LMFDB - Embedded newform 3549.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
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:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24698 q^{2} -1.00000 q^{3} +3.04892 q^{4} +2.24698 q^{6} +1.00000 q^{7} -2.35690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.24698 q^{2} -1.00000 q^{3} +3.04892 q^{4} +2.24698 q^{6} +1.00000 q^{7} -2.35690 q^{8} +1.00000 q^{9} +1.24698 q^{11} -3.04892 q^{12} -2.24698 q^{14} -0.801938 q^{16} +0.890084 q^{17} -2.24698 q^{18} +4.71379 q^{19} -1.00000 q^{21} -2.80194 q^{22} -0.225209 q^{23} +2.35690 q^{24} -5.00000 q^{25} -1.00000 q^{27} +3.04892 q^{28} -7.40581 q^{29} +0.396125 q^{31} +6.51573 q^{32} -1.24698 q^{33} -2.00000 q^{34} +3.04892 q^{36} +3.65279 q^{37} -10.5918 q^{38} -3.50604 q^{41} +2.24698 q^{42} +3.08815 q^{43} +3.80194 q^{44} +0.506041 q^{46} -8.81163 q^{47} +0.801938 q^{48} +1.00000 q^{49} +11.2349 q^{50} -0.890084 q^{51} -10.3666 q^{53} +2.24698 q^{54} -2.35690 q^{56} -4.71379 q^{57} +16.6407 q^{58} -7.20775 q^{59} -8.37196 q^{61} -0.890084 q^{62} +1.00000 q^{63} -13.0368 q^{64} +2.80194 q^{66} +9.15883 q^{67} +2.71379 q^{68} +0.225209 q^{69} -2.44504 q^{71} -2.35690 q^{72} -6.93362 q^{73} -8.20775 q^{74} +5.00000 q^{75} +14.3720 q^{76} +1.24698 q^{77} +5.12498 q^{79} +1.00000 q^{81} +7.87800 q^{82} +8.59179 q^{83} -3.04892 q^{84} -6.93900 q^{86} +7.40581 q^{87} -2.93900 q^{88} +0.670251 q^{89} -0.686645 q^{92} -0.396125 q^{93} +19.7995 q^{94} -6.51573 q^{96} +8.31767 q^{97} -2.24698 q^{98} +1.24698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 3 q^{3} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 2 q^{2} - 3 q^{3} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - q^{11} - 2 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 6 q^{19} - 3 q^{21} - 4 q^{22} + q^{23} + 3 q^{24} - 15 q^{25} - 3 q^{27} - 9 q^{29} + 10 q^{31} + 7 q^{32} + q^{33} - 6 q^{34} - 7 q^{37} - 4 q^{38} - 20 q^{41} + 2 q^{42} + 13 q^{43} + 7 q^{44} + 11 q^{46} - 2 q^{48} + 3 q^{49} + 10 q^{50} - 2 q^{51} - 5 q^{53} + 2 q^{54} - 3 q^{56} - 6 q^{57} + 13 q^{58} - 4 q^{59} + 4 q^{61} - 2 q^{62} + 3 q^{63} - 11 q^{64} + 4 q^{66} + 19 q^{67} - q^{69} - 7 q^{71} - 3 q^{72} - 14 q^{73} - 7 q^{74} + 15 q^{75} + 14 q^{76} - q^{77} - 9 q^{79} + 3 q^{81} + 4 q^{82} - 2 q^{83} - 11 q^{86} + 9 q^{87} + q^{88} - 10 q^{93} + 14 q^{94} - 7 q^{96} + 8 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - q^11 - 2 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 6 * q^19 - 3 * q^21 - 4 * q^22 + q^23 + 3 * q^24 - 15 * q^25 - 3 * q^27 - 9 * q^29 + 10 * q^31 + 7 * q^32 + q^33 - 6 * q^34 - 7 * q^37 - 4 * q^38 - 20 * q^41 + 2 * q^42 + 13 * q^43 + 7 * q^44 + 11 * q^46 - 2 * q^48 + 3 * q^49 + 10 * q^50 - 2 * q^51 - 5 * q^53 + 2 * q^54 - 3 * q^56 - 6 * q^57 + 13 * q^58 - 4 * q^59 + 4 * q^61 - 2 * q^62 + 3 * q^63 - 11 * q^64 + 4 * q^66 + 19 * q^67 - q^69 - 7 * q^71 - 3 * q^72 - 14 * q^73 - 7 * q^74 + 15 * q^75 + 14 * q^76 - q^77 - 9 * q^79 + 3 * q^81 + 4 * q^82 - 2 * q^83 - 11 * q^86 + 9 * q^87 + q^88 - 10 * q^93 + 14 * q^94 - 7 * q^96 + 8 * q^97 - 2 * q^98 - 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 $

$2$	−2.24698	−1.58885	−0.794427	−	0.607359i	$-0.792229\pi$
