LMFDB - Embedded newform 196.2.d.c.195.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("196.195");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.d (of order $2$, degree $1$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1212153856.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 $ x^8 - 4x^6 + 10x^4 - 16*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.8
Root			$-1.07072 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	196.195
Dual form			196.2.d.c.195.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 + 1.39897i) q^{2} +2.14144 q^{3} +(-1.91421 + 0.579471i) q^{4} +2.61313i q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +1.58579 q^{9} +O(q^{10})$	\(q+(0.207107 + 1.39897i) q^{2} +2.14144 q^{3} +(-1.91421 + 0.579471i) q^{4} +2.61313i q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +1.58579 q^{9} +(-3.65568 + 0.541196i) q^{10} -3.95687i q^{11} +(-4.09918 + 1.24090i) q^{12} +1.08239i q^{13} +5.59587i q^{15} +(3.32843 - 2.21846i) q^{16} +0.317025i q^{17} +(0.328427 + 2.21846i) q^{18} +5.16991 q^{19} +(-1.51423 - 5.00208i) q^{20} +(5.53553 - 0.819496i) q^{22} -2.31788i q^{23} +(-2.58495 - 5.47762i) q^{24} -1.82843 q^{25} +(-1.51423 + 0.224171i) q^{26} -3.02846 q^{27} -6.82843 q^{29} +(-7.82843 + 1.15894i) q^{30} +6.05692 q^{31} +(3.79289 + 4.19690i) q^{32} -8.47343i q^{33} +(-0.443508 + 0.0656581i) q^{34} +(-3.03553 + 0.918917i) q^{36} -4.00000 q^{37} +(1.07072 + 7.23252i) q^{38} +2.31788i q^{39} +(6.68414 - 3.15432i) q^{40} -2.29610i q^{41} -7.23486i q^{43} +(2.29289 + 7.57430i) q^{44} +4.14386i q^{45} +(3.24264 - 0.480049i) q^{46} -4.28289 q^{47} +(7.12764 - 4.75071i) q^{48} +(-0.378680 - 2.55791i) q^{50} +0.678892i q^{51} +(-0.627215 - 2.07193i) q^{52} +10.4853 q^{53} +(-0.627215 - 4.23671i) q^{54} +10.3398 q^{55} +11.0711 q^{57} +(-1.41421 - 9.55274i) q^{58} -11.2268 q^{59} +(-3.24264 - 10.7117i) q^{60} +5.41196i q^{61} +(1.25443 + 8.47343i) q^{62} +(-5.08579 + 6.17534i) q^{64} -2.82843 q^{65} +(11.8540 - 1.75490i) q^{66} +3.27798i q^{67} +(-0.183707 - 0.606854i) q^{68} -4.96362i q^{69} +(-1.91421 - 4.05630i) q^{72} -14.0167i q^{73} +(-0.828427 - 5.59587i) q^{74} -3.91548 q^{75} +(-9.89630 + 2.99581i) q^{76} +(-3.24264 + 0.480049i) q^{78} +7.91375i q^{79} +(5.79712 + 8.69760i) q^{80} -11.2426 q^{81} +(3.21217 - 0.475538i) q^{82} -9.45280 q^{83} -0.828427 q^{85} +(10.1213 - 1.49839i) q^{86} -14.6227 q^{87} +(-10.1213 + 4.77637i) q^{88} +5.99162i q^{89} +(-5.79712 + 0.858221i) q^{90} +(1.34315 + 4.43692i) q^{92} +12.9706 q^{93} +(-0.887016 - 5.99162i) q^{94} +13.5096i q^{95} +(8.12227 + 8.98743i) q^{96} +9.23880i q^{97} -6.27476i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 24 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 24 * q^9	$ 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 24 q^{9} + 4 q^{16} - 20 q^{18} + 16 q^{22} + 8 q^{25} - 32 q^{29} - 40 q^{30} + 36 q^{32} + 4 q^{36} - 32 q^{37} + 24 q^{44} - 8 q^{46} - 20 q^{50} + 16 q^{53} + 32 q^{57} + 8 q^{60} - 52 q^{64} - 4 q^{72} + 16 q^{74} + 8 q^{78} - 56 q^{81} + 16 q^{85} + 64 q^{86} - 64 q^{88} + 56 q^{92} - 32 q^{93}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 24 * q^9 + 4 * q^16 - 20 * q^18 + 16 * q^22 + 8 * q^25 - 32 * q^29 - 40 * q^30 + 36 * q^32 + 4 * q^36 - 32 * q^37 + 24 * q^44 - 8 * q^46 - 20 * q^50 + 16 * q^53 + 32 * q^57 + 8 * q^60 - 52 * q^64 - 4 * q^72 + 16 * q^74 + 8 * q^78 - 56 * q^81 + 16 * q^85 + 64 * q^86 - 64 * q^88 + 56 * q^92 - 32 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	0.207107	+	1.39897i	0.146447	+	0.989219i
$2$	0.207107	+	1.39897i	0.146447	+	0.989219i
$3$	2.14144			1.23636			0.618182	−	0.786035i	$-0.287870\pi$
$3$	2.14144			1.23636			0.618182	+	0.786035i	$0.287870\pi$
$4$	−1.91421	+	0.579471i	−0.957107	+	0.289735i
$5$			2.61313i			1.16863i	0.811529	+	0.584313i	$0.198636\pi$
$5$			2.61313i			1.16863i	−0.811529	+	0.584313i	$0.801364\pi$
$6$	0.443508	+	2.99581i	0.181061	+	1.22303i
$7$		0			0
$7$		0			0
$8$	−1.20711	−	2.55791i	−0.426777	−	0.904357i
$9$	1.58579			0.528595
$10$	−3.65568	+	0.541196i	−1.15603	+	0.171141i
$11$		−	3.95687i		−	1.19304i	−0.802597	−	0.596521i	$-0.796549\pi$
$11$		−	3.95687i		−	1.19304i	0.802597	−	0.596521i	$-0.203451\pi$
$12$	−4.09918	+	1.24090i	−1.18333	+	0.358218i
$13$			1.08239i			0.300202i	0.988671	+	0.150101i	$0.0479598\pi$
$13$			1.08239i			0.300202i	−0.988671	+	0.150101i	$0.952040\pi$
$14$		0			0
$15$			5.59587i			1.44485i
$16$	3.32843	−	2.21846i	0.832107	−	0.554615i
$17$			0.317025i			0.0768899i	0.999261	+	0.0384450i	$0.0122404\pi$
$17$			0.317025i			0.0768899i	−0.999261	+	0.0384450i	$0.987760\pi$
$18$	0.328427	+	2.21846i	0.0774110	+	0.522896i
$19$	5.16991			1.18606			0.593029	−	0.805181i	$-0.297932\pi$
$19$	5.16991			1.18606			0.593029	+	0.805181i	$0.297932\pi$
$20$	−1.51423	−	5.00208i	−0.338592	−	1.11850i
$21$		0			0
$22$	5.53553	−	0.819496i	1.18018	−	0.174717i
$23$		−	2.31788i		−	0.483312i	−0.970362	−	0.241656i	$-0.922309\pi$
$23$		−	2.31788i		−	0.483312i	0.970362	−	0.241656i	$-0.0776906\pi$
$24$	−2.58495	−	5.47762i	−0.527651	−	1.11811i
$25$	−1.82843			−0.365685
$26$	−1.51423	+	0.224171i	−0.296965	+	0.0439635i
$27$	−3.02846			−0.582827
$28$		0			0
$29$	−6.82843			−1.26801			−0.634004	−	0.773330i	$-0.718590\pi$
$29$	−6.82843			−1.26801			−0.634004	+	0.773330i	$0.718590\pi$
$30$	−7.82843	+	1.15894i	−1.42927	+	0.211593i
$31$	6.05692			1.08786			0.543928	−	0.839132i	$-0.316937\pi$
$31$	6.05692			1.08786			0.543928	+	0.839132i	$0.316937\pi$
$32$	3.79289	+	4.19690i	0.670495	+	0.741914i
$33$		−	8.47343i		−	1.47503i
$34$	−0.443508	+	0.0656581i	−0.0760610	+	0.0112603i
$35$		0			0
$36$	−3.03553	+	0.918917i	−0.505922	+	0.153153i
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	1.07072	+	7.23252i	0.173694	+	1.17327i
$39$			2.31788i			0.371158i
$40$	6.68414	−	3.15432i	1.05685	−	0.498742i
$41$		−	2.29610i		−	0.358591i	−0.983795	−	0.179295i	$-0.942618\pi$
$41$		−	2.29610i		−	0.358591i	0.983795	−	0.179295i	$-0.0573818\pi$
$42$		0			0
$43$		−	7.23486i		−	1.10331i	−0.834074	−	0.551653i	$-0.813997\pi$
$43$		−	7.23486i		−	1.10331i	0.834074	−	0.551653i	$-0.186003\pi$
$44$	2.29289	+	7.57430i	0.345667	+	1.14187i
$45$			4.14386i			0.617730i
$46$	3.24264	−	0.480049i	0.478101	−	0.0707794i
$47$	−4.28289			−0.624724			−0.312362	−	0.949963i	$-0.601120\pi$
$47$	−4.28289			−0.624724			−0.312362	+	0.949963i	$0.601120\pi$
$48$	7.12764	−	4.75071i	1.02879	−	0.685706i
$49$		0			0
$50$	−0.378680	−	2.55791i	−0.0535534	−	0.361743i
$51$			0.678892i			0.0950639i
$52$	−0.627215	−	2.07193i	−0.0869790	−	0.287325i
$53$	10.4853			1.44026			0.720132	−	0.693837i	$-0.244081\pi$
$53$	10.4853			1.44026			0.720132	+	0.693837i	$0.244081\pi$
$54$	−0.627215	−	4.23671i	−0.0853531	−	0.576544i
$55$	10.3398			1.39422
$56$		0			0
$57$	11.0711			1.46640
$58$	−1.41421	−	9.55274i	−0.185695	−	1.25434i
$59$	−11.2268			−1.46161			−0.730804	−	0.682587i	$-0.760855\pi$
$59$	−11.2268			−1.46161			−0.730804	+	0.682587i	$0.760855\pi$
$60$	−3.24264	−	10.7117i	−0.418623	−	1.38287i
$61$			5.41196i			0.692931i	0.938063	+	0.346465i	$0.112618\pi$
$61$			5.41196i			0.692931i	−0.938063	+	0.346465i	$0.887382\pi$
$62$	1.25443	+	8.47343i	0.159313	+	1.07613i
$63$		0			0
$64$	−5.08579	+	6.17534i	−0.635723	+	0.771917i
$65$	−2.82843			−0.350823
$66$	11.8540	−	1.75490i	1.45913	−	0.216014i
