LMFDB - Embedded newform 1920.2.bl.b.289.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (of order $4$, degree $2$, not 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.13
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.b.1249.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{3} +(-2.16437 - 0.561697i) q^{5} -4.51614 q^{7} -1.00000i q^{9} +(-3.44000 + 3.44000i) q^{11} +(0.113618 - 0.113618i) q^{13} +(-1.92762 + 1.13326i) q^{15} -5.03305i q^{17} +(-0.992498 - 0.992498i) q^{19} +(-3.19340 + 3.19340i) q^{21} +8.00517 q^{23} +(4.36899 + 2.43144i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(1.01722 + 1.01722i) q^{29} +6.42697 q^{31} +4.86490i q^{33} +(9.77461 + 2.53670i) q^{35} +(-1.63459 - 1.63459i) q^{37} -0.160680i q^{39} +3.35633i q^{41} +(5.68196 + 5.68196i) q^{43} +(-0.561697 + 2.16437i) q^{45} +9.10261i q^{47} +13.3956 q^{49} +(-3.55890 - 3.55890i) q^{51} +(-3.27113 - 3.27113i) q^{53} +(9.37767 - 5.51320i) q^{55} -1.40360 q^{57} +(-5.30843 + 5.30843i) q^{59} +(5.87487 + 5.87487i) q^{61} +4.51614i q^{63} +(-0.309729 + 0.182092i) q^{65} +(-1.87639 + 1.87639i) q^{67} +(5.66051 - 5.66051i) q^{69} +0.635312i q^{71} +6.14208 q^{73} +(4.80863 - 1.37006i) q^{75} +(15.5355 - 15.5355i) q^{77} -1.76500 q^{79} -1.00000 q^{81} +(-6.39170 + 6.39170i) q^{83} +(-2.82705 + 10.8934i) q^{85} +1.43857 q^{87} +0.579554i q^{89} +(-0.513114 + 0.513114i) q^{91} +(4.54455 - 4.54455i) q^{93} +(1.59065 + 2.70562i) q^{95} -15.2769i q^{97} +(3.44000 + 3.44000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{19} + 48 q^{31} + 24 q^{35} + 48 q^{49} + 8 q^{51} - 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} - 16 q^{75} + 96 q^{79} - 48 q^{81} - 32 q^{91} + 48 q^{95}+O(q^{100}) $ 48 * q + 8 * q^19 + 48 * q^31 + 24 * q^35 + 48 * q^49 + 8 * q^51 - 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 - 16 * q^75 + 96 * q^79 - 48 * q^81 - 32 * q^91 + 48 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−2.16437	−	0.561697i	−0.967936	−	0.251198i
$5$	−2.16437	−	0.561697i	−0.967936	−	0.251198i
$6$		0			0
$7$	−4.51614			−1.70694			−0.853471	−	0.521140i	$-0.825507\pi$
$7$	−4.51614			−1.70694			−0.853471	+	0.521140i	$0.825507\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.44000	+	3.44000i	−1.03720	+	1.03720i	−0.0379186	+	0.999281i	$0.512073\pi$
$11$	−3.44000	+	3.44000i	−1.03720	+	1.03720i	−0.999281	+	0.0379186i	$0.987927\pi$
$12$		0			0
$13$	0.113618	−	0.113618i	0.0315119	−	0.0315119i	−0.691175	−	0.722687i	$-0.742907\pi$
$13$	0.113618	−	0.113618i	0.0315119	−	0.0315119i	0.722687	+	0.691175i	$0.242907\pi$
$14$		0			0
$15$	−1.92762	+	1.13326i	−0.497709	+	0.292607i
$16$		0			0
$17$		−	5.03305i		−	1.22069i	−0.792134	−	0.610347i	$-0.791030\pi$
$17$		−	5.03305i		−	1.22069i	0.792134	−	0.610347i	$-0.208970\pi$
$18$		0			0
$19$	−0.992498	−	0.992498i	−0.227695	−	0.227695i	0.584034	−	0.811729i	$-0.301473\pi$
$19$	−0.992498	−	0.992498i	−0.227695	−	0.227695i	−0.811729	+	0.584034i	$0.801473\pi$
$20$		0			0
$21$	−3.19340	+	3.19340i	−0.696856	+	0.696856i
$22$		0			0
$23$	8.00517			1.66919			0.834596	−	0.550862i	$-0.185701\pi$
$23$	8.00517			1.66919			0.834596	+	0.550862i	$0.185701\pi$
$24$		0			0
$25$	4.36899	+	2.43144i	0.873799	+	0.486288i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$	1.01722	+	1.01722i	0.188894	+	0.188894i	0.795218	−	0.606324i	$-0.207357\pi$
$29$	1.01722	+	1.01722i	0.188894	+	0.188894i	−0.606324	+	0.795218i	$0.707357\pi$
$30$		0			0
$31$	6.42697			1.15432			0.577159	−	0.816632i	$-0.304161\pi$
$31$	6.42697			1.15432			0.577159	+	0.816632i	$0.304161\pi$
$32$		0			0
$33$			4.86490i			0.846870i
$34$		0			0
$35$	9.77461	+	2.53670i	1.65221	+	0.428781i
$36$		0			0
$37$	−1.63459	−	1.63459i	−0.268726	−	0.268726i	0.559861	−	0.828587i	$-0.310855\pi$
$37$	−1.63459	−	1.63459i	−0.268726	−	0.268726i	−0.828587	+	0.559861i	$0.810855\pi$
$38$		0			0
$39$		−	0.160680i		−	0.0257293i
$40$		0			0
$41$			3.35633i			0.524171i	0.965045	+	0.262086i	$0.0844103\pi$
$41$			3.35633i			0.524171i	−0.965045	+	0.262086i	$0.915590\pi$
$42$		0			0
$43$	5.68196	+	5.68196i	0.866491	+	0.866491i	0.992082	−	0.125591i	$-0.0400826\pi$
$43$	5.68196	+	5.68196i	0.866491	+	0.866491i	−0.125591	+	0.992082i	$0.540083\pi$
$44$		0			0
$45$	−0.561697	+	2.16437i	−0.0837328	+	0.322645i
$46$		0			0
$47$			9.10261i			1.32775i	0.747842	+	0.663876i	$0.231090\pi$
$47$			9.10261i			1.32775i	−0.747842	+	0.663876i	$0.768910\pi$
$48$		0			0
$49$	13.3956			1.91365
$50$		0			0
$51$	−3.55890	−	3.55890i	−0.498346	−	0.498346i
$52$		0			0
$53$	−3.27113	−	3.27113i	−0.449324	−	0.449324i	0.445806	−	0.895130i	$-0.352917\pi$
$53$	−3.27113	−	3.27113i	−0.449324	−	0.449324i	−0.895130	+	0.445806i	$0.852917\pi$
$54$		0			0
$55$	9.37767	−	5.51320i	1.26449	−	0.743399i
$56$		0			0
$57$	−1.40360			−0.185912
$58$		0			0
$59$	−5.30843	+	5.30843i	−0.691098	+	0.691098i	−0.962474	−	0.271375i	$-0.912522\pi$
$59$	−5.30843	+	5.30843i	−0.691098	+	0.691098i	0.271375	+	0.962474i	$0.412522\pi$
$60$		0			0
$61$	5.87487	+	5.87487i	0.752199	+	0.752199i	0.974889	−	0.222690i	$-0.0714837\pi$
$61$	5.87487	+	5.87487i	0.752199	+	0.752199i	−0.222690	+	0.974889i	$0.571484\pi$
$62$		0			0
$63$			4.51614i			0.568981i
$64$		0			0
$65$	−0.309729	+	0.182092i	−0.0384172	+	0.0225857i
$66$		0			0
$67$	−1.87639	+	1.87639i	−0.229238	+	0.229238i	−0.812374	−	0.583137i	$-0.801825\pi$
$67$	−1.87639	+	1.87639i	−0.229238	+	0.229238i	0.583137	+	0.812374i	$0.301825\pi$
$68$		0			0
$69$	5.66051	−	5.66051i	0.681445	−	0.681445i
$70$		0			0
$71$			0.635312i			0.0753977i	0.999289	+	0.0376988i	$0.0120028\pi$
$71$			0.635312i			0.0753977i	−0.999289	+	0.0376988i	$0.987997\pi$
$72$		0			0
$73$	6.14208			0.718876			0.359438	−	0.933169i	$-0.382968\pi$
$73$	6.14208			0.718876			0.359438	+	0.933169i	$0.382968\pi$
$74$		0			0
$75$	4.80863	−	1.37006i	0.555253	−	0.158201i
$76$		0			0
$77$	15.5355	−	15.5355i	1.77044	−	1.77044i
$78$		0			0
$79$	−1.76500			−0.198578			−0.0992888	−	0.995059i	$-0.531657\pi$
$79$	−1.76500			−0.198578			−0.0992888	+	0.995059i	$0.531657\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−6.39170	+	6.39170i	−0.701580	+	0.701580i	−0.964750	−	0.263169i	$-0.915232\pi$
$83$	−6.39170	+	6.39170i	−0.701580	+	0.701580i	0.263169	+	0.964750i	$0.415232\pi$
$84$		0			0
