LMFDB - Embedded newform 968.2.c.h.485.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(485,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("968.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.c (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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024 $ x^20 - x^18 - 2x^16 - 2x^15 - 4x^14 - 4x^13 + 12x^12 + 16x^11 + 32x^9 + 48x^8 - 32x^7 - 64x^6 - 64x^5 - 128x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			485.19
Root			$1.39771 + 0.215430i$ of defining polynomial
Character	$\chi$	$=$	968.485
Dual form			968.2.c.h.485.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39771 - 0.215430i) q^{2} -0.868641i q^{3} +(1.90718 - 0.602216i) q^{4} +3.67418i q^{5} +(-0.187131 - 1.21411i) q^{6} -1.19528 q^{7} +(2.53595 - 1.25259i) q^{8} +2.24546 q^{9} +(0.791527 + 5.13543i) q^{10} +(-0.523110 - 1.65665i) q^{12} +3.98051i q^{13} +(-1.67065 + 0.257499i) q^{14} +3.19154 q^{15} +(3.27467 - 2.29707i) q^{16} -3.17983 q^{17} +(3.13850 - 0.483739i) q^{18} +4.30609i q^{19} +(2.21265 + 7.00731i) q^{20} +1.03827i q^{21} +2.46096 q^{23} +(-1.08805 - 2.20283i) q^{24} -8.49956 q^{25} +(0.857521 + 5.56360i) q^{26} -4.55642i q^{27} +(-2.27962 + 0.719818i) q^{28} -3.84030i q^{29} +(4.46084 - 0.687553i) q^{30} +9.14861 q^{31} +(4.08218 - 3.91610i) q^{32} +(-4.44448 + 0.685031i) q^{34} -4.39167i q^{35} +(4.28250 - 1.35225i) q^{36} +5.33037i q^{37} +(0.927661 + 6.01866i) q^{38} +3.45764 q^{39} +(4.60222 + 9.31751i) q^{40} +0.533028 q^{41} +(0.223674 + 1.45120i) q^{42} -6.51729i q^{43} +8.25022i q^{45} +(3.43970 - 0.530164i) q^{46} +0.358873 q^{47} +(-1.99533 - 2.84451i) q^{48} -5.57130 q^{49} +(-11.8799 + 1.83106i) q^{50} +2.76213i q^{51} +(2.39713 + 7.59156i) q^{52} +2.42387i q^{53} +(-0.981589 - 6.36855i) q^{54} +(-3.03117 + 1.49719i) q^{56} +3.74045 q^{57} +(-0.827315 - 5.36762i) q^{58} -0.595680i q^{59} +(6.08684 - 1.92200i) q^{60} -7.28931i q^{61} +(12.7871 - 1.97088i) q^{62} -2.68396 q^{63} +(4.86206 - 6.35298i) q^{64} -14.6251 q^{65} -11.2692i q^{67} +(-6.06451 + 1.91495i) q^{68} -2.13769i q^{69} +(-0.946097 - 6.13828i) q^{70} +5.58709 q^{71} +(5.69437 - 2.81264i) q^{72} -2.67169 q^{73} +(1.14832 + 7.45030i) q^{74} +7.38307i q^{75} +(2.59320 + 8.21250i) q^{76} +(4.83277 - 0.744878i) q^{78} -11.5000 q^{79} +(8.43983 + 12.0317i) q^{80} +2.77849 q^{81} +(0.745018 - 0.114830i) q^{82} +1.00283i q^{83} +(0.625263 + 1.98017i) q^{84} -11.6833i q^{85} +(-1.40402 - 9.10928i) q^{86} -3.33584 q^{87} +13.6469 q^{89} +(1.77734 + 11.5314i) q^{90} -4.75783i q^{91} +(4.69349 - 1.48203i) q^{92} -7.94686i q^{93} +(0.501600 - 0.0773120i) q^{94} -15.8213 q^{95} +(-3.40168 - 3.54595i) q^{96} -5.95068 q^{97} +(-7.78706 + 1.20022i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) $ 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	1.39771	−	0.215430i	0.988329	−	0.152332i
$2$	1.39771	−	0.215430i	0.988329	−	0.152332i
$3$		−	0.868641i		−	0.501510i	−0.968051	−	0.250755i	$-0.919321\pi$
$3$		−	0.868641i		−	0.501510i	0.968051	−	0.250755i	$-0.0806789\pi$
$4$	1.90718	−	0.602216i	0.953590	−	0.301108i
$5$			3.67418i			1.64314i	0.570107	+	0.821571i	$0.306902\pi$
$5$			3.67418i			1.64314i	−0.570107	+	0.821571i	$0.693098\pi$
$6$	−0.187131	−	1.21411i	−0.0763960	−	0.495657i
$7$	−1.19528			−0.451774			−0.225887	−	0.974154i	$-0.572528\pi$
$7$	−1.19528			−0.451774			−0.225887	+	0.974154i	$0.572528\pi$
$8$	2.53595	−	1.25259i	0.896593	−	0.442856i
$9$	2.24546			0.748488
$10$	0.791527	+	5.13543i	0.250303	+	1.62396i
$11$		0			0
$11$		0			0
$12$	−0.523110	−	1.65665i	−0.151009	−	0.478235i
$13$			3.98051i			1.10400i	0.833845	+	0.551998i	$0.186134\pi$
$13$			3.98051i			1.10400i	−0.833845	+	0.551998i	$0.813866\pi$
$14$	−1.67065	+	0.257499i	−0.446501	+	0.0688195i
$15$	3.19154			0.824052
$16$	3.27467	−	2.29707i	0.818668	−	0.574267i
$17$	−3.17983			−0.771223			−0.385611	−	0.922661i	$-0.626009\pi$
$17$	−3.17983			−0.771223			−0.385611	+	0.922661i	$0.626009\pi$
$18$	3.13850	−	0.483739i	0.739752	−	0.114018i
$19$			4.30609i			0.987886i	0.869494	+	0.493943i	$0.164445\pi$
$19$			4.30609i			0.987886i	−0.869494	+	0.493943i	$0.835555\pi$
$20$	2.21265	+	7.00731i	0.494763	+	1.56688i
$21$			1.03827i			0.226569i
$22$		0			0
$23$	2.46096			0.513145			0.256573	−	0.966525i	$-0.417407\pi$
$23$	2.46096			0.513145			0.256573	+	0.966525i	$0.417407\pi$
$24$	−1.08805	−	2.20283i	−0.222097	−	0.449650i
$25$	−8.49956			−1.69991
$26$	0.857521	+	5.56360i	0.168174	+	1.09111i
$27$		−	4.55642i		−	0.876884i
$28$	−2.27962	+	0.719818i	−0.430807	+	0.136033i
$29$		−	3.84030i		−	0.713126i	−0.934271	−	0.356563i	$-0.883949\pi$
$29$		−	3.84030i		−	0.713126i	0.934271	−	0.356563i	$-0.116051\pi$
$30$	4.46084	−	0.687553i	0.814435	−	0.125529i
$31$	9.14861			1.64314			0.821570	−	0.570108i	$-0.193099\pi$
$31$	9.14861			1.64314			0.821570	+	0.570108i	$0.193099\pi$
$32$	4.08218	−	3.91610i	0.721634	−	0.692274i
$33$		0			0
$34$	−4.44448	+	0.685031i	−0.762222	+	0.117482i
$35$		−	4.39167i		−	0.742328i
$36$	4.28250	−	1.35225i	0.713750	−	0.225376i
$37$			5.33037i			0.876307i	0.898900	+	0.438153i	$0.144367\pi$
$37$			5.33037i			0.876307i	−0.898900	+	0.438153i	$0.855633\pi$
$38$	0.927661	+	6.01866i	0.150486	+	0.976356i
$39$	3.45764			0.553665
$40$	4.60222	+	9.31751i	0.727675	+	1.47323i
$41$	0.533028			0.0832450			0.0416225	−	0.999133i	$-0.486747\pi$
$41$	0.533028			0.0832450			0.0416225	+	0.999133i	$0.486747\pi$
$42$	0.223674	+	1.45120i	0.0345137	+	0.223925i
$43$		−	6.51729i		−	0.993878i	−0.867785	−	0.496939i	$-0.834457\pi$
$43$		−	6.51729i		−	0.993878i	0.867785	−	0.496939i	$-0.165543\pi$
$44$		0			0
$45$			8.25022i			1.22987i
$46$	3.43970	−	0.530164i	0.507157	−	0.0781684i
$47$	0.358873			0.0523471			0.0261735	−	0.999657i	$-0.491668\pi$
$47$	0.358873			0.0523471			0.0261735	+	0.999657i	$0.491668\pi$
$48$	−1.99533	−	2.84451i	−0.288001	−	0.410570i
$49$	−5.57130			−0.795900
$50$	−11.8799	+	1.83106i	−1.68007	+	0.258951i
$51$			2.76213i			0.386776i
$52$	2.39713	+	7.59156i	0.332422	+	1.05276i
$53$			2.42387i			0.332944i	0.986046	+	0.166472i	$0.0532375\pi$
$53$			2.42387i			0.332944i	−0.986046	+	0.166472i	$0.946762\pi$
$54$	−0.981589	−	6.36855i	−0.133577	−	0.866651i
$55$		0			0
$56$	−3.03117	+	1.49719i	−0.405057	+	0.200071i
$57$	3.74045			0.495435
$58$	−0.827315	−	5.36762i	−0.108632	−	0.704803i
$59$		−	0.595680i		−	0.0775510i	−0.999248	−	0.0387755i	$-0.987654\pi$
$59$		−	0.595680i		−	0.0775510i	0.999248	−	0.0387755i	$-0.0123457\pi$
$60$	6.08684	−	1.92200i	0.785808	−	0.248129i
$61$		−	7.28931i		−	0.933301i	−0.884442	−	0.466650i	$-0.845461\pi$
$61$		−	7.28931i		−	0.933301i	0.884442	−	0.466650i	$-0.154539\pi$
$62$	12.7871	−	1.97088i	1.62396	−	0.250302i
$63$	−2.68396			−0.338147
$64$	4.86206	−	6.35298i	0.607757	−	0.794123i
$65$	−14.6251			−1.81402
$66$		0			0
$67$		−	11.2692i		−	1.37675i	−0.725353	−	0.688377i	$-0.758323\pi$
$67$		−	11.2692i		−	1.37675i	0.725353	−	0.688377i	$-0.241677\pi$
$68$	−6.06451	+	1.91495i	−0.735430	+	0.232221i
$69$		−	2.13769i		−	0.257348i
$70$	−0.946097	−	6.13828i	−0.113080	−	0.733665i
$71$	5.58709			0.663066			0.331533	−	0.943444i	$-0.392434\pi$
$71$	5.58709			0.663066			0.331533	+	0.943444i	$0.392434\pi$
$72$	5.69437	−	2.81264i	0.671088	−	0.331472i
$73$	−2.67169			−0.312698			−0.156349	−	0.987702i	$-0.549972\pi$
$73$	−2.67169			−0.312698			−0.156349	+	0.987702i	$0.549972\pi$
$74$	1.14832	+	7.45030i	0.133489	+	0.866080i
$75$			7.38307i			0.852524i
$76$	2.59320	+	8.21250i	0.297460	+	0.942038i
$77$		0			0
$78$	4.83277	−	0.744878i	0.547204	−	0.0843408i
