LMFDB - Embedded newform 605.2.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(1,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.83094932229$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-1.00000 q^{2} -3.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} +3.00000 q^{6} -3.00000 q^{7} +3.00000 q^{8} +6.00000 q^{9} -1.00000 q^{10} +3.00000 q^{12} +4.00000 q^{13} +3.00000 q^{14} -3.00000 q^{15} -1.00000 q^{16} -6.00000 q^{18} +4.00000 q^{19} -1.00000 q^{20} +9.00000 q^{21} -8.00000 q^{23} -9.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} -9.00000 q^{27} +3.00000 q^{28} +6.00000 q^{29} +3.00000 q^{30} -2.00000 q^{31} -5.00000 q^{32} -3.00000 q^{35} -6.00000 q^{36} -8.00000 q^{37} -4.00000 q^{38} -12.0000 q^{39} +3.00000 q^{40} -5.00000 q^{41} -9.00000 q^{42} +5.00000 q^{43} +6.00000 q^{45} +8.00000 q^{46} -3.00000 q^{47} +3.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} -4.00000 q^{52} +4.00000 q^{53} +9.00000 q^{54} -9.00000 q^{56} -12.0000 q^{57} -6.00000 q^{58} -2.00000 q^{59} +3.00000 q^{60} -11.0000 q^{61} +2.00000 q^{62} -18.0000 q^{63} +7.00000 q^{64} +4.00000 q^{65} -13.0000 q^{67} +24.0000 q^{69} +3.00000 q^{70} +2.00000 q^{71} +18.0000 q^{72} -8.00000 q^{73} +8.00000 q^{74} -3.00000 q^{75} -4.00000 q^{76} +12.0000 q^{78} +10.0000 q^{79} -1.00000 q^{80} +9.00000 q^{81} +5.00000 q^{82} +4.00000 q^{83} -9.00000 q^{84} -5.00000 q^{86} -18.0000 q^{87} +1.00000 q^{89} -6.00000 q^{90} -12.0000 q^{91} +8.00000 q^{92} +6.00000 q^{93} +3.00000 q^{94} +4.00000 q^{95} +15.0000 q^{96} -8.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.00000	1.22474
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	3.00000	1.06066
$9$	6.00000	2.00000
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	3.00000	0.866025
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	3.00000	0.801784
$15$	−3.00000	−0.774597
$16$	−1.00000	−0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−6.00000	−1.41421
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−1.00000	−0.223607
$21$	9.00000	1.96396
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−9.00000	−1.83712
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	−9.00000	−1.73205
$28$	3.00000	0.566947
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	3.00000	0.547723
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	0	0
$35$	−3.00000	−0.507093
$36$	−6.00000	−1.00000
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	−4.00000	−0.648886
$39$	−12.0000	−1.92154
$40$	3.00000	0.474342
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	−9.00000	−1.38873
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	0	0
$45$	6.00000	0.894427
$46$	8.00000	1.17954
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	3.00000	0.433013
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−4.00000	−0.554700
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	9.00000	1.22474
$55$	0	0
$56$	−9.00000	−1.20268
$57$	−12.0000	−1.58944
$58$	−6.00000	−0.787839
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	3.00000	0.387298
$61$	−11.0000	−1.40841	−0.704203	−	0.709999i	$-0.748695\pi$
$61$	−11.0000	−1.40841	−0.704203	+	0.709999i	$0.748695\pi$
$62$	2.00000	0.254000
$63$	−18.0000	−2.26779
$64$	7.00000	0.875000
$65$	4.00000	0.496139
$66$	0	0
$67$	−13.0000	−1.58820	−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−13.0000	−1.58820	−0.794101	+	0.607785i	$0.792058\pi$
$68$	0	0
$69$	24.0000	2.88926
$70$	3.00000	0.358569
$71$	2.00000	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$72$	18.0000	2.12132
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	8.00000	0.929981
$75$	−3.00000	−0.346410
$76$	−4.00000	−0.458831
$77$	0	0
$78$	12.0000	1.35873
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	−1.00000	−0.111803
$81$	9.00000	1.00000
$82$	5.00000	0.552158
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−9.00000	−0.981981
$85$	0	0
$86$	−5.00000	−0.539164
$87$	−18.0000	−1.92980
$88$	0	0
$89$	1.00000	0.106000	0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000	0.106000	0.0529999	+	0.998595i	$0.483122\pi$
$90$	−6.00000	−0.632456
$91$	−12.0000	−1.25794
$92$	8.00000	0.834058
$93$	6.00000	0.622171
$94$	3.00000	0.309426
$95$	4.00000	0.410391
$96$	15.0000	1.53093
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−5.00000	−0.497519	−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000	−0.497519	−0.248759	+	0.968565i	$0.580023\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	12.0000	1.17670
