LMFDB - Embedded newform 850.2.h.i.251.1

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			251.1
Root			$-1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.i.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-2.15831 - 2.15831i) q^{3} -1.00000 q^{4} +(-2.15831 + 2.15831i) q^{6} +(-2.15831 + 2.15831i) q^{7} +1.00000i q^{8} +6.31662i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-2.15831 - 2.15831i) q^{3} -1.00000 q^{4} +(-2.15831 + 2.15831i) q^{6} +(-2.15831 + 2.15831i) q^{7} +1.00000i q^{8} +6.31662i q^{9} +(1.00000 - 1.00000i) q^{11} +(2.15831 + 2.15831i) q^{12} +1.00000 q^{13} +(2.15831 + 2.15831i) q^{14} +1.00000 q^{16} +(1.00000 - 4.00000i) q^{17} +6.31662 q^{18} +8.31662i q^{19} +9.31662 q^{21} +(-1.00000 - 1.00000i) q^{22} +(1.00000 - 1.00000i) q^{23} +(2.15831 - 2.15831i) q^{24} -1.00000i q^{26} +(7.15831 - 7.15831i) q^{27} +(2.15831 - 2.15831i) q^{28} +(-2.31662 - 2.31662i) q^{29} +(3.15831 + 3.15831i) q^{31} -1.00000i q^{32} -4.31662 q^{33} +(-4.00000 - 1.00000i) q^{34} -6.31662i q^{36} +(6.31662 + 6.31662i) q^{37} +8.31662 q^{38} +(-2.15831 - 2.15831i) q^{39} +(5.31662 - 5.31662i) q^{41} -9.31662i q^{42} -6.00000i q^{43} +(-1.00000 + 1.00000i) q^{44} +(-1.00000 - 1.00000i) q^{46} -10.9499 q^{47} +(-2.15831 - 2.15831i) q^{48} -2.31662i q^{49} +(-10.7916 + 6.47494i) q^{51} -1.00000 q^{52} +11.9499i q^{53} +(-7.15831 - 7.15831i) q^{54} +(-2.15831 - 2.15831i) q^{56} +(17.9499 - 17.9499i) q^{57} +(-2.31662 + 2.31662i) q^{58} -4.63325i q^{59} +(5.31662 - 5.31662i) q^{61} +(3.15831 - 3.15831i) q^{62} +(-13.6332 - 13.6332i) q^{63} -1.00000 q^{64} +4.31662i q^{66} -6.63325 q^{67} +(-1.00000 + 4.00000i) q^{68} -4.31662 q^{69} +(-6.15831 - 6.15831i) q^{71} -6.31662 q^{72} +(8.63325 + 8.63325i) q^{73} +(6.31662 - 6.31662i) q^{74} -8.31662i q^{76} +4.31662i q^{77} +(-2.15831 + 2.15831i) q^{78} +(4.47494 - 4.47494i) q^{79} -11.9499 q^{81} +(-5.31662 - 5.31662i) q^{82} +12.6332i q^{83} -9.31662 q^{84} -6.00000 q^{86} +10.0000i q^{87} +(1.00000 + 1.00000i) q^{88} +18.6332 q^{89} +(-2.15831 + 2.15831i) q^{91} +(-1.00000 + 1.00000i) q^{92} -13.6332i q^{93} +10.9499i q^{94} +(-2.15831 + 2.15831i) q^{96} +(2.00000 + 2.00000i) q^{97} -2.31662 q^{98} +(6.31662 + 6.31662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.906785\pi$
$3$	−2.15831	−	2.15831i	−1.24610	−	1.24610i	−0.288675	−	0.957427i	$-0.593215\pi$
$4$	−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	−0.985491	−	0.169726i	$-0.945712\pi$
$7$	−2.15831	+	2.15831i	−0.815765	+	0.815765i	0.169726	+	0.985491i	$0.445712\pi$
$8$			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	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	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	−0.595121	−	0.803636i	$-0.702896\pi$
$23$	1.00000	−	1.00000i	0.208514	−	0.208514i	0.803636	+	0.595121i	$0.202896\pi$
$24$	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	$0.0124860\pi$
$37$	6.31662	+	6.31662i	1.03845	+	1.03845i	0.0392160	+	0.999231i	$0.487514\pi$
$38$	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	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$	−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	$-0.794427\pi$
$47$	−10.9499			−1.59720			−0.798602	+	0.601860i	$0.794427\pi$
$48$	−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	$0.306428\pi$