$79$	−11.5000			−1.29385			−0.646925	−	0.762553i	$-0.723945\pi$
$79$	−11.5000			−1.29385			−0.646925	+	0.762553i	$0.723945\pi$
$80$	8.43983	+	12.0317i	0.943602	+	1.34519i
$81$	2.77849			0.308721
$82$	0.745018	−	0.114830i	0.0822735	−	0.0126809i
$83$			1.00283i			0.110075i	0.998484	+	0.0550376i	$0.0175279\pi$
$83$			1.00283i			0.110075i	−0.998484	+	0.0550376i	$0.982472\pi$
$84$	0.625263	+	1.98017i	0.0682218	+	0.216054i
$85$		−	11.6833i		−	1.26723i
$86$	−1.40402	−	9.10928i	−0.151399	−	0.982279i
$87$	−3.33584			−0.357640
$88$		0			0
$89$	13.6469			1.44657			0.723283	−	0.690551i	$-0.242632\pi$
$89$	13.6469			1.44657			0.723283	+	0.690551i	$0.242632\pi$
$90$	1.77734	+	11.5314i	0.187348	+	1.21552i
$91$		−	4.75783i		−	0.498757i
$92$	4.69349	−	1.48203i	0.489330	−	0.154512i
$93$		−	7.94686i		−	0.824051i
$94$	0.501600	−	0.0773120i	0.0517361	−	0.00797412i
$95$	−15.8213			−1.62324
$96$	−3.40168	−	3.54595i	−0.347183	−	0.361907i
$97$	−5.95068			−0.604200			−0.302100	−	0.953276i	$-0.597688\pi$
$97$	−5.95068			−0.604200			−0.302100	+	0.953276i	$0.597688\pi$
$98$	−7.78706	+	1.20022i	−0.786612	+	0.121241i
$99$		0			0
$100$	−16.2102	+	5.11857i	−1.62102	+	0.511857i
$101$		−	5.97512i		−	0.594547i	−0.954792	−	0.297273i	$-0.903923\pi$
$101$		−	5.97512i		−	0.594547i	0.954792	−	0.297273i	$-0.0960773\pi$
$102$	0.595046	+	3.86066i	0.0589183	+	0.382262i
$103$	−3.92564			−0.386805			−0.193402	−	0.981120i	$-0.561952\pi$
$103$	−3.92564			−0.386805			−0.193402	+	0.981120i	$0.561952\pi$
$104$	4.98594	+	10.0944i	0.488911	+	0.989835i
$105$	−3.81479			−0.372285
$106$	0.522173	+	3.38786i	0.0507180	+	0.329058i
$107$		−	12.8109i		−	1.23847i	−0.785205	−	0.619236i	$-0.787442\pi$
$107$		−	12.8109i		−	1.23847i	0.785205	−	0.619236i	$-0.212558\pi$
$108$	−2.74395	−	8.68992i	−0.264037	−	0.836188i
$109$		−	5.65346i		−	0.541504i	−0.962649	−	0.270752i	$-0.912728\pi$
$109$		−	5.65346i		−	0.541504i	0.962649	−	0.270752i	$-0.0872723\pi$
$110$		0			0
$111$	4.63018			0.439477
$112$	−3.91415	+	2.74564i	−0.369853	+	0.259439i
$113$	−15.9988			−1.50504			−0.752520	−	0.658570i	$-0.771162\pi$
$113$	−15.9988			−1.50504			−0.752520	+	0.658570i	$0.771162\pi$
$114$	5.22806	−	0.805804i	0.489653	−	0.0754705i
$115$			9.04200i			0.843170i
$116$	−2.31269	−	7.32414i	−0.214728	−	0.680029i
$117$			8.93810i			0.826327i
$118$	−0.128327	−	0.832588i	−0.0118135	−	0.0766459i
$119$	3.80079			0.348418
$120$	8.09358	−	3.99768i	0.738839	−	0.364936i
$121$		0			0
$122$	−1.57033	−	10.1883i	−0.142171	−	0.922408i
$123$		−	0.463010i		−	0.0417482i
$124$	17.4481	−	5.50944i	1.56688	−	0.494762i
$125$		−	12.8580i		−	1.15006i
$126$	−3.75139	+	0.578205i	−0.334201	+	0.0515106i
$127$	9.25691			0.821418			0.410709	−	0.911766i	$-0.365281\pi$
$127$	9.25691			0.821418			0.410709	+	0.911766i	$0.365281\pi$
$128$	5.42712	−	9.92705i	0.479694	−	0.877436i
$129$	−5.66119			−0.498440
$130$	−20.4416	+	3.15068i	−1.79285	+	0.276333i
$131$			13.3281i			1.16448i	0.813016	+	0.582241i	$0.197824\pi$
$131$			13.3281i			1.16448i	−0.813016	+	0.582241i	$0.802176\pi$
$132$		0			0
$133$		−	5.14699i		−	0.446301i
$134$	−2.42773	−	15.7511i	−0.209724	−	1.36069i
$135$	16.7411			1.44084
$136$	−8.06389	+	3.98301i	−0.691473	+	0.341541i
$137$	−9.70889			−0.829487			−0.414743	−	0.909938i	$-0.636129\pi$
$137$	−9.70889			−0.829487			−0.414743	+	0.909938i	$0.636129\pi$
$138$	−0.460522	−	2.98787i	−0.0392022	−	0.254344i
$139$		−	22.2550i		−	1.88764i	−0.330458	−	0.943821i	$-0.607203\pi$
$139$		−	22.2550i		−	1.88764i	0.330458	−	0.943821i	$-0.392797\pi$
$140$	−2.64474	−	8.37571i	−0.223521	−	0.707877i
$141$		−	0.311732i		−	0.0262526i
$142$	7.80913	−	1.20363i	0.655328	−	0.101006i
$143$		0			0
$144$	7.35315	−	5.15798i	0.612763	−	0.429832i
$145$	14.1099			1.17177
$146$	−3.73424	+	0.575561i	−0.309048	+	0.0476338i
$147$			4.83946i			0.399152i
$148$	3.21003	+	10.1660i	0.263863	+	0.835638i
$149$			12.6013i			1.03234i	0.856487	+	0.516169i	$0.172642\pi$
$149$			12.6013i			1.03234i	−0.856487	+	0.516169i	$0.827358\pi$
$150$	1.59053	+	10.3194i	0.129866	+	0.842574i
$151$	−15.1664			−1.23423			−0.617113	−	0.786875i	$-0.711698\pi$
$151$	−15.1664			−1.23423			−0.617113	+	0.786875i	$0.711698\pi$
$152$	5.39375	+	10.9200i	0.437491	+	0.885731i
$153$	−7.14020			−0.577251
$154$		0			0
$155$			33.6136i			2.69991i
$156$	6.59434	−	2.08225i	0.527970	−	0.166713i
$157$			1.52663i			0.121838i	0.998143	+	0.0609191i	$0.0194032\pi$
$157$			1.52663i			0.121838i	−0.998143	+	0.0609191i	$0.980597\pi$
$158$	−16.0736	+	2.47744i	−1.27875	+	0.197095i
$159$	2.10547			0.166975
$160$	14.3884	+	14.9986i	1.13750	+	1.18575i
$161$	−2.94154			−0.231826
$162$	3.88352	−	0.598570i	0.305118	−	0.0470281i
$163$		−	15.5362i		−	1.21689i	−0.793596	−	0.608444i	$-0.791794\pi$
$163$		−	15.5362i		−	1.21689i	0.793596	−	0.608444i	$-0.208206\pi$
$164$	1.01658	−	0.320998i	0.0793816	−	0.0250657i
$165$		0			0
$166$	0.216040	+	1.40167i	0.0167679	+	0.108791i
$167$	−8.39343			−0.649503			−0.324752	−	0.945799i	$-0.605281\pi$
$167$	−8.39343			−0.649503			−0.324752	+	0.945799i	$0.605281\pi$
$168$	1.30052	+	2.63300i	0.100338	+	0.203140i
$169$	−2.84450			−0.218808
$170$	−2.51692	−	16.3298i	−0.193039	−	1.25244i
$171$			9.66917i			0.739420i
$172$	−3.92482	−	12.4297i	−0.299265	−	0.947752i
$173$			24.8624i			1.89025i	0.326707	+	0.945126i	$0.394061\pi$
$173$			24.8624i			1.89025i	−0.326707	+	0.945126i	$0.605939\pi$
$174$	−4.66254	+	0.718639i	−0.353466	+	0.0544799i
$175$	10.1594			0.767976
$176$		0			0
$177$	−0.517432			−0.0388926
$178$	19.0744	−	2.93994i	1.42968	−	0.220358i
$179$			16.4860i			1.23222i	0.787660	+	0.616110i	$0.211292\pi$
$179$			16.4860i			1.23222i	−0.787660	+	0.616110i	$0.788708\pi$
$180$	4.96842	+	15.7347i	0.370324	+	1.17279i
$181$		−	9.17906i		−	0.682274i	−0.940014	−	0.341137i	$-0.889188\pi$
$181$		−	9.17906i		−	0.682274i	0.940014	−	0.341137i	$-0.110812\pi$
$182$	−1.02498	−	6.65007i	−0.0759765	−	0.492936i
$183$	−6.33179			−0.468060
$184$	6.24086	−	3.08256i	0.460082	−	0.227250i
$185$	−19.5847			−1.43990
$186$	−1.71199	−	11.1074i	−0.125529	−	0.814434i
$187$		0			0
$188$	0.684436	−	0.216119i	0.0499176	−	0.0157621i
$189$			5.44621i			0.396153i
$190$	−22.1136	+	3.40839i	−1.60429	+	0.247270i
$191$	−2.46982			−0.178710			−0.0893550	−	0.996000i	$-0.528481\pi$
$191$	−2.46982			−0.178710			−0.0893550	+	0.996000i	$0.528481\pi$
$192$	−5.51846	−	4.22338i	−0.398261	−	0.304796i
$193$	−10.0062			−0.720259			−0.360130	−	0.932902i	$-0.617268\pi$
$193$	−10.0062			−0.720259			−0.360130	+	0.932902i	$0.617268\pi$
$194$	−8.31732	+	1.28195i	−0.597149	+	0.0920389i
$195$			12.7040i			0.909750i
$196$	−10.6255	+	3.35513i	−0.758963	+	0.239652i
$197$		−	11.7936i		−	0.840260i	−0.907464	−	0.420130i	$-0.861985\pi$
$197$		−	11.7936i		−	0.840260i	0.907464	−	0.420130i	$-0.138015\pi$
$198$		0			0
$199$	−14.7867			−1.04820			−0.524101	−	0.851656i	$-0.675598\pi$
$199$	−14.7867			−1.04820			−0.524101	+	0.851656i	$0.675598\pi$
$200$	−21.5544	+	10.6464i	−1.52413	+	0.752817i
$201$	−9.78891			−0.690456
$202$	−1.28722	−	8.35148i	−0.0905684	−	0.587608i
$203$			4.59024i			0.322171i
$204$	1.66340	+	5.26789i	0.116461	+	0.368826i
$205$			1.95844i			0.136783i
$206$	−5.48690	+	0.845699i	−0.382290	+	0.0589227i
$207$	5.52599			0.384083
$208$	9.14352	+	13.0349i	0.633989	+	0.903806i
$209$		0			0
$210$	−5.33196	+	0.821819i	−0.367940	+	0.0567109i
$211$			8.50622i			0.585593i	0.956175	+	0.292796i	$0.0945858\pi$
$211$			8.50622i			0.585593i	−0.956175	+	0.292796i	$0.905414\pi$
$212$	1.45969	+	4.62275i	0.100252	+	0.317492i
$213$		−	4.85318i		−	0.332534i
