LMFDB - Embedded newform 1805.2.b.i.1084.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1084,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1084");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 $ x^16 + 22x^14 + 190x^12 + 820x^10 + 1862x^8 + 2154x^6 + 1163x^4 + 256*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.10
Root			$0.578047i$ of defining polynomial
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.i.1084.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.578047i q^{2} -0.551888i q^{3} +1.66586 q^{4} +(1.93245 + 1.12501i) q^{5} +0.319017 q^{6} -4.66297i q^{7} +2.11904i q^{8} +2.69542 q^{9} +O(q^{10})$	\(q+0.578047i q^{2} -0.551888i q^{3} +1.66586 q^{4} +(1.93245 + 1.12501i) q^{5} +0.319017 q^{6} -4.66297i q^{7} +2.11904i q^{8} +2.69542 q^{9} +(-0.650310 + 1.11705i) q^{10} -1.22659 q^{11} -0.919368i q^{12} -5.34538i q^{13} +2.69542 q^{14} +(0.620880 - 1.06649i) q^{15} +2.10682 q^{16} +1.41400i q^{17} +1.55808i q^{18} +(3.21919 + 1.87411i) q^{20} -2.57344 q^{21} -0.709029i q^{22} -1.95642i q^{23} +1.16947 q^{24} +(2.46870 + 4.34805i) q^{25} +3.08988 q^{26} -3.14323i q^{27} -7.76787i q^{28} -7.32776 q^{29} +(0.616484 + 0.358898i) q^{30} -1.83707 q^{31} +5.45592i q^{32} +0.676942i q^{33} -0.817358 q^{34} +(5.24590 - 9.01095i) q^{35} +4.49020 q^{36} -5.59033i q^{37} -2.95005 q^{39} +(-2.38395 + 4.09493i) q^{40} +8.29172 q^{41} -1.48757i q^{42} -8.30145i q^{43} -2.04333 q^{44} +(5.20875 + 3.03238i) q^{45} +1.13091 q^{46} +4.10272i q^{47} -1.16273i q^{48} -14.7433 q^{49} +(-2.51338 + 1.42702i) q^{50} +0.780368 q^{51} -8.90466i q^{52} +12.9816i q^{53} +1.81694 q^{54} +(-2.37033 - 1.37993i) q^{55} +9.88104 q^{56} -4.23579i q^{58} -3.76656 q^{59} +(1.03430 - 1.77663i) q^{60} -4.63515 q^{61} -1.06191i q^{62} -12.5687i q^{63} +1.05985 q^{64} +(6.01362 - 10.3297i) q^{65} -0.391304 q^{66} +4.65564i q^{67} +2.35552i q^{68} -1.07973 q^{69} +(5.20875 + 3.03238i) q^{70} -8.44003 q^{71} +5.71171i q^{72} +4.99385i q^{73} +3.23148 q^{74} +(2.39963 - 1.36244i) q^{75} +5.71957i q^{77} -1.70527i q^{78} +14.7216 q^{79} +(4.07131 + 2.37019i) q^{80} +6.35155 q^{81} +4.79301i q^{82} +1.02367i q^{83} -4.28699 q^{84} +(-1.59076 + 2.73248i) q^{85} +4.79863 q^{86} +4.04410i q^{87} -2.59920i q^{88} -3.94508 q^{89} +(-1.75286 + 3.01091i) q^{90} -24.9254 q^{91} -3.25913i q^{92} +1.01385i q^{93} -2.37156 q^{94} +3.01106 q^{96} +4.72554i q^{97} -8.52234i q^{98} -3.30618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) $ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9	$ 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} - 16 q^{10} - 22 q^{11} - 6 q^{14} + 10 q^{15} + 8 q^{16} - 14 q^{20} - 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} - 2 q^{29} - 12 q^{30} + 16 q^{31} + 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} + 38 q^{40} + 26 q^{41} + 64 q^{44} - 2 q^{45} + 2 q^{46} + 20 q^{49} - 48 q^{50} - 38 q^{51} + 12 q^{54} - 10 q^{55} + 6 q^{56} - 10 q^{59} - 10 q^{60} - 30 q^{61} + 16 q^{64} - 36 q^{65} + 4 q^{66} - 68 q^{69} - 2 q^{70} - 20 q^{71} + 40 q^{74} - 32 q^{75} - 12 q^{79} + 40 q^{80} - 48 q^{81} + 2 q^{84} - 2 q^{85} - 20 q^{86} + 30 q^{90} - 86 q^{91} + 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) $ 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 - 16 * q^10 - 22 * q^11 - 6 * q^14 + 10 * q^15 + 8 * q^16 - 14 * q^20 - 20 * q^21 + 14 * q^24 + 4 * q^25 - 16 * q^26 - 2 * q^29 - 12 * q^30 + 16 * q^31 + 8 * q^34 - 10 * q^35 + 18 * q^36 + 36 * q^39 + 38 * q^40 + 26 * q^41 + 64 * q^44 - 2 * q^45 + 2 * q^46 + 20 * q^49 - 48 * q^50 - 38 * q^51 + 12 * q^54 - 10 * q^55 + 6 * q^56 - 10 * q^59 - 10 * q^60 - 30 * q^61 + 16 * q^64 - 36 * q^65 + 4 * q^66 - 68 * q^69 - 2 * q^70 - 20 * q^71 + 40 * q^74 - 32 * q^75 - 12 * q^79 + 40 * q^80 - 48 * q^81 + 2 * q^84 - 2 * q^85 - 20 * q^86 + 30 * q^90 - 86 * q^91 + 38 * q^94 + 22 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			0.578047i			0.408741i	0.978894	+	0.204371i	$0.0655148\pi$
$2$			0.578047i			0.408741i	−0.978894	+	0.204371i	$0.934485\pi$
$3$		−	0.551888i		−	0.318632i	−0.987228	−	0.159316i	$-0.949071\pi$
$3$		−	0.551888i		−	0.318632i	0.987228	−	0.159316i	$-0.0509289\pi$
$4$	1.66586			0.832931
$5$	1.93245	+	1.12501i	0.864216	+	0.503120i
$5$	1.93245	+	1.12501i	0.864216	+	0.503120i
$6$	0.319017			0.130238
$7$		−	4.66297i		−	1.76244i	−0.472708	−	0.881219i	$-0.656723\pi$
$7$		−	4.66297i		−	1.76244i	0.472708	−	0.881219i	$-0.343277\pi$
$8$			2.11904i			0.749194i
$9$	2.69542			0.898473
$10$	−0.650310	+	1.11705i	−0.205646	+	0.353241i
$11$	−1.22659			−0.369832			−0.184916	−	0.982754i	$-0.559201\pi$
$11$	−1.22659			−0.369832			−0.184916	+	0.982754i	$0.559201\pi$
$12$		−	0.919368i		−	0.265399i
$13$		−	5.34538i		−	1.48254i	−0.671206	−	0.741271i	$-0.734223\pi$
$13$		−	5.34538i		−	1.48254i	0.671206	−	0.741271i	$-0.265777\pi$
$14$	2.69542			0.720381
$15$	0.620880	−	1.06649i	0.160311	−	0.275367i
$16$	2.10682			0.526704
$17$			1.41400i			0.342945i	0.985189	+	0.171472i	$0.0548525\pi$
$17$			1.41400i			0.342945i	−0.985189	+	0.171472i	$0.945148\pi$
$18$			1.55808i			0.367243i
$19$		0			0
$19$		0			0
$20$	3.21919	+	1.87411i	0.719832	+	0.419064i
$21$	−2.57344			−0.561570
$22$		−	0.709029i		−	0.151166i
$23$		−	1.95642i		−	0.407942i	−0.978977	−	0.203971i	$-0.934615\pi$
$23$		−	1.95642i		−	0.407942i	0.978977	−	0.203971i	$-0.0653849\pi$
$24$	1.16947			0.238718
$25$	2.46870	+	4.34805i	0.493740	+	0.869610i
$26$	3.08988			0.605976
$27$		−	3.14323i		−	0.604915i
$28$		−	7.76787i		−	1.46799i
$29$	−7.32776			−1.36073			−0.680366	−	0.732873i	$-0.738179\pi$
$29$	−7.32776			−1.36073			−0.680366	+	0.732873i	$0.738179\pi$
$30$	0.616484	+	0.358898i	0.112554	+	0.0655255i
$31$	−1.83707			−0.329947			−0.164973	−	0.986298i	$-0.552754\pi$
$31$	−1.83707			−0.329947			−0.164973	+	0.986298i	$0.552754\pi$
$32$			5.45592i			0.964480i
$33$			0.676942i			0.117840i
$34$	−0.817358			−0.140176
$35$	5.24590	−	9.01095i	0.886719	−	1.52313i
$36$	4.49020			0.748366
$37$		−	5.59033i		−	0.919045i	−0.888166	−	0.459522i	$-0.848021\pi$
$37$		−	5.59033i		−	0.919045i	0.888166	−	0.459522i	$-0.151979\pi$
$38$		0			0
$39$	−2.95005			−0.472386
$40$	−2.38395	+	4.09493i	−0.376935	+	0.647466i
$41$	8.29172			1.29495			0.647474	−	0.762087i	$-0.275825\pi$
$41$	8.29172			1.29495			0.647474	+	0.762087i	$0.275825\pi$
$42$		−	1.48757i		−	0.229537i
$43$		−	8.30145i		−	1.26596i	−0.774169	−	0.632980i	$-0.781832\pi$
$43$		−	8.30145i		−	1.26596i	0.774169	−	0.632980i	$-0.218168\pi$
$44$	−2.04333			−0.308044
$45$	5.20875	+	3.03238i	0.776475	+	0.452040i
$46$	1.13091			0.166743
$47$			4.10272i			0.598443i	0.954184	+	0.299221i	$0.0967269\pi$
$47$			4.10272i			0.598443i	−0.954184	+	0.299221i	$0.903273\pi$
$48$		−	1.16273i		−	0.167825i
$49$	−14.7433			−2.10619
$50$	−2.51338	+	1.42702i	−0.355445	+	0.201812i
$51$	0.780368			0.109273
$52$		−	8.90466i		−	1.23485i
$53$			12.9816i			1.78317i	0.452858	+	0.891583i	$0.350404\pi$
$53$			12.9816i			1.78317i	−0.452858	+	0.891583i	$0.649596\pi$
$54$	1.81694			0.247254