$67$			3.27798i			0.400469i	0.979748	+	0.200235i	$0.0641704\pi$
$67$			3.27798i			0.400469i	−0.979748	+	0.200235i	$0.935830\pi$
$68$	−0.183707	−	0.606854i	−0.0222777	−	0.0735919i
$69$		−	4.96362i		−	0.597550i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−1.91421	−	4.05630i	−0.225592	−	0.478039i
$73$		−	14.0167i		−	1.64053i	−0.571983	−	0.820266i	$-0.693826\pi$
$73$		−	14.0167i		−	1.64053i	0.571983	−	0.820266i	$-0.306174\pi$
$74$	−0.828427	−	5.59587i	−0.0963027	−	0.650506i
$75$	−3.91548			−0.452120
$76$	−9.89630	+	2.99581i	−1.13518	+	0.343643i
$77$		0			0
$78$	−3.24264	+	0.480049i	−0.367157	+	0.0543549i
$79$			7.91375i			0.890366i	0.895440	+	0.445183i	$0.146861\pi$
$79$			7.91375i			0.890366i	−0.895440	+	0.445183i	$0.853139\pi$
$80$	5.79712	+	8.69760i	0.648138	+	0.972421i
$81$	−11.2426			−1.24918
$82$	3.21217	−	0.475538i	0.354725	−	0.0525144i
$83$	−9.45280			−1.03758			−0.518790	−	0.854902i	$-0.673617\pi$
$83$	−9.45280			−1.03758			−0.518790	+	0.854902i	$0.673617\pi$
$84$		0			0
$85$	−0.828427			−0.0898555
$86$	10.1213	−	1.49839i	1.09141	−	0.161575i
$87$	−14.6227			−1.56772
$88$	−10.1213	+	4.77637i	−1.07894	+	0.509163i
$89$			5.99162i			0.635110i	0.948240	+	0.317555i	$0.102862\pi$
$89$			5.99162i			0.635110i	−0.948240	+	0.317555i	$0.897138\pi$
$90$	−5.79712	+	0.858221i	−0.611070	+	0.0904645i
$91$		0			0
$92$	1.34315	+	4.43692i	0.140033	+	0.462581i
$93$	12.9706			1.34498
$94$	−0.887016	−	5.99162i	−0.0914887	−	0.617988i
$95$			13.5096i			1.38606i
$96$	8.12227	+	8.98743i	0.828976	+	0.917276i
$97$			9.23880i			0.938058i	0.883183	+	0.469029i	$0.155396\pi$
$97$			9.23880i			0.938058i	−0.883183	+	0.469029i	$0.844604\pi$
$98$		0			0
$99$		−	6.27476i		−	0.630637i
$100$	3.50000	−	1.05952i	0.350000	−	0.105952i
$101$			15.2304i			1.51548i	0.652555	+	0.757741i	$0.273697\pi$
$101$			15.2304i			1.51548i	−0.652555	+	0.757741i	$0.726303\pi$
$102$	−0.949747	+	0.140603i	−0.0940390	+	0.0139218i
$103$	−12.1138			−1.19361			−0.596806	−	0.802385i	$-0.703564\pi$
$103$	−12.1138			−1.19361			−0.596806	+	0.802385i	$0.703564\pi$
$104$	2.76866	−	1.30656i	0.271489	−	0.128119i
$105$		0			0
$106$	2.17157	+	14.6686i	0.210922	+	1.42474i
$107$		−	2.31788i		−	0.224078i	−0.993704	−	0.112039i	$-0.964262\pi$
$107$		−	2.31788i		−	0.224078i	0.993704	−	0.112039i	$-0.0357382\pi$
$108$	5.79712	−	1.75490i	0.557828	−	0.168866i
$109$	−5.65685			−0.541828			−0.270914	−	0.962604i	$-0.587326\pi$
$109$	−5.65685			−0.541828			−0.270914	+	0.962604i	$0.587326\pi$
$110$	2.14144	+	14.4650i	0.204179	+	1.37919i
$111$	−8.56578			−0.813028
$112$		0			0
$113$	−4.24264			−0.399114			−0.199557	−	0.979886i	$-0.563950\pi$
$113$	−4.24264			−0.399114			−0.199557	+	0.979886i	$0.563950\pi$
$114$	2.29289	+	15.4881i	0.214749	+	1.45059i
$115$	6.05692			0.564811
$116$	13.0711	−	3.95687i	1.21362	−	0.367387i
$117$			1.71644i			0.158685i
$118$	−2.32515	−	15.7060i	−0.214048	−	1.44585i
$119$		0			0
$120$	14.3137	−	6.75481i	1.30666	−	0.616627i
$121$	−4.65685			−0.423350
$122$	−7.57115	+	1.12085i	−0.685460	+	0.101477i
$123$		−	4.91697i		−	0.443349i
$124$	−11.5942	+	3.50981i	−1.04119	+	0.315190i
$125$			8.28772i			0.741276i
$126$		0			0
$127$		−	10.2316i		−	0.907911i	−0.891024	−	0.453955i	$-0.850013\pi$
$127$		−	10.2316i		−	0.907911i	0.891024	−	0.453955i	$-0.149987\pi$
$128$	−9.69239	−	5.83589i	−0.856694	−	0.515825i
$129$		−	15.4930i		−	1.36409i
$130$	−0.585786	−	3.95687i	−0.0513769	−	0.347041i
$131$	−0.367414			−0.0321011			−0.0160505	−	0.999871i	$-0.505109\pi$
$131$	−0.367414			−0.0321011			−0.0160505	+	0.999871i	$0.505109\pi$
$132$	4.91010	+	16.2200i	0.427370	+	1.41177i
$133$		0			0
$134$	−4.58579	+	0.678892i	−0.396152	+	0.0586474i
$135$		−	7.91375i		−	0.681107i
$136$	0.810922	−	0.382683i	0.0695360	−	0.0328148i
$137$	−8.24264			−0.704216			−0.352108	−	0.935959i	$-0.614535\pi$
$137$	−8.24264			−0.704216			−0.352108	+	0.935959i	$0.614535\pi$
$138$	6.94394	−	1.02800i	0.591107	−	0.0875091i
$139$	22.8211			1.93566			0.967829	−	0.251610i	$-0.0809599\pi$
$139$	22.8211			1.93566			0.967829	+	0.251610i	$0.0809599\pi$
$140$		0			0
$141$	−9.17157			−0.772386
$142$		0			0
$143$	4.28289			0.358153
$144$	5.27817	−	3.51801i	0.439848	−	0.293167i
$145$		−	17.8435i		−	1.48183i
$146$	19.6089	−	2.90295i	1.62284	−	0.240250i
$147$		0			0
$148$	7.65685	−	2.31788i	0.629390	−	0.190529i
$149$	4.82843			0.395560			0.197780	−	0.980246i	$-0.436627\pi$
$149$	4.82843			0.395560			0.197780	+	0.980246i	$0.436627\pi$
$150$	−0.810922	−	5.47762i	−0.0662115	−	0.447246i
$151$		−	21.4234i		−	1.74341i	−0.490032	−	0.871704i	$-0.663015\pi$
$151$		−	21.4234i		−	1.74341i	0.490032	−	0.871704i	$-0.336985\pi$
$152$	−6.24063	−	13.2241i	−0.506182	−	1.07262i
$153$			0.502734i			0.0406437i
$154$		0			0
$155$			15.8275i			1.27130i
$156$	−1.34315	−	4.43692i	−0.107538	−	0.355238i
$157$			19.1886i			1.53141i	0.643189	+	0.765707i	$0.277611\pi$
$157$			19.1886i			1.53141i	−0.643189	+	0.765707i	$0.722389\pi$
$158$	−11.0711	+	1.63899i	−0.880767	+	0.130391i
$159$	22.4537			1.78069
$160$	−10.9670	+	9.91131i	−0.867019	+	0.783558i
$161$		0			0
$162$	−2.32843	−	15.7281i	−0.182939	−	1.23571i
$163$			15.1486i			1.18653i	0.805007	+	0.593265i	$0.202161\pi$
$163$			15.1486i			1.18653i	−0.805007	+	0.593265i	$0.797839\pi$
$164$	1.33052	+	4.39523i	0.103896	+	0.343210i
$165$	22.1421			1.72376
$166$	−1.95774	−	13.2241i	−0.151950	−	1.02639i
$167$	−7.83095			−0.605977			−0.302989	−	0.952994i	$-0.597984\pi$
$167$	−7.83095			−0.605977			−0.302989	+	0.952994i	$0.597984\pi$
$168$		0			0
$169$	11.8284			0.909879
$170$	−0.171573	−	1.15894i	−0.0131590	−	0.0888868i
$171$	8.19837			0.626945
$172$	4.19239	+	13.8491i	0.319667	+	1.05598i
$173$			6.57128i			0.499605i	0.968297	+	0.249802i	$0.0803657\pi$
$173$			6.57128i			0.499605i	−0.968297	+	0.249802i	$0.919634\pi$
$174$	−3.02846	−	20.4567i	−0.229587	−	1.55082i
$175$		0			0
$176$	−8.77817	−	13.1702i	−0.661680	−	0.992739i
$177$	−24.0416			−1.80708
$178$	−8.38207	+	1.24090i	−0.628263	+	0.0930098i
$179$			13.5096i			1.00976i	0.863191	+	0.504878i	$0.168463\pi$
$179$			13.5096i			1.00976i	−0.863191	+	0.504878i	$0.831537\pi$
$180$	−2.40125	−	7.93223i	−0.178978	−	0.591234i
$181$		−	21.9874i		−	1.63431i	−0.576418	−	0.817155i	$-0.695550\pi$
$181$		−	21.9874i		−	1.63431i	0.576418	−	0.817155i	$-0.304450\pi$
$182$		0			0
$183$			11.5894i			0.856714i
$184$	−5.92893	+	2.79793i	−0.437087	+	0.206266i
$185$		−	10.4525i		−	0.768483i
$186$	2.68629	+	18.1454i	0.196968	+	1.33048i
$187$	1.25443			0.0917330
$188$	8.19837	−	2.48181i	0.597927	−	0.181005i
$189$		0			0
$190$	−18.8995	+	2.79793i	−1.37111	+	0.202983i
$191$		−	6.55596i		−	0.474373i	−0.971464	−	0.237186i	$-0.923775\pi$
$191$		−	6.55596i		−	0.474373i	0.971464	−	0.237186i	$-0.0762252\pi$
$192$	−10.8909	+	13.2241i	−0.785985	+	0.954370i
$193$	14.5858			1.04991			0.524954	−	0.851131i	$-0.324083\pi$
$193$	14.5858			1.04991			0.524954	+	0.851131i	$0.324083\pi$
$194$	−12.9248	+	1.91342i	−0.927944	+	0.137375i
$195$	−6.05692			−0.433745
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	8.77817	−	1.29954i	0.623838	−	0.0923546i
$199$	17.1316			1.21442			0.607212	−	0.794540i	$-0.292288\pi$
$199$	17.1316			1.21442			0.607212	+	0.794540i	$0.292288\pi$
$200$	2.20711	+	4.67695i	0.156066	+	0.330710i
$201$			7.01962i			0.495126i
$202$	−21.3068	+	3.15432i	−1.49914	+	0.221937i
$203$		0			0