$214$	−2.75984	−	17.9058i	−0.188659	−	1.22402i
$215$	23.9457			1.63308
$216$	−5.70731	−	11.5549i	−0.388334	−	0.786208i
$217$	−10.9352			−0.742327
$218$	−1.21792	−	7.90190i	−0.0824882	−	0.535184i
$219$			2.32074i			0.156821i
$220$		0			0
$221$		−	12.6574i		−	0.851427i
$222$	6.47164	−	0.997478i	0.434348	−	0.0669463i
$223$	5.02295			0.336361			0.168181	−	0.985756i	$-0.446211\pi$
$223$	5.02295			0.336361			0.168181	+	0.985756i	$0.446211\pi$
$224$	−4.87935	+	4.68083i	−0.326015	+	0.312751i
$225$	−19.0855			−1.27236
$226$	−22.3616	+	3.44661i	−1.48747	+	0.229265i
$227$			18.0726i			1.19952i	0.800179	+	0.599761i	$0.204738\pi$
$227$			18.0726i			1.19952i	−0.800179	+	0.599761i	$0.795262\pi$
$228$	7.13371	−	2.25256i	0.472442	−	0.149179i
$229$		−	3.98259i		−	0.263177i	−0.991304	−	0.131589i	$-0.957992\pi$
$229$		−	3.98259i		−	0.263177i	0.991304	−	0.131589i	$-0.0420078\pi$
$230$	1.94791	+	12.6381i	0.128442	+	0.833330i
$231$		0			0
$232$	−4.81031	−	9.73880i	−0.315812	−	0.639383i
$233$	12.2853			0.804839			0.402420	−	0.915455i	$-0.368169\pi$
$233$	12.2853			0.804839			0.402420	+	0.915455i	$0.368169\pi$
$234$	1.92553	+	12.4929i	0.125876	+	0.816684i
$235$			1.31856i			0.0860136i
$236$	−0.358728	−	1.13607i	−0.0233512	−	0.0739518i
$237$			9.98937i			0.648879i
$238$	5.31240	−	0.818804i	0.344352	−	0.0530752i
$239$	20.9461			1.35489			0.677446	−	0.735572i	$-0.263087\pi$
$239$	20.9461			1.35489			0.677446	+	0.735572i	$0.263087\pi$
$240$	10.4512	−	7.33119i	0.674625	−	0.473226i
$241$	17.4490			1.12399			0.561996	−	0.827140i	$-0.310034\pi$
$241$	17.4490			1.12399			0.561996	+	0.827140i	$0.310034\pi$
$242$		0			0
$243$		−	16.0828i		−	1.03171i
$244$	−4.38974	−	13.9020i	−0.281024	−	0.889986i
$245$		−	20.4699i		−	1.30778i
$246$	−0.0997461	−	0.647153i	−0.00635958	−	0.0412610i
$247$	−17.1405			−1.09062
$248$	23.2004	−	11.4594i	1.47323	−	0.727674i
$249$	0.871101			0.0552038
$250$	−2.77000	−	17.9718i	−0.175190	−	1.13663i
$251$			5.95827i			0.376083i	0.982161	+	0.188041i	$0.0602139\pi$
$251$			5.95827i			0.376083i	−0.982161	+	0.188041i	$0.939786\pi$
$252$	−5.11879	+	1.61632i	−0.322454	+	0.101819i
$253$		0			0
$254$	12.9385	−	1.99421i	0.811832	−	0.125128i
$255$	−10.1486			−0.635528
$256$	5.44695	−	15.0443i	0.340434	−	0.940268i
$257$	−14.1682			−0.883789			−0.441894	−	0.897067i	$-0.645693\pi$
$257$	−14.1682			−0.883789			−0.441894	+	0.897067i	$0.645693\pi$
$258$	−7.91270	+	1.21959i	−0.492623	+	0.0759283i
$259$		−	6.37129i		−	0.395893i
$260$	−27.8927	+	8.80748i	−1.72983	+	0.546217i
$261$		−	8.62325i		−	0.533766i
$262$	2.87127	+	18.6288i	0.177388	+	1.15089i
$263$	11.0152			0.679225			0.339612	−	0.940566i	$-0.389704\pi$
$263$	11.0152			0.679225			0.339612	+	0.940566i	$0.389704\pi$
$264$		0			0
$265$	−8.90572			−0.547074
$266$	−1.10882	−	7.19400i	−0.0679858	−	0.441092i
$267$		−	11.8542i		−	0.725468i
$268$	−6.78651	−	21.4924i	−0.414552	−	1.31286i
$269$			2.48329i			0.151409i	0.997130	+	0.0757044i	$0.0241206\pi$
$269$			2.48329i			0.151409i	−0.997130	+	0.0757044i	$0.975879\pi$
$270$	23.3992	−	3.60653i	1.42403	−	0.219487i
$271$	0.307729			0.0186932			0.00934660	−	0.999956i	$-0.497025\pi$
$271$	0.307729			0.0186932			0.00934660	+	0.999956i	$0.497025\pi$
$272$	−10.4129	+	7.30430i	−0.631375	+	0.442888i
$273$	−4.13285			−0.250131
$274$	−13.5702	+	2.09158i	−0.819806	+	0.126357i
$275$		0			0
$276$	−1.28735	−	4.07696i	−0.0774895	−	0.245404i
$277$		−	2.50001i		−	0.150211i	−0.997176	−	0.0751056i	$-0.976071\pi$
$277$		−	2.50001i		−	0.150211i	0.997176	−	0.0751056i	$-0.0239294\pi$
$278$	−4.79438	−	31.1060i	−0.287548	−	1.86561i
$279$	20.5429			1.22987
$280$	−5.50095	−	11.1370i	−0.328744	−	0.665566i
$281$	−1.24314			−0.0741595			−0.0370798	−	0.999312i	$-0.511806\pi$
$281$	−1.24314			−0.0741595			−0.0370798	+	0.999312i	$0.511806\pi$
$282$	−0.0671564	−	0.435711i	−0.00399910	−	0.0259462i
$283$		−	13.8018i		−	0.820434i	−0.911988	−	0.410217i	$-0.865453\pi$
$283$		−	13.8018i		−	0.820434i	0.911988	−	0.410217i	$-0.134547\pi$
$284$	10.6556	−	3.36464i	0.632293	−	0.199655i
$285$			13.7431i			0.814069i
$286$		0			0
$287$	−0.637118			−0.0376079
$288$	9.16638	−	8.79345i	0.540134	−	0.518159i
$289$	−6.88867			−0.405216
$290$	19.7216	−	3.03970i	1.15809	−	0.178497i
$291$			5.16900i			0.303012i
$292$	−5.09539	+	1.60893i	−0.298185	+	0.0941557i
$293$		−	14.8846i		−	0.869566i	−0.900535	−	0.434783i	$-0.856825\pi$
$293$		−	14.8846i		−	0.869566i	0.900535	−	0.434783i	$-0.143175\pi$
$294$	1.04256	+	6.76416i	0.0608036	+	0.394494i
$295$	2.18863			0.127427
$296$	6.67674	+	13.5175i	0.388078	+	0.785690i
$297$		0			0
$298$	2.71469	+	17.6129i	0.157258	+	1.02029i
$299$			9.79588i			0.566511i
$300$	4.44620	+	14.0808i	0.256702	+	0.812958i
$301$			7.79000i			0.449008i
$302$	−21.1982	+	3.26730i	−1.21982	+	0.188012i
$303$	−5.19024			−0.298171
$304$	9.89139	+	14.1010i	0.567310	+	0.808750i
$305$	26.7822			1.53354
$306$	−9.97991	+	1.53821i	−0.570514	+	0.0879336i
$307$			8.40361i			0.479619i	0.970820	+	0.239810i	$0.0770850\pi$
$307$			8.40361i			0.479619i	−0.970820	+	0.239810i	$0.922915\pi$
$308$		0			0
$309$			3.40997i			0.193986i
$310$	7.24137	+	46.9820i	0.411282	+	2.66840i
$311$	25.6462			1.45426			0.727132	−	0.686498i	$-0.240853\pi$
$311$	25.6462			1.45426			0.727132	+	0.686498i	$0.240853\pi$
$312$	8.76839	−	4.33099i	0.496412	−	0.245194i
$313$	18.8824			1.06730			0.533648	−	0.845707i	$-0.320821\pi$
$313$	18.8824			1.06730			0.533648	+	0.845707i	$0.320821\pi$
$314$	0.328881	+	2.13378i	0.0185598	+	0.120416i
$315$		−	9.86134i		−	0.555623i
$316$	−21.9326	+	6.92548i	−1.23380	+	0.389589i
$317$		−	19.9628i		−	1.12122i	−0.828080	−	0.560611i	$-0.810566\pi$
$317$		−	19.9628i		−	1.12122i	0.828080	−	0.560611i	$-0.189434\pi$
$318$	2.94284	−	0.453581i	0.165026	−	0.0254356i
$319$		0			0
$320$	23.3420	+	17.8640i	1.30486	+	0.998631i
$321$	−11.1280			−0.621106
$322$	−4.11141	+	0.633695i	−0.229120	+	0.0353144i
$323$		−	13.6927i		−	0.761880i
$324$	5.29908	−	1.67325i	0.294393	−	0.0929584i
$325$		−	33.8326i		−	1.87670i
$326$	−3.34696	−	21.7151i	−0.185371	−	1.20269i
$327$	−4.91083			−0.271570
$328$	1.35173	−	0.667663i	0.0746368	−	0.0368655i
$329$	−0.428955			−0.0236490
$330$		0			0
$331$		−	18.8624i		−	1.03677i	−0.855147	−	0.518386i	$-0.826533\pi$
$331$		−	18.8624i		−	1.03677i	0.855147	−	0.518386i	$-0.173467\pi$
$332$	0.603922	+	1.91258i	0.0331445	+	0.104967i
$333$			11.9691i			0.655905i
$334$	−11.7316	+	1.80819i	−0.641923	+	0.0989400i
$335$	41.4051			2.26220
$336$	2.38498	+	3.39999i	0.130111	+	0.185485i
$337$	21.2837			1.15940			0.579698	−	0.814831i	$-0.303170\pi$
$337$	21.2837			1.15940			0.579698	+	0.814831i	$0.303170\pi$
$338$	−3.97578	+	0.612789i	−0.216254	+	0.0333314i
$339$			13.8972i			0.754793i
$340$	−7.03585	−	22.2821i	−0.381572	−	1.20842i
$341$		0			0
$342$	2.08303	+	13.5147i	0.112637	+	0.730791i
$343$	15.0262			0.811341
$344$	−8.16347	−	16.5275i	−0.440145	−	0.891104i
$345$	7.85425			0.422859
$346$	5.35609	+	34.7504i	0.287945	+	1.86819i
$347$		−	5.44703i		−	0.292412i	−0.989254	−	0.146206i	$-0.953294\pi$
$347$		−	5.44703i		−	0.292412i	0.989254	−	0.146206i	$-0.0467063\pi$
$348$	−6.36205	+	2.00890i	−0.341042	+	0.107688i
$349$		−	10.2084i		−	0.546446i	−0.961951	−	0.273223i	$-0.911910\pi$
$349$		−	10.2084i		−	0.546446i	0.961951	−	0.273223i	$-0.0880896\pi$
$350$	14.1998	−	2.18863i	0.759013	−	0.116987i
$351$	18.1369			0.968077
$352$		0			0
$353$	5.11121			0.272042			0.136021	−	0.990706i	$-0.456569\pi$
$353$	5.11121			0.272042			0.136021	+	0.990706i	$0.456569\pi$
$354$	−0.723220	+	0.111470i	−0.0384387	+	0.00592458i
$355$			20.5280i			1.08951i
