LMFDB - Embedded newform 850.2.h.l.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:	8.0.17572153600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 80x^{4} - 98x^{3} + 93x^{2} - 50x + 10 $ x^8 - 4x^7 + 18x^6 - 40x^5 + 80x^4 - 98x^3 + 93x^2 - 50*x + 10
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.4
Root			$0.500000 + 1.75824i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.l.701.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(2.25824 + 2.25824i) q^{3} -1.00000 q^{4} +(2.25824 - 2.25824i) q^{6} +(-3.11243 + 3.11243i) q^{7} +1.00000i q^{8} +7.19932i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(2.25824 + 2.25824i) q^{3} -1.00000 q^{4} +(2.25824 - 2.25824i) q^{6} +(-3.11243 + 3.11243i) q^{7} +1.00000i q^{8} +7.19932i q^{9} +(0.512764 - 0.512764i) q^{11} +(-2.25824 - 2.25824i) q^{12} -5.14954 q^{13} +(3.11243 + 3.11243i) q^{14} +1.00000 q^{16} +(2.27037 - 3.44172i) q^{17} +7.19932 q^{18} -0.658581i q^{19} -14.0572 q^{21} +(-0.512764 - 0.512764i) q^{22} +(-4.04978 + 4.04978i) q^{23} +(-2.25824 + 2.25824i) q^{24} +5.14954i q^{26} +(-9.48310 + 9.48310i) q^{27} +(3.11243 - 3.11243i) q^{28} +(5.49096 + 5.49096i) q^{29} +(-3.45385 - 3.45385i) q^{31} -1.00000i q^{32} +2.31589 q^{33} +(-3.44172 - 2.27037i) q^{34} -7.19932i q^{36} +(3.19932 + 3.19932i) q^{37} -0.658581 q^{38} +(-11.6289 - 11.6289i) q^{39} +(4.66230 - 4.66230i) q^{41} +14.0572i q^{42} +7.03297i q^{43} +(-0.512764 + 0.512764i) q^{44} +(4.04978 + 4.04978i) q^{46} +6.90769 q^{47} +(2.25824 + 2.25824i) q^{48} -12.3744i q^{49} +(12.8993 - 2.64518i) q^{51} +5.14954 q^{52} +5.37439i q^{53} +(9.48310 + 9.48310i) q^{54} +(-3.11243 - 3.11243i) q^{56} +(1.48724 - 1.48724i) q^{57} +(5.49096 - 5.49096i) q^{58} +0.733894i q^{59} +(3.36695 - 3.36695i) q^{61} +(-3.45385 + 3.45385i) q^{62} +(-22.4074 - 22.4074i) q^{63} -1.00000 q^{64} -2.31589i q^{66} +2.59180 q^{67} +(-2.27037 + 3.44172i) q^{68} -18.2908 q^{69} +(8.08690 + 8.08690i) q^{71} -7.19932 q^{72} +(1.14582 + 1.14582i) q^{73} +(3.19932 - 3.19932i) q^{74} +0.658581i q^{76} +3.19188i q^{77} +(-11.6289 + 11.6289i) q^{78} +(-6.60338 + 6.60338i) q^{79} -21.2323 q^{81} +(-4.66230 - 4.66230i) q^{82} +5.80685i q^{83} +14.0572 q^{84} +7.03297 q^{86} +24.7998i q^{87} +(0.512764 + 0.512764i) q^{88} -1.55883 q^{89} +(16.0276 - 16.0276i) q^{91} +(4.04978 - 4.04978i) q^{92} -15.5992i q^{93} -6.90769i q^{94} +(2.25824 - 2.25824i) q^{96} +(10.8324 + 10.8324i) q^{97} -12.3744 q^{98} +(3.69155 + 3.69155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^7	$ 8 q - 8 q^{4} - 2 q^{7} + 2 q^{11} - 12 q^{13} + 2 q^{14} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 32 q^{21} - 2 q^{22} - 20 q^{23} - 12 q^{27} + 2 q^{28} + 12 q^{29} - 2 q^{31} + 20 q^{33} - 6 q^{34} - 16 q^{37} - 8 q^{38} - 34 q^{39} + 6 q^{41} - 2 q^{44} + 20 q^{46} + 4 q^{47} + 22 q^{51} + 12 q^{52} + 12 q^{54} - 2 q^{56} + 14 q^{57} + 12 q^{58} + 20 q^{61} - 2 q^{62} - 32 q^{63} - 8 q^{64} - 32 q^{67} + 4 q^{68} + 44 q^{69} + 46 q^{71} - 16 q^{72} + 14 q^{73} - 16 q^{74} - 34 q^{78} + 2 q^{79} - 56 q^{81} - 6 q^{82} + 32 q^{84} - 16 q^{86} + 2 q^{88} - 32 q^{89} - 14 q^{91} + 20 q^{92} + 52 q^{97} - 24 q^{98} - 40 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^7 + 2 * q^11 - 12 * q^13 + 2 * q^14 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 32 * q^21 - 2 * q^22 - 20 * q^23 - 12 * q^27 + 2 * q^28 + 12 * q^29 - 2 * q^31 + 20 * q^33 - 6 * q^34 - 16 * q^37 - 8 * q^38 - 34 * q^39 + 6 * q^41 - 2 * q^44 + 20 * q^46 + 4 * q^47 + 22 * q^51 + 12 * q^52 + 12 * q^54 - 2 * q^56 + 14 * q^57 + 12 * q^58 + 20 * q^61 - 2 * q^62 - 32 * q^63 - 8 * q^64 - 32 * q^67 + 4 * q^68 + 44 * q^69 + 46 * q^71 - 16 * q^72 + 14 * q^73 - 16 * q^74 - 34 * q^78 + 2 * q^79 - 56 * q^81 - 6 * q^82 + 32 * q^84 - 16 * q^86 + 2 * q^88 - 32 * q^89 - 14 * q^91 + 20 * q^92 + 52 * q^97 - 24 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	2.25824	+	2.25824i	1.30380	+	1.30380i	0.925811	+	0.377986i	$0.123383\pi$
$3$	2.25824	+	2.25824i	1.30380	+	1.30380i	0.377986	+	0.925811i	$0.376617\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	2.25824	−	2.25824i	0.921924	−	0.921924i
$7$	−3.11243	+	3.11243i	−1.17639	+	1.17639i	−0.195728	+	0.980658i	$0.562707\pi$
$7$	−3.11243	+	3.11243i	−1.17639	+	1.17639i	−0.980658	+	0.195728i	$0.937293\pi$
$8$			1.00000i			0.353553i
$9$			7.19932i			2.39977i
$10$		0			0
$11$	0.512764	−	0.512764i	0.154604	−	0.154604i	−0.625567	−	0.780171i	$-0.715132\pi$
$11$	0.512764	−	0.512764i	0.154604	−	0.154604i	0.780171	+	0.625567i	$0.215132\pi$
$12$	−2.25824	−	2.25824i	−0.651899	−	0.651899i
$13$	−5.14954			−1.42823			−0.714113	−	0.700031i	$-0.753170\pi$
$13$	−5.14954			−1.42823			−0.714113	+	0.700031i	$0.753170\pi$
$14$	3.11243	+	3.11243i	0.831831	+	0.831831i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.27037	−	3.44172i	0.550646	−	0.834739i
$17$	2.27037	−	3.44172i	0.550646	−	0.834739i
$18$	7.19932			1.69690
$19$		−	0.658581i		−	0.151089i	−0.997142	−	0.0755444i	$-0.975931\pi$
$19$		−	0.658581i		−	0.151089i	0.997142	−	0.0755444i	$-0.0240695\pi$
$20$		0			0
$21$	−14.0572			−3.06754
$22$	−0.512764	−	0.512764i	−0.109322	−	0.109322i
$23$	−4.04978	+	4.04978i	−0.844438	+	0.844438i	−0.989433	−	0.144994i	$-0.953684\pi$
$23$	−4.04978	+	4.04978i	−0.844438	+	0.844438i	0.144994	+	0.989433i	$0.453684\pi$
$24$	−2.25824	+	2.25824i	−0.460962	+	0.460962i
$25$		0			0
$26$			5.14954i			1.00991i
$27$	−9.48310	+	9.48310i	−1.82502	+	1.82502i
$28$	3.11243	−	3.11243i	0.588193	−	0.588193i
$29$	5.49096	+	5.49096i	1.01965	+	1.01965i	0.999803	+	0.0198423i	$0.00631641\pi$
$29$	5.49096	+	5.49096i	1.01965	+	1.01965i	0.0198423	+	0.999803i	$0.493684\pi$
$30$		0			0
$31$	−3.45385	−	3.45385i	−0.620329	−	0.620329i	0.325287	−	0.945615i	$-0.394539\pi$
$31$	−3.45385	−	3.45385i	−0.620329	−	0.620329i	−0.945615	+	0.325287i	$0.894539\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.31589			0.403145
$34$	−3.44172	−	2.27037i	−0.590250	−	0.389366i
$35$		0			0
$36$		−	7.19932i		−	1.19989i
$37$	3.19932	+	3.19932i	0.525966	+	0.525966i	0.919367	−	0.393401i	$-0.128702\pi$
$37$	3.19932	+	3.19932i	0.525966	+	0.525966i	−0.393401	+	0.919367i	$0.628702\pi$
$38$	−0.658581			−0.106836
$39$	−11.6289	−	11.6289i	−1.86212	−	1.86212i
$40$		0			0
$41$	4.66230	−	4.66230i	0.728129	−	0.728129i	−0.242117	−	0.970247i	$-0.577842\pi$
$41$	4.66230	−	4.66230i	0.728129	−	0.728129i	0.970247	+	0.242117i	$0.0778419\pi$
$42$			14.0572i			2.16908i
$43$			7.03297i			1.07252i	0.844053	+	0.536259i	$0.180163\pi$
$43$			7.03297i			1.07252i	−0.844053	+	0.536259i	$0.819837\pi$
$44$	−0.512764	+	0.512764i	−0.0773021	+	0.0773021i
$45$		0			0
$46$	4.04978	+	4.04978i	0.597108	+	0.597108i
$47$	6.90769			1.00759			0.503795	−	0.863823i	$-0.331937\pi$
$47$	6.90769			1.00759			0.503795	+	0.863823i	$0.331937\pi$
$48$	2.25824	+	2.25824i	0.325949	+	0.325949i
$49$		−	12.3744i		−	1.76777i
$50$		0			0
$51$	12.8993	−	2.64518i	1.80626	−	0.370400i
$52$	5.14954			0.714113
$53$			5.37439i			0.738229i	0.929384	+	0.369115i	$0.120339\pi$
$53$			5.37439i			0.738229i	−0.929384	+	0.369115i	$0.879661\pi$
$54$	9.48310	+	9.48310i	1.29049	+	1.29049i
$55$		0			0
$56$	−3.11243	−	3.11243i	−0.415915	−	0.415915i
$57$	1.48724	−	1.48724i	0.196989	−	0.196989i
$58$	5.49096	−	5.49096i	0.720998	−	0.720998i
$59$			0.733894i			0.0955448i	0.998858	+	0.0477724i	$0.0152122\pi$
$59$			0.733894i			0.0955448i	−0.998858	+	0.0477724i	$0.984788\pi$
$60$		0			0
