LMFDB - Embedded newform 605.2.b.h.364.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(364,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("605.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.b (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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + x^{10} + 34 x^{9} - 123 x^{8} - 20 x^{7} + 516 x^{6} - 668 x^{5} - 67 x^{4} + \cdots + 1089 $ x^12 - 4x^11 + x^10 + 34x^9 - 123x^8 - 20x^7 + 516x^6 - 668x^5 - 67x^4 + 3848x^3 + 6697x^2 + 4398x + 1089
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.8
Root			$-2.40330 + 0.316825i$ of defining polynomial
Character	$\chi$	$=$	605.364
Dual form			605.2.b.h.364.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.328351i q^{2} +0.962000i q^{3} +1.89219 q^{4} +(-0.591185 + 2.15650i) q^{5} -0.315873 q^{6} -3.27259i q^{7} +1.27800i q^{8} +2.07456 q^{9} +O(q^{10})$	\(q+0.328351i q^{2} +0.962000i q^{3} +1.89219 q^{4} +(-0.591185 + 2.15650i) q^{5} -0.315873 q^{6} -3.27259i q^{7} +1.27800i q^{8} +2.07456 q^{9} +(-0.708089 - 0.194116i) q^{10} +1.82028i q^{12} +5.20729i q^{13} +1.07456 q^{14} +(-2.07456 - 0.568720i) q^{15} +3.36474 q^{16} -3.60094i q^{17} +0.681182i q^{18} +5.00941 q^{19} +(-1.11863 + 4.08050i) q^{20} +3.14823 q^{21} +5.84372i q^{23} -1.22944 q^{24} +(-4.30100 - 2.54978i) q^{25} -1.70982 q^{26} +4.88172i q^{27} -6.19234i q^{28} -2.04792 q^{29} +(0.186740 - 0.681182i) q^{30} -3.25693 q^{31} +3.66082i q^{32} +1.18237 q^{34} +(7.05734 + 1.93470i) q^{35} +3.92544 q^{36} -6.23700i q^{37} +1.64484i q^{38} -5.00941 q^{39} +(-2.75601 - 0.755535i) q^{40} -10.2056 q^{41} +1.03372i q^{42} +0.596820i q^{43} +(-1.22645 + 4.47378i) q^{45} -1.91879 q^{46} +0.962000i q^{47} +3.23688i q^{48} -3.70982 q^{49} +(0.837223 - 1.41224i) q^{50} +3.46410 q^{51} +9.85316i q^{52} +0.393280i q^{53} -1.60292 q^{54} +4.18237 q^{56} +4.81906i q^{57} -0.672437i q^{58} +0.527447 q^{59} +(-3.92544 - 1.07612i) q^{60} +5.32529 q^{61} -1.06941i q^{62} -6.78916i q^{63} +5.52745 q^{64} +(-11.2295 - 3.07847i) q^{65} -8.45057i q^{67} -6.81364i q^{68} -5.62166 q^{69} +(-0.635261 + 2.31728i) q^{70} +12.5274 q^{71} +2.65129i q^{72} -8.51527i q^{73} +2.04792 q^{74} +(2.45289 - 4.13756i) q^{75} +9.47874 q^{76} -1.64484i q^{78} +2.83235 q^{79} +(-1.98918 + 7.25607i) q^{80} +1.52745 q^{81} -3.35100i q^{82} +12.1407i q^{83} +5.95703 q^{84} +(7.76543 + 2.12882i) q^{85} -0.195966 q^{86} -1.97010i q^{87} -9.00000 q^{89} +(-1.46897 - 0.402704i) q^{90} +17.0413 q^{91} +11.0574i q^{92} -3.13316i q^{93} -0.315873 q^{94} +(-2.96149 + 10.8028i) q^{95} -3.52171 q^{96} -11.2942i q^{97} -1.21812i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9}+O(q^{10}) $ 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9	$ 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9} - 32 q^{14} + 20 q^{15} + 36 q^{16} + 26 q^{20} - 10 q^{25} + 20 q^{26} + 8 q^{31} + 12 q^{34} + 92 q^{36} - 18 q^{45} - 4 q^{49} + 48 q^{56} - 32 q^{59} - 92 q^{60} + 28 q^{64} - 16 q^{69} - 12 q^{70} + 112 q^{71} + 36 q^{75} - 106 q^{80} - 20 q^{81} - 56 q^{86} - 108 q^{89} + 72 q^{91}+O(q^{100}) $ 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9 - 32 * q^14 + 20 * q^15 + 36 * q^16 + 26 * q^20 - 10 * q^25 + 20 * q^26 + 8 * q^31 + 12 * q^34 + 92 * q^36 - 18 * q^45 - 4 * q^49 + 48 * q^56 - 32 * q^59 - 92 * q^60 + 28 * q^64 - 16 * q^69 - 12 * q^70 + 112 * q^71 + 36 * q^75 - 106 * q^80 - 20 * q^81 - 56 * q^86 - 108 * q^89 + 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			0.328351i			0.232179i	0.993239	+	0.116089i	$0.0370359\pi$
$2$			0.328351i			0.232179i	−0.993239	+	0.116089i	$0.962964\pi$
$3$			0.962000i			0.555411i	0.960666	+	0.277706i	$0.0895740\pi$
$3$			0.962000i			0.555411i	−0.960666	+	0.277706i	$0.910426\pi$
$4$	1.89219			0.946093
$5$	−0.591185	+	2.15650i	−0.264386	+	0.964417i
$5$	−0.591185	+	2.15650i	−0.264386	+	0.964417i
$6$	−0.315873			−0.128955
$7$		−	3.27259i		−	1.23692i	−0.785816	−	0.618461i	$-0.787757\pi$
$7$		−	3.27259i		−	1.23692i	0.785816	−	0.618461i	$-0.212243\pi$
$8$			1.27800i			0.451842i
$9$	2.07456			0.691518
$10$	−0.708089	−	0.194116i	−0.223917	−	0.0613848i
$11$		0			0
$11$		0			0
$12$			1.82028i			0.525471i
$13$			5.20729i			1.44424i	0.691767	+	0.722121i	$0.256833\pi$
$13$			5.20729i			1.44424i	−0.691767	+	0.722121i	$0.743167\pi$
$14$	1.07456			0.287187
$15$	−2.07456	−	0.568720i	−0.535648	−	0.146843i
$16$	3.36474			0.841185
$17$		−	3.60094i		−	0.873355i	−0.899618	−	0.436678i	$-0.856155\pi$
$17$		−	3.60094i		−	0.873355i	0.899618	−	0.436678i	$-0.143845\pi$
$18$			0.681182i			0.160556i
$19$	5.00941			1.14924			0.574619	−	0.818421i	$-0.305150\pi$
$19$	5.00941			1.14924			0.574619	+	0.818421i	$0.305150\pi$
$20$	−1.11863	+	4.08050i	−0.250134	+	0.912428i
$21$	3.14823			0.687000
$22$		0			0
$23$			5.84372i			1.21850i	0.792978	+	0.609250i	$0.208530\pi$
$23$			5.84372i			1.21850i	−0.792978	+	0.609250i	$0.791470\pi$
$24$	−1.22944			−0.250958
$25$	−4.30100	−	2.54978i	−0.860200	−	0.509956i
$26$	−1.70982			−0.335323
$27$			4.88172i			0.939488i
$28$		−	6.19234i		−	1.17024i
$29$	−2.04792			−0.380290			−0.190145	−	0.981756i	$-0.560896\pi$
$29$	−2.04792			−0.380290			−0.190145	+	0.981756i	$0.560896\pi$
$30$	0.186740	−	0.681182i	0.0340938	−	0.124366i
$31$	−3.25693			−0.584961			−0.292481	−	0.956271i	$-0.594481\pi$
$31$	−3.25693			−0.584961			−0.292481	+	0.956271i	$0.594481\pi$
$32$			3.66082i			0.647147i
$33$		0			0
$34$	1.18237			0.202775
$35$	7.05734	+	1.93470i	1.19291	+	0.327024i
$36$	3.92544			0.654241
$37$		−	6.23700i		−	1.02536i	−0.858581	−	0.512679i	$-0.828653\pi$
$37$		−	6.23700i		−	1.02536i	0.858581	−	0.512679i	$-0.171347\pi$
$38$			1.64484i			0.266829i
$39$	−5.00941			−0.802148
$40$	−2.75601	−	0.755535i	−0.435764	−	0.119461i
$41$	−10.2056			−1.59384			−0.796921	−	0.604084i	$-0.793539\pi$
$41$	−10.2056			−1.59384			−0.796921	+	0.604084i	$0.793539\pi$
$42$			1.03372i			0.159507i
$43$			0.596820i			0.0910142i	0.998964	+	0.0455071i	$0.0144904\pi$
$43$			0.596820i			0.0910142i	−0.998964	+	0.0455071i	$0.985510\pi$
$44$		0			0
$45$	−1.22645	+	4.47378i	−0.182828	+	0.666912i
$46$	−1.91879			−0.282910
$47$			0.962000i			0.140322i	0.997536	+	0.0701611i	$0.0223513\pi$
$47$			0.962000i			0.140322i	−0.997536	+	0.0701611i	$0.977649\pi$
$48$			3.23688i			0.467203i
$49$	−3.70982			−0.529974
$50$	0.837223	−	1.41224i	0.118401	−	0.199720i
$51$	3.46410			0.485071
$52$			9.85316i			1.36639i
$53$			0.393280i			0.0540212i	0.999635	+	0.0270106i	$0.00859879\pi$
$53$			0.393280i			0.0540212i	−0.999635	+	0.0270106i	$0.991401\pi$
$54$	−1.60292			−0.218129
$55$		0			0
$56$	4.18237			0.558893
$57$			4.81906i			0.638300i
$58$		−	0.672437i		−	0.0882953i
$59$	0.527447			0.0686677			0.0343339	−	0.999410i	$-0.489069\pi$
$59$	0.527447			0.0686677			0.0343339	+	0.999410i	$0.489069\pi$
$60$	−3.92544	−	1.07612i	−0.506773	−	0.138927i
$61$	5.32529			0.681833			0.340917	−	0.940094i	$-0.389263\pi$
$61$	5.32529			0.681833			0.340917	+	0.940094i	$0.389263\pi$
