LMFDB - Embedded newform 1815.2.c.i.364.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.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:	$14.4928479669$
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} + 21x^{10} + 164x^{8} + 589x^{6} + 965x^{4} + 576x^{2} + 4 $ x^12 + 21x^10 + 164x^8 + 589x^6 + 965x^4 + 576*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.5
Root			$-1.19557i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.i.364.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19557i q^{2} +1.00000i q^{3} +0.570614 q^{4} +(0.849151 - 2.06856i) q^{5} +1.19557 q^{6} +3.76208i q^{7} -3.07335i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.19557i q^{2} +1.00000i q^{3} +0.570614 q^{4} +(0.849151 - 2.06856i) q^{5} +1.19557 q^{6} +3.76208i q^{7} -3.07335i q^{8} -1.00000 q^{9} +(-2.47311 - 1.01522i) q^{10} +0.570614i q^{12} +1.11079i q^{13} +4.49782 q^{14} +(2.06856 + 0.849151i) q^{15} -2.53317 q^{16} +5.57117i q^{17} +1.19557i q^{18} +1.37094 q^{19} +(0.484538 - 1.18035i) q^{20} -3.76208 q^{21} -2.35369i q^{23} +3.07335 q^{24} +(-3.55789 - 3.51304i) q^{25} +1.32803 q^{26} -1.00000i q^{27} +2.14669i q^{28} +10.3637 q^{29} +(1.01522 - 2.47311i) q^{30} +9.94621 q^{31} -3.11811i q^{32} +6.66072 q^{34} +(7.78208 + 3.19457i) q^{35} -0.570614 q^{36} +4.01410i q^{37} -1.63905i q^{38} -1.11079 q^{39} +(-6.35740 - 2.60974i) q^{40} +3.94075 q^{41} +4.49782i q^{42} +7.78774i q^{43} +(-0.849151 + 2.06856i) q^{45} -2.81400 q^{46} -6.46038i q^{47} -2.53317i q^{48} -7.15321 q^{49} +(-4.20008 + 4.25370i) q^{50} -5.57117 q^{51} +0.633833i q^{52} +4.06788i q^{53} -1.19557 q^{54} +11.5622 q^{56} +1.37094i q^{57} -12.3905i q^{58} +4.28445 q^{59} +(1.18035 + 0.484538i) q^{60} -8.32914 q^{61} -11.8914i q^{62} -3.76208i q^{63} -8.79426 q^{64} +(2.29774 + 0.943230i) q^{65} -9.15868i q^{67} +3.17899i q^{68} +2.35369 q^{69} +(3.81933 - 9.30402i) q^{70} -2.85677 q^{71} +3.07335i q^{72} +11.6534i q^{73} +4.79913 q^{74} +(3.51304 - 3.55789i) q^{75} +0.782277 q^{76} +1.32803i q^{78} +3.07812 q^{79} +(-2.15104 + 5.24002i) q^{80} +1.00000 q^{81} -4.71144i q^{82} -4.64341i q^{83} -2.14669 q^{84} +(11.5243 + 4.73076i) q^{85} +9.31078 q^{86} +10.3637i q^{87} +16.5770 q^{89} +(2.47311 + 1.01522i) q^{90} -4.17888 q^{91} -1.34305i q^{92} +9.94621i q^{93} -7.72383 q^{94} +(1.16413 - 2.83587i) q^{95} +3.11811 q^{96} -18.1930i q^{97} +8.55216i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9	$ 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9} + 12 q^{10} + 20 q^{14} + 22 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{25} - 24 q^{29} - 8 q^{30} + 36 q^{31} + 2 q^{34} + 24 q^{35} + 18 q^{36} - 4 q^{39} - 22 q^{40} - 12 q^{41} + 2 q^{45} - 22 q^{46} - 24 q^{49} - 58 q^{50} + 4 q^{51} - 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} + 8 q^{61} - 44 q^{64} - 14 q^{65} - 24 q^{69} - 16 q^{70} + 8 q^{74} - 12 q^{75} - 40 q^{76} - 4 q^{79} - 58 q^{80} + 12 q^{81} + 48 q^{84} - 2 q^{85} + 56 q^{86} + 32 q^{89} - 12 q^{90} + 48 q^{91} - 6 q^{94} + 62 q^{96}+O(q^{100}) $ 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9 + 12 * q^10 + 20 * q^14 + 22 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^25 - 24 * q^29 - 8 * q^30 + 36 * q^31 + 2 * q^34 + 24 * q^35 + 18 * q^36 - 4 * q^39 - 22 * q^40 - 12 * q^41 + 2 * q^45 - 22 * q^46 - 24 * q^49 - 58 * q^50 + 4 * q^51 - 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 + 8 * q^61 - 44 * q^64 - 14 * q^65 - 24 * q^69 - 16 * q^70 + 8 * q^74 - 12 * q^75 - 40 * q^76 - 4 * q^79 - 58 * q^80 + 12 * q^81 + 48 * q^84 - 2 * q^85 + 56 * q^86 + 32 * q^89 - 12 * q^90 + 48 * q^91 - 6 * q^94 + 62 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.19557i		−	0.845395i	−0.906271	−	0.422698i	$-0.861083\pi$
$2$		−	1.19557i		−	0.845395i	0.906271	−	0.422698i	$-0.138917\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.570614			0.285307
$5$	0.849151	−	2.06856i	0.379752	−	0.925088i
$5$	0.849151	−	2.06856i	0.379752	−	0.925088i
$6$	1.19557			0.488089
$7$			3.76208i			1.42193i	0.703227	+	0.710965i	$0.251742\pi$
$7$			3.76208i			1.42193i	−0.703227	+	0.710965i	$0.748258\pi$
$8$		−	3.07335i		−	1.08659i
$9$	−1.00000			−0.333333
$10$	−2.47311	−	1.01522i	−0.782065	−	0.321040i
$11$		0			0
$11$		0			0
$12$			0.570614i			0.164722i
$13$			1.11079i			0.308078i	0.988065	+	0.154039i	$0.0492282\pi$
$13$			1.11079i			0.308078i	−0.988065	+	0.154039i	$0.950772\pi$
$14$	4.49782			1.20209
$15$	2.06856	+	0.849151i	0.534100	+	0.219250i
$16$	−2.53317			−0.633293
$17$			5.57117i			1.35121i	0.737265	+	0.675603i	$0.236117\pi$
$17$			5.57117i			1.35121i	−0.737265	+	0.675603i	$0.763883\pi$
$18$			1.19557i			0.281798i
$19$	1.37094			0.314515			0.157257	−	0.987558i	$-0.449735\pi$
$19$	1.37094			0.314515			0.157257	+	0.987558i	$0.449735\pi$
$20$	0.484538	−	1.18035i	0.108346	−	0.263934i
$21$	−3.76208			−0.820952
$22$		0			0
$23$		−	2.35369i		−	0.490779i	−0.969425	−	0.245390i	$-0.921084\pi$
$23$		−	2.35369i		−	0.490779i	0.969425	−	0.245390i	$-0.0789159\pi$
$24$	3.07335			0.627344
$25$	−3.55789	−	3.51304i	−0.711577	−	0.702608i
$26$	1.32803			0.260448
$27$		−	1.00000i		−	0.192450i
$28$			2.14669i			0.405687i
$29$	10.3637			1.92449			0.962244	−	0.272189i	$-0.0877477\pi$
$29$	10.3637			1.92449			0.962244	+	0.272189i	$0.0877477\pi$
$30$	1.01522	−	2.47311i	0.185353	−	0.451526i
$31$	9.94621			1.78639			0.893196	−	0.449667i	$-0.148457\pi$
$31$	9.94621			1.78639			0.893196	+	0.449667i	$0.148457\pi$
$32$		−	3.11811i		−	0.551210i
$33$		0			0
$34$	6.66072			1.14230
$35$	7.78208	+	3.19457i	1.31541	+	0.539981i
$36$	−0.570614			−0.0951024
$37$			4.01410i			0.659913i	0.943996	+	0.329957i	$0.107034\pi$
$37$			4.01410i			0.659913i	−0.943996	+	0.329957i	$0.892966\pi$
$38$		−	1.63905i		−	0.265889i
$39$	−1.11079			−0.177869
$40$	−6.35740	−	2.60974i	−1.00519	−	0.412635i
$41$	3.94075			0.615442			0.307721	−	0.951477i	$-0.400434\pi$
$41$	3.94075			0.615442			0.307721	+	0.951477i	$0.400434\pi$
$42$			4.49782i			0.694029i
$43$			7.78774i			1.18762i	0.804605	+	0.593810i	$0.202377\pi$
$43$			7.78774i			1.18762i	−0.804605	+	0.593810i	$0.797623\pi$
$44$		0			0
$45$	−0.849151	+	2.06856i	−0.126584	+	0.308363i
$46$	−2.81400			−0.414902
$47$		−	6.46038i		−	0.942343i	−0.882042	−	0.471171i	$-0.843831\pi$
$47$		−	6.46038i		−	0.942343i	0.882042	−	0.471171i	$-0.156169\pi$
$48$		−	2.53317i		−	0.365632i
$49$	−7.15321			−1.02189
$50$	−4.20008	+	4.25370i	−0.593981	+	0.601564i
$51$	−5.57117			−0.780120
$52$			0.633833i			0.0878969i
$53$			4.06788i			0.558766i	0.960180	+	0.279383i	$0.0901300\pi$
$53$			4.06788i			0.558766i	−0.960180	+	0.279383i	$0.909870\pi$
$54$	−1.19557			−0.162696
$55$		0			0
$56$	11.5622			1.54506
$57$			1.37094i			0.181585i
$58$		−	12.3905i		−	1.62695i
$59$	4.28445			0.557789			0.278894	−	0.960322i	$-0.410032\pi$
$59$	4.28445			0.557789			0.278894	+	0.960322i	$0.410032\pi$
