LMFDB - Embedded newform 400.2.y.c.129.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(129,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("400.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.y (of order $10$, degree $4$, not 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			129.2
Root			$-0.983224 - 0.644389i$ of defining polynomial
Character	$\chi$	$=$	400.129
Dual form			400.2.y.c.369.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.865190 - 1.19083i) q^{3} +(0.107666 - 2.23347i) q^{5} -3.26086i q^{7} +(0.257524 + 0.792578i) q^{9} +O(q^{10})$	\(q+(0.865190 - 1.19083i) q^{3} +(0.107666 - 2.23347i) q^{5} -3.26086i q^{7} +(0.257524 + 0.792578i) q^{9} +(-0.618034 + 1.90211i) q^{11} +(0.281873 - 0.0915860i) q^{13} +(-2.56654 - 2.06059i) q^{15} +(-3.03472 - 4.17693i) q^{17} +(-1.39991 + 1.01709i) q^{19} +(-3.88313 - 2.82126i) q^{21} +(-0.836161 - 0.271685i) q^{23} +(-4.97682 - 0.480938i) q^{25} +(5.36635 + 1.74363i) q^{27} +(4.78304 + 3.47508i) q^{29} +(4.93462 - 3.58521i) q^{31} +(1.73038 + 2.38166i) q^{33} +(-7.28304 - 0.351083i) q^{35} +(7.69215 - 2.49933i) q^{37} +(0.134810 - 0.414902i) q^{39} +(-0.313697 - 0.965461i) q^{41} +3.24199i q^{43} +(1.79793 - 0.489840i) q^{45} +(2.48043 - 3.41402i) q^{47} -3.63318 q^{49} -7.59963 q^{51} +(-4.76148 + 6.55362i) q^{53} +(4.18178 + 1.58516i) q^{55} +2.54703i q^{57} +(1.83443 + 5.64581i) q^{59} +(0.282941 - 0.870802i) q^{61} +(2.58448 - 0.839749i) q^{63} +(-0.174207 - 0.639416i) q^{65} +(-4.04870 - 5.57255i) q^{67} +(-1.04697 + 0.760668i) q^{69} +(-4.82884 - 3.50836i) q^{71} +(8.40107 + 2.72967i) q^{73} +(-4.87861 + 5.51045i) q^{75} +(6.20252 + 2.01532i) q^{77} +(6.27851 + 4.56161i) q^{79} +(4.69667 - 3.41233i) q^{81} +(8.53192 + 11.7432i) q^{83} +(-9.65580 + 6.32825i) q^{85} +(8.27647 - 2.68919i) q^{87} +(-2.32579 + 7.15805i) q^{89} +(-0.298649 - 0.919147i) q^{91} -8.97820i q^{93} +(2.12093 + 3.23616i) q^{95} +(3.95373 - 5.44184i) q^{97} -1.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} + q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 + q^9	$ 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.865190	−	1.19083i	0.499518	−	0.687527i	−0.482590	−	0.875846i	$-0.660304\pi$
$3$	0.865190	−	1.19083i	0.499518	−	0.687527i	0.982108	+	0.188319i	$0.0603039\pi$
$4$		0			0
$5$	0.107666	−	2.23347i	0.0481496	−	0.998840i
$5$	0.107666	−	2.23347i	0.0481496	−	0.998840i
$6$		0			0
$7$		−	3.26086i		−	1.23249i	−0.787555	−	0.616244i	$-0.788654\pi$
$7$		−	3.26086i		−	1.23249i	0.787555	−	0.616244i	$-0.211346\pi$
$8$		0			0
$9$	0.257524	+	0.792578i	0.0858414	+	0.264193i
$10$		0			0
$11$	−0.618034	+	1.90211i	−0.186344	+	0.573509i	−0.999969	−	0.00788181i	$-0.997491\pi$
$11$	−0.618034	+	1.90211i	−0.186344	+	0.573509i	0.813625	+	0.581390i	$0.197491\pi$
$12$		0			0
$13$	0.281873	−	0.0915860i	0.0781775	−	0.0254014i	−0.269667	−	0.962954i	$-0.586914\pi$
$13$	0.281873	−	0.0915860i	0.0781775	−	0.0254014i	0.347845	+	0.937552i	$0.386914\pi$
$14$		0			0
$15$	−2.56654	−	2.06059i	−0.662678	−	0.532042i
$16$		0			0
$17$	−3.03472	−	4.17693i	−0.736027	−	1.01305i	−0.998837	−	0.0482067i	$-0.984649\pi$
$17$	−3.03472	−	4.17693i	−0.736027	−	1.01305i	0.262810	−	0.964847i	$-0.415351\pi$
$18$		0			0
$19$	−1.39991	+	1.01709i	−0.321161	+	0.233337i	−0.736671	−	0.676252i	$-0.763603\pi$
$19$	−1.39991	+	1.01709i	−0.321161	+	0.233337i	0.415510	+	0.909589i	$0.363603\pi$
$20$		0			0
$21$	−3.88313	−	2.82126i	−0.847369	−	0.615649i
$22$		0			0
$23$	−0.836161	−	0.271685i	−0.174352	−	0.0566503i	0.220540	−	0.975378i	$-0.429218\pi$
$23$	−0.836161	−	0.271685i	−0.174352	−	0.0566503i	−0.394892	+	0.918728i	$0.629218\pi$
$24$		0			0
$25$	−4.97682	−	0.480938i	−0.995363	−	0.0961876i
$26$		0			0
$27$	5.36635	+	1.74363i	1.03276	+	0.335563i
$28$		0			0
$29$	4.78304	+	3.47508i	0.888188	+	0.645306i	0.935405	−	0.353578i	$-0.115035\pi$
$29$	4.78304	+	3.47508i	0.888188	+	0.645306i	−0.0472171	+	0.998885i	$0.515035\pi$
$30$		0			0
$31$	4.93462	−	3.58521i	0.886285	−	0.643923i	−0.0486220	−	0.998817i	$-0.515483\pi$
$31$	4.93462	−	3.58521i	0.886285	−	0.643923i	0.934907	+	0.354894i	$0.115483\pi$
$32$		0			0
$33$	1.73038	+	2.38166i	0.301220	+	0.414594i
$34$		0			0
$35$	−7.28304	−	0.351083i	−1.23106	−	0.0593438i
$36$		0			0
$37$	7.69215	−	2.49933i	1.26458	−	0.410887i	0.401457	−	0.915878i	$-0.368504\pi$
$37$	7.69215	−	2.49933i	1.26458	−	0.410887i	0.863125	+	0.504991i	$0.168504\pi$
$38$		0			0
$39$	0.134810	−	0.414902i	0.0215869	−	0.0664376i
$40$		0			0
$41$	−0.313697	−	0.965461i	−0.0489913	−	0.150780i	0.923568	−	0.383434i	$-0.125259\pi$
$41$	−0.313697	−	0.965461i	−0.0489913	−	0.150780i	−0.972559	+	0.232655i	$0.925259\pi$
$42$		0			0
$43$			3.24199i			0.494399i	0.968965	+	0.247200i	$0.0795103\pi$
$43$			3.24199i			0.494399i	−0.968965	+	0.247200i	$0.920490\pi$
$44$		0			0
$45$	1.79793	−	0.489840i	0.268019	−	0.0730210i
$46$		0			0
$47$	2.48043	−	3.41402i	0.361808	−	0.497986i	−0.588844	−	0.808247i	$-0.700417\pi$
$47$	2.48043	−	3.41402i	0.361808	−	0.497986i	0.950651	+	0.310261i	$0.100417\pi$
$48$		0			0
$49$	−3.63318			−0.519026
$50$		0			0
$51$	−7.59963			−1.06416
$52$		0			0
$53$	−4.76148	+	6.55362i	−0.654040	+	0.900209i	−0.999266	−	0.0383106i	$-0.987802\pi$
$53$	−4.76148	+	6.55362i	−0.654040	+	0.900209i	0.345226	+	0.938520i	$0.387802\pi$
$54$		0			0
$55$	4.18178	+	1.58516i	0.563871	+	0.213742i
$56$		0			0
$57$			2.54703i			0.337363i
$58$		0			0
$59$	1.83443	+	5.64581i	0.238823	+	0.735021i	0.996591	+	0.0824976i	$0.0262897\pi$
$59$	1.83443	+	5.64581i	0.238823	+	0.735021i	−0.757768	+	0.652524i	$0.773710\pi$
$60$		0			0
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	−0.931308	−	0.364233i	$-0.881331\pi$
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	0.967535	+	0.252738i	$0.0813312\pi$
$62$		0			0
$63$	2.58448	−	0.839749i	0.325614	−	0.105798i
$64$		0			0
$65$	−0.174207	−	0.639416i	−0.0216077	−	0.0793099i
$66$		0			0
$67$	−4.04870	−	5.57255i	−0.494627	−	0.680796i	0.486606	−	0.873622i	$-0.338235\pi$
$67$	−4.04870	−	5.57255i	−0.494627	−	0.680796i	−0.981233	+	0.192826i	$0.938235\pi$
$68$		0			0
$69$	−1.04697	+	0.760668i	−0.126040	+	0.0915737i
$70$		0			0
$71$	−4.82884	−	3.50836i	−0.573078	−	0.416366i	0.263144	−	0.964757i	$-0.415241\pi$
$71$	−4.82884	−	3.50836i	−0.573078	−	0.416366i	−0.836222	+	0.548391i	$0.815241\pi$
$72$		0			0
$73$	8.40107	+	2.72967i	0.983271	+	0.319484i	0.756161	−	0.654385i	$-0.227072\pi$
$73$	8.40107	+	2.72967i	0.983271	+	0.319484i	0.227110	+	0.973869i	$0.427072\pi$
$74$		0			0
$75$	−4.87861	+	5.51045i	−0.563333	+	0.636292i
$76$		0			0
$77$	6.20252	+	2.01532i	0.706842	+	0.229667i
$78$		0			0
$79$	6.27851	+	4.56161i	0.706388	+	0.513221i	0.882006	−	0.471237i	$-0.156192\pi$
$79$	6.27851	+	4.56161i	0.706388	+	0.513221i	−0.175618	+	0.984458i	$0.556192\pi$
$80$		0			0
$81$	4.69667	−	3.41233i	0.521852	−	0.379148i
$82$		0			0
