LMFDB - Embedded newform 400.2.u.e.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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, 4]))

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

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

chi := DirichletCharacter("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, 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 $\Q(\zeta_{5})$
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:	$ 5 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			161.1
Root			$1.17421 - 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	400.161
Dual form			400.2.u.e.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 - 0.587785i) q^{3} +(-1.39991 + 1.74363i) q^{5} -1.83337 q^{7} +(2.11803 + 1.53884i) q^{9} +O(q^{10})$	\(q+(0.190983 - 0.587785i) q^{3} +(-1.39991 + 1.74363i) q^{5} -1.83337 q^{7} +(2.11803 + 1.53884i) q^{9} +(4.19215 - 3.04577i) q^{11} +(2.22570 + 1.61707i) q^{13} +(0.757524 + 1.15585i) q^{15} +(2.02435 + 6.23030i) q^{17} +(2.20892 + 6.79837i) q^{19} +(-0.350142 + 1.07763i) q^{21} +(-3.57411 + 2.59675i) q^{23} +(-1.08052 - 4.88185i) q^{25} +(2.80902 - 2.04087i) q^{27} +(2.24075 - 6.89631i) q^{29} +(-0.240748 - 0.740947i) q^{31} +(-0.989632 - 3.04577i) q^{33} +(2.56654 - 3.19672i) q^{35} +(2.60314 + 1.89129i) q^{37} +(1.37556 - 0.999401i) q^{39} +(-2.84373 - 2.06609i) q^{41} -3.56029 q^{43} +(-5.64823 + 1.53884i) q^{45} +(-1.96177 + 6.03770i) q^{47} -3.63877 q^{49} +4.04870 q^{51} +(2.74364 - 8.44406i) q^{53} +(-0.557901 + 11.5734i) q^{55} +4.41785 q^{57} +(-0.345364 - 0.250922i) q^{59} +(1.55617 - 1.13063i) q^{61} +(-3.88313 - 2.82126i) q^{63} +(-5.93534 + 1.61707i) q^{65} +(-0.0382322 - 0.117667i) q^{67} +(0.843734 + 2.59675i) q^{69} +(3.97113 - 12.2219i) q^{71} +(0.472856 - 0.343550i) q^{73} +(-3.07584 - 0.297236i) q^{75} +(-7.68574 + 5.58402i) q^{77} +(-3.45888 + 10.6453i) q^{79} +(1.76393 + 5.42882i) q^{81} +(-5.47682 - 16.8559i) q^{83} +(-13.6973 - 5.19212i) q^{85} +(-3.62561 - 2.63416i) q^{87} +(6.23912 - 4.53298i) q^{89} +(-4.08052 - 2.96467i) q^{91} -0.481496 q^{93} +(-14.9462 - 5.66553i) q^{95} +(-2.10594 + 6.48141i) q^{97} +13.5661 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9	$ 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9} + 2 q^{11} + 8 q^{13} + 5 q^{15} + 10 q^{17} - 3 q^{19} - 3 q^{21} - 6 q^{23} - 5 q^{25} + 18 q^{27} + 6 q^{29} + 10 q^{31} - 16 q^{33} + 15 q^{35} - 2 q^{37} + q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47} - 4 q^{49} + 20 q^{51} - 13 q^{53} - 20 q^{55} - 6 q^{57} - 29 q^{59} + 15 q^{61} - 4 q^{63} - 50 q^{65} - 28 q^{67} - 12 q^{69} + 16 q^{71} + q^{73} - 15 q^{75} - 11 q^{77} - 23 q^{79} + 32 q^{81} - 14 q^{83} - 15 q^{85} - 3 q^{87} - 7 q^{89} - 29 q^{91} + 20 q^{93} - 45 q^{95} - 3 q^{97} + 22 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9 + 2 * q^11 + 8 * q^13 + 5 * q^15 + 10 * q^17 - 3 * q^19 - 3 * q^21 - 6 * q^23 - 5 * q^25 + 18 * q^27 + 6 * q^29 + 10 * q^31 - 16 * q^33 + 15 * q^35 - 2 * q^37 + q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 + 20 * q^51 - 13 * q^53 - 20 * q^55 - 6 * q^57 - 29 * q^59 + 15 * q^61 - 4 * q^63 - 50 * q^65 - 28 * q^67 - 12 * q^69 + 16 * q^71 + q^73 - 15 * q^75 - 11 * q^77 - 23 * q^79 + 32 * q^81 - 14 * q^83 - 15 * q^85 - 3 * q^87 - 7 * q^89 - 29 * q^91 + 20 * q^93 - 45 * q^95 - 3 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	−0.880666	−	0.473738i	$-0.842904\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	0.990930	+	0.134380i	$0.0429043\pi$
$4$		0			0
$5$	−1.39991	+	1.74363i	−0.626057	+	0.779777i
$5$	−1.39991	+	1.74363i	−0.626057	+	0.779777i
$6$		0			0
$7$	−1.83337			−0.692947			−0.346474	−	0.938060i	$-0.612621\pi$
$7$	−1.83337			−0.692947			−0.346474	+	0.938060i	$0.612621\pi$
$8$		0			0
$9$	2.11803	+	1.53884i	0.706011	+	0.512947i
$10$		0			0
$11$	4.19215	−	3.04577i	1.26398	−	0.918335i	0.265034	−	0.964239i	$-0.414617\pi$
$11$	4.19215	−	3.04577i	1.26398	−	0.918335i	0.998946	+	0.0459037i	$0.0146167\pi$
$12$		0			0
$13$	2.22570	+	1.61707i	0.617298	+	0.448493i	0.851977	−	0.523580i	$-0.175404\pi$
$13$	2.22570	+	1.61707i	0.617298	+	0.448493i	−0.234679	+	0.972073i	$0.575404\pi$
$14$		0			0
$15$	0.757524	+	1.15585i	0.195592	+	0.298439i
$16$		0			0
$17$	2.02435	+	6.23030i	0.490977	+	1.51107i	0.823134	+	0.567847i	$0.192223\pi$
$17$	2.02435	+	6.23030i	0.490977	+	1.51107i	−0.332158	+	0.943224i	$0.607777\pi$
$18$		0			0
$19$	2.20892	+	6.79837i	0.506762	+	1.55965i	0.797788	+	0.602938i	$0.206003\pi$
$19$	2.20892	+	6.79837i	0.506762	+	1.55965i	−0.291026	+	0.956715i	$0.593997\pi$
$20$		0			0
$21$	−0.350142	+	1.07763i	−0.0764072	+	0.235157i
$22$		0			0
$23$	−3.57411	+	2.59675i	−0.745254	+	0.541459i	−0.894352	−	0.447364i	$-0.852363\pi$
$23$	−3.57411	+	2.59675i	−0.745254	+	0.541459i	0.149098	+	0.988822i	$0.452363\pi$
$24$		0			0
$25$	−1.08052	−	4.88185i	−0.216104	−	0.976370i
$26$		0			0
$27$	2.80902	−	2.04087i	0.540596	−	0.392766i
$28$		0			0
$29$	2.24075	−	6.89631i	0.416096	−	1.28061i	−0.495170	−	0.868796i	$-0.664894\pi$
$29$	2.24075	−	6.89631i	0.416096	−	1.28061i	0.911266	−	0.411817i	$-0.135106\pi$
$30$		0			0
$31$	−0.240748	−	0.740947i	−0.0432396	−	0.133078i	0.927106	−	0.374799i	$-0.122288\pi$
$31$	−0.240748	−	0.740947i	−0.0432396	−	0.133078i	−0.970346	+	0.241721i	$0.922288\pi$
$32$		0			0
$33$	−0.989632	−	3.04577i	−0.172273	−	0.530201i
$34$		0			0
$35$	2.56654	−	3.19672i	0.433825	−	0.540344i
$36$		0			0
$37$	2.60314	+	1.89129i	0.427954	+	0.310927i	0.780830	−	0.624743i	$-0.214796\pi$
$37$	2.60314	+	1.89129i	0.427954	+	0.310927i	−0.352876	+	0.935670i	$0.614796\pi$
$38$		0			0
$39$	1.37556	−	0.999401i	0.220266	−	0.160032i
$40$		0			0
$41$	−2.84373	−	2.06609i	−0.444117	−	0.322670i	0.343152	−	0.939280i	$-0.388505\pi$
$41$	−2.84373	−	2.06609i	−0.444117	−	0.322670i	−0.787269	+	0.616610i	$0.788505\pi$
$42$		0			0
$43$	−3.56029			−0.542939			−0.271470	−	0.962447i	$-0.587510\pi$
$43$	−3.56029			−0.542939			−0.271470	+	0.962447i	$0.587510\pi$
$44$		0			0
$45$	−5.64823	+	1.53884i	−0.841988	+	0.229397i
$46$		0			0
$47$	−1.96177	+	6.03770i	−0.286153	+	0.880689i	0.699897	+	0.714243i	$0.253229\pi$
$47$	−1.96177	+	6.03770i	−0.286153	+	0.880689i	−0.986051	+	0.166446i	$0.946771\pi$
$48$		0			0
$49$	−3.63877			−0.519824
$50$		0			0
$51$	4.04870			0.566931
$52$		0			0
$53$	2.74364	−	8.44406i	0.376868	−	1.15988i	−0.565342	−	0.824857i	$-0.691256\pi$
$53$	2.74364	−	8.44406i	0.376868	−	1.15988i	0.942210	−	0.335024i	$-0.108744\pi$
$54$		0			0
$55$	−0.557901	+	11.5734i	−0.0752273	+	1.56055i
$56$		0			0
$57$	4.41785			0.585158
$58$		0			0
$59$	−0.345364	−	0.250922i	−0.0449626	−	0.0326673i	0.565077	−	0.825038i	$-0.308846\pi$
$59$	−0.345364	−	0.250922i	−0.0449626	−	0.0326673i	−0.610040	+	0.792371i	$0.708846\pi$
$60$		0			0
$61$	1.55617	−	1.13063i	0.199248	−	0.144762i	−0.483688	−	0.875241i	$-0.660703\pi$
$61$	1.55617	−	1.13063i	0.199248	−	0.144762i	0.682935	+	0.730479i	$0.260703\pi$
