LMFDB - Embedded newform 7800.2.a.bi.1.3

Newspace parameters

Level:	$ N $	$=$	$ 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7800.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$62.2833135766$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.940.1
Defining polynomial:	$ x^{3} - 7x - 4 $ x^3 - 7*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1560)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.29240$ of defining polynomial
Character	$\chi$	$=$	7800.1

$q$-expansion

$f(q)$	$=$	$q-1.00000 q^{3} +4.83991 q^{7} +1.00000 q^{9} +O(q^{10})$	$q-1.00000 q^{3} +4.83991 q^{7} +1.00000 q^{9} +2.25511 q^{11} +1.00000 q^{13} -6.32970 q^{17} -2.58480 q^{19} -4.83991 q^{21} -4.83991 q^{23} -1.00000 q^{27} +9.09501 q^{29} -0.510210 q^{31} -2.25511 q^{33} -4.25511 q^{37} -1.00000 q^{39} +0.255105 q^{41} -9.16961 q^{43} +4.51021 q^{47} +16.4247 q^{49} +6.32970 q^{51} +9.93492 q^{53} +2.58480 q^{57} +14.1900 q^{59} +9.93492 q^{61} +4.83991 q^{63} +13.1696 q^{67} +4.83991 q^{69} -5.74489 q^{71} -2.90499 q^{73} +10.9145 q^{77} +5.74489 q^{79} +1.00000 q^{81} -10.1900 q^{83} -9.09501 q^{87} +3.74489 q^{89} +4.83991 q^{91} +0.510210 q^{93} +12.5197 q^{97} +2.25511 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} - q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 - q^7 + 3 * q^9	$ 3 q - 3 q^{3} - q^{7} + 3 q^{9} + 5 q^{11} + 3 q^{13} - 7 q^{17} + 6 q^{19} + q^{21} + q^{23} - 3 q^{27} + 10 q^{29} + 2 q^{31} - 5 q^{33} - 11 q^{37} - 3 q^{39} - q^{41} + 10 q^{47} + 20 q^{49} + 7 q^{51} - 3 q^{53} - 6 q^{57} + 8 q^{59} - 3 q^{61} - q^{63} + 12 q^{67} - q^{69} - 19 q^{71} - 26 q^{73} + 7 q^{77} + 19 q^{79} + 3 q^{81} + 4 q^{83} - 10 q^{87} + 13 q^{89} - q^{91} - 2 q^{93} - 9 q^{97} + 5 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 - q^7 + 3 * q^9 + 5 * q^11 + 3 * q^13 - 7 * q^17 + 6 * q^19 + q^21 + q^23 - 3 * q^27 + 10 * q^29 + 2 * q^31 - 5 * q^33 - 11 * q^37 - 3 * q^39 - q^41 + 10 * q^47 + 20 * q^49 + 7 * q^51 - 3 * q^53 - 6 * q^57 + 8 * q^59 - 3 * q^61 - q^63 + 12 * q^67 - q^69 - 19 * q^71 - 26 * q^73 + 7 * q^77 + 19 * q^79 + 3 * q^81 + 4 * q^83 - 10 * q^87 + 13 * q^89 - q^91 - 2 * q^93 - 9 * q^97 + 5 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	4.83991	1.82931	0.914657	−	0.404232i	$-0.132461\pi$
$7$	4.83991	1.82931	0.914657	+	0.404232i	$0.132461\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	2.25511	0.679940	0.339970	−	0.940436i	$-0.389583\pi$
$11$	2.25511	0.679940	0.339970	+	0.940436i	$0.389583\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−6.32970	−1.53518	−0.767589	−	0.640943i	$-0.778544\pi$
$17$	−6.32970	−1.53518	−0.767589	+	0.640943i	$0.778544\pi$
$18$	0	0
$19$	−2.58480	−0.592995	−0.296497	−	0.955034i	$-0.595819\pi$
$19$	−2.58480	−0.592995	−0.296497	+	0.955034i	$0.595819\pi$
$20$	0	0
$21$	−4.83991	−1.05615
$22$	0	0
$23$	−4.83991	−1.00919	−0.504595	−	0.863356i	$-0.668358\pi$
$23$	−4.83991	−1.00919	−0.504595	+	0.863356i	$0.668358\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0	0
$29$	9.09501	1.68890	0.844451	−	0.535633i	$-0.179927\pi$
$29$	9.09501	1.68890	0.844451	+	0.535633i	$0.179927\pi$
$30$	0	0
$31$	−0.510210	−0.0916364	−0.0458182	−	0.998950i	$-0.514589\pi$
$31$	−0.510210	−0.0916364	−0.0458182	+	0.998950i	$0.514589\pi$
$32$	0	0
$33$	−2.25511	−0.392563
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−4.25511	−0.699535	−0.349767	−	0.936837i	$-0.613739\pi$
$37$	−4.25511	−0.699535	−0.349767	+	0.936837i	$0.613739\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	0.255105	0.0398407	0.0199204	−	0.999802i	$-0.493659\pi$
$41$	0.255105	0.0398407	0.0199204	+	0.999802i	$0.493659\pi$
$42$	0	0
$43$	−9.16961	−1.39835	−0.699176	−	0.714950i	$-0.746450\pi$
$43$	−9.16961	−1.39835	−0.699176	+	0.714950i	$0.746450\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	4.51021	0.657882	0.328941	−	0.944351i	$-0.393308\pi$
$47$	4.51021	0.657882	0.328941	+	0.944351i	$0.393308\pi$
$48$	0	0
$49$	16.4247	2.34639
$50$	0	0
$51$	6.32970	0.886335
$52$	0	0
$53$	9.93492	1.36467	0.682333	−	0.731041i	$-0.260965\pi$
$53$	9.93492	1.36467	0.682333	+	0.731041i	$0.260965\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	2.58480	0.342366
$58$	0	0
$59$	14.1900	1.84738	0.923692	−	0.383136i	$-0.125156\pi$
$59$	14.1900	1.84738	0.923692	+	0.383136i	$0.125156\pi$
$60$	0	0
$61$	9.93492	1.27204	0.636018	−	0.771674i	$-0.280580\pi$
$61$	9.93492	1.27204	0.636018	+	0.771674i	$0.280580\pi$
$62$	0	0
$63$	4.83991	0.609771
$64$	0	0
$65$	0	0
$66$	0	0
$67$	13.1696	1.60892	0.804462	−	0.594004i	$-0.202454\pi$