$83$	8.53192	+	11.7432i	0.936500	+	1.28898i	0.957269	+	0.289197i	$0.0933884\pi$
$83$	8.53192	+	11.7432i	0.936500	+	1.28898i	−0.0207694	+	0.999784i	$0.506612\pi$
$84$		0			0
$85$	−9.65580	+	6.32825i	−1.04732	+	0.686395i
$86$		0			0
$87$	8.27647	−	2.68919i	0.887331	−	0.288311i
$88$		0			0
$89$	−2.32579	+	7.15805i	−0.246534	+	0.758752i	0.748847	+	0.662743i	$0.230608\pi$
$89$	−2.32579	+	7.15805i	−0.246534	+	0.758752i	−0.995380	+	0.0960092i	$0.969392\pi$
$90$		0			0
$91$	−0.298649	−	0.919147i	−0.0313069	−	0.0963528i
$92$		0			0
$93$		−	8.97820i		−	0.930996i
$94$		0			0
$95$	2.12093	+	3.23616i	0.217602	+	0.332023i
$96$		0			0
$97$	3.95373	−	5.44184i	0.401440	−	0.552535i	−0.559664	−	0.828719i	$-0.689070\pi$
$97$	3.95373	−	5.44184i	0.401440	−	0.552535i	0.961105	+	0.276184i	$0.0890699\pi$
$98$		0			0
$99$	−1.66673			−0.167513
$100$		0			0
$101$	−12.1955			−1.21350			−0.606748	−	0.794894i	$-0.707526\pi$
$101$	−12.1955			−1.21350			−0.606748	+	0.794894i	$0.707526\pi$
$102$		0			0
$103$	−0.811969	+	1.11758i	−0.0800057	+	0.110118i	−0.847144	−	0.531363i	$-0.821680\pi$
$103$	−0.811969	+	1.11758i	−0.0800057	+	0.110118i	0.767138	+	0.641482i	$0.221680\pi$
$104$		0			0
$105$	−6.71929	+	8.36912i	−0.655736	+	0.816742i
$106$		0			0
$107$			15.8285i			1.53020i	0.643911	+	0.765101i	$0.277311\pi$
$107$			15.8285i			1.53020i	−0.643911	+	0.765101i	$0.722689\pi$
$108$		0			0
$109$	0.619199	+	1.90570i	0.0593085	+	0.182533i	0.976322	−	0.216324i	$-0.0694069\pi$
$109$	0.619199	+	1.90570i	0.0593085	+	0.182533i	−0.917013	+	0.398857i	$0.869407\pi$
$110$		0			0
$111$	3.67889	−	11.3225i	0.349185	−	1.07468i
$112$		0			0
$113$	9.91713	−	3.22227i	0.932925	−	0.303126i	0.197167	−	0.980370i	$-0.436826\pi$
$113$	9.91713	−	3.22227i	0.932925	−	0.303126i	0.735758	+	0.677244i	$0.236826\pi$
$114$		0			0
$115$	−0.696828	+	1.83829i	−0.0649795	+	0.171422i
$116$		0			0
$117$	0.145178	+	0.199821i	0.0134217	+	0.0184734i
$118$		0			0
$119$	−13.6204	+	9.89577i	−1.24858	+	0.907144i
$120$		0			0
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$		0			0
$123$	−1.42111	−	0.461746i	−0.128137	−	0.0416343i
$124$		0			0
$125$	−1.61000	+	11.0638i	−0.144002	+	0.989577i
$126$		0			0
$127$	−5.56375	−	1.80777i	−0.493703	−	0.160414i	0.0515752	−	0.998669i	$-0.483576\pi$
$127$	−5.56375	−	1.80777i	−0.493703	−	0.160414i	−0.545278	+	0.838255i	$0.683576\pi$
$128$		0			0
$129$	3.86067	+	2.80494i	0.339913	+	0.246961i
$130$		0			0
$131$	−1.21081	+	0.879704i	−0.105789	+	0.0768601i	−0.639422	−	0.768856i	$-0.720826\pi$
$131$	−1.21081	+	0.879704i	−0.105789	+	0.0768601i	0.533633	+	0.845716i	$0.320826\pi$
$132$		0			0
$133$	3.31659	+	4.56489i	0.287585	+	0.395827i
$134$		0			0
$135$	4.47214	−	11.7979i	0.384900	−	1.01540i
$136$		0			0
$137$	−7.46472	+	2.42543i	−0.637754	+	0.207219i	−0.610007	−	0.792396i	$-0.708833\pi$
$137$	−7.46472	+	2.42543i	−0.637754	+	0.207219i	−0.0277472	+	0.999615i	$0.508833\pi$
$138$		0			0
$139$	1.66607	−	5.12764i	0.141314	−	0.434921i	−0.855204	−	0.518291i	$-0.826568\pi$
$139$	1.66607	−	5.12764i	0.141314	−	0.434921i	0.996519	+	0.0833702i	$0.0265684\pi$
$140$		0			0
$141$	−1.91948	−	5.90755i	−0.161649	−	0.497505i
$142$		0			0
$143$			0.592757i			0.0495689i
$144$		0			0
$145$	8.27647	−	10.3086i	0.687324	−	0.856086i
$146$		0			0
$147$	−3.14339	+	4.32651i	−0.259262	+	0.356844i
$148$		0			0
$149$	−18.8229			−1.54203			−0.771015	−	0.636817i	$-0.780251\pi$
$149$	−18.8229			−1.54203			−0.771015	+	0.636817i	$0.780251\pi$
$150$		0			0
$151$	3.88797			0.316398			0.158199	−	0.987407i	$-0.449431\pi$
$151$	3.88797			0.316398			0.158199	+	0.987407i	$0.449431\pi$
$152$		0			0
$153$	2.52903	−	3.48091i	0.204460	−	0.281415i
$154$		0			0
$155$	−7.47619	−	11.4074i	−0.600502	−	0.916261i
$156$		0			0
$157$		−	4.28378i		−	0.341883i	−0.985281	−	0.170941i	$-0.945319\pi$
$157$		−	4.28378i		−	0.341883i	0.985281	−	0.170941i	$-0.0546808\pi$
$158$		0			0
$159$	3.68467	+	11.3403i	0.292214	+	0.899341i
$160$		0			0
$161$	−0.885926	+	2.72660i	−0.0698208	+	0.214886i
$162$		0			0
$163$	14.9566	−	4.85970i	1.17149	−	0.380641i	0.342293	−	0.939593i	$-0.388796\pi$
$163$	14.9566	−	4.85970i	1.17149	−	0.380641i	0.829200	+	0.558952i	$0.188796\pi$
$164$		0			0
$165$	5.50569	−	3.60834i	0.428617	−	0.280909i
$166$		0			0
$167$	−12.3629	−	17.0161i	−0.956670	−	1.31674i	−0.948500	−	0.316777i	$-0.897399\pi$
$167$	−12.3629	−	17.0161i	−0.956670	−	1.31674i	−0.00816967	−	0.999967i	$-0.502601\pi$
$168$		0			0
$169$	−10.4462	+	7.58958i	−0.803551	+	0.583814i
$170$		0			0
$171$	−1.16663	−	0.847609i	−0.0892148	−	0.0648183i
$172$		0			0
$173$	6.81587	+	2.21461i	0.518201	+	0.168374i	0.556429	−	0.830895i	$-0.312171\pi$
$173$	6.81587	+	2.21461i	0.518201	+	0.168374i	−0.0382277	+	0.999269i	$0.512171\pi$
$174$		0			0
$175$	−1.56827	+	16.2287i	−0.118550	+	1.22677i
$176$		0			0
$177$	8.31034	+	2.70019i	0.624643	+	0.202959i
$178$		0			0
$179$	−6.50396	−	4.72540i	−0.486129	−	0.353193i	0.317565	−	0.948237i	$-0.397135\pi$
$179$	−6.50396	−	4.72540i	−0.486129	−	0.353193i	−0.803694	+	0.595043i	$0.797135\pi$
$180$		0			0
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.242200	−	0.970226i	$-0.422131\pi$
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.997584	+	0.0694707i	$0.0221310\pi$
$182$		0			0
$183$	−0.792181	−	1.09034i	−0.0585597	−	0.0806005i
$184$		0			0
$185$	−4.75401	−	17.4493i	−0.349522	−	1.28290i
$186$		0			0
$187$	9.82055	−	3.19089i	0.718150	−	0.233341i
$188$		0			0
$189$	5.68574	−	17.4989i	0.413577	−	1.27286i
$190$		0			0
$191$	−5.57167	−	17.1478i	−0.403152	−	1.24077i	−0.922429	−	0.386167i	$-0.873799\pi$
$191$	−5.57167	−	17.1478i	−0.403152	−	1.24077i	0.519277	−	0.854606i	$-0.326201\pi$
$192$		0			0
$193$			6.78859i			0.488653i	0.969693	+	0.244327i	$0.0785669\pi$
$193$			6.78859i			0.488653i	−0.969693	+	0.244327i	$0.921433\pi$
$194$		0			0
$195$	−0.912160	−	0.345766i	−0.0653211	−	0.0247608i
$196$		0			0
$197$	−4.69956	+	6.46839i	−0.334830	+	0.460854i	−0.942923	−	0.333012i	$-0.891935\pi$
$197$	−4.69956	+	6.46839i	−0.334830	+	0.460854i	0.608092	+	0.793866i	$0.291935\pi$
$198$		0			0
$199$	−5.20485			−0.368962			−0.184481	−	0.982836i	$-0.559060\pi$
$199$	−5.20485			−0.368962			−0.184481	+	0.982836i	$0.559060\pi$
$200$		0			0
$201$	−10.1389			−0.715141
$202$		0			0
$203$	11.3317	−	15.5968i	0.795332	−	1.09468i
$204$		0			0
$205$	−2.19011	+	0.596687i	−0.152964	+	0.0416745i
$206$		0			0
$207$		−	0.732688i		−	0.0509254i
$208$		0			0
$209$	−1.06943	−	3.29138i	−0.0739743	−	0.227669i
$210$		0			0
$211$	−5.13029	+	15.7894i	−0.353184	+	1.08699i	0.603872	+	0.797082i	$0.293624\pi$
$211$	−5.13029	+	15.7894i	−0.353184	+	1.08699i	−0.957055	+	0.289906i	$0.906376\pi$
$212$		0			0
$213$	−8.35573	+	2.71494i	−0.572525	+	0.186025i
$214$		0			0
$215$	7.24091	+	0.349052i	0.493826	+	0.0238051i
$216$		0			0
$217$	−11.6909	−	16.0911i	−0.793628	−	1.09233i
$218$		0			0
$219$	10.5191	−	7.64258i	0.710815	−	0.516438i
$220$		0			0