$60$	1.18035	+	0.484538i	0.152383	+	0.0625536i
$61$	−8.32914			−1.06644			−0.533218	−	0.845978i	$-0.679018\pi$
$61$	−8.32914			−1.06644			−0.533218	+	0.845978i	$0.679018\pi$
$62$		−	11.8914i		−	1.51021i
$63$		−	3.76208i		−	0.473977i
$64$	−8.79426			−1.09928
$65$	2.29774	+	0.943230i	0.284999	+	0.116993i
$66$		0			0
$67$		−	9.15868i		−	1.11891i	−0.828860	−	0.559455i	$-0.811010\pi$
$67$		−	9.15868i		−	1.11891i	0.828860	−	0.559455i	$-0.188990\pi$
$68$			3.17899i			0.385509i
$69$	2.35369			0.283352
$70$	3.81933	−	9.30402i	0.456497	−	1.11204i
$71$	−2.85677			−0.339037			−0.169518	−	0.985527i	$-0.554221\pi$
$71$	−2.85677			−0.339037			−0.169518	+	0.985527i	$0.554221\pi$
$72$			3.07335i			0.362197i
$73$			11.6534i			1.36393i	0.731386	+	0.681963i	$0.238874\pi$
$73$			11.6534i			1.36393i	−0.731386	+	0.681963i	$0.761126\pi$
$74$	4.79913			0.557887
$75$	3.51304	−	3.55789i	0.405651	−	0.410829i
$76$	0.782277			0.0897333
$77$		0			0
$78$			1.32803i			0.150370i
$79$	3.07812			0.346315			0.173158	−	0.984894i	$-0.444603\pi$
$79$	3.07812			0.346315			0.173158	+	0.984894i	$0.444603\pi$
$80$	−2.15104	+	5.24002i	−0.240494	+	0.585852i
$81$	1.00000			0.111111
$82$		−	4.71144i		−	0.520291i
$83$		−	4.64341i		−	0.509680i	−0.966983	−	0.254840i	$-0.917977\pi$
$83$		−	4.64341i		−	0.509680i	0.966983	−	0.254840i	$-0.0820228\pi$
$84$	−2.14669			−0.234224
$85$	11.5243	+	4.73076i	1.24999	+	0.513123i
$86$	9.31078			1.00401
$87$			10.3637i			1.11110i
$88$		0			0
$89$	16.5770			1.75716			0.878582	−	0.477592i	$-0.158490\pi$
$89$	16.5770			1.75716			0.878582	+	0.477592i	$0.158490\pi$
$90$	2.47311	+	1.01522i	0.260688	+	0.107013i
$91$	−4.17888			−0.438066
$92$		−	1.34305i		−	0.140023i
$93$			9.94621i			1.03137i
$94$	−7.72383			−0.796652
$95$	1.16413	−	2.83587i	0.119438	−	0.290954i
$96$	3.11811			0.318241
$97$		−	18.1930i		−	1.84722i	−0.383337	−	0.923608i	$-0.625225\pi$
$97$		−	18.1930i		−	1.84722i	0.383337	−	0.923608i	$-0.374775\pi$
$98$			8.55216i			0.863899i
$99$		0			0
$100$	−2.03018	−	2.00459i	−0.203018	−	0.200459i
$101$	2.16756			0.215680			0.107840	−	0.994168i	$-0.465607\pi$
$101$	2.16756			0.215680			0.107840	+	0.994168i	$0.465607\pi$
$102$			6.66072i			0.659509i
$103$			11.5176i			1.13487i	0.823420	+	0.567433i	$0.192063\pi$
$103$			11.5176i			1.13487i	−0.823420	+	0.567433i	$0.807937\pi$
$104$	3.41385			0.334755
$105$	−3.19457	+	7.78208i	−0.311758	+	0.759453i
$106$	4.86343			0.472378
$107$		−	4.23880i		−	0.409780i	−0.978785	−	0.204890i	$-0.934316\pi$
$107$		−	4.23880i		−	0.409780i	0.978785	−	0.204890i	$-0.0656836\pi$
$108$		−	0.570614i		−	0.0549074i
$109$	−16.2407			−1.55557			−0.777786	−	0.628529i	$-0.783657\pi$
$109$	−16.2407			−1.55557			−0.777786	+	0.628529i	$0.783657\pi$
$110$		0			0
$111$	−4.01410			−0.381001
$112$		−	9.52998i		−	0.900498i
$113$			13.0953i			1.23190i	0.787784	+	0.615952i	$0.211229\pi$
$113$			13.0953i			1.23190i	−0.787784	+	0.615952i	$0.788771\pi$
$114$	1.63905			0.153511
$115$	−4.86876	−	1.99864i	−0.454014	−	0.186374i
$116$	5.91367			0.549070
$117$		−	1.11079i		−	0.102693i
$118$		−	5.12236i		−	0.471552i
$119$	−20.9592			−1.92132
$120$	2.60974	−	6.35740i	0.238235	−	0.580349i
$121$		0			0
$122$			9.95806i			0.901560i
$123$			3.94075i			0.355325i
$124$	5.67545			0.509671
$125$	−10.2881	+	4.37660i	−0.920197	+	0.391455i
$126$	−4.49782			−0.400698
$127$		−	8.72553i		−	0.774266i	−0.922024	−	0.387133i	$-0.873465\pi$
$127$		−	8.72553i		−	0.774266i	0.922024	−	0.387133i	$-0.126535\pi$
$128$			4.27792i			0.378118i
$129$	−7.78774			−0.685672
$130$	1.12770	−	2.74711i	0.0989055	−	0.240937i
$131$	−14.4100			−1.25901			−0.629504	−	0.776997i	$-0.716742\pi$
$131$	−14.4100			−1.25901			−0.629504	+	0.776997i	$0.716742\pi$
$132$		0			0
$133$			5.15757i			0.447218i
$134$	−10.9498			−0.945922
$135$	−2.06856	−	0.849151i	−0.178033	−	0.0730833i
$136$	17.1221			1.46821
$137$			9.98253i			0.852865i	0.904519	+	0.426433i	$0.140230\pi$
$137$			9.98253i			0.852865i	−0.904519	+	0.426433i	$0.859770\pi$
$138$		−	2.81400i		−	0.239544i
$139$	7.60360			0.644929			0.322465	−	0.946582i	$-0.395489\pi$
$139$	7.60360			0.644929			0.322465	+	0.946582i	$0.395489\pi$
$140$	4.44057	+	1.82287i	0.375296	+	0.154060i
$141$	6.46038			0.544062
$142$			3.41547i			0.286620i
$143$		0			0
$144$	2.53317			0.211098
$145$	8.80033	−	21.4379i	0.730828	−	1.78032i
$146$	13.9324			1.15306
$147$		−	7.15321i		−	0.589987i
$148$			2.29050i			0.188278i
$149$	−6.47125			−0.530146			−0.265073	−	0.964228i	$-0.585396\pi$
$149$	−6.47125			−0.530146			−0.265073	+	0.964228i	$0.585396\pi$
$150$	−4.25370	−	4.20008i	−0.347313	−	0.342935i
$151$	9.52872			0.775436			0.387718	−	0.921778i	$-0.373263\pi$
$151$	9.52872			0.775436			0.387718	+	0.921778i	$0.373263\pi$
$152$		−	4.21337i		−	0.341749i
$153$		−	5.57117i		−	0.450402i
$154$		0			0
$155$	8.44584	−	20.5743i	0.678386	−	1.65257i
$156$	−0.633833			−0.0507473
$157$			3.16690i			0.252746i	0.991983	+	0.126373i	$0.0403336\pi$
$157$			3.16690i			0.252746i	−0.991983	+	0.126373i	$0.959666\pi$
$158$		−	3.68010i		−	0.292773i
$159$	−4.06788			−0.322604
$160$	−6.45001	−	2.64775i	−0.509918	−	0.209323i
$161$	8.85478			0.697854
$162$		−	1.19557i		−	0.0939328i
$163$			9.02020i			0.706517i	0.935526	+	0.353258i	$0.114926\pi$
$163$			9.02020i			0.706517i	−0.935526	+	0.353258i	$0.885074\pi$
$164$	2.24865			0.175590
$165$		0			0
$166$	−5.55151			−0.430881
$167$		−	3.13597i		−	0.242669i	−0.992612	−	0.121334i	$-0.961283\pi$
$167$		−	3.13597i		−	0.242669i	0.992612	−	0.121334i	$-0.0387173\pi$
$168$			11.5622i			0.892040i
$169$	11.7661			0.905088
$170$	5.65596	−	13.7781i	0.433792	−	1.05673i
$171$	−1.37094			−0.104838
$172$			4.44380i			0.338836i
$173$		−	12.2424i		−	0.930776i	−0.885107	−	0.465388i	$-0.845915\pi$
$173$		−	12.2424i		−	0.930776i	0.885107	−	0.465388i	$-0.154085\pi$
$174$	12.3905			0.939321
$175$	13.2163	−	13.3850i	0.999060	−	1.01181i
$176$		0			0
$177$			4.28445i			0.322039i
$178$		−	19.8190i		−	1.48550i
$179$	8.46334			0.632579			0.316290	−	0.948663i	$-0.397563\pi$
$179$	8.46334			0.632579			0.316290	+	0.948663i	$0.397563\pi$
$180$	−0.484538	+	1.18035i	−0.0361153	+	0.0879781i
$181$	23.5514			1.75056			0.875282	−	0.483612i	$-0.160675\pi$
$181$	23.5514			1.75056			0.875282	+	0.483612i	$0.160675\pi$
$182$			4.99614i			0.370339i
$183$		−	8.32914i		−	0.615708i
$184$	−7.23372			−0.533277
$185$	8.30340	+	3.40857i	0.610478	+	0.250603i
$186$	11.8914			0.871919
$187$		0			0
$188$		−	3.68638i		−	0.268857i
$189$	3.76208			0.273651
$190$	−3.39048	−	1.39180i	−0.245971	−	0.100972i
$191$	−19.2179			−1.39056			−0.695278	−	0.718741i	$-0.744719\pi$
$191$	−19.2179			−1.39056			−0.695278	+	0.718741i	$0.744719\pi$
$192$		−	8.79426i		−	0.634671i
$193$		−	14.1416i		−	1.01794i	−0.860785	−	0.508969i	$-0.830027\pi$
$193$		−	14.1416i		−	1.01794i	0.860785	−	0.508969i	$-0.169973\pi$
$194$	−21.7510			−1.56163
$195$	−0.943230	+	2.29774i	−0.0675461	+	0.164544i