$2$	−2.24698	−1.58885	−0.794427	+	0.607359i	$0.792229\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.04892	1.52446
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	2.24698	0.917326
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.35690	−0.833289
$9$	1.00000	0.333333
$10$	0	0
$11$	1.24698	0.375978	0.187989	−	0.982171i	$-0.439803\pi$
$11$	1.24698	0.375978	0.187989	+	0.982171i	$0.439803\pi$
$12$	−3.04892	−0.880147
$13$	0	0
$13$	0	0
$14$	−2.24698	−0.600531
$15$	0	0
$16$	−0.801938	−0.200484
$17$	0.890084	0.215877	0.107939	−	0.994158i	$-0.465575\pi$
$17$	0.890084	0.215877	0.107939	+	0.994158i	$0.465575\pi$
$18$	−2.24698	−0.529618
$19$	4.71379	1.08142	0.540709	−	0.841210i	$-0.318156\pi$
$19$	4.71379	1.08142	0.540709	+	0.841210i	$0.318156\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−2.80194	−0.597375
$23$	−0.225209	−0.0469594	−0.0234797	−	0.999724i	$-0.507475\pi$
$23$	−0.225209	−0.0469594	−0.0234797	+	0.999724i	$0.507475\pi$
$24$	2.35690	0.481099
$25$	−5.00000	−1.00000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	3.04892	0.576191
$29$	−7.40581	−1.37522	−0.687612	−	0.726078i	$-0.741341\pi$
$29$	−7.40581	−1.37522	−0.687612	+	0.726078i	$0.741341\pi$
$30$	0	0
$31$	0.396125	0.0711461	0.0355730	−	0.999367i	$-0.488674\pi$
$31$	0.396125	0.0711461	0.0355730	+	0.999367i	$0.488674\pi$
$32$	6.51573	1.15183
$33$	−1.24698	−0.217071
$34$	−2.00000	−0.342997
$35$	0	0
$36$	3.04892	0.508153
$37$	3.65279	0.600515	0.300258	−	0.953858i	$-0.402927\pi$
$37$	3.65279	0.600515	0.300258	+	0.953858i	$0.402927\pi$
$38$	−10.5918	−1.71822
$39$	0	0
$40$	0	0
$41$	−3.50604	−0.547552	−0.273776	−	0.961794i	$-0.588273\pi$
$41$	−3.50604	−0.547552	−0.273776	+	0.961794i	$0.588273\pi$
$42$	2.24698	0.346716
$43$	3.08815	0.470938	0.235469	−	0.971882i	$-0.424337\pi$
$43$	3.08815	0.470938	0.235469	+	0.971882i	$0.424337\pi$
$44$	3.80194	0.573164
$45$	0	0
$46$	0.506041	0.0746116
$47$	−8.81163	−1.28531	−0.642654	−	0.766157i	$-0.722167\pi$
$47$	−8.81163	−1.28531	−0.642654	+	0.766157i	$0.722167\pi$
$48$	0.801938	0.115750
$49$	1.00000	0.142857
$50$	11.2349	1.58885
$51$	−0.890084	−0.124637
$52$	0	0
$53$	−10.3666	−1.42396	−0.711980	−	0.702200i	$-0.752201\pi$
$53$	−10.3666	−1.42396	−0.711980	+	0.702200i	$0.752201\pi$
$54$	2.24698	0.305775
$55$	0	0
$56$	−2.35690	−0.314953
$57$	−4.71379	−0.624357
$58$	16.6407	2.18503
$59$	−7.20775	−0.938369	−0.469185	−	0.883100i	$-0.655452\pi$
$59$	−7.20775	−0.938369	−0.469185	+	0.883100i	$0.655452\pi$
$60$	0	0
$61$	−8.37196	−1.07192	−0.535960	−	0.844243i	$-0.680050\pi$
$61$	−8.37196	−1.07192	−0.535960	+	0.844243i	$0.680050\pi$
$62$	−0.890084	−0.113041
$63$	1.00000	0.125988
$64$	−13.0368	−1.62960
$65$	0	0
$66$	2.80194	0.344895
$67$	9.15883	1.11893	0.559465	−	0.828854i	$-0.311007\pi$
$67$	9.15883	1.11893	0.559465	+	0.828854i	$0.311007\pi$
$68$	2.71379	0.329096
$69$	0.225209	0.0271120
$70$	0	0
$71$	−2.44504	−0.290173	−0.145087	−	0.989419i	$-0.546346\pi$
$71$	−2.44504	−0.290173	−0.145087	+	0.989419i	$0.546346\pi$
$72$	−2.35690	−0.277763
$73$	−6.93362	−0.811519	−0.405760	−	0.913980i	$-0.632993\pi$
$73$	−6.93362	−0.811519	−0.405760	+	0.913980i	$0.632993\pi$
$74$	−8.20775	−0.954132
$75$	5.00000	0.577350
$76$	14.3720	1.64858