$61$	3.36695	−	3.36695i	0.431093	−	0.431093i	−0.457907	−	0.889000i	$-0.651401\pi$
$61$	3.36695	−	3.36695i	0.431093	−	0.431093i	0.889000	+	0.457907i	$0.151401\pi$
$62$	−3.45385	+	3.45385i	−0.438639	+	0.438639i
$63$	−22.4074	−	22.4074i	−2.82306	−	2.82306i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		−	2.31589i		−	0.285066i
$67$	2.59180			0.316639			0.158319	−	0.987388i	$-0.449392\pi$
$67$	2.59180			0.316639			0.158319	+	0.987388i	$0.449392\pi$
$68$	−2.27037	+	3.44172i	−0.275323	+	0.417369i
$69$	−18.2908			−2.20195
$70$		0			0
$71$	8.08690	+	8.08690i	0.959738	+	0.959738i	0.999220	−	0.0394820i	$-0.0125708\pi$
$71$	8.08690	+	8.08690i	0.959738	+	0.959738i	−0.0394820	+	0.999220i	$0.512571\pi$
$72$	−7.19932			−0.848448
$73$	1.14582	+	1.14582i	0.134108	+	0.134108i	0.770974	−	0.636866i	$-0.219770\pi$
$73$	1.14582	+	1.14582i	0.134108	+	0.134108i	−0.636866	+	0.770974i	$0.719770\pi$
$74$	3.19932	−	3.19932i	0.371914	−	0.371914i
$75$		0			0
$76$			0.658581i			0.0755444i
$77$			3.19188i			0.363748i
$78$	−11.6289	+	11.6289i	−1.31672	+	1.31672i
$79$	−6.60338	+	6.60338i	−0.742939	+	0.742939i	−0.973142	−	0.230204i	$-0.926061\pi$
$79$	−6.60338	+	6.60338i	−0.742939	+	0.742939i	0.230204	+	0.973142i	$0.426061\pi$
$80$		0			0
$81$	−21.2323			−2.35914
$82$	−4.66230	−	4.66230i	−0.514865	−	0.514865i
$83$			5.80685i			0.637385i	0.947858	+	0.318692i	$0.103244\pi$
$83$			5.80685i			0.637385i	−0.947858	+	0.318692i	$0.896756\pi$
$84$	14.0572			1.53377
$85$		0			0
$86$	7.03297			0.758385
$87$			24.7998i			2.65882i
$88$	0.512764	+	0.512764i	0.0546608	+	0.0546608i
$89$	−1.55883			−0.165235			−0.0826176	−	0.996581i	$-0.526328\pi$
$89$	−1.55883			−0.165235			−0.0826176	+	0.996581i	$0.526328\pi$
$90$		0			0
$91$	16.0276	−	16.0276i	1.68014	−	1.68014i
$92$	4.04978	−	4.04978i	0.422219	−	0.422219i
$93$		−	15.5992i		−	1.61757i
$94$		−	6.90769i		−	0.712474i
$95$		0			0
$96$	2.25824	−	2.25824i	0.230481	−	0.230481i
$97$	10.8324	+	10.8324i	1.09986	+	1.09986i	0.994426	+	0.105435i	$0.0336235\pi$
$97$	10.8324	+	10.8324i	1.09986	+	1.09986i	0.105435	+	0.994426i	$0.466376\pi$
$98$	−12.3744			−1.25000
$99$	3.69155	+	3.69155i	0.371015	+	0.371015i
$100$		0			0
$101$	−11.5992			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$101$	−11.5992			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$102$	−2.64518	−	12.8993i	−0.261912	−	1.27722i
$103$	1.44244			0.142128			0.0710641	−	0.997472i	$-0.477360\pi$
$103$	1.44244			0.142128			0.0710641	+	0.997472i	$0.477360\pi$
$104$		−	5.14954i		−	0.504954i
$105$		0			0
$106$	5.37439			0.522007
$107$	−3.42459	−	3.42459i	−0.331068	−	0.331068i	0.521924	−	0.852992i	$-0.325214\pi$
$107$	−3.42459	−	3.42459i	−0.331068	−	0.331068i	−0.852992	+	0.521924i	$0.825214\pi$
$108$	9.48310	−	9.48310i	0.912511	−	0.912511i
$109$	14.0585	−	14.0585i	1.34656	−	1.34656i	0.457192	−	0.889368i	$-0.348855\pi$
$109$	14.0585	−	14.0585i	1.34656	−	1.34656i	0.889368	−	0.457192i	$-0.151145\pi$
$110$		0			0
$111$			14.4497i			1.37151i
$112$	−3.11243	+	3.11243i	−0.294097	+	0.294097i
$113$	10.1788	−	10.1788i	0.957540	−	0.957540i	−0.0415946	−	0.999135i	$-0.513244\pi$
$113$	10.1788	−	10.1788i	0.957540	−	0.957540i	0.999135	+	0.0415946i	$0.0132438\pi$
$114$	−1.48724	−	1.48724i	−0.139292	−	0.139292i
$115$		0			0
$116$	−5.49096	−	5.49096i	−0.509823	−	0.509823i
$117$		−	37.0732i		−	3.42742i
$118$	0.733894			0.0675604
$119$	3.64572	+	17.7785i	0.334203	+	1.62975i
$120$		0			0
$121$			10.4741i			0.952195i
$122$	−3.36695	−	3.36695i	−0.304829	−	0.304829i
$123$	21.0572			1.89867
$124$	3.45385	+	3.45385i	0.310164	+	0.310164i
$125$		0			0
$126$	−22.4074	+	22.4074i	−1.99621	+	1.99621i
$127$		−	4.39865i		−	0.390317i	−0.980772	−	0.195158i	$-0.937478\pi$
$127$		−	4.39865i		−	0.390317i	0.980772	−	0.195158i	$-0.0625221\pi$
$128$			1.00000i			0.0883883i
$129$	−15.8822	+	15.8822i	−1.39835	+	1.39835i
$130$		0			0
$131$	−3.42959	−	3.42959i	−0.299645	−	0.299645i	0.541230	−	0.840875i	$-0.317959\pi$
$131$	−3.42959	−	3.42959i	−0.299645	−	0.299645i	−0.840875	+	0.541230i	$0.817959\pi$
$132$	−2.31589			−0.201572
$133$	2.04978	+	2.04978i	0.177739	+	0.177739i
$134$		−	2.59180i		−	0.223897i
$135$		0			0
$136$	3.44172	+	2.27037i	0.295125	+	0.194683i
$137$	7.12528			0.608754			0.304377	−	0.952552i	$-0.401552\pi$
$137$	7.12528			0.608754			0.304377	+	0.952552i	$0.401552\pi$
$138$			18.2908i			1.55702i
$139$	0.691972	+	0.691972i	0.0586923	+	0.0586923i	0.735844	−	0.677151i	$-0.236786\pi$
$139$	0.691972	+	0.691972i	0.0586923	+	0.0586923i	−0.677151	+	0.735844i	$0.736786\pi$
$140$		0			0
$141$	15.5992	+	15.5992i	1.31369	+	1.31369i
$142$	8.08690	−	8.08690i	0.678637	−	0.678637i
$143$	−2.64050	+	2.64050i	−0.220810	+	0.220810i
$144$			7.19932i			0.599944i
$145$		0			0
$146$	1.14582	−	1.14582i	0.0948285	−	0.0948285i
$147$	27.9444	−	27.9444i	2.30481	−	2.30481i
$148$	−3.19932	−	3.19932i	−0.262983	−	0.262983i
$149$	14.2079			1.16395			0.581976	−	0.813206i	$-0.302280\pi$
$149$	14.2079			1.16395			0.581976	+	0.813206i	$0.302280\pi$
$150$		0			0
$151$			12.2249i			0.994844i	0.867509	+	0.497422i	$0.165720\pi$
$151$			12.2249i			0.994844i	−0.867509	+	0.497422i	$0.834280\pi$
$152$	0.658581			0.0534180
$153$	24.7780	+	16.3451i	2.00319	+	1.32143i
$154$	3.19188			0.257209
$155$		0			0
$156$	11.6289	+	11.6289i	0.931058	+	0.931058i
$157$	−11.6735			−0.931644			−0.465822	−	0.884878i	$-0.654241\pi$
$157$	−11.6735			−0.931644			−0.465822	+	0.884878i	$0.654241\pi$
$158$	6.60338	+	6.60338i	0.525337	+	0.525337i
$159$	−12.1367	+	12.1367i	−0.962502	+	0.962502i
$160$		0			0
$161$		−	25.2093i		−	1.98677i
$162$			21.2323i			1.66817i
$163$	−14.7747	+	14.7747i	−1.15725	+	1.15725i	−0.172181	+	0.985065i	$0.555081\pi$
$163$	−14.7747	+	14.7747i	−1.15725	+	1.15725i	−0.985065	+	0.172181i	$0.944919\pi$
$164$	−4.66230	+	4.66230i	−0.364065	+	0.364065i
$165$		0			0
$166$	5.80685			0.450699
$167$	−1.37439	−	1.37439i	−0.106354	−	0.106354i	0.651928	−	0.758281i	$-0.273961\pi$
$167$	−1.37439	−	1.37439i	−0.106354	−	0.106354i	−0.758281	+	0.651928i	$0.773961\pi$
$168$		−	14.0572i		−	1.08454i
$169$	13.5178			1.03983
$170$		0			0
$171$	4.74134			0.362579
$172$		−	7.03297i		−	0.536259i
$173$	−14.0572	−	14.0572i	−1.06875	−	1.06875i	−0.997455	−	0.0712962i	$-0.977286\pi$
$173$	−14.0572	−	14.0572i	−1.06875	−	1.06875i	−0.0712962	−	0.997455i	$-0.522714\pi$
$174$	24.7998			1.88007
$175$		0			0
$176$	0.512764	−	0.512764i	0.0386510	−	0.0386510i
$177$	−1.65731	+	1.65731i	−0.124571	+	0.124571i
$178$			1.55883i			0.116839i
$179$		−	5.64050i		−	0.421591i	−0.977530	−	0.210795i	$-0.932395\pi$
$179$		−	5.64050i		−	0.421591i	0.977530	−	0.210795i	$-0.0676054\pi$
$180$		0			0
$181$	2.75834	−	2.75834i	0.205025	−	0.205025i	−0.597124	−	0.802149i	$-0.703690\pi$
$181$	2.75834	−	2.75834i	0.205025	−	0.205025i	0.802149	+	0.597124i	$0.203690\pi$
$182$	−16.0276	−	16.0276i	−1.18804	−	1.18804i
$183$	15.2068			1.12412
$184$	−4.04978	−	4.04978i	−0.298554	−	0.298554i
$185$		0			0
$186$	−15.5992			−1.14379
$187$	−0.600623	−	2.92895i	−0.0439219	−	0.214186i
$188$	−6.90769			−0.503795
$189$		−	59.0309i		−	4.29386i
$190$		0			0
$191$	−19.8921			−1.43935			−0.719673	−	0.694313i	$-0.755708\pi$
$191$	−19.8921			−1.43935			−0.719673	+	0.694313i	$0.755708\pi$
$192$	−2.25824	−	2.25824i	−0.162975	−	0.162975i
$193$	14.6528	−	14.6528i	1.05473	−	1.05473i	0.0563150	−	0.998413i	$-0.482065\pi$
$193$	14.6528	−	14.6528i	1.05473	−	1.05473i	0.998413	−	0.0563150i	$-0.0179351\pi$
$194$	10.8324	−	10.8324i	0.777719	−	0.777719i
$195$		0			0
$196$			12.3744i			0.883885i
