LMFDB - Embedded newform 1815.2.c.h.364.12

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			364.12
Root			$2.73519i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.h.364.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73519i q^{2} +1.00000i q^{3} -5.48125 q^{4} +(-1.65271 + 1.50617i) q^{5} -2.73519 q^{6} -4.20410i q^{7} -9.52186i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.73519i q^{2} +1.00000i q^{3} -5.48125 q^{4} +(-1.65271 + 1.50617i) q^{5} -2.73519 q^{6} -4.20410i q^{7} -9.52186i q^{8} -1.00000 q^{9} +(-4.11965 - 4.52048i) q^{10} -5.48125i q^{12} -0.0784689i q^{13} +11.4990 q^{14} +(-1.50617 - 1.65271i) q^{15} +15.0816 q^{16} +0.0228569i q^{17} -2.73519i q^{18} +1.26627 q^{19} +(9.05893 - 8.25567i) q^{20} +4.20410 q^{21} +6.12996i q^{23} +9.52186 q^{24} +(0.462928 - 4.97852i) q^{25} +0.214627 q^{26} -1.00000i q^{27} +23.0437i q^{28} +5.85972 q^{29} +(4.52048 - 4.11965i) q^{30} -3.23929 q^{31} +22.2072i q^{32} -0.0625180 q^{34} +(6.33208 + 6.94818i) q^{35} +5.48125 q^{36} -8.67992i q^{37} +3.46349i q^{38} +0.0784689 q^{39} +(14.3415 + 15.7369i) q^{40} -3.84194 q^{41} +11.4990i q^{42} -0.859518i q^{43} +(1.65271 - 1.50617i) q^{45} -16.7666 q^{46} -1.89867i q^{47} +15.0816i q^{48} -10.6745 q^{49} +(13.6172 + 1.26619i) q^{50} -0.0228569 q^{51} +0.430108i q^{52} +4.55937i q^{53} +2.73519 q^{54} -40.0309 q^{56} +1.26627i q^{57} +16.0274i q^{58} +3.44174 q^{59} +(8.25567 + 9.05893i) q^{60} +8.13141 q^{61} -8.86007i q^{62} +4.20410i q^{63} -30.5777 q^{64} +(0.118187 + 0.129687i) q^{65} +0.406754i q^{67} -0.125285i q^{68} -6.12996 q^{69} +(-19.0046 + 17.3194i) q^{70} +8.40424 q^{71} +9.52186i q^{72} +15.1913i q^{73} +23.7412 q^{74} +(4.97852 + 0.462928i) q^{75} -6.94075 q^{76} +0.214627i q^{78} +13.2182 q^{79} +(-24.9255 + 22.7154i) q^{80} +1.00000 q^{81} -10.5084i q^{82} -14.4615i q^{83} -23.0437 q^{84} +(-0.0344264 - 0.0377760i) q^{85} +2.35094 q^{86} +5.85972i q^{87} +8.19755 q^{89} +(4.11965 + 4.52048i) q^{90} -0.329891 q^{91} -33.5998i q^{92} -3.23929i q^{93} +5.19323 q^{94} +(-2.09278 + 1.90722i) q^{95} -22.2072 q^{96} -1.64997i q^{97} -29.1967i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.73519i			1.93407i	0.254645	+	0.967035i	$0.418041\pi$
$2$			2.73519i			1.93407i	−0.254645	+	0.967035i	$0.581959\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−5.48125			−2.74062
$5$	−1.65271	+	1.50617i	−0.739116	+	0.673578i
$5$	−1.65271	+	1.50617i	−0.739116	+	0.673578i
$6$	−2.73519			−1.11664
$7$		−	4.20410i		−	1.58900i	−0.607263	−	0.794501i	$-0.707733\pi$
$7$		−	4.20410i		−	1.58900i	0.607263	−	0.794501i	$-0.292267\pi$
$8$		−	9.52186i		−	3.36649i
$9$	−1.00000			−0.333333
$10$	−4.11965	−	4.52048i	−1.30275	−	1.42950i
$11$		0			0
$11$		0			0
$12$		−	5.48125i		−	1.58230i
$13$		−	0.0784689i		−	0.0217634i	−0.999941	−	0.0108817i	$-0.996536\pi$
$13$		−	0.0784689i		−	0.0217634i	0.999941	−	0.0108817i	$-0.00346381\pi$
$14$	11.4990			3.07324
$15$	−1.50617	−	1.65271i	−0.388890	−	0.426729i
$16$	15.0816			3.77039
$17$			0.0228569i			0.00554362i	0.999996	+	0.00277181i	$0.000882296\pi$
$17$			0.0228569i			0.00554362i	−0.999996	+	0.00277181i	$0.999118\pi$
$18$		−	2.73519i		−	0.644690i
$19$	1.26627			0.290503			0.145251	−	0.989395i	$-0.453601\pi$
$19$	1.26627			0.290503			0.145251	+	0.989395i	$0.453601\pi$
$20$	9.05893	−	8.25567i	2.02564	−	1.84602i
$21$	4.20410			0.917410
$22$		0			0
$23$			6.12996i			1.27818i	0.769130	+	0.639092i	$0.220690\pi$
$23$			6.12996i			1.27818i	−0.769130	+	0.639092i	$0.779310\pi$
$24$	9.52186			1.94364
$25$	0.462928	−	4.97852i	0.0925855	−	0.995705i
$26$	0.214627			0.0420918
$27$		−	1.00000i		−	0.192450i
$28$			23.0437i			4.35485i
$29$	5.85972			1.08812			0.544061	−	0.839046i	$-0.316886\pi$
$29$	5.85972			1.08812			0.544061	+	0.839046i	$0.316886\pi$
$30$	4.52048	−	4.11965i	0.825323	−	0.752141i
$31$	−3.23929			−0.581794			−0.290897	−	0.956754i	$-0.593954\pi$
$31$	−3.23929			−0.581794			−0.290897	+	0.956754i	$0.593954\pi$
$32$			22.2072i			3.92572i
$33$		0			0
$34$	−0.0625180			−0.0107218
$35$	6.33208	+	6.94818i	1.07032	+	1.17446i
$36$	5.48125			0.913541
$37$		−	8.67992i		−	1.42697i	−0.700670	−	0.713485i	$-0.747116\pi$
$37$		−	8.67992i		−	1.42697i	0.700670	−	0.713485i	$-0.252884\pi$
$38$			3.46349i			0.561852i
$39$	0.0784689			0.0125651
$40$	14.3415	+	15.7369i	2.26759	+	2.48822i
$41$	−3.84194			−0.600010			−0.300005	−	0.953938i	$-0.596988\pi$
$41$	−3.84194			−0.600010			−0.300005	+	0.953938i	$0.596988\pi$
$42$			11.4990i			1.77434i
$43$		−	0.859518i		−	0.131075i	−0.997850	−	0.0655376i	$-0.979124\pi$
$43$		−	0.859518i		−	0.131075i	0.997850	−	0.0655376i	$-0.0208762\pi$
$44$		0			0
$45$	1.65271	−	1.50617i	0.246372	−	0.224526i
$46$	−16.7666			−2.47210
$47$		−	1.89867i		−	0.276950i	−0.990366	−	0.138475i	$-0.955780\pi$
$47$		−	1.89867i		−	0.276950i	0.990366	−	0.138475i	$-0.0442201\pi$
$48$			15.0816i			2.17684i
$49$	−10.6745			−1.52493
$50$	13.6172	+	1.26619i	1.92576	+	0.179067i
$51$	−0.0228569			−0.00320061
$52$			0.430108i			0.0596452i
$53$			4.55937i			0.626277i	0.949707	+	0.313139i	$0.101380\pi$
$53$			4.55937i			0.626277i	−0.949707	+	0.313139i	$0.898620\pi$
$54$	2.73519			0.372212
$55$		0			0
$56$	−40.0309			−5.34935
$57$			1.26627i			0.167722i
$58$			16.0274i			2.10450i
$59$	3.44174			0.448077			0.224038	−	0.974580i	$-0.428076\pi$
$59$	3.44174			0.448077			0.224038	+	0.974580i	$0.428076\pi$
$60$	8.25567	+	9.05893i	1.06580	+	1.16950i
$61$	8.13141			1.04112			0.520560	−	0.853825i	$-0.325723\pi$
$61$	8.13141			1.04112			0.520560	+	0.853825i	$0.325723\pi$
$62$		−	8.86007i		−	1.12523i
$63$			4.20410i			0.529667i
$64$	−30.5777			−3.82221
$65$	0.118187	+	0.129687i	0.0146593	+	0.0160857i
$66$		0			0
$67$			0.406754i			0.0496929i	0.999691	+	0.0248465i	$0.00790969\pi$
$67$			0.406754i			0.0496929i	−0.999691	+	0.0248465i	$0.992090\pi$
$68$		−	0.125285i		−	0.0151930i
$69$	−6.12996			−0.737960
$70$	−19.0046	+	17.3194i	−2.27148	+	2.07007i
$71$	8.40424			0.997399			0.498700	−	0.866775i	$-0.333811\pi$
$71$	8.40424			0.997399			0.498700	+	0.866775i	$0.333811\pi$
$72$			9.52186i			1.12216i
$73$			15.1913i			1.77800i	0.457905	+	0.889001i	$0.348600\pi$
$73$			15.1913i			1.77800i	−0.457905	+	0.889001i	$0.651400\pi$
$74$	23.7412			2.75986
$75$	4.97852	+	0.462928i	0.574870	+	0.0534543i
$76$	−6.94075			−0.796158
$77$		0			0
$78$			0.214627i			0.0243017i
$79$	13.2182			1.48717			0.743584	−	0.668642i	$-0.233124\pi$
$79$	13.2182			1.48717			0.743584	+	0.668642i	$0.233124\pi$
$80$	−24.9255	+	22.7154i	−2.78676	+	2.53965i
$81$	1.00000			0.111111
