + 10 $ x^8 - 4x^7 + 18x^6 - 40x^5 + 80x^4 - 98x^3 + 93x^2 - 50*x + 10
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.2
Root			$0.500000 + 0.0112831i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.m.701.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.511283 - 0.511283i) q^{3} -1.00000 q^{4} +(0.511283 - 0.511283i) q^{6} +(-2.15584 + 2.15584i) q^{7} -1.00000i q^{8} -2.47718i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.511283 - 0.511283i) q^{3} -1.00000 q^{4} +(0.511283 - 0.511283i) q^{6} +(-2.15584 + 2.15584i) q^{7} -1.00000i q^{8} -2.47718i q^{9} +(0.0827533 - 0.0827533i) q^{11} +(0.511283 + 0.511283i) q^{12} +5.60693 q^{13} +(-2.15584 - 2.15584i) q^{14} +1.00000 q^{16} +(4.11353 - 0.280900i) q^{17} +2.47718 q^{18} -3.74987i q^{19} +2.20449 q^{21} +(0.0827533 + 0.0827533i) q^{22} +(-6.08411 + 6.08411i) q^{23} +(-0.511283 + 0.511283i) q^{24} +5.60693i q^{26} +(-2.80039 + 2.80039i) q^{27} +(2.15584 - 2.15584i) q^{28} +(2.85706 + 2.85706i) q^{29} +(4.90571 + 4.90571i) q^{31} +1.00000i q^{32} -0.0846207 q^{33} +(0.280900 + 4.11353i) q^{34} +2.47718i q^{36} +(6.47718 + 6.47718i) q^{37} +3.74987 q^{38} +(-2.86673 - 2.86673i) q^{39} +(4.68969 - 4.68969i) q^{41} +2.20449i q^{42} -0.0451326i q^{43} +(-0.0827533 + 0.0827533i) q^{44} +(-6.08411 - 6.08411i) q^{46} +9.81142 q^{47} +(-0.511283 - 0.511283i) q^{48} -2.29526i q^{49} +(-2.24680 - 1.95956i) q^{51} -5.60693 q^{52} +4.70474i q^{53} +(-2.80039 - 2.80039i) q^{54} +(2.15584 + 2.15584i) q^{56} +(-1.91725 + 1.91725i) q^{57} +(-2.85706 + 2.85706i) q^{58} -7.16873i q^{59} +(-0.584366 + 0.584366i) q^{61} +(-4.90571 + 4.90571i) q^{62} +(5.34039 + 5.34039i) q^{63} -1.00000 q^{64} -0.0846207i q^{66} +11.8960 q^{67} +(-4.11353 + 0.280900i) q^{68} +6.22141 q^{69} +(3.67866 + 3.67866i) q^{71} -2.47718 q^{72} +(-4.66712 - 4.66712i) q^{73} +(-6.47718 + 6.47718i) q^{74} +3.74987i q^{76} +0.356805i q^{77} +(2.86673 - 2.86673i) q^{78} +(1.29878 - 1.29878i) q^{79} -4.56795 q^{81} +(4.68969 + 4.68969i) q^{82} -0.941680i q^{83} -2.20449 q^{84} +0.0451326 q^{86} -2.92153i q^{87} +(-0.0827533 - 0.0827533i) q^{88} +5.94117 q^{89} +(-12.0876 + 12.0876i) q^{91} +(6.08411 - 6.08411i) q^{92} -5.01641i q^{93} +9.81142i q^{94} +(0.511283 - 0.511283i) q^{96} +(-5.10719 - 5.10719i) q^{97} +2.29526 q^{98} +(-0.204995 - 0.204995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 2 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 + 2 * q^7	$ 8 q - 8 q^{4} + 2 q^{7} + 2 q^{11} + 12 q^{13} + 2 q^{14} + 8 q^{16} + 4 q^{17} - 16 q^{18} - 32 q^{21} + 2 q^{22} + 20 q^{23} + 12 q^{27} - 2 q^{28} + 12 q^{29} - 2 q^{31} - 20 q^{33} - 6 q^{34} + 16 q^{37} + 8 q^{38} - 34 q^{39} + 6 q^{41} - 2 q^{44} + 20 q^{46} - 4 q^{47} + 22 q^{51} - 12 q^{52} + 12 q^{54} - 2 q^{56} - 14 q^{57} - 12 q^{58} + 20 q^{61} + 2 q^{62} + 32 q^{63} - 8 q^{64} + 32 q^{67} - 4 q^{68} + 44 q^{69} + 46 q^{71} + 16 q^{72} - 14 q^{73} - 16 q^{74} + 34 q^{78} + 2 q^{79} - 56 q^{81} + 6 q^{82} + 32 q^{84} - 16 q^{86} - 2 q^{88} - 32 q^{89} - 14 q^{91} - 20 q^{92} - 52 q^{97} + 24 q^{98} - 40 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 2 * q^7 + 2 * q^11 + 12 * q^13 + 2 * q^14 + 8 * q^16 + 4 * q^17 - 16 * q^18 - 32 * q^21 + 2 * q^22 + 20 * q^23 + 12 * q^27 - 2 * q^28 + 12 * q^29 - 2 * q^31 - 20 * q^33 - 6 * q^34 + 16 * q^37 + 8 * q^38 - 34 * q^39 + 6 * q^41 - 2 * q^44 + 20 * q^46 - 4 * q^47 + 22 * q^51 - 12 * q^52 + 12 * q^54 - 2 * q^56 - 14 * q^57 - 12 * q^58 + 20 * q^61 + 2 * q^62 + 32 * q^63 - 8 * q^64 + 32 * q^67 - 4 * q^68 + 44 * q^69 + 46 * q^71 + 16 * q^72 - 14 * q^73 - 16 * q^74 + 34 * q^78 + 2 * q^79 - 56 * q^81 + 6 * q^82 + 32 * q^84 - 16 * q^86 - 2 * q^88 - 32 * q^89 - 14 * q^91 - 20 * q^92 - 52 * q^97 + 24 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.511283	−	0.511283i	−0.295189	−	0.295189i	0.543937	−	0.839126i	$-0.316933\pi$
$3$	−0.511283	−	0.511283i	−0.295189	−	0.295189i	−0.839126	+	0.543937i	$0.816933\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	0.511283	−	0.511283i	0.208730	−	0.208730i
$7$	−2.15584	+	2.15584i	−0.814830	+	0.814830i	−0.985354	−	0.170524i	$-0.945454\pi$
$7$	−2.15584	+	2.15584i	−0.814830	+	0.814830i	0.170524	+	0.985354i	$0.445454\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	2.47718i		−	0.825726i
$10$		0			0
$11$	0.0827533	−	0.0827533i	0.0249511	−	0.0249511i	−0.694521	−	0.719472i	$-0.744384\pi$
$11$	0.0827533	−	0.0827533i	0.0249511	−	0.0249511i	0.719472	+	0.694521i	$0.244384\pi$
$12$	0.511283	+	0.511283i	0.147595	+	0.147595i
$13$	5.60693			1.55508			0.777542	−	0.628831i	$-0.216466\pi$
$13$	5.60693			1.55508			0.777542	+	0.628831i	$0.216466\pi$
$14$	−2.15584	−	2.15584i	−0.576171	−	0.576171i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.11353	−	0.280900i	0.997677	−	0.0681282i
$17$	4.11353	−	0.280900i	0.997677	−	0.0681282i
$18$	2.47718			0.583877
$19$		−	3.74987i		−	0.860280i	−0.902762	−	0.430140i	$-0.858464\pi$
$19$		−	3.74987i		−	0.860280i	0.902762	−	0.430140i	$-0.141536\pi$
$20$		0			0
$21$	2.20449			0.481058
$22$	0.0827533	+	0.0827533i	0.0176431	+	0.0176431i
$23$	−6.08411	+	6.08411i	−1.26862	+	1.26862i	−0.321826	+	0.946799i	$0.604297\pi$
$23$	−6.08411	+	6.08411i	−1.26862	+	1.26862i	−0.946799	+	0.321826i	$0.895703\pi$
$24$	−0.511283	+	0.511283i	−0.104365	+	0.104365i
$25$		0			0
$26$			5.60693i			1.09961i
$27$	−2.80039	+	2.80039i	−0.538935	+	0.538935i
$28$	2.15584	−	2.15584i	0.407415	−	0.407415i
$29$	2.85706	+	2.85706i	0.530543	+	0.530543i	0.920734	−	0.390191i	$-0.127591\pi$
$29$	2.85706	+	2.85706i	0.530543	+	0.530543i	−0.390191	+	0.920734i	$0.627591\pi$
$30$		0			0
$31$	4.90571	+	4.90571i	0.881091	+	0.881091i	0.993646	−	0.112554i	$-0.0359032\pi$
$31$	4.90571	+	4.90571i	0.881091	+	0.881091i	−0.112554	+	0.993646i	$0.535903\pi$
$32$			1.00000i			0.176777i
$33$	−0.0846207			−0.0147306
$34$	0.280900	+	4.11353i	0.0481739	+	0.705464i
$35$		0			0
$36$			2.47718i			0.412863i
$37$	6.47718	+	6.47718i	1.06484	+	1.06484i	0.997747	+	0.0670951i	$0.0213731\pi$
$37$	6.47718	+	6.47718i	1.06484	+	1.06484i	0.0670951	+	0.997747i	$0.478627\pi$
$38$	3.74987			0.608310
$39$	−2.86673	−	2.86673i	−0.459044	−	0.459044i
$40$		0			0
$41$	4.68969	−	4.68969i	0.732406	−	0.732406i	−0.238690	−	0.971096i	$-0.576718\pi$
$41$	4.68969	−	4.68969i	0.732406	−	0.732406i	0.971096	+	0.238690i	$0.0767180\pi$
$42$			2.20449i			0.340159i
$43$		−	0.0451326i		−	0.00688265i	−0.999994	−	0.00344133i	$-0.998905\pi$
$43$		−	0.0451326i		−	0.00688265i	0.999994	−	0.00344133i	$-0.00109541\pi$
$44$	−0.0827533	+	0.0827533i	−0.0124755	+	0.0124755i
$45$		0			0
$46$	−6.08411	−	6.08411i	−0.897053	−	0.897053i
$47$	9.81142			1.43114			0.715571	−	0.698540i	$-0.246166\pi$
$47$	9.81142			1.43114			0.715571	+	0.698540i	$0.246166\pi$
$48$	−0.511283	−	0.511283i	−0.0737974	−	0.0737974i
$49$		−	2.29526i		−	0.327894i
$50$		0			0
$51$	−2.24680	−	1.95956i	−0.314614	−	0.274393i
$52$	−5.60693			−0.777542
$53$			4.70474i			0.646246i	0.946357	+	0.323123i	$0.104733\pi$
$53$			4.70474i			0.646246i	−0.946357	+	0.323123i	$0.895267\pi$
$54$	−2.80039	−	2.80039i	−0.381085	−	0.381085i
$55$		0			0
$56$	2.15584	+	2.15584i	0.288086	+	0.288086i
$57$	−1.91725	+	1.91725i	−0.253946	+	0.253946i
$58$	−2.85706	+	2.85706i	−0.375150	+	0.375150i
$59$		−	7.16873i		−	0.933289i	−0.884445	−	0.466645i	$-0.845463\pi$
$59$		−	7.16873i		−	0.933289i	0.884445	−	0.466645i	$-0.154537\pi$
$60$		0			0
$61$	−0.584366	+	0.584366i	−0.0748204	+	0.0748204i	−0.743527	−	0.668706i	$-0.766848\pi$
$61$	−0.584366	+	0.584366i	−0.0748204	+	0.0748204i	0.668706	+	0.743527i	$0.266848\pi$