$204$	−0.393398	−	1.29954i	−0.0275434	−	0.0909863i
$205$	6.00000			0.419058
$206$	−2.50886	−	16.9469i	−0.174800	−	1.18074i
$207$		−	3.67567i		−	0.255477i
$208$	2.40125	+	3.60266i	0.166496	+	0.249800i
$209$		−	20.4567i		−	1.41502i
$210$		0			0
$211$			14.4697i			0.996136i	0.867138	+	0.498068i	$0.165957\pi$
$211$			14.4697i			0.996136i	−0.867138	+	0.498068i	$0.834043\pi$
$212$	−20.0711	+	6.07591i	−1.37849	+	0.417296i
$213$		0			0
$214$	3.24264	−	0.480049i	0.221662	−	0.0328155i
$215$	18.9056			1.28935
$216$	3.65568	+	7.74652i	0.248737	+	0.527084i
$217$		0			0
$218$	−1.17157	−	7.91375i	−0.0793489	−	0.535987i
$219$		−	30.0160i		−	2.02829i
$220$	−19.7926	+	5.99162i	−1.33442	+	0.403955i
$221$	−0.343146			−0.0230825
$222$	−1.77403	−	11.9832i	−0.119065	−	0.804262i
$223$	−7.83095			−0.524399			−0.262200	−	0.965014i	$-0.584448\pi$
$223$	−7.83095			−0.524399			−0.262200	+	0.965014i	$0.584448\pi$
$224$		0			0
$225$	−2.89949			−0.193300
$226$	−0.878680	−	5.93531i	−0.0584489	−	0.394811i
$227$	9.97240			0.661891			0.330946	−	0.943650i	$-0.392632\pi$
$227$	9.97240			0.661891			0.330946	+	0.943650i	$0.392632\pi$
$228$	−21.1924	+	6.41536i	−1.40350	+	0.424868i
$229$		−	1.34502i		−	0.0888817i	−0.999012	−	0.0444409i	$-0.985849\pi$
$229$		−	1.34502i		−	0.0888817i	0.999012	−	0.0444409i	$-0.0141506\pi$
$230$	1.25443	+	8.47343i	0.0827146	+	0.558721i
$231$		0			0
$232$	8.24264	+	17.4665i	0.541156	+	1.14673i
$233$	16.2426			1.06409			0.532045	−	0.846716i	$-0.321424\pi$
$233$	16.2426			1.06409			0.532045	+	0.846716i	$0.321424\pi$
$234$	−2.40125	+	0.355487i	−0.156974	+	0.0232389i
$235$		−	11.1917i		−	0.730068i
$236$	21.4905	−	6.50562i	1.39892	−	0.423480i
$237$			16.9469i			1.10082i
$238$		0			0
$239$		−	10.2316i		−	0.661829i	−0.943661	−	0.330915i	$-0.892643\pi$
$239$		−	10.2316i		−	0.661829i	0.943661	−	0.330915i	$-0.107357\pi$
$240$	12.4142	+	18.6254i	0.801334	+	1.20227i
$241$			5.09494i			0.328194i	0.986444	+	0.164097i	$0.0524710\pi$
$241$			5.09494i			0.328194i	−0.986444	+	0.164097i	$0.947529\pi$
$242$	−0.964466	−	6.51478i	−0.0619982	−	0.418786i
$243$	−14.9901			−0.961616
$244$	−3.13607	−	10.3596i	−0.200767	−	0.663209i
$245$		0			0
$246$	6.87868	−	1.01834i	0.438569	−	0.0649269i
$247$			5.59587i			0.356056i
$248$	−7.31135	−	15.4930i	−0.464271	−	0.983809i
$249$	−20.2426			−1.28283
$250$	−11.5942	+	1.71644i	−0.733284	+	0.108557i
$251$	3.91548			0.247143			0.123571	−	0.992336i	$-0.460565\pi$
$251$	3.91548			0.247143			0.123571	+	0.992336i	$0.460565\pi$
$252$		0			0
$253$	−9.17157			−0.576612
$254$	14.3137	−	2.11904i	0.898122	−	0.132960i
$255$	−1.77403			−0.111094
$256$	6.15685	−	14.7680i	0.384803	−	0.922999i
$257$		−	19.0572i		−	1.18876i	−0.804185	−	0.594379i	$-0.797398\pi$
$257$		−	19.0572i		−	1.18876i	0.804185	−	0.594379i	$-0.202602\pi$
$258$	21.6743	−	3.20871i	1.34938	−	0.199766i
$259$		0			0
$260$	5.41421	−	1.63899i	0.335775	−	0.101646i
$261$	−10.8284			−0.670263
$262$	−0.0760939	−	0.514000i	−0.00470110	−	0.0317550i
$263$		−	25.6614i		−	1.58235i	−0.611588	−	0.791176i	$-0.709469\pi$
$263$		−	25.6614i		−	1.58235i	0.611588	−	0.791176i	$-0.290531\pi$
$264$	−21.6743	+	10.2283i	−1.33396	+	0.629510i
$265$			27.3994i			1.68313i
$266$		0			0
$267$			12.8307i			0.785227i
$268$	−1.89949	−	6.27476i	−0.116030	−	0.383292i
$269$		−	5.04054i		−	0.307327i	−0.988123	−	0.153664i	$-0.950893\pi$
$269$		−	5.04054i		−	0.307327i	0.988123	−	0.153664i	$-0.0491072\pi$
$270$	11.0711	−	1.63899i	0.673764	−	0.0997458i
$271$	−4.28289			−0.260167			−0.130084	−	0.991503i	$-0.541525\pi$
$271$	−4.28289			−0.260167			−0.130084	+	0.991503i	$0.541525\pi$
$272$	0.703309	+	1.05520i	0.0426443	+	0.0639806i
$273$		0			0
$274$	−1.70711	−	11.5312i	−0.103130	−	0.696624i
$275$			7.23486i			0.436278i
$276$	2.87627	+	9.50143i	0.173131	+	0.571919i
$277$	−4.14214			−0.248877			−0.124438	−	0.992227i	$-0.539713\pi$
$277$	−4.14214			−0.248877			−0.124438	+	0.992227i	$0.539713\pi$
$278$	4.72640	+	31.9259i	0.283470	+	1.91479i
$279$	9.60498			0.575035
$280$		0			0
$281$	10.3848			0.619504			0.309752	−	0.950817i	$-0.399754\pi$
$281$	10.3848			0.619504			0.309752	+	0.950817i	$0.399754\pi$
$282$	−1.89949	−	12.8307i	−0.113113	−	0.764058i
$283$	−3.39587			−0.201864			−0.100932	−	0.994893i	$-0.532182\pi$
$283$	−3.39587			−0.201864			−0.100932	+	0.994893i	$0.532182\pi$
$284$		0			0
$285$			28.9301i			1.71367i
$286$	0.887016	+	5.99162i	0.0524503	+	0.354292i
$287$		0			0
$288$	6.01472	+	6.65539i	0.354421	+	0.392172i
$289$	16.8995			0.994088
$290$	24.9625	−	3.69552i	1.46585	−	0.217008i
$291$			19.7844i			1.15978i
$292$	8.12227	+	26.8310i	0.475320	+	1.57016i
$293$			11.7975i			0.689219i	0.938746	+	0.344609i	$0.111989\pi$
$293$			11.7975i			0.689219i	−0.938746	+	0.344609i	$0.888011\pi$
$294$		0			0
$295$		−	29.3371i		−	1.70807i
$296$	4.82843	+	10.2316i	0.280647	+	0.594702i
$297$			11.9832i			0.695338i
$298$	1.00000	+	6.75481i	0.0579284	+	0.391295i
$299$	2.50886			0.145091
$300$	7.49506	−	2.26890i	0.432727	−	0.130995i
$301$		0			0
$302$	29.9706	−	4.43692i	1.72461	−	0.255316i
$303$			32.6151i			1.87369i
$304$	17.2077	−	11.4692i	0.986927	−	0.657806i
$305$	−14.1421			−0.809776
$306$	−0.703309	+	0.104120i	−0.0402055	+	0.00595213i
$307$	3.91548			0.223468			0.111734	−	0.993738i	$-0.464360\pi$
$307$	3.91548			0.223468			0.111734	+	0.993738i	$0.464360\pi$
$308$		0			0
$309$	−25.9411			−1.47574
$310$	−22.1421	+	3.27798i	−1.25759	+	0.186177i
$311$	−20.6796			−1.17263			−0.586317	−	0.810082i	$-0.699423\pi$
$311$	−20.6796			−1.17263			−0.586317	+	0.810082i	$0.699423\pi$
$312$	5.92893	−	2.79793i	0.335660	−	0.158402i
$313$			12.7486i			0.720594i	0.932838	+	0.360297i	$0.117325\pi$
$313$			12.7486i			0.720594i	−0.932838	+	0.360297i	$0.882675\pi$
$314$	−26.8442	+	3.97408i	−1.51490	+	0.224270i
$315$		0			0
$316$	−4.58579	−	15.1486i	−0.257971	−	0.852176i
$317$	−5.51472			−0.309737			−0.154869	−	0.987935i	$-0.549495\pi$
$317$	−5.51472			−0.309737			−0.154869	+	0.987935i	$0.549495\pi$
$318$	4.65030	+	31.4119i	0.260776	+	1.76149i
$319$			27.0192i			1.51279i
$320$	−16.1369	−	13.2898i	−0.902082	−	0.742922i
$321$		−	4.96362i		−	0.277042i
$322$		0			0
$323$			1.63899i			0.0911959i
$324$	21.5208	−	6.51478i	1.19560	−	0.361932i
$325$		−	1.97908i		−	0.109779i
$326$	−21.1924	+	3.13738i	−1.17374	+	0.173763i
$327$	−12.1138			−0.669897
$328$	−5.87321	+	2.77164i	−0.324294	+	0.153038i
$329$		0			0
$330$	4.58579	+	30.9761i	0.252439	+	1.70518i
$331$			15.1486i			0.832643i	0.909218	+	0.416321i	$0.136681\pi$
$331$			15.1486i			0.832643i	−0.909218	+	0.416321i	$0.863319\pi$
$332$	18.0947	−	5.47762i	0.993074	−	0.300623i
$333$	−6.34315			−0.347602
$334$	−1.62184	−	10.9552i	−0.0887433	−	0.599444i
$335$	−8.56578			−0.467999
$336$		0			0
$337$	10.8284			0.589862			0.294931	−	0.955519i	$-0.404703\pi$
$337$	10.8284			0.589862			0.294931	+	0.955519i	$0.404703\pi$
$338$	2.44975	+	16.5476i	0.133249	+	0.900069i
$339$	−9.08538			−0.493450
$340$	1.58579	−	0.480049i	0.0860013	−	0.0260343i
$341$		−	23.9665i		−	1.29786i
$342$	1.69794	+	11.4692i	0.0918139	+	0.620185i
$343$		0			0
$344$	−18.5061	+	8.73324i	−0.997782	+	0.470865i
$345$	12.9706			0.698312
$346$	−9.19299	+	1.36096i	−0.494218	+	0.0731654i
$347$		−	3.95687i		−	0.212416i	−0.994344	−	0.106208i	$-0.966129\pi$
$347$		−	3.95687i		−	0.212416i	0.994344	−	0.106208i	$-0.0338710\pi$
$348$	27.9910	−	8.47343i	1.50047	−	0.454223i
