LMFDB - Embedded newform 850.2.h.j.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:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.2
Root			$-1.65831 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.j.701.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(2.15831 + 2.15831i) q^{3} -1.00000 q^{4} +(-2.15831 + 2.15831i) q^{6} +(2.15831 - 2.15831i) q^{7} -1.00000i q^{8} +6.31662i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(2.15831 + 2.15831i) q^{3} -1.00000 q^{4} +(-2.15831 + 2.15831i) q^{6} +(2.15831 - 2.15831i) q^{7} -1.00000i q^{8} +6.31662i q^{9} +(1.00000 - 1.00000i) q^{11} +(-2.15831 - 2.15831i) q^{12} -1.00000 q^{13} +(2.15831 + 2.15831i) q^{14} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -6.31662 q^{18} +8.31662i q^{19} +9.31662 q^{21} +(1.00000 + 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(2.15831 - 2.15831i) q^{24} -1.00000i q^{26} +(-7.15831 + 7.15831i) q^{27} +(-2.15831 + 2.15831i) q^{28} +(-2.31662 - 2.31662i) q^{29} +(3.15831 + 3.15831i) q^{31} +1.00000i q^{32} +4.31662 q^{33} +(-4.00000 - 1.00000i) q^{34} -6.31662i q^{36} +(-6.31662 - 6.31662i) q^{37} -8.31662 q^{38} +(-2.15831 - 2.15831i) q^{39} +(5.31662 - 5.31662i) q^{41} +9.31662i q^{42} +6.00000i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} +10.9499 q^{47} +(2.15831 + 2.15831i) q^{48} -2.31662i q^{49} +(-10.7916 + 6.47494i) q^{51} +1.00000 q^{52} -11.9499i q^{53} +(-7.15831 - 7.15831i) q^{54} +(-2.15831 - 2.15831i) q^{56} +(-17.9499 + 17.9499i) q^{57} +(2.31662 - 2.31662i) q^{58} -4.63325i q^{59} +(5.31662 - 5.31662i) q^{61} +(-3.15831 + 3.15831i) q^{62} +(13.6332 + 13.6332i) q^{63} -1.00000 q^{64} +4.31662i q^{66} +6.63325 q^{67} +(1.00000 - 4.00000i) q^{68} -4.31662 q^{69} +(-6.15831 - 6.15831i) q^{71} +6.31662 q^{72} +(-8.63325 - 8.63325i) q^{73} +(6.31662 - 6.31662i) q^{74} -8.31662i q^{76} -4.31662i q^{77} +(2.15831 - 2.15831i) q^{78} +(4.47494 - 4.47494i) q^{79} -11.9499 q^{81} +(5.31662 + 5.31662i) q^{82} -12.6332i q^{83} -9.31662 q^{84} -6.00000 q^{86} -10.0000i q^{87} +(-1.00000 - 1.00000i) q^{88} +18.6332 q^{89} +(-2.15831 + 2.15831i) q^{91} +(1.00000 - 1.00000i) q^{92} +13.6332i q^{93} +10.9499i q^{94} +(-2.15831 + 2.15831i) q^{96} +(-2.00000 - 2.00000i) q^{97} +2.31662 q^{98} +(6.31662 + 6.31662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^4 - 2 * q^6 + 2 * q^7	$ 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{17} - 12 q^{18} + 24 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 22 q^{27} - 2 q^{28} + 4 q^{29} + 6 q^{31} + 4 q^{33} - 16 q^{34} - 12 q^{37} - 20 q^{38} - 2 q^{39} + 8 q^{41} - 4 q^{44} - 4 q^{46} + 4 q^{47} + 2 q^{48} - 10 q^{51} + 4 q^{52} - 22 q^{54} - 2 q^{56} - 32 q^{57} - 4 q^{58} + 8 q^{61} - 6 q^{62} + 28 q^{63} - 4 q^{64} + 4 q^{68} - 4 q^{69} - 18 q^{71} + 12 q^{72} - 8 q^{73} + 12 q^{74} + 2 q^{78} - 2 q^{79} - 8 q^{81} + 8 q^{82} - 24 q^{84} - 24 q^{86} - 4 q^{88} + 48 q^{89} - 2 q^{91} + 4 q^{92} - 2 q^{96} - 8 q^{97} - 4 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^4 - 2 * q^6 + 2 * q^7 + 4 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^17 - 12 * q^18 + 24 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 22 * q^27 - 2 * q^28 + 4 * q^29 + 6 * q^31 + 4 * q^33 - 16 * q^34 - 12 * q^37 - 20 * q^38 - 2 * q^39 + 8 * q^41 - 4 * q^44 - 4 * q^46 + 4 * q^47 + 2 * q^48 - 10 * q^51 + 4 * q^52 - 22 * q^54 - 2 * q^56 - 32 * q^57 - 4 * q^58 + 8 * q^61 - 6 * q^62 + 28 * q^63 - 4 * q^64 + 4 * q^68 - 4 * q^69 - 18 * q^71 + 12 * q^72 - 8 * q^73 + 12 * q^74 + 2 * q^78 - 2 * q^79 - 8 * q^81 + 8 * q^82 - 24 * q^84 - 24 * q^86 - 4 * q^88 + 48 * q^89 - 2 * q^91 + 4 * q^92 - 2 * q^96 - 8 * q^97 - 4 * q^98 + 12 * 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
$3$	2.15831	+	2.15831i	1.24610	+	1.24610i	0.957427	+	0.288675i	$0.0932147\pi$
$3$	2.15831	+	2.15831i	1.24610	+	1.24610i	0.288675	+	0.957427i	$0.406785\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−2.15831	+	2.15831i	−0.881127	+	0.881127i
$7$	2.15831	−	2.15831i	0.815765	−	0.815765i	−0.169726	−	0.985491i	$-0.554288\pi$
$7$	2.15831	−	2.15831i	0.815765	−	0.815765i	0.985491	+	0.169726i	$0.0542882\pi$
$8$		−	1.00000i		−	0.353553i
$9$			6.31662i			2.10554i
$10$		0			0
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	−0.540094	−	0.841605i	$-0.681611\pi$
$11$	1.00000	−	1.00000i	0.301511	−	0.301511i	0.841605	+	0.540094i	$0.181611\pi$
$12$	−2.15831	−	2.15831i	−0.623051	−	0.623051i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	2.15831	+	2.15831i	0.576833	+	0.576833i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$17$	−1.00000	+	4.00000i	−0.242536	+	0.970143i
$18$	−6.31662			−1.48884
$19$			8.31662i			1.90796i	0.299863	+	0.953982i	$0.403059\pi$
$19$			8.31662i			1.90796i	−0.299863	+	0.953982i	$0.596941\pi$
$20$		0			0
$21$	9.31662			2.03305
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	2.15831	−	2.15831i	0.440564	−	0.440564i
$25$		0			0
$26$		−	1.00000i		−	0.196116i
$27$	−7.15831	+	7.15831i	−1.37762	+	1.37762i
$28$	−2.15831	+	2.15831i	−0.407883	+	0.407883i
$29$	−2.31662	−	2.31662i	−0.430186	−	0.430186i	0.458505	−	0.888692i	$-0.348385\pi$
$29$	−2.31662	−	2.31662i	−0.430186	−	0.430186i	−0.888692	+	0.458505i	$0.848385\pi$
$30$		0			0
$31$	3.15831	+	3.15831i	0.567250	+	0.567250i	0.931357	−	0.364107i	$-0.118626\pi$
$31$	3.15831	+	3.15831i	0.567250	+	0.567250i	−0.364107	+	0.931357i	$0.618626\pi$
$32$			1.00000i			0.176777i
$33$	4.31662			0.751428
$34$	−4.00000	−	1.00000i	−0.685994	−	0.171499i
$35$		0			0
$36$		−	6.31662i		−	1.05277i
$37$	−6.31662	−	6.31662i	−1.03845	−	1.03845i	−0.999231	−	0.0392160i	$-0.987514\pi$
$37$	−6.31662	−	6.31662i	−1.03845	−	1.03845i	−0.0392160	−	0.999231i	$-0.512486\pi$
$38$	−8.31662			−1.34913
$39$	−2.15831	−	2.15831i	−0.345607	−	0.345607i
$40$		0			0
$41$	5.31662	−	5.31662i	0.830317	−	0.830317i	−0.157243	−	0.987560i	$-0.550260\pi$
$41$	5.31662	−	5.31662i	0.830317	−	0.830317i	0.987560	+	0.157243i	$0.0502605\pi$
$42$			9.31662i			1.43759i
$43$			6.00000i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$43$			6.00000i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$		0			0
$46$	−1.00000	−	1.00000i	−0.147442	−	0.147442i
$47$	10.9499			1.59720			0.798602	−	0.601860i	$-0.205573\pi$
$47$	10.9499			1.59720			0.798602	+	0.601860i	$0.205573\pi$
$48$	2.15831	+	2.15831i	0.311526	+	0.311526i
$49$		−	2.31662i		−	0.330946i
$50$		0			0
$51$	−10.7916	+	6.47494i	−1.51112	+	0.906673i
$52$	1.00000			0.138675
$53$		−	11.9499i		−	1.64144i	−0.571330	−	0.820721i	$-0.693572\pi$
$53$		−	11.9499i		−	1.64144i	0.571330	−	0.820721i	$-0.306428\pi$
$54$	−7.15831	−	7.15831i	−0.974123	−	0.974123i
$55$		0			0
$56$	−2.15831	−	2.15831i	−0.288417	−	0.288417i
$57$	−17.9499	+	17.9499i	−2.37752	+	2.37752i
$58$	2.31662	−	2.31662i	0.304188	−	0.304188i
$59$		−	4.63325i		−	0.603198i	−0.953435	−	0.301599i	$-0.902480\pi$
$59$		−	4.63325i		−	0.603198i	0.953435	−	0.301599i	$-0.0975203\pi$
$60$		0			0
$61$	5.31662	−	5.31662i	0.680724	−	0.680724i	−0.279439	−	0.960163i	$-0.590149\pi$
$61$	5.31662	−	5.31662i	0.680724	−	0.680724i	0.960163	+	0.279439i	$0.0901486\pi$
$62$	−3.15831	+	3.15831i	−0.401106	+	0.401106i
$63$	13.6332	+	13.6332i	1.71763	+	1.71763i
$64$	−1.00000			−0.125000
$65$		0			0
$66$			4.31662i			0.531340i
$67$	6.63325			0.810380			0.405190	−	0.914232i	$-0.367205\pi$
$67$	6.63325			0.810380			0.405190	+	0.914232i	$0.367205\pi$
