LMFDB - Embedded newform 196.2.d.c.195.3

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			195.3
Root			$1.36145 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	196.195
Dual form			196.2.d.c.195.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 + 0.736813i) q^{2} -2.72291 q^{3} +(0.914214 - 1.77882i) q^{4} -1.08239i q^{5} +(3.28684 - 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +4.41421 q^{9} +O(q^{10})$	\(q+(-1.20711 + 0.736813i) q^{2} -2.72291 q^{3} +(0.914214 - 1.77882i) q^{4} -1.08239i q^{5} +(3.28684 - 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +4.41421 q^{9} +(0.797521 + 1.30656i) q^{10} +2.08402i q^{11} +(-2.48932 + 4.84357i) q^{12} +2.61313i q^{13} +2.94725i q^{15} +(-2.32843 - 3.25245i) q^{16} +4.46088i q^{17} +(-5.32843 + 3.25245i) q^{18} +1.12786 q^{19} +(-1.92538 - 0.989538i) q^{20} +(-1.53553 - 2.51564i) q^{22} +7.11529i q^{23} +(-0.563932 - 7.68087i) q^{24} +3.82843 q^{25} +(-1.92538 - 3.15432i) q^{26} -3.85077 q^{27} -1.17157 q^{29} +(-2.17157 - 3.55765i) q^{30} +7.70154 q^{31} +(5.20711 + 2.21044i) q^{32} -5.67459i q^{33} +(-3.28684 - 5.38476i) q^{34} +(4.03553 - 7.85211i) q^{36} -4.00000 q^{37} +(-1.36145 + 0.831025i) q^{38} -7.11529i q^{39} +(3.05325 - 0.224171i) q^{40} +5.54328i q^{41} -7.97852i q^{43} +(3.70711 + 1.90524i) q^{44} -4.77791i q^{45} +(-5.24264 - 8.58892i) q^{46} +5.44581 q^{47} +(6.34009 + 8.85611i) q^{48} +(-4.62132 + 2.82083i) q^{50} -12.1466i q^{51} +(4.64829 + 2.38896i) q^{52} -6.48528 q^{53} +(4.64829 - 2.83730i) q^{54} +2.25573 q^{55} -3.07107 q^{57} +(1.41421 - 0.863230i) q^{58} -8.82940 q^{59} +(5.24264 + 2.69442i) q^{60} +13.0656i q^{61} +(-9.29658 + 5.67459i) q^{62} +(-7.91421 + 1.16843i) q^{64} +2.82843 q^{65} +(4.18111 + 6.84984i) q^{66} +10.0625i q^{67} +(7.93513 + 4.07820i) q^{68} -19.3743i q^{69} +(0.914214 + 12.4518i) q^{72} -7.97069i q^{73} +(4.82843 - 2.94725i) q^{74} -10.4244 q^{75} +(1.03111 - 2.00627i) q^{76} +(5.24264 + 8.58892i) q^{78} -4.16804i q^{79} +(-3.52043 + 2.52027i) q^{80} -2.75736 q^{81} +(-4.08436 - 6.69133i) q^{82} +4.31795 q^{83} +4.82843 q^{85} +(5.87868 + 9.63093i) q^{86} +3.19008 q^{87} +(-5.87868 + 0.431615i) q^{88} -4.01254i q^{89} +(3.52043 + 5.76745i) q^{90} +(12.6569 + 6.50490i) q^{92} -20.9706 q^{93} +(-6.57368 + 4.01254i) q^{94} -1.22079i q^{95} +(-14.1785 - 6.01882i) q^{96} +3.82683i q^{97} +9.19932i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.20711	+	0.736813i	−0.853553	+	0.521005i
$2$	−1.20711	+	0.736813i	−0.853553	+	0.521005i
$3$	−2.72291			−1.57207			−0.786035	−	0.618182i	$-0.787870\pi$
$3$	−2.72291			−1.57207			−0.786035	+	0.618182i	$0.787870\pi$
$4$	0.914214	−	1.77882i	0.457107	−	0.889412i
$5$		−	1.08239i		−	0.484061i	−0.970269	−	0.242030i	$-0.922187\pi$
$5$		−	1.08239i		−	0.484061i	0.970269	−	0.242030i	$-0.0778133\pi$
$6$	3.28684	−	2.00627i	1.34185	−	0.819057i
$7$		0			0
$7$		0			0
$8$	0.207107	+	2.82083i	0.0732233	+	0.997316i
$9$	4.41421			1.47140
$10$	0.797521	+	1.30656i	0.252198	+	0.413171i
$11$			2.08402i			0.628356i	0.949364	+	0.314178i	$0.101729\pi$
$11$			2.08402i			0.628356i	−0.949364	+	0.314178i	$0.898271\pi$
$12$	−2.48932	+	4.84357i	−0.718604	+	1.39822i
$13$			2.61313i			0.724751i	0.932032	+	0.362375i	$0.118034\pi$
$13$			2.61313i			0.724751i	−0.932032	+	0.362375i	$0.881966\pi$
$14$		0			0
$15$			2.94725i			0.760977i
$16$	−2.32843	−	3.25245i	−0.582107	−	0.813112i
$17$			4.46088i			1.08192i	0.841047	+	0.540962i	$0.181940\pi$
$17$			4.46088i			1.08192i	−0.841047	+	0.540962i	$0.818060\pi$
$18$	−5.32843	+	3.25245i	−1.25592	+	0.766610i
$19$	1.12786			0.258750			0.129375	−	0.991596i	$-0.458703\pi$
$19$	1.12786			0.258750			0.129375	+	0.991596i	$0.458703\pi$
$20$	−1.92538	−	0.989538i	−0.430529	−	0.221267i
$21$		0			0
$22$	−1.53553	−	2.51564i	−0.327377	−	0.536336i
$23$			7.11529i			1.48364i	0.670598	+	0.741821i	$0.266037\pi$
$23$			7.11529i			1.48364i	−0.670598	+	0.741821i	$0.733963\pi$
$24$	−0.563932	−	7.68087i	−0.115112	−	1.56785i
$25$	3.82843			0.765685
$26$	−1.92538	−	3.15432i	−0.377599	−	0.618613i
$27$	−3.85077			−0.741081
$28$		0			0
$29$	−1.17157			−0.217556			−0.108778	−	0.994066i	$-0.534694\pi$
$29$	−1.17157			−0.217556			−0.108778	+	0.994066i	$0.534694\pi$
$30$	−2.17157	−	3.55765i	−0.396473	−	0.649535i
$31$	7.70154			1.38324			0.691619	−	0.722263i	$-0.256898\pi$
$31$	7.70154			1.38324			0.691619	+	0.722263i	$0.256898\pi$
$32$	5.20711	+	2.21044i	0.920495	+	0.390754i
$33$		−	5.67459i		−	0.987820i
$34$	−3.28684	−	5.38476i	−0.563688	−	0.923479i
$35$		0			0
$36$	4.03553	−	7.85211i	0.672589	−	1.30868i
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	−1.36145	+	0.831025i	−0.220857	+	0.134810i
$39$		−	7.11529i		−	1.13936i
$40$	3.05325	−	0.224171i	0.482761	−	0.0354445i
$41$			5.54328i			0.865714i	0.901462	+	0.432857i	$0.142495\pi$
$41$			5.54328i			0.865714i	−0.901462	+	0.432857i	$0.857505\pi$
$42$		0			0
$43$		−	7.97852i		−	1.21671i	−0.793664	−	0.608357i	$-0.791829\pi$
$43$		−	7.97852i		−	1.21671i	0.793664	−	0.608357i	$-0.208171\pi$
$44$	3.70711	+	1.90524i	0.558867	+	0.287226i
$45$		−	4.77791i		−	0.712249i
$46$	−5.24264	−	8.58892i	−0.772985	−	1.26637i
$47$	5.44581			0.794353			0.397177	−	0.917742i	$-0.369990\pi$
$47$	5.44581			0.794353			0.397177	+	0.917742i	$0.369990\pi$
$48$	6.34009	+	8.85611i	0.915113	+	1.27827i
$49$		0			0
$50$	−4.62132	+	2.82083i	−0.653553	+	0.398926i
$51$		−	12.1466i		−	1.70086i
$52$	4.64829	+	2.38896i	0.644602	+	0.331288i
$53$	−6.48528			−0.890822			−0.445411	−	0.895326i	$-0.646942\pi$
$53$	−6.48528			−0.890822			−0.445411	+	0.895326i	$0.646942\pi$
$54$	4.64829	−	2.83730i	0.632552	−	0.386107i
$55$	2.25573			0.304162
$56$		0			0
$57$	−3.07107			−0.406773
$58$	1.41421	−	0.863230i	0.185695	−	0.113348i
$59$	−8.82940			−1.14949			−0.574745	−	0.818332i	$-0.694899\pi$
$59$	−8.82940			−1.14949			−0.574745	+	0.818332i	$0.694899\pi$
$60$	5.24264	+	2.69442i	0.676822	+	0.347848i
$61$			13.0656i			1.67288i	0.548057	+	0.836441i	$0.315368\pi$
$61$			13.0656i			1.67288i	−0.548057	+	0.836441i	$0.684632\pi$
$62$	−9.29658	+	5.67459i	−1.18067	+	0.720674i
$63$		0			0
$64$	−7.91421	+	1.16843i	−0.989277	+	0.146053i
$65$	2.82843			0.350823
$66$	4.18111	+	6.84984i	0.514659	+	0.843157i
$67$			10.0625i			1.22934i	0.788786	+	0.614668i	$0.210710\pi$
$67$			10.0625i			1.22934i	−0.788786	+	0.614668i	$0.789290\pi$
$68$	7.93513	+	4.07820i	0.962276	+	0.494555i
$69$		−	19.3743i		−	2.33239i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	0.914214	+	12.4518i	0.107741	+	1.46745i
$73$		−	7.97069i		−	0.932899i	−0.884548	−	0.466450i	$-0.845533\pi$
$73$		−	7.97069i		−	0.932899i	0.884548	−	0.466450i	$-0.154467\pi$
$74$	4.82843	−	2.94725i	0.561293	−	0.342611i
$75$	−10.4244			−1.20371
$76$	1.03111	−	2.00627i	0.118276	−	0.230135i
$77$		0			0
$78$	5.24264	+	8.58892i	0.593612	+	0.972504i
$79$		−	4.16804i		−	0.468941i	−0.972123	−	0.234471i	$-0.924664\pi$
$79$		−	4.16804i		−	0.468941i	0.972123	−	0.234471i	$-0.0753357\pi$
$80$	−3.52043	+	2.52027i	−0.393596	+	0.281775i
$81$	−2.75736			−0.306373
$82$	−4.08436	−	6.69133i	−0.451042	−	0.738934i