$55$	−2.37033	−	1.37993i	−0.319615	−	0.186070i
$56$	9.88104			1.32041
$57$		0			0
$58$		−	4.23579i		−	0.556187i
$59$	−3.76656			−0.490365			−0.245182	−	0.969477i	$-0.578848\pi$
$59$	−3.76656			−0.490365			−0.245182	+	0.969477i	$0.578848\pi$
$60$	1.03430	−	1.77663i	0.133528	−	0.229362i
$61$	−4.63515			−0.593470			−0.296735	−	0.954960i	$-0.595898\pi$
$61$	−4.63515			−0.593470			−0.296735	+	0.954960i	$0.595898\pi$
$62$		−	1.06191i		−	0.134863i
$63$		−	12.5687i		−	1.58350i
$64$	1.05985			0.132481
$65$	6.01362	−	10.3297i	0.745897	−	1.28124i
$66$	−0.391304			−0.0481662
$67$			4.65564i			0.568778i	0.958709	+	0.284389i	$0.0917906\pi$
$67$			4.65564i			0.568778i	−0.958709	+	0.284389i	$0.908209\pi$
$68$			2.35552i			0.285649i
$69$	−1.07973			−0.129984
$70$	5.20875	+	3.03238i	0.622565	+	0.362439i
$71$	−8.44003			−1.00165			−0.500824	−	0.865549i	$-0.666969\pi$
$71$	−8.44003			−1.00165			−0.500824	+	0.865549i	$0.666969\pi$
$72$			5.71171i			0.673131i
$73$			4.99385i			0.584486i	0.956344	+	0.292243i	$0.0944015\pi$
$73$			4.99385i			0.584486i	−0.956344	+	0.292243i	$0.905598\pi$
$74$	3.23148			0.375652
$75$	2.39963	−	1.36244i	0.277086	−	0.157321i
$76$		0			0
$77$			5.71957i			0.651806i
$78$		−	1.70527i		−	0.193084i
$79$	14.7216			1.65631			0.828155	−	0.560500i	$-0.189391\pi$
$79$	14.7216			1.65631			0.828155	+	0.560500i	$0.189391\pi$
$80$	4.07131	+	2.37019i	0.455186	+	0.264996i
$81$	6.35155			0.705728
$82$			4.79301i			0.529299i
$83$			1.02367i			0.112363i	0.998421	+	0.0561813i	$0.0178925\pi$
$83$			1.02367i			0.112363i	−0.998421	+	0.0561813i	$0.982108\pi$
$84$	−4.28699			−0.467749
$85$	−1.59076	+	2.73248i	−0.172543	+	0.296379i
$86$	4.79863			0.517450
$87$			4.04410i			0.433573i
$88$		−	2.59920i		−	0.277076i
$89$	−3.94508			−0.418178			−0.209089	−	0.977897i	$-0.567050\pi$
$89$	−3.94508			−0.418178			−0.209089	+	0.977897i	$0.567050\pi$
$90$	−1.75286	+	3.01091i	−0.184768	+	0.317377i
$91$	−24.9254			−2.61289
$92$		−	3.25913i		−	0.339788i
$93$			1.01385i			0.105132i
$94$	−2.37156			−0.244608
$95$		0			0
$96$	3.01106			0.307315
$97$			4.72554i			0.479806i	0.970797	+	0.239903i	$0.0771157\pi$
$97$			4.72554i			0.479806i	−0.970797	+	0.239903i	$0.922884\pi$
$98$		−	8.52234i		−	0.860887i
$99$	−3.30618			−0.332284
$100$	4.11251	+	7.24325i	0.411251	+	0.724325i
$101$	−2.69295			−0.267959			−0.133979	−	0.990984i	$-0.542776\pi$
$101$	−2.69295			−0.267959			−0.133979	+	0.990984i	$0.542776\pi$
$102$			0.451090i			0.0446645i
$103$			6.64948i			0.655193i	0.944818	+	0.327596i	$0.106239\pi$
$103$			6.64948i			0.655193i	−0.944818	+	0.327596i	$0.893761\pi$
$104$	11.3271			1.11071
$105$	−4.97303	−	2.89515i	−0.485318	−	0.282537i
$106$	−7.50400			−0.728853
$107$			9.70596i			0.938310i	0.883116	+	0.469155i	$0.155441\pi$
$107$			9.70596i			0.938310i	−0.883116	+	0.469155i	$0.844559\pi$
$108$		−	5.23619i		−	0.503852i
$109$	11.6767			1.11843			0.559214	−	0.829023i	$-0.311103\pi$
$109$	11.6767			1.11843			0.559214	+	0.829023i	$0.311103\pi$
$110$	0.797666	−	1.37016i	0.0760545	−	0.130640i
$111$	−3.08523			−0.292838
$112$		−	9.82403i		−	0.928284i
$113$		−	6.41337i		−	0.603319i	−0.953416	−	0.301659i	$-0.902459\pi$
$113$		−	6.41337i		−	0.603319i	0.953416	−	0.301659i	$-0.0975406\pi$
$114$		0			0
$115$	2.20100	−	3.78068i	0.205244	−	0.352550i
$116$	−12.2070			−1.13339
$117$		−	14.4080i		−	1.33202i
$118$		−	2.17725i		−	0.200432i
$119$	6.59344			0.604419
$120$	2.25994	+	1.31567i	0.206304	+	0.120104i
$121$	−9.49547			−0.863224
$122$		−	2.67933i		−	0.242576i
$123$		−	4.57610i		−	0.412613i
$124$	−3.06030			−0.274823
$125$	−0.120980	+	11.1797i	−0.0108207	+	0.999941i
$126$	7.26529			0.647243
$127$		−	13.1562i		−	1.16743i	−0.811960	−	0.583713i	$-0.801599\pi$
$127$		−	13.1562i		−	1.16743i	0.811960	−	0.583713i	$-0.198401\pi$
$128$			11.5245i			1.01863i
$129$	−4.58147			−0.403376
$130$	5.97103	+	3.47615i	0.523694	+	0.304879i
$131$	17.7707			1.55263			0.776317	−	0.630342i	$-0.217086\pi$
$131$	17.7707			1.55263			0.776317	+	0.630342i	$0.217086\pi$
$132$			1.12769i			0.0981529i
$133$		0			0
$134$	−2.69118			−0.232483
$135$	3.53617	−	6.07413i	0.304345	−	0.522778i
$136$	−2.99632			−0.256932
$137$			14.4889i			1.23787i	0.785441	+	0.618937i	$0.212436\pi$
$137$			14.4889i			1.23787i	−0.785441	+	0.618937i	$0.787564\pi$
$138$		−	0.624133i		−	0.0531297i
$139$	4.33776			0.367924			0.183962	−	0.982933i	$-0.441108\pi$
$139$	4.33776			0.367924			0.183962	+	0.982933i	$0.441108\pi$
$140$	8.73894	−	15.0110i	0.738575	−	1.26866i
$141$	2.26424			0.190683
$142$		−	4.87874i		−	0.409414i
$143$			6.55661i			0.548291i
$144$	5.67875			0.473230
$145$	−14.1605	−	8.24382i	−1.17597	−	0.684612i
$146$	−2.88668			−0.238903
$147$			8.13666i			0.671101i
$148$		−	9.31272i		−	0.765501i
$149$	11.3535			0.930113			0.465057	−	0.885281i	$-0.346034\pi$
$149$	11.3535			0.930113			0.465057	+	0.885281i	$0.346034\pi$
$150$	0.787557	+	1.38710i	0.0643038	+	0.113256i
$151$	17.0316			1.38601			0.693004	−	0.720933i	$-0.256287\pi$
$151$	17.0316			1.38601			0.693004	+	0.720933i	$0.256287\pi$
$152$		0			0
$153$			3.81132i			0.308127i
$154$	−3.30618			−0.266420
$155$	−3.55003	−	2.06672i	−0.285145	−	0.166003i
$156$	−4.91437			−0.393465
$157$		−	0.137360i		−	0.0109625i	−0.999985	−	0.00548127i	$-0.998255\pi$
$157$		−	0.137360i		−	0.0109625i	0.999985	−	0.00548127i	$-0.00174475\pi$
$158$			8.50978i			0.677002i
$159$	7.16440			0.568174
$160$	−6.13798	+	10.5433i	−0.485250	+	0.833519i
$161$	−9.12275			−0.718974
$162$			3.67150i			0.288460i
$163$			4.33952i			0.339897i	0.985453	+	0.169949i	$0.0543602\pi$
$163$			4.33952i			0.339897i	−0.985453	+	0.169949i	$0.945640\pi$
$164$	13.8128			1.07860
$165$	−0.761567	+	1.30815i	−0.0592879	+	0.101840i
$166$	−0.591731			−0.0459272
$167$		−	15.5934i		−	1.20665i	−0.797494	−	0.603327i	$-0.793841\pi$
$167$		−	15.5934i		−	1.20665i	0.797494	−	0.603327i	$-0.206159\pi$
$168$		−	5.45322i		−	0.420725i
$169$	−15.5731			−1.19793
$170$	−1.57950	−	0.919537i	−0.121142	−	0.0705253i
$171$		0			0
$172$		−	13.8291i		−	1.05446i
$173$			16.2544i			1.23580i	0.786257	+	0.617900i	$0.212016\pi$
$173$			16.2544i			1.23580i	−0.786257	+	0.617900i	$0.787984\pi$
$174$	−2.33768			−0.177219
$175$	20.2748	−	11.5115i	1.53263	−	0.870186i
$176$	−2.58421			−0.194792
$177$			2.07872i			0.156246i
$178$		−	2.28045i		−	0.170927i
$179$	13.8284			1.03358			0.516791	−	0.856112i	$-0.327126\pi$
$179$	13.8284			1.03358			0.516791	+	0.856112i	$0.327126\pi$
$180$	8.67706	+	5.05152i	0.646750	+	0.376518i
$181$	8.95858			0.665886			0.332943	−	0.942947i	$-0.391958\pi$
$181$	8.95858			0.665886			0.332943	+	0.942947i	$0.391958\pi$
$182$		−	14.4080i		−	1.06800i
$183$			2.55808i			0.189099i
$184$	4.14574			0.305628
$185$	6.28919	−	10.8030i	0.462390	−	0.794254i
$186$	−0.586055			−0.0429717
$187$		−	1.73440i		−	0.126832i
$188$			6.83456i			0.498461i
$189$	−14.6568			−1.06613
$190$		0			0
$191$	−5.51020			−0.398704			−0.199352	−	0.979928i	$-0.563884\pi$
$191$	−5.51020			−0.398704			−0.199352	+	0.979928i	$0.563884\pi$
$192$		−	0.584919i		−	0.0422129i