$62$		0			0
$63$	−3.88313	−	2.82126i	−0.489228	−	0.355445i
$64$		0			0
$65$	−5.93534	+	1.61707i	−0.736189	+	0.200572i
$66$		0			0
$67$	−0.0382322	−	0.117667i	−0.00467080	−	0.0143753i	0.948694	−	0.316196i	$-0.102406\pi$
$67$	−0.0382322	−	0.117667i	−0.00467080	−	0.0143753i	−0.953365	+	0.301821i	$0.902406\pi$
$68$		0			0
$69$	0.843734	+	2.59675i	0.101574	+	0.312611i
$70$		0			0
$71$	3.97113	−	12.2219i	0.471286	−	1.45047i	−0.379615	−	0.925144i	$-0.623944\pi$
$71$	3.97113	−	12.2219i	0.471286	−	1.45047i	0.850901	−	0.525325i	$-0.176056\pi$
$72$		0			0
$73$	0.472856	−	0.343550i	0.0553436	−	0.0402095i	−0.559770	−	0.828648i	$-0.689110\pi$
$73$	0.472856	−	0.343550i	0.0553436	−	0.0402095i	0.615113	+	0.788439i	$0.289110\pi$
$74$		0			0
$75$	−3.07584	−	0.297236i	−0.355168	−	0.0343218i
$76$		0			0
$77$	−7.68574	+	5.58402i	−0.875871	+	0.636358i
$78$		0			0
$79$	−3.45888	+	10.6453i	−0.389154	+	1.19769i	0.544268	+	0.838911i	$0.316808\pi$
$79$	−3.45888	+	10.6453i	−0.389154	+	1.19769i	−0.933422	+	0.358781i	$0.883192\pi$
$80$		0			0
$81$	1.76393	+	5.42882i	0.195992	+	0.603203i
$82$		0			0
$83$	−5.47682	−	16.8559i	−0.601159	−	1.85018i	−0.521307	−	0.853369i	$-0.674555\pi$
$83$	−5.47682	−	16.8559i	−0.601159	−	1.85018i	−0.0798520	−	0.996807i	$-0.525445\pi$
$84$		0			0
$85$	−13.6973	−	5.19212i	−1.48568	−	0.563165i
$86$		0			0
$87$	−3.62561	−	2.63416i	−0.388706	−	0.282411i
$88$		0			0
$89$	6.23912	−	4.53298i	0.661345	−	0.480495i	−0.205772	−	0.978600i	$-0.565970\pi$
$89$	6.23912	−	4.53298i	0.661345	−	0.480495i	0.867117	+	0.498105i	$0.165970\pi$
$90$		0			0
$91$	−4.08052	−	2.96467i	−0.427755	−	0.310782i
$92$		0			0
$93$	−0.481496			−0.0499288
$94$		0			0
$95$	−14.9462	−	5.66553i	−1.53344	−	0.581271i
$96$		0			0
$97$	−2.10594	+	6.48141i	−0.213826	+	0.658088i	0.785409	+	0.618977i	$0.212453\pi$
$97$	−2.10594	+	6.48141i	−0.213826	+	0.658088i	−0.999235	+	0.0391108i	$0.987547\pi$
$98$		0			0
$99$	13.5661			1.36344
$100$		0			0
$101$	−0.561416			−0.0558630			−0.0279315	−	0.999610i	$-0.508892\pi$
$101$	−0.561416			−0.0558630			−0.0279315	+	0.999610i	$0.508892\pi$
$102$		0			0
$103$	−1.21172	+	3.72929i	−0.119394	+	0.367458i	−0.992838	−	0.119467i	$-0.961881\pi$
$103$	−1.21172	+	3.72929i	−0.119394	+	0.367458i	0.873444	+	0.486925i	$0.161881\pi$
$104$		0			0
$105$	−1.38882	−	2.11909i	−0.135535	−	0.206802i
$106$		0			0
$107$	−0.172225			−0.0166496			−0.00832482	−	0.999965i	$-0.502650\pi$
$107$	−0.172225			−0.0166496			−0.00832482	+	0.999965i	$0.502650\pi$
$108$		0			0
$109$	11.9339	+	8.67049i	1.14306	+	0.830482i	0.987543	−	0.157351i	$-0.0502954\pi$
$109$	11.9339	+	8.67049i	1.14306	+	0.830482i	0.155518	+	0.987833i	$0.450295\pi$
$110$		0			0
$111$	1.60883	−	1.16888i	0.152703	−	0.110946i
$112$		0			0
$113$	−5.37393	−	3.90439i	−0.505537	−	0.367294i	0.305591	−	0.952163i	$-0.401146\pi$
$113$	−5.37393	−	3.90439i	−0.505537	−	0.367294i	−0.811128	+	0.584869i	$0.801146\pi$
$114$		0			0
$115$	0.475651	−	9.86715i	0.0443547	−	0.920116i
$116$		0			0
$117$	2.22570	+	6.85000i	0.205766	+	0.633283i
$118$		0			0
$119$	−3.71137	−	11.4224i	−0.340221	−	1.04709i
$120$		0			0
$121$	4.89818	−	15.0750i	0.445289	−	1.37046i
$122$		0			0
$123$	−1.75752	+	1.27692i	−0.158471	+	0.115136i
$124$		0			0
$125$	10.0248	+	4.95010i	0.896645	+	0.442751i
$126$		0			0
$127$	−8.82360	+	6.41072i	−0.782968	+	0.568859i	−0.905868	−	0.423560i	$-0.860780\pi$
$127$	−8.82360	+	6.41072i	−0.782968	+	0.568859i	0.122900	+	0.992419i	$0.460780\pi$
$128$		0			0
$129$	−0.679955	+	2.09269i	−0.0598667	+	0.184251i
$130$		0			0
$131$	−0.0775692	−	0.238733i	−0.00677725	−	0.0208582i	0.947611	−	0.319428i	$-0.103491\pi$
$131$	−0.0775692	−	0.238733i	−0.00677725	−	0.0208582i	−0.954388	+	0.298569i	$0.903491\pi$
$132$		0			0
$133$	−4.04977	−	12.4639i	−0.351159	−	1.08076i
$134$		0			0
$135$	−0.373830	+	7.75493i	−0.0321742	+	0.667438i
$136$		0			0
$137$	−17.7292	−	12.8810i	−1.51471	−	1.10050i	−0.964034	−	0.265778i	$-0.914371\pi$
$137$	−17.7292	−	12.8810i	−1.51471	−	1.10050i	−0.550673	−	0.834721i	$-0.685629\pi$
$138$		0			0
$139$	13.6615	−	9.92565i	1.15875	−	0.841883i	0.169133	−	0.985593i	$-0.445903\pi$
$139$	13.6615	−	9.92565i	1.15875	−	0.841883i	0.989620	+	0.143710i	$0.0459034\pi$
$140$		0			0
$141$	3.17421	+	2.30620i	0.267316	+	0.194217i
$142$		0			0
$143$	14.2557			1.19212
$144$		0			0
$145$	8.88781	+	13.5612i	0.738093	+	1.12620i
$146$		0			0
$147$	−0.694943	+	2.13882i	−0.0573180	+	0.176407i
$148$		0			0
$149$	−8.91185			−0.730087			−0.365043	−	0.930990i	$-0.618946\pi$
$149$	−8.91185			−0.730087			−0.365043	+	0.930990i	$0.618946\pi$
$150$		0			0
$151$	3.79403			0.308754			0.154377	−	0.988012i	$-0.450663\pi$
$151$	3.79403			0.308754			0.154377	+	0.988012i	$0.450663\pi$
$152$		0			0
$153$	−5.29981	+	16.3111i	−0.428465	+	1.31868i
$154$		0			0
$155$	1.62896	+	0.617479i	0.130842	+	0.0495971i
$156$		0			0
$157$	11.0058			0.878357			0.439179	−	0.898400i	$-0.355270\pi$
$157$	11.0058			0.878357			0.439179	+	0.898400i	$0.355270\pi$
$158$		0			0
$159$	−4.43930	−	3.22534i	−0.352060	−	0.255786i
$160$		0			0
$161$	6.55266	−	4.76078i	0.516422	−	0.375202i
$162$		0			0
$163$	−1.33352	−	0.968861i	−0.104450	−	0.0758870i	0.534335	−	0.845273i	$-0.320562\pi$
$163$	−1.33352	−	0.968861i	−0.104450	−	0.0758870i	−0.638784	+	0.769386i	$0.720562\pi$
$164$		0			0
$165$	6.69611	+	2.53824i	0.521291	+	0.197602i
$166$		0			0
$167$	0.0422895	+	0.130154i	0.00327246	+	0.0100716i	0.952679	−	0.303977i	$-0.0983146\pi$
$167$	0.0422895	+	0.130154i	0.00327246	+	0.0100716i	−0.949407	+	0.314048i	$0.898315\pi$
$168$		0			0
$169$	−1.67838	−	5.16553i	−0.129106	−	0.397348i
$170$		0			0
$171$	−5.78304	+	17.7984i	−0.442240	+	1.36107i
$172$		0			0
$173$	−7.89070	+	5.73293i	−0.599919	+	0.435867i	−0.845850	−	0.533421i	$-0.820906\pi$
$173$	−7.89070	+	5.73293i	−0.599919	+	0.435867i	0.245931	+	0.969287i	$0.420906\pi$
$174$		0			0
$175$	1.98099	+	8.95022i	0.149749	+	0.676573i
$176$		0			0
$177$	−0.213447	+	0.155078i	−0.0160437	+	0.0116564i
$178$		0			0
$179$	−6.43390	+	19.8015i	−0.480893	+	1.48004i	0.356950	+	0.934123i	$0.383817\pi$
$179$	−6.43390	+	19.8015i	−0.480893	+	1.48004i	−0.837843	+	0.545912i	$0.816183\pi$
$180$		0			0
$181$	−4.19504	−	12.9110i	−0.311815	−	0.959668i	−0.977046	−	0.213030i	$-0.931667\pi$
$181$	−4.19504	−	12.9110i	−0.311815	−	0.959668i	0.665231	−	0.746638i	$-0.268333\pi$
$182$		0			0
$183$	−0.367363	−	1.13063i	−0.0271562	−	0.0835783i
$184$		0			0
$185$	−6.94188	+	1.89129i	−0.510377	+	0.139051i
$186$		0			0
$187$	27.4625	+	19.9527i	2.00825	+	1.45908i
$188$		0			0
$189$	−5.14996	+	3.74166i	−0.374604	+	0.272166i
$190$		0			0
$191$	6.04625	+	4.39286i	0.437491	+	0.317856i	0.784637	−	0.619955i	$-0.212849\pi$
$191$	6.04625	+	4.39286i	0.437491	+	0.317856i	−0.347146	+	0.937811i	$0.612849\pi$
$192$		0			0
$193$	8.06710			0.580683			0.290341	−	0.956923i	$-0.406231\pi$
$193$	8.06710			0.580683			0.290341	+	0.956923i	$0.406231\pi$
$194$		0			0
$195$	−0.183062	+	3.79754i	−0.0131094	+	0.271947i