$83$	4.31795			0.473956			0.236978	−	0.971515i	$-0.423843\pi$
$83$	4.31795			0.473956			0.236978	+	0.971515i	$0.423843\pi$
$84$		0			0
$85$	4.82843			0.523716
$86$	5.87868	+	9.63093i	0.633914	+	1.03853i
$87$	3.19008			0.342013
$88$	−5.87868	+	0.431615i	−0.626669	+	0.0460103i
$89$		−	4.01254i		−	0.425329i	−0.977125	−	0.212664i	$-0.931786\pi$
$89$		−	4.01254i		−	0.425329i	0.977125	−	0.212664i	$-0.0682141\pi$
$90$	3.52043	+	5.76745i	0.371085	+	0.607942i
$91$		0			0
$92$	12.6569	+	6.50490i	1.31957	+	0.678183i
$93$	−20.9706			−2.17455
$94$	−6.57368	+	4.01254i	−0.678023	+	0.413862i
$95$		−	1.22079i		−	0.125251i
$96$	−14.1785	−	6.01882i	−1.44708	−	0.614293i
$97$			3.82683i			0.388556i	0.980946	+	0.194278i	$0.0622364\pi$
$97$			3.82683i			0.388556i	−0.980946	+	0.194278i	$0.937764\pi$
$98$		0			0
$99$			9.19932i			0.924566i
$100$	3.50000	−	6.81010i	0.350000	−	0.681010i
$101$		−	0.185709i		−	0.0184788i	−0.999957	−	0.00923938i	$-0.997059\pi$
$101$		−	0.185709i		−	0.0184788i	0.999957	−	0.00923938i	$-0.00294103\pi$
$102$	8.94975	+	14.6622i	0.886157	+	1.45177i
$103$	−15.4031			−1.51771			−0.758855	−	0.651259i	$-0.774241\pi$
$103$	−15.4031			−1.51771			−0.758855	+	0.651259i	$0.774241\pi$
$104$	−7.37120	+	0.541196i	−0.722805	+	0.0530686i
$105$		0			0
$106$	7.82843	−	4.77844i	0.760364	−	0.464123i
$107$			7.11529i			0.687861i	0.938995	+	0.343931i	$0.111759\pi$
$107$			7.11529i			0.687861i	−0.938995	+	0.343931i	$0.888241\pi$
$108$	−3.52043	+	6.84984i	−0.338753	+	0.659126i
$109$	5.65685			0.541828			0.270914	−	0.962604i	$-0.412674\pi$
$109$	5.65685			0.541828			0.270914	+	0.962604i	$0.412674\pi$
$110$	−2.72291	+	1.66205i	−0.259619	+	0.158470i
$111$	10.8916			1.03379
$112$		0			0
$113$	4.24264			0.399114			0.199557	−	0.979886i	$-0.436050\pi$
$113$	4.24264			0.399114			0.199557	+	0.979886i	$0.436050\pi$
$114$	3.70711	−	2.26280i	0.347202	−	0.211931i
$115$	7.70154			0.718172
$116$	−1.07107	+	2.08402i	−0.0994461	+	0.193497i
$117$			11.5349i			1.06640i
$118$	10.6580	−	6.50562i	0.981151	−	0.598891i
$119$		0			0
$120$	−8.31371	+	0.610396i	−0.758934	+	0.0557213i
$121$	6.65685			0.605169
$122$	−9.62692	−	15.7716i	−0.871581	−	1.42789i
$123$		−	15.0938i		−	1.36096i
$124$	7.04085	−	13.6997i	0.632287	−	1.23027i
$125$		−	9.55582i		−	0.854699i
$126$		0			0
$127$			11.2833i			1.00123i	0.865669	+	0.500617i	$0.166894\pi$
$127$			11.2833i			1.00123i	−0.865669	+	0.500617i	$0.833106\pi$
$128$	8.69239	−	7.24171i	0.768306	−	0.640083i
$129$			21.7248i			1.91276i
$130$	−3.41421	+	2.08402i	−0.299446	+	0.182781i
$131$	15.8703			1.38659			0.693295	−	0.720654i	$-0.256158\pi$
$131$	15.8703			1.38659			0.693295	+	0.720654i	$0.256158\pi$
$132$	−10.0941	−	5.18779i	−0.878579	−	0.451539i
$133$		0			0
$134$	−7.41421	−	12.1466i	−0.640490	−	1.04930i
$135$			4.16804i			0.358728i
$136$	−12.5834	+	0.923880i	−1.07902	+	0.0792220i
$137$	0.242641			0.0207302			0.0103651	−	0.999946i	$-0.496701\pi$
$137$	0.242641			0.0207302			0.0103651	+	0.999946i	$0.496701\pi$
$138$	14.2752	+	23.3868i	1.21519	+	1.99082i
$139$	1.78855			0.151703			0.0758515	−	0.997119i	$-0.475833\pi$
$139$	1.78855			0.151703			0.0758515	+	0.997119i	$0.475833\pi$
$140$		0			0
$141$	−14.8284			−1.24878
$142$		0			0
$143$	−5.44581			−0.455402
$144$	−10.2782	−	14.3570i	−0.856515	−	1.19642i
$145$			1.26810i			0.105310i
$146$	5.87291	+	9.62148i	0.486045	+	0.796279i
$147$		0			0
$148$	−3.65685	+	7.11529i	−0.300592	+	0.584874i
$149$	−0.828427			−0.0678674			−0.0339337	−	0.999424i	$-0.510804\pi$
$149$	−0.828427			−0.0678674			−0.0339337	+	0.999424i	$0.510804\pi$
$150$	12.5834	−	7.68087i	1.02743	−	0.627140i
$151$			5.38883i			0.438537i	0.975665	+	0.219269i	$0.0703671\pi$
$151$			5.38883i			0.438537i	−0.975665	+	0.219269i	$0.929633\pi$
$152$	0.233588	+	3.18152i	0.0189465	+	0.258055i
$153$			19.6913i			1.59195i
$154$		0			0
$155$		−	8.33609i		−	0.669571i
$156$	−12.6569	−	6.50490i	−1.01336	−	0.520809i
$157$		−	20.1940i		−	1.61166i	−0.592147	−	0.805830i	$-0.701720\pi$
$157$		−	20.1940i		−	1.61166i	0.592147	−	0.805830i	$-0.298280\pi$
$158$	3.07107	+	5.03127i	0.244321	+	0.400267i
$159$	17.6588			1.40043
$160$	2.39256	−	5.63613i	0.189149	−	0.445575i
$161$		0			0
$162$	3.32843	−	2.03166i	0.261506	−	0.159622i
$163$			3.81048i			0.298460i	0.988803	+	0.149230i	$0.0476795\pi$
$163$			3.81048i			0.298460i	−0.988803	+	0.149230i	$0.952321\pi$
$164$	9.86051	+	5.06774i	0.769977	+	0.395724i
$165$	−6.14214			−0.478165
$166$	−5.21222	+	3.18152i	−0.404547	+	0.246934i
$167$	−20.8489			−1.61334			−0.806668	−	0.591005i	$-0.798731\pi$
$167$	−20.8489			−1.61334			−0.806668	+	0.591005i	$0.798731\pi$
$168$		0			0
$169$	6.17157			0.474736
$170$	−5.82843	+	3.55765i	−0.447020	+	0.272859i
$171$	4.97863			0.380726
$172$	−14.1924	−	7.29408i	−1.08216	−	0.556168i
$173$		−	21.0907i		−	1.60350i	−0.597661	−	0.801749i	$-0.703903\pi$
$173$		−	21.0907i		−	1.60350i	0.597661	−	0.801749i	$-0.296097\pi$
$174$	−3.85077	+	2.35049i	−0.291926	+	0.178190i
$175$		0			0
$176$	6.77817	−	4.85249i	0.510924	−	0.365770i
$177$	24.0416			1.80708
$178$	2.95649	+	4.84357i	0.221599	+	0.363041i
$179$		−	1.22079i		−	0.0912462i	−0.998959	−	0.0456231i	$-0.985473\pi$
$179$		−	1.22079i		−	0.0912462i	0.998959	−	0.0456231i	$-0.0145273\pi$
$180$	−8.49906	−	4.36803i	−0.633483	−	0.325574i
$181$			6.04601i			0.449397i	0.974428	+	0.224698i	$0.0721396\pi$
$181$			6.04601i			0.449397i	−0.974428	+	0.224698i	$0.927860\pi$
$182$		0			0
$183$		−	35.5765i		−	2.62989i
$184$	−20.0711	+	1.47363i	−1.47966	+	0.108637i
$185$			4.32957i			0.318316i
$186$	25.3137	−	15.4514i	1.85609	−	1.13295i
$187$	−9.29658			−0.679833
$188$	4.97863	−	9.68714i	0.363104	−	0.706507i
$189$		0			0
$190$	0.899495	+	1.47363i	0.0652562	+	0.106908i
$191$		−	20.1251i		−	1.45620i	−0.685471	−	0.728100i	$-0.740404\pi$
$191$		−	20.1251i		−	1.45620i	0.685471	−	0.728100i	$-0.259596\pi$
$192$	21.5497	−	3.18152i	1.55521	−	0.229606i
$193$	17.4142			1.25350			0.626751	−	0.779219i	$-0.284384\pi$
$193$	17.4142			1.25350			0.626751	+	0.779219i	$0.284384\pi$
$194$	−2.81966	−	4.61940i	−0.202440	−	0.331653i
$195$	−7.70154			−0.551519
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−6.77817	−	11.1046i	−0.481704	−	0.789166i
$199$	−21.7832			−1.54417			−0.772087	−	0.635517i	$-0.780787\pi$
$199$	−21.7832			−1.54417			−0.772087	+	0.635517i	$0.780787\pi$
$200$	0.792893	+	10.7994i	0.0560660	+	0.763630i
$201$		−	27.3994i		−	1.93260i
$202$	0.136833	+	0.224171i	0.00962753	+	0.0157726i
$203$		0			0
$204$	−21.6066	−	11.1046i	−1.51276	−	0.777474i
$205$	6.00000			0.419058
$206$	18.5932	−	11.3492i	1.29545	−	0.790735i
$207$			31.4084i			2.18304i
$208$	8.49906	−	6.08447i	0.589304	−	0.421882i
$209$			2.35049i			0.162587i
$210$		0			0
$211$			15.9570i			1.09853i	0.835649	+	0.549264i	$0.185092\pi$
$211$			15.9570i			1.09853i	−0.835649	+	0.549264i	$0.814908\pi$
$212$	−5.92893	+	11.5362i	−0.407201	+	0.792308i
$213$		0			0
$214$	−5.24264	−	8.58892i	−0.358380	−	0.587127i
$215$	−8.63589			−0.588963
$216$	−0.797521	−	10.8624i	−0.0542644	−	0.739092i
$217$		0			0
$218$	−6.82843	+	4.16804i	−0.462479	+	0.282295i
$219$			21.7034i			1.46658i
$220$	2.06222	−	4.01254i	0.139035	−	0.270526i