$197$	5.36695	−	5.36695i	0.382379	−	0.382379i	−0.489580	−	0.871959i	$-0.662850\pi$
$197$	5.36695	−	5.36695i	0.382379	−	0.382379i	0.871959	+	0.489580i	$0.162850\pi$
$198$	3.69155	−	3.69155i	0.262347	−	0.262347i
$199$	2.97574	+	2.97574i	0.210945	+	0.210945i	0.804669	−	0.593724i	$-0.202343\pi$
$199$	2.97574	+	2.97574i	0.210945	+	0.210945i	−0.593724	+	0.804669i	$0.702343\pi$
$200$		0			0
$201$	5.85291	+	5.85291i	0.412833	+	0.412833i
$202$			11.5992i			0.816120i
$203$	−34.1804			−2.39899
$204$	−12.8993	+	2.64518i	−0.903131	+	0.185200i
$205$		0			0
$206$		−	1.44244i		−	0.100500i
$207$	−29.1557	−	29.1557i	−2.02646	−	2.02646i
$208$	−5.14954			−0.357056
$209$	−0.337697	−	0.337697i	−0.0233590	−	0.0233590i
$210$		0			0
$211$	14.6824	−	14.6824i	1.01078	−	1.01078i	0.0108382	−	0.999941i	$-0.496550\pi$
$211$	14.6824	−	14.6824i	1.01078	−	1.01078i	0.999941	−	0.0108382i	$-0.00344997\pi$
$212$		−	5.37439i		−	0.369115i
$213$			36.5244i			2.50261i
$214$	−3.42459	+	3.42459i	−0.234100	+	0.234100i
$215$		0			0
$216$	−9.48310	−	9.48310i	−0.645243	−	0.645243i
$217$	21.4997			1.45949
$218$	−14.0585	−	14.0585i	−0.952162	−	0.952162i
$219$			5.17507i			0.349699i
$220$		0			0
$221$	−11.6914	+	17.7233i	−0.786447	+	1.19220i
$222$	14.4497			0.969801
$223$		−	5.19188i		−	0.347674i	−0.984774	−	0.173837i	$-0.944383\pi$
$223$		−	5.19188i		−	0.347674i	0.984774	−	0.173837i	$-0.0556166\pi$
$224$	3.11243	+	3.11243i	0.207958	+	0.207958i
$225$		0			0
$226$	−10.1788	−	10.1788i	−0.677083	−	0.677083i
$227$	−11.4358	+	11.4358i	−0.759018	+	0.759018i	−0.976144	−	0.217126i	$-0.930332\pi$
$227$	−11.4358	+	11.4358i	−0.759018	+	0.759018i	0.217126	+	0.976144i	$0.430332\pi$
$228$	−1.48724	+	1.48724i	−0.0984946	+	0.0984946i
$229$		−	10.7169i		−	0.708192i	−0.935209	−	0.354096i	$-0.884789\pi$
$229$		−	10.7169i		−	0.708192i	0.935209	−	0.354096i	$-0.115211\pi$
$230$		0			0
$231$	−7.20804	+	7.20804i	−0.474254	+	0.474254i
$232$	−5.49096	+	5.49096i	−0.360499	+	0.360499i
$233$	−10.4254	−	10.4254i	−0.682994	−	0.682994i	0.277680	−	0.960674i	$-0.410435\pi$
$233$	−10.4254	−	10.4254i	−0.682994	−	0.682994i	−0.960674	+	0.277680i	$0.910435\pi$
$234$	−37.0732			−2.42355
$235$		0			0
$236$		−	0.733894i		−	0.0477724i
$237$	−29.8241			−1.93728
$238$	17.7785	−	3.64572i	1.15241	−	0.236317i
$239$	6.96703			0.450660			0.225330	−	0.974283i	$-0.427654\pi$
$239$	6.96703			0.450660			0.225330	+	0.974283i	$0.427654\pi$
$240$		0			0
$241$	−18.9189	−	18.9189i	−1.21867	−	1.21867i	−0.968098	−	0.250573i	$-0.919381\pi$
$241$	−18.9189	−	18.9189i	−1.21867	−	1.21867i	−0.250573	−	0.968098i	$-0.580619\pi$
$242$	10.4741			0.673304
$243$	−19.4984	−	19.4984i	−1.25082	−	1.25082i
$244$	−3.36695	+	3.36695i	−0.215547	+	0.215547i
$245$		0			0
$246$		−	21.0572i		−	1.34256i
$247$			3.39139i			0.215789i
$248$	3.45385	−	3.45385i	0.219319	−	0.219319i
$249$	−13.1133	+	13.1133i	−0.831020	+	0.831020i
$250$		0			0
$251$	1.85791			0.117270			0.0586350	−	0.998279i	$-0.481325\pi$
$251$	1.85791			0.117270			0.0586350	+	0.998279i	$0.481325\pi$
$252$	22.4074	+	22.4074i	1.41153	+	1.41153i
$253$			4.15317i			0.261107i
$254$	−4.39865			−0.275996
$255$		0			0
$256$	1.00000			0.0625000
$257$			13.9066i			0.867470i	0.901040	+	0.433735i	$0.142805\pi$
$257$			13.9066i			0.867470i	−0.901040	+	0.433735i	$0.857195\pi$
$258$	15.8822	+	15.8822i	0.988780	+	0.988780i
$259$	−19.9153			−1.23748
$260$		0			0
$261$	−39.5312	+	39.5312i	−2.44692	+	2.44692i
$262$	−3.42959	+	3.42959i	−0.211881	+	0.211881i
$263$		−	10.9334i		−	0.674183i	−0.941472	−	0.337091i	$-0.890557\pi$
$263$		−	10.9334i		−	0.674183i	0.941472	−	0.337091i	$-0.109443\pi$
$264$			2.31589i			0.142533i
$265$		0			0
$266$	2.04978	−	2.04978i	0.125680	−	0.125680i
$267$	−3.52021	−	3.52021i	−0.215433	−	0.215433i
$268$	−2.59180			−0.158319
$269$	−1.43373	−	1.43373i	−0.0874160	−	0.0874160i	0.662047	−	0.749463i	$-0.269688\pi$
$269$	−1.43373	−	1.43373i	−0.0874160	−	0.0874160i	−0.749463	+	0.662047i	$0.769688\pi$
$270$		0			0
$271$	20.9077			1.27005			0.635026	−	0.772491i	$-0.280989\pi$
$271$	20.9077			1.27005			0.635026	+	0.772491i	$0.280989\pi$
$272$	2.27037	−	3.44172i	0.137661	−	0.208685i
$273$	72.3883			4.38114
$274$		−	7.12528i		−	0.430454i
$275$		0			0
$276$	18.2908			1.10098
$277$	−8.34142	−	8.34142i	−0.501187	−	0.501187i	0.410619	−	0.911807i	$-0.365312\pi$
$277$	−8.34142	−	8.34142i	−0.501187	−	0.501187i	−0.911807	+	0.410619i	$0.865312\pi$
$278$	0.691972	−	0.691972i	0.0415017	−	0.0415017i
$279$	24.8654	−	24.8654i	1.48865	−	1.48865i
$280$		0			0
$281$		−	8.95003i		−	0.533914i	−0.963708	−	0.266957i	$-0.913982\pi$
$281$		−	8.95003i		−	0.533914i	0.963708	−	0.266957i	$-0.0860182\pi$
$282$	15.5992	−	15.5992i	0.928921	−	0.928921i
$283$	21.5774	−	21.5774i	1.28265	−	1.28265i	0.343489	−	0.939157i	$-0.388391\pi$
$283$	21.5774	−	21.5774i	1.28265	−	1.28265i	0.939157	−	0.343489i	$-0.111609\pi$
$284$	−8.08690	−	8.08690i	−0.479869	−	0.479869i
$285$		0			0
$286$	2.64050	+	2.64050i	0.156136	+	0.156136i
$287$			29.0221i			1.71312i
$288$	7.19932			0.424224
$289$	−6.69083	−	15.6280i	−0.393578	−	0.919291i
$290$		0			0
$291$			48.9243i			2.86799i
$292$	−1.14582	−	1.14582i	−0.0670539	−	0.0670539i
$293$	−17.1811			−1.00373			−0.501864	−	0.864947i	$-0.667352\pi$
$293$	−17.1811			−1.00373			−0.501864	+	0.864947i	$0.667352\pi$
$294$	−27.9444	−	27.9444i	−1.62975	−	1.62975i
$295$		0			0
$296$	−3.19932	+	3.19932i	−0.185957	+	0.185957i
$297$			9.72518i			0.564312i
$298$		−	14.2079i		−	0.823039i
$299$	20.8545	−	20.8545i	1.20605	−	1.20605i
$300$		0			0
$301$	−21.8896	−	21.8896i	−1.26170	−	1.26170i
$302$	12.2249			0.703461
$303$	−26.1939	−	26.1939i	−1.50480	−	1.50480i
$304$		−	0.658581i		−	0.0377722i
$305$		0			0
$306$	16.3451	−	24.7780i	0.934390	−	1.41647i
$307$	18.3002			1.04445			0.522223	−	0.852809i	$-0.325103\pi$
$307$	18.3002			1.04445			0.522223	+	0.852809i	$0.325103\pi$
$308$		−	3.19188i		−	0.181874i
$309$	3.25739	+	3.25739i	0.185306	+	0.185306i
$310$		0			0
$311$	4.31302	+	4.31302i	0.244569	+	0.244569i	0.818737	−	0.574168i	$-0.194674\pi$
$311$	4.31302	+	4.31302i	0.244569	+	0.244569i	−0.574168	+	0.818737i	$0.694674\pi$
$312$	11.6289	−	11.6289i	0.658358	−	0.658358i
$313$	−23.2908	+	23.2908i	−1.31647	+	1.31647i	−0.399926	+	0.916547i	$0.630964\pi$
$313$	−23.2908	+	23.2908i	−1.31647	+	1.31647i	−0.916547	+	0.399926i	$0.869036\pi$
$314$			11.6735i			0.658772i
$315$		0			0
$316$	6.60338	−	6.60338i	0.371469	−	0.371469i
$317$	−5.93195	+	5.93195i	−0.333171	+	0.333171i	−0.853790	−	0.520618i	$-0.825701\pi$
$317$	−5.93195	+	5.93195i	−0.333171	+	0.333171i	0.520618	+	0.853790i	$0.325701\pi$
$318$	12.1367	+	12.1367i	0.680591	+	0.680591i
$319$	5.63113			0.315283
$320$		0			0
$321$		−	15.4671i		−	0.863291i
$322$	−25.2093			−1.40486
$323$	−2.26665	−	1.49522i	−0.126120	−	0.0831965i
$324$	21.2323			1.17957
$325$		0			0
$326$	14.7747	+	14.7747i	0.818297	+	0.818297i
$327$	63.4950			3.51128
$328$	4.66230	+	4.66230i	0.257433	+	0.257433i
$329$	−21.4997	+	21.4997i	−1.18532	+	1.18532i
$330$		0			0
$331$		−	9.29781i		−	0.511054i	−0.966802	−	0.255527i	$-0.917751\pi$
$331$		−	9.29781i		−	0.511054i	0.966802	−	0.255527i	$-0.0822489\pi$
$332$		−	5.80685i		−	0.318692i
$333$	−23.0330	+	23.0330i	−1.26220	+	1.26220i
$334$	−1.37439	+	1.37439i	−0.0752034	+	0.0752034i
$335$		0			0
$336$	−14.0572			−0.766885
$337$	−13.5202	−	13.5202i	−0.736493	−	0.736493i	0.235405	−	0.971897i	$-0.424358\pi$
$337$	−13.5202	−	13.5202i	−0.736493	−	0.736493i	−0.971897	+	0.235405i	$0.924358\pi$
$338$		−	13.5178i		−	0.735269i