$62$		−	1.06941i		−	0.135816i
$63$		−	6.78916i		−	0.855354i
$64$	5.52745			0.690931
$65$	−11.2295	−	3.07847i	−1.39285	−	0.381837i
$66$		0			0
$67$		−	8.45057i		−	1.03240i	−0.856468	−	0.516201i	$-0.827346\pi$
$67$		−	8.45057i		−	1.03240i	0.856468	−	0.516201i	$-0.172654\pi$
$68$		−	6.81364i		−	0.826275i
$69$	−5.62166			−0.676769
$70$	−0.635261	+	2.31728i	−0.0759282	+	0.276968i
$71$	12.5274			1.48673			0.743367	−	0.668884i	$-0.233228\pi$
$71$	12.5274			1.48673			0.743367	+	0.668884i	$0.233228\pi$
$72$			2.65129i			0.312457i
$73$		−	8.51527i		−	0.996638i	−0.866994	−	0.498319i	$-0.833951\pi$
$73$		−	8.51527i		−	0.996638i	0.866994	−	0.498319i	$-0.166049\pi$
$74$	2.04792			0.238066
$75$	2.45289	−	4.13756i	0.283235	−	0.477765i
$76$	9.47874			1.08729
$77$		0			0
$78$		−	1.64484i		−	0.186242i
$79$	2.83235			0.318665			0.159332	−	0.987225i	$-0.449066\pi$
$79$	2.83235			0.318665			0.159332	+	0.987225i	$0.449066\pi$
$80$	−1.98918	+	7.25607i	−0.222397	+	0.811253i
$81$	1.52745			0.169716
$82$		−	3.35100i		−	0.370056i
$83$			12.1407i			1.33261i	0.745678	+	0.666307i	$0.232126\pi$
$83$			12.1407i			1.33261i	−0.745678	+	0.666307i	$0.767874\pi$
$84$	5.95703			0.649966
$85$	7.76543	+	2.12882i	0.842279	+	0.230903i
$86$	−0.195966			−0.0211316
$87$		−	1.97010i		−	0.211217i
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	−1.46897	−	0.402704i	−0.154843	−	0.0424487i
$91$	17.0413			1.78641
$92$			11.0574i			1.15281i
$93$		−	3.13316i		−	0.324894i
$94$	−0.315873			−0.0325799
$95$	−2.96149	+	10.8028i	−0.303842	+	1.10834i
$96$	−3.52171			−0.359433
$97$		−	11.2942i		−	1.14675i	−0.819293	−	0.573374i	$-0.805634\pi$
$97$		−	11.2942i		−	1.14675i	0.819293	−	0.573374i	$-0.194366\pi$
$98$		−	1.21812i		−	0.123049i
$99$		0			0
$100$	−8.13829	−	4.82466i	−0.813829	−	0.482466i
$101$	−13.1671			−1.31017			−0.655085	−	0.755555i	$-0.727367\pi$
$101$	−13.1671			−1.31017			−0.655085	+	0.755555i	$0.727367\pi$
$102$			1.13744i			0.112623i
$103$		−	2.78228i		−	0.274147i	−0.990561	−	0.137073i	$-0.956230\pi$
$103$		−	2.78228i		−	0.274147i	0.990561	−	0.137073i	$-0.0437696\pi$
$104$	−6.65492			−0.652569
$105$	−1.86118	+	6.78916i	−0.181633	+	0.662554i
$106$	−0.129134			−0.0125426
$107$		−	15.9502i		−	1.54197i	−0.636856	−	0.770983i	$-0.719765\pi$
$107$		−	15.9502i		−	1.54197i	0.636856	−	0.770983i	$-0.280235\pi$
$108$			9.23713i			0.888843i
$109$	−3.90911			−0.374425			−0.187212	−	0.982319i	$-0.559945\pi$
$109$	−3.90911			−0.374425			−0.187212	+	0.982319i	$0.559945\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		−	11.0114i		−	1.04048i
$113$		−	9.87757i		−	0.929204i	−0.885520	−	0.464602i	$-0.846197\pi$
$113$		−	9.87757i		−	0.929204i	0.885520	−	0.464602i	$-0.153803\pi$
$114$	−1.58234			−0.148200
$115$	−12.6020	−	3.45472i	−1.17514	−	0.322154i
$116$	−3.87505			−0.359790
$117$			10.8028i			0.998720i
$118$			0.173187i			0.0159432i
$119$	−11.7844			−1.08027
$120$	0.726825	−	2.65129i	0.0663497	−	0.242028i
$121$		0			0
$122$			1.74856i			0.158307i
$123$		−	9.81776i		−	0.885237i
$124$	−6.16271			−0.553427
$125$	8.04130	−	7.76772i	0.719235	−	0.694766i
$126$	2.22922			0.198595
$127$			5.41588i			0.480581i	0.970701	+	0.240291i	$0.0772428\pi$
$127$			5.41588i			0.480581i	−0.970701	+	0.240291i	$0.922757\pi$
$128$			9.13658i			0.807567i
$129$	−0.574141			−0.0505503
$130$	1.01082	−	3.68722i	0.0886545	−	0.323391i
$131$	19.1241			1.67088			0.835440	−	0.549582i	$-0.185213\pi$
$131$	19.1241			1.67088			0.835440	+	0.549582i	$0.185213\pi$
$132$		0			0
$133$		−	16.3937i		−	1.42152i
$134$	2.77475			0.239702
$135$	−10.5274	−	2.88600i	−0.906058	−	0.248387i
$136$	4.60200			0.394618
$137$		−	16.0429i		−	1.37063i	−0.728245	−	0.685317i	$-0.759664\pi$
$137$		−	16.0429i		−	1.37063i	0.728245	−	0.685317i	$-0.240336\pi$
$138$		−	1.84588i		−	0.157131i
$139$	−12.5694			−1.06612			−0.533060	−	0.846078i	$-0.678958\pi$
$139$	−12.5694			−1.06612			−0.533060	+	0.846078i	$0.678958\pi$
$140$	13.3538	+	3.66082i	1.12860	+	0.309396i
$141$	−0.925445			−0.0779365
$142$			4.11339i			0.345188i
$143$		0			0
$144$	6.98034			0.581695
$145$	1.21070	−	4.41635i	0.100543	−	0.366758i
$146$	2.79600			0.231398
$147$		−	3.56884i		−	0.294353i
$148$		−	11.8016i		−	0.970083i
$149$	13.9279			1.14102			0.570510	−	0.821290i	$-0.306745\pi$
$149$	13.9279			1.14102			0.570510	+	0.821290i	$0.306745\pi$
$150$	1.35857	+	0.805408i	0.110927	+	0.0657613i
$151$	−16.0335			−1.30478			−0.652392	−	0.757881i	$-0.726235\pi$
$151$	−16.0335			−1.30478			−0.652392	+	0.757881i	$0.726235\pi$
$152$			6.40204i			0.519274i
$153$		−	7.47034i		−	0.603941i
$154$		0			0
$155$	1.92544	−	7.02357i	0.154655	−	0.564146i
$156$	−9.47874			−0.758907
$157$		−	2.27488i		−	0.181555i	−0.995871	−	0.0907776i	$-0.971065\pi$
$157$		−	2.27488i		−	0.181555i	0.995871	−	0.0907776i	$-0.0289352\pi$
$158$			0.930005i			0.0739873i
$159$	−0.378336			−0.0300040
$160$	−7.89456	−	2.16422i	−0.624120	−	0.171097i
$161$	19.1241			1.50719
$162$			0.501538i			0.0394046i
$163$		−	22.5694i		−	1.76777i	−0.467701	−	0.883887i	$-0.654918\pi$
$163$		−	22.5694i		−	1.76777i	0.467701	−	0.883887i	$-0.345082\pi$
$164$	−19.3108			−1.50792
$165$		0			0
$166$	−3.98640			−0.309405
$167$		−	3.80952i		−	0.294790i	−0.989078	−	0.147395i	$-0.952911\pi$
$167$		−	3.80952i		−	0.294790i	0.989078	−	0.147395i	$-0.0470888\pi$
$168$			4.02344i			0.310415i
$169$	−14.1159			−1.08583
$170$	−0.698999	+	2.54978i	−0.0536108	+	0.195559i
$171$	10.3923			0.794719
$172$			1.12929i			0.0861079i
$173$		−	0.949651i		−	0.0722006i	−0.999348	−	0.0361003i	$-0.988506\pi$
$173$		−	0.949651i		−	0.0722006i	0.999348	−	0.0361003i	$-0.0114936\pi$
$174$	0.646885			0.0490402
$175$	−8.34438	+	14.0754i	−0.630776	+	1.06400i
$176$		0			0
$177$			0.507404i			0.0381388i
$178$		−	2.95516i		−	0.221498i
$179$	−3.63526			−0.271712			−0.135856	−	0.990729i	$-0.543378\pi$
$179$	−3.63526			−0.271712			−0.135856	+	0.990729i	$0.543378\pi$
$180$	−2.32066	+	8.46523i	−0.172972	+	0.630961i
$181$	12.5687			0.934227			0.467114	−	0.884197i	$-0.345294\pi$
$181$	12.5687			0.934227			0.467114	+	0.884197i	$0.345294\pi$
$182$			5.59552i			0.414768i
$183$			5.12293i			0.378698i
$184$	−7.46829			−0.550570
$185$	13.4501	+	3.68722i	0.988872	+	0.271090i
$186$	1.02878			0.0754335
$187$		0			0
$188$			1.82028i			0.132758i
$189$	15.9759			1.16207
$190$	−3.54711	−	0.972407i	−0.257334	−	0.0705458i
$191$	−2.67656			−0.193669			−0.0968345	−	0.995301i	$-0.530872\pi$
$191$	−2.67656			−0.193669			−0.0968345	+	0.995301i	$0.530872\pi$
$192$			5.31741i			0.383751i
$193$			0.388232i			0.0279455i	0.999902	+	0.0139728i	$0.00444781\pi$
$193$			0.388232i			0.0279455i	−0.999902	+	0.0139728i	$0.995552\pi$
$194$	3.70845			0.266251
$195$	2.96149	−	10.8028i	0.212077	−	0.773605i
$196$	−7.01966			−0.501404
$197$		−	18.5416i		−	1.32104i	−0.750810	−	0.660518i	$-0.770337\pi$
$197$		−	18.5416i		−	1.32104i	0.750810	−	0.660518i	$-0.229663\pi$
$198$		0			0
$199$	−10.1491			−0.719451			−0.359726	−	0.933058i	$-0.617130\pi$