$221$	−11.6569			−0.784125
$222$	−13.1474	+	8.02509i	−0.882392	+	0.538609i
$223$	−20.8489			−1.39614			−0.698072	−	0.716027i	$-0.745959\pi$
$223$	−20.8489			−1.39614			−0.698072	+	0.716027i	$0.745959\pi$
$224$		0			0
$225$	16.8995			1.12663
$226$	−5.12132	+	3.12603i	−0.340665	+	0.207941i
$227$	18.1260			1.20306			0.601532	−	0.798849i	$-0.294557\pi$
$227$	18.1260			1.20306			0.601532	+	0.798849i	$0.294557\pi$
$228$	−2.80761	+	5.46289i	−0.185939	+	0.361789i
$229$			18.9259i			1.25066i	0.780360	+	0.625330i	$0.215036\pi$
$229$			18.9259i			1.25066i	−0.780360	+	0.625330i	$0.784964\pi$
$230$	−9.29658	+	5.67459i	−0.612998	+	0.374172i
$231$		0			0
$232$	−0.242641	−	3.30481i	−0.0159301	−	0.216972i
$233$	7.75736			0.508202			0.254101	−	0.967178i	$-0.418221\pi$
$233$	7.75736			0.508202			0.254101	+	0.967178i	$0.418221\pi$
$234$	−8.49906	−	13.9239i	−0.555601	−	0.910231i
$235$		−	5.89450i		−	0.384515i
$236$	−8.07196	+	15.7060i	−0.525440	+	1.02237i
$237$			11.3492i			0.737209i
$238$		0			0
$239$			11.2833i			0.729858i	0.931035	+	0.364929i	$0.118907\pi$
$239$			11.2833i			0.729858i	−0.931035	+	0.364929i	$0.881093\pi$
$240$	9.58579	−	6.86246i	0.618760	−	0.442970i
$241$			8.60474i			0.554280i	0.960830	+	0.277140i	$0.0893866\pi$
$241$			8.60474i			0.554280i	−0.960830	+	0.277140i	$0.910613\pi$
$242$	−8.03553	+	4.90486i	−0.516544	+	0.315296i
$243$	19.0603			1.22272
$244$	23.2415	+	11.9448i	1.48788	+	0.764686i
$245$		0			0
$246$	11.1213	+	18.2199i	0.709069	+	1.16166i
$247$			2.94725i			0.187529i
$248$	1.59504	+	21.7248i	0.101285	+	1.37952i
$249$	−11.7574			−0.745092
$250$	7.04085	+	11.5349i	0.445303	+	0.729531i
$251$	10.4244			0.657985			0.328993	−	0.944333i	$-0.393291\pi$
$251$	10.4244			0.657985			0.328993	+	0.944333i	$0.393291\pi$
$252$		0			0
$253$	−14.8284			−0.932255
$254$	−8.31371	−	13.6202i	−0.521648	−	0.854607i
$255$	−13.1474			−0.823319
$256$	−5.15685	+	15.1462i	−0.322303	+	0.946636i
$257$			9.42450i			0.587884i	0.955823	+	0.293942i	$0.0949673\pi$
$257$			9.42450i			0.587884i	−0.955823	+	0.293942i	$0.905033\pi$
$258$	−16.0071	−	26.2241i	−0.996558	−	1.63264i
$259$		0			0
$260$	2.58579	−	5.03127i	0.160364	−	0.312026i
$261$	−5.17157			−0.320112
$262$	−19.1571	+	11.6934i	−1.18353	+	0.722421i
$263$		−	21.8516i		−	1.34742i	−0.738994	−	0.673712i	$-0.764699\pi$
$263$		−	21.8516i		−	1.34742i	0.738994	−	0.673712i	$-0.235301\pi$
$264$	16.0071	−	1.17525i	0.985168	−	0.0723314i
$265$			7.01962i			0.431212i
$266$		0			0
$267$			10.9258i			0.668647i
$268$	17.8995	+	9.19932i	1.09339	+	0.561938i
$269$			17.3952i			1.06060i	0.847809	+	0.530302i	$0.177921\pi$
$269$			17.3952i			1.06060i	−0.847809	+	0.530302i	$0.822079\pi$
$270$	−3.07107	−	5.03127i	−0.186899	−	0.306194i
$271$	5.44581			0.330809			0.165405	−	0.986226i	$-0.447107\pi$
$271$	5.44581			0.330809			0.165405	+	0.986226i	$0.447107\pi$
$272$	14.5088	−	10.3868i	0.879725	−	0.629795i
$273$		0			0
$274$	−0.292893	+	0.178781i	−0.0176943	+	0.0108005i
$275$			7.97852i			0.481123i
$276$	−34.4634	−	17.7122i	−2.07445	−	1.06615i
$277$	24.1421			1.45056			0.725280	−	0.688454i	$-0.241710\pi$
$277$	24.1421			1.45056			0.725280	+	0.688454i	$0.241710\pi$
$278$	−2.15897	+	1.31783i	−0.129487	+	0.0790381i
$279$	33.9962			2.03530
$280$		0			0
$281$	−26.3848			−1.57398			−0.786992	−	0.616963i	$-0.788363\pi$
$281$	−26.3848			−1.57398			−0.786992	+	0.616963i	$0.788363\pi$
$282$	17.8995	−	10.9258i	1.06590	−	0.650620i
$283$	12.0195			0.714484			0.357242	−	0.934012i	$-0.383717\pi$
$283$	12.0195			0.714484			0.357242	+	0.934012i	$0.383717\pi$
$284$		0			0
$285$			3.32410i			0.196903i
$286$	6.57368	−	4.01254i	0.388710	−	0.237267i
$287$		0			0
$288$	22.9853	+	9.75735i	1.35442	+	0.574957i
$289$	−2.89949			−0.170559
$290$	−0.934353	−	1.53073i	−0.0548671	−	0.0898878i
$291$		−	10.4201i		−	0.610838i
$292$	−14.1785	−	7.28692i	−0.829732	−	0.426435i
$293$		−	23.2555i		−	1.35860i	−0.733860	−	0.679300i	$-0.762283\pi$
$293$		−	23.2555i		−	1.35860i	0.733860	−	0.679300i	$-0.237717\pi$
$294$		0			0
$295$			9.55688i			0.556423i
$296$	−0.828427	−	11.2833i	−0.0481513	−	0.655831i
$297$		−	8.02509i		−	0.465663i
$298$	1.00000	−	0.610396i	0.0579284	−	0.0353593i
$299$	−18.5932			−1.07527
$300$	−9.53017	+	18.5432i	−0.550225	+	1.07059i
$301$		0			0
$302$	−3.97056	−	6.50490i	−0.228480	−	0.374315i
$303$			0.505668i			0.0290499i
$304$	−2.62615	−	3.66832i	−0.150620	−	0.210393i
$305$	14.1421			0.809776
$306$	−14.5088	−	23.7695i	−0.829413	−	1.35881i
$307$	10.4244			0.594954			0.297477	−	0.954729i	$-0.403855\pi$
$307$	10.4244			0.594954			0.297477	+	0.954729i	$0.403855\pi$
$308$		0			0
$309$	41.9411			2.38595
$310$	6.14214	+	10.0625i	0.348850	+	0.571514i
$311$	−4.51146			−0.255821			−0.127911	−	0.991786i	$-0.540827\pi$
$311$	−4.51146			−0.255821			−0.127911	+	0.991786i	$0.540827\pi$
$312$	20.0711	−	1.47363i	1.13630	−	0.0834276i
$313$		−	9.87285i		−	0.558046i	−0.960284	−	0.279023i	$-0.909989\pi$
$313$		−	9.87285i		−	0.558046i	0.960284	−	0.279023i	$-0.0900106\pi$
$314$	14.8792	+	24.3764i	0.839683	+	1.37564i
$315$		0			0
$316$	−7.41421	−	3.81048i	−0.417082	−	0.214356i
$317$	−22.4853			−1.26290			−0.631450	−	0.775417i	$-0.717540\pi$
$317$	−22.4853			−1.26290			−0.631450	+	0.775417i	$0.717540\pi$
$318$	−21.3161	+	13.0112i	−1.19535	+	0.729634i
$319$		−	2.44158i		−	0.136702i
$320$	1.26470	+	8.56628i	0.0706987	+	0.478870i
$321$		−	19.3743i		−	1.08137i
$322$		0			0
$323$			5.03127i			0.279948i
$324$	−2.52082	+	4.90486i	−0.140045	+	0.272492i
$325$			10.0042i			0.554931i
$326$	−2.80761	−	4.59966i	−0.155499	−	0.254751i
$327$	−15.4031			−0.851792
$328$	−15.6367	+	1.14805i	−0.863391	+	0.0633905i
$329$		0			0
$330$	7.41421	−	4.52560i	0.408139	−	0.249126i
$331$			3.81048i			0.209443i	0.994502	+	0.104722i	$0.0333951\pi$
$331$			3.81048i			0.209443i	−0.994502	+	0.104722i	$0.966605\pi$
$332$	3.94753	−	7.68087i	0.216649	−	0.421542i
$333$	−17.6569			−0.967590
$334$	25.1668	−	15.3617i	1.37707	−	0.840556i
$335$	10.8916			0.595073
$336$		0			0
$337$	5.17157			0.281714			0.140857	−	0.990030i	$-0.455014\pi$
$337$	5.17157			0.281714			0.140857	+	0.990030i	$0.455014\pi$
$338$	−7.44975	+	4.54729i	−0.405213	+	0.247340i
$339$	−11.5523			−0.627435
$340$	4.41421	−	8.58892i	0.239394	−	0.465800i
$341$			16.0502i			0.869166i
$342$	−6.00974	+	3.66832i	−0.324970	+	0.198360i
$343$		0			0
$344$	22.5061	−	1.65241i	1.21345	−	0.0890918i
$345$	−20.9706			−1.12902
$346$	15.5399	+	25.4587i	0.835431	+	1.36867i
$347$			2.08402i			0.111876i	0.998434	+	0.0559381i	$0.0178149\pi$
$347$			2.08402i			0.111876i	−0.998434	+	0.0559381i	$0.982185\pi$
$348$	2.91642	−	5.67459i	0.156336	−	0.304190i
$349$		−	5.67459i		−	0.303754i	−0.988399	−	0.151877i	$-0.951468\pi$
$349$		−	5.67459i		−	0.303754i	0.988399	−	0.151877i	$-0.0485318\pi$
$350$		0			0
$351$		−	10.0625i		−	0.537099i
$352$	−4.60660	+	10.8517i	−0.245533	+	0.578399i
$353$		−	27.9790i		−	1.48917i	−0.667526	−	0.744586i	$-0.732647\pi$
$353$		−	27.9790i		−	1.48917i	0.667526	−	0.744586i	$-0.267353\pi$
$354$	−29.0208	+	17.7142i	−1.54244	+	0.941498i
$355$		0			0
$356$	−7.13761	−	3.66832i	−0.378292	−	0.194421i
$357$		0			0