$196$		0			0
$197$	6.10701	−	18.7954i	0.435106	−	1.33912i	−0.457872	−	0.889018i	$-0.651388\pi$
$197$	6.10701	−	18.7954i	0.435106	−	1.33912i	0.892978	−	0.450101i	$-0.148612\pi$
$198$		0			0
$199$	−2.73271			−0.193717			−0.0968583	−	0.995298i	$-0.530879\pi$
$199$	−2.73271			−0.193717			−0.0968583	+	0.995298i	$0.530879\pi$
$200$		0			0
$201$	−0.0764644			−0.00539338
$202$		0			0
$203$	−4.10811	+	12.6435i	−0.288333	+	0.887397i
$204$		0			0
$205$	7.58347	−	2.06609i	0.529653	−	0.144302i
$206$		0			0
$207$	−11.5661			−0.803898
$208$		0			0
$209$	29.9664	+	21.7719i	2.07282	+	1.50599i
$210$		0			0
$211$	−8.66526	+	6.29568i	−0.596541	+	0.433412i	−0.844649	−	0.535320i	$-0.820191\pi$
$211$	−8.66526	+	6.29568i	−0.596541	+	0.433412i	0.248108	+	0.968732i	$0.420191\pi$
$212$		0			0
$213$	−6.42542	−	4.66834i	−0.440263	−	0.319869i
$214$		0			0
$215$	4.98407	−	6.20784i	0.339911	−	0.423371i
$216$		0			0
$217$	0.441379	+	1.35843i	0.0299628	+	0.0922160i
$218$		0			0
$219$	−0.111626	−	0.343550i	−0.00754299	−	0.0232149i
$220$		0			0
$221$	−5.56922	+	17.1403i	−0.374626	+	1.15298i
$222$		0			0
$223$	20.4215	−	14.8371i	1.36752	−	0.993565i	0.369599	−	0.929191i	$-0.379495\pi$
$223$	20.4215	−	14.8371i	1.36752	−	0.993565i	0.997926	−	0.0643735i	$-0.0205049\pi$
$224$		0			0
$225$	5.22382	−	12.0027i	0.348254	−	0.800179i
$226$		0			0
$227$	18.3220	−	13.3117i	1.21607	−	0.883528i	0.220304	−	0.975431i	$-0.429295\pi$
$227$	18.3220	−	13.3117i	1.21607	−	0.883528i	0.995768	+	0.0919034i	$0.0292951\pi$
$228$		0			0
$229$	−0.608831	+	1.87379i	−0.0402327	+	0.123823i	−0.969156	−	0.246450i	$-0.920736\pi$
$229$	−0.608831	+	1.87379i	−0.0402327	+	0.123823i	0.928923	+	0.370273i	$0.120736\pi$
$230$		0			0
$231$	1.81436	+	5.58402i	0.119376	+	0.367401i
$232$		0			0
$233$	−6.22281	−	19.1518i	−0.407670	−	1.25468i	−0.918645	−	0.395083i	$-0.870716\pi$
$233$	−6.22281	−	19.1518i	−0.407670	−	1.25468i	0.510976	−	0.859595i	$-0.329284\pi$
$234$		0			0
$235$	−7.78125	−	11.8728i	−0.507593	−	0.774498i
$236$		0			0
$237$	5.59658	+	4.06615i	0.363537	+	0.264125i
$238$		0			0
$239$	19.2533	−	13.9883i	1.24539	−	0.904830i	0.247446	−	0.968902i	$-0.420409\pi$
$239$	19.2533	−	13.9883i	1.24539	−	0.904830i	0.997945	+	0.0640715i	$0.0204086\pi$
$240$		0			0
$241$	3.33148	+	2.42046i	0.214600	+	0.155916i	0.689892	−	0.723912i	$-0.257658\pi$
$241$	3.33148	+	2.42046i	0.214600	+	0.155916i	−0.475293	+	0.879828i	$0.657658\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$		0			0
$245$	5.09394	−	6.34468i	0.325440	−	0.405347i
$246$		0			0
$247$	−6.07701	+	18.7031i	−0.386671	+	1.19005i
$248$		0			0
$249$	−10.9536			−0.694158
$250$		0			0
$251$	−25.7778			−1.62708			−0.813541	−	0.581507i	$-0.802463\pi$
$251$	−25.7778			−1.62708			−0.813541	+	0.581507i	$0.802463\pi$
$252$		0			0
$253$	−7.07411	+	21.7719i	−0.444746	+	1.36879i
$254$		0			0
$255$	−5.66780	+	7.05945i	−0.354931	+	0.442080i
$256$		0			0
$257$	−8.62200			−0.537825			−0.268913	−	0.963165i	$-0.586664\pi$
$257$	−8.62200			−0.537825			−0.268913	+	0.963165i	$0.586664\pi$
$258$		0			0
$259$	−4.77251	−	3.46743i	−0.296549	−	0.215456i
$260$		0			0
$261$	15.3583	−	11.1585i	0.950656	−	0.690692i
$262$		0			0
$263$	13.7537	+	9.99265i	0.848089	+	0.616173i	0.924619	−	0.380894i	$-0.124384\pi$
$263$	13.7537	+	9.99265i	0.848089	+	0.616173i	−0.0765291	+	0.997067i	$0.524384\pi$
$264$		0			0
$265$	10.8825	+	16.6048i	0.668507	+	1.02002i
$266$		0			0
$267$	−1.47286	−	4.53298i	−0.0901373	−	0.277414i
$268$		0			0
$269$	−2.54732	−	7.83984i	−0.155313	−	0.478003i	0.842880	−	0.538102i	$-0.180858\pi$
$269$	−2.54732	−	7.83984i	−0.155313	−	0.478003i	−0.998192	+	0.0600986i	$0.980858\pi$
$270$		0			0
$271$	1.62444	−	4.99952i	0.0986778	−	0.303699i	−0.889517	−	0.456902i	$-0.848959\pi$
$271$	1.62444	−	4.99952i	0.0986778	−	0.303699i	0.988195	+	0.153203i	$0.0489589\pi$
$272$		0			0
$273$	−2.52190	+	1.83227i	−0.152632	+	0.110894i
$274$		0			0
$275$	−19.3987	−	17.1744i	−1.16979	−	1.03566i
$276$		0			0
$277$	−16.8350	+	12.2313i	−1.01152	+	0.734909i	−0.964526	−	0.263986i	$-0.914963\pi$
$277$	−16.8350	+	12.2313i	−1.01152	+	0.734909i	−0.0469892	+	0.998895i	$0.514963\pi$
$278$		0			0
$279$	0.630287	−	1.93982i	0.0377343	−	0.116134i
$280$		0			0
$281$	1.16918	+	3.59836i	0.0697474	+	0.214660i	0.979854	−	0.199713i	$-0.0640009\pi$
$281$	1.16918	+	3.59836i	0.0697474	+	0.214660i	−0.910107	+	0.414373i	$0.864001\pi$
$282$		0			0
$283$	−6.43814	−	19.8146i	−0.382708	−	1.17785i	−0.938130	−	0.346284i	$-0.887443\pi$
$283$	−6.43814	−	19.8146i	−0.382708	−	1.17785i	0.555422	−	0.831569i	$-0.312557\pi$
$284$		0			0
$285$	−6.18458	+	7.70311i	−0.366343	+	0.456293i
$286$		0			0
$287$	5.21360	+	3.78791i	0.307749	+	0.223593i
$288$		0			0
$289$	−20.9654	+	15.2323i	−1.23326	+	0.896016i
$290$		0			0
$291$	3.40748	+	2.47568i	0.199750	+	0.145127i
$292$		0			0
$293$	19.5381			1.14143			0.570714	−	0.821149i	$-0.306666\pi$
$293$	19.5381			1.14143			0.570714	+	0.821149i	$0.306666\pi$
$294$		0			0
$295$	0.920994	−	0.250922i	0.0536224	−	0.0146092i
$296$		0			0
$297$	5.55979	−	17.1113i	0.322611	−	0.992896i
$298$		0			0
$299$	−12.1540			−0.702885
$300$		0			0
$301$	6.52731			0.376228
$302$		0			0
$303$	−0.107221	+	0.329992i	−0.00615968	+	0.0189575i
$304$		0			0
$305$	−0.207099	+	4.29617i	−0.0118585	+	0.245998i
$306$		0			0
$307$	−14.0671			−0.802852			−0.401426	−	0.915891i	$-0.631485\pi$
$307$	−14.0671			−0.802852			−0.401426	+	0.915891i	$0.631485\pi$
$308$		0			0
$309$	1.96060	+	1.42446i	0.111535	+	0.0810348i
$310$		0			0
$311$	13.0586	−	9.48763i	0.740485	−	0.537994i	−0.152378	−	0.988322i	$-0.548693\pi$
$311$	13.0586	−	9.48763i	0.740485	−	0.537994i	0.892863	+	0.450328i	$0.148693\pi$
$312$		0			0
$313$	13.6860	+	9.94346i	0.773578	+	0.562037i	0.903045	−	0.429546i	$-0.141327\pi$
$313$	13.6860	+	9.94346i	0.773578	+	0.562037i	−0.129467	+	0.991584i	$0.541327\pi$
$314$		0			0
$315$	10.3553	−	2.82126i	0.583453	−	0.158960i
$316$		0			0
$317$	−4.67034	−	14.3738i	−0.262313	−	0.807315i	−0.992300	−	0.123855i	$-0.960474\pi$
$317$	−4.67034	−	14.3738i	−0.262313	−	0.807315i	0.729988	−	0.683460i	$-0.239526\pi$
$318$		0			0
$319$	−11.6111	−	35.7352i	−0.650095	−	2.00079i
$320$		0			0
$321$	−0.0328921	+	0.101231i	−0.00183586	+	0.00565019i
$322$		0			0
$323$	−37.8843	+	27.5245i	−2.10794	+	1.53151i
$324$		0			0
$325$	5.48936	−	12.6128i	0.304495	−	0.699633i
$326$		0			0
$327$	7.37556	−	5.35866i	0.407869	−	0.296334i
$328$		0			0
$329$	3.59664	−	11.0693i	0.198289	−	0.610271i
$330$		0			0
$331$	2.57807	+	7.93450i	0.141704	+	0.436119i	0.996572	−	0.0827252i	$-0.0263624\pi$
$331$	2.57807	+	7.93450i	0.141704	+	0.436119i	−0.854869	+	0.518845i	$0.826362\pi$
$332$		0			0
$333$	2.60314	+	8.01165i	0.142651	+	0.439036i
$334$		0			0
$335$	0.258689	+	0.0980593i	0.0141337	+	0.00535755i
$336$		0			0
$337$	12.4416	+	9.03938i	0.677739	+	0.492406i	0.872607	−	0.488423i	$-0.162428\pi$
$337$	12.4416	+	9.03938i	0.677739	+	0.492406i	−0.194868	+	0.980830i	$0.562428\pi$
$338$		0			0