$221$	−1.23795	−	0.899425i	−0.0832737	−	0.0605019i
$222$		0			0
$223$	−6.30368	−	2.04819i	−0.422126	−	0.137157i	0.0902485	−	0.995919i	$-0.471234\pi$
$223$	−6.30368	−	2.04819i	−0.422126	−	0.137157i	−0.512374	+	0.858762i	$0.671234\pi$
$224$		0			0
$225$	−0.900470	−	4.06837i	−0.0600313	−	0.271224i
$226$		0			0
$227$	12.7365	+	4.13833i	0.845350	+	0.274671i	0.699497	−	0.714636i	$-0.253407\pi$
$227$	12.7365	+	4.13833i	0.845350	+	0.274671i	0.145853	+	0.989306i	$0.453407\pi$
$228$		0			0
$229$	8.16032	+	5.92882i	0.539249	+	0.391788i	0.823806	−	0.566872i	$-0.191846\pi$
$229$	8.16032	+	5.92882i	0.539249	+	0.391788i	−0.284557	+	0.958659i	$0.591846\pi$
$230$		0			0
$231$	7.76626	−	5.64252i	0.510983	−	0.371251i
$232$		0			0
$233$	−12.9345	−	17.8028i	−0.847368	−	1.16630i	−0.984437	−	0.175740i	$-0.943768\pi$
$233$	−12.9345	−	17.8028i	−0.847368	−	1.16630i	0.137069	−	0.990562i	$-0.456232\pi$
$234$		0			0
$235$	−7.35806	−	5.90755i	−0.479987	−	0.385366i
$236$		0			0
$237$	10.8642	−	3.53000i	0.705707	−	0.229298i
$238$		0			0
$239$	2.33626	−	7.19026i	0.151120	−	0.465099i	−0.846627	−	0.532187i	$-0.821371\pi$
$239$	2.33626	−	7.19026i	0.151120	−	0.465099i	0.997747	+	0.0670870i	$0.0213705\pi$
$240$		0			0
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	−0.920087	−	0.391713i	$-0.871883\pi$
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	0.514123	−	0.857716i	$-0.328117\pi$
$242$		0			0
$243$			8.38230i			0.537725i
$244$		0			0
$245$	−0.391169	+	8.11461i	−0.0249909	+	0.518424i
$246$		0			0
$247$	−0.301444	+	0.414902i	−0.0191804	+	0.0263996i
$248$		0			0
$249$	21.3659			1.35401
$250$		0			0
$251$	−10.5717			−0.667278			−0.333639	−	0.942701i	$-0.608277\pi$
$251$	−10.5717			−0.667278			−0.333639	+	0.942701i	$0.608277\pi$
$252$		0			0
$253$	1.03355	−	1.42256i	0.0649789	−	0.0894357i
$254$		0			0
$255$	−0.818220	+	16.9736i	−0.0512389	+	1.06293i
$256$		0			0
$257$			20.2700i			1.26441i	0.774801	+	0.632205i	$0.217850\pi$
$257$			20.2700i			1.26441i	−0.774801	+	0.632205i	$0.782150\pi$
$258$		0			0
$259$	−8.14996	−	25.0830i	−0.506414	−	1.55858i
$260$		0			0
$261$	−1.52252	+	4.68585i	−0.0942419	+	0.290047i
$262$		0			0
$263$	−26.7160	+	8.68056i	−1.64738	+	0.535267i	−0.978170	−	0.207806i	$-0.933368\pi$
$263$	−26.7160	+	8.68056i	−1.64738	+	0.535267i	−0.669211	+	0.743072i	$0.733368\pi$
$264$		0			0
$265$	14.1247	+	11.3403i	0.867673	+	0.696626i
$266$		0			0
$267$	6.51179	+	8.96271i	0.398515	+	0.548509i
$268$		0			0
$269$	16.4416	−	11.9455i	1.00246	−	0.728333i	0.0398490	−	0.999206i	$-0.487312\pi$
$269$	16.4416	−	11.9455i	1.00246	−	0.728333i	0.962615	+	0.270873i	$0.0873123\pi$
$270$		0			0
$271$	25.4409	+	18.4839i	1.54543	+	1.12282i	0.946816	+	0.321777i	$0.104280\pi$
$271$	25.4409	+	18.4839i	1.54543	+	1.12282i	0.598610	+	0.801041i	$0.295720\pi$
$272$		0			0
$273$	−1.35294	−	0.439596i	−0.0818835	−	0.0266056i
$274$		0			0
$275$	3.99064	−	9.16923i	0.240645	−	0.552925i
$276$		0			0
$277$	−13.2487	−	4.30475i	−0.796035	−	0.258648i	−0.117363	−	0.993089i	$-0.537444\pi$
$277$	−13.2487	−	4.30475i	−0.796035	−	0.258648i	−0.678672	+	0.734441i	$0.737444\pi$
$278$		0			0
$279$	4.11235	+	2.98779i	0.246200	+	0.178875i
$280$		0			0
$281$	−20.9355	+	15.2105i	−1.24891	+	0.907383i	−0.998158	−	0.0606690i	$-0.980677\pi$
$281$	−20.9355	+	15.2105i	−1.24891	+	0.907383i	−0.250748	+	0.968052i	$0.580677\pi$
$282$		0			0
$283$	−13.9491	−	19.1993i	−0.829188	−	1.14128i	−0.988074	−	0.153983i	$-0.950790\pi$
$283$	−13.9491	−	19.1993i	−0.829188	−	1.14128i	0.158885	−	0.987297i	$-0.449210\pi$
$284$		0			0
$285$	5.68873	+	0.274228i	0.336971	+	0.0162439i
$286$		0			0
$287$	−3.14823	+	1.02292i	−0.185834	+	0.0603811i
$288$		0			0
$289$	−2.98394	+	9.18363i	−0.175526	+	0.540214i
$290$		0			0
$291$	−3.05959	−	9.41645i	−0.179356	−	0.552002i
$292$		0			0
$293$			12.3029i			0.718742i	0.933195	+	0.359371i	$0.117009\pi$
$293$			12.3029i			0.718742i	−0.933195	+	0.359371i	$0.882991\pi$
$294$		0			0
$295$	12.8073	−	3.48930i	0.745668	−	0.203155i
$296$		0			0
$297$	−6.63318	+	9.12979i	−0.384896	+	0.529764i
$298$		0			0
$299$	−0.260574			−0.0150694
$300$		0			0
$301$	10.5717			0.609341
$302$		0			0
$303$	−10.5514	+	14.5228i	−0.606163	+	0.834311i
$304$		0			0
$305$	−1.91445	−	0.725696i	−0.109621	−	0.0415532i
$306$		0			0
$307$		−	4.28249i		−	0.244415i	−0.992505	−	0.122207i	$-0.961003\pi$
$307$		−	4.28249i		−	0.244415i	0.992505	−	0.122207i	$-0.0389973\pi$
$308$		0			0
$309$	0.628342	+	1.93384i	0.0357451	+	0.110012i
$310$		0			0
$311$	−7.92526	+	24.3915i	−0.449400	+	1.38311i	0.428185	+	0.903691i	$0.359153\pi$
$311$	−7.92526	+	24.3915i	−0.449400	+	1.38311i	−0.877585	+	0.479421i	$0.840847\pi$
$312$		0			0
$313$	−21.2573	+	6.90692i	−1.20153	+	0.390402i	−0.840325	−	0.542083i	$-0.817636\pi$
$313$	−21.2573	+	6.90692i	−1.20153	+	0.390402i	−0.361209	+	0.932485i	$0.617636\pi$
$314$		0			0
$315$	−1.59730	−	5.86279i	−0.0899975	−	0.330331i
$316$		0			0
$317$	−12.8859	−	17.7360i	−0.723746	−	0.996151i	−0.999391	−	0.0348911i	$-0.988892\pi$
$317$	−12.8859	−	17.7360i	−0.723746	−	0.996151i	0.275645	−	0.961259i	$-0.411108\pi$
$318$		0			0
$319$	−9.56608	+	6.95016i	−0.535597	+	0.389134i
$320$		0			0
$321$	18.8491	+	13.6947i	1.05205	+	0.764363i
$322$		0			0
$323$	8.49664	+	2.76073i	0.472766	+	0.153611i
$324$		0			0
$325$	−1.44688	+	0.320244i	−0.0802583	+	0.0177639i
$326$		0			0
$327$	2.80509	+	0.911429i	0.155122	+	0.0504021i
$328$		0			0
$329$	−11.1326	−	8.08832i	−0.613761	−	0.445923i
$330$		0			0
$331$	−7.25121	+	5.26831i	−0.398563	+	0.289573i	−0.768955	−	0.639303i	$-0.779223\pi$
$331$	−7.25121	+	5.26831i	−0.398563	+	0.289573i	0.370393	+	0.928875i	$0.379223\pi$
$332$		0			0
$333$	3.96183	+	5.45299i	0.217107	+	0.298822i
$334$		0			0
$335$	−12.8821	+	8.44269i	−0.703822	+	0.461273i
$336$		0			0
$337$	27.6601	−	8.98731i	1.50674	−	0.489570i	0.564766	−	0.825251i	$-0.308966\pi$
$337$	27.6601	−	8.98731i	1.50674	−	0.489570i	0.941976	+	0.335681i	$0.108966\pi$
$338$		0			0
$339$	4.74302	−	14.5975i	0.257605	−	0.792828i
$340$		0			0
$341$	3.76972	+	11.6020i	0.204142	+	0.628283i
$342$		0			0
$343$		−	10.9787i		−	0.592795i
$344$		0			0
$345$	1.58621	+	2.42028i	0.0853987	+	0.130303i
$346$		0			0
$347$	−8.40368	+	11.5667i	−0.451133	+	0.620931i	−0.972641	−	0.232315i	$-0.925370\pi$
$347$	−8.40368	+	11.5667i	−0.451133	+	0.620931i	0.521508	+	0.853247i	$0.325370\pi$
$348$		0			0
$349$	−5.62382			−0.301036			−0.150518	−	0.988607i	$-0.548094\pi$
$349$	−5.62382			−0.301036			−0.150518	+	0.988607i	$0.548094\pi$
$350$		0			0
$351$	1.67232			0.0892620
$352$		0			0
$353$	−1.12265	+	1.54520i	−0.0597529	+	0.0822427i	−0.837848	−	0.545904i	$-0.816186\pi$
$353$	−1.12265	+	1.54520i	−0.0597529	+	0.0822427i	0.778095	+	0.628147i	$0.216186\pi$
$354$		0			0
$355$	−8.35573	+	10.4074i	−0.443476	+	0.552366i
$356$		0			0
$357$			24.7813i			1.31156i
$358$		0			0
$359$	6.86161	+	21.1179i	0.362142	+	1.11456i	0.951751	+	0.306870i	$0.0992818\pi$