$358$	0.899495	+	1.47363i	0.0475398	+	0.0778835i
$359$		−	24.7988i		−	1.30883i	−0.756135	−	0.654415i	$-0.772915\pi$
$359$		−	24.7988i		−	1.30883i	0.756135	−	0.654415i	$-0.227085\pi$
$360$	13.4777	−	0.989538i	0.710337	−	0.0521532i
$361$	−17.7279			−0.933049
$362$	−4.45478	−	7.29818i	−0.234138	−	0.383584i
$363$	−18.1260			−0.951367
$364$		0			0
$365$	−8.62742			−0.451580
$366$	26.2132	+	42.9446i	1.37019	+	2.24475i
$367$	16.3374			0.852807			0.426404	−	0.904533i	$-0.359780\pi$
$367$	16.3374			0.852807			0.426404	+	0.904533i	$0.359780\pi$
$368$	23.1421	−	16.5674i	1.20637	−	0.863638i
$369$			24.4692i			1.27382i
$370$	−3.19008	−	5.22625i	−0.165844	−	0.271700i
$371$		0			0
$372$	−19.1716	+	37.3029i	−0.994000	+	1.93407i
$373$	8.14214			0.421584			0.210792	−	0.977531i	$-0.432396\pi$
$373$	8.14214			0.421584			0.210792	+	0.977531i	$0.432396\pi$
$374$	11.2220	−	6.84984i	0.580274	−	0.354197i
$375$			26.0196i			1.34365i
$376$	1.12786	+	15.3617i	0.0581652	+	0.792221i
$377$		−	3.06147i		−	0.157674i
$378$		0			0
$379$		−	23.9356i		−	1.22949i	−0.788727	−	0.614744i	$-0.789259\pi$
$379$		−	23.9356i		−	1.22949i	0.788727	−	0.614744i	$-0.210741\pi$
$380$	−2.17157	−	1.11606i	−0.111399	−	0.0572529i
$381$		−	30.7235i		−	1.57401i
$382$	14.8284	+	24.2931i	0.758688	+	1.24294i
$383$	−6.76719			−0.345787			−0.172894	−	0.984941i	$-0.555312\pi$
$383$	−6.76719			−0.345787			−0.172894	+	0.984941i	$0.555312\pi$
$384$	−23.6686	+	19.7185i	−1.20783	+	1.00626i
$385$		0			0
$386$	−21.0208	+	12.8310i	−1.06993	+	0.653082i
$387$		−	35.2189i		−	1.79028i
$388$	6.80726	+	3.49854i	0.345586	+	0.177612i
$389$	−14.1421			−0.717035			−0.358517	−	0.933523i	$-0.616718\pi$
$389$	−14.1421			−0.717035			−0.358517	+	0.933523i	$0.616718\pi$
$390$	9.29658	−	5.67459i	0.470751	−	0.287344i
$391$	−31.7405			−1.60519
$392$		0			0
$393$	−43.2132			−2.17982
$394$	−2.41421	+	1.47363i	−0.121626	+	0.0742402i
$395$	−4.51146			−0.226996
$396$	16.3640	+	8.41014i	0.822320	+	0.422625i
$397$		−	12.8030i		−	0.642564i	−0.946984	−	0.321282i	$-0.895886\pi$
$397$		−	12.8030i		−	0.642564i	0.946984	−	0.321282i	$-0.104114\pi$
$398$	26.2947	−	16.0502i	1.31803	−	0.804523i
$399$		0			0
$400$	−8.91421	−	12.4518i	−0.445711	−	0.622588i
$401$	−7.17157			−0.358131			−0.179066	−	0.983837i	$-0.557307\pi$
$401$	−7.17157			−0.358131			−0.179066	+	0.983837i	$0.557307\pi$
$402$	20.1882	+	33.0740i	1.00690	+	1.64958i
$403$			20.1251i			1.00250i
$404$	−0.330344	−	0.169778i	−0.0164352	−	0.00844676i
$405$			2.98454i			0.148303i
$406$		0			0
$407$		−	8.33609i		−	0.413204i
$408$	34.2635	−	2.51564i	1.69629	−	0.124543i
$409$		−	7.25972i		−	0.358970i	−0.983761	−	0.179485i	$-0.942557\pi$
$409$		−	7.25972i		−	0.358970i	0.983761	−	0.179485i	$-0.0574431\pi$
$410$	−7.24264	+	4.42088i	−0.357689	+	0.218332i
$411$	−0.660688			−0.0325893
$412$	−14.0817	+	27.3994i	−0.693756	+	1.34987i
$413$		0			0
$414$	−23.1421	−	37.9133i	−1.13737	−	1.86334i
$415$		−	4.67371i		−	0.229423i
$416$	−5.77615	+	13.6068i	−0.283199	+	0.667130i
$417$	−4.87006			−0.238488
$418$	−1.73187	−	2.83730i	−0.0847087	−	0.138777i
$419$	16.5309			0.807589			0.403795	−	0.914850i	$-0.367691\pi$
$419$	16.5309			0.807589			0.403795	+	0.914850i	$0.367691\pi$
$420$		0			0
$421$	6.48528			0.316073			0.158037	−	0.987433i	$-0.449484\pi$
$421$	6.48528			0.316073			0.158037	+	0.987433i	$0.449484\pi$
$422$	−11.7574	−	19.2619i	−0.572339	−	0.937653i
$423$	24.0390			1.16881
$424$	−1.34315	−	18.2939i	−0.0652289	−	0.888431i
$425$			17.0782i			0.828413i
$426$		0			0
$427$		0			0
$428$	12.6569	+	6.50490i	0.611792	+	0.314426i
$429$	14.8284			0.715923
$430$	10.4244	−	6.36304i	0.502711	−	0.306853i
$431$		−	17.1778i		−	0.827427i	−0.910407	−	0.413714i	$-0.864231\pi$
$431$		−	17.1778i		−	0.827427i	0.910407	−	0.413714i	$-0.135769\pi$
$432$	8.96624	+	12.5244i	0.431388	+	0.602582i
$433$		−	15.1760i		−	0.729313i	−0.931142	−	0.364657i	$-0.881186\pi$
$433$		−	15.1760i		−	0.729313i	0.931142	−	0.364657i	$-0.118814\pi$
$434$		0			0
$435$		−	3.45292i		−	0.165555i
$436$	5.17157	−	10.0625i	0.247673	−	0.481909i
$437$			8.02509i			0.383892i
$438$	−15.9914	−	26.1984i	−0.764098	−	1.25181i
$439$	17.6588			0.842809			0.421404	−	0.906873i	$-0.361537\pi$
$439$	17.6588			0.842809			0.421404	+	0.906873i	$0.361537\pi$
$440$	0.467177	+	6.36304i	0.0222718	+	0.303346i
$441$		0			0
$442$	14.0711	−	8.58892i	0.669292	−	0.408533i
$443$		−	26.7347i		−	1.27020i	−0.772428	−	0.635102i	$-0.780958\pi$
$443$		−	26.7347i		−	1.27020i	0.772428	−	0.635102i	$-0.219042\pi$
$444$	9.95727	−	19.3743i	0.472551	−	0.919462i
$445$	−4.34315			−0.205885
$446$	25.1668	−	15.3617i	1.19168	−	0.727399i
$447$	2.25573			0.106692
$448$		0			0
$449$	40.2843			1.90113			0.950566	−	0.310522i	$-0.100504\pi$
$449$	40.2843			1.90113			0.950566	+	0.310522i	$0.100504\pi$
$450$	−20.3995	+	12.4518i	−0.961641	+	0.586982i
$451$	−11.5523			−0.543977
$452$	3.87868	−	7.54691i	0.182438	−	0.354977i
$453$		−	14.6733i		−	0.689411i
$454$	−21.8800	+	13.3555i	−1.02688	+	0.626803i
$455$		0			0
$456$	−0.636039	−	8.66297i	−0.0297853	−	0.405681i
$457$	−24.7279			−1.15672			−0.578362	−	0.815780i	$-0.696308\pi$
$457$	−24.7279			−1.15672			−0.578362	+	0.815780i	$0.696308\pi$
$458$	−13.9449	−	22.8456i	−0.651601	−	1.06751i
$459$		−	17.1778i		−	0.801793i
$460$	7.04085	−	13.6997i	0.328281	−	0.638751i
$461$			27.4763i			1.27970i	0.768501	+	0.639849i	$0.221003\pi$
$461$			27.4763i			1.27970i	−0.768501	+	0.639849i	$0.778997\pi$
$462$		0			0
$463$		−	6.60963i		−	0.307175i	−0.988135	−	0.153588i	$-0.950917\pi$
$463$		−	6.60963i		−	0.307175i	0.988135	−	0.153588i	$-0.0490828\pi$
$464$	2.72792	+	3.81048i	0.126641	+	0.176897i
$465$			22.6984i			1.05261i
$466$	−9.36396	+	5.71572i	−0.433777	+	0.264776i
$467$	−7.50803			−0.347430			−0.173715	−	0.984796i	$-0.555577\pi$
$467$	−7.50803			−0.347430			−0.173715	+	0.984796i	$0.555577\pi$
$468$	20.5185	+	10.5454i	0.948470	+	0.487459i
$469$		0			0
$470$	4.34315	+	7.11529i	0.200334	+	0.328204i
$471$			54.9864i			2.53364i
$472$	−1.82863	−	24.9063i	−0.0841695	−	1.14640i
$473$	16.6274			0.764529
$474$	−8.36223	−	13.6997i	−0.384090	−	0.629247i
$475$	4.31795			0.198121
$476$		0			0
$477$	−28.6274			−1.31076
$478$	−8.31371	−	13.6202i	−0.380260	−	0.622973i
$479$	19.9145			0.909918			0.454959	−	0.890512i	$-0.349654\pi$
$479$	19.9145			0.909918			0.454959	+	0.890512i	$0.349654\pi$
$480$	−6.51472	+	15.3467i	−0.297355	+	0.700476i
$481$		−	10.4525i		−	0.476593i
$482$	−6.34009	−	10.3868i	−0.288783	−	0.473108i
$483$		0			0
$484$	6.08579	−	11.8414i	0.276627	−	0.538244i
$485$	4.14214			0.188085
$486$	−23.0079	+	14.0439i	−1.04366	+	0.637044i
$487$		−	39.7445i		−	1.80100i	−0.434860	−	0.900498i	$-0.643202\pi$
$487$		−	39.7445i		−	1.80100i	0.434860	−	0.900498i	$-0.356798\pi$
$488$	−36.8560	+	2.70598i	−1.66839	+	0.122494i
$489$		−	10.3756i		−	0.469200i
$490$		0			0
$491$		−	15.9570i		−	0.720132i	−0.932927	−	0.360066i	$-0.882754\pi$
$491$		−	15.9570i		−	0.720132i	0.932927	−	0.360066i	$-0.117246\pi$
$492$	−26.8492	−	13.7990i	−1.21046	−	0.622106i
$493$		−	5.22625i		−	0.235379i
$494$	−2.17157	−	3.55765i	−0.0977037	−	0.160066i
$495$	9.95727			0.447546