$196$	−4.08173			−0.291552
$197$		−	10.2965i		−	0.733593i	−0.930301	−	0.366796i	$-0.880455\pi$
$197$		−	10.2965i		−	0.733593i	0.930301	−	0.366796i	$-0.119545\pi$
$198$		0			0
$199$	−26.3053			−1.86473			−0.932367	−	0.361514i	$-0.882260\pi$
$199$	−26.3053			−1.86473			−0.932367	+	0.361514i	$0.882260\pi$
$200$	−10.7968	+	10.9346i	−0.763449	+	0.773194i
$201$	9.15868			0.646003
$202$		−	2.59147i		−	0.182335i
$203$			38.9890i			2.73649i
$204$	−3.17899			−0.222574
$205$	3.34629	−	8.15168i	0.233715	−	0.569338i
$206$	13.7701			0.959410
$207$			2.35369i			0.163593i
$208$		−	2.81382i		−	0.195104i
$209$		0			0
$210$	9.30402	+	3.81933i	0.642038	+	0.263559i
$211$	−0.360214			−0.0247981			−0.0123991	−	0.999923i	$-0.503947\pi$
$211$	−0.360214			−0.0247981			−0.0123991	+	0.999923i	$0.503947\pi$
$212$			2.32119i			0.159420i
$213$		−	2.85677i		−	0.195743i
$214$	−5.06777			−0.346426
$215$	16.1094	+	6.61297i	1.09865	+	0.451001i
$216$	−3.07335			−0.209115
$217$			37.4184i			2.54013i
$218$			19.4168i			1.31507i
$219$	−11.6534			−0.787463
$220$		0			0
$221$	−6.18841			−0.416277
$222$			4.79913i			0.322096i
$223$		−	26.4883i		−	1.77379i	−0.461971	−	0.886895i	$-0.652858\pi$
$223$		−	26.4883i		−	1.77379i	0.461971	−	0.886895i	$-0.347142\pi$
$224$	11.7306			0.783782
$225$	3.55789	+	3.51304i	0.237192	+	0.234203i
$226$	15.6564			1.04145
$227$		−	23.3780i		−	1.55165i	−0.630946	−	0.775827i	$-0.717333\pi$
$227$		−	23.3780i		−	1.55165i	0.630946	−	0.775827i	$-0.282667\pi$
$228$			0.782277i			0.0518075i
$229$	10.1085			0.667986			0.333993	−	0.942576i	$-0.391604\pi$
$229$	10.1085			0.667986			0.333993	+	0.942576i	$0.391604\pi$
$230$	−2.38951	+	5.82094i	−0.157560	+	0.383821i
$231$		0			0
$232$		−	31.8512i		−	2.09113i
$233$			4.17456i			0.273485i	0.990607	+	0.136742i	$0.0436633\pi$
$233$			4.17456i			0.273485i	−0.990607	+	0.136742i	$0.956337\pi$
$234$	−1.32803			−0.0868159
$235$	−13.3637	−	5.48584i	−0.871751	−	0.357857i
$236$	2.44477			0.159141
$237$			3.07812i			0.199945i
$238$			25.0581i			1.62428i
$239$	−23.8799			−1.54466			−0.772332	−	0.635219i	$-0.780910\pi$
$239$	−23.8799			−1.54466			−0.772332	+	0.635219i	$0.780910\pi$
$240$	−5.24002	−	2.15104i	−0.338242	−	0.138849i
$241$	−15.6656			−1.00911			−0.504555	−	0.863380i	$-0.668343\pi$
$241$	−15.6656			−1.00911			−0.504555	+	0.863380i	$0.668343\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	−4.75273			−0.304262
$245$	−6.07416	+	14.7969i	−0.388064	+	0.945336i
$246$	4.71144			0.300390
$247$			1.52283i			0.0968951i
$248$		−	30.5682i		−	1.94108i
$249$	4.64341			0.294264
$250$	5.23253	+	12.3002i	0.330934	+	0.777930i
$251$	−6.30803			−0.398160			−0.199080	−	0.979983i	$-0.563795\pi$
$251$	−6.30803			−0.398160			−0.199080	+	0.979983i	$0.563795\pi$
$252$		−	2.14669i		−	0.135229i
$253$		0			0
$254$	−10.4320			−0.654561
$255$	−4.73076	+	11.5243i	−0.296252	+	0.721680i
$256$	−12.4740			−0.779623
$257$		−	8.20364i		−	0.511729i	−0.966713	−	0.255865i	$-0.917640\pi$
$257$		−	8.20364i		−	0.511729i	0.966713	−	0.255865i	$-0.0823601\pi$
$258$			9.31078i			0.579664i
$259$	−15.1013			−0.938351
$260$	1.31112	+	0.538220i	0.0813124	+	0.0333790i
$261$	−10.3637			−0.641496
$262$			17.2282i			1.06436i
$263$			9.84566i			0.607109i	0.952814	+	0.303555i	$0.0981735\pi$
$263$			9.84566i			0.607109i	−0.952814	+	0.303555i	$0.901826\pi$
$264$		0			0
$265$	8.41466	+	3.45425i	0.516908	+	0.212193i
$266$	6.16623			0.378076
$267$			16.5770i			1.01450i
$268$		−	5.22607i		−	0.319233i
$269$	−17.6147			−1.07399			−0.536994	−	0.843586i	$-0.680440\pi$
$269$	−17.6147			−1.07399			−0.536994	+	0.843586i	$0.680440\pi$
$270$	−1.01522	+	2.47311i	−0.0617842	+	0.150509i
$271$	−1.25356			−0.0761484			−0.0380742	−	0.999275i	$-0.512122\pi$
$271$	−1.25356			−0.0761484			−0.0380742	+	0.999275i	$0.512122\pi$
$272$		−	14.1127i		−	0.855709i
$273$		−	4.17888i		−	0.252917i
$274$	11.9348			0.721008
$275$		0			0
$276$	1.34305			0.0808422
$277$			16.3707i			0.983623i	0.870702	+	0.491811i	$0.163665\pi$
$277$			16.3707i			0.983623i	−0.870702	+	0.491811i	$0.836335\pi$
$278$		−	9.09063i		−	0.545220i
$279$	−9.94621			−0.595464
$280$	9.81802	−	23.9170i	0.586739	−	1.42932i
$281$	11.7669			0.701953			0.350977	−	0.936384i	$-0.385850\pi$
$281$	11.7669			0.701953			0.350977	+	0.936384i	$0.385850\pi$
$282$		−	7.72383i		−	0.459947i
$283$		−	3.16579i		−	0.188186i	−0.995563	−	0.0940932i	$-0.970005\pi$
$283$		−	3.16579i		−	0.188186i	0.995563	−	0.0940932i	$-0.0299952\pi$
$284$	−1.63012			−0.0967296
$285$	2.83587	+	1.16413i	0.167982	+	0.0689573i
$286$		0			0
$287$			14.8254i			0.875115i
$288$			3.11811i			0.183737i
$289$	−14.0379			−0.825760
$290$	−25.6305	−	10.5214i	−1.50507	−	0.617838i
$291$	18.1930			1.06649
$292$			6.64959i			0.389138i
$293$			19.0522i			1.11304i	0.830834	+	0.556521i	$0.187864\pi$
$293$			19.0522i			1.11304i	−0.830834	+	0.556521i	$0.812136\pi$
$294$	−8.55216			−0.498772
$295$	3.63815	−	8.86265i	0.211821	−	0.516004i
$296$	12.3367			0.717057
$297$		0			0
$298$			7.73683i			0.448183i
$299$	2.61446			0.151198
$300$	2.00459	−	2.03018i	0.115735	−	0.117213i
$301$	−29.2981			−1.68871
$302$		−	11.3922i		−	0.655550i
$303$			2.16756i			0.124523i
$304$	−3.47282			−0.199180
$305$	−7.07270	+	17.2293i	−0.404981	+	0.986548i
$306$	−6.66072			−0.380768
$307$		−	10.6573i		−	0.608242i	−0.952633	−	0.304121i	$-0.901637\pi$
$307$		−	10.6573i		−	0.608242i	0.952633	−	0.304121i	$-0.0983627\pi$
$308$		0			0
$309$	−11.5176			−0.655215
$310$	−24.5981	−	10.0976i	−1.39708	−	0.573504i
$311$	−11.4350			−0.648420			−0.324210	−	0.945985i	$-0.605098\pi$
$311$	−11.4350			−0.648420			−0.324210	+	0.945985i	$0.605098\pi$
$312$			3.41385i			0.193271i
$313$		−	0.0233313i		−	0.00131876i	−1.00000		0.000659382i	$-0.999790\pi$
$313$		−	0.0233313i		−	0.00131876i	1.00000		0.000659382i	$-0.000209888\pi$
$314$	3.78624			0.213670
$315$	−7.78208	−	3.19457i	−0.438471	−	0.179994i
$316$	1.75642			0.0988063
$317$		−	1.54123i		−	0.0865640i	−0.999063	−	0.0432820i	$-0.986219\pi$
$317$		−	1.54123i		−	0.0865640i	0.999063	−	0.0432820i	$-0.0137814\pi$
$318$			4.86343i			0.272728i
$319$		0			0
$320$	−7.46766	+	18.1915i	−0.417455	+	1.01693i
$321$	4.23880			0.236586
$322$		−	10.5865i		−	0.589962i
$323$			7.63772i			0.424974i
$324$	0.570614			0.0317008
$325$	3.90225	−	3.95207i	0.216458	−	0.219221i
$326$	10.7843			0.597286
$327$		−	16.2407i		−	0.898110i
$328$		−	12.1113i		−	0.668734i
$329$	24.3044			1.33995
$330$		0			0
$331$	−5.57394			−0.306372			−0.153186	−	0.988197i	$-0.548953\pi$
$331$	−5.57394			−0.306372			−0.153186	+	0.988197i	$0.548953\pi$
$332$		−	2.64959i		−	0.145415i
$333$		−	4.01410i		−	0.219971i
$334$	−3.74927			−0.205151
$335$	−18.9453	−	7.77710i	−1.03509	−	0.424908i
$336$	9.52998			0.519903
$337$			15.5366i			0.846335i	0.906052	+	0.423167i	$0.139082\pi$
$337$			15.5366i			0.846335i	−0.906052	+	0.423167i	$0.860918\pi$
$338$		−	14.0672i		−	0.765157i
$339$	−13.0953			−0.711240