$68$	1.00000	−	4.00000i	0.121268	−	0.485071i
$69$	−4.31662			−0.519661
$70$		0			0
$71$	−6.15831	−	6.15831i	−0.730857	−	0.730857i	0.239932	−	0.970790i	$-0.422875\pi$
$71$	−6.15831	−	6.15831i	−0.730857	−	0.730857i	−0.970790	+	0.239932i	$0.922875\pi$
$72$	6.31662			0.744421
$73$	−8.63325	−	8.63325i	−1.01045	−	1.01045i	−0.999945	−	0.0105006i	$-0.996658\pi$
$73$	−8.63325	−	8.63325i	−1.01045	−	1.01045i	−0.0105006	−	0.999945i	$-0.503342\pi$
$74$	6.31662	−	6.31662i	0.734293	−	0.734293i
$75$		0			0
$76$		−	8.31662i		−	0.953982i
$77$		−	4.31662i		−	0.491925i
$78$	2.15831	−	2.15831i	0.244381	−	0.244381i
$79$	4.47494	−	4.47494i	0.503470	−	0.503470i	−0.409045	−	0.912514i	$-0.634138\pi$
$79$	4.47494	−	4.47494i	0.503470	−	0.503470i	0.912514	+	0.409045i	$0.134138\pi$
$80$		0			0
$81$	−11.9499			−1.32776
$82$	5.31662	+	5.31662i	0.587123	+	0.587123i
$83$		−	12.6332i		−	1.38668i	−0.720611	−	0.693340i	$-0.756139\pi$
$83$		−	12.6332i		−	1.38668i	0.720611	−	0.693340i	$-0.243861\pi$
$84$	−9.31662			−1.01653
$85$		0			0
$86$	−6.00000			−0.646997
$87$		−	10.0000i		−	1.07211i
$88$	−1.00000	−	1.00000i	−0.106600	−	0.106600i
$89$	18.6332			1.97512			0.987560	−	0.157241i	$-0.0502600\pi$
$89$	18.6332			1.97512			0.987560	+	0.157241i	$0.0502600\pi$
$90$		0			0
$91$	−2.15831	+	2.15831i	−0.226253	+	0.226253i
$92$	1.00000	−	1.00000i	0.104257	−	0.104257i
$93$			13.6332i			1.41370i
$94$			10.9499i			1.12939i
$95$		0			0
$96$	−2.15831	+	2.15831i	−0.220282	+	0.220282i
$97$	−2.00000	−	2.00000i	−0.203069	−	0.203069i	0.598244	−	0.801314i	$-0.295865\pi$
$97$	−2.00000	−	2.00000i	−0.203069	−	0.203069i	−0.801314	+	0.598244i	$0.795865\pi$
$98$	2.31662			0.234014
$99$	6.31662	+	6.31662i	0.634845	+	0.634845i
$100$		0			0
$101$	5.63325			0.560529			0.280265	−	0.959923i	$-0.409578\pi$
$101$	5.63325			0.560529			0.280265	+	0.959923i	$0.409578\pi$
$102$	−6.47494	−	10.7916i	−0.641114	−	1.06852i
$103$	−17.5831			−1.73252			−0.866258	−	0.499596i	$-0.833482\pi$
$103$	−17.5831			−1.73252			−0.866258	+	0.499596i	$0.833482\pi$
$104$			1.00000i			0.0980581i
$105$		0			0
$106$	11.9499			1.16067
$107$	−9.15831	−	9.15831i	−0.885367	−	0.885367i	0.108706	−	0.994074i	$-0.465329\pi$
$107$	−9.15831	−	9.15831i	−0.885367	−	0.885367i	−0.994074	+	0.108706i	$0.965329\pi$
$108$	7.15831	−	7.15831i	0.688809	−	0.688809i
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	−0.796372	−	0.604807i	$-0.793250\pi$
$109$	−2.00000	+	2.00000i	−0.191565	+	0.191565i	0.604807	+	0.796372i	$0.293250\pi$
$110$		0			0
$111$		−	27.2665i		−	2.58802i
$112$	2.15831	−	2.15831i	0.203941	−	0.203941i
$113$	−13.2665	+	13.2665i	−1.24801	+	1.24801i	−0.291409	+	0.956599i	$0.594124\pi$
$113$	−13.2665	+	13.2665i	−1.24801	+	1.24801i	−0.956599	+	0.291409i	$0.905876\pi$
$114$	−17.9499	−	17.9499i	−1.68116	−	1.68116i
$115$		0			0
$116$	2.31662	+	2.31662i	0.215093	+	0.215093i
$117$		−	6.31662i		−	0.583972i
$118$	4.63325			0.426525
$119$	6.47494	+	10.7916i	0.593557	+	0.989261i
$120$		0			0
$121$			9.00000i			0.818182i
$122$	5.31662	+	5.31662i	0.481345	+	0.481345i
$123$	22.9499			2.06932
$124$	−3.15831	−	3.15831i	−0.283625	−	0.283625i
$125$		0			0
$126$	−13.6332	+	13.6332i	−1.21455	+	1.21455i
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−12.9499	+	12.9499i	−1.14017	+	1.14017i
$130$		0			0
$131$	1.79156	+	1.79156i	0.156529	+	0.156529i	0.781027	−	0.624497i	$-0.214696\pi$
$131$	1.79156	+	1.79156i	0.156529	+	0.156529i	−0.624497	+	0.781027i	$0.714696\pi$
$132$	−4.31662			−0.375714
$133$	17.9499	+	17.9499i	1.55645	+	1.55645i
$134$			6.63325i			0.573025i
$135$		0			0
$136$	4.00000	+	1.00000i	0.342997	+	0.0857493i
$137$	0.0501256			0.00428252			0.00214126	−	0.999998i	$-0.499318\pi$
$137$	0.0501256			0.00428252			0.00214126	+	0.999998i	$0.499318\pi$
$138$		−	4.31662i		−	0.367456i
$139$	2.79156	+	2.79156i	0.236777	+	0.236777i	0.815514	−	0.578737i	$-0.196454\pi$
$139$	2.79156	+	2.79156i	0.236777	+	0.236777i	−0.578737	+	0.815514i	$0.696454\pi$
$140$		0			0
$141$	23.6332	+	23.6332i	1.99028	+	1.99028i
$142$	6.15831	−	6.15831i	0.516794	−	0.516794i
$143$	−1.00000	+	1.00000i	−0.0836242	+	0.0836242i
$144$			6.31662i			0.526385i
$145$		0			0
$146$	8.63325	−	8.63325i	0.714493	−	0.714493i
$147$	5.00000	−	5.00000i	0.412393	−	0.412393i
$148$	6.31662	+	6.31662i	0.519223	+	0.519223i
$149$	2.05013			0.167953			0.0839764	−	0.996468i	$-0.473238\pi$
$149$	2.05013			0.167953			0.0839764	+	0.996468i	$0.473238\pi$
$150$		0			0
$151$			14.3166i			1.16507i	0.812805	+	0.582535i	$0.197939\pi$
$151$			14.3166i			1.16507i	−0.812805	+	0.582535i	$0.802061\pi$
$152$	8.31662			0.674567
$153$	−25.2665	−	6.31662i	−2.04268	−	0.510669i
$154$	4.31662			0.347844
$155$		0			0
$156$	2.15831	+	2.15831i	0.172803	+	0.172803i
$157$	8.68338			0.693009			0.346504	−	0.938048i	$-0.387369\pi$
$157$	8.68338			0.693009			0.346504	+	0.938048i	$0.387369\pi$
$158$	4.47494	+	4.47494i	0.356007	+	0.356007i
$159$	25.7916	−	25.7916i	2.04540	−	2.04540i
$160$		0			0
$161$			4.31662i			0.340198i
$162$		−	11.9499i		−	0.938871i
$163$	6.15831	−	6.15831i	0.482356	−	0.482356i	−0.423527	−	0.905883i	$-0.639208\pi$
$163$	6.15831	−	6.15831i	0.482356	−	0.482356i	0.905883	+	0.423527i	$0.139208\pi$
$164$	−5.31662	+	5.31662i	−0.415159	+	0.415159i
$165$		0			0
$166$	12.6332			0.980530
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	0.382344	−	0.924020i	$-0.375117\pi$
$167$	−7.00000	−	7.00000i	−0.541676	−	0.541676i	−0.924020	+	0.382344i	$0.875117\pi$
$168$		−	9.31662i		−	0.718793i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−52.5330			−4.01730
$172$		−	6.00000i		−	0.457496i
$173$	−10.6834	−	10.6834i	−0.812242	−	0.812242i	0.172728	−	0.984970i	$-0.444742\pi$
$173$	−10.6834	−	10.6834i	−0.812242	−	0.812242i	−0.984970	+	0.172728i	$0.944742\pi$
$174$	10.0000			0.758098
$175$		0			0
$176$	1.00000	−	1.00000i	0.0753778	−	0.0753778i
$177$	10.0000	−	10.0000i	0.751646	−	0.751646i
$178$			18.6332i			1.39662i
$179$		−	1.68338i		−	0.125821i	−0.998019	−	0.0629107i	$-0.979962\pi$
$179$		−	1.68338i		−	0.125821i	0.998019	−	0.0629107i	$-0.0200383\pi$
$180$		0			0
$181$	−17.6332	+	17.6332i	−1.31067	+	1.31067i	−0.389747	+	0.920922i	$0.627438\pi$
$181$	−17.6332	+	17.6332i	−1.31067	+	1.31067i	−0.920922	+	0.389747i	$0.872562\pi$
$182$	−2.15831	−	2.15831i	−0.159985	−	0.159985i
$183$	22.9499			1.69650
$184$	1.00000	+	1.00000i	0.0737210	+	0.0737210i
$185$		0			0
$186$	−13.6332			−0.999638
$187$	3.00000	+	5.00000i	0.219382	+	0.365636i
$188$	−10.9499			−0.798602
$189$			30.8997i			2.24763i
$190$		0			0
$191$	−10.9499			−0.792305			−0.396153	−	0.918185i	$-0.629655\pi$
$191$	−10.9499			−0.792305			−0.396153	+	0.918185i	$0.629655\pi$
$192$	−2.15831	−	2.15831i	−0.155763	−	0.155763i
$193$	−0.316625	+	0.316625i	−0.0227912	+	0.0227912i	−0.718411	−	0.695619i	$-0.755130\pi$
$193$	−0.316625	+	0.316625i	−0.0227912	+	0.0227912i	0.695619	+	0.718411i	$0.255130\pi$
$194$	2.00000	−	2.00000i	0.143592	−	0.143592i
$195$		0			0
$196$			2.31662i			0.165473i
$197$	−0.683375	+	0.683375i	−0.0486885	+	0.0486885i	−0.731032	−	0.682343i	$-0.760961\pi$
$197$	−0.683375	+	0.683375i	−0.0486885	+	0.0486885i	0.682343	+	0.731032i	$0.260961\pi$
$198$	−6.31662	+	6.31662i	−0.448903	+	0.448903i
$199$	−1.63325	−	1.63325i	−0.115778	−	0.115778i	0.646844	−	0.762622i	$-0.276088\pi$
$199$	−1.63325	−	1.63325i	−0.115778	−	0.115778i	−0.762622	+	0.646844i	$0.776088\pi$
$200$		0			0
$201$	14.3166	+	14.3166i	1.00982	+	1.00982i