$62$	−4.90571	+	4.90571i	−0.623026	+	0.623026i
$63$	5.34039	+	5.34039i	0.672826	+	0.672826i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	0.0846207i		−	0.0104161i
$67$	11.8960			1.45333			0.726666	−	0.686991i	$-0.241069\pi$
$67$	11.8960			1.45333			0.726666	+	0.686991i	$0.241069\pi$
$68$	−4.11353	+	0.280900i	−0.498838	+	0.0340641i
$69$	6.22141			0.748969
$70$		0			0
$71$	3.67866	+	3.67866i	0.436576	+	0.436576i	0.890858	−	0.454282i	$-0.150104\pi$
$71$	3.67866	+	3.67866i	0.436576	+	0.436576i	−0.454282	+	0.890858i	$0.650104\pi$
$72$	−2.47718			−0.291938
$73$	−4.66712	−	4.66712i	−0.546245	−	0.546245i	0.379108	−	0.925353i	$-0.376231\pi$
$73$	−4.66712	−	4.66712i	−0.546245	−	0.546245i	−0.925353	+	0.379108i	$0.876231\pi$
$74$	−6.47718	+	6.47718i	−0.752957	+	0.752957i
$75$		0			0
$76$			3.74987i			0.430140i
$77$			0.356805i			0.0406617i
$78$	2.86673	−	2.86673i	0.324593	−	0.324593i
$79$	1.29878	−	1.29878i	0.146124	−	0.146124i	−0.630260	−	0.776384i	$-0.717052\pi$
$79$	1.29878	−	1.29878i	0.146124	−	0.146124i	0.776384	+	0.630260i	$0.217052\pi$
$80$		0			0
$81$	−4.56795			−0.507550
$82$	4.68969	+	4.68969i	0.517889	+	0.517889i
$83$		−	0.941680i		−	0.103363i	−0.998664	−	0.0516814i	$-0.983542\pi$
$83$		−	0.941680i		−	0.103363i	0.998664	−	0.0516814i	$-0.0164580\pi$
$84$	−2.20449			−0.240529
$85$		0			0
$86$	0.0451326			0.00486677
$87$		−	2.92153i		−	0.313221i
$88$	−0.0827533	−	0.0827533i	−0.00882153	−	0.00882153i
$89$	5.94117			0.629763			0.314881	−	0.949131i	$-0.398035\pi$
$89$	5.94117			0.629763			0.314881	+	0.949131i	$0.398035\pi$
$90$		0			0
$91$	−12.0876	+	12.0876i	−1.26713	+	1.26713i
$92$	6.08411	−	6.08411i	0.634312	−	0.634312i
$93$		−	5.01641i		−	0.520178i
$94$			9.81142i			1.01197i
$95$		0			0
$96$	0.511283	−	0.511283i	0.0521826	−	0.0521826i
$97$	−5.10719	−	5.10719i	−0.518556	−	0.518556i	0.398578	−	0.917134i	$-0.369504\pi$
$97$	−5.10719	−	5.10719i	−0.518556	−	0.518556i	−0.917134	+	0.398578i	$0.869504\pi$
$98$	2.29526			0.231856
$99$	−0.204995	−	0.204995i	−0.0206027	−	0.0206027i
$100$		0			0
$101$	9.01641			0.897167			0.448583	−	0.893741i	$-0.351929\pi$
$101$	9.01641			0.897167			0.448583	+	0.893741i	$0.351929\pi$
$102$	1.95956	−	2.24680i	0.194025	−	0.222466i
$103$	−17.3563			−1.71017			−0.855083	−	0.518491i	$-0.826494\pi$
$103$	−17.3563			−1.71017			−0.855083	+	0.518491i	$0.826494\pi$
$104$		−	5.60693i		−	0.549805i
$105$		0			0
$106$	−4.70474			−0.456965
$107$	−1.01103	−	1.01103i	−0.0977398	−	0.0977398i	0.656546	−	0.754286i	$-0.272017\pi$
$107$	−1.01103	−	1.01103i	−0.0977398	−	0.0977398i	−0.754286	+	0.656546i	$0.772017\pi$
$108$	2.80039	−	2.80039i	0.269468	−	0.269468i
$109$	6.21064	−	6.21064i	0.594871	−	0.594871i	−0.344072	−	0.938943i	$-0.611806\pi$
$109$	6.21064	−	6.21064i	0.594871	−	0.594871i	0.938943	+	0.344072i	$0.111806\pi$
$110$		0			0
$111$		−	6.62335i		−	0.628660i
$112$	−2.15584	+	2.15584i	−0.203707	+	0.203707i
$113$	−6.71225	+	6.71225i	−0.631436	+	0.631436i	−0.948428	−	0.316992i	$-0.897327\pi$
$113$	−6.71225	+	6.71225i	−0.631436	+	0.631436i	0.316992	+	0.948428i	$0.397327\pi$
$114$	−1.91725	−	1.91725i	−0.179567	−	0.179567i
$115$		0			0
$116$	−2.85706	−	2.85706i	−0.265271	−	0.265271i
$117$		−	13.8894i		−	1.28407i
$118$	7.16873			0.659935
$119$	−8.26251	+	9.47366i	−0.757423	+	0.868449i
$120$		0			0
$121$			10.9863i			0.998755i
$122$	−0.584366	−	0.584366i	−0.0529060	−	0.0529060i
$123$	−4.79551			−0.432397
$124$	−4.90571	−	4.90571i	−0.440546	−	0.440546i
$125$		0			0
$126$	−5.34039	+	5.34039i	−0.475760	+	0.475760i
$127$		−	14.9544i		−	1.32698i	−0.748183	−	0.663492i	$-0.769074\pi$
$127$		−	14.9544i		−	1.32698i	0.748183	−	0.663492i	$-0.230926\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−0.0230755	+	0.0230755i	−0.00203169	+	0.00203169i
$130$		0			0
$131$	−4.34391	−	4.34391i	−0.379529	−	0.379529i	0.491403	−	0.870932i	$-0.336484\pi$
$131$	−4.34391	−	4.34391i	−0.379529	−	0.379529i	−0.870932	+	0.491403i	$0.836484\pi$
$132$	0.0846207			0.00736529
$133$	8.08411	+	8.08411i	0.700981	+	0.700981i
$134$			11.8960i			1.02766i
$135$		0			0
$136$	−0.280900	−	4.11353i	−0.0240870	−	0.352732i
$137$	−16.8566			−1.44015			−0.720076	−	0.693895i	$-0.755893\pi$
$137$	−16.8566			−1.44015			−0.720076	+	0.693895i	$0.755893\pi$
$138$			6.22141i			0.529601i
$139$	12.5728	+	12.5728i	1.06641	+	1.06641i	0.997632	+	0.0687816i	$0.0219112\pi$
$139$	12.5728	+	12.5728i	1.06641	+	1.06641i	0.0687816	+	0.997632i	$0.478089\pi$
$140$		0			0
$141$	−5.01641	−	5.01641i	−0.422458	−	0.422458i
$142$	−3.67866	+	3.67866i	−0.308706	+	0.308706i
$143$	0.463992	−	0.463992i	0.0388010	−	0.0388010i
$144$		−	2.47718i		−	0.206432i
$145$		0			0
$146$	4.66712	−	4.66712i	0.386254	−	0.386254i
$147$	−1.17353	+	1.17353i	−0.0967909	+	0.0967909i
$148$	−6.47718	−	6.47718i	−0.532421	−	0.532421i
$149$	−24.0417			−1.96957			−0.984786	−	0.173770i	$-0.944405\pi$
$149$	−24.0417			−1.96957			−0.984786	+	0.173770i	$0.944405\pi$
$150$		0			0
$151$			1.68833i			0.137394i	0.997638	+	0.0686971i	$0.0218842\pi$
$151$			1.68833i			0.137394i	−0.997638	+	0.0686971i	$0.978116\pi$
$152$	−3.74987			−0.304155
$153$	−0.695839	−	10.1899i	−0.0562553	−	0.823808i
$154$	−0.356805			−0.0287522
$155$		0			0
$156$	2.86673	+	2.86673i	0.229522	+	0.229522i
$157$	2.50912			0.200250			0.100125	−	0.994975i	$-0.468076\pi$
$157$	2.50912			0.200250			0.100125	+	0.994975i	$0.468076\pi$
$158$	1.29878	+	1.29878i	0.103325	+	0.103325i
$159$	2.40545	−	2.40545i	0.190765	−	0.190765i
$160$		0			0
$161$		−	26.2327i		−	2.06743i
$162$		−	4.56795i		−	0.358892i
$163$	9.53385	−	9.53385i	0.746749	−	0.746749i	−0.227118	−	0.973867i	$-0.572930\pi$
$163$	9.53385	−	9.53385i	0.746749	−	0.746749i	0.973867	+	0.227118i	$0.0729304\pi$
$164$	−4.68969	+	4.68969i	−0.366203	+	0.366203i
$165$		0			0
$166$	0.941680			0.0730886
$167$	−8.70474	−	8.70474i	−0.673593	−	0.673593i	0.284950	−	0.958543i	$-0.408023\pi$
$167$	−8.70474	−	8.70474i	−0.673593	−	0.673593i	−0.958543	+	0.284950i	$0.908023\pi$
$168$		−	2.20449i		−	0.170080i
$169$	18.4377			1.41828
$170$		0			0
$171$	−9.28911			−0.710356
$172$			0.0451326i			0.00344133i
$173$	−2.20449	−	2.20449i	−0.167604	−	0.167604i	0.618321	−	0.785925i	$-0.287813\pi$
$173$	−2.20449	−	2.20449i	−0.167604	−	0.167604i	−0.785925	+	0.618321i	$0.787813\pi$
$174$	2.92153			0.221481
$175$		0			0
$176$	0.0827533	−	0.0827533i	0.00623776	−	0.00623776i
$177$	−3.66525	+	3.66525i	−0.275497	+	0.275497i
$178$			5.94117i			0.445310i
$179$		−	3.46399i		−	0.258911i	−0.991585	−	0.129455i	$-0.958677\pi$
$179$		−	3.46399i		−	0.258911i	0.991585	−	0.129455i	$-0.0413229\pi$
$180$		0			0
$181$	16.4409	−	16.4409i	1.22204	−	1.22204i	0.255139	−	0.966904i	$-0.417879\pi$
$181$	16.4409	−	16.4409i	1.22204	−	1.22204i	0.966904	−	0.255139i	$-0.0821214\pi$
$182$	−12.0876	−	12.0876i	−0.895995	−	0.895995i
$183$	0.597553			0.0441724
$184$	6.08411	+	6.08411i	0.448527	+	0.448527i
$185$		0			0
$186$	5.01641			0.367821
$187$	0.317162	−	0.363653i	0.0231932	−	0.0265930i
$188$	−9.81142			−0.715571
$189$		−	12.0744i		−	0.878281i
$190$		0			0
$191$	−14.7330			−1.06604			−0.533019	−	0.846103i	$-0.678943\pi$
$191$	−14.7330			−1.06604			−0.533019	+	0.846103i	$0.678943\pi$
$192$	0.511283	+	0.511283i	0.0368987	+	0.0368987i
$193$	19.1607	−	19.1607i	1.37922	−	1.37922i	0.533278	−	0.845940i	$-0.320960\pi$
$193$	19.1607	−	19.1607i	1.37922	−	1.37922i	0.845940	−	0.533278i	$-0.179040\pi$
$194$	5.10719	−	5.10719i	0.366675	−	0.366675i
$195$		0			0
$196$			2.29526i			0.163947i
$197$	−1.41563	+	1.41563i	−0.100860	+	0.100860i	−0.755736	−	0.654876i	$-0.772721\pi$