$77$	1.24698	0.142107
$78$	0	0
$79$	5.12498	0.576605	0.288303	−	0.957539i	$-0.406909\pi$
$79$	5.12498	0.576605	0.288303	+	0.957539i	$0.406909\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	7.87800	0.869980
$83$	8.59179	0.943072	0.471536	−	0.881847i	$-0.343700\pi$
$83$	8.59179	0.943072	0.471536	+	0.881847i	$0.343700\pi$
$84$	−3.04892	−0.332664
$85$	0	0
$86$	−6.93900	−0.748252
$87$	7.40581	0.793987
$88$	−2.93900	−0.313299
$89$	0.670251	0.0710465	0.0355232	−	0.999369i	$-0.488690\pi$
$89$	0.670251	0.0710465	0.0355232	+	0.999369i	$0.488690\pi$
$90$	0	0
$91$	0	0
$92$	−0.686645	−0.0715877
$93$	−0.396125	−0.0410762
$94$	19.7995	2.04217
$95$	0	0
$96$	−6.51573	−0.665009
$97$	8.31767	0.844531	0.422266	−	0.906472i	$-0.361235\pi$
$97$	8.31767	0.844531	0.422266	+	0.906472i	$0.361235\pi$
$98$	−2.24698	−0.226979
$99$	1.24698	0.125326
$100$	−15.2446	−1.52446
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	2.00000	0.198030
$103$	−1.06638	−0.105073	−0.0525366	−	0.998619i	$-0.516731\pi$
$103$	−1.06638	−0.105073	−0.0525366	+	0.998619i	$0.516731\pi$
$104$	0	0
$105$	0	0
$106$	23.2935	2.26247
$107$	−19.7409	−1.90843	−0.954214	−	0.299124i	$-0.903306\pi$
$107$	−19.7409	−1.90843	−0.954214	+	0.299124i	$0.903306\pi$
$108$	−3.04892	−0.293382
$109$	2.31336	0.221579	0.110790	−	0.993844i	$-0.464662\pi$
$109$	2.31336	0.221579	0.110790	+	0.993844i	$0.464662\pi$
$110$	0	0
$111$	−3.65279	−0.346708
$112$	−0.801938	−0.0757760
$113$	13.0465	1.22731	0.613657	−	0.789573i	$-0.289698\pi$
$113$	13.0465	1.22731	0.613657	+	0.789573i	$0.289698\pi$
$114$	10.5918	0.992012
$115$	0	0
$116$	−22.5797	−2.09647
$117$	0	0
$118$	16.1957	1.49093
$119$	0.890084	0.0815938
$120$	0	0
$121$	−9.44504	−0.858640
$122$	18.8116	1.70312
$123$	3.50604	0.316129
$124$	1.20775	0.108459
$125$	0	0
$126$	−2.24698	−0.200177
$127$	−9.70410	−0.861100	−0.430550	−	0.902567i	$-0.641680\pi$
$127$	−9.70410	−0.861100	−0.430550	+	0.902567i	$0.641680\pi$
$128$	16.2620	1.43738
$129$	−3.08815	−0.271896
$130$	0	0
$131$	−14.2741	−1.24714	−0.623568	−	0.781769i	$-0.714318\pi$
$131$	−14.2741	−1.24714	−0.623568	+	0.781769i	$0.714318\pi$
$132$	−3.80194	−0.330916
$133$	4.71379	0.408738
$134$	−20.5797	−1.77782
$135$	0	0
$136$	−2.09783	−0.179888
$137$	−13.8388	−1.18233	−0.591163	−	0.806552i	$-0.701331\pi$
$137$	−13.8388	−1.18233	−0.591163	+	0.806552i	$0.701331\pi$
$138$	−0.506041	−0.0430771
$139$	17.7017	1.50144	0.750720	−	0.660621i	$-0.229707\pi$
$139$	17.7017	1.50144	0.750720	+	0.660621i	$0.229707\pi$
$140$	0	0
$141$	8.81163	0.742073
$142$	5.49396	0.461043
$143$	0	0
$144$	−0.801938	−0.0668281
$145$	0	0
$146$	15.5797	1.28939
$147$	−1.00000	−0.0824786
$148$	11.1371	0.915461
$149$	4.63773	0.379937	0.189969	−	0.981790i	$-0.439161\pi$
$149$	4.63773	0.379937	0.189969	+	0.981790i	$0.439161\pi$
$150$	−11.2349	−0.917326
$151$	0.0760644	0.00619003	0.00309502	−	0.999995i	$-0.499015\pi$
$151$	0.0760644	0.00619003	0.00309502	+	0.999995i	$0.499015\pi$
$152$	−11.1099	−0.901133
$153$	0.890084	0.0719590
$154$	−2.80194	−0.225787
$155$	0	0
$156$	0	0
$157$	19.3599	1.54509	0.772543	−	0.634962i	$-0.218984\pi$
$157$	19.3599	1.54509	0.772543	+	0.634962i	$0.218984\pi$
$158$	−11.5157	−0.916142
$159$	10.3666	0.822124
$160$	0	0
$161$	−0.225209	−0.0177490