$349$		−	8.47343i		−	0.453572i	−0.973945	−	0.226786i	$-0.927178\pi$
$349$		−	8.47343i		−	0.453572i	0.973945	−	0.226786i	$-0.0728218\pi$
$350$		0			0
$351$		−	3.27798i		−	0.174966i
$352$	16.6066	−	15.0080i	0.885135	−	0.799929i
$353$		−	10.0586i		−	0.535363i	−0.963507	−	0.267681i	$-0.913743\pi$
$353$		−	10.0586i		−	0.535363i	0.963507	−	0.267681i	$-0.0862575\pi$
$354$	−4.97918	−	33.6334i	−0.264641	−	1.78760i
$355$		0			0
$356$	−3.47197	−	11.4692i	−0.184014	−	0.607868i
$357$		0			0
$358$	−18.8995	+	2.79793i	−0.998869	+	0.147875i
$359$		−	31.2573i		−	1.64970i	−0.565353	−	0.824849i	$-0.691260\pi$
$359$		−	31.2573i		−	1.64970i	0.565353	−	0.824849i	$-0.308740\pi$
$360$	10.5996	−	5.00208i	0.558649	−	0.263633i
$361$	7.72792			0.406733
$362$	30.7596	−	4.55374i	1.61669	−	0.239339i
$363$	−9.97240			−0.523415
$364$		0			0
$365$	36.6274			1.91717
$366$	−16.2132	+	2.40025i	−0.847478	+	0.125463i
$367$	−12.8487			−0.670695			−0.335348	−	0.942094i	$-0.608854\pi$
$367$	−12.8487			−0.670695			−0.335348	+	0.942094i	$0.608854\pi$
$368$	−5.14214	−	7.71491i	−0.268052	−	0.402167i
$369$		−	3.64113i		−	0.189549i
$370$	14.6227	−	2.16478i	0.760198	−	0.112542i
$371$		0			0
$372$	−24.8284	+	7.51606i	−1.28729	+	0.389690i
$373$	−20.1421			−1.04292			−0.521460	−	0.853276i	$-0.674612\pi$
$373$	−20.1421			−1.04292			−0.521460	+	0.853276i	$0.674612\pi$
$374$	0.259801	+	1.75490i	0.0134340	+	0.0907440i
$375$			17.7477i			0.916487i
$376$	5.16991	+	10.9552i	0.266618	+	0.564973i
$377$		−	7.39104i		−	0.380658i
$378$		0			0
$379$		−	21.7046i		−	1.11489i	−0.830214	−	0.557444i	$-0.811782\pi$
$379$		−	21.7046i		−	1.11489i	0.830214	−	0.557444i	$-0.188218\pi$
$380$	−7.82843	−	25.8603i	−0.401590	−	1.32660i
$381$		−	21.9105i		−	1.12251i
$382$	9.17157	−	1.35778i	0.469258	−	0.0694703i
$383$	−31.0194			−1.58502			−0.792509	−	0.609860i	$-0.791226\pi$
$383$	−31.0194			−1.58502			−0.792509	+	0.609860i	$0.791226\pi$
$384$	−20.7557	−	12.4972i	−1.05919	−	0.637747i
$385$		0			0
$386$	3.02082	+	20.4050i	0.153755	+	1.03859i
$387$		−	11.4729i		−	0.583202i
$388$	−5.35361	−	17.6850i	−0.271788	−	0.897821i
$389$	14.1421			0.717035			0.358517	−	0.933523i	$-0.383282\pi$
$389$	14.1421			0.717035			0.358517	+	0.933523i	$0.383282\pi$
$390$	−1.25443	−	8.47343i	−0.0635205	−	0.429069i
$391$	0.734828			0.0371618
$392$		0			0
$393$	−0.786797			−0.0396886
$394$	0.414214	+	2.79793i	0.0208678	+	0.140958i
$395$	−20.6796			−1.04050
$396$	3.63604	+	12.0112i	0.182718	+	0.603587i
$397$			16.1271i			0.809396i	0.914450	+	0.404698i	$0.132623\pi$
$397$			16.1271i			0.809396i	−0.914450	+	0.404698i	$0.867377\pi$
$398$	3.54806	+	23.9665i	0.177848	+	1.20133i
$399$		0			0
$400$	−6.08579	+	4.05630i	−0.304289	+	0.202815i
$401$	−12.8284			−0.640621			−0.320311	−	0.947313i	$-0.603787\pi$
$401$	−12.8284			−0.640621			−0.320311	+	0.947313i	$0.603787\pi$
$402$	−9.82021	+	1.45381i	−0.489788	+	0.0725095i
$403$			6.55596i			0.326576i
$404$	−8.82558	−	29.1543i	−0.439089	−	1.45048i
$405$		−	29.3784i		−	1.45983i
$406$		0			0
$407$			15.8275i			0.784540i
$408$	1.73654	−	0.819496i	0.0859717	−	0.0405711i
$409$			13.8310i			0.683899i	0.939718	+	0.341949i	$0.111087\pi$
$409$			13.8310i			0.683899i	−0.939718	+	0.341949i	$0.888913\pi$
$410$	1.24264	+	8.39380i	0.0613696	+	0.414540i
$411$	−17.6512			−0.870668
$412$	23.1885	−	7.01962i	1.14241	−	0.345832i
$413$		0			0
$414$	5.14214	−	0.761256i	0.252722	−	0.0374137i
$415$		−	24.7013i		−	1.21254i
$416$	−4.54269	+	4.10540i	−0.222724	+	0.201284i
$417$	48.8701			2.39318
$418$	28.6182	−	4.23671i	1.39976	−	0.207224i
$419$	17.2837			0.844366			0.422183	−	0.906511i	$-0.361264\pi$
$419$	17.2837			0.844366			0.422183	+	0.906511i	$0.361264\pi$
$420$		0			0
$421$	−10.4853			−0.511021			−0.255511	−	0.966806i	$-0.582244\pi$
$421$	−10.4853			−0.511021			−0.255511	+	0.966806i	$0.582244\pi$
$422$	−20.2426	+	2.99678i	−0.985396	+	0.145881i
$423$	−6.79175			−0.330226
$424$	−12.6569	−	26.8204i	−0.614671	−	1.30251i
$425$		−	0.579658i		−	0.0281175i
$426$		0			0
$427$		0			0
$428$	1.34315	+	4.43692i	0.0649234	+	0.214467i
$429$	9.17157			0.442808
$430$	3.91548	+	26.4483i	0.188821	+	1.27545i
$431$		−	0.960099i		−	0.0462463i	−0.999733	−	0.0231232i	$-0.992639\pi$
$431$		−	0.960099i		−	0.0462463i	0.999733	−	0.0231232i	$-0.00736099\pi$
$432$	−10.0800	+	6.71852i	−0.484975	+	0.323245i
$433$		−	26.1857i		−	1.25840i	−0.777243	−	0.629201i	$-0.783382\pi$
$433$		−	26.1857i		−	1.25840i	0.777243	−	0.629201i	$-0.216618\pi$
$434$		0			0
$435$		−	38.2110i		−	1.83208i
$436$	10.8284	−	3.27798i	0.518588	−	0.156987i
$437$		−	11.9832i		−	0.573236i
$438$	41.9914	−	6.21652i	2.00643	−	0.297037i
$439$	22.4537			1.07165			0.535827	−	0.844328i	$-0.320000\pi$
$439$	22.4537			1.07165			0.535827	+	0.844328i	$0.320000\pi$
$440$	−12.4813	−	26.4483i	−0.595021	−	1.26087i
$441$		0			0
$442$	−0.0710678	−	0.480049i	−0.00338035	−	0.0228336i
$443$			28.3770i			1.34823i	0.738625	+	0.674116i	$0.235475\pi$
$443$			28.3770i			1.34823i	−0.738625	+	0.674116i	$0.764525\pi$
$444$	16.3967	−	4.96362i	0.778154	−	0.235563i
$445$	−15.6569			−0.742206
$446$	−1.62184	−	10.9552i	−0.0767965	−	0.518746i
$447$	10.3398			0.489056
$448$		0			0
$449$	−16.2843			−0.768502			−0.384251	−	0.923229i	$-0.625540\pi$
$449$	−16.2843			−0.768502			−0.384251	+	0.923229i	$0.625540\pi$
$450$	−0.600505	−	4.05630i	−0.0283081	−	0.191216i
$451$	−9.08538			−0.427814
$452$	8.12132	−	2.45849i	0.381995	−	0.115637i
$453$		−	45.8770i		−	2.15549i
$454$	2.06535	+	13.9510i	0.0969317	+	0.654755i
$455$		0			0
$456$	−13.3640	−	28.3188i	−0.625825	−	1.32615i
$457$	0.727922			0.0340508			0.0170254	−	0.999855i	$-0.494580\pi$
$457$	0.727922			0.0340508			0.0170254	+	0.999855i	$0.494580\pi$
$458$	1.88164	−	0.278564i	0.0879235	−	0.0130164i
$459$		−	0.960099i		−	0.0448136i
$460$	−11.5942	+	3.50981i	−0.540584	+	0.163646i
$461$			29.7499i			1.38559i	0.721135	+	0.692794i	$0.243621\pi$
$461$			29.7499i			1.38559i	−0.721135	+	0.692794i	$0.756379\pi$
$462$		0			0
$463$			34.9330i			1.62347i	0.584024	+	0.811737i	$0.301477\pi$
$463$			34.9330i			1.62347i	−0.584024	+	0.811737i	$0.698523\pi$
$464$	−22.7279	+	15.1486i	−1.05512	+	0.703256i
$465$			33.8937i			1.57178i
$466$	3.36396	+	22.7229i	0.155832	+	1.05262i
$467$	24.0755			1.11408			0.557041	−	0.830485i	$-0.311937\pi$
$467$	24.0755			1.11408			0.557041	+	0.830485i	$0.311937\pi$
$468$	−0.994629	−	3.28564i	−0.0459767	−	0.151879i
$469$		0			0
$470$	15.6569	−	2.31788i	0.722197	−	0.106916i
$471$			41.0913i			1.89339i
$472$	13.5520	+	28.7172i	0.623780	+	1.32182i
$473$	−28.6274			−1.31629
$474$	−23.7081	+	3.50981i	−1.08895	+	0.161211i
$475$	−9.45280			−0.433724
$476$		0			0
$477$	16.6274			0.761317
$478$	14.3137	−	2.11904i	0.654694	−	0.0969226i
$479$	32.7935			1.49837			0.749186	−	0.662360i	$-0.230445\pi$
$479$	32.7935			1.49837			0.749186	+	0.662360i	$0.230445\pi$
$480$	−23.4853	+	21.2245i	−1.07195	+	0.968762i
$481$		−	4.32957i		−	0.197411i
$482$	−7.12764	+	1.05520i	−0.324655	+	0.0480628i
$483$		0			0
$484$	8.91421	−	2.69851i	0.405192	−	0.122660i
$485$	−24.1421			−1.09624
$486$	−3.10455	−	20.9707i	−0.140825	−	0.951249i
$487$			19.5032i			0.883773i	0.897071	+	0.441886i	$0.145691\pi$
$487$			19.5032i			0.883773i	−0.897071	+	0.441886i	$0.854309\pi$
$488$	13.8433	−	6.53281i	0.626657	−	0.295727i
$489$			32.4399i			1.46698i
$490$		0			0
$491$		−	14.4697i		−	0.653009i	−0.945196	−	0.326504i	$-0.894129\pi$
