LMFDB - Embedded newform 850.2.h.n.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("850.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.23045668864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 237x^{4} + 892x^{2} + 1156 $ x^8 + 26x^6 + 237x^4 + 892*x^2 + 1156
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.4
Root			$-2.26843i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.n.701.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(2.31113 + 2.31113i) q^{3} -1.00000 q^{4} +(2.31113 - 2.31113i) q^{6} +(3.26843 - 3.26843i) q^{7} +1.00000i q^{8} +7.68265i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(2.31113 + 2.31113i) q^{3} -1.00000 q^{4} +(2.31113 - 2.31113i) q^{6} +(3.26843 - 3.26843i) q^{7} +1.00000i q^{8} +7.68265i q^{9} +(-1.82843 + 1.82843i) q^{11} +(-2.31113 - 2.31113i) q^{12} +0.145782 q^{13} +(-3.26843 - 3.26843i) q^{14} +1.00000 q^{16} +(3.31113 + 2.45691i) q^{17} +7.68265 q^{18} -2.06038i q^{19} +15.1075 q^{21} +(1.82843 + 1.82843i) q^{22} +(3.41421 - 3.41421i) q^{23} +(-2.31113 + 2.31113i) q^{24} -0.145782i q^{26} +(-10.8222 + 10.8222i) q^{27} +(-3.26843 + 3.26843i) q^{28} +(2.10308 + 2.10308i) q^{29} +(-2.78573 - 2.78573i) q^{31} -1.00000i q^{32} -8.45147 q^{33} +(2.45691 - 3.31113i) q^{34} -7.68265i q^{36} +(2.44000 + 2.44000i) q^{37} -2.06038 q^{38} +(0.336921 + 0.336921i) q^{39} +(-5.53686 + 5.53686i) q^{41} -15.1075i q^{42} -0.622260i q^{43} +(1.82843 - 1.82843i) q^{44} +(-3.41421 - 3.41421i) q^{46} -8.47648 q^{47} +(2.31113 + 2.31113i) q^{48} -14.3653i q^{49} +(1.97421 + 13.3307i) q^{51} -0.145782 q^{52} -6.68265i q^{53} +(10.8222 + 10.8222i) q^{54} +(3.26843 + 3.26843i) q^{56} +(4.76182 - 4.76182i) q^{57} +(2.10308 - 2.10308i) q^{58} +5.71724i q^{59} +(2.63995 - 2.63995i) q^{61} +(-2.78573 + 2.78573i) q^{62} +(25.1102 + 25.1102i) q^{63} -1.00000 q^{64} +8.45147i q^{66} -1.58767 q^{67} +(-3.31113 - 2.45691i) q^{68} +15.7814 q^{69} +(1.83653 + 1.83653i) q^{71} -7.68265 q^{72} +(5.82220 + 5.82220i) q^{73} +(2.44000 - 2.44000i) q^{74} +2.06038i q^{76} +11.9522i q^{77} +(0.336921 - 0.336921i) q^{78} +(3.29344 - 3.29344i) q^{79} -26.9751 q^{81} +(5.53686 + 5.53686i) q^{82} -8.91382i q^{83} -15.1075 q^{84} -0.622260 q^{86} +9.72100i q^{87} +(-1.82843 - 1.82843i) q^{88} -15.9787 q^{89} +(0.476478 - 0.476478i) q^{91} +(-3.41421 + 3.41421i) q^{92} -12.8764i q^{93} +8.47648i q^{94} +(2.31113 - 2.31113i) q^{96} +(-12.5814 - 12.5814i) q^{97} -14.3653 q^{98} +(-14.0472 - 14.0472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 + 4 * q^7	$ 8 q - 8 q^{4} + 4 q^{7} + 8 q^{11} + 12 q^{13} - 4 q^{14} + 8 q^{16} + 8 q^{17} + 28 q^{18} + 16 q^{21} - 8 q^{22} + 16 q^{23} - 12 q^{27} - 4 q^{28} + 24 q^{29} + 4 q^{31} - 16 q^{33} + 12 q^{34} + 20 q^{37} - 20 q^{38} - 4 q^{39} - 8 q^{44} - 16 q^{46} - 20 q^{47} + 4 q^{51} - 12 q^{52} + 12 q^{54} + 4 q^{56} - 40 q^{57} + 24 q^{58} - 16 q^{61} + 4 q^{62} + 64 q^{63} - 8 q^{64} + 16 q^{67} - 8 q^{68} + 8 q^{69} + 4 q^{71} - 28 q^{72} - 28 q^{73} + 20 q^{74} - 4 q^{78} + 8 q^{79} - 8 q^{81} - 16 q^{84} + 32 q^{86} + 8 q^{88} - 44 q^{89} - 44 q^{91} - 16 q^{92} - 20 q^{97} - 48 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^7 + 8 * q^11 + 12 * q^13 - 4 * q^14 + 8 * q^16 + 8 * q^17 + 28 * q^18 + 16 * q^21 - 8 * q^22 + 16 * q^23 - 12 * q^27 - 4 * q^28 + 24 * q^29 + 4 * q^31 - 16 * q^33 + 12 * q^34 + 20 * q^37 - 20 * q^38 - 4 * q^39 - 8 * q^44 - 16 * q^46 - 20 * q^47 + 4 * q^51 - 12 * q^52 + 12 * q^54 + 4 * q^56 - 40 * q^57 + 24 * q^58 - 16 * q^61 + 4 * q^62 + 64 * q^63 - 8 * q^64 + 16 * q^67 - 8 * q^68 + 8 * q^69 + 4 * q^71 - 28 * q^72 - 28 * q^73 + 20 * q^74 - 4 * q^78 + 8 * q^79 - 8 * q^81 - 16 * q^84 + 32 * q^86 + 8 * q^88 - 44 * q^89 - 44 * q^91 - 16 * q^92 - 20 * q^97 - 48 * q^98 - 4 * 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
$3$	2.31113	+	2.31113i	1.33433	+	1.33433i	0.901451	+	0.432880i	$0.142503\pi$
$3$	2.31113	+	2.31113i	1.33433	+	1.33433i	0.432880	+	0.901451i	$0.357497\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	2.31113	−	2.31113i	0.943515	−	0.943515i
$7$	3.26843	−	3.26843i	1.23535	−	1.23535i	0.273471	−	0.961880i	$-0.411828\pi$
$7$	3.26843	−	3.26843i	1.23535	−	1.23535i	0.961880	−	0.273471i	$-0.0881717\pi$
$8$			1.00000i			0.353553i
$9$			7.68265i			2.56088i
$10$		0			0
$11$	−1.82843	+	1.82843i	−0.551292	+	0.551292i	−0.926813	−	0.375522i	$-0.877463\pi$
$11$	−1.82843	+	1.82843i	−0.551292	+	0.551292i	0.375522	+	0.926813i	$0.377463\pi$
$12$	−2.31113	−	2.31113i	−0.667166	−	0.667166i
$13$	0.145782			0.0404326			0.0202163	−	0.999796i	$-0.493565\pi$
$13$	0.145782			0.0404326			0.0202163	+	0.999796i	$0.493565\pi$
$14$	−3.26843	−	3.26843i	−0.873525	−	0.873525i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.31113	+	2.45691i	0.803067	+	0.595889i
$17$	3.31113	+	2.45691i	0.803067	+	0.595889i
$18$	7.68265			1.81082
$19$		−	2.06038i		−	0.472685i	−0.971670	−	0.236342i	$-0.924051\pi$
$19$		−	2.06038i		−	0.472685i	0.971670	−	0.236342i	$-0.0759487\pi$
$20$		0			0
$21$	15.1075			3.29674
$22$	1.82843	+	1.82843i	0.389822	+	0.389822i
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	−0.255022	−	0.966935i	$-0.582083\pi$
$23$	3.41421	−	3.41421i	0.711913	−	0.711913i	0.966935	+	0.255022i	$0.0820828\pi$
$24$	−2.31113	+	2.31113i	−0.471757	+	0.471757i
$25$		0			0
$26$		−	0.145782i		−	0.0285902i
$27$	−10.8222	+	10.8222i	−2.08273	+	2.08273i
$28$	−3.26843	+	3.26843i	−0.617676	+	0.617676i
$29$	2.10308	+	2.10308i	0.390533	+	0.390533i	0.874877	−	0.484345i	$-0.160942\pi$
$29$	2.10308	+	2.10308i	0.390533	+	0.390533i	−0.484345	+	0.874877i	$0.660942\pi$
$30$		0			0
$31$	−2.78573	−	2.78573i	−0.500332	−	0.500332i	0.411209	−	0.911541i	$-0.365107\pi$
$31$	−2.78573	−	2.78573i	−0.500332	−	0.500332i	−0.911541	+	0.411209i	$0.865107\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−8.45147			−1.47121
$34$	2.45691	−	3.31113i	0.421357	−	0.567854i
$35$		0			0
$36$		−	7.68265i		−	1.28044i
$37$	2.44000	+	2.44000i	0.401134	+	0.401134i	0.878633	−	0.477498i	$-0.158456\pi$
$37$	2.44000	+	2.44000i	0.401134	+	0.401134i	−0.477498	+	0.878633i	$0.658456\pi$
$38$	−2.06038			−0.334239
$39$	0.336921	+	0.336921i	0.0539505	+	0.0539505i
$40$		0			0
$41$	−5.53686	+	5.53686i	−0.864713	+	0.864713i	−0.991881	−	0.127168i	$-0.959411\pi$
$41$	−5.53686	+	5.53686i	−0.864713	+	0.864713i	0.127168	+	0.991881i	$0.459411\pi$
$42$		−	15.1075i		−	2.33114i
$43$		−	0.622260i		−	0.0948938i	−0.998874	−	0.0474469i	$-0.984892\pi$
$43$		−	0.622260i		−	0.0948938i	0.998874	−	0.0474469i	$-0.0151085\pi$
$44$	1.82843	−	1.82843i	0.275646	−	0.275646i
$45$		0			0
$46$	−3.41421	−	3.41421i	−0.503398	−	0.503398i
$47$	−8.47648			−1.23642			−0.618211	−	0.786012i	$-0.712142\pi$
$47$	−8.47648			−1.23642			−0.618211	+	0.786012i	$0.712142\pi$
$48$	2.31113	+	2.31113i	0.333583	+	0.333583i
$49$		−	14.3653i		−	2.05218i
$50$		0			0
$51$	1.97421	+	13.3307i	0.276445	+	1.86667i
$52$	−0.145782			−0.0202163
$53$		−	6.68265i		−	0.917932i	−0.888454	−	0.458966i	$-0.848220\pi$
$53$		−	6.68265i		−	0.917932i	0.888454	−	0.458966i	$-0.151780\pi$
$54$	10.8222	+	10.8222i	1.47272	+	1.47272i
$55$		0			0
$56$	3.26843	+	3.26843i	0.436763	+	0.436763i
$57$	4.76182	−	4.76182i	0.630718	−	0.630718i
$58$	2.10308	−	2.10308i	0.276148	−	0.276148i
$59$			5.71724i			0.744321i	0.928168	+	0.372161i	$0.121383\pi$
$59$			5.71724i			0.744321i	−0.928168	+	0.372161i	$0.878617\pi$
$60$		0			0
$61$	2.63995	−	2.63995i	0.338011	−	0.338011i	−0.517608	−	0.855618i	$-0.673177\pi$
$61$	2.63995	−	2.63995i	0.338011	−	0.338011i	0.855618	+	0.517608i	$0.173177\pi$