$197$	−1.41563	+	1.41563i	−0.100860	+	0.100860i	0.654876	+	0.755736i	$0.272721\pi$
$198$	0.204995	−	0.204995i	0.0145683	−	0.0145683i
$199$	12.2496	+	12.2496i	0.868352	+	0.868352i	0.992290	−	0.123938i	$-0.0395523\pi$
$199$	12.2496	+	12.2496i	0.868352	+	0.868352i	−0.123938	+	0.992290i	$0.539552\pi$
$200$		0			0
$201$	−6.08224	−	6.08224i	−0.429008	−	0.429008i
$202$			9.01641i			0.634393i
$203$	−12.3187			−0.864604
$204$	2.24680	+	1.95956i	0.157307	+	0.137196i
$205$		0			0
$206$		−	17.3563i		−	1.20927i
$207$	15.0714	+	15.0714i	1.04754	+	1.04754i
$208$	5.60693			0.388771
$209$	−0.310314	−	0.310314i	−0.0214649	−	0.0214649i
$210$		0			0
$211$	−7.27757	+	7.27757i	−0.501008	+	0.501008i	−0.911751	−	0.410743i	$-0.865269\pi$
$211$	−7.27757	+	7.27757i	−0.501008	+	0.501008i	0.410743	+	0.911751i	$0.365269\pi$
$212$		−	4.70474i		−	0.323123i
$213$		−	3.76167i		−	0.257745i
$214$	1.01103	−	1.01103i	0.0691125	−	0.0691125i
$215$		0			0
$216$	2.80039	+	2.80039i	0.190542	+	0.190542i
$217$	−21.1518			−1.43588
$218$	6.21064	+	6.21064i	0.420638	+	0.420638i
$219$			4.77244i			0.322492i
$220$		0			0
$221$	23.0643	−	1.57499i	1.55147	−	0.105945i
$222$	6.62335			0.444530
$223$			1.64319i			0.110036i	0.998485	+	0.0550182i	$0.0175217\pi$
$223$			1.64319i			0.110036i	−0.998485	+	0.0550182i	$0.982478\pi$
$224$	−2.15584	−	2.15584i	−0.144043	−	0.144043i
$225$		0			0
$226$	−6.71225	−	6.71225i	−0.446492	−	0.446492i
$227$	−2.19159	+	2.19159i	−0.145461	+	0.145461i	−0.776087	−	0.630626i	$-0.782798\pi$
$227$	−2.19159	+	2.19159i	−0.145461	+	0.145461i	0.630626	+	0.776087i	$0.282798\pi$
$228$	1.91725	−	1.91725i	0.126973	−	0.126973i
$229$			24.8988i			1.64536i	0.568508	+	0.822678i	$0.307521\pi$
$229$			24.8988i			1.64536i	−0.568508	+	0.822678i	$0.692479\pi$
$230$		0			0
$231$	0.182428	−	0.182428i	0.0120029	−	0.0120029i
$232$	2.85706	−	2.85706i	0.187575	−	0.187575i
$233$	−1.37373	−	1.37373i	−0.0899958	−	0.0899958i	0.660676	−	0.750671i	$-0.270270\pi$
$233$	−1.37373	−	1.37373i	−0.0899958	−	0.0899958i	−0.750671	+	0.660676i	$0.770270\pi$
$234$	13.8894			0.907977
$235$		0			0
$236$			7.16873i			0.466645i
$237$	−1.32809			−0.0862684
$238$	−9.47366	−	8.26251i	−0.614086	−	0.535579i
$239$	13.9549			0.902665			0.451333	−	0.892356i	$-0.350949\pi$
$239$	13.9549			0.902665			0.451333	+	0.892356i	$0.350949\pi$
$240$		0			0
$241$	6.99198	+	6.99198i	0.450393	+	0.450393i	0.895485	−	0.445092i	$-0.146829\pi$
$241$	6.99198	+	6.99198i	0.450393	+	0.450393i	−0.445092	+	0.895485i	$0.646829\pi$
$242$	−10.9863			−0.706226
$243$	10.7367	+	10.7367i	0.688759	+	0.688759i
$244$	0.584366	−	0.584366i	0.0374102	−	0.0374102i
$245$		0			0
$246$		−	4.79551i		−	0.305751i
$247$		−	21.0253i		−	1.33781i
$248$	4.90571	−	4.90571i	0.311513	−	0.311513i
$249$	−0.481465	+	0.481465i	−0.0305116	+	0.0305116i
$250$		0			0
$251$	−4.72731			−0.298385			−0.149192	−	0.988808i	$-0.547667\pi$
$251$	−4.72731			−0.298385			−0.149192	+	0.988808i	$0.547667\pi$
$252$	−5.34039	−	5.34039i	−0.336413	−	0.336413i
$253$			1.00696i			0.0633071i
$254$	14.9544			0.938320
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	19.6327i		−	1.22466i	−0.790604	−	0.612328i	$-0.790233\pi$
$257$		−	19.6327i		−	1.22466i	0.790604	−	0.612328i	$-0.209767\pi$
$258$	−0.0230755	−	0.0230755i	−0.00143662	−	0.00143662i
$259$	−27.9275			−1.73533
$260$		0			0
$261$	7.07745	−	7.07745i	0.438083	−	0.438083i
$262$	4.34391	−	4.34391i	0.268368	−	0.268368i
$263$			24.2134i			1.49306i	0.665352	+	0.746530i	$0.268281\pi$
$263$			24.2134i			1.49306i	−0.665352	+	0.746530i	$0.731719\pi$
$264$			0.0846207i			0.00520805i
$265$		0			0
$266$	−8.08411	+	8.08411i	−0.495669	+	0.495669i
$267$	−3.03762	−	3.03762i	−0.185899	−	0.185899i
$268$	−11.8960			−0.726666
$269$	−15.0615	−	15.0615i	−0.918319	−	0.918319i	0.0785885	−	0.996907i	$-0.474959\pi$
$269$	−15.0615	−	15.0615i	−0.918319	−	0.918319i	−0.996907	+	0.0785885i	$0.974959\pi$
$270$		0			0
$271$	4.18858			0.254438			0.127219	−	0.991875i	$-0.459395\pi$
$271$	4.18858			0.254438			0.127219	+	0.991875i	$0.459395\pi$
$272$	4.11353	−	0.280900i	0.249419	−	0.0170321i
$273$	12.3604			0.748086
$274$		−	16.8566i		−	1.01834i
$275$		0			0
$276$	−6.22141			−0.374485
$277$	5.25013	+	5.25013i	0.315450	+	0.315450i	0.847016	−	0.531567i	$-0.178397\pi$
$277$	5.25013	+	5.25013i	0.315450	+	0.315450i	−0.531567	+	0.847016i	$0.678397\pi$
$278$	−12.5728	+	12.5728i	−0.754068	+	0.754068i
$279$	12.1523	−	12.1523i	0.727540	−	0.727540i
$280$		0			0
$281$			11.7752i			0.702447i	0.936292	+	0.351223i	$0.114234\pi$
$281$			11.7752i			0.702447i	−0.936292	+	0.351223i	$0.885766\pi$
$282$	5.01641	−	5.01641i	0.298723	−	0.298723i
$283$	1.24211	−	1.24211i	0.0738355	−	0.0738355i	−0.669225	−	0.743060i	$-0.733374\pi$
$283$	1.24211	−	1.24211i	0.0738355	−	0.0738355i	0.743060	+	0.669225i	$0.233374\pi$
$284$	−3.67866	−	3.67866i	−0.218288	−	0.218288i
$285$		0			0
$286$	0.463992	+	0.463992i	0.0274364	+	0.0274364i
$287$			20.2204i			1.19357i
$288$	2.47718			0.145969
$289$	16.8422	−	2.31098i	0.990717	−	0.135940i
$290$		0			0
$291$			5.22244i			0.306145i
$292$	4.66712	+	4.66712i	0.273123	+	0.273123i
$293$	−28.6223			−1.67213			−0.836067	−	0.548627i	$-0.815151\pi$
$293$	−28.6223			−1.67213			−0.836067	+	0.548627i	$0.815151\pi$
$294$	−1.17353	−	1.17353i	−0.0684415	−	0.0684415i
$295$		0			0
$296$	6.47718	−	6.47718i	0.376478	−	0.376478i
$297$			0.463483i			0.0268940i
$298$		−	24.0417i		−	1.39270i
$299$	−34.1132	+	34.1132i	−1.97282	+	1.97282i
$300$		0			0
$301$	0.0972985	+	0.0972985i	0.00560819	+	0.00560819i
$302$	−1.68833			−0.0971523
$303$	−4.60994	−	4.60994i	−0.264834	−	0.264834i
$304$		−	3.74987i		−	0.215070i
$305$		0			0
$306$	10.1899	−	0.695839i	0.582520	−	0.0397785i
$307$	3.23028			0.184362			0.0921808	−	0.995742i	$-0.470616\pi$
$307$	3.23028			0.184362			0.0921808	+	0.995742i	$0.470616\pi$
$308$		−	0.356805i		−	0.0203309i
$309$	8.87398	+	8.87398i	0.504823	+	0.504823i
$310$		0			0
$311$	−2.21789	−	2.21789i	−0.125765	−	0.125765i	0.641423	−	0.767188i	$-0.278345\pi$
$311$	−2.21789	−	2.21789i	−0.125765	−	0.125765i	−0.767188	+	0.641423i	$0.778345\pi$
$312$	−2.86673	+	2.86673i	−0.162297	+	0.162297i
$313$	−1.22141	+	1.22141i	−0.0690380	+	0.0690380i	−0.740783	−	0.671745i	$-0.765545\pi$
$313$	−1.22141	+	1.22141i	−0.0690380	+	0.0690380i	0.671745	+	0.740783i	$0.265545\pi$
$314$			2.50912i			0.141598i
$315$		0			0
$316$	−1.29878	+	1.29878i	−0.0730619	+	0.0730619i
$317$	−20.0610	+	20.0610i	−1.12674	+	1.12674i	−0.136036	+	0.990704i	$0.543436\pi$
$317$	−20.0610	+	20.0610i	−1.12674	+	1.12674i	−0.990704	+	0.136036i	$0.956564\pi$
$318$	2.40545	+	2.40545i	0.134891	+	0.134891i
$319$	0.472862			0.0264752
$320$		0			0
$321$			1.03384i			0.0577035i
$322$	26.2327			1.46189
$323$	−1.05334	−	15.4252i	−0.0586093	−	0.858281i
$324$	4.56795			0.253775
$325$		0			0
$326$	9.53385	+	9.53385i	0.528031	+	0.528031i
$327$	−6.35079			−0.351200
$328$	−4.68969	−	4.68969i	−0.258945	−	0.258945i
$329$	−21.1518	+	21.1518i	−1.16614	+	1.16614i
$330$		0			0
$331$		−	1.79874i		−	0.0988677i	−0.998777	−	0.0494339i	$-0.984258\pi$
$331$		−	1.79874i		−	0.0988677i	0.998777	−	0.0494339i	$-0.0157417\pi$
$332$			0.941680i			0.0516814i
$333$	16.0451	−	16.0451i	0.879268	−	0.879268i
$334$	8.70474	−	8.70474i	0.476302	−	0.476302i
$335$		0			0
$336$	2.20449			0.120265
$337$	6.96238	+	6.96238i	0.379265	+	0.379265i	0.870837	−	0.491572i	$-0.163578\pi$
$337$	6.96238	+	6.96238i	0.379265	+	0.379265i	−0.491572	+	0.870837i	$0.663578\pi$
$338$			18.4377i			1.00288i
$339$	6.86372			0.372786
$340$		0			0
$341$	0.811927			0.0439683
$342$		−	9.28911i		−	0.502297i
