LMFDB - Embedded newform 7605.2.a.bq.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7605,2,Mod(1,7605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7605, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7605 = 3^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7605.a (trivial)

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:	yes
Analytic conductor:	$60.7262307372$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2535)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	7605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.445042 q^{2} -1.80194 q^{4} +1.00000 q^{5} -0.554958 q^{7} +1.69202 q^{8} +O(q^{10})$	$q-0.445042 q^{2} -1.80194 q^{4} +1.00000 q^{5} -0.554958 q^{7} +1.69202 q^{8} -0.445042 q^{10} -1.00000 q^{11} +0.246980 q^{14} +2.85086 q^{16} +3.10992 q^{17} +6.40581 q^{19} -1.80194 q^{20} +0.445042 q^{22} -3.24698 q^{23} +1.00000 q^{25} +1.00000 q^{28} -4.51573 q^{29} -7.09783 q^{31} -4.65279 q^{32} -1.38404 q^{34} -0.554958 q^{35} -3.58211 q^{37} -2.85086 q^{38} +1.69202 q^{40} -7.44504 q^{41} -5.44504 q^{43} +1.80194 q^{44} +1.44504 q^{46} -1.76271 q^{47} -6.69202 q^{49} -0.445042 q^{50} +7.92692 q^{53} -1.00000 q^{55} -0.939001 q^{56} +2.00969 q^{58} +4.71917 q^{59} +7.72886 q^{61} +3.15883 q^{62} -3.63102 q^{64} +2.14914 q^{67} -5.60388 q^{68} +0.246980 q^{70} +7.07606 q^{71} -12.0640 q^{73} +1.59419 q^{74} -11.5429 q^{76} +0.554958 q^{77} +1.48858 q^{79} +2.85086 q^{80} +3.31336 q^{82} +16.1196 q^{83} +3.10992 q^{85} +2.42327 q^{86} -1.69202 q^{88} -9.39373 q^{89} +5.85086 q^{92} +0.784479 q^{94} +6.40581 q^{95} +15.2935 q^{97} +2.97823 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - q^{4} + 3 q^{5} - 2 q^{7}+O(q^{10}) $ 3 * q - q^2 - q^4 + 3 * q^5 - 2 * q^7	$ 3 q - q^{2} - q^{4} + 3 q^{5} - 2 q^{7} - q^{10} - 3 q^{11} - 4 q^{14} - 5 q^{16} + 10 q^{17} + 6 q^{19} - q^{20} + q^{22} - 5 q^{23} + 3 q^{25} + 3 q^{28} - q^{29} - 3 q^{31} + 4 q^{32} + 6 q^{34} - 2 q^{35} - 5 q^{37} + 5 q^{38} - 22 q^{41} - 16 q^{43} + q^{44} + 4 q^{46} + 12 q^{47} - 15 q^{49} - q^{50} - 5 q^{53} - 3 q^{55} + 7 q^{56} - 16 q^{58} + 3 q^{59} - 10 q^{61} + q^{62} + 4 q^{64} + 20 q^{67} - 8 q^{68} - 4 q^{70} + 6 q^{71} - 2 q^{73} + 18 q^{74} - 16 q^{76} + 2 q^{77} - 2 q^{79} - 5 q^{80} + 12 q^{82} + 27 q^{83} + 10 q^{85} + 10 q^{86} + 4 q^{89} + 4 q^{92} - 18 q^{94} + 6 q^{95} - 9 q^{97} + 12 q^{98}+O(q^{100}) $ 3 * q - q^2 - q^4 + 3 * q^5 - 2 * q^7 - q^10 - 3 * q^11 - 4 * q^14 - 5 * q^16 + 10 * q^17 + 6 * q^19 - q^20 + q^22 - 5 * q^23 + 3 * q^25 + 3 * q^28 - q^29 - 3 * q^31 + 4 * q^32 + 6 * q^34 - 2 * q^35 - 5 * q^37 + 5 * q^38 - 22 * q^41 - 16 * q^43 + q^44 + 4 * q^46 + 12 * q^47 - 15 * q^49 - q^50 - 5 * q^53 - 3 * q^55 + 7 * q^56 - 16 * q^58 + 3 * q^59 - 10 * q^61 + q^62 + 4 * q^64 + 20 * q^67 - 8 * q^68 - 4 * q^70 + 6 * q^71 - 2 * q^73 + 18 * q^74 - 16 * q^76 + 2 * q^77 - 2 * q^79 - 5 * q^80 + 12 * q^82 + 27 * q^83 + 10 * q^85 + 10 * q^86 + 4 * q^89 + 4 * q^92 - 18 * q^94 + 6 * q^95 - 9 * q^97 + 12 * q^98

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 $

$2$	−0.445042	−0.314692	−0.157346	−	0.987544i	$-0.550294\pi$
$2$	−0.445042	−0.314692	−0.157346	+	0.987544i	$0.550294\pi$
$3$	0	0
$3$	0	0
$4$	−1.80194	−0.900969
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−0.554958	−0.209754	−0.104877	−	0.994485i	$-0.533445\pi$
$7$	−0.554958	−0.209754	−0.104877	+	0.994485i	$0.533445\pi$
$8$	1.69202	0.598220
$9$	0	0
$10$	−0.445042	−0.140735
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	0.246980	0.0660081
$15$	0	0
$16$	2.85086	0.712714
$17$	3.10992	0.754265	0.377133	−	0.926159i	$-0.376910\pi$
$17$	3.10992	0.754265	0.377133	+	0.926159i	$0.376910\pi$
$18$	0	0
$19$	6.40581	1.46959	0.734797	−	0.678287i	$-0.237277\pi$
$19$	6.40581	1.46959	0.734797	+	0.678287i	$0.237277\pi$
$20$	−1.80194	−0.402926
$21$	0	0
$22$	0.445042	0.0948832
$23$	−3.24698	−0.677042	−0.338521	−	0.940959i	$-0.609927\pi$
$23$	−3.24698	−0.677042	−0.338521	+	0.940959i	$0.609927\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	1.00000	0.188982
$29$	−4.51573	−0.838550	−0.419275	−	0.907859i	$-0.637716\pi$
$29$	−4.51573	−0.838550	−0.419275	+	0.907859i	$0.637716\pi$
$30$	0	0
$31$	−7.09783	−1.27481	−0.637404	−	0.770529i	$-0.719992\pi$
$31$	−7.09783	−1.27481	−0.637404	+	0.770529i	$0.719992\pi$
$32$	−4.65279	−0.822505
$33$	0	0
$34$	−1.38404	−0.237361
$35$	−0.554958	−0.0938050
$36$	0	0
$37$	−3.58211	−0.588894	−0.294447	−	0.955668i	$-0.595136\pi$
$37$	−3.58211	−0.588894	−0.294447	+	0.955668i	$0.595136\pi$
$38$	−2.85086	−0.462470
$39$	0	0
$40$	1.69202	0.267532
$41$	−7.44504	−1.16272	−0.581360	−	0.813646i	$-0.697479\pi$
$41$	−7.44504	−1.16272	−0.581360	+	0.813646i	$0.697479\pi$
$42$	0	0
$43$	−5.44504	−0.830361	−0.415181	−	0.909739i	$-0.636282\pi$
$43$	−5.44504	−0.830361	−0.415181	+	0.909739i	$0.636282\pi$
$44$	1.80194	0.271652
$45$	0	0
$46$	1.44504	0.213060
$47$	−1.76271	−0.257118	−0.128559	−	0.991702i	$-0.541035\pi$
$47$	−1.76271	−0.257118	−0.128559	+	0.991702i	$0.541035\pi$
$48$	0	0
$49$	−6.69202	−0.956003
$50$	−0.445042	−0.0629384
$51$	0	0
$52$	0	0