$85$	−2.82705	+	10.8934i	−0.306636	+	1.18155i
$86$		0			0
$87$	1.43857			0.154231
$88$		0			0
$89$			0.579554i			0.0614326i	0.999528	+	0.0307163i	$0.00977884\pi$
$89$			0.579554i			0.0614326i	−0.999528	+	0.0307163i	$0.990221\pi$
$90$		0			0
$91$	−0.513114	+	0.513114i	−0.0537889	+	0.0537889i
$92$		0			0
$93$	4.54455	−	4.54455i	0.471248	−	0.471248i
$94$		0			0
$95$	1.59065	+	2.70562i	0.163197	+	0.277590i
$96$		0			0
$97$		−	15.2769i		−	1.55113i	−0.631265	−	0.775567i	$-0.717464\pi$
$97$		−	15.2769i		−	1.55113i	0.631265	−	0.775567i	$-0.282536\pi$
$98$		0			0
$99$	3.44000	+	3.44000i	0.345733	+	0.345733i
$100$		0			0
$101$	2.60639	−	2.60639i	0.259346	−	0.259346i	−0.565442	−	0.824788i	$-0.691294\pi$
$101$	2.60639	−	2.60639i	0.259346	−	0.259346i	0.824788	+	0.565442i	$0.191294\pi$
$102$		0			0
$103$	9.26272			0.912683			0.456341	−	0.889805i	$-0.349160\pi$
$103$	9.26272			0.912683			0.456341	+	0.889805i	$0.349160\pi$
$104$		0			0
$105$	8.70541	−	5.11797i	0.849561	−	0.499463i
$106$		0			0
$107$	4.72776	+	4.72776i	0.457050	+	0.457050i	0.897686	−	0.440636i	$-0.145247\pi$
$107$	4.72776	+	4.72776i	0.457050	+	0.457050i	−0.440636	+	0.897686i	$0.645247\pi$
$108$		0			0
$109$	−0.160713	−	0.160713i	−0.0153935	−	0.0153935i	0.699368	−	0.714762i	$-0.253465\pi$
$109$	−0.160713	−	0.160713i	−0.0153935	−	0.0153935i	−0.714762	+	0.699368i	$0.753465\pi$
$110$		0			0
$111$	−2.31167			−0.219414
$112$		0			0
$113$		−	1.02489i		−	0.0964131i	−0.998837	−	0.0482066i	$-0.984649\pi$
$113$		−	1.02489i		−	0.0964131i	0.998837	−	0.0482066i	$-0.0153506\pi$
$114$		0			0
$115$	−17.3261	−	4.49648i	−1.61567	−	0.419298i
$116$		0			0
$117$	−0.113618	−	0.113618i	−0.0105040	−	0.0105040i
$118$		0			0
$119$			22.7300i			2.08365i
$120$		0			0
$121$		−	12.6672i		−	1.15157i
$122$		0			0
$123$	2.37329	+	2.37329i	0.213992	+	0.213992i
$124$		0			0
$125$	−8.09039	−	7.71658i	−0.723626	−	0.690192i
$126$		0			0
$127$		−	9.29167i		−	0.824502i	−0.911070	−	0.412251i	$-0.864743\pi$
$127$		−	9.29167i		−	0.824502i	0.911070	−	0.412251i	$-0.135257\pi$
$128$		0			0
$129$	8.03551			0.707487
$130$		0			0
$131$	−4.53759	−	4.53759i	−0.396451	−	0.396451i	0.480528	−	0.876979i	$-0.340445\pi$
$131$	−4.53759	−	4.53759i	−0.396451	−	0.396451i	−0.876979	+	0.480528i	$0.840445\pi$
$132$		0			0
$133$	4.48226	+	4.48226i	0.388662	+	0.388662i
$134$		0			0
$135$	1.13326	+	1.92762i	0.0975356	+	0.165903i
$136$		0			0
$137$	0.448842			0.0383471			0.0191736	−	0.999816i	$-0.493896\pi$
$137$	0.448842			0.0383471			0.0191736	+	0.999816i	$0.493896\pi$
$138$		0			0
$139$	−5.12669	+	5.12669i	−0.434840	+	0.434840i	−0.890271	−	0.455431i	$-0.849485\pi$
$139$	−5.12669	+	5.12669i	−0.434840	+	0.434840i	0.455431	+	0.890271i	$0.349485\pi$
$140$		0			0
$141$	6.43652	+	6.43652i	0.542053	+	0.542053i
$142$		0			0
$143$			0.781690i			0.0653682i
$144$		0			0
$145$	−1.63028	−	2.77302i	−0.135387	−	0.230287i
$146$		0			0
$147$	9.47209	−	9.47209i	0.781245	−	0.781245i
$148$		0			0
$149$	−4.56510	+	4.56510i	−0.373988	+	0.373988i	−0.868927	−	0.494940i	$-0.835190\pi$
$149$	−4.56510	+	4.56510i	−0.373988	+	0.373988i	0.494940	+	0.868927i	$0.335190\pi$
$150$		0			0
$151$			6.84317i			0.556890i	0.960452	+	0.278445i	$0.0898189\pi$
$151$			6.84317i			0.556890i	−0.960452	+	0.278445i	$0.910181\pi$
$152$		0			0
$153$	−5.03305			−0.406898
$154$		0			0
$155$	−13.9103	−	3.61001i	−1.11730	−	0.289963i
$156$		0			0
$157$	1.85978	−	1.85978i	0.148426	−	0.148426i	−0.628988	−	0.777415i	$-0.716531\pi$
$157$	1.85978	−	1.85978i	0.148426	−	0.148426i	0.777415	+	0.628988i	$0.216531\pi$
$158$		0			0
$159$	−4.62608			−0.366872
$160$		0			0
$161$	−36.1525			−2.84922
$162$		0			0
$163$	9.43033	−	9.43033i	0.738641	−	0.738641i	−0.233674	−	0.972315i	$-0.575075\pi$
$163$	9.43033	−	9.43033i	0.738641	−	0.738641i	0.972315	+	0.233674i	$0.0750750\pi$
$164$		0			0
$165$	2.73260	−	10.5294i	0.212732	−	0.819715i
$166$		0			0
$167$	−21.2570			−1.64492			−0.822459	−	0.568824i	$-0.807398\pi$
$167$	−21.2570			−1.64492			−0.822459	+	0.568824i	$0.807398\pi$
$168$		0			0
$169$			12.9742i			0.998014i
$170$		0			0
$171$	−0.992498	+	0.992498i	−0.0758982	+	0.0758982i
$172$		0			0
$173$	−3.90989	+	3.90989i	−0.297263	+	0.297263i	−0.839941	−	0.542678i	$-0.817410\pi$
$173$	−3.90989	+	3.90989i	−0.297263	+	0.297263i	0.542678	+	0.839941i	$0.317410\pi$
$174$		0			0
$175$	−19.7310	−	10.9807i	−1.49152	−	0.830065i
$176$		0			0
$177$			7.50725i			0.564279i
$178$		0			0
$179$	16.8281	+	16.8281i	1.25779	+	1.25779i	0.952144	+	0.305651i	$0.0988740\pi$
$179$	16.8281	+	16.8281i	1.25779	+	1.25779i	0.305651	+	0.952144i	$0.401126\pi$
$180$		0			0
$181$	10.4003	−	10.4003i	0.773050	−	0.773050i	−0.205588	−	0.978639i	$-0.565911\pi$
$181$	10.4003	−	10.4003i	0.773050	−	0.773050i	0.978639	+	0.205588i	$0.0659108\pi$
$182$		0			0
$183$	8.30831			0.614168
$184$		0			0
$185$	2.61972	+	4.45601i	0.192606	+	0.327613i
$186$		0			0
$187$	17.3137	+	17.3137i	1.26610	+	1.26610i
$188$		0			0
$189$	3.19340	+	3.19340i	0.232285	+	0.232285i
$190$		0			0
$191$	−20.8245			−1.50681			−0.753404	−	0.657558i	$-0.771589\pi$
$191$	−20.8245			−1.50681			−0.753404	+	0.657558i	$0.771589\pi$
$192$		0			0
$193$		−	5.82531i		−	0.419315i	−0.977775	−	0.209657i	$-0.932765\pi$
$193$		−	5.82531i		−	0.419315i	0.977775	−	0.209657i	$-0.0672349\pi$
$194$		0			0
$195$	−0.0902532	+	0.347770i	−0.00646317	+	0.0249043i
$196$		0			0
$197$	11.0656	+	11.0656i	0.788391	+	0.788391i	0.981230	−	0.192839i	$-0.0617695\pi$
$197$	11.0656	+	11.0656i	0.788391	+	0.788391i	−0.192839	+	0.981230i	$0.561770\pi$
$198$		0			0
$199$			7.04564i			0.499452i	0.968317	+	0.249726i	$0.0803406\pi$
$199$			7.04564i			0.499452i	−0.968317	+	0.249726i	$0.919659\pi$
$200$		0			0
$201$			2.65362i			0.187172i
$202$		0			0
$203$	−4.59393	−	4.59393i	−0.322430	−	0.322430i
$204$		0			0
$205$	1.88524	−	7.26435i	0.131671	−	0.507364i
$206$		0			0
$207$		−	8.00517i		−	0.556398i
$208$		0			0
$209$	6.82839			0.472329
$210$		0			0
$211$	0.158025	+	0.158025i	0.0108789	+	0.0108789i	0.712525	−	0.701646i	$-0.247551\pi$
$211$	0.158025	+	0.158025i	0.0108789	+	0.0108789i	−0.701646	+	0.712525i	$0.747551\pi$
$212$		0			0
$213$	0.449234	+	0.449234i	0.0307810	+	0.0307810i
$214$		0			0
$215$	−9.10633	−	15.4894i	−0.621047	−	1.05637i
$216$		0			0
$217$	−29.0251			−1.97035
$218$		0			0
