LMFDB - Embedded newform 1805.2.b.j.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.j.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	$0.343277\pi$
$7$			4.66297i			1.76244i	−0.472708	+	0.881219i	$0.656723\pi$
$8$			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	$-0.945148\pi$
$17$		−	1.41400i		−	0.342945i	0.985189	−	0.171472i	$-0.0548525\pi$
$18$			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	$0.0653849\pi$
$23$			1.95642i			0.407942i	−0.978977	+	0.203971i	$0.934615\pi$
$24$	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	$-0.261821\pi$
$29$	7.32776			1.36073			0.680366	+	0.732873i	$0.261821\pi$
$30$	0.616484	−	0.358898i	0.112554	−	0.0655255i
$31$	1.83707			0.329947			0.164973	−	0.986298i	$-0.447246\pi$
$31$	1.83707			0.329947			0.164973	+	0.986298i	$0.447246\pi$
$32$			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	$-0.724175\pi$
$41$	−8.29172			−1.29495			−0.647474	+	0.762087i	$0.724175\pi$
$42$			1.48757i			0.229537i
$43$			8.30145i			1.26596i	0.774169	+	0.632980i	$0.218168\pi$
$43$			8.30145i			1.26596i	−0.774169	+	0.632980i	$0.781832\pi$
$44$	−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	$-0.903273\pi$
$47$		−	4.10272i		−	0.598443i	0.954184	−	0.299221i	$-0.0967269\pi$
$48$		−	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	$-0.421152\pi$
$59$	3.76656			0.490365			0.245182	+	0.969477i	$0.421152\pi$
$60$	−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	$-0.333031\pi$
$71$	8.44003			1.00165			0.500824	+	0.865549i	$0.333031\pi$
$72$			5.71171i			0.673131i
$73$		−	4.99385i		−	0.584486i	−0.956344	−	0.292243i	$-0.905598\pi$
$73$		−	4.99385i		−	0.584486i	0.956344	−	0.292243i	$-0.0944015\pi$
$74$	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	$-0.810609\pi$
$79$	−14.7216			−1.65631			−0.828155	+	0.560500i	$0.810609\pi$
$80$	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	$-0.982108\pi$
$83$		−	1.02367i		−	0.112363i	0.998421	−	0.0561813i	$-0.0178925\pi$
$84$	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	$-0.432950\pi$
$89$	3.94508			0.418178			0.209089	+	0.977897i	$0.432950\pi$
$90$	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	$-0.688897\pi$
$109$	−11.6767			−1.11843			−0.559214	+	0.829023i	$0.688897\pi$
$110$	−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	$-0.787564\pi$
$137$		−	14.4889i		−	1.23787i	0.785441	−	0.618937i	$-0.212436\pi$
$138$			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	$-0.743713\pi$
$151$	−17.0316			−1.38601			−0.693004	+	0.720933i	$0.743713\pi$
$152$		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	$0.00174475\pi$
$157$			0.137360i			0.0109625i	−0.999985	+	0.00548127i	$0.998255\pi$
$158$		−	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	$-0.945640\pi$
$163$		−	4.33952i		−	0.339897i	0.985453	−	0.169949i	$-0.0543602\pi$
$164$	−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	$-0.672874\pi$
$179$	−13.8284			−1.03358			−0.516791	+	0.856112i	$0.672874\pi$
$180$	8.67706	−	5.05152i	0.646750	−	0.376518i
$181$	−8.95858			−0.665886			−0.332943	−	0.942947i	$-0.608042\pi$
$181$	−8.95858			−0.665886			−0.332943	+	0.942947i	$0.608042\pi$
$182$			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	$-0.955879\pi$
$197$		−	3.87849i		−	0.276331i	0.990409	−	0.138166i	$-0.0441206\pi$
$198$		−	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	$-0.624648\pi$
$211$	−11.0879			−0.763322			−0.381661	+	0.924302i	$0.624648\pi$
$212$			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	$-0.977532\pi$
$233$		−	2.15309i		−	0.141054i	0.997510	−	0.0705269i	$-0.0224681\pi$
$234$	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	$-0.571935\pi$
$241$	−6.95703			−0.448141			−0.224071	+	0.974573i	$0.571935\pi$
$242$		−	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	$0.146489\pi$
$263$			14.4054i			0.888272i	−0.895959	+	0.444136i	$0.853511\pi$
$264$	−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	$-0.440088\pi$
$269$	6.13766			0.374220			0.187110	+	0.982339i	$0.440088\pi$
$270$	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	$-0.773166\pi$
$277$		−	21.7634i		−	1.30764i	0.756651	−	0.653819i	$-0.226834\pi$