$82$		−	10.5084i		−	1.16046i
$83$		−	14.4615i		−	1.58736i	−0.608338	−	0.793678i	$-0.708164\pi$
$83$		−	14.4615i		−	1.58736i	0.608338	−	0.793678i	$-0.291836\pi$
$84$	−23.0437			−2.51428
$85$	−0.0344264	−	0.0377760i	−0.00373406	−	0.00409738i
$86$	2.35094			0.253508
$87$			5.85972i			0.628228i
$88$		0			0
$89$	8.19755			0.868938			0.434469	−	0.900687i	$-0.356936\pi$
$89$	8.19755			0.868938			0.434469	+	0.900687i	$0.356936\pi$
$90$	4.11965	+	4.52048i	0.434249	+	0.476501i
$91$	−0.329891			−0.0345820
$92$		−	33.5998i		−	3.50302i
$93$		−	3.23929i		−	0.335899i
$94$	5.19323			0.535641
$95$	−2.09278	+	1.90722i	−0.214715	+	0.195676i
$96$	−22.2072			−2.26651
$97$		−	1.64997i		−	0.167529i	−0.996486	−	0.0837644i	$-0.973306\pi$
$97$		−	1.64997i		−	0.167529i	0.996486	−	0.0837644i	$-0.0266943\pi$
$98$		−	29.1967i		−	2.94931i
$99$		0			0
$100$	−2.53742	+	27.2885i	−0.253742	+	2.72885i
$101$	16.0533			1.59736			0.798681	−	0.601754i	$-0.205531\pi$
$101$	16.0533			1.59736			0.798681	+	0.601754i	$0.205531\pi$
$102$		−	0.0625180i		−	0.00619021i
$103$		−	16.3100i		−	1.60707i	−0.595256	−	0.803536i	$-0.702949\pi$
$103$		−	16.3100i		−	1.60707i	0.595256	−	0.803536i	$-0.297051\pi$
$104$	−0.747170			−0.0732661
$105$	−6.94818	+	6.33208i	−0.678073	+	0.617947i
$106$	−12.4707			−1.21126
$107$			1.74174i			0.168380i	0.996450	+	0.0841900i	$0.0268303\pi$
$107$			1.74174i			0.168380i	−0.996450	+	0.0841900i	$0.973170\pi$
$108$			5.48125i			0.527433i
$109$	−5.52731			−0.529420			−0.264710	−	0.964328i	$-0.585276\pi$
$109$	−5.52731			−0.529420			−0.264710	+	0.964328i	$0.585276\pi$
$110$		0			0
$111$	8.67992			0.823862
$112$		−	63.4045i		−	5.99116i
$113$			8.38535i			0.788827i	0.918933	+	0.394414i	$0.129052\pi$
$113$			8.38535i			0.788827i	−0.918933	+	0.394414i	$0.870948\pi$
$114$	−3.46349			−0.324385
$115$	−9.23273	−	10.1311i	−0.860957	−	0.944727i
$116$	−32.1186			−2.98213
$117$			0.0784689i			0.00725445i
$118$			9.41381i			0.866611i
$119$	0.0960930			0.00880883
$120$	−15.7369	+	14.3415i	−1.43658	+	1.30919i
$121$		0			0
$122$			22.2409i			2.01360i
$123$		−	3.84194i		−	0.346416i
$124$	17.7554			1.59448
$125$	6.73340	+	8.92532i	0.602253	+	0.798305i
$126$	−11.4990			−1.02441
$127$			1.82850i			0.162253i	0.996704	+	0.0811264i	$0.0258518\pi$
$127$			1.82850i			0.162253i	−0.996704	+	0.0811264i	$0.974148\pi$
$128$		−	39.2214i		−	3.46671i
$129$	0.859518			0.0756763
$130$	−0.354717	+	0.323264i	−0.0311108	+	0.0283521i
$131$	1.09407			0.0955894			0.0477947	−	0.998857i	$-0.484781\pi$
$131$	1.09407			0.0955894			0.0477947	+	0.998857i	$0.484781\pi$
$132$		0			0
$133$		−	5.32354i		−	0.461609i
$134$	−1.11255			−0.0961095
$135$	1.50617	+	1.65271i	0.129630	+	0.142243i
$136$	0.217641			0.0186625
$137$		−	17.0599i		−	1.45752i	−0.684768	−	0.728761i	$-0.740097\pi$
$137$		−	17.0599i		−	1.45752i	0.684768	−	0.728761i	$-0.259903\pi$
$138$		−	16.7666i		−	1.42727i
$139$	−14.3029			−1.21316			−0.606579	−	0.795024i	$-0.707458\pi$
$139$	−14.3029			−1.21316			−0.606579	+	0.795024i	$0.707458\pi$
$140$	−34.7077	−	38.0847i	−2.93333	−	3.21874i
$141$	1.89867			0.159897
$142$			22.9872i			1.92904i
$143$		0			0
$144$	−15.0816			−1.25680
$145$	−9.68444	+	8.82571i	−0.804249	+	0.732935i
$146$	−41.5509			−3.43878
$147$		−	10.6745i		−	0.880416i
$148$			47.5768i			3.91079i
$149$	16.6189			1.36147			0.680735	−	0.732530i	$-0.261660\pi$
$149$	16.6189			1.36147			0.680735	+	0.732530i	$0.261660\pi$
$150$	−1.26619	+	13.6172i	−0.103384	+	1.11184i
$151$	6.89775			0.561331			0.280666	−	0.959806i	$-0.409445\pi$
$151$	6.89775			0.561331			0.280666	+	0.959806i	$0.409445\pi$
$152$		−	12.0573i		−	0.977973i
$153$		−	0.0228569i		−	0.00184787i
$154$		0			0
$155$	5.35362	−	4.87891i	0.430013	−	0.391884i
$156$	−0.430108			−0.0344362
$157$		−	16.3071i		−	1.30145i	−0.759315	−	0.650723i	$-0.774466\pi$
$157$		−	16.3071i		−	1.30145i	0.759315	−	0.650723i	$-0.225534\pi$
$158$			36.1544i			2.87629i
$159$	−4.55937			−0.361581
$160$	−33.4477	−	36.7022i	−2.64428	−	2.90156i
$161$	25.7710			2.03104
$162$			2.73519i			0.214897i
$163$			14.7366i			1.15426i	0.816651	+	0.577132i	$0.195828\pi$
$163$			14.7366i			1.15426i	−0.816651	+	0.577132i	$0.804172\pi$
$164$	21.0586			1.64440
$165$		0			0
$166$	39.5549			3.07006
$167$			0.810790i			0.0627408i	0.999508	+	0.0313704i	$0.00998715\pi$
$167$			0.810790i			0.0627408i	−0.999508	+	0.0313704i	$0.990013\pi$
$168$		−	40.0309i		−	3.08845i
$169$	12.9938			0.999526
$170$	0.103324	−	0.0941625i	0.00792462	−	0.00722194i
$171$	−1.26627			−0.0968342
$172$			4.71123i			0.359228i
$173$			17.1474i			1.30369i	0.758352	+	0.651845i	$0.226005\pi$
$173$			17.1474i			1.30369i	−0.758352	+	0.651845i	$0.773995\pi$
$174$	−16.0274			−1.21504
$175$	−20.9302	−	1.94620i	−1.58218	−	0.147119i
$176$		0			0
$177$			3.44174i			0.258697i
$178$			22.4218i			1.68059i
$179$	3.77163			0.281905			0.140953	−	0.990016i	$-0.454983\pi$
$179$	3.77163			0.281905			0.140953	+	0.990016i	$0.454983\pi$
$180$	−9.05893	+	8.25567i	−0.675213	+	0.615341i
$181$	−5.17637			−0.384756			−0.192378	−	0.981321i	$-0.561620\pi$
$181$	−5.17637			−0.384756			−0.192378	+	0.981321i	$0.561620\pi$
$182$		−	0.902314i		−	0.0668840i
$183$			8.13141i			0.601091i
$184$	58.3686			4.30299
$185$	13.0734	+	14.3454i	0.961176	+	1.05470i
$186$	8.86007			0.649652
$187$		0			0
$188$			10.4071i			0.759016i
$189$	−4.20410			−0.305803
$190$	−5.21659	−	5.72416i	−0.378451	−	0.415274i
$191$	−26.1298			−1.89069			−0.945345	−	0.326073i	$-0.894275\pi$
$191$	−26.1298			−1.89069			−0.945345	+	0.326073i	$0.894275\pi$
$192$		−	30.5777i		−	2.20676i
$193$			12.3391i			0.888191i	0.895980	+	0.444095i	$0.146475\pi$
$193$			12.3391i			0.888191i	−0.895980	+	0.444095i	$0.853525\pi$
$194$	4.51297			0.324012
$195$	−0.129687	+	0.118187i	−0.00928706	+	0.00846356i
$196$	58.5094			4.17925
$197$		−	5.16530i		−	0.368013i	−0.982925	−	0.184006i	$-0.941093\pi$
$197$		−	5.16530i		−	0.368013i	0.982925	−	0.184006i	$-0.0589067\pi$
$198$		0			0
$199$	−7.92806			−0.562005			−0.281003	−	0.959707i	$-0.590667\pi$
$199$	−7.92806			−0.562005			−0.281003	+	0.959707i	$0.590667\pi$
$200$	−47.4048	−	4.40793i	−3.35203	−	0.311688i
$201$	−0.406754			−0.0286902
$202$			43.9088i			3.08941i
$203$		−	24.6349i		−	1.72903i
$204$	0.125285			0.00877168
$205$	6.34963	−	5.78660i	0.443477	−	0.404154i
$206$	44.6109			3.10819
$207$		−	6.12996i		−	0.426062i
$208$		−	1.18344i		−	0.0820565i
$209$		0			0
$210$	−17.3194	−	19.0046i	−1.19515	−	1.31144i
$211$	20.5882			1.41735			0.708677	−	0.705533i	$-0.249293\pi$
$211$	20.5882			1.41735			0.708677	+	0.705533i	$0.249293\pi$
$212$		−	24.9910i		−	1.71639i