$53$			11.9499i			1.64144i	−0.571330	+	0.820721i	$0.693572\pi$
$54$	−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	$-0.632795\pi$
$67$	−6.63325			−0.810380			−0.405190	+	0.914232i	$0.632795\pi$
$68$	−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	$0.00334250\pi$
$73$	8.63325	+	8.63325i	1.01045	+	1.01045i	0.0105006	+	0.999945i	$0.496658\pi$
$74$	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	$0.243861\pi$
$83$			12.6332i			1.38668i	−0.720611	+	0.693340i	$0.756139\pi$
$84$	−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	0.801314	−	0.598244i	$-0.204135\pi$
$97$	2.00000	+	2.00000i	0.203069	+	0.203069i	−0.598244	+	0.801314i	$0.704135\pi$
$98$	−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	$-0.166518\pi$
$103$	17.5831			1.73252			0.866258	+	0.499596i	$0.166518\pi$
$104$			1.00000i			0.0980581i
$105$		0			0
$106$	11.9499			1.16067
$107$	9.15831	+	9.15831i	0.885367	+	0.885367i	0.994074	−	0.108706i	$-0.0346708\pi$
$107$	9.15831	+	9.15831i	0.885367	+	0.885367i	−0.108706	+	0.994074i	$0.534671\pi$
$108$	−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	$-0.405876\pi$
$113$	13.2665	−	13.2665i	1.24801	−	1.24801i	0.956599	−	0.291409i	$-0.0941239\pi$
$114$	−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	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$			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	$-0.500682\pi$
$137$	−0.0501256			−0.00428252			−0.00214126	+	0.999998i	$0.500682\pi$
$138$			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	$-0.612631\pi$
$157$	−8.68338			−0.693009			−0.346504	+	0.938048i	$0.612631\pi$
$158$	−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	−0.905883	−	0.423527i	$-0.860792\pi$
$163$	−6.15831	+	6.15831i	−0.482356	+	0.482356i	0.423527	+	0.905883i	$0.360792\pi$
$164$	−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	0.924020	−	0.382344i	$-0.124883\pi$
$167$	7.00000	+	7.00000i	0.541676	+	0.541676i	−0.382344	+	0.924020i	$0.624883\pi$
$168$			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	0.984970	−	0.172728i	$-0.0552580\pi$
$173$	10.6834	+	10.6834i	0.812242	+	0.812242i	−0.172728	+	0.984970i	$0.555258\pi$
$174$	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	−0.695619	−	0.718411i	$-0.744870\pi$
$193$	0.316625	−	0.316625i	0.0227912	−	0.0227912i	0.718411	+	0.695619i	$0.244870\pi$
$194$	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	−0.682343	−	0.731032i	$-0.739039\pi$
$197$	0.683375	−	0.683375i	0.0486885	−	0.0486885i	0.731032	+	0.682343i	$0.239039\pi$
$198$	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	$0.0598560\pi$
$223$			5.58312i			0.373874i	−0.982372	+	0.186937i	$0.940144\pi$
$224$	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	−0.775096	−	0.631844i	$-0.782298\pi$
$227$	−2.15831	+	2.15831i	−0.143252	+	0.143252i	0.631844	+	0.775096i	$0.282298\pi$
$228$	−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	0.603847	−	0.797100i	$-0.293634\pi$
$233$	−2.94987	−	2.94987i	−0.193253	−	0.193253i	−0.797100	+	0.603847i	$0.793634\pi$
$234$	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	$0.0266712\pi$
$257$			2.68338i			0.167384i	−0.996492	+	0.0836922i	$0.973329\pi$
$258$	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	$0.0393559\pi$
$263$			4.00000i			0.246651i	−0.992366	+	0.123325i	$0.960644\pi$