$67$	13.1696	1.60892	0.804462	+	0.594004i	$0.202454\pi$
$68$	0	0
$69$	4.83991	0.582656
$70$	0	0
$71$	−5.74489	−0.681794	−0.340897	−	0.940101i	$-0.610731\pi$
$71$	−5.74489	−0.681794	−0.340897	+	0.940101i	$0.610731\pi$
$72$	0	0
$73$	−2.90499	−0.340003	−0.170001	−	0.985444i	$-0.554377\pi$
$73$	−2.90499	−0.340003	−0.170001	+	0.985444i	$0.554377\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	10.9145	1.24382
$78$	0	0
$79$	5.74489	0.646351	0.323176	−	0.946339i	$-0.395250\pi$
$79$	5.74489	0.646351	0.323176	+	0.946339i	$0.395250\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−10.1900	−1.11850	−0.559250	−	0.828999i	$-0.688911\pi$
$83$	−10.1900	−1.11850	−0.559250	+	0.828999i	$0.688911\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−9.09501	−0.975088
$88$	0	0
$89$	3.74489	0.396958	0.198479	−	0.980105i	$-0.436400\pi$
$89$	3.74489	0.396958	0.198479	+	0.980105i	$0.436400\pi$
$90$	0	0
$91$	4.83991	0.507360
$92$	0	0
$93$	0.510210	0.0529063
$94$	0	0
$95$	0	0
$96$	0	0
$97$	12.5197	1.27119	0.635593	−	0.772025i	$-0.280756\pi$
$97$	12.5197	1.27119	0.635593	+	0.772025i	$0.280756\pi$
$98$	0	0
$99$	2.25511	0.226647
$100$	0	0
$101$	−17.6052	−1.75179	−0.875893	−	0.482506i	$-0.839727\pi$
$101$	−17.6052	−1.75179	−0.875893	+	0.482506i	$0.839727\pi$
$102$	0	0
$103$	17.1696	1.69177	0.845886	−	0.533364i	$-0.179072\pi$
$103$	17.1696	1.69177	0.845886	+	0.533364i	$0.179072\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−6.91450	−0.668450	−0.334225	−	0.942493i	$-0.608475\pi$
$107$	−6.91450	−0.668450	−0.334225	+	0.942493i	$0.608475\pi$
$108$	0	0
$109$	3.41520	0.327117	0.163558	−	0.986534i	$-0.447703\pi$
$109$	3.41520	0.327117	0.163558	+	0.986534i	$0.447703\pi$
$110$	0	0
$111$	4.25511	0.403877
$112$	0	0
$113$	−5.09501	−0.479299	−0.239649	−	0.970860i	$-0.577032\pi$
$113$	−5.09501	−0.479299	−0.239649	+	0.970860i	$0.577032\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	1.00000	0.0924500
$118$	0	0
$119$	−30.6352	−2.80832
$120$	0	0
$121$	−5.91450	−0.537682
$122$	0	0
$123$	−0.255105	−0.0230020
$124$	0	0
$125$	0	0
$126$	0	0
$127$	12.6594	1.12334	0.561670	−	0.827361i	$-0.310159\pi$
$127$	12.6594	1.12334	0.561670	+	0.827361i	$0.310159\pi$
$128$	0	0
$129$	9.16961	0.807339
$130$	0	0
$131$	−16.7748	−1.46562	−0.732812	−	0.680431i	$-0.761792\pi$
$131$	−16.7748	−1.46562	−0.732812	+	0.680431i	$0.761792\pi$
$132$	0	0
$133$	−12.5102	−1.08477
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	0	0
$139$	5.23468	0.444000	0.222000	−	0.975047i	$-0.428741\pi$
$139$	5.23468	0.444000	0.222000	+	0.975047i	$0.428741\pi$
$140$	0	0
$141$	−4.51021	−0.379828
$142$	0	0
$143$	2.25511	0.188581
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−16.4247	−1.35469
$148$	0	0
$149$	3.74489	0.306794	0.153397	−	0.988165i	$-0.450979\pi$
$149$	3.74489	0.306794	0.153397	+	0.988165i	$0.450979\pi$
$150$	0	0
$151$	15.3596	1.24995	0.624975	−	0.780645i	$-0.285109\pi$
$151$	15.3596	1.24995	0.624975	+	0.780645i	$0.285109\pi$
$152$	0	0
$153$	−6.32970	−0.511726
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−0.979580	−0.0781790	−0.0390895	−	0.999236i	$-0.512446\pi$
$157$	−0.979580	−0.0781790	−0.0390895	+	0.999236i	$0.512446\pi$
$158$	0	0
$159$	−9.93492	−0.787891
$160$	0	0
$161$	−23.4247	−1.84613
$162$	0	0
$163$	−7.42471	−0.581548	−0.290774	−	0.956792i	$-0.593913\pi$
$163$	−7.42471	−0.581548	−0.290774	+	0.956792i	$0.593913\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	21.1696	1.63815	0.819077	−	0.573684i	$-0.194486\pi$
$167$	21.1696	1.63815	0.819077	+	0.573684i	$0.194486\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−2.58480	−0.197665
$172$	0	0
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−14.1900	−1.06659
$178$	0	0
$179$	8.77483	0.655862	0.327931	−	0.944702i	$-0.393649\pi$
$179$	8.77483	0.655862	0.327931	+	0.944702i	$0.393649\pi$
$180$	0	0
$181$	23.1045	1.71735	0.858673	−	0.512524i	$-0.171289\pi$
$181$	23.1045	1.71735	0.858673	+	0.512524i	$0.171289\pi$
$182$	0	0
$183$	−9.93492	−0.734411
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−14.2741	−1.04383
$188$	0	0
$189$	−4.83991	−0.352052
$190$	0	0
$191$	19.3596	1.40081	0.700407	−	0.713744i	$-0.253002\pi$
$191$	19.3596	1.40081	0.700407	+	0.713744i	$0.253002\pi$
$192$	0	0
$193$	−6.18051	−0.444883	−0.222441	−	0.974946i	$-0.571403\pi$
$193$	−6.18051	−0.444883	−0.222441	+	0.974946i	$0.571403\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−21.8698	−1.55816	−0.779081	−	0.626923i	$-0.784314\pi$
$197$	−21.8698	−1.55816	−0.779081	+	0.626923i	$0.784314\pi$
$198$	0	0
$199$	2.83039	0.200641	0.100321	−	0.994955i	$-0.468013\pi$