$496$	−17.9325	−	25.0489i	−0.805192	−	1.12473i
$497$		0			0
$498$	14.1924	−	8.66297i	0.635976	−	0.388197i
$499$			18.3986i			0.823636i	0.911266	+	0.411818i	$0.135106\pi$
$499$			18.3986i			0.823636i	−0.911266	+	0.411818i	$0.864894\pi$
$500$	−16.9981	−	8.73606i	−0.760179	−	0.390689i
$501$	56.7696			2.53628
$502$	−12.5834	+	7.68087i	−0.561625	+	0.342814i
$503$	20.8489			0.929606			0.464803	−	0.885414i	$-0.346125\pi$
$503$	20.8489			0.929606			0.464803	+	0.885414i	$0.346125\pi$
$504$		0			0
$505$	−0.201010			−0.00894483
$506$	17.8995	−	10.9258i	0.795730	−	0.485710i
$507$	−16.8046			−0.746319
$508$	20.0711	+	10.3154i	0.890510	+	0.457671i
$509$		−	21.0907i		−	0.934830i	−0.884038	−	0.467415i	$-0.845185\pi$
$509$		−	21.0907i		−	0.934830i	0.884038	−	0.467415i	$-0.154815\pi$
$510$	15.8703	−	9.68714i	0.702747	−	0.428954i
$511$		0			0
$512$	−4.93503	−	22.0827i	−0.218100	−	0.975927i
$513$	−4.34315			−0.191755
$514$	−6.94410	−	11.3764i	−0.306291	−	0.501791i
$515$			16.6722i			0.734664i
$516$	38.6445	+	19.8611i	1.70123	+	0.874335i
$517$			11.3492i			0.499137i
$518$		0			0
$519$			57.4280i			2.52081i
$520$	0.585786	+	7.97852i	0.0256884	+	0.349881i
$521$		−	17.9749i		−	0.787493i	−0.919219	−	0.393746i	$-0.871179\pi$
$521$		−	17.9749i		−	0.787493i	0.919219	−	0.393746i	$-0.128821\pi$
$522$	6.24264	−	3.81048i	0.273233	−	0.166780i
$523$	36.7191			1.60562			0.802808	−	0.596238i	$-0.203338\pi$
$523$	36.7191			1.60562			0.802808	+	0.596238i	$0.203338\pi$
$524$	14.5088	−	28.2304i	0.633820	−	1.23325i
$525$		0			0
$526$	16.1005	+	26.3772i	0.702015	+	1.15010i
$527$			34.3557i			1.49656i
$528$	−18.4563	+	13.2129i	−0.803209	+	0.575017i
$529$	−27.6274			−1.20119
$530$	−5.17214	−	8.47343i	−0.224664	−	0.368062i
$531$	−38.9749			−1.69137
$532$		0			0
$533$	−14.4853			−0.627427
$534$	−8.05025	−	13.1886i	−0.348368	−	0.570726i
$535$	7.70154			0.332967
$536$	−28.3848	+	2.08402i	−1.22604	+	0.0900160i
$537$			3.32410i			0.143445i
$538$	−12.8170	−	20.9979i	−0.552580	−	0.905282i
$539$		0			0
$540$	7.41421	+	3.81048i	0.319057	+	0.163977i
$541$	22.6863			0.975360			0.487680	−	0.873023i	$-0.337843\pi$
$541$	22.6863			0.975360			0.487680	+	0.873023i	$0.337843\pi$
$542$	−6.57368	+	4.01254i	−0.282364	+	0.172353i
$543$		−	16.4627i		−	0.706483i
$544$	−9.86051	+	23.2283i	−0.422766	+	0.995905i
$545$		−	6.12293i		−	0.262278i
$546$		0			0
$547$		−	14.5882i		−	0.623744i	−0.950124	−	0.311872i	$-0.899044\pi$
$547$		−	14.5882i		−	0.623744i	0.950124	−	0.311872i	$-0.100956\pi$
$548$	0.221825	−	0.431615i	0.00947591	−	0.0184377i
$549$			57.6745i			2.46149i
$550$	−5.87868	−	9.63093i	−0.250668	−	0.410664i
$551$	−1.32138			−0.0562925
$552$	54.6516	−	4.01254i	2.32613	−	0.170785i
$553$		0			0
$554$	−29.1421	+	17.7882i	−1.23813	+	0.755750i
$555$		−	11.7890i		−	0.500415i
$556$	1.63512	−	3.18152i	0.0693445	−	0.134926i
$557$	−8.34315			−0.353510			−0.176755	−	0.984255i	$-0.556560\pi$
$557$	−8.34315			−0.353510			−0.176755	+	0.984255i	$0.556560\pi$
$558$	−41.0371	+	25.0489i	−1.73724	+	1.06040i
$559$	20.8489			0.881814
$560$		0			0
$561$	25.3137			1.06875
$562$	31.8492	−	19.4406i	1.34348	−	0.820054i
$563$	−11.3588			−0.478716			−0.239358	−	0.970931i	$-0.576937\pi$
$563$	−11.3588			−0.478716			−0.239358	+	0.970931i	$0.576937\pi$
$564$	−13.5563	+	26.3772i	−0.570825	+	1.11068i
$565$		−	4.59220i		−	0.193195i
$566$	−14.5088	+	8.85611i	−0.609850	+	0.372250i
$567$		0			0
$568$		0			0
$569$	13.1716			0.552181			0.276091	−	0.961132i	$-0.410961\pi$
$569$	13.1716			0.552181			0.276091	+	0.961132i	$0.410961\pi$
$570$	−2.44924	−	4.01254i	−0.102587	−	0.168067i
$571$			40.6077i			1.69938i	0.527282	+	0.849691i	$0.323211\pi$
$571$			40.6077i			1.69938i	−0.527282	+	0.849691i	$0.676789\pi$
$572$	−4.97863	+	9.68714i	−0.208167	+	0.405040i
$573$			54.7987i			2.28925i
$574$		0			0
$575$			27.2404i			1.13600i
$576$	−34.9350	+	5.15769i	−1.45563	+	0.214904i
$577$			38.6172i			1.60766i	0.594862	+	0.803828i	$0.297207\pi$
$577$			38.6172i			1.60766i	−0.594862	+	0.803828i	$0.702793\pi$
$578$	3.50000	−	2.13639i	0.145581	−	0.0888619i
$579$	−47.4173			−1.97059
$580$	2.25573	+	1.15932i	0.0936640	+	0.0481380i
$581$		0			0
$582$	7.67767	+	12.5782i	0.318250	+	0.521382i
$583$		−	13.5155i		−	0.559753i
$584$	22.4840	−	1.65078i	0.930395	−	0.0683100i
$585$	12.4853			0.516203
$586$	17.1350	+	28.0719i	0.707838	+	1.15964i
$587$	−1.78855			−0.0738214			−0.0369107	−	0.999319i	$-0.511752\pi$
$587$	−1.78855			−0.0738214			−0.0369107	+	0.999319i	$0.511752\pi$
$588$		0			0
$589$	8.68629			0.357912
$590$	−7.04163	−	11.5362i	−0.289899	−	0.474937i
$591$	−5.44581			−0.224011
$592$	9.31371	+	13.0098i	0.382791	+	0.534699i
$593$			34.9986i			1.43722i	0.695412	+	0.718611i	$0.255222\pi$
$593$			34.9986i			1.43722i	−0.695412	+	0.718611i	$0.744778\pi$
$594$	5.91299	+	9.68714i	0.242613	+	0.397468i
$595$		0			0
$596$	−0.757359	+	1.47363i	−0.0310226	+	0.0603621i
$597$	59.3137			2.42755
$598$	22.4439	−	13.6997i	0.917801	−	0.560222i
$599$			41.9766i			1.71512i	0.514385	+	0.857560i	$0.328020\pi$
$599$			41.9766i			1.71512i	−0.514385	+	0.857560i	$0.671980\pi$
$600$	−2.15897	−	29.4056i	−0.0881397	−	1.20048i
$601$			6.25425i			0.255116i	0.991831	+	0.127558i	$0.0407139\pi$
$601$			6.25425i			0.255116i	−0.991831	+	0.127558i	$0.959286\pi$
$602$		0			0
$603$			44.4182i			1.80885i
$604$	9.58579	+	4.92655i	0.390040	+	0.200458i
$605$		−	7.20533i		−	0.292938i
$606$	−0.372583	−	0.610396i	−0.0151351	−	0.0247956i
$607$	−15.4031			−0.625192			−0.312596	−	0.949886i	$-0.601199\pi$
$607$	−15.4031			−0.625192			−0.312596	+	0.949886i	$0.601199\pi$
$608$	5.87291	+	2.49307i	0.238178	+	0.101108i
$609$		0			0
$610$	−17.0711	+	10.4201i	−0.691187	+	0.421898i
$611$			14.2306i			0.575708i
$612$	35.0273	+	18.0021i	1.41590	+	0.727690i
$613$	−31.3137			−1.26475			−0.632374	−	0.774663i	$-0.717920\pi$
$613$	−31.3137			−1.26475			−0.632374	+	0.774663i	$0.717920\pi$
$614$	−12.5834	+	7.68087i	−0.507825	+	0.309974i
$615$	−16.3374			−0.658789
$616$		0			0
$617$	15.4558			0.622229			0.311114	−	0.950372i	$-0.399298\pi$
$617$	15.4558			0.622229			0.311114	+	0.950372i	$0.399298\pi$
$618$	−50.6274	+	30.9028i	−2.03653	+	1.24309i
$619$	−44.4207			−1.78542			−0.892709	−	0.450634i	$-0.851198\pi$
$619$	−44.4207			−1.78542			−0.892709	+	0.450634i	$0.851198\pi$
$620$	−14.8284	−	7.62096i	−0.595524	−	0.306065i
$621$		−	27.3994i		−	1.09950i
$622$	5.44581	−	3.32410i	0.218357	−	0.133284i
$623$		0			0
$624$	−23.1421	+	16.5674i	−0.926427	+	0.663229i
$625$	8.79899			0.351960
$626$	7.27444	+	11.9176i	0.290745	+	0.476322i
$627$		−	6.40017i		−	0.255598i
$628$	−35.9216	−	18.4617i	−1.43343	−	0.736700i
$629$		−	17.8435i		−	0.711469i
$630$		0			0
$631$		−	22.5667i		−	0.898365i	−0.893440	−	0.449183i	$-0.851715\pi$
$631$		−	22.5667i		−	0.898365i	0.893440	−	0.449183i	$-0.148285\pi$
$632$	11.7574	−	0.863230i	0.467683	−	0.0343374i
$633$		−	43.4495i		−	1.72696i
$634$	27.1421	−	16.5674i	1.07795	−	0.657977i
$635$	12.2130			0.484658
$636$	16.1439	−	31.4119i	0.640148	−	1.24556i
$637$		0			0
$638$	1.79899	+	2.94725i	0.0712227	+	0.116683i
$639$		0			0
$640$	−7.83837	−	9.40857i	−0.309839	−	0.371907i