$339$	45.9724			2.49688
$340$		0			0
$341$	−3.54201			−0.191811
$342$		−	4.74134i		−	0.256382i
$343$	16.7274	+	16.7274i	0.903194	+	0.903194i
$344$	−7.03297			−0.379192
$345$		0			0
$346$	−14.0572	+	14.0572i	−0.755721	+	0.755721i
$347$	9.72367	−	9.72367i	0.521994	−	0.521994i	−0.396179	−	0.918173i	$-0.629664\pi$
$347$	9.72367	−	9.72367i	0.521994	−	0.521994i	0.918173	+	0.396179i	$0.129664\pi$
$348$		−	24.7998i		−	1.32941i
$349$			32.1083i			1.71872i	0.511374	+	0.859359i	$0.329137\pi$
$349$			32.1083i			1.71872i	−0.511374	+	0.859359i	$0.670863\pi$
$350$		0			0
$351$	48.8336	−	48.8336i	2.60654	−	2.60654i
$352$	−0.512764	−	0.512764i	−0.0273304	−	0.0273304i
$353$	−18.1825			−0.967757			−0.483879	−	0.875135i	$-0.660772\pi$
$353$	−18.1825			−0.967757			−0.483879	+	0.875135i	$0.660772\pi$
$354$	1.65731	+	1.65731i	0.0880850	+	0.0880850i
$355$		0			0
$356$	1.55883			0.0826176
$357$	−31.9151	+	48.3810i	−1.68913	+	2.56059i
$358$	−5.64050			−0.298110
$359$			9.60542i			0.506955i	0.967341	+	0.253477i	$0.0815743\pi$
$359$			9.60542i			0.506955i	−0.967341	+	0.253477i	$0.918426\pi$
$360$		0			0
$361$	18.5663			0.977172
$362$	−2.75834	−	2.75834i	−0.144975	−	0.144975i
$363$	−23.6532	+	23.6532i	−1.24147	+	1.24147i
$364$	−16.0276	+	16.0276i	−0.840072	+	0.840072i
$365$		0			0
$366$		−	15.2068i		−	0.794871i
$367$	−9.06264	+	9.06264i	−0.473066	+	0.473066i	−0.902905	−	0.429839i	$-0.858570\pi$
$367$	−9.06264	+	9.06264i	−0.473066	+	0.473066i	0.429839	+	0.902905i	$0.358570\pi$
$368$	−4.04978	+	4.04978i	−0.211110	+	0.211110i
$369$	33.5654	+	33.5654i	1.74735	+	1.74735i
$370$		0			0
$371$	−16.7274	−	16.7274i	−0.868443	−	0.868443i
$372$			15.5992i			0.808783i
$373$	25.9830			1.34535			0.672674	−	0.739939i	$-0.265145\pi$
$373$	25.9830			1.34535			0.672674	+	0.739939i	$0.265145\pi$
$374$	−2.92895	+	0.600623i	−0.151453	+	0.0310575i
$375$		0			0
$376$			6.90769i			0.356237i
$377$	−28.2759	−	28.2759i	−1.45628	−	1.45628i
$378$	−59.0309			−3.03622
$379$	4.73348	+	4.73348i	0.243142	+	0.243142i	0.818149	−	0.575007i	$-0.195000\pi$
$379$	4.73348	+	4.73348i	0.243142	+	0.243142i	−0.575007	+	0.818149i	$0.695000\pi$
$380$		0			0
$381$	9.93322	−	9.93322i	0.508894	−	0.508894i
$382$			19.8921i			1.01777i
$383$			8.22231i			0.420140i	0.977686	+	0.210070i	$0.0673693\pi$
$383$			8.22231i			0.420140i	−0.977686	+	0.210070i	$0.932631\pi$
$384$	−2.25824	+	2.25824i	−0.115240	+	0.115240i
$385$		0			0
$386$	−14.6528	−	14.6528i	−0.745805	−	0.745805i
$387$	−50.6327			−2.57380
$388$	−10.8324	−	10.8324i	−0.549931	−	0.549931i
$389$			36.0320i			1.82689i	0.406960	+	0.913446i	$0.366589\pi$
$389$			36.0320i			1.82689i	−0.406960	+	0.913446i	$0.633411\pi$
$390$		0			0
$391$	4.74369	+	23.1327i	0.239899	+	1.16987i
$392$	12.3744			0.625001
$393$		−	15.4897i		−	0.781351i
$394$	−5.36695	−	5.36695i	−0.270383	−	0.270383i
$395$		0			0
$396$	−3.69155	−	3.69155i	−0.185508	−	0.185508i
$397$	19.6162	−	19.6162i	0.984511	−	0.984511i	−0.0153709	−	0.999882i	$-0.504893\pi$
$397$	19.6162	−	19.6162i	0.984511	−	0.984511i	0.999882	+	0.0153709i	$0.00489292\pi$
$398$	2.97574	−	2.97574i	0.149161	−	0.149161i
$399$			9.25782i			0.463471i
$400$		0			0
$401$	2.46171	−	2.46171i	0.122932	−	0.122932i	−0.642964	−	0.765896i	$-0.722296\pi$
$401$	2.46171	−	2.46171i	0.122932	−	0.122932i	0.765896	+	0.642964i	$0.222296\pi$
$402$	5.85291	−	5.85291i	0.291917	−	0.291917i
$403$	17.7857	+	17.7857i	0.885969	+	0.885969i
$404$	11.5992			0.577084
$405$		0			0
$406$			34.1804i			1.69634i
$407$	3.28100			0.162633
$408$	2.64518	+	12.8993i	0.130956	+	0.638610i
$409$	10.6599			0.527096			0.263548	−	0.964646i	$-0.415107\pi$
$409$	10.6599			0.527096			0.263548	+	0.964646i	$0.415107\pi$
$410$		0			0
$411$	16.0906	+	16.0906i	0.793692	+	0.793692i
$412$	−1.44244			−0.0710641
$413$	−2.28419	−	2.28419i	−0.112398	−	0.112398i
$414$	−29.1557	+	29.1557i	−1.43293	+	1.43293i
$415$		0			0
$416$			5.14954i			0.252477i
$417$			3.12528i			0.153046i
$418$	−0.337697	+	0.337697i	−0.0165173	+	0.0165173i
$419$	14.8278	−	14.8278i	0.724386	−	0.724386i	−0.245109	−	0.969495i	$-0.578824\pi$
$419$	14.8278	−	14.8278i	0.724386	−	0.724386i	0.969495	+	0.245109i	$0.0788238\pi$
$420$		0			0
$421$	7.30016			0.355788			0.177894	−	0.984050i	$-0.443072\pi$
$421$	7.30016			0.355788			0.177894	+	0.984050i	$0.443072\pi$
$422$	−14.6824	−	14.6824i	−0.714729	−	0.714729i
$423$			49.7307i			2.41799i
$424$	−5.37439			−0.261004
$425$		0			0
$426$	36.5244			1.76961
$427$			20.9587i			1.01426i
$428$	3.42459	+	3.42459i	0.165534	+	0.165534i
$429$	−11.9258			−0.575782
$430$		0			0
$431$	−7.91183	+	7.91183i	−0.381099	+	0.381099i	−0.871498	−	0.490399i	$-0.836851\pi$
$431$	−7.91183	+	7.91183i	−0.381099	+	0.381099i	0.490399	+	0.871498i	$0.336851\pi$
$432$	−9.48310	+	9.48310i	−0.456256	+	0.456256i
$433$			7.86535i			0.377985i	0.981979	+	0.188992i	$0.0605221\pi$
$433$			7.86535i			0.377985i	−0.981979	+	0.188992i	$0.939478\pi$
$434$		−	21.4997i		−	1.03202i
$435$		0			0
$436$	−14.0585	+	14.0585i	−0.673280	+	0.673280i
$437$	2.66711	+	2.66711i	0.127585	+	0.127585i
$438$	5.17507			0.247274
$439$	−9.58040	−	9.58040i	−0.457247	−	0.457247i	0.440503	−	0.897751i	$-0.354800\pi$
$439$	−9.58040	−	9.58040i	−0.457247	−	0.457247i	−0.897751	+	0.440503i	$0.854800\pi$
$440$		0			0
$441$	89.0873			4.24225
$442$	17.7233	+	11.6914i	0.843009	+	0.556102i
$443$	29.5994			1.40631			0.703156	−	0.711036i	$-0.251774\pi$
$443$	29.5994			1.40631			0.703156	+	0.711036i	$0.251774\pi$
$444$		−	14.4497i		−	0.685753i
$445$		0			0
$446$	−5.19188			−0.245843
$447$	32.0848	+	32.0848i	1.51756	+	1.51756i
$448$	3.11243	−	3.11243i	0.147048	−	0.147048i
$449$	−5.81184	+	5.81184i	−0.274278	+	0.274278i	−0.830820	−	0.556542i	$-0.812128\pi$
$449$	−5.81184	+	5.81184i	−0.274278	+	0.274278i	0.556542	+	0.830820i	$0.312128\pi$
$450$		0			0
$451$		−	4.78132i		−	0.225144i
$452$	−10.1788	+	10.1788i	−0.478770	+	0.478770i
$453$	−27.6067	+	27.6067i	−1.29708	+	1.29708i
$454$	11.4358	+	11.4358i	0.536707	+	0.536707i
$455$		0			0
$456$	1.48724	+	1.48724i	0.0696462	+	0.0696462i
$457$			6.79221i			0.317726i	0.987301	+	0.158863i	$0.0507828\pi$
$457$			6.79221i			0.317726i	−0.987301	+	0.158863i	$0.949217\pi$
$458$	−10.7169			−0.500768
$459$	11.1080	+	54.1683i	0.518476	+	2.52836i
$460$		0			0
$461$		−	1.36822i		−	0.0637243i	−0.999492	−	0.0318621i	$-0.989856\pi$
$461$		−	1.36822i		−	0.0637243i	0.999492	−	0.0318621i	$-0.0101437\pi$
$462$	7.20804	+	7.20804i	0.335348	+	0.335348i
$463$	−0.933403			−0.0433789			−0.0216895	−	0.999765i	$-0.506905\pi$
$463$	−0.933403			−0.0433789			−0.0216895	+	0.999765i	$0.506905\pi$
$464$	5.49096	+	5.49096i	0.254911	+	0.254911i
$465$		0			0
$466$	−10.4254	+	10.4254i	−0.482950	+	0.482950i
$467$		−	12.7256i		−	0.588871i	−0.955671	−	0.294436i	$-0.904868\pi$
$467$		−	12.7256i		−	0.588871i	0.955671	−	0.294436i	$-0.0951316\pi$
$468$			37.0732i			1.71371i
$469$	−8.06678	+	8.06678i	−0.372489	+	0.372489i
$470$		0			0
$471$	−26.3615	−	26.3615i	−1.21468	−	1.21468i
$472$	−0.733894			−0.0337802
$473$	3.60625	+	3.60625i	0.165816	+	0.165816i
$474$			29.8241i			1.36987i
$475$		0			0
$476$	−3.64572	−	17.7785i	−0.167102	−	0.814874i
$477$	−38.6920			−1.77158
$478$		−	6.96703i		−	0.318664i
$479$	4.51031	+	4.51031i	0.206081	+	0.206081i	0.802600	−	0.596518i	$-0.203450\pi$
$479$	4.51031	+	4.51031i	0.206081	+	0.206081i	−0.596518	+	0.802600i	$0.703450\pi$
$480$		0			0
$481$	−16.4750	−	16.4750i	−0.751197	−	0.751197i
$482$	−18.9189	+	18.9189i	−0.861730	+	0.861730i
$483$	56.9288	−	56.9288i	2.59035	−	2.59035i