$162$	−2.24698	−0.176539
$163$	16.0761	1.25917	0.629587	−	0.776930i	$-0.283224\pi$
$163$	16.0761	1.25917	0.629587	+	0.776930i	$0.283224\pi$
$164$	−10.6896	−0.834720
$165$	0	0
$166$	−19.3056	−1.49840
$167$	23.2814	1.80157	0.900785	−	0.434265i	$-0.142992\pi$
$167$	23.2814	1.80157	0.900785	+	0.434265i	$0.142992\pi$
$168$	2.35690	0.181838
$169$	0	0
$170$	0	0
$171$	4.71379	0.360473
$172$	9.41550	0.717925
$173$	1.65817	0.126068	0.0630342	−	0.998011i	$-0.479922\pi$
$173$	1.65817	0.126068	0.0630342	+	0.998011i	$0.479922\pi$
$174$	−16.6407	−1.26153
$175$	−5.00000	−0.377964
$176$	−1.00000	−0.0753778
$177$	7.20775	0.541768
$178$	−1.50604	−0.112883
$179$	−9.52111	−0.711641	−0.355820	−	0.934554i	$-0.615799\pi$
$179$	−9.52111	−0.711641	−0.355820	+	0.934554i	$0.615799\pi$
$180$	0	0
$181$	26.3913	1.96165	0.980826	−	0.194884i	$-0.0624329\pi$
$181$	26.3913	1.96165	0.980826	+	0.194884i	$0.0624329\pi$
$182$	0	0
$183$	8.37196	0.618873
$184$	0.530795	0.0391307
$185$	0	0
$186$	0.890084	0.0652641
$187$	1.10992	0.0811651
$188$	−26.8659	−1.95940
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	15.5036	1.12180	0.560902	−	0.827882i	$-0.310454\pi$
$191$	15.5036	1.12180	0.560902	+	0.827882i	$0.310454\pi$
$192$	13.0368	0.940853
$193$	−13.2054	−0.950542	−0.475271	−	0.879839i	$-0.657650\pi$
$193$	−13.2054	−0.950542	−0.475271	+	0.879839i	$0.657650\pi$
$194$	−18.6896	−1.34184
$195$	0	0
$196$	3.04892	0.217780
$197$	4.65950	0.331975	0.165988	−	0.986128i	$-0.446919\pi$
$197$	4.65950	0.331975	0.165988	+	0.986128i	$0.446919\pi$
$198$	−2.80194	−0.199125
$199$	−20.9095	−1.48223	−0.741116	−	0.671377i	$-0.765703\pi$
$199$	−20.9095	−1.48223	−0.741116	+	0.671377i	$0.765703\pi$
$200$	11.7845	0.833289
$201$	−9.15883	−0.646014
$202$	13.4819	0.948582
$203$	−7.40581	−0.519786
$204$	−2.71379	−0.190003
$205$	0	0
$206$	2.39612	0.166946
$207$	−0.225209	−0.0156531
$208$	0	0
$209$	5.87800	0.406590
$210$	0	0
$211$	−15.4765	−1.06545	−0.532723	−	0.846290i	$-0.678831\pi$
$211$	−15.4765	−1.06545	−0.532723	+	0.846290i	$0.678831\pi$
$212$	−31.6069	−2.17077
$213$	2.44504	0.167532
$214$	44.3575	3.03222
$215$	0	0
$216$	2.35690	0.160366
$217$	0.396125	0.0268907
$218$	−5.19806	−0.352057
$219$	6.93362	0.468531
$220$	0	0
$221$	0	0
$222$	8.20775	0.550868
$223$	−6.17629	−0.413595	−0.206798	−	0.978384i	$-0.566304\pi$
$223$	−6.17629	−0.413595	−0.206798	+	0.978384i	$0.566304\pi$
$224$	6.51573	0.435350
$225$	−5.00000	−0.333333
$226$	−29.3153	−1.95002
$227$	−23.6582	−1.57025	−0.785124	−	0.619339i	$-0.787401\pi$
$227$	−23.6582	−1.57025	−0.785124	+	0.619339i	$0.787401\pi$
$228$	−14.3720	−0.951806
$229$	−18.3961	−1.21565	−0.607825	−	0.794071i	$-0.707958\pi$
$229$	−18.3961	−1.21565	−0.607825	+	0.794071i	$0.707958\pi$
$230$	0	0
$231$	−1.24698	−0.0820452
$232$	17.4547	1.14596
$233$	25.7778	1.68876	0.844379	−	0.535746i	$-0.179970\pi$
$233$	25.7778	1.68876	0.844379	+	0.535746i	$0.179970\pi$
$234$	0	0
$235$	0	0
$236$	−21.9758	−1.43051
$237$	−5.12498	−0.332903
$238$	−2.00000	−0.129641
$239$	−5.28382	−0.341782	−0.170891	−	0.985290i	$-0.554665\pi$
$239$	−5.28382	−0.341782	−0.170891	+	0.985290i	$0.554665\pi$
$240$	0	0
$241$	−22.8418	−1.47137	−0.735683	−	0.677326i	$-0.763139\pi$
$241$	−22.8418	−1.47137	−0.735683	+	0.677326i	$0.763139\pi$