$193$			16.2322i			1.16842i	0.811602	+	0.584211i	$0.198596\pi$
$193$			16.2322i			1.16842i	−0.811602	+	0.584211i	$0.801404\pi$
$194$	−2.73159			−0.196117
$195$	−5.70081	−	3.31884i	−0.408244	−	0.237667i
$196$	−24.5603			−1.75431
$197$			3.87849i			0.276331i	0.990409	+	0.138166i	$0.0441206\pi$
$197$			3.87849i			0.276331i	−0.990409	+	0.138166i	$0.955879\pi$
$198$		−	1.91113i		−	0.135818i
$199$	5.13881			0.364281			0.182140	−	0.983273i	$-0.441697\pi$
$199$	5.13881			0.364281			0.182140	+	0.983273i	$0.441697\pi$
$200$	−9.21370	+	5.23127i	−0.651507	+	0.369907i
$201$	2.56939			0.181231
$202$		−	1.55665i		−	0.109526i
$203$			34.1692i			2.39821i
$204$	1.29998			0.0910171
$205$	16.0233	+	9.32828i	1.11912	+	0.651515i
$206$	−3.84372			−0.267804
$207$		−	5.27338i		−	0.366525i
$208$		−	11.2617i		−	0.780861i
$209$		0			0
$210$	1.67353	−	2.87465i	0.115485	−	0.198369i
$211$	11.0879			0.763322			0.381661	−	0.924302i	$-0.375352\pi$
$211$	11.0879			0.763322			0.381661	+	0.924302i	$0.375352\pi$
$212$			21.6256i			1.48525i
$213$			4.65795i			0.319157i
$214$	−5.61050			−0.383526
$215$	9.33923	−	16.0421i	0.636930	−	1.09406i
$216$	6.66064			0.453199
$217$			8.56619i			0.581511i
$218$			6.74970i			0.457148i
$219$	2.75604			0.186236
$220$	−3.94863	−	2.29878i	−0.266217	−	0.154983i
$221$	7.55836			0.508430
$222$		−	1.78341i		−	0.119695i
$223$		−	17.6708i		−	1.18333i	−0.806185	−	0.591664i	$-0.798471\pi$
$223$		−	17.6708i		−	1.18333i	0.806185	−	0.591664i	$-0.201529\pi$
$224$	25.4408			1.69984
$225$	6.65418	+	11.7198i	0.443612	+	0.781321i
$226$	3.70723			0.246601
$227$			14.1375i			0.938341i	0.883108	+	0.469170i	$0.155447\pi$
$227$			14.1375i			0.938341i	−0.883108	+	0.469170i	$0.844553\pi$
$228$		0			0
$229$	1.60567			0.106106			0.0530528	−	0.998592i	$-0.483105\pi$
$229$	1.60567			0.106106			0.0530528	+	0.998592i	$0.483105\pi$
$230$	2.18541	+	1.27228i	0.144102	+	0.0838918i
$231$	3.15656			0.207687
$232$		−	15.5278i		−	1.01945i
$233$			2.15309i			0.141054i	0.997510	+	0.0705269i	$0.0224681\pi$
$233$			2.15309i			0.141054i	−0.997510	+	0.0705269i	$0.977532\pi$
$234$	8.32853			0.544453
$235$	−4.61560	+	7.92828i	−0.301089	+	0.517184i
$236$	−6.27457			−0.408440
$237$		−	8.12467i		−	0.527754i
$238$			3.81132i			0.247051i
$239$	11.6863			0.755927			0.377963	−	0.925821i	$-0.376625\pi$
$239$	11.6863			0.755927			0.377963	+	0.925821i	$0.376625\pi$
$240$	1.30808	−	2.24690i	0.0844362	−	0.145037i
$241$	6.95703			0.448141			0.224071	−	0.974573i	$-0.428065\pi$
$241$	6.95703			0.448141			0.224071	+	0.974573i	$0.428065\pi$
$242$		−	5.48883i		−	0.352835i
$243$		−	12.9350i		−	0.829783i
$244$	−7.72151			−0.494319
$245$	−28.4907	−	16.5864i	−1.82020	−	1.05967i
$246$	2.64520			0.168652
$247$		0			0
$248$		−	3.89282i		−	0.247194i
$249$	0.564952			0.0358024
$250$	−6.46239	−	0.0699319i	−0.408717	−	0.00442288i
$251$	−17.6254			−1.11250			−0.556252	−	0.831013i	$-0.687761\pi$
$251$	−17.6254			−1.11250			−0.556252	+	0.831013i	$0.687761\pi$
$252$		−	20.9377i		−	1.31895i
$253$			2.39974i			0.150870i
$254$	7.60491			0.477175
$255$	1.50802	+	0.877923i	0.0944358	+	0.0549777i
$256$	−4.54200			−0.283875
$257$		−	16.3856i		−	1.02210i	−0.859550	−	0.511052i	$-0.829256\pi$
$257$		−	16.3856i		−	1.02210i	0.859550	−	0.511052i	$-0.170744\pi$
$258$		−	2.64830i		−	0.164876i
$259$	−26.0676			−1.61976
$260$	10.0178	−	17.2078i	0.621281	−	1.06718i
$261$	−19.7514			−1.22258
$262$			10.2723i			0.634626i
$263$		−	14.4054i		−	0.888272i	−0.895959	−	0.444136i	$-0.853511\pi$
$263$		−	14.4054i		−	0.888272i	0.895959	−	0.444136i	$-0.146489\pi$
$264$	−1.43447			−0.0882854
$265$	−14.6045	+	25.0863i	−0.897147	+	1.54104i
$266$		0			0
$267$			2.17724i			0.133245i
$268$			7.75566i			0.473752i
$269$	−6.13766			−0.374220			−0.187110	−	0.982339i	$-0.559912\pi$
$269$	−6.13766			−0.374220			−0.187110	+	0.982339i	$0.559912\pi$
$270$	3.51113	+	2.04407i	0.213681	+	0.124398i
$271$	−21.2762			−1.29244			−0.646218	−	0.763153i	$-0.723650\pi$
$271$	−21.2762			−1.29244			−0.646218	+	0.763153i	$0.723650\pi$
$272$			2.97903i			0.180630i
$273$			13.7560i			0.832551i
$274$	−8.37529			−0.505970
$275$	−3.02809	−	5.33329i	−0.182601	−	0.321609i
$276$	−1.79867			−0.108267
$277$			21.7634i			1.30764i	0.756651	+	0.653819i	$0.226834\pi$
$277$			21.7634i			1.30764i	−0.756651	+	0.653819i	$0.773166\pi$
$278$			2.50743i			0.150386i
$279$	−4.95166			−0.296448
$280$	19.0946	+	11.1163i	1.14112	+	0.664325i
$281$	−17.0673			−1.01815			−0.509076	−	0.860722i	$-0.670013\pi$
$281$	−17.0673			−1.01815			−0.509076	+	0.860722i	$0.670013\pi$
$282$			1.30884i			0.0779401i
$283$			14.9760i			0.890229i	0.895474	+	0.445115i	$0.146837\pi$
$283$			14.9760i			0.890229i	−0.895474	+	0.445115i	$0.853163\pi$
$284$	−14.0599			−0.834303
$285$		0			0
$286$	−3.79003			−0.224109
$287$		−	38.6641i		−	2.28227i
$288$			14.7060i			0.866560i
$289$	15.0006			0.882389
$290$	4.76532	−	8.18544i	0.279829	−	0.480666i
$291$	2.60797			0.152882
$292$			8.31906i			0.486836i
$293$		−	14.9548i		−	0.873669i	−0.899542	−	0.436834i	$-0.856100\pi$
$293$		−	14.9548i		−	0.873669i	0.899542	−	0.436834i	$-0.143900\pi$
$294$	−4.70338			−0.274306
$295$	−7.27868	−	4.23743i	−0.423781	−	0.246712i
$296$	11.8461			0.688543
$297$			3.85547i			0.223717i
$298$			6.56285i			0.380176i
$299$	−10.4578			−0.604792
$300$	3.99746	−	2.26964i	0.230793	−	0.131038i
$301$	−38.7094			−2.23118
$302$			9.84505i			0.566519i
$303$			1.48621i			0.0853804i
$304$		0			0
$305$	−8.95717	−	5.21460i	−0.512886	−	0.298587i
$306$	−2.20312			−0.125944
$307$		−	20.1616i		−	1.15068i	−0.817914	−	0.575341i	$-0.804869\pi$
$307$		−	20.1616i		−	1.15068i	0.817914	−	0.575341i	$-0.195131\pi$
$308$			9.52802i			0.542909i
$309$	3.66977			0.208766
$310$	1.19466	−	2.05209i	0.0678523	−	0.116551i
$311$	−33.3688			−1.89217			−0.946084	−	0.323921i	$-0.894999\pi$
$311$	−33.3688			−1.89217			−0.946084	+	0.323921i	$0.894999\pi$
$312$		−	6.25128i		−	0.353909i
$313$			24.3153i			1.37438i	0.726476	+	0.687191i	$0.241157\pi$
$313$			24.3153i			1.37438i	−0.726476	+	0.687191i	$0.758843\pi$
$314$	0.0794007			0.00448084
$315$	14.1399	−	24.2883i	0.796693	−	1.36849i
$316$	24.5241			1.37959
$317$			0.777616i			0.0436753i	0.999762	+	0.0218376i	$0.00695169\pi$
$317$			0.777616i			0.0436753i	−0.999762	+	0.0218376i	$0.993048\pi$
$318$			4.14137i			0.232236i
$319$	8.98819			0.503242
$320$	2.04811	+	1.19234i	0.114493	+	0.0666541i
$321$	5.35660			0.298976
$322$		−	5.27338i		−	0.293874i
$323$		0			0
$324$	10.5808			0.587822
$325$	23.2420	−	13.1961i	1.28923	−	0.731990i
$326$	−2.50845			−0.138930
$327$		−	6.44424i		−	0.356367i
$328$			17.5705i			0.970168i
$329$	19.1309			1.05472
$330$	−0.756175	−	0.440222i	−0.0416260	−	0.0242334i
$331$	−19.5153			−1.07266			−0.536328	−	0.844009i	$-0.680189\pi$
$331$	−19.5153			−1.07266			−0.536328	+	0.844009i	$0.680189\pi$
$332$			1.70530i			0.0935903i
$333$		−	15.0683i		−	0.825737i
$334$	9.01373			0.493209
$335$	−5.23765	+	8.99678i	−0.286164	+	0.491547i
$336$	−5.42176			−0.295781
$337$			16.3254i			0.889300i	0.895704	+	0.444650i	$0.146672\pi$
$337$			16.3254i			0.889300i	−0.895704	+	0.444650i	$0.853328\pi$