$359$	6.86161	+	21.1179i	0.362142	+	1.11456i	−0.589609	+	0.807689i	$0.700718\pi$
$360$		0			0
$361$	−4.94606	+	15.2224i	−0.260319	+	0.801179i
$362$		0			0
$363$	9.79935	−	3.18400i	0.514332	−	0.167117i
$364$		0			0
$365$	7.00116	−	18.4697i	0.366458	−	0.966748i
$366$		0			0
$367$	−12.6050	−	17.3493i	−0.657978	−	0.905629i	0.341435	−	0.939906i	$-0.389087\pi$
$367$	−12.6050	−	17.3493i	−0.657978	−	0.905629i	−0.999412	+	0.0342768i	$0.989087\pi$
$368$		0			0
$369$	0.684418	−	0.497259i	0.0356294	−	0.0258863i
$370$		0			0
$371$	21.3704	+	15.5265i	1.10950	+	0.806096i
$372$		0			0
$373$	−22.0074	−	7.15063i	−1.13950	−	0.370245i	−0.322320	−	0.946631i	$-0.604463\pi$
$373$	−22.0074	−	7.15063i	−1.13950	−	0.370245i	−0.817178	+	0.576385i	$0.804463\pi$
$374$		0			0
$375$	11.7822	+	11.4895i	0.608430	+	0.593317i
$376$		0			0
$377$	1.66648	+	0.541471i	0.0858279	+	0.0278872i
$378$		0			0
$379$	17.5153	+	12.7256i	0.899702	+	0.653672i	0.938390	−	0.345579i	$-0.112318\pi$
$379$	17.5153	+	12.7256i	0.899702	+	0.653672i	−0.0386872	+	0.999251i	$0.512318\pi$
$380$		0			0
$381$	−6.96645	+	5.06142i	−0.356902	+	0.259304i
$382$		0			0
$383$	−3.32381	−	4.57484i	−0.169839	−	0.233763i	0.715610	−	0.698500i	$-0.246149\pi$
$383$	−3.32381	−	4.57484i	−0.169839	−	0.233763i	−0.885449	+	0.464737i	$0.846149\pi$
$384$		0			0
$385$	5.16896	−	13.6362i	0.263435	−	0.694964i
$386$		0			0
$387$	−2.56953	+	0.834891i	−0.130617	+	0.0424399i
$388$		0			0
$389$	2.51109	−	7.72833i	0.127317	−	0.391842i	−0.866999	−	0.498310i	$-0.833954\pi$
$389$	2.51109	−	7.72833i	0.127317	−	0.391842i	0.994316	+	0.106468i	$0.0339541\pi$
$390$		0			0
$391$	1.40270	+	4.31707i	0.0709377	+	0.218324i
$392$		0			0
$393$			2.20298i			0.111126i
$394$		0			0
$395$	10.8642	−	13.5318i	0.546638	−	0.680857i
$396$		0			0
$397$	−12.2076	+	16.8024i	−0.612684	+	0.843287i	−0.996795	−	0.0799998i	$-0.974508\pi$
$397$	−12.2076	+	16.8024i	−0.612684	+	0.843287i	0.384111	+	0.923287i	$0.374508\pi$
$398$		0			0
$399$	8.30550			0.415795
$400$		0			0
$401$	30.1195			1.50410			0.752049	−	0.659107i	$-0.229066\pi$
$401$	30.1195			1.50410			0.752049	+	0.659107i	$0.229066\pi$
$402$		0			0
$403$	1.06258	−	1.46252i	0.0529309	−	0.0728532i
$404$		0			0
$405$	−7.11568	−	10.8573i	−0.353581	−	0.539503i
$406$		0			0
$407$			16.1760i			0.801815i
$408$		0			0
$409$	−3.41317	−	10.5046i	−0.168770	−	0.519421i	0.830524	−	0.556983i	$-0.188041\pi$
$409$	−3.41317	−	10.5046i	−0.168770	−	0.519421i	−0.999294	+	0.0375613i	$0.988041\pi$
$410$		0			0
$411$	−3.57012	+	10.9877i	−0.176101	+	0.541983i
$412$		0			0
$413$	18.4102	−	5.98182i	0.905905	−	0.294346i
$414$		0			0
$415$	27.1467	−	17.7915i	1.33258	−	0.873350i
$416$		0			0
$417$	−4.66469	−	6.42039i	−0.228431	−	0.314408i
$418$		0			0
$419$	26.6338	−	19.3506i	1.30115	−	0.945337i	0.301179	−	0.953568i	$-0.402620\pi$
$419$	26.6338	−	19.3506i	1.30115	−	0.945337i	0.999966	+	0.00823011i	$0.00261975\pi$
$420$		0			0
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	0.910626	−	0.413231i	$-0.135600\pi$
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	−0.111607	+	0.993752i	$0.535600\pi$
$422$		0			0
$423$	3.34464	+	1.08674i	0.162622	+	0.0528392i
$424$		0			0
$425$	13.0944	+	22.2473i	0.635171	+	1.07915i
$426$		0			0
$427$	−2.83956	−	0.922629i	−0.137416	−	0.0446491i
$428$		0			0
$429$	0.705874	+	0.512848i	0.0340799	+	0.0247605i
$430$		0			0
$431$	5.78873	−	4.20576i	0.278833	−	0.202584i	−0.439575	−	0.898206i	$-0.644871\pi$
$431$	5.78873	−	4.20576i	0.278833	−	0.202584i	0.718408	+	0.695622i	$0.244871\pi$
$432$		0			0
$433$	−3.22262	−	4.43555i	−0.154869	−	0.213159i	0.724531	−	0.689242i	$-0.242056\pi$
$433$	−3.22262	−	4.43555i	−0.154869	−	0.213159i	−0.879400	+	0.476083i	$0.842056\pi$
$434$		0			0
$435$	−5.11514	−	18.7748i	−0.245252	−	0.900184i
$436$		0			0
$437$	1.44688	−	0.470119i	0.0692135	−	0.0224888i
$438$		0			0
$439$	−9.50415	+	29.2508i	−0.453609	+	1.39606i	0.419153	+	0.907916i	$0.362327\pi$
$439$	−9.50415	+	29.2508i	−0.453609	+	1.39606i	−0.872761	+	0.488148i	$0.837673\pi$
$440$		0			0
$441$	−0.935631	−	2.87958i	−0.0445539	−	0.137123i
$442$		0			0
$443$			11.3527i			0.539381i	0.962947	+	0.269691i	$0.0869214\pi$
$443$			11.3527i			0.539381i	−0.962947	+	0.269691i	$0.913079\pi$
$444$		0			0
$445$	15.7369	+	5.96528i	0.746002	+	0.282781i
$446$		0			0
$447$	−16.2854	+	22.4149i	−0.770271	+	1.06019i
$448$		0			0
$449$	15.7661			0.744050			0.372025	−	0.928223i	$-0.378664\pi$
$449$	15.7661			0.744050			0.372025	+	0.928223i	$0.378664\pi$
$450$		0			0
$451$	2.03029			0.0956027
$452$		0			0
$453$	3.36383	−	4.62992i	0.158047	−	0.217532i
$454$		0			0
$455$	−2.08504	+	0.568064i	−0.0977484	+	0.0266312i
$456$		0			0
$457$		−	4.16714i		−	0.194931i	−0.995239	−	0.0974653i	$-0.968926\pi$
$457$		−	4.16714i		−	0.194931i	0.995239	−	0.0974653i	$-0.0310735\pi$
$458$		0			0
$459$	−9.00233	−	27.7063i	−0.420193	−	1.29322i
$460$		0			0
$461$	−7.40758	+	22.7982i	−0.345005	+	1.06182i	0.616576	+	0.787296i	$0.288519\pi$
$461$	−7.40758	+	22.7982i	−0.345005	+	1.06182i	−0.961581	+	0.274521i	$0.911481\pi$
$462$		0			0
$463$	−39.3021	+	12.7700i	−1.82652	+	0.593473i	−0.827013	+	0.562183i	$0.809962\pi$
$463$	−39.3021	+	12.7700i	−1.82652	+	0.593473i	−0.999510	+	0.0312899i	$0.990038\pi$
$464$		0			0
$465$	−20.0526	−	0.966645i	−0.929916	−	0.0448271i
$466$		0			0
$467$	−6.11096	−	8.41102i	−0.282782	−	0.389216i	0.643871	−	0.765134i	$-0.277327\pi$
$467$	−6.11096	−	8.41102i	−0.282782	−	0.389216i	−0.926653	+	0.375918i	$0.877327\pi$
$468$		0			0
$469$	−18.1713	+	13.2022i	−0.839072	+	0.609622i
$470$		0			0
$471$	−5.10126	−	3.70628i	−0.235054	−	0.170776i
$472$		0			0
$473$	−6.16663	−	2.00366i	−0.283542	−	0.0921284i
$474$		0			0
$475$	7.45624	−	4.38861i	0.342116	−	0.201363i
$476$		0			0
$477$	−6.42045	−	2.08613i	−0.293972	−	0.0955174i
$478$		0			0
$479$	−29.1312	−	21.1650i	−1.33104	−	0.967055i	−0.999723	−	0.0235349i	$-0.992508\pi$
$479$	−29.1312	−	21.1650i	−1.33104	−	0.967055i	−0.331314	−	0.943520i	$-0.607492\pi$
$480$		0			0
$481$	1.93930	−	1.40899i	0.0884246	−	0.0642443i
$482$		0			0
$483$	2.48043	+	3.41402i	0.112863	+	0.155343i
$484$		0			0
$485$	−11.7285	−	9.41645i	−0.532565	−	0.427579i
$486$		0			0
$487$	10.1172	−	3.28726i	0.458452	−	0.148960i	−0.0706809	−	0.997499i	$-0.522517\pi$
$487$	10.1172	−	3.28726i	0.458452	−	0.148960i	0.529133	+	0.848539i	$0.322517\pi$
$488$		0			0
$489$	7.15323	−	22.0154i	0.323480	−	0.995570i
$490$		0			0
$491$	5.46010	+	16.8045i	0.246411	+	0.758375i	0.995401	+	0.0957938i	$0.0305389\pi$
$491$	5.46010	+	16.8045i	0.246411	+	0.758375i	−0.748990	+	0.662581i	$0.769461\pi$
$492$		0			0
$493$		−	30.5243i		−	1.37475i
$494$		0			0
$495$	−0.179450	+	3.72260i	−0.00806568	+	0.167319i
$496$		0			0
$497$	−11.4403	+	15.7462i	−0.513166	+	0.706312i
$498$		0			0
$499$	−9.41734			−0.421578			−0.210789	−	0.977532i	$-0.567603\pi$
$499$	−9.41734			−0.421578			−0.210789	+	0.977532i	$0.567603\pi$