$264$		−	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	0.452268	−	0.891882i	$-0.350615\pi$
$277$	−7.31662	−	7.31662i	−0.439613	−	0.439613i	−0.891882	+	0.452268i	$0.850615\pi$
$278$	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	−0.981753	−	0.190162i	$-0.939099\pi$
$283$	−13.3166	+	13.3166i	−0.791591	+	0.791591i	0.190162	+	0.981753i	$0.439099\pi$
$284$	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	$-0.697447\pi$
$293$	−19.8997			−1.16256			−0.581278	+	0.813705i	$0.697447\pi$
$294$	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	$-0.226587\pi$
$307$	26.5330			1.51432			0.757159	+	0.653231i	$0.226587\pi$
$308$		−	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	−0.192754	−	0.981247i	$-0.561742\pi$
$313$	13.9499	−	13.9499i	0.788494	−	0.788494i	0.981247	+	0.192754i	$0.0617418\pi$
$314$			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	−0.552611	−	0.833439i	$-0.686369\pi$
$317$	5.00000	−	5.00000i	0.280828	−	0.280828i	0.833439	+	0.552611i	$0.186369\pi$
$318$	−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	0.641189	−	0.767383i	$-0.278442\pi$
$337$	−2.31662	−	2.31662i	−0.126195	−	0.126195i	−0.767383	+	0.641189i	$0.778442\pi$
$338$			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	−0.989850	−	0.142115i	$-0.954610\pi$
$347$	−15.7916	+	15.7916i	−0.847735	+	0.847735i	0.142115	+	0.989850i	$0.454610\pi$
$348$		−	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	$-0.228975\pi$
$353$	28.2665			1.50447			0.752237	+	0.658893i	$0.228975\pi$
$354$	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	$-0.430727\pi$
$367$	22.8417	−	22.8417i	1.19233	−	1.19233i	0.976412	−	0.215914i	$-0.0692731\pi$
$368$	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	$-0.834682\pi$
$373$	−33.5330			−1.73627			−0.868136	+	0.496326i	$0.834682\pi$
$374$	−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	$0.142562\pi$
$383$			16.9499i			0.866098i	−0.901370	+	0.433049i	$0.857438\pi$
$384$	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	−0.982778	−	0.184792i	$-0.940839\pi$
$397$	−15.8997	+	15.8997i	−0.797986	+	0.797986i	0.184792	+	0.982778i	$0.440839\pi$
$398$	−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	$-0.885633\pi$
$433$		−	14.6332i		−	0.703229i	0.936145	−	0.351615i	$-0.114367\pi$
$434$			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	$-0.476916\pi$
$443$	3.05013			0.144916			0.0724579	+	0.997371i	$0.476916\pi$
$444$			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	$-0.779386\pi$
$457$		−	27.3166i		−	1.27782i	0.769282	−	0.638909i	$-0.220614\pi$
$458$	−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	$-0.700654\pi$
$463$	−25.3668			−1.17889			−0.589446	+	0.807807i	$0.700654\pi$
$464$	−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	$0.0365351\pi$
$467$			4.94987i			0.229053i	−0.993420	+	0.114526i	$0.963465\pi$
$468$		−	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	$-0.425524\pi$
$487$	26.5831	−	26.5831i	1.20460	−	1.20460i	0.972753	−	0.231843i	$-0.0744756\pi$
$488$	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	−0.458941	−	0.888467i	$-0.651771\pi$
$503$	9.63325	−	9.63325i	0.429525	−	0.429525i	0.888467	+	0.458941i	$0.151771\pi$
$504$	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	$-0.664774\pi$
$523$	−22.6332			−0.989683			−0.494841	+	0.868983i	$0.664774\pi$