$199$	−10.1491			−0.719451			−0.359726	+	0.933058i	$0.617130\pi$
$200$	3.25863	−	5.49669i	0.230420	−	0.388674i
$201$	8.12945			0.573407
$202$		−	4.32341i		−	0.304194i
$203$			6.70201i			0.470389i
$204$	6.55472			0.458922
$205$	6.03337	−	22.0083i	0.421389	−	1.53713i
$206$	0.913565			0.0636511
$207$			12.1231i			0.842616i
$208$			17.5212i			1.21487i
$209$		0			0
$210$	−2.22922	−	0.611121i	−0.153831	−	0.0421714i
$211$	−8.47351			−0.583341			−0.291670	−	0.956519i	$-0.594211\pi$
$211$	−8.47351			−0.583341			−0.291670	+	0.956519i	$0.594211\pi$
$212$			0.744160i			0.0511091i
$213$			12.0514i			0.825749i
$214$	5.23726			0.358012
$215$	−1.28704	−	0.352831i	−0.0877756	−	0.0240629i
$216$	−6.23885			−0.424500
$217$			10.6586i			0.723551i
$218$		−	1.28356i		−	0.0869335i
$219$	8.19170			0.553544
$220$		0			0
$221$	18.7511			1.26134
$222$			1.97010i			0.132225i
$223$			23.7069i			1.58753i	0.608225	+	0.793764i	$0.291882\pi$
$223$			23.7069i			1.58753i	−0.608225	+	0.793764i	$0.708118\pi$
$224$	11.9803			0.800470
$225$	−8.92267	−	5.28966i	−0.594844	−	0.352644i
$226$	3.24331			0.215742
$227$			0.716582i			0.0475612i	0.999717	+	0.0237806i	$0.00757032\pi$
$227$			0.716582i			0.0475612i	−0.999717	+	0.0237806i	$0.992430\pi$
$228$			9.11855i			0.603891i
$229$	−13.1491			−0.868918			−0.434459	−	0.900692i	$-0.643060\pi$
$229$	−13.1491			−0.868918			−0.434459	+	0.900692i	$0.643060\pi$
$230$	1.13436	−	4.13788i	0.0747975	−	0.272843i
$231$		0			0
$232$		−	2.61725i		−	0.171831i
$233$			26.9327i			1.76442i	0.470858	+	0.882209i	$0.343944\pi$
$233$			26.9327i			1.76442i	−0.470858	+	0.882209i	$0.656056\pi$
$234$	−3.54711			−0.231882
$235$	−2.07456	−	0.568720i	−0.135329	−	0.0370992i
$236$	0.998027			0.0649660
$237$			2.72473i			0.176990i
$238$		−	3.86941i		−	0.250816i
$239$	5.00941			0.324032			0.162016	−	0.986788i	$-0.448200\pi$
$239$	5.00941			0.324032			0.162016	+	0.986788i	$0.448200\pi$
$240$	−6.98034	−	1.91359i	−0.450579	−	0.123522i
$241$	4.69354			0.302337			0.151169	−	0.988508i	$-0.451696\pi$
$241$	4.69354			0.302337			0.151169	+	0.988508i	$0.451696\pi$
$242$		0			0
$243$			16.1146i			1.03375i
$244$	10.0764			0.645077
$245$	2.19319	−	8.00023i	0.140118	−	0.511116i
$246$	3.22367			0.205533
$247$			26.0855i			1.65978i
$248$		−	4.16236i		−	0.264310i
$249$	−11.6793			−0.740149
$250$	2.55054	+	2.64036i	0.161310	+	0.166991i
$251$	4.37834			0.276358			0.138179	−	0.990407i	$-0.455875\pi$
$251$	4.37834			0.276358			0.138179	+	0.990407i	$0.455875\pi$
$252$		−	12.8464i		−	0.809244i
$253$		0			0
$254$	−1.77831			−0.111581
$255$	−2.04792	+	7.47034i	−0.128246	+	0.467811i
$256$	8.05489			0.503431
$257$			6.51616i			0.406467i	0.979130	+	0.203233i	$0.0651450\pi$
$257$			6.51616i			0.406467i	−0.979130	+	0.203233i	$0.934855\pi$
$258$		−	0.188520i		−	0.0117367i
$259$	−20.4111			−1.26829
$260$	−21.2484	−	5.82504i	−1.31777	−	0.361253i
$261$	−4.24853			−0.262978
$262$			6.27941i			0.387943i
$263$		−	4.28212i		−	0.264047i	−0.991247	−	0.132023i	$-0.957853\pi$
$263$		−	4.28212i		−	0.264047i	0.991247	−	0.132023i	$-0.0421474\pi$
$264$		0			0
$265$	−0.848110	−	0.232501i	−0.0520990	−	0.0142824i
$266$	5.38289			0.330046
$267$		−	8.65800i		−	0.529861i
$268$		−	15.9900i		−	0.976747i
$269$	−10.6217			−0.647614			−0.323807	−	0.946123i	$-0.604963\pi$
$269$	−10.6217			−0.647614			−0.323807	+	0.946123i	$0.604963\pi$
$270$	0.947620	−	3.45669i	0.0576703	−	0.210368i
$271$	−10.6506			−0.646976			−0.323488	−	0.946232i	$-0.604856\pi$
$271$	−10.6506			−0.646976			−0.323488	+	0.946232i	$0.604856\pi$
$272$		−	12.1162i		−	0.734653i
$273$			16.3937i			0.992194i
$274$	5.26768			0.318232
$275$		0			0
$276$	−10.6372			−0.640286
$277$			7.35058i			0.441654i	0.975313	+	0.220827i	$0.0708755\pi$
$277$			7.35058i			0.441654i	−0.975313	+	0.220827i	$0.929124\pi$
$278$		−	4.12716i		−	0.247530i
$279$	−6.75667			−0.404511
$280$	−2.47255	+	9.01929i	−0.147763	+	0.539006i
$281$	−28.2293			−1.68402			−0.842011	−	0.539461i	$-0.818628\pi$
$281$	−28.2293			−1.68402			−0.842011	+	0.539461i	$0.818628\pi$
$282$		−	0.303870i		−	0.0180952i
$283$			10.0617i			0.598109i	0.954236	+	0.299054i	$0.0966712\pi$
$283$			10.0617i			0.598109i	−0.954236	+	0.299054i	$0.903329\pi$
$284$	23.7043			1.40659
$285$	−10.3923	−	2.84895i	−0.615587	−	0.168757i
$286$		0			0
$287$			33.3986i			1.97146i
$288$			7.59457i			0.447514i
$289$	4.03326			0.237251
$290$	1.45011	+	0.397535i	0.0851535	+	0.0233440i
$291$	10.8650			0.636917
$292$		−	16.1125i		−	0.942912i
$293$		−	0.0244803i		−	0.00143016i	−1.00000		0.000715078i	$-0.999772\pi$
$293$		−	0.0244803i		−	0.00143016i	1.00000		0.000715078i	$-0.000227616\pi$
$294$	1.17183			0.0683426
$295$	−0.311818	+	1.13744i	−0.0181548	+	0.0662243i
$296$	7.97090			0.463299
$297$		0			0
$298$			4.57325i			0.264921i
$299$	−30.4300			−1.75981
$300$	4.64133	−	7.82904i	0.267967	−	0.452010i
$301$	1.95314			0.112577
$302$		−	5.26460i		−	0.302944i
$303$		−	12.6667i		−	0.727683i
$304$	16.8554			0.966722
$305$	−3.14823	+	11.4840i	−0.180267	+	0.657571i
$306$	2.45289			0.140222
$307$			32.9698i			1.88169i	0.338839	+	0.940844i	$0.389966\pi$
$307$			32.9698i			1.88169i	−0.338839	+	0.940844i	$0.610034\pi$
$308$		0			0
$309$	2.67656			0.152264
$310$	2.30619	+	0.632221i	0.130983	+	0.0359077i
$311$	−4.82567			−0.273639			−0.136819	−	0.990596i	$-0.543688\pi$
$311$	−4.82567			−0.273639			−0.136819	+	0.990596i	$0.543688\pi$
$312$		−	6.40204i		−	0.362444i
$313$			17.0662i			0.964637i	0.875996	+	0.482318i	$0.160205\pi$
$313$			17.0662i			0.964637i	−0.875996	+	0.482318i	$0.839795\pi$
$314$	0.746958			0.0421533
$315$	14.6408	+	4.01365i	0.824918	+	0.226143i
$316$	5.35934			0.301487
$317$			1.71657i			0.0964120i	0.998837	+	0.0482060i	$0.0153504\pi$
$317$			1.71657i			0.0964120i	−0.998837	+	0.0482060i	$0.984650\pi$
$318$		−	0.124227i		−	0.00696629i
$319$		0			0
$320$	−3.26774	+	11.9199i	−0.182672	+	0.666345i
$321$	15.3441			0.856425
$322$			6.27941i			0.349938i
$323$		−	18.0386i		−	1.00369i
$324$	2.89021			0.160567
$325$	13.2775	−	22.3966i	0.736501	−	1.24234i
$326$	7.41068			0.410440
$327$		−	3.76056i		−	0.207960i
$328$		−	13.0427i		−	0.720164i
$329$	3.14823			0.173567
$330$		0			0
$331$	0.892186			0.0490390			0.0245195	−	0.999699i	$-0.492194\pi$
$331$	0.892186			0.0490390			0.0245195	+	0.999699i	$0.492194\pi$
$332$			22.9724i			1.26078i
$333$		−	12.9390i		−	0.709053i
$334$	1.25086			0.0684440
$335$	18.2237	+	4.99585i	0.995665	+	0.272952i
$336$	10.5930			0.577894
$337$		−	18.7856i		−	1.02332i	−0.859189	−	0.511659i	$-0.829031\pi$
$337$		−	18.7856i		−	1.02332i	0.859189	−	0.511659i	$-0.170969\pi$
$338$		−	4.63495i		−	0.252108i
$339$	9.50223			0.516090
$340$	14.6936	+	4.02812i	0.796874	+	0.218456i
$341$		0			0
$342$			3.41232i			0.184517i
$343$		−	10.7674i		−	0.581385i
$344$	−0.762737			−0.0411240
$345$	3.32344	−	12.1231i	0.178928	−	0.652687i
$346$	0.311818			0.0167635
$347$		−	20.9598i		−	1.12518i	−0.826735	−	0.562591i	$-0.809804\pi$
$347$		−	20.9598i		−	1.12518i	0.826735	−	0.562591i	$-0.190196\pi$