$202$			5.63325i			0.396354i
$203$	−10.0000			−0.701862
$204$	10.7916	−	6.47494i	0.755560	−	0.453336i
$205$		0			0
$206$		−	17.5831i		−	1.22507i
$207$	−6.31662	−	6.31662i	−0.439036	−	0.439036i
$208$	−1.00000			−0.0693375
$209$	8.31662	+	8.31662i	0.575273	+	0.575273i
$210$		0			0
$211$	6.10819	−	6.10819i	0.420505	−	0.420505i	−0.464873	−	0.885378i	$-0.653900\pi$
$211$	6.10819	−	6.10819i	0.420505	−	0.420505i	0.885378	+	0.464873i	$0.153900\pi$
$212$			11.9499i			0.820721i
$213$		−	26.5831i		−	1.82145i
$214$	9.15831	−	9.15831i	0.626049	−	0.626049i
$215$		0			0
$216$	7.15831	+	7.15831i	0.487061	+	0.487061i
$217$	13.6332			0.925485
$218$	−2.00000	−	2.00000i	−0.135457	−	0.135457i
$219$		−	37.2665i		−	2.51824i
$220$		0			0
$221$	1.00000	−	4.00000i	0.0672673	−	0.269069i
$222$	27.2665			1.83001
$223$		−	5.58312i		−	0.373874i	−0.982372	−	0.186937i	$-0.940144\pi$
$223$		−	5.58312i		−	0.373874i	0.982372	−	0.186937i	$-0.0598560\pi$
$224$	2.15831	+	2.15831i	0.144208	+	0.144208i
$225$		0			0
$226$	−13.2665	−	13.2665i	−0.882474	−	0.882474i
$227$	2.15831	−	2.15831i	0.143252	−	0.143252i	−0.631844	−	0.775096i	$-0.717702\pi$
$227$	2.15831	−	2.15831i	0.143252	−	0.143252i	0.775096	+	0.631844i	$0.217702\pi$
$228$	17.9499	−	17.9499i	1.18876	−	1.18876i
$229$		−	16.8997i		−	1.11677i	−0.829583	−	0.558383i	$-0.811422\pi$
$229$		−	16.8997i		−	1.11677i	0.829583	−	0.558383i	$-0.188578\pi$
$230$		0			0
$231$	9.31662	−	9.31662i	0.612989	−	0.612989i
$232$	−2.31662	+	2.31662i	−0.152094	+	0.152094i
$233$	2.94987	+	2.94987i	0.193253	+	0.193253i	0.797100	−	0.603847i	$-0.206366\pi$
$233$	2.94987	+	2.94987i	0.193253	+	0.193253i	−0.603847	+	0.797100i	$0.706366\pi$
$234$	6.31662			0.412931
$235$		0			0
$236$			4.63325i			0.301599i
$237$	19.3166			1.25475
$238$	−10.7916	+	6.47494i	−0.699513	+	0.419708i
$239$	8.63325			0.558438			0.279219	−	0.960227i	$-0.409924\pi$
$239$	8.63325			0.558438			0.279219	+	0.960227i	$0.409924\pi$
$240$		0			0
$241$	6.68338	+	6.68338i	0.430514	+	0.430514i	0.888803	−	0.458289i	$-0.151538\pi$
$241$	6.68338	+	6.68338i	0.430514	+	0.430514i	−0.458289	+	0.888803i	$0.651538\pi$
$242$	−9.00000			−0.578542
$243$	−4.31662	−	4.31662i	−0.276912	−	0.276912i
$244$	−5.31662	+	5.31662i	−0.340362	+	0.340362i
$245$		0			0
$246$			22.9499i			1.46323i
$247$		−	8.31662i		−	0.529174i
$248$	3.15831	−	3.15831i	0.200553	−	0.200553i
$249$	27.2665	−	27.2665i	1.72794	−	1.72794i
$250$		0			0
$251$	19.2665			1.21609			0.608045	−	0.793902i	$-0.291954\pi$
$251$	19.2665			1.21609			0.608045	+	0.793902i	$0.291954\pi$
$252$	−13.6332	−	13.6332i	−0.858814	−	0.858814i
$253$			2.00000i			0.125739i
$254$	2.00000			0.125491
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	2.68338i		−	0.167384i	−0.996492	−	0.0836922i	$-0.973329\pi$
$257$		−	2.68338i		−	0.167384i	0.996492	−	0.0836922i	$-0.0266712\pi$
$258$	−12.9499	−	12.9499i	−0.806224	−	0.806224i
$259$	−27.2665			−1.69426
$260$		0			0
$261$	14.6332	−	14.6332i	0.905775	−	0.905775i
$262$	−1.79156	+	1.79156i	−0.110683	+	0.110683i
$263$		−	4.00000i		−	0.246651i	−0.992366	−	0.123325i	$-0.960644\pi$
$263$		−	4.00000i		−	0.246651i	0.992366	−	0.123325i	$-0.0393559\pi$
$264$		−	4.31662i		−	0.265670i
$265$		0			0
$266$	−17.9499	+	17.9499i	−1.10058	+	1.10058i
$267$	40.2164	+	40.2164i	2.46120	+	2.46120i
$268$	−6.63325			−0.405190
$269$	−10.2665	−	10.2665i	−0.625960	−	0.625960i	0.321089	−	0.947049i	$-0.395951\pi$
$269$	−10.2665	−	10.2665i	−0.625960	−	0.625960i	−0.947049	+	0.321089i	$0.895951\pi$
$270$		0			0
$271$	13.5831			0.825116			0.412558	−	0.910931i	$-0.364635\pi$
$271$	13.5831			0.825116			0.412558	+	0.910931i	$0.364635\pi$
$272$	−1.00000	+	4.00000i	−0.0606339	+	0.242536i
$273$	−9.31662			−0.563868
$274$			0.0501256i			0.00302820i
$275$		0			0
$276$	4.31662			0.259830
$277$	7.31662	+	7.31662i	0.439613	+	0.439613i	0.891882	−	0.452268i	$-0.149385\pi$
$277$	7.31662	+	7.31662i	0.439613	+	0.439613i	−0.452268	+	0.891882i	$0.649385\pi$
$278$	−2.79156	+	2.79156i	−0.167427	+	0.167427i
$279$	−19.9499	+	19.9499i	−1.19437	+	1.19437i
$280$		0			0
$281$		−	5.00000i		−	0.298275i	−0.988816	−	0.149137i	$-0.952350\pi$
$281$		−	5.00000i		−	0.298275i	0.988816	−	0.149137i	$-0.0476497\pi$
$282$	−23.6332	+	23.6332i	−1.40734	+	1.40734i
$283$	13.3166	−	13.3166i	0.791591	−	0.791591i	−0.190162	−	0.981753i	$-0.560901\pi$
$283$	13.3166	−	13.3166i	0.791591	−	0.791591i	0.981753	+	0.190162i	$0.0609012\pi$
$284$	6.15831	+	6.15831i	0.365429	+	0.365429i
$285$		0			0
$286$	−1.00000	−	1.00000i	−0.0591312	−	0.0591312i
$287$		−	22.9499i		−	1.35469i
$288$	−6.31662			−0.372211
$289$	−15.0000	−	8.00000i	−0.882353	−	0.470588i
$290$		0			0
$291$		−	8.63325i		−	0.506090i
$292$	8.63325	+	8.63325i	0.505223	+	0.505223i
$293$	19.8997			1.16256			0.581278	−	0.813705i	$-0.302553\pi$
$293$	19.8997			1.16256			0.581278	+	0.813705i	$0.302553\pi$
$294$	5.00000	+	5.00000i	0.291606	+	0.291606i
$295$		0			0
$296$	−6.31662	+	6.31662i	−0.367146	+	0.367146i
$297$			14.3166i			0.830735i
$298$			2.05013i			0.118761i
$299$	1.00000	−	1.00000i	0.0578315	−	0.0578315i
$300$		0			0
$301$	12.9499	+	12.9499i	0.746418	+	0.746418i
$302$	−14.3166			−0.823829
$303$	12.1583	+	12.1583i	0.698477	+	0.698477i
$304$			8.31662i			0.476991i
$305$		0			0
$306$	6.31662	−	25.2665i	0.361097	−	1.44439i
$307$	−26.5330			−1.51432			−0.757159	−	0.653231i	$-0.773413\pi$
$307$	−26.5330			−1.51432			−0.757159	+	0.653231i	$0.773413\pi$
$308$			4.31662i			0.245963i
$309$	−37.9499	−	37.9499i	−2.15889	−	2.15889i
$310$		0			0
$311$	−6.84169	−	6.84169i	−0.387957	−	0.387957i	0.486001	−	0.873958i	$-0.338455\pi$
$311$	−6.84169	−	6.84169i	−0.387957	−	0.387957i	−0.873958	+	0.486001i	$0.838455\pi$
$312$	−2.15831	+	2.15831i	−0.122190	+	0.122190i
$313$	−13.9499	+	13.9499i	−0.788494	+	0.788494i	−0.981247	−	0.192754i	$-0.938258\pi$
$313$	−13.9499	+	13.9499i	−0.788494	+	0.788494i	0.192754	+	0.981247i	$0.438258\pi$
$314$			8.68338i			0.490031i
$315$		0			0
$316$	−4.47494	+	4.47494i	−0.251735	+	0.251735i
$317$	−5.00000	+	5.00000i	−0.280828	+	0.280828i	−0.833439	−	0.552611i	$-0.813631\pi$
$317$	−5.00000	+	5.00000i	−0.280828	+	0.280828i	0.552611	+	0.833439i	$0.313631\pi$
$318$	25.7916	+	25.7916i	1.44632	+	1.44632i
$319$	−4.63325			−0.259412
$320$		0			0
$321$		−	39.5330i		−	2.20652i
$322$	−4.31662			−0.240556
$323$	−33.2665	−	8.31662i	−1.85100	−	0.462749i
$324$	11.9499			0.663882
$325$		0			0
$326$	6.15831	+	6.15831i	0.341077	+	0.341077i
$327$	−8.63325			−0.477420
$328$	−5.31662	−	5.31662i	−0.293561	−	0.293561i
$329$	23.6332	−	23.6332i	1.30294	−	1.30294i
$330$		0			0
$331$			11.5831i			0.636666i	0.947979	+	0.318333i	$0.103123\pi$
$331$			11.5831i			0.636666i	−0.947979	+	0.318333i	$0.896877\pi$
$332$			12.6332i			0.693340i
$333$	39.8997	−	39.8997i	2.18649	−	2.18649i
$334$	7.00000	−	7.00000i	0.383023	−	0.383023i
$335$		0			0
$336$	9.31662			0.508264
$337$	2.31662	+	2.31662i	0.126195	+	0.126195i	0.767383	−	0.641189i	$-0.221558\pi$
$337$	2.31662	+	2.31662i	0.126195	+	0.126195i	−0.641189	+	0.767383i	$0.721558\pi$
$338$		−	12.0000i		−	0.652714i
$339$	−57.2665			−3.11029
$340$		0			0
$341$	6.31662			0.342064
$342$		−	52.5330i		−	2.84066i
$343$	10.1082	+	10.1082i	0.545791	+	0.545791i
$344$	6.00000			0.323498
$345$		0			0
$346$	10.6834	−	10.6834i	0.574342	−	0.574342i
$347$	15.7916	−	15.7916i	0.847735	−	0.847735i	−0.142115	−	0.989850i	$-0.545390\pi$
$347$	15.7916	−	15.7916i	0.847735	−	0.847735i	0.989850	+	0.142115i	$0.0453902\pi$