$339$	−3.32127	+	2.41304i	−0.180387	+	0.131059i
$340$		0			0
$341$	−3.26601	−	2.37289i	−0.176864	−	0.128499i
$342$		0			0
$343$	19.5048			1.05316
$344$		0			0
$345$	−5.70892	−	2.16404i	−0.307358	−	0.116508i
$346$		0			0
$347$	5.32705	−	16.3950i	0.285971	−	0.880129i	−0.700135	−	0.714011i	$-0.746877\pi$
$347$	5.32705	−	16.3950i	0.285971	−	0.880129i	0.986106	−	0.166118i	$-0.0531233\pi$
$348$		0			0
$349$	−32.5092			−1.74018			−0.870089	−	0.492894i	$-0.835939\pi$
$349$	−32.5092			−1.74018			−0.870089	+	0.492894i	$0.835939\pi$
$350$		0			0
$351$	9.55225			0.509861
$352$		0			0
$353$	−0.186926	+	0.575298i	−0.00994905	+	0.0306200i	−0.955908	−	0.293667i	$-0.905124\pi$
$353$	−0.186926	+	0.575298i	−0.00994905	+	0.0306200i	0.945959	+	0.324287i	$0.105124\pi$
$354$		0			0
$355$	15.7513	+	24.0337i	0.835991	+	1.27558i
$356$		0			0
$357$	−7.42274			−0.392853
$358$		0			0
$359$	−13.8191	−	10.0401i	−0.729343	−	0.529899i	0.160013	−	0.987115i	$-0.448847\pi$
$359$	−13.8191	−	10.0401i	−0.729343	−	0.529899i	−0.889356	+	0.457216i	$0.848847\pi$
$360$		0			0
$361$	−25.9671	+	18.8662i	−1.36669	+	0.992960i
$362$		0			0
$363$	−7.92542	−	5.75815i	−0.415977	−	0.302225i
$364$		0			0
$365$	−0.0629287	+	1.30543i	−0.00329384	+	0.0683291i
$366$		0			0
$367$	−11.3239	−	34.8513i	−0.591102	−	1.81923i	−0.573244	−	0.819385i	$-0.694315\pi$
$367$	−11.3239	−	34.8513i	−0.591102	−	1.81923i	−0.0178581	−	0.999841i	$-0.505685\pi$
$368$		0			0
$369$	−2.84373	−	8.75211i	−0.148039	−	0.455617i
$370$		0			0
$371$	−5.03010	+	15.4810i	−0.261150	+	0.803736i
$372$		0			0
$373$	−10.9523	+	7.95732i	−0.567089	+	0.412014i	−0.834047	−	0.551694i	$-0.813982\pi$
$373$	−10.9523	+	7.95732i	−0.567089	+	0.412014i	0.266958	+	0.963708i	$0.413982\pi$
$374$		0			0
$375$	4.82416	−	4.94704i	0.249119	−	0.255464i
$376$		0			0
$377$	16.1390	−	11.7257i	0.831202	−	0.603904i
$378$		0			0
$379$	−9.56485	+	29.4376i	−0.491313	+	1.51211i	0.331311	+	0.943522i	$0.392509\pi$
$379$	−9.56485	+	29.4376i	−0.491313	+	1.51211i	−0.822624	+	0.568585i	$0.807491\pi$
$380$		0			0
$381$	2.08297	+	6.41072i	0.106714	+	0.328431i
$382$		0			0
$383$	7.49447	+	23.0656i	0.382949	+	1.17860i	0.937957	+	0.346752i	$0.112715\pi$
$383$	7.49447	+	23.0656i	0.382949	+	1.17860i	−0.555007	+	0.831845i	$0.687285\pi$
$384$		0			0
$385$	1.02284	−	21.2182i	0.0521285	−	1.08138i
$386$		0			0
$387$	−7.54082	−	5.47872i	−0.383321	−	0.278499i
$388$		0			0
$389$	18.7779	−	13.6429i	0.952077	−	0.691724i	0.000779726	−	1.00000i	$-0.499752\pi$
$389$	18.7779	−	13.6429i	0.952077	−	0.691724i	0.951297	+	0.308275i	$0.0997518\pi$
$390$		0			0
$391$	−23.4138	−	17.0111i	−1.18409	−	0.860288i
$392$		0			0
$393$	−0.155138			−0.00782570
$394$		0			0
$395$	−13.7194	−	20.9335i	−0.690300	−	1.05328i
$396$		0			0
$397$	0.202731	−	0.623942i	0.0101748	−	0.0313147i	−0.945840	−	0.324632i	$-0.894759\pi$
$397$	0.202731	−	0.623942i	0.0101748	−	0.0313147i	0.956015	+	0.293318i	$0.0947594\pi$
$398$		0			0
$399$	−8.09953			−0.405484
$400$		0			0
$401$	−19.5996			−0.978759			−0.489379	−	0.872071i	$-0.662777\pi$
$401$	−19.5996			−0.978759			−0.489379	+	0.872071i	$0.662777\pi$
$402$		0			0
$403$	0.662326	−	2.03843i	0.0329928	−	0.101541i
$404$		0			0
$405$	−11.9352	−	4.52420i	−0.593066	−	0.224809i
$406$		0			0
$407$	16.6732			0.826460
$408$		0			0
$409$	−27.7007	−	20.1257i	−1.36971	−	0.995153i	−0.997760	−	0.0669001i	$-0.978689\pi$
$409$	−27.7007	−	20.1257i	−1.36971	−	0.995153i	−0.371950	−	0.928253i	$-0.621311\pi$
$410$		0			0
$411$	−10.9572	+	7.96090i	−0.540481	+	0.392682i
$412$		0			0
$413$	0.633179	+	0.460032i	0.0311567	+	0.0226367i
$414$		0			0
$415$	37.0576	+	14.0471i	1.81908	+	0.689547i
$416$		0			0
$417$	−3.22504	−	9.92565i	−0.157931	−	0.486061i
$418$		0			0
$419$	1.18712	+	3.65358i	0.0579946	+	0.178489i	0.975857	−	0.218409i	$-0.0700867\pi$
$419$	1.18712	+	3.65358i	0.0579946	+	0.178489i	−0.917863	+	0.396898i	$0.870087\pi$
$420$		0			0
$421$	2.82117	−	8.68268i	0.137496	−	0.423168i	−0.858474	−	0.512857i	$-0.828587\pi$
$421$	2.82117	−	8.68268i	0.137496	−	0.423168i	0.995970	+	0.0896888i	$0.0285873\pi$
$422$		0			0
$423$	−13.4462	+	9.76920i	−0.653775	+	0.474995i
$424$		0			0
$425$	28.2281	−	16.6145i	1.36926	−	0.805924i
$426$		0			0
$427$	−2.85303	+	2.07285i	−0.138068	+	0.100312i
$428$		0			0
$429$	2.72259	−	8.37928i	0.131448	−	0.404555i
$430$		0			0
$431$	−4.76582	−	14.6677i	−0.229561	−	0.706517i	−0.997796	−	0.0663493i	$-0.978865\pi$
$431$	−4.76582	−	14.6677i	−0.229561	−	0.706517i	0.768235	−	0.640168i	$-0.221135\pi$
$432$		0			0
$433$	−1.48963	−	4.58462i	−0.0715871	−	0.220323i	0.908861	−	0.417098i	$-0.136953\pi$
$433$	−1.48963	−	4.58462i	−0.0715871	−	0.220323i	−0.980449	+	0.196776i	$0.936953\pi$
$434$		0			0
$435$	9.66852	−	2.63416i	0.463570	−	0.126298i
$436$		0			0
$437$	−25.5486	−	18.5621i	−1.22215	−	0.887947i
$438$		0			0
$439$	−12.2341	+	8.88861i	−0.583903	+	0.424230i	−0.840129	−	0.542386i	$-0.817521\pi$
$439$	−12.2341	+	8.88861i	−0.583903	+	0.424230i	0.256226	+	0.966617i	$0.417521\pi$
$440$		0			0
$441$	−7.70704	−	5.59949i	−0.367002	−	0.266642i
$442$		0			0
$443$	−7.19925			−0.342047			−0.171023	−	0.985267i	$-0.554707\pi$
$443$	−7.19925			−0.342047			−0.171023	+	0.985267i	$0.554707\pi$
$444$		0			0
$445$	−0.830316	+	17.2245i	−0.0393608	+	0.816519i
$446$		0			0
$447$	−1.70201	+	5.23825i	−0.0805024	+	0.247761i
$448$		0			0
$449$	8.03243			0.379074			0.189537	−	0.981874i	$-0.439301\pi$
$449$	8.03243			0.379074			0.189537	+	0.981874i	$0.439301\pi$
$450$		0			0
$451$	−18.2142			−0.857673
$452$		0			0
$453$	0.724595	−	2.23007i	0.0340444	−	0.104778i
$454$		0			0
$455$	10.8817	−	2.96467i	0.510140	−	0.138986i
$456$		0			0
$457$	13.9713			0.653550			0.326775	−	0.945102i	$-0.394038\pi$
$457$	13.9713			0.653550			0.326775	+	0.945102i	$0.394038\pi$
$458$		0			0
$459$	18.4017	+	13.3696i	0.858917	+	0.624039i
$460$		0			0
$461$	−22.8169	+	16.5774i	−1.06269	+	0.772088i	−0.974584	−	0.224023i	$-0.928081\pi$
$461$	−22.8169	+	16.5774i	−1.06269	+	0.772088i	−0.0881043	+	0.996111i	$0.528081\pi$
$462$		0			0
$463$	20.4596	+	14.8648i	0.950837	+	0.690824i	0.951005	−	0.309176i	$-0.100053\pi$
$463$	20.4596	+	14.8648i	0.950837	+	0.690824i	−0.000167644		1.00000i	$0.500053\pi$
$464$		0			0
$465$	0.674050	−	0.839554i	0.0312583	−	0.0389334i
$466$		0			0
$467$	2.62831	+	8.08909i	0.121623	+	0.374319i	0.993271	−	0.115815i	$-0.0369480\pi$
$467$	2.62831	+	8.08909i	0.121623	+	0.374319i	−0.871647	+	0.490134i	$0.836948\pi$
$468$		0			0
$469$	0.0700936	+	0.215726i	0.00323662	+	0.00996129i
$470$		0			0
$471$	2.10192	−	6.46904i	0.0968513	−	0.298078i
$472$		0			0
$473$	−14.9253	+	10.8438i	−0.686264	+	0.498600i
$474$		0			0
$475$	30.8018	−	18.1294i	1.41329	−	0.831835i
$476$		0			0
$477$	18.8052	−	13.6628i	0.861031	−	0.625575i
$478$		0			0
$479$	−4.29475	+	13.2179i	−0.196232	+	0.603940i	0.803728	+	0.594997i	$0.202847\pi$
$479$	−4.29475	+	13.2179i	−0.196232	+	0.603940i	−0.999960	+	0.00894324i	$0.997153\pi$
$480$		0			0
$481$	2.73547	+	8.41890i	0.124727	+	0.383869i