$213$			8.40424i			0.575849i
$214$	−4.76397			−0.325659
$215$	1.29458	+	1.42054i	0.0882894	+	0.0968798i
$216$	−9.52186			−0.647881
$217$			13.6183i			0.924471i
$218$		−	15.1182i		−	1.02394i
$219$	−15.1913			−1.02653
$220$		0			0
$221$	0.00179356			0.000120648
$222$			23.7412i			1.59341i
$223$			6.43212i			0.430726i	0.976534	+	0.215363i	$0.0690935\pi$
$223$			6.43212i			0.430726i	−0.976534	+	0.215363i	$0.930906\pi$
$224$	93.3614			6.23797
$225$	−0.462928	+	4.97852i	−0.0308618	+	0.331902i
$226$	−22.9355			−1.52565
$227$		−	14.5875i		−	0.968206i	−0.875011	−	0.484103i	$-0.839146\pi$
$227$		−	14.5875i		−	0.968206i	0.875011	−	0.484103i	$-0.160854\pi$
$228$		−	6.94075i		−	0.459662i
$229$	16.1992			1.07047			0.535237	−	0.844702i	$-0.320222\pi$
$229$	16.1992			1.07047			0.535237	+	0.844702i	$0.320222\pi$
$230$	27.7104	−	25.2533i	1.82717	−	1.66515i
$231$		0			0
$232$		−	55.7954i		−	3.66315i
$233$		−	8.58800i		−	0.562619i	−0.959617	−	0.281309i	$-0.909231\pi$
$233$		−	8.58800i		−	0.562619i	0.959617	−	0.281309i	$-0.0907687\pi$
$234$	−0.214627			−0.0140306
$235$	2.85972	+	3.13797i	0.186547	+	0.204698i
$236$	−18.8650			−1.22801
$237$			13.2182i			0.858617i
$238$			0.262832i			0.0170369i
$239$	−6.29874			−0.407432			−0.203716	−	0.979030i	$-0.565302\pi$
$239$	−6.29874			−0.407432			−0.203716	+	0.979030i	$0.565302\pi$
$240$	−22.7154	−	24.9255i	−1.46627	−	1.60894i
$241$	1.13776			0.0732899			0.0366449	−	0.999328i	$-0.488333\pi$
$241$	1.13776			0.0732899			0.0366449	+	0.999328i	$0.488333\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$	−44.5703			−2.85332
$245$	17.6419	−	16.0775i	1.12710	−	1.02716i
$246$	10.5084			0.669992
$247$		−	0.0993630i		−	0.00632231i
$248$			30.8441i			1.95860i
$249$	14.4615			0.916460
$250$	−24.4124	+	18.4171i	−1.54398	+	1.16480i
$251$	3.82996			0.241745			0.120873	−	0.992668i	$-0.461431\pi$
$251$	3.82996			0.241745			0.120873	+	0.992668i	$0.461431\pi$
$252$		−	23.0437i		−	1.45162i
$253$		0			0
$254$	−5.00128			−0.313808
$255$	0.0377760	−	0.0344264i	0.00236562	−	0.00215586i
$256$	46.1223			2.88264
$257$		−	9.67810i		−	0.603703i	−0.953355	−	0.301852i	$-0.902395\pi$
$257$		−	9.67810i		−	0.603703i	0.953355	−	0.301852i	$-0.0976048\pi$
$258$			2.35094i			0.146363i
$259$	−36.4913			−2.26746
$260$	−0.647813	−	0.710845i	−0.0401757	−	0.0440847i
$261$	−5.85972			−0.362707
$262$			2.99249i			0.184877i
$263$			19.0954i			1.17747i	0.808326	+	0.588735i	$0.200374\pi$
$263$			19.0954i			1.17747i	−0.808326	+	0.588735i	$0.799626\pi$
$264$		0			0
$265$	−6.86716	−	7.53533i	−0.421847	−	0.462892i
$266$	14.5609			0.892784
$267$			8.19755i			0.501682i
$268$		−	2.22952i		−	0.136190i
$269$	−17.4899			−1.06638			−0.533190	−	0.845996i	$-0.679007\pi$
$269$	−17.4899			−1.06638			−0.533190	+	0.845996i	$0.679007\pi$
$270$	−4.52048	+	4.11965i	−0.275108	+	0.250714i
$271$	23.8385			1.44809			0.724043	−	0.689755i	$-0.242282\pi$
$271$	23.8385			1.44809			0.724043	+	0.689755i	$0.242282\pi$
$272$			0.344719i			0.0209017i
$273$		−	0.329891i		−	0.0199659i
$274$	46.6619			2.81895
$275$		0			0
$276$	33.5998			2.02247
$277$			4.93692i			0.296631i	0.988940	+	0.148315i	$0.0473851\pi$
$277$			4.93692i			0.296631i	−0.988940	+	0.148315i	$0.952615\pi$
$278$		−	39.1211i		−	2.34633i
$279$	3.23929			0.193931
$280$	66.1596	−	60.2932i	3.95379	−	3.60321i
$281$	2.13091			0.127120			0.0635598	−	0.997978i	$-0.479755\pi$
$281$	2.13091			0.127120			0.0635598	+	0.997978i	$0.479755\pi$
$282$			5.19323i			0.309252i
$283$		−	17.2239i		−	1.02385i	−0.859029	−	0.511926i	$-0.828932\pi$
$283$		−	17.2239i		−	1.02385i	0.859029	−	0.511926i	$-0.171068\pi$
$284$	−46.0657			−2.73350
$285$	−1.90722	−	2.09278i	−0.112974	−	0.123966i
$286$		0			0
$287$			16.1519i			0.953417i
$288$		−	22.2072i		−	1.30857i
$289$	16.9995			0.999969
$290$	−24.1400	−	26.4888i	−1.41755	−	1.55547i
$291$	1.64997			0.0967228
$292$		−	83.2671i		−	4.87284i
$293$		−	19.1742i		−	1.12017i	−0.828436	−	0.560084i	$-0.810769\pi$
$293$		−	19.1742i		−	1.12017i	0.828436	−	0.560084i	$-0.189231\pi$
$294$	29.1967			1.70279
$295$	−5.68822	+	5.18384i	−0.331181	+	0.301815i
$296$	−82.6490			−4.80388
$297$		0			0
$298$			45.4557i			2.63318i
$299$	0.481011			0.0278176
$300$	−27.2885	−	2.53742i	−1.57550	−	0.146498i
$301$	−3.61350			−0.208279
$302$			18.8666i			1.08565i
$303$			16.0533i			0.922238i
$304$	19.0974			1.09531
$305$	−13.4389	+	12.2473i	−0.769509	+	0.701276i
$306$	0.0625180			0.00357392
$307$		−	12.0936i		−	0.690217i	−0.938563	−	0.345108i	$-0.887842\pi$
$307$		−	12.0936i		−	0.690217i	0.938563	−	0.345108i	$-0.112158\pi$
$308$		0			0
$309$	16.3100			0.927843
$310$	13.3447	+	14.6432i	0.757930	+	0.831675i
$311$	10.5043			0.595644			0.297822	−	0.954621i	$-0.403740\pi$
$311$	10.5043			0.595644			0.297822	+	0.954621i	$0.403740\pi$
$312$		−	0.747170i		−	0.0423002i
$313$			0.223857i			0.0126532i	0.999980	+	0.00632658i	$0.00201383\pi$
$313$			0.223857i			0.0126532i	−0.999980	+	0.00632658i	$0.997986\pi$
$314$	44.6029			2.51709
$315$	−6.33208	−	6.94818i	−0.356772	−	0.391486i
$316$	−72.4525			−4.07577
$317$			11.0776i			0.622179i	0.950381	+	0.311090i	$0.100694\pi$
$317$			11.0776i			0.622179i	−0.950381	+	0.311090i	$0.899306\pi$
$318$		−	12.4707i		−	0.699323i
$319$		0			0
$320$	50.5362	−	46.0551i	2.82506	−	2.57456i
$321$	−1.74174			−0.0972142
$322$			70.4884i			3.92817i
$323$			0.0289431i			0.00161044i
$324$	−5.48125			−0.304514
$325$	−0.390659	−	0.0363254i	−0.0216699	−	0.00201497i
$326$	−40.3075			−2.23242
$327$		−	5.52731i		−	0.305661i
$328$			36.5824i			2.01993i
$329$	−7.98222			−0.440074
$330$		0			0
$331$	27.0860			1.48878			0.744390	−	0.667745i	$-0.232741\pi$
$331$	27.0860			1.48878			0.744390	+	0.667745i	$0.232741\pi$
$332$			79.2671i			4.35035i
$333$			8.67992i			0.475657i
$334$	−2.21766			−0.121345
$335$	−0.612639	−	0.672248i	−0.0334720	−	0.0367288i
$336$	63.4045			3.45900
$337$		−	20.9072i		−	1.13889i	−0.822030	−	0.569444i	$-0.807159\pi$
$337$		−	20.9072i		−	1.13889i	0.822030	−	0.569444i	$-0.192841\pi$
$338$			35.5406i			1.93315i
$339$	−8.38535			−0.455430
$340$	0.188699	+	0.207060i	0.0102337	+	0.0112294i
$341$		0			0
$342$		−	3.46349i		−	0.187284i
$343$			15.4479i			0.834107i
$344$	−8.18421			−0.441263
$345$	10.1311	−	9.23273i	0.545438	−	0.497074i
$346$	−46.9013			−2.52143
$347$		−	15.3060i		−	0.821667i	−0.911710	−	0.410833i	$-0.865238\pi$
$347$		−	15.3060i		−	0.821667i	0.911710	−	0.410833i	$-0.134762\pi$
$348$		−	32.1186i		−	1.72174i
$349$	0.634549			0.0339666			0.0169833	−	0.999856i	$-0.494594\pi$
$349$	0.634549			0.0339666			0.0169833	+	0.999856i	$0.494594\pi$