$53$	7.92692	1.08885	0.544423	−	0.838811i	$-0.316749\pi$
$53$	7.92692	1.08885	0.544423	+	0.838811i	$0.316749\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	−0.939001	−0.125479
$57$	0	0
$58$	2.00969	0.263885
$59$	4.71917	0.614383	0.307192	−	0.951648i	$-0.400611\pi$
$59$	4.71917	0.614383	0.307192	+	0.951648i	$0.400611\pi$
$60$	0	0
$61$	7.72886	0.989579	0.494789	−	0.869013i	$-0.335245\pi$
$61$	7.72886	0.989579	0.494789	+	0.869013i	$0.335245\pi$
$62$	3.15883	0.401172
$63$	0	0
$64$	−3.63102	−0.453878
$65$	0	0
$66$	0	0
$67$	2.14914	0.262560	0.131280	−	0.991345i	$-0.458091\pi$
$67$	2.14914	0.262560	0.131280	+	0.991345i	$0.458091\pi$
$68$	−5.60388	−0.679570
$69$	0	0
$70$	0.246980	0.0295197
$71$	7.07606	0.839774	0.419887	−	0.907576i	$-0.362070\pi$
$71$	7.07606	0.839774	0.419887	+	0.907576i	$0.362070\pi$
$72$	0	0
$73$	−12.0640	−1.41198	−0.705991	−	0.708221i	$-0.749498\pi$
$73$	−12.0640	−1.41198	−0.705991	+	0.708221i	$0.749498\pi$
$74$	1.59419	0.185320
$75$	0	0
$76$	−11.5429	−1.32406
$77$	0.554958	0.0632433
$78$	0	0
$79$	1.48858	0.167479	0.0837393	−	0.996488i	$-0.473314\pi$
$79$	1.48858	0.167479	0.0837393	+	0.996488i	$0.473314\pi$
$80$	2.85086	0.318735
$81$	0	0
$82$	3.31336	0.365899
$83$	16.1196	1.76936	0.884678	−	0.466202i	$-0.154378\pi$
$83$	16.1196	1.76936	0.884678	+	0.466202i	$0.154378\pi$
$84$	0	0
$85$	3.10992	0.337318
$86$	2.42327	0.261308
$87$	0	0
$88$	−1.69202	−0.180370
$89$	−9.39373	−0.995734	−0.497867	−	0.867254i	$-0.665883\pi$
$89$	−9.39373	−0.995734	−0.497867	+	0.867254i	$0.665883\pi$
$90$	0	0
$91$	0	0
$92$	5.85086	0.609994
$93$	0	0
$94$	0.784479	0.0809129
$95$	6.40581	0.657223
$96$	0	0
$97$	15.2935	1.55282	0.776410	−	0.630228i	$-0.217039\pi$
$97$	15.2935	1.55282	0.776410	+	0.630228i	$0.217039\pi$
$98$	2.97823	0.300847
$99$	0	0
$100$	−1.80194	−0.180194
$101$	16.6843	1.66015	0.830073	−	0.557655i	$-0.188299\pi$
$101$	16.6843	1.66015	0.830073	+	0.557655i	$0.188299\pi$
$102$	0	0
$103$	−9.87263	−0.972779	−0.486389	−	0.873742i	$-0.661686\pi$
$103$	−9.87263	−0.972779	−0.486389	+	0.873742i	$0.661686\pi$
$104$	0	0
$105$	0	0
$106$	−3.52781	−0.342651
$107$	−11.5483	−1.11641	−0.558206	−	0.829702i	$-0.688510\pi$
$107$	−11.5483	−1.11641	−0.558206	+	0.829702i	$0.688510\pi$
$108$	0	0
$109$	8.76809	0.839830	0.419915	−	0.907563i	$-0.362060\pi$
$109$	8.76809	0.839830	0.419915	+	0.907563i	$0.362060\pi$
$110$	0.445042	0.0424331
$111$	0	0
$112$	−1.58211	−0.149495
$113$	12.4112	1.16755	0.583773	−	0.811917i	$-0.301576\pi$
$113$	12.4112	1.16755	0.583773	+	0.811917i	$0.301576\pi$
$114$	0	0
$115$	−3.24698	−0.302782
$116$	8.13706	0.755507
$117$	0	0
$118$	−2.10023	−0.193342
$119$	−1.72587	−0.158211
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−3.43967	−0.311413
$123$	0	0
$124$	12.7899	1.14856
$125$	1.00000	0.0894427
$126$	0	0
$127$	−4.56704	−0.405259	−0.202630	−	0.979255i	$-0.564949\pi$
$127$	−4.56704	−0.405259	−0.202630	+	0.979255i	$0.564949\pi$
$128$	10.9215	0.965337
$129$	0	0
$130$	0	0
$131$	9.83877	0.859618	0.429809	−	0.902920i	$-0.358581\pi$
$131$	9.83877	0.859618	0.429809	+	0.902920i	$0.358581\pi$
$132$	0	0
$133$	−3.55496	−0.308254
$134$	−0.956459	−0.0826255
$135$	0	0
$136$	5.26205	0.451217
$137$	−5.19269	−0.443641	−0.221821	−	0.975088i	$-0.571200\pi$
$137$	−5.19269	−0.443641	−0.221821	+	0.975088i	$0.571200\pi$
$138$	0	0
$139$	−10.2591	−0.870162	−0.435081	−	0.900391i	$-0.643280\pi$
$139$	−10.2591	−0.870162	−0.435081	+	0.900391i	$0.643280\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	−3.14914	−0.264270
$143$	0	0
$144$	0	0
$145$	−4.51573	−0.375011
$146$	5.36898	0.444340
$147$	0	0
$148$	6.45473	0.530576
$149$	−4.34721	−0.356137	−0.178069	−	0.984018i	$-0.556985\pi$
$149$	−4.34721	−0.356137	−0.178069	+	0.984018i	$0.556985\pi$
$150$	0	0
$151$	5.48427	0.446304	0.223152	−	0.974784i	$-0.428365\pi$
$151$	5.48427	0.446304	0.223152	+	0.974784i	$0.428365\pi$
$152$	10.8388	0.879141
$153$	0	0
$154$	−0.246980	−0.0199022
$155$	−7.09783	−0.570112
$156$	0	0
$157$	−15.6431	−1.24846	−0.624228	−	0.781242i	$-0.714586\pi$
$157$	−15.6431	−1.24846	−0.624228	+	0.781242i	$0.714586\pi$
$158$	−0.662481	−0.0527042
$159$	0	0
$160$	−4.65279	−0.367836
$161$	1.80194	0.142013
$162$	0	0
$163$	−6.72587	−0.526811	−0.263406	−	0.964685i	$-0.584846\pi$
$163$	−6.72587	−0.526811	−0.263406	+	0.964685i	$0.584846\pi$
$164$	13.4155	1.04757
$165$	0	0
$166$	−7.17390	−0.556803
$167$	−16.5254	−1.27878	−0.639388	−	0.768885i	$-0.720812\pi$
$167$	−16.5254	−1.27878	−0.639388	+	0.768885i	$0.720812\pi$
$168$	0	0
$169$	0	0
$170$	−1.38404	−0.106151
$171$	0	0
$172$	9.81163	0.748130
$173$	−0.432960	−0.0329174	−0.0164587	−	0.999865i	$-0.505239\pi$
$173$	−0.432960	−0.0329174	−0.0164587	+	0.999865i	$0.505239\pi$
$174$	0	0
$175$	−0.554958	−0.0419509
$176$	−2.85086	−0.214891
$177$	0	0
$178$	4.18060	0.313350
$179$	21.9734	1.64237	0.821186	−	0.570660i	$-0.193313\pi$
$179$	21.9734	1.64237	0.821186	+	0.570660i	$0.193313\pi$
$180$	0	0
$181$	−16.8334	−1.25122	−0.625608	−	0.780137i	$-0.715149\pi$
$181$	−16.8334	−1.25122	−0.625608	+	0.780137i	$0.715149\pi$
$182$	0	0
$183$	0	0
$184$	−5.49396	−0.405020
$185$	−3.58211	−0.263362