$242$	21.2228	1.36425
$243$	−1.00000	−0.0641500
$244$	−25.5254	−1.63410
$245$	0	0
$246$	−7.87800	−0.502283
$247$	0	0
$248$	−0.933624	−0.0592852
$249$	−8.59179	−0.544483
$250$	0	0
$251$	−17.2862	−1.09110	−0.545548	−	0.838080i	$-0.683678\pi$
$251$	−17.2862	−1.09110	−0.545548	+	0.838080i	$0.683678\pi$
$252$	3.04892	0.192064
$253$	−0.280831	−0.0176557
$254$	21.8049	1.36816
$255$	0	0
$256$	−10.4668	−0.654176
$257$	−6.76809	−0.422182	−0.211091	−	0.977466i	$-0.567702\pi$
$257$	−6.76809	−0.422182	−0.211091	+	0.977466i	$0.567702\pi$
$258$	6.93900	0.432003
$259$	3.65279	0.226974
$260$	0	0
$261$	−7.40581	−0.458408
$262$	32.0737	1.98152
$263$	5.71678	0.352511	0.176256	−	0.984344i	$-0.443601\pi$
$263$	5.71678	0.352511	0.176256	+	0.984344i	$0.443601\pi$
$264$	2.93900	0.180883
$265$	0	0
$266$	−10.5918	−0.649425
$267$	−0.670251	−0.0410187
$268$	27.9245	1.70576
$269$	2.15213	0.131218	0.0656088	−	0.997845i	$-0.479101\pi$
$269$	2.15213	0.131218	0.0656088	+	0.997845i	$0.479101\pi$
$270$	0	0
$271$	−10.0435	−0.610102	−0.305051	−	0.952336i	$-0.598673\pi$
$271$	−10.0435	−0.610102	−0.305051	+	0.952336i	$0.598673\pi$
$272$	−0.713792	−0.0432800
$273$	0	0
$274$	31.0954	1.87854
$275$	−6.23490	−0.375978
$276$	0.686645	0.0413312
$277$	22.6746	1.36238	0.681191	−	0.732106i	$-0.261462\pi$
$277$	22.6746	1.36238	0.681191	+	0.732106i	$0.261462\pi$
$278$	−39.7754	−2.38557
$279$	0.396125	0.0237154
$280$	0	0
$281$	−16.6112	−0.990939	−0.495470	−	0.868625i	$-0.665004\pi$
$281$	−16.6112	−0.990939	−0.495470	+	0.868625i	$0.665004\pi$
$282$	−19.7995	−1.17905
$283$	−33.4470	−1.98822	−0.994108	−	0.108397i	$-0.965428\pi$
$283$	−33.4470	−1.98822	−0.994108	+	0.108397i	$0.965428\pi$
$284$	−7.45473	−0.442357
$285$	0	0
$286$	0	0
$287$	−3.50604	−0.206955
$288$	6.51573	0.383943
$289$	−16.2078	−0.953397
$290$	0	0
$291$	−8.31767	−0.487590
$292$	−21.1400	−1.23713
$293$	19.3599	1.13102	0.565508	−	0.824743i	$-0.308680\pi$
$293$	19.3599	1.13102	0.565508	+	0.824743i	$0.308680\pi$
$294$	2.24698	0.131047
$295$	0	0
$296$	−8.60925	−0.500403
$297$	−1.24698	−0.0723571
$298$	−10.4209	−0.603665
$299$	0	0
$300$	15.2446	0.880147
$301$	3.08815	0.177998
$302$	−0.170915	−0.00983506
$303$	6.00000	0.344691
$304$	−3.78017	−0.216807
$305$	0	0
$306$	−2.00000	−0.114332
$307$	−16.7681	−0.957005	−0.478503	−	0.878086i	$-0.658820\pi$
$307$	−16.7681	−0.957005	−0.478503	+	0.878086i	$0.658820\pi$
$308$	3.80194	0.216636
$309$	1.06638	0.0606640
$310$	0	0
$311$	1.62325	0.0920462	0.0460231	−	0.998940i	$-0.485345\pi$
$311$	1.62325	0.0920462	0.0460231	+	0.998940i	$0.485345\pi$
$312$	0	0
$313$	−17.7125	−1.00117	−0.500584	−	0.865688i	$-0.666881\pi$
$313$	−17.7125	−1.00117	−0.500584	+	0.865688i	$0.666881\pi$
$314$	−43.5013	−2.45492
$315$	0	0
$316$	15.6256	0.879011
$317$	−18.3569	−1.03103	−0.515513	−	0.856882i	$-0.672399\pi$
$317$	−18.3569	−1.03103	−0.515513	+	0.856882i	$0.672399\pi$
$318$	−23.2935	−1.30623
$319$	−9.23490	−0.517055
$320$	0	0
$321$	19.7409	1.10183
$322$	0.506041	0.0282006
$323$	4.19567	0.233453
$324$	3.04892	0.169384
$325$	0	0
$326$	−36.1226	−2.00065
$327$	−2.31336	−0.127929
$328$	8.26337	0.456268
$329$	−8.81163	−0.485801
$330$	0	0
$331$	18.2446	1.00281	0.501407	−	0.865212i	$-0.332816\pi$