$500$		0			0
$501$	−30.9595			−1.38317
$502$		0			0
$503$	−10.5879	+	14.5730i	−0.472093	+	0.649780i	−0.976961	−	0.213416i	$-0.931541\pi$
$503$	−10.5879	+	14.5730i	−0.472093	+	0.649780i	0.504869	+	0.863196i	$0.331541\pi$
$504$		0			0
$505$	−1.31304	+	27.2383i	−0.0584294	+	1.21209i
$506$		0			0
$507$			19.0060i			0.844088i
$508$		0			0
$509$	4.95926	+	15.2630i	0.219815	+	0.676522i	0.998777	+	0.0494500i	$0.0157469\pi$
$509$	4.95926	+	15.2630i	0.219815	+	0.676522i	−0.778961	+	0.627072i	$0.784253\pi$
$510$		0			0
$511$	8.90107	−	27.3947i	0.393760	−	1.21187i
$512$		0			0
$513$	−9.28583	+	3.01715i	−0.409980	+	0.133210i
$514$		0			0
$515$	2.40867	+	1.93384i	0.106138	+	0.0852151i
$516$		0			0
$517$	4.96086	+	6.82803i	0.218178	+	0.300297i
$518$		0			0
$519$	8.53425	−	6.20050i	0.374612	−	0.272172i
$520$		0			0
$521$	1.78040	+	1.29354i	0.0780007	+	0.0566708i	0.626102	−	0.779741i	$-0.284649\pi$
$521$	1.78040	+	1.29354i	0.0780007	+	0.0566708i	−0.548102	+	0.836412i	$0.684649\pi$
$522$		0			0
$523$	−7.07194	−	2.29781i	−0.309234	−	0.100476i	0.150289	−	0.988642i	$-0.451980\pi$
$523$	−7.07194	−	2.29781i	−0.309234	−	0.100476i	−0.459523	+	0.888166i	$0.651980\pi$
$524$		0			0
$525$	17.9688	+	15.9084i	0.784222	+	0.694301i
$526$		0			0
$527$	−29.9504	−	9.73147i	−1.30466	−	0.423909i
$528$		0			0
$529$	−17.9820	−	13.0647i	−0.781828	−	0.568031i
$530$		0			0
$531$	−4.00233	+	2.90786i	−0.173686	+	0.126190i
$532$		0			0
$533$	−0.176845	−	0.243407i	−0.00766003	−	0.0105431i
$534$		0			0
$535$	35.3526	+	1.70419i	1.52843	+	0.0736786i
$536$		0			0
$537$	−11.2543	+	3.65675i	−0.485660	+	0.157800i
$538$		0			0
$539$	2.24543	−	6.91072i	0.0967174	−	0.297666i
$540$		0			0
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	0.989400	+	0.145216i	$0.0463878\pi$
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	−0.715085	+	0.699037i	$0.753612\pi$
$542$		0			0
$543$		−	30.3473i		−	1.30233i
$544$		0			0
$545$	4.32299	−	1.17779i	0.185177	−	0.0504508i
$546$		0			0
$547$	−18.4424	+	25.3839i	−0.788542	+	1.08534i	0.205746	+	0.978605i	$0.434038\pi$
$547$	−18.4424	+	25.3839i	−0.788542	+	1.08534i	−0.994288	+	0.106730i	$0.965962\pi$
$548$		0			0
$549$	0.763042			0.0325658
$550$		0			0
$551$	−10.2303			−0.435825
$552$		0			0
$553$	14.8747	−	20.4733i	0.632538	−	0.870615i
$554$		0			0
$555$	−24.8923	−	9.43574i	−1.05662	−	0.400525i
$556$		0			0
$557$		−	22.3515i		−	0.947064i	−0.880776	−	0.473532i	$-0.842979\pi$
$557$		−	22.3515i		−	0.947064i	0.880776	−	0.473532i	$-0.157021\pi$
$558$		0			0
$559$	0.296921	+	0.913829i	0.0125584	+	0.0386509i
$560$		0			0
$561$	4.69683	−	14.4554i	0.198300	−	0.610305i
$562$		0			0
$563$	32.6843	−	10.6198i	1.37748	−	0.447570i	0.475639	−	0.879640i	$-0.342217\pi$
$563$	32.6843	−	10.6198i	1.37748	−	0.447570i	0.901840	+	0.432070i	$0.142217\pi$
$564$		0			0
$565$	−6.12912	−	22.4966i	−0.257854	−	0.946438i
$566$		0			0
$567$	−11.1271	−	15.3152i	−0.467295	−	0.643177i
$568$		0			0
$569$	26.0230	−	18.9068i	1.09094	−	0.792615i	0.111383	−	0.993778i	$-0.464472\pi$
$569$	26.0230	−	18.9068i	1.09094	−	0.792615i	0.979558	+	0.201162i	$0.0644718\pi$
$570$		0			0
$571$	−21.9784	−	15.9683i	−0.919768	−	0.668251i	0.0236979	−	0.999719i	$-0.492456\pi$
$571$	−21.9784	−	15.9683i	−0.919768	−	0.668251i	−0.943466	+	0.331468i	$0.892456\pi$
$572$		0			0
$573$	−25.2407	−	8.20121i	−1.05445	−	0.342610i
$574$		0			0
$575$	4.03076	+	1.75427i	0.168094	+	0.0731581i
$576$		0			0
$577$	13.1724	+	4.27998i	0.548375	+	0.178178i	0.570084	−	0.821586i	$-0.306911\pi$
$577$	13.1724	+	4.27998i	0.548375	+	0.178178i	−0.0217089	+	0.999764i	$0.506911\pi$
$578$		0			0
$579$	8.08407	+	5.87342i	0.335963	+	0.244091i
$580$		0			0
$581$	38.2928	−	27.8214i	1.58865	−	1.15422i
$582$		0			0
$583$	−9.52297	−	13.1072i	−0.394401	−	0.542847i
$584$		0			0
$585$	0.461925	−	0.302738i	0.0190982	−	0.0125167i
$586$		0			0
$587$	41.9890	−	13.6431i	1.73307	−	0.563110i	0.739185	−	0.673502i	$-0.235211\pi$
$587$	41.9890	−	13.6431i	1.73307	−	0.563110i	0.993888	+	0.110392i	$0.0352107\pi$
$588$		0			0
$589$	−3.26152	+	10.0379i	−0.134389	+	0.413606i
$590$		0			0
$591$	3.63675	+	11.1928i	0.149596	+	0.460409i
$592$		0			0
$593$			16.2531i			0.667437i	0.942673	+	0.333718i	$0.108303\pi$
$593$			16.2531i			0.667437i	−0.942673	+	0.333718i	$0.891697\pi$
$594$		0			0
$595$	20.6355	+	31.4862i	0.845973	+	1.29081i
$596$		0			0
$597$	−4.50318	+	6.19810i	−0.184303	+	0.253671i
$598$		0			0
$599$	30.4822			1.24547			0.622734	−	0.782433i	$-0.286022\pi$
$599$	30.4822			1.24547			0.622734	+	0.782433i	$0.286022\pi$
$600$		0			0
$601$	−28.9162			−1.17952			−0.589758	−	0.807580i	$-0.700777\pi$
$601$	−28.9162			−1.17952			−0.589758	+	0.807580i	$0.700777\pi$
$602$		0			0
$603$	3.37405	−	4.64398i	0.137402	−	0.189117i
$604$		0			0
$605$	9.79935	−	12.2054i	0.398400	−	0.496222i
$606$		0			0
$607$		−	8.23276i		−	0.334157i	−0.985944	−	0.167079i	$-0.946567\pi$
$607$		−	8.23276i		−	0.334157i	0.985944	−	0.167079i	$-0.0534334\pi$
$608$		0			0
$609$	−8.76906	−	26.9884i	−0.355340	−	1.09362i
$610$		0			0
$611$	0.386489	−	1.18949i	0.0156357	−	0.0481217i
$612$		0			0
$613$	4.56327	−	1.48270i	0.184309	−	0.0598856i	−0.215408	−	0.976524i	$-0.569108\pi$
$613$	4.56327	−	1.48270i	0.184309	−	0.0598856i	0.399717	+	0.916638i	$0.369108\pi$
$614$		0			0
$615$	−1.18430	+	3.12430i	−0.0477557	+	0.125984i
$616$		0			0
$617$	1.19428	+	1.64379i	0.0480800	+	0.0661765i	0.832380	−	0.554205i	$-0.186978\pi$
$617$	1.19428	+	1.64379i	0.0480800	+	0.0661765i	−0.784300	+	0.620382i	$0.786978\pi$
$618$		0			0
$619$	−6.58621	+	4.78516i	−0.264722	+	0.192332i	−0.712226	−	0.701950i	$-0.752313\pi$
$619$	−6.58621	+	4.78516i	−0.264722	+	0.192332i	0.447504	+	0.894282i	$0.352313\pi$
$620$		0			0
$621$	−4.01342	−	2.91592i	−0.161053	−	0.117012i
$622$		0			0
$623$	23.3414	+	7.58408i	0.935153	+	0.303850i
$624$		0			0
$625$	24.5374	+	4.78708i	0.981496	+	0.191483i
$626$		0			0
$627$	−4.84474	−	1.57415i	−0.193480	−	0.0628656i
$628$		0			0
$629$	−33.7830	−	24.5448i	−1.34702	−	0.978665i
$630$		0			0
$631$	26.9279	−	19.5643i	1.07198	−	0.778841i	0.0957154	−	0.995409i	$-0.469486\pi$
$631$	26.9279	−	19.5643i	1.07198	−	0.778841i	0.976268	+	0.216567i	$0.0694861\pi$
$632$		0			0
$633$	14.3638	+	19.7701i	0.570912	+	0.785793i
$634$		0			0
$635$	−4.63663	+	12.2318i	−0.183999	+	0.485406i
$636$		0			0
$637$	−1.02409	+	0.332749i	−0.0405761	+	0.0131840i
$638$		0			0
$639$	1.53710	−	4.73072i	0.0608069	−	0.187144i
$640$		0			0
$641$	−12.3755	−	38.0880i	−0.488804	−	1.50439i	−0.826394	−	0.563092i	$-0.809612\pi$
$641$	−12.3755	−	38.0880i	−0.488804	−	1.50439i	0.337590	−	0.941293i	$-0.390388\pi$
$642$		0			0
$643$		−	11.6870i		−	0.460890i	−0.973085	−	0.230445i	$-0.925982\pi$
$643$		−	11.6870i		−	0.460890i	0.973085	−	0.230445i	$-0.0740182\pi$
$644$		0			0
$645$	6.68042	−	8.32070i	0.263041	−	0.327627i
$646$		0			0
$647$	4.67252	−	6.43117i	0.183696	−	0.252835i	−0.707231	−	0.706982i	$-0.750056\pi$