$482$		0			0
$483$	−1.54687	−	4.76078i	−0.0703851	−	0.216623i
$484$		0			0
$485$	−8.35309	−	12.7454i	−0.379294	−	0.578737i
$486$		0			0
$487$	−33.4909	−	24.3326i	−1.51762	−	1.10261i	−0.962652	−	0.270743i	$-0.912731\pi$
$487$	−33.4909	−	24.3326i	−1.51762	−	1.10261i	−0.554967	−	0.831872i	$-0.687269\pi$
$488$		0			0
$489$	−0.824162	+	0.598789i	−0.0372699	+	0.0270782i
$490$		0			0
$491$	28.3015	+	20.5623i	1.27723	+	0.927962i	0.999466	−	0.0326876i	$-0.0104066\pi$
$491$	28.3015	+	20.5623i	1.27723	+	0.927962i	0.277764	+	0.960649i	$0.410407\pi$
$492$		0			0
$493$	47.5022			2.13939
$494$		0			0
$495$	−18.9912	+	23.6543i	−0.853593	+	1.06318i
$496$		0			0
$497$	−7.28053	+	22.4072i	−0.326576	+	1.00510i
$498$		0			0
$499$	9.42740			0.422028			0.211014	−	0.977483i	$-0.432323\pi$
$499$	9.42740			0.422028			0.211014	+	0.977483i	$0.432323\pi$
$500$		0			0
$501$	0.0845790			0.00377871
$502$		0			0
$503$	−4.90707	+	15.1024i	−0.218796	+	0.673383i	0.780067	+	0.625696i	$0.215185\pi$
$503$	−4.90707	+	15.1024i	−0.218796	+	0.673383i	−0.998862	+	0.0476871i	$0.984815\pi$
$504$		0			0
$505$	0.785930	−	0.978904i	0.0349734	−	0.0435607i
$506$		0			0
$507$	−3.35676			−0.149079
$508$		0			0
$509$	2.69830	+	1.96043i	0.119600	+	0.0868946i	0.645977	−	0.763357i	$-0.276450\pi$
$509$	2.69830	+	1.96043i	0.119600	+	0.0868946i	−0.526377	+	0.850251i	$0.676450\pi$
$510$		0			0
$511$	−0.866918	+	0.629853i	−0.0383502	+	0.0278630i
$512$		0			0
$513$	20.0795	+	14.5886i	0.886531	+	0.644103i
$514$		0			0
$515$	−4.80622	−	7.33345i	−0.211787	−	0.323151i
$516$		0			0
$517$	10.1654	+	31.2860i	0.447076	+	1.37596i
$518$		0			0
$519$	1.86274	+	5.73293i	0.0817653	+	0.251648i
$520$		0			0
$521$	−8.30286	+	25.5536i	−0.363755	+	1.11952i	0.587002	+	0.809586i	$0.300308\pi$
$521$	−8.30286	+	25.5536i	−0.363755	+	1.11952i	−0.950757	+	0.309937i	$0.899692\pi$
$522$		0			0
$523$	3.84546	−	2.79389i	0.168150	−	0.122168i	−0.500527	−	0.865721i	$-0.666861\pi$
$523$	3.84546	−	2.79389i	0.168150	−	0.122168i	0.668678	+	0.743552i	$0.266861\pi$
$524$		0			0
$525$	5.63914	+	0.544942i	0.246112	+	0.0237832i
$526$		0			0
$527$	4.12896	−	2.99987i	0.179861	−	0.130676i
$528$		0			0
$529$	−1.07619	+	3.31217i	−0.0467908	+	0.144007i
$530$		0			0
$531$	−0.345364	−	1.06292i	−0.0149875	−	0.0461269i
$532$		0			0
$533$	−2.98829	−	9.19701i	−0.129437	−	0.398367i
$534$		0			0
$535$	0.241099	−	0.300298i	0.0104236	−	0.0129830i
$536$		0			0
$537$	10.4103	+	7.56351i	0.449237	+	0.326389i
$538$		0			0
$539$	−15.2543	+	11.0829i	−0.657048	+	0.477373i
$540$		0			0
$541$	−17.0316	−	12.3742i	−0.732246	−	0.532008i	0.158027	−	0.987435i	$-0.449487\pi$
$541$	−17.0316	−	12.3742i	−0.732246	−	0.532008i	−0.890273	+	0.455427i	$0.849487\pi$
$542$		0			0
$543$	−8.39008			−0.360053
$544$		0			0
$545$	−31.8245	+	8.67049i	−1.36321	+	0.371403i
$546$		0			0
$547$	8.41913	−	25.9114i	0.359976	−	1.10789i	−0.593092	−	0.805135i	$-0.702093\pi$
$547$	8.41913	−	25.9114i	0.359976	−	1.10789i	0.953068	−	0.302757i	$-0.0979072\pi$
$548$		0			0
$549$	5.03588			0.214926
$550$		0			0
$551$	51.8333			2.20817
$552$		0			0
$553$	6.34138	−	19.5168i	0.269663	−	0.829938i
$554$		0			0
$555$	−0.214107	+	4.44154i	−0.00908833	+	0.188533i
$556$		0			0
$557$	27.1225			1.14922			0.574608	−	0.818429i	$-0.305154\pi$
$557$	27.1225			1.14922			0.574608	+	0.818429i	$0.305154\pi$
$558$		0			0
$559$	−7.92414	−	5.75722i	−0.335155	−	0.243505i
$560$		0			0
$561$	16.9727	−	12.3314i	0.716590	−	0.520633i
$562$		0			0
$563$	−2.20949	−	1.60529i	−0.0931188	−	0.0676547i	0.540252	−	0.841503i	$-0.318329\pi$
$563$	−2.20949	−	1.60529i	−0.0931188	−	0.0676547i	−0.633370	+	0.773849i	$0.718329\pi$
$564$		0			0
$565$	14.3308	−	3.90439i	0.602902	−	0.164259i
$566$		0			0
$567$	−3.23393	−	9.95302i	−0.135812	−	0.417988i
$568$		0			0
$569$	−9.14444	−	28.1437i	−0.383355	−	1.17984i	−0.937667	−	0.347536i	$-0.887019\pi$
$569$	−9.14444	−	28.1437i	−0.383355	−	1.17984i	0.554312	−	0.832309i	$-0.312981\pi$
$570$		0			0
$571$	2.68530	−	8.26449i	0.112376	−	0.345858i	−0.879015	−	0.476795i	$-0.841798\pi$
$571$	2.68530	−	8.26449i	0.112376	−	0.345858i	0.991391	+	0.130937i	$0.0417985\pi$
$572$		0			0
$573$	3.73679	−	2.71494i	0.156107	−	0.113418i
$574$		0			0
$575$	16.5388	+	14.6425i	0.689717	+	0.610632i
$576$		0			0
$577$	−19.7734	+	14.3662i	−0.823176	+	0.598072i	−0.917621	−	0.397458i	$-0.869893\pi$
$577$	−19.7734	+	14.3662i	−0.823176	+	0.598072i	0.0944444	+	0.995530i	$0.469893\pi$
$578$		0			0
$579$	1.54068	−	4.74172i	0.0640285	−	0.197059i
$580$		0			0
$581$	10.0410	+	30.9030i	0.416571	+	1.28207i
$582$		0			0
$583$	−14.2169	−	43.7552i	−0.588806	−	1.81216i
$584$		0			0
$585$	−15.0597	−	5.70855i	−0.622641	−	0.236020i
$586$		0			0
$587$	−11.2806	−	8.19583i	−0.465600	−	0.338278i	0.330124	−	0.943938i	$-0.392909\pi$
$587$	−11.2806	−	8.19583i	−0.465600	−	0.338278i	−0.795724	+	0.605659i	$0.792909\pi$
$588$		0			0
$589$	4.50543	−	3.27339i	0.185643	−	0.134878i
$590$		0			0
$591$	−9.88134	−	7.17922i	−0.406464	−	0.295313i
$592$		0			0
$593$	24.6781			1.01341			0.506704	−	0.862120i	$-0.330864\pi$
$593$	24.6781			1.01341			0.506704	+	0.862120i	$0.330864\pi$
$594$		0			0
$595$	25.1121	+	9.51906i	1.02950	+	0.390243i
$596$		0			0
$597$	−0.521901	+	1.60625i	−0.0213600	+	0.0657393i
$598$		0			0
$599$	−16.1948			−0.661701			−0.330851	−	0.943683i	$-0.607336\pi$
$599$	−16.1948			−0.661701			−0.330851	+	0.943683i	$0.607336\pi$
$600$		0			0
$601$	4.66188			0.190162			0.0950810	−	0.995470i	$-0.469689\pi$
$601$	4.66188			0.190162			0.0950810	+	0.995470i	$0.469689\pi$
$602$		0			0
$603$	0.100093	−	0.308055i	0.00407611	−	0.0125450i
$604$		0			0
$605$	19.4284	+	29.6443i	0.789876	+	1.20521i
$606$		0			0
$607$	4.79441			0.194599			0.0972996	−	0.995255i	$-0.468980\pi$
$607$	4.79441			0.194599			0.0972996	+	0.995255i	$0.468980\pi$
$608$		0			0
$609$	6.64706	+	4.82937i	0.269353	+	0.195696i
$610$		0			0
$611$	−14.1297	+	10.2658i	−0.571625	+	0.415310i
$612$		0			0
$613$	−1.63842	−	1.19038i	−0.0661753	−	0.0480791i	0.554206	−	0.832380i	$-0.313022\pi$
$613$	−1.63842	−	1.19038i	−0.0661753	−	0.0480791i	−0.620381	+	0.784301i	$0.713022\pi$
$614$		0			0
$615$	0.233895	−	4.85204i	0.00943157	−	0.195653i
$616$		0			0
$617$	2.23562	+	6.88054i	0.0900028	+	0.277000i	0.985919	−	0.167223i	$-0.0534799\pi$
$617$	2.23562	+	6.88054i	0.0900028	+	0.277000i	−0.895916	+	0.444223i	$0.853480\pi$
$618$		0			0
$619$	−0.527529	−	1.62357i	−0.0212032	−	0.0652567i	0.939895	−	0.341463i	$-0.110923\pi$
$619$	−0.527529	−	1.62357i	−0.0212032	−	0.0652567i	−0.961098	+	0.276207i	$0.910923\pi$
$620$		0			0
$621$	−4.74013	+	14.5886i	−0.190215	+	0.585421i
$622$		0			0
$623$	−11.4386	+	8.31062i	−0.458277	+	0.332958i
$624$		0			0
$625$	−22.6649	+	10.5499i	−0.906598	+	0.421996i
$626$		0			0
$627$	18.5203	−	13.4558i	0.739628	−	0.537371i
$628$		0			0
$629$	−6.51367	+	20.0470i	−0.259717	+	0.799327i
$630$		0			0
$631$	6.38944	+	19.6647i	0.254360	+	0.782839i	0.993955	+	0.109787i	$0.0350168\pi$