$186$	0	0
$187$	−3.10992	−0.227420
$188$	3.17629	0.231655
$189$	0	0
$190$	−2.85086	−0.206823
$191$	−15.6843	−1.13487	−0.567436	−	0.823417i	$-0.692065\pi$
$191$	−15.6843	−1.13487	−0.567436	+	0.823417i	$0.692065\pi$
$192$	0	0
$193$	−17.0804	−1.22947	−0.614736	−	0.788733i	$-0.710738\pi$
$193$	−17.0804	−1.22947	−0.614736	+	0.788733i	$0.710738\pi$
$194$	−6.80625	−0.488660
$195$	0	0
$196$	12.0586	0.861329
$197$	−7.92261	−0.564462	−0.282231	−	0.959346i	$-0.591075\pi$
$197$	−7.92261	−0.564462	−0.282231	+	0.959346i	$0.591075\pi$
$198$	0	0
$199$	−27.7928	−1.97018	−0.985091	−	0.172034i	$-0.944966\pi$
$199$	−27.7928	−1.97018	−0.985091	+	0.172034i	$0.944966\pi$
$200$	1.69202	0.119644
$201$	0	0
$202$	−7.42519	−0.522435
$203$	2.50604	0.175890
$204$	0	0
$205$	−7.44504	−0.519984
$206$	4.39373	0.306126
$207$	0	0
$208$	0	0
$209$	−6.40581	−0.443099
$210$	0	0
$211$	−16.8823	−1.16223	−0.581113	−	0.813823i	$-0.697383\pi$
$211$	−16.8823	−1.16223	−0.581113	+	0.813823i	$0.697383\pi$
$212$	−14.2838	−0.981016
$213$	0	0
$214$	5.13946	0.351326
$215$	−5.44504	−0.371349
$216$	0	0
$217$	3.93900	0.267397
$218$	−3.90217	−0.264288
$219$	0	0
$220$	1.80194	0.121487
$221$	0	0
$222$	0	0
$223$	17.8146	1.19295	0.596477	−	0.802630i	$-0.296567\pi$
$223$	17.8146	1.19295	0.596477	+	0.802630i	$0.296567\pi$
$224$	2.58211	0.172524
$225$	0	0
$226$	−5.52350	−0.367418
$227$	8.45473	0.561160	0.280580	−	0.959831i	$-0.409473\pi$
$227$	8.45473	0.561160	0.280580	+	0.959831i	$0.409473\pi$
$228$	0	0
$229$	9.73125	0.643059	0.321530	−	0.946900i	$-0.395803\pi$
$229$	9.73125	0.643059	0.321530	+	0.946900i	$0.395803\pi$
$230$	1.44504	0.0952832
$231$	0	0
$232$	−7.64071	−0.501637
$233$	5.39612	0.353512	0.176756	−	0.984255i	$-0.443440\pi$
$233$	5.39612	0.353512	0.176756	+	0.984255i	$0.443440\pi$
$234$	0	0
$235$	−1.76271	−0.114986
$236$	−8.50365	−0.553540
$237$	0	0
$238$	0.768086	0.0497876
$239$	−16.3013	−1.05444	−0.527221	−	0.849728i	$-0.676766\pi$
$239$	−16.3013	−1.05444	−0.527221	+	0.849728i	$0.676766\pi$
$240$	0	0
$241$	−7.08038	−0.456087	−0.228044	−	0.973651i	$-0.573233\pi$
$241$	−7.08038	−0.456087	−0.228044	+	0.973651i	$0.573233\pi$
$242$	4.45042	0.286084
$243$	0	0
$244$	−13.9269	−0.891580
$245$	−6.69202	−0.427538
$246$	0	0
$247$	0	0
$248$	−12.0097	−0.762616
$249$	0	0
$250$	−0.445042	−0.0281469
$251$	−25.1075	−1.58477	−0.792386	−	0.610019i	$-0.791162\pi$
$251$	−25.1075	−1.58477	−0.792386	+	0.610019i	$0.791162\pi$
$252$	0	0
$253$	3.24698	0.204136
$254$	2.03252	0.127532
$255$	0	0
$256$	2.40150	0.150094
$257$	−18.9312	−1.18090	−0.590449	−	0.807075i	$-0.701049\pi$
$257$	−18.9312	−1.18090	−0.590449	+	0.807075i	$0.701049\pi$
$258$	0	0
$259$	1.98792	0.123523
$260$	0	0
$261$	0	0
$262$	−4.37867	−0.270515
$263$	−4.70948	−0.290399	−0.145199	−	0.989402i	$-0.546382\pi$
$263$	−4.70948	−0.290399	−0.145199	+	0.989402i	$0.546382\pi$
$264$	0	0
$265$	7.92692	0.486947
$266$	1.58211	0.0970051
$267$	0	0
$268$	−3.87263	−0.236558
$269$	8.10023	0.493880	0.246940	−	0.969031i	$-0.420575\pi$
$269$	8.10023	0.493880	0.246940	+	0.969031i	$0.420575\pi$
$270$	0	0
$271$	0.692021	0.0420373	0.0210187	−	0.999779i	$-0.493309\pi$
$271$	0.692021	0.0420373	0.0210187	+	0.999779i	$0.493309\pi$
$272$	8.86592	0.537575
$273$	0	0
$274$	2.31096	0.139610
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	−28.7633	−1.72822	−0.864110	−	0.503304i	$-0.832118\pi$
$277$	−28.7633	−1.72822	−0.864110	+	0.503304i	$0.832118\pi$
$278$	4.56571	0.273833
$279$	0	0
$280$	−0.939001	−0.0561160
$281$	8.47889	0.505808	0.252904	−	0.967491i	$-0.418614\pi$
$281$	8.47889	0.505808	0.252904	+	0.967491i	$0.418614\pi$
$282$	0	0
$283$	27.7482	1.64946	0.824731	−	0.565526i	$-0.191327\pi$
$283$	27.7482	1.64946	0.824731	+	0.565526i	$0.191327\pi$
$284$	−12.7506	−0.756611
$285$	0	0
$286$	0	0
$287$	4.13169	0.243886
$288$	0	0
$289$	−7.32842	−0.431084
$290$	2.00969	0.118013
$291$	0	0
$292$	21.7385	1.27215
$293$	29.4349	1.71960	0.859802	−	0.510628i	$-0.170587\pi$
$293$	29.4349	1.71960	0.859802	+	0.510628i	$0.170587\pi$
$294$	0	0
$295$	4.71917	0.274761
$296$	−6.06100	−0.352288
$297$	0	0
$298$	1.93469	0.112074
$299$	0	0
$300$	0	0
$301$	3.02177	0.174172
$302$	−2.44073	−0.140448
$303$	0	0
$304$	18.2620	1.04740
$305$	7.72886	0.442553
$306$	0	0
$307$	3.71678	0.212128	0.106064	−	0.994359i	$-0.466175\pi$
$307$	3.71678	0.212128	0.106064	+	0.994359i	$0.466175\pi$
$308$	−1.00000	−0.0569803
$309$	0	0
$310$	3.15883	0.179410
$311$	−14.4426	−0.818967	−0.409484	−	0.912317i	$-0.634291\pi$
$311$	−14.4426	−0.818967	−0.409484	+	0.912317i	$0.634291\pi$
$312$	0	0
$313$	−34.4577	−1.94767	−0.973833	−	0.227267i	$-0.927021\pi$
$313$	−34.4577	−1.94767	−0.973833	+	0.227267i	$0.927021\pi$
$314$	6.96184	0.392879
$315$	0	0
$316$	−2.68233	−0.150893
$317$	13.4494	0.755391	0.377695	−	0.925930i	$-0.376717\pi$
$317$	13.4494	0.755391	0.377695	+	0.925930i	$0.376717\pi$
$318$	0	0
$319$	4.51573	0.252832
$320$	−3.63102	−0.202980
$321$	0	0
$322$	−0.801938	−0.0446902
$323$	19.9215	1.10846
$324$	0	0
$325$	0	0
$326$	2.99330	0.165783
$327$	0	0
$328$	−12.5972	−0.695562
$329$	0.978230	0.0539316
$330$	0	0
$331$	−3.52004	−0.193479	−0.0967395	−	0.995310i	$-0.530841\pi$