$647$	4.67252	−	6.43117i	0.183696	−	0.252835i	0.890927	+	0.454147i	$0.150056\pi$
$648$		0			0
$649$	−11.8727			−0.466044
$650$		0			0
$651$	−29.2766			−1.14744
$652$		0			0
$653$	−1.96165	+	2.69998i	−0.0767653	+	0.105658i	−0.845673	−	0.533702i	$-0.820801\pi$
$653$	−1.96165	+	2.69998i	−0.0767653	+	0.105658i	0.768908	+	0.639360i	$0.220801\pi$
$654$		0			0
$655$	1.83443	+	2.79902i	0.0716772	+	0.109367i
$656$		0			0
$657$			7.36146i			0.287198i
$658$		0			0
$659$	−9.28621	−	28.5800i	−0.361739	−	1.11332i	−0.951998	−	0.306105i	$-0.900974\pi$
$659$	−9.28621	−	28.5800i	−0.361739	−	1.11332i	0.590259	−	0.807214i	$-0.299026\pi$
$660$		0			0
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	−0.982796	−	0.184693i	$-0.940871\pi$
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	0.903659	+	0.428253i	$0.140871\pi$
$662$		0			0
$663$	−2.14213	+	0.696020i	−0.0831934	+	0.0270312i
$664$		0			0
$665$	10.5527	−	6.91604i	0.409215	−	0.268192i
$666$		0			0
$667$	−3.05526	−	4.20521i	−0.118300	−	0.162826i
$668$		0			0
$669$	−7.89293	+	5.73455i	−0.305158	+	0.221711i
$670$		0			0
$671$	1.48150	+	1.07637i	0.0571925	+	0.0415528i
$672$		0			0
$673$	−6.40194	−	2.08012i	−0.246777	−	0.0801826i	0.183017	−	0.983110i	$-0.441414\pi$
$673$	−6.40194	−	2.08012i	−0.246777	−	0.0801826i	−0.429794	+	0.902927i	$0.641414\pi$
$674$		0			0
$675$	−25.8688	−	11.2586i	−0.995690	−	0.433345i
$676$		0			0
$677$	12.9799	+	4.21741i	0.498857	+	0.162088i	0.547629	−	0.836722i	$-0.315531\pi$
$677$	12.9799	+	4.21741i	0.498857	+	0.162088i	−0.0487718	+	0.998810i	$0.515531\pi$
$678$		0			0
$679$	−17.7451	−	12.8925i	−0.680993	−	0.494770i
$680$		0			0
$681$	15.9475	−	11.5866i	0.611111	−	0.443998i
$682$		0			0
$683$	−0.689001	−	0.948329i	−0.0263639	−	0.0362868i	0.795632	−	0.605781i	$-0.207139\pi$
$683$	−0.689001	−	0.948329i	−0.0263639	−	0.0362868i	−0.821995	+	0.569494i	$0.807139\pi$
$684$		0			0
$685$	4.61345	+	16.9334i	0.176271	+	0.646992i
$686$		0			0
$687$	14.1205	−	4.58802i	0.538729	−	0.175044i
$688$		0			0
$689$	−0.741913	+	2.28337i	−0.0282646	+	0.0869896i
$690$		0			0
$691$	−3.79083	−	11.6670i	−0.144210	−	0.443832i	0.852699	−	0.522403i	$-0.174964\pi$
$691$	−3.79083	−	11.6670i	−0.144210	−	0.443832i	−0.996909	+	0.0785709i	$0.974964\pi$
$692$		0			0
$693$			5.43497i			0.206457i
$694$		0			0
$695$	−11.2731	−	4.27320i	−0.427612	−	0.162092i
$696$		0			0
$697$	−3.08068	+	4.24019i	−0.116689	+	0.160609i
$698$		0			0
$699$	−32.3910			−1.22514
$700$		0			0
$701$	−20.0271			−0.756415			−0.378207	−	0.925721i	$-0.623459\pi$
$701$	−20.0271			−0.756415			−0.378207	+	0.925721i	$0.623459\pi$
$702$		0			0
$703$	−8.22624	+	11.3225i	−0.310259	+	0.427034i
$704$		0			0
$705$	−13.4010	+	3.65106i	−0.504711	+	0.137507i
$706$		0			0
$707$			39.7677i			1.49562i
$708$		0			0
$709$	1.35816	+	4.17998i	0.0510067	+	0.156983i	0.973315	−	0.229471i	$-0.0736998\pi$
$709$	1.35816	+	4.17998i	0.0510067	+	0.156983i	−0.922309	+	0.386454i	$0.873700\pi$
$710$		0			0
$711$	−1.99856	+	6.15094i	−0.0749519	+	0.230678i
$712$		0			0
$713$	−5.10019	+	1.65715i	−0.191004	+	0.0620608i
$714$		0			0
$715$	1.32391	+	0.0638197i	0.0495114	+	0.00238672i
$716$		0			0
$717$	−6.54109	−	9.00303i	−0.244281	−	0.336224i
$718$		0			0
$719$	8.84119	−	6.42350i	0.329721	−	0.239556i	−0.410591	−	0.911819i	$-0.634678\pi$
$719$	8.84119	−	6.42350i	0.329721	−	0.239556i	0.740312	+	0.672263i	$0.234678\pi$
$720$		0			0
$721$	3.64427	+	2.64772i	0.135720	+	0.0986061i
$722$		0			0
$723$	−28.5505	−	9.27661i	−1.06180	−	0.345001i
$724$		0			0
$725$	−22.1330	−	19.5952i	−0.821999	−	0.727747i
$726$		0			0
$727$	31.2928	+	10.1677i	1.16059	+	0.377097i	0.825122	−	0.564955i	$-0.191107\pi$
$727$	31.2928	+	10.1677i	1.16059	+	0.377097i	0.335465	+	0.942053i	$0.391107\pi$
$728$		0			0
$729$	24.0719	+	17.4893i	0.891553	+	0.647751i
$730$		0			0
$731$	13.5416	−	9.83853i	0.500853	−	0.363891i
$732$		0			0
$733$	−8.08190	−	11.1238i	−0.298512	−	0.410866i	0.633244	−	0.773952i	$-0.281723\pi$
$733$	−8.08190	−	11.1238i	−0.298512	−	0.410866i	−0.931756	+	0.363086i	$0.881723\pi$
$734$		0			0
$735$	9.32470	+	7.48650i	0.343947	+	0.276144i
$736$		0			0
$737$	13.1019	−	4.25705i	0.482613	−	0.156811i
$738$		0			0
$739$	−13.3462	+	41.0754i	−0.490949	+	1.51098i	0.332228	+	0.943199i	$0.392200\pi$
$739$	−13.3462	+	41.0754i	−0.490949	+	1.51098i	−0.823177	+	0.567785i	$0.807800\pi$
$740$		0			0
$741$	0.233273	+	0.717939i	0.00856948	+	0.0263741i
$742$		0			0
$743$		−	31.8479i		−	1.16838i	−0.811615	−	0.584192i	$-0.801411\pi$
$743$		−	31.8479i		−	1.16838i	0.811615	−	0.584192i	$-0.198589\pi$
$744$		0			0
$745$	−2.02658	+	42.0404i	−0.0742482	+	1.54024i
$746$		0			0
$747$	−7.11021	+	9.78637i	−0.260149	+	0.358064i
$748$		0			0
$749$	51.6145			1.88595
$750$		0			0
$751$	29.5952			1.07995			0.539973	−	0.841682i	$-0.318435\pi$
$751$	29.5952			1.07995			0.539973	+	0.841682i	$0.318435\pi$
$752$		0			0
$753$	−9.14650	+	12.5891i	−0.333317	+	0.458771i
$754$		0			0
$755$	0.418601	−	8.68368i	0.0152345	−	0.316031i
$756$		0			0
$757$			0.0984401i			0.00357786i	0.999998	+	0.00178893i	$0.000569435\pi$
$757$			0.0984401i			0.00357786i	−0.999998	+	0.00178893i	$0.999431\pi$
$758$		0			0
$759$	−0.799814	−	2.46157i	−0.0290314	−	0.0893495i
$760$		0			0
$761$	−1.09516	+	3.37056i	−0.0396996	+	0.122183i	−0.968942	−	0.247287i	$-0.920461\pi$
$761$	−1.09516	+	3.37056i	−0.0396996	+	0.122183i	0.929243	+	0.369470i	$0.120461\pi$
$762$		0			0
$763$	6.21421	−	2.01912i	0.224969	−	0.0730970i
$764$		0			0
$765$	−7.50223	−	6.02330i	−0.271244	−	0.217773i
$766$		0			0
$767$	1.03415	+	1.42339i	0.0373411	+	0.0513957i
$768$		0			0
$769$	1.15494	−	0.839116i	0.0416484	−	0.0302593i	−0.566766	−	0.823879i	$-0.691806\pi$
$769$	1.15494	−	0.839116i	0.0416484	−	0.0302593i	0.608415	+	0.793619i	$0.291806\pi$
$770$		0			0
$771$	24.1382	+	17.5374i	0.869316	+	0.631595i
$772$		0			0
$773$	32.1274	+	10.4388i	1.15554	+	0.375458i	0.823228	−	0.567711i	$-0.192171\pi$
$773$	32.1274	+	10.4388i	1.15554	+	0.375458i	0.332313	+	0.943169i	$0.392171\pi$
$774$		0			0
$775$	−26.2830	+	15.4697i	−0.944113	+	0.555688i
$776$		0			0
$777$	−36.9209	−	11.9963i	−1.32453	−	0.430366i
$778$		0			0
$779$	1.42111	+	1.03250i	0.0509165	+	0.0369930i
$780$		0			0
$781$	9.65769	−	7.01672i	0.345579	−	0.251078i
$782$		0			0
$783$	19.6082	+	26.9884i	0.700740	+	0.964486i
$784$		0			0
$785$	−9.56771	−	0.461216i	−0.341486	−	0.0164615i
$786$		0			0
$787$	−2.07358	+	0.673749i	−0.0739153	+	0.0240165i	−0.345741	−	0.938330i	$-0.612373\pi$
$787$	−2.07358	+	0.673749i	−0.0739153	+	0.0240165i	0.271826	+	0.962346i	$0.412373\pi$
$788$		0			0
$789$	−12.7773	+	39.3246i	−0.454886	+	1.39999i
$790$		0			0
$791$	−10.5074	−	32.3383i	−0.373599	−	1.14982i
$792$		0			0
$793$		−	0.271369i		−	0.00963659i
$794$		0			0
$795$	25.7249	−	7.00866i	0.912368	−	0.248572i
$796$		0			0
$797$	−13.8082	+	19.0053i	−0.489110	+	0.673203i	−0.980224	−	0.197893i	$-0.936590\pi$