$343$	−10.1426	−	10.1426i	−0.547652	−	0.547652i
$344$	−0.0451326			−0.00243339
$345$		0			0
$346$	2.20449	−	2.20449i	0.118514	−	0.118514i
$347$	−6.20284	+	6.20284i	−0.332986	+	0.332986i	−0.853719	−	0.520734i	$-0.825659\pi$
$347$	−6.20284	+	6.20284i	−0.332986	+	0.332986i	0.520734	+	0.853719i	$0.325659\pi$
$348$			2.92153i			0.156611i
$349$			14.1265i			0.756176i	0.925770	+	0.378088i	$0.123418\pi$
$349$			14.1265i			0.756176i	−0.925770	+	0.378088i	$0.876582\pi$
$350$		0			0
$351$	−15.7016	+	15.7016i	−0.838089	+	0.838089i
$352$	0.0827533	+	0.0827533i	0.00441077	+	0.00441077i
$353$	11.6521			0.620177			0.310088	−	0.950708i	$-0.399641\pi$
$353$	11.6521			0.620177			0.310088	+	0.950708i	$0.399641\pi$
$354$	−3.66525	−	3.66525i	−0.194806	−	0.194806i
$355$		0			0
$356$	−5.94117			−0.314881
$357$	9.06821	−	0.619240i	0.479940	−	0.0327736i
$358$	3.46399			0.183078
$359$		−	25.5519i		−	1.34858i	−0.738467	−	0.674289i	$-0.764450\pi$
$359$		−	25.5519i		−	1.34858i	0.738467	−	0.674289i	$-0.235550\pi$
$360$		0			0
$361$	4.93845			0.259919
$362$	16.4409	+	16.4409i	0.864115	+	0.864115i
$363$	5.61711	−	5.61711i	0.294822	−	0.294822i
$364$	12.0876	−	12.0876i	0.633564	−	0.633564i
$365$		0			0
$366$			0.597553i			0.0312346i
$367$	13.9283	−	13.9283i	0.727050	−	0.727050i	−0.242981	−	0.970031i	$-0.578125\pi$
$367$	13.9283	−	13.9283i	0.727050	−	0.727050i	0.970031	+	0.242981i	$0.0781253\pi$
$368$	−6.08411	+	6.08411i	−0.317156	+	0.317156i
$369$	−11.6172	−	11.6172i	−0.604767	−	0.604767i
$370$		0			0
$371$	−10.1426	−	10.1426i	−0.526580	−	0.526580i
$372$			5.01641i			0.260089i
$373$	1.73002			0.0895772			0.0447886	−	0.998996i	$-0.485739\pi$
$373$	1.73002			0.0895772			0.0447886	+	0.998996i	$0.485739\pi$
$374$	0.363653	+	0.317162i	0.0188041	+	0.0164001i
$375$		0			0
$376$		−	9.81142i		−	0.505985i
$377$	16.0193	+	16.0193i	0.825038	+	0.825038i
$378$	12.0744			0.621038
$379$	−18.9466	−	18.9466i	−0.973219	−	0.973219i	0.0264315	−	0.999651i	$-0.491586\pi$
$379$	−18.9466	−	18.9466i	−0.973219	−	0.973219i	−0.999651	+	0.0264315i	$0.991586\pi$
$380$		0			0
$381$	−7.64591	+	7.64591i	−0.391712	+	0.391712i
$382$		−	14.7330i		−	0.753803i
$383$			19.1419i			0.978107i	0.872254	+	0.489053i	$0.162658\pi$
$383$			19.1419i			0.978107i	−0.872254	+	0.489053i	$0.837342\pi$
$384$	−0.511283	+	0.511283i	−0.0260913	+	0.0260913i
$385$		0			0
$386$	19.1607	+	19.1607i	0.975255	+	0.975255i
$387$	−0.111801			−0.00568319
$388$	5.10719	+	5.10719i	0.259278	+	0.259278i
$389$		−	33.3698i		−	1.69192i	−0.533250	−	0.845958i	$-0.679030\pi$
$389$		−	33.3698i		−	1.69192i	0.533250	−	0.845958i	$-0.320970\pi$
$390$		0			0
$391$	−23.3181	+	26.7362i	−1.17925	+	1.35211i
$392$	−2.29526			−0.115928
$393$			4.44194i			0.224066i
$394$	−1.41563	−	1.41563i	−0.0713186	−	0.0713186i
$395$		0			0
$396$	0.204995	+	0.204995i	0.0103014	+	0.0103014i
$397$	−26.7136	+	26.7136i	−1.34072	+	1.34072i	−0.445372	+	0.895346i	$0.646929\pi$
$397$	−26.7136	+	26.7136i	−1.34072	+	1.34072i	−0.895346	+	0.445372i	$0.853071\pi$
$398$	−12.2496	+	12.2496i	−0.614018	+	0.614018i
$399$		−	8.26654i		−	0.413845i
$400$		0			0
$401$	3.75174	−	3.75174i	0.187353	−	0.187353i	−0.607198	−	0.794551i	$-0.707706\pi$
$401$	3.75174	−	3.75174i	0.187353	−	0.187353i	0.794551	+	0.607198i	$0.207706\pi$
$402$	6.08224	−	6.08224i	0.303355	−	0.303355i
$403$	27.5060	+	27.5060i	1.37017	+	1.37017i
$404$	−9.01641			−0.448583
$405$		0			0
$406$		−	12.3187i		−	0.611367i
$407$	1.07202			0.0531378
$408$	−1.95956	+	2.24680i	−0.0970125	+	0.111233i
$409$	22.1650			1.09599			0.547994	−	0.836482i	$-0.315392\pi$
$409$	22.1650			1.09599			0.547994	+	0.836482i	$0.315392\pi$
$410$		0			0
$411$	8.61847	+	8.61847i	0.425118	+	0.425118i
$412$	17.3563			0.855083
$413$	15.4546	+	15.4546i	0.760472	+	0.760472i
$414$	−15.0714	+	15.0714i	−0.740721	+	0.740721i
$415$		0			0
$416$			5.60693i			0.274902i
$417$		−	12.8566i		−	0.629588i
$418$	0.310314	−	0.310314i	0.0151780	−	0.0151780i
$419$	−19.3883	+	19.3883i	−0.947179	+	0.947179i	−0.998673	−	0.0514942i	$-0.983602\pi$
$419$	−19.3883	+	19.3883i	−0.947179	+	0.947179i	0.0514942	+	0.998673i	$0.483602\pi$
$420$		0			0
$421$	−14.2303			−0.693541			−0.346771	−	0.937950i	$-0.612722\pi$
$421$	−14.2303			−0.693541			−0.346771	+	0.937950i	$0.612722\pi$
$422$	−7.27757	−	7.27757i	−0.354266	−	0.354266i
$423$		−	24.3046i		−	1.18173i
$424$	4.70474			0.228482
$425$		0			0
$426$	3.76167			0.182254
$427$		−	2.51960i		−	0.121932i
$428$	1.01103	+	1.01103i	0.0488699	+	0.0488699i
$429$	−0.474463			−0.0229073
$430$		0			0
$431$	−3.90622	+	3.90622i	−0.188156	+	0.188156i	−0.794898	−	0.606743i	$-0.792476\pi$
$431$	−3.90622	+	3.90622i	−0.188156	+	0.188156i	0.606743	+	0.794898i	$0.292476\pi$
$432$	−2.80039	+	2.80039i	−0.134734	+	0.134734i
$433$			4.84768i			0.232965i	0.993193	+	0.116482i	$0.0371618\pi$
$433$			4.84768i			0.232965i	−0.993193	+	0.116482i	$0.962838\pi$
$434$		−	21.1518i		−	1.01532i
$435$		0			0
$436$	−6.21064	+	6.21064i	−0.297436	+	0.297436i
$437$	22.8146	+	22.8146i	1.09137	+	1.09137i
$438$	−4.77244			−0.228036
$439$	−19.3660	−	19.3660i	−0.924287	−	0.924287i	0.0730417	−	0.997329i	$-0.476729\pi$
$439$	−19.3660	−	19.3660i	−0.924287	−	0.924287i	−0.997329	+	0.0730417i	$0.976729\pi$
$440$		0			0
$441$	−5.68577			−0.270751
$442$	1.57499	+	23.0643i	0.0749145	+	1.09706i
$443$	−39.8429			−1.89299			−0.946496	−	0.322717i	$-0.895404\pi$
$443$	−39.8429			−1.89299			−0.946496	+	0.322717i	$0.895404\pi$
$444$			6.62335i			0.314330i
$445$		0			0
$446$	−1.64319			−0.0778075
$447$	12.2921	+	12.2921i	0.581397	+	0.581397i
$448$	2.15584	−	2.15584i	0.101854	−	0.101854i
$449$	−6.29662	+	6.29662i	−0.297156	+	0.297156i	−0.839899	−	0.542743i	$-0.817386\pi$
$449$	−6.29662	+	6.29662i	−0.297156	+	0.297156i	0.542743	+	0.839899i	$0.317386\pi$
$450$		0			0
$451$		−	0.776174i		−	0.0365486i
$452$	6.71225	−	6.71225i	0.315718	−	0.315718i
$453$	0.863213	−	0.863213i	0.0405573	−	0.0405573i
$454$	−2.19159	−	2.19159i	−0.102856	−	0.102856i
$455$		0			0
$456$	1.91725	+	1.91725i	0.0897833	+	0.0897833i
$457$			39.8174i			1.86258i	0.364282	+	0.931289i	$0.381314\pi$
$457$			39.8174i			1.86258i	−0.364282	+	0.931289i	$0.618686\pi$
$458$	−24.8988			−1.16344
$459$	−10.7328	+	12.3061i	−0.500966	+	0.574400i
$460$		0			0
$461$		−	5.83076i		−	0.271565i	−0.990739	−	0.135783i	$-0.956645\pi$
$461$		−	5.83076i		−	0.271565i	0.990739	−	0.135783i	$-0.0433549\pi$
$462$	0.182428	+	0.182428i	0.00848734	+	0.00848734i
$463$	14.2134			0.660551			0.330275	−	0.943885i	$-0.392858\pi$
$463$	14.2134			0.660551			0.330275	+	0.943885i	$0.392858\pi$
$464$	2.85706	+	2.85706i	0.132636	+	0.132636i
$465$		0			0
$466$	1.37373	−	1.37373i	0.0636367	−	0.0636367i
$467$		−	20.6040i		−	0.953440i	−0.879055	−	0.476720i	$-0.841826\pi$
$467$		−	20.6040i		−	0.953440i	0.879055	−	0.476720i	$-0.158174\pi$
$468$			13.8894i			0.642037i
$469$	−25.6459	+	25.6459i	−1.18422	+	1.18422i
$470$		0			0
$471$	−1.28287	−	1.28287i	−0.0591117	−	0.0591117i
$472$	−7.16873			−0.329968
$473$	−0.00373487	−	0.00373487i	−0.000171730	−	0.000171730i
$474$		−	1.32809i		−	0.0610010i
$475$		0			0
$476$	8.26251	−	9.47366i	0.378712	−	0.434225i
$477$	11.6545			0.533622
$478$			13.9549i			0.638281i
$479$	15.5581	+	15.5581i	0.710866	+	0.710866i	0.966716	−	0.255850i	$-0.0823554\pi$
$479$	15.5581	+	15.5581i	0.710866	+	0.710866i	−0.255850	+	0.966716i	$0.582355\pi$
$480$		0			0
$481$	36.3171	+	36.3171i	1.65592	+	1.65592i
$482$	−6.99198	+	6.99198i	−0.318476	+	0.318476i
$483$	−13.4123	+	13.4123i	−0.610282	+	0.610282i
$484$		−	10.9863i		−	0.499377i
$485$		0			0
$486$	−10.7367	+	10.7367i	−0.487026	+	0.487026i