$641$	−1.45584			−0.0575024			−0.0287512	−	0.999587i	$-0.509153\pi$
$641$	−1.45584			−0.0575024			−0.0287512	+	0.999587i	$0.509153\pi$
$642$	14.2752	+	23.3868i	0.563398	+	0.923004i
$643$	6.84734			0.270033			0.135016	−	0.990843i	$-0.456891\pi$
$643$	6.84734			0.270033			0.135016	+	0.990843i	$0.456891\pi$
$644$		0			0
$645$	23.5147			0.925891
$646$	−3.70711	−	6.07328i	−0.145854	−	0.238950i
$647$	−9.57025			−0.376245			−0.188123	−	0.982146i	$-0.560240\pi$
$647$	−9.57025			−0.376245			−0.188123	+	0.982146i	$0.560240\pi$
$648$	−0.571068	−	7.77805i	−0.0224337	−	0.305551i
$649$		−	18.4007i		−	0.722289i
$650$	−7.37120	−	12.0761i	−0.289122	−	0.473663i
$651$		0			0
$652$	6.77817	+	3.48359i	0.265454	+	0.136428i
$653$	15.7990			0.618262			0.309131	−	0.951019i	$-0.399962\pi$
$653$	15.7990			0.618262			0.309131	+	0.951019i	$0.399962\pi$
$654$	18.5932	−	11.3492i	0.727050	−	0.443788i
$655$		−	17.1778i		−	0.671194i
$656$	18.0292	−	12.9071i	0.703923	−	0.503938i
$657$		−	35.1843i		−	1.37267i
$658$		0			0
$659$		−	30.5452i		−	1.18987i	−0.803773	−	0.594936i	$-0.797177\pi$
$659$		−	30.5452i		−	1.18987i	0.803773	−	0.594936i	$-0.202823\pi$
$660$	−5.61522	+	10.9258i	−0.218572	+	0.425285i
$661$			12.5404i			0.487764i	0.969805	+	0.243882i	$0.0784209\pi$
$661$			12.5404i			0.487764i	−0.969805	+	0.243882i	$0.921579\pi$
$662$	−2.80761	−	4.59966i	−0.109121	−	0.178771i
$663$	31.7405			1.23270
$664$	0.894276	+	12.1802i	0.0347046	+	0.472684i
$665$		0			0
$666$	21.3137	−	13.0098i	0.825889	−	0.504119i
$667$		−	8.33609i		−	0.322775i
$668$	−19.0603	+	37.0865i	−0.737467	+	1.43492i
$669$	56.7696			2.19484
$670$	−13.1474	+	8.02509i	−0.507926	+	0.310036i
$671$	−27.2291			−1.05117
$672$		0			0
$673$	−26.3848			−1.01706			−0.508529	−	0.861045i	$-0.669811\pi$
$673$	−26.3848			−1.01706			−0.508529	+	0.861045i	$0.669811\pi$
$674$	−6.24264	+	3.81048i	−0.240458	+	0.146774i
$675$	−14.7424			−0.567435
$676$	5.64214	−	10.9781i	0.217005	−	0.422236i
$677$		−	40.0936i		−	1.54092i	−0.637488	−	0.770461i	$-0.720026\pi$
$677$		−	40.0936i		−	1.54092i	0.637488	−	0.770461i	$-0.279974\pi$
$678$	13.9449	−	8.51189i	0.535550	−	0.326897i
$679$		0			0
$680$	1.00000	+	13.6202i	0.0383482	+	0.522311i
$681$	−49.3553			−1.89130
$682$	−11.8260	−	19.3743i	−0.452840	−	0.741879i
$683$			41.9766i			1.60619i	0.595850	+	0.803096i	$0.296815\pi$
$683$			41.9766i			1.60619i	−0.595850	+	0.803096i	$0.703185\pi$
$684$	4.55153	−	8.85611i	0.174032	−	0.338622i
$685$		−	0.262632i		−	0.0100347i
$686$		0			0
$687$		−	51.5335i		−	1.96613i
$688$	−25.9497	+	18.5774i	−0.989325	+	0.708257i
$689$		−	16.9469i		−	0.645624i
$690$	25.3137	−	15.4514i	0.963676	−	0.588224i
$691$	−4.97863			−0.189396			−0.0946981	−	0.995506i	$-0.530189\pi$
$691$	−4.97863			−0.189396			−0.0946981	+	0.995506i	$0.530189\pi$
$692$	−37.5167	−	19.2814i	−1.42617	−	0.732970i
$693$		0			0
$694$	−1.53553	−	2.51564i	−0.0582881	−	0.0954923i
$695$		−	1.93591i		−	0.0734334i
$696$	0.660688	+	8.99869i	0.0250433	+	0.341095i
$697$	−24.7279			−0.936637
$698$	4.18111	+	6.84984i	0.158257	+	0.259270i
$699$	−21.1226			−0.798928
$700$		0			0
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$	7.41421	+	12.1466i	0.279831	+	0.458443i
$703$	−4.51146			−0.170153
$704$	−2.43503	−	16.4934i	−0.0917736	−	0.621618i
$705$			16.0502i			0.604485i
$706$	20.6153	+	33.7737i	0.775867	+	1.27109i
$707$		0			0
$708$	21.9792	−	42.7658i	0.826028	−	1.60724i
$709$	−1.37258			−0.0515484			−0.0257742	−	0.999668i	$-0.508205\pi$
$709$	−1.37258			−0.0515484			−0.0257742	+	0.999668i	$0.508205\pi$
$710$		0			0
$711$		−	18.3986i		−	0.690003i
$712$	11.3187	−	0.831025i	0.424187	−	0.0311440i
$713$			54.7987i			2.05223i
$714$		0			0
$715$			5.89450i			0.220442i
$716$	−2.17157	−	1.11606i	−0.0811555	−	0.0417093i
$717$		−	30.7235i		−	1.14739i
$718$	18.2721	+	29.9348i	0.681908	+	1.11716i
$719$	−11.8260			−0.441034			−0.220517	−	0.975383i	$-0.570775\pi$
$719$	−11.8260			−0.441034			−0.220517	+	0.975383i	$0.570775\pi$
$720$	−15.5399	+	11.1250i	−0.579138	+	0.414605i
$721$		0			0
$722$	21.3995	−	13.0622i	0.796407	−	0.486123i
$723$		−	23.4299i		−	0.871368i
$724$	10.7548	+	5.52735i	0.399699	+	0.205422i
$725$	−4.48528			−0.166579
$726$	21.8800	−	13.3555i	0.812043	−	0.495668i
$727$	38.1207			1.41382			0.706909	−	0.707305i	$-0.250089\pi$
$727$	38.1207			1.41382			0.706909	+	0.707305i	$0.250089\pi$
$728$		0			0
$729$	−43.6274			−1.61583
$730$	10.4142	−	6.35679i	0.385447	−	0.235275i
$731$	35.5913			1.31639
$732$	−63.2843	−	32.5245i	−2.33905	−	1.20214i
$733$			2.35049i			0.0868175i	0.999057	+	0.0434087i	$0.0138218\pi$
$733$			2.35049i			0.0868175i	−0.999057	+	0.0434087i	$0.986178\pi$
$734$	−19.7210	+	12.0376i	−0.727916	+	0.444317i
$735$		0			0
$736$	−15.7279	+	37.0501i	−0.579739	+	1.36568i
$737$	−20.9706			−0.772461
$738$	−18.0292	−	29.5369i	−0.663665	−	1.08727i
$739$		−	52.3968i		−	1.92745i	−0.266905	−	0.963723i	$-0.586001\pi$
$739$		−	52.3968i		−	1.92745i	0.266905	−	0.963723i	$-0.413999\pi$
$740$	7.70154	+	3.95815i	0.283114	+	0.145505i
$741$		−	8.02509i		−	0.294809i
$742$		0			0
$743$			17.8930i			0.656429i	0.944603	+	0.328215i	$0.106447\pi$
$743$			17.8930i			0.656429i	−0.944603	+	0.328215i	$0.893553\pi$
$744$	−4.34315	−	59.1545i	−0.159227	−	2.16871i
$745$			0.896683i			0.0328519i
$746$	−9.82843	+	5.99923i	−0.359844	+	0.219647i
$747$	19.0603			0.697381
$748$	−8.49906	+	16.5370i	−0.310756	+	0.604652i
$749$		0			0
$750$	−19.1716	−	31.4084i	−0.700047	−	1.14687i
$751$			13.7249i			0.500829i	0.968139	+	0.250415i	$0.0805670\pi$
$751$			13.7249i			0.500829i	−0.968139	+	0.250415i	$0.919433\pi$
$752$	−12.6802	−	17.7122i	−0.462398	−	0.645898i
$753$	−28.3848			−1.03440
$754$	2.25573	+	3.69552i	0.0821488	+	0.134583i
$755$	5.83283			0.212279
$756$		0			0
$757$	12.2843			0.446479			0.223240	−	0.974764i	$-0.428337\pi$
$757$	12.2843			0.446479			0.223240	+	0.974764i	$0.428337\pi$
$758$	17.6360	+	28.8928i	0.640570	+	1.04943i
$759$	40.3764			1.46557
$760$	3.44365	−	0.252834i	0.124914	−	0.00917126i
$761$			25.9999i			0.942497i	0.882000	+	0.471249i	$0.156197\pi$
$761$			25.9999i			0.942497i	−0.882000	+	0.471249i	$0.843803\pi$
$762$	22.6374	+	37.0865i	0.820068	+	1.34350i
$763$		0			0
$764$	−35.7990	−	18.3986i	−1.29516	−	0.665639i
$765$	21.3137			0.770599
$766$	8.16872	−	4.98615i	0.295148	−	0.180157i
$767$		−	23.0723i		−	0.833094i
$768$	14.0416	−	41.2416i	0.506684	−	1.48818i
$769$		−	46.1940i		−	1.66580i	−0.553425	−	0.832899i	$-0.686680\pi$
$769$		−	46.1940i		−	1.66580i	0.553425	−	0.832899i	$-0.313320\pi$
$770$		0			0
$771$		−	25.6620i		−	0.924196i
$772$	15.9203	−	30.9768i	0.572985	−	1.11488i
$773$			52.9735i			1.90532i	0.304031	+	0.952662i	$0.401667\pi$
$773$			52.9735i			1.90532i	−0.304031	+	0.952662i	$0.598333\pi$
$774$	25.9497	+	42.5130i	0.932744	+	1.52810i
$775$	29.4848			1.05912
$776$	−10.7949	+	0.792563i	−0.387513	+	0.0284514i
$777$		0			0
$778$	17.0711	−	10.4201i	0.612027	−	0.373579i
$779$			6.25206i			0.224003i
$780$	−7.04085	+	13.6997i	−0.252103	+	0.490527i
$781$		0			0
$782$	38.3142	−	23.3868i	1.37011	−	0.836311i
$783$	4.51146			0.161226
$784$		0			0
$785$	−21.8579			−0.780141