$484$		−	10.4741i		−	0.476098i
$485$		0			0
$486$	−19.4984	+	19.4984i	−0.884466	+	0.884466i
$487$	10.9575	−	10.9575i	0.496531	−	0.496531i	−0.413826	−	0.910356i	$-0.635808\pi$
$487$	10.9575	−	10.9575i	0.496531	−	0.496531i	0.910356	+	0.413826i	$0.135808\pi$
$488$	3.36695	+	3.36695i	0.152415	+	0.152415i
$489$	−66.7299			−3.01763
$490$		0			0
$491$			31.0840i			1.40280i	0.712767	+	0.701401i	$0.247442\pi$
$491$			31.0840i			1.40280i	−0.712767	+	0.701401i	$0.752558\pi$
$492$	−21.0572			−0.949333
$493$	31.3648	−	6.43181i	1.41260	−	0.289674i
$494$	3.39139			0.152586
$495$		0			0
$496$	−3.45385	−	3.45385i	−0.155082	−	0.155082i
$497$	−50.3397			−2.25805
$498$	13.1133	+	13.1133i	0.587620	+	0.587620i
$499$	−17.9473	+	17.9473i	−0.803434	+	0.803434i	−0.983631	−	0.180197i	$-0.942326\pi$
$499$	−17.9473	+	17.9473i	−0.803434	+	0.803434i	0.180197	+	0.983631i	$0.442326\pi$
$500$		0			0
$501$		−	6.20742i		−	0.277327i
$502$		−	1.85791i		−	0.0829224i
$503$	12.7426	−	12.7426i	0.568165	−	0.568165i	−0.363449	−	0.931614i	$-0.618401\pi$
$503$	12.7426	−	12.7426i	0.568165	−	0.568165i	0.931614	+	0.363449i	$0.118401\pi$
$504$	22.4074	−	22.4074i	0.998103	−	0.998103i
$505$		0			0
$506$	4.15317			0.184631
$507$	30.5264	+	30.5264i	1.35572	+	1.35572i
$508$			4.39865i			0.195158i
$509$	15.2238			0.674782			0.337391	−	0.941365i	$-0.390456\pi$
$509$	15.2238			0.674782			0.337391	+	0.941365i	$0.390456\pi$
$510$		0			0
$511$	−7.13254			−0.315525
$512$		−	1.00000i		−	0.0441942i
$513$	6.24539	+	6.24539i	0.275741	+	0.275741i
$514$	13.9066			0.613394
$515$		0			0
$516$	15.8822	−	15.8822i	0.699173	−	0.699173i
$517$	3.54201	−	3.54201i	0.155778	−	0.155778i
$518$			19.9153i			0.875029i
$519$		−	63.4893i		−	2.78687i
$520$		0			0
$521$	−25.4596	+	25.4596i	−1.11541	+	1.11541i	−0.122998	+	0.992407i	$0.539251\pi$
$521$	−25.4596	+	25.4596i	−1.11541	+	1.11541i	−0.992407	+	0.122998i	$0.960749\pi$
$522$	39.5312	+	39.5312i	1.73023	+	1.73023i
$523$	−30.5918			−1.33769			−0.668843	−	0.743404i	$-0.733210\pi$
$523$	−30.5918			−1.33769			−0.668843	+	0.743404i	$0.733210\pi$
$524$	3.42959	+	3.42959i	0.149822	+	0.149822i
$525$		0			0
$526$	−10.9334			−0.476719
$527$	−19.7287	+	4.04564i	−0.859394	+	0.176231i
$528$	2.31589			0.100786
$529$		−	9.80151i		−	0.426153i
$530$		0			0
$531$	−5.28354			−0.229286
$532$	−2.04978	−	2.04978i	−0.0888694	−	0.0888694i
$533$	−24.0087	+	24.0087i	−1.03993	+	1.03993i
$534$	−3.52021	+	3.52021i	−0.152334	+	0.152334i
$535$		0			0
$536$			2.59180i			0.111949i
$537$	12.7376	−	12.7376i	0.549669	−	0.549669i
$538$	−1.43373	+	1.43373i	−0.0618124	+	0.0618124i
$539$	−6.34514	−	6.34514i	−0.273305	−	0.273305i
$540$		0			0
$541$	7.41673	+	7.41673i	0.318870	+	0.318870i	0.848333	−	0.529463i	$-0.177607\pi$
$541$	7.41673	+	7.41673i	0.318870	+	0.318870i	−0.529463	+	0.848333i	$0.677607\pi$
$542$		−	20.9077i		−	0.898062i
$543$	12.4580			0.534623
$544$	−3.44172	−	2.27037i	−0.147562	−	0.0973414i
$545$		0			0
$546$		−	72.3883i		−	3.09793i
$547$	−7.13550	−	7.13550i	−0.305092	−	0.305092i	0.537910	−	0.843002i	$-0.319214\pi$
$547$	−7.13550	−	7.13550i	−0.305092	−	0.305092i	−0.843002	+	0.537910i	$0.819214\pi$
$548$	−7.12528			−0.304377
$549$	24.2397	+	24.2397i	1.03453	+	1.03453i
$550$		0			0
$551$	3.61624	−	3.61624i	0.154057	−	0.154057i
$552$		−	18.2908i		−	0.778508i
$553$		−	41.1051i		−	1.74797i
$554$	−8.34142	+	8.34142i	−0.354393	+	0.354393i
$555$		0			0
$556$	−0.691972	−	0.691972i	−0.0293462	−	0.0293462i
$557$	−35.0794			−1.48636			−0.743180	−	0.669091i	$-0.766684\pi$
$557$	−35.0794			−1.48636			−0.743180	+	0.669091i	$0.766684\pi$
$558$	−24.8654	−	24.8654i	−1.05263	−	1.05263i
$559$		−	36.2166i		−	1.53180i
$560$		0			0
$561$	5.25793	−	7.97064i	0.221990	−	0.336521i
$562$	−8.95003			−0.377534
$563$		−	15.9917i		−	0.673971i	−0.941510	−	0.336985i	$-0.890593\pi$
$563$		−	15.9917i		−	0.673971i	0.941510	−	0.336985i	$-0.109407\pi$
$564$	−15.5992	−	15.5992i	−0.656847	−	0.656847i
$565$		0			0
$566$	−21.5774	−	21.5774i	−0.906967	−	0.906967i
$567$	66.0840	−	66.0840i	2.77527	−	2.77527i
$568$	−8.08690	+	8.08690i	−0.339319	+	0.339319i
$569$			27.8750i			1.16858i	0.811545	+	0.584290i	$0.198627\pi$
$569$			27.8750i			1.16858i	−0.811545	+	0.584290i	$0.801373\pi$
$570$		0			0
$571$	−15.7453	+	15.7453i	−0.658920	+	0.658920i	−0.955125	−	0.296205i	$-0.904279\pi$
$571$	−15.7453	+	15.7453i	−0.658920	+	0.658920i	0.296205	+	0.955125i	$0.404279\pi$
$572$	2.64050	−	2.64050i	0.110405	−	0.110405i
$573$	−44.9213	−	44.9213i	−1.87661	−	1.87661i
$574$	29.0221			1.21136
$575$		0			0
$576$		−	7.19932i		−	0.299972i
$577$	18.0160			0.750015			0.375007	−	0.927022i	$-0.377640\pi$
$577$	18.0160			0.750015			0.375007	+	0.927022i	$0.377640\pi$
$578$	−15.6280	+	6.69083i	−0.650037	+	0.278302i
$579$	66.1789			2.75030
$580$		0			0
$581$	−18.0734	−	18.0734i	−0.749811	−	0.749811i
$582$	48.9243			2.02798
$583$	2.75579	+	2.75579i	0.114133	+	0.114133i
$584$	−1.14582	+	1.14582i	−0.0474142	+	0.0474142i
$585$		0			0
$586$			17.1811i			0.709743i
$587$			14.0134i			0.578396i	0.957269	+	0.289198i	$0.0933886\pi$
$587$			14.0134i			0.578396i	−0.957269	+	0.289198i	$0.906611\pi$
$588$	−27.9444	+	27.9444i	−1.15241	+	1.15241i
$589$	−2.27464	+	2.27464i	−0.0937248	+	0.0937248i
$590$		0			0
$591$	24.2397			0.997090
$592$	3.19932	+	3.19932i	0.131491	+	0.131491i
$593$		−	35.3721i		−	1.45256i	−0.687400	−	0.726279i	$-0.741248\pi$
$593$		−	35.3721i		−	1.45256i	0.687400	−	0.726279i	$-0.258752\pi$
$594$	9.72518			0.399029
$595$		0			0
$596$	−14.2079			−0.581976
$597$			13.4399i			0.550059i
$598$	−20.8545	−	20.8545i	−0.852805	−	0.852805i
$599$	−15.8179			−0.646303			−0.323151	−	0.946347i	$-0.604742\pi$
$599$	−15.8179			−0.646303			−0.323151	+	0.946347i	$0.604742\pi$
$600$		0			0
$601$	9.17860	−	9.17860i	0.374403	−	0.374403i	−0.494675	−	0.869078i	$-0.664713\pi$
$601$	9.17860	−	9.17860i	0.374403	−	0.374403i	0.869078	+	0.494675i	$0.164713\pi$
$602$	−21.8896	+	21.8896i	−0.892154	+	0.892154i
$603$			18.6592i			0.759861i
$604$		−	12.2249i		−	0.497422i
$605$		0			0
$606$	−26.1939	+	26.1939i	−1.06405	+	1.06405i
$607$	10.0471	+	10.0471i	0.407799	+	0.407799i	0.880970	−	0.473171i	$-0.156891\pi$
$607$	10.0471	+	10.0471i	0.407799	+	0.407799i	−0.473171	+	0.880970i	$0.656891\pi$
$608$	−0.658581			−0.0267090
$609$	−77.1877	−	77.1877i	−3.12780	−	3.12780i
$610$		0			0
$611$	−35.5714			−1.43907
$612$	−24.7780	−	16.3451i	−1.00159	−	0.660713i
$613$	8.93958			0.361066			0.180533	−	0.983569i	$-0.442218\pi$
$613$	8.93958			0.361066			0.180533	+	0.983569i	$0.442218\pi$
$614$		−	18.3002i		−	0.738535i
$615$		0			0
$616$	−3.19188			−0.128604
$617$	6.65858	+	6.65858i	0.268064	+	0.268064i	0.828320	−	0.560255i	$-0.189297\pi$
$617$	6.65858	+	6.65858i	0.268064	+	0.268064i	−0.560255	+	0.828320i	$0.689297\pi$
$618$	3.25739	−	3.25739i	0.131031	−	0.131031i
$619$	−2.54946	+	2.54946i	−0.102471	+	0.102471i	−0.756484	−	0.654012i	$-0.773084\pi$
$619$	−2.54946	+	2.54946i	−0.102471	+	0.102471i	0.654012	+	0.756484i	$0.273084\pi$
$620$		0			0
$621$		−	76.8090i		−	3.08224i
$622$	4.31302	−	4.31302i	0.172936	−	0.172936i
$623$	4.85173	−	4.85173i	0.194381	−	0.194381i
$624$	−11.6289	−	11.6289i	−0.465529	−	0.465529i
$625$		0			0
$626$	23.2908	+	23.2908i	0.930887	+	0.930887i
$627$		−	1.52520i		−	0.0609107i
$628$	11.6735			0.465822
$629$	18.2748	−	3.74751i	0.728665	−	0.149423i
$630$		0			0
$631$		−	7.16654i		−	0.285295i	−0.989774	−	0.142648i	$-0.954438\pi$
$631$		−	7.16654i		−	0.285295i	0.989774	−	0.142648i	$-0.0455616\pi$