$105$	9.00000	0.878310
$106$	−4.00000	−0.388514
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	9.00000	0.866025
$109$	−9.00000	−0.862044	−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000	−0.862044	−0.431022	+	0.902342i	$0.641847\pi$
$110$	0	0
$111$	24.0000	2.27798
$112$	3.00000	0.283473
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	12.0000	1.12390
$115$	−8.00000	−0.746004
$116$	−6.00000	−0.557086
$117$	24.0000	2.21880
$118$	2.00000	0.184115
$119$	0	0
$120$	−9.00000	−0.821584
$121$	0	0
$122$	11.0000	0.995893
$123$	15.0000	1.35250
$124$	2.00000	0.179605
$125$	1.00000	0.0894427
$126$	18.0000	1.60357
$127$	11.0000	0.976092	0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000	0.976092	0.488046	+	0.872818i	$0.337710\pi$
$128$	3.00000	0.265165
$129$	−15.0000	−1.32068
$130$	−4.00000	−0.350823
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−12.0000	−1.04053
$134$	13.0000	1.12303
$135$	−9.00000	−0.774597
$136$	0	0
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	−24.0000	−2.04302
$139$	−18.0000	−1.52674	−0.763370	−	0.645961i	$-0.776457\pi$
$139$	−18.0000	−1.52674	−0.763370	+	0.645961i	$0.776457\pi$
$140$	3.00000	0.253546
$141$	9.00000	0.757937
$142$	−2.00000	−0.167836
$143$	0	0
$144$	−6.00000	−0.500000
$145$	6.00000	0.498273
$146$	8.00000	0.662085
$147$	−6.00000	−0.494872
$148$	8.00000	0.657596
$149$	−17.0000	−1.39269	−0.696347	−	0.717705i	$-0.745193\pi$
$149$	−17.0000	−1.39269	−0.696347	+	0.717705i	$0.745193\pi$
$150$	3.00000	0.244949
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	12.0000	0.973329
$153$	0	0
$154$	0	0
$155$	−2.00000	−0.160644
$156$	12.0000	0.960769
$157$	−8.00000	−0.638470	−0.319235	−	0.947676i	$-0.603426\pi$
$157$	−8.00000	−0.638470	−0.319235	+	0.947676i	$0.603426\pi$
$158$	−10.0000	−0.795557
$159$	−12.0000	−0.951662
$160$	−5.00000	−0.395285
$161$	24.0000	1.89146
$162$	−9.00000	−0.707107
$163$	−17.0000	−1.33154	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000	−1.33154	−0.665771	+	0.746156i	$0.731897\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−7.00000	−0.541676	−0.270838	−	0.962625i	$-0.587301\pi$
$167$	−7.00000	−0.541676	−0.270838	+	0.962625i	$0.587301\pi$
$168$	27.0000	2.08310
$169$	3.00000	0.230769
$170$	0	0
$171$	24.0000	1.83533
$172$	−5.00000	−0.381246
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	18.0000	1.36458
$175$	−3.00000	−0.226779
$176$	0	0
$177$	6.00000	0.450988
$178$	−1.00000	−0.0749532
$179$	−26.0000	−1.94333	−0.971666	−	0.236360i	$-0.924046\pi$
$179$	−26.0000	−1.94333	−0.971666	+	0.236360i	$0.924046\pi$
$180$	−6.00000	−0.447214
$181$	−19.0000	−1.41226	−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−19.0000	−1.41226	−0.706129	+	0.708083i	$0.749560\pi$
$182$	12.0000	0.889499
$183$	33.0000	2.43943
$184$	−24.0000	−1.76930
$185$	−8.00000	−0.588172
$186$	−6.00000	−0.439941
$187$	0	0
$188$	3.00000	0.218797
$189$	27.0000	1.96396
$190$	−4.00000	−0.290191
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	−21.0000	−1.51554
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	8.00000	0.574367
$195$	−12.0000	−0.859338
$196$	−2.00000	−0.142857
$197$	−14.0000	−0.997459	−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000	−0.997459	−0.498729	+	0.866758i	$0.666200\pi$
$198$	0	0
$199$	−6.00000	−0.425329	−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000	−0.425329	−0.212664	+	0.977125i	$0.568214\pi$
$200$	3.00000	0.212132
$201$	39.0000	2.75085
$202$	5.00000	0.351799
$203$	−18.0000	−1.26335
$204$	0	0
$205$	−5.00000	−0.349215
$206$	−8.00000	−0.557386
$207$	−48.0000	−3.33623
$208$	−4.00000	−0.277350
$209$	0	0
$210$	−9.00000	−0.621059
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	−4.00000	−0.274721
$213$	−6.00000	−0.411113
$214$	−9.00000	−0.615227
$215$	5.00000	0.340997
$216$	−27.0000	−1.83712
$217$	6.00000	0.407307
$218$	9.00000	0.609557
$219$	24.0000	1.62177
$220$	0	0
$221$	0	0
$222$	−24.0000	−1.61077
$223$	5.00000	0.334825	0.167412	−	0.985887i	$-0.446459\pi$
$223$	5.00000	0.334825	0.167412	+	0.985887i	$0.446459\pi$
$224$	15.0000	1.00223
$225$	6.00000	0.400000
$226$	−6.00000	−0.399114
$227$	−1.00000	−0.0663723	−0.0331862	−	0.999449i	$-0.510565\pi$
$227$	−1.00000	−0.0663723	−0.0331862	+	0.999449i	$0.510565\pi$
$228$	12.0000	0.794719
$229$	−1.00000	−0.0660819	−0.0330409	−	0.999454i	$-0.510519\pi$