$340$	6.57593	+	2.69944i	0.356630	+	0.146398i
$341$		0			0
$342$			1.63905i			0.0886297i
$343$		−	0.576403i		−	0.0311228i
$344$	23.9344			1.29046
$345$	1.99864	−	4.86876i	0.107603	−	0.262125i
$346$	−14.6367			−0.786873
$347$		−	2.00456i		−	0.107611i	−0.998551	−	0.0538053i	$-0.982865\pi$
$347$		−	2.00456i		−	0.107611i	0.998551	−	0.0538053i	$-0.0171350\pi$
$348$			5.91367i			0.317006i
$349$	−29.4300			−1.57535			−0.787675	−	0.616090i	$-0.788716\pi$
$349$	−29.4300			−1.57535			−0.787675	+	0.616090i	$0.788716\pi$
$350$	−16.0027	−	15.8010i	−0.855382	−	0.844601i
$351$	1.11079			0.0592896
$352$		0			0
$353$			25.0526i			1.33342i	0.745319	+	0.666708i	$0.232297\pi$
$353$			25.0526i			1.33342i	−0.745319	+	0.666708i	$0.767703\pi$
$354$	5.12236			0.272250
$355$	−2.42583	+	5.90941i	−0.128750	+	0.313639i
$356$	9.45910			0.501331
$357$		−	20.9592i		−	1.10928i
$358$		−	10.1185i		−	0.534780i
$359$	−20.4849			−1.08115			−0.540576	−	0.841295i	$-0.681794\pi$
$359$	−20.4849			−1.08115			−0.540576	+	0.841295i	$0.681794\pi$
$360$	6.35740	+	2.60974i	0.335065	+	0.137545i
$361$	−17.1205			−0.901081
$362$		−	28.1574i		−	1.47992i
$363$		0			0
$364$	−2.38453			−0.124983
$365$	24.1058	+	9.89549i	1.26175	+	0.517954i
$366$	−9.95806			−0.520516
$367$			14.5810i			0.761119i	0.924756	+	0.380560i	$0.124269\pi$
$367$			14.5810i			0.761119i	−0.924756	+	0.380560i	$0.875731\pi$
$368$			5.96231i			0.310807i
$369$	−3.94075			−0.205147
$370$	4.07519	−	9.92729i	0.211859	−	0.516095i
$371$	−15.3037			−0.794527
$372$			5.67545i			0.294259i
$373$			1.60074i			0.0828829i	0.999141	+	0.0414415i	$0.0131950\pi$
$373$			1.60074i			0.0828829i	−0.999141	+	0.0414415i	$0.986805\pi$
$374$		0			0
$375$	−4.37660	−	10.2881i	−0.226007	−	0.531276i
$376$	−19.8550			−1.02394
$377$			11.5119i			0.592892i
$378$		−	4.49782i		−	0.231343i
$379$	−14.2870			−0.733875			−0.366938	−	0.930246i	$-0.619594\pi$
$379$	−14.2870			−0.733875			−0.366938	+	0.930246i	$0.619594\pi$
$380$	0.664271	−	1.61819i	0.0340764	−	0.0830112i
$381$	8.72553			0.447023
$382$			22.9763i			1.17557i
$383$		−	6.52801i		−	0.333566i	−0.985994	−	0.166783i	$-0.946662\pi$
$383$		−	6.52801i		−	0.333566i	0.985994	−	0.166783i	$-0.0533379\pi$
$384$	−4.27792			−0.218307
$385$		0			0
$386$	−16.9073			−0.860560
$387$		−	7.78774i		−	0.395873i
$388$		−	10.3812i		−	0.527024i
$389$	27.3227			1.38532			0.692658	−	0.721266i	$-0.256439\pi$
$389$	27.3227			1.38532			0.692658	+	0.721266i	$0.256439\pi$
$390$	2.74711	+	1.12770i	0.139105	+	0.0571031i
$391$	13.1128			0.663144
$392$			21.9843i			1.11038i
$393$		−	14.4100i		−	0.726889i
$394$	−12.3101			−0.620176
$395$	2.61379	−	6.36727i	0.131514	−	0.320372i
$396$		0			0
$397$			3.24918i			0.163072i	0.996670	+	0.0815359i	$0.0259825\pi$
$397$			3.24918i			0.163072i	−0.996670	+	0.0815359i	$0.974017\pi$
$398$			31.4498i			1.57644i
$399$	−5.15757			−0.258201
$400$	9.01273	+	8.89913i	0.450636	+	0.444957i
$401$	11.2464			0.561620			0.280810	−	0.959763i	$-0.409397\pi$
$401$	11.2464			0.561620			0.280810	+	0.959763i	$0.409397\pi$
$402$		−	10.9498i		−	0.546128i
$403$			11.0482i			0.550348i
$404$	1.23684			0.0615351
$405$	0.849151	−	2.06856i	0.0421947	−	0.102788i
$406$	46.6140			2.31341
$407$		0			0
$408$			17.1221i			0.847672i
$409$	−14.4206			−0.713052			−0.356526	−	0.934285i	$-0.616039\pi$
$409$	−14.4206			−0.713052			−0.356526	+	0.934285i	$0.616039\pi$
$410$	−9.74589	−	4.00072i	−0.481315	−	0.197582i
$411$	−9.98253			−0.492402
$412$			6.57213i			0.323785i
$413$			16.1184i			0.793137i
$414$	2.81400			0.138301
$415$	−9.60517	−	3.94295i	−0.471499	−	0.193552i
$416$	3.46357			0.169816
$417$			7.60360i			0.372350i
$418$		0			0
$419$	−34.6547			−1.69299			−0.846496	−	0.532396i	$-0.821292\pi$
$419$	−34.6547			−1.69299			−0.846496	+	0.532396i	$0.821292\pi$
$420$	−1.82287	+	4.44057i	−0.0889468	+	0.216678i
$421$	4.87769			0.237724			0.118862	−	0.992911i	$-0.462075\pi$
$421$	4.87769			0.237724			0.118862	+	0.992911i	$0.462075\pi$
$422$			0.430661i			0.0209642i
$423$			6.46038i			0.314114i
$424$	12.5020			0.607151
$425$	19.5717	−	19.8216i	0.949369	−	0.961488i
$426$	−3.41547			−0.165480
$427$		−	31.3348i		−	1.51640i
$428$		−	2.41872i		−	0.116913i
$429$		0			0
$430$	7.90626	−	19.2599i	0.381274	−	0.928796i
$431$	12.1129			0.583458			0.291729	−	0.956501i	$-0.405769\pi$
$431$	12.1129			0.583458			0.291729	+	0.956501i	$0.405769\pi$
$432$			2.53317i			0.121877i
$433$			31.2618i			1.50234i	0.660107	+	0.751172i	$0.270511\pi$
$433$			31.2618i			1.50234i	−0.660107	+	0.751172i	$0.729489\pi$
$434$	44.7363			2.14741
$435$	21.4379	+	8.80033i	1.02787	+	0.421944i
$436$	−9.26715			−0.443816
$437$		−	3.22677i		−	0.154357i
$438$			13.9324i			0.665718i
$439$	−25.6088			−1.22224			−0.611122	−	0.791537i	$-0.709281\pi$
$439$	−25.6088			−1.22224			−0.611122	+	0.791537i	$0.709281\pi$
$440$		0			0
$441$	7.15321			0.340629
$442$			7.39867i			0.351919i
$443$		−	2.26739i		−	0.107727i	−0.998548	−	0.0538635i	$-0.982846\pi$
$443$		−	2.26739i		−	0.107727i	0.998548	−	0.0538635i	$-0.0171536\pi$
$444$	−2.29050			−0.108702
$445$	14.0764	−	34.2906i	0.667286	−	1.62553i
$446$	−31.6686			−1.49955
$447$		−	6.47125i		−	0.306080i
$448$		−	33.0847i		−	1.56310i
$449$	13.7183			0.647406			0.323703	−	0.946159i	$-0.395072\pi$
$449$	13.7183			0.647406			0.323703	+	0.946159i	$0.395072\pi$
$450$	4.20008	−	4.25370i	0.197994	−	0.200521i
$451$		0			0
$452$			7.47238i			0.351471i
$453$			9.52872i			0.447698i
$454$	−27.9500			−1.31176
$455$	−3.54850	+	8.64427i	−0.166356	+	0.405250i
$456$	4.21337			0.197309
$457$			16.1017i			0.753208i	0.926374	+	0.376604i	$0.122908\pi$
$457$			16.1017i			0.753208i	−0.926374	+	0.376604i	$0.877092\pi$
$458$		−	12.0854i		−	0.564712i
$459$	5.57117			0.260040
$460$	−2.77818	−	1.14045i	−0.129533	−	0.0531739i
$461$	−0.225594			−0.0105070			−0.00525348	−	0.999986i	$-0.501672\pi$
$461$	−0.225594			−0.0105070			−0.00525348	+	0.999986i	$0.501672\pi$
$462$		0			0
$463$			14.6080i			0.678893i	0.940625	+	0.339446i	$0.110240\pi$
$463$			14.6080i			0.678893i	−0.940625	+	0.339446i	$0.889760\pi$
$464$	−26.2530			−1.21876
$465$	20.5743	+	8.44584i	0.954112	+	0.391666i
$466$	4.99098			0.231203
$467$		−	39.8942i		−	1.84608i	−0.384699	−	0.923042i	$-0.625695\pi$
$467$		−	39.8942i		−	1.84608i	0.384699	−	0.923042i	$-0.374305\pi$
$468$		−	0.633833i		−	0.0292990i
$469$	34.4556			1.59101
$470$	−6.55870	+	15.9772i	−0.302530	+	0.736974i
$471$	−3.16690			−0.145923
$472$		−	13.1676i		−	0.606089i
$473$		0			0
$474$	3.68010			0.169033
$475$	−4.87764	−	4.81616i	−0.223801	−	0.220981i
$476$	−11.9596			−0.548167
$477$		−	4.06788i		−	0.186255i
$478$			28.5501i			1.30585i
$479$	31.2539			1.42803			0.714013	−	0.700132i	$-0.246876\pi$
$479$	31.2539			1.42803			0.714013	+	0.700132i	$0.246876\pi$
$480$	2.64775	−	6.45001i	0.120853	−	0.294401i
$481$	−4.45882			−0.203305
$482$			18.7293i			0.853096i
$483$			8.85478i			0.402906i
$484$		0			0