$348$		−	3.72780i		−	0.199831i
$349$	27.1866			1.45527			0.727634	−	0.685966i	$-0.240620\pi$
$349$	27.1866			1.45527			0.727634	+	0.685966i	$0.240620\pi$
$350$	−4.62166	−	2.73988i	−0.247038	−	0.146453i
$351$	−25.4205			−1.35685
$352$		0			0
$353$		−	8.66841i		−	0.461373i	−0.973028	−	0.230686i	$-0.925903\pi$
$353$		−	8.66841i		−	0.461373i	0.973028	−	0.230686i	$-0.0740972\pi$
$354$	−0.166606			−0.00885503
$355$	−7.40604	+	27.0155i	−0.393072	+	1.43383i
$356$	−17.0297			−0.902571
$357$		−	11.3366i		−	0.599995i
$358$		−	1.19364i		−	0.0630858i
$359$	6.90465			0.364414			0.182207	−	0.983260i	$-0.441676\pi$
$359$	6.90465			0.364414			0.182207	+	0.983260i	$0.441676\pi$
$360$	−5.71750	−	1.56740i	−0.301339	−	0.0826092i
$361$	6.09422			0.320748
$362$			4.12695i			0.216908i
$363$		0			0
$364$	32.2453			1.69011
$365$	18.3632	+	5.03410i	0.961174	+	0.263497i
$366$	−1.68212			−0.0879256
$367$			16.2900i			0.850332i	0.905115	+	0.425166i	$0.139784\pi$
$367$			16.2900i			0.850332i	−0.905115	+	0.425166i	$0.860216\pi$
$368$			19.6626i			1.02498i
$369$	−21.1720			−1.10217
$370$	−1.21070	+	4.41635i	−0.0629414	+	0.229595i
$371$	1.28704			0.0668200
$372$		−	5.92853i		−	0.307380i
$373$			3.69622i			0.191383i	0.995411	+	0.0956915i	$0.0305062\pi$
$373$			3.69622i			0.191383i	−0.995411	+	0.0956915i	$0.969494\pi$
$374$		0			0
$375$	7.47255	+	7.73573i	0.385881	+	0.399471i
$376$	−1.22944			−0.0634034
$377$		−	10.6641i		−	0.549231i
$378$			5.24568i			0.269809i
$379$	3.70178			0.190148			0.0950738	−	0.995470i	$-0.469691\pi$
$379$	3.70178			0.190148			0.0950738	+	0.995470i	$0.469691\pi$
$380$	−5.60369	+	20.4409i	−0.287463	+	1.04860i
$381$	−5.21007			−0.266920
$382$		−	0.878849i		−	0.0449658i
$383$			31.3709i			1.60298i	0.598011	+	0.801488i	$0.295958\pi$
$383$			31.3709i			1.60298i	−0.598011	+	0.801488i	$0.704042\pi$
$384$	−8.78939			−0.448532
$385$		0			0
$386$	−0.127476			−0.00648836
$387$			1.23814i			0.0629380i
$388$		−	21.3707i		−	1.08493i
$389$	13.8257			0.700989			0.350495	−	0.936565i	$-0.386013\pi$
$389$	13.8257			0.700989			0.350495	+	0.936565i	$0.386013\pi$
$390$	3.54711	+	0.972407i	0.179615	+	0.0492397i
$391$	21.0429			1.06418
$392$		−	4.74115i		−	0.239464i
$393$			18.3974i			0.928025i
$394$	6.08815			0.306717
$395$	−1.67445	+	6.10798i	−0.0842505	+	0.307326i
$396$		0			0
$397$		−	9.73413i		−	0.488542i	−0.969707	−	0.244271i	$-0.921451\pi$
$397$		−	9.73413i		−	0.488542i	0.969707	−	0.244271i	$-0.0785486\pi$
$398$		−	3.33247i		−	0.167041i
$399$	15.7708			0.789526
$400$	−14.4717	−	8.57935i	−0.723587	−	0.428968i
$401$	−26.1768			−1.30721			−0.653604	−	0.756837i	$-0.726744\pi$
$401$	−26.1768			−1.30721			−0.653604	+	0.756837i	$0.726744\pi$
$402$			2.66931i			0.133133i
$403$		−	16.9597i		−	0.844825i
$404$	−24.9145			−1.23954
$405$	−0.903003	+	3.29394i	−0.0448706	+	0.163677i
$406$	−2.20061			−0.109214
$407$		0			0
$408$			4.42713i			0.219175i
$409$	−2.64562			−0.130817			−0.0654086	−	0.997859i	$-0.520835\pi$
$409$	−2.64562			−0.130817			−0.0654086	+	0.997859i	$0.520835\pi$
$410$	7.22645	+	1.98106i	0.356889	+	0.0978377i
$411$	15.4332			0.761265
$412$		−	5.26460i		−	0.259368i
$413$		−	1.72611i		−	0.0849365i
$414$	−3.98064			−0.195638
$415$	−26.1814	−	7.17739i	−1.28520	−	0.352324i
$416$	−19.0629			−0.934637
$417$		−	12.0917i		−	0.592135i
$418$		0			0
$419$	−24.3118			−1.18771			−0.593855	−	0.804572i	$-0.702395\pi$
$419$	−24.3118			−1.18771			−0.593855	+	0.804572i	$0.702395\pi$
$420$	−3.52171	+	12.8464i	−0.171842	+	0.626838i
$421$	−27.8922			−1.35938			−0.679691	−	0.733499i	$-0.737886\pi$
$421$	−27.8922			−1.35938			−0.679691	+	0.733499i	$0.737886\pi$
$422$		−	2.78228i		−	0.135439i
$423$			1.99572i			0.0970354i
$424$	−0.502613			−0.0244090
$425$	−9.18160	+	15.4876i	−0.445373	+	0.751260i
$426$	−3.95709			−0.191721
$427$		−	17.4275i		−	0.843374i
$428$		−	30.1808i		−	1.45884i
$429$		0			0
$430$	0.115852	−	0.422602i	0.00558689	−	0.0203797i
$431$	20.0377			0.965180			0.482590	−	0.875846i	$-0.339696\pi$
$431$	20.0377			0.965180			0.482590	+	0.875846i	$0.339696\pi$
$432$			16.4257i			0.790283i
$433$			4.38473i			0.210716i	0.994434	+	0.105358i	$0.0335989\pi$
$433$			4.38473i			0.210716i	−0.994434	+	0.105358i	$0.966401\pi$
$434$	−3.49975			−0.167993
$435$	4.24853	+	1.16470i	0.203702	+	0.0558429i
$436$	−7.39676			−0.354241
$437$			29.2736i			1.40035i
$438$			2.68975i			0.128521i
$439$	34.2675			1.63550			0.817750	−	0.575573i	$-0.195221\pi$
$439$	34.2675			1.63550			0.817750	+	0.575573i	$0.195221\pi$
$440$		0			0
$441$	−7.69622			−0.366487
$442$			6.15694i			0.292856i
$443$			18.4932i			0.878637i	0.898331	+	0.439319i	$0.144780\pi$
$443$			18.4932i			0.878637i	−0.898331	+	0.439319i	$0.855220\pi$
$444$	11.3531			0.538795
$445$	5.32066	−	19.4085i	0.252224	−	0.920052i
$446$	−7.78416			−0.368591
$447$			13.3987i			0.633736i
$448$		−	18.0890i		−	0.854627i
$449$	−18.7708			−0.885848			−0.442924	−	0.896559i	$-0.646059\pi$
$449$	−18.7708			−0.885848			−0.442924	+	0.896559i	$0.646059\pi$
$450$	1.73686	−	2.92976i	0.0818766	−	0.138110i
$451$		0			0
$452$		−	18.6902i		−	0.879113i
$453$		−	15.4242i		−	0.724692i
$454$	−0.235290			−0.0110427
$455$	−10.0746	+	36.7496i	−0.472302	+	1.72285i
$456$	−6.15876			−0.288410
$457$			14.4990i			0.678236i	0.940744	+	0.339118i	$0.110129\pi$
$457$			14.4990i			0.678236i	−0.940744	+	0.339118i	$0.889871\pi$
$458$		−	4.31752i		−	0.201744i
$459$	17.5788			0.820507
$460$	−23.8453	−	6.53697i	−1.11179	−	0.304788i
$461$	−15.2150			−0.708632			−0.354316	−	0.935126i	$-0.615286\pi$
$461$	−15.2150			−0.708632			−0.354316	+	0.935126i	$0.615286\pi$
$462$		0			0
$463$		−	9.08060i		−	0.422011i	−0.977485	−	0.211006i	$-0.932326\pi$
$463$		−	9.08060i		−	0.422011i	0.977485	−	0.211006i	$-0.0676739\pi$
$464$	−6.89073			−0.319894
$465$	6.75667	+	1.85228i	0.313333	+	0.0858973i
$466$	−8.84336			−0.409661
$467$			17.2840i			0.799809i	0.916557	+	0.399904i	$0.130957\pi$
$467$			17.2840i			0.799809i	−0.916557	+	0.399904i	$0.869043\pi$
$468$			20.4409i			0.944882i
$469$	−27.6552			−1.27700
$470$	0.186740	−	0.681182i	0.00861365	−	0.0314206i
$471$	2.18843			0.100838
$472$			0.674078i			0.0310269i
$473$		0			0
$474$	−0.894665			−0.0410933
$475$	−21.5455	−	12.7729i	−0.988575	−	0.586061i
$476$	−22.2982			−1.02204
$477$			0.815882i			0.0373567i
$478$			1.64484i			0.0752334i
$479$	32.6306			1.49093			0.745464	−	0.666546i	$-0.232228\pi$
$479$	32.6306			1.49093			0.745464	+	0.666546i	$0.232228\pi$
$480$	2.08198	−	7.59457i	0.0950289	−	0.346643i
$481$	32.4779			1.48086
$482$			1.54113i			0.0701964i
$483$			18.3974i			0.837110i
$484$		0			0
$485$	24.3559	+	6.67694i	1.10594	+	0.303184i
$486$	−5.29123			−0.240015
$487$			15.2563i			0.691329i	0.938358	+	0.345664i	$0.112346\pi$
$487$			15.2563i			0.691329i	−0.938358	+	0.345664i	$0.887654\pi$
$488$			6.80572i			0.308081i
$489$	21.7118			0.981841
$490$	2.62688	+	0.720134i	0.118670	+	0.0325324i
$491$	−6.66994			−0.301010			−0.150505	−	0.988609i	$-0.548090\pi$