$62$	−2.78573	+	2.78573i	−0.353788	+	0.353788i
$63$	25.1102	+	25.1102i	3.16359	+	3.16359i
$64$	−1.00000			−0.125000
$65$		0			0
$66$			8.45147i			1.04030i
$67$	−1.58767			−0.193964			−0.0969822	−	0.995286i	$-0.530919\pi$
$67$	−1.58767			−0.193964			−0.0969822	+	0.995286i	$0.530919\pi$
$68$	−3.31113	−	2.45691i	−0.401534	−	0.297944i
$69$	15.7814			1.89986
$70$		0			0
$71$	1.83653	+	1.83653i	0.217956	+	0.217956i	0.807637	−	0.589680i	$-0.200746\pi$
$71$	1.83653	+	1.83653i	0.217956	+	0.217956i	−0.589680	+	0.807637i	$0.700746\pi$
$72$	−7.68265			−0.905408
$73$	5.82220	+	5.82220i	0.681437	+	0.681437i	0.960324	−	0.278887i	$-0.0899654\pi$
$73$	5.82220	+	5.82220i	0.681437	+	0.681437i	−0.278887	+	0.960324i	$0.589965\pi$
$74$	2.44000	−	2.44000i	0.283645	−	0.283645i
$75$		0			0
$76$			2.06038i			0.236342i
$77$			11.9522i			1.36208i
$78$	0.336921	−	0.336921i	0.0381488	−	0.0381488i
$79$	3.29344	−	3.29344i	0.370541	−	0.370541i	−0.497133	−	0.867674i	$-0.665614\pi$
$79$	3.29344	−	3.29344i	0.370541	−	0.370541i	0.867674	+	0.497133i	$0.165614\pi$
$80$		0			0
$81$	−26.9751			−2.99723
$82$	5.53686	+	5.53686i	0.611444	+	0.611444i
$83$		−	8.91382i		−	0.978419i	−0.872166	−	0.489210i	$-0.837285\pi$
$83$		−	8.91382i		−	0.978419i	0.872166	−	0.489210i	$-0.162715\pi$
$84$	−15.1075			−1.64837
$85$		0			0
$86$	−0.622260			−0.0671001
$87$			9.72100i			1.04220i
$88$	−1.82843	−	1.82843i	−0.194911	−	0.194911i
$89$	−15.9787			−1.69374			−0.846872	−	0.531797i	$-0.821517\pi$
$89$	−15.9787			−1.69374			−0.846872	+	0.531797i	$0.821517\pi$
$90$		0			0
$91$	0.476478	−	0.476478i	0.0499485	−	0.0499485i
$92$	−3.41421	+	3.41421i	−0.355956	+	0.355956i
$93$		−	12.8764i		−	1.33522i
$94$			8.47648i			0.874282i
$95$		0			0
$96$	2.31113	−	2.31113i	0.235879	−	0.235879i
$97$	−12.5814	−	12.5814i	−1.27745	−	1.27745i	−0.942089	−	0.335363i	$-0.891141\pi$
$97$	−12.5814	−	12.5814i	−1.27745	−	1.27745i	−0.335363	−	0.942089i	$-0.608859\pi$
$98$	−14.3653			−1.45111
$99$	−14.0472	−	14.0472i	−1.41179	−	1.41179i
$100$		0			0
$101$	7.65685			0.761885			0.380943	−	0.924599i	$-0.375599\pi$
$101$	7.65685			0.761885			0.380943	+	0.924599i	$0.375599\pi$
$102$	13.3307	−	1.97421i	1.31994	−	0.195476i
$103$	−8.07295			−0.795451			−0.397726	−	0.917504i	$-0.630200\pi$
$103$	−8.07295			−0.795451			−0.397726	+	0.917504i	$0.630200\pi$
$104$			0.145782i			0.0142951i
$105$		0			0
$106$	−6.68265			−0.649076
$107$	−1.68265	−	1.68265i	−0.162667	−	0.162667i	0.621080	−	0.783747i	$-0.286694\pi$
$107$	−1.68265	−	1.68265i	−0.162667	−	0.162667i	−0.783747	+	0.621080i	$0.786694\pi$
$108$	10.8222	−	10.8222i	1.04137	−	1.04137i
$109$	−2.10308	+	2.10308i	−0.201439	+	0.201439i	−0.800616	−	0.599177i	$-0.795494\pi$
$109$	−2.10308	+	2.10308i	−0.201439	+	0.201439i	0.599177	+	0.800616i	$0.295494\pi$
$110$		0			0
$111$			11.2783i			1.07049i
$112$	3.26843	−	3.26843i	0.308838	−	0.308838i
$113$	7.19994	−	7.19994i	0.677314	−	0.677314i	−0.282078	−	0.959391i	$-0.591024\pi$
$113$	7.19994	−	7.19994i	0.677314	−	0.677314i	0.959391	+	0.282078i	$0.0910237\pi$
$114$	−4.76182	−	4.76182i	−0.445985	−	0.445985i
$115$		0			0
$116$	−2.10308	−	2.10308i	−0.195266	−	0.195266i
$117$			1.11999i			0.103543i
$118$	5.71724			0.526315
$119$	18.8525	−	2.79195i	1.72820	−	0.255938i
$120$		0			0
$121$			4.31371i			0.392155i
$122$	−2.63995	−	2.63995i	−0.239010	−	0.239010i
$123$	−25.5928			−2.30763
$124$	2.78573	+	2.78573i	0.250166	+	0.250166i
$125$		0			0
$126$	25.1102	−	25.1102i	2.23699	−	2.23699i
$127$		−	11.1841i		−	0.992432i	−0.868199	−	0.496216i	$-0.834722\pi$
$127$		−	11.1841i		−	0.992432i	0.868199	−	0.496216i	$-0.165278\pi$
$128$			1.00000i			0.0883883i
$129$	1.43812	−	1.43812i	0.126620	−	0.126620i
$130$		0			0
$131$	10.5715	+	10.5715i	0.923633	+	0.923633i	0.997284	−	0.0736515i	$-0.0234653\pi$
$131$	10.5715	+	10.5715i	0.923633	+	0.923633i	−0.0736515	+	0.997284i	$0.523465\pi$
$132$	8.45147			0.735606
$133$	−6.73423	−	6.73423i	−0.583932	−	0.583932i
$134$			1.58767i			0.137153i
$135$		0			0
$136$	−2.45691	+	3.31113i	−0.210678	+	0.283927i
$137$	14.1583			1.20963			0.604815	−	0.796366i	$-0.293247\pi$
$137$	14.1583			1.20963			0.604815	+	0.796366i	$0.293247\pi$
$138$		−	15.7814i		−	1.34340i
$139$	−15.0729	−	15.0729i	−1.27847	−	1.27847i	−0.941524	−	0.336947i	$-0.890606\pi$
$139$	−15.0729	−	15.0729i	−1.27847	−	1.27847i	−0.336947	−	0.941524i	$-0.609394\pi$
$140$		0			0
$141$	−19.5902	−	19.5902i	−1.64980	−	1.64980i
$142$	1.83653	−	1.83653i	0.154118	−	0.154118i
$143$	−0.266552	+	0.266552i	−0.0222902	+	0.0222902i
$144$			7.68265i			0.640220i
$145$		0			0
$146$	5.82220	−	5.82220i	0.481849	−	0.481849i
$147$	33.2001	−	33.2001i	2.73829	−	2.73829i
$148$	−2.44000	−	2.44000i	−0.200567	−	0.200567i
$149$	−10.2791			−0.842098			−0.421049	−	0.907038i	$-0.638338\pi$
$149$	−10.2791			−0.842098			−0.421049	+	0.907038i	$0.638338\pi$
$150$		0			0
$151$		−	6.53686i		−	0.531962i	−0.963978	−	0.265981i	$-0.914304\pi$
$151$		−	6.53686i		−	0.531962i	0.963978	−	0.265981i	$-0.0856959\pi$
$152$	2.06038			0.167119
$153$	−18.8756	+	25.4382i	−1.52600	+	2.05656i
$154$	11.9522			0.963134
$155$		0			0
$156$	−0.336921	−	0.336921i	−0.0269753	−	0.0269753i
$157$	−12.4337			−0.992317			−0.496159	−	0.868232i	$-0.665257\pi$
$157$	−12.4337			−0.992317			−0.496159	+	0.868232i	$0.665257\pi$
$158$	−3.29344	−	3.29344i	−0.262012	−	0.262012i
$159$	15.4445	−	15.4445i	1.22483	−	1.22483i
$160$		0			0
$161$		−	22.3182i		−	1.75892i
$162$			26.9751i			2.11936i
$163$	0.562654	−	0.562654i	0.0440705	−	0.0440705i	−0.684728	−	0.728799i	$-0.740079\pi$
$163$	0.562654	−	0.562654i	0.0440705	−	0.0440705i	0.728799	+	0.684728i	$0.240079\pi$
$164$	5.53686	−	5.53686i	0.432356	−	0.432356i
$165$		0			0
$166$	−8.91382			−0.691847
$167$	3.36263	+	3.36263i	0.260208	+	0.260208i	0.825139	−	0.564930i	$-0.191097\pi$
$167$	3.36263	+	3.36263i	0.260208	+	0.260208i	−0.564930	+	0.825139i	$0.691097\pi$
$168$			15.1075i			1.16557i
$169$	−12.9787			−0.998365
$170$		0			0
$171$	15.8292			1.21049
$172$			0.622260i			0.0474469i
$173$	−9.00188	−	9.00188i	−0.684400	−	0.684400i	0.276588	−	0.960989i	$-0.410796\pi$
$173$	−9.00188	−	9.00188i	−0.684400	−	0.684400i	−0.960989	+	0.276588i	$0.910796\pi$
$174$	9.72100			0.736947
$175$		0			0
$176$	−1.82843	+	1.82843i	−0.137823	+	0.137823i
$177$	−13.2133	+	13.2133i	−0.993171	+	0.993171i
$178$			15.9787i			1.19766i
$179$			0.170794i			0.0127658i	0.999980	+	0.00638288i	$0.00203175\pi$
$179$			0.170794i			0.0127658i	−0.999980	+	0.00638288i	$0.997968\pi$
$180$		0			0
$181$	3.32882	−	3.32882i	0.247429	−	0.247429i	−0.572486	−	0.819915i	$-0.694021\pi$
$181$	3.32882	−	3.32882i	0.247429	−	0.247429i	0.819915	+	0.572486i	$0.194021\pi$
$182$	−0.476478	−	0.476478i	−0.0353189	−	0.0353189i
$183$	12.2025			0.902036
$184$	3.41421	+	3.41421i	0.251699	+	0.251699i
$185$		0			0
$186$	−12.8764			−0.944141
$187$	−10.5464	+	1.56188i	−0.771232	+	0.114216i
$188$	8.47648			0.618211
$189$			70.7433i			5.14581i
$190$		0			0
$191$	4.79461			0.346926			0.173463	−	0.984840i	$-0.444504\pi$
$191$	4.79461			0.346926			0.173463	+	0.984840i	$0.444504\pi$
$192$	−2.31113	−	2.31113i	−0.166791	−	0.166791i
$193$	−10.6819	+	10.6819i	−0.768898	+	0.768898i	−0.977912	−	0.209015i	$-0.932974\pi$
$193$	−10.6819	+	10.6819i	−0.768898	+	0.768898i	0.209015	+	0.977912i	$0.432974\pi$
$194$	−12.5814	+	12.5814i	−0.903295	+	0.903295i
$195$		0			0
$196$			14.3653i			1.02609i
$197$	−4.85610	+	4.85610i	−0.345983	+	0.345983i	−0.858611	−	0.512628i	$-0.828672\pi$
$197$	−4.85610	+	4.85610i	−0.345983	+	0.345983i	0.512628	+	0.858611i	$0.328672\pi$