$487$	15.8955	−	15.8955i	0.720295	−	0.720295i	−0.248370	−	0.968665i	$-0.579895\pi$
$487$	15.8955	−	15.8955i	0.720295	−	0.720295i	0.968665	+	0.248370i	$0.0798949\pi$
$488$	0.584366	+	0.584366i	0.0264530	+	0.0264530i
$489$	−9.74899			−0.440865
$490$		0			0
$491$			22.3761i			1.00982i	0.863172	+	0.504911i	$0.168475\pi$
$491$			22.3761i			1.00982i	−0.863172	+	0.504911i	$0.831525\pi$
$492$	4.79551			0.216198
$493$	12.5551	+	10.9500i	0.565455	+	0.493165i
$494$	21.0253			0.945972
$495$		0			0
$496$	4.90571	+	4.90571i	0.220273	+	0.220273i
$497$	−15.8612			−0.711470
$498$	−0.481465	−	0.481465i	−0.0215750	−	0.0215750i
$499$	−23.7816	+	23.7816i	−1.06461	+	1.06461i	−0.0668474	+	0.997763i	$0.521294\pi$
$499$	−23.7816	+	23.7816i	−1.06461	+	1.06461i	−0.997763	+	0.0668474i	$0.978706\pi$
$500$		0			0
$501$			8.90117i			0.397675i
$502$		−	4.72731i		−	0.210990i
$503$	−7.12602	+	7.12602i	−0.317733	+	0.317733i	−0.847896	−	0.530163i	$-0.822131\pi$
$503$	−7.12602	+	7.12602i	−0.317733	+	0.317733i	0.530163	+	0.847896i	$0.322131\pi$
$504$	5.34039	−	5.34039i	0.237880	−	0.237880i
$505$		0			0
$506$	−1.00696			−0.0447649
$507$	−9.42688	−	9.42688i	−0.418662	−	0.418662i
$508$			14.9544i			0.663492i
$509$	27.1325			1.20263			0.601313	−	0.799014i	$-0.294645\pi$
$509$	27.1325			1.20263			0.601313	+	0.799014i	$0.294645\pi$
$510$		0			0
$511$	20.1231			0.890193
$512$			1.00000i			0.0441942i
$513$	10.5011	+	10.5011i	0.463635	+	0.463635i
$514$	19.6327			0.865962
$515$		0			0
$516$	0.0230755	−	0.0230755i	0.00101584	−	0.00101584i
$517$	0.811927	−	0.811927i	0.0357085	−	0.0357085i
$518$		−	27.9275i		−	1.22706i
$519$			2.25423i			0.0989498i
$520$		0			0
$521$	13.2190	−	13.2190i	0.579136	−	0.579136i	−0.355529	−	0.934665i	$-0.615699\pi$
$521$	13.2190	−	13.2190i	0.579136	−	0.579136i	0.934665	+	0.355529i	$0.115699\pi$
$522$	7.07745	+	7.07745i	0.309772	+	0.309772i
$523$	16.1040			0.704177			0.352089	−	0.935967i	$-0.385472\pi$
$523$	16.1040			0.704177			0.352089	+	0.935967i	$0.385472\pi$
$524$	4.34391	+	4.34391i	0.189765	+	0.189765i
$525$		0			0
$526$	−24.2134			−1.05575
$527$	21.5578	+	18.8017i	0.939071	+	0.819017i
$528$	−0.0846207			−0.00368264
$529$		−	51.0328i		−	2.21882i
$530$		0			0
$531$	−17.7582			−0.770642
$532$	−8.08411	−	8.08411i	−0.350491	−	0.350491i
$533$	26.2948	−	26.2948i	1.13895	−	1.13895i
$534$	3.03762	−	3.03762i	0.131451	−	0.131451i
$535$		0			0
$536$		−	11.8960i		−	0.513831i
$537$	−1.77108	+	1.77108i	−0.0764278	+	0.0764278i
$538$	15.0615	−	15.0615i	0.649349	−	0.649349i
$539$	−0.189940	−	0.189940i	−0.00818131	−	0.00818131i
$540$		0			0
$541$	−6.66848	−	6.66848i	−0.286700	−	0.286700i	0.549074	−	0.835774i	$-0.314981\pi$
$541$	−6.66848	−	6.66848i	−0.286700	−	0.286700i	−0.835774	+	0.549074i	$0.814981\pi$
$542$			4.18858i			0.179915i
$543$	−16.8119			−0.721469
$544$	0.280900	+	4.11353i	0.0120435	+	0.176366i
$545$		0			0
$546$			12.3604i			0.528976i
$547$	12.4850	+	12.4850i	0.533819	+	0.533819i	0.921707	−	0.387887i	$-0.126795\pi$
$547$	12.4850	+	12.4850i	0.533819	+	0.533819i	−0.387887	+	0.921707i	$0.626795\pi$
$548$	16.8566			0.720076
$549$	1.44758	+	1.44758i	0.0617812	+	0.0617812i
$550$		0			0
$551$	10.7136	−	10.7136i	0.456415	−	0.456415i
$552$		−	6.22141i		−	0.264801i
$553$			5.59990i			0.238132i
$554$	−5.25013	+	5.25013i	−0.223057	+	0.223057i
$555$		0			0
$556$	−12.5728	−	12.5728i	−0.533207	−	0.533207i
$557$	−30.4249			−1.28914			−0.644572	−	0.764544i	$-0.722964\pi$
$557$	−30.4249			−1.28914			−0.644572	+	0.764544i	$0.722964\pi$
$558$	12.1523	+	12.1523i	0.514449	+	0.514449i
$559$		−	0.253055i		−	0.0107031i
$560$		0			0
$561$	−0.348090	+	0.0237700i	−0.0146964	+	0.00100357i
$562$	−11.7752			−0.496705
$563$		−	9.43527i		−	0.397649i	−0.980035	−	0.198825i	$-0.936288\pi$
$563$		−	9.43527i		−	0.397649i	0.980035	−	0.198825i	$-0.0637124\pi$
$564$	5.01641	+	5.01641i	0.211229	+	0.211229i
$565$		0			0
$566$	1.24211	+	1.24211i	0.0522096	+	0.0522096i
$567$	9.84776	−	9.84776i	0.413567	−	0.413567i
$568$	3.67866	−	3.67866i	0.154353	−	0.154353i
$569$		−	35.8563i		−	1.50318i	−0.659633	−	0.751588i	$-0.729288\pi$
$569$		−	35.8563i		−	1.50318i	0.659633	−	0.751588i	$-0.270712\pi$
$570$		0			0
$571$	16.4307	−	16.4307i	0.687605	−	0.687605i	−0.274097	−	0.961702i	$-0.588379\pi$
$571$	16.4307	−	16.4307i	0.687605	−	0.687605i	0.961702	+	0.274097i	$0.0883790\pi$
$572$	−0.463992	+	0.463992i	−0.0194005	+	0.0194005i
$573$	7.53271	+	7.53271i	0.314683	+	0.314683i
$574$	−20.2204			−0.843983
$575$		0			0
$576$			2.47718i			0.103216i
$577$	16.6849			0.694601			0.347301	−	0.937754i	$-0.387098\pi$
$577$	16.6849			0.694601			0.347301	+	0.937754i	$0.387098\pi$
$578$	2.31098	+	16.8422i	0.0961240	+	0.700543i
$579$	−19.5931			−0.814261
$580$		0			0
$581$	2.03011	+	2.03011i	0.0842231	+	0.0842231i
$582$	−5.22244			−0.216477
$583$	0.389333	+	0.389333i	0.0161245	+	0.0161245i
$584$	−4.66712	+	4.66712i	−0.193127	+	0.193127i
$585$		0			0
$586$		−	28.6223i		−	1.18238i
$587$			37.5151i			1.54842i	0.632932	+	0.774208i	$0.281851\pi$
$587$			37.5151i			1.54842i	−0.632932	+	0.774208i	$0.718149\pi$
$588$	1.17353	−	1.17353i	0.0483955	−	0.0483955i
$589$	18.3958	−	18.3958i	0.757985	−	0.757985i
$590$		0			0
$591$	1.44758			0.0595455
$592$	6.47718	+	6.47718i	0.266210	+	0.266210i
$593$		−	45.5348i		−	1.86989i	−0.354794	−	0.934945i	$-0.615449\pi$
$593$		−	45.5348i		−	1.86989i	0.354794	−	0.934945i	$-0.384551\pi$
$594$	−0.463483			−0.0190169
$595$		0			0
$596$	24.0417			0.984786
$597$		−	12.5260i		−	0.512657i
$598$	−34.1132	−	34.1132i	−1.39499	−	1.39499i
$599$	0.792586			0.0323842			0.0161921	−	0.999869i	$-0.494846\pi$
$599$	0.792586			0.0323842			0.0161921	+	0.999869i	$0.494846\pi$
$600$		0			0
$601$	−25.1470	+	25.1470i	−1.02577	+	1.02577i	−0.0261090	+	0.999659i	$0.508312\pi$
$601$	−25.1470	+	25.1470i	−1.02577	+	1.02577i	−0.999659	+	0.0261090i	$0.991688\pi$
$602$	−0.0972985	+	0.0972985i	−0.00396559	+	0.00396559i
$603$		−	29.4686i		−	1.20005i
$604$		−	1.68833i		−	0.0686971i
$605$		0			0
$606$	4.60994	−	4.60994i	0.187266	−	0.187266i
$607$	−26.4726	−	26.4726i	−1.07449	−	1.07449i	−0.996992	−	0.0774990i	$-0.975307\pi$
$607$	−26.4726	−	26.4726i	−1.07449	−	1.07449i	−0.0774990	−	0.996992i	$-0.524693\pi$
$608$	3.74987			0.152077
$609$	6.29835	+	6.29835i	0.255222	+	0.255222i
$610$		0			0
$611$	55.0120			2.22555
$612$	0.695839	+	10.1899i	0.0281276	+	0.411904i
$613$	−7.67786			−0.310106			−0.155053	−	0.987906i	$-0.549555\pi$
$613$	−7.67786			−0.310106			−0.155053	+	0.987906i	$0.549555\pi$
$614$			3.23028i			0.130363i
$615$		0			0
$616$	0.356805			0.0143761
$617$	−9.74987	−	9.74987i	−0.392515	−	0.392515i	0.483068	−	0.875583i	$-0.339522\pi$
$617$	−9.74987	−	9.74987i	−0.392515	−	0.392515i	−0.875583	+	0.483068i	$0.839522\pi$
$618$	−8.87398	+	8.87398i	−0.356964	+	0.356964i
$619$	7.93230	−	7.93230i	0.318826	−	0.318826i	−0.529490	−	0.848316i	$-0.677617\pi$
$619$	7.93230	−	7.93230i	0.318826	−	0.318826i	0.848316	+	0.529490i	$0.177617\pi$
$620$		0			0
$621$		−	34.0758i		−	1.36741i
$622$	2.21789	−	2.21789i	0.0889293	−	0.0889293i
$623$	−12.8082	+	12.8082i	−0.513149	+	0.513149i
$624$	−2.86673	−	2.86673i	−0.114761	−	0.114761i
$625$		0			0
$626$	−1.22141	−	1.22141i	−0.0488173	−	0.0488173i
$627$			0.317317i			0.0126724i
$628$	−2.50912			−0.100125
$629$	28.4635	+	24.8246i	1.13491	+	0.989822i
$630$		0			0
$631$		−	35.3370i		−	1.40674i	−0.710823	−	0.703371i	$-0.751677\pi$
$631$		−	35.3370i		−	1.40674i	0.710823	−	0.703371i	$-0.248323\pi$
$632$	−1.29878	−	1.29878i	−0.0516626	−	0.0516626i
$633$	7.44180			0.295785
$634$	−20.0610	−	20.0610i	−0.796726	−	0.796726i