$491$	−6.66994			−0.301010			−0.150505	+	0.988609i	$0.548090\pi$
$492$		−	18.5770i		−	0.837517i
$493$			7.37444i			0.332128i
$494$	−8.56518			−0.385365
$495$		0			0
$496$	−10.9587			−0.492060
$497$		−	40.9971i		−	1.83897i
$498$		−	3.83492i		−	0.171847i
$499$	6.14911			0.275272			0.137636	−	0.990483i	$-0.456050\pi$
$499$	6.14911			0.275272			0.137636	+	0.990483i	$0.456050\pi$
$500$	15.2156	−	14.6980i	0.680464	−	0.657314i
$501$	3.66476			0.163730
$502$			1.43763i			0.0641645i
$503$		−	25.7081i		−	1.14627i	−0.819462	−	0.573134i	$-0.805728\pi$
$503$		−	25.7081i		−	1.14627i	0.819462	−	0.573134i	$-0.194272\pi$
$504$	8.67656			0.386485
$505$	7.78416	−	28.3948i	0.346391	−	1.26355i
$506$		0			0
$507$		−	13.5795i		−	0.603085i
$508$			10.2478i			0.454675i
$509$	16.8453			0.746656			0.373328	−	0.927699i	$-0.378217\pi$
$509$	16.8453			0.746656			0.373328	+	0.927699i	$0.378217\pi$
$510$	−2.45289	−	0.672437i	−0.108616	−	0.0297760i
$511$	−27.8670			−1.23276
$512$			20.9180i			0.924453i
$513$			24.4546i			1.07970i
$514$	−2.13959			−0.0943731
$515$	6.00000	+	1.64484i	0.264392	+	0.0724805i
$516$	−1.08638			−0.0478253
$517$		0			0
$518$		−	6.70201i		−	0.294469i
$519$	0.913565			0.0401010
$520$	3.93429	−	14.3514i	0.172530	−	0.629349i
$521$	−25.1707			−1.10275			−0.551375	−	0.834257i	$-0.685897\pi$
$521$	−25.1707			−1.10275			−0.551375	+	0.834257i	$0.685897\pi$
$522$		−	1.39501i		−	0.0610578i
$523$			17.9094i			0.783123i	0.920152	+	0.391562i	$0.128065\pi$
$523$			17.9094i			0.783123i	−0.920152	+	0.391562i	$0.871935\pi$
$524$	36.1863			1.58081
$525$	−13.5405	−	8.02730i	−0.590957	−	0.350340i
$526$	1.40604			0.0613061
$527$			11.7280i			0.510879i
$528$		0			0
$529$	−11.1491			−0.484744
$530$	0.0763420	−	0.278477i	0.00331608	−	0.0120963i
$531$	1.09422			0.0474850
$532$		−	31.0200i		−	1.34489i
$533$		−	53.1433i		−	2.30189i
$534$	2.84286			0.123023
$535$	34.3967	+	9.42952i	1.48710	+	0.407674i
$536$	10.7998			0.466482
$537$		−	3.49712i		−	0.150912i
$538$		−	3.48763i		−	0.150362i
$539$		0			0
$540$	−19.9199	−	5.46085i	−0.857215	−	0.234998i
$541$	9.44468			0.406059			0.203029	−	0.979173i	$-0.434921\pi$
$541$	9.44468			0.406059			0.203029	+	0.979173i	$0.434921\pi$
$542$		−	3.49712i		−	0.150214i
$543$			12.0911i			0.518880i
$544$	13.1824			0.565189
$545$	2.31101	−	8.43000i	0.0989926	−	0.361102i
$546$	−5.38289			−0.230367
$547$			15.3044i			0.654370i	0.944960	+	0.327185i	$0.106100\pi$
$547$			15.3044i			0.654370i	−0.944960	+	0.327185i	$0.893900\pi$
$548$		−	30.3561i		−	1.29675i
$549$	11.0476			0.471500
$550$		0			0
$551$	−10.2589			−0.437044
$552$		−	7.18450i		−	0.305792i
$553$		−	9.26912i		−	0.394163i
$554$	−2.41357			−0.102543
$555$	−3.54711	+	12.9390i	−0.150566	+	0.549230i
$556$	−23.7836			−1.00865
$557$			9.94844i			0.421529i	0.977537	+	0.210764i	$0.0675953\pi$
$557$			9.94844i			0.421529i	−0.977537	+	0.210764i	$0.932405\pi$
$558$		−	2.21856i		−	0.0939190i
$559$	−3.10781			−0.131447
$560$	23.7461	+	6.50977i	1.00346	+	0.275088i
$561$		0			0
$562$		−	9.26912i		−	0.390994i
$563$		−	28.0419i		−	1.18183i	−0.806735	−	0.590914i	$-0.798767\pi$
$563$		−	28.0419i		−	1.18183i	0.806735	−	0.590914i	$-0.201233\pi$
$564$	−1.75111			−0.0737352
$565$	21.3010	+	5.83947i	0.896140	+	0.245668i
$566$	−3.30378			−0.138868
$567$		−	4.99870i		−	0.209926i
$568$			16.0101i			0.671769i
$569$	−20.3771			−0.854251			−0.427126	−	0.904192i	$-0.640474\pi$
$569$	−20.3771			−0.854251			−0.427126	+	0.904192i	$0.640474\pi$
$570$	0.935455	−	3.41232i	0.0391819	−	0.142926i
$571$	−43.6546			−1.82689			−0.913444	−	0.406964i	$-0.866588\pi$
$571$	−43.6546			−1.82689			−0.913444	+	0.406964i	$0.866588\pi$
$572$		0			0
$573$		−	2.57485i		−	0.107566i
$574$	−10.9664			−0.457731
$575$	14.9002	−	25.1339i	0.621382	−	1.04815i
$576$	11.4670			0.477791
$577$		−	37.4644i		−	1.55966i	−0.625989	−	0.779832i	$-0.715304\pi$
$577$		−	37.4644i		−	1.55966i	0.625989	−	0.779832i	$-0.284696\pi$
$578$			1.32432i			0.0550846i
$579$	−0.373479			−0.0155213
$580$	2.29087	−	8.35656i	0.0951233	−	0.346987i
$581$	39.7315			1.64834
$582$			3.56753i			0.147879i
$583$		0			0
$584$	10.8825			0.450322
$585$	−23.2963	−	6.38646i	−0.963183	−	0.264047i
$586$	0.00803813			0.000332052
$587$		−	6.01916i		−	0.248437i	−0.992255	−	0.124219i	$-0.960358\pi$
$587$		−	6.01916i		−	0.248437i	0.992255	−	0.124219i	$-0.0396425\pi$
$588$		−	6.75292i		−	0.278486i
$589$	−16.3153			−0.672259
$590$	−0.373479	−	0.102386i	−0.0153759	−	0.00421516i
$591$	17.8370			0.733718
$592$		−	20.9859i		−	0.862515i
$593$			14.3574i			0.589589i	0.955561	+	0.294794i	$0.0952511\pi$
$593$			14.3574i			0.589589i	−0.955561	+	0.294794i	$0.904749\pi$
$594$		0			0
$595$	6.96674	−	25.4130i	0.285609	−	1.04183i
$596$	26.3542			1.07951
$597$		−	9.76345i		−	0.399591i
$598$		−	9.99169i		−	0.408591i
$599$	−27.9471			−1.14189			−0.570943	−	0.820989i	$-0.693422\pi$
$599$	−27.9471			−1.14189			−0.570943	+	0.820989i	$0.693422\pi$
$600$	5.28781	+	3.13480i	0.215874	+	0.127978i
$601$	20.5638			0.838815			0.419408	−	0.907798i	$-0.362238\pi$
$601$	20.5638			0.838815			0.419408	+	0.907798i	$0.362238\pi$
$602$			0.641316i			0.0261381i
$603$		−	17.5312i		−	0.713925i
$604$	−30.3383			−1.23445
$605$		0			0
$606$	4.15912			0.168953
$607$		−	19.1738i		−	0.778242i	−0.921187	−	0.389121i	$-0.872779\pi$
$607$		−	19.1738i		−	0.778242i	0.921187	−	0.389121i	$-0.127221\pi$
$608$			18.3385i			0.743726i
$609$	−6.44733			−0.261259
$610$	−3.77078	−	1.03372i	−0.152674	−	0.0418542i
$611$	−5.00941			−0.202659
$612$		−	14.1353i		−	0.571385i
$613$			18.0536i			0.729180i	0.931168	+	0.364590i	$0.118791\pi$
$613$			18.0536i			0.729180i	−0.931168	+	0.364590i	$0.881209\pi$
$614$	−10.8257			−0.436888
$615$	21.1720	+	5.80411i	0.853738	+	0.234044i
$616$		0			0
$617$		−	32.0433i		−	1.29001i	−0.764176	−	0.645007i	$-0.776854\pi$
$617$		−	32.0433i		−	1.29001i	0.764176	−	0.645007i	$-0.223146\pi$
$618$			0.878849i			0.0353525i
$619$	5.30985			0.213421			0.106710	−	0.994290i	$-0.465968\pi$
$619$	5.30985			0.213421			0.106710	+	0.994290i	$0.465968\pi$
$620$	3.64330	−	13.2899i	0.146318	−	0.533735i
$621$	−28.5274			−1.14477
$622$		−	1.58451i		−	0.0635331i
$623$			29.4533i			1.18002i
$624$	−16.8554			−0.674755
$625$	11.9972	+	21.9332i	0.479889	+	0.877329i
$626$	−5.60369			−0.223968
$627$		0			0
$628$		−	4.30450i		−	0.171768i
$629$	−22.4591			−0.895501
$630$	−1.31788	+	4.80733i	−0.0525057	+	0.191529i
$631$	39.3924			1.56819			0.784094	−	0.620642i	$-0.213128\pi$
$631$	39.3924			1.56819			0.784094	+	0.620642i	$0.213128\pi$
$632$			3.61975i			0.143986i
$633$		−	8.15152i		−	0.323994i
$634$	−0.563636			−0.0223848
$635$	−11.6793	−	3.20178i	−0.463481	−	0.127059i
$636$	−0.715882			−0.0283866
$637$		−	19.3181i		−	0.765410i
$638$		0			0
$639$	25.9889			1.02810
$640$	−19.7030	−	5.40140i	−0.778831	−	0.213509i
$641$	−47.2650			−1.86685			−0.933427	−	0.358768i	$-0.883197\pi$
$641$	−47.2650			−1.86685			−0.933427	+	0.358768i	$0.883197\pi$
$642$			5.03825i			0.198844i