$485$	−37.6333	−	15.4486i	−1.70884	−	0.701484i
$486$	1.19557			0.0542321
$487$		−	19.7837i		−	0.896487i	−0.893911	−	0.448244i	$-0.852050\pi$
$487$		−	19.7837i		−	0.896487i	0.893911	−	0.448244i	$-0.147950\pi$
$488$			25.5983i			1.15878i
$489$	−9.02020			−0.407908
$490$	17.6907	+	7.26208i	0.799183	+	0.328067i
$491$	−24.6747			−1.11355			−0.556777	−	0.830662i	$-0.687962\pi$
$491$	−24.6747			−1.11355			−0.556777	+	0.830662i	$0.687962\pi$
$492$			2.24865i			0.101377i
$493$			57.7378i			2.60038i
$494$	1.82064			0.0819146
$495$		0			0
$496$	−25.1955			−1.13131
$497$		−	10.7474i		−	0.482087i
$498$		−	5.55151i		−	0.248769i
$499$	−32.8239			−1.46940			−0.734700	−	0.678392i	$-0.762677\pi$
$499$	−32.8239			−1.46940			−0.734700	+	0.678392i	$0.762677\pi$
$500$	−5.87055	+	2.49735i	−0.262539	+	0.111685i
$501$	3.13597			0.140105
$502$			7.54169i			0.336602i
$503$			5.72294i			0.255173i	0.991827	+	0.127587i	$0.0407231\pi$
$503$			5.72294i			0.255173i	−0.991827	+	0.127587i	$0.959277\pi$
$504$	−11.5622			−0.515020
$505$	1.84058	−	4.48373i	0.0819049	−	0.199523i
$506$		0			0
$507$			11.7661i			0.522553i
$508$		−	4.97891i		−	0.220904i
$509$	−19.9144			−0.882690			−0.441345	−	0.897337i	$-0.645499\pi$
$509$	−19.9144			−0.882690			−0.441345	+	0.897337i	$0.645499\pi$
$510$	13.7781	+	5.65596i	0.610104	+	0.250450i
$511$	−43.8410			−1.93941
$512$			23.4693i			1.03721i
$513$		−	1.37094i		−	0.0605284i
$514$	−9.80802			−0.432613
$515$	23.8249	+	9.78021i	1.04985	+	0.430968i
$516$	−4.44380			−0.195627
$517$		0			0
$518$			18.0547i			0.793277i
$519$	12.2424			0.537384
$520$	2.89887	−	7.06175i	0.127124	−	0.309678i
$521$	−12.5924			−0.551681			−0.275841	−	0.961203i	$-0.588956\pi$
$521$	−12.5924			−0.551681			−0.275841	+	0.961203i	$0.588956\pi$
$522$			12.3905i			0.542317i
$523$		−	38.5086i		−	1.68386i	−0.539584	−	0.841931i	$-0.681419\pi$
$523$		−	38.5086i		−	1.68386i	0.539584	−	0.841931i	$-0.318581\pi$
$524$	−8.22256			−0.359204
$525$	13.3850	+	13.2163i	0.584171	+	0.576808i
$526$	11.7712			0.513247
$527$			55.4120i			2.41379i
$528$		0			0
$529$	17.4601			0.759136
$530$	4.12979	−	10.0603i	0.179387	−	0.436992i
$531$	−4.28445			−0.185930
$532$			2.94298i			0.127595i
$533$			4.37735i			0.189604i
$534$	19.8190			0.857652
$535$	−8.76820	−	3.59938i	−0.379083	−	0.155615i
$536$	−28.1478			−1.21580
$537$			8.46334i			0.365220i
$538$			21.0596i			0.907944i
$539$		0			0
$540$	−1.18035	−	0.484538i	−0.0507942	−	0.0208512i
$541$	−11.7649			−0.505812			−0.252906	−	0.967491i	$-0.581386\pi$
$541$	−11.7649			−0.505812			−0.252906	+	0.967491i	$0.581386\pi$
$542$			1.49872i			0.0643755i
$543$			23.5514i			1.01069i
$544$	17.3715			0.744799
$545$	−13.7908	+	33.5948i	−0.590732	+	1.43904i
$546$	−4.99614			−0.213815
$547$			14.6981i			0.628444i	0.949350	+	0.314222i	$0.101744\pi$
$547$			14.6981i			0.628444i	−0.949350	+	0.314222i	$0.898256\pi$
$548$			5.69618i			0.243329i
$549$	8.32914			0.355479
$550$		0			0
$551$	14.2080			0.605279
$552$		−	7.23372i		−	0.307888i
$553$			11.5801i			0.492437i
$554$	19.5724			0.831550
$555$	−3.40857	+	8.30340i	−0.144686	+	0.352460i
$556$	4.33873			0.184003
$557$		−	33.6038i		−	1.42384i	−0.702261	−	0.711920i	$-0.747826\pi$
$557$		−	33.6038i		−	1.42384i	0.702261	−	0.711920i	$-0.252174\pi$
$558$			11.8914i			0.503403i
$559$	−8.65056			−0.365880
$560$	−19.7133	−	8.09239i	−0.833041	−	0.341966i
$561$		0			0
$562$		−	14.0681i		−	0.593428i
$563$		−	23.3225i		−	0.982928i	−0.870898	−	0.491464i	$-0.836462\pi$
$563$		−	23.3225i		−	0.982928i	0.870898	−	0.491464i	$-0.163538\pi$
$564$	3.68638			0.155225
$565$	27.0885	+	11.1199i	1.13962	+	0.467818i
$566$	−3.78492			−0.159092
$567$			3.76208i			0.157992i
$568$			8.77986i			0.368395i
$569$	15.6575			0.656396			0.328198	−	0.944609i	$-0.393559\pi$
$569$	15.6575			0.656396			0.328198	+	0.944609i	$0.393559\pi$
$570$	1.39180	−	3.39048i	0.0582961	−	0.142011i
$571$	0.295842			0.0123806			0.00619029	−	0.999981i	$-0.498030\pi$
$571$	0.295842			0.0123806			0.00619029	+	0.999981i	$0.498030\pi$
$572$		0			0
$573$		−	19.2179i		−	0.802838i
$574$	17.7248			0.739818
$575$	−8.26862	+	8.37417i	−0.344825	+	0.349227i
$576$	8.79426			0.366428
$577$		−	5.59077i		−	0.232747i	−0.993206	−	0.116373i	$-0.962873\pi$
$577$		−	5.59077i		−	0.232747i	0.993206	−	0.116373i	$-0.0371269\pi$
$578$			16.7833i			0.698094i
$579$	14.1416			0.587707
$580$	5.02160	−	12.2328i	0.208510	−	0.507938i
$581$	17.4688			0.724730
$582$		−	21.7510i		−	0.901606i
$583$		0			0
$584$	35.8149			1.48203
$585$	−2.29774	−	0.943230i	−0.0949998	−	0.0389977i
$586$	22.7782			0.940960
$587$		−	22.3983i		−	0.924477i	−0.886756	−	0.462239i	$-0.847046\pi$
$587$		−	22.3983i		−	0.924477i	0.886756	−	0.462239i	$-0.152954\pi$
$588$		−	4.08173i		−	0.168328i
$589$	13.6356			0.561847
$590$	−10.5959	−	4.34966i	−0.436227	−	0.179073i
$591$	10.2965			0.423540
$592$		−	10.1684i		−	0.417918i
$593$			0.445411i			0.0182908i	0.999958	+	0.00914542i	$0.00291112\pi$
$593$			0.445411i			0.0182908i	−0.999958	+	0.00914542i	$0.997089\pi$
$594$		0			0
$595$	−17.7975	+	43.3553i	−0.729626	+	1.77739i
$596$	−3.69259			−0.151254
$597$		−	26.3053i		−	1.07660i
$598$		−	3.12577i		−	0.127822i
$599$	23.5775			0.963350			0.481675	−	0.876350i	$-0.340029\pi$
$599$	23.5775			0.963350			0.481675	+	0.876350i	$0.340029\pi$
$600$	−10.9346	−	10.7968i	−0.446404	−	0.440777i
$601$	−5.95640			−0.242967			−0.121483	−	0.992593i	$-0.538765\pi$
$601$	−5.95640			−0.242967			−0.121483	+	0.992593i	$0.538765\pi$
$602$			35.0279i			1.42763i
$603$			9.15868i			0.372970i
$604$	5.43722			0.221237
$605$		0			0
$606$	2.59147			0.105271
$607$			43.9090i			1.78221i	0.453796	+	0.891106i	$0.350069\pi$
$607$			43.9090i			1.78221i	−0.453796	+	0.891106i	$0.649931\pi$
$608$		−	4.27474i		−	0.173364i
$609$	−38.9890			−1.57991
$610$	20.5988	+	8.45590i	0.834023	+	0.342369i
$611$	7.17613			0.290315
$612$		−	3.17899i		−	0.128503i
$613$			29.3033i			1.18355i	0.806104	+	0.591774i	$0.201572\pi$
$613$			29.3033i			1.18355i	−0.806104	+	0.591774i	$0.798428\pi$
$614$	−12.7415			−0.514204
$615$	8.15168	+	3.34629i	0.328707	+	0.134935i
$616$		0			0
$617$		−	18.1925i		−	0.732402i	−0.930536	−	0.366201i	$-0.880658\pi$
$617$		−	18.1925i		−	0.732402i	0.930536	−	0.366201i	$-0.119342\pi$
$618$			13.7701i			0.553916i
$619$	30.7056			1.23416			0.617081	−	0.786899i	$-0.288315\pi$
$619$	30.7056			1.23416			0.617081	+	0.786899i	$0.288315\pi$
$620$	4.81932	−	11.7400i	0.193548	−	0.471490i
$621$	−2.35369			−0.0944505
$622$			13.6713i			0.548171i
$623$			62.3641i			2.49857i
$624$	2.81382			0.112643
$625$	0.317092	+	24.9980i	0.0126837	+	0.999920i
$626$	−0.0278942			−0.00111488
$627$		0			0
$628$			1.80708i			0.0721102i
$629$	−22.3632			−0.891679
$630$	−3.81933	+	9.30402i	−0.152166	+	0.370681i
$631$	11.8334			0.471080			0.235540	−	0.971865i	$-0.424314\pi$
$631$	11.8334			0.471080			0.235540	+	0.971865i	$0.424314\pi$
$632$		−	9.46013i		−	0.376304i