$786$	52.1630	−	31.8400i	1.86059	−	1.13570i
$787$	29.2913			1.04412			0.522061	−	0.852908i	$-0.325164\pi$
$787$	29.2913			1.04412			0.522061	+	0.852908i	$0.325164\pi$
$788$	1.82843	−	3.55765i	0.0651350	−	0.126736i
$789$			59.4997i			2.11825i
$790$	5.44581	−	3.32410i	0.193753	−	0.118266i
$791$		0			0
$792$	−25.9497	+	1.90524i	−0.922084	+	0.0676998i
$793$	−34.1421			−1.21242
$794$	9.43341	+	15.4546i	0.334779	+	0.548463i
$795$		−	19.1138i		−	0.677895i
$796$	−19.9145	+	38.7485i	−0.705852	+	1.37341i
$797$			19.1886i			0.679694i	0.940481	+	0.339847i	$0.110375\pi$
$797$			19.1886i			0.679694i	−0.940481	+	0.339847i	$0.889625\pi$
$798$		0			0
$799$			24.2931i			0.859429i
$800$	19.9350	+	8.46250i	0.704810	+	0.299195i
$801$		−	17.7122i		−	0.625831i
$802$	8.65685	−	5.28411i	0.305684	−	0.186588i
$803$	16.6111			0.586193
$804$	−48.7386	−	25.0489i	−1.71888	−	0.883405i
$805$		0			0
$806$	−14.8284	−	24.2931i	−0.522309	−	0.855689i
$807$		−	47.3655i		−	1.66734i
$808$	0.523855	−	0.0384616i	0.0184291	−	0.00135308i
$809$	48.0416			1.68905			0.844527	−	0.535513i	$-0.179882\pi$
$809$	48.0416			1.68905			0.844527	+	0.535513i	$0.179882\pi$
$810$	−2.19905	−	3.60266i	−0.0772668	−	0.126585i
$811$	42.4386			1.49022			0.745111	−	0.666941i	$-0.232397\pi$
$811$	42.4386			1.49022			0.745111	+	0.666941i	$0.232397\pi$
$812$		0			0
$813$	−14.8284			−0.520056
$814$	6.14214	+	10.0625i	0.215282	+	0.352692i
$815$	4.12444			0.144473
$816$	−39.5061	+	28.2824i	−1.38299	+	0.990082i
$817$		−	8.99869i		−	0.314824i
$818$	5.34906	+	8.76326i	0.187025	+	0.306400i
$819$		0			0
$820$	5.48528	−	10.6729i	0.191554	−	0.372715i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$	0.797521	−	0.486803i	0.0278167	−	0.0169792i
$823$			32.6292i			1.13738i	0.822551	+	0.568692i	$0.192550\pi$
$823$			32.6292i			1.13738i	−0.822551	+	0.568692i	$0.807450\pi$
$824$	−3.19008	−	43.4495i	−0.111132	−	1.51364i
$825$		−	21.7248i		−	0.756359i
$826$		0			0
$827$			17.8930i			0.622199i	0.950377	+	0.311100i	$0.100697\pi$
$827$			17.8930i			0.622199i	−0.950377	+	0.311100i	$0.899303\pi$
$828$	55.8701	+	28.7140i	1.94162	+	0.997881i
$829$			4.25265i			0.147700i	0.997269	+	0.0738502i	$0.0235287\pi$
$829$			4.25265i			0.147700i	−0.997269	+	0.0738502i	$0.976471\pi$
$830$	3.44365	+	5.64167i	0.119531	+	0.195825i
$831$	−65.7368			−2.28038
$832$	−3.05325	−	20.6808i	−0.105852	−	0.716979i
$833$		0			0
$834$	5.87868	−	3.58832i	0.203562	−	0.124253i
$835$			22.5667i			0.780952i
$836$	4.18111	+	2.14885i	0.144607	+	0.0743196i
$837$	−29.6569			−1.02509
$838$	−19.9546	+	12.1802i	−0.689321	+	0.420758i
$839$	−53.9108			−1.86121			−0.930603	−	0.366029i	$-0.880717\pi$
$839$	−53.9108			−1.86121			−0.930603	+	0.366029i	$0.880717\pi$
$840$		0			0
$841$	−27.6274			−0.952670
$842$	−7.82843	+	4.77844i	−0.269785	+	0.164676i
$843$	71.8432			2.47441
$844$	28.3848	+	14.5882i	0.977044	+	0.502145i
$845$		−	6.68006i		−	0.229801i
$846$	−29.0176	+	17.7122i	−0.997646	+	0.608959i
$847$		0			0
$848$	15.1005	+	21.0930i	0.518553	+	0.724338i
$849$	−32.7279			−1.12322
$850$	−12.5834	−	20.6152i	−0.431608	−	0.707095i
$851$		−	28.4612i		−	0.975637i
$852$		0			0
$853$			3.61859i			0.123898i	0.998079	+	0.0619492i	$0.0197317\pi$
$853$			3.61859i			0.123898i	−0.998079	+	0.0619492i	$0.980268\pi$
$854$		0			0
$855$		−	5.38883i		−	0.184294i
$856$	−20.0711	+	1.47363i	−0.686015	+	0.0503675i
$857$		−	39.6996i		−	1.35611i	−0.735010	−	0.678057i	$-0.762822\pi$
$857$		−	39.6996i		−	1.35611i	0.735010	−	0.678057i	$-0.237178\pi$
$858$	−17.8995	+	10.9258i	−0.611079	+	0.373000i
$859$	−19.7210			−0.672873			−0.336436	−	0.941706i	$-0.609222\pi$
$859$	−19.7210			−0.672873			−0.336436	+	0.941706i	$0.609222\pi$
$860$	−7.89505	+	15.3617i	−0.269219	+	0.523831i
$861$		0			0
$862$	12.6569	+	20.7355i	0.431094	+	0.706254i
$863$			18.3986i			0.626297i	0.949704	+	0.313148i	$0.101384\pi$
$863$			18.3986i			0.626297i	−0.949704	+	0.313148i	$0.898616\pi$
$864$	−20.0514	−	8.51189i	−0.682161	−	0.289580i
$865$	−22.8284			−0.776190
$866$	11.1819	+	18.3191i	0.379976	+	0.622508i
$867$	7.89505			0.268130
$868$		0			0
$869$	8.68629			0.294662
$870$	2.54416	+	4.16804i	0.0862550	+	0.141310i
$871$	−26.2947			−0.890962
$872$	1.17157	+	15.9570i	0.0396745	+	0.540374i
$873$			16.8925i			0.571723i
$874$	−5.91299	−	9.68714i	−0.200010	−	0.327672i
$875$		0			0
$876$	38.6066	+	19.8416i	1.30440	+	0.670385i
$877$	−54.4264			−1.83785			−0.918925	−	0.394433i	$-0.870941\pi$
$877$	−54.4264			−1.83785			−0.918925	+	0.394433i	$0.870941\pi$
$878$	−21.3161	+	13.0112i	−0.719382	+	0.439108i
$879$			63.3225i			2.13582i
$880$	−5.25230	−	7.33664i	−0.177055	−	0.247318i
$881$		−	15.1760i		−	0.511293i	−0.966770	−	0.255647i	$-0.917712\pi$
$881$		−	15.1760i		−	0.511293i	0.966770	−	0.255647i	$-0.0822883\pi$
$882$		0			0
$883$			4.67371i			0.157283i	0.996903	+	0.0786415i	$0.0250582\pi$
$883$			4.67371i			0.157283i	−0.996903	+	0.0786415i	$0.974942\pi$
$884$	−10.6569	+	20.7355i	−0.358429	+	0.697410i
$885$		−	26.0225i		−	0.874736i
$886$	19.6985	+	32.2717i	0.661784	+	1.08419i
$887$	17.6588			0.592925			0.296462	−	0.955045i	$-0.404193\pi$
$887$	17.6588			0.592925			0.296462	+	0.955045i	$0.404193\pi$
$888$	2.25573	+	30.7235i	0.0756973	+	1.03101i
$889$		0			0
$890$	5.24264	−	3.20009i	0.175734	−	0.107267i
$891$		−	5.74640i		−	0.192512i
$892$	−19.0603	+	37.0865i	−0.638187	+	1.24175i
$893$	6.14214			0.205539
$894$	−2.72291	+	1.66205i	−0.0910676	+	0.0555873i
$895$	−1.32138			−0.0441687
$896$		0			0
$897$	50.6274			1.69040
$898$	−48.6274	+	29.6820i	−1.62272	+	0.990500i
$899$	−9.02291			−0.300931
$900$	15.4497	−	30.0612i	0.514992	−	1.00204i
$901$		−	28.9301i		−	0.963801i
$902$	13.9449	−	8.51189i	0.464313	−	0.283415i
$903$		0			0
$904$	0.878680	+	11.9678i	0.0292245	+	0.398043i
$905$	6.54416			0.217535
$906$	10.8115	+	17.7122i	0.359187	+	0.588449i
$907$		−	23.7875i		−	0.789850i	−0.918713	−	0.394925i	$-0.870771\pi$
$907$		−	23.7875i		−	0.789850i	0.918713	−	0.394925i	$-0.129229\pi$
$908$	16.5710	−	32.2429i	0.549929	−	1.07002i
$909$		−	0.819760i		−	0.0271897i
$910$		0			0
$911$		−	43.1974i		−	1.43119i	−0.698513	−	0.715597i	$-0.746155\pi$
$911$		−	43.1974i		−	1.43119i	0.698513	−	0.715597i	$-0.253845\pi$
$912$	7.15076	+	9.98849i	0.236785	+	0.330752i
$913$			8.99869i			0.297813i
$914$	29.8492	−	18.2199i	0.987325	−	0.602659i
$915$	−38.5077			−1.27303
$916$	33.6659	+	17.3023i	1.11235	+	0.571686i
$917$		0			0
$918$	12.6569	+	20.7355i	0.417738	+	0.684373i
$919$		−	49.3014i		−	1.62630i	−0.582052	−	0.813151i	$-0.697750\pi$
$919$		−	49.3014i		−	1.62630i	0.582052	−	0.813151i	$-0.302250\pi$
$920$	1.59504	+	21.7248i	0.0525869	+	0.716244i
$921$	−28.3848			−0.935310
$922$	−20.2449	−	33.1668i	−0.666730	−	1.09229i
$923$		0			0
$924$		0			0
$925$	−15.3137			−0.503512
$926$	4.87006	+	7.97852i	0.160040	+	0.262191i
$927$	−67.9925			−2.23317
$928$	−6.10051	−	2.58969i	−0.200259	−	0.0850107i
$929$			16.7068i			0.548131i	0.961711	+	0.274065i	$0.0883685\pi$
$929$			16.7068i			0.548131i	−0.961711	+	0.274065i	$0.911632\pi$
$930$	−16.7245	−	27.3994i	−0.548416	−	0.898460i
$931$		0			0
$932$	7.09188	−	13.7990i	0.232302	−	0.452000i