$229$	−1.00000	−0.0660819	−0.0330409	+	0.999454i	$0.510519\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	18.0000	1.18176
$233$	−24.0000	−1.57229	−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000	−1.57229	−0.786146	+	0.618041i	$0.787927\pi$
$234$	−24.0000	−1.56893
$235$	−3.00000	−0.195698
$236$	2.00000	0.130189
$237$	−30.0000	−1.94871
$238$	0	0
$239$	4.00000	0.258738	0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000	0.258738	0.129369	+	0.991596i	$0.458705\pi$
$240$	3.00000	0.193649
$241$	23.0000	1.48156	0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000	1.48156	0.740780	+	0.671748i	$0.234456\pi$
$242$	0	0
$243$	0	0
$244$	11.0000	0.704203
$245$	2.00000	0.127775
$246$	−15.0000	−0.956365
$247$	16.0000	1.01806
$248$	−6.00000	−0.381000
$249$	−12.0000	−0.760469
$250$	−1.00000	−0.0632456
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	18.0000	1.13389
$253$	0	0
$254$	−11.0000	−0.690201
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	15.0000	0.933859
$259$	24.0000	1.49129
$260$	−4.00000	−0.248069
$261$	36.0000	2.22834
$262$	0	0
$263$	12.0000	0.739952	0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000	0.739952	0.369976	+	0.929041i	$0.379366\pi$
$264$	0	0
$265$	4.00000	0.245718
$266$	12.0000	0.735767
$267$	−3.00000	−0.183597
$268$	13.0000	0.794101
$269$	21.0000	1.28039	0.640196	−	0.768211i	$-0.278853\pi$
$269$	21.0000	1.28039	0.640196	+	0.768211i	$0.278853\pi$
$270$	9.00000	0.547723
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	36.0000	2.17882
$274$	0	0
$275$	0	0
$276$	−24.0000	−1.44463
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	18.0000	1.07957
$279$	−12.0000	−0.718421
$280$	−9.00000	−0.537853
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	−9.00000	−0.535942
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	−2.00000	−0.118678
$285$	−12.0000	−0.710819
$286$	0	0
$287$	15.0000	0.885422
$288$	−30.0000	−1.76777
$289$	−17.0000	−1.00000
$290$	−6.00000	−0.352332
$291$	24.0000	1.40690
$292$	8.00000	0.468165
$293$	−34.0000	−1.98630	−0.993151	−	0.116841i	$-0.962723\pi$
$293$	−34.0000	−1.98630	−0.993151	+	0.116841i	$0.962723\pi$
$294$	6.00000	0.349927
$295$	−2.00000	−0.116445
$296$	−24.0000	−1.39497
$297$	0	0
$298$	17.0000	0.984784
$299$	−32.0000	−1.85061
$300$	3.00000	0.173205
$301$	−15.0000	−0.864586
$302$	14.0000	0.805609
$303$	15.0000	0.861727
$304$	−4.00000	−0.229416
$305$	−11.0000	−0.629858
$306$	0	0
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	0	0
$309$	−24.0000	−1.36531
$310$	2.00000	0.113592
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	−36.0000	−2.03810
$313$	8.00000	0.452187	0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000	0.452187	0.226093	+	0.974106i	$0.427405\pi$
$314$	8.00000	0.451466
$315$	−18.0000	−1.01419
$316$	−10.0000	−0.562544
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	12.0000	0.672927
$319$	0	0
$320$	7.00000	0.391312
$321$	−27.0000	−1.50699
$322$	−24.0000	−1.33747
$323$	0	0
$324$	−9.00000	−0.500000
$325$	4.00000	0.221880
$326$	17.0000	0.941543
$327$	27.0000	1.49310
$328$	−15.0000	−0.828236
$329$	9.00000	0.496186
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−4.00000	−0.219529
$333$	−48.0000	−2.63038
$334$	7.00000	0.383023
$335$	−13.0000	−0.710266
$336$	−9.00000	−0.490990
$337$	−12.0000	−0.653682	−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000	−0.653682	−0.326841	+	0.945079i	$0.605984\pi$
$338$	−3.00000	−0.163178
$339$	−18.0000	−0.977626
$340$	0	0
$341$	0	0
$342$	−24.0000	−1.29777
$343$	15.0000	0.809924
$344$	15.0000	0.808746
$345$	24.0000	1.29212
$346$	−24.0000	−1.29025
$347$	7.00000	0.375780	0.187890	−	0.982190i	$-0.439835\pi$
$347$	7.00000	0.375780	0.187890	+	0.982190i	$0.439835\pi$
$348$	18.0000	0.964901
$349$	22.0000	1.17763	0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000	1.17763	0.588817	+	0.808267i	$0.299594\pi$
$350$	3.00000	0.160357
$351$	−36.0000	−1.92154
$352$	0	0
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	−6.00000	−0.318896
$355$	2.00000	0.106149
$356$	−1.00000	−0.0529999
$357$	0	0
$358$	26.0000	1.37414
$359$	−28.0000	−1.47778	−0.738892	−	0.673824i	$-0.764651\pi$
$359$	−28.0000	−1.47778	−0.738892	+	0.673824i	$0.764651\pi$
$360$	18.0000	0.948683
$361$	−3.00000	−0.157895
$362$	19.0000	0.998618
$363$	0	0
$364$	12.0000	0.628971
$365$	−8.00000	−0.418739
$366$	−33.0000	−1.72494