$331$	−3.52004	−0.193479	−0.0967395	+	0.995310i	$0.530841\pi$
$332$	−29.0465	−1.59414
$333$	0	0
$334$	7.35450	0.402420
$335$	2.14914	0.117420
$336$	0	0
$337$	3.61894	0.197136	0.0985681	−	0.995130i	$-0.468574\pi$
$337$	3.61894	0.197136	0.0985681	+	0.995130i	$0.468574\pi$
$338$	0	0
$339$	0	0
$340$	−5.60388	−0.303913
$341$	7.09783	0.384369
$342$	0	0
$343$	7.59850	0.410280
$344$	−9.21313	−0.496739
$345$	0	0
$346$	0.192685	0.0103588
$347$	−35.9487	−1.92983	−0.964913	−	0.262568i	$-0.915430\pi$
$347$	−35.9487	−1.92983	−0.964913	+	0.262568i	$0.915430\pi$
$348$	0	0
$349$	32.6069	1.74541	0.872703	−	0.488252i	$-0.162365\pi$
$349$	32.6069	1.74541	0.872703	+	0.488252i	$0.162365\pi$
$350$	0.246980	0.0132016
$351$	0	0
$352$	4.65279	0.247995
$353$	4.79225	0.255066	0.127533	−	0.991834i	$-0.459294\pi$
$353$	4.79225	0.255066	0.127533	+	0.991834i	$0.459294\pi$
$354$	0	0
$355$	7.07606	0.375559
$356$	16.9269	0.897125
$357$	0	0
$358$	−9.77910	−0.516842
$359$	−9.89546	−0.522262	−0.261131	−	0.965303i	$-0.584096\pi$
$359$	−9.89546	−0.522262	−0.261131	+	0.965303i	$0.584096\pi$
$360$	0	0
$361$	22.0344	1.15971
$362$	7.49157	0.393748
$363$	0	0
$364$	0	0
$365$	−12.0640	−0.631458
$366$	0	0
$367$	−32.1661	−1.67906	−0.839529	−	0.543315i	$-0.817169\pi$
$367$	−32.1661	−1.67906	−0.839529	+	0.543315i	$0.817169\pi$
$368$	−9.25667	−0.482537
$369$	0	0
$370$	1.59419	0.0828778
$371$	−4.39911	−0.228390
$372$	0	0
$373$	21.8756	1.13268	0.566338	−	0.824173i	$-0.308360\pi$
$373$	21.8756	1.13268	0.566338	+	0.824173i	$0.308360\pi$
$374$	1.38404	0.0715672
$375$	0	0
$376$	−2.98254	−0.153813
$377$	0	0
$378$	0	0
$379$	−26.2325	−1.34747	−0.673737	−	0.738972i	$-0.735312\pi$
$379$	−26.2325	−1.34747	−0.673737	+	0.738972i	$0.735312\pi$
$380$	−11.5429	−0.592137
$381$	0	0
$382$	6.98015	0.357135
$383$	26.8799	1.37350	0.686750	−	0.726894i	$-0.259037\pi$
$383$	26.8799	1.37350	0.686750	+	0.726894i	$0.259037\pi$
$384$	0	0
$385$	0.554958	0.0282833
$386$	7.60148	0.386905
$387$	0	0
$388$	−27.5579	−1.39904
$389$	−24.6437	−1.24948	−0.624742	−	0.780831i	$-0.714796\pi$
$389$	−24.6437	−1.24948	−0.624742	+	0.780831i	$0.714796\pi$
$390$	0	0
$391$	−10.0978	−0.510669
$392$	−11.3230	−0.571900
$393$	0	0
$394$	3.52589	0.177632
$395$	1.48858	0.0748987
$396$	0	0
$397$	−12.1438	−0.609478	−0.304739	−	0.952436i	$-0.598569\pi$
$397$	−12.1438	−0.609478	−0.304739	+	0.952436i	$0.598569\pi$
$398$	12.3690	0.620001
$399$	0	0
$400$	2.85086	0.142543
$401$	−5.90946	−0.295104	−0.147552	−	0.989054i	$-0.547139\pi$
$401$	−5.90946	−0.295104	−0.147552	+	0.989054i	$0.547139\pi$
$402$	0	0
$403$	0	0
$404$	−30.0640	−1.49574
$405$	0	0
$406$	−1.11529	−0.0553511
$407$	3.58211	0.177558
$408$	0	0
$409$	0.155850	0.00770627	0.00385314	−	0.999993i	$-0.498774\pi$
$409$	0.155850	0.00770627	0.00385314	+	0.999993i	$0.498774\pi$
$410$	3.31336	0.163635
$411$	0	0
$412$	17.7899	0.876443
$413$	−2.61894	−0.128870
$414$	0	0
$415$	16.1196	0.791280
$416$	0	0
$417$	0	0
$418$	2.85086	0.139440
$419$	9.88099	0.482718	0.241359	−	0.970436i	$-0.422407\pi$
$419$	9.88099	0.482718	0.241359	+	0.970436i	$0.422407\pi$
$420$	0	0
$421$	24.6939	1.20351	0.601755	−	0.798681i	$-0.294469\pi$
$421$	24.6939	1.20351	0.601755	+	0.798681i	$0.294469\pi$
$422$	7.51334	0.365744
$423$	0	0
$424$	13.4125	0.651369
$425$	3.10992	0.150853
$426$	0	0
$427$	−4.28919	−0.207569
$428$	20.8092	1.00585
$429$	0	0
$430$	2.42327	0.116861
$431$	−3.98493	−0.191948	−0.0959738	−	0.995384i	$-0.530596\pi$
$431$	−3.98493	−0.191948	−0.0959738	+	0.995384i	$0.530596\pi$
$432$	0	0
$433$	−17.1032	−0.821928	−0.410964	−	0.911652i	$-0.634808\pi$
$433$	−17.1032	−0.821928	−0.410964	+	0.911652i	$0.634808\pi$
$434$	−1.75302	−0.0841477
$435$	0	0
$436$	−15.7995	−0.756661
$437$	−20.7995	−0.994977
$438$	0	0
$439$	−10.4383	−0.498195	−0.249097	−	0.968478i	$-0.580134\pi$
$439$	−10.4383	−0.498195	−0.249097	+	0.968478i	$0.580134\pi$
$440$	−1.69202	−0.0806640
$441$	0	0
$442$	0	0
$443$	−6.11662	−0.290609	−0.145305	−	0.989387i	$-0.546416\pi$
$443$	−6.11662	−0.290609	−0.145305	+	0.989387i	$0.546416\pi$
$444$	0	0
$445$	−9.39373	−0.445306
$446$	−7.92825	−0.375413
$447$	0	0
$448$	2.01507	0.0952029
$449$	−12.7385	−0.601169	−0.300585	−	0.953755i	$-0.597182\pi$
$449$	−12.7385	−0.601169	−0.300585	+	0.953755i	$0.597182\pi$
$450$	0	0
$451$	7.44504	0.350573
$452$	−22.3642	−1.05192
$453$	0	0
$454$	−3.76271	−0.176593
$455$	0	0
$456$	0	0
$457$	−36.5176	−1.70822	−0.854112	−	0.520089i	$-0.825899\pi$
$457$	−36.5176	−1.70822	−0.854112	+	0.520089i	$0.825899\pi$
$458$	−4.33081	−0.202366
$459$	0	0
$460$	5.85086	0.272798
$461$	−3.86054	−0.179803	−0.0899017	−	0.995951i	$-0.528655\pi$
$461$	−3.86054	−0.179803	−0.0899017	+	0.995951i	$0.528655\pi$
$462$	0	0
$463$	24.1172	1.12082	0.560411	−	0.828215i	$-0.310643\pi$
$463$	24.1172	1.12082	0.560411	+	0.828215i	$0.310643\pi$
$464$	−12.8737	−0.597646
$465$	0	0
$466$	−2.40150	−0.111247
$467$	−7.40821	−0.342811	−0.171405	−	0.985201i	$-0.554831\pi$
$467$	−7.40821	−0.342811	−0.171405	+	0.985201i	$0.554831\pi$
$468$	0	0
$469$	−1.19269	−0.0550731
$470$	0.784479	0.0361853
$471$	0	0
$472$	7.98493	0.367536