$356$	26.0271	−	8.21837i	1.37943	−	0.435573i
$357$		−	3.30153i		−	0.174735i
$358$	3.55157	+	23.0426i	0.187706	+	1.21784i
$359$	20.9801			1.10729			0.553644	−	0.832753i	$-0.313237\pi$
$359$	20.9801			1.10729			0.553644	+	0.832753i	$0.313237\pi$
$360$	10.3341	+	20.9221i	0.544656	+	1.10269i
$361$	0.457560			0.0240821
$362$	−1.97744	−	12.8296i	−0.103932	−	0.674311i
$363$		0			0
$364$	−2.86524	−	9.07405i	−0.150180	−	0.475609i
$365$		−	9.81625i		−	0.513806i
$366$	−8.85000	+	1.36406i	−0.462597	+	0.0713004i
$367$	−31.5290			−1.64580			−0.822901	−	0.568185i	$-0.807646\pi$
$367$	−31.5290			−1.64580			−0.822901	+	0.568185i	$0.807646\pi$
$368$	8.05883	−	5.65299i	0.420096	−	0.294683i
$369$	1.19689			0.0623078
$370$	−27.3737	+	4.21913i	−1.42309	+	0.219342i
$371$		−	2.89720i		−	0.150415i
$372$	−4.78573	−	15.1561i	−0.248128	−	0.785807i
$373$			24.8244i			1.28536i	0.766136	+	0.642678i	$0.222177\pi$
$373$			24.8244i			1.28536i	−0.766136	+	0.642678i	$0.777823\pi$
$374$		0			0
$375$	−11.1690			−0.576765
$376$	0.910084	−	0.449520i	0.0469340	−	0.0231822i
$377$	15.2864			0.787288
$378$	1.17328	+	7.61221i	0.0603468	+	0.391530i
$379$		−	35.7411i		−	1.83590i	−0.396699	−	0.917949i	$-0.629844\pi$
$379$		−	35.7411i		−	1.83590i	0.396699	−	0.917949i	$-0.370156\pi$
$380$	−30.1741	+	9.52787i	−1.54790	+	0.488769i
$381$		−	8.04093i		−	0.411950i
$382$	−3.45209	+	0.532073i	−0.176624	+	0.0272232i
$383$	−19.0377			−0.972782			−0.486391	−	0.873741i	$-0.661687\pi$
$383$	−19.0377			−0.972782			−0.486391	+	0.873741i	$0.661687\pi$
$384$	−8.62305	−	4.71422i	−0.440043	−	0.240571i
$385$		0			0
$386$	−13.9857	+	2.15562i	−0.711853	+	0.109718i
$387$		−	14.6343i		−	0.743905i
$388$	−11.3490	+	3.58359i	−0.576159	+	0.181929i
$389$			32.5699i			1.65136i	0.564141	+	0.825679i	$0.309207\pi$
$389$			32.5699i			1.65136i	−0.564141	+	0.825679i	$0.690793\pi$
$390$	2.73681	+	17.7565i	0.138584	+	0.899133i
$391$	−7.82544			−0.395749
$392$	−14.1285	+	6.97854i	−0.713599	+	0.352469i
$393$	11.5773			0.584000
$394$	−2.54069	−	16.4840i	−0.127998	−	0.830453i
$395$		−	42.2530i		−	2.12598i
$396$		0			0
$397$			13.0143i			0.653167i	0.945168	+	0.326584i	$0.105897\pi$
$397$			13.0143i			0.653167i	−0.945168	+	0.326584i	$0.894103\pi$
$398$	−20.6675	+	3.18549i	−1.03597	+	0.159674i
$399$	−4.47089			−0.223824
$400$	−27.8333	+	19.5241i	−1.39166	+	0.976204i
$401$	20.5539			1.02641			0.513206	−	0.858266i	$-0.328458\pi$
$401$	20.5539			1.02641			0.513206	+	0.858266i	$0.328458\pi$
$402$	−13.6820	+	2.10882i	−0.682398	+	0.105178i
$403$			36.4162i			1.81402i
$404$	−3.59831	−	11.3956i	−0.179023	−	0.566954i
$405$			10.2087i			0.507272i
$406$	0.988874	+	6.41581i	0.0490770	+	0.318412i
$407$		0			0
$408$	3.45981	+	7.00462i	0.171286	+	0.346781i
$409$	9.86091			0.487590			0.243795	−	0.969827i	$-0.421608\pi$
$409$	9.86091			0.487590			0.243795	+	0.969827i	$0.421608\pi$
$410$	0.421906	+	2.73733i	0.0208364	+	0.135187i
$411$			8.43354i			0.415996i
$412$	−7.48690	+	2.36408i	−0.368853	+	0.116470i
$413$			0.712005i			0.0350355i
$414$	7.72373	−	1.19046i	0.379601	−	0.0585081i
$415$	−3.68458			−0.180869
$416$	15.5881	+	16.2492i	0.764268	+	0.796682i
$417$	−19.3316			−0.946671
$418$		0			0
$419$			0.169087i			0.00826046i	0.999991	+	0.00413023i	$0.00131470\pi$
$419$			0.169087i			0.00826046i	−0.999991	+	0.00413023i	$0.998685\pi$
$420$	−7.27549	+	2.29733i	−0.355007	+	0.112098i
$421$			23.5128i			1.14594i	0.819575	+	0.572972i	$0.194210\pi$
$421$			23.5128i			1.14594i	−0.819575	+	0.572972i	$0.805790\pi$
$422$	1.83249	+	11.8892i	0.0892044	+	0.578758i
$423$	0.805837			0.0391811
$424$	3.03610	+	6.14680i	0.147446	+	0.298515i
$425$	27.0272			1.31101
$426$	−1.04552	−	6.78333i	−0.0506556	−	0.328653i
$427$			8.71277i			0.421641i
$428$	−7.71490	−	24.4326i	−0.372914	−	1.18099i
$429$		0			0
$430$	33.4691	−	5.15861i	1.61402	−	0.248770i
$431$	−7.29273			−0.351278			−0.175639	−	0.984455i	$-0.556199\pi$
$431$	−7.29273			−0.351278			−0.175639	+	0.984455i	$0.556199\pi$
$432$	−10.4664	−	14.9208i	−0.503566	−	0.717877i
$433$	2.33830			0.112372			0.0561858	−	0.998420i	$-0.482106\pi$
$433$	2.33830			0.112372			0.0561858	+	0.998420i	$0.482106\pi$
$434$	−15.2842	+	2.35576i	−0.733664	+	0.113080i
$435$		−	12.2565i		−	0.587653i
$436$	−3.40461	−	10.7822i	−0.163051	−	0.516372i
$437$			10.5971i			0.506929i
$438$	0.499956	+	3.24372i	0.0238888	+	0.154991i
$439$	−1.21401			−0.0579413			−0.0289707	−	0.999580i	$-0.509223\pi$
$439$	−1.21401			−0.0579413			−0.0289707	+	0.999580i	$0.509223\pi$
$440$		0			0
$441$	−12.5102			−0.595722
$442$	−2.72677	−	17.6913i	−0.129699	−	0.841490i
$443$		−	4.61876i		−	0.219444i	−0.993962	−	0.109722i	$-0.965004\pi$
$443$		−	4.61876i		−	0.219444i	0.993962	−	0.109722i	$-0.0349961\pi$
$444$	8.83058	−	2.78837i	0.419081	−	0.132330i
$445$			50.1410i			2.37691i
$446$	7.02062	−	1.08209i	0.332436	−	0.0512385i
$447$	10.9460			0.517728
$448$	−5.81152	+	7.59360i	−0.274569	+	0.358764i
$449$	5.86880			0.276966			0.138483	−	0.990365i	$-0.455777\pi$
$449$	5.86880			0.276966			0.138483	+	0.990365i	$0.455777\pi$
$450$	−26.6759	+	4.11157i	−1.25751	+	0.193821i
$451$		0			0
$452$	−30.5126	+	9.63473i	−1.43519	+	0.453180i
$453$			13.1742i			0.618976i
$454$	3.89338	+	25.2603i	0.182725	+	1.18552i
$455$	17.4811			0.819527
$456$	9.48558	−	4.68524i	0.444203	−	0.219406i
$457$	−24.4974			−1.14594			−0.572969	−	0.819577i	$-0.694209\pi$
$457$	−24.4974			−1.14594			−0.572969	+	0.819577i	$0.694209\pi$
$458$	−0.857969	−	5.56651i	−0.0400903	−	0.260106i
$459$			14.4887i			0.676273i
$460$	5.44524	+	17.2447i	0.253885	+	0.804039i
$461$		−	6.59878i		−	0.307336i	−0.988123	−	0.153668i	$-0.950891\pi$
$461$		−	6.59878i		−	0.307336i	0.988123	−	0.153668i	$-0.0491086\pi$
$462$		0			0
$463$	−14.4202			−0.670163			−0.335081	−	0.942189i	$-0.608764\pi$
$463$	−14.4202			−0.670163			−0.335081	+	0.942189i	$0.608764\pi$
$464$	−8.82143	−	12.5757i	−0.409525	−	0.583813i
$465$	29.1982			1.35403
$466$	17.1713	−	2.64663i	0.795447	−	0.122603i
$467$			5.48879i			0.253991i	0.991903	+	0.126996i	$0.0405334\pi$
$467$			5.48879i			0.253991i	−0.991903	+	0.126996i	$0.959467\pi$
$468$	5.38267	+	17.0466i	0.248814	+	0.787978i
$469$			13.4699i			0.621982i
$470$	0.284058	+	1.84297i	0.0131026	+	0.0850098i
$471$	1.32609			0.0611031
$472$	−0.746141	−	1.51061i	−0.0343439	−	0.0695316i
$473$		0			0
$474$	2.15201	+	13.9622i	0.0988450	+	0.641307i
$475$		−	36.5999i		−	1.67932i
$476$	7.24880	−	2.28890i	0.332248	−	0.104912i
$477$			5.44271i			0.249204i
$478$	29.2766	−	4.51242i	1.33908	−	0.206393i
$479$	−29.8638			−1.36451			−0.682255	−	0.731114i	$-0.739001\pi$
$479$	−29.8638			−1.36451			−0.682255	+	0.731114i	$0.739001\pi$
$480$	13.0284	−	12.4984i	0.594664	−	0.570470i
$481$	−21.2176			−0.967440
$482$	24.3887	−	3.75904i	1.11087	−	0.171220i
$483$			2.55514i			0.116263i
$484$		0			0
$485$		−	21.8638i		−	0.992786i
$486$	−3.46471	−	22.4790i	−0.157162	−	1.01967i
$487$	−2.97753			−0.134925			−0.0674624	−	0.997722i	$-0.521490\pi$
$487$	−2.97753			−0.134925			−0.0674624	+	0.997722i	$0.521490\pi$
$488$	−9.13049	−	18.4853i	−0.413318	−	0.836790i
$489$	−13.4954			−0.610282
$490$	−4.40983	−	28.6110i	−0.199216	−	1.29251i
$491$		−	2.98055i		−	0.134511i	−0.997736	−	0.0672553i	$-0.978576\pi$
$491$		−	2.98055i		−	0.134511i	0.997736	−	0.0672553i	$-0.0214242\pi$
$492$	−0.278832	−	0.883043i	−0.0125707	−	0.0398107i
$493$			12.2115i			0.549979i
$494$	−23.9574	+	3.69257i	−1.07789	+	0.166136i
$495$		0			0
$496$	29.9587	−	21.0150i	1.34519	−	0.943601i
$497$	−6.67815			−0.299556
$498$	1.21755	−	0.187661i	0.0545595	−	0.00840930i