$338$		−	9.00199i		−	0.489643i
$339$	−3.53946			−0.192237
$340$	−2.64999	+	4.55193i	−0.143716	+	0.246863i
$341$	2.25333			0.122025
$342$		0			0
$343$			36.1070i			1.94959i
$344$	17.5911			0.948449
$345$	−2.08651	−	1.21470i	−0.112334	−	0.0653975i
$346$	−9.39582			−0.505122
$347$			27.2858i			1.46478i	0.680886	+	0.732390i	$0.261595\pi$
$347$			27.2858i			1.46478i	−0.680886	+	0.732390i	$0.738405\pi$
$348$			6.73691i			0.361136i
$349$	−16.9079			−0.905060			−0.452530	−	0.891749i	$-0.649479\pi$
$349$	−16.9079			−0.905060			−0.452530	+	0.891749i	$0.649479\pi$
$350$	6.65418	+	11.7198i	0.355681	+	0.626451i
$351$	−16.8018			−0.896812
$352$		−	6.69220i		−	0.356695i
$353$		−	15.5056i		−	0.825282i	−0.910894	−	0.412641i	$-0.864606\pi$
$353$		−	15.5056i		−	0.825282i	0.910894	−	0.412641i	$-0.135394\pi$
$354$	−1.20160			−0.0638642
$355$	−16.3099	−	9.49513i	−0.865640	−	0.503949i
$356$	−6.57196			−0.348313
$357$		−	3.63884i		−	0.192588i
$358$			7.99346i			0.422468i
$359$	−4.25751			−0.224703			−0.112351	−	0.993669i	$-0.535838\pi$
$359$	−4.25751			−0.224703			−0.112351	+	0.993669i	$0.535838\pi$
$360$	−6.42574	+	11.0376i	−0.338666	+	0.581731i
$361$		0			0
$362$			5.17848i			0.272175i
$363$			5.24043i			0.275051i
$364$	−41.5222			−2.17636
$365$	−5.61814	+	9.65034i	−0.294067	+	0.505122i
$366$	−1.47869			−0.0772924
$367$		−	10.1206i		−	0.528294i	−0.964482	−	0.264147i	$-0.914910\pi$
$367$		−	10.1206i		−	0.528294i	0.964482	−	0.264147i	$-0.0850903\pi$
$368$		−	4.12182i		−	0.214865i
$369$	22.3497			1.16348
$370$	6.24466	+	3.63545i	0.324644	+	0.188998i
$371$	60.5331			3.14272
$372$			1.68894i			0.0875674i
$373$			21.1191i			1.09351i	0.837294	+	0.546753i	$0.184136\pi$
$373$			21.1191i			1.09351i	−0.837294	+	0.546753i	$0.815864\pi$
$374$	1.00257			0.0518415
$375$	6.16993	+	0.0667671i	0.318614	+	0.00344784i
$376$	−8.69383			−0.448350
$377$			39.1697i			2.01734i
$378$		−	8.47233i		−	0.435770i
$379$	11.6942			0.600692			0.300346	−	0.953830i	$-0.402898\pi$
$379$	11.6942			0.600692			0.300346	+	0.953830i	$0.402898\pi$
$380$		0			0
$381$	−7.26075			−0.371980
$382$		−	3.18516i		−	0.162967i
$383$		−	1.70745i		−	0.0872465i	−0.999048	−	0.0436233i	$-0.986110\pi$
$383$		−	1.70745i		−	0.0872465i	0.999048	−	0.0436233i	$-0.0138901\pi$
$384$	6.36022			0.324569
$385$	−6.43459	+	11.0528i	−0.327937	+	0.563301i
$386$	−9.38300			−0.477582
$387$		−	22.3759i		−	1.13743i
$388$			7.87210i			0.399645i
$389$	−24.3284			−1.23350			−0.616751	−	0.787159i	$-0.711551\pi$
$389$	−24.3284			−1.23350			−0.616751	+	0.787159i	$0.711551\pi$
$390$	1.91845	−	3.29534i	0.0971443	−	0.166866i
$391$	2.76638			0.139902
$392$		−	31.2417i		−	1.57795i
$393$		−	9.80744i		−	0.494720i
$394$	−2.24195			−0.112948
$395$	28.4487	+	16.5620i	1.43141	+	0.833323i
$396$	−5.50765			−0.276770
$397$			18.4591i			0.926433i	0.886245	+	0.463217i	$0.153305\pi$
$397$			18.4591i			0.926433i	−0.886245	+	0.463217i	$0.846695\pi$
$398$			2.97048i			0.148896i
$399$		0			0
$400$	5.20109	+	9.16054i	0.260055	+	0.458027i
$401$	−5.16001			−0.257679			−0.128839	−	0.991665i	$-0.541125\pi$
$401$	−5.16001			−0.257679			−0.128839	+	0.991665i	$0.541125\pi$
$402$			1.48523i			0.0740766i
$403$			9.81982i			0.489160i
$404$	−4.48609			−0.223191
$405$	12.2740	+	7.14557i	0.609901	+	0.355066i
$406$	−19.7514			−0.980245
$407$			6.85707i			0.339892i
$408$			1.65363i			0.0818670i
$409$	−10.1477			−0.501772			−0.250886	−	0.968017i	$-0.580722\pi$
$409$	−10.1477			−0.501772			−0.250886	+	0.968017i	$0.580722\pi$
$410$	−5.39219	+	9.26223i	−0.266301	+	0.457429i
$411$	7.99626			0.394427
$412$			11.0771i			0.545730i
$413$			17.5634i			0.864237i
$414$	3.04826			0.149814
$415$	−1.15164	+	1.97819i	−0.0565319	+	0.0971056i
$416$	29.1640			1.42988
$417$		−	2.39396i		−	0.117233i
$418$		0			0
$419$	−8.33923			−0.407398			−0.203699	−	0.979034i	$-0.565296\pi$
$419$	−8.33923			−0.407398			−0.203699	+	0.979034i	$0.565296\pi$
$420$	−8.28438	−	4.82291i	−0.404236	−	0.235334i
$421$	−9.94235			−0.484560			−0.242280	−	0.970206i	$-0.577895\pi$
$421$	−9.94235			−0.484560			−0.242280	+	0.970206i	$0.577895\pi$
$422$			6.40933i			0.312001i
$423$			11.0585i			0.537685i
$424$	−27.5086			−1.33594
$425$	−6.14813	+	3.49073i	−0.298228	+	0.169325i
$426$	−2.69251			−0.130453
$427$			21.6136i			1.04595i
$428$			16.1688i			0.781547i
$429$	3.61851			0.174703
$430$	9.27310	+	5.39852i	0.447188	+	0.260340i
$431$	−37.2668			−1.79508			−0.897540	−	0.440934i	$-0.854647\pi$
$431$	−37.2668			−1.79508			−0.897540	+	0.440934i	$0.854647\pi$
$432$		−	6.62221i		−	0.318611i
$433$			5.56925i			0.267641i	0.991006	+	0.133821i	$0.0427246\pi$
$433$			5.56925i			0.267641i	−0.991006	+	0.133821i	$0.957275\pi$
$434$	−4.95166			−0.237687
$435$	−4.54966	+	7.81501i	−0.218140	+	0.374701i
$436$	19.4518			0.931573
$437$		0			0
$438$			1.59312i			0.0761224i
$439$	21.7559			1.03835			0.519177	−	0.854666i	$-0.326238\pi$
$439$	21.7559			1.03835			0.519177	+	0.854666i	$0.326238\pi$
$440$	2.92413	−	5.02282i	0.139403	−	0.239454i
$441$	−39.7395			−1.89236
$442$			4.36909i			0.207816i
$443$			1.61620i			0.0767880i	0.999263	+	0.0383940i	$0.0122242\pi$
$443$			1.61620i			0.0767880i	−0.999263	+	0.0383940i	$0.987776\pi$
$444$	−5.13957			−0.243913
$445$	−7.62366	−	4.43827i	−0.361396	−	0.210394i
$446$	10.2146			0.483675
$447$		−	6.26584i		−	0.296364i
$448$		−	4.94206i		−	0.233490i
$449$	−3.07122			−0.144940			−0.0724700	−	0.997371i	$-0.523088\pi$
$449$	−3.07122			−0.144940			−0.0724700	+	0.997371i	$0.523088\pi$
$450$	−6.77461	+	3.84643i	−0.319358	+	0.181322i
$451$	−10.1706			−0.478913
$452$		−	10.6838i		−	0.502523i
$453$		−	9.39950i		−	0.441627i
$454$	−8.17216			−0.383539
$455$	−48.1669	−	28.0413i	−2.25810	−	1.31460i
$456$		0			0
$457$			5.23234i			0.244759i	0.992483	+	0.122379i	$0.0390524\pi$
$457$			5.23234i			0.244759i	−0.992483	+	0.122379i	$0.960948\pi$
$458$			0.928152i			0.0433697i
$459$	4.44452			0.207453
$460$	3.66656	−	6.29809i	0.170954	−	0.293650i
$461$	−13.5378			−0.630519			−0.315259	−	0.949006i	$-0.602092\pi$
$461$	−13.5378			−0.630519			−0.315259	+	0.949006i	$0.602092\pi$
$462$			1.82464i			0.0848900i
$463$			22.3863i			1.04038i	0.854050	+	0.520191i	$0.174139\pi$
$463$			22.3863i			1.04038i	−0.854050	+	0.520191i	$0.825861\pi$
$464$	−15.4382			−0.716703
$465$	−1.14060	+	1.95922i	−0.0528939	+	0.0908566i
$466$	−1.24459			−0.0576545
$467$		−	34.7898i		−	1.60988i	−0.593356	−	0.804940i	$-0.702198\pi$
$467$		−	34.7898i		−	1.60988i	0.593356	−	0.804940i	$-0.297802\pi$
$468$		−	24.0018i		−	1.10948i
$469$	21.7092			1.00244
$470$	−4.58292	−	2.66804i	−0.211394	−	0.123067i
$471$	−0.0758074			−0.00349302
$472$		−	7.98150i		−	0.367378i
$473$			10.1825i			0.468192i
$474$	4.69644			0.215715
$475$		0			0
$476$	10.9838			0.503439
$477$			34.9910i			1.60213i
$478$			6.75526i			0.308978i
$479$	17.7814			0.812454			0.406227	−	0.913772i	$-0.366844\pi$
$479$	17.7814			0.812454			0.406227	+	0.913772i	$0.366844\pi$
$480$	5.81870	+	3.38747i	0.265586	+	0.154616i
$481$	−29.8825			−1.36252
$482$			4.02149i			0.183174i