$797$	−13.8082	+	19.0053i	−0.489110	+	0.673203i	0.491113	+	0.871096i	$0.336590\pi$
$798$		0			0
$799$	−21.7875			−0.770787
$800$		0			0
$801$	−6.27226			−0.221620
$802$		0			0
$803$	−10.3843	+	14.2928i	−0.366454	+	0.504380i
$804$		0			0
$805$	5.99441	+	2.27226i	0.211275	+	0.0800865i
$806$		0			0
$807$		−	29.9144i		−	1.05304i
$808$		0			0
$809$	11.7893	+	36.2837i	0.414489	+	1.27567i	0.912707	+	0.408615i	$0.133988\pi$
$809$	11.7893	+	36.2837i	0.414489	+	1.27567i	−0.498217	+	0.867052i	$0.666012\pi$
$810$		0			0
$811$	−14.8040	+	45.5622i	−0.519840	+	1.59990i	0.254458	+	0.967084i	$0.418103\pi$
$811$	−14.8040	+	45.5622i	−0.519840	+	1.59990i	−0.774298	+	0.632821i	$0.781897\pi$
$812$		0			0
$813$	44.0224	−	14.3038i	1.54393	−	0.501655i
$814$		0			0
$815$	−9.24370	−	33.9285i	−0.323793	−	1.18846i
$816$		0			0
$817$	−3.29740	−	4.53849i	−0.115362	−	0.158782i
$818$		0			0
$819$	0.651586	−	0.473405i	0.0227683	−	0.0165421i
$820$		0			0
$821$	−15.3558	−	11.1566i	−0.535920	−	0.389369i	0.286647	−	0.958036i	$-0.407459\pi$
$821$	−15.3558	−	11.1566i	−0.535920	−	0.389369i	−0.822568	+	0.568667i	$0.807459\pi$
$822$		0			0
$823$	21.0831	+	6.85033i	0.734912	+	0.238787i	0.652476	−	0.757809i	$-0.273730\pi$
$823$	21.0831	+	6.85033i	0.734912	+	0.238787i	0.0824356	+	0.996596i	$0.473730\pi$
$824$		0			0
$825$	−7.46635	−	12.6853i	−0.259945	−	0.441646i
$826$		0			0
$827$	−4.49790	−	1.46146i	−0.156407	−	0.0508199i	0.229767	−	0.973246i	$-0.426204\pi$
$827$	−4.49790	−	1.46146i	−0.156407	−	0.0508199i	−0.386174	+	0.922426i	$0.626204\pi$
$828$		0			0
$829$	13.3003	+	9.66320i	0.461937	+	0.335617i	0.794291	−	0.607538i	$-0.207843\pi$
$829$	13.3003	+	9.66320i	0.461937	+	0.335617i	−0.332354	+	0.943155i	$0.607843\pi$
$830$		0			0
$831$	−16.5889	+	12.0525i	−0.575461	+	0.418097i
$832$		0			0
$833$	11.0257	+	15.1755i	0.382017	+	0.525801i
$834$		0			0
$835$	−39.3360	+	25.7802i	−1.36128	+	0.892160i
$836$		0			0
$837$	32.7322	−	10.6354i	1.13139	−	0.367611i
$838$		0			0
$839$	−1.73075	+	5.32671i	−0.0597522	+	0.183898i	−0.976477	−	0.215620i	$-0.930823\pi$
$839$	−1.73075	+	5.32671i	−0.0597522	+	0.183898i	0.916725	+	0.399519i	$0.130823\pi$
$840$		0			0
$841$	1.83977	+	5.66224i	0.0634405	+	0.195250i
$842$		0			0
$843$			38.0906i			1.31191i
$844$		0			0
$845$	15.8264	+	24.1484i	0.544446	+	0.830729i
$846$		0			0
$847$	13.4168	−	18.4666i	0.461006	−	0.634520i
$848$		0			0
$849$	−34.9318			−1.19886
$850$		0			0
$851$	−7.11091			−0.243759
$852$		0			0
$853$	−10.5158	+	14.4737i	−0.360053	+	0.495571i	−0.950164	−	0.311752i	$-0.899084\pi$
$853$	−10.5158	+	14.4737i	−0.360053	+	0.495571i	0.590110	+	0.807323i	$0.299084\pi$
$854$		0			0
$855$	−2.01872	+	2.51439i	−0.0690388	+	0.0859903i
$856$		0			0
$857$		−	3.19536i		−	0.109151i	−0.998510	−	0.0545757i	$-0.982619\pi$
$857$		−	3.19536i		−	0.109151i	0.998510	−	0.0545757i	$-0.0173806\pi$
$858$		0			0
$859$	13.4174	+	41.2945i	0.457795	+	1.40895i	0.867822	+	0.496875i	$0.165519\pi$
$859$	13.4174	+	41.2945i	0.457795	+	1.40895i	−0.410027	+	0.912073i	$0.634481\pi$
$860$		0			0
$861$	−1.50569	+	4.63403i	−0.0513137	+	0.157927i
$862$		0			0
$863$	41.1545	−	13.3719i	1.40091	−	0.455185i	0.491428	−	0.870918i	$-0.336475\pi$
$863$	41.1545	−	13.3719i	1.40091	−	0.455185i	0.909486	+	0.415734i	$0.136475\pi$
$864$		0			0
$865$	5.68011	−	14.9846i	0.193130	−	0.509493i
$866$		0			0
$867$	8.35449	+	11.4990i	0.283733	+	0.390525i
$868$		0			0
$869$	−12.5570	+	9.12322i	−0.425968	+	0.309484i
$870$		0			0
$871$	−1.65159	−	1.19995i	−0.0559619	−	0.0406587i
$872$		0			0
$873$	5.33126	+	1.73223i	0.180436	+	0.0586272i
$874$		0			0
$875$	36.0775	+	5.24996i	1.21964	+	0.177481i
$876$		0			0
$877$	−32.5584	−	10.5789i	−1.09942	−	0.357223i	−0.297540	−	0.954709i	$-0.596166\pi$
$877$	−32.5584	−	10.5789i	−1.09942	−	0.357223i	−0.801879	+	0.597487i	$0.796166\pi$
$878$		0			0
$879$	14.6507	+	10.6443i	0.494154	+	0.359024i
$880$		0			0
$881$	−22.3507	+	16.2388i	−0.753016	+	0.547098i	−0.896760	−	0.442517i	$-0.854086\pi$
$881$	−22.3507	+	16.2388i	−0.753016	+	0.547098i	0.143744	+	0.989615i	$0.454086\pi$
$882$		0			0
$883$	15.2231	+	20.9527i	0.512297	+	0.705116i	0.984305	−	0.176478i	$-0.0564706\pi$
$883$	15.2231	+	20.9527i	0.512297	+	0.705116i	−0.472008	+	0.881594i	$0.656471\pi$
$884$		0			0
$885$	6.92555	−	18.2702i	0.232800	−	0.614146i
$886$		0			0
$887$	−16.4009	+	5.32897i	−0.550688	+	0.178929i	−0.571127	−	0.820862i	$-0.693494\pi$
$887$	−16.4009	+	5.32897i	−0.550688	+	0.178929i	0.0204392	+	0.999791i	$0.493494\pi$
$888$		0			0
$889$	−5.89488	+	18.1426i	−0.197708	+	0.608482i
$890$		0			0
$891$	3.58794	+	11.0425i	0.120200	+	0.369939i
$892$		0			0
$893$			7.30213i			0.244356i
$894$		0			0
$895$	−11.2543	+	14.0177i	−0.376191	+	0.468559i
$896$		0			0
$897$	−0.225446	+	0.310299i	−0.00752741	+	0.0103606i
$898$		0			0
$899$	36.0614			1.20271
$900$		0			0
$901$	41.8238			1.39335
$902$		0			0
$903$	9.14650	−	12.5891i	0.304376	−	0.418938i
$904$		0			0
$905$	−25.2704	−	38.5582i	−0.840016	−	1.28172i
$906$		0			0
$907$		−	57.0465i		−	1.89420i	−0.320940	−	0.947099i	$-0.603999\pi$
$907$		−	57.0465i		−	1.89420i	0.320940	−	0.947099i	$-0.396001\pi$
$908$		0			0
$909$	−3.14063	−	9.66587i	−0.104168	−	0.320597i
$910$		0			0
$911$	−6.13965	+	18.8959i	−0.203416	+	0.626049i	0.796359	+	0.604824i	$0.206757\pi$
$911$	−6.13965	+	18.8959i	−0.203416	+	0.626049i	−0.999775	+	0.0212248i	$0.993243\pi$
$912$		0			0
$913$	−27.6099	+	8.97099i	−0.913754	+	0.296897i
$914$		0			0
$915$	−2.52055	+	1.65192i	−0.0833267	+	0.0546109i
$916$		0			0
$917$	2.86859	+	3.94827i	0.0947291	+	0.130383i
$918$		0			0
$919$	−22.6350	+	16.4453i	−0.746661	+	0.542481i	−0.894790	−	0.446487i	$-0.852675\pi$
$919$	−22.6350	+	16.4453i	−0.746661	+	0.542481i	0.148129	+	0.988968i	$0.452675\pi$
$920$		0			0
$921$	−5.09972	−	3.70517i	−0.168042	−	0.122089i
$922$		0			0
$923$	−1.68244	−	0.546657i	−0.0553781	−	0.0179934i
$924$		0			0
$925$	−39.4844	+	8.73926i	−1.29824	+	0.287345i
$926$		0			0
$927$	−1.09487	−	0.355745i	−0.0359603	−	0.0116842i
$928$		0			0
$929$	−11.4273	−	8.30242i	−0.374918	−	0.272394i	0.384329	−	0.923196i	$-0.374433\pi$
$929$	−11.4273	−	8.30242i	−0.374918	−	0.272394i	−0.759247	+	0.650802i	$0.774433\pi$
$930$		0			0
$931$	5.08611	−	3.69528i	0.166691	−	0.121108i
$932$		0			0
$933$	22.1893	+	30.5409i	0.726444	+	0.999864i
$934$		0			0
$935$	−6.06943	−	22.2775i	−0.198492	−	0.728552i
$936$		0			0
$937$	34.1949	−	11.1106i	1.11710	−	0.362967i	0.308438	−	0.951244i	$-0.400194\pi$
$937$	34.1949	−	11.1106i	1.11710	−	0.362967i	0.808659	+	0.588277i	$0.200194\pi$
$938$		0			0
$939$	−10.1666	+	31.2897i	−0.331776	+	1.02110i
$940$		0			0
$941$	8.25011	+	25.3912i	0.268946	+	0.827730i	0.990758	+	0.135641i	$0.0433094\pi$
$941$	8.25011	+	25.3912i	0.268946	+	0.827730i	−0.721812	+	0.692089i	$0.756691\pi$
$942$		0			0
$943$			0.892508i			0.0290640i
$944$		0			0
$945$	−38.4712	−	14.5830i	−1.25147	−	0.474385i