$491$		−	14.4697i		−	0.653009i	0.945196	−	0.326504i	$-0.105871\pi$
$492$	2.84924	+	9.41214i	0.128454	+	0.424332i
$493$		−	2.16478i		−	0.0974970i
$494$	−7.82843	+	1.15894i	−0.352218	+	0.0521433i
$495$	16.3967			0.736978
$496$	20.1600	−	13.4370i	0.905212	−	0.603341i
$497$		0			0
$498$	−4.19239	−	28.3188i	−0.187865	−	1.26899i
$499$		−	12.5495i		−	0.561793i	−0.959738	−	0.280897i	$-0.909368\pi$
$499$		−	12.5495i		−	0.561793i	0.959738	−	0.280897i	$-0.0906318\pi$
$500$	−4.80249	−	15.8645i	−0.214774	−	0.709480i
$501$	−16.7696			−0.749208
$502$	0.810922	+	5.47762i	0.0361932	+	0.244478i
$503$	7.83095			0.349165			0.174582	−	0.984643i	$-0.444142\pi$
$503$	7.83095			0.349165			0.174582	+	0.984643i	$0.444142\pi$
$504$		0			0
$505$	−39.7990			−1.77103
$506$	−1.89949	−	12.8307i	−0.0844428	−	0.570395i
$507$	25.3299			1.12494
$508$	5.92893	+	19.5855i	0.263054	+	0.868967i
$509$			6.57128i			0.291267i	0.989339	+	0.145633i	$0.0465220\pi$
$509$			6.57128i			0.291267i	−0.989339	+	0.145633i	$0.953478\pi$
$510$	−0.367414	−	2.48181i	−0.0162694	−	0.109896i
$511$		0			0
$512$	21.9350	+	5.55468i	0.969400	+	0.245485i
$513$	−15.6569			−0.691267
$514$	26.6604	−	3.94689i	1.17594	−	0.174090i
$515$		−	31.6550i		−	1.39489i
$516$	8.97777	+	29.6570i	0.395224	+	1.30558i
$517$			16.9469i			0.745322i
$518$		0			0
$519$			14.0720i			0.617693i
$520$	3.41421	+	7.23486i	0.149723	+	0.317269i
$521$		−	12.0376i		−	0.527378i	−0.964608	−	0.263689i	$-0.915061\pi$
$521$		−	12.0376i		−	0.527378i	0.964608	−	0.263689i	$-0.0849393\pi$
$522$	−2.24264	−	15.1486i	−0.0981577	−	0.663036i
$523$	7.46354			0.326358			0.163179	−	0.986597i	$-0.447825\pi$
$523$	7.46354			0.326358			0.163179	+	0.986597i	$0.447825\pi$
$524$	0.703309	−	0.212906i	0.0307242	−	0.00930083i
$525$		0			0
$526$	35.8995	−	5.31466i	1.56529	−	0.231730i
$527$			1.92020i			0.0836451i
$528$	−18.7980	−	28.2032i	−0.818077	−	1.22739i
$529$	17.6274			0.766409
$530$	−38.3308	+	5.67459i	−1.66498	+	0.246489i
$531$	−17.8033			−0.772600
$532$		0			0
$533$	2.48528			0.107649
$534$	−17.9497	+	2.65733i	−0.776762	+	0.114994i
$535$	6.05692			0.261864
$536$	8.38478	−	3.95687i	0.362167	−	0.170911i
$537$			28.9301i			1.24843i
$538$	7.05155	−	1.04393i	0.304014	−	0.0450070i
$539$		0			0
$540$	4.58579	+	15.1486i	0.197341	+	0.651892i
$541$	45.3137			1.94819			0.974094	−	0.226142i	$-0.0726115\pi$
$541$	45.3137			1.94819			0.974094	+	0.226142i	$0.0726115\pi$
$542$	−0.887016	−	5.99162i	−0.0381006	−	0.257362i
$543$		−	47.0848i		−	2.02060i
$544$	−1.33052	+	1.20244i	−0.0570457	+	0.0515543i
$545$		−	14.7821i		−	0.633194i
$546$		0			0
$547$			27.6981i			1.18429i	0.805833	+	0.592143i	$0.201718\pi$
$547$			27.6981i			1.18429i	−0.805833	+	0.592143i	$0.798282\pi$
$548$	15.7782	−	4.77637i	0.674010	−	0.204036i
$549$			8.58221i			0.366280i
$550$	−10.1213	+	1.49839i	−0.431575	+	0.0638915i
$551$	−35.3023			−1.50393
$552$	−12.6965	+	5.99162i	−0.540398	+	0.255020i
$553$		0			0
$554$	−0.857864	−	5.79471i	−0.0364472	−	0.246194i
$555$		−	22.3835i		−	0.950125i
$556$	−43.6844	+	13.2241i	−1.85263	+	0.560829i
$557$	−19.6569			−0.832888			−0.416444	−	0.909161i	$-0.636724\pi$
$557$	−19.6569			−0.832888			−0.416444	+	0.909161i	$0.636724\pi$
$558$	1.98926	+	13.4370i	0.0842120	+	0.568836i
$559$	7.83095			0.331214
$560$		0			0
$561$	2.68629			0.113415
$562$	2.15076	+	14.5280i	0.0907242	+	0.612825i
$563$	21.0470			0.887027			0.443513	−	0.896268i	$-0.353732\pi$
$563$	21.0470			0.887027			0.443513	+	0.896268i	$0.353732\pi$
$564$	17.5563	−	5.31466i	0.739256	−	0.223788i
$565$		−	11.0866i		−	0.466415i
$566$	−0.703309	−	4.75071i	−0.0295623	−	0.199687i
$567$		0			0
$568$		0			0
$569$	18.8284			0.789329			0.394664	−	0.918825i	$-0.370861\pi$
$569$	18.8284			0.789329			0.394664	+	0.918825i	$0.370861\pi$
$570$	−40.4722	+	5.99162i	−1.69520	+	0.250961i
$571$		−	9.95043i		−	0.416412i	−0.978085	−	0.208206i	$-0.933237\pi$
$571$		−	9.95043i		−	0.416412i	0.978085	−	0.208206i	$-0.0667625\pi$
$572$	−8.19837	+	2.48181i	−0.342791	+	0.103770i
$573$		−	14.0392i		−	0.586497i
$574$		0			0
$575$			4.23808i			0.176740i
$576$	−8.06497	+	9.79276i	−0.336040	+	0.408032i
$577$		−	0.842290i		−	0.0350650i	−0.999846	−	0.0175325i	$-0.994419\pi$
$577$		−	0.842290i		−	0.0350650i	0.999846	−	0.0175325i	$-0.00558105\pi$
$578$	3.50000	+	23.6418i	0.145581	+	0.983370i
$579$	31.2347			1.29807
$580$	10.3398	+	34.1563i	0.429337	+	1.41827i
$581$		0			0
$582$	−27.6777	+	4.09748i	−1.14728	+	0.169846i
$583$		−	41.4889i		−	1.71830i
$584$	−35.8534	+	16.9197i	−1.48363	+	0.700141i
$585$	−4.48528			−0.185444
$586$	−16.5043	+	2.44335i	−0.681788	+	0.100934i
$587$	−22.8211			−0.941926			−0.470963	−	0.882153i	$-0.656094\pi$
$587$	−22.8211			−0.941926			−0.470963	+	0.882153i	$0.656094\pi$
$588$		0			0
$589$	31.3137			1.29026
$590$	41.0416	−	6.07591i	1.68966	−	0.250141i
$591$	4.28289			0.176175
$592$	−13.3137	+	8.87385i	−0.547190	+	0.364713i
$593$			37.4579i			1.53821i	0.639121	+	0.769106i	$0.279298\pi$
$593$			37.4579i			1.53821i	−0.639121	+	0.769106i	$0.720702\pi$
$594$	−16.7641	+	2.48181i	−0.687841	+	0.101830i
$595$		0			0
$596$	−9.24264	+	2.79793i	−0.378593	+	0.114608i
$597$	36.6863			1.50147
$598$	0.519602	+	3.50981i	0.0212481	+	0.143527i
$599$			32.2174i			1.31637i	0.752857	+	0.658184i	$0.228675\pi$
$599$			32.2174i			1.31637i	−0.752857	+	0.658184i	$0.771325\pi$
$600$	4.72640	+	10.0154i	0.192954	+	0.408878i
$601$			25.5516i			1.04227i	0.853474	+	0.521136i	$0.174491\pi$
$601$			25.5516i			1.04227i	−0.853474	+	0.521136i	$0.825509\pi$
$602$		0			0
$603$			5.19818i			0.211686i
$604$	12.4142	+	41.0089i	0.505127	+	1.66863i
$605$		−	12.1689i		−	0.494738i
$606$	−45.6274	+	6.75481i	−1.85349	+	0.274395i
$607$	−12.1138			−0.491686			−0.245843	−	0.969310i	$-0.579065\pi$
$607$	−12.1138			−0.491686			−0.245843	+	0.969310i	$0.579065\pi$
$608$	19.6089	+	21.6976i	0.795246	+	0.879953i
$609$		0			0
$610$	−2.92893	−	19.7844i	−0.118589	−	0.801046i
$611$		−	4.63577i		−	0.187543i
$612$	−0.291320	−	0.962341i	−0.0117759	−	0.0389003i
$613$	−8.68629			−0.350836			−0.175418	−	0.984494i	$-0.556128\pi$
$613$	−8.68629			−0.350836			−0.175418	+	0.984494i	$0.556128\pi$
$614$	0.810922	+	5.47762i	0.0327261	+	0.221059i
$615$	12.8487			0.518108
$616$		0			0
$617$	−35.4558			−1.42740			−0.713699	−	0.700452i	$-0.752982\pi$
$617$	−35.4558			−1.42740			−0.713699	+	0.700452i	$0.752982\pi$
$618$	−5.37258	−	36.2908i	−0.216117	−	1.45983i
$619$	−13.5205			−0.543433			−0.271717	−	0.962377i	$-0.587591\pi$
$619$	−13.5205			−0.543433			−0.271717	+	0.962377i	$0.587591\pi$
$620$	−9.17157	−	30.2972i	−0.368339	−	1.21677i
$621$			7.01962i			0.281688i
$622$	−4.28289	−	28.9301i	−0.171728	−	1.15999i
$623$		0			0
$624$	5.14214	+	7.71491i	0.205850	+	0.308843i
$625$	−30.7990			−1.23196
$626$	−17.8349	+	2.64032i	−0.712825	+	0.105529i
$627$		−	43.8068i		−	1.74948i
$628$	−11.1192	−	36.7310i	−0.443705	−	1.46573i
$629$		−	1.26810i		−	0.0505625i
$630$		0			0
$631$			20.4633i			0.814630i	0.913288	+	0.407315i	$0.133535\pi$
$631$			20.4633i			0.814630i	−0.913288	+	0.407315i	$0.866465\pi$
$632$	20.2426	−	9.55274i	0.805209	−	0.379988i
$633$			30.9861i			1.23159i
$634$	−1.14214	−	7.71491i	−0.0453600	−	0.306398i
$635$	26.7365			1.06101
$636$	−42.9811	+	13.0112i	−1.70431	+	0.515929i
$637$		0			0
$638$	−37.7990	+	5.59587i	−1.49648	+	0.221542i
$639$		0			0
$640$	15.2499	−	25.3274i	0.602806	−	1.00115i