$199$	2.83039	0.200641	0.100321	+	0.994955i	$0.468013\pi$
$200$	0	0
$201$	−13.1696	−0.928912
$202$	0	0
$203$	44.0190	3.08953
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−4.83991	−0.336397
$208$	0	0
$209$	−5.82900	−0.403201
$210$	0	0
$211$	−22.3392	−1.53789	−0.768947	−	0.639312i	$-0.779219\pi$
$211$	−22.3392	−1.53789	−0.768947	+	0.639312i	$0.779219\pi$
$212$	0	0
$213$	5.74489	0.393634
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−2.46937	−0.167632
$218$	0	0
$219$	2.90499	0.196301
$220$	0	0
$221$	−6.32970	−0.425782
$222$	0	0
$223$	23.0950	1.54656	0.773278	−	0.634067i	$-0.218616\pi$
$223$	23.0950	1.54656	0.773278	+	0.634067i	$0.218616\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0.510210	0.0338638	0.0169319	−	0.999857i	$-0.494610\pi$
$227$	0.510210	0.0338638	0.0169319	+	0.999857i	$0.494610\pi$
$228$	0	0
$229$	−1.09501	−0.0723605	−0.0361803	−	0.999345i	$-0.511519\pi$
$229$	−1.09501	−0.0723605	−0.0361803	+	0.999345i	$0.511519\pi$
$230$	0	0
$231$	−10.9145	−0.718121
$232$	0	0
$233$	−1.81949	−0.119199	−0.0595993	−	0.998222i	$-0.518982\pi$
$233$	−1.81949	−0.119199	−0.0595993	+	0.998222i	$0.518982\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−5.74489	−0.373171
$238$	0	0
$239$	8.44513	0.546270	0.273135	−	0.961976i	$-0.411939\pi$
$239$	8.44513	0.546270	0.273135	+	0.961976i	$0.411939\pi$
$240$	0	0
$241$	20.3392	1.31016	0.655082	−	0.755558i	$-0.272634\pi$
$241$	20.3392	1.31016	0.655082	+	0.755558i	$0.272634\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−2.58480	−0.164467
$248$	0	0
$249$	10.1900	0.645767
$250$	0	0
$251$	−17.4342	−1.10044	−0.550219	−	0.835020i	$-0.685456\pi$
$251$	−17.4342	−1.10044	−0.550219	+	0.835020i	$0.685456\pi$
$252$	0	0
$253$	−10.9145	−0.686189
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−15.4342	−0.962761	−0.481380	−	0.876512i	$-0.659864\pi$
$257$	−15.4342	−0.962761	−0.481380	+	0.876512i	$0.659864\pi$
$258$	0	0
$259$	−20.5943	−1.27967
$260$	0	0
$261$	9.09501	0.562967
$262$	0	0
$263$	8.90499	0.549105	0.274553	−	0.961572i	$-0.411470\pi$
$263$	8.90499	0.549105	0.274553	+	0.961572i	$0.411470\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−3.74489	−0.229184
$268$	0	0
$269$	−16.5848	−1.01119	−0.505597	−	0.862770i	$-0.668728\pi$
$269$	−16.5848	−1.01119	−0.505597	+	0.862770i	$0.668728\pi$
$270$	0	0
$271$	17.8290	1.08303	0.541517	−	0.840690i	$-0.317850\pi$
$271$	17.8290	1.08303	0.541517	+	0.840690i	$0.317850\pi$
$272$	0	0
$273$	−4.83991	−0.292925
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−22.3801	−1.34469	−0.672344	−	0.740239i	$-0.734712\pi$
$277$	−22.3801	−1.34469	−0.672344	+	0.740239i	$0.734712\pi$
$278$	0	0
$279$	−0.510210	−0.0305455
$280$	0	0
$281$	−24.1900	−1.44306	−0.721528	−	0.692385i	$-0.756560\pi$
$281$	−24.1900	−1.44306	−0.721528	+	0.692385i	$0.756560\pi$
$282$	0	0
$283$	26.1900	1.55684	0.778418	−	0.627747i	$-0.216023\pi$
$283$	26.1900	1.55684	0.778418	+	0.627747i	$0.216023\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	1.23468	0.0728811
$288$	0	0
$289$	23.0651	1.35677
$290$	0	0
$291$	−12.5197	−0.733919
$292$	0	0
$293$	5.48979	0.320717	0.160358	−	0.987059i	$-0.448735\pi$
$293$	5.48979	0.320717	0.160358	+	0.987059i	$0.448735\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−2.25511	−0.130854
$298$	0	0
$299$	−4.83991	−0.279899
$300$	0	0
$301$	−44.3801	−2.55802
$302$	0	0
$303$	17.6052	1.01139
$304$	0	0
$305$	0	0
$306$	0	0
$307$	6.76532	0.386117	0.193058	−	0.981187i	$-0.438159\pi$
$307$	6.76532	0.386117	0.193058	+	0.981187i	$0.438159\pi$
$308$	0	0
$309$	−17.1696	−0.976745
$310$	0	0
$311$	−17.0204	−0.965139	−0.482570	−	0.875858i	$-0.660297\pi$
$311$	−17.0204	−0.965139	−0.482570	+	0.875858i	$0.660297\pi$
$312$	0	0
$313$	−12.8304	−0.725217	−0.362608	−	0.931942i	$-0.618114\pi$
$313$	−12.8304	−0.725217	−0.362608	+	0.931942i	$0.618114\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	13.4898	0.757662	0.378831	−	0.925466i	$-0.376326\pi$
$317$	13.4898	0.757662	0.378831	+	0.925466i	$0.376326\pi$
$318$	0	0
$319$	20.5102	1.14835
$320$	0	0
$321$	6.91450	0.385930
$322$	0	0
$323$	16.3610	0.910352
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−3.41520	−0.188861
$328$	0	0
$329$	21.8290	1.20347
$330$	0	0
$331$	−14.0746	−0.773610	−0.386805	−	0.922162i	$-0.626421\pi$
$331$	−14.0746	−0.773610	−0.386805	+	0.922162i	$0.626421\pi$
$332$	0	0
$333$	−4.25511	−0.233178
$334$	0	0
$335$	0	0
$336$	0	0
$337$	22.6594	1.23434	0.617168	−	0.786831i	$-0.288280\pi$
$337$	22.6594	1.23434	0.617168	+	0.786831i	$0.288280\pi$
$338$	0	0
$339$	5.09501	0.276723