$499$		−	15.1943i		−	0.680191i	−0.940391	−	0.340095i	$-0.889541\pi$
$499$		−	15.1943i		−	0.680191i	0.940391	−	0.340095i	$-0.110459\pi$
$500$	−7.74330	−	24.5225i	−0.346291	−	1.09668i
$501$			7.29088i			0.325732i
$502$	1.28359	+	8.32793i	0.0572894	+	0.371694i
$503$	32.9216			1.46790			0.733951	−	0.679202i	$-0.237674\pi$
$503$	32.9216			1.46790			0.733951	+	0.679202i	$0.237674\pi$
$504$	−6.80638	+	3.36189i	−0.303180	+	0.149750i
$505$	21.9536			0.976924
$506$		0			0
$507$			2.47085i			0.109734i
$508$	17.6546	−	5.57466i	0.783296	−	0.247336i
$509$		−	13.4791i		−	0.597450i	−0.954339	−	0.298725i	$-0.903439\pi$
$509$		−	13.4791i		−	0.597450i	0.954339	−	0.298725i	$-0.0965614\pi$
$510$	−14.1847	+	2.18630i	−0.628111	+	0.0968111i
$511$	3.19342			0.141269
$512$	4.37226	−	22.2010i	0.193228	−	0.981154i
$513$	19.6204			0.866261
$514$	−19.8030	+	3.05225i	−0.873475	+	0.134629i
$515$		−	14.4235i		−	0.635575i
$516$	−10.7969	+	3.40926i	−0.475307	+	0.150084i
$517$		0			0
$518$	−1.37256	−	8.90520i	−0.0603070	−	0.391272i
$519$	21.5965			0.947980
$520$	−37.0885	+	18.3192i	−1.62644	+	0.803350i
$521$	9.30652			0.407726			0.203863	−	0.978999i	$-0.434650\pi$
$521$	9.30652			0.407726			0.203863	+	0.978999i	$0.434650\pi$
$522$	−1.85770	−	12.0528i	−0.0813095	−	0.527536i
$523$			14.3312i			0.626660i	0.949644	+	0.313330i	$0.101445\pi$
$523$			14.3312i			0.626660i	−0.949644	+	0.313330i	$0.898555\pi$
$524$	8.02640	+	25.4191i	0.350635	+	1.11044i
$525$		−	8.82484i		−	0.385148i
$526$	15.3960	−	2.37300i	0.671298	−	0.103468i
$527$	−29.0911			−1.26723
$528$		0			0
$529$	−16.9437			−0.736682
$530$	−12.4476	+	1.91856i	−0.540689	+	0.0833368i
$531$		−	1.33758i		−	0.0580459i
$532$	−3.09960	−	9.81624i	−0.134385	−	0.425588i
$533$			2.12173i			0.0919021i
$534$	−2.55376	−	16.5688i	−0.110512	−	0.717001i
$535$	47.0693			2.03498
$536$	−14.1157	−	28.5781i	−0.609704	−	1.23439i
$537$	14.3204			0.617970
$538$	0.534975	+	3.47092i	0.0230644	+	0.149642i
$539$		0			0
$540$	31.9283	−	10.0818i	1.37398	−	0.433850i
$541$			23.1240i			0.994180i	0.867699	+	0.497090i	$0.165598\pi$
$541$			23.1240i			0.994180i	−0.867699	+	0.497090i	$0.834402\pi$
$542$	0.430115	−	0.0662940i	0.0184750	−	0.00284757i
$543$	−7.97330			−0.342167
$544$	−12.9806	+	12.4525i	−0.556541	+	0.533898i
$545$	20.7718			0.889767
$546$	−5.77652	+	0.890339i	−0.247212	+	0.0381030i
$547$			9.04146i			0.386585i	0.981141	+	0.193292i	$0.0619166\pi$
$547$			9.04146i			0.386585i	−0.981141	+	0.193292i	$0.938083\pi$
$548$	−18.5166	+	5.84685i	−0.790990	+	0.249765i
$549$		−	16.3679i		−	0.698564i
$550$		0			0
$551$	16.5367			0.704487
$552$	−2.67764	−	5.42107i	−0.113968	−	0.230736i
$553$	13.7457			0.584528
$554$	−0.538577	−	3.49429i	−0.0228819	−	0.148458i
$555$			17.0121i			0.722122i
$556$	−13.4023	−	42.4442i	−0.568384	−	1.80004i
$557$			27.8071i			1.17822i	0.808052	+	0.589112i	$0.200522\pi$
$557$			27.8071i			1.17822i	−0.808052	+	0.589112i	$0.799478\pi$
$558$	28.7129	−	4.42554i	1.21552	−	0.187348i
$559$	25.9422			1.09724
$560$	−10.0880	−	14.3813i	−0.426295	−	0.607720i
$561$		0			0
$562$	−1.73755	+	0.267809i	−0.0732940	+	0.0112969i
$563$			35.3346i			1.48918i	0.667524	+	0.744588i	$0.267354\pi$
$563$			35.3346i			1.48918i	−0.667524	+	0.744588i	$0.732646\pi$
$564$	−0.187730	−	0.594529i	−0.00790486	−	0.0250342i
$565$		−	58.7824i		−	2.47299i
$566$	−2.97333	−	19.2909i	−0.124978	−	0.810859i
$567$	−3.32108			−0.139472
$568$	14.1686	−	6.99832i	0.594500	−	0.293643i
$569$	32.7054			1.37108			0.685540	−	0.728035i	$-0.259566\pi$
$569$	32.7054			1.37108			0.685540	+	0.728035i	$0.259566\pi$
$570$	2.96067	+	19.2088i	0.124009	+	0.804568i
$571$			32.0987i			1.34329i	0.740874	+	0.671644i	$0.234412\pi$
$571$			32.0987i			1.34329i	−0.740874	+	0.671644i	$0.765588\pi$
$572$		0			0
$573$			2.14539i			0.0896249i
$574$	−0.890506	+	0.137254i	−0.0371690	+	0.00572888i
$575$	−20.9171			−0.872303
$576$	10.9176	−	14.2654i	0.454899	−	0.594391i
$577$	21.1935			0.882298			0.441149	−	0.897434i	$-0.354571\pi$
$577$	21.1935			0.882298			0.441149	+	0.897434i	$0.354571\pi$
$578$	−9.62835	+	1.48402i	−0.400486	+	0.0617272i
$579$			8.69176i			0.361217i
$580$	26.9102	−	8.49723i	1.11738	−	0.352828i
$581$		−	1.19867i		−	0.0497291i
$582$	1.11356	+	7.22476i	0.0461584	+	0.299476i
$583$		0			0
$584$	−6.77526	+	3.34652i	−0.280362	+	0.138480i
$585$	−32.8401			−1.35777
$586$	−3.20658	−	20.8043i	−0.132463	−	0.859418i
$587$		−	6.76248i		−	0.279118i	−0.990214	−	0.139559i	$-0.955432\pi$
$587$		−	6.76248i		−	0.279118i	0.990214	−	0.139559i	$-0.0445684\pi$
$588$	2.91440	+	9.22973i	0.120188	+	0.380628i
$589$			39.3948i			1.62323i
$590$	3.05907	−	0.471497i	0.125940	−	0.0194112i
$591$	−10.2444			−0.421399
$592$	12.2442	+	17.4552i	0.503234	+	0.717404i
$593$	8.93648			0.366977			0.183489	−	0.983022i	$-0.441261\pi$
$593$	8.93648			0.366977			0.183489	+	0.983022i	$0.441261\pi$
$594$		0			0
$595$			13.9648i			0.572500i
$596$	7.58870	+	24.0329i	0.310845	+	0.984427i
$597$			12.8443i			0.525684i
$598$	2.11032	+	13.6918i	0.0862976	+	0.559899i
$599$	−5.66385			−0.231419			−0.115709	−	0.993283i	$-0.536914\pi$
$599$	−5.66385			−0.231419			−0.115709	+	0.993283i	$0.536914\pi$
$600$	9.24793	+	18.7231i	0.377545	+	0.764366i
$601$	−34.3297			−1.40034			−0.700170	−	0.713976i	$-0.746892\pi$
$601$	−34.3297			−1.40034			−0.700170	+	0.713976i	$0.746892\pi$
$602$	1.67820	+	10.8882i	0.0683982	+	0.443768i
$603$		−	25.3046i		−	1.03048i
$604$	−28.9251	+	9.13346i	−1.17694	+	0.371635i
$605$		0			0
$606$	−7.25444	+	1.11813i	−0.294691	+	0.0454210i
$607$	−40.4456			−1.64163			−0.820817	−	0.571191i	$-0.806482\pi$
$607$	−40.4456			−1.64163			−0.820817	+	0.571191i	$0.806482\pi$
$608$	16.8631	+	17.5782i	0.683888	+	0.712892i
$609$	3.98727			0.161572
$610$	37.4337	−	5.76968i	1.51565	−	0.233608i
$611$			1.42850i			0.0577910i
$612$	−13.6176	+	4.29994i	−0.550460	+	0.173815i
$613$			14.5003i			0.585663i	0.956164	+	0.292831i	$0.0945974\pi$
$613$			14.5003i			0.585663i	−0.956164	+	0.292831i	$0.905403\pi$
$614$	1.81039	+	11.7458i	0.0730613	+	0.474022i
$615$	1.70118			0.0685982
$616$		0			0
$617$	−17.5018			−0.704595			−0.352297	−	0.935888i	$-0.614599\pi$
$617$	−17.5018			−0.704595			−0.352297	+	0.935888i	$0.614599\pi$
$618$	0.734609	+	4.76615i	0.0295503	+	0.191723i
$619$		−	28.0738i		−	1.12838i	−0.825645	−	0.564190i	$-0.809188\pi$
$619$		−	28.0738i		−	1.12838i	0.825645	−	0.564190i	$-0.190812\pi$
$620$	20.2427	+	64.1072i	0.812965	+	2.57461i
$621$		−	11.2132i		−	0.449969i
$622$	35.8460	−	5.52496i	1.43729	−	0.221531i
$623$	−16.3119			−0.653521
$624$	11.3226	−	7.94244i	0.453268	−	0.317952i
$625$	4.74477			0.189791
$626$	26.3921	−	4.06783i	1.05484	−	0.162583i
$627$		0			0
$628$	0.919360	+	2.91155i	0.0366864	+	0.116184i
$629$		−	16.9497i		−	0.675828i
$630$	−2.12443	−	13.7833i	−0.0846391	−	0.549139i
$631$	17.9240			0.713543			0.356771	−	0.934192i	$-0.383877\pi$
$631$	17.9240			0.713543			0.356771	+	0.934192i	$0.383877\pi$
$632$	−29.1634	+	14.4047i	−1.16006	+	0.572990i
$633$	7.38885			0.293681
$634$	−4.30058	−	27.9021i	−0.170798	−	1.10814i
$635$			34.0115i			1.34971i
$636$	4.01551	−	1.26795i	0.159225	−	0.0502774i
$637$		−	22.1767i		−	0.878671i
$638$		0			0
$639$	12.5456			0.496297
$640$	36.4737	+	19.9402i	1.44175	+	0.788205i
$641$	3.54460			0.140003			0.0700017	−	0.997547i	$-0.477700\pi$
$641$	3.54460			0.140003			0.0700017	+	0.997547i	$0.477700\pi$
$642$	−15.5537	+	2.39731i	−0.613858	+	0.0946142i
$643$			15.6401i			0.616786i	0.951259	+	0.308393i	$0.0997911\pi$
$643$			15.6401i			0.616786i	−0.951259	+	0.308393i	$0.900209\pi$
$644$	−5.61004	+	1.77144i	−0.221067	+	0.0698046i