$198$	−14.0472	+	14.0472i	−0.998288	+	0.998288i
$199$	−2.12810	−	2.12810i	−0.150857	−	0.150857i	0.627644	−	0.778501i	$-0.284019\pi$
$199$	−2.12810	−	2.12810i	−0.150857	−	0.150857i	−0.778501	+	0.627644i	$0.784019\pi$
$200$		0			0
$201$	−3.66930	−	3.66930i	−0.258813	−	0.258813i
$202$		−	7.65685i		−	0.538734i
$203$	13.7476			0.964890
$204$	−1.97421	−	13.3307i	−0.138222	−	0.933335i
$205$		0			0
$206$			8.07295i			0.562469i
$207$	26.2302	+	26.2302i	1.82312	+	1.82312i
$208$	0.145782			0.0101082
$209$	3.76726	+	3.76726i	0.260587	+	0.260587i
$210$		0			0
$211$	−1.47648	+	1.47648i	−0.101645	+	0.101645i	−0.756100	−	0.654456i	$-0.772898\pi$
$211$	−1.47648	+	1.47648i	−0.101645	+	0.101645i	0.654456	+	0.756100i	$0.272898\pi$
$212$			6.68265i			0.458966i
$213$			8.48893i			0.581652i
$214$	−1.68265	+	1.68265i	−0.115023	+	0.115023i
$215$		0			0
$216$	−10.8222	−	10.8222i	−0.736358	−	0.736358i
$217$	−18.2099			−1.23617
$218$	2.10308	+	2.10308i	0.142439	+	0.142439i
$219$			26.9117i			1.81853i
$220$		0			0
$221$	0.482703	+	0.358173i	0.0324701	+	0.0240934i
$222$	11.2783			0.756952
$223$		−	22.6186i		−	1.51465i	−0.653036	−	0.757327i	$-0.726505\pi$
$223$		−	22.6186i		−	1.51465i	0.653036	−	0.757327i	$-0.273495\pi$
$224$	−3.26843	−	3.26843i	−0.218381	−	0.218381i
$225$		0			0
$226$	−7.19994	−	7.19994i	−0.478933	−	0.478933i
$227$	8.29868	−	8.29868i	0.550803	−	0.550803i	−0.375870	−	0.926673i	$-0.622656\pi$
$227$	8.29868	−	8.29868i	0.550803	−	0.550803i	0.926673	+	0.375870i	$0.122656\pi$
$228$	−4.76182	+	4.76182i	−0.315359	+	0.315359i
$229$		−	25.8897i		−	1.71084i	−0.517935	−	0.855420i	$-0.673299\pi$
$229$		−	25.8897i		−	1.71084i	0.517935	−	0.855420i	$-0.326701\pi$
$230$		0			0
$231$	−27.6230	+	27.6230i	−1.81746	+	1.81746i
$232$	−2.10308	+	2.10308i	−0.138074	+	0.138074i
$233$	−9.65141	−	9.65141i	−0.632285	−	0.632285i	0.316356	−	0.948641i	$-0.397541\pi$
$233$	−9.65141	−	9.65141i	−0.632285	−	0.632285i	−0.948641	+	0.316356i	$0.897541\pi$
$234$	1.11999			0.0732161
$235$		0			0
$236$		−	5.71724i		−	0.372161i
$237$	15.2232			0.988850
$238$	−2.79195	−	18.8525i	−0.180975	−	1.22202i
$239$	−25.4736			−1.64775			−0.823875	−	0.566771i	$-0.808192\pi$
$239$	−25.4736			−1.64775			−0.823875	+	0.566771i	$0.808192\pi$
$240$		0			0
$241$	5.65763	+	5.65763i	0.364440	+	0.364440i	0.865445	−	0.501005i	$-0.167036\pi$
$241$	5.65763	+	5.65763i	0.364440	+	0.364440i	−0.501005	+	0.865445i	$0.667036\pi$
$242$	4.31371			0.277296
$243$	−29.8764	−	29.8764i	−1.91657	−	1.91657i
$244$	−2.63995	+	2.63995i	−0.169005	+	0.169005i
$245$		0			0
$246$			25.5928i			1.63174i
$247$		−	0.300367i		−	0.0191119i
$248$	2.78573	−	2.78573i	0.176894	−	0.176894i
$249$	20.6010	−	20.6010i	1.30554	−	1.30554i
$250$		0			0
$251$	8.60981			0.543446			0.271723	−	0.962375i	$-0.412406\pi$
$251$	8.60981			0.543446			0.271723	+	0.962375i	$0.412406\pi$
$252$	−25.1102	−	25.1102i	−1.58179	−	1.58179i
$253$			12.4853i			0.784943i
$254$	−11.1841			−0.701755
$255$		0			0
$256$	1.00000			0.0625000
$257$			13.7976i			0.860670i	0.902669	+	0.430335i	$0.141605\pi$
$257$			13.7976i			0.860670i	−0.902669	+	0.430335i	$0.858395\pi$
$258$	−1.43812	−	1.43812i	−0.0895337	−	0.0895337i
$259$	15.9500			0.991083
$260$		0			0
$261$	−16.1572	+	16.1572i	−1.00011	+	1.00011i
$262$	10.5715	−	10.5715i	0.653107	−	0.653107i
$263$			22.3271i			1.37674i	0.725357	+	0.688372i	$0.241675\pi$
$263$			22.3271i			1.37674i	−0.725357	+	0.688372i	$0.758325\pi$
$264$		−	8.45147i		−	0.520152i
$265$		0			0
$266$	−6.73423	+	6.73423i	−0.412902	+	0.412902i
$267$	−36.9290	−	36.9290i	−2.26002	−	2.26002i
$268$	1.58767			0.0969822
$269$	11.2747	+	11.2747i	0.687428	+	0.687428i	0.961663	−	0.274235i	$-0.0884246\pi$
$269$	11.2747	+	11.2747i	0.687428	+	0.687428i	−0.274235	+	0.961663i	$0.588425\pi$
$270$		0			0
$271$	−30.8765			−1.87561			−0.937806	−	0.347159i	$-0.887146\pi$
$271$	−30.8765			−1.87561			−0.937806	+	0.347159i	$0.887146\pi$
$272$	3.31113	+	2.45691i	0.200767	+	0.148972i
$273$	2.20241			0.133296
$274$		−	14.1583i		−	0.855337i
$275$		0			0
$276$	−15.7814			−0.949928
$277$	19.7325	+	19.7325i	1.18561	+	1.18561i	0.978269	+	0.207340i	$0.0664805\pi$
$277$	19.7325	+	19.7325i	1.18561	+	1.18561i	0.207340	+	0.978269i	$0.433519\pi$
$278$	−15.0729	+	15.0729i	−0.904015	+	0.904015i
$279$	21.4018	−	21.4018i	1.28129	−	1.28129i
$280$		0			0
$281$		−	10.2879i		−	0.613726i	−0.951754	−	0.306863i	$-0.900721\pi$
$281$		−	10.2879i		−	0.613726i	0.951754	−	0.306863i	$-0.0992793\pi$
$282$	−19.5902	+	19.5902i	−1.16658	+	1.16658i
$283$	8.51730	−	8.51730i	0.506301	−	0.506301i	−0.407088	−	0.913389i	$-0.633456\pi$
$283$	8.51730	−	8.51730i	0.506301	−	0.506301i	0.913389	+	0.407088i	$0.133456\pi$
$284$	−1.83653	−	1.83653i	−0.108978	−	0.108978i
$285$		0			0
$286$	0.266552	+	0.266552i	0.0157615	+	0.0157615i
$287$			36.1937i			2.13645i
$288$	7.68265			0.452704
$289$	4.92717	+	16.2703i	0.289833	+	0.957077i
$290$		0			0
$291$		−	58.1547i		−	3.40909i
$292$	−5.82220	−	5.82220i	−0.340719	−	0.340719i
$293$	30.6024			1.78781			0.893906	−	0.448255i	$-0.147954\pi$
$293$	30.6024			1.78781			0.893906	+	0.448255i	$0.147954\pi$
$294$	−33.2001	−	33.2001i	−1.93627	−	1.93627i
$295$		0			0
$296$	−2.44000	+	2.44000i	−0.141822	+	0.141822i
$297$		−	39.5752i		−	2.29639i
$298$			10.2791i			0.595453i
$299$	0.497731	−	0.497731i	0.0287845	−	0.0287845i
$300$		0			0
$301$	−2.03382	−	2.03382i	−0.117227	−	0.117227i
$302$	−6.53686			−0.376154
$303$	17.6960	+	17.6960i	1.01661	+	1.01661i
$304$		−	2.06038i		−	0.118171i
$305$		0			0
$306$	25.4382	+	18.8756i	1.45421	+	1.07905i
$307$	13.6268			0.777722			0.388861	−	0.921296i	$-0.372869\pi$
$307$	13.6268			0.777722			0.388861	+	0.921296i	$0.372869\pi$
$308$		−	11.9522i		−	0.681039i
$309$	−18.6576	−	18.6576i	−1.06140	−	1.06140i
$310$		0			0
$311$	8.72792	+	8.72792i	0.494915	+	0.494915i	0.909851	−	0.414936i	$-0.136196\pi$
$311$	8.72792	+	8.72792i	0.494915	+	0.494915i	−0.414936	+	0.909851i	$0.636196\pi$
$312$	−0.336921	+	0.336921i	−0.0190744	+	0.0190744i
$313$	8.73345	−	8.73345i	0.493644	−	0.493644i	−0.415809	−	0.909452i	$-0.636501\pi$
$313$	8.73345	−	8.73345i	0.493644	−	0.493644i	0.909452	+	0.415809i	$0.136501\pi$
$314$			12.4337i			0.701674i
$315$		0			0
$316$	−3.29344	+	3.29344i	−0.185271	+	0.185271i
$317$	−11.3288	+	11.3288i	−0.636290	+	0.636290i	−0.949638	−	0.313348i	$-0.898549\pi$
$317$	−11.3288	+	11.3288i	−0.636290	+	0.636290i	0.313348	+	0.949638i	$0.398549\pi$
$318$	−15.4445	−	15.4445i	−0.866082	−	0.866082i
$319$	−7.69067			−0.430595
$320$		0			0
$321$		−	7.77762i		−	0.434105i
$322$	−22.3182			−1.24375
$323$	5.06218	−	6.82220i	0.281667	−	0.379597i
$324$	26.9751			1.49862
$325$		0			0
$326$	−0.562654	−	0.562654i	−0.0311625	−	0.0311625i
$327$	−9.72100			−0.537572
$328$	−5.53686	−	5.53686i	−0.305722	−	0.305722i
$329$	−27.7048	+	27.7048i	−1.52741	+	1.52741i
$330$		0			0
$331$			10.5494i			0.579849i	0.957050	+	0.289924i	$0.0936302\pi$
$331$			10.5494i			0.579849i	−0.957050	+	0.289924i	$0.906370\pi$
$332$			8.91382i			0.489210i
$333$	−18.7457	+	18.7457i	−1.02726	+	1.02726i
$334$	3.36263	−	3.36263i	0.183995	−	0.183995i
$335$		0			0
$336$	15.1075			0.824184
$337$	−8.95840	−	8.95840i	−0.487995	−	0.487995i	0.419678	−	0.907673i	$-0.362143\pi$
$337$	−8.95840	−	8.95840i	−0.487995	−	0.487995i	−0.907673	+	0.419678i	$0.862143\pi$
$338$			12.9787i			0.705951i
$339$	33.2800			1.80752
$340$		0			0
$341$	10.1870			0.551657
$342$		−	15.8292i		−	0.855945i
$343$	−24.0729	−	24.0729i	−1.29982	−	1.29982i
$344$	0.622260			0.0335500
$345$		0			0
$346$	−9.00188	+	9.00188i	−0.483944	+	0.483944i