$340$	0	0
$341$	−1.15058	−0.0623073
$342$	0	0
$343$	45.6147	2.46296
$344$	0	0
$345$	0	0
$346$	0	0
$347$	8.59432	0.461367	0.230684	−	0.973029i	$-0.425904\pi$
$347$	8.59432	0.461367	0.230684	+	0.973029i	$0.425904\pi$
$348$	0	0
$349$	−23.9444	−1.28172	−0.640858	−	0.767659i	$-0.721421\pi$
$349$	−23.9444	−1.28172	−0.640858	+	0.767659i	$0.721421\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	30.6352	1.62138
$358$	0	0
$359$	−1.80997	−0.0955268	−0.0477634	−	0.998859i	$-0.515209\pi$
$359$	−1.80997	−0.0955268	−0.0477634	+	0.998859i	$0.515209\pi$
$360$	0	0
$361$	−12.3188	−0.648358
$362$	0	0
$363$	5.91450	0.310431
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−9.16961	−0.478650	−0.239325	−	0.970940i	$-0.576926\pi$
$367$	−9.16961	−0.478650	−0.239325	+	0.970940i	$0.576926\pi$
$368$	0	0
$369$	0.255105	0.0132802
$370$	0	0
$371$	48.0841	2.49640
$372$	0	0
$373$	28.8494	1.49377	0.746883	−	0.664955i	$-0.231549\pi$
$373$	28.8494	1.49377	0.746883	+	0.664955i	$0.231549\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	9.09501	0.468417
$378$	0	0
$379$	21.9444	1.12721	0.563605	−	0.826044i	$-0.309414\pi$
$379$	21.9444	1.12721	0.563605	+	0.826044i	$0.309414\pi$
$380$	0	0
$381$	−12.6594	−0.648561
$382$	0	0
$383$	6.32018	0.322946	0.161473	−	0.986877i	$-0.448375\pi$
$383$	6.32018	0.322946	0.161473	+	0.986877i	$0.448375\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−9.16961	−0.466117
$388$	0	0
$389$	−17.6052	−0.892620	−0.446310	−	0.894878i	$-0.647262\pi$
$389$	−17.6052	−0.892620	−0.446310	+	0.894878i	$0.647262\pi$
$390$	0	0
$391$	30.6352	1.54929
$392$	0	0
$393$	16.7748	0.846178
$394$	0	0
$395$	0	0
$396$	0	0
$397$	30.0841	1.50988	0.754939	−	0.655795i	$-0.227666\pi$
$397$	30.0841	1.50988	0.754939	+	0.655795i	$0.227666\pi$
$398$	0	0
$399$	12.5102	0.626294
$400$	0	0
$401$	22.5292	1.12506	0.562528	−	0.826778i	$-0.309829\pi$
$401$	22.5292	1.12506	0.562528	+	0.826778i	$0.309829\pi$
$402$	0	0
$403$	−0.510210	−0.0254154
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−9.59571	−0.475642
$408$	0	0
$409$	23.1696	1.14566	0.572832	−	0.819673i	$-0.305845\pi$
$409$	23.1696	1.14566	0.572832	+	0.819673i	$0.305845\pi$
$410$	0	0
$411$	2.00000	0.0986527
$412$	0	0
$413$	68.6784	3.37944
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−5.23468	−0.256344
$418$	0	0
$419$	9.56438	0.467251	0.233625	−	0.972327i	$-0.424941\pi$
$419$	9.56438	0.467251	0.233625	+	0.972327i	$0.424941\pi$
$420$	0	0
$421$	−35.7952	−1.74455	−0.872277	−	0.489012i	$-0.837357\pi$
$421$	−35.7952	−1.74455	−0.872277	+	0.489012i	$0.837357\pi$
$422$	0	0
$423$	4.51021	0.219294
$424$	0	0
$425$	0	0
$426$	0	0
$427$	48.0841	2.32695
$428$	0	0
$429$	−2.25511	−0.108877
$430$	0	0
$431$	28.3801	1.36702	0.683510	−	0.729942i	$-0.260453\pi$
$431$	28.3801	1.36702	0.683510	+	0.729942i	$0.260453\pi$
$432$	0	0
$433$	−19.6798	−0.945752	−0.472876	−	0.881129i	$-0.656784\pi$
$433$	−19.6798	−0.945752	−0.472876	+	0.881129i	$0.656784\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	12.5102	0.598445
$438$	0	0
$439$	33.7639	1.61146	0.805732	−	0.592280i	$-0.201772\pi$
$439$	33.7639	1.61146	0.805732	+	0.592280i	$0.201772\pi$
$440$	0	0
$441$	16.4247	0.782129
$442$	0	0
$443$	−29.1045	−1.38280	−0.691399	−	0.722473i	$-0.743005\pi$
$443$	−29.1045	−1.38280	−0.691399	+	0.722473i	$0.743005\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−3.74489	−0.177127
$448$	0	0
$449$	−22.4642	−1.06015	−0.530075	−	0.847951i	$-0.677836\pi$
$449$	−22.4642	−1.06015	−0.530075	+	0.847951i	$0.677836\pi$
$450$	0	0
$451$	0.575289	0.0270893
$452$	0	0
$453$	−15.3596	−0.721659
$454$	0	0
$455$	0	0
$456$	0	0
$457$	11.4993	0.537915	0.268957	−	0.963152i	$-0.413321\pi$
$457$	11.4993	0.537915	0.268957	+	0.963152i	$0.413321\pi$
$458$	0	0
$459$	6.32970	0.295445
$460$	0	0
$461$	16.7843	0.781725	0.390862	−	0.920449i	$-0.372177\pi$
$461$	16.7843	0.781725	0.390862	+	0.920449i	$0.372177\pi$
$462$	0	0
$463$	−19.6893	−0.915041	−0.457520	−	0.889199i	$-0.651262\pi$
$463$	−19.6893	−0.915041	−0.457520	+	0.889199i	$0.651262\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	1.38387	0.0640379	0.0320190	−	0.999487i	$-0.489806\pi$
$467$	1.38387	0.0640379	0.0320190	+	0.999487i	$0.489806\pi$
$468$	0	0
$469$	63.7397	2.94323
$470$	0	0
$471$	0.979580	0.0451367
$472$	0	0
$473$	−20.6784	−0.950795
$474$	0	0
$475$	0	0
$476$	0	0
$477$	9.93492	0.454889
$478$	0	0
$479$	28.9553	1.32300	0.661502	−	0.749944i	$-0.269919\pi$
$479$	28.9553	1.32300	0.661502	+	0.749944i	$0.269919\pi$
$480$	0	0
$481$	−4.25511	−0.194016
$482$	0	0
$483$	23.4247	1.06586
$484$	0	0