$219$	4.34311	−	4.34311i	0.293480	−	0.293480i
$220$		0			0
$221$	−0.571843	−	0.571843i	−0.0384663	−	0.0384663i
$222$		0			0
$223$			8.38138i			0.561259i	0.959816	+	0.280629i	$0.0905432\pi$
$223$			8.38138i			0.561259i	−0.959816	+	0.280629i	$0.909457\pi$
$224$		0			0
$225$	2.43144	−	4.36899i	0.162096	−	0.291266i
$226$		0			0
$227$	6.73568	−	6.73568i	0.447063	−	0.447063i	−0.447314	−	0.894377i	$-0.647619\pi$
$227$	6.73568	−	6.73568i	0.447063	−	0.447063i	0.894377	+	0.447314i	$0.147619\pi$
$228$		0			0
$229$	13.6770	−	13.6770i	0.903800	−	0.903800i	−0.0919626	−	0.995762i	$-0.529314\pi$
$229$	13.6770	−	13.6770i	0.903800	−	0.903800i	0.995762	+	0.0919626i	$0.0293140\pi$
$230$		0			0
$231$		−	21.9706i		−	1.44556i
$232$		0			0
$233$	−1.62741			−0.106615			−0.0533077	−	0.998578i	$-0.516976\pi$
$233$	−1.62741			−0.106615			−0.0533077	+	0.998578i	$0.516976\pi$
$234$		0			0
$235$	5.11291	−	19.7014i	0.333529	−	1.28518i
$236$		0			0
$237$	−1.24804	+	1.24804i	−0.0810690	+	0.0810690i
$238$		0			0
$239$	12.6908			0.820902			0.410451	−	0.911883i	$-0.365371\pi$
$239$	12.6908			0.820902			0.410451	+	0.911883i	$0.365371\pi$
$240$		0			0
$241$	21.1033			1.35938			0.679692	−	0.733498i	$-0.262114\pi$
$241$	21.1033			1.35938			0.679692	+	0.733498i	$0.262114\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−28.9930	−	7.52424i	−1.85229	−	0.480706i
$246$		0			0
$247$	−0.225531			−0.0143502
$248$		0			0
$249$			9.03923i			0.572838i
$250$		0			0
$251$	17.4935	−	17.4935i	1.10418	−	1.10418i	0.110282	−	0.993900i	$-0.464824\pi$
$251$	17.4935	−	17.4935i	1.10418	−	1.10418i	0.993900	−	0.110282i	$-0.0351755\pi$
$252$		0			0
$253$	−27.5378	+	27.5378i	−1.73129	+	1.73129i
$254$		0			0
$255$	5.70376	+	9.70181i	0.357183	+	0.607551i
$256$		0			0
$257$			7.80177i			0.486661i	0.969943	+	0.243331i	$0.0782400\pi$
$257$			7.80177i			0.486661i	−0.969943	+	0.243331i	$0.921760\pi$
$258$		0			0
$259$	7.38207	+	7.38207i	0.458699	+	0.458699i
$260$		0			0
$261$	1.01722	−	1.01722i	0.0629645	−	0.0629645i
$262$		0			0
$263$	−11.9238			−0.735252			−0.367626	−	0.929974i	$-0.619829\pi$
$263$	−11.9238			−0.735252			−0.367626	+	0.929974i	$0.619829\pi$
$264$		0			0
$265$	5.24255	+	8.91732i	0.322047	+	0.547787i
$266$		0			0
$267$	0.409807	+	0.409807i	0.0250798	+	0.0250798i
$268$		0			0
$269$	8.24368	+	8.24368i	0.502626	+	0.502626i	0.912253	−	0.409627i	$-0.134341\pi$
$269$	8.24368	+	8.24368i	0.502626	+	0.502626i	−0.409627	+	0.912253i	$0.634341\pi$
$270$		0			0
$271$	26.8960			1.63381			0.816907	−	0.576770i	$-0.195687\pi$
$271$	26.8960			1.63381			0.816907	+	0.576770i	$0.195687\pi$
$272$		0			0
$273$			0.725652i			0.0439185i
$274$		0			0
$275$	−23.3935	+	6.66519i	−1.41068	+	0.401926i
$276$		0			0
$277$	15.8294	+	15.8294i	0.951099	+	0.951099i	0.998859	−	0.0477597i	$-0.0152082\pi$
$277$	15.8294	+	15.8294i	0.951099	+	0.951099i	−0.0477597	+	0.998859i	$0.515208\pi$
$278$		0			0
$279$		−	6.42697i		−	0.384772i
$280$		0			0
$281$			27.8550i			1.66169i	0.556503	+	0.830845i	$0.312143\pi$
$281$			27.8550i			1.66169i	−0.556503	+	0.830845i	$0.687857\pi$
$282$		0			0
$283$	2.62285	+	2.62285i	0.155913	+	0.155913i	0.780753	−	0.624840i	$-0.214836\pi$
$283$	2.62285	+	2.62285i	0.155913	+	0.155913i	−0.624840	+	0.780753i	$0.714836\pi$
$284$		0			0
$285$	3.03792	+	0.788400i	0.179951	+	0.0467008i
$286$		0			0
$287$		−	15.1577i		−	0.894730i
$288$		0			0
$289$	−8.33160			−0.490094
$290$		0			0
$291$	−10.8024	−	10.8024i	−0.633248	−	0.633248i
$292$		0			0
$293$	−7.75559	−	7.75559i	−0.453086	−	0.453086i	0.443291	−	0.896378i	$-0.353811\pi$
$293$	−7.75559	−	7.75559i	−0.453086	−	0.453086i	−0.896378	+	0.443291i	$0.853811\pi$
$294$		0			0
$295$	14.4711	−	8.50767i	0.842541	−	0.495336i
$296$		0			0
$297$	4.86490			0.282290
$298$		0			0
$299$	0.909528	−	0.909528i	0.0525994	−	0.0525994i
$300$		0			0
$301$	−25.6606	−	25.6606i	−1.47905	−	1.47905i
$302$		0			0
$303$		−	3.68600i		−	0.211755i
$304$		0			0
$305$	−9.41549	−	16.0153i	−0.539129	−	0.917032i
$306$		0			0
$307$	−2.60764	+	2.60764i	−0.148826	+	0.148826i	−0.777593	−	0.628767i	$-0.783560\pi$
$307$	−2.60764	+	2.60764i	−0.148826	+	0.148826i	0.628767	+	0.777593i	$0.283560\pi$
$308$		0			0
$309$	6.54973	−	6.54973i	0.372601	−	0.372601i
$310$		0			0
$311$			20.1642i			1.14340i	0.820461	+	0.571702i	$0.193717\pi$
$311$			20.1642i			1.14340i	−0.820461	+	0.571702i	$0.806283\pi$
$312$		0			0
$313$	23.2572			1.31457			0.657286	−	0.753641i	$-0.271704\pi$
$313$	23.2572			1.31457			0.657286	+	0.753641i	$0.271704\pi$
$314$		0			0
$315$	2.53670	−	9.77461i	0.142927	−	0.550737i
$316$		0			0
$317$	−17.1360	+	17.1360i	−0.962451	+	0.962451i	−0.999320	−	0.0368693i	$-0.988261\pi$
$317$	−17.1360	+	17.1360i	−0.962451	+	0.962451i	0.0368693	+	0.999320i	$0.488261\pi$
$318$		0			0
$319$	−6.99850			−0.391841
$320$		0			0
$321$	6.68607			0.373180
$322$		0			0
$323$	−4.99529	+	4.99529i	−0.277945	+	0.277945i
$324$		0			0
$325$	0.772649	−	0.220140i	0.0428589	−	0.0122112i
$326$		0			0
$327$	−0.227282			−0.0125687
$328$		0			0
$329$		−	41.1087i		−	2.26640i
$330$		0			0
$331$	−2.06668	+	2.06668i	−0.113595	+	0.113595i	−0.761619	−	0.648025i	$-0.775595\pi$
$331$	−2.06668	+	2.06668i	−0.113595	+	0.113595i	0.648025	+	0.761619i	$0.275595\pi$
$332$		0			0
$333$	−1.63459	+	1.63459i	−0.0895752	+	0.0895752i
$334$		0			0
$335$	5.11517	−	3.00724i	0.279471	−	0.164303i
$336$		0			0
$337$			35.2657i			1.92105i	0.278201	+	0.960523i	$0.410262\pi$
$337$			35.2657i			1.92105i	−0.278201	+	0.960523i	$0.589738\pi$
$338$		0			0
$339$	−0.724704	−	0.724704i	−0.0393605	−	0.0393605i
$340$		0			0
$341$	−22.1088	+	22.1088i	−1.19726	+	1.19726i
$342$		0			0
$343$	−28.8833			−1.55955
$344$		0			0
$345$	−15.4309	+	9.07194i	−0.830773	+	0.488417i
$346$		0			0
$347$	2.03686	+	2.03686i	0.109344	+	0.109344i	0.759662	−	0.650318i	$-0.225364\pi$
$347$	2.03686	+	2.03686i	0.109344	+	0.109344i	−0.650318	+	0.759662i	$0.725364\pi$
$348$		0			0
$349$	19.7731	+	19.7731i	1.05843	+	1.05843i	0.998184	+	0.0602455i	$0.0191884\pi$
$349$	19.7731	+	19.7731i	1.05843	+	1.05843i	0.0602455	+	0.998184i	$0.480812\pi$
$350$		0			0
$351$	−0.160680			−0.00857644
$352$		0			0
$353$		−	10.5799i		−	0.563110i	−0.959545	−	0.281555i	$-0.909150\pi$
$353$		−	10.5799i		−	0.563110i	0.959545	−	0.281555i	$-0.0908502\pi$
$354$		0			0