$483$			5.03473i			0.229088i
$484$	−15.8181			−0.719006
$485$	−5.31629	+	9.13186i	−0.241400	+	0.414656i
$486$	7.47706			0.339166
$487$			2.42918i			0.110077i	0.998484	+	0.0550383i	$0.0175281\pi$
$487$			2.42918i			0.110077i	−0.998484	+	0.0550383i	$0.982472\pi$
$488$		−	9.82207i		−	0.444624i
$489$	2.39492			0.108302
$490$	9.58774	−	16.4690i	0.433130	−	0.743992i
$491$	−35.1354			−1.58564			−0.792819	−	0.609457i	$-0.791388\pi$
$491$	−35.1354			−1.58564			−0.792819	+	0.609457i	$0.791388\pi$
$492$		−	7.62314i		−	0.343678i
$493$		−	10.3614i		−	0.466656i
$494$		0			0
$495$	−6.38902	−	3.71950i	−0.287165	−	0.167179i
$496$	−3.87036			−0.173784
$497$			39.3556i			1.76534i
$498$			0.326569i			0.0146339i
$499$	−26.0749			−1.16727			−0.583636	−	0.812015i	$-0.698371\pi$
$499$	−26.0749			−1.16727			−0.583636	+	0.812015i	$0.698371\pi$
$500$	−0.201535	+	18.6238i	−0.00901293	+	0.832882i
$501$	−8.60581			−0.384479
$502$		−	10.1883i		−	0.454727i
$503$		−	43.7728i		−	1.95173i	−0.218367	−	0.975867i	$-0.570073\pi$
$503$		−	43.7728i		−	1.95173i	0.218367	−	0.975867i	$-0.429927\pi$
$504$	26.6335			1.18635
$505$	−5.20399	−	3.02960i	−0.231574	−	0.134816i
$506$	−1.38716			−0.0616668
$507$			8.59460i			0.381699i
$508$		−	21.9164i		−	0.972384i
$509$	−4.01256			−0.177854			−0.0889268	−	0.996038i	$-0.528344\pi$
$509$	−4.01256			−0.177854			−0.0889268	+	0.996038i	$0.528344\pi$
$510$	−0.507481	+	0.871707i	−0.0224716	+	0.0385998i
$511$	23.2862			1.03012
$512$			20.4235i			0.902599i
$513$		0			0
$514$	9.47164			0.417776
$515$	−7.48074	+	12.8498i	−0.329641	+	0.566228i
$516$	−7.63209			−0.335984
$517$		−	5.03237i		−	0.221323i
$518$		−	15.0683i		−	0.662063i
$519$	8.97060			0.393766
$520$	21.8890	+	12.7431i	0.959895	+	0.558822i
$521$	2.54253			0.111390			0.0556951	−	0.998448i	$-0.482263\pi$
$521$	2.54253			0.111390			0.0556951	+	0.998448i	$0.482263\pi$
$522$		−	11.4172i		−	0.499719i
$523$		−	25.2632i		−	1.10468i	−0.833618	−	0.552341i	$-0.813735\pi$
$523$		−	25.2632i		−	1.10468i	0.833618	−	0.552341i	$-0.186265\pi$
$524$	29.6035			1.29324
$525$	−6.35304	−	11.1894i	−0.277269	−	0.488347i
$526$	8.32698			0.363073
$527$		−	2.59761i		−	0.113154i
$528$			1.42619i			0.0620670i
$529$	19.1724			0.833583
$530$	−14.5011	−	8.44209i	−0.629887	−	0.366701i
$531$	−10.1525			−0.440579
$532$		0			0
$533$		−	44.3224i		−	1.91982i
$534$	−1.25855			−0.0544628
$535$	−10.9193	+	18.7562i	−0.472083	+	0.810903i
$536$	−9.86550			−0.426125
$537$		−	7.63171i		−	0.329333i
$538$		−	3.54786i		−	0.152959i
$539$	18.0841			0.778936
$540$	5.89077	−	10.1187i	0.253498	−	0.435437i
$541$	−24.6342			−1.05911			−0.529553	−	0.848277i	$-0.677640\pi$
$541$	−24.6342			−1.05911			−0.529553	+	0.848277i	$0.677640\pi$
$542$		−	12.2986i		−	0.528272i
$543$		−	4.94413i		−	0.212173i
$544$	−7.71466			−0.330764
$545$	22.5647	+	13.1365i	0.966564	+	0.562704i
$546$	−7.95162			−0.340298
$547$			17.4853i			0.747616i	0.927506	+	0.373808i	$0.121948\pi$
$547$			17.4853i			0.747616i	−0.927506	+	0.373808i	$0.878052\pi$
$548$			24.1366i			1.03106i
$549$	−12.4937			−0.533217
$550$	3.08289	−	1.75038i	0.131455	−	0.0746364i
$551$		0			0
$552$		−	2.28798i		−	0.0973830i
$553$		−	68.6464i		−	2.91914i
$554$	−12.5803			−0.534485
$555$	−5.96205	−	3.47092i	−0.253075	−	0.147333i
$556$	7.22611			0.306455
$557$		−	11.4576i		−	0.485472i	−0.970092	−	0.242736i	$-0.921955\pi$
$557$		−	11.4576i		−	0.485472i	0.970092	−	0.242736i	$-0.0780449\pi$
$558$		−	2.86230i		−	0.121171i
$559$	−44.3744			−1.87684
$560$	11.0521	−	18.9844i	0.467039	−	0.802238i
$561$	−0.957194			−0.0404128
$562$		−	9.86573i		−	0.416161i
$563$		−	24.0351i		−	1.01296i	−0.862252	−	0.506479i	$-0.830947\pi$
$563$		−	24.0351i		−	1.01296i	0.862252	−	0.506479i	$-0.169053\pi$
$564$	3.77191			0.158826
$565$	7.21511	−	12.3935i	0.303542	−	0.521398i
$566$	−8.65682			−0.363873
$567$		−	29.6171i		−	1.24380i
$568$		−	17.8848i		−	0.750428i
$569$	9.61664			0.403151			0.201575	−	0.979473i	$-0.435394\pi$
$569$	9.61664			0.403151			0.201575	+	0.979473i	$0.435394\pi$
$570$		0			0
$571$	−27.2898			−1.14204			−0.571021	−	0.820936i	$-0.693452\pi$
$571$	−27.2898			−1.14204			−0.571021	+	0.820936i	$0.693452\pi$
$572$			10.9224i			0.456689i
$573$			3.04101i			0.127040i
$574$	22.3497			0.932857
$575$	8.50662	−	4.82982i	0.354751	−	0.201417i
$576$	2.85674			0.119031
$577$			28.7657i			1.19753i	0.800924	+	0.598766i	$0.204342\pi$
$577$			28.7657i			1.19753i	−0.800924	+	0.598766i	$0.795658\pi$
$578$			8.67106i			0.360669i
$579$	8.95837			0.372297
$580$	−23.5894	−	13.7331i	−0.979498	−	0.570234i
$581$	4.77336			0.198032
$582$			1.50753i			0.0624891i
$583$		−	15.9232i		−	0.659471i
$584$	−10.5822			−0.437893
$585$	16.2092	−	27.8428i	0.670169	−	1.15116i
$586$	8.64458			0.357104
$587$		−	18.5265i		−	0.764669i	−0.924024	−	0.382335i	$-0.875120\pi$
$587$		−	18.5265i		−	0.764669i	0.924024	−	0.382335i	$-0.124880\pi$
$588$			13.5545i			0.558980i
$589$		0			0
$590$	2.44943	−	4.20742i	0.100842	−	0.173217i
$591$	2.14049			0.0880481
$592$		−	11.7778i		−	0.484065i
$593$		−	35.2510i		−	1.44758i	−0.690018	−	0.723792i	$-0.742398\pi$
$593$		−	35.2510i		−	1.44758i	0.690018	−	0.723792i	$-0.257602\pi$
$594$	−2.22864			−0.0914423
$595$	12.7415	+	7.41769i	0.522349	+	0.304096i
$596$	18.9133			0.774720
$597$		−	2.83605i		−	0.116072i
$598$		−	6.04512i		−	0.247203i
$599$	−21.8274			−0.891845			−0.445922	−	0.895072i	$-0.647124\pi$
$599$	−21.8274			−0.891845			−0.445922	+	0.895072i	$0.647124\pi$
$600$	2.88707	+	5.08492i	0.117864	+	0.207591i
$601$	36.9139			1.50575			0.752875	−	0.658164i	$-0.228667\pi$
$601$	36.9139			1.50575			0.752875	+	0.658164i	$0.228667\pi$
$602$		−	22.3759i		−	0.911973i
$603$			12.5489i			0.511031i
$604$	28.3722			1.15445
$605$	−18.3495	−	10.6825i	−0.746013	−	0.434306i
$606$	−0.859098			−0.0348985
$607$		−	14.6393i		−	0.594192i	−0.954848	−	0.297096i	$-0.903982\pi$
$607$		−	14.6393i		−	0.594192i	0.954848	−	0.297096i	$-0.0960182\pi$
$608$		0			0
$609$	18.8575			0.764146
$610$	3.01428	−	5.17767i	0.122045	−	0.209638i
$611$	21.9306			0.887216
$612$			6.34913i			0.256648i
$613$		−	32.3507i		−	1.30663i	−0.757085	−	0.653317i	$-0.773377\pi$
$613$		−	32.3507i		−	1.30663i	0.757085	−	0.653317i	$-0.226623\pi$
$614$	11.6543			0.470331
$615$	5.14816	−	8.84306i	0.207594	−	0.356587i
$616$	−12.1200			−0.488329
$617$			23.3753i			0.941054i	0.882386	+	0.470527i	$0.155936\pi$
$617$			23.3753i			0.941054i	−0.882386	+	0.470527i	$0.844064\pi$
$618$			2.12130i			0.0853311i
$619$	−33.0099			−1.32678			−0.663390	−	0.748274i	$-0.730883\pi$
$619$	−33.0099			−1.32678			−0.663390	+	0.748274i	$0.730883\pi$
$620$	−5.91386	−	3.44287i	−0.237506	−	0.138269i
$621$	−6.14949			−0.246771
$622$		−	19.2887i		−	0.773407i
$623$			18.3958i			0.737013i
$624$	−6.21521			−0.248808
$625$	−12.8111	+	21.4680i	−0.512442	+	0.858722i
$626$	−14.0554			−0.561767
$627$		0			0
$628$		−	0.228823i		−	0.00913103i
$629$	7.90472			0.315182
$630$	14.0398	+	8.17354i	0.559358	+	0.325641i
$631$	15.2167			0.605768			0.302884	−	0.953027i	$-0.402050\pi$
$631$	15.2167			0.605768			0.302884	+	0.953027i	$0.402050\pi$