$632$	−6.60338	−	6.60338i	−0.262669	−	0.262669i
$633$	66.3129			2.63570
$634$	5.93195	+	5.93195i	0.235588	+	0.235588i
$635$		0			0
$636$	12.1367	−	12.1367i	0.481251	−	0.481251i
$637$			63.7224i			2.52477i
$638$		−	5.63113i		−	0.222939i
$639$	−58.2202	+	58.2202i	−2.30316	+	2.30316i
$640$		0			0
$641$	23.2227	+	23.2227i	0.917243	+	0.917243i	0.996828	−	0.0795848i	$-0.0253595\pi$
$641$	23.2227	+	23.2227i	0.917243	+	0.917243i	−0.0795848	+	0.996828i	$0.525359\pi$
$642$	−15.4671			−0.610439
$643$	9.30431	+	9.30431i	0.366926	+	0.366926i	0.866355	−	0.499429i	$-0.166457\pi$
$643$	9.30431	+	9.30431i	0.366926	+	0.366926i	−0.499429	+	0.866355i	$0.666457\pi$
$644$			25.2093i			0.993386i
$645$		0			0
$646$	−1.49522	+	2.26665i	−0.0588288	+	0.0891801i
$647$	7.18360			0.282416			0.141208	−	0.989980i	$-0.454901\pi$
$647$	7.18360			0.282416			0.141208	+	0.989980i	$0.454901\pi$
$648$		−	21.2323i		−	0.834083i
$649$	0.376314	+	0.376314i	0.0147716	+	0.0147716i
$650$		0			0
$651$	48.5515	+	48.5515i	1.90288	+	1.90288i
$652$	14.7747	−	14.7747i	0.578623	−	0.578623i
$653$	−17.0889	+	17.0889i	−0.668742	+	0.668742i	−0.957425	−	0.288683i	$-0.906783\pi$
$653$	−17.0889	+	17.0889i	−0.668742	+	0.668742i	0.288683	+	0.957425i	$0.406783\pi$
$654$		−	63.4950i		−	2.48285i
$655$		0			0
$656$	4.66230	−	4.66230i	0.182032	−	0.182032i
$657$	−8.24911	+	8.24911i	−0.321828	+	0.321828i
$658$	21.4997	+	21.4997i	0.838145	+	0.838145i
$659$	28.1901			1.09813			0.549066	−	0.835779i	$-0.314984\pi$
$659$	28.1901			1.09813			0.549066	+	0.835779i	$0.314984\pi$
$660$		0			0
$661$		−	16.4895i		−	0.641367i	−0.947186	−	0.320684i	$-0.896087\pi$
$661$		−	16.4895i		−	0.641367i	0.947186	−	0.320684i	$-0.103913\pi$
$662$	−9.29781			−0.361370
$663$	−66.4254	+	13.6215i	−2.57975	+	0.529014i
$664$	−5.80685			−0.225349
$665$		0			0
$666$	23.0330	+	23.0330i	0.892510	+	0.892510i
$667$	−44.4744			−1.72206
$668$	1.37439	+	1.37439i	0.0531768	+	0.0531768i
$669$	11.7245	−	11.7245i	0.453296	−	0.453296i
$670$		0			0
$671$		−	3.45290i		−	0.133298i
$672$			14.0572i			0.542269i
$673$	22.2553	−	22.2553i	0.857878	−	0.857878i	−0.133210	−	0.991088i	$-0.542528\pi$
$673$	22.2553	−	22.2553i	0.857878	−	0.857878i	0.991088	+	0.133210i	$0.0425284\pi$
$674$	−13.5202	+	13.5202i	−0.520779	+	0.520779i
$675$		0			0
$676$	−13.5178			−0.519914
$677$	15.5420	+	15.5420i	0.597328	+	0.597328i	0.939601	−	0.342273i	$-0.111197\pi$
$677$	15.5420	+	15.5420i	0.597328	+	0.597328i	−0.342273	+	0.939601i	$0.611197\pi$
$678$		−	45.9724i		−	1.76556i
$679$	−67.4299			−2.58772
$680$		0			0
$681$	−51.6495			−1.97921
$682$			3.54201i			0.135631i
$683$	32.6499	+	32.6499i	1.24931	+	1.24931i	0.956024	+	0.293289i	$0.0947499\pi$
$683$	32.6499	+	32.6499i	1.24931	+	1.24931i	0.293289	+	0.956024i	$0.405250\pi$
$684$	−4.74134			−0.181290
$685$		0			0
$686$	16.7274	−	16.7274i	0.638655	−	0.638655i
$687$	24.2014	−	24.2014i	0.923339	−	0.923339i
$688$			7.03297i			0.268130i
$689$		−	27.6756i		−	1.05436i
$690$		0			0
$691$	10.1670	−	10.1670i	0.386772	−	0.386772i	−0.486763	−	0.873534i	$-0.661822\pi$
$691$	10.1670	−	10.1670i	0.386772	−	0.386772i	0.873534	+	0.486763i	$0.161822\pi$
$692$	14.0572	+	14.0572i	0.534376	+	0.534376i
$693$	−22.9794			−0.872914
$694$	−9.72367	−	9.72367i	−0.369106	−	0.369106i
$695$		0			0
$696$	−24.7998			−0.940035
$697$	−5.46117	−	26.6315i	−0.206856	−	1.00874i
$698$	32.1083			1.21532
$699$		−	47.0864i		−	1.78097i
$700$		0			0
$701$	−35.1985			−1.32943			−0.664714	−	0.747098i	$-0.731447\pi$
$701$	−35.1985			−1.32943			−0.664714	+	0.747098i	$0.731447\pi$
$702$	−48.8336	−	48.8336i	−1.84310	−	1.84310i
$703$	2.10701	−	2.10701i	0.0794675	−	0.0794675i
$704$	−0.512764	+	0.512764i	−0.0193255	+	0.0193255i
$705$		0			0
$706$			18.1825i			0.684308i
$707$	36.1018	−	36.1018i	1.35775	−	1.35775i
$708$	1.65731	−	1.65731i	0.0622855	−	0.0622855i
$709$	−7.30016	−	7.30016i	−0.274163	−	0.274163i	0.556610	−	0.830774i	$-0.312102\pi$
$709$	−7.30016	−	7.30016i	−0.274163	−	0.274163i	−0.830774	+	0.556610i	$0.812102\pi$
$710$		0			0
$711$	−47.5399	−	47.5399i	−1.78289	−	1.78289i
$712$		−	1.55883i		−	0.0584195i
$713$	27.9747			1.04766
$714$	48.3810	+	31.9151i	1.81061	+	1.19439i
$715$		0			0
$716$			5.64050i			0.210795i
$717$	15.7332	+	15.7332i	0.587569	+	0.587569i
$718$	9.60542			0.358471
$719$	−22.7859	−	22.7859i	−0.849771	−	0.849771i	0.140334	−	0.990104i	$-0.455182\pi$
$719$	−22.7859	−	22.7859i	−0.849771	−	0.849771i	−0.990104	+	0.140334i	$0.955182\pi$
$720$		0			0
$721$	−4.48950	+	4.48950i	−0.167198	+	0.167198i
$722$		−	18.5663i		−	0.690965i
$723$		−	85.4468i		−	3.17780i
$724$	−2.75834	+	2.75834i	−0.102513	+	0.102513i
$725$		0			0
$726$	23.6532	+	23.6532i	0.877851	+	0.877851i
$727$	23.2578			0.862585			0.431292	−	0.902212i	$-0.358058\pi$
$727$	23.2578			0.862585			0.431292	+	0.902212i	$0.358058\pi$
$728$	16.0276	+	16.0276i	0.594021	+	0.594021i
$729$		−	24.3674i		−	0.902496i
$730$		0			0
$731$	24.2055	+	15.9675i	0.895273	+	0.590578i
$732$	−15.2068			−0.562058
$733$			10.2053i			0.376942i	0.982079	+	0.188471i	$0.0603531\pi$
$733$			10.2053i			0.376942i	−0.982079	+	0.188471i	$0.939647\pi$
$734$	9.06264	+	9.06264i	0.334508	+	0.334508i
$735$		0			0
$736$	4.04978	+	4.04978i	0.149277	+	0.149277i
$737$	1.32898	−	1.32898i	0.0489536	−	0.0489536i
$738$	33.5654	−	33.5654i	1.23556	−	1.23556i
$739$			20.0891i			0.738990i	0.929233	+	0.369495i	$0.120469\pi$
$739$			20.0891i			0.738990i	−0.929233	+	0.369495i	$0.879531\pi$
$740$		0			0
$741$	−7.65858	+	7.65858i	−0.281345	+	0.281345i
$742$	−16.7274	+	16.7274i	−0.614082	+	0.614082i
$743$	0.896290	+	0.896290i	0.0328817	+	0.0328817i	0.723356	−	0.690475i	$-0.242598\pi$
$743$	0.896290	+	0.896290i	0.0328817	+	0.0328817i	−0.690475	+	0.723356i	$0.742598\pi$
$744$	15.5992			0.571896
$745$		0			0
$746$		−	25.9830i		−	0.951305i
$747$	−41.8054			−1.52958
$748$	0.600623	+	2.92895i	0.0219610	+	0.107093i
$749$	21.3176			0.778928
$750$		0			0
$751$	−1.20888	−	1.20888i	−0.0441125	−	0.0441125i	0.684706	−	0.728819i	$-0.259930\pi$
$751$	−1.20888	−	1.20888i	−0.0441125	−	0.0441125i	−0.728819	+	0.684706i	$0.759930\pi$
$752$	6.90769			0.251898
$753$	4.19560	+	4.19560i	0.152896	+	0.152896i
$754$	−28.2759	+	28.2759i	−1.02975	+	1.02975i
$755$		0			0
$756$			59.0309i			2.14693i
$757$		−	39.8962i		−	1.45005i	−0.688721	−	0.725026i	$-0.741828\pi$
$757$		−	39.8962i		−	1.45005i	0.688721	−	0.725026i	$-0.258172\pi$
$758$	4.73348	−	4.73348i	0.171928	−	0.171928i
$759$	−9.37886	+	9.37886i	−0.340431	+	0.340431i
$760$		0			0
$761$	−4.97683			−0.180410			−0.0902049	−	0.995923i	$-0.528752\pi$
$761$	−4.97683			−0.180410			−0.0902049	+	0.995923i	$0.528752\pi$
$762$	−9.93322	−	9.93322i	−0.359843	−	0.359843i
$763$			87.5121i			3.16815i
$764$	19.8921			0.719673
$765$		0			0
$766$	8.22231			0.297084
$767$		−	3.77921i		−	0.136460i
$768$	2.25824	+	2.25824i	0.0814873	+	0.0814873i
$769$	12.5591			0.452892			0.226446	−	0.974024i	$-0.427289\pi$
$769$	12.5591			0.452892			0.226446	+	0.974024i	$0.427289\pi$
$770$		0			0
$771$	−31.4045	+	31.4045i	−1.13101	+	1.13101i
$772$	−14.6528	+	14.6528i	−0.527364	+	0.527364i
$773$		−	20.1315i		−	0.724078i	−0.932163	−	0.362039i	$-0.882081\pi$
$773$		−	20.1315i		−	0.724078i	0.932163	−	0.362039i	$-0.117919\pi$
$774$			50.6327i			1.81995i
$775$		0			0
$776$	−10.8324	+	10.8324i	−0.388860	+	0.388860i
$777$	−44.9736	−	44.9736i	−1.61342	−	1.61342i
$778$	36.0320			1.29181
$779$	−3.07050	−	3.07050i	−0.110012	−	0.110012i
$780$		0			0
$781$	8.29334			0.296759
$782$	23.1327	−	4.74369i	0.827225	−	0.169634i