$355$	0.356853	−	1.37505i	0.0189398	−	0.0729801i
$356$		0			0
$357$	16.0725	+	16.0725i	0.850648	+	0.850648i
$358$		0			0
$359$			32.7257i			1.72719i	0.504183	+	0.863597i	$0.331794\pi$
$359$			32.7257i			1.72719i	−0.504183	+	0.863597i	$0.668206\pi$
$360$		0			0
$361$		−	17.0299i		−	0.896310i
$362$		0			0
$363$	−8.95708	−	8.95708i	−0.470125	−	0.470125i
$364$		0			0
$365$	−13.2937	−	3.44999i	−0.695826	−	0.180581i
$366$		0			0
$367$			22.0267i			1.14978i	0.818230	+	0.574891i	$0.194956\pi$
$367$			22.0267i			1.14978i	−0.818230	+	0.574891i	$0.805044\pi$
$368$		0			0
$369$	3.35633			0.174724
$370$		0			0
$371$	14.7729	+	14.7729i	0.766971	+	0.766971i
$372$		0			0
$373$	−9.69407	−	9.69407i	−0.501940	−	0.501940i	0.410100	−	0.912040i	$-0.365494\pi$
$373$	−9.69407	−	9.69407i	−0.501940	−	0.501940i	−0.912040	+	0.410100i	$0.865494\pi$
$374$		0			0
$375$	−11.1772	+	0.264320i	−0.577189	+	0.0136494i
$376$		0			0
$377$	0.231149			0.0119048
$378$		0			0
$379$	−7.44766	+	7.44766i	−0.382560	+	0.382560i	−0.872024	−	0.489463i	$-0.837193\pi$
$379$	−7.44766	+	7.44766i	−0.382560	+	0.382560i	0.489463	+	0.872024i	$0.337193\pi$
$380$		0			0
$381$	−6.57020	−	6.57020i	−0.336602	−	0.336602i
$382$		0			0
$383$			7.30581i			0.373309i	0.982426	+	0.186655i	$0.0597645\pi$
$383$			7.30581i			0.373309i	−0.982426	+	0.186655i	$0.940235\pi$
$384$		0			0
$385$	−42.3509	+	24.8984i	−2.15840	+	1.26894i
$386$		0			0
$387$	5.68196	−	5.68196i	0.288830	−	0.288830i
$388$		0			0
$389$	10.6571	−	10.6571i	0.540338	−	0.540338i	−0.383290	−	0.923628i	$-0.625209\pi$
$389$	10.6571	−	10.6571i	0.540338	−	0.540338i	0.923628	+	0.383290i	$0.125209\pi$
$390$		0			0
$391$		−	40.2904i		−	2.03757i
$392$		0			0
$393$	−6.41712			−0.323701
$394$		0			0
$395$	3.82011	+	0.991393i	0.192210	+	0.0498824i
$396$		0			0
$397$	3.10102	−	3.10102i	0.155636	−	0.155636i	−0.624994	−	0.780630i	$-0.714899\pi$
$397$	3.10102	−	3.10102i	0.155636	−	0.155636i	0.780630	+	0.624994i	$0.214899\pi$
$398$		0			0
$399$	6.33888			0.317341
$400$		0			0
$401$	−9.88608			−0.493687			−0.246844	−	0.969055i	$-0.579393\pi$
$401$	−9.88608			−0.493687			−0.246844	+	0.969055i	$0.579393\pi$
$402$		0			0
$403$	0.730217	−	0.730217i	0.0363747	−	0.0363747i
$404$		0			0
$405$	2.16437	+	0.561697i	0.107548	+	0.0279109i
$406$		0			0
$407$	11.2460			0.557444
$408$		0			0
$409$		−	11.6903i		−	0.578048i	−0.957322	−	0.289024i	$-0.906669\pi$
$409$		−	11.6903i		−	0.578048i	0.957322	−	0.289024i	$-0.0933307\pi$
$410$		0			0
$411$	0.317379	−	0.317379i	0.0156552	−	0.0156552i
$412$		0			0
$413$	23.9736	−	23.9736i	1.17966	−	1.17966i
$414$		0			0
$415$	17.4242	−	10.2438i	0.855321	−	0.502849i
$416$		0			0
$417$			7.25024i			0.355046i
$418$		0			0
$419$	5.66521	+	5.66521i	0.276764	+	0.276764i	0.831816	−	0.555052i	$-0.187302\pi$
$419$	5.66521	+	5.66521i	0.276764	+	0.276764i	−0.555052	+	0.831816i	$0.687302\pi$
$420$		0			0
$421$	−19.7440	+	19.7440i	−0.962263	+	0.962263i	−0.999313	−	0.0370502i	$-0.988204\pi$
$421$	−19.7440	+	19.7440i	−0.962263	+	0.962263i	0.0370502	+	0.999313i	$0.488204\pi$
$422$		0			0
$423$	9.10261			0.442584
$424$		0			0
$425$	12.2376	−	21.9894i	0.593609	−	1.06664i
$426$		0			0
$427$	−26.5317	−	26.5317i	−1.28396	−	1.28396i
$428$		0			0
$429$	0.552738	+	0.552738i	0.0266864	+	0.0266864i
$430$		0			0
$431$	10.8449			0.522382			0.261191	−	0.965287i	$-0.415885\pi$
$431$	10.8449			0.522382			0.261191	+	0.965287i	$0.415885\pi$
$432$		0			0
$433$			15.4885i			0.744330i	0.928167	+	0.372165i	$0.121384\pi$
$433$			15.4885i			0.744330i	−0.928167	+	0.372165i	$0.878616\pi$
$434$		0			0
$435$	−3.11360	−	0.808040i	−0.149286	−	0.0387426i
$436$		0			0
$437$	−7.94511	−	7.94511i	−0.380066	−	0.380066i
$438$		0			0
$439$		−	10.4685i		−	0.499633i	−0.968293	−	0.249816i	$-0.919630\pi$
$439$		−	10.4685i		−	0.499633i	0.968293	−	0.249816i	$-0.0803702\pi$
$440$		0			0
$441$		−	13.3956i		−	0.637884i
$442$		0			0
$443$	−15.6375	−	15.6375i	−0.742961	−	0.742961i	0.230186	−	0.973147i	$-0.426067\pi$
$443$	−15.6375	−	15.6375i	−0.742961	−	0.742961i	−0.973147	+	0.230186i	$0.926067\pi$
$444$		0			0
$445$	0.325534	−	1.25437i	0.0154318	−	0.0594628i
$446$		0			0
$447$			6.45603i			0.305360i
$448$		0			0
$449$	22.2119			1.04825			0.524123	−	0.851642i	$-0.324393\pi$
$449$	22.2119			1.04825			0.524123	+	0.851642i	$0.324393\pi$
$450$		0			0
$451$	−11.5458	−	11.5458i	−0.543670	−	0.543670i
$452$		0			0
$453$	4.83885	+	4.83885i	0.227349	+	0.227349i
$454$		0			0
$455$	1.39878	−	0.822354i	0.0655759	−	0.0385525i
$456$		0			0
$457$	−28.4752			−1.33201			−0.666006	−	0.745946i	$-0.731998\pi$
$457$	−28.4752			−1.33201			−0.666006	+	0.745946i	$0.731998\pi$
$458$		0			0
$459$	−3.55890	+	3.55890i	−0.166115	+	0.166115i
$460$		0			0
$461$	−22.7778	−	22.7778i	−1.06087	−	1.06087i	−0.998023	−	0.0628456i	$-0.979982\pi$
$461$	−22.7778	−	22.7778i	−1.06087	−	1.06087i	−0.0628456	−	0.998023i	$-0.520018\pi$
$462$		0			0
$463$		−	24.5804i		−	1.14235i	−0.820829	−	0.571174i	$-0.806488\pi$
$463$		−	24.5804i		−	1.14235i	0.820829	−	0.571174i	$-0.193512\pi$
$464$		0			0
$465$	−12.3888	+	7.28343i	−0.574515	+	0.337761i
$466$		0			0
$467$	15.6837	−	15.6837i	0.725757	−	0.725757i	−0.244015	−	0.969772i	$-0.578464\pi$
$467$	15.6837	−	15.6837i	0.725757	−	0.725757i	0.969772	+	0.244015i	$0.0784645\pi$
$468$		0			0
$469$	8.47405	−	8.47405i	0.391295	−	0.391295i
$470$		0			0
$471$		−	2.63012i		−	0.121190i
$472$		0			0
$473$	−39.0919			−1.79745
$474$		0			0
$475$	−1.92302	−	6.74941i	−0.0882342	−	0.309684i
$476$		0			0
$477$	−3.27113	+	3.27113i	−0.149775	+	0.149775i
$478$		0			0
$479$	9.45943			0.432212			0.216106	−	0.976370i	$-0.430664\pi$
$479$	9.45943			0.432212			0.216106	+	0.976370i	$0.430664\pi$
$480$		0			0
$481$	−0.371438			−0.0169361
$482$		0			0
$483$	−25.5637	+	25.5637i	−1.16319	+	1.16319i
$484$		0			0
$485$	−8.58099	+	33.0649i	−0.389643	+	1.50140i
$486$		0			0
$487$	−9.95957			−0.451311			−0.225656	−	0.974207i	$-0.572452\pi$
$487$	−9.95957			−0.451311			−0.225656	+	0.974207i	$0.572452\pi$
$488$		0			0
$489$		−	13.3365i		−	0.603097i
$490$		0			0
$491$	4.35184	−	4.35184i	0.196396	−	0.196396i	−0.602057	−	0.798453i	$-0.705652\pi$
$491$	4.35184	−	4.35184i	0.196396	−	0.196396i	0.798453	+	0.602057i	$0.205652\pi$
$492$		0			0
$493$	5.11973	−	5.11973i	0.230581	−	0.230581i
$494$		0			0