$473$	5.44504	0.250363
$474$	0	0
$475$	6.40581	0.293919
$476$	3.10992	0.142543
$477$	0	0
$478$	7.25475	0.331825
$479$	−42.1081	−1.92397	−0.961984	−	0.273104i	$-0.911950\pi$
$479$	−42.1081	−1.92397	−0.961984	+	0.273104i	$0.911950\pi$
$480$	0	0
$481$	0	0
$482$	3.15106	0.143527
$483$	0	0
$484$	18.0194	0.819063
$485$	15.2935	0.694442
$486$	0	0
$487$	−22.5265	−1.02077	−0.510386	−	0.859945i	$-0.670498\pi$
$487$	−22.5265	−1.02077	−0.510386	+	0.859945i	$0.670498\pi$
$488$	13.0774	0.591986
$489$	0	0
$490$	2.97823	0.134543
$491$	−33.2325	−1.49976	−0.749881	−	0.661573i	$-0.769889\pi$
$491$	−33.2325	−1.49976	−0.749881	+	0.661573i	$0.769889\pi$
$492$	0	0
$493$	−14.0435	−0.632489
$494$	0	0
$495$	0	0
$496$	−20.2349	−0.908574
$497$	−3.92692	−0.176146
$498$	0	0
$499$	7.90217	0.353750	0.176875	−	0.984233i	$-0.443401\pi$
$499$	7.90217	0.353750	0.176875	+	0.984233i	$0.443401\pi$
$500$	−1.80194	−0.0805851
$501$	0	0
$502$	11.1739	0.498716
$503$	29.6534	1.32218	0.661090	−	0.750307i	$-0.270094\pi$
$503$	29.6534	1.32218	0.661090	+	0.750307i	$0.270094\pi$
$504$	0	0
$505$	16.6843	0.742439
$506$	−1.44504	−0.0642399
$507$	0	0
$508$	8.22952	0.365126
$509$	40.7904	1.80800	0.904002	−	0.427527i	$-0.140615\pi$
$509$	40.7904	1.80800	0.904002	+	0.427527i	$0.140615\pi$
$510$	0	0
$511$	6.69501	0.296170
$512$	−22.9119	−1.01257
$513$	0	0
$514$	8.42519	0.371619
$515$	−9.87263	−0.435040
$516$	0	0
$517$	1.76271	0.0775239
$518$	−0.884707	−0.0388718
$519$	0	0
$520$	0	0
$521$	38.4209	1.68325	0.841625	−	0.540063i	$-0.181600\pi$
$521$	38.4209	1.68325	0.841625	+	0.540063i	$0.181600\pi$
$522$	0	0
$523$	−13.9903	−0.611754	−0.305877	−	0.952071i	$-0.598950\pi$
$523$	−13.9903	−0.611754	−0.305877	+	0.952071i	$0.598950\pi$
$524$	−17.7289	−0.774489
$525$	0	0
$526$	2.09592	0.0913863
$527$	−22.0737	−0.961544
$528$	0	0
$529$	−12.4571	−0.541614
$530$	−3.52781	−0.153238
$531$	0	0
$532$	6.40581	0.277727
$533$	0	0
$534$	0	0
$535$	−11.5483	−0.499275
$536$	3.63640	0.157069
$537$	0	0
$538$	−3.60494	−0.155420
$539$	6.69202	0.288246
$540$	0	0
$541$	25.9457	1.11549	0.557747	−	0.830011i	$-0.311666\pi$
$541$	25.9457	1.11549	0.557747	+	0.830011i	$0.311666\pi$
$542$	−0.307979	−0.0132288
$543$	0	0
$544$	−14.4698	−0.620387
$545$	8.76809	0.375584
$546$	0	0
$547$	16.4698	0.704198	0.352099	−	0.935963i	$-0.385468\pi$
$547$	16.4698	0.704198	0.352099	+	0.935963i	$0.385468\pi$
$548$	9.35690	0.399707
$549$	0	0
$550$	0.445042	0.0189766
$551$	−28.9269	−1.23233
$552$	0	0
$553$	−0.826101	−0.0351294
$554$	12.8009	0.543857
$555$	0	0
$556$	18.4862	0.783989
$557$	26.3351	1.11586	0.557928	−	0.829890i	$-0.311597\pi$
$557$	26.3351	1.11586	0.557928	+	0.829890i	$0.311597\pi$
$558$	0	0
$559$	0	0
$560$	−1.58211	−0.0668561
$561$	0	0
$562$	−3.77346	−0.159174
$563$	−31.5273	−1.32872	−0.664359	−	0.747413i	$-0.731296\pi$
$563$	−31.5273	−1.32872	−0.664359	+	0.747413i	$0.731296\pi$
$564$	0	0
$565$	12.4112	0.522143
$566$	−12.3491	−0.519072
$567$	0	0
$568$	11.9729	0.502370
$569$	27.5690	1.15575	0.577875	−	0.816125i	$-0.303882\pi$
$569$	27.5690	1.15575	0.577875	+	0.816125i	$0.303882\pi$
$570$	0	0
$571$	−8.24890	−0.345206	−0.172603	−	0.984992i	$-0.555218\pi$
$571$	−8.24890	−0.345206	−0.172603	+	0.984992i	$0.555218\pi$
$572$	0	0
$573$	0	0
$574$	−1.83877	−0.0767489
$575$	−3.24698	−0.135408
$576$	0	0
$577$	−42.5512	−1.77143	−0.885716	−	0.464228i	$-0.846332\pi$
$577$	−42.5512	−1.77143	−0.885716	+	0.464228i	$0.846332\pi$
$578$	3.26145	0.135659
$579$	0	0
$580$	8.13706	0.337873
$581$	−8.94571	−0.371130
$582$	0	0
$583$	−7.92692	−0.328299
$584$	−20.4125	−0.844676
$585$	0	0
$586$	−13.0998	−0.541146
$587$	−14.3472	−0.592173	−0.296086	−	0.955161i	$-0.595682\pi$
$587$	−14.3472	−0.592173	−0.296086	+	0.955161i	$0.595682\pi$
$588$	0	0
$589$	−45.4674	−1.87345
$590$	−2.10023	−0.0864650
$591$	0	0
$592$	−10.2121	−0.419713
$593$	−43.1497	−1.77195	−0.885974	−	0.463736i	$-0.846509\pi$
$593$	−43.1497	−1.77195	−0.885974	+	0.463736i	$0.846509\pi$
$594$	0	0
$595$	−1.72587	−0.0707539
$596$	7.83340	0.320868
$597$	0	0
$598$	0	0
$599$	−36.0355	−1.47237	−0.736185	−	0.676780i	$-0.763375\pi$
$599$	−36.0355	−1.47237	−0.736185	+	0.676780i	$0.763375\pi$
$600$	0	0
$601$	−29.9573	−1.22198	−0.610992	−	0.791637i	$-0.709229\pi$
$601$	−29.9573	−1.22198	−0.610992	+	0.791637i	$0.709229\pi$
$602$	−1.34481	−0.0548105
$603$	0	0
$604$	−9.88231	−0.402106
$605$	−10.0000	−0.406558
$606$	0	0
$607$	−32.8635	−1.33389	−0.666945	−	0.745107i	$-0.732398\pi$
$607$	−32.8635	−1.33389	−0.666945	+	0.745107i	$0.732398\pi$
$608$	−29.8049	−1.20875
$609$	0	0
$610$	−3.43967	−0.139268
$611$	0	0
$612$	0	0
$613$	−25.8732	−1.04501	−0.522505	−	0.852636i	$-0.675002\pi$
$613$	−25.8732	−1.04501	−0.522505	+	0.852636i	$0.675002\pi$
$614$	−1.65412	−0.0667549
$615$	0	0
$616$	0.939001	0.0378334
$617$	36.7362	1.47894	0.739471	−	0.673189i	$-0.235076\pi$
$617$	36.7362	1.47894	0.739471	+	0.673189i	$0.235076\pi$
$618$	0	0
$619$	2.88876	0.116109	0.0580544	−	0.998313i	$-0.481510\pi$
$619$	2.88876	0.116109	0.0580544	+	0.998313i	$0.481510\pi$
$620$	12.7899	0.513653
$621$	0	0
$622$	6.42758	0.257723
$623$	5.21313	0.208860
$624$	0	0
$625$	1.00000	0.0400000