$331$	18.2446	1.00281	0.501407	+	0.865212i	$0.332816\pi$
$332$	26.1957	1.43767
$333$	3.65279	0.200172
$334$	−52.3129	−2.86243
$335$	0	0
$336$	0.801938	0.0437493
$337$	31.8649	1.73579	0.867895	−	0.496748i	$-0.165473\pi$
$337$	31.8649	1.73579	0.867895	+	0.496748i	$0.165473\pi$
$338$	0	0
$339$	−13.0465	−0.708590
$340$	0	0
$341$	0.493959	0.0267494
$342$	−10.5918	−0.572739
$343$	1.00000	0.0539949
$344$	−7.27844	−0.392427
$345$	0	0
$346$	−3.72587	−0.200304
$347$	−30.9933	−1.66381	−0.831904	−	0.554920i	$-0.812749\pi$
$347$	−30.9933	−1.66381	−0.831904	+	0.554920i	$0.812749\pi$
$348$	22.5797	1.21040
$349$	−30.1280	−1.61271	−0.806357	−	0.591430i	$-0.798564\pi$
$349$	−30.1280	−1.61271	−0.806357	+	0.591430i	$0.798564\pi$
$350$	11.2349	0.600531
$351$	0	0
$352$	8.12498	0.433063
$353$	16.7681	0.892475	0.446238	−	0.894915i	$-0.352764\pi$
$353$	16.7681	0.892475	0.446238	+	0.894915i	$0.352764\pi$
$354$	−16.1957	−0.860790
$355$	0	0
$356$	2.04354	0.108307
$357$	−0.890084	−0.0471082
$358$	21.3937	1.13069
$359$	9.30021	0.490846	0.245423	−	0.969416i	$-0.421073\pi$
$359$	9.30021	0.490846	0.245423	+	0.969416i	$0.421073\pi$
$360$	0	0
$361$	3.21983	0.169465
$362$	−59.3008	−3.11678
$363$	9.44504	0.495736
$364$	0	0
$365$	0	0
$366$	−18.8116	−0.983299
$367$	12.7245	0.664216	0.332108	−	0.943241i	$-0.392240\pi$
$367$	12.7245	0.664216	0.332108	+	0.943241i	$0.392240\pi$
$368$	0.180604	0.00941463
$369$	−3.50604	−0.182517
$370$	0	0
$371$	−10.3666	−0.538206
$372$	−1.20775	−0.0626190
$373$	3.35929	0.173937	0.0869687	−	0.996211i	$-0.472282\pi$
$373$	3.35929	0.173937	0.0869687	+	0.996211i	$0.472282\pi$
$374$	−2.49396	−0.128960
$375$	0	0
$376$	20.7681	1.07103
$377$	0	0
$378$	2.24698	0.115572
$379$	−17.4601	−0.896865	−0.448433	−	0.893817i	$-0.648018\pi$
$379$	−17.4601	−0.896865	−0.448433	+	0.893817i	$0.648018\pi$
$380$	0	0
$381$	9.70410	0.497156
$382$	−34.8364	−1.78238
$383$	7.34913	0.375523	0.187761	−	0.982215i	$-0.439877\pi$
$383$	7.34913	0.375523	0.187761	+	0.982215i	$0.439877\pi$
$384$	−16.2620	−0.829869
$385$	0	0
$386$	29.6722	1.51027
$387$	3.08815	0.156979
$388$	25.3599	1.28745
$389$	−28.0586	−1.42263	−0.711314	−	0.702874i	$-0.751900\pi$
$389$	−28.0586	−1.42263	−0.711314	+	0.702874i	$0.751900\pi$
$390$	0	0
$391$	−0.200455	−0.0101375
$392$	−2.35690	−0.119041
$393$	14.2741	0.720034
$394$	−10.4698	−0.527461
$395$	0	0
$396$	3.80194	0.191055
$397$	−34.4698	−1.72999	−0.864995	−	0.501781i	$-0.832678\pi$
$397$	−34.4698	−1.72999	−0.864995	+	0.501781i	$0.832678\pi$
$398$	46.9831	2.35505
$399$	−4.71379	−0.235985
$400$	4.00969	0.200484
$401$	−18.1739	−0.907561	−0.453781	−	0.891113i	$-0.649925\pi$
$401$	−18.1739	−0.907561	−0.453781	+	0.891113i	$0.649925\pi$
$402$	20.5797	1.02642
$403$	0	0
$404$	−18.2935	−0.910136
$405$	0	0
$406$	16.6407	0.825865
$407$	4.55496	0.225781
$408$	2.09783	0.103858
$409$	−3.69096	−0.182506	−0.0912530	−	0.995828i	$-0.529087\pi$
$409$	−3.69096	−0.182506	−0.0912530	+	0.995828i	$0.529087\pi$
$410$	0	0
$411$	13.8388	0.682616
$412$	−3.25129	−0.160180
$413$	−7.20775	−0.354670
$414$	0.506041	0.0248705
$415$	0	0
$416$	0	0
$417$	−17.7017	−0.866856
$418$	−13.2078	−0.646012
$419$	14.2500	0.696156	0.348078	−	0.937466i	$-0.386834\pi$
$419$	14.2500	0.696156	0.348078	+	0.937466i	$0.386834\pi$
$420$	0	0