$933$	12.2843			0.402169
$934$	9.06299	−	5.53201i	0.296550	−	0.181013i
$935$			10.0625i			0.329080i
$936$	−32.5380	+	2.38896i	−1.06354	+	0.0780854i
$937$		−	53.4762i		−	1.74699i	−0.486831	−	0.873496i	$-0.661847\pi$
$937$		−	53.4762i		−	1.74699i	0.486831	−	0.873496i	$-0.338153\pi$
$938$		0			0
$939$			26.8828i			0.877288i
$940$	−10.4853	−	5.38883i	−0.341992	−	0.175764i
$941$			8.10201i			0.264118i	0.991242	+	0.132059i	$0.0421588\pi$
$941$			8.10201i			0.264118i	−0.991242	+	0.132059i	$0.957841\pi$
$942$	−40.5147	−	66.3745i	−1.32004	−	2.16260i
$943$	−39.4421			−1.28441
$944$	20.5586	+	28.7172i	0.669126	+	0.934665i
$945$		0			0
$946$	−20.0711	+	12.2513i	−0.652567	+	0.398324i
$947$			42.3342i			1.37568i	0.725864	+	0.687838i	$0.241440\pi$
$947$			42.3342i			1.37568i	−0.725864	+	0.687838i	$0.758560\pi$
$948$	20.1882	+	10.3756i	0.655682	+	0.336983i
$949$	20.8284			0.676119
$950$	−5.21222	+	3.18152i	−0.169107	+	0.103222i
$951$	61.2253			1.98537
$952$		0			0
$953$	37.6569			1.21983			0.609913	−	0.792469i	$-0.291205\pi$
$953$	37.6569			1.21983			0.609913	+	0.792469i	$0.291205\pi$
$954$	34.5563	−	21.0930i	1.11880	−	0.682913i
$955$	−21.7832			−0.704889
$956$	20.0711	+	10.3154i	0.649145	+	0.333623i
$957$			6.64820i			0.214906i
$958$	−24.0390	+	14.6733i	−0.776664	+	0.474072i
$959$		0			0
$960$	−3.44365	−	23.3252i	−0.111143	−	0.752817i
$961$	28.3137			0.913345
$962$	7.70154	+	12.6173i	0.248308	+	0.406798i
$963$			31.4084i			1.01212i
$964$	15.3063	+	7.86657i	0.492983	+	0.253365i
$965$		−	18.8490i		−	0.606771i
$966$		0			0
$967$			17.8930i			0.575399i	0.957721	+	0.287699i	$0.0928904\pi$
$967$			17.8930i			0.575399i	−0.957721	+	0.287699i	$0.907110\pi$
$968$	1.37868	+	18.7779i	0.0443124	+	0.603544i
$969$		−	13.6997i		−	0.440097i
$970$	−5.00000	+	3.05198i	−0.160540	+	0.0979931i
$971$	21.9768			0.705268			0.352634	−	0.935761i	$-0.385286\pi$
$971$	21.9768			0.705268			0.352634	+	0.935761i	$0.385286\pi$
$972$	17.4252	−	33.9050i	0.558914	−	1.08750i
$973$		0			0
$974$	29.2843	+	47.9759i	0.938329	+	1.53725i
$975$		−	27.2404i		−	0.872391i
$976$	42.4953	−	30.4224i	1.36024	−	0.973796i
$977$	54.3848			1.73992			0.869962	−	0.493120i	$-0.164143\pi$
$977$	54.3848			1.73992			0.869962	+	0.493120i	$0.164143\pi$
$978$	7.64486	+	12.5244i	0.244456	+	0.400487i
$979$	8.36223			0.267258
$980$		0			0
$981$	24.9706			0.797249
$982$	11.7574	+	19.2619i	0.375192	+	0.614671i
$983$	−33.9962			−1.08431			−0.542156	−	0.840278i	$-0.682392\pi$
$983$	−33.9962			−1.08431			−0.542156	+	0.840278i	$0.682392\pi$
$984$	42.5772	−	3.12603i	1.35731	−	0.0996543i
$985$		−	2.16478i		−	0.0689758i
$986$	3.85077	+	6.30864i	0.122633	+	0.200908i
$987$		0			0
$988$	5.24264	+	2.69442i	0.166791	+	0.0857208i
$989$	56.7696			1.80517
$990$	−12.0195	+	7.33664i	−0.382004	+	0.233174i
$991$		−	21.8516i		−	0.694137i	−0.937840	−	0.347069i	$-0.887177\pi$
$991$		−	21.8516i		−	0.694137i	0.937840	−	0.347069i	$-0.112823\pi$
$992$	40.1027	+	17.0238i	1.27326	+	0.540506i
$993$		−	10.3756i		−	0.329259i
$994$		0			0
$995$			23.5780i			0.747473i
$996$	−10.7487	+	20.9143i	−0.340587	+	0.662694i
$997$			6.68006i			0.211560i	0.994390	+	0.105780i	$0.0337339\pi$
$997$			6.68006i			0.211560i	−0.994390	+	0.105780i	$0.966266\pi$
$998$	−13.5563	−	22.2091i	−0.429119	−	0.703017i
$999$	15.4031			0.487332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.d.c.195.3	yes	8
3.2	odd	2		1764.2.b.k.1567.6		8
4.3	odd	2	inner	196.2.d.c.195.2	yes	8
7.2	even	3		196.2.f.d.31.8		16
7.3	odd	6		196.2.f.d.19.3		16
7.4	even	3		196.2.f.d.19.4		16
7.5	odd	6		196.2.f.d.31.7		16
7.6	odd	2	inner	196.2.d.c.195.4	yes	8
8.3	odd	2		3136.2.f.i.3135.2		8
8.5	even	2		3136.2.f.i.3135.8		8
12.11	even	2		1764.2.b.k.1567.8		8
21.20	even	2		1764.2.b.k.1567.5		8
28.3	even	6		196.2.f.d.19.8		16
28.11	odd	6		196.2.f.d.19.7		16
28.19	even	6		196.2.f.d.31.4		16
28.23	odd	6		196.2.f.d.31.3		16
28.27	even	2	inner	196.2.d.c.195.1	✓	8
56.13	odd	2		3136.2.f.i.3135.1		8
56.27	even	2		3136.2.f.i.3135.7		8
84.83	odd	2		1764.2.b.k.1567.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.d.c.195.1	✓	8	28.27	even	2	inner
196.2.d.c.195.2	yes	8	4.3	odd	2	inner
196.2.d.c.195.3	yes	8	1.1	even	1	trivial
196.2.d.c.195.4	yes	8	7.6	odd	2	inner
196.2.f.d.19.3		16	7.3	odd	6
196.2.f.d.19.4		16	7.4	even	3
196.2.f.d.19.7		16	28.11	odd	6
196.2.f.d.19.8		16	28.3	even	6
196.2.f.d.31.3		16	28.23	odd	6
196.2.f.d.31.4		16	28.19	even	6
196.2.f.d.31.7		16	7.5	odd	6
196.2.f.d.31.8		16	7.2	even	3
1764.2.b.k.1567.5		8	21.20	even	2
1764.2.b.k.1567.6		8	3.2	odd	2
1764.2.b.k.1567.7		8	84.83	odd	2
1764.2.b.k.1567.8		8	12.11	even	2
3136.2.f.i.3135.1		8	56.13	odd	2
3136.2.f.i.3135.2		8	8.3	odd	2
3136.2.f.i.3135.7		8	56.27	even	2
3136.2.f.i.3135.8		8	8.5	even	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)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 0.736813i) q^{2} -2.72291 q^{3} +(0.914214 - 1.77882i) q^{4} -1.08239i q^{5} +(3.28684 - 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +4.41421 q^{9} +O(q^{10})\)	\(q+(-1.20711 + 0.736813i) q^{2} -2.72291 q^{3} +(0.914214 - 1.77882i) q^{4} -1.08239i q^{5} +(3.28684 - 2.00627i) q^{6} +(0.207107 + 2.82083i) q^{8} +4.41421 q^{9} +(0.797521 + 1.30656i) q^{10} +2.08402i q^{11} +(-2.48932 + 4.84357i) q^{12} +2.61313i q^{13} +2.94725i q^{15} +(-2.32843 - 3.25245i) q^{16} +4.46088i q^{17} +(-5.32843 + 3.25245i) q^{18} +1.12786 q^{19} +(-1.92538 - 0.989538i) q^{20} +(-1.53553 - 2.51564i) q^{22} +7.11529i q^{23} +(-0.563932 - 7.68087i) q^{24} +3.82843 q^{25} +(-1.92538 - 3.15432i) q^{26} -3.85077 q^{27} -1.17157 q^{29} +(-2.17157 - 3.55765i) q^{30} +7.70154 q^{31} +(5.20711 + 2.21044i) q^{32} -5.67459i q^{33} +(-3.28684 - 5.38476i) q^{34} +(4.03553 - 7.85211i) q^{36} -4.00000 q^{37} +(-1.36145 + 0.831025i) q^{38} -7.11529i q^{39} +(3.05325 - 0.224171i) q^{40} +5.54328i q^{41} -7.97852i q^{43} +(3.70711 + 1.90524i) q^{44} -4.77791i q^{45} +(-5.24264 - 8.58892i) q^{46} +5.44581 q^{47} +(6.34009 + 8.85611i) q^{48} +(-4.62132 + 2.82083i) q^{50} -12.1466i q^{51} +(4.64829 + 2.38896i) q^{52} -6.48528 q^{53} +(4.64829 - 2.83730i) q^{54} +2.25573 q^{55} -3.07107 q^{57} +(1.41421 - 0.863230i) q^{58} -8.82940 q^{59} +(5.24264 + 2.69442i) q^{60} +13.0656i q^{61} +(-9.29658 + 5.67459i) q^{62} +(-7.91421 + 1.16843i) q^{64} +2.82843 q^{65} +(4.18111 + 6.84984i) q^{66} +10.0625i q^{67} +(7.93513 + 4.07820i) q^{68} -19.3743i q^{69} +(0.914214 + 12.4518i) q^{72} -7.97069i q^{73} +(4.82843 - 2.94725i) q^{74} -10.4244 q^{75} +(1.03111 - 2.00627i) q^{76} +(5.24264 + 8.58892i) q^{78} -4.16804i q^{79} +(-3.52043 + 2.52027i) q^{80} -2.75736 q^{81} +(-4.08436 - 6.69133i) q^{82} +4.31795 q^{83} +4.82843 q^{85} +(5.87868 + 9.63093i) q^{86} +3.19008 q^{87} +(-5.87868 + 0.431615i) q^{88} -4.01254i q^{89} +(3.52043 + 5.76745i) q^{90} +(12.6569 + 6.50490i) q^{92} -20.9706 q^{93} +(-6.57368 + 4.01254i) q^{94} -1.22079i q^{95} +(-14.1785 - 6.01882i) q^{96} +3.82683i q^{97} +9.19932i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) 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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