$641$	49.4558			1.95339			0.976694	−	0.214636i	$-0.0688564\pi$
$641$	49.4558			1.95339			0.976694	+	0.214636i	$0.0688564\pi$
$642$	6.94394	−	1.02800i	0.274055	−	0.0405719i
$643$	−41.7267			−1.64554			−0.822769	−	0.568375i	$-0.807572\pi$
$643$	−41.7267			−1.64554			−0.822769	+	0.568375i	$0.807572\pi$
$644$		0			0
$645$	40.4853			1.59411
$646$	−2.29289	+	0.339446i	−0.0902127	+	0.0133553i
$647$	43.8681			1.72463			0.862317	−	0.506370i	$-0.169013\pi$
$647$	43.8681			1.72463			0.862317	+	0.506370i	$0.169013\pi$
$648$	13.5711	+	28.7576i	0.533122	+	1.12971i
$649$			44.4231i			1.74376i
$650$	2.76866	−	0.409880i	0.108596	−	0.0160768i
$651$		0			0
$652$	−8.77817	−	28.9977i	−0.343780	−	1.13564i
$653$	−23.7990			−0.931326			−0.465663	−	0.884962i	$-0.654184\pi$
$653$	−23.7990			−0.931326			−0.465663	+	0.884962i	$0.654184\pi$
$654$	−2.50886	−	16.9469i	−0.0981041	−	0.662675i
$655$		−	0.960099i		−	0.0375142i
$656$	−5.09381	−	7.64240i	−0.198880	−	0.298386i
$657$		−	22.2275i		−	0.867177i
$658$		0			0
$659$			13.2284i			0.515306i	0.966238	+	0.257653i	$0.0829491\pi$
$659$			13.2284i			0.515306i	−0.966238	+	0.257653i	$0.917051\pi$
$660$	−42.3848	+	12.8307i	−1.64983	+	0.499435i
$661$		−	37.6662i		−	1.46504i	−0.680744	−	0.732522i	$-0.738343\pi$
$661$		−	37.6662i		−	1.46504i	0.680744	−	0.732522i	$-0.261657\pi$
$662$	−21.1924	+	3.13738i	−0.823666	+	0.121938i
$663$	−0.734828			−0.0285383
$664$	11.4105	+	24.1794i	0.442815	+	0.938342i
$665$		0			0
$666$	−1.31371	−	8.87385i	−0.0509052	−	0.343855i
$667$			15.8275i			0.612843i
$668$	14.9901	−	4.53781i	0.579985	−	0.175573i
$669$	−16.7696			−0.648348
$670$	−1.77403	−	11.9832i	−0.0685368	−	0.462953i
$671$	21.4144			0.826696
$672$		0			0
$673$	10.3848			0.400304			0.200152	−	0.979765i	$-0.435856\pi$
$673$	10.3848			0.400304			0.200152	+	0.979765i	$0.435856\pi$
$674$	2.24264	+	15.1486i	0.0863833	+	0.583502i
$675$	5.53732			0.213132
$676$	−22.6421	+	6.85423i	−0.870851	+	0.263624i
$677$		−	28.8532i		−	1.10892i	−0.832211	−	0.554459i	$-0.812925\pi$
$677$		−	28.8532i		−	1.10892i	0.832211	−	0.554459i	$-0.187075\pi$
$678$	−1.88164	−	12.7101i	−0.0722641	−	0.488130i
$679$		0			0
$680$	1.00000	+	2.11904i	0.0383482	+	0.0812615i
$681$	21.3553			0.818338
$682$	33.5283	−	4.96362i	1.28386	−	0.190067i
$683$			32.2174i			1.23276i	0.787447	+	0.616382i	$0.211402\pi$
$683$			32.2174i			1.23276i	−0.787447	+	0.616382i	$0.788598\pi$
$684$	−15.6934	+	4.75071i	−0.600053	+	0.181648i
$685$		−	21.5391i		−	0.822965i
$686$		0			0
$687$		−	2.88030i		−	0.109890i
$688$	−16.0503	−	24.0807i	−0.611910	−	0.918068i
$689$			11.3492i			0.432370i
$690$	2.68629	+	18.1454i	0.102265	+	0.690783i
$691$	−8.19837			−0.311881			−0.155940	−	0.987766i	$-0.549841\pi$
$691$	−8.19837			−0.311881			−0.155940	+	0.987766i	$0.549841\pi$
$692$	−3.80786	−	12.5788i	−0.144753	−	0.478175i
$693$		0			0
$694$	5.53553	−	0.819496i	0.210126	−	0.0311076i
$695$			59.6343i			2.26206i
$696$	17.6512	+	37.4035i	0.669066	+	1.41778i
$697$	0.727922			0.0275720
$698$	11.8540	−	1.75490i	0.448682	−	0.0664241i
$699$	34.7827			1.31560
$700$		0			0
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$	4.58579	−	0.678892i	0.173079	−	0.0256231i
$703$	−20.6796			−0.779947
$704$	24.4350	+	20.1238i	0.920930	+	0.758445i
$705$		−	23.9665i		−	0.902630i
$706$	14.0716	−	2.08319i	0.529591	−	0.0784021i
$707$		0			0
$708$	46.0208	−	13.9314i	1.72957	−	0.523575i
$709$	−46.6274			−1.75113			−0.875565	−	0.483101i	$-0.839510\pi$
$709$	−46.6274			−1.75113			−0.875565	+	0.483101i	$0.839510\pi$
$710$		0			0
$711$			12.5495i			0.470644i
$712$	15.3260	−	7.23252i	0.574366	−	0.271050i
$713$		−	14.0392i		−	0.525774i
$714$		0			0
$715$			11.1917i			0.418547i
$716$	−7.82843	−	25.8603i	−0.292562	−	0.966444i
$717$		−	21.9105i		−	0.818262i
$718$	43.7279	−	6.47360i	1.63191	−	0.241593i
$719$	33.5283			1.25039			0.625197	−	0.780467i	$-0.285019\pi$
$719$	33.5283			1.25039			0.625197	+	0.780467i	$0.285019\pi$
$720$	9.19299	+	13.7925i	0.342603	+	0.514017i
$721$		0			0
$722$	1.60051	+	10.8111i	0.0595646	+	0.402348i
$723$			10.9105i			0.405767i
$724$	12.7411	+	42.0886i	0.473518	+	1.56421i
$725$	12.4853			0.463692
$726$	−2.06535	−	13.9510i	−0.0766524	−	0.517772i
$727$	−29.9802			−1.11191			−0.555953	−	0.831214i	$-0.687646\pi$
$727$	−29.9802			−1.11191			−0.555953	+	0.831214i	$0.687646\pi$
$728$		0			0
$729$	1.62742			0.0602747
$730$	7.58579	+	51.2405i	0.280763	+	1.89650i
$731$	2.29363			0.0848331
$732$	−6.71573	−	22.1846i	−0.248220	−	0.819967i
$733$		−	20.4567i		−	0.755584i	−0.925890	−	0.377792i	$-0.876683\pi$
$733$		−	20.4567i		−	0.755584i	0.925890	−	0.377792i	$-0.123317\pi$
$734$	−2.66105	−	17.9749i	−0.0982210	−	0.663464i
$735$		0			0
$736$	9.72792	−	8.79148i	0.358576	−	0.324058i
$737$	12.9706			0.477777
$738$	5.09381	−	0.754102i	0.187506	−	0.0277589i
$739$		−	12.4330i		−	0.457357i	−0.973502	−	0.228678i	$-0.926560\pi$
$739$		−	12.4330i		−	0.457357i	0.973502	−	0.228678i	$-0.0734404\pi$
$740$	6.05692	+	20.0083i	0.222657	+	0.735521i
$741$			11.9832i			0.440215i
$742$		0			0
$743$		−	45.1646i		−	1.65693i	−0.560042	−	0.828464i	$-0.689215\pi$
$743$		−	45.1646i		−	1.65693i	0.560042	−	0.828464i	$-0.310785\pi$
$744$	−15.6569	−	33.1775i	−0.574008	−	1.21635i
$745$			12.6173i			0.462262i
$746$	−4.17157	−	28.1782i	−0.152732	−	1.03168i
$747$	−14.9901			−0.548460
$748$	−2.40125	+	0.726905i	−0.0877982	+	0.0265783i
$749$		0			0
$750$	−24.8284	+	3.67567i	−0.906606	+	0.134216i
$751$		−	37.2509i		−	1.35930i	−0.733535	−	0.679652i	$-0.762131\pi$
$751$		−	37.2509i		−	1.35930i	0.733535	−	0.679652i	$-0.237869\pi$
$752$	−14.2553	+	9.50143i	−0.519837	+	0.346481i
$753$	8.38478			0.305558
$754$	10.3398	−	1.53073i	0.376554	−	0.0557460i
$755$	55.9819			2.03739
$756$		0			0
$757$	−44.2843			−1.60954			−0.804770	−	0.593587i	$-0.797711\pi$
$757$	−44.2843			−1.60954			−0.804770	+	0.593587i	$0.797711\pi$
$758$	30.3640	−	4.49516i	1.10287	−	0.163272i
$759$	−19.6404			−0.712902
$760$	34.5563	−	16.3075i	1.25349	−	0.591537i
$761$			0.0543929i			0.00197174i	1.00000		0.000985871i	$0.000313813\pi$
$761$			0.0543929i			0.00197174i	−1.00000		0.000985871i	$0.999686\pi$
$762$	30.6520	−	4.53781i	1.11041	−	0.164387i
$763$		0			0
$764$	3.79899	+	12.5495i	0.137443	+	0.454026i
$765$	−1.31371			−0.0474972
$766$	−6.42433	−	43.3951i	−0.232121	−	1.56793i
$767$		−	12.1518i		−	0.438777i
$768$	13.1846	−	31.6248i	0.475757	−	1.14116i
$769$			19.1342i			0.689996i	0.938603	+	0.344998i	$0.112120\pi$
$769$			19.1342i			0.689996i	−0.938603	+	0.344998i	$0.887880\pi$
$770$		0			0
$771$		−	40.8100i		−	1.46974i
$772$	−27.9203	+	8.45204i	−1.00487	+	0.304195i
$773$			49.4955i			1.78023i	0.455735	+	0.890116i	$0.349376\pi$
$773$			49.4955i			1.78023i	−0.455735	+	0.890116i	$0.650624\pi$
$774$	16.0503	−	2.37612i	0.576914	−	0.0854080i
$775$	−11.0746			−0.397813
$776$	23.6320	−	11.1522i	0.848339	−	0.400341i
$777$		0			0
$778$	2.92893	+	19.7844i	0.105007	+	0.709304i
$779$		−	11.8706i		−	0.425309i
$780$	11.5942	−	3.50981i	0.415140	−	0.125671i
$781$		0			0
$782$	0.152188	+	1.02800i	0.00544222	+	0.0367612i
$783$	20.6796			0.739029
$784$		0			0
$785$	−50.1421			−1.78965
$786$	−0.162951	−	1.10070i	−0.00581227	−	0.0392607i
$787$	−41.2071			−1.46887			−0.734436	−	0.678677i	$-0.762553\pi$
$787$	−41.2071			−1.46887			−0.734436	+	0.678677i	$0.762553\pi$
$788$	−3.82843	+	1.15894i	−0.136382	+	0.0412856i