$495$	−5.51320	−	9.37767i	−0.247800	−	0.421495i
$496$		0			0
$497$		−	2.86916i		−	0.128700i
$498$		0			0
$499$	3.09455	+	3.09455i	0.138531	+	0.138531i	0.772972	−	0.634440i	$-0.218769\pi$
$499$	3.09455	+	3.09455i	0.138531	+	0.138531i	−0.634440	+	0.772972i	$0.718769\pi$
$500$		0			0
$501$	−15.0310	+	15.0310i	−0.671535	+	0.671535i
$502$		0			0
$503$	−5.84356			−0.260552			−0.130276	−	0.991478i	$-0.541586\pi$
$503$	−5.84356			−0.260552			−0.130276	+	0.991478i	$0.541586\pi$
$504$		0			0
$505$	−7.10520	+	4.17720i	−0.316177	+	0.185883i
$506$		0			0
$507$	9.17413	+	9.17413i	0.407438	+	0.407438i
$508$		0			0
$509$	−2.16459	−	2.16459i	−0.0959436	−	0.0959436i	0.657506	−	0.753449i	$-0.271611\pi$
$509$	−2.16459	−	2.16459i	−0.0959436	−	0.0959436i	−0.753449	+	0.657506i	$0.771611\pi$
$510$		0			0
$511$	−27.7385			−1.22708
$512$		0			0
$513$			1.40360i			0.0619706i
$514$		0			0
$515$	−20.0479	−	5.20284i	−0.883418	−	0.229264i
$516$		0			0
$517$	−31.3130	−	31.3130i	−1.37714	−	1.37714i
$518$		0			0
$519$			5.52941i			0.242714i
$520$		0			0
$521$		−	4.80746i		−	0.210619i	−0.994440	−	0.105309i	$-0.966417\pi$
$521$		−	4.80746i		−	0.210619i	0.994440	−	0.105309i	$-0.0335833\pi$
$522$		0			0
$523$	−23.6204	−	23.6204i	−1.03285	−	1.03285i	−0.999442	−	0.0334047i	$-0.989365\pi$
$523$	−23.6204	−	23.6204i	−1.03285	−	1.03285i	−0.0334047	−	0.999442i	$-0.510635\pi$
$524$		0			0
$525$	−21.7165	+	6.18738i	−0.947785	+	0.270039i
$526$		0			0
$527$		−	32.3473i		−	1.40907i
$528$		0			0
$529$	41.0827			1.78620
$530$		0			0
$531$	5.30843	+	5.30843i	0.230366	+	0.230366i
$532$		0			0
$533$	0.381339	+	0.381339i	0.0165176	+	0.0165176i
$534$		0			0
$535$	−7.57706	−	12.8882i	−0.327585	−	0.557205i
$536$		0			0
$537$	23.7986			1.02698
$538$		0			0
$539$	−46.0808	+	46.0808i	−1.98484	+	1.98484i
$540$		0			0
$541$	22.9002	+	22.9002i	0.984558	+	0.984558i	0.999883	−	0.0153248i	$-0.00487822\pi$
$541$	22.9002	+	22.9002i	0.984558	+	0.984558i	−0.0153248	+	0.999883i	$0.504878\pi$
$542$		0			0
$543$		−	14.7083i		−	0.631193i
$544$		0			0
$545$	0.257570	+	0.438114i	0.0110331	+	0.0187667i
$546$		0			0
$547$	−24.1611	+	24.1611i	−1.03306	+	1.03306i	−0.0336209	+	0.999435i	$0.510704\pi$
$547$	−24.1611	+	24.1611i	−1.03306	+	1.03306i	−0.999435	+	0.0336209i	$0.989296\pi$
$548$		0			0
$549$	5.87487	−	5.87487i	0.250733	−	0.250733i
$550$		0			0
$551$		−	2.01918i		−	0.0860201i
$552$		0			0
$553$	7.97098			0.338961
$554$		0			0
$555$	5.00330	+	1.29846i	0.212378	+	0.0551164i
$556$		0			0
$557$	−4.87106	+	4.87106i	−0.206393	+	0.206393i	−0.802733	−	0.596339i	$-0.796621\pi$
$557$	−4.87106	+	4.87106i	−0.206393	+	0.206393i	0.596339	+	0.802733i	$0.296621\pi$
$558$		0			0
$559$	1.29114			0.0546095
$560$		0			0
$561$	24.4853			1.03377
$562$		0			0
$563$	−1.64374	+	1.64374i	−0.0692752	+	0.0692752i	−0.740896	−	0.671620i	$-0.765599\pi$
$563$	−1.64374	+	1.64374i	−0.0692752	+	0.0692752i	0.671620	+	0.740896i	$0.265599\pi$
$564$		0			0
$565$	−0.575675	+	2.21823i	−0.0242188	+	0.0933217i
$566$		0			0
$567$	4.51614			0.189660
$568$		0			0
$569$			30.0890i			1.26140i	0.776028	+	0.630699i	$0.217232\pi$
$569$			30.0890i			1.26140i	−0.776028	+	0.630699i	$0.782768\pi$
$570$		0			0
$571$	12.4422	−	12.4422i	0.520688	−	0.520688i	−0.397091	−	0.917779i	$-0.629980\pi$
$571$	12.4422	−	12.4422i	0.520688	−	0.520688i	0.917779	+	0.397091i	$0.129980\pi$
$572$		0			0
$573$	−14.7251	+	14.7251i	−0.615151	+	0.615151i
$574$		0			0
$575$	34.9745	+	19.4641i	1.45854	+	0.811708i
$576$		0			0
$577$		−	38.4529i		−	1.60081i	−0.599457	−	0.800407i	$-0.704617\pi$
$577$		−	38.4529i		−	1.60081i	0.599457	−	0.800407i	$-0.295383\pi$
$578$		0			0
$579$	−4.11912	−	4.11912i	−0.171185	−	0.171185i
$580$		0			0
$581$	28.8659	−	28.8659i	1.19756	−	1.19756i
$582$		0			0
$583$	22.5054			0.932078
$584$		0			0
$585$	0.182092	+	0.309729i	0.00752858	+	0.0128057i
$586$		0			0
$587$	−20.0374	−	20.0374i	−0.827031	−	0.827031i	0.160074	−	0.987105i	$-0.448827\pi$
$587$	−20.0374	−	20.0374i	−0.827031	−	0.827031i	−0.987105	+	0.160074i	$0.948827\pi$
$588$		0			0
$589$	−6.37875	−	6.37875i	−0.262832	−	0.262832i
$590$		0			0
$591$	15.6491			0.643719
$592$		0			0
$593$			39.5143i			1.62266i	0.584590	+	0.811329i	$0.301255\pi$
$593$			39.5143i			1.62266i	−0.584590	+	0.811329i	$0.698745\pi$
$594$		0			0
$595$	12.7674	−	49.1961i	0.523411	−	2.01684i
$596$		0			0
$597$	4.98202	+	4.98202i	0.203901	+	0.203901i
$598$		0			0
$599$		−	46.6476i		−	1.90597i	−0.303022	−	0.952984i	$-0.597996\pi$
$599$		−	46.6476i		−	1.90597i	0.303022	−	0.952984i	$-0.402004\pi$
$600$		0			0
$601$			39.8224i			1.62439i	0.583386	+	0.812195i	$0.301727\pi$
$601$			39.8224i			1.62439i	−0.583386	+	0.812195i	$0.698273\pi$
$602$		0			0
$603$	1.87639	+	1.87639i	0.0764125	+	0.0764125i
$604$		0			0
$605$	−7.11514	+	27.4165i	−0.289271	+	1.11464i
$606$		0			0
$607$			29.2165i			1.18586i	0.805254	+	0.592930i	$0.202029\pi$
$607$			29.2165i			1.18586i	−0.805254	+	0.592930i	$0.797971\pi$
$608$		0			0
$609$	−6.49679			−0.263263
$610$		0			0
$611$	1.03422	+	1.03422i	0.0418400	+	0.0418400i
$612$		0			0
$613$	19.6885	+	19.6885i	0.795212	+	0.795212i	0.982336	−	0.187124i	$-0.0599167\pi$
$613$	19.6885	+	19.6885i	0.795212	+	0.795212i	−0.187124	+	0.982336i	$0.559917\pi$
$614$		0			0
$615$	−3.80360	−	6.46973i	−0.153376	−	0.260885i
$616$		0			0
$617$	−10.8873			−0.438306			−0.219153	−	0.975691i	$-0.570329\pi$
$617$	−10.8873			−0.438306			−0.219153	+	0.975691i	$0.570329\pi$
$618$		0			0
$619$	31.2108	−	31.2108i	1.25447	−	1.25447i	0.300773	−	0.953696i	$-0.402755\pi$
$619$	31.2108	−	31.2108i	1.25447	−	1.25447i	0.953696	−	0.300773i	$-0.0972445\pi$
$620$		0			0
$621$	−5.66051	−	5.66051i	−0.227148	−	0.227148i
$622$		0			0
$623$		−	2.61735i		−	0.104862i
$624$		0			0
$625$	13.1762	+	21.2459i	0.527048	+	0.849835i
$626$		0			0
$627$	4.82840	−	4.82840i	0.192828	−	0.192828i
$628$		0			0
$629$	−8.22700	+	8.22700i	−0.328032	+	0.328032i
$630$		0			0
$631$		−	15.8570i		−	0.631257i	−0.948883	−	0.315629i	$-0.897785\pi$
$631$		−	15.8570i		−	0.631257i	0.948883	−	0.315629i	$-0.102215\pi$
$632$		0			0
$633$	0.223481			0.00888257
$634$		0			0
$635$	−5.21910	+	20.1106i	−0.207114	+	0.798065i
$636$		0			0
$637$	1.52197	−	1.52197i	0.0603027	−	0.0603027i
$638$		0			0
$639$	0.635312			0.0251326
$640$		0			0