$626$	15.3351	0.612915
$627$	0	0
$628$	28.1879	1.12482
$629$	−11.1400	−0.444183
$630$	0	0
$631$	−16.9196	−0.673560	−0.336780	−	0.941583i	$-0.609338\pi$
$631$	−16.9196	−0.673560	−0.336780	+	0.941583i	$0.609338\pi$
$632$	2.51871	0.100189
$633$	0	0
$634$	−5.98553	−0.237716
$635$	−4.56704	−0.181237
$636$	0	0
$637$	0	0
$638$	−2.00969	−0.0795643
$639$	0	0
$640$	10.9215	0.431712
$641$	−8.61894	−0.340428	−0.170214	−	0.985407i	$-0.554446\pi$
$641$	−8.61894	−0.340428	−0.170214	+	0.985407i	$0.554446\pi$
$642$	0	0
$643$	−15.2064	−0.599683	−0.299841	−	0.953989i	$-0.596934\pi$
$643$	−15.2064	−0.599683	−0.299841	+	0.953989i	$0.596934\pi$
$644$	−3.24698	−0.127949
$645$	0	0
$646$	−8.86592	−0.348825
$647$	−24.9323	−0.980190	−0.490095	−	0.871669i	$-0.663038\pi$
$647$	−24.9323	−0.980190	−0.490095	+	0.871669i	$0.663038\pi$
$648$	0	0
$649$	−4.71917	−0.185244
$650$	0	0
$651$	0	0
$652$	12.1196	0.474640
$653$	21.8616	0.855511	0.427755	−	0.903895i	$-0.359304\pi$
$653$	21.8616	0.855511	0.427755	+	0.903895i	$0.359304\pi$
$654$	0	0
$655$	9.83877	0.384433
$656$	−21.2247	−0.828687
$657$	0	0
$658$	−0.435353	−0.0169718
$659$	37.4174	1.45758	0.728788	−	0.684740i	$-0.240084\pi$
$659$	37.4174	1.45758	0.728788	+	0.684740i	$0.240084\pi$
$660$	0	0
$661$	−22.0084	−0.856026	−0.428013	−	0.903773i	$-0.640786\pi$
$661$	−22.0084	−0.856026	−0.428013	+	0.903773i	$0.640786\pi$
$662$	1.56657	0.0608863
$663$	0	0
$664$	27.2747	1.05846
$665$	−3.55496	−0.137855
$666$	0	0
$667$	14.6625	0.567734
$668$	29.7778	1.15214
$669$	0	0
$670$	−0.956459	−0.0369513
$671$	−7.72886	−0.298369
$672$	0	0
$673$	3.83340	0.147767	0.0738833	−	0.997267i	$-0.476461\pi$
$673$	3.83340	0.147767	0.0738833	+	0.997267i	$0.476461\pi$
$674$	−1.61058	−0.0620372
$675$	0	0
$676$	0	0
$677$	−6.82238	−0.262205	−0.131103	−	0.991369i	$-0.541852\pi$
$677$	−6.82238	−0.262205	−0.131103	+	0.991369i	$0.541852\pi$
$678$	0	0
$679$	−8.48725	−0.325711
$680$	5.26205	0.201790
$681$	0	0
$682$	−3.15883	−0.120958
$683$	27.0877	1.03648	0.518240	−	0.855235i	$-0.326587\pi$
$683$	27.0877	1.03648	0.518240	+	0.855235i	$0.326587\pi$
$684$	0	0
$685$	−5.19269	−0.198402
$686$	−3.38165	−0.129112
$687$	0	0
$688$	−15.5230	−0.591810
$689$	0	0
$690$	0	0
$691$	−9.72156	−0.369826	−0.184913	−	0.982755i	$-0.559200\pi$
$691$	−9.72156	−0.369826	−0.184913	+	0.982755i	$0.559200\pi$
$692$	0.780167	0.0296575
$693$	0	0
$694$	15.9987	0.607301
$695$	−10.2591	−0.389148
$696$	0	0
$697$	−23.1535	−0.877000
$698$	−14.5114	−0.549265
$699$	0	0
$700$	1.00000	0.0377964
$701$	11.8823	0.448789	0.224394	−	0.974498i	$-0.427960\pi$
$701$	11.8823	0.448789	0.224394	+	0.974498i	$0.427960\pi$
$702$	0	0
$703$	−22.9463	−0.865436
$704$	3.63102	0.136849
$705$	0	0
$706$	−2.13275	−0.0802672
$707$	−9.25906	−0.348223
$708$	0	0
$709$	18.4765	0.693900	0.346950	−	0.937884i	$-0.387217\pi$
$709$	18.4765	0.693900	0.346950	+	0.937884i	$0.387217\pi$
$710$	−3.14914	−0.118185
$711$	0	0
$712$	−15.8944	−0.595668
$713$	23.0465	0.863099
$714$	0	0
$715$	0	0
$716$	−39.5948	−1.47973
$717$	0	0
$718$	4.40389	0.164352
$719$	−27.7506	−1.03492	−0.517462	−	0.855706i	$-0.673123\pi$
$719$	−27.7506	−1.03492	−0.517462	+	0.855706i	$0.673123\pi$
$720$	0	0
$721$	5.47889	0.204045
$722$	−9.80625	−0.364951
$723$	0	0
$724$	30.3327	1.12731
$725$	−4.51573	−0.167710
$726$	0	0
$727$	−6.01985	−0.223264	−0.111632	−	0.993750i	$-0.535608\pi$
$727$	−6.01985	−0.223264	−0.111632	+	0.993750i	$0.535608\pi$
$728$	0	0
$729$	0	0
$730$	5.36898	0.198715
$731$	−16.9336	−0.626313
$732$	0	0
$733$	−16.0731	−0.593673	−0.296836	−	0.954928i	$-0.595932\pi$
$733$	−16.0731	−0.593673	−0.296836	+	0.954928i	$0.595932\pi$
$734$	14.3153	0.528386
$735$	0	0
$736$	15.1075	0.556871
$737$	−2.14914	−0.0791648
$738$	0	0
$739$	25.8595	0.951256	0.475628	−	0.879646i	$-0.342221\pi$
$739$	25.8595	0.951256	0.475628	+	0.879646i	$0.342221\pi$
$740$	6.45473	0.237281
$741$	0	0
$742$	1.95779	0.0718726
$743$	−23.4741	−0.861181	−0.430591	−	0.902547i	$-0.641695\pi$
$743$	−23.4741	−0.861181	−0.430591	+	0.902547i	$0.641695\pi$
$744$	0	0
$745$	−4.34721	−0.159269
$746$	−9.73556	−0.356444
$747$	0	0
$748$	5.60388	0.204898
$749$	6.40880	0.234172
$750$	0	0
$751$	40.2626	1.46920	0.734602	−	0.678498i	$-0.237369\pi$
$751$	40.2626	1.46920	0.734602	+	0.678498i	$0.237369\pi$
$752$	−5.02523	−0.183251
$753$	0	0
$754$	0	0
$755$	5.48427	0.199593
$756$	0	0
$757$	−8.23596	−0.299341	−0.149671	−	0.988736i	$-0.547821\pi$
$757$	−8.23596	−0.299341	−0.149671	+	0.988736i	$0.547821\pi$
$758$	11.6746	0.424039
$759$	0	0
$760$	10.8388	0.393164
$761$	42.0183	1.52316	0.761581	−	0.648069i	$-0.224423\pi$
$761$	42.0183	1.52316	0.761581	+	0.648069i	$0.224423\pi$
$762$	0	0
$763$	−4.86592	−0.176158
$764$	28.2620	1.02248
$765$	0	0
$766$	−11.9627	−0.432230
$767$	0	0
$768$	0	0
$769$	0.586891	0.0211638	0.0105819	−	0.999944i	$-0.496632\pi$
$769$	0.586891	0.0211638	0.0105819	+	0.999944i	$0.496632\pi$
$770$	−0.246980	−0.00890053
$771$	0	0
$772$	30.7778	1.10772
$773$	−29.0713	−1.04562	−0.522811	−	0.852449i	$-0.675117\pi$
$773$	−29.0713	−1.04562	−0.522811	+	0.852449i	$0.675117\pi$
$774$	0	0
$775$	−7.09783	−0.254962
$776$	25.8769	0.928928