$643$		−	2.37860i		−	0.0938027i	−0.998900	−	0.0469014i	$-0.985065\pi$
$643$		−	2.37860i		−	0.0938027i	0.998900	−	0.0469014i	$-0.0149346\pi$
$644$	36.1863			1.42594
$645$	0.339423	−	1.23814i	0.0133648	−	0.0487516i
$646$	5.92298			0.233036
$647$		−	0.890278i		−	0.0350004i	−0.999847	−	0.0175002i	$-0.994429\pi$
$647$		−	0.890278i		−	0.0350004i	0.999847	−	0.0175002i	$-0.00557078\pi$
$648$			1.95208i			0.0766849i
$649$		0			0
$650$	7.35392	+	4.35966i	0.288445	+	0.171000i
$651$	−10.2535			−0.401868
$652$		−	42.7055i		−	1.67248i
$653$			13.0531i			0.510809i	0.966834	+	0.255404i	$0.0822086\pi$
$653$			13.0531i			0.510809i	−0.966834	+	0.255404i	$0.917791\pi$
$654$	1.23478			0.0482839
$655$	−11.3059	+	41.2411i	−0.441757	+	1.61142i
$656$	−34.3391			−1.34072
$657$		−	17.6654i		−	0.689193i
$658$			1.03372i			0.0402987i
$659$	24.8805			0.969205			0.484603	−	0.874734i	$-0.338964\pi$
$659$	24.8805			0.969205			0.484603	+	0.874734i	$0.338964\pi$
$660$		0			0
$661$	−33.1788			−1.29051			−0.645253	−	0.763969i	$-0.723248\pi$
$661$	−33.1788			−1.29051			−0.645253	+	0.763969i	$0.723248\pi$
$662$			0.292950i			0.0113858i
$663$			18.0386i			0.700560i
$664$	−15.5158			−0.602131
$665$	35.3531	+	9.69173i	1.37094	+	0.375829i
$666$	4.24853			0.164627
$667$		−	11.9675i		−	0.463384i
$668$		−	7.20833i		−	0.278899i
$669$	−22.8060			−0.881731
$670$	−1.64039	+	5.98375i	−0.0633738	+	0.231173i
$671$		0			0
$672$			11.5251i			0.444590i
$673$			23.8197i			0.918182i	0.888389	+	0.459091i	$0.151825\pi$
$673$			23.8197i			0.918182i	−0.888389	+	0.459091i	$0.848175\pi$
$674$	6.16827			0.237593
$675$	12.4473	−	20.9963i	0.479098	−	0.808148i
$676$	−26.7098			−1.02730
$677$			1.87036i			0.0718837i	0.999354	+	0.0359418i	$0.0114431\pi$
$677$			1.87036i			0.0718837i	−0.999354	+	0.0359418i	$0.988557\pi$
$678$			3.12006i			0.119825i
$679$	−36.9611			−1.41844
$680$	−2.72063	+	9.92423i	−0.104332	+	0.380577i
$681$	−0.689352			−0.0264160
$682$		0			0
$683$			9.51629i			0.364131i	0.983286	+	0.182065i	$0.0582782\pi$
$683$			9.51629i			0.364131i	−0.983286	+	0.182065i	$0.941722\pi$
$684$	19.6642			0.751878
$685$	34.5964	+	9.48429i	1.32186	+	0.362376i
$686$	3.53548			0.134985
$687$		−	12.6494i		−	0.482607i
$688$			2.00814i			0.0765598i
$689$	−2.04792			−0.0780197
$690$	3.98064	+	1.09125i	0.151540	+	0.0415433i
$691$	−4.56677			−0.173728			−0.0868641	−	0.996220i	$-0.527685\pi$
$691$	−4.56677			−0.173728			−0.0868641	+	0.996220i	$0.527685\pi$
$692$		−	1.79692i		−	0.0683085i
$693$		0			0
$694$	6.88217			0.261244
$695$	7.43082	−	27.1059i	0.281867	−	1.02818i
$696$	2.51780			0.0954368
$697$			36.7496i			1.39199i
$698$			8.92675i			0.337883i
$699$	−25.9092			−0.979977
$700$	−15.7891	+	26.6333i	−0.596773	+	1.00664i
$701$	28.7555			1.08608			0.543040	−	0.839707i	$-0.317273\pi$
$701$	28.7555			1.08608			0.543040	+	0.839707i	$0.317273\pi$
$702$		−	8.34685i		−	0.315032i
$703$		−	31.2437i		−	1.17838i
$704$		0			0
$705$	0.547109	−	1.99572i	0.0206053	−	0.0751633i
$706$	2.84628			0.107121
$707$			43.0903i			1.62058i
$708$			0.960102i			0.0360829i
$709$	36.4141			1.36756			0.683780	−	0.729689i	$-0.260335\pi$
$709$	36.4141			1.36756			0.683780	+	0.729689i	$0.260335\pi$
$710$	−8.87054	−	2.43178i	−0.332906	−	0.0912629i
$711$	5.87588			0.220363
$712$		−	11.5020i		−	0.431056i
$713$		−	19.0326i		−	0.712775i
$714$	3.72237			0.139306
$715$		0			0
$716$	−6.87859			−0.257065
$717$			4.81906i			0.179971i
$718$			2.26715i			0.0846092i
$719$	−39.1239			−1.45907			−0.729537	−	0.683941i	$-0.760265\pi$
$719$	−39.1239			−1.45907			−0.729537	+	0.683941i	$0.760265\pi$
$720$	−4.12667	+	15.0531i	−0.153792	+	0.560996i
$721$	−9.10526			−0.339098
$722$			2.00104i			0.0744710i
$723$			4.51519i			0.167922i
$724$	23.7824			0.883866
$725$	8.80812	+	5.22176i	0.327126	+	0.193931i
$726$		0			0
$727$			32.8912i			1.21987i	0.792453	+	0.609933i	$0.208804\pi$
$727$			32.8912i			1.21987i	−0.792453	+	0.609933i	$0.791196\pi$
$728$			21.7788i			0.807176i
$729$	−10.9199			−0.404440
$730$	−1.65295	+	6.02957i	−0.0611784	+	0.223164i
$731$	2.14911			0.0794877
$732$			9.69353i			0.358283i
$733$		−	11.9256i		−	0.440484i	−0.975445	−	0.220242i	$-0.929315\pi$
$733$		−	11.9256i		−	0.440484i	0.975445	−	0.220242i	$-0.0706847\pi$
$734$	−5.34884			−0.197429
$735$	7.69622	+	2.10985i	0.283879	+	0.0778229i
$736$	−21.3928			−0.788549
$737$		0			0
$738$		−	6.95184i		−	0.255901i
$739$	37.2429			1.37000			0.685002	−	0.728541i	$-0.259801\pi$
$739$	37.2429			1.37000			0.685002	+	0.728541i	$0.259801\pi$
$740$	25.4501	+	6.97691i	0.935565	+	0.256476i
$741$	−25.0942			−0.921859
$742$			0.422602i			0.0155142i
$743$		−	13.3453i		−	0.489590i	−0.969575	−	0.244795i	$-0.921279\pi$
$743$		−	13.3453i		−	0.489590i	0.969575	−	0.244795i	$-0.0787206\pi$
$744$	4.00419			0.146801
$745$	−8.23398	+	30.0356i	−0.301670	+	1.10042i
$746$	−1.21366			−0.0444351
$747$			25.1865i			0.921527i
$748$		0			0
$749$	−52.1984			−1.90729
$750$	−2.54003	+	2.45362i	−0.0927488	+	0.0895934i
$751$	0.795996			0.0290463			0.0145231	−	0.999895i	$-0.495377\pi$
$751$	0.795996			0.0290463			0.0145231	+	0.999895i	$0.495377\pi$
$752$			3.23688i			0.118037i
$753$			4.21196i			0.153492i
$754$	3.50157			0.127520
$755$	9.47874	−	34.5762i	0.344967	−	1.25836i
$756$	30.2293			1.09943
$757$			40.6693i			1.47815i	0.673622	+	0.739076i	$0.264737\pi$
$757$			40.6693i			1.47815i	−0.673622	+	0.739076i	$0.735263\pi$
$758$			1.21548i			0.0441483i
$759$		0			0
$760$	−13.8060	−	3.78479i	−0.500796	−	0.137289i
$761$	−5.77029			−0.209173			−0.104586	−	0.994516i	$-0.533352\pi$
$761$	−5.77029			−0.209173			−0.104586	+	0.994516i	$0.533352\pi$
$762$		−	1.71073i		−	0.0619733i
$763$			12.7929i			0.463134i
$764$	−5.06454			−0.183229
$765$	16.1098	+	4.41635i	0.582451	+	0.159674i
$766$	−10.3006			−0.372177
$767$			2.74657i			0.0991728i
$768$			7.74881i			0.279611i
$769$	16.4209			0.592152			0.296076	−	0.955164i	$-0.404322\pi$
$769$	16.4209			0.592152			0.296076	+	0.955164i	$0.404322\pi$
$770$		0			0
$771$	−6.26855			−0.225756
$772$			0.734607i			0.0264391i
$773$		−	24.5841i		−	0.884227i	−0.896959	−	0.442114i	$-0.854229\pi$
$773$		−	24.5841i		−	0.884227i	0.896959	−	0.442114i	$-0.145771\pi$
$774$	−0.406543			−0.0146129
$775$	14.0080	+	8.30445i	0.503184	+	0.298305i
$776$	14.4340			0.518149
$777$		−	19.6355i		−	0.704420i
$778$			4.53967i			0.162755i
$779$	−51.1239			−1.83170
$780$	5.60369	−	20.4409i	0.200644	−	0.731902i
$781$		0			0
$782$			6.90944i			0.247081i
$783$		−	9.99740i		−	0.357278i
$784$	−12.4826			−0.445806
$785$	4.90578	+	1.34487i	0.175095	+	0.0480006i
$786$	−6.04079			−0.215468
$787$		−	1.83496i		−	0.0654091i	−0.999465	−	0.0327046i	$-0.989588\pi$
$787$		−	1.83496i		−	0.0654091i	0.999465	−	0.0327046i	$-0.0104120\pi$
$788$		−	35.0842i		−	1.24982i
$789$	4.11940			0.146654
$790$	−2.00556	−	0.549805i	−0.0713546	−	0.0195612i
$791$	−32.3252			−1.14935
$792$		0			0
$793$			27.7303i			0.984732i
$794$	3.19621			0.113429
$795$	0.223666	−	0.815882i	0.00793263	−	0.0289363i
$796$	−19.2040			−0.680668