$367$	1.00000	0.0521996	0.0260998	−	0.999659i	$-0.491691\pi$
$367$	1.00000	0.0521996	0.0260998	+	0.999659i	$0.491691\pi$
$368$	8.00000	0.417029
$369$	−30.0000	−1.56174
$370$	8.00000	0.415900
$371$	−12.0000	−0.623009
$372$	−6.00000	−0.311086
$373$	18.0000	0.932005	0.466002	−	0.884783i	$-0.345694\pi$
$373$	18.0000	0.932005	0.466002	+	0.884783i	$0.345694\pi$
$374$	0	0
$375$	−3.00000	−0.154919
$376$	−9.00000	−0.464140
$377$	24.0000	1.23606
$378$	−27.0000	−1.38873
$379$	−22.0000	−1.13006	−0.565032	−	0.825069i	$-0.691136\pi$
$379$	−22.0000	−1.13006	−0.565032	+	0.825069i	$0.691136\pi$
$380$	−4.00000	−0.205196
$381$	−33.0000	−1.69064
$382$	−8.00000	−0.409316
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−9.00000	−0.459279
$385$	0	0
$386$	10.0000	0.508987
$387$	30.0000	1.52499
$388$	8.00000	0.406138
$389$	−3.00000	−0.152106	−0.0760530	−	0.997104i	$-0.524232\pi$
$389$	−3.00000	−0.152106	−0.0760530	+	0.997104i	$0.524232\pi$
$390$	12.0000	0.607644
$391$	0	0
$392$	6.00000	0.303046
$393$	0	0
$394$	14.0000	0.705310
$395$	10.0000	0.503155
$396$	0	0
$397$	−12.0000	−0.602263	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000	−0.602263	−0.301131	+	0.953583i	$0.597364\pi$
$398$	6.00000	0.300753
$399$	36.0000	1.80225
$400$	−1.00000	−0.0500000
$401$	−37.0000	−1.84769	−0.923846	−	0.382765i	$-0.874972\pi$
$401$	−37.0000	−1.84769	−0.923846	+	0.382765i	$0.874972\pi$
$402$	−39.0000	−1.94514
$403$	−8.00000	−0.398508
$404$	5.00000	0.248759
$405$	9.00000	0.447214
$406$	18.0000	0.893325
$407$	0	0
$408$	0	0
$409$	21.0000	1.03838	0.519192	−	0.854658i	$-0.326233\pi$
$409$	21.0000	1.03838	0.519192	+	0.854658i	$0.326233\pi$
$410$	5.00000	0.246932
$411$	0	0
$412$	−8.00000	−0.394132
$413$	6.00000	0.295241
$414$	48.0000	2.35907
$415$	4.00000	0.196352
$416$	−20.0000	−0.980581
$417$	54.0000	2.64439
$418$	0	0
$419$	32.0000	1.56330	0.781651	−	0.623716i	$-0.214378\pi$
$419$	32.0000	1.56330	0.781651	+	0.623716i	$0.214378\pi$
$420$	−9.00000	−0.439155
$421$	3.00000	0.146211	0.0731055	−	0.997324i	$-0.476709\pi$
$421$	3.00000	0.146211	0.0731055	+	0.997324i	$0.476709\pi$
$422$	22.0000	1.07094
$423$	−18.0000	−0.875190
$424$	12.0000	0.582772
$425$	0	0
$426$	6.00000	0.290701
$427$	33.0000	1.59698
$428$	−9.00000	−0.435031
$429$	0	0
$430$	−5.00000	−0.241121
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	9.00000	0.433013
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	−6.00000	−0.288009
$435$	−18.0000	−0.863034
$436$	9.00000	0.431022
$437$	−32.0000	−1.53077
$438$	−24.0000	−1.14676
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	0	0
$443$	−25.0000	−1.18779	−0.593893	−	0.804544i	$-0.702410\pi$
$443$	−25.0000	−1.18779	−0.593893	+	0.804544i	$0.702410\pi$
$444$	−24.0000	−1.13899
$445$	1.00000	0.0474045
$446$	−5.00000	−0.236757
$447$	51.0000	2.41222
$448$	−21.0000	−0.992157
$449$	−13.0000	−0.613508	−0.306754	−	0.951789i	$-0.599243\pi$
$449$	−13.0000	−0.613508	−0.306754	+	0.951789i	$0.599243\pi$
$450$	−6.00000	−0.282843
$451$	0	0
$452$	−6.00000	−0.282216
$453$	42.0000	1.97333
$454$	1.00000	0.0469323
$455$	−12.0000	−0.562569
$456$	−36.0000	−1.68585
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	1.00000	0.0467269
$459$	0	0
$460$	8.00000	0.373002
$461$	7.00000	0.326023	0.163011	−	0.986624i	$-0.447879\pi$
$461$	7.00000	0.326023	0.163011	+	0.986624i	$0.447879\pi$
$462$	0	0
$463$	−15.0000	−0.697109	−0.348555	−	0.937288i	$-0.613327\pi$
$463$	−15.0000	−0.697109	−0.348555	+	0.937288i	$0.613327\pi$
$464$	−6.00000	−0.278543
$465$	6.00000	0.278243
$466$	24.0000	1.11178
$467$	27.0000	1.24941	0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000	1.24941	0.624705	+	0.780860i	$0.285219\pi$
$468$	−24.0000	−1.10940
$469$	39.0000	1.80085
$470$	3.00000	0.138380
$471$	24.0000	1.10586
$472$	−6.00000	−0.276172
$473$	0	0
$474$	30.0000	1.37795
$475$	4.00000	0.183533
$476$	0	0
$477$	24.0000	1.09888
$478$	−4.00000	−0.182956
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	15.0000	0.684653
$481$	−32.0000	−1.45907
$482$	−23.0000	−1.04762
$483$	−72.0000	−3.27611
$484$	0	0
$485$	−8.00000	−0.363261
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	−33.0000	−1.49384
$489$	51.0000	2.30630
$490$	−2.00000	−0.0903508
$491$	22.0000	0.992846	0.496423	−	0.868081i	$-0.334646\pi$
$491$	22.0000	0.992846	0.496423	+	0.868081i	$0.334646\pi$
$492$	−15.0000	−0.676252
$493$	0	0
$494$	−16.0000	−0.719874
$495$	0	0
$496$	2.00000	0.0898027
$497$	−6.00000	−0.269137