$632$			31.1957i			1.24090i
$633$		−	6.11927i		−	0.243219i
$634$	−0.449499			−0.0178519
$635$	14.8009	−	25.4237i	0.587356	−	1.00891i
$636$	11.9349			0.473250
$637$			78.8087i			3.12252i
$638$			5.19560i			0.205696i
$639$	−22.7494			−0.899953
$640$	−12.9652	+	22.2705i	−0.512494	+	0.880317i
$641$	−11.0717			−0.437307			−0.218654	−	0.975803i	$-0.570167\pi$
$641$	−11.0717			−0.437307			−0.218654	+	0.975803i	$0.570167\pi$
$642$			3.09637i			0.122204i
$643$			36.4492i			1.43742i	0.695312	+	0.718708i	$0.255266\pi$
$643$			36.4492i			1.43742i	−0.695312	+	0.718708i	$0.744734\pi$
$644$	−15.1972			−0.598855
$645$	−8.85344	−	5.15420i	−0.348604	−	0.202947i
$646$		0			0
$647$		−	17.2616i		−	0.678624i	−0.940674	−	0.339312i	$-0.889806\pi$
$647$		−	17.2616i		−	0.678624i	0.940674	−	0.339312i	$-0.110194\pi$
$648$			13.4592i			0.528727i
$649$	4.62004			0.181352
$650$	7.62799	+	13.4350i	0.299194	+	0.526963i
$651$	4.72757			0.185288
$652$			7.22903i			0.283111i
$653$		−	43.0613i		−	1.68512i	−0.538605	−	0.842559i	$-0.681048\pi$
$653$		−	43.0613i		−	1.68512i	0.538605	−	0.842559i	$-0.318952\pi$
$654$	3.72508			0.145662
$655$	34.3409	+	19.9923i	1.34181	+	0.781162i
$656$	17.4691			0.682055
$657$			13.4605i			0.525145i
$658$			11.0585i			0.431107i
$659$	7.86198			0.306259			0.153130	−	0.988206i	$-0.451065\pi$
$659$	7.86198			0.306259			0.153130	+	0.988206i	$0.451065\pi$
$660$	−1.26867	+	2.17920i	−0.0493827	+	0.0848253i
$661$	−21.6266			−0.841177			−0.420588	−	0.907252i	$-0.638176\pi$
$661$	−21.6266			−0.841177			−0.420588	+	0.907252i	$0.638176\pi$
$662$		−	11.2808i		−	0.438439i
$663$		−	4.17136i		−	0.162002i
$664$	−2.16920			−0.0841814
$665$		0			0
$666$	8.71019			0.337513
$667$			14.3362i			0.555100i
$668$		−	25.9765i		−	1.00506i
$669$	−9.75232			−0.377046
$670$	−5.20057	−	3.02761i	−0.200915	−	0.116967i
$671$	5.68544			0.219484
$672$		−	14.0405i		−	0.541623i
$673$		−	2.49031i		−	0.0959943i	−0.998847	−	0.0479971i	$-0.984716\pi$
$673$		−	2.49031i		−	0.0959943i	0.998847	−	0.0479971i	$-0.0152838\pi$
$674$	−9.43684			−0.363494
$675$	13.6669	−	7.75969i	0.526040	−	0.298671i
$676$	−25.9426			−0.997793
$677$			17.5426i			0.674216i	0.941466	+	0.337108i	$0.109449\pi$
$677$			17.5426i			0.674216i	−0.941466	+	0.337108i	$0.890551\pi$
$678$		−	2.04597i		−	0.0785752i
$679$	22.0351			0.845629
$680$	−5.79023	−	3.37090i	−0.222045	−	0.129268i
$681$	7.80233			0.298986
$682$			1.30253i			0.0498766i
$683$			42.8977i			1.64143i	0.571334	+	0.820717i	$0.306426\pi$
$683$			42.8977i			1.64143i	−0.571334	+	0.820717i	$0.693574\pi$
$684$		0			0
$685$	−16.3002	+	27.9991i	−0.622799	+	1.06979i
$686$	−20.8715			−0.796879
$687$		−	0.886148i		−	0.0338087i
$688$		−	17.4896i		−	0.666786i
$689$	69.3918			2.64362
$690$	0.702156	−	1.20610i	0.0267306	−	0.0459155i
$691$	−21.9873			−0.836435			−0.418218	−	0.908347i	$-0.637345\pi$
$691$	−21.9873			−0.836435			−0.418218	+	0.908347i	$0.637345\pi$
$692$			27.0776i			1.02934i
$693$			15.4167i			0.585630i
$694$	−15.7725			−0.598716
$695$	8.38249	+	4.88003i	0.317966	+	0.185110i
$696$	−8.56962			−0.324831
$697$			11.7245i			0.444096i
$698$		−	9.77358i		−	0.369935i
$699$	1.18827			0.0449443
$700$	33.7751	−	19.1765i	1.27658	−	0.724804i
$701$	−4.73849			−0.178970			−0.0894851	−	0.995988i	$-0.528522\pi$
$701$	−4.73849			−0.178970			−0.0894851	+	0.995988i	$0.528522\pi$
$702$		−	9.71222i		−	0.366564i
$703$		0			0
$704$	−1.30001			−0.0489958
$705$	4.37552	+	2.54729i	0.164792	+	0.0959367i
$706$	8.96299			0.337327
$707$			12.5572i			0.472261i
$708$			3.46286i			0.130142i
$709$	4.81018			0.180650			0.0903251	−	0.995912i	$-0.471209\pi$
$709$	4.81018			0.180650			0.0903251	+	0.995912i	$0.471209\pi$
$710$	5.48864	−	9.42790i	0.205985	−	0.353823i
$711$	39.6809			1.48815
$712$		−	8.35980i		−	0.313297i
$713$			3.59408i			0.134599i
$714$	2.10342			0.0787185
$715$	−7.37626	+	12.6703i	−0.275857	+	0.473842i
$716$	23.0362			0.860902
$717$		−	6.44955i		−	0.240863i
$718$		−	2.46104i		−	0.0918454i
$719$	49.7230			1.85436			0.927178	−	0.374621i	$-0.122227\pi$
$719$	49.7230			1.85436			0.927178	+	0.374621i	$0.122227\pi$
$720$	10.9739	+	6.38867i	0.408973	+	0.238091i
$721$	31.0064			1.15474
$722$		0			0
$723$		−	3.83950i		−	0.142792i
$724$	14.9237			0.554637
$725$	−18.0900	−	31.8615i	−0.671847	−	1.18331i
$726$	−3.02922			−0.112425
$727$			15.2548i			0.565769i	0.959154	+	0.282885i	$0.0912914\pi$
$727$			15.2548i			0.565769i	−0.959154	+	0.282885i	$0.908709\pi$
$728$		−	52.8179i		−	1.95756i
$729$	11.9160			0.441332
$730$	−5.57835	−	3.24755i	−0.206464	−	0.120197i
$731$	11.7382			0.434154
$732$			4.26141i			0.157506i
$733$			17.1375i			0.632989i	0.948594	+	0.316495i	$0.102506\pi$
$733$			17.1375i			0.632989i	−0.948594	+	0.316495i	$0.897494\pi$
$734$	5.85021			0.215935
$735$	−9.15384	+	15.7237i	−0.337644	+	0.579976i
$736$	10.6741			0.393452
$737$		−	5.71058i		−	0.210352i
$738$			12.9192i			0.475561i
$739$	10.0760			0.370651			0.185326	−	0.982677i	$-0.440666\pi$
$739$	10.0760			0.370651			0.185326	+	0.982677i	$0.440666\pi$
$740$	10.4769	−	17.9963i	0.385139	−	0.661558i
$741$		0			0
$742$			34.9910i			1.28456i
$743$			2.20803i			0.0810049i	0.999179	+	0.0405024i	$0.0128959\pi$
$743$			2.20803i			0.0810049i	−0.999179	+	0.0405024i	$0.987104\pi$
$744$	−2.14840			−0.0787641
$745$	21.9400	+	12.7728i	0.803819	+	0.467959i
$746$	−12.2079			−0.446961
$747$			2.75923i			0.100955i
$748$		−	2.88927i		−	0.105642i
$749$	45.2586			1.65371
$750$	−0.0385946	+	3.56651i	−0.00140927	+	0.130231i
$751$	−24.9684			−0.911109			−0.455555	−	0.890208i	$-0.650559\pi$
$751$	−24.9684			−0.911109			−0.455555	+	0.890208i	$0.650559\pi$
$752$			8.64367i			0.315202i
$753$			9.72723i			0.354480i
$754$	−22.6419			−0.824570
$755$	32.9126	+	19.1607i	1.19781	+	0.697329i
$756$	−24.4162			−0.888009
$757$		−	26.5524i		−	0.965062i	−0.875879	−	0.482531i	$-0.839718\pi$
$757$		−	26.5524i		−	0.965062i	0.875879	−	0.482531i	$-0.160282\pi$
$758$			6.75981i			0.245527i
$759$	1.32438			0.0480721
$760$		0			0
$761$	15.5905			0.565154			0.282577	−	0.959245i	$-0.408811\pi$
$761$	15.5905			0.565154			0.282577	+	0.959245i	$0.408811\pi$
$762$		−	4.19706i		−	0.152043i
$763$		−	54.4483i		−	1.97116i
$764$	−9.17923			−0.332093
$765$	−4.28778	+	7.36517i	−0.155025	+	0.266288i
$766$	0.986986			0.0356612
$767$			20.1337i			0.726986i
$768$			2.50667i			0.0904517i
$769$	10.4030			0.375142			0.187571	−	0.982251i	$-0.439938\pi$
$769$	10.4030			0.375142			0.187571	+	0.982251i	$0.439938\pi$
$770$	−6.38902	−	3.71950i	−0.230244	−	0.134041i
$771$	−9.04299			−0.325675
$772$			27.0407i			0.973214i
$773$		−	54.7882i		−	1.97060i	−0.170845	−	0.985298i	$-0.554650\pi$
$773$		−	54.7882i		−	1.97060i	0.170845	−	0.985298i	$-0.445350\pi$
$774$	12.9343			0.464915
$775$	−4.53516	−	7.98765i	−0.162908	−	0.286925i
$776$	−10.0136			−0.359468
$777$			14.3864i			0.516108i
$778$		−	14.0630i		−	0.504183i
$779$		0			0
$780$	−9.49676	−	5.52873i	−0.340039	−	0.197960i
$781$	10.3525			0.370441
$782$			1.59910i			0.0571836i
$783$			23.0329i			0.823127i
$784$	−31.0615			−1.10934