$641$	−10.9256			−0.431535			−0.215767	−	0.976445i	$-0.569225\pi$
$641$	−10.9256			−0.431535			−0.215767	+	0.976445i	$0.569225\pi$
$642$		0			0
$643$	34.9865	−	34.9865i	1.37973	−	1.37973i	0.534675	−	0.845058i	$-0.320434\pi$
$643$	34.9865	−	34.9865i	1.37973	−	1.37973i	0.845058	−	0.534675i	$-0.179566\pi$
$644$		0			0
$645$	−17.3918	−	4.51352i	−0.684802	−	0.177720i
$646$		0			0
$647$	−8.60364			−0.338244			−0.169122	−	0.985595i	$-0.554093\pi$
$647$	−8.60364			−0.338244			−0.169122	+	0.985595i	$0.554093\pi$
$648$		0			0
$649$		−	36.5220i		−	1.43361i
$650$		0			0
$651$	−20.5239	+	20.5239i	−0.804393	+	0.804393i
$652$		0			0
$653$	−9.44853	+	9.44853i	−0.369750	+	0.369750i	−0.867386	−	0.497636i	$-0.834201\pi$
$653$	−9.44853	+	9.44853i	−0.369750	+	0.369750i	0.497636	+	0.867386i	$0.334201\pi$
$654$		0			0
$655$	7.27227	+	12.3698i	0.284151	+	0.483327i
$656$		0			0
$657$		−	6.14208i		−	0.239625i
$658$		0			0
$659$	−4.77731	−	4.77731i	−0.186098	−	0.186098i	0.607909	−	0.794007i	$-0.292009\pi$
$659$	−4.77731	−	4.77731i	−0.186098	−	0.186098i	−0.794007	+	0.607909i	$0.792009\pi$
$660$		0			0
$661$	−14.2928	+	14.2928i	−0.555927	+	0.555927i	−0.928145	−	0.372218i	$-0.878597\pi$
$661$	−14.2928	+	14.2928i	−0.555927	+	0.555927i	0.372218	+	0.928145i	$0.378597\pi$
$662$		0			0
$663$	−0.808709			−0.0314076
$664$		0			0
$665$	−7.18360	−	12.2189i	−0.278568	−	0.473831i
$666$		0			0
$667$	8.14304	+	8.14304i	0.315300	+	0.315300i
$668$		0			0
$669$	5.92653	+	5.92653i	0.229133	+	0.229133i
$670$		0			0
$671$	−40.4191			−1.56036
$672$		0			0
$673$			19.6076i			0.755818i	0.925843	+	0.377909i	$0.123357\pi$
$673$			19.6076i			0.755818i	−0.925843	+	0.377909i	$0.876643\pi$
$674$		0			0
$675$	−1.37006	−	4.80863i	−0.0527336	−	0.185084i
$676$		0			0
$677$	1.22231	+	1.22231i	0.0469773	+	0.0469773i	0.730205	−	0.683228i	$-0.239424\pi$
$677$	1.22231	+	1.22231i	0.0469773	+	0.0469773i	−0.683228	+	0.730205i	$0.739424\pi$
$678$		0			0
$679$			68.9927i			2.64770i
$680$		0			0
$681$		−	9.52569i		−	0.365025i
$682$		0			0
$683$	27.1537	+	27.1537i	1.03901	+	1.03901i	0.999208	+	0.0398011i	$0.0126724\pi$
$683$	27.1537	+	27.1537i	1.03901	+	1.03901i	0.0398011	+	0.999208i	$0.487328\pi$
$684$		0			0
$685$	−0.971460	−	0.252113i	−0.0371176	−	0.00963274i
$686$		0			0
$687$		−	19.3422i		−	0.737950i
$688$		0			0
$689$	−0.743316			−0.0283181
$690$		0			0
$691$	14.8065	+	14.8065i	0.563266	+	0.563266i	0.930234	−	0.366968i	$-0.119604\pi$
$691$	14.8065	+	14.8065i	0.563266	+	0.563266i	−0.366968	+	0.930234i	$0.619604\pi$
$692$		0			0
$693$	−15.5355	−	15.5355i	−0.590147	−	0.590147i
$694$		0			0
$695$	13.9757	−	8.21641i	0.530129	−	0.311666i
$696$		0			0
$697$	16.8926			0.639853
$698$		0			0
$699$	−1.15076	+	1.15076i	−0.0435256	+	0.0435256i
$700$		0			0
$701$	0.259714	+	0.259714i	0.00980927	+	0.00980927i	0.711994	−	0.702185i	$-0.247792\pi$
$701$	0.259714	+	0.259714i	0.00980927	+	0.00980927i	−0.702185	+	0.711994i	$0.747792\pi$
$702$		0			0
$703$			3.24466i			0.122375i
$704$		0			0
$705$	−10.3156	−	17.5464i	−0.388509	−	0.660835i
$706$		0			0
$707$	−11.7708	+	11.7708i	−0.442688	+	0.442688i
$708$		0			0
$709$	16.6998	−	16.6998i	0.627173	−	0.627173i	−0.320183	−	0.947356i	$-0.603744\pi$
$709$	16.6998	−	16.6998i	0.627173	−	0.627173i	0.947356	+	0.320183i	$0.103744\pi$
$710$		0			0
$711$			1.76500i			0.0661925i
$712$		0			0
$713$	51.4489			1.92678
$714$		0			0
$715$	0.439073	−	1.69187i	0.0164204	−	0.0632722i
$716$		0			0
$717$	8.97378	−	8.97378i	0.335132	−	0.335132i
$718$		0			0
$719$	−0.0356124			−0.00132812			−0.000664059	−	1.00000i	$-0.500211\pi$
$719$	−0.0356124			−0.00132812			−0.000664059		1.00000i	$0.500211\pi$
$720$		0			0
$721$	−41.8318			−1.55790
$722$		0			0
$723$	14.9223	−	14.9223i	0.554966	−	0.554966i
$724$		0			0
$725$	1.97093	+	6.91755i	0.0731983	+	0.256912i
$726$		0			0
$727$	−35.1597			−1.30400			−0.652000	−	0.758219i	$-0.726070\pi$
$727$	−35.1597			−1.30400			−0.652000	+	0.758219i	$0.726070\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	28.5976	−	28.5976i	1.05772	−	1.05772i
$732$		0			0
$733$	27.9959	−	27.9959i	1.03405	−	1.03405i	0.0346524	−	0.999399i	$-0.488968\pi$
$733$	27.9959	−	27.9959i	1.03405	−	1.03405i	0.999399	−	0.0346524i	$-0.0110324\pi$
$734$		0			0
$735$	−25.8216	+	15.1807i	−0.952443	+	0.559947i
$736$		0			0
$737$		−	12.9096i		−	0.475530i
$738$		0			0
$739$	22.3803	+	22.3803i	0.823274	+	0.823274i	0.986576	−	0.163302i	$-0.0522145\pi$
$739$	22.3803	+	22.3803i	0.823274	+	0.823274i	−0.163302	+	0.986576i	$0.552215\pi$
$740$		0			0
$741$	−0.159474	+	0.159474i	−0.00585843	+	0.00585843i
$742$		0			0
$743$	−11.3806			−0.417514			−0.208757	−	0.977968i	$-0.566942\pi$
$743$	−11.3806			−0.417514			−0.208757	+	0.977968i	$0.566942\pi$
$744$		0			0
$745$	12.4448	−	7.31637i	0.455941	−	0.268051i
$746$		0			0
$747$	6.39170	+	6.39170i	0.233860	+	0.233860i
$748$		0			0
$749$	−21.3513	−	21.3513i	−0.780158	−	0.780158i
$750$		0			0
$751$	−54.6781			−1.99523			−0.997616	−	0.0690113i	$-0.978016\pi$
$751$	−54.6781			−1.99523			−0.997616	+	0.0690113i	$0.978016\pi$
$752$		0			0
$753$		−	24.7396i		−	0.901561i
$754$		0			0
$755$	3.84379	−	14.8112i	0.139890	−	0.539033i
$756$		0			0
$757$	−32.3418	−	32.3418i	−1.17548	−	1.17548i	−0.980882	−	0.194602i	$-0.937658\pi$
$757$	−32.3418	−	32.3418i	−1.17548	−	1.17548i	−0.194602	−	0.980882i	$-0.562342\pi$
$758$		0			0
$759$			38.9443i			1.41359i
$760$		0			0
$761$		−	0.392110i		−	0.0142140i	−0.999975	−	0.00710700i	$-0.997738\pi$
$761$		−	0.392110i		−	0.0142140i	0.999975	−	0.00710700i	$-0.00226225\pi$
$762$		0			0
$763$	0.725803	+	0.725803i	0.0262758	+	0.0262758i
$764$		0			0
$765$	10.8934	+	2.82705i	0.393851	+	0.102212i
$766$		0			0
$767$			1.20626i			0.0435556i
$768$		0			0
$769$	−4.36080			−0.157255			−0.0786273	−	0.996904i	$-0.525054\pi$
$769$	−4.36080			−0.157255			−0.0786273	+	0.996904i	$0.525054\pi$
$770$		0			0
$771$	5.51668	+	5.51668i	0.198679	+	0.198679i
$772$		0			0
$773$	17.2357	+	17.2357i	0.619923	+	0.619923i	0.945512	−	0.325588i	$-0.105562\pi$
$773$	17.2357	+	17.2357i	0.619923	+	0.619923i	−0.325588	+	0.945512i	$0.605562\pi$
$774$		0			0
$775$	28.0794	+	15.6268i	1.00864	+	0.561330i
$776$		0			0
$777$	10.4398			0.374526
$778$		0			0
$779$	3.33115	−	3.33115i	0.119351	−	0.119351i
$780$		0			0
$781$	−2.18548	−	2.18548i	−0.0782024	−	0.0782024i