$498$	12.0000	0.537733
$499$	−42.0000	−1.88018	−0.940089	−	0.340929i	$-0.889258\pi$
$499$	−42.0000	−1.88018	−0.940089	+	0.340929i	$0.889258\pi$
$500$	−1.00000	−0.0447214
$501$	21.0000	0.938211
$502$	−18.0000	−0.803379
$503$	13.0000	0.579641	0.289821	−	0.957081i	$-0.406404\pi$
$503$	13.0000	0.579641	0.289821	+	0.957081i	$0.406404\pi$
$504$	−54.0000	−2.40535
$505$	−5.00000	−0.222497
$506$	0	0
$507$	−9.00000	−0.399704
$508$	−11.0000	−0.488046
$509$	23.0000	1.01946	0.509729	−	0.860335i	$-0.329746\pi$
$509$	23.0000	1.01946	0.509729	+	0.860335i	$0.329746\pi$
$510$	0	0
$511$	24.0000	1.06170
$512$	11.0000	0.486136
$513$	−36.0000	−1.58944
$514$	6.00000	0.264649
$515$	8.00000	0.352522
$516$	15.0000	0.660338
$517$	0	0
$518$	−24.0000	−1.05450
$519$	−72.0000	−3.16045
$520$	12.0000	0.526235
$521$	15.0000	0.657162	0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000	0.657162	0.328581	+	0.944476i	$0.393430\pi$
$522$	−36.0000	−1.57568
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	0	0
$525$	9.00000	0.392792
$526$	−12.0000	−0.523225
$527$	0	0
$528$	0	0
$529$	41.0000	1.78261
$530$	−4.00000	−0.173749
$531$	−12.0000	−0.520756
$532$	12.0000	0.520266
$533$	−20.0000	−0.866296
$534$	3.00000	0.129823
$535$	9.00000	0.389104
$536$	−39.0000	−1.68454
$537$	78.0000	3.36595
$538$	−21.0000	−0.905374
$539$	0	0
$540$	9.00000	0.387298
$541$	31.0000	1.33279	0.666397	−	0.745597i	$-0.267836\pi$
$541$	31.0000	1.33279	0.666397	+	0.745597i	$0.267836\pi$
$542$	0	0
$543$	57.0000	2.44610
$544$	0	0
$545$	−9.00000	−0.385518
$546$	−36.0000	−1.54066
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	0	0
$549$	−66.0000	−2.81681
$550$	0	0
$551$	24.0000	1.02243
$552$	72.0000	3.06452
$553$	−30.0000	−1.27573
$554$	−14.0000	−0.594803
$555$	24.0000	1.01874
$556$	18.0000	0.763370
$557$	−28.0000	−1.18640	−0.593199	−	0.805056i	$-0.702135\pi$
$557$	−28.0000	−1.18640	−0.593199	+	0.805056i	$0.702135\pi$
$558$	12.0000	0.508001
$559$	20.0000	0.845910
$560$	3.00000	0.126773
$561$	0	0
$562$	6.00000	0.253095
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	−9.00000	−0.378968
$565$	6.00000	0.252422
$566$	13.0000	0.546431
$567$	−27.0000	−1.13389
$568$	6.00000	0.251754
$569$	−11.0000	−0.461144	−0.230572	−	0.973055i	$-0.574060\pi$
$569$	−11.0000	−0.461144	−0.230572	+	0.973055i	$0.574060\pi$
$570$	12.0000	0.502625
$571$	−18.0000	−0.753277	−0.376638	−	0.926360i	$-0.622920\pi$
$571$	−18.0000	−0.753277	−0.376638	+	0.926360i	$0.622920\pi$
$572$	0	0
$573$	−24.0000	−1.00261
$574$	−15.0000	−0.626088
$575$	−8.00000	−0.333623
$576$	42.0000	1.75000
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	17.0000	0.707107
$579$	30.0000	1.24676
$580$	−6.00000	−0.249136
$581$	−12.0000	−0.497844
$582$	−24.0000	−0.994832
$583$	0	0
$584$	−24.0000	−0.993127
$585$	24.0000	0.992278
$586$	34.0000	1.40453
$587$	21.0000	0.866763	0.433381	−	0.901211i	$-0.357320\pi$
$587$	21.0000	0.866763	0.433381	+	0.901211i	$0.357320\pi$
$588$	6.00000	0.247436
$589$	−8.00000	−0.329634
$590$	2.00000	0.0823387
$591$	42.0000	1.72765
$592$	8.00000	0.328798
$593$	44.0000	1.80686	0.903432	−	0.428732i	$-0.141040\pi$
$593$	44.0000	1.80686	0.903432	+	0.428732i	$0.141040\pi$
$594$	0	0
$595$	0	0
$596$	17.0000	0.696347
$597$	18.0000	0.736691
$598$	32.0000	1.30858
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	−9.00000	−0.367423
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	15.0000	0.611354
$603$	−78.0000	−3.17641
$604$	14.0000	0.569652
$605$	0	0
$606$	−15.0000	−0.609333
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	−20.0000	−0.811107
$609$	54.0000	2.18819
$610$	11.0000	0.445377
$611$	−12.0000	−0.485468
$612$	0	0
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	8.00000	0.322854
$615$	15.0000	0.604858
$616$	0	0
$617$	26.0000	1.04672	0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000	1.04672	0.523360	+	0.852111i	$0.324678\pi$
$618$	24.0000	0.965422
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	2.00000	0.0803219
$621$	72.0000	2.88926
$622$	−24.0000	−0.962312
$623$	−3.00000	−0.120192
$624$	12.0000	0.480384
$625$	1.00000	0.0400000
$626$	−8.00000	−0.319744
$627$	0	0
$628$	8.00000	0.319235
$629$	0	0
$630$	18.0000	0.717137
$631$	−44.0000	−1.75161	−0.875806	−	0.482663i	$-0.839670\pi$
$631$	−44.0000	−1.75161	−0.875806	+	0.482663i	$0.839670\pi$
$632$	30.0000	1.19334
$633$	66.0000	2.62326
$634$	−18.0000	−0.714871
$635$	11.0000	0.436522
$636$	12.0000	0.475831