$350$	5.32321	−	57.2481i	0.284537	−	3.06004i
$351$	−0.0784689			−0.00418836
$352$		0			0
$353$			18.5583i			0.987759i	0.869530	+	0.493879i	$0.164422\pi$
$353$			18.5583i			0.987759i	−0.869530	+	0.493879i	$0.835578\pi$
$354$	−9.41381			−0.500338
$355$	−13.8898	+	12.6582i	−0.737194	+	0.671826i
$356$	−44.9328			−2.38143
$357$			0.0960930i			0.00508578i
$358$			10.3161i			0.545224i
$359$	−16.8668			−0.890196			−0.445098	−	0.895482i	$-0.646831\pi$
$359$	−16.8668			−0.890196			−0.445098	+	0.895482i	$0.646831\pi$
$360$	−14.3415	−	15.7369i	−0.755864	−	0.829408i
$361$	−17.3966			−0.915608
$362$		−	14.1583i		−	0.744146i
$363$		0			0
$364$	1.80822			0.0947763
$365$	−22.8806	−	25.1068i	−1.19762	−	1.31415i
$366$	−22.2409			−1.16255
$367$		−	12.3622i		−	0.645301i	−0.946518	−	0.322651i	$-0.895426\pi$
$367$		−	12.3622i		−	0.645301i	0.946518	−	0.322651i	$-0.104574\pi$
$368$			92.4494i			4.81926i
$369$	3.84194			0.200003
$370$	−39.2374	+	35.7582i	−2.03986	+	1.85898i
$371$	19.1680			0.995155
$372$			17.7554i			0.920572i
$373$			13.0097i			0.673615i	0.941574	+	0.336807i	$0.109347\pi$
$373$			13.0097i			0.673615i	−0.941574	+	0.336807i	$0.890653\pi$
$374$		0			0
$375$	−8.92532	+	6.73340i	−0.460902	+	0.347711i
$376$	−18.0789			−0.932349
$377$		−	0.459806i		−	0.0236812i
$378$		−	11.4990i		−	0.591445i
$379$	27.2309			1.39876			0.699380	−	0.714750i	$-0.253460\pi$
$379$	27.2309			1.39876			0.699380	+	0.714750i	$0.253460\pi$
$380$	11.4711	−	10.4539i	0.588454	−	0.536275i
$381$	−1.82850			−0.0936767
$382$		−	71.4700i		−	3.65672i
$383$		−	11.5059i		−	0.587924i	−0.955817	−	0.293962i	$-0.905026\pi$
$383$		−	11.5059i		−	0.587924i	0.955817	−	0.293962i	$-0.0949738\pi$
$384$	39.2214			2.00151
$385$		0			0
$386$	−33.7498			−1.71782
$387$			0.859518i			0.0436917i
$388$			9.04388i			0.459133i
$389$	−23.0264			−1.16749			−0.583743	−	0.811939i	$-0.698412\pi$
$389$	−23.0264			−1.16749			−0.583743	+	0.811939i	$0.698412\pi$
$390$	−0.323264	−	0.354717i	−0.0163691	−	0.0179618i
$391$	−0.140112			−0.00708577
$392$			101.641i			5.13364i
$393$			1.09407i			0.0551886i
$394$	14.1281			0.711762
$395$	−21.8460	+	19.9089i	−1.09919	+	1.00172i
$396$		0			0
$397$			8.37468i			0.420313i	0.977668	+	0.210157i	$0.0673974\pi$
$397$			8.37468i			0.420313i	−0.977668	+	0.210157i	$0.932603\pi$
$398$		−	21.6847i		−	1.08696i
$399$	5.32354			0.266510
$400$	6.98168	−	75.0840i	0.349084	−	3.75420i
$401$	38.3767			1.91644			0.958221	−	0.286029i	$-0.0923354\pi$
$401$	38.3767			1.91644			0.958221	+	0.286029i	$0.0923354\pi$
$402$		−	1.11255i		−	0.0554889i
$403$			0.254184i			0.0126618i
$404$	−87.9921			−4.37777
$405$	−1.65271	+	1.50617i	−0.0821240	+	0.0748420i
$406$	67.3809			3.34406
$407$		0			0
$408$			0.217641i			0.0107748i
$409$	35.6631			1.76343			0.881713	−	0.471786i	$-0.156391\pi$
$409$	35.6631			1.76343			0.881713	+	0.471786i	$0.156391\pi$
$410$	15.8274	+	17.3674i	0.781661	+	0.857715i
$411$	17.0599			0.841501
$412$			89.3991i			4.40438i
$413$		−	14.4694i		−	0.711994i
$414$	16.7666			0.824032
$415$	21.7814	+	23.9007i	1.06921	+	1.17324i
$416$	1.74258			0.0854368
$417$		−	14.3029i		−	0.700417i
$418$		0			0
$419$	−28.0750			−1.37155			−0.685777	−	0.727812i	$-0.740537\pi$
$419$	−28.0750			−1.37155			−0.685777	+	0.727812i	$0.740537\pi$
$420$	38.0847	−	34.7077i	1.85834	−	1.69356i
$421$	−40.2965			−1.96393			−0.981965	−	0.189065i	$-0.939454\pi$
$421$	−40.2965			−1.96393			−0.981965	+	0.189065i	$0.939454\pi$
$422$			56.3127i			2.74126i
$423$			1.89867i			0.0923167i
$424$	43.4137			2.10835
$425$	0.113794	+	0.0105811i	0.00551981	+	0.000513259i
$426$	−22.9872			−1.11373
$427$		−	34.1853i		−	1.65434i
$428$		−	9.54689i		−	0.461466i
$429$		0			0
$430$	−3.88543	+	3.54091i	−0.187372	+	0.170758i
$431$	17.2384			0.830346			0.415173	−	0.909743i	$-0.363721\pi$
$431$	17.2384			0.830346			0.415173	+	0.909743i	$0.363721\pi$
$432$		−	15.0816i		−	0.725613i
$433$		−	17.0888i		−	0.821237i	−0.911807	−	0.410619i	$-0.865313\pi$
$433$		−	17.0888i		−	0.821237i	0.911807	−	0.410619i	$-0.134687\pi$
$434$	−37.2486			−1.78799
$435$	−8.82571	−	9.68444i	−0.423160	−	0.464333i
$436$	30.2966			1.45094
$437$			7.76219i			0.371316i
$438$		−	41.5509i		−	1.98538i
$439$	−1.97449			−0.0942371			−0.0471185	−	0.998889i	$-0.515004\pi$
$439$	−1.97449			−0.0942371			−0.0471185	+	0.998889i	$0.515004\pi$
$440$		0			0
$441$	10.6745			0.508308
$442$			0.00490572i			0.000233341i
$443$		−	26.2675i		−	1.24801i	−0.781422	−	0.624003i	$-0.785505\pi$
$443$		−	26.2675i		−	1.24801i	0.781422	−	0.624003i	$-0.214495\pi$
$444$	−47.5768			−2.25790
$445$	−13.5482	+	12.3469i	−0.642246	+	0.585297i
$446$	−17.5930			−0.833055
$447$			16.6189i			0.786045i
$448$			128.552i			6.07350i
$449$	−6.76495			−0.319258			−0.159629	−	0.987177i	$-0.551030\pi$
$449$	−6.76495			−0.319258			−0.159629	+	0.987177i	$0.551030\pi$
$450$	−13.6172	−	1.26619i	−0.641921	−	0.0596889i
$451$		0			0
$452$		−	45.9622i		−	2.16188i
$453$			6.89775i			0.324085i
$454$	39.8995			1.87258
$455$	0.545216	−	0.496871i	0.0255601	−	0.0232937i
$456$	12.0573			0.564633
$457$			25.1897i			1.17832i	0.808016	+	0.589161i	$0.200542\pi$
$457$			25.1897i			1.17832i	−0.808016	+	0.589161i	$0.799458\pi$
$458$			44.3078i			2.07037i
$459$	0.0228569			0.00106687
$460$	50.6069	+	55.5309i	2.35956	+	2.58914i
$461$	39.8293			1.85504			0.927518	−	0.373778i	$-0.121938\pi$
$461$	39.8293			1.85504			0.927518	+	0.373778i	$0.121938\pi$
$462$		0			0
$463$		−	38.6388i		−	1.79570i	−0.440303	−	0.897849i	$-0.645129\pi$
$463$		−	38.6388i		−	1.79570i	0.440303	−	0.897849i	$-0.354871\pi$
$464$	88.3738			4.10265
$465$	4.87891	+	5.35362i	0.226254	+	0.248268i
$466$	23.4898			1.08814
$467$		−	10.6309i		−	0.491940i	−0.969277	−	0.245970i	$-0.920894\pi$
$467$		−	10.6309i		−	0.491940i	0.969277	−	0.245970i	$-0.0791064\pi$
$468$		−	0.430108i		−	0.0198817i
$469$	1.71004			0.0789621
$470$	−8.58292	+	7.82186i	−0.395901	+	0.360796i
$471$	16.3071			0.751391
$472$		−	32.7718i		−	1.50844i
$473$		0			0
$474$	−36.1544			−1.66062
$475$	0.586192	−	6.30416i	0.0268963	−	0.289255i
$476$	−0.526709			−0.0241417
$477$		−	4.55937i		−	0.208759i
$478$		−	17.2282i		−	0.788002i
$479$	37.6760			1.72146			0.860730	−	0.509062i	$-0.170008\pi$
$479$	37.6760			1.72146			0.860730	+	0.509062i	$0.170008\pi$
$480$	36.7022	−	33.4477i	1.67522	−	1.52667i
$481$	−0.681104			−0.0310557
$482$			3.11200i			0.141748i
$483$			25.7710i			1.17262i
$484$		0			0
$485$	2.48513	+	2.72692i	0.112844	+	0.123823i
$486$	−2.73519			−0.124071
$487$			33.8739i			1.53498i	0.641064	+	0.767488i	$0.278493\pi$
$487$			33.8739i			1.53498i	−0.641064	+	0.767488i	$0.721507\pi$