$777$	0	0
$778$	10.9675	0.393203
$779$	−47.6915	−1.70873
$780$	0	0
$781$	−7.07606	−0.253201
$782$	4.49396	0.160704
$783$	0	0
$784$	−19.0780	−0.681357
$785$	−15.6431	−0.558326
$786$	0	0
$787$	−19.6606	−0.700823	−0.350412	−	0.936596i	$-0.613958\pi$
$787$	−19.6606	−0.700823	−0.350412	+	0.936596i	$0.613958\pi$
$788$	14.2760	0.508563
$789$	0	0
$790$	−0.662481	−0.0235700
$791$	−6.88769	−0.244898
$792$	0	0
$793$	0	0
$794$	5.40449	0.191798
$795$	0	0
$796$	50.0810	1.77507
$797$	30.4926	1.08010	0.540052	−	0.841632i	$-0.318404\pi$
$797$	30.4926	1.08010	0.540052	+	0.841632i	$0.318404\pi$
$798$	0	0
$799$	−5.48188	−0.193935
$800$	−4.65279	−0.164501
$801$	0	0
$802$	2.62996	0.0928670
$803$	12.0640	0.425729
$804$	0	0
$805$	1.80194	0.0635100
$806$	0	0
$807$	0	0
$808$	28.2301	0.993132
$809$	22.6823	0.797468	0.398734	−	0.917067i	$-0.369450\pi$
$809$	22.6823	0.797468	0.398734	+	0.917067i	$0.369450\pi$
$810$	0	0
$811$	10.5254	0.369597	0.184799	−	0.982776i	$-0.440837\pi$
$811$	10.5254	0.369597	0.184799	+	0.982776i	$0.440837\pi$
$812$	−4.51573	−0.158471
$813$	0	0
$814$	−1.59419	−0.0558762
$815$	−6.72587	−0.235597
$816$	0	0
$817$	−34.8799	−1.22029
$818$	−0.0693596	−0.00242510
$819$	0	0
$820$	13.4155	0.468490
$821$	−45.2573	−1.57949	−0.789745	−	0.613436i	$-0.789787\pi$
$821$	−45.2573	−1.57949	−0.789745	+	0.613436i	$0.789787\pi$
$822$	0	0
$823$	28.7985	1.00385	0.501926	−	0.864911i	$-0.332625\pi$
$823$	28.7985	1.00385	0.501926	+	0.864911i	$0.332625\pi$
$824$	−16.7047	−0.581936
$825$	0	0
$826$	1.16554	0.0405543
$827$	−42.1957	−1.46729	−0.733644	−	0.679534i	$-0.762182\pi$
$827$	−42.1957	−1.46729	−0.733644	+	0.679534i	$0.762182\pi$
$828$	0	0
$829$	12.4741	0.433244	0.216622	−	0.976256i	$-0.430496\pi$
$829$	12.4741	0.433244	0.216622	+	0.976256i	$0.430496\pi$
$830$	−7.17390	−0.249010
$831$	0	0
$832$	0	0
$833$	−20.8116	−0.721080
$834$	0	0
$835$	−16.5254	−0.571886
$836$	11.5429	0.399219
$837$	0	0
$838$	−4.39745	−0.151907
$839$	39.7488	1.37228	0.686141	−	0.727469i	$-0.259303\pi$
$839$	39.7488	1.37228	0.686141	+	0.727469i	$0.259303\pi$
$840$	0	0
$841$	−8.60819	−0.296834
$842$	−10.9898	−0.378735
$843$	0	0
$844$	30.4209	1.04713
$845$	0	0
$846$	0	0
$847$	5.54958	0.190686
$848$	22.5985	0.776036
$849$	0	0
$850$	−1.38404	−0.0474723
$851$	11.6310	0.398706
$852$	0	0
$853$	−8.92500	−0.305586	−0.152793	−	0.988258i	$-0.548827\pi$
$853$	−8.92500	−0.305586	−0.152793	+	0.988258i	$0.548827\pi$
$854$	1.90887	0.0653202
$855$	0	0
$856$	−19.5399	−0.667860
$857$	35.5666	1.21493	0.607465	−	0.794346i	$-0.292186\pi$
$857$	35.5666	1.21493	0.607465	+	0.794346i	$0.292186\pi$
$858$	0	0
$859$	38.9842	1.33012	0.665062	−	0.746788i	$-0.268405\pi$
$859$	38.9842	1.33012	0.665062	+	0.746788i	$0.268405\pi$
$860$	9.81163	0.334574
$861$	0	0
$862$	1.77346	0.0604044
$863$	44.8829	1.52783	0.763916	−	0.645316i	$-0.223274\pi$
$863$	44.8829	1.52783	0.763916	+	0.645316i	$0.223274\pi$
$864$	0	0
$865$	−0.432960	−0.0147211
$866$	7.61165	0.258654
$867$	0	0
$868$	−7.09783	−0.240916
$869$	−1.48858	−0.0504967
$870$	0	0
$871$	0	0
$872$	14.8358	0.502403
$873$	0	0
$874$	9.25667	0.313111
$875$	−0.554958	−0.0187610
$876$	0	0
$877$	17.3588	0.586166	0.293083	−	0.956087i	$-0.405319\pi$
$877$	17.3588	0.586166	0.293083	+	0.956087i	$0.405319\pi$
$878$	4.64550	0.156778
$879$	0	0
$880$	−2.85086	−0.0961023
$881$	18.1142	0.610284	0.305142	−	0.952307i	$-0.401296\pi$
$881$	18.1142	0.610284	0.305142	+	0.952307i	$0.401296\pi$
$882$	0	0
$883$	−47.1726	−1.58748	−0.793742	−	0.608255i	$-0.791870\pi$
$883$	−47.1726	−1.58748	−0.793742	+	0.608255i	$0.791870\pi$
$884$	0	0
$885$	0	0
$886$	2.72215	0.0914525
$887$	−3.52409	−0.118327	−0.0591637	−	0.998248i	$-0.518843\pi$
$887$	−3.52409	−0.118327	−0.0591637	+	0.998248i	$0.518843\pi$
$888$	0	0
$889$	2.53452	0.0850049
$890$	4.18060	0.140134
$891$	0	0
$892$	−32.1008	−1.07481
$893$	−11.2916	−0.377858
$894$	0	0
$895$	21.9734	0.734491
$896$	−6.06100	−0.202484
$897$	0	0
$898$	5.66919	0.189183
$899$	32.0519	1.06899
$900$	0	0
$901$	24.6521	0.821279
$902$	−3.31336	−0.110323
$903$	0	0
$904$	21.0000	0.698450
$905$	−16.8334	−0.559561
$906$	0	0
$907$	−42.1788	−1.40052	−0.700262	−	0.713886i	$-0.746934\pi$
$907$	−42.1788	−1.40052	−0.700262	+	0.713886i	$0.746934\pi$
$908$	−15.2349	−0.505588
$909$	0	0
$910$	0	0
$911$	33.4547	1.10840	0.554202	−	0.832382i	$-0.313023\pi$
$911$	33.4547	1.10840	0.554202	+	0.832382i	$0.313023\pi$
$912$	0	0
$913$	−16.1196	−0.533481
$914$	16.2519	0.537564
$915$	0	0
$916$	−17.5351	−0.579376
$917$	−5.46011	−0.180309
$918$	0	0
$919$	13.8401	0.456543	0.228271	−	0.973598i	$-0.426693\pi$
$919$	13.8401	0.456543	0.228271	+	0.973598i	$0.426693\pi$
$920$	−5.49396	−0.181130
$921$	0	0
$922$	1.71810	0.0565827
$923$	0	0
$924$	0	0
$925$	−3.58211	−0.117779
$926$	−10.7332	−0.352714
$927$	0	0
$928$	21.0108	0.689712
$929$	−56.7271	−1.86115	−0.930577	−	0.366096i	$-0.880694\pi$
$929$	−56.7271	−1.86115	−0.930577	+	0.366096i	$0.880694\pi$
$930$	0	0
$931$	−42.8678	−1.40494
$932$	−9.72348	−0.318503
$933$	0	0
$934$	3.29696	0.107880
$935$	−3.10992	−0.101705
$936$	0	0
$937$	10.0291	0.327635	0.163818	−	0.986491i	$-0.447619\pi$