$797$			42.0057i			1.48792i	0.668226	+	0.743959i	$0.267054\pi$
$797$			42.0057i			1.48792i	−0.668226	+	0.743959i	$0.732946\pi$
$798$			5.17834i			0.183311i
$799$	3.46410			0.122551
$800$	9.33429	−	15.7452i	0.330017	−	0.556676i
$801$	−18.6710			−0.659707
$802$		−	8.59517i		−	0.303506i
$803$		0			0
$804$	15.3824			0.542496
$805$	−11.3059	+	41.2411i	−0.398480	+	1.45356i
$806$	5.56874			0.196151
$807$		−	10.2180i		−	0.359692i
$808$		−	16.8275i		−	0.591990i
$809$	27.0811			0.952120			0.476060	−	0.879413i	$-0.342065\pi$
$809$	27.0811			0.952120			0.476060	+	0.879413i	$0.342065\pi$
$810$	−1.08157	−	0.296502i	−0.0380024	−	0.0104180i
$811$	1.02878			0.0361252			0.0180626	−	0.999837i	$-0.494250\pi$
$811$	1.02878			0.0361252			0.0180626	+	0.999837i	$0.494250\pi$
$812$			12.6814i			0.445031i
$813$		−	10.2459i		−	0.359338i
$814$		0			0
$815$	48.6710	+	13.3427i	1.70487	+	0.467374i
$816$	11.6558			0.408035
$817$			2.98972i			0.104597i
$818$		−	0.868689i		−	0.0303730i
$819$	35.3531			1.23534
$820$	11.4163	−	41.6438i	0.398673	−	1.45427i
$821$	−11.5065			−0.401581			−0.200790	−	0.979634i	$-0.564351\pi$
$821$	−11.5065			−0.401581			−0.200790	+	0.979634i	$0.564351\pi$
$822$			5.06751i			0.176750i
$823$			28.7640i			1.00265i	0.865259	+	0.501325i	$0.167154\pi$
$823$			28.7640i			1.00265i	−0.865259	+	0.501325i	$0.832846\pi$
$824$	3.55576			0.123871
$825$		0			0
$826$	0.566771			0.0197205
$827$			54.0494i			1.87948i	0.341885	+	0.939742i	$0.388935\pi$
$827$			54.0494i			1.87948i	−0.341885	+	0.939742i	$0.611065\pi$
$828$			22.9392i			0.797193i
$829$	−4.64886			−0.161461			−0.0807307	−	0.996736i	$-0.525725\pi$
$829$	−4.64886			−0.161461			−0.0807307	+	0.996736i	$0.525725\pi$
$830$	2.35670	−	8.59669i	0.0818023	−	0.298395i
$831$	−7.07126			−0.245299
$832$			28.7830i			0.997871i
$833$			13.3588i			0.462855i
$834$	3.97033			0.137481
$835$	8.21525	+	2.25213i	0.284300	+	0.0779383i
$836$		0			0
$837$		−	15.8994i		−	0.549564i
$838$		−	7.98280i		−	0.275761i
$839$	−4.94511			−0.170724			−0.0853620	−	0.996350i	$-0.527205\pi$
$839$	−4.94511			−0.170724			−0.0853620	+	0.996350i	$0.527205\pi$
$840$	−8.67656	−	2.37860i	−0.299370	−	0.0820694i
$841$	−24.8060			−0.855380
$842$		−	9.15842i		−	0.315620i
$843$		−	27.1566i		−	0.935324i
$844$	−16.0335			−0.551895
$845$	8.34508	−	30.4409i	0.287079	−	1.04720i
$846$	−0.655297			−0.0225296
$847$		0			0
$848$			1.32329i			0.0454418i
$849$	−9.67940			−0.332196
$850$	−5.08537	−	3.01478i	−0.174427	−	0.103406i
$851$	36.4473			1.24940
$852$			22.8035i			0.781235i
$853$		−	29.3155i		−	1.00374i	−0.864942	−	0.501872i	$-0.832645\pi$
$853$		−	29.3155i		−	1.00374i	0.864942	−	0.501872i	$-0.167355\pi$
$854$	5.72232			0.195814
$855$	−6.14377	+	22.4110i	−0.210113	+	0.766441i
$856$	20.3844			0.696724
$857$		−	0.656701i		−	0.0224325i	−0.999937	−	0.0112162i	$-0.996430\pi$
$857$		−	0.656701i		−	0.0224325i	0.999937	−	0.0112162i	$-0.00357032\pi$
$858$		0			0
$859$	40.0569			1.36672			0.683361	−	0.730080i	$-0.260517\pi$
$859$	40.0569			1.36672			0.683361	+	0.730080i	$0.260517\pi$
$860$	−2.43533	−	0.667622i	−0.0830439	−	0.0227657i
$861$	−32.1294			−1.09497
$862$			6.57938i			0.224094i
$863$			19.9306i			0.678445i	0.940706	+	0.339222i	$0.110164\pi$
$863$			19.9306i			0.678445i	−0.940706	+	0.339222i	$0.889836\pi$
$864$	−17.8711			−0.607987
$865$	2.04792	+	0.561419i	0.0696315	+	0.0190888i
$866$	−1.43973			−0.0489239
$867$			3.88000i			0.131772i
$868$			20.1680i			0.684546i
$869$		0			0
$870$	−0.382428	+	1.39501i	−0.0129655	+	0.0472952i
$871$	44.0045			1.49104
$872$		−	4.99585i		−	0.169181i
$873$		−	23.4304i		−	0.792998i
$874$	−9.61201			−0.325131
$875$	−25.4205	−	26.3158i	−0.859371	−	0.889637i
$876$	15.5002			0.523704
$877$		−	4.79011i		−	0.161751i	−0.996724	−	0.0808753i	$-0.974228\pi$
$877$		−	4.79011i		−	0.161751i	0.996724	−	0.0808753i	$-0.0257716\pi$
$878$			11.2518i			0.379729i
$879$	0.0235501			0.000794325
$880$		0			0
$881$	33.9748			1.14464			0.572320	−	0.820031i	$-0.306044\pi$
$881$	33.9748			1.14464			0.572320	+	0.820031i	$0.306044\pi$
$882$		−	2.52706i		−	0.0850905i
$883$		−	39.2743i		−	1.32169i	−0.750524	−	0.660843i	$-0.770199\pi$
$883$		−	39.2743i		−	1.32169i	0.750524	−	0.660843i	$-0.229801\pi$
$884$	35.4806			1.19334
$885$	−1.09422	−	0.299969i	−0.0367817	−	0.0100834i
$886$	−6.07224			−0.204001
$887$			33.2519i			1.11649i	0.829677	+	0.558244i	$0.188525\pi$
$887$			33.2519i			1.11649i	−0.829677	+	0.558244i	$0.811475\pi$
$888$			7.66801i			0.257322i
$889$	17.7239			0.594441
$890$	6.37280	+	1.74704i	0.213617	+	0.0585610i
$891$		0			0
$892$			44.8578i			1.50195i
$893$			4.81906i			0.161264i
$894$	−4.39946			−0.147140
$895$	2.14911	−	7.83945i	0.0718369	−	0.262044i
$896$	29.9002			0.998896
$897$		−	29.2736i		−	0.977418i
$898$		−	6.16340i		−	0.205675i
$899$	6.66994			0.222455
$900$	−16.8833	−	10.0090i	−0.562778	−	0.333634i
$901$	1.41618			0.0471797
$902$		0			0
$903$			1.87893i			0.0625267i
$904$	12.6236			0.419853
$905$	−7.43045	+	27.1045i	−0.246997	+	0.900985i
$906$	5.06454			0.168258
$907$			18.3497i			0.609293i	0.952466	+	0.304646i	$0.0985383\pi$
$907$			18.3497i			0.609293i	−0.952466	+	0.304646i	$0.901462\pi$
$908$			1.35591i			0.0449974i
$909$	−27.3158			−0.906007
$910$	−12.0667	−	3.30799i	−0.400009	−	0.109659i
$911$	38.8121			1.28590			0.642951	−	0.765908i	$-0.277710\pi$
$911$	38.8121			1.28590			0.642951	+	0.765908i	$0.277710\pi$
$912$			16.2149i			0.536928i
$913$		0			0
$914$	−4.76076			−0.157472
$915$	−11.0476	−	3.02860i	−0.365222	−	0.100122i
$916$	−24.8806			−0.822077
$917$		−	62.5852i		−	2.06675i
$918$			5.77200i			0.190504i
$919$	0.981676			0.0323825			0.0161912	−	0.999869i	$-0.494846\pi$
$919$	0.981676			0.0323825			0.0161912	+	0.999869i	$0.494846\pi$
$920$	4.41514	−	16.1054i	0.145563	−	0.530979i
$921$	−31.7170			−1.04511
$922$		−	4.99585i		−	0.164529i
$923$			65.2340i			2.14720i
$924$		0			0
$925$	−15.9030	+	26.8254i	−0.522888	+	0.882012i
$926$	2.98162			0.0979822
$927$		−	5.77200i		−	0.189577i
$928$		−	7.49708i		−	0.246104i
$929$	−35.0100			−1.14864			−0.574321	−	0.818630i	$-0.694734\pi$
$929$	−35.0100			−1.14864			−0.574321	+	0.818630i	$0.694734\pi$
$930$	−0.608197	+	2.21856i	−0.0199436	+	0.0727494i
$931$	−18.5840			−0.609066
$932$			50.9616i			1.66930i
$933$		−	4.64229i		−	0.151982i
$934$	−5.67522			−0.185699
$935$		0			0
$936$	−13.8060			−0.451263
$937$			30.8555i			1.00801i	0.863702	+	0.504003i	$0.168140\pi$
$937$			30.8555i			1.00801i	−0.863702	+	0.504003i	$0.831860\pi$
$938$		−	9.08060i		−	0.296492i
$939$	−16.4177			−0.535770
$940$	−3.92544	−	1.07612i	−0.128034	−	0.0350993i
$941$	−30.0766			−0.980469			−0.490235	−	0.871590i	$-0.663089\pi$
$941$	−30.0766			−0.980469			−0.490235	+	0.871590i	$0.663089\pi$
$942$			0.718574i			0.0234124i
$943$		−	59.6385i		−	1.94210i
$944$	1.77472			0.0577622
$945$	−9.44468	+	34.4520i	−0.307236	+	1.12072i
$946$		0			0
$947$		−	10.1860i		−	0.331002i	−0.986210	−	0.165501i	$-0.947076\pi$