$488$		−	77.4262i		−	3.50492i
$489$	−14.7366			−0.666414
$490$	43.9751	+	48.2538i	1.98659	+	2.17988i
$491$	4.46216			0.201375			0.100687	−	0.994918i	$-0.467896\pi$
$491$	4.46216			0.201375			0.100687	+	0.994918i	$0.467896\pi$
$492$			21.0586i			0.949396i
$493$			0.133935i			0.00603214i
$494$	0.271776			0.0122278
$495$		0			0
$496$	−48.8536			−2.19359
$497$		−	35.3323i		−	1.58487i
$498$			39.5549i			1.77250i
$499$	30.5968			1.36970			0.684851	−	0.728683i	$-0.259867\pi$
$499$	30.5968			1.36970			0.684851	+	0.728683i	$0.259867\pi$
$500$	−36.9074	−	48.9219i	−1.65055	−	2.18785i
$501$	−0.810790			−0.0362234
$502$			10.4757i			0.467552i
$503$		−	33.2223i		−	1.48131i	−0.671886	−	0.740655i	$-0.734516\pi$
$503$		−	33.2223i		−	1.48131i	0.671886	−	0.740655i	$-0.265484\pi$
$504$	40.0309			1.78312
$505$	−26.5315	+	24.1789i	−1.18064	+	1.07595i
$506$		0			0
$507$			12.9938i			0.577077i
$508$		−	10.0224i		−	0.444674i
$509$	−1.42863			−0.0633228			−0.0316614	−	0.999499i	$-0.510080\pi$
$509$	−1.42863			−0.0633228			−0.0316614	+	0.999499i	$0.510080\pi$
$510$	0.0941625	+	0.103324i	0.00416959	+	0.00457528i
$511$	63.8656			2.82525
$512$			47.7104i			2.10852i
$513$		−	1.26627i		−	0.0559073i
$514$	26.4714			1.16760
$515$	24.5656	+	26.9558i	1.08249	+	1.18781i
$516$	−4.71123			−0.207400
$517$		0			0
$518$		−	99.8105i		−	4.38542i
$519$	−17.1474			−0.752686
$520$	1.23486	−	1.12536i	0.0541521	−	0.0493504i
$521$	11.4588			0.502020			0.251010	−	0.967985i	$-0.419237\pi$
$521$	11.4588			0.502020			0.251010	+	0.967985i	$0.419237\pi$
$522$		−	16.0274i		−	0.701501i
$523$		−	29.5781i		−	1.29336i	−0.762761	−	0.646680i	$-0.776157\pi$
$523$		−	29.5781i		−	1.29336i	0.762761	−	0.646680i	$-0.223843\pi$
$524$	−5.99687			−0.261975
$525$	1.94620	−	20.9302i	0.0849389	−	0.913470i
$526$	−52.2294			−2.27731
$527$		−	0.0740403i		−	0.00322525i
$528$		0			0
$529$	−14.5764			−0.633756
$530$	20.6105	−	18.7830i	0.895265	−	0.815880i
$531$	−3.44174			−0.149359
$532$			29.1796i			1.26510i
$533$			0.301473i			0.0130582i
$534$	−22.4218			−0.970287
$535$	−2.62334	−	2.87859i	−0.113417	−	0.124452i
$536$	3.87306			0.167291
$537$			3.77163i			0.162758i
$538$		−	47.8382i		−	2.06245i
$539$		0			0
$540$	−8.25567	−	9.05893i	−0.355267	−	0.389834i
$541$	−25.4976			−1.09623			−0.548115	−	0.836403i	$-0.684654\pi$
$541$	−25.4976			−1.09623			−0.548115	+	0.836403i	$0.684654\pi$
$542$			65.2028i			2.80070i
$543$		−	5.17637i		−	0.222139i
$544$	−0.507589			−0.0217627
$545$	9.13506	−	8.32505i	0.391303	−	0.356606i
$546$	0.902314			0.0386155
$547$		−	6.72363i		−	0.287482i	−0.989615	−	0.143741i	$-0.954087\pi$
$547$		−	6.72363i		−	0.287482i	0.989615	−	0.143741i	$-0.0459132\pi$
$548$			93.5093i			3.99452i
$549$	−8.13141			−0.347040
$550$		0			0
$551$	7.41999			0.316102
$552$			58.3686i			2.48433i
$553$		−	55.5708i		−	2.36311i
$554$	−13.5034			−0.573705
$555$	−14.3454	+	13.0734i	−0.608930	+	0.554935i
$556$	78.3978			3.32481
$557$			18.7697i			0.795299i	0.917537	+	0.397650i	$0.130174\pi$
$557$			18.7697i			0.795299i	−0.917537	+	0.397650i	$0.869826\pi$
$558$			8.86007i			0.375077i
$559$	−0.0674454			−0.00285264
$560$	95.4977	+	104.790i	4.03551	+	4.42817i
$561$		0			0
$562$			5.82844i			0.245858i
$563$			10.7917i			0.454818i	0.973799	+	0.227409i	$0.0730254\pi$
$563$			10.7917i			0.454818i	−0.973799	+	0.227409i	$0.926975\pi$
$564$	−10.4071			−0.438218
$565$	−12.6297	−	13.8586i	−0.531337	−	0.583035i
$566$	47.1105			1.98020
$567$		−	4.20410i		−	0.176556i
$568$		−	80.0240i		−	3.35773i
$569$	−14.1026			−0.591211			−0.295606	−	0.955310i	$-0.595521\pi$
$569$	−14.1026			−0.591211			−0.295606	+	0.955310i	$0.595521\pi$
$570$	5.72416	−	5.21659i	0.239759	−	0.218499i
$571$	22.1590			0.927325			0.463662	−	0.886012i	$-0.346535\pi$
$571$	22.1590			0.927325			0.463662	+	0.886012i	$0.346535\pi$
$572$		0			0
$573$		−	26.1298i		−	1.09159i
$574$	−44.1785			−1.84397
$575$	30.5181	+	2.83773i	1.27269	+	0.118341i
$576$	30.5777			1.27407
$577$			31.5239i			1.31236i	0.754605	+	0.656179i	$0.227828\pi$
$577$			31.5239i			1.31236i	−0.754605	+	0.656179i	$0.772172\pi$
$578$			46.4967i			1.93401i
$579$	−12.3391			−0.512797
$580$	53.0828	−	48.3759i	2.20414	−	2.00870i
$581$	−60.7976			−2.52231
$582$			4.51297i			0.187069i
$583$		0			0
$584$	144.649			5.98562
$585$	−0.118187	−	0.129687i	−0.00488644	−	0.00536188i
$586$	52.4450			2.16648
$587$			31.2905i			1.29150i	0.763551	+	0.645748i	$0.223454\pi$
$587$			31.2905i			1.29150i	−0.763551	+	0.645748i	$0.776546\pi$
$588$			58.5094i			2.41289i
$589$	−4.10182			−0.169013
$590$	−14.1788	−	15.5583i	−0.583730	−	0.640526i
$591$	5.16530			0.212472
$592$		−	130.907i		−	5.38024i
$593$		−	10.6328i		−	0.436635i	−0.975878	−	0.218318i	$-0.929943\pi$
$593$		−	10.6328i		−	0.436635i	0.975878	−	0.218318i	$-0.0700569\pi$
$594$		0			0
$595$	−0.158814	+	0.144732i	−0.00651075	+	0.00593343i
$596$	−91.0921			−3.73128
$597$		−	7.92806i		−	0.324474i
$598$			1.31566i			0.0538011i
$599$	33.0858			1.35185			0.675924	−	0.736971i	$-0.263745\pi$
$599$	33.0858			1.35185			0.675924	+	0.736971i	$0.263745\pi$
$600$	4.40793	−	47.4048i	0.179953	−	1.93529i
$601$	−0.0517727			−0.00211185			−0.00105593	−	0.999999i	$-0.500336\pi$
$601$	−0.0517727			−0.00211185			−0.00105593	+	0.999999i	$0.500336\pi$
$602$		−	9.88360i		−	0.402825i
$603$		−	0.406754i		−	0.0165643i
$604$	−37.8083			−1.53840
$605$		0			0
$606$	−43.9088			−1.78367
$607$		−	10.7914i		−	0.438008i	−0.975724	−	0.219004i	$-0.929719\pi$
$607$		−	10.7914i		−	0.438008i	0.975724	−	0.219004i	$-0.0702807\pi$
$608$			28.1204i			1.14043i
$609$	24.6349			0.998255
$610$	−33.4985	−	36.7579i	−1.35632	−	1.48828i
$611$	−0.148987			−0.00602736
$612$			0.125285i			0.00506433i
$613$			6.69877i			0.270561i	0.990807	+	0.135280i	$0.0431935\pi$
$613$			6.69877i			0.270561i	−0.990807	+	0.135280i	$0.956806\pi$
$614$	33.0782			1.33493
$615$	5.78660	+	6.34963i	0.233338	+	0.256042i
$616$		0			0
$617$			17.4561i			0.702755i	0.936234	+	0.351377i	$0.114287\pi$
$617$			17.4561i			0.702755i	−0.936234	+	0.351377i	$0.885713\pi$
$618$			44.6109i			1.79451i
$619$	−31.1598			−1.25242			−0.626209	−	0.779655i	$-0.715394\pi$
$619$	−31.1598			−1.25242			−0.626209	+	0.779655i	$0.715394\pi$
$620$	−29.3445	+	26.7425i	−1.17850	+	1.07401i
$621$	6.12996			0.245987
$622$			28.7312i			1.15202i
$623$		−	34.4633i		−	1.38074i
$624$	1.18344			0.0473753
$625$	−24.5714	−	4.60939i	−0.982856	−	0.184376i
$626$	−0.612291			−0.0244721
$627$		0			0
$628$			89.3831i			3.56678i
$629$	0.198397			0.00791059
$630$	19.0046	−	17.3194i	0.757160	−	0.690022i