$524$	−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	0.658316	−	0.752742i	$-0.271269\pi$
$547$	−2.20844	−	2.20844i	−0.0944260	−	0.0944260i	−0.752742	+	0.658316i	$0.771269\pi$
$548$	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	$-0.328125\pi$
$557$	24.2665			1.02820			0.514102	+	0.857729i	$0.328125\pi$
$558$	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	$-0.920819\pi$
$563$		−	11.6834i		−	0.492396i	0.969220	−	0.246198i	$-0.0791813\pi$
$564$	−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	$-0.571722\pi$
$577$	−10.7335			−0.446841			−0.223421	+	0.974722i	$0.571722\pi$
$578$	−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	$-0.765697\pi$
$587$		−	32.5330i		−	1.34278i	0.741104	−	0.671390i	$-0.234303\pi$
$588$	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	$0.117925\pi$
$593$			17.6332i			0.724111i	−0.932157	+	0.362055i	$0.882075\pi$
$594$	−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	0.868105	−	0.496381i	$-0.165338\pi$
$607$	9.15831	+	9.15831i	0.371724	+	0.371724i	−0.496381	+	0.868105i	$0.665338\pi$
$608$	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	$-0.790943\pi$
$613$	−39.2164			−1.58393			−0.791967	+	0.610564i	$0.790943\pi$
$614$		−	26.5330i		−	1.07078i
$615$		0			0
$616$	−4.31662			−0.173922
$617$	7.68338	+	7.68338i	0.309321	+	0.309321i	0.844646	−	0.535325i	$-0.179811\pi$
$617$	7.68338	+	7.68338i	0.309321	+	0.309321i	−0.535325	+	0.844646i	$0.679811\pi$
$618$	−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	$0.0459491\pi$
$643$	28.7414	+	28.7414i	1.13345	+	1.13345i	0.143852	+	0.989599i	$0.454051\pi$
$644$		−	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	$-0.450370\pi$
$647$	7.89975			0.310571			0.155286	+	0.987870i	$0.450370\pi$
$648$		−	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	−0.579894	−	0.814692i	$-0.696906\pi$
$653$	6.00000	−	6.00000i	0.234798	−	0.234798i	0.814692	+	0.579894i	$0.196906\pi$
$654$		−	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	−0.122013	−	0.992528i	$-0.538935\pi$
$673$	22.5831	−	22.5831i	0.870515	−	0.870515i	0.992528	+	0.122013i	$0.0389350\pi$
$674$	−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	$-0.971839\pi$
$677$	−28.2164	−	28.2164i	−1.08444	−	1.08444i	−0.0883542	−	0.996089i	$-0.528161\pi$
$678$			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	0.870561	−	0.492061i	$-0.163756\pi$
$683$	9.89181	+	9.89181i	0.378500	+	0.378500i	−0.492061	+	0.870561i	$0.663756\pi$
$684$	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	$-0.186305\pi$
$727$	44.9499			1.66710			0.833549	+	0.552445i	$0.186305\pi$
$728$	−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	$-0.804417\pi$
$733$		−	31.2164i		−	1.15300i	0.817096	−	0.576502i	$-0.195583\pi$
$734$	−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	0.849033	−	0.528340i	$-0.177186\pi$
$743$	8.74144	+	8.74144i	0.320692	+	0.320692i	−0.528340	+	0.849033i	$0.677186\pi$
$744$	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	$0.0194874\pi$
$757$			3.36675i			0.122367i	−0.998127	+	0.0611833i	$0.980513\pi$
$758$	−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	$0.0863473\pi$
$773$			14.8997i			0.535907i	−0.963432	+	0.267953i	$0.913653\pi$
$774$		−	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	0.679403	−	0.733765i	$-0.262239\pi$