$637$	8.00000	0.316972
$638$	0	0
$639$	12.0000	0.474713
$640$	3.00000	0.118585
$641$	−14.0000	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$642$	27.0000	1.06561
$643$	35.0000	1.38027	0.690133	−	0.723683i	$-0.257552\pi$
$643$	35.0000	1.38027	0.690133	+	0.723683i	$0.257552\pi$
$644$	−24.0000	−0.945732
$645$	−15.0000	−0.590624
$646$	0	0
$647$	−25.0000	−0.982851	−0.491426	−	0.870919i	$-0.663524\pi$
$647$	−25.0000	−0.982851	−0.491426	+	0.870919i	$0.663524\pi$
$648$	27.0000	1.06066
$649$	0	0
$650$	−4.00000	−0.156893
$651$	−18.0000	−0.705476
$652$	17.0000	0.665771
$653$	−34.0000	−1.33052	−0.665261	−	0.746611i	$-0.731680\pi$
$653$	−34.0000	−1.33052	−0.665261	+	0.746611i	$0.731680\pi$
$654$	−27.0000	−1.05578
$655$	0	0
$656$	5.00000	0.195217
$657$	−48.0000	−1.87266
$658$	−9.00000	−0.350857
$659$	−42.0000	−1.63609	−0.818044	−	0.575156i	$-0.804941\pi$
$659$	−42.0000	−1.63609	−0.818044	+	0.575156i	$0.804941\pi$
$660$	0	0
$661$	−37.0000	−1.43913	−0.719567	−	0.694423i	$-0.755660\pi$
$661$	−37.0000	−1.43913	−0.719567	+	0.694423i	$0.755660\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	12.0000	0.465690
$665$	−12.0000	−0.465340
$666$	48.0000	1.85996
$667$	−48.0000	−1.85857
$668$	7.00000	0.270838
$669$	−15.0000	−0.579934
$670$	13.0000	0.502234
$671$	0	0
$672$	−45.0000	−1.73591
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	12.0000	0.462223
$675$	−9.00000	−0.346410
$676$	−3.00000	−0.115385
$677$	−28.0000	−1.07613	−0.538064	−	0.842904i	$-0.680844\pi$
$677$	−28.0000	−1.07613	−0.538064	+	0.842904i	$0.680844\pi$
$678$	18.0000	0.691286
$679$	24.0000	0.921035
$680$	0	0
$681$	3.00000	0.114960
$682$	0	0
$683$	47.0000	1.79841	0.899203	−	0.437533i	$-0.144148\pi$
$683$	47.0000	1.79841	0.899203	+	0.437533i	$0.144148\pi$
$684$	−24.0000	−0.917663
$685$	0	0
$686$	−15.0000	−0.572703
$687$	3.00000	0.114457
$688$	−5.00000	−0.190623
$689$	16.0000	0.609551
$690$	−24.0000	−0.913664
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	−24.0000	−0.912343
$693$	0	0
$694$	−7.00000	−0.265716
$695$	−18.0000	−0.682779
$696$	−54.0000	−2.04686
$697$	0	0
$698$	−22.0000	−0.832712
$699$	72.0000	2.72329
$700$	3.00000	0.113389
$701$	38.0000	1.43524	0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000	1.43524	0.717620	+	0.696435i	$0.245231\pi$
$702$	36.0000	1.35873
$703$	−32.0000	−1.20690
$704$	0	0
$705$	9.00000	0.338960
$706$	−6.00000	−0.225813
$707$	15.0000	0.564133
$708$	−6.00000	−0.225494
$709$	−25.0000	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$710$	−2.00000	−0.0750587
$711$	60.0000	2.25018
$712$	3.00000	0.112430
$713$	16.0000	0.599205
$714$	0	0
$715$	0	0
$716$	26.0000	0.971666
$717$	−12.0000	−0.448148
$718$	28.0000	1.04495
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	−6.00000	−0.223607
$721$	−24.0000	−0.893807
$722$	3.00000	0.111648
$723$	−69.0000	−2.56614
$724$	19.0000	0.706129
$725$	6.00000	0.222834
$726$	0	0
$727$	−17.0000	−0.630495	−0.315248	−	0.949009i	$-0.602088\pi$
$727$	−17.0000	−0.630495	−0.315248	+	0.949009i	$0.602088\pi$
$728$	−36.0000	−1.33425
$729$	−27.0000	−1.00000
$730$	8.00000	0.296093
$731$	0	0
$732$	−33.0000	−1.21972
$733$	36.0000	1.32969	0.664845	−	0.746981i	$-0.268498\pi$
$733$	36.0000	1.32969	0.664845	+	0.746981i	$0.268498\pi$
$734$	−1.00000	−0.0369107
$735$	−6.00000	−0.221313
$736$	40.0000	1.47442
$737$	0	0
$738$	30.0000	1.10432
$739$	−10.0000	−0.367856	−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000	−0.367856	−0.183928	+	0.982940i	$0.558881\pi$
$740$	8.00000	0.294086
$741$	−48.0000	−1.76332
$742$	12.0000	0.440534
$743$	−7.00000	−0.256805	−0.128403	−	0.991722i	$-0.540985\pi$
$743$	−7.00000	−0.256805	−0.128403	+	0.991722i	$0.540985\pi$
$744$	18.0000	0.659912
$745$	−17.0000	−0.622832
$746$	−18.0000	−0.659027
$747$	24.0000	0.878114
$748$	0	0
$749$	−27.0000	−0.986559
$750$	3.00000	0.109545
$751$	10.0000	0.364905	0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000	0.364905	0.182453	+	0.983215i	$0.441596\pi$
$752$	3.00000	0.109399
$753$	−54.0000	−1.96787
$754$	−24.0000	−0.874028
$755$	−14.0000	−0.509512
$756$	−27.0000	−0.981981
$757$	−12.0000	−0.436147	−0.218074	−	0.975932i	$-0.569977\pi$
$757$	−12.0000	−0.436147	−0.218074	+	0.975932i	$0.569977\pi$
$758$	22.0000	0.799076
$759$	0	0
$760$	12.0000	0.435286
$761$	26.0000	0.942499	0.471250	−	0.882000i	$-0.343803\pi$
$761$	26.0000	0.942499	0.471250	+	0.882000i	$0.343803\pi$
$762$	33.0000	1.19546