$278$			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	$-0.329987\pi$
$281$	17.0673			1.01815			0.509076	+	0.860722i	$0.329987\pi$
$282$		−	1.30884i		−	0.0779401i
$283$		−	14.9760i		−	0.890229i	−0.895474	−	0.445115i	$-0.853163\pi$
$283$		−	14.9760i		−	0.890229i	0.895474	−	0.445115i	$-0.146837\pi$
$284$	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	$-0.758843\pi$
$313$		−	24.3153i		−	1.37438i	0.726476	−	0.687191i	$-0.241157\pi$
$314$	−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	$-0.319811\pi$
$331$	19.5153			1.07266			0.536328	+	0.844009i	$0.319811\pi$
$332$		−	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	$-0.738405\pi$
$347$		−	27.2858i		−	1.46478i	0.680886	−	0.732390i	$-0.261595\pi$
$348$		−	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	$0.135394\pi$
$353$			15.5056i			0.825282i	−0.910894	+	0.412641i	$0.864606\pi$
$354$	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	$0.0850903\pi$
$367$			10.1206i			0.528294i	−0.964482	+	0.264147i	$0.914910\pi$
$368$			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	$-0.597102\pi$
$379$	−11.6942			−0.600692			−0.300346	+	0.953830i	$0.597102\pi$
$380$		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	$-0.846695\pi$
$397$		−	18.4591i		−	0.926433i	0.886245	−	0.463217i	$-0.153305\pi$
$398$			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	$-0.458875\pi$
$401$	5.16001			0.257679			0.128839	+	0.991665i	$0.458875\pi$
$402$			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	$-0.419278\pi$
$409$	10.1477			0.501772			0.250886	+	0.968017i	$0.419278\pi$
$410$	−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	$-0.422105\pi$
$421$	9.94235			0.484560			0.242280	+	0.970206i	$0.422105\pi$
$422$		−	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	$-0.145353\pi$
$431$	37.2668			1.79508			0.897540	+	0.440934i	$0.145353\pi$
$432$		−	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	$-0.673762\pi$
$439$	−21.7559			−1.03835			−0.519177	+	0.854666i	$0.673762\pi$
$440$	−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	$-0.987776\pi$
$443$		−	1.61620i		−	0.0767880i	0.999263	−	0.0383940i	$-0.0122242\pi$
$444$	−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	$-0.476912\pi$
$449$	3.07122			0.144940			0.0724700	+	0.997371i	$0.476912\pi$
$450$	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	$-0.960948\pi$
$457$		−	5.23234i		−	0.244759i	0.992483	−	0.122379i	$-0.0390524\pi$
$458$			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	$-0.825861\pi$
$463$		−	22.3863i		−	1.04038i	0.854050	−	0.520191i	$-0.174139\pi$
$464$	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	$0.297802\pi$
$467$			34.7898i			1.60988i	−0.593356	+	0.804940i	$0.702198\pi$
$468$		−	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	$0.429927\pi$
$503$			43.7728i			1.95173i	−0.218367	+	0.975867i	$0.570073\pi$
$504$	−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	$-0.471656\pi$
$509$	4.01256			0.177854			0.0889268	+	0.996038i	$0.471656\pi$
$510$	−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	$-0.517737\pi$
$521$	−2.54253			−0.111390			−0.0556951	+	0.998448i	$0.517737\pi$
$522$			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	$0.0780449\pi$
$557$			11.4576i			0.485472i	−0.970092	+	0.242736i	$0.921955\pi$
$558$			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	$-0.564606\pi$
$569$	−9.61664			−0.403151			−0.201575	+	0.979473i	$0.564606\pi$
$570$		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	$-0.795658\pi$
$577$		−	28.7657i		−	1.19753i	0.800924	−	0.598766i	$-0.204342\pi$
$578$			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	$0.124880\pi$
$587$			18.5265i			0.764669i	−0.924024	+	0.382335i	$0.875120\pi$
$588$			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	$0.257602\pi$
$593$			35.2510i			1.44758i	−0.690018	+	0.723792i	$0.742398\pi$
$594$	−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	$-0.352876\pi$
$599$	21.8274			0.891845			0.445922	+	0.895072i	$0.352876\pi$
$600$	2.88707	−	5.08492i	0.117864	−	0.207591i
$601$	−36.9139			−1.50575			−0.752875	−	0.658164i	$-0.771333\pi$
$601$	−36.9139			−1.50575			−0.752875	+	0.658164i	$0.771333\pi$