$633$		−	0.360214i		−	0.0143172i
$634$	−1.84265			−0.0731808
$635$	−18.0493	−	7.40930i	−0.716264	−	0.294029i
$636$	−2.32119			−0.0920412
$637$		−	7.94573i		−	0.314821i
$638$		0			0
$639$	2.85677			0.113012
$640$	8.84914	+	3.63260i	0.349793	+	0.143591i
$641$	−38.6152			−1.52521			−0.762604	−	0.646865i	$-0.776080\pi$
$641$	−38.6152			−1.52521			−0.762604	+	0.646865i	$0.776080\pi$
$642$		−	5.06777i		−	0.200009i
$643$			12.6400i			0.498473i	0.968443	+	0.249236i	$0.0801796\pi$
$643$			12.6400i			0.498473i	−0.968443	+	0.249236i	$0.919820\pi$
$644$	5.05266			0.199103
$645$	−6.61297	+	16.1094i	−0.260385	+	0.634308i
$646$	9.13143			0.359271
$647$		−	18.3632i		−	0.721933i	−0.932579	−	0.360967i	$-0.882447\pi$
$647$		−	18.3632i		−	0.721933i	0.932579	−	0.360967i	$-0.117553\pi$
$648$		−	3.07335i		−	0.120732i
$649$		0			0
$650$	−4.72497	−	4.66542i	−0.185329	−	0.182993i
$651$	−37.4184			−1.46654
$652$			5.14706i			0.201574i
$653$		−	16.7800i		−	0.656653i	−0.944564	−	0.328327i	$-0.893515\pi$
$653$		−	16.7800i		−	0.656653i	0.944564	−	0.328327i	$-0.106485\pi$
$654$	−19.4168			−0.759258
$655$	−12.2363	+	29.8080i	−0.478111	+	1.16469i
$656$	−9.98259			−0.389755
$657$		−	11.6534i		−	0.454642i
$658$		−	29.0576i		−	1.13278i
$659$	28.8939			1.12554			0.562772	−	0.826612i	$-0.309735\pi$
$659$	28.8939			1.12554			0.562772	+	0.826612i	$0.309735\pi$
$660$		0			0
$661$	31.6886			1.23254			0.616272	−	0.787534i	$-0.288642\pi$
$661$	31.6886			1.23254			0.616272	+	0.787534i	$0.288642\pi$
$662$			6.66403i			0.259005i
$663$		−	6.18841i		−	0.240338i
$664$	−14.2708			−0.553815
$665$	10.6687	+	4.37956i	0.413716	+	0.169832i
$666$	−4.79913			−0.185962
$667$		−	24.3929i		−	0.944498i
$668$		−	1.78943i		−	0.0692351i
$669$	26.4883			1.02410
$670$	−9.29806	+	22.6504i	−0.359216	+	0.875061i
$671$		0			0
$672$			11.7306i			0.452517i
$673$		−	40.4250i		−	1.55827i	−0.626857	−	0.779134i	$-0.715659\pi$
$673$		−	40.4250i		−	1.55827i	0.626857	−	0.779134i	$-0.284341\pi$
$674$	18.5751			0.715487
$675$	−3.51304	+	3.55789i	−0.135217	+	0.136943i
$676$	6.71393			0.258228
$677$		−	38.3568i		−	1.47417i	−0.675798	−	0.737087i	$-0.736201\pi$
$677$		−	38.3568i		−	1.47417i	0.675798	−	0.737087i	$-0.263799\pi$
$678$			15.6564i			0.601279i
$679$	68.4434			2.62661
$680$	14.5393	−	35.4182i	0.557556	−	1.35823i
$681$	23.3780			0.895848
$682$		0			0
$683$		−	15.0969i		−	0.577668i	−0.957379	−	0.288834i	$-0.906732\pi$
$683$		−	15.0969i		−	0.577668i	0.957379	−	0.288834i	$-0.0932675\pi$
$684$	−0.782277			−0.0299111
$685$	20.6495	+	8.47668i	0.788976	+	0.323877i
$686$	−0.689130			−0.0263111
$687$			10.1085i			0.385662i
$688$		−	19.7277i		−	0.752111i
$689$	−4.51857			−0.172144
$690$	−5.82094	−	2.38951i	−0.221599	−	0.0909673i
$691$	−36.0997			−1.37330			−0.686648	−	0.726990i	$-0.740919\pi$
$691$	−36.0997			−1.37330			−0.686648	+	0.726990i	$0.740919\pi$
$692$		−	6.98572i		−	0.265557i
$693$		0			0
$694$	−2.39660			−0.0909735
$695$	6.45661	−	15.7285i	0.244913	−	0.596617i
$696$	31.8512			1.20732
$697$			21.9546i			0.831589i
$698$			35.1856i			1.33179i
$699$	−4.17456			−0.157897
$700$	7.54143	−	7.63769i	0.285039	−	0.288678i
$701$	−34.0391			−1.28564			−0.642820	−	0.766017i	$-0.722236\pi$
$701$	−34.0391			−1.28564			−0.642820	+	0.766017i	$0.722236\pi$
$702$		−	1.32803i		−	0.0501232i
$703$			5.50307i			0.207552i
$704$		0			0
$705$	5.48584	−	13.3637i	0.206609	−	0.503305i
$706$	29.9521			1.12726
$707$			8.15452i			0.306682i
$708$			2.44477i			0.0918801i
$709$	1.10539			0.0415139			0.0207569	−	0.999785i	$-0.493392\pi$
$709$	1.10539			0.0415139			0.0207569	+	0.999785i	$0.493392\pi$
$710$	7.06511	+	2.90025i	0.265149	+	0.108844i
$711$	−3.07812			−0.115438
$712$		−	50.9470i		−	1.90932i
$713$		−	23.4103i		−	0.876724i
$714$	−25.0581			−0.937777
$715$		0			0
$716$	4.82930			0.180479
$717$		−	23.8799i		−	0.891812i
$718$			24.4911i			0.914001i
$719$	24.7383			0.922582			0.461291	−	0.887249i	$-0.347386\pi$
$719$	24.7383			0.922582			0.461291	+	0.887249i	$0.347386\pi$
$720$	2.15104	−	5.24002i	0.0801647	−	0.195284i
$721$	−43.3302			−1.61370
$722$			20.4688i			0.761769i
$723$		−	15.6656i		−	0.582609i
$724$	13.4388			0.499449
$725$	−36.8728	−	36.4080i	−1.36942	−	1.35216i
$726$		0			0
$727$			6.81327i			0.252690i	0.991986	+	0.126345i	$0.0403246\pi$
$727$			6.81327i			0.252690i	−0.991986	+	0.126345i	$0.959675\pi$
$728$			12.8432i			0.475999i
$729$	−1.00000			−0.0370370
$730$	11.8307	−	28.8201i	0.437876	−	1.06668i
$731$	−43.3868			−1.60472
$732$		−	4.75273i		−	0.175666i
$733$		−	32.9294i		−	1.21628i	−0.793831	−	0.608138i	$-0.791917\pi$
$733$		−	32.9294i		−	1.21628i	0.793831	−	0.608138i	$-0.208083\pi$
$734$	17.4325			0.643447
$735$	−14.7969	−	6.07416i	−0.545790	−	0.224049i
$736$	−7.33909			−0.270522
$737$		0			0
$738$			4.71144i			0.173430i
$739$	25.6642			0.944072			0.472036	−	0.881579i	$-0.343519\pi$
$739$	25.6642			0.944072			0.472036	+	0.881579i	$0.343519\pi$
$740$	4.73804	+	1.94498i	0.174174	+	0.0714989i
$741$	−1.52283			−0.0559424
$742$			18.2966i			0.671690i
$743$		−	19.7267i		−	0.723701i	−0.932236	−	0.361850i	$-0.882145\pi$
$743$		−	19.7267i		−	0.723701i	0.932236	−	0.361850i	$-0.117855\pi$
$744$	30.5682			1.12068
$745$	−5.49507	+	13.3862i	−0.201324	+	0.490432i
$746$	1.91379			0.0700688
$747$			4.64341i			0.169893i
$748$		0			0
$749$	15.9467			0.582679
$750$	−12.3002	+	5.23253i	−0.449138	+	0.191065i
$751$	−15.3758			−0.561072			−0.280536	−	0.959843i	$-0.590512\pi$
$751$	−15.3758			−0.561072			−0.280536	+	0.959843i	$0.590512\pi$
$752$			16.3652i			0.596779i
$753$		−	6.30803i		−	0.229878i
$754$	13.7633			0.501228
$755$	8.09132	−	19.7107i	0.294473	−	0.717347i
$756$	2.14669			0.0780745
$757$		−	34.9995i		−	1.27208i	−0.771657	−	0.636039i	$-0.780572\pi$
$757$		−	34.9995i		−	1.27208i	0.771657	−	0.636039i	$-0.219428\pi$
$758$			17.0811i			0.620414i
$759$		0			0
$760$	−8.71560	−	3.57778i	−0.316148	−	0.129780i
$761$	20.7260			0.751319			0.375659	−	0.926758i	$-0.377416\pi$
$761$	20.7260			0.751319			0.375659	+	0.926758i	$0.377416\pi$
$762$		−	10.4320i		−	0.377911i
$763$		−	61.0986i		−	2.21192i
$764$	−10.9660			−0.396735
$765$	−11.5243	−	4.73076i	−0.416662	−	0.171041i
$766$	−7.80469			−0.281995
$767$			4.75913i			0.171842i
$768$		−	12.4740i		−	0.450116i
$769$	13.6328			0.491613			0.245806	−	0.969319i	$-0.420947\pi$
$769$	13.6328			0.491613			0.245806	+	0.969319i	$0.420947\pi$
$770$		0			0
$771$	8.20364			0.295447
$772$		−	8.06943i		−	0.290425i
$773$			1.37046i			0.0492919i	0.999696	+	0.0246460i	$0.00784585\pi$
$773$			1.37046i			0.0492919i	−0.999696	+	0.0246460i	$0.992154\pi$
$774$	−9.31078			−0.334669
$775$	−35.3875	−	34.9415i	−1.27116	−	1.25513i
$776$	−55.9133			−2.00717
$777$		−	15.1013i		−	0.541757i
$778$		−	32.6662i		−	1.17114i
$779$	5.40252			0.193565
$780$	−0.538220	+	1.31112i	−0.0192714	+	0.0469457i
$781$		0			0
$782$		−	15.6773i		−	0.560619i
$783$		−	10.3637i		−	0.370368i