$631$	6.55952			0.261130			0.130565	−	0.991440i	$-0.458321\pi$
$631$	6.55952			0.261130			0.130565	+	0.991440i	$0.458321\pi$
$632$		−	125.862i		−	5.00653i
$633$			20.5882i			0.818309i
$634$	−30.2993			−1.20334
$635$	−2.75402	−	3.02198i	−0.109290	−	0.119924i
$636$	24.9910			0.990958
$637$			0.837615i			0.0331875i
$638$		0			0
$639$	−8.40424			−0.332466
$640$	59.0739	+	64.8217i	2.33510	+	2.56230i
$641$	9.17095			0.362231			0.181115	−	0.983462i	$-0.442029\pi$
$641$	9.17095			0.362231			0.181115	+	0.983462i	$0.442029\pi$
$642$		−	4.76397i		−	0.188019i
$643$		−	10.8962i		−	0.429704i	−0.976647	−	0.214852i	$-0.931073\pi$
$643$		−	10.8962i		−	0.429704i	0.976647	−	0.214852i	$-0.0689269\pi$
$644$	−141.257			−5.56631
$645$	−1.42054	+	1.29458i	−0.0559336	+	0.0509739i
$646$	−0.0791648			−0.00311470
$647$		−	2.47728i		−	0.0973921i	−0.998814	−	0.0486960i	$-0.984493\pi$
$647$		−	2.47728i		−	0.0973921i	0.998814	−	0.0486960i	$-0.0155066\pi$
$648$		−	9.52186i		−	0.374054i
$649$		0			0
$650$	0.0993568	−	1.06853i	0.00389710	−	0.0419111i
$651$	−13.6183			−0.533744
$652$		−	80.7752i		−	3.16340i
$653$			27.9010i			1.09185i	0.837833	+	0.545926i	$0.183822\pi$
$653$			27.9010i			1.09185i	−0.837833	+	0.545926i	$0.816178\pi$
$654$	15.1182			0.591169
$655$	−1.80819	+	1.64785i	−0.0706517	+	0.0643869i
$656$	−57.9425			−2.26227
$657$		−	15.1913i		−	0.592668i
$658$		−	21.8329i		−	0.851134i
$659$	−3.19475			−0.124450			−0.0622250	−	0.998062i	$-0.519820\pi$
$659$	−3.19475			−0.124450			−0.0622250	+	0.998062i	$0.519820\pi$
$660$		0			0
$661$	−14.8273			−0.576717			−0.288358	−	0.957523i	$-0.593109\pi$
$661$	−14.8273			−0.576717			−0.288358	+	0.957523i	$0.593109\pi$
$662$			74.0852i			2.87940i
$663$			0.00179356i			6.96561e-5i
$664$	−137.700			−5.34381
$665$	8.01813	+	8.79828i	0.310930	+	0.341183i
$666$	−23.7412			−0.919953
$667$			35.9198i			1.39082i
$668$		−	4.44414i		−	0.171949i
$669$	−6.43212			−0.248680
$670$	1.83872	−	1.67568i	0.0710361	−	0.0647373i
$671$		0			0
$672$			93.3614i			3.60149i
$673$		−	22.7828i		−	0.878211i	−0.898436	−	0.439105i	$-0.855295\pi$
$673$		−	22.7828i		−	0.878211i	0.898436	−	0.439105i	$-0.144705\pi$
$674$	57.1851			2.20269
$675$	−4.97852	−	0.462928i	−0.191623	−	0.0178181i
$676$	−71.2225			−2.73933
$677$			18.8485i			0.724405i	0.932099	+	0.362203i	$0.117975\pi$
$677$			18.8485i			0.724405i	−0.932099	+	0.362203i	$0.882025\pi$
$678$		−	22.9355i		−	0.880832i
$679$	−6.93663			−0.266204
$680$	−0.359698	+	0.327803i	−0.0137938	+	0.0125707i
$681$	14.5875			0.558994
$682$		0			0
$683$		−	18.3894i		−	0.703650i	−0.936066	−	0.351825i	$-0.885561\pi$
$683$		−	18.3894i		−	0.703650i	0.936066	−	0.351825i	$-0.114439\pi$
$684$	6.94075			0.265386
$685$	25.6950	+	28.1951i	0.981754	+	1.07728i
$686$	−42.2528			−1.61322
$687$			16.1992i			0.618038i
$688$		−	12.9629i		−	0.494205i
$689$	0.357769			0.0136299
$690$	25.2533	+	27.7104i	0.961375	+	1.05492i
$691$	−18.0662			−0.687269			−0.343635	−	0.939103i	$-0.611658\pi$
$691$	−18.0662			−0.687269			−0.343635	+	0.939103i	$0.611658\pi$
$692$		−	93.9890i		−	3.57292i
$693$		0			0
$694$	41.8647			1.58916
$695$	23.6386	−	21.5426i	0.896664	−	0.817156i
$696$	55.7954			2.11492
$697$		−	0.0878150i		−	0.00332623i
$698$			1.73561i			0.0656938i
$699$	8.58800			0.324828
$700$	114.724	+	10.6676i	4.33615	+	0.403197i
$701$	−22.5834			−0.852963			−0.426481	−	0.904496i	$-0.640247\pi$
$701$	−22.5834			−0.852963			−0.426481	+	0.904496i	$0.640247\pi$
$702$		−	0.214627i		−	0.00810058i
$703$		−	10.9911i		−	0.414539i
$704$		0			0
$705$	−3.13797	+	2.85972i	−0.118183	+	0.107703i
$706$	−50.7604			−1.91039
$707$		−	67.4897i		−	2.53821i
$708$		−	18.8650i		−	0.708992i
$709$	−39.7417			−1.49253			−0.746266	−	0.665648i	$-0.768155\pi$
$709$	−39.7417			−1.49253			−0.746266	+	0.665648i	$0.768155\pi$
$710$	−34.6225	−	37.9912i	−1.29936	−	1.42578i
$711$	−13.2182			−0.495723
$712$		−	78.0559i		−	2.92527i
$713$		−	19.8567i		−	0.743640i
$714$	−0.262832			−0.00983625
$715$		0			0
$716$	−20.6733			−0.772596
$717$		−	6.29874i		−	0.235231i
$718$		−	46.1339i		−	1.72170i
$719$	13.2796			0.495247			0.247624	−	0.968856i	$-0.420350\pi$
$719$	13.2796			0.495247			0.247624	+	0.968856i	$0.420350\pi$
$720$	24.9255	−	22.7154i	0.928920	−	0.846552i
$721$	−68.5689			−2.55364
$722$		−	47.5828i		−	1.77085i
$723$			1.13776i			0.0423139i
$724$	28.3730			1.05447
$725$	2.71263	−	29.1727i	0.100744	−	1.08345i
$726$		0			0
$727$		−	40.1610i		−	1.48949i	−0.667349	−	0.744745i	$-0.732571\pi$
$727$		−	40.1610i		−	1.48949i	0.667349	−	0.744745i	$-0.267429\pi$
$728$			3.14118i			0.116420i
$729$	−1.00000			−0.0370370
$730$	68.6718	−	62.5826i	2.54166	−	2.31629i
$731$	0.0196459			0.000726632
$732$		−	44.5703i		−	1.64736i
$733$		−	16.6840i		−	0.616237i	−0.951348	−	0.308119i	$-0.900301\pi$
$733$		−	16.6840i		−	0.616237i	0.951348	−	0.308119i	$-0.0996994\pi$
$734$	33.8129			1.24806
$735$	16.0775	+	17.6419i	0.593029	+	0.650730i
$736$	−136.129			−5.01779
$737$		0			0
$738$			10.5084i			0.386820i
$739$	−30.0698			−1.10614			−0.553068	−	0.833136i	$-0.686543\pi$
$739$	−30.0698			−1.10614			−0.553068	+	0.833136i	$0.686543\pi$
$740$	−71.6586	−	78.6309i	−2.63422	−	2.89053i
$741$	0.0993630			0.00365019
$742$			52.4282i			1.92470i
$743$			8.68420i			0.318593i	0.987231	+	0.159296i	$0.0509225\pi$
$743$			8.68420i			0.318593i	−0.987231	+	0.159296i	$0.949077\pi$
$744$	−30.8441			−1.13080
$745$	−27.4662	+	25.0308i	−1.00628	+	0.917056i
$746$	−35.5839			−1.30282
$747$			14.4615i			0.529119i
$748$		0			0
$749$	7.32244			0.267556
$750$	−18.4171	−	24.4124i	−0.672497	−	0.891416i
$751$	−34.1267			−1.24530			−0.622651	−	0.782500i	$-0.713944\pi$
$751$	−34.1267			−1.24530			−0.622651	+	0.782500i	$0.713944\pi$
$752$		−	28.6350i		−	1.04421i
$753$			3.82996i			0.139572i
$754$	1.25765			0.0458011
$755$	−11.4000	+	10.3892i	−0.414889	+	0.378100i
$756$	23.0437			0.838092
$757$		−	36.1782i		−	1.31492i	−0.753490	−	0.657459i	$-0.771631\pi$
$757$		−	36.1782i		−	1.31492i	0.753490	−	0.657459i	$-0.228369\pi$
$758$			74.4817i			2.70530i
$759$		0			0
$760$	18.1602	+	19.9272i	0.658741	+	0.722836i
$761$	22.4924			0.815350			0.407675	−	0.913127i	$-0.366340\pi$
$761$	22.4924			0.815350			0.407675	+	0.913127i	$0.366340\pi$
$762$		−	5.00128i		−	0.181177i
$763$			23.2374i			0.841250i
$764$	143.224			5.18167
$765$	0.0344264	+	0.0377760i	0.00124469	+	0.00136579i
$766$	31.4708			1.13708
$767$		−	0.270070i		−	0.00975165i
$768$			46.1223i			1.66429i
$769$	−12.2384			−0.441327			−0.220664	−	0.975350i	$-0.570822\pi$
$769$	−12.2384			−0.441327			−0.220664	+	0.975350i	$0.570822\pi$
$770$		0			0