$635$		0			0
$636$	−2.40545	+	2.40545i	−0.0953825	+	0.0953825i
$637$		−	12.8694i		−	0.509903i
$638$			0.472862i			0.0187208i
$639$	9.11269	−	9.11269i	0.360493	−	0.360493i
$640$		0			0
$641$	−27.2824	−	27.2824i	−1.07759	−	1.07759i	−0.996725	−	0.0808668i	$-0.974231\pi$
$641$	−27.2824	−	27.2824i	−1.07759	−	1.07759i	−0.0808668	−	0.996725i	$-0.525769\pi$
$642$	−1.03384			−0.0408026
$643$	−0.487359	−	0.487359i	−0.0192195	−	0.0192195i	0.697432	−	0.716651i	$-0.254326\pi$
$643$	−0.487359	−	0.487359i	−0.0192195	−	0.0192195i	−0.716651	+	0.697432i	$0.754326\pi$
$644$			26.2327i			1.03371i
$645$		0			0
$646$	15.4252	−	1.05334i	0.606896	−	0.0414431i
$647$	21.7921			0.856735			0.428367	−	0.903605i	$-0.359089\pi$
$647$	21.7921			0.856735			0.428367	+	0.903605i	$0.359089\pi$
$648$			4.56795i			0.179446i
$649$	−0.593236	−	0.593236i	−0.0232866	−	0.0232866i
$650$		0			0
$651$	10.8146	+	10.8146i	0.423856	+	0.423856i
$652$	−9.53385	+	9.53385i	−0.373374	+	0.373374i
$653$	−14.5745	+	14.5745i	−0.570343	+	0.570343i	−0.932224	−	0.361881i	$-0.882135\pi$
$653$	−14.5745	+	14.5745i	−0.570343	+	0.570343i	0.361881	+	0.932224i	$0.382135\pi$
$654$		−	6.35079i		−	0.248336i
$655$		0			0
$656$	4.68969	−	4.68969i	0.183101	−	0.183101i
$657$	−11.5613	+	11.5613i	−0.451049	+	0.451049i
$658$	−21.1518	−	21.1518i	−0.824583	−	0.824583i
$659$	46.3910			1.80714			0.903568	−	0.428446i	$-0.140939\pi$
$659$	46.3910			1.80714			0.903568	+	0.428446i	$0.140939\pi$
$660$		0			0
$661$			25.4173i			0.988620i	0.869286	+	0.494310i	$0.164579\pi$
$661$			25.4173i			0.988620i	−0.869286	+	0.494310i	$0.835421\pi$
$662$	1.79874			0.0699100
$663$	−12.5976	−	10.9871i	−0.489252	−	0.426704i
$664$	−0.941680			−0.0365443
$665$		0			0
$666$	16.0451	+	16.0451i	0.621736	+	0.621736i
$667$	−34.7653			−1.34612
$668$	8.70474	+	8.70474i	0.336797	+	0.336797i
$669$	0.840138	−	0.840138i	0.0324816	−	0.0324816i
$670$		0			0
$671$			0.0967164i			0.00373370i
$672$			2.20449i			0.0850399i
$673$	12.0968	−	12.0968i	0.466297	−	0.466297i	−0.434416	−	0.900713i	$-0.643045\pi$
$673$	12.0968	−	12.0968i	0.466297	−	0.466297i	0.900713	+	0.434416i	$0.143045\pi$
$674$	−6.96238	+	6.96238i	−0.268181	+	0.268181i
$675$		0			0
$676$	−18.4377			−0.709142
$677$	−11.1881	−	11.1881i	−0.429993	−	0.429993i	0.458633	−	0.888626i	$-0.348339\pi$
$677$	−11.1881	−	11.1881i	−0.429993	−	0.429993i	−0.888626	+	0.458633i	$0.848339\pi$
$678$			6.86372i			0.263600i
$679$	22.0205			0.845070
$680$		0			0
$681$	2.24105			0.0858771
$682$			0.811927i			0.0310903i
$683$	5.46322	+	5.46322i	0.209044	+	0.209044i	0.803861	−	0.594817i	$-0.202775\pi$
$683$	5.46322	+	5.46322i	0.209044	+	0.209044i	−0.594817	+	0.803861i	$0.702775\pi$
$684$	9.28911			0.355178
$685$		0			0
$686$	10.1426	−	10.1426i	0.387248	−	0.387248i
$687$	12.7303	−	12.7303i	0.485692	−	0.485692i
$688$		−	0.0451326i		−	0.00172066i
$689$			26.3792i			1.00497i
$690$		0			0
$691$	−30.7443	+	30.7443i	−1.16957	+	1.16957i	−0.187256	+	0.982311i	$0.559959\pi$
$691$	−30.7443	+	30.7443i	−1.16957	+	1.16957i	−0.982311	+	0.187256i	$0.940041\pi$
$692$	2.20449	+	2.20449i	0.0838020	+	0.0838020i
$693$	0.883870			0.0335754
$694$	−6.20284	−	6.20284i	−0.235456	−	0.235456i
$695$		0			0
$696$	−2.92153			−0.110740
$697$	17.9738	−	20.6085i	0.680807	−	0.780602i
$698$	−14.1265			−0.534697
$699$			1.40473i			0.0531316i
$700$		0			0
$701$	6.03283			0.227857			0.113928	−	0.993489i	$-0.463657\pi$
$701$	6.03283			0.227857			0.113928	+	0.993489i	$0.463657\pi$
$702$	−15.7016	−	15.7016i	−0.592618	−	0.592618i
$703$	24.2886	−	24.2886i	0.916062	−	0.916062i
$704$	−0.0827533	+	0.0827533i	−0.00311888	+	0.00311888i
$705$		0			0
$706$			11.6521i			0.438531i
$707$	−19.4379	+	19.4379i	−0.731038	+	0.731038i
$708$	3.66525	−	3.66525i	0.137749	−	0.137749i
$709$	14.2303	+	14.2303i	0.534429	+	0.534429i	0.921887	−	0.387458i	$-0.126647\pi$
$709$	14.2303	+	14.2303i	0.534429	+	0.534429i	−0.387458	+	0.921887i	$0.626647\pi$
$710$		0			0
$711$	−3.21730	−	3.21730i	−0.120658	−	0.120658i
$712$		−	5.94117i		−	0.222655i
$713$	−59.6938			−2.23555
$714$	0.619240	+	9.06821i	0.0231745	+	0.339369i
$715$		0			0
$716$			3.46399i			0.129455i
$717$	−7.13489	−	7.13489i	−0.266457	−	0.266457i
$718$	25.5519			0.953589
$719$	−8.35329	−	8.35329i	−0.311525	−	0.311525i	0.533975	−	0.845500i	$-0.320698\pi$
$719$	−8.35329	−	8.35329i	−0.311525	−	0.311525i	−0.845500	+	0.533975i	$0.820698\pi$
$720$		0			0
$721$	37.4173	−	37.4173i	1.39349	−	1.39349i
$722$			4.93845i			0.183790i
$723$		−	7.14976i		−	0.265903i
$724$	−16.4409	+	16.4409i	−0.611022	+	0.611022i
$725$		0			0
$726$	5.61711	+	5.61711i	0.208471	+	0.208471i
$727$	−5.73346			−0.212642			−0.106321	−	0.994332i	$-0.533907\pi$
$727$	−5.73346			−0.212642			−0.106321	+	0.994332i	$0.533907\pi$
$728$	12.0876	+	12.0876i	0.447997	+	0.447997i
$729$			2.72489i			0.100922i
$730$		0			0
$731$	−0.0126777	−	0.185654i	−0.000468903	−	0.00686666i
$732$	−0.597553			−0.0220862
$733$			44.8719i			1.65738i	0.559706	+	0.828692i	$0.310914\pi$
$733$			44.8719i			1.65738i	−0.559706	+	0.828692i	$0.689086\pi$
$734$	13.9283	+	13.9283i	0.514102	+	0.514102i
$735$		0			0
$736$	−6.08411	−	6.08411i	−0.224263	−	0.224263i
$737$	0.984436	−	0.984436i	0.0362622	−	0.0362622i
$738$	11.6172	−	11.6172i	0.427635	−	0.427635i
$739$			19.2848i			0.709402i	0.934980	+	0.354701i	$0.115417\pi$
$739$			19.2848i			0.709402i	−0.934980	+	0.354701i	$0.884583\pi$
$740$		0			0
$741$	−10.7499	+	10.7499i	−0.394906	+	0.394906i
$742$	10.1426	−	10.1426i	0.372348	−	0.372348i
$743$	−8.45059	−	8.45059i	−0.310022	−	0.310022i	0.534896	−	0.844918i	$-0.320351\pi$
$743$	−8.45059	−	8.45059i	−0.310022	−	0.310022i	−0.844918	+	0.534896i	$0.820351\pi$
$744$	−5.01641			−0.183911
$745$		0			0
$746$			1.73002i			0.0633406i
$747$	−2.33271			−0.0853494
$748$	−0.317162	+	0.363653i	−0.0115966	+	0.0132965i
$749$	4.35922			0.159283
$750$		0			0
$751$	−25.3732	−	25.3732i	−0.925882	−	0.925882i	0.0715548	−	0.997437i	$-0.477204\pi$
$751$	−25.3732	−	25.3732i	−0.925882	−	0.925882i	−0.997437	+	0.0715548i	$0.977204\pi$
$752$	9.81142			0.357786
$753$	2.41699	+	2.41699i	0.0880801	+	0.0880801i
$754$	−16.0193	+	16.0193i	−0.583390	+	0.583390i
$755$		0			0
$756$			12.0744i			0.439140i
$757$		−	19.7733i		−	0.718673i	−0.933208	−	0.359337i	$-0.883003\pi$
$757$		−	19.7733i		−	0.718673i	0.933208	−	0.359337i	$-0.116997\pi$
$758$	18.9466	−	18.9466i	0.688170	−	0.688170i
$759$	0.514842	−	0.514842i	0.0186876	−	0.0186876i
$760$		0			0
$761$	8.19452			0.297051			0.148526	−	0.988909i	$-0.452547\pi$
$761$	8.19452			0.297051			0.148526	+	0.988909i	$0.452547\pi$
$762$	−7.64591	−	7.64591i	−0.276982	−	0.276982i
$763$			26.7782i			0.969437i
$764$	14.7330			0.533019
$765$		0			0
$766$	−19.1419			−0.691626
$767$		−	40.1946i		−	1.45134i
$768$	−0.511283	−	0.511283i	−0.0184493	−	0.0184493i
$769$	−48.9410			−1.76486			−0.882428	−	0.470447i	$-0.844093\pi$
$769$	−48.9410			−1.76486			−0.882428	+	0.470447i	$0.844093\pi$
$770$		0			0
$771$	−10.0379	+	10.0379i	−0.361505	+	0.361505i
$772$	−19.1607	+	19.1607i	−0.689609	+	0.689609i
$773$			15.3211i			0.551060i	0.961292	+	0.275530i	$0.0888533\pi$
$773$			15.3211i			0.551060i	−0.961292	+	0.275530i	$0.911147\pi$
$774$		−	0.111801i		−	0.00401862i
$775$		0			0
$776$	−5.10719	+	5.10719i	−0.183337	+	0.183337i
$777$	14.2788	+	14.2788i	0.512251	+	0.512251i
$778$	33.3698			1.19636
$779$	−17.5857	−	17.5857i	−0.630074	−	0.630074i
$780$		0			0
$781$	0.608842			0.0217861
$782$	−26.7362	−	23.3181i	−0.956084	−	0.833854i
$783$	−16.0018			−0.571856
$784$		−	2.29526i		−	0.0819736i
$785$		0			0
$786$	−4.44194			−0.158439