$602$		−	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	$0.226623\pi$
$613$			32.3507i			1.30663i	−0.757085	+	0.653317i	$0.773377\pi$
$614$	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	$-0.844064\pi$
$617$		−	23.3753i		−	0.941054i	0.882386	−	0.470527i	$-0.155936\pi$
$618$			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	$-0.429833\pi$
$641$	11.0717			0.437307			0.218654	+	0.975803i	$0.429833\pi$
$642$			3.09637i			0.122204i
$643$		−	36.4492i		−	1.43742i	−0.695312	−	0.718708i	$-0.744734\pi$
$643$		−	36.4492i		−	1.43742i	0.695312	−	0.718708i	$-0.255266\pi$
$644$	−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	$0.110194\pi$
$647$			17.2616i			0.678624i	−0.940674	+	0.339312i	$0.889806\pi$
$648$			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	$0.318952\pi$
$653$			43.0613i			1.68512i	−0.538605	+	0.842559i	$0.681048\pi$
$654$	−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	$-0.548935\pi$
$659$	−7.86198			−0.306259			−0.153130	+	0.988206i	$0.548935\pi$
$660$	1.26867	+	2.17920i	0.0493827	+	0.0848253i
$661$	21.6266			0.841177			0.420588	−	0.907252i	$-0.361824\pi$
$661$	21.6266			0.841177			0.420588	+	0.907252i	$0.361824\pi$
$662$			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	$-0.908709\pi$
$727$		−	15.2548i		−	0.565769i	0.959154	−	0.282885i	$-0.0912914\pi$
$728$			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	$-0.897494\pi$
$733$		−	17.1375i		−	0.632989i	0.948594	−	0.316495i	$-0.102506\pi$
$734$	−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	$-0.349441\pi$
$751$	24.9684			0.911109			0.455555	+	0.890208i	$0.349441\pi$
$752$		−	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	$0.160282\pi$
$757$			26.5524i			0.965062i	−0.875879	+	0.482531i	$0.839718\pi$
$758$		−	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	$-0.474708\pi$
$811$	4.52088			0.158750			0.0793748	+	0.996845i	$0.474708\pi$
$812$			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	$-0.734249\pi$
$823$		−	42.5280i		−	1.48243i	0.671267	−	0.741216i	$-0.265751\pi$
$824$	−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	$-0.520916\pi$
$829$	−3.78122			−0.131327			−0.0656637	+	0.997842i	$0.520916\pi$
$830$	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	$-0.828638\pi$
$839$	−49.7370			−1.71711			−0.858557	+	0.512719i	$0.828638\pi$
$840$	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	$0.119928\pi$
$853$			21.4908i			0.735831i	−0.929859	+	0.367916i	$0.880072\pi$
$854$	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	$0.0466738\pi$
$883$			8.68312i			0.292210i	−0.989269	+	0.146105i	$0.953326\pi$
$884$	−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	$-0.725733\pi$
$911$	−39.3098			−1.30239			−0.651196	+	0.758909i	$0.725733\pi$
$912$		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	$0.0669132\pi$
$937$			12.7749i			0.417339i	−0.977986	+	0.208669i	$0.933087\pi$
$938$		−	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	$-0.504730\pi$
$941$	−0.911554			−0.0297158			−0.0148579	+	0.999890i	$0.504730\pi$
$942$			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	$-0.923322\pi$
$947$		−	14.6832i		−	0.477139i	0.971125	−	0.238569i	$-0.0766784\pi$
$948$			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	$0.242161\pi$
$967$			42.8810i			1.37896i	−0.724305	+	0.689480i	$0.757839\pi$
$968$		−	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	$-0.251146\pi$
$971$	43.9092			1.40911			0.704556	+	0.709648i	$0.251146\pi$
$972$		−	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	$-0.536453\pi$
$991$	−7.19452			−0.228542			−0.114271	+	0.993450i	$0.536453\pi$
$992$			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	$0.296331\pi$
$997$			50.6587i			1.60438i	−0.597071	+	0.802189i	$0.703669\pi$
$998$		−	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.j.1084.10	yes	16
5.2	odd	4		9025.2.a.ck.1.7		16
5.3	odd	4		9025.2.a.ck.1.10		16
5.4	even	2	inner	1805.2.b.j.1084.7	yes	16
19.18	odd	2		1805.2.b.i.1084.7	✓	16
95.18	even	4		9025.2.a.cl.1.7		16
95.37	even	4		9025.2.a.cl.1.10		16
95.94	odd	2		1805.2.b.i.1084.10	yes	16

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