$348$			10.0000i			0.536056i
$349$			31.9499i			1.71024i	0.518432	+	0.855119i	$0.326516\pi$
$349$			31.9499i			1.71024i	−0.518432	+	0.855119i	$0.673484\pi$
$350$		0			0
$351$	7.15831	−	7.15831i	0.382082	−	0.382082i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	−28.2665			−1.50447			−0.752237	−	0.658893i	$-0.771025\pi$
$353$	−28.2665			−1.50447			−0.752237	+	0.658893i	$0.771025\pi$
$354$	10.0000	+	10.0000i	0.531494	+	0.531494i
$355$		0			0
$356$	−18.6332			−0.987560
$357$	−9.31662	+	37.2665i	−0.493088	+	1.97235i
$358$	1.68338			0.0889691
$359$			18.3166i			0.966714i	0.875423	+	0.483357i	$0.160583\pi$
$359$			18.3166i			0.966714i	−0.875423	+	0.483357i	$0.839417\pi$
$360$		0			0
$361$	−50.1662			−2.64033
$362$	−17.6332	−	17.6332i	−0.926783	−	0.926783i
$363$	−19.4248	+	19.4248i	−1.01954	+	1.01954i
$364$	2.15831	−	2.15831i	0.113126	−	0.113126i
$365$		0			0
$366$			22.9499i			1.19961i
$367$	−22.8417	+	22.8417i	−1.19233	+	1.19233i	−0.215914	+	0.976412i	$0.569273\pi$
$367$	−22.8417	+	22.8417i	−1.19233	+	1.19233i	−0.976412	+	0.215914i	$0.930727\pi$
$368$	−1.00000	+	1.00000i	−0.0521286	+	0.0521286i
$369$	33.5831	+	33.5831i	1.74827	+	1.74827i
$370$		0			0
$371$	−25.7916	−	25.7916i	−1.33903	−	1.33903i
$372$		−	13.6332i		−	0.706851i
$373$	33.5330			1.73627			0.868136	−	0.496326i	$-0.165318\pi$
$373$	33.5330			1.73627			0.868136	+	0.496326i	$0.165318\pi$
$374$	−5.00000	+	3.00000i	−0.258544	+	0.155126i
$375$		0			0
$376$		−	10.9499i		−	0.564697i
$377$	2.31662	+	2.31662i	0.119312	+	0.119312i
$378$	−30.8997			−1.58931
$379$	−6.52506	−	6.52506i	−0.335170	−	0.335170i	0.519376	−	0.854546i	$-0.326164\pi$
$379$	−6.52506	−	6.52506i	−0.335170	−	0.335170i	−0.854546	+	0.519376i	$0.826164\pi$
$380$		0			0
$381$	4.31662	−	4.31662i	0.221147	−	0.221147i
$382$		−	10.9499i		−	0.560244i
$383$		−	16.9499i		−	0.866098i	−0.901370	−	0.433049i	$-0.857438\pi$
$383$		−	16.9499i		−	0.866098i	0.901370	−	0.433049i	$-0.142562\pi$
$384$	2.15831	−	2.15831i	0.110141	−	0.110141i
$385$		0			0
$386$	−0.316625	−	0.316625i	−0.0161158	−	0.0161158i
$387$	−37.8997			−1.92655
$388$	2.00000	+	2.00000i	0.101535	+	0.101535i
$389$			1.26650i			0.0642141i	0.999484	+	0.0321070i	$0.0102217\pi$
$389$			1.26650i			0.0642141i	−0.999484	+	0.0321070i	$0.989778\pi$
$390$		0			0
$391$	−3.00000	−	5.00000i	−0.151717	−	0.252861i
$392$	−2.31662			−0.117007
$393$			7.73350i			0.390104i
$394$	−0.683375	−	0.683375i	−0.0344279	−	0.0344279i
$395$		0			0
$396$	−6.31662	−	6.31662i	−0.317422	−	0.317422i
$397$	15.8997	−	15.8997i	0.797986	−	0.797986i	−0.184792	−	0.982778i	$-0.559161\pi$
$397$	15.8997	−	15.8997i	0.797986	−	0.797986i	0.982778	+	0.184792i	$0.0591612\pi$
$398$	1.63325	−	1.63325i	0.0818674	−	0.0818674i
$399$			77.4829i			3.87900i
$400$		0			0
$401$	−10.5831	+	10.5831i	−0.528496	+	0.528496i	−0.920124	−	0.391628i	$-0.871912\pi$
$401$	−10.5831	+	10.5831i	−0.528496	+	0.528496i	0.391628	+	0.920124i	$0.371912\pi$
$402$	−14.3166	+	14.3166i	−0.714048	+	0.714048i
$403$	−3.15831	−	3.15831i	−0.157327	−	0.157327i
$404$	−5.63325			−0.280265
$405$		0			0
$406$		−	10.0000i		−	0.496292i
$407$	−12.6332			−0.626207
$408$	6.47494	+	10.7916i	0.320557	+	0.534262i
$409$	10.8997			0.538958			0.269479	−	0.963006i	$-0.413149\pi$
$409$	10.8997			0.538958			0.269479	+	0.963006i	$0.413149\pi$
$410$		0			0
$411$	0.108187	+	0.108187i	0.00533646	+	0.00533646i
$412$	17.5831			0.866258
$413$	−10.0000	−	10.0000i	−0.492068	−	0.492068i
$414$	6.31662	−	6.31662i	0.310445	−	0.310445i
$415$		0			0
$416$		−	1.00000i		−	0.0490290i
$417$			12.0501i			0.590097i
$418$	−8.31662	+	8.31662i	−0.406779	+	0.406779i
$419$	−7.00000	+	7.00000i	−0.341972	+	0.341972i	−0.857108	−	0.515136i	$-0.827741\pi$
$419$	−7.00000	+	7.00000i	−0.341972	+	0.341972i	0.515136	+	0.857108i	$0.327741\pi$
$420$		0			0
$421$	15.6332			0.761918			0.380959	−	0.924592i	$-0.375594\pi$
$421$	15.6332			0.761918			0.380959	+	0.924592i	$0.375594\pi$
$422$	6.10819	+	6.10819i	0.297342	+	0.297342i
$423$			69.1662i			3.36298i
$424$	−11.9499			−0.580337
$425$		0			0
$426$	26.5831			1.28796
$427$		−	22.9499i		−	1.11062i
$428$	9.15831	+	9.15831i	0.442684	+	0.442684i
$429$	−4.31662			−0.208409
$430$		0			0
$431$	−18.4248	+	18.4248i	−0.887492	+	0.887492i	−0.994282	−	0.106790i	$-0.965943\pi$
$431$	−18.4248	+	18.4248i	−0.887492	+	0.887492i	0.106790	+	0.994282i	$0.465943\pi$
$432$	−7.15831	+	7.15831i	−0.344404	+	0.344404i
$433$			14.6332i			0.703229i	0.936145	+	0.351615i	$0.114367\pi$
$433$			14.6332i			0.703229i	−0.936145	+	0.351615i	$0.885633\pi$
$434$			13.6332i			0.654417i
$435$		0			0
$436$	2.00000	−	2.00000i	0.0957826	−	0.0957826i
$437$	−8.31662	−	8.31662i	−0.397838	−	0.397838i
$438$	37.2665			1.78066
$439$	−0.158312	−	0.158312i	−0.00755584	−	0.00755584i	0.703319	−	0.710875i	$-0.251701\pi$
$439$	−0.158312	−	0.158312i	−0.00755584	−	0.00755584i	−0.710875	+	0.703319i	$0.751701\pi$
$440$		0			0
$441$	14.6332			0.696821
$442$	4.00000	+	1.00000i	0.190261	+	0.0475651i
$443$	−3.05013			−0.144916			−0.0724579	−	0.997371i	$-0.523084\pi$
$443$	−3.05013			−0.144916			−0.0724579	+	0.997371i	$0.523084\pi$
$444$			27.2665i			1.29401i
$445$		0			0
$446$	5.58312			0.264369
$447$	4.42481	+	4.42481i	0.209286	+	0.209286i
$448$	−2.15831	+	2.15831i	−0.101971	+	0.101971i
$449$	−7.68338	+	7.68338i	−0.362601	+	0.362601i	−0.864770	−	0.502169i	$-0.832536\pi$
$449$	−7.68338	+	7.68338i	−0.362601	+	0.362601i	0.502169	+	0.864770i	$0.332536\pi$
$450$		0			0
$451$		−	10.6332i		−	0.500700i
$452$	13.2665	−	13.2665i	0.624004	−	0.624004i
$453$	−30.8997	+	30.8997i	−1.45180	+	1.45180i
$454$	2.15831	+	2.15831i	0.101295	+	0.101295i
$455$		0			0
$456$	17.9499	+	17.9499i	0.840580	+	0.840580i
$457$			27.3166i			1.27782i	0.769282	+	0.638909i	$0.220614\pi$
$457$			27.3166i			1.27782i	−0.769282	+	0.638909i	$0.779386\pi$
$458$	16.8997			0.789673
$459$	−21.4749	−	35.7916i	−1.00236	−	1.67061i
$460$		0			0
$461$			35.8997i			1.67202i	0.548716	+	0.836009i	$0.315117\pi$
$461$			35.8997i			1.67202i	−0.548716	+	0.836009i	$0.684883\pi$
$462$	9.31662	+	9.31662i	0.433449	+	0.433449i
$463$	25.3668			1.17889			0.589446	−	0.807807i	$-0.299346\pi$
$463$	25.3668			1.17889			0.589446	+	0.807807i	$0.299346\pi$
$464$	−2.31662	−	2.31662i	−0.107547	−	0.107547i
$465$		0			0
$466$	−2.94987	+	2.94987i	−0.136650	+	0.136650i
$467$		−	4.94987i		−	0.229053i	−0.993420	−	0.114526i	$-0.963465\pi$
$467$		−	4.94987i		−	0.229053i	0.993420	−	0.114526i	$-0.0365351\pi$
$468$			6.31662i			0.291986i
$469$	14.3166	−	14.3166i	0.661080	−	0.661080i
$470$		0			0
$471$	18.7414	+	18.7414i	0.863560	+	0.863560i
$472$	−4.63325			−0.213263
$473$	6.00000	+	6.00000i	0.275880	+	0.275880i
$474$			19.3166i			0.887242i
$475$		0			0
$476$	−6.47494	−	10.7916i	−0.296778	−	0.494630i
$477$	75.4829			3.45612
$478$			8.63325i			0.394876i
$479$	−17.3166	−	17.3166i	−0.791217	−	0.791217i	0.190475	−	0.981692i	$-0.438997\pi$
$479$	−17.3166	−	17.3166i	−0.791217	−	0.791217i	−0.981692	+	0.190475i	$0.938997\pi$
$480$		0			0
$481$	6.31662	+	6.31662i	0.288013	+	0.288013i
$482$	−6.68338	+	6.68338i	−0.304419	+	0.304419i
$483$	−9.31662	+	9.31662i	−0.423921	+	0.423921i
$484$		−	9.00000i		−	0.409091i
$485$		0			0
$486$	4.31662	−	4.31662i	0.195806	−	0.195806i
$487$	−26.5831	+	26.5831i	−1.20460	+	1.20460i	−0.231843	+	0.972753i	$0.574476\pi$
$487$	−26.5831	+	26.5831i	−1.20460	+	1.20460i	−0.972753	+	0.231843i	$0.925524\pi$