$784$	18.1203			0.647154
$785$	6.55091	+	2.68917i	0.233812	+	0.0959807i
$786$	−17.2282			−0.614508
$787$		−	23.6626i		−	0.843482i	−0.906716	−	0.421741i	$-0.861419\pi$
$787$		−	23.6626i		−	0.843482i	0.906716	−	0.421741i	$-0.138581\pi$
$788$		−	5.87531i		−	0.209299i
$789$	−9.84566			−0.350515
$790$	−7.61252	−	3.12496i	−0.270841	−	0.111181i
$791$	−49.2656			−1.75168
$792$		0			0
$793$		−	9.25193i		−	0.328546i
$794$	3.88462			0.137860
$795$	−3.45425	+	8.41466i	−0.122509	+	0.298437i
$796$	−15.0102			−0.532022
$797$		−	17.9874i		−	0.637146i	−0.947898	−	0.318573i	$-0.896796\pi$
$797$		−	17.9874i		−	0.637146i	0.947898	−	0.318573i	$-0.103204\pi$
$798$			6.16623i			0.218282i
$799$	35.9919			1.27330
$800$	−10.9541	+	11.0939i	−0.387285	+	0.392228i
$801$	−16.5770			−0.585721
$802$		−	13.4459i		−	0.474790i
$803$		0			0
$804$	5.22607			0.184309
$805$	7.51904	−	18.3166i	0.265011	−	0.645577i
$806$	13.2088			0.465262
$807$		−	17.6147i		−	0.620067i
$808$		−	6.66166i		−	0.234356i
$809$	−48.0286			−1.68860			−0.844298	−	0.535873i	$-0.819982\pi$
$809$	−48.0286			−1.68860			−0.844298	+	0.535873i	$0.819982\pi$
$810$	−2.47311	−	1.01522i	−0.0868961	−	0.0356712i
$811$	−17.3727			−0.610038			−0.305019	−	0.952346i	$-0.598663\pi$
$811$	−17.3727			−0.610038			−0.305019	+	0.952346i	$0.598663\pi$
$812$			22.2477i			0.780740i
$813$		−	1.25356i		−	0.0439643i
$814$		0			0
$815$	18.6588	+	7.65951i	0.653590	+	0.268301i
$816$	14.1127			0.494044
$817$			10.6765i			0.373524i
$818$			17.2408i			0.602810i
$819$	4.17888			0.146022
$820$	1.90944	−	4.65146i	0.0666806	−	0.162436i
$821$	4.97342			0.173573			0.0867867	−	0.996227i	$-0.472340\pi$
$821$	4.97342			0.173573			0.0867867	+	0.996227i	$0.472340\pi$
$822$			11.9348i			0.416274i
$823$			32.6485i			1.13806i	0.822318	+	0.569028i	$0.192681\pi$
$823$			32.6485i			1.13806i	−0.822318	+	0.569028i	$0.807319\pi$
$824$	35.3977			1.23314
$825$		0			0
$826$	19.2707			0.670514
$827$		−	12.9363i		−	0.449839i	−0.974377	−	0.224920i	$-0.927788\pi$
$827$		−	12.9363i		−	0.449839i	0.974377	−	0.224920i	$-0.0722119\pi$
$828$			1.34305i			0.0466743i
$829$	−32.7103			−1.13607			−0.568037	−	0.823003i	$-0.692297\pi$
$829$	−32.7103			−1.13607			−0.568037	+	0.823003i	$0.692297\pi$
$830$	−4.71407	+	11.4836i	−0.163628	+	0.398603i
$831$	−16.3707			−0.567895
$832$		−	9.76859i		−	0.338665i
$833$		−	39.8518i		−	1.38078i
$834$	9.09063			0.314783
$835$	−6.48695	−	2.66291i	−0.224490	−	0.0921539i
$836$		0			0
$837$		−	9.94621i		−	0.343791i
$838$			41.4321i			1.43125i
$839$	−16.2411			−0.560707			−0.280353	−	0.959897i	$-0.590452\pi$
$839$	−16.2411			−0.560707			−0.280353	+	0.959897i	$0.590452\pi$
$840$	23.9170	+	9.81802i	0.825216	+	0.338754i
$841$	78.4059			2.70365
$842$		−	5.83162i		−	0.200971i
$843$			11.7669i			0.405273i
$844$	−0.205543			−0.00707509
$845$	9.99123	−	24.3390i	0.343709	−	0.837286i
$846$	7.72383			0.265551
$847$		0			0
$848$		−	10.3046i		−	0.353863i
$849$	3.16579			0.108649
$850$	−23.6981	−	23.3994i	−0.812837	−	0.802592i
$851$	9.44795			0.323872
$852$		−	1.63012i		−	0.0558469i
$853$		−	6.01751i		−	0.206035i	−0.994680	−	0.103018i	$-0.967150\pi$
$853$		−	6.01751i		−	0.206035i	0.994680	−	0.103018i	$-0.0328498\pi$
$854$	−37.4630			−1.28196
$855$	−1.16413	+	2.83587i	−0.0398125	+	0.0969846i
$856$	−13.0273			−0.445264
$857$			1.48842i			0.0508436i	0.999677	+	0.0254218i	$0.00809288\pi$
$857$			1.48842i			0.0508436i	−0.999677	+	0.0254218i	$0.991907\pi$
$858$		0			0
$859$	6.62548			0.226059			0.113029	−	0.993592i	$-0.463945\pi$
$859$	6.62548			0.226059			0.113029	+	0.993592i	$0.463945\pi$
$860$	9.19226	+	3.77346i	0.313454	+	0.128674i
$861$	−14.8254			−0.505248
$862$		−	14.4818i		−	0.493252i
$863$		−	25.6159i		−	0.871976i	−0.899953	−	0.435988i	$-0.856399\pi$
$863$		−	25.6159i		−	0.871976i	0.899953	−	0.435988i	$-0.143601\pi$
$864$	−3.11811			−0.106080
$865$	−25.3242	−	10.3957i	−0.861050	−	0.353464i
$866$	37.3756			1.27007
$867$		−	14.0379i		−	0.476753i
$868$			21.3515i			0.724717i
$869$		0			0
$870$	10.5214	−	25.6305i	0.356709	−	0.868955i
$871$	10.1734			0.344712
$872$			49.9132i			1.69027i
$873$			18.1930i			0.615739i
$874$	−3.85782			−0.130493
$875$	−16.4651	−	38.7047i	−0.556622	−	1.30846i
$876$	−6.64959			−0.224669
$877$		−	24.6934i		−	0.833838i	−0.908944	−	0.416919i	$-0.863110\pi$
$877$		−	24.6934i		−	0.833838i	0.908944	−	0.416919i	$-0.136890\pi$
$878$			30.6171i			1.03328i
$879$	−19.0522			−0.642615
$880$		0			0
$881$	−16.6177			−0.559866			−0.279933	−	0.960020i	$-0.590312\pi$
$881$	−16.6177			−0.559866			−0.279933	+	0.960020i	$0.590312\pi$
$882$		−	8.55216i		−	0.287966i
$883$			17.9632i			0.604511i	0.953227	+	0.302255i	$0.0977396\pi$
$883$			17.9632i			0.604511i	−0.953227	+	0.302255i	$0.902260\pi$
$884$	−3.53119			−0.118767
$885$	8.86265	+	3.63815i	0.297915	+	0.122295i
$886$	−2.71082			−0.0910719
$887$			41.3644i			1.38888i	0.719551	+	0.694440i	$0.244348\pi$
$887$			41.3644i			1.38888i	−0.719551	+	0.694440i	$0.755652\pi$
$888$			12.3367i			0.413993i
$889$	32.8261			1.10095
$890$	−40.9968	−	16.8293i	−1.37422	−	0.564120i
$891$		0			0
$892$		−	15.1146i		−	0.506075i
$893$		−	8.85677i		−	0.296381i
$894$	−7.73683			−0.258758
$895$	7.18665	−	17.5069i	0.240223	−	0.585192i
$896$	−16.0939			−0.537658
$897$			2.61446i			0.0872944i
$898$		−	16.4012i		−	0.547313i
$899$	103.079			3.43789
$900$	2.03018	+	2.00459i	0.0676727	+	0.0668197i
$901$	−22.6629			−0.755009
$902$		0			0
$903$		−	29.2981i		−	0.974979i
$904$	40.2465			1.33858
$905$	19.9987	−	48.7176i	0.664780	−	1.61943i
$906$	11.3922			0.378482
$907$			43.8277i			1.45528i	0.685962	+	0.727638i	$0.259382\pi$
$907$			43.8277i			1.45528i	−0.685962	+	0.727638i	$0.740618\pi$
$908$		−	13.3398i		−	0.442698i
$909$	−2.16756			−0.0718934
$910$	10.3348	+	4.24248i	0.342596	+	0.140637i
$911$	−3.01368			−0.0998477			−0.0499239	−	0.998753i	$-0.515898\pi$
$911$	−3.01368			−0.0998477			−0.0499239	+	0.998753i	$0.515898\pi$
$912$		−	3.47282i		−	0.114997i
$913$		0			0
$914$	19.2508			0.636758
$915$	−17.2293	−	7.07270i	−0.569584	−	0.233816i
$916$	5.76803			0.190581
$917$		−	54.2115i		−	1.79022i
$918$		−	6.66072i		−	0.219836i
$919$	0.579650			0.0191209			0.00956045	−	0.999954i	$-0.496957\pi$
$919$	0.579650			0.0191209			0.00956045	+	0.999954i	$0.496957\pi$
$920$	−6.14252	+	14.9634i	−0.202513	+	0.493328i
$921$	10.6573			0.351168
$922$			0.269713i			0.00888253i
$923$		−	3.17328i		−	0.104450i
$924$		0			0
$925$	14.1017	−	14.2817i	0.463660	−	0.469579i
$926$	17.4649			0.573933
$927$		−	11.5176i		−	0.378289i
$928$		−	32.3151i		−	1.06080i
$929$	7.38827			0.242401			0.121201	−	0.992628i	$-0.461326\pi$
$929$	7.38827			0.242401			0.121201	+	0.992628i	$0.461326\pi$
$930$	10.0976	−	24.5981i	0.331113	−	0.806602i
$931$	−9.80661			−0.321399
$932$			2.38207i			0.0780272i
$933$		−	11.4350i		−	0.374365i
$934$	−47.6963			−1.56067
$935$		0			0
$936$	−3.41385			−0.111585
$937$			22.3759i			0.730990i	0.930813	+	0.365495i	$0.119100\pi$