$485$	0	0
$486$	0	0
$487$	26.3705	1.19496	0.597482	−	0.801883i	$-0.296168\pi$
$487$	26.3705	1.19496	0.597482	+	0.801883i	$0.296168\pi$
$488$	0	0
$489$	7.42471	0.335757
$490$	0	0
$491$	5.05417	0.228092	0.114046	−	0.993475i	$-0.463619\pi$
$491$	5.05417	0.228092	0.114046	+	0.993475i	$0.463619\pi$
$492$	0	0
$493$	−57.5687	−2.59276
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−27.8048	−1.24721
$498$	0	0
$499$	−15.7544	−0.705264	−0.352632	−	0.935762i	$-0.614713\pi$
$499$	−15.7544	−0.705264	−0.352632	+	0.935762i	$0.614713\pi$
$500$	0	0
$501$	−21.1696	−0.945788
$502$	0	0
$503$	9.92541	0.442552	0.221276	−	0.975211i	$-0.428978\pi$
$503$	9.92541	0.442552	0.221276	+	0.975211i	$0.428978\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−1.00000	−0.0444116
$508$	0	0
$509$	−25.4247	−1.12693	−0.563465	−	0.826140i	$-0.690532\pi$
$509$	−25.4247	−1.12693	−0.563465	+	0.826140i	$0.690532\pi$
$510$	0	0
$511$	−14.0599	−0.621972
$512$	0	0
$513$	2.58480	0.114122
$514$	0	0
$515$	0	0
$516$	0	0
$517$	10.1710	0.447320
$518$	0	0
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−14.5292	−0.636538	−0.318269	−	0.948001i	$-0.603101\pi$
$521$	−14.5292	−0.636538	−0.318269	+	0.948001i	$0.603101\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	3.22948	0.140678
$528$	0	0
$529$	0.424711	0.0184657
$530$	0	0
$531$	14.1900	0.615795
$532$	0	0
$533$	0.255105	0.0110498
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−8.77483	−0.378662
$538$	0	0
$539$	37.0394	1.59540
$540$	0	0
$541$	6.11543	0.262923	0.131462	−	0.991321i	$-0.458033\pi$
$541$	6.11543	0.262923	0.131462	+	0.991321i	$0.458033\pi$
$542$	0	0
$543$	−23.1045	−0.991510
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−15.3596	−0.656730	−0.328365	−	0.944551i	$-0.606498\pi$
$547$	−15.3596	−0.656730	−0.328365	+	0.944551i	$0.606498\pi$
$548$	0	0
$549$	9.93492	0.424012
$550$	0	0
$551$	−23.5088	−1.00151
$552$	0	0
$553$	27.8048	1.18238
$554$	0	0
$555$	0	0
$556$	0	0
$557$	22.3801	0.948273	0.474137	−	0.880451i	$-0.342760\pi$
$557$	22.3801	0.948273	0.474137	+	0.880451i	$0.342760\pi$
$558$	0	0
$559$	−9.16961	−0.387833
$560$	0	0
$561$	14.2741	0.602654
$562$	0	0
$563$	−17.7449	−0.747858	−0.373929	−	0.927457i	$-0.621990\pi$
$563$	−17.7449	−0.747858	−0.373929	+	0.927457i	$0.621990\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	4.83991	0.203257
$568$	0	0
$569$	−10.0190	−0.420020	−0.210010	−	0.977699i	$-0.567350\pi$
$569$	−10.0190	−0.420020	−0.210010	+	0.977699i	$0.567350\pi$
$570$	0	0
$571$	−17.6147	−0.737154	−0.368577	−	0.929597i	$-0.620155\pi$
$571$	−17.6147	−0.737154	−0.368577	+	0.929597i	$0.620155\pi$
$572$	0	0
$573$	−19.3596	−0.808760
$574$	0	0
$575$	0	0
$576$	0	0
$577$	15.3501	0.639034	0.319517	−	0.947581i	$-0.396479\pi$
$577$	15.3501	0.639034	0.319517	+	0.947581i	$0.396479\pi$
$578$	0	0
$579$	6.18051	0.256853
$580$	0	0
$581$	−49.3188	−2.04609
$582$	0	0
$583$	22.4043	0.927891
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−23.4898	−0.969527	−0.484764	−	0.874645i	$-0.661094\pi$
$587$	−23.4898	−0.969527	−0.484764	+	0.874645i	$0.661094\pi$
$588$	0	0
$589$	1.31879	0.0543399
$590$	0	0
$591$	21.8698	0.899605
$592$	0	0
$593$	5.63898	0.231565	0.115782	−	0.993275i	$-0.463062\pi$
$593$	5.63898	0.231565	0.115782	+	0.993275i	$0.463062\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−2.83039	−0.115840
$598$	0	0
$599$	−10.0408	−0.410258	−0.205129	−	0.978735i	$-0.565761\pi$
$599$	−10.0408	−0.410258	−0.205129	+	0.978735i	$0.565761\pi$
$600$	0	0
$601$	5.04466	0.205776	0.102888	−	0.994693i	$-0.467192\pi$
$601$	5.04466	0.205776	0.102888	+	0.994693i	$0.467192\pi$
$602$	0	0
$603$	13.1696	0.536308
$604$	0	0
$605$	0	0
$606$	0	0
$607$	2.19003	0.0888904	0.0444452	−	0.999012i	$-0.485848\pi$
$607$	2.19003	0.0888904	0.0444452	+	0.999012i	$0.485848\pi$
$608$	0	0
$609$	−44.0190	−1.78374
$610$	0	0
$611$	4.51021	0.182464
$612$	0	0
$613$	−45.4437	−1.83546	−0.917728	−	0.397210i	$-0.869978\pi$
$613$	−45.4437	−1.83546	−0.917728	+	0.397210i	$0.869978\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	7.31879	0.294643	0.147322	−	0.989089i	$-0.452935\pi$
$617$	7.31879	0.294643	0.147322	+	0.989089i	$0.452935\pi$
$618$	0	0
$619$	20.6256	0.829015	0.414507	−	0.910046i	$-0.363954\pi$
$619$	20.6256	0.829015	0.414507	+	0.910046i	$0.363954\pi$
$620$	0	0
$621$	4.83991	0.194219
$622$	0	0
$623$	18.1249	0.726161
$624$	0	0
$625$	0	0
$626$	0	0
$627$	5.82900	0.232788
$628$	0	0
$629$	26.9335	1.07391
$630$	0	0
$631$	14.8304	0.590389	0.295194	−	0.955437i	$-0.404616\pi$
$631$	14.8304	0.590389	0.295194	+	0.955437i	$0.404616\pi$