$771$	9.67810			0.348548
$772$		−	67.6339i		−	2.43420i
$773$			41.3335i			1.48666i	0.668923	+	0.743332i	$0.266756\pi$
$773$			41.3335i			1.48666i	−0.668923	+	0.743332i	$0.733244\pi$
$774$	−2.35094			−0.0845028
$775$	−1.49956	+	16.1269i	−0.0538657	+	0.579295i
$776$	−15.7108			−0.563984
$777$		−	36.4913i		−	1.30912i
$778$		−	62.9815i		−	2.25800i
$779$	−4.86494			−0.174304
$780$	0.710845	−	0.647813i	0.0254523	−	0.0231954i
$781$		0			0
$782$		−	0.383233i		−	0.0137044i
$783$		−	5.85972i		−	0.209409i
$784$	−160.988			−5.74957
$785$	24.5612	+	26.9509i	0.876626	+	0.961920i
$786$	−2.99249			−0.106739
$787$			9.26481i			0.330255i	0.986272	+	0.165127i	$0.0528035\pi$
$787$			9.26481i			0.330255i	−0.986272	+	0.165127i	$0.947196\pi$
$788$			28.3123i			1.00858i
$789$	−19.0954			−0.679813
$790$	−54.4545	−	59.7528i	−1.93740	−	2.12591i
$791$	35.2529			1.25345
$792$		0			0
$793$		−	0.638063i		−	0.0226583i
$794$	−22.9063			−0.812915
$795$	7.53533	−	6.86716i	0.267251	−	0.243553i
$796$	43.4557			1.54024
$797$			46.0523i			1.63126i	0.578577	+	0.815628i	$0.303608\pi$
$797$			46.0523i			1.63126i	−0.578577	+	0.815628i	$0.696392\pi$
$798$			14.5609i			0.515449i
$799$	0.0433979			0.00153531
$800$	110.559	+	10.2803i	3.90886	+	0.363465i
$801$	−8.19755			−0.289646
$802$			104.967i			3.70653i
$803$		0			0
$804$	2.22952			0.0786291
$805$	−42.5920	+	38.8154i	−1.50117	+	1.36806i
$806$	−0.695240			−0.0244888
$807$		−	17.4899i		−	0.615675i
$808$		−	152.857i		−	5.37750i
$809$	2.69777			0.0948485			0.0474243	−	0.998875i	$-0.484899\pi$
$809$	2.69777			0.0948485			0.0474243	+	0.998875i	$0.484899\pi$
$810$	−4.11965	−	4.52048i	−0.144750	−	0.158834i
$811$	25.1697			0.883828			0.441914	−	0.897057i	$-0.354300\pi$
$811$	25.1697			0.883828			0.441914	+	0.897057i	$0.354300\pi$
$812$			135.030i			4.73862i
$813$			23.8385i			0.836053i
$814$		0			0
$815$	−22.1958	−	24.3555i	−0.777486	−	0.853135i
$816$	−0.344719			−0.0120676
$817$		−	1.08838i		−	0.0380777i
$818$			97.5452i			3.41059i
$819$	0.329891			0.0115273
$820$	−34.8039	+	31.7178i	−1.21540	+	1.10763i
$821$	16.3843			0.571814			0.285907	−	0.958257i	$-0.407705\pi$
$821$	16.3843			0.571814			0.285907	+	0.958257i	$0.407705\pi$
$822$			46.6619i			1.62752i
$823$			37.9024i			1.32120i	0.750740	+	0.660598i	$0.229697\pi$
$823$			37.9024i			1.32120i	−0.750740	+	0.660598i	$0.770303\pi$
$824$	−155.302			−5.41019
$825$		0			0
$826$	39.5766			1.37705
$827$		−	38.4533i		−	1.33715i	−0.743644	−	0.668575i	$-0.766904\pi$
$827$		−	38.4533i		−	1.33715i	0.743644	−	0.668575i	$-0.233096\pi$
$828$			33.5998i			1.16767i
$829$	−31.9916			−1.11111			−0.555557	−	0.831479i	$-0.687495\pi$
$829$	−31.9916			−1.11111			−0.555557	+	0.831479i	$0.687495\pi$
$830$	−65.3730	+	59.5763i	−2.26913	+	2.06792i
$831$	−4.93692			−0.171260
$832$			2.39940i			0.0831842i
$833$		−	0.243986i		−	0.00845361i
$834$	39.1211			1.35465
$835$	−1.22118	−	1.34000i	−0.0422608	−	0.0463728i
$836$		0			0
$837$			3.23929i			0.111966i
$838$		−	76.7904i		−	2.65268i
$839$	28.5217			0.984680			0.492340	−	0.870403i	$-0.336142\pi$
$839$	28.5217			0.984680			0.492340	+	0.870403i	$0.336142\pi$
$840$	60.2932	+	66.1596i	2.08031	+	2.28272i
$841$	5.33630			0.184010
$842$		−	110.218i		−	3.79838i
$843$			2.13091i			0.0733925i
$844$	−112.849			−3.88443
$845$	−21.4751	+	19.5709i	−0.738766	+	0.673259i
$846$	−5.19323			−0.178547
$847$		0			0
$848$			68.7625i			2.36131i
$849$	17.2239			0.591121
$850$	−0.0289413	+	0.311247i	−0.000992679	+	0.0106757i
$851$	53.2076			1.82393
$852$		−	46.0657i		−	1.57818i
$853$		−	15.4094i		−	0.527607i	−0.964576	−	0.263804i	$-0.915023\pi$
$853$		−	15.4094i		−	0.527607i	0.964576	−	0.263804i	$-0.0849771\pi$
$854$	93.5031			3.19961
$855$	2.09278	−	1.90722i	0.0715717	−	0.0652254i
$856$	16.5846			0.566849
$857$		−	33.8611i		−	1.15667i	−0.815798	−	0.578336i	$-0.803702\pi$
$857$		−	33.8611i		−	1.15667i	0.815798	−	0.578336i	$-0.196298\pi$
$858$		0			0
$859$	−44.0831			−1.50410			−0.752048	−	0.659109i	$-0.770934\pi$
$859$	−44.0831			−1.50410			−0.752048	+	0.659109i	$0.770934\pi$
$860$	−7.09589	−	7.78631i	−0.241968	−	0.265511i
$861$	−16.1519			−0.550455
$862$			47.1503i			1.60595i
$863$		−	9.86583i		−	0.335837i	−0.985801	−	0.167918i	$-0.946295\pi$
$863$		−	9.86583i		−	0.335837i	0.985801	−	0.167918i	$-0.0537045\pi$
$864$	22.2072			0.755505
$865$	−25.8268	−	28.3397i	−0.878137	−	0.963579i
$866$	46.7412			1.58833
$867$			16.9995i			0.577333i
$868$		−	74.6453i		−	2.53363i
$869$		0			0
$870$	26.4888	−	24.1400i	0.898053	−	0.818421i
$871$	0.0319175			0.00108148
$872$			52.6303i			1.78229i
$873$			1.64997i			0.0558429i
$874$	−21.2310			−0.718151
$875$	37.5230	−	28.3079i	1.26851	−	0.956981i
$876$	83.2671			2.81333
$877$			33.4906i			1.13090i	0.824784	+	0.565449i	$0.191297\pi$
$877$			33.4906i			1.13090i	−0.824784	+	0.565449i	$0.808703\pi$
$878$		−	5.40059i		−	0.182261i
$879$	19.1742			0.646729
$880$		0			0
$881$	0.0156474			0.000527176			0.000263588	−	1.00000i	$-0.499916\pi$
$881$	0.0156474			0.000527176			0.000263588		1.00000i	$0.499916\pi$
$882$			29.1967i			0.983104i
$883$		−	10.5718i		−	0.355768i	−0.984051	−	0.177884i	$-0.943075\pi$
$883$		−	10.5718i		−	0.355768i	0.984051	−	0.177884i	$-0.0569253\pi$
$884$	−0.00983095			−0.000330651
$885$	−5.18384	−	5.68822i	−0.174253	−	0.191207i
$886$	71.8465			2.41373
$887$			38.9927i			1.30925i	0.755955	+	0.654623i	$0.227173\pi$
$887$			38.9927i			1.30925i	−0.755955	+	0.654623i	$0.772827\pi$
$888$		−	82.6490i		−	2.77352i
$889$	7.68719			0.257820
$890$	−33.7710	−	37.0569i	−1.13201	−	1.24215i
$891$		0			0
$892$		−	35.2560i		−	1.18046i
$893$		−	2.40424i		−	0.0804547i
$894$	−45.4557			−1.52027
$895$	−6.23343	+	5.68071i	−0.208361	+	0.189885i
$896$	−164.891			−5.50861
$897$			0.481011i			0.0160605i
$898$		−	18.5034i		−	0.617467i
$899$	−18.9813			−0.633063
$900$	2.53742	−	27.2885i	0.0845807	−	0.909617i
$901$	−0.104213			−0.00347185
$902$		0			0
$903$		−	3.61350i		−	0.120250i
$904$	79.8441			2.65558
$905$	8.55506	−	7.79647i	0.284380	−	0.259163i
$906$	−18.8666			−0.626802
$907$		−	28.0569i		−	0.931614i	−0.884886	−	0.465807i	$-0.845764\pi$
$907$		−	28.0569i		−	0.931614i	0.884886	−	0.465807i	$-0.154236\pi$
$908$			79.9576i			2.65349i
$909$	−16.0533			−0.532454
$910$	1.35904	+	1.49127i	0.0450516	+	0.0494350i
$911$	19.9816			0.662018			0.331009	−	0.943628i	$-0.392611\pi$
$911$	19.9816			0.662018			0.331009	+	0.943628i	$0.392611\pi$
$912$			19.0974i			0.632377i
$913$		0			0
$914$	−68.8984			−2.27896
$915$	−12.2473	−	13.4389i	−0.404882	−	0.444276i
$916$	−88.7918			−2.93376
$917$		−	4.59959i		−	0.151892i