$347$	−2.59024	+	2.59024i	−0.139052	+	0.139052i	−0.773206	−	0.634155i	$-0.781348\pi$
$347$	−2.59024	+	2.59024i	−0.139052	+	0.139052i	0.634155	+	0.773206i	$0.281348\pi$
$348$		−	9.72100i		−	0.521100i
$349$			28.5120i			1.52621i	0.646274	+	0.763105i	$0.276326\pi$
$349$			28.5120i			1.52621i	−0.646274	+	0.763105i	$0.723674\pi$
$350$		0			0
$351$	−1.57768	+	1.57768i	−0.0842104	+	0.0842104i
$352$	1.82843	+	1.82843i	0.0974555	+	0.0974555i
$353$	9.22691			0.491099			0.245550	−	0.969384i	$-0.421032\pi$
$353$	9.22691			0.491099			0.245550	+	0.969384i	$0.421032\pi$
$354$	13.2133	+	13.2133i	0.702278	+	0.702278i
$355$		0			0
$356$	15.9787			0.846872
$357$	50.0230	+	37.1179i	2.64750	+	1.96449i
$358$	0.170794			0.00902675
$359$			23.1576i			1.22221i	0.791550	+	0.611105i	$0.209275\pi$
$359$			23.1576i			1.22221i	−0.791550	+	0.611105i	$0.790725\pi$
$360$		0			0
$361$	14.7548			0.776569
$362$	−3.32882	−	3.32882i	−0.174959	−	0.174959i
$363$	−9.96954	+	9.96954i	−0.523265	+	0.523265i
$364$	−0.476478	+	0.476478i	−0.0249743	+	0.0249743i
$365$		0			0
$366$		−	12.2025i		−	0.637836i
$367$	5.65951	−	5.65951i	0.295424	−	0.295424i	−0.543794	−	0.839219i	$-0.683013\pi$
$367$	5.65951	−	5.65951i	0.295424	−	0.295424i	0.839219	+	0.543794i	$0.183013\pi$
$368$	3.41421	−	3.41421i	0.177978	−	0.177978i
$369$	−42.5378	−	42.5378i	−2.21443	−	2.21443i
$370$		0			0
$371$	−21.8418	−	21.8418i	−1.13397	−	1.13397i
$372$			12.8764i			0.667608i
$373$	16.1245			0.834896			0.417448	−	0.908701i	$-0.362925\pi$
$373$	16.1245			0.834896			0.417448	+	0.908701i	$0.362925\pi$
$374$	1.56188	+	10.5464i	0.0807627	+	0.545344i
$375$		0			0
$376$		−	8.47648i		−	0.437141i
$377$	0.306592	+	0.306592i	0.0157903	+	0.0157903i
$378$	70.7433			3.63864
$379$	23.6577	+	23.6577i	1.21522	+	1.21522i	0.969288	+	0.245929i	$0.0790930\pi$
$379$	23.6577	+	23.6577i	1.21522	+	1.21522i	0.245929	+	0.969288i	$0.420907\pi$
$380$		0			0
$381$	25.8480	−	25.8480i	1.32423	−	1.32423i
$382$		−	4.79461i		−	0.245314i
$383$		−	17.5273i		−	0.895602i	−0.894133	−	0.447801i	$-0.852207\pi$
$383$		−	17.5273i		−	0.895602i	0.894133	−	0.447801i	$-0.147793\pi$
$384$	−2.31113	+	2.31113i	−0.117939	+	0.117939i
$385$		0			0
$386$	10.6819	+	10.6819i	0.543693	+	0.543693i
$387$	4.78061			0.243012
$388$	12.5814	+	12.5814i	0.638726	+	0.638726i
$389$			5.39395i			0.273484i	0.990607	+	0.136742i	$0.0436631\pi$
$389$			5.39395i			0.273484i	−0.990607	+	0.136742i	$0.956337\pi$
$390$		0			0
$391$	19.6933	−	2.91648i	0.995934	−	0.147493i
$392$	14.3653			0.725557
$393$			48.8640i			2.46486i
$394$	4.85610	+	4.85610i	0.244647	+	0.244647i
$395$		0			0
$396$	14.0472	+	14.0472i	0.705896	+	0.705896i
$397$	−22.1572	+	22.1572i	−1.11204	+	1.11204i	−0.119166	+	0.992874i	$0.538022\pi$
$397$	−22.1572	+	22.1572i	−1.11204	+	1.11204i	−0.992874	+	0.119166i	$0.961978\pi$
$398$	−2.12810	+	2.12810i	−0.106672	+	0.106672i
$399$		−	31.1274i		−	1.55832i
$400$		0			0
$401$	−27.5332	+	27.5332i	−1.37494	+	1.37494i	−0.521994	+	0.852949i	$0.674812\pi$
$401$	−27.5332	+	27.5332i	−1.37494	+	1.37494i	−0.852949	+	0.521994i	$0.825188\pi$
$402$	−3.66930	+	3.66930i	−0.183008	+	0.183008i
$403$	−0.406109	−	0.406109i	−0.0202297	−	0.0202297i
$404$	−7.65685			−0.380943
$405$		0			0
$406$		−	13.7476i		−	0.682280i
$407$	−8.92274			−0.442284
$408$	−13.3307	+	1.97421i	−0.659968	+	0.0977379i
$409$	16.6326			0.822430			0.411215	−	0.911538i	$-0.365105\pi$
$409$	16.6326			0.822430			0.411215	+	0.911538i	$0.365105\pi$
$410$		0			0
$411$	32.7218	+	32.7218i	1.61405	+	1.61405i
$412$	8.07295			0.397726
$413$	18.6864	+	18.6864i	0.919498	+	0.919498i
$414$	26.2302	−	26.2302i	1.28914	−	1.28914i
$415$		0			0
$416$		−	0.145782i		−	0.00714755i
$417$		−	69.6711i		−	3.41181i
$418$	3.76726	−	3.76726i	0.184263	−	0.184263i
$419$	20.3049	−	20.3049i	0.991960	−	0.991960i	−0.00800839	−	0.999968i	$-0.502549\pi$
$419$	20.3049	−	20.3049i	0.991960	−	0.991960i	0.999968	+	0.00800839i	$0.00254918\pi$
$420$		0			0
$421$	28.5974			1.39375			0.696875	−	0.717193i	$-0.254573\pi$
$421$	28.5974			1.39375			0.696875	+	0.717193i	$0.254573\pi$
$422$	1.47648	+	1.47648i	0.0718738	+	0.0718738i
$423$		−	65.1218i		−	3.16633i
$424$	6.68265			0.324538
$425$		0			0
$426$	8.48893			0.411290
$427$		−	17.2570i		−	0.835123i
$428$	1.68265	+	1.68265i	0.0813337	+	0.0813337i
$429$	−1.23207			−0.0594850
$430$		0			0
$431$	1.39800	−	1.39800i	0.0673395	−	0.0673395i	−0.672635	−	0.739974i	$-0.734838\pi$
$431$	1.39800	−	1.39800i	0.0673395	−	0.0673395i	0.739974	+	0.672635i	$0.234838\pi$
$432$	−10.8222	+	10.8222i	−0.520683	+	0.520683i
$433$			35.6444i			1.71296i	0.516180	+	0.856480i	$0.327354\pi$
$433$			35.6444i			1.71296i	−0.516180	+	0.856480i	$0.672646\pi$
$434$			18.2099i			0.874104i
$435$		0			0
$436$	2.10308	−	2.10308i	0.100719	−	0.100719i
$437$	−7.03459	−	7.03459i	−0.336510	−	0.336510i
$438$	26.9117			1.28589
$439$	−10.9165	−	10.9165i	−0.521015	−	0.521015i	0.396863	−	0.917878i	$-0.370099\pi$
$439$	−10.9165	−	10.9165i	−0.521015	−	0.521015i	−0.917878	+	0.396863i	$0.870099\pi$
$440$		0			0
$441$	110.363			5.25540
$442$	0.358173	−	0.482703i	0.0170366	−	0.0229598i
$443$	8.63471			0.410247			0.205124	−	0.978736i	$-0.434240\pi$
$443$	8.63471			0.410247			0.205124	+	0.978736i	$0.434240\pi$
$444$		−	11.2783i		−	0.535246i
$445$		0			0
$446$	−22.6186			−1.07102
$447$	−23.7564	−	23.7564i	−1.12364	−	1.12364i
$448$	−3.26843	+	3.26843i	−0.154419	+	0.154419i
$449$	5.98677	−	5.98677i	0.282533	−	0.282533i	−0.551585	−	0.834119i	$-0.685977\pi$
$449$	5.98677	−	5.98677i	0.282533	−	0.282533i	0.834119	+	0.551585i	$0.185977\pi$
$450$		0			0
$451$		−	20.2475i		−	0.953418i
$452$	−7.19994	+	7.19994i	−0.338657	+	0.338657i
$453$	15.1075	−	15.1075i	0.709814	−	0.709814i
$454$	−8.29868	−	8.29868i	−0.389476	−	0.389476i
$455$		0			0
$456$	4.76182	+	4.76182i	0.222993	+	0.222993i
$457$		−	33.1305i		−	1.54978i	−0.632097	−	0.774889i	$-0.717806\pi$
$457$		−	33.1305i		−	1.54978i	0.632097	−	0.774889i	$-0.282194\pi$
$458$	−25.8897			−1.20975
$459$	−62.4229	+	9.24452i	−2.91365	+	0.431497i
$460$		0			0
$461$			12.8035i			0.596320i	0.954516	+	0.298160i	$0.0963729\pi$
$461$			12.8035i			0.596320i	−0.954516	+	0.298160i	$0.903627\pi$
$462$	27.6230	+	27.6230i	1.28514	+	1.28514i
$463$	−25.9877			−1.20775			−0.603875	−	0.797079i	$-0.706377\pi$
$463$	−25.9877			−1.20775			−0.603875	+	0.797079i	$0.706377\pi$
$464$	2.10308	+	2.10308i	0.0976332	+	0.0976332i
$465$		0			0
$466$	−9.65141	+	9.65141i	−0.447093	+	0.447093i
$467$			11.1805i			0.517371i	0.965962	+	0.258686i	$0.0832894\pi$
$467$			11.1805i			0.517371i	−0.965962	+	0.258686i	$0.916711\pi$
$468$		−	1.11999i		−	0.0517716i
$469$	−5.18918	+	5.18918i	−0.239614	+	0.239614i
$470$		0			0
$471$	−28.7359	−	28.7359i	−1.32408	−	1.32408i
$472$	−5.71724			−0.263157
$473$	1.13776	+	1.13776i	0.0523142	+	0.0523142i
$474$		−	15.2232i		−	0.699223i
$475$		0			0
$476$	−18.8525	+	2.79195i	−0.864101	+	0.127969i
$477$	51.3404			2.35072
$478$			25.4736i			1.16514i
$479$	−7.57878	−	7.57878i	−0.346283	−	0.346283i	0.512440	−	0.858723i	$-0.328742\pi$
$479$	−7.57878	−	7.57878i	−0.346283	−	0.346283i	−0.858723	+	0.512440i	$0.828742\pi$
$480$		0			0
$481$	0.355709	+	0.355709i	0.0162189	+	0.0162189i
$482$	5.65763	−	5.65763i	0.257698	−	0.257698i
$483$	51.5804	−	51.5804i	2.34699	−	2.34699i
$484$		−	4.31371i		−	0.196078i
$485$		0			0
$486$	−29.8764	+	29.8764i	−1.35522	+	1.35522i
$487$	19.9761	−	19.9761i	0.905203	−	0.905203i	−0.0906773	−	0.995880i	$-0.528903\pi$
$487$	19.9761	−	19.9761i	0.905203	−	0.905203i	0.995880	+	0.0906773i	$0.0289032\pi$
$488$	2.63995	+	2.63995i	0.119505	+	0.119505i