$488$	−5.31662	−	5.31662i	−0.240672	−	0.240672i
$489$	26.5831			1.20213
$490$		0			0
$491$		−	25.8997i		−	1.16884i	−0.811452	−	0.584420i	$-0.801322\pi$
$491$		−	25.8997i		−	1.16884i	0.811452	−	0.584420i	$-0.198678\pi$
$492$	−22.9499			−1.03466
$493$	11.5831	−	6.94987i	0.521678	−	0.313007i
$494$	8.31662			0.374183
$495$		0			0
$496$	3.15831	+	3.15831i	0.141812	+	0.141812i
$497$	−26.5831			−1.19242
$498$	27.2665	+	27.2665i	1.22184	+	1.22184i
$499$	−1.42481	+	1.42481i	−0.0637833	+	0.0637833i	−0.738279	−	0.674496i	$-0.764361\pi$
$499$	−1.42481	+	1.42481i	−0.0637833	+	0.0637833i	0.674496	+	0.738279i	$0.264361\pi$
$500$		0			0
$501$		−	30.2164i		−	1.34997i
$502$			19.2665i			0.859906i
$503$	−9.63325	+	9.63325i	−0.429525	+	0.429525i	−0.888467	−	0.458941i	$-0.848229\pi$
$503$	−9.63325	+	9.63325i	−0.429525	+	0.429525i	0.458941	+	0.888467i	$0.348229\pi$
$504$	13.6332	−	13.6332i	0.607273	−	0.607273i
$505$		0			0
$506$	−2.00000			−0.0889108
$507$	−25.8997	−	25.8997i	−1.15025	−	1.15025i
$508$			2.00000i			0.0887357i
$509$	−12.0501			−0.534112			−0.267056	−	0.963681i	$-0.586051\pi$
$509$	−12.0501			−0.534112			−0.267056	+	0.963681i	$0.586051\pi$
$510$		0			0
$511$	−37.2665			−1.64857
$512$			1.00000i			0.0441942i
$513$	−59.5330	−	59.5330i	−2.62845	−	2.62845i
$514$	2.68338			0.118359
$515$		0			0
$516$	12.9499	−	12.9499i	0.570086	−	0.570086i
$517$	10.9499	−	10.9499i	0.481575	−	0.481575i
$518$		−	27.2665i		−	1.19802i
$519$		−	46.1161i		−	2.02427i
$520$		0			0
$521$	6.68338	−	6.68338i	0.292804	−	0.292804i	−0.545383	−	0.838187i	$-0.683616\pi$
$521$	6.68338	−	6.68338i	0.292804	−	0.292804i	0.838187	+	0.545383i	$0.183616\pi$
$522$	14.6332	+	14.6332i	0.640480	+	0.640480i
$523$	22.6332			0.989683			0.494841	−	0.868983i	$-0.335226\pi$
$523$	22.6332			0.989683			0.494841	+	0.868983i	$0.335226\pi$
$524$	−1.79156	−	1.79156i	−0.0782647	−	0.0782647i
$525$		0			0
$526$	4.00000			0.174408
$527$	−15.7916	+	9.47494i	−0.687891	+	0.412735i
$528$	4.31662			0.187857
$529$			21.0000i			0.913043i
$530$		0			0
$531$	29.2665			1.27006
$532$	−17.9499	−	17.9499i	−0.778226	−	0.778226i
$533$	−5.31662	+	5.31662i	−0.230289	+	0.230289i
$534$	−40.2164	+	40.2164i	−1.74033	+	1.74033i
$535$		0			0
$536$		−	6.63325i		−	0.286513i
$537$	3.63325	−	3.63325i	0.156786	−	0.156786i
$538$	10.2665	−	10.2665i	0.442620	−	0.442620i
$539$	−2.31662	−	2.31662i	−0.0997841	−	0.0997841i
$540$		0			0
$541$	−1.26650	−	1.26650i	−0.0544511	−	0.0544511i	0.679357	−	0.733808i	$-0.262259\pi$
$541$	−1.26650	−	1.26650i	−0.0544511	−	0.0544511i	−0.733808	+	0.679357i	$0.762259\pi$
$542$			13.5831i			0.583445i
$543$	−76.1161			−3.26646
$544$	−4.00000	−	1.00000i	−0.171499	−	0.0428746i
$545$		0			0
$546$		−	9.31662i		−	0.398715i
$547$	2.20844	+	2.20844i	0.0944260	+	0.0944260i	0.752742	−	0.658316i	$-0.228731\pi$
$547$	2.20844	+	2.20844i	0.0944260	+	0.0944260i	−0.658316	+	0.752742i	$0.728731\pi$
$548$	−0.0501256			−0.00214126
$549$	33.5831	+	33.5831i	1.43329	+	1.43329i
$550$		0			0
$551$	19.2665	−	19.2665i	0.820780	−	0.820780i
$552$			4.31662i			0.183728i
$553$		−	19.3166i		−	0.821426i
$554$	−7.31662	+	7.31662i	−0.310854	+	0.310854i
$555$		0			0
$556$	−2.79156	−	2.79156i	−0.118389	−	0.118389i
$557$	−24.2665			−1.02820			−0.514102	−	0.857729i	$-0.671875\pi$
$557$	−24.2665			−1.02820			−0.514102	+	0.857729i	$0.671875\pi$
$558$	−19.9499	−	19.9499i	−0.844546	−	0.844546i
$559$		−	6.00000i		−	0.253773i
$560$		0			0
$561$	−4.31662	+	17.2665i	−0.182248	+	0.728992i
$562$	5.00000			0.210912
$563$			11.6834i			0.492396i	0.969220	+	0.246198i	$0.0791813\pi$
$563$			11.6834i			0.492396i	−0.969220	+	0.246198i	$0.920819\pi$
$564$	−23.6332	−	23.6332i	−0.995139	−	0.995139i
$565$		0			0
$566$	13.3166	+	13.3166i	0.559739	+	0.559739i
$567$	−25.7916	+	25.7916i	−1.08314	+	1.08314i
$568$	−6.15831	+	6.15831i	−0.258397	+	0.258397i
$569$		−	1.89975i		−	0.0796416i	−0.999207	−	0.0398208i	$-0.987321\pi$
$569$		−	1.89975i		−	0.0796416i	0.999207	−	0.0398208i	$-0.0126787\pi$
$570$		0			0
$571$	13.8417	−	13.8417i	0.579257	−	0.579257i	−0.355442	−	0.934698i	$-0.615670\pi$
$571$	13.8417	−	13.8417i	0.579257	−	0.579257i	0.934698	+	0.355442i	$0.115670\pi$
$572$	1.00000	−	1.00000i	0.0418121	−	0.0418121i
$573$	−23.6332	−	23.6332i	−0.987293	−	0.987293i
$574$	22.9499			0.957909
$575$		0			0
$576$		−	6.31662i		−	0.263193i
$577$	10.7335			0.446841			0.223421	−	0.974722i	$-0.428278\pi$
$577$	10.7335			0.446841			0.223421	+	0.974722i	$0.428278\pi$
$578$	8.00000	−	15.0000i	0.332756	−	0.623918i
$579$	−1.36675			−0.0568002
$580$		0			0
$581$	−27.2665	−	27.2665i	−1.13120	−	1.13120i
$582$	8.63325			0.357860
$583$	−11.9499	−	11.9499i	−0.494913	−	0.494913i
$584$	−8.63325	+	8.63325i	−0.357246	+	0.357246i
$585$		0			0
$586$			19.8997i			0.822051i
$587$			32.5330i			1.34278i	0.741104	+	0.671390i	$0.234303\pi$
$587$			32.5330i			1.34278i	−0.741104	+	0.671390i	$0.765697\pi$
$588$	−5.00000	+	5.00000i	−0.206197	+	0.206197i
$589$	−26.2665	+	26.2665i	−1.08229	+	1.08229i
$590$		0			0
$591$	−2.94987			−0.121342
$592$	−6.31662	−	6.31662i	−0.259612	−	0.259612i
$593$		−	17.6332i		−	0.724111i	−0.932157	−	0.362055i	$-0.882075\pi$
$593$		−	17.6332i		−	0.724111i	0.932157	−	0.362055i	$-0.117925\pi$
$594$	−14.3166			−0.587418
$595$		0			0
$596$	−2.05013			−0.0839764
$597$		−	7.05013i		−	0.288542i
$598$	1.00000	+	1.00000i	0.0408930	+	0.0408930i
$599$	−14.5330			−0.593802			−0.296901	−	0.954908i	$-0.595953\pi$
$599$	−14.5330			−0.593802			−0.296901	+	0.954908i	$0.595953\pi$
$600$		0			0
$601$	−8.31662	+	8.31662i	−0.339242	+	0.339242i	−0.856082	−	0.516840i	$-0.827108\pi$
$601$	−8.31662	+	8.31662i	−0.339242	+	0.339242i	0.516840	+	0.856082i	$0.327108\pi$
$602$	−12.9499	+	12.9499i	−0.527797	+	0.527797i
$603$			41.8997i			1.70629i
$604$		−	14.3166i		−	0.582535i
$605$		0			0
$606$	−12.1583	+	12.1583i	−0.493898	+	0.493898i
$607$	−9.15831	−	9.15831i	−0.371724	−	0.371724i	0.496381	−	0.868105i	$-0.334662\pi$
$607$	−9.15831	−	9.15831i	−0.371724	−	0.371724i	−0.868105	+	0.496381i	$0.834662\pi$
$608$	−8.31662			−0.337284
$609$	−21.5831	−	21.5831i	−0.874592	−	0.874592i
$610$		0			0
$611$	−10.9499			−0.442985
$612$	25.2665	+	6.31662i	1.02134	+	0.255334i
$613$	39.2164			1.58393			0.791967	−	0.610564i	$-0.209057\pi$
$613$	39.2164			1.58393			0.791967	+	0.610564i	$0.209057\pi$
$614$		−	26.5330i		−	1.07078i
$615$		0			0
$616$	−4.31662			−0.173922
$617$	−7.68338	−	7.68338i	−0.309321	−	0.309321i	0.535325	−	0.844646i	$-0.320189\pi$
$617$	−7.68338	−	7.68338i	−0.309321	−	0.309321i	−0.844646	+	0.535325i	$0.820189\pi$
$618$	37.9499	−	37.9499i	1.52657	−	1.52657i
$619$	28.8997	−	28.8997i	1.16158	−	1.16158i	0.177449	−	0.984130i	$-0.443216\pi$
$619$	28.8997	−	28.8997i	1.16158	−	1.16158i	0.984130	−	0.177449i	$-0.0567845\pi$
$620$		0			0
$621$		−	14.3166i		−	0.574506i
$622$	6.84169	−	6.84169i	0.274327	−	0.274327i
$623$	40.2164	−	40.2164i	1.61123	−	1.61123i
$624$	−2.15831	−	2.15831i	−0.0864016	−	0.0864016i
$625$		0			0
$626$	−13.9499	−	13.9499i	−0.557549	−	0.557549i
$627$			35.8997i			1.43370i
$628$	−8.68338			−0.346504
$629$	31.5831	−	18.9499i	1.25930	−	0.755581i
$630$		0			0
$631$			38.6332i			1.53797i	0.639270	+	0.768983i	$0.279237\pi$
$631$			38.6332i			1.53797i	−0.639270	+	0.768983i	$0.720763\pi$
$632$	−4.47494	−	4.47494i	−0.178003	−	0.178003i
$633$	26.3668			1.04798
$634$	−5.00000	−	5.00000i	−0.198575	−	0.198575i
$635$		0			0
$636$	−25.7916	+	25.7916i	−1.02270	+	1.02270i