$937$			22.3759i			0.730990i	−0.930813	+	0.365495i	$0.880900\pi$
$938$		−	41.1941i		−	1.34504i
$939$	0.0233313			0.000761388
$940$	−7.62551	−	3.13030i	−0.248717	−	0.102099i
$941$	30.8195			1.00469			0.502343	−	0.864668i	$-0.332471\pi$
$941$	30.8195			1.00469			0.502343	+	0.864668i	$0.332471\pi$
$942$			3.78624i			0.123362i
$943$		−	9.27532i		−	0.302046i
$944$	−10.8533			−0.353243
$945$	3.19457	−	7.78208i	0.103919	−	0.253151i
$946$		0			0
$947$		−	6.42672i		−	0.208840i	−0.994533	−	0.104420i	$-0.966701\pi$
$947$		−	6.42672i		−	0.208840i	0.994533	−	0.104420i	$-0.0332987\pi$
$948$			1.75642i			0.0570458i
$949$	−12.9445			−0.420196
$950$	−5.75805	+	5.83155i	−0.186816	+	0.189201i
$951$	1.54123			0.0499778
$952$			64.4148i			2.08769i
$953$		−	33.1383i		−	1.07345i	−0.843756	−	0.536727i	$-0.819660\pi$
$953$		−	33.1383i		−	1.07345i	0.843756	−	0.536727i	$-0.180340\pi$
$954$	−4.86343			−0.157459
$955$	−16.3189	+	39.7533i	−0.528066	+	1.28639i
$956$	−13.6262			−0.440704
$957$		0			0
$958$		−	37.3662i		−	1.20725i
$959$	−37.5550			−1.21272
$960$	−18.1915	−	7.46766i	−0.587127	−	0.241018i
$961$	67.9272			2.19120
$962$			5.33083i			0.171873i
$963$			4.23880i			0.136593i
$964$	−8.93901			−0.287906
$965$	−29.2528	−	12.0084i	−0.941682	−	0.386564i
$966$	10.5865			0.340615
$967$		−	34.8065i		−	1.11930i	−0.828728	−	0.559651i	$-0.810935\pi$
$967$		−	34.8065i		−	1.11930i	0.828728	−	0.559651i	$-0.189065\pi$
$968$		0			0
$969$	−7.63772			−0.245359
$970$	−18.4699	+	44.9932i	−0.593031	+	1.44464i
$971$	45.2026			1.45062			0.725310	−	0.688423i	$-0.241697\pi$
$971$	45.2026			1.45062			0.725310	+	0.688423i	$0.241697\pi$
$972$			0.570614i			0.0183025i
$973$			28.6053i			0.917045i
$974$	−23.6528			−0.757886
$975$	3.95207	+	3.90225i	0.126567	+	0.124972i
$976$	21.0991			0.675366
$977$			36.8788i			1.17986i	0.807455	+	0.589929i	$0.200844\pi$
$977$			36.8788i			1.17986i	−0.807455	+	0.589929i	$0.799156\pi$
$978$			10.7843i			0.344843i
$979$		0			0
$980$	−3.46600	+	8.44330i	−0.110717	+	0.269711i
$981$	16.2407			0.518524
$982$			29.5003i			0.941393i
$983$		−	9.80072i		−	0.312594i	−0.987710	−	0.156297i	$-0.950044\pi$
$983$		−	9.80072i		−	0.312594i	0.987710	−	0.156297i	$-0.0499558\pi$
$984$	12.1113			0.386094
$985$	−21.2989	−	8.74325i	−0.678638	−	0.278583i
$986$	69.0296			2.19835
$987$			24.3044i			0.773619i
$988$			0.868946i			0.0276449i
$989$	18.3300			0.582859
$990$		0			0
$991$	52.5716			1.66999			0.834995	−	0.550257i	$-0.185470\pi$
$991$	52.5716			1.66999			0.834995	+	0.550257i	$0.185470\pi$
$992$		−	31.0134i		−	0.984677i
$993$		−	5.57394i		−	0.176884i
$994$	−12.8493			−0.407554
$995$	−22.3372	+	54.4141i	−0.708136	+	1.72504i
$996$	2.64959			0.0839556
$997$		−	9.95697i		−	0.315340i	−0.987492	−	0.157670i	$-0.949602\pi$
$997$		−	9.95697i		−	0.315340i	0.987492	−	0.157670i	$-0.0503983\pi$
$998$			39.2433i			1.24222i
$999$	4.01410			0.127000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.i.364.5	yes	12
5.2	odd	4		9075.2.a.ds.1.4		6
5.3	odd	4		9075.2.a.do.1.3		6
5.4	even	2	inner	1815.2.c.i.364.8	yes	12
11.10	odd	2		1815.2.c.h.364.8	yes	12
55.32	even	4		9075.2.a.dp.1.3		6
55.43	even	4		9075.2.a.dr.1.4		6
55.54	odd	2		1815.2.c.h.364.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.h.364.5	✓	12	55.54	odd	2
1815.2.c.h.364.8	yes	12	11.10	odd	2
1815.2.c.i.364.5	yes	12	1.1	even	1	trivial
1815.2.c.i.364.8	yes	12	5.4	even	2	inner
9075.2.a.do.1.3		6	5.3	odd	4
9075.2.a.dp.1.3		6	55.32	even	4
9075.2.a.dr.1.4		6	55.43	even	4
9075.2.a.ds.1.4		6	5.2	odd	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.19557i q^{2} +1.00000i q^{3} +0.570614 q^{4} +(0.849151 - 2.06856i) q^{5} +1.19557 q^{6} +3.76208i q^{7} -3.07335i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.19557i q^{2} +1.00000i q^{3} +0.570614 q^{4} +(0.849151 - 2.06856i) q^{5} +1.19557 q^{6} +3.76208i q^{7} -3.07335i q^{8} -1.00000 q^{9} +(-2.47311 - 1.01522i) q^{10} +0.570614i q^{12} +1.11079i q^{13} +4.49782 q^{14} +(2.06856 + 0.849151i) q^{15} -2.53317 q^{16} +5.57117i q^{17} +1.19557i q^{18} +1.37094 q^{19} +(0.484538 - 1.18035i) q^{20} -3.76208 q^{21} -2.35369i q^{23} +3.07335 q^{24} +(-3.55789 - 3.51304i) q^{25} +1.32803 q^{26} -1.00000i q^{27} +2.14669i q^{28} +10.3637 q^{29} +(1.01522 - 2.47311i) q^{30} +9.94621 q^{31} -3.11811i q^{32} +6.66072 q^{34} +(7.78208 + 3.19457i) q^{35} -0.570614 q^{36} +4.01410i q^{37} -1.63905i q^{38} -1.11079 q^{39} +(-6.35740 - 2.60974i) q^{40} +3.94075 q^{41} +4.49782i q^{42} +7.78774i q^{43} +(-0.849151 + 2.06856i) q^{45} -2.81400 q^{46} -6.46038i q^{47} -2.53317i q^{48} -7.15321 q^{49} +(-4.20008 + 4.25370i) q^{50} -5.57117 q^{51} +0.633833i q^{52} +4.06788i q^{53} -1.19557 q^{54} +11.5622 q^{56} +1.37094i q^{57} -12.3905i q^{58} +4.28445 q^{59} +(1.18035 + 0.484538i) q^{60} -8.32914 q^{61} -11.8914i q^{62} -3.76208i q^{63} -8.79426 q^{64} +(2.29774 + 0.943230i) q^{65} -9.15868i q^{67} +3.17899i q^{68} +2.35369 q^{69} +(3.81933 - 9.30402i) q^{70} -2.85677 q^{71} +3.07335i q^{72} +11.6534i q^{73} +4.79913 q^{74} +(3.51304 - 3.55789i) q^{75} +0.782277 q^{76} +1.32803i q^{78} +3.07812 q^{79} +(-2.15104 + 5.24002i) q^{80} +1.00000 q^{81} -4.71144i q^{82} -4.64341i q^{83} -2.14669 q^{84} +(11.5243 + 4.73076i) q^{85} +9.31078 q^{86} +10.3637i q^{87} +16.5770 q^{89} +(2.47311 + 1.01522i) q^{90} -4.17888 q^{91} -1.34305i q^{92} +9.94621i q^{93} -7.72383 q^{94} +(1.16413 - 2.83587i) q^{95} +3.11811 q^{96} -18.1930i q^{97} +8.55216i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9	\( 12 q - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{9} + 12 q^{10} + 20 q^{14} + 22 q^{16} + 4 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{25} - 24 q^{29} - 8 q^{30} + 36 q^{31} + 2 q^{34} + 24 q^{35} + 18 q^{36} - 4 q^{39} - 22 q^{40} - 12 q^{41} + 2 q^{45} - 22 q^{46} - 24 q^{49} - 58 q^{50} + 4 q^{51} - 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} + 8 q^{61} - 44 q^{64} - 14 q^{65} - 24 q^{69} - 16 q^{70} + 8 q^{74} - 12 q^{75} - 40 q^{76} - 4 q^{79} - 58 q^{80} + 12 q^{81} + 48 q^{84} - 2 q^{85} + 56 q^{86} + 32 q^{89} - 12 q^{90} + 48 q^{91} - 6 q^{94} + 62 q^{96}+O(q^{100}) \) 12 * q - 18 * q^4 - 2 * q^5 + 2 * q^6 - 12 * q^9 + 12 * q^10 + 20 * q^14 + 22 * q^16 + 4 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^25 - 24 * q^29 - 8 * q^30 + 36 * q^31 + 2 * q^34 + 24 * q^35 + 18 * q^36 - 4 * q^39 - 22 * q^40 - 12 * q^41 + 2 * q^45 - 22 * q^46 - 24 * q^49 - 58 * q^50 + 4 * q^51 - 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 + 8 * q^61 - 44 * q^64 - 14 * q^65 - 24 * q^69 - 16 * q^70 + 8 * q^74 - 12 * q^75 - 40 * q^76 - 4 * q^79 - 58 * q^80 + 12 * q^81 + 48 * q^84 - 2 * q^85 + 56 * q^86 + 32 * q^89 - 12 * q^90 + 48 * q^91 - 6 * q^94 + 62 * q^96

Introduction

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Database

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