$489$	2.60073			0.117609
$490$		0			0
$491$			9.08253i			0.409889i	0.978774	+	0.204944i	$0.0657014\pi$
$491$			9.08253i			0.409889i	−0.978774	+	0.204944i	$0.934299\pi$
$492$	25.5928			1.15381
$493$	1.79649	+	12.1307i	0.0809099	+	0.546338i
$494$	−0.300367			−0.0135141
$495$		0			0
$496$	−2.78573	−	2.78573i	−0.125083	−	0.125083i
$497$	12.0052			0.538505
$498$	−20.6010	−	20.6010i	−0.923153	−	0.923153i
$499$	−2.62304	+	2.62304i	−0.117423	+	0.117423i	−0.763377	−	0.645953i	$-0.776460\pi$
$499$	−2.62304	+	2.62304i	−0.117423	+	0.117423i	0.645953	+	0.763377i	$0.276460\pi$
$500$		0			0
$501$			15.5430i			0.694408i
$502$		−	8.60981i		−	0.384275i
$503$	−2.84354	+	2.84354i	−0.126787	+	0.126787i	−0.767653	−	0.640866i	$-0.778575\pi$
$503$	−2.84354	+	2.84354i	−0.126787	+	0.126787i	0.640866	+	0.767653i	$0.278575\pi$
$504$	−25.1102	+	25.1102i	−1.11850	+	1.11850i
$505$		0			0
$506$	12.4853			0.555038
$507$	−29.9956	−	29.9956i	−1.33215	−	1.33215i
$508$			11.1841i			0.496216i
$509$	21.0221			0.931790			0.465895	−	0.884840i	$-0.345732\pi$
$509$	21.0221			0.931790			0.465895	+	0.884840i	$0.345732\pi$
$510$		0			0
$511$	38.0589			1.68363
$512$		−	1.00000i		−	0.0441942i
$513$	22.2979	+	22.2979i	0.984476	+	0.984476i
$514$	13.7976			0.608586
$515$		0			0
$516$	−1.43812	+	1.43812i	−0.0633099	+	0.0633099i
$517$	15.4986	−	15.4986i	0.681629	−	0.681629i
$518$		−	15.9500i		−	0.700802i
$519$		−	41.6090i		−	1.82643i
$520$		0			0
$521$	−3.14578	+	3.14578i	−0.137819	+	0.137819i	−0.772651	−	0.634831i	$-0.781070\pi$
$521$	−3.14578	+	3.14578i	−0.137819	+	0.137819i	0.634831	+	0.772651i	$0.281070\pi$
$522$	16.1572	+	16.1572i	0.707183	+	0.707183i
$523$	2.55823			0.111864			0.0559318	−	0.998435i	$-0.482187\pi$
$523$	2.55823			0.111864			0.0559318	+	0.998435i	$0.482187\pi$
$524$	−10.5715	−	10.5715i	−0.461816	−	0.461816i
$525$		0			0
$526$	22.3271			0.973506
$527$	−2.37962	−	16.0682i	−0.103658	−	0.699942i
$528$	−8.45147			−0.367803
$529$		−	0.313708i		−	0.0136395i
$530$		0			0
$531$	−43.9235			−1.90612
$532$	6.73423	+	6.73423i	0.291966	+	0.291966i
$533$	−0.807175	+	0.807175i	−0.0349626	+	0.0349626i
$534$	−36.9290	+	36.9290i	−1.59807	+	1.59807i
$535$		0			0
$536$		−	1.58767i		−	0.0685767i
$537$	−0.394728	+	0.394728i	−0.0170338	+	0.0170338i
$538$	11.2747	−	11.2747i	0.486085	−	0.486085i
$539$	26.2659	+	26.2659i	1.13135	+	1.13135i
$540$		0			0
$541$	−20.3318	−	20.3318i	−0.874132	−	0.874132i	0.118787	−	0.992920i	$-0.462099\pi$
$541$	−20.3318	−	20.3318i	−0.874132	−	0.874132i	−0.992920	+	0.118787i	$0.962099\pi$
$542$			30.8765i			1.32626i
$543$	15.3867			0.660305
$544$	2.45691	−	3.31113i	0.105339	−	0.141964i
$545$		0			0
$546$		−	2.20241i		−	0.0942543i
$547$	7.93417	+	7.93417i	0.339241	+	0.339241i	0.856081	−	0.516841i	$-0.172892\pi$
$547$	7.93417	+	7.93417i	0.339241	+	0.339241i	−0.516841	+	0.856081i	$0.672892\pi$
$548$	−14.1583			−0.604815
$549$	20.2818	+	20.2818i	0.865605	+	0.865605i
$550$		0			0
$551$	4.33316	−	4.33316i	0.184599	−	0.184599i
$552$			15.7814i			0.671700i
$553$		−	21.5288i		−	0.915497i
$554$	19.7325	−	19.7325i	0.838352	−	0.838352i
$555$		0			0
$556$	15.0729	+	15.0729i	0.639235	+	0.639235i
$557$	−37.4862			−1.58834			−0.794170	−	0.607696i	$-0.792094\pi$
$557$	−37.4862			−1.58834			−0.794170	+	0.607696i	$0.792094\pi$
$558$	−21.4018	−	21.4018i	−0.906009	−	0.906009i
$559$		−	0.0907143i		−	0.00383681i
$560$		0			0
$561$	−27.9839	−	20.7645i	−1.18148	−	0.876678i
$562$	−10.2879			−0.433970
$563$			21.9751i			0.926140i	0.886322	+	0.463070i	$0.153252\pi$
$563$			21.9751i			0.926140i	−0.886322	+	0.463070i	$0.846748\pi$
$564$	19.5902	+	19.5902i	0.824898	+	0.824898i
$565$		0			0
$566$	−8.51730	−	8.51730i	−0.358009	−	0.358009i
$567$	−88.1663	+	88.1663i	−3.70264	+	3.70264i
$568$	−1.83653	+	1.83653i	−0.0770592	+	0.0770592i
$569$			15.3425i			0.643190i	0.946877	+	0.321595i	$0.104219\pi$
$569$			15.3425i			0.643190i	−0.946877	+	0.321595i	$0.895781\pi$
$570$		0			0
$571$	1.57068	−	1.57068i	0.0657308	−	0.0657308i	−0.673477	−	0.739208i	$-0.735200\pi$
$571$	1.57068	−	1.57068i	0.0657308	−	0.0657308i	0.739208	+	0.673477i	$0.235200\pi$
$572$	0.266552	−	0.266552i	0.0111451	−	0.0111451i
$573$	11.0810	+	11.0810i	0.462914	+	0.462914i
$574$	36.1937			1.51070
$575$		0			0
$576$		−	7.68265i		−	0.320110i
$577$	−1.36685			−0.0569026			−0.0284513	−	0.999595i	$-0.509058\pi$
$577$	−1.36685			−0.0569026			−0.0284513	+	0.999595i	$0.509058\pi$
$578$	16.2703	−	4.92717i	0.676756	−	0.204943i
$579$	−49.3744			−2.05193
$580$		0			0
$581$	−29.1342	−	29.1342i	−1.20869	−	1.20869i
$582$	−58.1547			−2.41059
$583$	12.2187	+	12.2187i	0.506048	+	0.506048i
$584$	−5.82220	+	5.82220i	−0.240924	+	0.240924i
$585$		0			0
$586$		−	30.6024i		−	1.26417i
$587$			36.4050i			1.50260i	0.659963	+	0.751298i	$0.270572\pi$
$587$			36.4050i			1.50260i	−0.659963	+	0.751298i	$0.729428\pi$
$588$	−33.2001	+	33.2001i	−1.36915	+	1.36915i
$589$	−5.73967	+	5.73967i	−0.236499	+	0.236499i
$590$		0			0
$591$	−22.4461			−0.923311
$592$	2.44000	+	2.44000i	0.100284	+	0.100284i
$593$		−	20.7822i		−	0.853421i	−0.904388	−	0.426711i	$-0.859672\pi$
$593$		−	20.7822i		−	0.853421i	0.904388	−	0.426711i	$-0.140328\pi$
$594$	−39.5752			−1.62379
$595$		0			0
$596$	10.2791			0.421049
$597$		−	9.83661i		−	0.402586i
$598$	−0.497731	−	0.497731i	−0.0203537	−	0.0203537i
$599$	11.2961			0.461546			0.230773	−	0.973008i	$-0.425874\pi$
$599$	11.2961			0.461546			0.230773	+	0.973008i	$0.425874\pi$
$600$		0			0
$601$	−30.6356	+	30.6356i	−1.24965	+	1.24965i	−0.293779	+	0.955873i	$0.594913\pi$
$601$	−30.6356	+	30.6356i	−1.24965	+	1.24965i	−0.955873	+	0.293779i	$0.905087\pi$
$602$	−2.03382	+	2.03382i	−0.0828921	+	0.0828921i
$603$		−	12.1975i		−	0.496720i
$604$			6.53686i			0.265981i
$605$		0			0
$606$	17.6960	−	17.6960i	0.718850	−	0.718850i
$607$	28.6035	+	28.6035i	1.16098	+	1.16098i	0.984261	+	0.176719i	$0.0565484\pi$
$607$	28.6035	+	28.6035i	1.16098	+	1.16098i	0.176719	+	0.984261i	$0.443452\pi$
$608$	−2.06038			−0.0835596
$609$	31.7724	+	31.7724i	1.28748	+	1.28748i
$610$		0			0
$611$	−1.23572			−0.0499918
$612$	18.8756	−	25.4382i	0.763000	−	1.02828i
$613$	6.73799			0.272145			0.136072	−	0.990699i	$-0.456552\pi$
$613$	6.73799			0.272145			0.136072	+	0.990699i	$0.456552\pi$
$614$		−	13.6268i		−	0.549933i
$615$		0			0
$616$	−11.9522			−0.481567
$617$	−17.4915	−	17.4915i	−0.704182	−	0.704182i	0.261124	−	0.965305i	$-0.415907\pi$
$617$	−17.4915	−	17.4915i	−0.704182	−	0.704182i	−0.965305	+	0.261124i	$0.915907\pi$
$618$	−18.6576	+	18.6576i	−0.750520	+	0.750520i
$619$	15.9442	−	15.9442i	0.640850	−	0.640850i	−0.309915	−	0.950764i	$-0.600301\pi$
$619$	15.9442	−	15.9442i	0.640850	−	0.640850i	0.950764	+	0.309915i	$0.100301\pi$
$620$		0			0
$621$			73.8986i			2.96545i
$622$	8.72792	−	8.72792i	0.349958	−	0.349958i
$623$	−52.2254	+	52.2254i	−2.09237	+	2.09237i
$624$	0.336921	+	0.336921i	0.0134876	+	0.0134876i
$625$		0			0
$626$	−8.73345	−	8.73345i	−0.349059	−	0.349059i
$627$			17.4133i			0.695419i
$628$	12.4337			0.496159
$629$	2.08430	+	14.0740i	0.0831063	+	0.561169i
$630$		0			0
$631$			5.83297i			0.232207i	0.993237	+	0.116103i	$0.0370404\pi$
$631$			5.83297i			0.232207i	−0.993237	+	0.116103i	$0.962960\pi$
$632$	3.29344	+	3.29344i	0.131006	+	0.131006i
$633$	−6.82467			−0.271256
$634$	11.3288	+	11.3288i	0.449925	+	0.449925i
$635$		0			0
$636$	−15.4445	+	15.4445i	−0.612413	+	0.612413i
$637$		−	2.09420i		−	0.0829752i
$638$			7.69067i			0.304477i
$639$	−14.1094	+	14.1094i	−0.558160	+	0.558160i
$640$		0			0
$641$	8.08629	+	8.08629i	0.319389	+	0.319389i	0.848532	−	0.529143i	$-0.177487\pi$