$637$			2.31662i			0.0917880i
$638$		−	4.63325i		−	0.183432i
$639$	38.8997	−	38.8997i	1.53885	−	1.53885i
$640$		0			0
$641$	−24.2164	−	24.2164i	−0.956489	−	0.956489i	0.0426028	−	0.999092i	$-0.486435\pi$
$641$	−24.2164	−	24.2164i	−0.956489	−	0.956489i	−0.999092	+	0.0426028i	$0.986435\pi$
$642$	39.5330			1.56024
$643$	−28.7414	−	28.7414i	−1.13345	−	1.13345i	−0.989599	−	0.143852i	$-0.954051\pi$
$643$	−28.7414	−	28.7414i	−1.13345	−	1.13345i	−0.143852	−	0.989599i	$-0.545949\pi$
$644$		−	4.31662i		−	0.170099i
$645$		0			0
$646$	8.31662	−	33.2665i	0.327213	−	1.30885i
$647$	−7.89975			−0.310571			−0.155286	−	0.987870i	$-0.549630\pi$
$647$	−7.89975			−0.310571			−0.155286	+	0.987870i	$0.549630\pi$
$648$			11.9499i			0.469435i
$649$	−4.63325	−	4.63325i	−0.181871	−	0.181871i
$650$		0			0
$651$	29.4248	+	29.4248i	1.15325	+	1.15325i
$652$	−6.15831	+	6.15831i	−0.241178	+	0.241178i
$653$	−6.00000	+	6.00000i	−0.234798	+	0.234798i	−0.814692	−	0.579894i	$-0.803094\pi$
$653$	−6.00000	+	6.00000i	−0.234798	+	0.234798i	0.579894	+	0.814692i	$0.303094\pi$
$654$		−	8.63325i		−	0.337587i
$655$		0			0
$656$	5.31662	−	5.31662i	0.207579	−	0.207579i
$657$	54.5330	−	54.5330i	2.12753	−	2.12753i
$658$	23.6332	+	23.6332i	0.921320	+	0.921320i
$659$	12.9499			0.504455			0.252228	−	0.967668i	$-0.418837\pi$
$659$	12.9499			0.504455			0.252228	+	0.967668i	$0.418837\pi$
$660$		0			0
$661$			46.5831i			1.81187i	0.423413	+	0.905937i	$0.360832\pi$
$661$			46.5831i			1.81187i	−0.423413	+	0.905937i	$0.639168\pi$
$662$	−11.5831			−0.450191
$663$	10.7916	−	6.47494i	0.419110	−	0.251466i
$664$	−12.6332			−0.490265
$665$		0			0
$666$	39.8997	+	39.8997i	1.54608	+	1.54608i
$667$	4.63325			0.179400
$668$	7.00000	+	7.00000i	0.270838	+	0.270838i
$669$	12.0501	−	12.0501i	0.465885	−	0.465885i
$670$		0			0
$671$		−	10.6332i		−	0.410492i
$672$			9.31662i			0.359397i
$673$	−22.5831	+	22.5831i	−0.870515	+	0.870515i	−0.992528	−	0.122013i	$-0.961065\pi$
$673$	−22.5831	+	22.5831i	−0.870515	+	0.870515i	0.122013	+	0.992528i	$0.461065\pi$
$674$	−2.31662	+	2.31662i	−0.0892331	+	0.0892331i
$675$		0			0
$676$	12.0000			0.461538
$677$	28.2164	+	28.2164i	1.08444	+	1.08444i	0.996089	+	0.0883542i	$0.0281607\pi$
$677$	28.2164	+	28.2164i	1.08444	+	1.08444i	0.0883542	+	0.996089i	$0.471839\pi$
$678$		−	57.2665i		−	2.19931i
$679$	−8.63325			−0.331314
$680$		0			0
$681$	9.31662			0.357014
$682$			6.31662i			0.241876i
$683$	−9.89181	−	9.89181i	−0.378500	−	0.378500i	0.492061	−	0.870561i	$-0.336244\pi$
$683$	−9.89181	−	9.89181i	−0.378500	−	0.378500i	−0.870561	+	0.492061i	$0.836244\pi$
$684$	52.5330			2.00865
$685$		0			0
$686$	−10.1082	+	10.1082i	−0.385932	+	0.385932i
$687$	36.4749	−	36.4749i	1.39161	−	1.39161i
$688$			6.00000i			0.228748i
$689$			11.9499i			0.455254i
$690$		0			0
$691$	29.0581	−	29.0581i	1.10542	−	1.10542i	0.111676	−	0.993745i	$-0.464378\pi$
$691$	29.0581	−	29.0581i	1.10542	−	1.10542i	0.993745	−	0.111676i	$-0.0356219\pi$
$692$	10.6834	+	10.6834i	0.406121	+	0.406121i
$693$	27.2665			1.03577
$694$	15.7916	+	15.7916i	0.599439	+	0.599439i
$695$		0			0
$696$	−10.0000			−0.379049
$697$	15.9499	+	26.5831i	0.604145	+	1.00691i
$698$	−31.9499			−1.20932
$699$			12.7335i			0.481625i
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$	7.15831	+	7.15831i	0.270173	+	0.270173i
$703$	52.5330	−	52.5330i	1.98132	−	1.98132i
$704$	−1.00000	+	1.00000i	−0.0376889	+	0.0376889i
$705$		0			0
$706$		−	28.2665i		−	1.06382i
$707$	12.1583	−	12.1583i	0.457260	−	0.457260i
$708$	−10.0000	+	10.0000i	−0.375823	+	0.375823i
$709$	−11.6332	−	11.6332i	−0.436896	−	0.436896i	0.454070	−	0.890966i	$-0.349972\pi$
$709$	−11.6332	−	11.6332i	−0.436896	−	0.436896i	−0.890966	+	0.454070i	$0.849972\pi$
$710$		0			0
$711$	28.2665	+	28.2665i	1.06008	+	1.06008i
$712$		−	18.6332i		−	0.698311i
$713$	−6.31662			−0.236559
$714$	−37.2665	−	9.31662i	−1.39466	−	0.348666i
$715$		0			0
$716$			1.68338i			0.0629107i
$717$	18.6332	+	18.6332i	0.695871	+	0.695871i
$718$	−18.3166			−0.683570
$719$	29.1583	+	29.1583i	1.08742	+	1.08742i	0.995793	+	0.0916283i	$0.0292072\pi$
$719$	29.1583	+	29.1583i	1.08742	+	1.08742i	0.0916283	+	0.995793i	$0.470793\pi$
$720$		0			0
$721$	−37.9499	+	37.9499i	−1.41333	+	1.41333i
$722$		−	50.1662i		−	1.86699i
$723$			28.8496i			1.07293i
$724$	17.6332	−	17.6332i	0.655335	−	0.655335i
$725$		0			0
$726$	−19.4248	−	19.4248i	−0.720922	−	0.720922i
$727$	−44.9499			−1.66710			−0.833549	−	0.552445i	$-0.813695\pi$
$727$	−44.9499			−1.66710			−0.833549	+	0.552445i	$0.813695\pi$
$728$	2.15831	+	2.15831i	0.0799924	+	0.0799924i
$729$			17.2164i			0.637643i
$730$		0			0
$731$	−24.0000	−	6.00000i	−0.887672	−	0.221918i
$732$	−22.9499			−0.848252
$733$			31.2164i			1.15300i	0.817096	+	0.576502i	$0.195583\pi$
$733$			31.2164i			1.15300i	−0.817096	+	0.576502i	$0.804417\pi$
$734$	−22.8417	−	22.8417i	−0.843102	−	0.843102i
$735$		0			0
$736$	−1.00000	−	1.00000i	−0.0368605	−	0.0368605i
$737$	6.63325	−	6.63325i	0.244339	−	0.244339i
$738$	−33.5831	+	33.5831i	−1.23621	+	1.23621i
$739$		−	4.41688i		−	0.162477i	−0.996695	−	0.0812387i	$-0.974112\pi$
$739$		−	4.41688i		−	0.162477i	0.996695	−	0.0812387i	$-0.0258876\pi$
$740$		0			0
$741$	17.9499	−	17.9499i	0.659405	−	0.659405i
$742$	25.7916	−	25.7916i	0.946838	−	0.946838i
$743$	−8.74144	−	8.74144i	−0.320692	−	0.320692i	0.528340	−	0.849033i	$-0.322814\pi$
$743$	−8.74144	−	8.74144i	−0.320692	−	0.320692i	−0.849033	+	0.528340i	$0.822814\pi$
$744$	13.6332			0.499819
$745$		0			0
$746$			33.5330i			1.22773i
$747$	79.7995			2.91971
$748$	−3.00000	−	5.00000i	−0.109691	−	0.182818i
$749$	−39.5330			−1.44450
$750$		0			0
$751$	−24.8997	−	24.8997i	−0.908605	−	0.908605i	0.0875550	−	0.996160i	$-0.472095\pi$
$751$	−24.8997	−	24.8997i	−0.908605	−	0.908605i	−0.996160	+	0.0875550i	$0.972095\pi$
$752$	10.9499			0.399301
$753$	41.5831	+	41.5831i	1.51537	+	1.51537i
$754$	−2.31662	+	2.31662i	−0.0843665	+	0.0843665i
$755$		0			0
$756$		−	30.8997i		−	1.12381i
$757$		−	3.36675i		−	0.122367i	−0.998127	−	0.0611833i	$-0.980513\pi$
$757$		−	3.36675i		−	0.122367i	0.998127	−	0.0611833i	$-0.0194874\pi$
$758$	6.52506	−	6.52506i	0.237001	−	0.237001i
$759$	−4.31662	+	4.31662i	−0.156684	+	0.156684i
$760$		0			0
$761$	−1.41688			−0.0513617			−0.0256809	−	0.999670i	$-0.508175\pi$
$761$	−1.41688			−0.0513617			−0.0256809	+	0.999670i	$0.508175\pi$
$762$	4.31662	+	4.31662i	0.156375	+	0.156375i
$763$			8.63325i			0.312545i
$764$	10.9499			0.396153
$765$		0			0
$766$	16.9499			0.612424
$767$			4.63325i			0.167297i
$768$	2.15831	+	2.15831i	0.0778814	+	0.0778814i
$769$	16.5831			0.598003			0.299001	−	0.954253i	$-0.403346\pi$
$769$	16.5831			0.598003			0.299001	+	0.954253i	$0.403346\pi$
$770$		0			0
$771$	5.79156	−	5.79156i	0.208578	−	0.208578i
$772$	0.316625	−	0.316625i	0.0113956	−	0.0113956i
$773$		−	14.8997i		−	0.535907i	−0.963432	−	0.267953i	$-0.913653\pi$
$773$		−	14.8997i		−	0.535907i	0.963432	−	0.267953i	$-0.0863473\pi$
$774$		−	37.8997i		−	1.36228i
$775$		0			0
$776$	−2.00000	+	2.00000i	−0.0717958	+	0.0717958i
$777$	−58.8496	−	58.8496i	−2.11122	−	2.11122i
$778$	−1.26650			−0.0454062
$779$	44.2164	+	44.2164i	1.58422	+	1.58422i
$780$		0			0
$781$	−12.3166			−0.440723
$782$	5.00000	−	3.00000i	0.178800	−	0.107280i
$783$	33.1662			1.18527
$784$		−	2.31662i		−	0.0827366i
$785$		0			0
$786$	−7.73350			−0.275845
$787$	1.52506	+	1.52506i	0.0543626	+	0.0543626i	0.733765	−	0.679403i	$-0.237761\pi$