$632$	0	0
$633$	22.3392	0.887904
$634$	0	0
$635$	0	0
$636$	0	0
$637$	16.4247	0.650771
$638$	0	0
$639$	−5.74489	−0.227265
$640$	0	0
$641$	−28.8494	−1.13948	−0.569742	−	0.821824i	$-0.692957\pi$
$641$	−28.8494	−1.13948	−0.569742	+	0.821824i	$0.692957\pi$
$642$	0	0
$643$	29.7449	1.17302	0.586512	−	0.809940i	$-0.300501\pi$
$643$	29.7449	1.17302	0.586512	+	0.809940i	$0.300501\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−2.13967	−0.0841192	−0.0420596	−	0.999115i	$-0.513392\pi$
$647$	−2.13967	−0.0841192	−0.0420596	+	0.999115i	$0.513392\pi$
$648$	0	0
$649$	32.0000	1.25611
$650$	0	0
$651$	2.46937	0.0967822
$652$	0	0
$653$	13.2104	0.516965	0.258482	−	0.966016i	$-0.416778\pi$
$653$	13.2104	0.516965	0.258482	+	0.966016i	$0.416778\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−2.90499	−0.113334
$658$	0	0
$659$	−48.6447	−1.89493	−0.947464	−	0.319863i	$-0.896363\pi$
$659$	−48.6447	−1.89493	−0.947464	+	0.319863i	$0.896363\pi$
$660$	0	0
$661$	−24.7340	−0.962041	−0.481020	−	0.876709i	$-0.659734\pi$
$661$	−24.7340	−0.962041	−0.481020	+	0.876709i	$0.659734\pi$
$662$	0	0
$663$	6.32970	0.245825
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−44.0190	−1.70442
$668$	0	0
$669$	−23.0950	−0.892905
$670$	0	0
$671$	22.4043	0.864908
$672$	0	0
$673$	−39.6988	−1.53028	−0.765139	−	0.643865i	$-0.777330\pi$
$673$	−39.6988	−1.53028	−0.765139	+	0.643865i	$0.777330\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−28.5535	−1.09740	−0.548700	−	0.836020i	$-0.684877\pi$
$677$	−28.5535	−1.09740	−0.548700	+	0.836020i	$0.684877\pi$
$678$	0	0
$679$	60.5943	2.32540
$680$	0	0
$681$	−0.510210	−0.0195513
$682$	0	0
$683$	−15.8508	−0.606515	−0.303257	−	0.952909i	$-0.598074\pi$
$683$	−15.8508	−0.606515	−0.303257	+	0.952909i	$0.598074\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	1.09501	0.0417774
$688$	0	0
$689$	9.93492	0.378490
$690$	0	0
$691$	−28.6256	−1.08897	−0.544485	−	0.838770i	$-0.683275\pi$
$691$	−28.6256	−1.08897	−0.544485	+	0.838770i	$0.683275\pi$
$692$	0	0
$693$	10.9145	0.414608
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−1.61474	−0.0611626
$698$	0	0
$699$	1.81949	0.0688194
$700$	0	0
$701$	−8.58480	−0.324244	−0.162122	−	0.986771i	$-0.551834\pi$
$701$	−8.58480	−0.324244	−0.162122	+	0.986771i	$0.551834\pi$
$702$	0	0
$703$	10.9986	0.414820
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−85.2077	−3.20456
$708$	0	0
$709$	−3.56438	−0.133863	−0.0669316	−	0.997758i	$-0.521321\pi$
$709$	−3.56438	−0.133863	−0.0669316	+	0.997758i	$0.521321\pi$
$710$	0	0
$711$	5.74489	0.215450
$712$	0	0
$713$	2.46937	0.0924786
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−8.44513	−0.315389
$718$	0	0
$719$	22.1900	0.827548	0.413774	−	0.910380i	$-0.364210\pi$
$719$	22.1900	0.827548	0.413774	+	0.910380i	$0.364210\pi$
$720$	0	0
$721$	83.0993	3.09478
$722$	0	0
$723$	−20.3392	−0.756423
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−9.82900	−0.364538	−0.182269	−	0.983249i	$-0.558344\pi$
$727$	−9.82900	−0.364538	−0.182269	+	0.983249i	$0.558344\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	58.0408	2.14672
$732$	0	0
$733$	29.0637	1.07349	0.536746	−	0.843744i	$-0.319653\pi$
$733$	29.0637	1.07349	0.536746	+	0.843744i	$0.319653\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	29.6988	1.09397
$738$	0	0
$739$	28.9240	1.06399	0.531994	−	0.846748i	$-0.321443\pi$
$739$	28.9240	1.06399	0.531994	+	0.846748i	$0.321443\pi$
$740$	0	0
$741$	2.58480	0.0949551
$742$	0	0
$743$	20.0190	0.734427	0.367213	−	0.930137i	$-0.380312\pi$
$743$	20.0190	0.734427	0.367213	+	0.930137i	$0.380312\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−10.1900	−0.372834
$748$	0	0
$749$	−33.4656	−1.22280
$750$	0	0
$751$	−22.2741	−0.812795	−0.406397	−	0.913696i	$-0.633215\pi$
$751$	−22.2741	−0.812795	−0.406397	+	0.913696i	$0.633215\pi$
$752$	0	0
$753$	17.4342	0.635339
$754$	0	0
$755$	0	0
$756$	0	0
$757$	23.1886	0.842805	0.421403	−	0.906874i	$-0.361538\pi$
$757$	23.1886	0.842805	0.421403	+	0.906874i	$0.361538\pi$
$758$	0	0
$759$	10.9145	0.396171
$760$	0	0
$761$	47.5497	1.72367	0.861837	−	0.507186i	$-0.169314\pi$
$761$	47.5497	1.72367	0.861837	+	0.507186i	$0.169314\pi$
$762$	0	0
$763$	16.5292	0.598399
$764$	0	0
$765$	0	0
$766$	0	0
$767$	14.1900	0.512372
$768$	0	0
$769$	−21.8698	−0.788647	−0.394323	−	0.918972i	$-0.629021\pi$
$769$	−21.8698	−0.788647	−0.394323	+	0.918972i	$0.629021\pi$
$770$	0	0
$771$	15.4342	0.555850
$772$	0	0
$773$	8.84942	0.318292	0.159146	−	0.987255i	$-0.449126\pi$
$773$	8.84942	0.318292	0.159146	+	0.987255i	$0.449126\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	20.5943	0.738817