$645$		−	20.8002i		−	0.819007i
$646$	−2.94981	−	19.1383i	−0.116059	−	0.752988i
$647$	−27.7363			−1.09043			−0.545213	−	0.838297i	$-0.683551\pi$
$647$	−27.7363			−1.09043			−0.545213	+	0.838297i	$0.683551\pi$
$648$	7.04611	−	3.48030i	0.276797	−	0.136719i
$649$		0			0
$650$	−7.28856	−	47.2882i	−0.285881	−	1.85480i
$651$			9.49873i			0.372285i
$652$	−9.35615	−	29.6303i	−0.366415	−	1.16041i
$653$			4.43599i			0.173594i	0.996226	+	0.0867969i	$0.0276631\pi$
$653$			4.43599i			0.173594i	−0.996226	+	0.0867969i	$0.972337\pi$
$654$	−6.86391	+	1.05794i	−0.268400	+	0.0413687i
$655$	−48.9698			−1.91341
$656$	1.74549	−	1.22440i	0.0681500	−	0.0478049i
$657$	−5.99918			−0.234050
$658$	−0.599554	+	0.0924096i	−0.0233730	+	0.00360250i
$659$			14.0037i			0.545506i	0.962084	+	0.272753i	$0.0879341\pi$
$659$			14.0037i			0.545506i	−0.962084	+	0.272753i	$0.912066\pi$
$660$		0			0
$661$			33.4719i			1.30191i	0.759118	+	0.650953i	$0.225631\pi$
$661$			33.4719i			1.30191i	−0.759118	+	0.650953i	$0.774369\pi$
$662$	−4.06352	−	26.3641i	−0.157933	−	1.02467i
$663$	−10.9947			−0.426999
$664$	1.25613	+	2.54313i	0.0487474	+	0.0986926i
$665$	18.9109			0.733335
$666$	2.57851	+	16.7294i	0.0999152	+	0.648250i
$667$		−	9.45082i		−	0.365937i
$668$	−16.0078	+	5.05466i	−0.619360	+	0.195571i
$669$		−	4.36314i		−	0.168689i
$670$	57.8723	−	8.91989i	2.23580	−	0.344605i
$671$		0			0
$672$	4.06597	+	4.23841i	0.156848	+	0.163500i
$673$	−1.01007			−0.0389352			−0.0194676	−	0.999810i	$-0.506197\pi$
$673$	−1.01007			−0.0389352			−0.0194676	+	0.999810i	$0.506197\pi$
$674$	29.7484	−	4.58514i	1.14587	−	0.176613i
$675$			38.7276i			1.49063i
$676$	−5.42497	+	1.71300i	−0.208653	+	0.0658847i
$677$		−	31.2927i		−	1.20268i	−0.798995	−	0.601338i	$-0.794635\pi$
$677$		−	31.2927i		−	1.20268i	0.798995	−	0.601338i	$-0.205365\pi$
$678$	2.99387	+	19.4242i	0.114979	+	0.745984i
$679$	7.11273			0.272962
$680$	−14.6343	−	29.6281i	−0.561199	−	1.13619i
$681$	15.6986			0.601573
$682$		0			0
$683$		−	12.2698i		−	0.469491i	−0.972057	−	0.234745i	$-0.924574\pi$
$683$		−	12.2698i		−	0.469491i	0.972057	−	0.234745i	$-0.0754256\pi$
$684$	5.82293	+	18.4409i	0.222645	+	0.705104i
$685$		−	35.6722i		−	1.36296i
$686$	21.0023	−	3.23710i	0.801872	−	0.123593i
$687$	−3.45944			−0.131986
$688$	−14.9707	−	21.3420i	−0.570752	−	0.813656i
$689$	−9.64824			−0.367569
$690$	10.9780	−	1.69204i	0.417924	−	0.0644148i
$691$			10.5030i			0.399554i	0.979841	+	0.199777i	$0.0640218\pi$
$691$			10.5030i			0.399554i	−0.979841	+	0.199777i	$0.935978\pi$
$692$	14.9725	+	47.4170i	0.569170	+	1.80252i
$693$		0			0
$694$	−1.17345	−	7.61337i	−0.0445437	−	0.288999i
$695$	81.7686			3.10166
$696$	−8.45952	+	4.17843i	−0.320657	+	0.158383i
$697$	−1.69494			−0.0642004
$698$	−2.19920	−	14.2684i	−0.0832411	−	0.540068i
$699$		−	10.6716i		−	0.403635i
$700$	19.3757	−	6.11814i	0.732334	−	0.231244i
$701$			5.79354i			0.218819i	0.993997	+	0.109410i	$0.0348960\pi$
$701$			5.79354i			0.218819i	−0.993997	+	0.109410i	$0.965104\pi$
$702$	25.3501	−	3.90723i	0.956779	−	0.147469i
$703$	−22.9531			−0.865691
$704$		0			0
$705$	1.14536			0.0431367
$706$	7.14398	−	1.10111i	0.268867	−	0.0414407i
$707$			7.14195i			0.268601i
$708$	−0.986837	+	0.311606i	−0.0370876	+	0.0117109i
$709$		−	45.5576i		−	1.71095i	−0.517843	−	0.855475i	$-0.673265\pi$
$709$		−	45.5576i		−	1.71095i	0.517843	−	0.855475i	$-0.326735\pi$
$710$	4.42233	+	28.6921i	0.165967	+	1.07680i
$711$	−25.8228			−0.968431
$712$	34.6078	−	17.0939i	1.29698	−	0.640621i
$713$	22.5144			0.843169
$714$	−0.711247	−	4.61457i	−0.0266177	−	0.172696i
$715$		0			0
$716$	9.92812	+	31.4417i	0.371031	+	1.17503i
$717$		−	18.1947i		−	0.679492i
$718$	29.3241	−	4.51974i	1.09437	−	0.168675i
$719$	2.93095			0.109306			0.0546530	−	0.998505i	$-0.482595\pi$
$719$	2.93095			0.109306			0.0546530	+	0.998505i	$0.482595\pi$
$720$	18.9513	+	27.0168i	0.706275	+	1.00686i
$721$	4.69224			0.174748
$722$	0.639536	−	0.0985721i	0.0238011	−	0.00366847i
$723$		−	15.1570i		−	0.563693i
$724$	−5.52778	−	17.5061i	−0.205438	−	0.650610i
$725$			32.6409i			1.21225i
$726$		0			0
$727$	−24.5751			−0.911438			−0.455719	−	0.890124i	$-0.650618\pi$
$727$	−24.5751			−0.911438			−0.455719	+	0.890124i	$0.650618\pi$
$728$	−5.95960	−	12.0656i	−0.220877	−	0.447181i
$729$	−5.63470			−0.208692
$730$	−2.11471	−	13.7203i	−0.0782690	−	0.507810i
$731$			20.7239i			0.766501i
$732$	−12.0759	+	3.81311i	−0.446337	+	0.140937i
$733$			20.8045i			0.768430i	0.923244	+	0.384215i	$0.125528\pi$
$733$			20.8045i			0.768430i	−0.923244	+	0.384215i	$0.874472\pi$
$734$	−44.0684	+	6.79229i	−1.62659	+	0.250708i
$735$	−17.7810			−0.655863
$736$	10.0461	−	9.63735i	0.370303	−	0.355237i
$737$		0			0
$738$	1.67291	−	0.257847i	0.0615807	−	0.00949147i
$739$			2.75118i			0.101204i	0.998719	+	0.0506020i	$0.0161140\pi$
$739$			2.75118i			0.101204i	−0.998719	+	0.0506020i	$0.983886\pi$
$740$	−37.3516	+	11.7942i	−1.37307	+	0.433564i
$741$			14.8889i			0.546958i
$742$	−0.624144	−	4.04945i	−0.0229130	−	0.148660i
$743$	44.9780			1.65008			0.825041	−	0.565073i	$-0.191152\pi$
$743$	44.9780			1.65008			0.825041	+	0.565073i	$0.191152\pi$
$744$	−9.95413	−	20.1528i	−0.364936	−	0.738838i
$745$	−46.2993			−1.69628
$746$	5.34791	+	34.6972i	0.195801	+	1.27036i
$747$			2.25182i			0.0823899i
$748$		0			0
$749$			15.3126i			0.559509i
$750$	−15.6110	+	2.40613i	−0.570033	+	0.0878596i
$751$	−35.2762			−1.28725			−0.643624	−	0.765342i	$-0.722570\pi$
$751$	−35.2762			−1.28725			−0.643624	+	0.765342i	$0.722570\pi$
$752$	1.17519	−	0.824357i	0.0428549	−	0.0300612i
$753$	5.17560			0.188609
$754$	21.3659	−	3.29314i	0.778100	−	0.119929i
$755$		−	55.7241i		−	2.02801i
$756$	3.27979	+	10.3869i	0.119285	+	0.377768i
$757$			46.8943i			1.70440i	0.523216	+	0.852200i	$0.324732\pi$
$757$			46.8943i			1.70440i	−0.523216	+	0.852200i	$0.675268\pi$
$758$	−7.69970	−	49.9557i	−0.279666	−	1.81447i
$759$		0			0
$760$	−40.1221	+	19.8176i	−1.45538	+	0.718860i
$761$	4.42256			0.160318			0.0801588	−	0.996782i	$-0.474457\pi$
$761$	4.42256			0.160318			0.0801588	+	0.996782i	$0.474457\pi$
$762$	−1.73226	−	11.2389i	−0.0627530	−	0.407142i
$763$			6.75748i			0.244637i
$764$	−4.71039	+	1.48737i	−0.170416	+	0.0538110i
$765$		−	26.2343i		−	0.948504i
$766$	−26.6092	+	4.10129i	−0.961429	+	0.148186i
$767$	2.37111			0.0856160
$768$	−13.0681	−	4.73144i	−0.471554	−	0.170731i
$769$	53.6158			1.93344			0.966718	−	0.255844i	$-0.0823534\pi$
$769$	53.6158			1.93344			0.966718	+	0.255844i	$0.0823534\pi$
$770$		0			0
$771$			12.3071i			0.443229i
$772$	−19.0836	+	6.02587i	−0.686832	+	0.216876i
$773$			42.9848i			1.54606i	0.634372	+	0.773028i	$0.281259\pi$
$773$			42.9848i			1.54606i	−0.634372	+	0.773028i	$0.718741\pi$
$774$	−3.15267	−	20.4545i	−0.113320	−	0.735224i
$775$	−77.7592			−2.79319
$776$	−15.0906	+	7.45374i	−0.541721	+	0.267574i
$777$	−5.53436			−0.198544
$778$	7.01652	+	45.5232i	0.251554	+	1.63208i
$779$			2.29527i			0.0822365i
$780$	7.65054	+	24.2288i	0.273933	+	0.867529i
$781$		0			0
$782$	−10.9377	+	1.68583i	−0.391131	+	0.0602852i
$783$	−17.4980			−0.625329
$784$	−18.2442	+	12.7977i	−0.651578	+	0.457060i
$785$	−5.60910			−0.200197
$786$	16.1818	−	2.49410i	0.577184	−	0.0889617i
$787$			15.2371i			0.543145i	0.962418	+	0.271573i	$0.0875437\pi$
$787$			15.2371i			0.543145i	−0.962418	+	0.271573i	$0.912456\pi$
$788$	−7.10230	−	22.4925i	−0.253009	−	0.801263i
$789$		−	9.56823i		−	0.340638i
$790$	−9.10255	−	59.0574i	−0.323854	−	2.10117i
$791$	19.1230			0.679937
$792$		0			0
$793$	29.0152			1.03036
$794$	2.80366	+	18.1902i	0.0994982	+	0.645545i