$787$	1.52506	+	1.52506i	0.0543626	+	0.0543626i	−0.679403	+	0.733765i	$0.737761\pi$
$788$	0.683375	−	0.683375i	0.0243442	−	0.0243442i
$789$	8.63325	−	8.63325i	0.307352	−	0.307352i
$790$		0			0
$791$			57.2665i			2.03616i
$792$	6.31662	−	6.31662i	0.224451	−	0.224451i
$793$	−5.31662	+	5.31662i	−0.188799	+	0.188799i
$794$	15.8997	+	15.8997i	0.564261	+	0.564261i
$795$		0			0
$796$	1.63325	+	1.63325i	0.0578890	+	0.0578890i
$797$		−	38.5831i		−	1.36668i	−0.730098	−	0.683342i	$-0.760526\pi$
$797$		−	38.5831i		−	1.36668i	0.730098	−	0.683342i	$-0.239474\pi$
$798$	−77.4829			−2.74286
$799$	−10.9499	+	43.7995i	−0.387379	+	1.54951i
$800$		0			0
$801$			117.699i			4.15870i
$802$	−10.5831	−	10.5831i	−0.373703	−	0.373703i
$803$	−17.2665			−0.609322
$804$	−14.3166	−	14.3166i	−0.504908	−	0.504908i
$805$		0			0
$806$	3.15831	−	3.15831i	0.111247	−	0.111247i
$807$		−	44.3166i		−	1.56002i
$808$		−	5.63325i		−	0.198177i
$809$	−8.58312	+	8.58312i	−0.301767	+	0.301767i	−0.841705	−	0.539938i	$-0.818448\pi$
$809$	−8.58312	+	8.58312i	−0.301767	+	0.301767i	0.539938	+	0.841705i	$0.318448\pi$
$810$		0			0
$811$	−29.1082	−	29.1082i	−1.02213	−	1.02213i	−0.999750	−	0.0223771i	$-0.992877\pi$
$811$	−29.1082	−	29.1082i	−1.02213	−	1.02213i	−0.0223771	−	0.999750i	$-0.507123\pi$
$812$	10.0000			0.350931
$813$	29.3166	+	29.3166i	1.02818	+	1.02818i
$814$		−	12.6332i		−	0.442795i
$815$		0			0
$816$	−10.7916	+	6.47494i	−0.377780	+	0.226668i
$817$	−49.8997			−1.74577
$818$			10.8997i			0.381101i
$819$	−13.6332	−	13.6332i	−0.476384	−	0.476384i
$820$		0			0
$821$	−20.3668	−	20.3668i	−0.710804	−	0.710804i	0.255899	−	0.966704i	$-0.417629\pi$
$821$	−20.3668	−	20.3668i	−0.710804	−	0.710804i	−0.966704	+	0.255899i	$0.917629\pi$
$822$	−0.108187	+	0.108187i	−0.00377345	+	0.00377345i
$823$	26.1583	−	26.1583i	0.911821	−	0.911821i	−0.0845940	−	0.996415i	$-0.526959\pi$
$823$	26.1583	−	26.1583i	0.911821	−	0.911821i	0.996415	+	0.0845940i	$0.0269593\pi$
$824$			17.5831i			0.612537i
$825$		0			0
$826$	10.0000	−	10.0000i	0.347945	−	0.347945i
$827$	6.36675	−	6.36675i	0.221394	−	0.221394i	−0.587691	−	0.809085i	$-0.699963\pi$
$827$	6.36675	−	6.36675i	0.221394	−	0.221394i	0.809085	+	0.587691i	$0.199963\pi$
$828$	6.31662	+	6.31662i	0.219518	+	0.219518i
$829$	−5.21637			−0.181172			−0.0905861	−	0.995889i	$-0.528874\pi$
$829$	−5.21637			−0.181172			−0.0905861	+	0.995889i	$0.528874\pi$
$830$		0			0
$831$			31.5831i			1.09561i
$832$	1.00000			0.0346688
$833$	9.26650	+	2.31662i	0.321065	+	0.0802663i
$834$	−12.0501			−0.417262
$835$		0			0
$836$	−8.31662	−	8.31662i	−0.287636	−	0.287636i
$837$	−45.2164			−1.56291
$838$	−7.00000	−	7.00000i	−0.241811	−	0.241811i
$839$	−6.42481	+	6.42481i	−0.221809	+	0.221809i	−0.809260	−	0.587451i	$-0.800132\pi$
$839$	−6.42481	+	6.42481i	−0.221809	+	0.221809i	0.587451	+	0.809260i	$0.300132\pi$
$840$		0			0
$841$		−	18.2665i		−	0.629879i
$842$			15.6332i			0.538757i
$843$	10.7916	−	10.7916i	0.371681	−	0.371681i
$844$	−6.10819	+	6.10819i	−0.210252	+	0.210252i
$845$		0			0
$846$	−69.1662			−2.37798
$847$	19.4248	+	19.4248i	0.667444	+	0.667444i
$848$		−	11.9499i		−	0.410360i
$849$	57.4829			1.97281
$850$		0			0
$851$	12.6332			0.433062
$852$			26.5831i			0.910723i
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	0.402034	−	0.915625i	$-0.368303\pi$
$853$	−15.0000	−	15.0000i	−0.513590	−	0.513590i	−0.915625	+	0.402034i	$0.868303\pi$
$854$	22.9499			0.785329
$855$		0			0
$856$	−9.15831	+	9.15831i	−0.313025	+	0.313025i
$857$	27.2665	−	27.2665i	0.931406	−	0.931406i	−0.0663880	−	0.997794i	$-0.521148\pi$
$857$	27.2665	−	27.2665i	0.931406	−	0.931406i	0.997794	+	0.0663880i	$0.0211475\pi$
$858$		−	4.31662i		−	0.147367i
$859$		−	11.6834i		−	0.398632i	−0.979935	−	0.199316i	$-0.936128\pi$
$859$		−	11.6834i		−	0.398632i	0.979935	−	0.199316i	$-0.0638720\pi$
$860$		0			0
$861$	49.5330	−	49.5330i	1.68808	−	1.68808i
$862$	−18.4248	−	18.4248i	−0.627552	−	0.627552i
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$	−7.15831	−	7.15831i	−0.243531	−	0.243531i
$865$		0			0
$866$	−14.6332			−0.497258
$867$	−15.1082	−	49.6412i	−0.513101	−	1.68590i
$868$	−13.6332			−0.462743
$869$		−	8.94987i		−	0.303604i
$870$		0			0
$871$	−6.63325			−0.224759
$872$	2.00000	+	2.00000i	0.0677285	+	0.0677285i
$873$	12.6332	−	12.6332i	0.427571	−	0.427571i
$874$	8.31662	−	8.31662i	0.281314	−	0.281314i
$875$		0			0
$876$			37.2665i			1.25912i
$877$	−2.94987	+	2.94987i	−0.0996102	+	0.0996102i	−0.755156	−	0.655545i	$-0.772439\pi$
$877$	−2.94987	+	2.94987i	−0.0996102	+	0.0996102i	0.655545	+	0.755156i	$0.272439\pi$
$878$	0.158312	−	0.158312i	0.00534278	−	0.00534278i
$879$	42.9499	+	42.9499i	1.44866	+	1.44866i
$880$		0			0
$881$	25.3166	+	25.3166i	0.852939	+	0.852939i	0.990494	−	0.137555i	$-0.0439245\pi$
$881$	25.3166	+	25.3166i	0.852939	+	0.852939i	−0.137555	+	0.990494i	$0.543924\pi$
$882$			14.6332i			0.492727i
$883$	−7.58312			−0.255192			−0.127596	−	0.991826i	$-0.540726\pi$
$883$	−7.58312			−0.255192			−0.127596	+	0.991826i	$0.540726\pi$
$884$	−1.00000	+	4.00000i	−0.0336336	+	0.134535i
$885$		0			0
$886$		−	3.05013i		−	0.102471i
$887$	−9.15831	−	9.15831i	−0.307506	−	0.307506i	0.536435	−	0.843941i	$-0.319771\pi$
$887$	−9.15831	−	9.15831i	−0.307506	−	0.307506i	−0.843941	+	0.536435i	$0.819771\pi$
$888$	−27.2665			−0.915004
$889$	−4.31662	−	4.31662i	−0.144775	−	0.144775i
$890$		0			0
$891$	−11.9499	+	11.9499i	−0.400336	+	0.400336i
$892$			5.58312i			0.186937i
$893$			91.0660i			3.04741i
$894$	−4.42481	+	4.42481i	−0.147988	+	0.147988i
$895$		0			0
$896$	−2.15831	−	2.15831i	−0.0721042	−	0.0721042i
$897$	4.31662			0.144128
$898$	−7.68338	−	7.68338i	−0.256398	−	0.256398i
$899$		−	14.6332i		−	0.488046i
$900$		0			0
$901$	47.7995	+	11.9499i	1.59243	+	0.398108i
$902$	10.6332			0.354048
$903$			55.8997i			1.86023i
$904$	13.2665	+	13.2665i	0.441237	+	0.441237i
$905$		0			0
$906$	−30.8997	−	30.8997i	−1.02658	−	1.02658i
$907$	−26.3668	+	26.3668i	−0.875494	+	0.875494i	−0.993064	−	0.117571i	$-0.962489\pi$
$907$	−26.3668	+	26.3668i	−0.875494	+	0.875494i	0.117571	+	0.993064i	$0.462489\pi$
$908$	−2.15831	+	2.15831i	−0.0716261	+	0.0716261i
$909$			35.5831i			1.18022i
$910$		0			0
$911$	8.15831	−	8.15831i	0.270297	−	0.270297i	−0.558923	−	0.829220i	$-0.688785\pi$
$911$	8.15831	−	8.15831i	0.270297	−	0.270297i	0.829220	+	0.558923i	$0.188785\pi$
$912$	−17.9499	+	17.9499i	−0.594380	+	0.594380i
$913$	−12.6332	−	12.6332i	−0.418100	−	0.418100i
$914$	−27.3166			−0.903554
$915$		0			0
$916$			16.8997i			0.558383i
$917$	7.73350			0.255383
$918$	35.7916	−	21.4749i	1.18130	−	0.708779i
$919$	−23.1662			−0.764184			−0.382092	−	0.924124i	$-0.624796\pi$
$919$	−23.1662			−0.764184			−0.382092	+	0.924124i	$0.624796\pi$
$920$		0			0
$921$	−57.2665	−	57.2665i	−1.88700	−	1.88700i
$922$	−35.8997			−1.18230
$923$	6.15831	+	6.15831i	0.202703	+	0.202703i
$924$	−9.31662	+	9.31662i	−0.306494	+	0.306494i
$925$		0			0
$926$			25.3668i			0.833603i
$927$		−	111.066i		−	3.64789i
$928$	2.31662	−	2.31662i	0.0760469	−	0.0760469i
$929$	−17.8997	+	17.8997i	−0.587272	+	0.587272i	−0.936892	−	0.349620i	$-0.886311\pi$
$929$	−17.8997	+	17.8997i	−0.587272	+	0.587272i	0.349620	+	0.936892i	$0.386311\pi$
$930$		0			0
$931$	19.2665			0.631434
$932$	−2.94987	−	2.94987i	−0.0966263	−	0.0966263i
$933$		−	29.5330i		−	0.966867i
$934$	4.94987			0.161965
$935$		0			0
$936$	−6.31662			−0.206465