$783$	−104.143			−3.72175
$784$		−	12.3744i		−	0.441943i
$785$		0			0
$786$	−15.4897			−0.552499
$787$	−2.55341	−	2.55341i	−0.0910194	−	0.0910194i	0.660131	−	0.751150i	$-0.270501\pi$
$787$	−2.55341	−	2.55341i	−0.0910194	−	0.0910194i	−0.751150	+	0.660131i	$0.770501\pi$
$788$	−5.36695	+	5.36695i	−0.191190	+	0.191190i
$789$	24.6903	−	24.6903i	0.878997	−	0.878997i
$790$		0			0
$791$			63.3615i			2.25287i
$792$	−3.69155	+	3.69155i	−0.131174	+	0.131174i
$793$	−17.3382	+	17.3382i	−0.615698	+	0.615698i
$794$	−19.6162	−	19.6162i	−0.696154	−	0.696154i
$795$		0			0
$796$	−2.97574	−	2.97574i	−0.105472	−	0.105472i
$797$		−	1.45653i		−	0.0515929i	−0.999667	−	0.0257965i	$-0.991788\pi$
$797$		−	1.45653i		−	0.0515929i	0.999667	−	0.0257965i	$-0.00821218\pi$
$798$	9.25782			0.327723
$799$	15.6830	−	23.7743i	0.554825	−	0.841075i
$800$		0			0
$801$		−	11.2225i		−	0.396527i
$802$	−2.46171	−	2.46171i	−0.0869259	−	0.0869259i
$803$	1.17507			0.0414672
$804$	−5.85291	−	5.85291i	−0.206416	−	0.206416i
$805$		0			0
$806$	17.7857	−	17.7857i	0.626475	−	0.626475i
$807$		−	6.47542i		−	0.227945i
$808$		−	11.5992i		−	0.408060i
$809$	−36.2727	+	36.2727i	−1.27528	+	1.27528i	−0.332002	+	0.943279i	$0.607724\pi$
$809$	−36.2727	+	36.2727i	−1.27528	+	1.27528i	−0.943279	+	0.332002i	$0.892276\pi$
$810$		0			0
$811$	16.2924	+	16.2924i	0.572103	+	0.572103i	0.932716	−	0.360612i	$-0.117432\pi$
$811$	16.2924	+	16.2924i	0.572103	+	0.572103i	−0.360612	+	0.932716i	$0.617432\pi$
$812$	34.1804			1.19950
$813$	47.2146	+	47.2146i	1.65589	+	1.65589i
$814$		−	3.28100i		−	0.114999i
$815$		0			0
$816$	12.8993	−	2.64518i	0.451565	−	0.0925999i
$817$	4.63178			0.162046
$818$		−	10.6599i		−	0.372713i
$819$	115.388	+	115.388i	4.03197	+	4.03197i
$820$		0			0
$821$	10.3742	+	10.3742i	0.362062	+	0.362062i	0.864572	−	0.502509i	$-0.167590\pi$
$821$	10.3742	+	10.3742i	0.362062	+	0.362062i	−0.502509	+	0.864572i	$0.667590\pi$
$822$	16.0906	−	16.0906i	0.561225	−	0.561225i
$823$	−34.0193	+	34.0193i	−1.18584	+	1.18584i	−0.207630	+	0.978207i	$0.566575\pi$
$823$	−34.0193	+	34.0193i	−1.18584	+	1.18584i	−0.978207	+	0.207630i	$0.933425\pi$
$824$			1.44244i			0.0502499i
$825$		0			0
$826$	−2.28419	+	2.28419i	−0.0794771	+	0.0794771i
$827$	−22.4366	+	22.4366i	−0.780198	+	0.780198i	−0.979864	−	0.199666i	$-0.936014\pi$
$827$	−22.4366	+	22.4366i	−0.780198	+	0.780198i	0.199666	+	0.979864i	$0.436014\pi$
$828$	29.1557	+	29.1557i	1.01323	+	1.01323i
$829$	−28.3053			−0.983082			−0.491541	−	0.870854i	$-0.663566\pi$
$829$	−28.3053			−0.983082			−0.491541	+	0.870854i	$0.663566\pi$
$830$		0			0
$831$		−	37.6739i		−	1.30689i
$832$	5.14954			0.178528
$833$	−42.5891	−	28.0945i	−1.47563	−	0.973416i
$834$	3.12528			0.108220
$835$		0			0
$836$	0.337697	+	0.337697i	0.0116795	+	0.0116795i
$837$	65.5063			2.26423
$838$	−14.8278	−	14.8278i	−0.512218	−	0.512218i
$839$	24.9291	−	24.9291i	0.860647	−	0.860647i	−0.130766	−	0.991413i	$-0.541744\pi$
$839$	24.9291	−	24.9291i	0.860647	−	0.860647i	0.991413	+	0.130766i	$0.0417436\pi$
$840$		0			0
$841$			31.3013i			1.07935i
$842$		−	7.30016i		−	0.251580i
$843$	20.2113	−	20.2113i	0.696116	−	0.696116i
$844$	−14.6824	+	14.6824i	−0.505390	+	0.505390i
$845$		0			0
$846$	49.7307			1.70978
$847$	−32.6000	−	32.6000i	−1.12015	−	1.12015i
$848$			5.37439i			0.184557i
$849$	97.4542			3.34462
$850$		0			0
$851$	−25.9131			−0.888291
$852$		−	36.5244i		−	1.25130i
$853$	−29.7573	−	29.7573i	−1.01887	−	1.01887i	−0.999818	−	0.0190525i	$-0.993935\pi$
$853$	−29.7573	−	29.7573i	−1.01887	−	1.01887i	−0.0190525	−	0.999818i	$-0.506065\pi$
$854$	20.9587			0.717194
$855$		0			0
$856$	3.42459	−	3.42459i	0.117050	−	0.117050i
$857$	−6.39703	+	6.39703i	−0.218519	+	0.218519i	−0.807874	−	0.589355i	$-0.799382\pi$
$857$	−6.39703	+	6.39703i	−0.218519	+	0.218519i	0.589355	+	0.807874i	$0.299382\pi$
$858$			11.9258i			0.407139i
$859$			48.9796i			1.67116i	0.549366	+	0.835582i	$0.314869\pi$
$859$			48.9796i			1.67116i	−0.549366	+	0.835582i	$0.685131\pi$
$860$		0			0
$861$	−65.5391	+	65.5391i	−2.23357	+	2.23357i
$862$	7.91183	+	7.91183i	0.269478	+	0.269478i
$863$	34.7637			1.18337			0.591685	−	0.806170i	$-0.298463\pi$
$863$	34.7637			1.18337			0.591685	+	0.806170i	$0.298463\pi$
$864$	9.48310	+	9.48310i	0.322621	+	0.322621i
$865$		0			0
$866$	7.86535			0.267275
$867$	20.1822	−	50.4012i	0.685424	−	1.71172i
$868$	−21.4997			−0.729746
$869$			6.77195i			0.229723i
$870$		0			0
$871$	−13.3466			−0.452231
$872$	14.0585	+	14.0585i	0.476081	+	0.476081i
$873$	−77.9858	+	77.9858i	−2.63942	+	2.63942i
$874$	2.66711	−	2.66711i	0.0902164	−	0.0902164i
$875$		0			0
$876$		−	5.17507i		−	0.174849i
$877$	16.5750	−	16.5750i	0.559698	−	0.559698i	−0.369524	−	0.929221i	$-0.620479\pi$
$877$	16.5750	−	16.5750i	0.559698	−	0.559698i	0.929221	+	0.369524i	$0.120479\pi$
$878$	−9.58040	+	9.58040i	−0.323323	+	0.323323i
$879$	−38.7990	−	38.7990i	−1.30866	−	1.30866i
$880$		0			0
$881$	23.1402	+	23.1402i	0.779612	+	0.779612i	0.979765	−	0.200153i	$-0.0641438\pi$
$881$	23.1402	+	23.1402i	0.779612	+	0.779612i	−0.200153	+	0.979765i	$0.564144\pi$
$882$		−	89.0873i		−	2.99972i
$883$	28.0513			0.944002			0.472001	−	0.881598i	$-0.343532\pi$
$883$	28.0513			0.944002			0.472001	+	0.881598i	$0.343532\pi$
$884$	11.6914	−	17.7233i	0.393223	−	0.596098i
$885$		0			0
$886$		−	29.5994i		−	0.994412i
$887$	−8.07027	−	8.07027i	−0.270973	−	0.270973i	0.558519	−	0.829492i	$-0.311370\pi$
$887$	−8.07027	−	8.07027i	−0.270973	−	0.270973i	−0.829492	+	0.558519i	$0.811370\pi$
$888$	−14.4497			−0.484900
$889$	13.6905	+	13.6905i	0.459164	+	0.459164i
$890$		0			0
$891$	−10.8872	+	10.8872i	−0.364733	+	0.364733i
$892$			5.19188i			0.173837i
$893$		−	4.54927i		−	0.152236i
$894$	32.0848	−	32.0848i	1.07308	−	1.07308i
$895$		0			0
$896$	−3.11243	−	3.11243i	−0.103979	−	0.103979i
$897$	94.1892			3.14489
$898$	5.81184	+	5.81184i	0.193944	+	0.193944i
$899$		−	37.9298i		−	1.26503i
$900$		0			0
$901$	18.4971	+	12.2019i	0.616229	+	0.406503i
$902$	−4.78132			−0.159201
$903$		−	98.8641i		−	3.28999i
$904$	10.1788	+	10.1788i	0.338542	+	0.338542i
$905$		0			0
$906$	27.6067	+	27.6067i	0.917171	+	0.917171i
$907$	−29.2982	+	29.2982i	−0.972832	+	0.972832i	−0.999641	−	0.0268084i	$-0.991466\pi$
$907$	−29.2982	+	29.2982i	−0.972832	+	0.972832i	0.0268084	+	0.999641i	$0.491466\pi$
$908$	11.4358	−	11.4358i	0.379509	−	0.379509i
$909$		−	83.5067i		−	2.76974i
$910$		0			0
$911$	22.8125	−	22.8125i	0.755812	−	0.755812i	−0.219745	−	0.975557i	$-0.570523\pi$
$911$	22.8125	−	22.8125i	0.755812	−	0.755812i	0.975557	+	0.219745i	$0.0705226\pi$
$912$	1.48724	−	1.48724i	0.0492473	−	0.0492473i
$913$	2.97754	+	2.97754i	0.0985423	+	0.0985423i
$914$	6.79221			0.224666
$915$		0			0
$916$			10.7169i			0.354096i
$917$	21.3487			0.704995
$918$	54.1683	−	11.1080i	1.78782	−	0.366618i
$919$	44.5645			1.47005			0.735024	−	0.678041i	$-0.237171\pi$
$919$	44.5645			1.47005			0.735024	+	0.678041i	$0.237171\pi$
$920$		0			0
$921$	41.3262	+	41.3262i	1.36175	+	1.36175i
$922$	−1.36822			−0.0450598
$923$	−41.6438	−	41.6438i	−1.37072	−	1.37072i
$924$	7.20804	−	7.20804i	0.237127	−	0.237127i
$925$		0			0
$926$			0.933403i			0.0306735i
$927$			10.3846i			0.341076i
$928$	5.49096	−	5.49096i	0.180250	−	0.180250i
$929$	16.9979	−	16.9979i	0.557683	−	0.557683i	−0.370964	−	0.928647i	$-0.620973\pi$
$929$	16.9979	−	16.9979i	0.557683	−	0.557683i	0.928647	+	0.370964i	$0.120973\pi$
$930$		0			0
$931$	−8.14954			−0.267090
$932$	10.4254	+	10.4254i	0.341497	+	0.341497i
$933$			19.4797i			0.637737i