$789$		−	54.9526i		−	1.95636i
$790$	−4.28289	−	28.9301i	−0.152378	−	1.02929i
$791$		0			0
$792$	−16.0503	+	7.57430i	−0.570321	+	0.269141i
$793$	−5.85786			−0.208019
$794$	−22.5613	+	3.34003i	−0.800669	+	0.118533i
$795$			58.6742i			2.08096i
$796$	−32.7935	+	9.92724i	−1.16233	+	0.351862i
$797$			20.1940i			0.715309i	0.933854	+	0.357655i	$0.116424\pi$
$797$			20.1940i			0.715309i	−0.933854	+	0.357655i	$0.883576\pi$
$798$		0			0
$799$		−	1.35778i		−	0.0480350i
$800$	−6.93503	−	7.67372i	−0.245190	−	0.271307i
$801$			9.50143i			0.335716i
$802$	−2.65685	−	17.9465i	−0.0938168	−	0.633714i
$803$	−55.4623			−1.95722
$804$	−4.06766	−	13.4370i	−0.143455	−	0.473888i
$805$		0			0
$806$	−9.17157	+	1.35778i	−0.323055	+	0.0478259i
$807$		−	10.7940i		−	0.379968i
$808$	38.9580	−	18.3847i	1.37054	−	0.646773i
$809$	−0.0416306			−0.00146365			−0.000731826	−	1.00000i	$-0.500233\pi$
$809$	−0.0416306			−0.00146365			−0.000731826		1.00000i	$0.500233\pi$
$810$	41.0994	−	6.08447i	1.44409	−	0.213787i
$811$	−39.4330			−1.38468			−0.692340	−	0.721571i	$-0.743420\pi$
$811$	−39.4330			−1.38468			−0.692340	+	0.721571i	$0.743420\pi$
$812$		0			0
$813$	−9.17157			−0.321661
$814$	−22.1421	+	3.27798i	−0.776081	+	0.114893i
$815$	−39.5852			−1.38661
$816$	1.50610	+	2.25964i	0.0527239	+	0.0791033i
$817$		−	37.4035i		−	1.30858i
$818$	−19.3491	+	2.86449i	−0.676525	+	0.100155i
$819$		0			0
$820$	−11.4853	+	3.47682i	−0.401083	+	0.121416i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$	−3.65568	−	24.6934i	−0.127506	−	0.861281i
$823$		−	17.1853i		−	0.599041i	−0.954090	−	0.299521i	$-0.903173\pi$
$823$		−	17.1853i		−	0.599041i	0.954090	−	0.299521i	$-0.0968267\pi$
$824$	14.6227	+	30.9861i	0.509406	+	1.07945i
$825$			15.4930i			0.539399i
$826$		0			0
$827$		−	45.1646i		−	1.57053i	−0.619162	−	0.785264i	$-0.712527\pi$
$827$		−	45.1646i		−	1.57053i	0.619162	−	0.785264i	$-0.287473\pi$
$828$	2.12994	+	7.03601i	0.0740206	+	0.244518i
$829$		−	47.2220i		−	1.64009i	−0.572301	−	0.820044i	$-0.693949\pi$
$829$		−	47.2220i		−	1.64009i	0.572301	−	0.820044i	$-0.306051\pi$
$830$	34.5563	−	5.11582i	1.19947	−	0.177573i
$831$	−8.87016			−0.307702
$832$	−6.68414	−	5.50482i	−0.231731	−	0.190845i
$833$		0			0
$834$	10.1213	+	68.3676i	0.350473	+	2.36738i
$835$		−	20.4633i		−	0.708160i
$836$	11.8540	+	39.1584i	0.409981	+	1.35432i
$837$	−18.3431			−0.634032
$838$	3.57958	+	24.1794i	0.123655	+	0.835263i
$839$	−42.3984			−1.46376			−0.731878	−	0.681435i	$-0.761356\pi$
$839$	−42.3984			−1.46376			−0.731878	+	0.681435i	$0.761356\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$	−2.17157	−	14.6686i	−0.0748373	−	0.505512i
$843$	22.2384			0.765932
$844$	−8.38478	−	27.6981i	−0.288616	−	0.953409i
$845$			30.9092i			1.06331i
$846$	−1.40662	−	9.50143i	−0.0483605	−	0.326666i
$847$		0			0
$848$	34.8995	−	23.2612i	1.19845	−	0.798793i
$849$	−7.27208			−0.249577
$850$	0.810922	−	0.120051i	0.0278144	−	0.00411772i
$851$			9.27153i			0.317824i
$852$		0			0
$853$		−	38.3002i		−	1.31137i	−0.755033	−	0.655687i	$-0.772379\pi$
$853$		−	38.3002i		−	1.31137i	0.755033	−	0.655687i	$-0.227621\pi$
$854$		0			0
$855$			21.4234i			0.732664i
$856$	−5.92893	+	2.79793i	−0.202647	+	0.0956314i
$857$			3.45542i			0.118035i	0.998257	+	0.0590174i	$0.0187967\pi$
$857$			3.45542i			0.118035i	−0.998257	+	0.0590174i	$0.981203\pi$
$858$	1.89949	+	12.8307i	0.0648477	+	0.438034i
$859$	−2.66105			−0.0907937			−0.0453969	−	0.998969i	$-0.514455\pi$
$859$	−2.66105			−0.0907937			−0.0453969	+	0.998969i	$0.514455\pi$
$860$	−36.1893	+	10.9552i	−1.23405	+	0.373571i
$861$		0			0
$862$	1.34315	−	0.198843i	0.0457477	−	0.00677262i
$863$		−	12.5495i		−	0.427190i	−0.976922	−	0.213595i	$-0.931483\pi$
$863$		−	12.5495i		−	0.427190i	0.976922	−	0.213595i	$-0.0685174\pi$
$864$	−11.4866	−	12.7101i	−0.390783	−	0.432408i
$865$	−17.1716			−0.583851
$866$	36.6328	−	5.42323i	1.24483	−	0.184289i
$867$	36.1893			1.22905
$868$		0			0
$869$	31.3137			1.06224
$870$	53.4558	−	7.91375i	1.81232	−	0.268301i
$871$	−3.54806			−0.120221
$872$	6.82843	+	14.4697i	0.231240	+	0.490006i
$873$			14.6508i			0.495853i
$874$	16.7641	−	2.48181i	0.567056	−	0.0839485i
$875$		0			0
$876$	17.3934	+	57.4570i	0.587668	+	1.94129i
$877$	30.4264			1.02743			0.513713	−	0.857962i	$-0.328269\pi$
$877$	30.4264			1.02743			0.513713	+	0.857962i	$0.328269\pi$
$878$	4.65030	+	31.4119i	0.156940	+	1.06010i
$879$			25.2638i			0.852125i
$880$	34.4153	−	22.9385i	1.16014	−	0.773256i
$881$		−	26.1857i		−	0.882217i	−0.897454	−	0.441109i	$-0.854585\pi$
$881$		−	26.1857i		−	0.882217i	0.897454	−	0.441109i	$-0.145415\pi$
$882$		0			0
$883$			24.7013i			0.831266i	0.909532	+	0.415633i	$0.136440\pi$
$883$			24.7013i			0.831266i	−0.909532	+	0.415633i	$0.863560\pi$
$884$	0.656854	−	0.198843i	0.0220924	−	0.00668781i
$885$		−	62.8238i		−	2.11180i
$886$	−39.6985	+	5.87707i	−1.33370	+	0.197444i
$887$	22.4537			0.753920			0.376960	−	0.926230i	$-0.376969\pi$
$887$	22.4537			0.753920			0.376960	+	0.926230i	$0.376969\pi$
$888$	10.3398	+	21.9105i	0.346981	+	0.735267i
$889$		0			0
$890$	−3.24264	−	21.9034i	−0.108694	−	0.734204i
$891$			44.4857i			1.49033i
$892$	14.9901	−	4.53781i	0.501906	−	0.151937i
$893$	−22.1421			−0.740958
$894$	2.14144	+	14.4650i	0.0716206	+	0.483784i
$895$	−35.3023			−1.18003
$896$		0			0
$897$	5.37258			0.179385
$898$	−3.37258	−	22.7811i	−0.112545	−	0.760217i
$899$	−41.3592			−1.37941
$900$	5.55025	−	1.68017i	0.185008	−	0.0560058i
$901$			3.32410i			0.110742i
$902$	−1.88164	−	12.7101i	−0.0626519	−	0.423201i
$903$		0			0
$904$	5.12132	+	10.8523i	0.170333	+	0.360942i
$905$	57.4558			1.90990
$906$	64.1803	−	9.50143i	2.13225	−	0.315664i
$907$			33.9729i			1.12805i	0.825757	+	0.564025i	$0.190748\pi$
$907$			33.9729i			1.12805i	−0.825757	+	0.564025i	$0.809252\pi$
$908$	−19.0893	+	5.77871i	−0.633501	+	0.191773i
$909$			24.1522i			0.801077i
$910$		0			0
$911$		−	18.7078i		−	0.619817i	−0.950766	−	0.309908i	$-0.899702\pi$
$911$		−	18.7078i		−	0.619817i	0.950766	−	0.309908i	$-0.100298\pi$
$912$	36.8492	−	24.5607i	1.22020	−	0.813287i
$913$			37.4035i			1.23788i
$914$	0.150758	+	1.01834i	0.00498662	+	0.0336836i
$915$	−30.2846			−1.00118
$916$	0.779403	+	2.57466i	0.0257522	+	0.0850693i
$917$		0			0
$918$	1.34315	−	0.198843i	0.0443304	−	0.00656280i
$919$			48.8403i			1.61109i	0.592533	+	0.805546i	$0.298128\pi$
$919$			48.8403i			1.61109i	−0.592533	+	0.805546i	$0.701872\pi$
$920$	−7.31135	−	15.4930i	−0.241048	−	0.510791i
$921$	8.38478			0.276288
$922$	−41.6190	+	6.16140i	−1.37065	+	0.202915i
$923$		0			0
$924$		0			0
$925$	7.31371			0.240473
$926$	−48.8701	+	7.23486i	−1.60597	+	0.237752i
$927$	−19.2100			−0.630938
$928$	−25.8995	−	28.6582i	−0.850193	−	0.940752i
$929$			29.8812i			0.980369i	0.871619	+	0.490185i	$0.163071\pi$
$929$			29.8812i			0.980369i	−0.871619	+	0.490185i	$0.836929\pi$
$930$	−47.4162	+	7.01962i	−1.55484	+	0.230182i
$931$		0			0
$932$	−31.0919	+	9.41214i	−1.01845	+	0.308305i
$933$	−44.2843			−1.44980
$934$	4.98620	+	33.6808i	0.163153	+	1.10207i
$935$			3.27798i			0.107201i
$936$	4.39050	−	2.07193i	0.143508	−	0.0677231i
$937$		−	29.8042i		−	0.973662i	−0.873496	−	0.486831i	$-0.838153\pi$
$937$		−	29.8042i		−	0.973662i	0.873496	−	0.486831i	$-0.161847\pi$
$938$		0			0
$939$			27.3004i			0.890916i
$940$	6.48528	+	21.4234i	0.211527	+	0.698753i
$941$			24.7862i			0.808008i	0.914757	+	0.404004i	$0.132382\pi$