$778$	0	0
$779$	−0.659396	−0.0236253
$780$	0	0
$781$	−12.9553	−0.463579
$782$	0	0
$783$	−9.09501	−0.325029
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−9.02042	−0.321543	−0.160772	−	0.986992i	$-0.551398\pi$
$787$	−9.02042	−0.321543	−0.160772	+	0.986992i	$0.551398\pi$
$788$	0	0
$789$	−8.90499	−0.317026
$790$	0	0
$791$	−24.6594	−0.876787
$792$	0	0
$793$	9.93492	0.352799
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−9.55487	−0.338451	−0.169225	−	0.985577i	$-0.554127\pi$
$797$	−9.55487	−0.338451	−0.169225	+	0.985577i	$0.554127\pi$
$798$	0	0
$799$	−28.5483	−1.00997
$800$	0	0
$801$	3.74489	0.132319
$802$	0	0
$803$	−6.55105	−0.231182
$804$	0	0
$805$	0	0
$806$	0	0
$807$	16.5848	0.583813
$808$	0	0
$809$	53.3596	1.87602	0.938012	−	0.346602i	$-0.112664\pi$
$809$	53.3596	1.87602	0.938012	+	0.346602i	$0.112664\pi$
$810$	0	0
$811$	10.9458	0.384360	0.192180	−	0.981360i	$-0.438444\pi$
$811$	10.9458	0.384360	0.192180	+	0.981360i	$0.438444\pi$
$812$	0	0
$813$	−17.8290	−0.625290
$814$	0	0
$815$	0	0
$816$	0	0
$817$	23.7016	0.829215
$818$	0	0
$819$	4.83991	0.169120
$820$	0	0
$821$	35.6147	1.24296	0.621481	−	0.783429i	$-0.286531\pi$
$821$	35.6147	1.24296	0.621481	+	0.783429i	$0.286531\pi$
$822$	0	0
$823$	−10.1900	−0.355202	−0.177601	−	0.984103i	$-0.556834\pi$
$823$	−10.1900	−0.355202	−0.177601	+	0.984103i	$0.556834\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	25.0394	0.870707	0.435353	−	0.900260i	$-0.356623\pi$
$827$	25.0394	0.870707	0.435353	+	0.900260i	$0.356623\pi$
$828$	0	0
$829$	−36.3392	−1.26211	−0.631057	−	0.775737i	$-0.717378\pi$
$829$	−36.3392	−1.26211	−0.631057	+	0.775737i	$0.717378\pi$
$830$	0	0
$831$	22.3801	0.776355
$832$	0	0
$833$	−103.963	−3.60212
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0.510210	0.0176354
$838$	0	0
$839$	38.4043	1.32586	0.662932	−	0.748680i	$-0.269312\pi$
$839$	38.4043	1.32586	0.662932	+	0.748680i	$0.269312\pi$
$840$	0	0
$841$	53.7193	1.85239
$842$	0	0
$843$	24.1900	0.833149
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−28.6256	−0.983589
$848$	0	0
$849$	−26.1900	−0.898839
$850$	0	0
$851$	20.5943	0.705964
$852$	0	0
$853$	−22.7245	−0.778071	−0.389036	−	0.921223i	$-0.627192\pi$
$853$	−22.7245	−0.778071	−0.389036	+	0.921223i	$0.627192\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	10.3297	0.352856	0.176428	−	0.984314i	$-0.443546\pi$
$857$	10.3297	0.352856	0.176428	+	0.984314i	$0.443546\pi$
$858$	0	0
$859$	2.40429	0.0820334	0.0410167	−	0.999158i	$-0.486940\pi$
$859$	2.40429	0.0820334	0.0410167	+	0.999158i	$0.486940\pi$
$860$	0	0
$861$	−1.23468	−0.0420779
$862$	0	0
$863$	−17.6798	−0.601828	−0.300914	−	0.953651i	$-0.597292\pi$
$863$	−17.6798	−0.601828	−0.300914	+	0.953651i	$0.597292\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−23.0651	−0.783331
$868$	0	0
$869$	12.9553	0.439480
$870$	0	0
$871$	13.1696	0.446235
$872$	0	0
$873$	12.5197	0.423728
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−50.7601	−1.71405	−0.857023	−	0.515277i	$-0.827689\pi$
$877$	−50.7601	−1.71405	−0.857023	+	0.515277i	$0.827689\pi$
$878$	0	0
$879$	−5.48979	−0.185166
$880$	0	0
$881$	−49.5905	−1.67075	−0.835373	−	0.549683i	$-0.814748\pi$
$881$	−49.5905	−1.67075	−0.835373	+	0.549683i	$0.814748\pi$
$882$	0	0
$883$	−21.3188	−0.717434	−0.358717	−	0.933446i	$-0.616786\pi$
$883$	−21.3188	−0.717434	−0.358717	+	0.933446i	$0.616786\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	16.9891	0.570438	0.285219	−	0.958462i	$-0.407934\pi$
$887$	16.9891	0.570438	0.285219	+	0.958462i	$0.407934\pi$
$888$	0	0
$889$	61.2703	2.05494
$890$	0	0
$891$	2.25511	0.0755489
$892$	0	0
$893$	−11.6580	−0.390120
$894$	0	0
$895$	0	0
$896$	0	0
$897$	4.83991	0.161600
$898$	0	0
$899$	−4.64037	−0.154765
$900$	0	0
$901$	−62.8851	−2.09500
$902$	0	0
$903$	44.3801	1.47688
$904$	0	0
$905$	0	0
$906$	0	0
$907$	36.6594	1.21726	0.608628	−	0.793456i	$-0.291720\pi$
$907$	36.6594	1.21726	0.608628	+	0.793456i	$0.291720\pi$
$908$	0	0
$909$	−17.6052	−0.583928
$910$	0	0
$911$	22.1900	0.735188	0.367594	−	0.929986i	$-0.380182\pi$
$911$	22.1900	0.735188	0.367594	+	0.929986i	$0.380182\pi$
$912$	0	0
$913$	−22.9796	−0.760513
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−81.1886	−2.68108
$918$	0	0
$919$	25.5957	0.844325	0.422162	−	0.906520i	$-0.361271\pi$
$919$	25.5957	0.844325	0.422162	+	0.906520i	$0.361271\pi$
$920$	0	0
$921$	−6.76532	−0.222925
$922$	0	0
$923$	−5.74489	−0.189096
$924$	0	0
$925$	0	0
$926$	0	0
$927$	17.1696	0.563924
$928$	0	0
$929$	9.40568	0.308590	0.154295	−	0.988025i	$-0.450689\pi$