$631$	6.38944	+	19.6647i	0.254360	+	0.782839i	−0.739595	+	0.673052i	$0.764983\pi$
$632$		0			0
$633$	2.04559	+	6.29568i	0.0813049	+	0.250231i
$634$		0			0
$635$	1.17426	−	24.3595i	0.0465993	−	0.966679i
$636$		0			0
$637$	−8.09881	−	5.88413i	−0.320887	−	0.233138i
$638$		0			0
$639$	27.2185	−	19.7754i	1.07675	−	0.782303i
$640$		0			0
$641$	35.0795	+	25.4867i	1.38556	+	1.00667i	0.996336	+	0.0855202i	$0.0272552\pi$
$641$	35.0795	+	25.4867i	1.38556	+	1.00667i	0.389219	+	0.921145i	$0.372745\pi$
$642$		0			0
$643$	9.91631			0.391061			0.195531	−	0.980698i	$-0.437357\pi$
$643$	9.91631			0.391061			0.195531	+	0.980698i	$0.437357\pi$
$644$		0			0
$645$	−2.69701	−	4.11516i	−0.106195	−	0.162034i
$646$		0			0
$647$	−6.30874	+	19.4163i	−0.248022	+	0.763334i	0.747102	+	0.664709i	$0.231444\pi$
$647$	−6.30874	+	19.4163i	−0.248022	+	0.763334i	−0.995125	+	0.0986250i	$0.968556\pi$
$648$		0			0
$649$	−2.21207			−0.0868314
$650$		0			0
$651$	0.882759			0.0345980
$652$		0			0
$653$	−9.23372	+	28.4185i	−0.361343	+	1.11210i	0.590896	+	0.806748i	$0.298774\pi$
$653$	−9.23372	+	28.4185i	−0.361343	+	1.11210i	−0.952239	+	0.305353i	$0.901226\pi$
$654$		0			0
$655$	0.524854	+	0.198952i	0.0205077	+	0.00777371i
$656$		0			0
$657$	1.53019			0.0596985
$658$		0			0
$659$	10.6885	+	7.76563i	0.416364	+	0.302506i	0.776173	−	0.630520i	$-0.217158\pi$
$659$	10.6885	+	7.76563i	0.416364	+	0.302506i	−0.359809	+	0.933026i	$0.617158\pi$
$660$		0			0
$661$	−21.5135	+	15.6305i	−0.836780	+	0.607956i	−0.921469	−	0.388451i	$-0.873010\pi$
$661$	−21.5135	+	15.6305i	−0.836780	+	0.607956i	0.0846893	+	0.996407i	$0.473010\pi$
$662$		0			0
$663$	9.01119	+	6.54701i	0.349965	+	0.254265i
$664$		0			0
$665$	27.4018	+	10.3870i	1.06260	+	0.402790i
$666$		0			0
$667$	9.89928	+	30.4669i	0.383302	+	1.17968i
$668$		0			0
$669$	−4.82086	−	14.8371i	−0.186385	−	0.573635i
$670$		0			0
$671$	3.08008	−	9.47950i	0.118905	−	0.365952i
$672$		0			0
$673$	1.80286	−	1.30986i	0.0694953	−	0.0504913i	−0.552495	−	0.833516i	$-0.686324\pi$
$673$	1.80286	−	1.30986i	0.0694953	−	0.0504913i	0.621990	+	0.783025i	$0.286324\pi$
$674$		0			0
$675$	−12.9984	−	11.5080i	−0.500310	−	0.442943i
$676$		0			0
$677$	7.87631	−	5.72248i	0.302711	−	0.219933i	−0.426051	−	0.904699i	$-0.640096\pi$
$677$	7.87631	−	5.72248i	0.302711	−	0.219933i	0.728763	+	0.684766i	$0.240096\pi$
$678$		0			0
$679$	3.86095	−	11.8828i	0.148170	−	0.456020i
$680$		0			0
$681$	−4.32523	−	13.3117i	−0.165743	−	0.510105i
$682$		0			0
$683$	9.49775	+	29.2311i	0.363421	+	1.11850i	0.950964	+	0.309302i	$0.100095\pi$
$683$	9.49775	+	29.2311i	0.363421	+	1.11850i	−0.587543	+	0.809193i	$0.699905\pi$
$684$		0			0
$685$	47.2790	−	12.8810i	1.80644	−	0.492158i
$686$		0			0
$687$	0.985109	+	0.715723i	0.0375842	+	0.0273065i
$688$		0			0
$689$	19.7611	−	14.3573i	0.752839	−	0.546969i
$690$		0			0
$691$	−12.6860	−	9.21691i	−0.482598	−	0.350628i	0.319733	−	0.947508i	$-0.396407\pi$
$691$	−12.6860	−	9.21691i	−0.482598	−	0.350628i	−0.802331	+	0.596880i	$0.796407\pi$
$692$		0			0
$693$	−24.8716			−0.944793
$694$		0			0
$695$	−1.81810	+	37.7156i	−0.0689646	+	1.43064i
$696$		0			0
$697$	7.11568	−	21.8998i	0.269526	−	0.829515i
$698$		0			0
$699$	−12.4456			−0.470736
$700$		0			0
$701$	−18.6041			−0.702667			−0.351333	−	0.936250i	$-0.614272\pi$
$701$	−18.6041			−0.702667			−0.351333	+	0.936250i	$0.614272\pi$
$702$		0			0
$703$	−7.10757	+	21.8748i	−0.268067	+	0.825025i
$704$		0			0
$705$	−8.46476	+	2.30620i	−0.318801	+	0.0868564i
$706$		0			0
$707$	1.02928			0.0387101
$708$		0			0
$709$	7.34414	+	5.33583i	0.275815	+	0.200391i	0.717090	−	0.696981i	$-0.245474\pi$
$709$	7.34414	+	5.33583i	0.275815	+	0.200391i	−0.441275	+	0.897372i	$0.645474\pi$
$710$		0			0
$711$	−23.7075	+	17.2245i	−0.889100	+	0.645969i
$712$		0			0
$713$	2.78451	+	2.02307i	0.104281	+	0.0757644i
$714$		0			0
$715$	−19.9566	+	24.8567i	−0.746335	+	0.929588i
$716$		0			0
$717$	−4.54508	−	13.9883i	−0.169739	−	0.522404i
$718$		0			0
$719$	7.37490	+	22.6976i	0.275037	+	0.846478i	0.989210	+	0.146508i	$0.0468033\pi$
$719$	7.37490	+	22.6976i	0.275037	+	0.846478i	−0.714172	+	0.699970i	$0.753197\pi$
$720$		0			0
$721$	2.22152	−	6.83715i	0.0827339	−	0.254629i
$722$		0			0
$723$	2.05897	−	1.49593i	0.0765739	−	0.0556342i
$724$		0			0
$725$	−36.0880	−	3.48738i	−1.34027	−	0.129518i
$726$		0			0
$727$	−32.0955	+	23.3188i	−1.19036	+	0.864846i	−0.993302	−	0.115547i	$-0.963138\pi$
$727$	−32.0955	+	23.3188i	−1.19036	+	0.864846i	−0.197056	+	0.980392i	$0.563138\pi$
$728$		0			0
$729$	−2.62868	+	8.09024i	−0.0973584	+	0.299638i
$730$		0			0
$731$	−7.20727	−	22.1817i	−0.266570	−	0.820420i
$732$		0			0
$733$	−7.06196	−	21.7345i	−0.260839	−	0.802781i	−0.992623	−	0.121244i	$-0.961312\pi$
$733$	−7.06196	−	21.7345i	−0.260839	−	0.802781i	0.731783	−	0.681537i	$-0.238688\pi$
$734$		0			0
$735$	−2.75646	−	4.20587i	−0.101673	−	0.155136i
$736$		0			0
$737$	−0.518661	−	0.376829i	−0.0191051	−	0.0138807i
$738$		0			0
$739$	14.7392	−	10.7087i	0.542191	−	0.393925i	−0.282707	−	0.959206i	$-0.591232\pi$
$739$	14.7392	−	10.7087i	0.542191	−	0.393925i	0.824898	+	0.565282i	$0.191232\pi$
$740$		0			0
$741$	9.83280	+	7.14395i	0.361217	+	0.262440i
$742$		0			0
$743$	47.9825			1.76031			0.880153	−	0.474690i	$-0.157440\pi$
$743$	47.9825			1.76031			0.880153	+	0.474690i	$0.157440\pi$
$744$		0			0
$745$	12.4758	−	15.5390i	0.457076	−	0.569305i
$746$		0			0
$747$	14.3385	−	44.1293i	0.524618	−	1.61461i
$748$		0			0
$749$	0.315752			0.0115373
$750$		0			0
$751$	−23.0826			−0.842295			−0.421147	−	0.906992i	$-0.638372\pi$
$751$	−23.0826			−0.842295			−0.421147	+	0.906992i	$0.638372\pi$
$752$		0			0
$753$	−4.92313	+	15.1518i	−0.179409	+	0.552163i
$754$		0			0
$755$	−5.31129	+	6.61540i	−0.193298	+	0.240759i
$756$		0			0
$757$	−29.8449			−1.08473			−0.542366	−	0.840142i	$-0.682472\pi$
$757$	−29.8449			−1.08473			−0.542366	+	0.840142i	$0.682472\pi$
$758$		0			0
$759$	11.4462	+	8.31612i	0.415469	+	0.301856i
$760$		0			0
$761$	4.23082	−	3.07387i	0.153367	−	0.111428i	−0.508455	−	0.861088i	$-0.669783\pi$
$761$	4.23082	−	3.07387i	0.153367	−	0.111428i	0.661822	+	0.749661i	$0.269783\pi$
$762$		0			0
$763$	−21.8792	−	15.8962i	−0.792081	−	0.575480i
$764$		0			0
$765$	−21.0214	−	32.0750i	−0.760032	−	1.15968i
$766$		0			0
$767$	−0.362920	−	1.11695i	−0.0131043	−	0.0403309i
$768$		0			0
$769$	0.368899	+	1.13536i	0.0133029	+	0.0409420i	0.957488	−	0.288474i	$-0.0931480\pi$
$769$	0.368899	+	1.13536i	0.0133029	+	0.0409420i	−0.944185	+	0.329416i	$0.893148\pi$
$770$		0			0
$771$	−1.64666	+	5.06788i	−0.0593028	+	0.182515i
$772$		0			0
$773$	9.71750	−	7.06018i	0.349514	−	0.253937i	−0.399151	−	0.916885i	$-0.630695\pi$
$773$	9.71750	−	7.06018i	0.349514	−	0.253937i	0.748665	+	0.662948i	$0.230695\pi$
$774$		0			0
$775$	−3.35706	+	1.97591i	−0.120589	+	0.0709766i
$776$		0			0
$777$	−2.94957	+	2.14299i	−0.105815	+	0.0768794i
$778$		0			0
$779$	7.76447	−	23.8966i	0.278191	−	0.856184i
$780$		0			0
$781$	−20.5775	−	63.3311i	−0.736321	−	2.26616i