$641$	8.08629	+	8.08629i	0.319389	+	0.319389i	−0.529143	+	0.848532i	$0.677487\pi$
$642$	−7.77762			−0.306958
$643$	2.42192	+	2.42192i	0.0955110	+	0.0955110i	0.753248	−	0.657737i	$-0.228486\pi$
$643$	2.42192	+	2.42192i	0.0955110	+	0.0955110i	−0.657737	+	0.753248i	$0.728486\pi$
$644$			22.3182i			0.879462i
$645$		0			0
$646$	−6.82220	−	5.06218i	−0.268416	−	0.199169i
$647$	−32.9671			−1.29607			−0.648035	−	0.761611i	$-0.724409\pi$
$647$	−32.9671			−1.29607			−0.648035	+	0.761611i	$0.724409\pi$
$648$		−	26.9751i		−	1.05968i
$649$	−10.4536	−	10.4536i	−0.410338	−	0.410338i
$650$		0			0
$651$	−42.0855	−	42.0855i	−1.64946	−	1.64946i
$652$	−0.562654	+	0.562654i	−0.0220352	+	0.0220352i
$653$	−2.47382	+	2.47382i	−0.0968080	+	0.0968080i	−0.753852	−	0.657044i	$-0.771807\pi$
$653$	−2.47382	+	2.47382i	−0.0968080	+	0.0968080i	0.657044	+	0.753852i	$0.271807\pi$
$654$			9.72100i			0.380121i
$655$		0			0
$656$	−5.53686	+	5.53686i	−0.216178	+	0.216178i
$657$	−44.7299	+	44.7299i	−1.74508	+	1.74508i
$658$	27.7048	+	27.7048i	1.08005	+	1.08005i
$659$	38.0355			1.48165			0.740826	−	0.671697i	$-0.234434\pi$
$659$	38.0355			1.48165			0.740826	+	0.671697i	$0.234434\pi$
$660$		0			0
$661$			16.7077i			0.649853i	0.945739	+	0.324926i	$0.105339\pi$
$661$			16.7077i			0.649853i	−0.945739	+	0.324926i	$0.894661\pi$
$662$	10.5494			0.410015
$663$	0.287804	+	1.94337i	0.0111774	+	0.0754744i
$664$	8.91382			0.345923
$665$		0			0
$666$	18.7457	+	18.7457i	0.726381	+	0.726381i
$667$	14.3608			0.556051
$668$	−3.36263	−	3.36263i	−0.130104	−	0.130104i
$669$	52.2746	−	52.2746i	2.02105	−	2.02105i
$670$		0			0
$671$			9.65390i			0.372685i
$672$		−	15.1075i		−	0.582786i
$673$	−21.0829	+	21.0829i	−0.812687	+	0.812687i	−0.985036	−	0.172349i	$-0.944864\pi$
$673$	−21.0829	+	21.0829i	−0.812687	+	0.812687i	0.172349	+	0.985036i	$0.444864\pi$
$674$	−8.95840	+	8.95840i	−0.345065	+	0.345065i
$675$		0			0
$676$	12.9787			0.499183
$677$	−7.32517	−	7.32517i	−0.281529	−	0.281529i	0.552189	−	0.833719i	$-0.313792\pi$
$677$	−7.32517	−	7.32517i	−0.281529	−	0.281529i	−0.833719	+	0.552189i	$0.813792\pi$
$678$		−	33.2800i		−	1.27811i
$679$	−82.2432			−3.15620
$680$		0			0
$681$	38.3587			1.46991
$682$		−	10.1870i		−	0.390081i
$683$	20.1403	+	20.1403i	0.770649	+	0.770649i	0.978220	−	0.207571i	$-0.0665559\pi$
$683$	20.1403	+	20.1403i	0.770649	+	0.770649i	−0.207571	+	0.978220i	$0.566556\pi$
$684$	−15.8292			−0.605245
$685$		0			0
$686$	−24.0729	+	24.0729i	−0.919109	+	0.919109i
$687$	59.8345	−	59.8345i	2.28283	−	2.28283i
$688$		−	0.622260i		−	0.0237235i
$689$		−	0.974209i		−	0.0371144i
$690$		0			0
$691$	34.6090	−	34.6090i	1.31659	−	1.31659i	0.400132	−	0.916457i	$-0.368964\pi$
$691$	34.6090	−	34.6090i	1.31659	−	1.31659i	0.916457	−	0.400132i	$-0.131036\pi$
$692$	9.00188	+	9.00188i	0.342200	+	0.342200i
$693$	−91.8243			−3.48812
$694$	2.59024	+	2.59024i	0.0983243	+	0.0983243i
$695$		0			0
$696$	−9.72100			−0.368474
$697$	−31.9369	+	4.72969i	−1.20969	+	0.179150i
$698$	28.5120			1.07919
$699$		−	44.6113i		−	1.68736i
$700$		0			0
$701$	−8.53155			−0.322232			−0.161116	−	0.986935i	$-0.551509\pi$
$701$	−8.53155			−0.322232			−0.161116	+	0.986935i	$0.551509\pi$
$702$	1.57768	+	1.57768i	0.0595458	+	0.0595458i
$703$	5.02735	−	5.02735i	0.189610	−	0.189610i
$704$	1.82843	−	1.82843i	0.0689114	−	0.0689114i
$705$		0			0
$706$		−	9.22691i		−	0.347260i
$707$	25.0259	−	25.0259i	0.941196	−	0.941196i
$708$	13.2133	−	13.2133i	0.496586	−	0.496586i
$709$	9.95226	+	9.95226i	0.373765	+	0.373765i	0.868846	−	0.495082i	$-0.164862\pi$
$709$	9.95226	+	9.95226i	0.373765	+	0.373765i	−0.495082	+	0.868846i	$0.664862\pi$
$710$		0			0
$711$	25.3024	+	25.3024i	0.948913	+	0.948913i
$712$		−	15.9787i		−	0.598829i
$713$	−19.0221			−0.712385
$714$	37.1179	−	50.0230i	1.38910	−	1.87207i
$715$		0			0
$716$		−	0.170794i		−	0.00638288i
$717$	−58.8728	−	58.8728i	−2.19865	−	2.19865i
$718$	23.1576			0.864233
$719$	2.74660	+	2.74660i	0.102431	+	0.102431i	0.756465	−	0.654034i	$-0.226925\pi$
$719$	2.74660	+	2.74660i	0.102431	+	0.102431i	−0.654034	+	0.756465i	$0.726925\pi$
$720$		0			0
$721$	−26.3859	+	26.3859i	−0.982661	+	0.982661i
$722$		−	14.7548i		−	0.549117i
$723$			26.1511i			0.972568i
$724$	−3.32882	+	3.32882i	−0.123714	+	0.123714i
$725$		0			0
$726$	9.96954	+	9.96954i	0.370004	+	0.370004i
$727$	43.7477			1.62251			0.811256	−	0.584691i	$-0.198784\pi$
$727$	43.7477			1.62251			0.811256	+	0.584691i	$0.198784\pi$
$728$	0.476478	+	0.476478i	0.0176595	+	0.0176595i
$729$		−	57.1710i		−	2.11745i
$730$		0			0
$731$	1.52884	−	2.06038i	0.0565461	−	0.0762061i
$732$	−12.2025			−0.451018
$733$		−	27.1945i		−	1.00445i	−0.864737	−	0.502226i	$-0.832515\pi$
$733$		−	27.1945i		−	1.00445i	0.864737	−	0.502226i	$-0.167485\pi$
$734$	−5.65951	−	5.65951i	−0.208896	−	0.208896i
$735$		0			0
$736$	−3.41421	−	3.41421i	−0.125850	−	0.125850i
$737$	2.90293	−	2.90293i	0.106931	−	0.106931i
$738$	−42.5378	+	42.5378i	−1.56584	+	1.56584i
$739$			14.5227i			0.534228i	0.963665	+	0.267114i	$0.0860700\pi$
$739$			14.5227i			0.534228i	−0.963665	+	0.267114i	$0.913930\pi$
$740$		0			0
$741$	0.694187	−	0.694187i	0.0255016	−	0.0255016i
$742$	−21.8418	+	21.8418i	−0.801837	+	0.801837i
$743$	−36.1912	−	36.1912i	−1.32773	−	1.32773i	−0.907351	−	0.420375i	$-0.861899\pi$
$743$	−36.1912	−	36.1912i	−1.32773	−	1.32773i	−0.420375	−	0.907351i	$-0.638101\pi$
$744$	12.8764			0.472070
$745$		0			0
$746$		−	16.1245i		−	0.590361i
$747$	68.4817			2.50562
$748$	10.5464	−	1.56188i	0.385616	−	0.0571078i
$749$	−10.9992			−0.401903
$750$		0			0
$751$	12.4234	+	12.4234i	0.453337	+	0.453337i	0.896461	−	0.443124i	$-0.146130\pi$
$751$	12.4234	+	12.4234i	0.453337	+	0.453337i	−0.443124	+	0.896461i	$0.646130\pi$
$752$	−8.47648			−0.309105
$753$	19.8984	+	19.8984i	0.725138	+	0.725138i
$754$	0.306592	−	0.306592i	0.0111654	−	0.0111654i
$755$		0			0
$756$		−	70.7433i		−	2.57291i
$757$			37.5091i			1.36329i	0.731682	+	0.681646i	$0.238735\pi$
$757$			37.5091i			1.36329i	−0.731682	+	0.681646i	$0.761265\pi$
$758$	23.6577	−	23.6577i	0.859288	−	0.859288i
$759$	−28.8551	+	28.8551i	−1.04737	+	1.04737i
$760$		0			0
$761$	−31.7851			−1.15221			−0.576105	−	0.817375i	$-0.695428\pi$
$761$	−31.7851			−1.15221			−0.576105	+	0.817375i	$0.695428\pi$
$762$	−25.8480	−	25.8480i	−0.936374	−	0.936374i
$763$			13.7476i			0.497695i
$764$	−4.79461			−0.173463
$765$		0			0
$766$	−17.5273			−0.633286
$767$			0.833470i			0.0300949i
$768$	2.31113	+	2.31113i	0.0833957	+	0.0833957i
$769$	−31.9023			−1.15043			−0.575213	−	0.818004i	$-0.695081\pi$
$769$	−31.9023			−1.15043			−0.575213	+	0.818004i	$0.695081\pi$
$770$		0			0
$771$	−31.8880	+	31.8880i	−1.14842	+	1.14842i
$772$	10.6819	−	10.6819i	0.384449	−	0.384449i
$773$			27.0913i			0.974408i	0.873288	+	0.487204i	$0.161983\pi$
$773$			27.0913i			0.974408i	−0.873288	+	0.487204i	$0.838017\pi$
$774$		−	4.78061i		−	0.171835i
$775$		0			0
$776$	12.5814	−	12.5814i	0.451647	−	0.451647i
$777$	36.8625	+	36.8625i	1.32243	+	1.32243i
$778$	5.39395			0.193382
$779$	11.4081	+	11.4081i	0.408736	+	0.408736i
$780$		0			0
$781$	−6.71593			−0.240315
$782$	−2.91648	−	19.6933i	−0.104293	−	0.704232i
$783$	−45.5200			−1.62675
$784$		−	14.3653i		−	0.513046i
$785$		0			0
$786$	48.8640			1.74292
$787$	37.0771	+	37.0771i	1.32166	+	1.32166i	0.912436	+	0.409219i	$0.134199\pi$
$787$	37.0771	+	37.0771i	1.32166	+	1.32166i	0.409219	+	0.912436i	$0.365801\pi$
$788$	4.85610	−	4.85610i	0.172991	−	0.172991i
$789$	−51.6007	+	51.6007i	−1.83703	+	1.83703i
$790$		0			0
$791$		−	47.0650i		−	1.67344i