$421$	27.5362	1.34203	0.671015	−	0.741443i	$-0.265858\pi$
$421$	27.5362	1.34203	0.671015	+	0.741443i	$0.265858\pi$
$422$	34.7754	1.69284
$423$	−8.81163	−0.428436
$424$	24.4330	1.18657
$425$	−4.45042	−0.215877
$426$	−5.49396	−0.266183
$427$	−8.37196	−0.405148
$428$	−60.1885	−2.90932
$429$	0	0
$430$	0	0
$431$	−25.1202	−1.21000	−0.604999	−	0.796227i	$-0.706826\pi$
$431$	−25.1202	−1.21000	−0.604999	+	0.796227i	$0.706826\pi$
$432$	0.801938	0.0385832
$433$	13.3405	0.641104	0.320552	−	0.947231i	$-0.396132\pi$
$433$	13.3405	0.641104	0.320552	+	0.947231i	$0.396132\pi$
$434$	−0.890084	−0.0427254
$435$	0	0
$436$	7.05323	0.337788
$437$	−1.06159	−0.0507827
$438$	−15.5797	−0.744427
$439$	−30.3129	−1.44675	−0.723377	−	0.690453i	$-0.757411\pi$
$439$	−30.3129	−1.44675	−0.723377	+	0.690453i	$0.757411\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	−35.8998	−1.70565	−0.852825	−	0.522197i	$-0.825113\pi$
$443$	−35.8998	−1.70565	−0.852825	+	0.522197i	$0.825113\pi$
$444$	−11.1371	−0.528542
$445$	0	0
$446$	13.8780	0.657142
$447$	−4.63773	−0.219357
$448$	−13.0368	−0.615933
$449$	−0.695005	−0.0327993	−0.0163997	−	0.999866i	$-0.505220\pi$
$449$	−0.695005	−0.0327993	−0.0163997	+	0.999866i	$0.505220\pi$
$450$	11.2349	0.529618
$451$	−4.37196	−0.205868
$452$	39.7778	1.87099
$453$	−0.0760644	−0.00357382
$454$	53.1594	2.49490
$455$	0	0
$456$	11.1099	0.520269
$457$	−10.1564	−0.475098	−0.237549	−	0.971376i	$-0.576344\pi$
$457$	−10.1564	−0.475098	−0.237549	+	0.971376i	$0.576344\pi$
$458$	41.3357	1.93149
$459$	−0.890084	−0.0415456
$460$	0	0
$461$	−29.1642	−1.35831	−0.679156	−	0.733994i	$-0.737654\pi$
$461$	−29.1642	−1.35831	−0.679156	+	0.733994i	$0.737654\pi$
$462$	2.80194	0.130358
$463$	−16.5284	−0.768140	−0.384070	−	0.923304i	$-0.625478\pi$
$463$	−16.5284	−0.768140	−0.384070	+	0.923304i	$0.625478\pi$
$464$	5.93900	0.275711
$465$	0	0
$466$	−57.9221	−2.68319
$467$	6.50471	0.301002	0.150501	−	0.988610i	$-0.451911\pi$
$467$	6.50471	0.301002	0.150501	+	0.988610i	$0.451911\pi$
$468$	0	0
$469$	9.15883	0.422916
$470$	0	0
$471$	−19.3599	−0.892056
$472$	16.9879	0.781932
$473$	3.85086	0.177063
$474$	11.5157	0.528935
$475$	−23.5690	−1.08142
$476$	2.71379	0.124386
$477$	−10.3666	−0.474653
$478$	11.8726	0.543041
$479$	−17.5797	−0.803238	−0.401619	−	0.915807i	$-0.631552\pi$
$479$	−17.5797	−0.803238	−0.401619	+	0.915807i	$0.631552\pi$
$480$	0	0
$481$	0	0
$482$	51.3250	2.33779
$483$	0.225209	0.0102474
$484$	−28.7972	−1.30896
$485$	0	0
$486$	2.24698	0.101925
$487$	39.2664	1.77933	0.889664	−	0.456615i	$-0.150938\pi$
$487$	39.2664	1.77933	0.889664	+	0.456615i	$0.150938\pi$
$488$	19.7318	0.893218
$489$	−16.0761	−0.726985
$490$	0	0
$491$	15.9221	0.718556	0.359278	−	0.933231i	$-0.383023\pi$
$491$	15.9221	0.718556	0.359278	+	0.933231i	$0.383023\pi$
$492$	10.6896	0.481926
$493$	−6.59179	−0.296879
$494$	0	0
$495$	0	0
$496$	−0.317667	−0.0142637
$497$	−2.44504	−0.109675
$498$	19.3056	0.865104
$499$	20.3153	0.909437	0.454718	−	0.890635i	$-0.349740\pi$
$499$	20.3153	0.909437	0.454718	+	0.890635i	$0.349740\pi$
$500$	0	0
$501$	−23.2814	−1.04014
$502$	38.8418	1.73359
$503$	−7.10992	−0.317015	−0.158508	−	0.987358i	$-0.550668\pi$
$503$	−7.10992	−0.317015	−0.158508	+	0.987358i	$0.550668\pi$