$937$	10.0291	0.327635	0.163818	+	0.986491i	$0.447619\pi$
$938$	0.530795	0.0173311
$939$	0	0
$940$	3.17629	0.103599
$941$	−15.7356	−0.512965	−0.256482	−	0.966549i	$-0.582564\pi$
$941$	−15.7356	−0.512965	−0.256482	+	0.966549i	$0.582564\pi$
$942$	0	0
$943$	24.1739	0.787210
$944$	13.4537	0.437880
$945$	0	0
$946$	−2.42327	−0.0787874
$947$	−20.4782	−0.665451	−0.332725	−	0.943024i	$-0.607968\pi$
$947$	−20.4782	−0.665451	−0.332725	+	0.943024i	$0.607968\pi$
$948$	0	0
$949$	0	0
$950$	−2.85086	−0.0924940
$951$	0	0
$952$	−2.92021	−0.0946447
$953$	−19.7845	−0.640882	−0.320441	−	0.947268i	$-0.603831\pi$
$953$	−19.7845	−0.640882	−0.320441	+	0.947268i	$0.603831\pi$
$954$	0	0
$955$	−15.6843	−0.507530
$956$	29.3739	0.950019
$957$	0	0
$958$	18.7399	0.605458
$959$	2.88172	0.0930557
$960$	0	0
$961$	19.3793	0.625137
$962$	0	0
$963$	0	0
$964$	12.7584	0.410920
$965$	−17.0804	−0.549837
$966$	0	0
$967$	−31.2562	−1.00513	−0.502566	−	0.864539i	$-0.667611\pi$
$967$	−31.2562	−1.00513	−0.502566	+	0.864539i	$0.667611\pi$
$968$	−16.9202	−0.543836
$969$	0	0
$970$	−6.80625	−0.218536
$971$	12.7764	0.410016	0.205008	−	0.978760i	$-0.434278\pi$
$971$	12.7764	0.410016	0.205008	+	0.978760i	$0.434278\pi$
$972$	0	0
$973$	5.69335	0.182520
$974$	10.0252	0.321229
$975$	0	0
$976$	22.0339	0.705286
$977$	−17.8340	−0.570560	−0.285280	−	0.958444i	$-0.592087\pi$
$977$	−17.8340	−0.570560	−0.285280	+	0.958444i	$0.592087\pi$
$978$	0	0
$979$	9.39373	0.300225
$980$	12.0586	0.385198
$981$	0	0
$982$	14.7899	0.471963
$983$	6.20344	0.197859	0.0989295	−	0.995094i	$-0.468458\pi$
$983$	6.20344	0.197859	0.0989295	+	0.995094i	$0.468458\pi$
$984$	0	0
$985$	−7.92261	−0.252435
$986$	6.24996	0.199039
$987$	0	0
$988$	0	0
$989$	17.6799	0.562189
$990$	0	0
$991$	13.6200	0.432654	0.216327	−	0.976321i	$-0.430592\pi$
$991$	13.6200	0.432654	0.216327	+	0.976321i	$0.430592\pi$
$992$	33.0248	1.04854
$993$	0	0
$994$	1.74764	0.0554319
$995$	−27.7928	−0.881092
$996$	0	0
$997$	29.2646	0.926818	0.463409	−	0.886145i	$-0.346626\pi$
$997$	29.2646	0.926818	0.463409	+	0.886145i	$0.346626\pi$
$998$	−3.51679	−0.111322
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.bq.1.2		3
3.2	odd	2		2535.2.a.bd.1.2	yes	3
13.12	even	2		7605.2.a.bz.1.2		3
39.38	odd	2		2535.2.a.v.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.2.a.v.1.2	✓	3	39.38	odd	2
2535.2.a.bd.1.2	yes	3	3.2	odd	2
7605.2.a.bq.1.2		3	1.1	even	1	trivial
7605.2.a.bz.1.2		3	13.12	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:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)

\(f(q)\)	\(=\)	\(q-0.445042 q^{2} -1.80194 q^{4} +1.00000 q^{5} -0.554958 q^{7} +1.69202 q^{8} +O(q^{10})\)	\(q-0.445042 q^{2} -1.80194 q^{4} +1.00000 q^{5} -0.554958 q^{7} +1.69202 q^{8} -0.445042 q^{10} -1.00000 q^{11} +0.246980 q^{14} +2.85086 q^{16} +3.10992 q^{17} +6.40581 q^{19} -1.80194 q^{20} +0.445042 q^{22} -3.24698 q^{23} +1.00000 q^{25} +1.00000 q^{28} -4.51573 q^{29} -7.09783 q^{31} -4.65279 q^{32} -1.38404 q^{34} -0.554958 q^{35} -3.58211 q^{37} -2.85086 q^{38} +1.69202 q^{40} -7.44504 q^{41} -5.44504 q^{43} +1.80194 q^{44} +1.44504 q^{46} -1.76271 q^{47} -6.69202 q^{49} -0.445042 q^{50} +7.92692 q^{53} -1.00000 q^{55} -0.939001 q^{56} +2.00969 q^{58} +4.71917 q^{59} +7.72886 q^{61} +3.15883 q^{62} -3.63102 q^{64} +2.14914 q^{67} -5.60388 q^{68} +0.246980 q^{70} +7.07606 q^{71} -12.0640 q^{73} +1.59419 q^{74} -11.5429 q^{76} +0.554958 q^{77} +1.48858 q^{79} +2.85086 q^{80} +3.31336 q^{82} +16.1196 q^{83} +3.10992 q^{85} +2.42327 q^{86} -1.69202 q^{88} -9.39373 q^{89} +5.85086 q^{92} +0.784479 q^{94} +6.40581 q^{95} +15.2935 q^{97} +2.97823 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - q^{4} + 3 q^{5} - 2 q^{7}+O(q^{10}) \) 3 * q - q^2 - q^4 + 3 * q^5 - 2 * q^7	\( 3 q - q^{2} - q^{4} + 3 q^{5} - 2 q^{7} - q^{10} - 3 q^{11} - 4 q^{14} - 5 q^{16} + 10 q^{17} + 6 q^{19} - q^{20} + q^{22} - 5 q^{23} + 3 q^{25} + 3 q^{28} - q^{29} - 3 q^{31} + 4 q^{32} + 6 q^{34} - 2 q^{35} - 5 q^{37} + 5 q^{38} - 22 q^{41} - 16 q^{43} + q^{44} + 4 q^{46} + 12 q^{47} - 15 q^{49} - q^{50} - 5 q^{53} - 3 q^{55} + 7 q^{56} - 16 q^{58} + 3 q^{59} - 10 q^{61} + q^{62} + 4 q^{64} + 20 q^{67} - 8 q^{68} - 4 q^{70} + 6 q^{71} - 2 q^{73} + 18 q^{74} - 16 q^{76} + 2 q^{77} - 2 q^{79} - 5 q^{80} + 12 q^{82} + 27 q^{83} + 10 q^{85} + 10 q^{86} + 4 q^{89} + 4 q^{92} - 18 q^{94} + 6 q^{95} - 9 q^{97} + 12 q^{98}+O(q^{100}) \) 3 * q - q^2 - q^4 + 3 * q^5 - 2 * q^7 - q^10 - 3 * q^11 - 4 * q^14 - 5 * q^16 + 10 * q^17 + 6 * q^19 - q^20 + q^22 - 5 * q^23 + 3 * q^25 + 3 * q^28 - q^29 - 3 * q^31 + 4 * q^32 + 6 * q^34 - 2 * q^35 - 5 * q^37 + 5 * q^38 - 22 * q^41 - 16 * q^43 + q^44 + 4 * q^46 + 12 * q^47 - 15 * q^49 - q^50 - 5 * q^53 - 3 * q^55 + 7 * q^56 - 16 * q^58 + 3 * q^59 - 10 * q^61 + q^62 + 4 * q^64 + 20 * q^67 - 8 * q^68 - 4 * q^70 + 6 * q^71 - 2 * q^73 + 18 * q^74 - 16 * q^76 + 2 * q^77 - 2 * q^79 - 5 * q^80 + 12 * q^82 + 27 * q^83 + 10 * q^85 + 10 * q^86 + 4 * q^89 + 4 * q^92 - 18 * q^94 + 6 * q^95 - 9 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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