$785$	0.154532	−	0.265441i	0.00551548	−	0.00947400i
$786$	5.66916			0.202212
$787$			3.32906i			0.118668i	0.998238	+	0.0593341i	$0.0188977\pi$
$787$			3.32906i			0.118668i	−0.998238	+	0.0593341i	$0.981102\pi$
$788$			6.46103i			0.230165i
$789$	−7.95014			−0.283032
$790$	−9.57360	+	16.4447i	−0.340613	+	0.585076i
$791$	−29.9054			−1.06331
$792$		−	7.00594i		−	0.248945i
$793$			24.7766i			0.879844i
$794$	−10.6702			−0.378672
$795$	13.8448	+	8.06004i	0.491025	+	0.285860i
$796$	8.56055			0.303420
$797$			28.1743i			0.997985i	0.866606	+	0.498993i	$0.166297\pi$
$797$			28.1743i			0.997985i	−0.866606	+	0.498993i	$0.833703\pi$
$798$		0			0
$799$	−5.80123			−0.205233
$800$	−23.7226	+	13.4690i	−0.838721	+	0.476202i
$801$	−10.6337			−0.375722
$802$		−	2.98273i		−	0.105324i
$803$		−	6.12542i		−	0.216161i
$804$	4.28025			0.150953
$805$	−17.6292	−	10.2632i	−0.621349	−	0.361730i
$806$	−5.67632			−0.199940
$807$			3.38730i			0.119239i
$808$		−	5.70648i		−	0.200753i
$809$	−13.5668			−0.476983			−0.238492	−	0.971145i	$-0.576653\pi$
$809$	−13.5668			−0.476983			−0.238492	+	0.971145i	$0.576653\pi$
$810$	−4.13048	+	7.09497i	−0.145130	+	0.249292i
$811$	−4.52088			−0.158750			−0.0793748	−	0.996845i	$-0.525292\pi$
$811$	−4.52088			−0.158750			−0.0793748	+	0.996845i	$0.525292\pi$
$812$			56.9211i			1.99754i
$813$			11.7421i			0.411812i
$814$	−3.96371			−0.138928
$815$	−4.88201	+	8.38588i	−0.171009	+	0.293745i
$816$	1.64409			0.0575547
$817$		0			0
$818$		−	5.86586i		−	0.205095i
$819$	−67.1844			−2.34761
$820$	26.6926	+	15.5396i	0.932146	+	0.542667i
$821$	−20.1939			−0.704771			−0.352386	−	0.935855i	$-0.614629\pi$
$821$	−20.1939			−0.704771			−0.352386	+	0.935855i	$0.614629\pi$
$822$			4.62222i			0.161218i
$823$			42.5280i			1.48243i	0.671267	+	0.741216i	$0.265751\pi$
$823$			42.5280i			1.48243i	−0.671267	+	0.741216i	$0.734249\pi$
$824$	−14.0905			−0.490867
$825$	−2.94338	+	1.67116i	−0.102475	+	0.0581825i
$826$	−10.1525			−0.353249
$827$		−	42.2171i		−	1.46803i	−0.679131	−	0.734017i	$-0.737643\pi$
$827$		−	42.2171i		−	1.46803i	0.679131	−	0.734017i	$-0.262357\pi$
$828$		−	8.78472i		−	0.305290i
$829$	3.78122			0.131327			0.0656637	−	0.997842i	$-0.479084\pi$
$829$	3.78122			0.131327			0.0656637	+	0.997842i	$0.479084\pi$
$830$	−1.14349	−	0.665704i	−0.0396911	−	0.0231069i
$831$	12.0110			0.416656
$832$		−	5.66531i		−	0.196409i
$833$		−	20.8470i		−	0.722307i
$834$	1.38382			0.0479178
$835$	17.5428	−	30.1334i	0.607092	−	1.04281i
$836$		0			0
$837$			5.77432i			0.199590i
$838$		−	4.82047i		−	0.166520i
$839$	49.7370			1.71711			0.858557	−	0.512719i	$-0.171362\pi$
$839$	49.7370			1.71711			0.858557	+	0.512719i	$0.171362\pi$
$840$	6.13494	−	10.5381i	0.211675	−	0.363598i
$841$	24.6961			0.851590
$842$		−	5.74715i		−	0.198060i
$843$			9.41925i			0.324416i
$844$	18.4709			0.635794
$845$	−30.0942	−	17.5199i	−1.03527	−	0.602703i
$846$	−6.39236			−0.219774
$847$			44.2771i			1.52138i
$848$			27.3499i			0.939200i
$849$	8.26505			0.283656
$850$	−2.01781	−	3.55391i	−0.0692103	−	0.121898i
$851$	−10.9371			−0.374917
$852$			7.75949i			0.265836i
$853$		−	21.4908i		−	0.735831i	−0.929859	−	0.367916i	$-0.880072\pi$
$853$		−	21.4908i		−	0.735831i	0.929859	−	0.367916i	$-0.119928\pi$
$854$	−12.4937			−0.427525
$855$		0			0
$856$	−20.5673			−0.702977
$857$			2.96612i			0.101321i	0.998716	+	0.0506604i	$0.0161326\pi$
$857$			2.96612i			0.101321i	−0.998716	+	0.0506604i	$0.983867\pi$
$858$			2.09167i			0.0714085i
$859$	21.3696			0.729120			0.364560	−	0.931180i	$-0.381219\pi$
$859$	21.3696			0.729120			0.364560	+	0.931180i	$0.381219\pi$
$860$	15.5579	−	26.7239i	0.530518	−	0.911278i
$861$	−21.3382			−0.727204
$862$		−	21.5420i		−	0.733723i
$863$			8.17747i			0.278364i	0.990267	+	0.139182i	$0.0444474\pi$
$863$			8.17747i			0.278364i	−0.990267	+	0.139182i	$0.955553\pi$
$864$	17.1492			0.583429
$865$	−18.2864	+	31.4108i	−0.621756	+	1.06800i
$866$	−3.21929			−0.109396
$867$		−	8.27865i		−	0.281158i
$868$			14.2701i			0.484358i
$869$	−18.0574			−0.612556
$870$	−4.51744	−	2.62992i	−0.153156	−	0.0891626i
$871$	24.8862			0.843236
$872$			24.7435i			0.837920i
$873$			12.7373i			0.431093i
$874$		0			0
$875$	52.1306	+	0.564125i	1.76234	+	0.0190709i
$876$	4.59118			0.155122
$877$		−	7.84379i		−	0.264866i	−0.991192	−	0.132433i	$-0.957721\pi$
$877$		−	7.84379i		−	0.264866i	0.991192	−	0.132433i	$-0.0422789\pi$
$878$			12.5760i			0.424418i
$879$	−8.25337			−0.278379
$880$	−4.99384	−	2.90726i	−0.168342	−	0.0980038i
$881$	27.9372			0.941229			0.470614	−	0.882339i	$-0.344032\pi$
$881$	27.9372			0.941229			0.470614	+	0.882339i	$0.344032\pi$
$882$		−	22.9713i		−	0.773484i
$883$		−	8.68312i		−	0.292210i	−0.989269	−	0.146105i	$-0.953326\pi$
$883$		−	8.68312i		−	0.292210i	0.989269	−	0.146105i	$-0.0466738\pi$
$884$	12.5912			0.423487
$885$	−2.33858	+	4.01701i	−0.0786106	+	0.135030i
$886$	−0.934240			−0.0313864
$887$			52.7474i			1.77108i	0.464559	+	0.885542i	$0.346213\pi$
$887$			52.7474i			1.77108i	−0.464559	+	0.885542i	$0.653787\pi$
$888$		−	6.53774i		−	0.219392i
$889$	−61.3471			−2.05752
$890$	2.56553	−	4.40684i	0.0859967	−	0.147718i
$891$	−7.79077			−0.261001
$892$		−	29.4372i		−	0.985629i
$893$		0			0
$894$	3.62195			0.121136
$895$	26.7226	+	15.5571i	0.893238	+	0.520016i
$896$	53.7384			1.79527
$897$			5.77154i			0.192706i
$898$		−	1.77531i		−	0.0592429i
$899$	13.4616			0.448969
$900$	11.0849	+	19.5236i	0.369498	+	0.650786i
$901$	−18.3560			−0.611528
$902$		−	5.87907i		−	0.195752i
$903$			21.3633i			0.710925i
$904$	13.5902			0.452003
$905$	17.3120	+	10.0785i	0.575469	+	0.335021i
$906$	5.43336			0.180511
$907$		−	11.6721i		−	0.387567i	−0.981044	−	0.193783i	$-0.937924\pi$
$907$		−	11.6721i		−	0.387567i	0.981044	−	0.193783i	$-0.0620759\pi$
$908$			23.5512i			0.781573i
$909$	−7.25864			−0.240754
$910$	16.2092	−	27.8428i	0.537330	−	0.922979i
$911$	39.3098			1.30239			0.651196	−	0.758909i	$-0.274267\pi$
$911$	39.3098			1.30239			0.651196	+	0.758909i	$0.274267\pi$
$912$		0			0
$913$		−	1.25563i		−	0.0415553i
$914$	−3.02454			−0.100043
$915$	−2.87787	+	4.94335i	−0.0951395	+	0.163422i
$916$	2.67482			0.0883785
$917$		−	82.8644i		−	2.73642i
$918$			2.56915i			0.0847944i
$919$	48.2908			1.59297			0.796483	−	0.604660i	$-0.206691\pi$
$919$	48.2908			1.59297			0.796483	+	0.604660i	$0.206691\pi$
$920$	8.01142	+	4.66401i	0.264129	+	0.153768i
$921$	−11.1269			−0.366644
$922$		−	7.82550i		−	0.257719i
$923$			45.1152i			1.48498i
$924$	5.25839			0.172988
$925$	24.3070	−	13.8008i	0.799211	−	0.453769i
$926$	−12.9404			−0.425247
$927$			17.9231i			0.588673i
$928$		−	39.9797i		−	1.31240i
$929$	50.1999			1.64700			0.823502	−	0.567314i	$-0.192017\pi$
$929$	50.1999			1.64700			0.823502	+	0.567314i	$0.192017\pi$
$930$	−1.13252	−	0.659319i	−0.0371368	−	0.0216199i
$931$		0			0
$932$			3.58676i			0.117488i
$933$			18.4158i			0.602906i
$934$	20.1101			0.658024
$935$	1.95122	−	3.35164i	0.0638118	−	0.109610i
$936$	30.5312			0.997945
$937$		−	12.7749i		−	0.417339i	−0.977986	−	0.208669i	$-0.933087\pi$