$792$	14.0472	−	14.0472i	0.499144	−	0.499144i
$793$	0.384857	−	0.384857i	0.0136667	−	0.0136667i
$794$	22.1572	+	22.1572i	0.786331	+	0.786331i
$795$		0			0
$796$	2.12810	+	2.12810i	0.0754284	+	0.0754284i
$797$			34.4375i			1.21984i	0.792464	+	0.609919i	$0.208798\pi$
$797$			34.4375i			1.21984i	−0.792464	+	0.609919i	$0.791202\pi$
$798$	−31.1274			−1.10190
$799$	−28.0667	−	20.8260i	−0.992929	−	0.736770i
$800$		0			0
$801$		−	122.759i		−	4.33748i
$802$	27.5332	+	27.5332i	0.972232	+	0.972232i
$803$	−21.2909			−0.751341
$804$	3.66930	+	3.66930i	0.129406	+	0.129406i
$805$		0			0
$806$	−0.406109	+	0.406109i	−0.0143046	+	0.0143046i
$807$			52.1144i			1.83451i
$808$			7.65685i			0.269367i
$809$	−4.90215	+	4.90215i	−0.172351	+	0.172351i	−0.788011	−	0.615661i	$-0.788889\pi$
$809$	−4.90215	+	4.90215i	−0.172351	+	0.172351i	0.615661	+	0.788011i	$0.288889\pi$
$810$		0			0
$811$	−16.9360	−	16.9360i	−0.594702	−	0.594702i	0.344196	−	0.938898i	$-0.388152\pi$
$811$	−16.9360	−	16.9360i	−0.594702	−	0.594702i	−0.938898	+	0.344196i	$0.888152\pi$
$812$	−13.7476			−0.482445
$813$	−71.3596	−	71.3596i	−2.50269	−	2.50269i
$814$			8.92274i			0.312742i
$815$		0			0
$816$	1.97421	+	13.3307i	0.0691111	+	0.466668i
$817$	−1.28210			−0.0448549
$818$		−	16.6326i		−	0.581546i
$819$	3.66061	+	3.66061i	0.127912	+	0.127912i
$820$		0			0
$821$	14.1244	+	14.1244i	0.492947	+	0.492947i	0.909233	−	0.416287i	$-0.136669\pi$
$821$	14.1244	+	14.1244i	0.492947	+	0.492947i	−0.416287	+	0.909233i	$0.636669\pi$
$822$	32.7218	−	32.7218i	1.14130	−	1.14130i
$823$	−4.17345	+	4.17345i	−0.145477	+	0.145477i	−0.776094	−	0.630617i	$-0.782802\pi$
$823$	−4.17345	+	4.17345i	−0.145477	+	0.145477i	0.630617	+	0.776094i	$0.282802\pi$
$824$		−	8.07295i		−	0.281234i
$825$		0			0
$826$	18.6864	−	18.6864i	0.650183	−	0.650183i
$827$	18.0258	−	18.0258i	0.626818	−	0.626818i	−0.320448	−	0.947266i	$-0.603833\pi$
$827$	18.0258	−	18.0258i	0.626818	−	0.626818i	0.947266	+	0.320448i	$0.103833\pi$
$828$	−26.2302	−	26.2302i	−0.911562	−	0.911562i
$829$	18.4375			0.640359			0.320180	−	0.947357i	$-0.396257\pi$
$829$	18.4375			0.640359			0.320180	+	0.947357i	$0.396257\pi$
$830$		0			0
$831$			91.2086i			3.16399i
$832$	−0.145782			−0.00505408
$833$	35.2943	−	47.5653i	1.22287	−	1.64804i
$834$	−69.6711			−2.41251
$835$		0			0
$836$	−3.76726	−	3.76726i	−0.130294	−	0.130294i
$837$	60.2954			2.08412
$838$	−20.3049	−	20.3049i	−0.701421	−	0.701421i
$839$	8.28424	−	8.28424i	0.286004	−	0.286004i	−0.549494	−	0.835498i	$-0.685179\pi$
$839$	8.28424	−	8.28424i	0.286004	−	0.286004i	0.835498	+	0.549494i	$0.185179\pi$
$840$		0			0
$841$		−	20.1541i		−	0.694968i
$842$		−	28.5974i		−	0.985530i
$843$	23.7767	−	23.7767i	0.818914	−	0.818914i
$844$	1.47648	−	1.47648i	0.0508225	−	0.0508225i
$845$		0			0
$846$	−65.1218			−2.23893
$847$	14.0991	+	14.0991i	0.484449	+	0.484449i
$848$		−	6.68265i		−	0.229483i
$849$	39.3692			1.35115
$850$		0			0
$851$	16.6614			0.571145
$852$		−	8.48893i		−	0.290826i
$853$	−9.64915	−	9.64915i	−0.330381	−	0.330381i	0.522350	−	0.852731i	$-0.325055\pi$
$853$	−9.64915	−	9.64915i	−0.330381	−	0.330381i	−0.852731	+	0.522350i	$0.825055\pi$
$854$	−17.2570			−0.590521
$855$		0			0
$856$	1.68265	−	1.68265i	0.0575116	−	0.0575116i
$857$	−22.9313	+	22.9313i	−0.783318	+	0.783318i	−0.980389	−	0.197071i	$-0.936857\pi$
$857$	−22.9313	+	22.9313i	−0.783318	+	0.783318i	0.197071	+	0.980389i	$0.436857\pi$
$858$			1.23207i			0.0420622i
$859$		−	14.1902i		−	0.484164i	−0.970256	−	0.242082i	$-0.922170\pi$
$859$		−	14.1902i		−	0.484164i	0.970256	−	0.242082i	$-0.0778304\pi$
$860$		0			0
$861$	−83.6484	+	83.6484i	−2.85073	+	2.85073i
$862$	−1.39800	−	1.39800i	−0.0476162	−	0.0476162i
$863$	52.0480			1.77174			0.885868	−	0.463937i	$-0.153564\pi$
$863$	52.0480			1.77174			0.885868	+	0.463937i	$0.153564\pi$
$864$	10.8222	+	10.8222i	0.368179	+	0.368179i
$865$		0			0
$866$	35.6444			1.21125
$867$	−26.2155	+	48.9901i	−0.890325	+	1.66379i
$868$	18.2099			0.618085
$869$			12.0436i			0.408553i
$870$		0			0
$871$	−0.231453			−0.00784249
$872$	−2.10308	−	2.10308i	−0.0712194	−	0.0712194i
$873$	96.6588	−	96.6588i	3.27140	−	3.27140i
$874$	−7.03459	+	7.03459i	−0.237949	+	0.237949i
$875$		0			0
$876$		−	26.9117i		−	0.909263i
$877$	−3.85156	+	3.85156i	−0.130058	+	0.130058i	−0.769139	−	0.639081i	$-0.779315\pi$
$877$	−3.85156	+	3.85156i	−0.130058	+	0.130058i	0.639081	+	0.769139i	$0.279315\pi$
$878$	−10.9165	+	10.9165i	−0.368413	+	0.368413i
$879$	70.7261	+	70.7261i	2.38553	+	2.38553i
$880$		0			0
$881$	12.6672	+	12.6672i	0.426769	+	0.426769i	0.887526	−	0.460757i	$-0.152422\pi$
$881$	12.6672	+	12.6672i	0.426769	+	0.426769i	−0.460757	+	0.887526i	$0.652422\pi$
$882$		−	110.363i		−	3.71613i
$883$	−15.1362			−0.509374			−0.254687	−	0.967024i	$-0.581972\pi$
$883$	−15.1362			−0.509374			−0.254687	+	0.967024i	$0.581972\pi$
$884$	−0.482703	−	0.358173i	−0.0162351	−	0.0120467i
$885$		0			0
$886$		−	8.63471i		−	0.290089i
$887$	29.5122	+	29.5122i	0.990922	+	0.990922i	0.999959	−	0.00903736i	$-0.00287672\pi$
$887$	29.5122	+	29.5122i	0.990922	+	0.990922i	−0.00903736	+	0.999959i	$0.502877\pi$
$888$	−11.2783			−0.378476
$889$	−36.5546	−	36.5546i	−1.22600	−	1.22600i
$890$		0			0
$891$	49.3220	−	49.3220i	1.65235	−	1.65235i
$892$			22.6186i			0.757327i
$893$			17.4648i			0.584438i
$894$	−23.7564	+	23.7564i	−0.794532	+	0.794532i
$895$		0			0
$896$	3.26843	+	3.26843i	0.109191	+	0.109191i
$897$	2.30064			0.0768162
$898$	−5.98677	−	5.98677i	−0.199781	−	0.199781i
$899$		−	11.7172i		−	0.390792i
$900$		0			0
$901$	16.4187	−	22.1271i	0.546985	−	0.737161i
$902$	−20.2475			−0.674168
$903$		−	9.40082i		−	0.312840i
$904$	7.19994	+	7.19994i	0.239467	+	0.239467i
$905$		0			0
$906$	−15.1075	−	15.1075i	−0.501914	−	0.501914i
$907$	9.65865	−	9.65865i	0.320710	−	0.320710i	−0.528329	−	0.849040i	$-0.677181\pi$
$907$	9.65865	−	9.65865i	0.320710	−	0.320710i	0.849040	+	0.528329i	$0.177181\pi$
$908$	−8.29868	+	8.29868i	−0.275401	+	0.275401i
$909$			58.8249i			1.95110i
$910$		0			0
$911$	0.866458	−	0.866458i	0.0287070	−	0.0287070i	−0.692608	−	0.721315i	$-0.743538\pi$
$911$	0.866458	−	0.866458i	0.0287070	−	0.0287070i	0.721315	+	0.692608i	$0.243538\pi$
$912$	4.76182	−	4.76182i	0.157680	−	0.157680i
$913$	16.2983	+	16.2983i	0.539394	+	0.539394i
$914$	−33.1305			−1.09586
$915$		0			0
$916$			25.8897i			0.855420i
$917$	69.1042			2.28202
$918$	9.24452	+	62.4229i	0.305115	+	2.06026i
$919$	21.7152			0.716317			0.358158	−	0.933661i	$-0.383405\pi$
$919$	21.7152			0.716317			0.358158	+	0.933661i	$0.383405\pi$
$920$		0			0
$921$	31.4933	+	31.4933i	1.03774	+	1.03774i
$922$	12.8035			0.421662
$923$	0.267733	+	0.267733i	0.00881255	+	0.00881255i
$924$	27.6230	−	27.6230i	0.908731	−	0.908731i
$925$		0			0
$926$			25.9877i			0.854008i
$927$		−	62.0216i		−	2.03706i
$928$	2.10308	−	2.10308i	0.0690371	−	0.0690371i
$929$	−14.9022	+	14.9022i	−0.488924	+	0.488924i	−0.907967	−	0.419043i	$-0.862366\pi$
$929$	−14.9022	+	14.9022i	−0.488924	+	0.488924i	0.419043	+	0.907967i	$0.362366\pi$
$930$		0			0
$931$	−29.5980			−0.970036
$932$	9.65141	+	9.65141i	0.316142	+	0.316142i
$933$			40.3427i			1.32076i
$934$	11.1805			0.365837
$935$		0			0
$936$	−1.11999			−0.0366081
$937$		−	48.3234i		−	1.57866i	−0.613971	−	0.789328i	$-0.710429\pi$
$937$		−	48.3234i		−	1.57866i	0.613971	−	0.789328i	$-0.289571\pi$
$938$	5.18918	+	5.18918i	0.169433	+	0.169433i
$939$	40.3683			1.31737
$940$		0			0
$941$	11.0045	−	11.0045i	0.358735	−	0.358735i	−0.504611	−	0.863347i	$-0.668364\pi$
$941$	11.0045	−	11.0045i	0.358735	−	0.358735i	0.863347	+	0.504611i	$0.168364\pi$