$941$			24.7862i			0.808008i	−0.914757	+	0.404004i	$0.867618\pi$
$942$	−57.4853	+	8.51028i	−1.87297	+	0.277280i
$943$	−5.32209			−0.173311
$944$	−37.3677	+	24.9063i	−1.21621	+	0.810631i
$945$		0			0
$946$	−5.92893	−	40.0488i	−0.192766	−	1.30210i
$947$			9.15505i			0.297499i	0.988875	+	0.148750i	$0.0475249\pi$
$947$			9.15505i			0.297499i	−0.988875	+	0.148750i	$0.952475\pi$
$948$	−9.82021	−	32.4399i	−0.318946	−	1.05360i
$949$	15.1716			0.492490
$950$	−1.95774	−	13.2241i	−0.0635174	−	0.429048i
$951$	−11.8095			−0.382948
$952$		0			0
$953$	26.3431			0.853338			0.426669	−	0.904408i	$-0.359687\pi$
$953$	26.3431			0.853338			0.426669	+	0.904408i	$0.359687\pi$
$954$	3.44365	+	23.2612i	0.111492	+	0.753109i
$955$	17.1316			0.554364
$956$	5.92893	+	19.5855i	0.191755	+	0.633441i
$957$			57.8602i			1.87035i
$958$	6.79175	+	45.8770i	0.219431	+	1.48222i
$959$		0			0
$960$	−34.5563	−	28.4594i	−1.11530	−	0.918522i
$961$	5.68629			0.183429
$962$	6.05692	−	0.896683i	0.195283	−	0.0289102i
$963$		−	3.67567i		−	0.118447i
$964$	−2.95237	−	9.75279i	−0.0950893	−	0.314116i
$965$			38.1145i			1.22695i
$966$		0			0
$967$		−	45.1646i		−	1.45240i	−0.687486	−	0.726198i	$-0.741286\pi$
$967$		−	45.1646i		−	1.45240i	0.687486	−	0.726198i	$-0.258714\pi$
$968$	5.62132	+	11.9118i	0.180676	+	0.382860i
$969$			3.50981i			0.112751i
$970$	−5.00000	−	33.7740i	−0.160540	−	1.08442i
$971$	13.0009			0.417217			0.208609	−	0.977999i	$-0.433106\pi$
$971$	13.0009			0.417217			0.208609	+	0.977999i	$0.433106\pi$
$972$	28.6943	−	8.68633i	0.920369	−	0.278614i
$973$		0			0
$974$	−27.2843	+	4.03924i	−0.874244	+	0.129426i
$975$		−	4.23808i		−	0.135727i
$976$	12.0062	+	18.0133i	0.384310	+	0.576592i
$977$	17.6152			0.563561			0.281780	−	0.959479i	$-0.409075\pi$
$977$	17.6152			0.563561			0.281780	+	0.959479i	$0.409075\pi$
$978$	−45.3823	+	6.71852i	−1.45117	+	0.214835i
$979$	23.7081			0.757714
$980$		0			0
$981$	−8.97056			−0.286408
$982$	20.2426	−	2.99678i	0.645969	−	0.0956310i
$983$	−9.60498			−0.306351			−0.153176	−	0.988199i	$-0.548950\pi$
$983$	−9.60498			−0.306351			−0.153176	+	0.988199i	$0.548950\pi$
$984$	−12.5772	+	5.93531i	−0.400945	+	0.189211i
$985$			5.22625i			0.166522i
$986$	3.02846	−	0.448342i	0.0964458	−	0.0142781i
$987$		0			0
$988$	−3.24264	−	10.7117i	−0.103162	−	0.340784i
$989$	−16.7696			−0.533241
$990$	3.39587	+	22.9385i	0.107928	+	0.729033i
$991$		−	25.6614i		−	0.815163i	−0.913169	−	0.407581i	$-0.866372\pi$
$991$		−	25.6614i		−	0.815163i	0.913169	−	0.407581i	$-0.133628\pi$
$992$	22.9733	+	25.4203i	0.729402	+	0.807095i
$993$			32.4399i			1.02945i
$994$		0			0
$995$			44.7669i			1.41921i
$996$	38.7487	−	11.7300i	1.22780	−	0.371680i
$997$		−	30.9092i		−	0.978903i	−0.872030	−	0.489452i	$-0.837197\pi$
$997$		−	30.9092i		−	0.978903i	0.872030	−	0.489452i	$-0.162803\pi$
$998$	17.5563	−	2.59909i	0.555737	−	0.0822727i
$999$	12.1138			0.383265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.d.c.195.8	yes	8
3.2	odd	2		1764.2.b.k.1567.1		8
4.3	odd	2	inner	196.2.d.c.195.5	✓	8
7.2	even	3		196.2.f.d.31.5		16
7.3	odd	6		196.2.f.d.19.2		16
7.4	even	3		196.2.f.d.19.1		16
7.5	odd	6		196.2.f.d.31.6		16
7.6	odd	2	inner	196.2.d.c.195.7	yes	8
8.3	odd	2		3136.2.f.i.3135.5		8
8.5	even	2		3136.2.f.i.3135.3		8
12.11	even	2		1764.2.b.k.1567.3		8
21.20	even	2		1764.2.b.k.1567.2		8
28.3	even	6		196.2.f.d.19.5		16
28.11	odd	6		196.2.f.d.19.6		16
28.19	even	6		196.2.f.d.31.1		16
28.23	odd	6		196.2.f.d.31.2		16
28.27	even	2	inner	196.2.d.c.195.6	yes	8
56.13	odd	2		3136.2.f.i.3135.6		8
56.27	even	2		3136.2.f.i.3135.4		8
84.83	odd	2		1764.2.b.k.1567.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.d.c.195.5	✓	8	4.3	odd	2	inner
196.2.d.c.195.6	yes	8	28.27	even	2	inner
196.2.d.c.195.7	yes	8	7.6	odd	2	inner
196.2.d.c.195.8	yes	8	1.1	even	1	trivial
196.2.f.d.19.1		16	7.4	even	3
196.2.f.d.19.2		16	7.3	odd	6
196.2.f.d.19.5		16	28.3	even	6
196.2.f.d.19.6		16	28.11	odd	6
196.2.f.d.31.1		16	28.19	even	6
196.2.f.d.31.2		16	28.23	odd	6
196.2.f.d.31.5		16	7.2	even	3
196.2.f.d.31.6		16	7.5	odd	6
1764.2.b.k.1567.1		8	3.2	odd	2
1764.2.b.k.1567.2		8	21.20	even	2
1764.2.b.k.1567.3		8	12.11	even	2
1764.2.b.k.1567.4		8	84.83	odd	2
3136.2.f.i.3135.3		8	8.5	even	2
3136.2.f.i.3135.4		8	56.27	even	2
3136.2.f.i.3135.5		8	8.3	odd	2
3136.2.f.i.3135.6		8	56.13	odd	2

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 + 1.39897i) q^{2} +2.14144 q^{3} +(-1.91421 + 0.579471i) q^{4} +2.61313i q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +1.58579 q^{9} +O(q^{10})\)	\(q+(0.207107 + 1.39897i) q^{2} +2.14144 q^{3} +(-1.91421 + 0.579471i) q^{4} +2.61313i q^{5} +(0.443508 + 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +1.58579 q^{9} +(-3.65568 + 0.541196i) q^{10} -3.95687i q^{11} +(-4.09918 + 1.24090i) q^{12} +1.08239i q^{13} +5.59587i q^{15} +(3.32843 - 2.21846i) q^{16} +0.317025i q^{17} +(0.328427 + 2.21846i) q^{18} +5.16991 q^{19} +(-1.51423 - 5.00208i) q^{20} +(5.53553 - 0.819496i) q^{22} -2.31788i q^{23} +(-2.58495 - 5.47762i) q^{24} -1.82843 q^{25} +(-1.51423 + 0.224171i) q^{26} -3.02846 q^{27} -6.82843 q^{29} +(-7.82843 + 1.15894i) q^{30} +6.05692 q^{31} +(3.79289 + 4.19690i) q^{32} -8.47343i q^{33} +(-0.443508 + 0.0656581i) q^{34} +(-3.03553 + 0.918917i) q^{36} -4.00000 q^{37} +(1.07072 + 7.23252i) q^{38} +2.31788i q^{39} +(6.68414 - 3.15432i) q^{40} -2.29610i q^{41} -7.23486i q^{43} +(2.29289 + 7.57430i) q^{44} +4.14386i q^{45} +(3.24264 - 0.480049i) q^{46} -4.28289 q^{47} +(7.12764 - 4.75071i) q^{48} +(-0.378680 - 2.55791i) q^{50} +0.678892i q^{51} +(-0.627215 - 2.07193i) q^{52} +10.4853 q^{53} +(-0.627215 - 4.23671i) q^{54} +10.3398 q^{55} +11.0711 q^{57} +(-1.41421 - 9.55274i) q^{58} -11.2268 q^{59} +(-3.24264 - 10.7117i) q^{60} +5.41196i q^{61} +(1.25443 + 8.47343i) q^{62} +(-5.08579 + 6.17534i) q^{64} -2.82843 q^{65} +(11.8540 - 1.75490i) q^{66} +3.27798i q^{67} +(-0.183707 - 0.606854i) q^{68} -4.96362i q^{69} +(-1.91421 - 4.05630i) q^{72} -14.0167i q^{73} +(-0.828427 - 5.59587i) q^{74} -3.91548 q^{75} +(-9.89630 + 2.99581i) q^{76} +(-3.24264 + 0.480049i) q^{78} +7.91375i q^{79} +(5.79712 + 8.69760i) q^{80} -11.2426 q^{81} +(3.21217 - 0.475538i) q^{82} -9.45280 q^{83} -0.828427 q^{85} +(10.1213 - 1.49839i) q^{86} -14.6227 q^{87} +(-10.1213 + 4.77637i) q^{88} +5.99162i q^{89} +(-5.79712 + 0.858221i) q^{90} +(1.34315 + 4.43692i) q^{92} +12.9706 q^{93} +(-0.887016 - 5.99162i) q^{94} +13.5096i q^{95} +(8.12227 + 8.98743i) q^{96} +9.23880i q^{97} -6.27476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 24 * q^9	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 24 q^{9} + 4 q^{16} - 20 q^{18} + 16 q^{22} + 8 q^{25} - 32 q^{29} - 40 q^{30} + 36 q^{32} + 4 q^{36} - 32 q^{37} + 24 q^{44} - 8 q^{46} - 20 q^{50} + 16 q^{53} + 32 q^{57} + 8 q^{60} - 52 q^{64} - 4 q^{72} + 16 q^{74} + 8 q^{78} - 56 q^{81} + 16 q^{85} + 64 q^{86} - 64 q^{88} + 56 q^{92} - 32 q^{93}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 + 24 * q^9 + 4 * q^16 - 20 * q^18 + 16 * q^22 + 8 * q^25 - 32 * q^29 - 40 * q^30 + 36 * q^32 + 4 * q^36 - 32 * q^37 + 24 * q^44 - 8 * q^46 - 20 * q^50 + 16 * q^53 + 32 * q^57 + 8 * q^60 - 52 * q^64 - 4 * q^72 + 16 * q^74 + 8 * q^78 - 56 * q^81 + 16 * q^85 + 64 * q^86 - 64 * q^88 + 56 * q^92 - 32 * q^93

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