$763$	27.0000	0.977466
$764$	−8.00000	−0.289430
$765$	0	0
$766$	0	0
$767$	−8.00000	−0.288863
$768$	51.0000	1.84030
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	18.0000	0.648254
$772$	10.0000	0.359908
$773$	−22.0000	−0.791285	−0.395643	−	0.918405i	$-0.629478\pi$
$773$	−22.0000	−0.791285	−0.395643	+	0.918405i	$0.629478\pi$
$774$	−30.0000	−1.07833
$775$	−2.00000	−0.0718421
$776$	−24.0000	−0.861550
$777$	−72.0000	−2.58299
$778$	3.00000	0.107555
$779$	−20.0000	−0.716574
$780$	12.0000	0.429669
$781$	0	0
$782$	0	0
$783$	−54.0000	−1.92980
$784$	−2.00000	−0.0714286
$785$	−8.00000	−0.285532
$786$	0	0
$787$	−43.0000	−1.53278	−0.766392	−	0.642373i	$-0.777950\pi$
$787$	−43.0000	−1.53278	−0.766392	+	0.642373i	$0.777950\pi$
$788$	14.0000	0.498729
$789$	−36.0000	−1.28163
$790$	−10.0000	−0.355784
$791$	−18.0000	−0.640006
$792$	0	0
$793$	−44.0000	−1.56249
$794$	12.0000	0.425864
$795$	−12.0000	−0.425596
$796$	6.00000	0.212664
$797$	−50.0000	−1.77109	−0.885545	−	0.464553i	$-0.846215\pi$
$797$	−50.0000	−1.77109	−0.885545	+	0.464553i	$0.846215\pi$
$798$	−36.0000	−1.27439
$799$	0	0
$800$	−5.00000	−0.176777
$801$	6.00000	0.212000
$802$	37.0000	1.30652
$803$	0	0
$804$	−39.0000	−1.37542
$805$	24.0000	0.845889
$806$	8.00000	0.281788
$807$	−63.0000	−2.21771
$808$	−15.0000	−0.527698
$809$	54.0000	1.89854	0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000	1.89854	0.949269	+	0.314464i	$0.101825\pi$
$810$	−9.00000	−0.316228
$811$	42.0000	1.47482	0.737410	−	0.675446i	$-0.236049\pi$
$811$	42.0000	1.47482	0.737410	+	0.675446i	$0.236049\pi$
$812$	18.0000	0.631676
$813$	0	0
$814$	0	0
$815$	−17.0000	−0.595484
$816$	0	0
$817$	20.0000	0.699711
$818$	−21.0000	−0.734248
$819$	−72.0000	−2.51588
$820$	5.00000	0.174608
$821$	−3.00000	−0.104701	−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000	−0.104701	−0.0523504	+	0.998629i	$0.516671\pi$
$822$	0	0
$823$	51.0000	1.77775	0.888874	−	0.458151i	$-0.151488\pi$
$823$	51.0000	1.77775	0.888874	+	0.458151i	$0.151488\pi$
$824$	24.0000	0.836080
$825$	0	0
$826$	−6.00000	−0.208767
$827$	45.0000	1.56480	0.782402	−	0.622774i	$-0.213994\pi$
$827$	45.0000	1.56480	0.782402	+	0.622774i	$0.213994\pi$
$828$	48.0000	1.66812
$829$	13.0000	0.451509	0.225754	−	0.974184i	$-0.427515\pi$
$829$	13.0000	0.451509	0.225754	+	0.974184i	$0.427515\pi$
$830$	−4.00000	−0.138842
$831$	−42.0000	−1.45696
$832$	28.0000	0.970725
$833$	0	0
$834$	−54.0000	−1.86987
$835$	−7.00000	−0.242245
$836$	0	0
$837$	18.0000	0.622171
$838$	−32.0000	−1.10542
$839$	−14.0000	−0.483334	−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000	−0.483334	−0.241667	+	0.970359i	$0.577694\pi$
$840$	27.0000	0.931589
$841$	7.00000	0.241379
$842$	−3.00000	−0.103387
$843$	18.0000	0.619953
$844$	22.0000	0.757271
$845$	3.00000	0.103203
$846$	18.0000	0.618853
$847$	0	0
$848$	−4.00000	−0.137361
$849$	39.0000	1.33848
$850$	0	0
$851$	64.0000	2.19389
$852$	6.00000	0.205557
$853$	−32.0000	−1.09566	−0.547830	−	0.836590i	$-0.684546\pi$
$853$	−32.0000	−1.09566	−0.547830	+	0.836590i	$0.684546\pi$
$854$	−33.0000	−1.12924
$855$	24.0000	0.820783
$856$	27.0000	0.922841
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	−5.00000	−0.170499
$861$	−45.0000	−1.53360
$862$	−18.0000	−0.613082
$863$	31.0000	1.05525	0.527626	−	0.849477i	$-0.323082\pi$
$863$	31.0000	1.05525	0.527626	+	0.849477i	$0.323082\pi$
$864$	45.0000	1.53093
$865$	24.0000	0.816024
$866$	−14.0000	−0.475739
$867$	51.0000	1.73205
$868$	−6.00000	−0.203653
$869$	0	0
$870$	18.0000	0.610257
$871$	−52.0000	−1.76195
$872$	−27.0000	−0.914335
$873$	−48.0000	−1.62455
$874$	32.0000	1.08242
$875$	−3.00000	−0.101419
$876$	−24.0000	−0.810885
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	−8.00000	−0.269987
$879$	102.000	3.44037
$880$	0	0
$881$	−15.0000	−0.505363	−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000	−0.505363	−0.252681	+	0.967550i	$0.581312\pi$
$882$	−12.0000	−0.404061
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	0	0
$885$	6.00000	0.201688
$886$	25.0000	0.839891
$887$	1.00000	0.0335767	0.0167884	−	0.999859i	$-0.494656\pi$
$887$	1.00000	0.0335767	0.0167884	+	0.999859i	$0.494656\pi$
$888$	72.0000	2.41616
$889$	−33.0000	−1.10678
$890$	−1.00000	−0.0335201
$891$	0	0
$892$	−5.00000	−0.167412
$893$	−12.0000	−0.401565
$894$	−51.0000	−1.70570
$895$	−26.0000	−0.869084
$896$	−9.00000	−0.300669
$897$	96.0000	3.20535
$898$	13.0000	0.433816
$899$	−12.0000	−0.400222