$787$	−26.0739	−	26.0739i	−0.929435	−	0.929435i	0.0682340	−	0.997669i	$-0.478264\pi$
$787$	−26.0739	−	26.0739i	−0.929435	−	0.929435i	−0.997669	+	0.0682340i	$0.978264\pi$
$788$	1.41563	−	1.41563i	0.0504299	−	0.0504299i
$789$	12.3799	−	12.3799i	0.440735	−	0.440735i
$790$		0			0
$791$		−	28.9410i		−	1.02902i
$792$	−0.204995	+	0.204995i	−0.00728417	+	0.00728417i
$793$	−3.27650	+	3.27650i	−0.116352	+	0.116352i
$794$	−26.7136	−	26.7136i	−0.948031	−	0.948031i
$795$		0			0
$796$	−12.2496	−	12.2496i	−0.434176	−	0.434176i
$797$		−	33.4625i		−	1.18530i	−0.805460	−	0.592651i	$-0.798081\pi$
$797$		−	33.4625i		−	1.18530i	0.805460	−	0.592651i	$-0.201919\pi$
$798$	8.26654			0.292632
$799$	40.3595	−	2.75603i	1.42782	−	0.0975012i
$800$		0			0
$801$		−	14.7173i		−	0.520012i
$802$	3.75174	+	3.75174i	0.132479	+	0.132479i
$803$	−0.772439			−0.0272588
$804$	6.08224	+	6.08224i	0.214504	+	0.214504i
$805$		0			0
$806$	−27.5060	+	27.5060i	−0.968857	+	0.968857i
$807$			15.4014i			0.542156i
$808$		−	9.01641i		−	0.317196i
$809$	−6.49271	+	6.49271i	−0.228272	+	0.228272i	−0.811970	−	0.583699i	$-0.801605\pi$
$809$	−6.49271	+	6.49271i	−0.228272	+	0.228272i	0.583699	+	0.811970i	$0.301605\pi$
$810$		0			0
$811$	−12.3340	−	12.3340i	−0.433106	−	0.433106i	0.456578	−	0.889684i	$-0.349075\pi$
$811$	−12.3340	−	12.3340i	−0.433106	−	0.433106i	−0.889684	+	0.456578i	$0.849075\pi$
$812$	12.3187			0.432302
$813$	−2.14155	−	2.14155i	−0.0751075	−	0.0751075i
$814$			1.07202i			0.0375741i
$815$		0			0
$816$	−2.24680	−	1.95956i	−0.0786536	−	0.0685982i
$817$	−0.169241			−0.00592101
$818$			22.1650i			0.774981i
$819$	29.9432	+	29.9432i	1.04630	+	1.04630i
$820$		0			0
$821$	−30.5640	−	30.5640i	−1.06669	−	1.06669i	−0.997611	−	0.0690801i	$-0.977994\pi$
$821$	−30.5640	−	30.5640i	−1.06669	−	1.06669i	−0.0690801	−	0.997611i	$-0.522006\pi$
$822$	−8.61847	+	8.61847i	−0.300604	+	0.300604i
$823$	−19.5229	+	19.5229i	−0.680526	+	0.680526i	−0.960119	−	0.279593i	$-0.909800\pi$
$823$	−19.5229	+	19.5229i	−0.680526	+	0.680526i	0.279593	+	0.960119i	$0.409800\pi$
$824$			17.3563i			0.604635i
$825$		0			0
$826$	−15.4546	+	15.4546i	−0.537735	+	0.537735i
$827$	1.44571	−	1.44571i	0.0502723	−	0.0502723i	−0.681524	−	0.731796i	$-0.738682\pi$
$827$	1.44571	−	1.44571i	0.0502723	−	0.0502723i	0.731796	+	0.681524i	$0.238682\pi$
$828$	−15.0714	−	15.0714i	−0.523769	−	0.523769i
$829$	−14.6784			−0.509801			−0.254900	−	0.966967i	$-0.582043\pi$
$829$	−14.6784			−0.509801			−0.254900	+	0.966967i	$0.582043\pi$
$830$		0			0
$831$		−	5.36860i		−	0.186235i
$832$	−5.60693			−0.194385
$833$	−0.644738	−	9.44161i	−0.0223389	−	0.327132i
$834$	12.8566			0.445186
$835$		0			0
$836$	0.310314	+	0.310314i	0.0107324	+	0.0107324i
$837$	−27.4758			−0.949702
$838$	−19.3883	−	19.3883i	−0.669757	−	0.669757i
$839$	−5.36355	+	5.36355i	−0.185170	+	0.185170i	−0.793604	−	0.608434i	$-0.791798\pi$
$839$	−5.36355	+	5.36355i	−0.185170	+	0.185170i	0.608434	+	0.793604i	$0.291798\pi$
$840$		0			0
$841$		−	12.6744i		−	0.437049i
$842$		−	14.2303i		−	0.490408i
$843$	6.02044	−	6.02044i	0.207355	−	0.207355i
$844$	7.27757	−	7.27757i	0.250504	−	0.250504i
$845$		0			0
$846$	24.3046			0.835611
$847$	−23.6847	−	23.6847i	−0.813815	−	0.813815i
$848$			4.70474i			0.161561i
$849$	−1.27014			−0.0435910
$850$		0			0
$851$	−78.8158			−2.70177
$852$			3.76167i			0.128873i
$853$	−18.9740	−	18.9740i	−0.649657	−	0.649657i	0.303253	−	0.952910i	$-0.401927\pi$
$853$	−18.9740	−	18.9740i	−0.649657	−	0.649657i	−0.952910	+	0.303253i	$0.901927\pi$
$854$	2.51960			0.0862188
$855$		0			0
$856$	−1.01103	+	1.01103i	−0.0345562	+	0.0345562i
$857$	30.0766	−	30.0766i	1.02740	−	1.02740i	0.0277831	−	0.999614i	$-0.491155\pi$
$857$	30.0766	−	30.0766i	1.02740	−	1.02740i	0.999614	−	0.0277831i	$-0.00884477\pi$
$858$		−	0.474463i		−	0.0161979i
$859$		−	27.1159i		−	0.925183i	−0.886571	−	0.462592i	$-0.846920\pi$
$859$		−	27.1159i		−	0.925183i	0.886571	−	0.462592i	$-0.153080\pi$
$860$		0			0
$861$	10.3383	−	10.3383i	0.352330	−	0.352330i
$862$	−3.90622	−	3.90622i	−0.133046	−	0.133046i
$863$	−2.34977			−0.0799872			−0.0399936	−	0.999200i	$-0.512734\pi$
$863$	−2.34977			−0.0799872			−0.0399936	+	0.999200i	$0.512734\pi$
$864$	−2.80039	−	2.80039i	−0.0952712	−	0.0952712i
$865$		0			0
$866$	−4.84768			−0.164731
$867$	−9.79269	−	7.42956i	−0.332577	−	0.252321i
$868$	21.1518			0.717939
$869$		−	0.214956i		−	0.00729189i
$870$		0			0
$871$	66.7003			2.26005
$872$	−6.21064	−	6.21064i	−0.210319	−	0.210319i
$873$	−12.6514	+	12.6514i	−0.428186	+	0.428186i
$874$	−22.8146	+	22.8146i	−0.771717	+	0.771717i
$875$		0			0
$876$		−	4.77244i		−	0.161246i
$877$	−5.23321	+	5.23321i	−0.176713	+	0.176713i	−0.789921	−	0.613208i	$-0.789879\pi$
$877$	−5.23321	+	5.23321i	−0.176713	+	0.176713i	0.613208	+	0.789921i	$0.289879\pi$
$878$	19.3660	−	19.3660i	0.653570	−	0.653570i
$879$	14.6341	+	14.6341i	0.493596	+	0.493596i
$880$		0			0
$881$	20.6158	+	20.6158i	0.694564	+	0.694564i	0.963233	−	0.268669i	$-0.0865837\pi$
$881$	20.6158	+	20.6158i	0.694564	+	0.694564i	−0.268669	+	0.963233i	$0.586584\pi$
$882$		−	5.68577i		−	0.191450i
$883$	27.6688			0.931128			0.465564	−	0.885014i	$-0.345851\pi$
$883$	27.6688			0.931128			0.465564	+	0.885014i	$0.345851\pi$
$884$	−23.0643	+	1.57499i	−0.775735	+	0.0529725i
$885$		0			0
$886$		−	39.8429i		−	1.33855i
$887$	37.6672	+	37.6672i	1.26474	+	1.26474i	0.948769	+	0.315971i	$0.102330\pi$
$887$	37.6672	+	37.6672i	1.26474	+	1.26474i	0.315971	+	0.948769i	$0.397670\pi$
$888$	−6.62335			−0.222265
$889$	32.2391	+	32.2391i	1.08127	+	1.08127i
$890$		0			0
$891$	−0.378013	+	0.378013i	−0.0126639	+	0.0126639i
$892$		−	1.64319i		−	0.0550182i
$893$		−	36.7916i		−	1.23118i
$894$	−12.2921	+	12.2921i	−0.411110	+	0.411110i
$895$		0			0
$896$	2.15584	+	2.15584i	0.0720214	+	0.0720214i
$897$	34.8830			1.16471
$898$	−6.29662	−	6.29662i	−0.210121	−	0.210121i
$899$			28.0318i			0.934913i
$900$		0			0
$901$	1.32156	+	19.3531i	0.0440276	+	0.644744i
$902$	0.776174			0.0258438
$903$		−	0.0994941i		−	0.00331096i
$904$	6.71225	+	6.71225i	0.223246	+	0.223246i
$905$		0			0
$906$	0.863213	+	0.863213i	0.0286783	+	0.0286783i
$907$	−1.34178	+	1.34178i	−0.0445531	+	0.0445531i	−0.729032	−	0.684479i	$-0.760030\pi$
$907$	−1.34178	+	1.34178i	−0.0445531	+	0.0445531i	0.684479	+	0.729032i	$0.260030\pi$
$908$	2.19159	−	2.19159i	0.0727305	−	0.0727305i
$909$		−	22.3353i		−	0.740814i
$910$		0			0
$911$	−14.9253	+	14.9253i	−0.494499	+	0.494499i	−0.909720	−	0.415222i	$-0.863704\pi$
$911$	−14.9253	+	14.9253i	−0.494499	+	0.494499i	0.415222	+	0.909720i	$0.363704\pi$
$912$	−1.91725	+	1.91725i	−0.0634864	+	0.0634864i
$913$	−0.0779272	−	0.0779272i	−0.00257901	−	0.00257901i
$914$	−39.8174			−1.31704
$915$		0			0
$916$		−	24.8988i		−	0.822678i
$917$	18.7295			0.618503
$918$	−12.3061	−	10.7328i	−0.406162	−	0.354237i
$919$	52.6862			1.73796			0.868979	−	0.494849i	$-0.164777\pi$
$919$	52.6862			1.73796			0.868979	+	0.494849i	$0.164777\pi$
$920$		0			0
$921$	−1.65159	−	1.65159i	−0.0544216	−	0.0544216i
$922$	5.83076			0.192026
$923$	20.6260	+	20.6260i	0.678912	+	0.678912i
$924$	−0.182428	+	0.182428i	−0.00600145	+	0.00600145i
$925$		0			0
$926$			14.2134i			0.467080i
$927$			42.9947i			1.41213i
$928$	−2.85706	+	2.85706i	−0.0937876	+	0.0937876i
$929$	−22.9708	+	22.9708i	−0.753647	+	0.753647i	−0.975158	−	0.221511i	$-0.928901\pi$
$929$	−22.9708	+	22.9708i	−0.753647	+	0.753647i	0.221511	+	0.975158i	$0.428901\pi$
$930$		0			0
$931$	−8.60693			−0.282081
$932$	1.37373	+	1.37373i	0.0449979	+	0.0449979i
$933$			2.26794i			0.0742490i
$934$	20.6040			0.674184
$935$		0			0