$937$			16.1662i			0.528128i	0.964505	+	0.264064i	$0.0850631\pi$
$937$			16.1662i			0.528128i	−0.964505	+	0.264064i	$0.914937\pi$
$938$	14.3166	+	14.3166i	0.467454	+	0.467454i
$939$	−60.2164			−1.96509
$940$		0			0
$941$	−23.3166	+	23.3166i	−0.760100	+	0.760100i	−0.976340	−	0.216240i	$-0.930621\pi$
$941$	−23.3166	+	23.3166i	−0.760100	+	0.760100i	0.216240	+	0.976340i	$0.430621\pi$
$942$	−18.7414	+	18.7414i	−0.610629	+	0.610629i
$943$			10.6332i			0.346266i
$944$		−	4.63325i		−	0.150799i
$945$		0			0
$946$	−6.00000	+	6.00000i	−0.195077	+	0.195077i
$947$	−24.2665	−	24.2665i	−0.788555	−	0.788555i	0.192702	−	0.981257i	$-0.438275\pi$
$947$	−24.2665	−	24.2665i	−0.788555	−	0.788555i	−0.981257	+	0.192702i	$0.938275\pi$
$948$	−19.3166			−0.627375
$949$	8.63325	+	8.63325i	0.280247	+	0.280247i
$950$		0			0
$951$	−21.5831			−0.699881
$952$	10.7916	−	6.47494i	0.349757	−	0.209854i
$953$	39.2164			1.27034			0.635171	−	0.772371i	$-0.280929\pi$
$953$	39.2164			1.27034			0.635171	+	0.772371i	$0.280929\pi$
$954$			75.4829i			2.44385i
$955$		0			0
$956$	−8.63325			−0.279219
$957$	−10.0000	−	10.0000i	−0.323254	−	0.323254i
$958$	17.3166	−	17.3166i	0.559475	−	0.559475i
$959$	0.108187	−	0.108187i	0.00349353	−	0.00349353i
$960$		0			0
$961$		−	11.0501i		−	0.356456i
$962$	−6.31662	+	6.31662i	−0.203656	+	0.203656i
$963$	57.8496	−	57.8496i	1.86418	−	1.86418i
$964$	−6.68338	−	6.68338i	−0.215257	−	0.215257i
$965$		0			0
$966$	−9.31662	−	9.31662i	−0.299757	−	0.299757i
$967$			36.6332i			1.17805i	0.808116	+	0.589023i	$0.200487\pi$
$967$			36.6332i			1.17805i	−0.808116	+	0.589023i	$0.799513\pi$
$968$	9.00000			0.289271
$969$	−53.8496	−	89.7494i	−1.72990	−	2.88317i
$970$		0			0
$971$		−	27.2665i		−	0.875024i	−0.899213	−	0.437512i	$-0.855860\pi$
$971$		−	27.2665i		−	0.875024i	0.899213	−	0.437512i	$-0.144140\pi$
$972$	4.31662	+	4.31662i	0.138456	+	0.138456i
$973$	12.0501			0.386309
$974$	−26.5831	−	26.5831i	−0.851778	−	0.851778i
$975$		0			0
$976$	5.31662	−	5.31662i	0.170181	−	0.170181i
$977$			28.8997i			0.924585i	0.886728	+	0.462292i	$0.152973\pi$
$977$			28.8997i			0.924585i	−0.886728	+	0.462292i	$0.847027\pi$
$978$			26.5831i			0.850035i
$979$	18.6332	−	18.6332i	0.595521	−	0.595521i
$980$		0			0
$981$	−12.6332	−	12.6332i	−0.403349	−	0.403349i
$982$	25.8997			0.826494
$983$	27.8417	+	27.8417i	0.888012	+	0.888012i	0.994332	−	0.106320i	$-0.0339068\pi$
$983$	27.8417	+	27.8417i	0.888012	+	0.888012i	−0.106320	+	0.994332i	$0.533907\pi$
$984$		−	22.9499i		−	0.731615i
$985$		0			0
$986$	6.94987	+	11.5831i	0.221329	+	0.368882i
$987$	102.016			3.24720
$988$			8.31662i			0.264587i
$989$	−6.00000	−	6.00000i	−0.190789	−	0.190789i
$990$		0			0
$991$	1.57519	+	1.57519i	0.0500375	+	0.0500375i	0.731683	−	0.681645i	$-0.238735\pi$
$991$	1.57519	+	1.57519i	0.0500375	+	0.0500375i	−0.681645	+	0.731683i	$0.738735\pi$
$992$	−3.15831	+	3.15831i	−0.100277	+	0.100277i
$993$	−25.0000	+	25.0000i	−0.793351	+	0.793351i
$994$		−	26.5831i		−	0.843165i
$995$		0			0
$996$	−27.2665	+	27.2665i	−0.863972	+	0.863972i
$997$	11.5831	−	11.5831i	0.366841	−	0.366841i	−0.499483	−	0.866324i	$-0.666477\pi$
$997$	11.5831	−	11.5831i	0.366841	−	0.366841i	0.866324	+	0.499483i	$0.166477\pi$
$998$	−1.42481	−	1.42481i	−0.0451016	−	0.0451016i
$999$	90.4327			2.86117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.j.251.2	yes	4
5.2	odd	4		850.2.g.f.149.2		4
5.3	odd	4		850.2.g.g.149.1		4
5.4	even	2		850.2.h.i.251.1	✓	4
17.4	even	4	inner	850.2.h.j.701.2	yes	4
85.4	even	4		850.2.h.i.701.1	yes	4
85.38	odd	4		850.2.g.f.599.2		4
85.72	odd	4		850.2.g.g.599.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.g.f.149.2		4	5.2	odd	4
850.2.g.f.599.2		4	85.38	odd	4
850.2.g.g.149.1		4	5.3	odd	4
850.2.g.g.599.1		4	85.72	odd	4
850.2.h.i.251.1	✓	4	5.4	even	2
850.2.h.i.701.1	yes	4	85.4	even	4
850.2.h.j.251.2	yes	4	1.1	even	1	trivial
850.2.h.j.701.2	yes	4	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(2.15831 + 2.15831i) q^{3} -1.00000 q^{4} +(-2.15831 + 2.15831i) q^{6} +(2.15831 - 2.15831i) q^{7} -1.00000i q^{8} +6.31662i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(2.15831 + 2.15831i) q^{3} -1.00000 q^{4} +(-2.15831 + 2.15831i) q^{6} +(2.15831 - 2.15831i) q^{7} -1.00000i q^{8} +6.31662i q^{9} +(1.00000 - 1.00000i) q^{11} +(-2.15831 - 2.15831i) q^{12} -1.00000 q^{13} +(2.15831 + 2.15831i) q^{14} +1.00000 q^{16} +(-1.00000 + 4.00000i) q^{17} -6.31662 q^{18} +8.31662i q^{19} +9.31662 q^{21} +(1.00000 + 1.00000i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(2.15831 - 2.15831i) q^{24} -1.00000i q^{26} +(-7.15831 + 7.15831i) q^{27} +(-2.15831 + 2.15831i) q^{28} +(-2.31662 - 2.31662i) q^{29} +(3.15831 + 3.15831i) q^{31} +1.00000i q^{32} +4.31662 q^{33} +(-4.00000 - 1.00000i) q^{34} -6.31662i q^{36} +(-6.31662 - 6.31662i) q^{37} -8.31662 q^{38} +(-2.15831 - 2.15831i) q^{39} +(5.31662 - 5.31662i) q^{41} +9.31662i q^{42} +6.00000i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} +10.9499 q^{47} +(2.15831 + 2.15831i) q^{48} -2.31662i q^{49} +(-10.7916 + 6.47494i) q^{51} +1.00000 q^{52} -11.9499i q^{53} +(-7.15831 - 7.15831i) q^{54} +(-2.15831 - 2.15831i) q^{56} +(-17.9499 + 17.9499i) q^{57} +(2.31662 - 2.31662i) q^{58} -4.63325i q^{59} +(5.31662 - 5.31662i) q^{61} +(-3.15831 + 3.15831i) q^{62} +(13.6332 + 13.6332i) q^{63} -1.00000 q^{64} +4.31662i q^{66} +6.63325 q^{67} +(1.00000 - 4.00000i) q^{68} -4.31662 q^{69} +(-6.15831 - 6.15831i) q^{71} +6.31662 q^{72} +(-8.63325 - 8.63325i) q^{73} +(6.31662 - 6.31662i) q^{74} -8.31662i q^{76} -4.31662i q^{77} +(2.15831 - 2.15831i) q^{78} +(4.47494 - 4.47494i) q^{79} -11.9499 q^{81} +(5.31662 + 5.31662i) q^{82} -12.6332i q^{83} -9.31662 q^{84} -6.00000 q^{86} -10.0000i q^{87} +(-1.00000 - 1.00000i) q^{88} +18.6332 q^{89} +(-2.15831 + 2.15831i) q^{91} +(1.00000 - 1.00000i) q^{92} +13.6332i q^{93} +10.9499i q^{94} +(-2.15831 + 2.15831i) q^{96} +(-2.00000 - 2.00000i) q^{97} +2.31662 q^{98} +(6.31662 + 6.31662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^4 - 2 * q^6 + 2 * q^7	\( 4 q + 2 q^{3} - 4 q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{17} - 12 q^{18} + 24 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 22 q^{27} - 2 q^{28} + 4 q^{29} + 6 q^{31} + 4 q^{33} - 16 q^{34} - 12 q^{37} - 20 q^{38} - 2 q^{39} + 8 q^{41} - 4 q^{44} - 4 q^{46} + 4 q^{47} + 2 q^{48} - 10 q^{51} + 4 q^{52} - 22 q^{54} - 2 q^{56} - 32 q^{57} - 4 q^{58} + 8 q^{61} - 6 q^{62} + 28 q^{63} - 4 q^{64} + 4 q^{68} - 4 q^{69} - 18 q^{71} + 12 q^{72} - 8 q^{73} + 12 q^{74} + 2 q^{78} - 2 q^{79} - 8 q^{81} + 8 q^{82} - 24 q^{84} - 24 q^{86} - 4 q^{88} + 48 q^{89} - 2 q^{91} + 4 q^{92} - 2 q^{96} - 8 q^{97} - 4 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^4 - 2 * q^6 + 2 * q^7 + 4 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^17 - 12 * q^18 + 24 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 22 * q^27 - 2 * q^28 + 4 * q^29 + 6 * q^31 + 4 * q^33 - 16 * q^34 - 12 * q^37 - 20 * q^38 - 2 * q^39 + 8 * q^41 - 4 * q^44 - 4 * q^46 + 4 * q^47 + 2 * q^48 - 10 * q^51 + 4 * q^52 - 22 * q^54 - 2 * q^56 - 32 * q^57 - 4 * q^58 + 8 * q^61 - 6 * q^62 + 28 * q^63 - 4 * q^64 + 4 * q^68 - 4 * q^69 - 18 * q^71 + 12 * q^72 - 8 * q^73 + 12 * q^74 + 2 * q^78 - 2 * q^79 - 8 * q^81 + 8 * q^82 - 24 * q^84 - 24 * q^86 - 4 * q^88 + 48 * q^89 - 2 * q^91 + 4 * q^92 - 2 * q^96 - 8 * q^97 - 4 * q^98 + 12 * q^99

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