$782$		0			0
$783$		−	1.43857i		−	0.0514103i
$784$		0			0
$785$	−5.06988	+	2.98062i	−0.180952	+	0.106383i
$786$		0			0
$787$	−24.9814	+	24.9814i	−0.890490	+	0.890490i	−0.994569	−	0.104079i	$-0.966811\pi$
$787$	−24.9814	+	24.9814i	−0.890490	+	0.890490i	0.104079	+	0.994569i	$0.466811\pi$
$788$		0			0
$789$	−8.43139	+	8.43139i	−0.300165	+	0.300165i
$790$		0			0
$791$			4.62853i			0.164572i
$792$		0			0
$793$	1.33498			0.0474064
$794$		0			0
$795$	10.0125	+	2.59845i	0.355108	+	0.0921576i
$796$		0			0
$797$	−18.8067	+	18.8067i	−0.666166	+	0.666166i	−0.956826	−	0.290660i	$-0.906125\pi$
$797$	−18.8067	+	18.8067i	−0.666166	+	0.666166i	0.290660	+	0.956826i	$0.406125\pi$
$798$		0			0
$799$	45.8139			1.62078
$800$		0			0
$801$	0.579554			0.0204775
$802$		0			0
$803$	−21.1288	+	21.1288i	−0.745618	+	0.745618i
$804$		0			0
$805$	78.2474	+	20.3067i	2.75786	+	0.715718i
$806$		0			0
$807$	11.6583			0.410392
$808$		0			0
$809$			48.5593i			1.70726i	0.520883	+	0.853628i	$0.325603\pi$
$809$			48.5593i			1.70726i	−0.520883	+	0.853628i	$0.674397\pi$
$810$		0			0
$811$	−14.4543	+	14.4543i	−0.507560	+	0.507560i	−0.913777	−	0.406217i	$-0.866848\pi$
$811$	−14.4543	+	14.4543i	−0.507560	+	0.507560i	0.406217	+	0.913777i	$0.366848\pi$
$812$		0			0
$813$	19.0183	−	19.0183i	0.667002	−	0.667002i
$814$		0			0
$815$	−25.7077	+	15.1137i	−0.900502	+	0.529411i
$816$		0			0
$817$		−	11.2787i		−	0.394591i
$818$		0			0
$819$	0.513114	+	0.513114i	0.0179296	+	0.0179296i
$820$		0			0
$821$	29.1579	−	29.1579i	1.01762	−	1.01762i	0.0177763	−	0.999842i	$-0.494341\pi$
$821$	29.1579	−	29.1579i	1.01762	−	1.01762i	0.999842	−	0.0177763i	$-0.00565868\pi$
$822$		0			0
$823$	−7.17233			−0.250012			−0.125006	−	0.992156i	$-0.539895\pi$
$823$	−7.17233			−0.250012			−0.125006	+	0.992156i	$0.539895\pi$
$824$		0			0
$825$	−11.8287	+	21.2547i	−0.411822	+	0.739994i
$826$		0			0
$827$	−21.6132	−	21.6132i	−0.751564	−	0.751564i	0.223207	−	0.974771i	$-0.428347\pi$
$827$	−21.6132	−	21.6132i	−0.751564	−	0.751564i	−0.974771	+	0.223207i	$0.928347\pi$
$828$		0			0
$829$	21.3762	+	21.3762i	0.742424	+	0.742424i	0.973044	−	0.230620i	$-0.0740753\pi$
$829$	21.3762	+	21.3762i	0.742424	+	0.742424i	−0.230620	+	0.973044i	$0.574075\pi$
$830$		0			0
$831$	22.3862			0.776569
$832$		0			0
$833$		−	67.4205i		−	2.33598i
$834$		0			0
$835$	46.0081	+	11.9400i	1.59217	+	0.413201i
$836$		0			0
$837$	−4.54455	−	4.54455i	−0.157083	−	0.157083i
$838$		0			0
$839$			1.15350i			0.0398234i	0.999802	+	0.0199117i	$0.00633851\pi$
$839$			1.15350i			0.0398234i	−0.999802	+	0.0199117i	$0.993661\pi$
$840$		0			0
$841$		−	26.9305i		−	0.928638i
$842$		0			0
$843$	19.6965	+	19.6965i	0.678382	+	0.678382i
$844$		0			0
$845$	7.28755	−	28.0809i	0.250700	−	0.966013i
$846$		0			0
$847$			57.2070i			1.96566i
$848$		0			0
$849$	3.70928			0.127302
$850$		0			0
$851$	−13.0852	−	13.0852i	−0.448555	−	0.448555i
$852$		0			0
$853$	−27.6979	−	27.6979i	−0.948358	−	0.948358i	0.0503728	−	0.998730i	$-0.483959\pi$
$853$	−27.6979	−	27.6979i	−0.948358	−	0.948358i	−0.998730	+	0.0503728i	$0.983959\pi$
$854$		0			0
$855$	2.70562	−	1.59065i	0.0925301	−	0.0543991i
$856$		0			0
$857$	49.0796			1.67653			0.838263	−	0.545266i	$-0.183571\pi$
$857$	49.0796			1.67653			0.838263	+	0.545266i	$0.183571\pi$
$858$		0			0
$859$	−28.4421	+	28.4421i	−0.970433	+	0.970433i	−0.999575	−	0.0291421i	$-0.990722\pi$
$859$	−28.4421	+	28.4421i	−0.970433	+	0.970433i	0.0291421	+	0.999575i	$0.490722\pi$
$860$		0			0
$861$	−10.7181	−	10.7181i	−0.365272	−	0.365272i
$862$		0			0
$863$		−	24.2991i		−	0.827151i	−0.910470	−	0.413576i	$-0.864280\pi$
$863$		−	24.2991i		−	0.827151i	0.910470	−	0.413576i	$-0.135720\pi$
$864$		0			0
$865$	10.6586	−	6.26627i	0.362404	−	0.213060i
$866$		0			0
$867$	−5.89133	+	5.89133i	−0.200080	+	0.200080i
$868$		0			0
$869$	6.07159	−	6.07159i	0.205965	−	0.205965i
$870$		0			0
$871$			0.426382i			0.0144474i
$872$		0			0
$873$	−15.2769			−0.517045
$874$		0			0
$875$	36.5374	+	34.8492i	1.23519	+	1.17812i
$876$		0			0
$877$	14.7778	−	14.7778i	0.499010	−	0.499010i	−0.412120	−	0.911130i	$-0.635211\pi$
$877$	14.7778	−	14.7778i	0.499010	−	0.499010i	0.911130	+	0.412120i	$0.135211\pi$
$878$		0			0
$879$	−10.9681			−0.369943
$880$		0			0
$881$	29.8866			1.00691			0.503453	−	0.864023i	$-0.332063\pi$
$881$	29.8866			1.00691			0.503453	+	0.864023i	$0.332063\pi$
$882$		0			0
$883$	−16.5411	+	16.5411i	−0.556653	+	0.556653i	−0.928353	−	0.371700i	$-0.878775\pi$
$883$	−16.5411	+	16.5411i	−0.556653	+	0.556653i	0.371700	+	0.928353i	$0.378775\pi$
$884$		0			0
$885$	4.21680	−	16.2485i	0.141746	−	0.546186i
$886$		0			0
$887$	36.8915			1.23870			0.619348	−	0.785116i	$-0.287397\pi$
$887$	36.8915			1.23870			0.619348	+	0.785116i	$0.287397\pi$
$888$		0			0
$889$			41.9625i			1.40738i
$890$		0			0
$891$	3.44000	−	3.44000i	0.115244	−	0.115244i
$892$		0			0
$893$	9.03432	−	9.03432i	0.302322	−	0.302322i
$894$		0			0
$895$	−26.9700	−	45.8746i	−0.901508	−	1.53342i
$896$		0			0
$897$		−	1.28627i		−	0.0429472i
$898$		0			0
$899$	6.53766	+	6.53766i	0.218043	+	0.218043i
$900$		0			0
$901$	−16.4638	+	16.4638i	−0.548487	+	0.548487i
$902$		0			0
$903$	−36.2895			−1.20764
$904$		0			0
$905$	−28.3520	+	16.6683i	−0.942452	+	0.554074i
$906$		0			0
$907$	19.6564	+	19.6564i	0.652679	+	0.652679i	0.953637	−	0.300958i	$-0.0973064\pi$
$907$	19.6564	+	19.6564i	0.652679	+	0.652679i	−0.300958	+	0.953637i	$0.597306\pi$
$908$		0			0
$909$	−2.60639	−	2.60639i	−0.0864486	−	0.0864486i
$910$		0			0
$911$	10.4327			0.345650			0.172825	−	0.984953i	$-0.444711\pi$
$911$	10.4327			0.345650			0.172825	+	0.984953i	$0.444711\pi$
$912$		0			0
$913$		−	43.9749i		−	1.45536i
$914$		0			0
$915$	−17.9823	−	4.66675i	−0.594475	−	0.154278i
$916$		0			0
$917$	20.4924	+	20.4924i	0.676719	+	0.676719i
$918$		0			0
$919$			21.6666i			0.714715i	0.933968	+	0.357357i	$0.116322\pi$
$919$			21.6666i			0.714715i	−0.933968	+	0.357357i	$0.883678\pi$
$920$		0			0
$921$			3.68777i			0.121516i
$922$		0			0
$923$	0.0721827	+	0.0721827i	0.00237592	+	0.00237592i
$924$		0			0
$925$	−3.16712	−	11.1160i	−0.104134	−	0.365490i
$926$		0			0
$927$		−	9.26272i		−	0.304228i
$928$		0			0
$929$	6.46931			0.212251			0.106126	−	0.994353i	$-0.466155\pi$
$929$	6.46931			0.212251			0.106126	+	0.994353i	$0.466155\pi$