$900$	−6.00000	−0.200000
$901$	0	0
$902$	0	0
$903$	45.0000	1.49751
$904$	18.0000	0.598671
$905$	−19.0000	−0.631581
$906$	−42.0000	−1.39536
$907$	−43.0000	−1.42779	−0.713896	−	0.700252i	$-0.753071\pi$
$907$	−43.0000	−1.42779	−0.713896	+	0.700252i	$0.753071\pi$
$908$	1.00000	0.0331862
$909$	−30.0000	−0.995037
$910$	12.0000	0.397796
$911$	−34.0000	−1.12647	−0.563235	−	0.826297i	$-0.690443\pi$
$911$	−34.0000	−1.12647	−0.563235	+	0.826297i	$0.690443\pi$
$912$	12.0000	0.397360
$913$	0	0
$914$	−26.0000	−0.860004
$915$	33.0000	1.09095
$916$	1.00000	0.0330409
$917$	0	0
$918$	0	0
$919$	12.0000	0.395843	0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000	0.395843	0.197922	+	0.980218i	$0.436581\pi$
$920$	−24.0000	−0.791257
$921$	24.0000	0.790827
$922$	−7.00000	−0.230533
$923$	8.00000	0.263323
$924$	0	0
$925$	−8.00000	−0.263038
$926$	15.0000	0.492931
$927$	48.0000	1.57653
$928$	−30.0000	−0.984798
$929$	−26.0000	−0.853032	−0.426516	−	0.904480i	$-0.640259\pi$
$929$	−26.0000	−0.853032	−0.426516	+	0.904480i	$0.640259\pi$
$930$	−6.00000	−0.196748
$931$	8.00000	0.262189
$932$	24.0000	0.786146
$933$	−72.0000	−2.35717
$934$	−27.0000	−0.883467
$935$	0	0
$936$	72.0000	2.35339
$937$	−18.0000	−0.588034	−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000	−0.588034	−0.294017	+	0.955800i	$0.594992\pi$
$938$	−39.0000	−1.27340
$939$	−24.0000	−0.783210
$940$	3.00000	0.0978492
$941$	−13.0000	−0.423788	−0.211894	−	0.977293i	$-0.567963\pi$
$941$	−13.0000	−0.423788	−0.211894	+	0.977293i	$0.567963\pi$
$942$	−24.0000	−0.781962
$943$	40.0000	1.30258
$944$	2.00000	0.0650945
$945$	27.0000	0.878310
$946$	0	0
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	30.0000	0.974355
$949$	−32.0000	−1.03876
$950$	−4.00000	−0.129777
$951$	−54.0000	−1.75107
$952$	0	0
$953$	−36.0000	−1.16615	−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000	−1.16615	−0.583077	+	0.812417i	$0.698151\pi$
$954$	−24.0000	−0.777029
$955$	8.00000	0.258874
$956$	−4.00000	−0.129369
$957$	0	0
$958$	−6.00000	−0.193851
$959$	0	0
$960$	−21.0000	−0.677772
$961$	−27.0000	−0.870968
$962$	32.0000	1.03172
$963$	54.0000	1.74013
$964$	−23.0000	−0.740780
$965$	−10.0000	−0.321911
$966$	72.0000	2.31656
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	0	0
$969$	0	0
$970$	8.00000	0.256865
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	0	0
$973$	54.0000	1.73116
$974$	8.00000	0.256337
$975$	−12.0000	−0.384308
$976$	11.0000	0.352101
$977$	28.0000	0.895799	0.447900	−	0.894084i	$-0.352172\pi$
$977$	28.0000	0.895799	0.447900	+	0.894084i	$0.352172\pi$
$978$	−51.0000	−1.63080
$979$	0	0
$980$	−2.00000	−0.0638877
$981$	−54.0000	−1.72409
$982$	−22.0000	−0.702048
$983$	−61.0000	−1.94560	−0.972799	−	0.231651i	$-0.925587\pi$
$983$	−61.0000	−1.94560	−0.972799	+	0.231651i	$0.925587\pi$
$984$	45.0000	1.43455
$985$	−14.0000	−0.446077
$986$	0	0
$987$	−27.0000	−0.859419
$988$	−16.0000	−0.509028
$989$	−40.0000	−1.27193
$990$	0	0
$991$	20.0000	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$992$	10.0000	0.317500
$993$	60.0000	1.90404
$994$	6.00000	0.190308
$995$	−6.00000	−0.190213
$996$	12.0000	0.380235
$997$	52.0000	1.64686	0.823428	−	0.567420i	$-0.192059\pi$
$997$	52.0000	1.64686	0.823428	+	0.567420i	$0.192059\pi$
$998$	42.0000	1.32949
$999$	72.0000	2.27798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.a.1.1	✓	1
3.2	odd	2		5445.2.a.h.1.1		1
4.3	odd	2		9680.2.a.bf.1.1		1
5.4	even	2		3025.2.a.g.1.1		1
11.2	odd	10		605.2.g.b.81.1		4
11.3	even	5		605.2.g.d.251.1		4
11.4	even	5		605.2.g.d.511.1		4
11.5	even	5		605.2.g.d.366.1		4
11.6	odd	10		605.2.g.b.366.1		4
11.7	odd	10		605.2.g.b.511.1		4
11.8	odd	10		605.2.g.b.251.1		4
11.9	even	5		605.2.g.d.81.1		4
11.10	odd	2		605.2.a.c.1.1	yes	1
33.32	even	2		5445.2.a.d.1.1		1
44.43	even	2		9680.2.a.be.1.1		1
55.54	odd	2		3025.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.a.1.1	✓	1	1.1	even	1	trivial
605.2.a.c.1.1	yes	1	11.10	odd	2
605.2.g.b.81.1		4	11.2	odd	10
605.2.g.b.251.1		4	11.8	odd	10
605.2.g.b.366.1		4	11.6	odd	10
605.2.g.b.511.1		4	11.7	odd	10
605.2.g.d.81.1		4	11.9	even	5
605.2.g.d.251.1		4	11.3	even	5
605.2.g.d.366.1		4	11.5	even	5
605.2.g.d.511.1		4	11.4	even	5
3025.2.a.c.1.1		1	55.54	odd	2
3025.2.a.g.1.1		1	5.4	even	2
5445.2.a.d.1.1		1	33.32	even	2
5445.2.a.h.1.1		1	3.2	odd	2
9680.2.a.be.1.1		1	44.43	even	2
9680.2.a.bf.1.1		1	4.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more