$934$	−12.7256			−0.416395
$935$		0			0
$936$	37.0732			1.21178
$937$		−	41.9118i		−	1.36920i	−0.728920	−	0.684599i	$-0.759977\pi$
$937$		−	41.9118i		−	1.36920i	0.728920	−	0.684599i	$-0.240023\pi$
$938$	8.06678	+	8.06678i	0.263390	+	0.263390i
$939$	−105.193			−3.43283
$940$		0			0
$941$	12.0721	−	12.0721i	0.393540	−	0.393540i	−0.482407	−	0.875947i	$-0.660237\pi$
$941$	12.0721	−	12.0721i	0.393540	−	0.393540i	0.875947	+	0.482407i	$0.160237\pi$
$942$	−26.3615	+	26.3615i	−0.858905	+	0.858905i
$943$			37.7627i			1.22972i
$944$			0.733894i			0.0238862i
$945$		0			0
$946$	3.60625	−	3.60625i	0.117249	−	0.117249i
$947$	31.4803	+	31.4803i	1.02297	+	1.02297i	0.999730	+	0.0232431i	$0.00739918\pi$
$947$	31.4803	+	31.4803i	1.02297	+	1.02297i	0.0232431	+	0.999730i	$0.492601\pi$
$948$	29.8241			0.968642
$949$	−5.90043	−	5.90043i	−0.191536	−	0.191536i
$950$		0			0
$951$	−26.7916			−0.868776
$952$	−17.7785	+	3.64572i	−0.576203	+	0.118159i
$953$	15.1175			0.489703			0.244851	−	0.969561i	$-0.421261\pi$
$953$	15.1175			0.489703			0.244851	+	0.969561i	$0.421261\pi$
$954$			38.6920i			1.25270i
$955$		0			0
$956$	−6.96703			−0.225330
$957$	12.7165	+	12.7165i	0.411065	+	0.411065i
$958$	4.51031	−	4.51031i	0.145722	−	0.145722i
$959$	−22.1769	+	22.1769i	−0.716130	+	0.716130i
$960$		0			0
$961$		−	7.14191i		−	0.230384i
$962$	−16.4750	+	16.4750i	−0.531177	+	0.531177i
$963$	24.6548	−	24.6548i	0.794489	−	0.794489i
$964$	18.9189	+	18.9189i	0.609335	+	0.609335i
$965$		0			0
$966$	−56.9288	−	56.9288i	−1.83165	−	1.83165i
$967$		−	56.0954i		−	1.80390i	−0.431835	−	0.901952i	$-0.642134\pi$
$967$		−	56.0954i		−	1.80390i	0.431835	−	0.901952i	$-0.357866\pi$
$968$	−10.4741			−0.336652
$969$	−1.74207	−	8.49522i	−0.0559632	−	0.272906i
$970$		0			0
$971$		−	54.5752i		−	1.75140i	−0.482853	−	0.875701i	$-0.660400\pi$
$971$		−	54.5752i		−	1.75140i	0.482853	−	0.875701i	$-0.339600\pi$
$972$	19.4984	+	19.4984i	0.625412	+	0.625412i
$973$	−4.30742			−0.138090
$974$	−10.9575	−	10.9575i	−0.351100	−	0.351100i
$975$		0			0
$976$	3.36695	−	3.36695i	0.107773	−	0.107773i
$977$			46.4565i			1.48628i	0.669139	+	0.743138i	$0.266663\pi$
$977$			46.4565i			1.48628i	−0.669139	+	0.743138i	$0.733337\pi$
$978$			66.7299i			2.13379i
$979$	−0.799310	+	0.799310i	−0.0255461	+	0.0255461i
$980$		0			0
$981$	101.212	+	101.212i	3.23144	+	3.23144i
$982$	31.0840			0.991931
$983$	−9.91800	−	9.91800i	−0.316335	−	0.316335i	0.531022	−	0.847358i	$-0.321808\pi$
$983$	−9.91800	−	9.91800i	−0.316335	−	0.316335i	−0.847358	+	0.531022i	$0.821808\pi$
$984$			21.0572i			0.671280i
$985$		0			0
$986$	−6.43181	−	31.3648i	−0.204830	−	0.998860i
$987$	−97.1030			−3.09082
$988$		−	3.39139i		−	0.107894i
$989$	−28.4820	−	28.4820i	−0.905676	−	0.905676i
$990$		0			0
$991$	−24.1773	−	24.1773i	−0.768017	−	0.768017i	0.209740	−	0.977757i	$-0.432738\pi$
$991$	−24.1773	−	24.1773i	−0.768017	−	0.768017i	−0.977757	+	0.209740i	$0.932738\pi$
$992$	−3.45385	+	3.45385i	−0.109660	+	0.109660i
$993$	20.9967	−	20.9967i	0.666310	−	0.666310i
$994$			50.3397i			1.59668i
$995$		0			0
$996$	13.1133	−	13.1133i	0.415510	−	0.415510i
$997$	0.757065	−	0.757065i	0.0239765	−	0.0239765i	−0.695017	−	0.718993i	$-0.744603\pi$
$997$	0.757065	−	0.757065i	0.0239765	−	0.0239765i	0.718993	+	0.695017i	$0.244603\pi$
$998$	17.9473	+	17.9473i	0.568113	+	0.568113i
$999$	−60.6790			−1.91980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.l.251.4	✓	8
5.2	odd	4		850.2.g.k.149.4		8
5.3	odd	4		850.2.g.j.149.1		8
5.4	even	2		850.2.h.m.251.1	yes	8
17.4	even	4	inner	850.2.h.l.701.4	yes	8
85.4	even	4		850.2.h.m.701.1	yes	8
85.38	odd	4		850.2.g.k.599.4		8
85.72	odd	4		850.2.g.j.599.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.g.j.149.1		8	5.3	odd	4
850.2.g.j.599.1		8	85.72	odd	4
850.2.g.k.149.4		8	5.2	odd	4
850.2.g.k.599.4		8	85.38	odd	4
850.2.h.l.251.4	✓	8	1.1	even	1	trivial
850.2.h.l.701.4	yes	8	17.4	even	4	inner
850.2.h.m.251.1	yes	8	5.4	even	2
850.2.h.m.701.1	yes	8	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(2.25824 + 2.25824i) q^{3} -1.00000 q^{4} +(2.25824 - 2.25824i) q^{6} +(-3.11243 + 3.11243i) q^{7} +1.00000i q^{8} +7.19932i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(2.25824 + 2.25824i) q^{3} -1.00000 q^{4} +(2.25824 - 2.25824i) q^{6} +(-3.11243 + 3.11243i) q^{7} +1.00000i q^{8} +7.19932i q^{9} +(0.512764 - 0.512764i) q^{11} +(-2.25824 - 2.25824i) q^{12} -5.14954 q^{13} +(3.11243 + 3.11243i) q^{14} +1.00000 q^{16} +(2.27037 - 3.44172i) q^{17} +7.19932 q^{18} -0.658581i q^{19} -14.0572 q^{21} +(-0.512764 - 0.512764i) q^{22} +(-4.04978 + 4.04978i) q^{23} +(-2.25824 + 2.25824i) q^{24} +5.14954i q^{26} +(-9.48310 + 9.48310i) q^{27} +(3.11243 - 3.11243i) q^{28} +(5.49096 + 5.49096i) q^{29} +(-3.45385 - 3.45385i) q^{31} -1.00000i q^{32} +2.31589 q^{33} +(-3.44172 - 2.27037i) q^{34} -7.19932i q^{36} +(3.19932 + 3.19932i) q^{37} -0.658581 q^{38} +(-11.6289 - 11.6289i) q^{39} +(4.66230 - 4.66230i) q^{41} +14.0572i q^{42} +7.03297i q^{43} +(-0.512764 + 0.512764i) q^{44} +(4.04978 + 4.04978i) q^{46} +6.90769 q^{47} +(2.25824 + 2.25824i) q^{48} -12.3744i q^{49} +(12.8993 - 2.64518i) q^{51} +5.14954 q^{52} +5.37439i q^{53} +(9.48310 + 9.48310i) q^{54} +(-3.11243 - 3.11243i) q^{56} +(1.48724 - 1.48724i) q^{57} +(5.49096 - 5.49096i) q^{58} +0.733894i q^{59} +(3.36695 - 3.36695i) q^{61} +(-3.45385 + 3.45385i) q^{62} +(-22.4074 - 22.4074i) q^{63} -1.00000 q^{64} -2.31589i q^{66} +2.59180 q^{67} +(-2.27037 + 3.44172i) q^{68} -18.2908 q^{69} +(8.08690 + 8.08690i) q^{71} -7.19932 q^{72} +(1.14582 + 1.14582i) q^{73} +(3.19932 - 3.19932i) q^{74} +0.658581i q^{76} +3.19188i q^{77} +(-11.6289 + 11.6289i) q^{78} +(-6.60338 + 6.60338i) q^{79} -21.2323 q^{81} +(-4.66230 - 4.66230i) q^{82} +5.80685i q^{83} +14.0572 q^{84} +7.03297 q^{86} +24.7998i q^{87} +(0.512764 + 0.512764i) q^{88} -1.55883 q^{89} +(16.0276 - 16.0276i) q^{91} +(4.04978 - 4.04978i) q^{92} -15.5992i q^{93} -6.90769i q^{94} +(2.25824 - 2.25824i) q^{96} +(10.8324 + 10.8324i) q^{97} -12.3744 q^{98} +(3.69155 + 3.69155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^7	\( 8 q - 8 q^{4} - 2 q^{7} + 2 q^{11} - 12 q^{13} + 2 q^{14} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 32 q^{21} - 2 q^{22} - 20 q^{23} - 12 q^{27} + 2 q^{28} + 12 q^{29} - 2 q^{31} + 20 q^{33} - 6 q^{34} - 16 q^{37} - 8 q^{38} - 34 q^{39} + 6 q^{41} - 2 q^{44} + 20 q^{46} + 4 q^{47} + 22 q^{51} + 12 q^{52} + 12 q^{54} - 2 q^{56} + 14 q^{57} + 12 q^{58} + 20 q^{61} - 2 q^{62} - 32 q^{63} - 8 q^{64} - 32 q^{67} + 4 q^{68} + 44 q^{69} + 46 q^{71} - 16 q^{72} + 14 q^{73} - 16 q^{74} - 34 q^{78} + 2 q^{79} - 56 q^{81} - 6 q^{82} + 32 q^{84} - 16 q^{86} + 2 q^{88} - 32 q^{89} - 14 q^{91} + 20 q^{92} + 52 q^{97} - 24 q^{98} - 40 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^7 + 2 * q^11 - 12 * q^13 + 2 * q^14 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 32 * q^21 - 2 * q^22 - 20 * q^23 - 12 * q^27 + 2 * q^28 + 12 * q^29 - 2 * q^31 + 20 * q^33 - 6 * q^34 - 16 * q^37 - 8 * q^38 - 34 * q^39 + 6 * q^41 - 2 * q^44 + 20 * q^46 + 4 * q^47 + 22 * q^51 + 12 * q^52 + 12 * q^54 - 2 * q^56 + 14 * q^57 + 12 * q^58 + 20 * q^61 - 2 * q^62 - 32 * q^63 - 8 * q^64 - 32 * q^67 + 4 * q^68 + 44 * q^69 + 46 * q^71 - 16 * q^72 + 14 * q^73 - 16 * q^74 - 34 * q^78 + 2 * q^79 - 56 * q^81 - 6 * q^82 + 32 * q^84 - 16 * q^86 + 2 * q^88 - 32 * q^89 - 14 * q^91 + 20 * q^92 + 52 * q^97 - 24 * q^98 - 40 * q^99

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