$947$		−	10.1860i		−	0.331002i	0.986210	−	0.165501i	$-0.0529241\pi$
$948$			5.15569i			0.167449i
$949$	44.3415			1.43939
$950$	4.19399	−	7.07447i	0.136071	−	0.229526i
$951$	−1.65134			−0.0535483
$952$		−	15.0604i		−	0.488112i
$953$		−	40.1472i		−	1.30050i	−0.759722	−	0.650248i	$-0.774665\pi$
$953$		−	40.1472i		−	1.30050i	0.759722	−	0.650248i	$-0.225335\pi$
$954$	−0.267895			−0.00867343
$955$	1.58234	−	5.77200i	0.0512033	−	0.186778i
$956$	9.47874			0.306564
$957$		0			0
$958$			10.7143i			0.346162i
$959$	−52.5016			−1.69537
$960$	−11.4670	−	3.14357i	−0.370096	−	0.101458i
$961$	−20.3924			−0.657821
$962$			10.6641i			0.343825i
$963$		−	33.0896i		−	1.06630i
$964$	8.88105			0.286039
$965$	−0.837223	−	0.229517i	−0.0269511	−	0.00738840i
$966$	−6.04079			−0.194359
$967$		−	58.0856i		−	1.86791i	−0.357395	−	0.933953i	$-0.616335\pi$
$967$		−	58.0856i		−	1.86791i	0.357395	−	0.933953i	$-0.383665\pi$
$968$		0			0
$969$	17.3531			0.557462
$970$	−2.19238	+	7.99727i	−0.0703930	+	0.256777i
$971$	32.8121			1.05299			0.526495	−	0.850178i	$-0.323506\pi$
$971$	32.8121			1.05299			0.526495	+	0.850178i	$0.323506\pi$
$972$			30.4918i			0.978024i
$973$			41.1343i			1.31871i
$974$	−5.00941			−0.160512
$975$	21.5455	+	12.7729i	0.690008	+	0.409061i
$976$	17.9182			0.573548
$977$			17.9245i			0.573454i	0.958012	+	0.286727i	$0.0925673\pi$
$977$			17.9245i			0.573454i	−0.958012	+	0.286727i	$0.907433\pi$
$978$			7.12908i			0.227963i
$979$		0			0
$980$	4.14992	−	15.1379i	0.132564	−	0.483563i
$981$	−8.10966			−0.258922
$982$		−	2.19008i		−	0.0698882i
$983$		−	17.0766i		−	0.544658i	−0.962204	−	0.272329i	$-0.912206\pi$
$983$		−	17.0766i		−	0.544658i	0.962204	−	0.272329i	$-0.0877939\pi$
$984$	12.5471			0.399987
$985$	39.9850	+	10.9615i	1.27403	+	0.349263i
$986$	−2.42140			−0.0771132
$987$			3.02860i			0.0964013i
$988$			49.3585i			1.57030i
$989$	−3.48765			−0.110901
$990$		0			0
$991$	17.5551			0.557658			0.278829	−	0.960341i	$-0.410054\pi$
$991$	17.5551			0.557658			0.278829	+	0.960341i	$0.410054\pi$
$992$		−	11.9230i		−	0.378556i
$993$			0.858283i			0.0272368i
$994$	13.4614			0.426971
$995$	6.00000	−	21.8866i	0.190213	−	0.693851i
$996$	−22.0995			−0.700249
$997$			15.2047i			0.481537i	0.970583	+	0.240769i	$0.0773995\pi$
$997$			15.2047i			0.481537i	−0.970583	+	0.240769i	$0.922600\pi$
$998$			2.01906i			0.0639124i
$999$	30.4473			0.963311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.b.h.364.8	yes	12
5.2	odd	4		3025.2.a.bo.1.6		12
5.3	odd	4		3025.2.a.bo.1.7		12
5.4	even	2	inner	605.2.b.h.364.5	✓	12
11.2	odd	10		605.2.j.k.444.6		48
11.3	even	5		605.2.j.k.9.7		48
11.4	even	5		605.2.j.k.269.6		48
11.5	even	5		605.2.j.k.124.5		48
11.6	odd	10		605.2.j.k.124.7		48
11.7	odd	10		605.2.j.k.269.8		48
11.8	odd	10		605.2.j.k.9.5		48
11.9	even	5		605.2.j.k.444.8		48
11.10	odd	2	inner	605.2.b.h.364.6	yes	12
55.4	even	10		605.2.j.k.269.7		48
55.9	even	10		605.2.j.k.444.5		48
55.14	even	10		605.2.j.k.9.6		48
55.19	odd	10		605.2.j.k.9.8		48
55.24	odd	10		605.2.j.k.444.7		48
55.29	odd	10		605.2.j.k.269.5		48
55.32	even	4		3025.2.a.bo.1.8		12
55.39	odd	10		605.2.j.k.124.6		48
55.43	even	4		3025.2.a.bo.1.5		12
55.49	even	10		605.2.j.k.124.8		48
55.54	odd	2	inner	605.2.b.h.364.7	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.h.364.5	✓	12	5.4	even	2	inner
605.2.b.h.364.6	yes	12	11.10	odd	2	inner
605.2.b.h.364.7	yes	12	55.54	odd	2	inner
605.2.b.h.364.8	yes	12	1.1	even	1	trivial
605.2.j.k.9.5		48	11.8	odd	10
605.2.j.k.9.6		48	55.14	even	10
605.2.j.k.9.7		48	11.3	even	5
605.2.j.k.9.8		48	55.19	odd	10
605.2.j.k.124.5		48	11.5	even	5
605.2.j.k.124.6		48	55.39	odd	10
605.2.j.k.124.7		48	11.6	odd	10
605.2.j.k.124.8		48	55.49	even	10
605.2.j.k.269.5		48	55.29	odd	10
605.2.j.k.269.6		48	11.4	even	5
605.2.j.k.269.7		48	55.4	even	10
605.2.j.k.269.8		48	11.7	odd	10
605.2.j.k.444.5		48	55.9	even	10
605.2.j.k.444.6		48	11.2	odd	10
605.2.j.k.444.7		48	55.24	odd	10
605.2.j.k.444.8		48	11.9	even	5
3025.2.a.bo.1.5		12	55.43	even	4
3025.2.a.bo.1.6		12	5.2	odd	4
3025.2.a.bo.1.7		12	5.3	odd	4
3025.2.a.bo.1.8		12	55.32	even	4

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.328351i q^{2} +0.962000i q^{3} +1.89219 q^{4} +(-0.591185 + 2.15650i) q^{5} -0.315873 q^{6} -3.27259i q^{7} +1.27800i q^{8} +2.07456 q^{9} +O(q^{10})\)	\(q+0.328351i q^{2} +0.962000i q^{3} +1.89219 q^{4} +(-0.591185 + 2.15650i) q^{5} -0.315873 q^{6} -3.27259i q^{7} +1.27800i q^{8} +2.07456 q^{9} +(-0.708089 - 0.194116i) q^{10} +1.82028i q^{12} +5.20729i q^{13} +1.07456 q^{14} +(-2.07456 - 0.568720i) q^{15} +3.36474 q^{16} -3.60094i q^{17} +0.681182i q^{18} +5.00941 q^{19} +(-1.11863 + 4.08050i) q^{20} +3.14823 q^{21} +5.84372i q^{23} -1.22944 q^{24} +(-4.30100 - 2.54978i) q^{25} -1.70982 q^{26} +4.88172i q^{27} -6.19234i q^{28} -2.04792 q^{29} +(0.186740 - 0.681182i) q^{30} -3.25693 q^{31} +3.66082i q^{32} +1.18237 q^{34} +(7.05734 + 1.93470i) q^{35} +3.92544 q^{36} -6.23700i q^{37} +1.64484i q^{38} -5.00941 q^{39} +(-2.75601 - 0.755535i) q^{40} -10.2056 q^{41} +1.03372i q^{42} +0.596820i q^{43} +(-1.22645 + 4.47378i) q^{45} -1.91879 q^{46} +0.962000i q^{47} +3.23688i q^{48} -3.70982 q^{49} +(0.837223 - 1.41224i) q^{50} +3.46410 q^{51} +9.85316i q^{52} +0.393280i q^{53} -1.60292 q^{54} +4.18237 q^{56} +4.81906i q^{57} -0.672437i q^{58} +0.527447 q^{59} +(-3.92544 - 1.07612i) q^{60} +5.32529 q^{61} -1.06941i q^{62} -6.78916i q^{63} +5.52745 q^{64} +(-11.2295 - 3.07847i) q^{65} -8.45057i q^{67} -6.81364i q^{68} -5.62166 q^{69} +(-0.635261 + 2.31728i) q^{70} +12.5274 q^{71} +2.65129i q^{72} -8.51527i q^{73} +2.04792 q^{74} +(2.45289 - 4.13756i) q^{75} +9.47874 q^{76} -1.64484i q^{78} +2.83235 q^{79} +(-1.98918 + 7.25607i) q^{80} +1.52745 q^{81} -3.35100i q^{82} +12.1407i q^{83} +5.95703 q^{84} +(7.76543 + 2.12882i) q^{85} -0.195966 q^{86} -1.97010i q^{87} -9.00000 q^{89} +(-1.46897 - 0.402704i) q^{90} +17.0413 q^{91} +11.0574i q^{92} -3.13316i q^{93} -0.315873 q^{94} +(-2.96149 + 10.8028i) q^{95} -3.52171 q^{96} -11.2942i q^{97} -1.21812i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9}+O(q^{10}) \) 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9	\( 12 q - 20 q^{4} - 6 q^{5} - 20 q^{9} - 32 q^{14} + 20 q^{15} + 36 q^{16} + 26 q^{20} - 10 q^{25} + 20 q^{26} + 8 q^{31} + 12 q^{34} + 92 q^{36} - 18 q^{45} - 4 q^{49} + 48 q^{56} - 32 q^{59} - 92 q^{60} + 28 q^{64} - 16 q^{69} - 12 q^{70} + 112 q^{71} + 36 q^{75} - 106 q^{80} - 20 q^{81} - 56 q^{86} - 108 q^{89} + 72 q^{91}+O(q^{100}) \) 12 * q - 20 * q^4 - 6 * q^5 - 20 * q^9 - 32 * q^14 + 20 * q^15 + 36 * q^16 + 26 * q^20 - 10 * q^25 + 20 * q^26 + 8 * q^31 + 12 * q^34 + 92 * q^36 - 18 * q^45 - 4 * q^49 + 48 * q^56 - 32 * q^59 - 92 * q^60 + 28 * q^64 - 16 * q^69 - 12 * q^70 + 112 * q^71 + 36 * q^75 - 106 * q^80 - 20 * q^81 - 56 * q^86 - 108 * q^89 + 72 * q^91

Introduction

L-functions

Modular forms

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Database

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