$946$		0			0
$947$	10.1747	−	14.0042i	0.330633	−	0.455077i	−0.611044	−	0.791597i	$-0.709250\pi$
$947$	10.1747	−	14.0042i	0.330633	−	0.455077i	0.941676	+	0.336520i	$0.109250\pi$
$948$		0			0
$949$	2.61803			0.0849850
$950$		0			0
$951$	−32.2693			−1.04640
$952$		0			0
$953$	14.2610	−	19.6286i	0.461959	−	0.635831i	−0.512955	−	0.858416i	$-0.671449\pi$
$953$	14.2610	−	19.6286i	0.461959	−	0.635831i	0.974913	+	0.222584i	$0.0714492\pi$
$954$		0			0
$955$	−38.8991	+	10.5979i	−1.25875	+	0.342941i
$956$		0			0
$957$			17.4048i			0.562617i
$958$		0			0
$959$	7.90899	+	24.3414i	0.255395	+	0.786024i
$960$		0			0
$961$	1.91722	−	5.90061i	0.0618460	−	0.190342i
$962$		0			0
$963$	−12.5453	+	4.07623i	−0.404268	+	0.131355i
$964$		0			0
$965$	15.1621	+	0.730899i	0.488087	+	0.0235285i
$966$		0			0
$967$	18.2885	+	25.1720i	0.588120	+	0.809477i	0.994556	−	0.104202i	$-0.0332288\pi$
$967$	18.2885	+	25.1720i	0.588120	+	0.809477i	−0.406437	+	0.913679i	$0.633229\pi$
$968$		0			0
$969$	10.6388	−	7.72952i	0.341767	−	0.248308i
$970$		0			0
$971$	−14.0543	−	10.2111i	−0.451025	−	0.327689i	0.338975	−	0.940795i	$-0.389920\pi$
$971$	−14.0543	−	10.2111i	−0.451025	−	0.327689i	−0.790000	+	0.613106i	$0.789920\pi$
$972$		0			0
$973$	−16.7205	−	5.43282i	−0.536034	−	0.174168i
$974$		0			0
$975$	−0.870467	+	2.00006i	−0.0278773	+	0.0640531i
$976$		0			0
$977$	40.7936	+	13.2546i	1.30510	+	0.424054i	0.877354	−	0.479844i	$-0.159307\pi$
$977$	40.7936	+	13.2546i	1.30510	+	0.424054i	0.427749	+	0.903898i	$0.359307\pi$
$978$		0			0
$979$	−12.1780	−	8.84784i	−0.389211	−	0.282778i
$980$		0			0
$981$	−1.35096	+	0.981527i	−0.0431327	+	0.0313377i
$982$		0			0
$983$	−22.0145	−	30.3003i	−0.702153	−	0.966431i	−0.999930	−	0.0117954i	$-0.996245\pi$
$983$	−22.0145	−	30.3003i	−0.702153	−	0.966431i	0.297777	−	0.954635i	$-0.403755\pi$
$984$		0			0
$985$	13.9410	+	11.1928i	0.444198	+	0.356632i
$986$		0			0
$987$	−19.2637	+	6.25914i	−0.613169	+	0.199231i
$988$		0			0
$989$	0.880801	−	2.71083i	0.0280078	−	0.0861993i
$990$		0			0
$991$	−5.17987	−	15.9420i	−0.164544	−	0.506415i	0.834458	−	0.551071i	$-0.185781\pi$
$991$	−5.17987	−	15.9420i	−0.164544	−	0.506415i	−0.999002	+	0.0446564i	$0.985781\pi$
$992$		0			0
$993$			13.1931i			0.418669i
$994$		0			0
$995$	−0.560384	+	11.6249i	−0.0177654	+	0.368534i
$996$		0			0
$997$	35.1845	−	48.4273i	1.11430	−	1.53371i	0.299388	−	0.954132i	$-0.403218\pi$
$997$	35.1845	−	48.4273i	1.11430	−	1.53371i	0.814917	−	0.579577i	$-0.196782\pi$
$998$		0			0
$999$	45.6367			1.44388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.y.c.129.2		8
4.3	odd	2		25.2.e.a.4.2	✓	8
12.11	even	2		225.2.m.a.154.1		8
20.3	even	4		125.2.d.b.101.3		16
20.7	even	4		125.2.d.b.101.2		16
20.19	odd	2		125.2.e.b.24.1		8
25.12	odd	20		10000.2.a.bj.1.6		8
25.13	odd	20		10000.2.a.bj.1.3		8
25.19	even	10	inner	400.2.y.c.369.2		8
100.3	even	20		625.2.d.o.251.2		16
100.11	odd	10		625.2.e.a.249.2		8
100.19	odd	10		25.2.e.a.19.2	yes	8
100.23	even	20		625.2.d.o.376.2		16
100.27	even	20		625.2.d.o.376.3		16
100.31	odd	10		125.2.e.b.99.1		8
100.39	odd	10		625.2.e.i.249.1		8
100.47	even	20		625.2.d.o.251.3		16
100.59	odd	10		625.2.b.c.624.4		8
100.63	even	20		625.2.a.f.1.5		8
100.67	even	20		125.2.d.b.26.2		16
100.71	odd	10		625.2.e.i.374.1		8
100.79	odd	10		625.2.e.a.374.2		8
100.83	even	20		125.2.d.b.26.3		16
100.87	even	20		625.2.a.f.1.4		8
100.91	odd	10		625.2.b.c.624.5		8
300.119	even	10		225.2.m.a.19.1		8
300.263	odd	20		5625.2.a.x.1.4		8
300.287	odd	20		5625.2.a.x.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.2	✓	8	4.3	odd	2
25.2.e.a.19.2	yes	8	100.19	odd	10
125.2.d.b.26.2		16	100.67	even	20
125.2.d.b.26.3		16	100.83	even	20
125.2.d.b.101.2		16	20.7	even	4
125.2.d.b.101.3		16	20.3	even	4
125.2.e.b.24.1		8	20.19	odd	2
125.2.e.b.99.1		8	100.31	odd	10
225.2.m.a.19.1		8	300.119	even	10
225.2.m.a.154.1		8	12.11	even	2
400.2.y.c.129.2		8	1.1	even	1	trivial
400.2.y.c.369.2		8	25.19	even	10	inner
625.2.a.f.1.4		8	100.87	even	20
625.2.a.f.1.5		8	100.63	even	20
625.2.b.c.624.4		8	100.59	odd	10
625.2.b.c.624.5		8	100.91	odd	10
625.2.d.o.251.2		16	100.3	even	20
625.2.d.o.251.3		16	100.47	even	20
625.2.d.o.376.2		16	100.23	even	20
625.2.d.o.376.3		16	100.27	even	20
625.2.e.a.249.2		8	100.11	odd	10
625.2.e.a.374.2		8	100.79	odd	10
625.2.e.i.249.1		8	100.39	odd	10
625.2.e.i.374.1		8	100.71	odd	10
5625.2.a.x.1.4		8	300.263	odd	20
5625.2.a.x.1.5		8	300.287	odd	20
10000.2.a.bj.1.3		8	25.13	odd	20
10000.2.a.bj.1.6		8	25.12	odd	20

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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.y (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.865190 - 1.19083i) q^{3} +(0.107666 - 2.23347i) q^{5} -3.26086i q^{7} +(0.257524 + 0.792578i) q^{9} +O(q^{10})\)	\(q+(0.865190 - 1.19083i) q^{3} +(0.107666 - 2.23347i) q^{5} -3.26086i q^{7} +(0.257524 + 0.792578i) q^{9} +(-0.618034 + 1.90211i) q^{11} +(0.281873 - 0.0915860i) q^{13} +(-2.56654 - 2.06059i) q^{15} +(-3.03472 - 4.17693i) q^{17} +(-1.39991 + 1.01709i) q^{19} +(-3.88313 - 2.82126i) q^{21} +(-0.836161 - 0.271685i) q^{23} +(-4.97682 - 0.480938i) q^{25} +(5.36635 + 1.74363i) q^{27} +(4.78304 + 3.47508i) q^{29} +(4.93462 - 3.58521i) q^{31} +(1.73038 + 2.38166i) q^{33} +(-7.28304 - 0.351083i) q^{35} +(7.69215 - 2.49933i) q^{37} +(0.134810 - 0.414902i) q^{39} +(-0.313697 - 0.965461i) q^{41} +3.24199i q^{43} +(1.79793 - 0.489840i) q^{45} +(2.48043 - 3.41402i) q^{47} -3.63318 q^{49} -7.59963 q^{51} +(-4.76148 + 6.55362i) q^{53} +(4.18178 + 1.58516i) q^{55} +2.54703i q^{57} +(1.83443 + 5.64581i) q^{59} +(0.282941 - 0.870802i) q^{61} +(2.58448 - 0.839749i) q^{63} +(-0.174207 - 0.639416i) q^{65} +(-4.04870 - 5.57255i) q^{67} +(-1.04697 + 0.760668i) q^{69} +(-4.82884 - 3.50836i) q^{71} +(8.40107 + 2.72967i) q^{73} +(-4.87861 + 5.51045i) q^{75} +(6.20252 + 2.01532i) q^{77} +(6.27851 + 4.56161i) q^{79} +(4.69667 - 3.41233i) q^{81} +(8.53192 + 11.7432i) q^{83} +(-9.65580 + 6.32825i) q^{85} +(8.27647 - 2.68919i) q^{87} +(-2.32579 + 7.15805i) q^{89} +(-0.298649 - 0.919147i) q^{91} -8.97820i q^{93} +(2.12093 + 3.23616i) q^{95} +(3.95373 - 5.44184i) q^{97} -1.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 + q^9	\( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 + q^9 + 4 * q^11 - 5 * q^13 - 15 * q^15 - 10 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^23 - 10 * q^25 + 5 * q^27 - 5 * q^29 + 9 * q^31 + 10 * q^33 - 15 * q^35 + 30 * q^37 + 3 * q^39 - 4 * q^41 - 15 * q^45 + 14 * q^49 + 4 * q^51 - 10 * q^53 + 10 * q^55 - 9 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 + 17 * q^69 - 6 * q^71 + 15 * q^73 + 10 * q^75 + 10 * q^77 - 15 * q^79 + 28 * q^81 + 45 * q^83 - 15 * q^85 + 20 * q^87 - 25 * q^89 - 6 * q^91 - 15 * q^95 - 60 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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