$795$			7.73587i			0.274363i
$796$	−28.2009	+	8.90479i	−0.999554	+	0.315622i
$797$		−	32.3077i		−	1.14440i	−0.820115	−	0.572199i	$-0.806091\pi$
$797$		−	32.3077i		−	1.14440i	0.820115	−	0.572199i	$-0.193909\pi$
$798$	−6.24900	+	0.963162i	−0.221212	+	0.0340956i
$799$	−1.14116			−0.0403712
$800$	−34.6968	+	33.2851i	−1.22672	+	1.17681i
$801$	30.6436			1.08274
$802$	28.7283	−	4.42792i	1.01443	−	0.156355i
$803$		0			0
$804$	−18.6692	+	5.89504i	−0.658412	+	0.207902i
$805$		−	10.8077i		−	0.380922i
$806$	7.84513	+	50.8992i	0.276333	+	1.79285i
$807$	2.15709			0.0759331
$808$	−7.48435	−	15.1526i	−0.263299	−	0.533066i
$809$	50.3552			1.77040			0.885198	−	0.465215i	$-0.154023\pi$
$809$	50.3552			1.77040			0.885198	+	0.465215i	$0.154023\pi$
$810$	2.19925	+	14.2687i	0.0772737	+	0.501352i
$811$		−	43.6584i		−	1.53305i	−0.642213	−	0.766526i	$-0.721984\pi$
$811$		−	43.6584i		−	1.53305i	0.642213	−	0.766526i	$-0.278016\pi$
$812$	2.76431	+	8.75441i	0.0970084	+	0.307219i
$813$		−	0.267306i		−	0.00937483i
$814$		0			0
$815$	57.0827			1.99952
$816$	6.34481	+	9.04508i	0.222113	+	0.316641i
$817$	28.0641			0.981838
$818$	13.7827	−	2.12433i	0.481900	−	0.0742755i
$819$		−	10.6835i		−	0.373313i
$820$	1.17940	+	3.73509i	0.0411865	+	0.130435i
$821$			18.9987i			0.663059i	0.943445	+	0.331530i	$0.107565\pi$
$821$			18.9987i			0.663059i	−0.943445	+	0.331530i	$0.892435\pi$
$822$	1.81684	+	11.7876i	0.0633694	+	0.411141i
$823$	−13.2125			−0.460558			−0.230279	−	0.973125i	$-0.573964\pi$
$823$	−13.2125			−0.460558			−0.230279	+	0.973125i	$0.573964\pi$
$824$	−9.95521	+	4.91720i	−0.346806	+	0.171299i
$825$		0			0
$826$	0.153387	+	0.995176i	0.00533702	+	0.0346266i
$827$			17.7503i			0.617239i	0.951186	+	0.308619i	$0.0998669\pi$
$827$			17.7503i			0.617239i	−0.951186	+	0.308619i	$0.900133\pi$
$828$	10.5391	−	3.32784i	0.366258	−	0.115650i
$829$			8.56368i			0.297429i	0.988880	+	0.148714i	$0.0475135\pi$
$829$			8.56368i			0.297429i	−0.988880	+	0.148714i	$0.952486\pi$
$830$	−5.14997	+	0.793769i	−0.178758	+	0.0275521i
$831$	−2.17161			−0.0753324
$832$	25.2881	+	19.3535i	0.876709	+	0.670961i
$833$	17.7158			0.613816
$834$	−27.0199	+	4.16460i	−0.935623	+	0.144208i
$835$		−	30.8389i		−	1.06723i
$836$		0			0
$837$		−	41.6850i		−	1.44084i
$838$	0.0364265	+	0.236335i	0.00125833	+	0.00816406i
$839$	−38.0668			−1.31421			−0.657106	−	0.753798i	$-0.728220\pi$
$839$	−38.0668			−1.31421			−0.657106	+	0.753798i	$0.728220\pi$
$840$	−9.67410	+	4.77835i	−0.333788	+	0.164869i
$841$	14.2521			0.491452
$842$	5.06536	+	32.8641i	0.174564	+	1.13257i
$843$			1.07984i			0.0371918i
$844$	5.12258	+	16.2229i	0.176327	+	0.558415i
$845$		−	10.4512i		−	0.359532i
$846$	1.12633	−	0.173601i	0.0387239	−	0.00596853i
$847$		0			0
$848$	5.56779	+	7.93737i	0.191199	+	0.272571i
$849$	−11.9888			−0.411456
$850$	37.7761	−	5.82246i	1.29571	−	0.199709i
$851$			13.1178i			0.449673i
$852$	−2.92266	−	9.25589i	−0.100129	−	0.317101i
$853$			34.2480i			1.17263i	0.810084	+	0.586314i	$0.199422\pi$
$853$			34.2480i			1.17263i	−0.810084	+	0.586314i	$0.800578\pi$
$854$	1.87699	+	12.1779i	0.0642293	+	0.416720i
$855$	−35.5262			−1.21497
$856$	−16.0467	−	32.4876i	−0.548465	−	1.11040i
$857$	−52.8215			−1.80435			−0.902174	−	0.431371i	$-0.858030\pi$
$857$	−52.8215			−1.80435			−0.902174	+	0.431371i	$0.858030\pi$
$858$		0			0
$859$		−	8.91497i		−	0.304175i	−0.988367	−	0.152087i	$-0.951400\pi$
$859$		−	8.91497i		−	0.304175i	0.988367	−	0.152087i	$-0.0485995\pi$
$860$	45.6687	−	14.4205i	1.55729	−	0.491734i
$861$			0.553427i			0.0188607i
$862$	−10.1931	+	1.57107i	−0.347179	+	0.0535109i
$863$	−1.04860			−0.0356949			−0.0178475	−	0.999841i	$-0.505681\pi$
$863$	−1.04860			−0.0356949			−0.0178475	+	0.999841i	$0.505681\pi$
$864$	−17.8434	−	18.6001i	−0.607045	−	0.632790i
$865$	−91.3487			−3.10595
$866$	3.26826	−	0.503740i	0.111060	−	0.0171178i
$867$			5.98378i			0.203220i
$868$	−20.8553	+	6.58533i	−0.707876	+	0.223521i
$869$		0			0
$870$	−2.64041	−	17.1310i	−0.0895182	−	0.580794i
$871$	44.8573			1.51993
$872$	−7.08145	−	14.3369i	−0.239808	−	0.485508i
$873$	−13.3620			−0.452236
$874$	2.28293	+	14.8117i	0.0772214	+	0.501013i
$875$			15.3689i			0.519565i
$876$	1.39759	+	4.42607i	0.0472201	+	0.149543i
$877$		−	12.0834i		−	0.408026i	−0.978968	−	0.204013i	$-0.934601\pi$
$877$		−	12.0834i		−	0.408026i	0.978968	−	0.204013i	$-0.0653986\pi$
$878$	−1.69683	+	0.261533i	−0.0572651	+	0.00882631i
$879$	−12.9294			−0.436096
$880$		0			0
$881$	11.8356			0.398752			0.199376	−	0.979923i	$-0.436109\pi$
$881$	11.8356			0.398752			0.199376	+	0.979923i	$0.436109\pi$
$882$	−17.4856	+	2.69506i	−0.588769	+	0.0907474i
$883$		−	51.1300i		−	1.72066i	−0.509737	−	0.860330i	$-0.670257\pi$
$883$		−	51.1300i		−	1.72066i	0.509737	−	0.860330i	$-0.329743\pi$
$884$	−7.62247	−	24.1399i	−0.256371	−	0.811912i
$885$		−	1.90114i		−	0.0639060i
$886$	−0.995019	−	6.45569i	−0.0334283	−	0.216883i
$887$	16.9859			0.570330			0.285165	−	0.958478i	$-0.407952\pi$
$887$	16.9859			0.570330			0.285165	+	0.958478i	$0.407952\pi$
$888$	11.7419	−	5.79969i	0.394032	−	0.194625i
$889$	−11.0646			−0.371095
$890$	10.8019	+	70.0826i	0.362080	+	2.34917i
$891$		0			0
$892$	9.57966	−	3.02490i	0.320751	−	0.101281i
$893$			1.54534i			0.0517129i
$894$	15.2993	−	2.35809i	0.511686	−	0.0788664i
$895$	−60.5723			−2.02471
$896$	−6.48693	+	11.8656i	−0.216713	+	0.396403i
$897$	8.50911			0.284111
$898$	8.20288	−	1.26432i	0.273734	−	0.0421907i
$899$		−	35.1334i		−	1.17176i
$900$	−36.3994	+	11.4936i	−1.21331	+	0.383119i
$901$		−	7.70750i		−	0.256774i
$902$		0			0
$903$	6.76671			0.225182
$904$	−40.5721	+	20.0399i	−1.34941	+	0.666516i
$905$	33.7255			1.12107
$906$	2.83811	+	18.4137i	0.0942898	+	0.611753i
$907$		−	14.4036i		−	0.478262i	−0.970987	−	0.239131i	$-0.923137\pi$
$907$		−	14.4036i		−	0.478262i	0.970987	−	0.239131i	$-0.0768626\pi$
$908$	10.8836	+	34.4678i	0.361186	+	1.14385i
$909$		−	13.4169i		−	0.445011i
$910$	24.4335	−	3.76595i	0.809963	−	0.124840i
$911$	−39.9889			−1.32489			−0.662445	−	0.749110i	$-0.730481\pi$
$911$	−39.9889			−1.32489			−0.662445	+	0.749110i	$0.730481\pi$
$912$	12.2487	−	8.59207i	0.405596	−	0.284512i
$913$		0			0
$914$	−34.2402	+	5.27746i	−1.13256	+	0.174563i
$915$		−	23.2641i		−	0.769088i
$916$	−2.39838	−	7.59552i	−0.0792448	−	0.250963i
$917$		−	15.9308i		−	0.526083i
$918$	3.12129	+	20.2509i	0.103018	+	0.668381i
$919$	−7.07907			−0.233517			−0.116758	−	0.993160i	$-0.537250\pi$
$919$	−7.07907			−0.233517			−0.116758	+	0.993160i	$0.537250\pi$
$920$	11.3259	+	22.9300i	0.373403	+	0.755980i
$921$	7.29972			0.240534
$922$	−1.42157	−	9.22317i	−0.0468170	−	0.303749i
$923$			22.2395i			0.732022i
$924$		0			0
$925$		−	45.3058i		−	1.48965i
$926$	−20.1552	+	3.10654i	−0.662341	+	0.102087i
$927$	−8.81488			−0.289519
$928$	−15.0390	−	15.6768i	−0.493679	−	0.514616i
$929$	−38.3373			−1.25781			−0.628904	−	0.777483i	$-0.716496\pi$
$929$	−38.3373			−1.25781			−0.628904	+	0.777483i	$0.716496\pi$
$930$	40.8105	−	6.29015i	1.33823	−	0.206262i
$931$		−	23.9906i		−	0.786259i
$932$	23.4304	−	7.39843i	0.767487	−	0.242344i
$933$		−	22.2774i		−	0.729328i
$934$	1.18245	+	7.67174i	0.0386909	+	0.251027i
$935$		0			0
$936$	11.1957	+	22.6665i	0.365944	+	0.740879i
$937$	−58.0159			−1.89530			−0.947648	−	0.319317i	$-0.896546\pi$
$937$	−58.0159			−1.89530			−0.947648	+	0.319317i	$0.896546\pi$
$938$	2.90181	+	18.8270i	0.0947476	+	0.614723i
$939$		−	16.4020i		−	0.535259i
$940$	0.794060	+	2.51474i	0.0258994	+	0.0820217i
$941$			11.0380i			0.359827i	0.983682	+	0.179914i	$0.0575818\pi$