$782$		0			0
$783$	−7.78018	−	23.9449i	−0.278041	−	0.855722i
$784$		0			0
$785$	−15.4071	+	19.1901i	−0.549902	+	0.684923i
$786$		0			0
$787$	40.6304	+	29.5197i	1.44832	+	1.05226i	0.986221	+	0.165435i	$0.0529027\pi$
$787$	40.6304	+	29.5197i	1.44832	+	1.05226i	0.462097	+	0.886830i	$0.347097\pi$
$788$		0			0
$789$	8.50025	−	6.17580i	0.302617	−	0.219864i
$790$		0			0
$791$	9.85237	+	7.15817i	0.350310	+	0.254515i
$792$		0			0
$793$	5.29187			0.187920
$794$		0			0
$795$	11.8384	−	3.22534i	0.419866	−	0.114391i
$796$		0			0
$797$	−6.94555	+	21.3762i	−0.246024	+	0.757185i	0.749442	+	0.662070i	$0.230322\pi$
$797$	−6.94555	+	21.3762i	−0.246024	+	0.757185i	−0.995466	+	0.0951147i	$0.969678\pi$
$798$		0			0
$799$	−41.5880			−1.47128
$800$		0			0
$801$	20.1902			0.713386
$802$		0			0
$803$	0.935906	−	2.88042i	0.0330274	−	0.101648i
$804$		0			0
$805$	−0.872043	+	18.0901i	−0.0307355	+	0.637592i
$806$		0			0
$807$	−5.09464			−0.179340
$808$		0			0
$809$	−10.8493	−	7.88250i	−0.381442	−	0.277134i	0.380498	−	0.924782i	$-0.375753\pi$
$809$	−10.8493	−	7.88250i	−0.381442	−	0.277134i	−0.761940	+	0.647648i	$0.775753\pi$
$810$		0			0
$811$	43.9946	−	31.9639i	1.54486	−	1.12241i	0.597664	−	0.801747i	$-0.296096\pi$
$811$	43.9946	−	31.9639i	1.54486	−	1.12241i	0.947195	−	0.320659i	$-0.103904\pi$
$812$		0			0
$813$	−2.62840	−	1.90965i	−0.0921821	−	0.0669742i
$814$		0			0
$815$	3.55615	−	0.968861i	0.124566	−	0.0339377i
$816$		0			0
$817$	−7.86441	−	24.2042i	−0.275141	−	0.846797i
$818$		0			0
$819$	−4.08052	−	12.5586i	−0.142585	−	0.438831i
$820$		0			0
$821$	15.4210	−	47.4609i	0.538196	−	1.65640i	−0.198443	−	0.980112i	$-0.563588\pi$
$821$	15.4210	−	47.4609i	0.538196	−	1.65640i	0.736639	−	0.676286i	$-0.236412\pi$
$822$		0			0
$823$	−11.4411	+	8.31246i	−0.398813	+	0.289754i	−0.769057	−	0.639180i	$-0.779274\pi$
$823$	−11.4411	+	8.31246i	−0.398813	+	0.289754i	0.370245	+	0.928934i	$0.379274\pi$
$824$		0			0
$825$	−13.7997	+	8.12226i	−0.480444	+	0.282781i
$826$		0			0
$827$	−18.4876	+	13.4320i	−0.642878	+	0.467078i	−0.860838	−	0.508880i	$-0.830060\pi$
$827$	−18.4876	+	13.4320i	−0.642878	+	0.467078i	0.217960	+	0.975958i	$0.430060\pi$
$828$		0			0
$829$	−8.79447	+	27.0666i	−0.305445	+	0.940062i	0.674066	+	0.738671i	$0.264546\pi$
$829$	−8.79447	+	27.0666i	−0.305445	+	0.940062i	−0.979511	+	0.201391i	$0.935454\pi$
$830$		0			0
$831$	3.97420	+	12.2313i	0.137863	+	0.424300i
$832$		0			0
$833$	−7.36614	−	22.6706i	−0.255222	−	0.785491i
$834$		0			0
$835$	−0.286142	−	0.108466i	−0.00990235	−	0.00375361i
$836$		0			0
$837$	−2.18844	−	1.59000i	−0.0756436	−	0.0549583i
$838$		0			0
$839$	−4.38856	+	3.18848i	−0.151510	+	0.110079i	−0.660958	−	0.750423i	$-0.729850\pi$
$839$	−4.38856	+	3.18848i	−0.151510	+	0.110079i	0.509448	+	0.860502i	$0.329850\pi$
$840$		0			0
$841$	−19.0767	−	13.8600i	−0.657817	−	0.477932i
$842$		0			0
$843$	2.33836			0.0805373
$844$		0			0
$845$	11.3564	+	4.30478i	0.390671	+	0.148089i
$846$		0			0
$847$	−8.98015	+	27.6381i	−0.308562	+	0.949655i
$848$		0			0
$849$	−12.8763			−0.441913
$850$		0			0
$851$	−14.2151			−0.487289
$852$		0			0
$853$	10.1803	−	31.3316i	0.348566	−	1.07277i	−0.611081	−	0.791568i	$-0.709265\pi$
$853$	10.1803	−	31.3316i	0.348566	−	1.07277i	0.959647	−	0.281207i	$-0.0907348\pi$
$854$		0			0
$855$	−22.9381	−	34.9995i	−0.784467	−	1.19696i
$856$		0			0
$857$	−34.1264			−1.16573			−0.582867	−	0.812567i	$-0.698069\pi$
$857$	−34.1264			−1.16573			−0.582867	+	0.812567i	$0.698069\pi$
$858$		0			0
$859$	35.5346	+	25.8174i	1.21242	+	0.880878i	0.995449	−	0.0952987i	$-0.0303806\pi$
$859$	35.5346	+	25.8174i	1.21242	+	0.880878i	0.216976	+	0.976177i	$0.430381\pi$
$860$		0			0
$861$	3.22218	−	2.34105i	0.109812	−	0.0797829i
$862$		0			0
$863$	−39.8099	−	28.9236i	−1.35514	−	0.984569i	−0.998737	−	0.0502379i	$-0.984002\pi$
$863$	−39.8099	−	28.9236i	−1.35514	−	0.984569i	−0.356406	−	0.934331i	$-0.615998\pi$
$864$		0			0
$865$	1.05011	−	21.7841i	0.0357049	−	0.740681i
$866$		0			0
$867$	4.94926	+	15.2323i	0.168086	+	0.517315i
$868$		0			0
$869$	17.9231	+	55.1617i	0.608001	+	1.87123i
$870$		0			0
$871$	0.105181	−	0.323714i	0.00356393	−	0.0109686i
$872$		0			0
$873$	−14.4343	+	10.4871i	−0.488528	+	0.354936i
$874$		0			0
$875$	−18.3791	−	9.07535i	−0.621327	−	0.306803i
$876$		0			0
$877$	20.6659	−	15.0146i	0.697836	−	0.507008i	−0.181390	−	0.983411i	$-0.558060\pi$
$877$	20.6659	−	15.0146i	0.697836	−	0.507008i	0.879227	+	0.476403i	$0.158060\pi$
$878$		0			0
$879$	3.73145	−	11.4842i	0.125859	−	0.387353i
$880$		0			0
$881$	−6.31888	−	19.4475i	−0.212889	−	0.655204i	−0.999297	−	0.0374964i	$-0.988062\pi$
$881$	−6.31888	−	19.4475i	−0.212889	−	0.655204i	0.786408	−	0.617707i	$-0.211938\pi$
$882$		0			0
$883$	−10.3964	−	31.9968i	−0.349866	−	1.07678i	−0.958927	−	0.283653i	$-0.908454\pi$
$883$	−10.3964	−	31.9968i	−0.349866	−	1.07678i	0.609061	−	0.793123i	$-0.291546\pi$
$884$		0			0
$885$	0.0284060	−	0.589269i	0.000954858	−	0.0198080i
$886$		0			0
$887$	−5.83763	−	4.24129i	−0.196009	−	0.142409i	0.485452	−	0.874263i	$-0.338655\pi$
$887$	−5.83763	−	4.24129i	−0.196009	−	0.142409i	−0.681461	+	0.731855i	$0.738655\pi$
$888$		0			0
$889$	16.1769	−	11.7532i	0.542555	−	0.394189i
$890$		0			0
$891$	23.9296	+	17.3859i	0.801673	+	0.582449i
$892$		0			0
$893$	−45.3799			−1.51858
$894$		0			0
$895$	−25.5197	−	38.9387i	−0.853031	−	1.30158i
$896$		0			0
$897$	−2.32121	+	7.14395i	−0.0775029	+	0.238530i
$898$		0			0
$899$	−5.64926			−0.188413
$900$		0			0
$901$	58.1631			1.93770
$902$		0			0
$903$	1.24661	−	3.83666i	0.0414845	−	0.127676i
$904$		0			0
$905$	28.3847	+	10.7596i	0.943541	+	0.357661i
$906$		0			0
$907$	−3.13960			−0.104249			−0.0521244	−	0.998641i	$-0.516599\pi$
$907$	−3.13960			−0.104249			−0.0521244	+	0.998641i	$0.516599\pi$
$908$		0			0
$909$	−1.18910	−	0.863930i	−0.0394399	−	0.0286548i
$910$		0			0
$911$	−14.4189	+	10.4759i	−0.477718	+	0.347082i	−0.800442	−	0.599411i	$-0.795402\pi$
$911$	−14.4189	+	10.4759i	−0.477718	+	0.347082i	0.322724	+	0.946493i	$0.395402\pi$
$912$		0			0
$913$	−74.2989	−	53.9813i	−2.45893	−	1.78652i
$914$		0			0
$915$	2.48567	+	0.942225i	0.0821738	+	0.0311490i
$916$		0			0
$917$	0.142213	+	0.437686i	0.00469628	+	0.0144537i
$918$		0			0
$919$	0.498872	+	1.53537i	0.0164563	+	0.0506472i	0.958947	−	0.283584i	$-0.0915234\pi$
$919$	0.498872	+	1.53537i	0.0164563	+	0.0506472i	−0.942491	+	0.334231i	$0.891523\pi$
$920$		0			0
$921$	−2.68658	+	8.26844i	−0.0885257	+	0.272454i
$922$		0			0
$923$	28.6021	−	20.7807i	0.941450	−	0.684003i
$924$		0			0
$925$	6.42026	−	14.7517i	0.211097	−	0.485034i
$926$		0			0
$927$	−8.30525	+	6.03412i	−0.272780	+	0.198186i
$928$		0			0
$929$	−17.5670	+	54.0656i	−0.576354	+	1.77384i	0.0551673	+	0.998477i	$0.482431\pi$
$929$	−17.5670	+	54.0656i	−0.576354	+	1.77384i	−0.631521	+	0.775358i	$0.717569\pi$
$930$		0			0
$931$	−8.03777	−	24.7377i	−0.263427	−	0.810745i
$932$		0			0
$933$	−3.08272	−	9.48763i	−0.100924	−	0.310611i
$934$		0			0