$937$		−	12.7749i		−	0.417339i	0.977986	−	0.208669i	$-0.0669132\pi$
$938$			12.5489i			0.409737i
$939$	13.4193			0.437923
$940$	−7.68896	+	13.2074i	−0.250786	+	0.430778i
$941$	0.911554			0.0297158			0.0148579	−	0.999890i	$-0.495270\pi$
$941$	0.911554			0.0297158			0.0148579	+	0.999890i	$0.495270\pi$
$942$		−	0.0438203i		−	0.00142774i
$943$		−	16.2221i		−	0.528264i
$944$	−7.93545			−0.258277
$945$	−28.3235	−	16.4891i	−0.921363	−	0.536390i
$946$	−5.88597			−0.191369
$947$			14.6832i			0.477139i	0.971125	+	0.238569i	$0.0766784\pi$
$947$			14.6832i			0.477139i	−0.971125	+	0.238569i	$0.923322\pi$
$948$		−	13.5346i		−	0.439582i
$949$	26.6940			0.866524
$950$		0			0
$951$	0.429157			0.0139164
$952$			13.9718i			0.452828i
$953$			17.0223i			0.551406i	0.961243	+	0.275703i	$0.0889107\pi$
$953$			17.0223i			0.551406i	−0.961243	+	0.275703i	$0.911089\pi$
$954$	−20.2264			−0.654855
$955$	−10.6482	−	6.19904i	−0.344567	−	0.200596i
$956$	19.4678			0.629635
$957$		−	4.96047i		−	0.160349i
$958$			10.2785i			0.332083i
$959$	67.5615			2.18168
$960$	0.658040	−	1.13032i	0.0212382	−	0.0364810i
$961$	−27.6252			−0.891135
$962$		−	17.2735i		−	0.556919i
$963$			26.1616i			0.843047i
$964$	11.5894			0.373271
$965$	−18.2615	+	31.3679i	−0.587857	+	1.00977i
$966$	−2.91031			−0.0936378
$967$		−	42.8810i		−	1.37896i	−0.724305	−	0.689480i	$-0.757839\pi$
$967$		−	42.8810i		−	1.37896i	0.724305	−	0.689480i	$-0.242161\pi$
$968$		−	20.1213i		−	0.646723i
$969$		0			0
$970$	−5.27865	−	3.07307i	−0.169487	−	0.0986703i
$971$	−43.9092			−1.40911			−0.704556	−	0.709648i	$-0.748854\pi$
$971$	−43.9092			−1.40911			−0.704556	+	0.709648i	$0.748854\pi$
$972$		−	21.5480i		−	0.691152i
$973$		−	20.2269i		−	0.648444i
$974$	−1.40418			−0.0449928
$975$	−7.28278	−	12.8270i	−0.233236	−	0.410791i
$976$	−9.76540			−0.312583
$977$		−	18.8399i		−	0.602740i	−0.953507	−	0.301370i	$-0.902556\pi$
$977$		−	18.8399i		−	0.602740i	0.953507	−	0.301370i	$-0.0974440\pi$
$978$			1.38438i			0.0442676i
$979$	4.83901			0.154656
$980$	−47.4615	−	27.6307i	−1.51610	−	0.882629i
$981$	31.4737			1.00488
$982$		−	20.3099i		−	0.648116i
$983$		−	48.3532i		−	1.54223i	−0.636697	−	0.771114i	$-0.719700\pi$
$983$		−	48.3532i		−	1.54223i	0.636697	−	0.771114i	$-0.280300\pi$
$984$	9.69694			0.309127
$985$	−4.36335	+	7.49498i	−0.139028	+	0.238810i
$986$	5.98941			0.190742
$987$		−	10.5581i		−	0.336068i
$988$		0			0
$989$	−16.2411			−0.516438
$990$	2.15005	−	3.69316i	0.0683329	−	0.117376i
$991$	7.19452			0.228542			0.114271	−	0.993450i	$-0.463547\pi$
$991$	7.19452			0.228542			0.114271	+	0.993450i	$0.463547\pi$
$992$		−	10.0229i		−	0.318227i
$993$			10.7702i			0.341783i
$994$	−22.7494			−0.721568
$995$	9.93048	+	5.78122i	0.314817	+	0.183277i
$996$	0.941132			0.0298209
$997$		−	50.6587i		−	1.60438i	−0.597071	−	0.802189i	$-0.703669\pi$
$997$		−	50.6587i		−	1.60438i	0.597071	−	0.802189i	$-0.296331\pi$
$998$		−	15.0725i		−	0.477112i
$999$	−17.5717			−0.555944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.i.1084.10	yes	16
5.2	odd	4		9025.2.a.cl.1.7		16
5.3	odd	4		9025.2.a.cl.1.10		16
5.4	even	2	inner	1805.2.b.i.1084.7	✓	16
19.18	odd	2		1805.2.b.j.1084.7	yes	16
95.18	even	4		9025.2.a.ck.1.7		16
95.37	even	4		9025.2.a.ck.1.10		16
95.94	odd	2		1805.2.b.j.1084.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.i.1084.7	✓	16	5.4	even	2	inner
1805.2.b.i.1084.10	yes	16	1.1	even	1	trivial
1805.2.b.j.1084.7	yes	16	19.18	odd	2
1805.2.b.j.1084.10	yes	16	95.94	odd	2
9025.2.a.ck.1.7		16	95.18	even	4
9025.2.a.ck.1.10		16	95.37	even	4
9025.2.a.cl.1.7		16	5.2	odd	4
9025.2.a.cl.1.10		16	5.3	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.578047i q^{2} -0.551888i q^{3} +1.66586 q^{4} +(1.93245 + 1.12501i) q^{5} +0.319017 q^{6} -4.66297i q^{7} +2.11904i q^{8} +2.69542 q^{9} +O(q^{10})\)	\(q+0.578047i q^{2} -0.551888i q^{3} +1.66586 q^{4} +(1.93245 + 1.12501i) q^{5} +0.319017 q^{6} -4.66297i q^{7} +2.11904i q^{8} +2.69542 q^{9} +(-0.650310 + 1.11705i) q^{10} -1.22659 q^{11} -0.919368i q^{12} -5.34538i q^{13} +2.69542 q^{14} +(0.620880 - 1.06649i) q^{15} +2.10682 q^{16} +1.41400i q^{17} +1.55808i q^{18} +(3.21919 + 1.87411i) q^{20} -2.57344 q^{21} -0.709029i q^{22} -1.95642i q^{23} +1.16947 q^{24} +(2.46870 + 4.34805i) q^{25} +3.08988 q^{26} -3.14323i q^{27} -7.76787i q^{28} -7.32776 q^{29} +(0.616484 + 0.358898i) q^{30} -1.83707 q^{31} +5.45592i q^{32} +0.676942i q^{33} -0.817358 q^{34} +(5.24590 - 9.01095i) q^{35} +4.49020 q^{36} -5.59033i q^{37} -2.95005 q^{39} +(-2.38395 + 4.09493i) q^{40} +8.29172 q^{41} -1.48757i q^{42} -8.30145i q^{43} -2.04333 q^{44} +(5.20875 + 3.03238i) q^{45} +1.13091 q^{46} +4.10272i q^{47} -1.16273i q^{48} -14.7433 q^{49} +(-2.51338 + 1.42702i) q^{50} +0.780368 q^{51} -8.90466i q^{52} +12.9816i q^{53} +1.81694 q^{54} +(-2.37033 - 1.37993i) q^{55} +9.88104 q^{56} -4.23579i q^{58} -3.76656 q^{59} +(1.03430 - 1.77663i) q^{60} -4.63515 q^{61} -1.06191i q^{62} -12.5687i q^{63} +1.05985 q^{64} +(6.01362 - 10.3297i) q^{65} -0.391304 q^{66} +4.65564i q^{67} +2.35552i q^{68} -1.07973 q^{69} +(5.20875 + 3.03238i) q^{70} -8.44003 q^{71} +5.71171i q^{72} +4.99385i q^{73} +3.23148 q^{74} +(2.39963 - 1.36244i) q^{75} +5.71957i q^{77} -1.70527i q^{78} +14.7216 q^{79} +(4.07131 + 2.37019i) q^{80} +6.35155 q^{81} +4.79301i q^{82} +1.02367i q^{83} -4.28699 q^{84} +(-1.59076 + 2.73248i) q^{85} +4.79863 q^{86} +4.04410i q^{87} -2.59920i q^{88} -3.94508 q^{89} +(-1.75286 + 3.01091i) q^{90} -24.9254 q^{91} -3.25913i q^{92} +1.01385i q^{93} -2.37156 q^{94} +3.01106 q^{96} +4.72554i q^{97} -8.52234i q^{98} -3.30618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9	\( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} - 16 q^{10} - 22 q^{11} - 6 q^{14} + 10 q^{15} + 8 q^{16} - 14 q^{20} - 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} - 2 q^{29} - 12 q^{30} + 16 q^{31} + 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} + 38 q^{40} + 26 q^{41} + 64 q^{44} - 2 q^{45} + 2 q^{46} + 20 q^{49} - 48 q^{50} - 38 q^{51} + 12 q^{54} - 10 q^{55} + 6 q^{56} - 10 q^{59} - 10 q^{60} - 30 q^{61} + 16 q^{64} - 36 q^{65} + 4 q^{66} - 68 q^{69} - 2 q^{70} - 20 q^{71} + 40 q^{74} - 32 q^{75} - 12 q^{79} + 40 q^{80} - 48 q^{81} + 2 q^{84} - 2 q^{85} - 20 q^{86} + 30 q^{90} - 86 q^{91} + 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) \) 16 * q - 12 * q^4 + 4 * q^5 - 10 * q^6 - 6 * q^9 - 16 * q^10 - 22 * q^11 - 6 * q^14 + 10 * q^15 + 8 * q^16 - 14 * q^20 - 20 * q^21 + 14 * q^24 + 4 * q^25 - 16 * q^26 - 2 * q^29 - 12 * q^30 + 16 * q^31 + 8 * q^34 - 10 * q^35 + 18 * q^36 + 36 * q^39 + 38 * q^40 + 26 * q^41 + 64 * q^44 - 2 * q^45 + 2 * q^46 + 20 * q^49 - 48 * q^50 - 38 * q^51 + 12 * q^54 - 10 * q^55 + 6 * q^56 - 10 * q^59 - 10 * q^60 - 30 * q^61 + 16 * q^64 - 36 * q^65 + 4 * q^66 - 68 * q^69 - 2 * q^70 - 20 * q^71 + 40 * q^74 - 32 * q^75 - 12 * q^79 + 40 * q^80 - 48 * q^81 + 2 * q^84 - 2 * q^85 - 20 * q^86 + 30 * q^90 - 86 * q^91 + 38 * q^94 + 22 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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