$936$	−13.8894			−0.453988
$937$		−	29.3177i		−	0.957767i	−0.877878	−	0.478884i	$-0.841042\pi$
$937$		−	29.3177i		−	0.957767i	0.877878	−	0.478884i	$-0.158958\pi$
$938$	−25.6459	−	25.6459i	−0.837369	−	0.837369i
$939$	1.24897			0.0407586
$940$		0			0
$941$	−16.4452	+	16.4452i	−0.536099	+	0.536099i	−0.922381	−	0.386282i	$-0.873759\pi$
$941$	−16.4452	+	16.4452i	−0.536099	+	0.536099i	0.386282	+	0.922381i	$0.373759\pi$
$942$	1.28287	−	1.28287i	0.0417983	−	0.0417983i
$943$			57.0651i			1.85830i
$944$		−	7.16873i		−	0.233322i
$945$		0			0
$946$	0.00373487	−	0.00373487i	0.000121431	−	0.000121431i
$947$	−17.4508	−	17.4508i	−0.567075	−	0.567075i	0.364233	−	0.931308i	$-0.381331\pi$
$947$	−17.4508	−	17.4508i	−0.567075	−	0.567075i	−0.931308	+	0.364233i	$0.881331\pi$
$948$	1.32809			0.0431342
$949$	−26.1682	−	26.1682i	−0.849456	−	0.849456i
$950$		0			0
$951$	20.5137			0.665204
$952$	9.47366	+	8.26251i	0.307043	+	0.267790i
$953$	30.7416			0.995818			0.497909	−	0.867229i	$-0.334101\pi$
$953$	30.7416			0.995818			0.497909	+	0.867229i	$0.334101\pi$
$954$			11.6545i			0.377328i
$955$		0			0
$956$	−13.9549			−0.451333
$957$	−0.241766	−	0.241766i	−0.00781520	−	0.00781520i
$958$	−15.5581	+	15.5581i	−0.502658	+	0.502658i
$959$	36.3400	−	36.3400i	1.17348	−	1.17348i
$960$		0			0
$961$			17.1320i			0.552644i
$962$	−36.3171	+	36.3171i	−1.17091	+	1.17091i
$963$	−2.50450	+	2.50450i	−0.0807063	+	0.0807063i
$964$	−6.99198	−	6.99198i	−0.225196	−	0.225196i
$965$		0			0
$966$	−13.4123	−	13.4123i	−0.431535	−	0.431535i
$967$		−	44.1098i		−	1.41847i	−0.704970	−	0.709237i	$-0.749040\pi$
$967$		−	44.1098i		−	1.41847i	0.704970	−	0.709237i	$-0.250960\pi$
$968$	10.9863			0.353113
$969$	−7.34809	+	8.42520i	−0.236055	+	0.270656i
$970$		0			0
$971$			10.7666i			0.345516i	0.984964	+	0.172758i	$0.0552679\pi$
$971$			10.7666i			0.345516i	−0.984964	+	0.172758i	$0.944732\pi$
$972$	−10.7367	−	10.7367i	−0.344379	−	0.344379i
$973$	−54.2099			−1.73789
$974$	15.8955	+	15.8955i	0.509326	+	0.509326i
$975$		0			0
$976$	−0.584366	+	0.584366i	−0.0187051	+	0.0187051i
$977$		−	18.5599i		−	0.593784i	−0.954911	−	0.296892i	$-0.904050\pi$
$977$		−	18.5599i		−	0.593784i	0.954911	−	0.296892i	$-0.0959501\pi$
$978$		−	9.74899i		−	0.311738i
$979$	0.491651	−	0.491651i	0.0157132	−	0.0157132i
$980$		0			0
$981$	−15.3849	−	15.3849i	−0.491201	−	0.491201i
$982$	−22.3761			−0.714052
$983$	−8.62928	−	8.62928i	−0.275231	−	0.275231i	0.555971	−	0.831202i	$-0.312347\pi$
$983$	−8.62928	−	8.62928i	−0.275231	−	0.275231i	−0.831202	+	0.555971i	$0.812347\pi$
$984$			4.79551i			0.152875i
$985$		0			0
$986$	−10.9500	+	12.5551i	−0.348720	+	0.399837i
$987$	21.6291			0.688463
$988$			21.0253i			0.668903i
$989$	0.274592	+	0.274592i	0.00873151	+	0.00873151i
$990$		0			0
$991$	−27.3786	−	27.3786i	−0.869709	−	0.869709i	0.122731	−	0.992440i	$-0.460835\pi$
$991$	−27.3786	−	27.3786i	−0.869709	−	0.869709i	−0.992440	+	0.122731i	$0.960835\pi$
$992$	−4.90571	+	4.90571i	−0.155756	+	0.155756i
$993$	−0.919666	+	0.919666i	−0.0291847	+	0.0291847i
$994$		−	15.8612i		−	0.503086i
$995$		0			0
$996$	0.481465	−	0.481465i	0.0152558	−	0.0152558i
$997$	−6.02579	+	6.02579i	−0.190839	+	0.190839i	−0.796058	−	0.605220i	$-0.793085\pi$
$997$	−6.02579	+	6.02579i	−0.190839	+	0.190839i	0.605220	+	0.796058i	$0.293085\pi$
$998$	−23.7816	−	23.7816i	−0.752793	−	0.752793i
$999$	−36.2772			−1.14776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.m.251.2	yes	8
5.2	odd	4		850.2.g.j.149.2		8
5.3	odd	4		850.2.g.k.149.3		8
5.4	even	2		850.2.h.l.251.3	✓	8
17.4	even	4	inner	850.2.h.m.701.2	yes	8
85.4	even	4		850.2.h.l.701.3	yes	8
85.38	odd	4		850.2.g.j.599.2		8
85.72	odd	4		850.2.g.k.599.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.g.j.149.2		8	5.2	odd	4
850.2.g.j.599.2		8	85.38	odd	4
850.2.g.k.149.3		8	5.3	odd	4
850.2.g.k.599.3		8	85.72	odd	4
850.2.h.l.251.3	✓	8	5.4	even	2
850.2.h.l.701.3	yes	8	85.4	even	4
850.2.h.m.251.2	yes	8	1.1	even	1	trivial
850.2.h.m.701.2	yes	8	17.4	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.511283 - 0.511283i) q^{3} -1.00000 q^{4} +(0.511283 - 0.511283i) q^{6} +(-2.15584 + 2.15584i) q^{7} -1.00000i q^{8} -2.47718i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.511283 - 0.511283i) q^{3} -1.00000 q^{4} +(0.511283 - 0.511283i) q^{6} +(-2.15584 + 2.15584i) q^{7} -1.00000i q^{8} -2.47718i q^{9} +(0.0827533 - 0.0827533i) q^{11} +(0.511283 + 0.511283i) q^{12} +5.60693 q^{13} +(-2.15584 - 2.15584i) q^{14} +1.00000 q^{16} +(4.11353 - 0.280900i) q^{17} +2.47718 q^{18} -3.74987i q^{19} +2.20449 q^{21} +(0.0827533 + 0.0827533i) q^{22} +(-6.08411 + 6.08411i) q^{23} +(-0.511283 + 0.511283i) q^{24} +5.60693i q^{26} +(-2.80039 + 2.80039i) q^{27} +(2.15584 - 2.15584i) q^{28} +(2.85706 + 2.85706i) q^{29} +(4.90571 + 4.90571i) q^{31} +1.00000i q^{32} -0.0846207 q^{33} +(0.280900 + 4.11353i) q^{34} +2.47718i q^{36} +(6.47718 + 6.47718i) q^{37} +3.74987 q^{38} +(-2.86673 - 2.86673i) q^{39} +(4.68969 - 4.68969i) q^{41} +2.20449i q^{42} -0.0451326i q^{43} +(-0.0827533 + 0.0827533i) q^{44} +(-6.08411 - 6.08411i) q^{46} +9.81142 q^{47} +(-0.511283 - 0.511283i) q^{48} -2.29526i q^{49} +(-2.24680 - 1.95956i) q^{51} -5.60693 q^{52} +4.70474i q^{53} +(-2.80039 - 2.80039i) q^{54} +(2.15584 + 2.15584i) q^{56} +(-1.91725 + 1.91725i) q^{57} +(-2.85706 + 2.85706i) q^{58} -7.16873i q^{59} +(-0.584366 + 0.584366i) q^{61} +(-4.90571 + 4.90571i) q^{62} +(5.34039 + 5.34039i) q^{63} -1.00000 q^{64} -0.0846207i q^{66} +11.8960 q^{67} +(-4.11353 + 0.280900i) q^{68} +6.22141 q^{69} +(3.67866 + 3.67866i) q^{71} -2.47718 q^{72} +(-4.66712 - 4.66712i) q^{73} +(-6.47718 + 6.47718i) q^{74} +3.74987i q^{76} +0.356805i q^{77} +(2.86673 - 2.86673i) q^{78} +(1.29878 - 1.29878i) q^{79} -4.56795 q^{81} +(4.68969 + 4.68969i) q^{82} -0.941680i q^{83} -2.20449 q^{84} +0.0451326 q^{86} -2.92153i q^{87} +(-0.0827533 - 0.0827533i) q^{88} +5.94117 q^{89} +(-12.0876 + 12.0876i) q^{91} +(6.08411 - 6.08411i) q^{92} -5.01641i q^{93} +9.81142i q^{94} +(0.511283 - 0.511283i) q^{96} +(-5.10719 - 5.10719i) q^{97} +2.29526 q^{98} +(-0.204995 - 0.204995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 2 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 + 2 * q^7	\( 8 q - 8 q^{4} + 2 q^{7} + 2 q^{11} + 12 q^{13} + 2 q^{14} + 8 q^{16} + 4 q^{17} - 16 q^{18} - 32 q^{21} + 2 q^{22} + 20 q^{23} + 12 q^{27} - 2 q^{28} + 12 q^{29} - 2 q^{31} - 20 q^{33} - 6 q^{34} + 16 q^{37} + 8 q^{38} - 34 q^{39} + 6 q^{41} - 2 q^{44} + 20 q^{46} - 4 q^{47} + 22 q^{51} - 12 q^{52} + 12 q^{54} - 2 q^{56} - 14 q^{57} - 12 q^{58} + 20 q^{61} + 2 q^{62} + 32 q^{63} - 8 q^{64} + 32 q^{67} - 4 q^{68} + 44 q^{69} + 46 q^{71} + 16 q^{72} - 14 q^{73} - 16 q^{74} + 34 q^{78} + 2 q^{79} - 56 q^{81} + 6 q^{82} + 32 q^{84} - 16 q^{86} - 2 q^{88} - 32 q^{89} - 14 q^{91} - 20 q^{92} - 52 q^{97} + 24 q^{98} - 40 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 2 * q^7 + 2 * q^11 + 12 * q^13 + 2 * q^14 + 8 * q^16 + 4 * q^17 - 16 * q^18 - 32 * q^21 + 2 * q^22 + 20 * q^23 + 12 * q^27 - 2 * q^28 + 12 * q^29 - 2 * q^31 - 20 * q^33 - 6 * q^34 + 16 * q^37 + 8 * q^38 - 34 * q^39 + 6 * q^41 - 2 * q^44 + 20 * q^46 - 4 * q^47 + 22 * q^51 - 12 * q^52 + 12 * q^54 - 2 * q^56 - 14 * q^57 - 12 * q^58 + 20 * q^61 + 2 * q^62 + 32 * q^63 - 8 * q^64 + 32 * q^67 - 4 * q^68 + 44 * q^69 + 46 * q^71 + 16 * q^72 - 14 * q^73 - 16 * q^74 + 34 * q^78 + 2 * q^79 - 56 * q^81 + 6 * q^82 + 32 * q^84 - 16 * q^86 - 2 * q^88 - 32 * q^89 - 14 * q^91 - 20 * q^92 - 52 * q^97 + 24 * q^98 - 40 * q^99

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