$935$	−73.2350	+	19.9527i	−2.39504	+	0.652521i
$936$		0			0
$937$	40.5800	+	29.4831i	1.32569	+	0.963172i	0.999842	+	0.0177499i	$0.00565028\pi$
$937$	40.5800	+	29.4831i	1.32569	+	0.963172i	0.325850	+	0.945422i	$0.394350\pi$
$938$		0			0
$939$	8.45841	−	6.14539i	0.276030	−	0.200547i
$940$		0			0
$941$	12.9142	+	9.38274i	0.420992	+	0.305869i	0.778037	−	0.628219i	$-0.216216\pi$
$941$	12.9142	+	9.38274i	0.420992	+	0.305869i	−0.357045	+	0.934087i	$0.616216\pi$
$942$		0			0
$943$	15.5289			0.505692
$944$		0			0
$945$	0.685368	−	14.2176i	0.0222950	−	0.462499i
$946$		0			0
$947$	2.25164	−	6.92984i	0.0731685	−	0.225190i	−0.907784	−	0.419439i	$-0.862227\pi$
$947$	2.25164	−	6.92984i	0.0731685	−	0.225190i	0.980952	+	0.194249i	$0.0622270\pi$
$948$		0			0
$949$	1.60798			0.0521972
$950$		0			0
$951$	−9.34069			−0.302893
$952$		0			0
$953$	−9.29362	+	28.6028i	−0.301050	+	0.926537i	0.680072	+	0.733146i	$0.261949\pi$
$953$	−9.29362	+	28.6028i	−0.301050	+	0.926537i	−0.981122	+	0.193391i	$0.938051\pi$
$954$		0			0
$955$	−16.1237	+	4.39286i	−0.521751	+	0.142150i
$956$		0			0
$957$	−23.2221			−0.750665
$958$		0			0
$959$	32.5041	+	23.6156i	1.04961	+	0.762588i
$960$		0			0
$961$	24.5885	−	17.8646i	0.793177	−	0.576277i
$962$		0			0
$963$	−0.364779	−	0.265027i	−0.0117548	−	0.00854039i
$964$		0			0
$965$	−11.2932	+	14.0661i	−0.363541	+	0.452803i
$966$		0			0
$967$	13.7553	+	42.3346i	0.442342	+	1.36139i	0.885373	+	0.464881i	$0.153903\pi$
$967$	13.7553	+	42.3346i	0.442342	+	1.36139i	−0.443031	+	0.896506i	$0.646097\pi$
$968$		0			0
$969$	8.94326	+	27.5245i	0.287299	+	0.884216i
$970$		0			0
$971$	−4.60912	+	14.1854i	−0.147914	+	0.455231i	−0.997374	−	0.0724208i	$-0.976928\pi$
$971$	−4.60912	+	14.1854i	−0.147914	+	0.455231i	0.849461	+	0.527652i	$0.176928\pi$
$972$		0			0
$973$	−25.0465	+	18.1974i	−0.802954	+	0.583380i
$974$		0			0
$975$	−6.36525	−	5.63540i	−0.203851	−	0.180477i
$976$		0			0
$977$	−0.362552	+	0.263409i	−0.0115991	+	0.00842720i	−0.593570	−	0.804783i	$-0.702282\pi$
$977$	−0.362552	+	0.263409i	−0.0115991	+	0.00842720i	0.581971	+	0.813210i	$0.302282\pi$
$978$		0			0
$979$	12.3489	−	38.0059i	0.394671	−	1.21467i
$980$		0			0
$981$	11.9339	+	36.7288i	0.381020	+	1.17266i
$982$		0			0
$983$	0.727835	+	2.24005i	0.0232143	+	0.0714464i	0.961993	−	0.273076i	$-0.0880410\pi$
$983$	0.727835	+	2.24005i	0.0232143	+	0.0714464i	−0.938778	+	0.344522i	$0.888041\pi$
$984$		0			0
$985$	24.2231	+	36.9602i	0.771813	+	1.17765i
$986$		0			0
$987$	−5.81948	−	4.22810i	−0.185236	−	0.134582i
$988$		0			0
$989$	12.7249	−	9.24517i	0.404628	−	0.293979i
$990$		0			0
$991$	−15.0508	−	10.9350i	−0.478104	−	0.347363i	0.322487	−	0.946574i	$-0.395481\pi$
$991$	−15.0508	−	10.9350i	−0.478104	−	0.347363i	−0.800591	+	0.599211i	$0.795481\pi$
$992$		0			0
$993$	5.15615			0.163625
$994$		0			0
$995$	3.82554	−	4.76485i	0.121278	−	0.151056i
$996$		0			0
$997$	−13.0443	+	40.1463i	−0.413118	+	1.27145i	0.500805	+	0.865560i	$0.333037\pi$
$997$	−13.0443	+	40.1463i	−0.413118	+	1.27145i	−0.913923	+	0.405887i	$0.866963\pi$
$998$		0			0
$999$	11.1722			0.353471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.e.161.1		8
4.3	odd	2		200.2.m.b.161.1	yes	8
20.3	even	4		1000.2.q.b.449.1		16
20.7	even	4		1000.2.q.b.449.4		16
20.19	odd	2		1000.2.m.b.801.1		8
25.4	even	10		10000.2.a.z.1.2		4
25.16	even	5	inner	400.2.u.e.241.1		8
25.21	even	5		10000.2.a.q.1.3		4
100.59	odd	10		1000.2.m.b.201.1		8
100.63	even	20		1000.2.q.b.49.3		16
100.71	odd	10		5000.2.a.i.1.2		4
100.79	odd	10		5000.2.a.f.1.3		4
100.87	even	20		1000.2.q.b.49.2		16
100.91	odd	10		200.2.m.b.41.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.b.41.1	✓	8	100.91	odd	10
200.2.m.b.161.1	yes	8	4.3	odd	2
400.2.u.e.161.1		8	1.1	even	1	trivial
400.2.u.e.241.1		8	25.16	even	5	inner
1000.2.m.b.201.1		8	100.59	odd	10
1000.2.m.b.801.1		8	20.19	odd	2
1000.2.q.b.49.2		16	100.87	even	20
1000.2.q.b.49.3		16	100.63	even	20
1000.2.q.b.449.1		16	20.3	even	4
1000.2.q.b.449.4		16	20.7	even	4
5000.2.a.f.1.3		4	100.79	odd	10
5000.2.a.i.1.2		4	100.71	odd	10
10000.2.a.q.1.3		4	25.21	even	5
10000.2.a.z.1.2		4	25.4	even	10

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.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{3} +(-1.39991 + 1.74363i) q^{5} -1.83337 q^{7} +(2.11803 + 1.53884i) q^{9} +O(q^{10})\)	\(q+(0.190983 - 0.587785i) q^{3} +(-1.39991 + 1.74363i) q^{5} -1.83337 q^{7} +(2.11803 + 1.53884i) q^{9} +(4.19215 - 3.04577i) q^{11} +(2.22570 + 1.61707i) q^{13} +(0.757524 + 1.15585i) q^{15} +(2.02435 + 6.23030i) q^{17} +(2.20892 + 6.79837i) q^{19} +(-0.350142 + 1.07763i) q^{21} +(-3.57411 + 2.59675i) q^{23} +(-1.08052 - 4.88185i) q^{25} +(2.80902 - 2.04087i) q^{27} +(2.24075 - 6.89631i) q^{29} +(-0.240748 - 0.740947i) q^{31} +(-0.989632 - 3.04577i) q^{33} +(2.56654 - 3.19672i) q^{35} +(2.60314 + 1.89129i) q^{37} +(1.37556 - 0.999401i) q^{39} +(-2.84373 - 2.06609i) q^{41} -3.56029 q^{43} +(-5.64823 + 1.53884i) q^{45} +(-1.96177 + 6.03770i) q^{47} -3.63877 q^{49} +4.04870 q^{51} +(2.74364 - 8.44406i) q^{53} +(-0.557901 + 11.5734i) q^{55} +4.41785 q^{57} +(-0.345364 - 0.250922i) q^{59} +(1.55617 - 1.13063i) q^{61} +(-3.88313 - 2.82126i) q^{63} +(-5.93534 + 1.61707i) q^{65} +(-0.0382322 - 0.117667i) q^{67} +(0.843734 + 2.59675i) q^{69} +(3.97113 - 12.2219i) q^{71} +(0.472856 - 0.343550i) q^{73} +(-3.07584 - 0.297236i) q^{75} +(-7.68574 + 5.58402i) q^{77} +(-3.45888 + 10.6453i) q^{79} +(1.76393 + 5.42882i) q^{81} +(-5.47682 - 16.8559i) q^{83} +(-13.6973 - 5.19212i) q^{85} +(-3.62561 - 2.63416i) q^{87} +(6.23912 - 4.53298i) q^{89} +(-4.08052 - 2.96467i) q^{91} -0.481496 q^{93} +(-14.9462 - 5.66553i) q^{95} +(-2.10594 + 6.48141i) q^{97} +13.5661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9	\( 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9} + 2 q^{11} + 8 q^{13} + 5 q^{15} + 10 q^{17} - 3 q^{19} - 3 q^{21} - 6 q^{23} - 5 q^{25} + 18 q^{27} + 6 q^{29} + 10 q^{31} - 16 q^{33} + 15 q^{35} - 2 q^{37} + q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47} - 4 q^{49} + 20 q^{51} - 13 q^{53} - 20 q^{55} - 6 q^{57} - 29 q^{59} + 15 q^{61} - 4 q^{63} - 50 q^{65} - 28 q^{67} - 12 q^{69} + 16 q^{71} + q^{73} - 15 q^{75} - 11 q^{77} - 23 q^{79} + 32 q^{81} - 14 q^{83} - 15 q^{85} - 3 q^{87} - 7 q^{89} - 29 q^{91} + 20 q^{93} - 45 q^{95} - 3 q^{97} + 22 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9 + 2 * q^11 + 8 * q^13 + 5 * q^15 + 10 * q^17 - 3 * q^19 - 3 * q^21 - 6 * q^23 - 5 * q^25 + 18 * q^27 + 6 * q^29 + 10 * q^31 - 16 * q^33 + 15 * q^35 - 2 * q^37 + q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 + 20 * q^51 - 13 * q^53 - 20 * q^55 - 6 * q^57 - 29 * q^59 + 15 * q^61 - 4 * q^63 - 50 * q^65 - 28 * q^67 - 12 * q^69 + 16 * q^71 + q^73 - 15 * q^75 - 11 * q^77 - 23 * q^79 + 32 * q^81 - 14 * q^83 - 15 * q^85 - 3 * q^87 - 7 * q^89 - 29 * q^91 + 20 * q^93 - 45 * q^95 - 3 * q^97 + 22 * q^99

Introduction

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