$941$			11.0380i			0.359827i	−0.983682	+	0.179914i	$0.942418\pi$
$942$	1.85349	−	0.285680i	0.0603900	−	0.00930794i
$943$	1.31176			0.0427168
$944$	−1.36832	−	1.95066i	−0.0445350	−	0.0634885i
$945$	−20.0103			−0.650936
$946$		0			0
$947$		−	15.5478i		−	0.505235i	−0.967566	−	0.252617i	$-0.918709\pi$
$947$		−	15.5478i		−	0.505235i	0.967566	−	0.252617i	$-0.0812914\pi$
$948$	6.01576	+	19.0515i	0.195383	+	0.618765i
$949$		−	10.6347i		−	0.345217i
$950$	−7.88471	−	51.1560i	−0.255814	−	1.65972i
$951$	−17.3405			−0.562304
$952$	9.63861	−	4.76082i	0.312389	−	0.154299i
$953$	7.82561			0.253496			0.126748	−	0.991935i	$-0.459546\pi$
$953$	7.82561			0.253496			0.126748	+	0.991935i	$0.459546\pi$
$954$	1.17252	+	7.60732i	0.0379618	+	0.246296i
$955$		−	9.07455i		−	0.293646i
$956$	39.9480	−	12.6141i	1.29201	−	0.407969i
$957$		0			0
$958$	−41.7408	+	6.43354i	−1.34858	+	0.207858i
$959$	11.6049			0.374740
$960$	15.5174	−	20.2758i	0.500823	−	0.654399i
$961$	52.6971			1.69991
$962$	−29.6560	+	4.57090i	−0.956149	+	0.147372i
$963$		−	28.7663i		−	0.926981i
$964$	33.2785	−	10.5081i	1.07183	−	0.338443i
$965$		−	36.7644i		−	1.18349i
$966$	0.550453	+	3.57134i	0.0177105	+	0.114906i
$967$	−47.0564			−1.51323			−0.756615	−	0.653860i	$-0.773148\pi$
$967$	−47.0564			−1.51323			−0.756615	+	0.653860i	$0.773148\pi$
$968$		0			0
$969$	−11.8940			−0.382090
$970$	−4.71012	−	30.5593i	−0.151233	−	0.981199i
$971$			38.7883i			1.24478i	0.782708	+	0.622389i	$0.213838\pi$
$971$			38.7883i			1.24478i	−0.782708	+	0.622389i	$0.786162\pi$
$972$	−9.68531	−	30.6728i	−0.310657	−	0.983829i
$973$			26.6009i			0.852787i
$974$	−4.16172	+	0.641449i	−0.133350	+	0.0205533i
$975$	−29.3884			−0.941183
$976$	−16.7440	−	23.8701i	−0.535964	−	0.764063i
$977$	−39.0383			−1.24894			−0.624472	−	0.781047i	$-0.714686\pi$
$977$	−39.0383			−1.24894			−0.624472	+	0.781047i	$0.714686\pi$
$978$	−18.8626	+	2.90731i	−0.603160	+	0.0929654i
$979$		0			0
$980$	−12.3273	−	39.0399i	−0.393782	−	1.24708i
$981$		−	12.6946i		−	0.405309i
$982$	−0.642100	−	4.16595i	−0.0204902	−	0.132941i
$983$	5.62407			0.179380			0.0896899	−	0.995970i	$-0.471412\pi$
$983$	5.62407			0.179380			0.0896899	+	0.995970i	$0.471412\pi$
$984$	−0.579960	−	1.17417i	−0.0184884	−	0.0374311i
$985$	43.3318			1.38067
$986$	2.63072	+	17.0681i	0.0837793	+	0.543560i
$987$			0.372608i			0.0118602i
$988$	−32.6900	+	10.3223i	−1.04001	+	0.328395i
$989$		−	16.0388i		−	0.510004i
$990$		0			0
$991$	7.34032			0.233173			0.116586	−	0.993181i	$-0.462805\pi$
$991$	7.34032			0.233173			0.116586	+	0.993181i	$0.462805\pi$
$992$	37.3463	−	35.8268i	1.18575	−	1.13750i
$993$	−16.3847			−0.519951
$994$	−9.33411	+	1.43867i	−0.296060	+	0.0456319i
$995$		−	54.3289i		−	1.72234i
$996$	1.66135	−	0.524591i	0.0526418	−	0.0166223i
$997$		−	56.9391i		−	1.80328i	−0.432488	−	0.901640i	$-0.642364\pi$
$997$		−	56.9391i		−	1.80328i	0.432488	−	0.901640i	$-0.357636\pi$
$998$	−3.27331	−	21.2372i	−0.103615	−	0.672252i
$999$	24.2874			0.768420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.c.h.485.19		20
4.3	odd	2		3872.2.c.h.1937.14		20
8.3	odd	2		3872.2.c.h.1937.7		20
8.5	even	2	inner	968.2.c.h.485.20		20
11.2	odd	10		968.2.o.i.565.8		40
11.3	even	5		968.2.o.j.493.6		40
11.4	even	5		968.2.o.j.269.7		40
11.5	even	5		88.2.o.a.69.4	yes	40
11.6	odd	10		968.2.o.i.245.7		40
11.7	odd	10		968.2.o.d.269.4		40
11.8	odd	10		968.2.o.d.493.5		40
11.9	even	5		88.2.o.a.37.3	✓	40
11.10	odd	2		968.2.c.i.485.2		20
33.5	odd	10		792.2.br.b.685.7		40
33.20	odd	10		792.2.br.b.37.8		40
44.27	odd	10		352.2.w.a.113.4		40
44.31	odd	10		352.2.w.a.81.7		40
44.43	even	2		3872.2.c.i.1937.14		20
88.5	even	10		88.2.o.a.69.3	yes	40
88.13	odd	10		968.2.o.i.565.7		40
88.21	odd	2		968.2.c.i.485.1		20
88.27	odd	10		352.2.w.a.113.7		40
88.29	odd	10		968.2.o.d.269.5		40
88.37	even	10		968.2.o.j.269.6		40
88.43	even	2		3872.2.c.i.1937.7		20
88.53	even	10		88.2.o.a.37.4	yes	40
88.61	odd	10		968.2.o.i.245.8		40
88.69	even	10		968.2.o.j.493.7		40
88.75	odd	10		352.2.w.a.81.4		40
88.85	odd	10		968.2.o.d.493.4		40
264.5	odd	10		792.2.br.b.685.8		40
264.53	odd	10		792.2.br.b.37.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.3	✓	40	11.9	even	5
88.2.o.a.37.4	yes	40	88.53	even	10
88.2.o.a.69.3	yes	40	88.5	even	10
88.2.o.a.69.4	yes	40	11.5	even	5
352.2.w.a.81.4		40	88.75	odd	10
352.2.w.a.81.7		40	44.31	odd	10
352.2.w.a.113.4		40	44.27	odd	10
352.2.w.a.113.7		40	88.27	odd	10
792.2.br.b.37.7		40	264.53	odd	10
792.2.br.b.37.8		40	33.20	odd	10
792.2.br.b.685.7		40	33.5	odd	10
792.2.br.b.685.8		40	264.5	odd	10
968.2.c.h.485.19		20	1.1	even	1	trivial
968.2.c.h.485.20		20	8.5	even	2	inner
968.2.c.i.485.1		20	88.21	odd	2
968.2.c.i.485.2		20	11.10	odd	2
968.2.o.d.269.4		40	11.7	odd	10
968.2.o.d.269.5		40	88.29	odd	10
968.2.o.d.493.4		40	88.85	odd	10
968.2.o.d.493.5		40	11.8	odd	10
968.2.o.i.245.7		40	11.6	odd	10
968.2.o.i.245.8		40	88.61	odd	10
968.2.o.i.565.7		40	88.13	odd	10
968.2.o.i.565.8		40	11.2	odd	10
968.2.o.j.269.6		40	88.37	even	10
968.2.o.j.269.7		40	11.4	even	5
968.2.o.j.493.6		40	11.3	even	5
968.2.o.j.493.7		40	88.69	even	10
3872.2.c.h.1937.7		20	8.3	odd	2
3872.2.c.h.1937.14		20	4.3	odd	2
3872.2.c.i.1937.7		20	88.43	even	2
3872.2.c.i.1937.14		20	44.43	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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39771 - 0.215430i) q^{2} -0.868641i q^{3} +(1.90718 - 0.602216i) q^{4} +3.67418i q^{5} +(-0.187131 - 1.21411i) q^{6} -1.19528 q^{7} +(2.53595 - 1.25259i) q^{8} +2.24546 q^{9} +(0.791527 + 5.13543i) q^{10} +(-0.523110 - 1.65665i) q^{12} +3.98051i q^{13} +(-1.67065 + 0.257499i) q^{14} +3.19154 q^{15} +(3.27467 - 2.29707i) q^{16} -3.17983 q^{17} +(3.13850 - 0.483739i) q^{18} +4.30609i q^{19} +(2.21265 + 7.00731i) q^{20} +1.03827i q^{21} +2.46096 q^{23} +(-1.08805 - 2.20283i) q^{24} -8.49956 q^{25} +(0.857521 + 5.56360i) q^{26} -4.55642i q^{27} +(-2.27962 + 0.719818i) q^{28} -3.84030i q^{29} +(4.46084 - 0.687553i) q^{30} +9.14861 q^{31} +(4.08218 - 3.91610i) q^{32} +(-4.44448 + 0.685031i) q^{34} -4.39167i q^{35} +(4.28250 - 1.35225i) q^{36} +5.33037i q^{37} +(0.927661 + 6.01866i) q^{38} +3.45764 q^{39} +(4.60222 + 9.31751i) q^{40} +0.533028 q^{41} +(0.223674 + 1.45120i) q^{42} -6.51729i q^{43} +8.25022i q^{45} +(3.43970 - 0.530164i) q^{46} +0.358873 q^{47} +(-1.99533 - 2.84451i) q^{48} -5.57130 q^{49} +(-11.8799 + 1.83106i) q^{50} +2.76213i q^{51} +(2.39713 + 7.59156i) q^{52} +2.42387i q^{53} +(-0.981589 - 6.36855i) q^{54} +(-3.03117 + 1.49719i) q^{56} +3.74045 q^{57} +(-0.827315 - 5.36762i) q^{58} -0.595680i q^{59} +(6.08684 - 1.92200i) q^{60} -7.28931i q^{61} +(12.7871 - 1.97088i) q^{62} -2.68396 q^{63} +(4.86206 - 6.35298i) q^{64} -14.6251 q^{65} -11.2692i q^{67} +(-6.06451 + 1.91495i) q^{68} -2.13769i q^{69} +(-0.946097 - 6.13828i) q^{70} +5.58709 q^{71} +(5.69437 - 2.81264i) q^{72} -2.67169 q^{73} +(1.14832 + 7.45030i) q^{74} +7.38307i q^{75} +(2.59320 + 8.21250i) q^{76} +(4.83277 - 0.744878i) q^{78} -11.5000 q^{79} +(8.43983 + 12.0317i) q^{80} +2.77849 q^{81} +(0.745018 - 0.114830i) q^{82} +1.00283i q^{83} +(0.625263 + 1.98017i) q^{84} -11.6833i q^{85} +(-1.40402 - 9.10928i) q^{86} -3.33584 q^{87} +13.6469 q^{89} +(1.77734 + 11.5314i) q^{90} -4.75783i q^{91} +(4.69349 - 1.48203i) q^{92} -7.94686i q^{93} +(0.501600 - 0.0773120i) q^{94} -15.8213 q^{95} +(-3.40168 - 3.54595i) q^{96} -5.95068 q^{97} +(-7.78706 + 1.20022i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) \) 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

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