$918$			0.0625180i			0.00206340i
$919$	29.0321			0.957681			0.478840	−	0.877902i	$-0.341057\pi$
$919$	29.0321			0.957681			0.478840	+	0.877902i	$0.341057\pi$
$920$	−96.4666	+	87.9128i	−3.18041	+	2.89840i
$921$	12.0936			0.398497
$922$			108.941i			3.58777i
$923$		−	0.659471i		−	0.0217068i
$924$		0			0
$925$	−43.2132	−	4.01818i	−1.42084	−	0.132117i
$926$	105.684			3.47301
$927$			16.3100i			0.535691i
$928$			130.128i			4.27166i
$929$	−10.8422			−0.355721			−0.177860	−	0.984056i	$-0.556918\pi$
$929$	−10.8422			−0.355721			−0.177860	+	0.984056i	$0.556918\pi$
$930$	−14.6432	+	13.3447i	−0.480168	+	0.437591i
$931$	−13.5168			−0.442995
$932$			47.0729i			1.54193i
$933$			10.5043i			0.343895i
$934$	29.0775			0.951446
$935$		0			0
$936$	0.747170			0.0244220
$937$		−	37.2335i		−	1.21637i	−0.793797	−	0.608183i	$-0.791899\pi$
$937$		−	37.2335i		−	1.21637i	0.793797	−	0.608183i	$-0.208101\pi$
$938$			4.67727i			0.152718i
$939$	−0.223857			−0.00730530
$940$	−15.6748	−	17.2000i	−0.511256	−	0.561001i
$941$	−27.3449			−0.891419			−0.445709	−	0.895178i	$-0.647049\pi$
$941$	−27.3449			−0.891419			−0.445709	+	0.895178i	$0.647049\pi$
$942$			44.6029i			1.45324i
$943$		−	23.5509i		−	0.766924i
$944$	51.9069			1.68943
$945$	6.94818	−	6.33208i	0.226024	−	0.205982i
$946$		0			0
$947$		−	10.7746i		−	0.350126i	−0.984557	−	0.175063i	$-0.943987\pi$
$947$		−	10.7746i		−	0.350126i	0.984557	−	0.175063i	$-0.0560130\pi$
$948$		−	72.4525i		−	2.35315i
$949$	1.19204			0.0386953
$950$	17.2431	+	1.60335i	0.559439	+	0.0520194i
$951$	−11.0776			−0.359215
$952$		−	0.914984i		−	0.0296548i
$953$		−	0.814050i		−	0.0263697i	−0.999913	−	0.0131848i	$-0.995803\pi$
$953$		−	0.814050i		−	0.0263697i	0.999913	−	0.0131848i	$-0.00419698\pi$
$954$	12.4707			0.403755
$955$	43.1852	−	39.3559i	1.39744	−	1.27353i
$956$	34.5250			1.11662
$957$		0			0
$958$			103.051i			3.32942i
$959$	−71.7214			−2.31600
$960$	46.0551	+	50.5362i	1.48642	+	1.63105i
$961$	−20.5070			−0.661516
$962$		−	1.86295i		−	0.0600638i
$963$		−	1.74174i		−	0.0561267i
$964$	−6.23637			−0.200860
$965$	−18.5848	−	20.3931i	−0.598266	−	0.656476i
$966$	−70.4884			−2.26793
$967$			3.35764i			0.107974i	0.998542	+	0.0539872i	$0.0171930\pi$
$967$			3.35764i			0.107974i	−0.998542	+	0.0539872i	$0.982807\pi$
$968$		0			0
$969$	−0.0289431			−0.000929786
$970$	−7.45865	+	6.79728i	−0.239483	+	0.218248i
$971$	−56.1483			−1.80189			−0.900943	−	0.433937i	$-0.857124\pi$
$971$	−56.1483			−1.80189			−0.900943	+	0.433937i	$0.857124\pi$
$972$		−	5.48125i		−	0.175811i
$973$			60.1309i			1.92771i
$974$	−92.6516			−2.96875
$975$	0.0363254	−	0.390659i	0.00116334	−	0.0125111i
$976$	122.634			3.92543
$977$		−	48.9637i		−	1.56649i	−0.621716	−	0.783243i	$-0.713564\pi$
$977$		−	48.9637i		−	1.56649i	0.621716	−	0.783243i	$-0.286436\pi$
$978$		−	40.3075i		−	1.28889i
$979$		0			0
$980$	−96.6994	+	88.1249i	−3.08895	+	2.81505i
$981$	5.52731			0.176473
$982$			12.2049i			0.389473i
$983$		−	1.28160i		−	0.0408768i	−0.999791	−	0.0204384i	$-0.993494\pi$
$983$		−	1.28160i		−	0.0408768i	0.999791	−	0.0204384i	$-0.00650620\pi$
$984$	−36.5824			−1.16620
$985$	7.77980	+	8.53677i	0.247885	+	0.272004i
$986$	−0.366338			−0.0116666
$987$		−	7.98222i		−	0.254077i
$988$			0.544633i			0.0173271i
$989$	5.26881			0.167538
$990$		0			0
$991$	21.4347			0.680896			0.340448	−	0.940263i	$-0.389421\pi$
$991$	21.4347			0.680896			0.340448	+	0.940263i	$0.389421\pi$
$992$		−	71.9356i		−	2.28396i
$993$			27.0860i			0.859547i
$994$	96.6404			3.06525
$995$	13.1028	−	11.9410i	0.415387	−	0.378554i
$996$	−79.2671			−2.51167
$997$		−	43.1737i		−	1.36732i	−0.729799	−	0.683662i	$-0.760386\pi$
$997$		−	43.1737i		−	1.36732i	0.729799	−	0.683662i	$-0.239614\pi$
$998$			83.6880i			2.64910i
$999$	−8.67992			−0.274621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.h.364.12	yes	12
5.2	odd	4		9075.2.a.dp.1.1		6
5.3	odd	4		9075.2.a.dr.1.6		6
5.4	even	2	inner	1815.2.c.h.364.1	✓	12
11.10	odd	2		1815.2.c.i.364.1	yes	12
55.32	even	4		9075.2.a.ds.1.6		6
55.43	even	4		9075.2.a.do.1.1		6
55.54	odd	2		1815.2.c.i.364.12	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.h.364.1	✓	12	5.4	even	2	inner
1815.2.c.h.364.12	yes	12	1.1	even	1	trivial
1815.2.c.i.364.1	yes	12	11.10	odd	2
1815.2.c.i.364.12	yes	12	55.54	odd	2
9075.2.a.do.1.1		6	55.43	even	4
9075.2.a.dp.1.1		6	5.2	odd	4
9075.2.a.dr.1.6		6	5.3	odd	4
9075.2.a.ds.1.6		6	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.73519i q^{2} +1.00000i q^{3} -5.48125 q^{4} +(-1.65271 + 1.50617i) q^{5} -2.73519 q^{6} -4.20410i q^{7} -9.52186i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.73519i q^{2} +1.00000i q^{3} -5.48125 q^{4} +(-1.65271 + 1.50617i) q^{5} -2.73519 q^{6} -4.20410i q^{7} -9.52186i q^{8} -1.00000 q^{9} +(-4.11965 - 4.52048i) q^{10} -5.48125i q^{12} -0.0784689i q^{13} +11.4990 q^{14} +(-1.50617 - 1.65271i) q^{15} +15.0816 q^{16} +0.0228569i q^{17} -2.73519i q^{18} +1.26627 q^{19} +(9.05893 - 8.25567i) q^{20} +4.20410 q^{21} +6.12996i q^{23} +9.52186 q^{24} +(0.462928 - 4.97852i) q^{25} +0.214627 q^{26} -1.00000i q^{27} +23.0437i q^{28} +5.85972 q^{29} +(4.52048 - 4.11965i) q^{30} -3.23929 q^{31} +22.2072i q^{32} -0.0625180 q^{34} +(6.33208 + 6.94818i) q^{35} +5.48125 q^{36} -8.67992i q^{37} +3.46349i q^{38} +0.0784689 q^{39} +(14.3415 + 15.7369i) q^{40} -3.84194 q^{41} +11.4990i q^{42} -0.859518i q^{43} +(1.65271 - 1.50617i) q^{45} -16.7666 q^{46} -1.89867i q^{47} +15.0816i q^{48} -10.6745 q^{49} +(13.6172 + 1.26619i) q^{50} -0.0228569 q^{51} +0.430108i q^{52} +4.55937i q^{53} +2.73519 q^{54} -40.0309 q^{56} +1.26627i q^{57} +16.0274i q^{58} +3.44174 q^{59} +(8.25567 + 9.05893i) q^{60} +8.13141 q^{61} -8.86007i q^{62} +4.20410i q^{63} -30.5777 q^{64} +(0.118187 + 0.129687i) q^{65} +0.406754i q^{67} -0.125285i q^{68} -6.12996 q^{69} +(-19.0046 + 17.3194i) q^{70} +8.40424 q^{71} +9.52186i q^{72} +15.1913i q^{73} +23.7412 q^{74} +(4.97852 + 0.462928i) q^{75} -6.94075 q^{76} +0.214627i q^{78} +13.2182 q^{79} +(-24.9255 + 22.7154i) q^{80} +1.00000 q^{81} -10.5084i q^{82} -14.4615i q^{83} -23.0437 q^{84} +(-0.0344264 - 0.0377760i) q^{85} +2.35094 q^{86} +5.85972i q^{87} +8.19755 q^{89} +(4.11965 + 4.52048i) q^{90} -0.329891 q^{91} -33.5998i q^{92} -3.23929i q^{93} +5.19323 q^{94} +(-2.09278 + 1.90722i) q^{95} -22.2072 q^{96} -1.64997i q^{97} -29.1967i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 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

L-functions

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Database

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