$942$	−28.7359	+	28.7359i	−0.936266	+	0.936266i
$943$			37.8081i			1.23120i
$944$			5.71724i			0.186080i
$945$		0			0
$946$	1.13776	−	1.13776i	0.0369917	−	0.0369917i
$947$	−21.4879	−	21.4879i	−0.698262	−	0.698262i	0.265774	−	0.964035i	$-0.414373\pi$
$947$	−21.4879	−	21.4879i	−0.698262	−	0.698262i	−0.964035	+	0.265774i	$0.914373\pi$
$948$	−15.2232			−0.494425
$949$	0.848772	+	0.848772i	0.0275523	+	0.0275523i
$950$		0			0
$951$	−52.3647			−1.69804
$952$	2.79195	+	18.8525i	0.0904877	+	0.611011i
$953$	18.6150			0.602998			0.301499	−	0.953467i	$-0.402513\pi$
$953$	18.6150			0.602998			0.301499	+	0.953467i	$0.402513\pi$
$954$		−	51.3404i		−	1.66221i
$955$		0			0
$956$	25.4736			0.823875
$957$	−17.7741	−	17.7741i	−0.574556	−	0.574556i
$958$	−7.57878	+	7.57878i	−0.244859	+	0.244859i
$959$	46.2756	−	46.2756i	1.49432	−	1.49432i
$960$		0			0
$961$		−	15.4794i		−	0.499337i
$962$	0.355709	−	0.355709i	0.0114685	−	0.0114685i
$963$	12.9272	−	12.9272i	0.416572	−	0.416572i
$964$	−5.65763	−	5.65763i	−0.182220	−	0.182220i
$965$		0			0
$966$	−51.5804	−	51.5804i	−1.65957	−	1.65957i
$967$		−	24.1990i		−	0.778188i	−0.921198	−	0.389094i	$-0.872788\pi$
$967$		−	24.1990i		−	0.778188i	0.921198	−	0.389094i	$-0.127212\pi$
$968$	−4.31371			−0.138648
$969$	27.4664	−	4.06763i	0.882347	−	0.130671i
$970$		0			0
$971$			23.8896i			0.766653i	0.923613	+	0.383327i	$0.125222\pi$
$971$			23.8896i			0.766653i	−0.923613	+	0.383327i	$0.874778\pi$
$972$	29.8764	+	29.8764i	0.958285	+	0.958285i
$973$	−98.5298			−3.15872
$974$	−19.9761	−	19.9761i	−0.640075	−	0.640075i
$975$		0			0
$976$	2.63995	−	2.63995i	0.0845026	−	0.0845026i
$977$		−	23.3337i		−	0.746510i	−0.927729	−	0.373255i	$-0.878242\pi$
$977$		−	23.3337i		−	0.746510i	0.927729	−	0.373255i	$-0.121758\pi$
$978$		−	2.60073i		−	0.0831623i
$979$	29.2160	−	29.2160i	0.933747	−	0.933747i
$980$		0			0
$981$	−16.1572	−	16.1572i	−0.515861	−	0.515861i
$982$	9.08253			0.289835
$983$	−37.4373	−	37.4373i	−1.19406	−	1.19406i	−0.975916	−	0.218147i	$-0.929999\pi$
$983$	−37.4373	−	37.4373i	−1.19406	−	1.19406i	−0.218147	−	0.975916i	$-0.570001\pi$
$984$		−	25.5928i		−	0.815869i
$985$		0			0
$986$	12.1307	−	1.79649i	0.386319	−	0.0572120i
$987$	−128.059			−4.07615
$988$			0.300367i			0.00955595i
$989$	−2.12453	−	2.12453i	−0.0675561	−	0.0675561i
$990$		0			0
$991$	39.1164	+	39.1164i	1.24257	+	1.24257i	0.958929	+	0.283645i	$0.0915436\pi$
$991$	39.1164	+	39.1164i	1.24257	+	1.24257i	0.283645	+	0.958929i	$0.408456\pi$
$992$	−2.78573	+	2.78573i	−0.0884470	+	0.0884470i
$993$	−24.3811	+	24.3811i	−0.773711	+	0.773711i
$994$		−	12.0052i		−	0.380780i
$995$		0			0
$996$	−20.6010	+	20.6010i	−0.652768	+	0.652768i
$997$	−36.7958	+	36.7958i	−1.16534	+	1.16534i	−0.182045	+	0.983290i	$0.558272\pi$
$997$	−36.7958	+	36.7958i	−1.16534	+	1.16534i	−0.983290	+	0.182045i	$0.941728\pi$
$998$	2.62304	+	2.62304i	0.0830308	+	0.0830308i
$999$	−52.8124			−1.67091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.n.251.4		8
5.2	odd	4		850.2.g.l.149.4		8
5.3	odd	4		850.2.g.i.149.1		8
5.4	even	2		170.2.h.b.81.1	yes	8
15.14	odd	2		1530.2.q.g.1441.1		8
17.4	even	4	inner	850.2.h.n.701.4		8
20.19	odd	2		1360.2.bt.b.81.4		8
85.4	even	4		170.2.h.b.21.1	✓	8
85.9	even	8		2890.2.b.o.2311.1		8
85.19	even	8		2890.2.a.bd.1.1		4
85.38	odd	4		850.2.g.l.599.4		8
85.49	even	8		2890.2.a.be.1.4		4
85.59	even	8		2890.2.b.o.2311.8		8
85.72	odd	4		850.2.g.i.599.1		8
255.89	odd	4		1530.2.q.g.361.1		8
340.259	odd	4		1360.2.bt.b.1041.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.h.b.21.1	✓	8	85.4	even	4
170.2.h.b.81.1	yes	8	5.4	even	2
850.2.g.i.149.1		8	5.3	odd	4
850.2.g.i.599.1		8	85.72	odd	4
850.2.g.l.149.4		8	5.2	odd	4
850.2.g.l.599.4		8	85.38	odd	4
850.2.h.n.251.4		8	1.1	even	1	trivial
850.2.h.n.701.4		8	17.4	even	4	inner
1360.2.bt.b.81.4		8	20.19	odd	2
1360.2.bt.b.1041.4		8	340.259	odd	4
1530.2.q.g.361.1		8	255.89	odd	4
1530.2.q.g.1441.1		8	15.14	odd	2
2890.2.a.bd.1.1		4	85.19	even	8
2890.2.a.be.1.4		4	85.49	even	8
2890.2.b.o.2311.1		8	85.9	even	8
2890.2.b.o.2311.8		8	85.59	even	8

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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(2.31113 + 2.31113i) q^{3} -1.00000 q^{4} +(2.31113 - 2.31113i) q^{6} +(3.26843 - 3.26843i) q^{7} +1.00000i q^{8} +7.68265i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(2.31113 + 2.31113i) q^{3} -1.00000 q^{4} +(2.31113 - 2.31113i) q^{6} +(3.26843 - 3.26843i) q^{7} +1.00000i q^{8} +7.68265i q^{9} +(-1.82843 + 1.82843i) q^{11} +(-2.31113 - 2.31113i) q^{12} +0.145782 q^{13} +(-3.26843 - 3.26843i) q^{14} +1.00000 q^{16} +(3.31113 + 2.45691i) q^{17} +7.68265 q^{18} -2.06038i q^{19} +15.1075 q^{21} +(1.82843 + 1.82843i) q^{22} +(3.41421 - 3.41421i) q^{23} +(-2.31113 + 2.31113i) q^{24} -0.145782i q^{26} +(-10.8222 + 10.8222i) q^{27} +(-3.26843 + 3.26843i) q^{28} +(2.10308 + 2.10308i) q^{29} +(-2.78573 - 2.78573i) q^{31} -1.00000i q^{32} -8.45147 q^{33} +(2.45691 - 3.31113i) q^{34} -7.68265i q^{36} +(2.44000 + 2.44000i) q^{37} -2.06038 q^{38} +(0.336921 + 0.336921i) q^{39} +(-5.53686 + 5.53686i) q^{41} -15.1075i q^{42} -0.622260i q^{43} +(1.82843 - 1.82843i) q^{44} +(-3.41421 - 3.41421i) q^{46} -8.47648 q^{47} +(2.31113 + 2.31113i) q^{48} -14.3653i q^{49} +(1.97421 + 13.3307i) q^{51} -0.145782 q^{52} -6.68265i q^{53} +(10.8222 + 10.8222i) q^{54} +(3.26843 + 3.26843i) q^{56} +(4.76182 - 4.76182i) q^{57} +(2.10308 - 2.10308i) q^{58} +5.71724i q^{59} +(2.63995 - 2.63995i) q^{61} +(-2.78573 + 2.78573i) q^{62} +(25.1102 + 25.1102i) q^{63} -1.00000 q^{64} +8.45147i q^{66} -1.58767 q^{67} +(-3.31113 - 2.45691i) q^{68} +15.7814 q^{69} +(1.83653 + 1.83653i) q^{71} -7.68265 q^{72} +(5.82220 + 5.82220i) q^{73} +(2.44000 - 2.44000i) q^{74} +2.06038i q^{76} +11.9522i q^{77} +(0.336921 - 0.336921i) q^{78} +(3.29344 - 3.29344i) q^{79} -26.9751 q^{81} +(5.53686 + 5.53686i) q^{82} -8.91382i q^{83} -15.1075 q^{84} -0.622260 q^{86} +9.72100i q^{87} +(-1.82843 - 1.82843i) q^{88} -15.9787 q^{89} +(0.476478 - 0.476478i) q^{91} +(-3.41421 + 3.41421i) q^{92} -12.8764i q^{93} +8.47648i q^{94} +(2.31113 - 2.31113i) q^{96} +(-12.5814 - 12.5814i) q^{97} -14.3653 q^{98} +(-14.0472 - 14.0472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 + 4 * q^7	\( 8 q - 8 q^{4} + 4 q^{7} + 8 q^{11} + 12 q^{13} - 4 q^{14} + 8 q^{16} + 8 q^{17} + 28 q^{18} + 16 q^{21} - 8 q^{22} + 16 q^{23} - 12 q^{27} - 4 q^{28} + 24 q^{29} + 4 q^{31} - 16 q^{33} + 12 q^{34} + 20 q^{37} - 20 q^{38} - 4 q^{39} - 8 q^{44} - 16 q^{46} - 20 q^{47} + 4 q^{51} - 12 q^{52} + 12 q^{54} + 4 q^{56} - 40 q^{57} + 24 q^{58} - 16 q^{61} + 4 q^{62} + 64 q^{63} - 8 q^{64} + 16 q^{67} - 8 q^{68} + 8 q^{69} + 4 q^{71} - 28 q^{72} - 28 q^{73} + 20 q^{74} - 4 q^{78} + 8 q^{79} - 8 q^{81} - 16 q^{84} + 32 q^{86} + 8 q^{88} - 44 q^{89} - 44 q^{91} - 16 q^{92} - 20 q^{97} - 48 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^7 + 8 * q^11 + 12 * q^13 - 4 * q^14 + 8 * q^16 + 8 * q^17 + 28 * q^18 + 16 * q^21 - 8 * q^22 + 16 * q^23 - 12 * q^27 - 4 * q^28 + 24 * q^29 + 4 * q^31 - 16 * q^33 + 12 * q^34 + 20 * q^37 - 20 * q^38 - 4 * q^39 - 8 * q^44 - 16 * q^46 - 20 * q^47 + 4 * q^51 - 12 * q^52 + 12 * q^54 + 4 * q^56 - 40 * q^57 + 24 * q^58 - 16 * q^61 + 4 * q^62 + 64 * q^63 - 8 * q^64 + 16 * q^67 - 8 * q^68 + 8 * q^69 + 4 * q^71 - 28 * q^72 - 28 * q^73 + 20 * q^74 - 4 * q^78 + 8 * q^79 - 8 * q^81 - 16 * q^84 + 32 * q^86 + 8 * q^88 - 44 * q^89 - 44 * q^91 - 16 * q^92 - 20 * q^97 - 48 * q^98 - 4 * q^99

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