$787$	−1.52506	−	1.52506i	−0.0543626	−	0.0543626i	−0.733765	+	0.679403i	$0.762239\pi$
$788$	−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	$0.239474\pi$
$797$			38.5831i			1.36668i	−0.730098	+	0.683342i	$0.760526\pi$
$798$	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	−0.996415	−	0.0845940i	$-0.973041\pi$
$823$	−26.1583	+	26.1583i	−0.911821	+	0.911821i	0.0845940	+	0.996415i	$0.473041\pi$
$824$			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	−0.809085	−	0.587691i	$-0.800037\pi$
$827$	−6.36675	+	6.36675i	−0.221394	+	0.221394i	0.587691	+	0.809085i	$0.300037\pi$
$828$	−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	0.915625	−	0.402034i	$-0.131697\pi$
$853$	15.0000	+	15.0000i	0.513590	+	0.513590i	−0.402034	+	0.915625i	$0.631697\pi$
$854$	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	−0.997794	−	0.0663880i	$-0.978852\pi$
$857$	−27.2665	+	27.2665i	−0.931406	+	0.931406i	0.0663880	+	0.997794i	$0.478852\pi$
$858$			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	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$	−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	−0.655545	−	0.755156i	$-0.727561\pi$
$877$	2.94987	−	2.94987i	0.0996102	−	0.0996102i	0.755156	+	0.655545i	$0.227561\pi$
$878$	−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	$-0.459274\pi$
$883$	7.58312			0.255192			0.127596	+	0.991826i	$0.459274\pi$
$884$	−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	0.843941	−	0.536435i	$-0.180229\pi$
$887$	9.15831	+	9.15831i	0.307506	+	0.307506i	−0.536435	+	0.843941i	$0.680229\pi$
$888$	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	−0.117571	−	0.993064i	$-0.537511\pi$
$907$	26.3668	−	26.3668i	0.875494	−	0.875494i	0.993064	+	0.117571i	$0.0375107\pi$
$908$	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	$-0.914937\pi$
$937$		−	16.1662i		−	0.528128i	0.964505	−	0.264064i	$-0.0850631\pi$
$938$	−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	0.981257	−	0.192702i	$-0.0617251\pi$
$947$	24.2665	+	24.2665i	0.788555	+	0.788555i	−0.192702	+	0.981257i	$0.561725\pi$
$948$	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	$-0.719071\pi$
$953$	−39.2164			−1.27034			−0.635171	+	0.772371i	$0.719071\pi$
$954$			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	$-0.799513\pi$
$967$		−	36.6332i		−	1.17805i	0.808116	−	0.589023i	$-0.200487\pi$
$968$	−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	$-0.847027\pi$
$977$		−	28.8997i		−	0.924585i	0.886728	−	0.462292i	$-0.152973\pi$
$978$		−	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	0.106320	−	0.994332i	$-0.466093\pi$
$983$	−27.8417	−	27.8417i	−0.888012	−	0.888012i	−0.994332	+	0.106320i	$0.966093\pi$
$984$		−	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	−0.866324	−	0.499483i	$-0.833523\pi$
$997$	−11.5831	+	11.5831i	−0.366841	+	0.366841i	0.499483	+	0.866324i	$0.333523\pi$
$998$	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.i.251.1	✓	4
5.2	odd	4		850.2.g.g.149.1		4
5.3	odd	4		850.2.g.f.149.2		4
5.4	even	2		850.2.h.j.251.2	yes	4
17.4	even	4	inner	850.2.h.i.701.1	yes	4
85.4	even	4		850.2.h.j.701.2	yes	4
85.38	odd	4		850.2.g.g.599.1		4
85.72	odd	4		850.2.g.f.599.2		4

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

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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