$930$		0			0
$931$	−13.2951	−	13.2951i	−0.435728	−	0.435728i
$932$		0			0
$933$	14.2582	+	14.2582i	0.466793	+	0.466793i
$934$		0			0
$935$	−27.7482	−	47.1983i	−0.907463	−	1.54355i
$936$		0			0
$937$	20.4235			0.667208			0.333604	−	0.942713i	$-0.391735\pi$
$937$	20.4235			0.667208			0.333604	+	0.942713i	$0.391735\pi$
$938$		0			0
$939$	16.4453	−	16.4453i	0.536672	−	0.536672i
$940$		0			0
$941$	28.2871	+	28.2871i	0.922134	+	0.922134i	0.997180	−	0.0750464i	$-0.0239105\pi$
$941$	28.2871	+	28.2871i	0.922134	+	0.922134i	−0.0750464	+	0.997180i	$0.523910\pi$
$942$		0			0
$943$			26.8680i			0.874943i
$944$		0			0
$945$	−5.11797	−	8.70541i	−0.166488	−	0.283187i
$946$		0			0
$947$	−8.81881	+	8.81881i	−0.286573	+	0.286573i	−0.835723	−	0.549151i	$-0.814951\pi$
$947$	−8.81881	+	8.81881i	−0.286573	+	0.286573i	0.549151	+	0.835723i	$0.314951\pi$
$948$		0			0
$949$	0.697849	−	0.697849i	0.0226531	−	0.0226531i
$950$		0			0
$951$			24.2339i			0.785838i
$952$		0			0
$953$	−43.7042			−1.41572			−0.707858	−	0.706354i	$-0.750339\pi$
$953$	−43.7042			−1.41572			−0.707858	+	0.706354i	$0.750339\pi$
$954$		0			0
$955$	45.0719	+	11.6970i	1.45849	+	0.378508i
$956$		0			0
$957$	−4.94868	+	4.94868i	−0.159968	+	0.159968i
$958$		0			0
$959$	−2.02703			−0.0654564
$960$		0			0
$961$	10.3059			0.332449
$962$		0			0
$963$	4.72776	−	4.72776i	0.152350	−	0.152350i
$964$		0			0
$965$	−3.27206	+	12.6081i	−0.105331	+	0.405870i
$966$		0			0
$967$	24.4130			0.785068			0.392534	−	0.919738i	$-0.371599\pi$
$967$	24.4130			0.785068			0.392534	+	0.919738i	$0.371599\pi$
$968$		0			0
$969$			7.06441i			0.226942i
$970$		0			0
$971$	−3.61271	+	3.61271i	−0.115937	+	0.115937i	−0.762695	−	0.646758i	$-0.776124\pi$
$971$	−3.61271	+	3.61271i	−0.115937	+	0.115937i	0.646758	+	0.762695i	$0.276124\pi$
$972$		0			0
$973$	23.1529	−	23.1529i	0.742247	−	0.742247i
$974$		0			0
$975$	0.390683	−	0.702008i	0.0125119	−	0.0224823i
$976$		0			0
$977$			52.1693i			1.66904i	0.550975	+	0.834522i	$0.314256\pi$
$977$			52.1693i			1.66904i	−0.550975	+	0.834522i	$0.685744\pi$
$978$		0			0
$979$	−1.99367	−	1.99367i	−0.0637179	−	0.0637179i
$980$		0			0
$981$	−0.160713	+	0.160713i	−0.00513117	+	0.00513117i
$982$		0			0
$983$	43.2396			1.37913			0.689564	−	0.724225i	$-0.257802\pi$
$983$	43.2396			1.37913			0.689564	+	0.724225i	$0.257802\pi$
$984$		0			0
$985$	−17.7345	−	30.1656i	−0.565069	−	0.961155i
$986$		0			0
$987$	−29.0683	−	29.0683i	−0.925253	−	0.925253i
$988$		0			0
$989$	45.4851	+	45.4851i	1.44634	+	1.44634i
$990$		0			0
$991$	48.9048			1.55351			0.776756	−	0.629802i	$-0.216864\pi$
$991$	48.9048			1.55351			0.776756	+	0.629802i	$0.216864\pi$
$992$		0			0
$993$			2.92273i			0.0927499i
$994$		0			0
$995$	3.95751	−	15.2494i	0.125462	−	0.483438i
$996$		0			0
$997$	−41.0281	−	41.0281i	−1.29937	−	1.29937i	−0.928806	−	0.370565i	$-0.879164\pi$
$997$	−41.0281	−	41.0281i	−1.29937	−	1.29937i	−0.370565	−	0.928806i	$-0.620836\pi$
$998$		0			0
$999$			2.31167i			0.0731379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.b.289.13		48
4.3	odd	2		1920.2.bl.a.289.12		48
5.4	even	2	inner	1920.2.bl.b.289.12		48
8.3	odd	2		240.2.bl.a.109.12	✓	48
8.5	even	2		960.2.bl.a.529.12		48
16.3	odd	4		240.2.bl.a.229.13	yes	48
16.5	even	4	inner	1920.2.bl.b.1249.12		48
16.11	odd	4		1920.2.bl.a.1249.13		48
16.13	even	4		960.2.bl.a.49.18		48
20.19	odd	2		1920.2.bl.a.289.13		48
24.11	even	2		720.2.bm.h.109.13		48
40.19	odd	2		240.2.bl.a.109.13	yes	48
40.29	even	2		960.2.bl.a.529.18		48
48.35	even	4		720.2.bm.h.469.12		48
80.19	odd	4		240.2.bl.a.229.12	yes	48
80.29	even	4		960.2.bl.a.49.12		48
80.59	odd	4		1920.2.bl.a.1249.12		48
80.69	even	4	inner	1920.2.bl.b.1249.13		48
120.59	even	2		720.2.bm.h.109.12		48
240.179	even	4		720.2.bm.h.469.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.12	✓	48	8.3	odd	2
240.2.bl.a.109.13	yes	48	40.19	odd	2
240.2.bl.a.229.12	yes	48	80.19	odd	4
240.2.bl.a.229.13	yes	48	16.3	odd	4
720.2.bm.h.109.12		48	120.59	even	2
720.2.bm.h.109.13		48	24.11	even	2
720.2.bm.h.469.12		48	48.35	even	4
720.2.bm.h.469.13		48	240.179	even	4
960.2.bl.a.49.12		48	80.29	even	4
960.2.bl.a.49.18		48	16.13	even	4
960.2.bl.a.529.12		48	8.5	even	2
960.2.bl.a.529.18		48	40.29	even	2
1920.2.bl.a.289.12		48	4.3	odd	2
1920.2.bl.a.289.13		48	20.19	odd	2
1920.2.bl.a.1249.12		48	80.59	odd	4
1920.2.bl.a.1249.13		48	16.11	odd	4
1920.2.bl.b.289.12		48	5.4	even	2	inner
1920.2.bl.b.289.13		48	1.1	even	1	trivial
1920.2.bl.b.1249.12		48	16.5	even	4	inner
1920.2.bl.b.1249.13		48	80.69	even	4	inner

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.16437 - 0.561697i) q^{5} -4.51614 q^{7} -1.00000i q^{9} +(-3.44000 + 3.44000i) q^{11} +(0.113618 - 0.113618i) q^{13} +(-1.92762 + 1.13326i) q^{15} -5.03305i q^{17} +(-0.992498 - 0.992498i) q^{19} +(-3.19340 + 3.19340i) q^{21} +8.00517 q^{23} +(4.36899 + 2.43144i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(1.01722 + 1.01722i) q^{29} +6.42697 q^{31} +4.86490i q^{33} +(9.77461 + 2.53670i) q^{35} +(-1.63459 - 1.63459i) q^{37} -0.160680i q^{39} +3.35633i q^{41} +(5.68196 + 5.68196i) q^{43} +(-0.561697 + 2.16437i) q^{45} +9.10261i q^{47} +13.3956 q^{49} +(-3.55890 - 3.55890i) q^{51} +(-3.27113 - 3.27113i) q^{53} +(9.37767 - 5.51320i) q^{55} -1.40360 q^{57} +(-5.30843 + 5.30843i) q^{59} +(5.87487 + 5.87487i) q^{61} +4.51614i q^{63} +(-0.309729 + 0.182092i) q^{65} +(-1.87639 + 1.87639i) q^{67} +(5.66051 - 5.66051i) q^{69} +0.635312i q^{71} +6.14208 q^{73} +(4.80863 - 1.37006i) q^{75} +(15.5355 - 15.5355i) q^{77} -1.76500 q^{79} -1.00000 q^{81} +(-6.39170 + 6.39170i) q^{83} +(-2.82705 + 10.8934i) q^{85} +1.43857 q^{87} +0.579554i q^{89} +(-0.513114 + 0.513114i) q^{91} +(4.54455 - 4.54455i) q^{93} +(1.59065 + 2.70562i) q^{95} -15.2769i q^{97} +(3.44000 + 3.44000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{19} + 48 q^{31} + 24 q^{35} + 48 q^{49} + 8 q^{51} - 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} - 16 q^{75} + 96 q^{79} - 48 q^{81} - 32 q^{91} + 48 q^{95}+O(q^{100}) \) 48 * q + 8 * q^19 + 48 * q^31 + 24 * q^35 + 48 * q^49 + 8 * q^51 - 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 - 16 * q^75 + 96 * q^79 - 48 * q^81 - 32 * q^91 + 48 * q^95

Introduction

L-functions

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