$929$	9.40568	0.308590	0.154295	+	0.988025i	$0.450689\pi$
$930$	0	0
$931$	−42.4546	−1.39139
$932$	0	0
$933$	17.0204	0.557224
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−50.7601	−1.65826	−0.829130	−	0.559056i	$-0.811164\pi$
$937$	−50.7601	−1.65826	−0.829130	+	0.559056i	$0.811164\pi$
$938$	0	0
$939$	12.8304	0.418704
$940$	0	0
$941$	−30.5943	−0.997346	−0.498673	−	0.866790i	$-0.666179\pi$
$941$	−30.5943	−0.997346	−0.498673	+	0.866790i	$0.666179\pi$
$942$	0	0
$943$	−1.23468	−0.0402069
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−7.12877	−0.231654	−0.115827	−	0.993269i	$-0.536952\pi$
$947$	−7.12877	−0.231654	−0.115827	+	0.993269i	$0.536952\pi$
$948$	0	0
$949$	−2.90499	−0.0942999
$950$	0	0
$951$	−13.4898	−0.437436
$952$	0	0
$953$	−3.99049	−0.129265	−0.0646323	−	0.997909i	$-0.520587\pi$
$953$	−3.99049	−0.129265	−0.0646323	+	0.997909i	$0.520587\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−20.5102	−0.663001
$958$	0	0
$959$	−9.67982	−0.312578
$960$	0	0
$961$	−30.7397	−0.991603
$962$	0	0
$963$	−6.91450	−0.222817
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−27.4751	−0.883539	−0.441769	−	0.897129i	$-0.645649\pi$
$967$	−27.4751	−0.883539	−0.441769	+	0.897129i	$0.645649\pi$
$968$	0	0
$969$	−16.3610	−0.525592
$970$	0	0
$971$	29.5834	0.949377	0.474688	−	0.880154i	$-0.342561\pi$
$971$	29.5834	0.949377	0.474688	+	0.880154i	$0.342561\pi$
$972$	0	0
$973$	25.3354	0.812215
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1.72066	0.0550487	0.0275243	−	0.999621i	$-0.491238\pi$
$977$	1.72066	0.0550487	0.0275243	+	0.999621i	$0.491238\pi$
$978$	0	0
$979$	8.44513	0.269908
$980$	0	0
$981$	3.41520	0.109039
$982$	0	0
$983$	−27.8889	−0.889517	−0.444758	−	0.895651i	$-0.646710\pi$
$983$	−27.8889	−0.889517	−0.444758	+	0.895651i	$0.646710\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−21.8290	−0.694825
$988$	0	0
$989$	44.3801	1.41120
$990$	0	0
$991$	45.6147	1.44900	0.724500	−	0.689275i	$-0.242071\pi$
$991$	45.6147	1.44900	0.724500	+	0.689275i	$0.242071\pi$
$992$	0	0
$993$	14.0746	0.446644
$994$	0	0
$995$	0	0
$996$	0	0
$997$	19.8290	0.627991	0.313995	−	0.949425i	$-0.398332\pi$
$997$	19.8290	0.627991	0.313995	+	0.949425i	$0.398332\pi$
$998$	0	0
$999$	4.25511	0.134626

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7800.2.a.bi.1.3		3
5.4	even	2		1560.2.a.q.1.1	✓	3
15.14	odd	2		4680.2.a.bh.1.1		3
20.19	odd	2		3120.2.a.bi.1.3		3
60.59	even	2		9360.2.a.cy.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.a.q.1.1	✓	3	5.4	even	2
3120.2.a.bi.1.3		3	20.19	odd	2
4680.2.a.bh.1.1		3	15.14	odd	2
7800.2.a.bi.1.3		3	1.1	even	1	trivial
9360.2.a.cy.1.3		3	60.59	even	2

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:	\( N \)	\(=\)	\( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7800.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +4.83991 q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +4.83991 q^{7} +1.00000 q^{9} +2.25511 q^{11} +1.00000 q^{13} -6.32970 q^{17} -2.58480 q^{19} -4.83991 q^{21} -4.83991 q^{23} -1.00000 q^{27} +9.09501 q^{29} -0.510210 q^{31} -2.25511 q^{33} -4.25511 q^{37} -1.00000 q^{39} +0.255105 q^{41} -9.16961 q^{43} +4.51021 q^{47} +16.4247 q^{49} +6.32970 q^{51} +9.93492 q^{53} +2.58480 q^{57} +14.1900 q^{59} +9.93492 q^{61} +4.83991 q^{63} +13.1696 q^{67} +4.83991 q^{69} -5.74489 q^{71} -2.90499 q^{73} +10.9145 q^{77} +5.74489 q^{79} +1.00000 q^{81} -10.1900 q^{83} -9.09501 q^{87} +3.74489 q^{89} +4.83991 q^{91} +0.510210 q^{93} +12.5197 q^{97} +2.25511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} - q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 - q^7 + 3 * q^9	\( 3 q - 3 q^{3} - q^{7} + 3 q^{9} + 5 q^{11} + 3 q^{13} - 7 q^{17} + 6 q^{19} + q^{21} + q^{23} - 3 q^{27} + 10 q^{29} + 2 q^{31} - 5 q^{33} - 11 q^{37} - 3 q^{39} - q^{41} + 10 q^{47} + 20 q^{49} + 7 q^{51} - 3 q^{53} - 6 q^{57} + 8 q^{59} - 3 q^{61} - q^{63} + 12 q^{67} - q^{69} - 19 q^{71} - 26 q^{73} + 7 q^{77} + 19 q^{79} + 3 q^{81} + 4 q^{83} - 10 q^{87} + 13 q^{89} - q^{91} - 2 q^{93} - 9 q^{97} + 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 - q^7 + 3 * q^9 + 5 * q^11 + 3 * q^13 - 7 * q^17 + 6 * q^19 + q^21 + q^23 - 3 * q^27 + 10 * q^29 + 2 * q^31 - 5 * q^33 - 11 * q^37 - 3 * q^39 - q^41 + 10 * q^47 + 20 * q^49 + 7 * q^51 - 3 * q^53 - 6 * q^57 + 8 * q^59 - 3 * q^61 - q^63 + 12 * q^67 - q^69 - 19 * q^71 - 26 * q^73 + 7 * q^77 + 19 * q^79 + 3 * q^81 + 4 * q^83 - 10 * q^87 + 13 * q^89 - q^91 - 2 * q^93 - 9 * q^97 + 5 * q^99

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