$504$	−2.35690	−0.104984
$505$	0	0
$506$	0.631023	0.0280524
$507$	0	0
$508$	−29.5870	−1.31271
$509$	5.92633	0.262680	0.131340	−	0.991337i	$-0.458072\pi$
$509$	5.92633	0.262680	0.131340	+	0.991337i	$0.458072\pi$
$510$	0	0
$511$	−6.93362	−0.306725
$512$	−9.00538	−0.397985
$513$	−4.71379	−0.208119
$514$	15.2078	0.670785
$515$	0	0
$516$	−9.41550	−0.414494
$517$	−10.9879	−0.483248
$518$	−8.20775	−0.360628
$519$	−1.65817	−0.0727856
$520$	0	0
$521$	−12.9987	−0.569482	−0.284741	−	0.958604i	$-0.591908\pi$
$521$	−12.9987	−0.569482	−0.284741	+	0.958604i	$0.591908\pi$
$522$	16.6407	0.728344
$523$	−17.1943	−0.751856	−0.375928	−	0.926649i	$-0.622676\pi$
$523$	−17.1943	−0.751856	−0.375928	+	0.926649i	$0.622676\pi$
$524$	−43.5206	−1.90121
$525$	5.00000	0.218218
$526$	−12.8455	−0.560089
$527$	0.352584	0.0153588
$528$	1.00000	0.0435194
$529$	−22.9493	−0.997795
$530$	0	0
$531$	−7.20775	−0.312790
$532$	14.3720	0.623104
$533$	0	0
$534$	1.50604	0.0651728
$535$	0	0
$536$	−21.5864	−0.932391
$537$	9.52111	0.410866
$538$	−4.83579	−0.208486
$539$	1.24698	0.0537112
$540$	0	0
$541$	24.1420	1.03794	0.518972	−	0.854791i	$-0.326315\pi$
$541$	24.1420	1.03794	0.518972	+	0.854791i	$0.326315\pi$
$542$	22.5676	0.969363
$543$	−26.3913	−1.13256
$544$	5.79954	0.248653
$545$	0	0
$546$	0	0
$547$	−12.8025	−0.547397	−0.273698	−	0.961816i	$-0.588247\pi$
$547$	−12.8025	−0.547397	−0.273698	+	0.961816i	$0.588247\pi$
$548$	−42.1933	−1.80241
$549$	−8.37196	−0.357307
$550$	14.0097	0.597375
$551$	−34.9095	−1.48719
$552$	−0.530795	−0.0225921
$553$	5.12498	0.217936
$554$	−50.9493	−2.16463
$555$	0	0
$556$	53.9711	2.28888
$557$	−2.32783	−0.0986333	−0.0493167	−	0.998783i	$-0.515704\pi$
$557$	−2.32783	−0.0986333	−0.0493167	+	0.998783i	$0.515704\pi$
$558$	−0.890084	−0.0376802
$559$	0	0
$560$	0	0
$561$	−1.10992	−0.0468607
$562$	37.3250	1.57446
$563$	−3.98062	−0.167763	−0.0838816	−	0.996476i	$-0.526732\pi$
$563$	−3.98062	−0.167763	−0.0838816	+	0.996476i	$0.526732\pi$
$564$	26.8659	1.13126
$565$	0	0
$566$	75.1546	3.15899
$567$	1.00000	0.0419961
$568$	5.76271	0.241798
$569$	−9.39911	−0.394031	−0.197016	−	0.980400i	$-0.563125\pi$
$569$	−9.39911	−0.394031	−0.197016	+	0.980400i	$0.563125\pi$
$570$	0	0
$571$	−8.75973	−0.366583	−0.183292	−	0.983059i	$-0.558675\pi$
$571$	−8.75973	−0.366583	−0.183292	+	0.983059i	$0.558675\pi$
$572$	0	0
$573$	−15.5036	−0.647674
$574$	7.87800	0.328821
$575$	1.12605	0.0469594
$576$	−13.0368	−0.543201
$577$	−2.72455	−0.113424	−0.0567122	−	0.998391i	$-0.518062\pi$
$577$	−2.72455	−0.113424	−0.0567122	+	0.998391i	$0.518062\pi$
$578$	36.4185	1.51481
$579$	13.2054	0.548796
$580$	0	0
$581$	8.59179	0.356448
$582$	18.6896	0.774710
$583$	−12.9269	−0.535378
$584$	16.3418	0.676230
$585$	0	0
$586$	−43.5013	−1.79702
$587$	27.9866	1.15513	0.577565	−	0.816345i	$-0.304003\pi$
$587$	27.9866	1.15513	0.577565	+	0.816345i	$0.304003\pi$
$588$	−3.04892	−0.125735
$589$	1.86725	0.0769386
$590$	0	0
$591$	−4.65950	−0.191666
$592$	−2.92931	−0.120394
$593$	24.4784	1.00521	0.502604	−	0.864517i	$-0.332375\pi$
$593$	24.4784	1.00521	0.502604	+	0.864517i	$0.332375\pi$
$594$	2.80194	0.114965
$595$	0	0
$596$	14.1400	0.579199
$597$	20.9095	0.855767
$598$	0	0
$599$	−25.6752	−1.04906	−0.524529	−	0.851392i	$-0.675759\pi$
$599$	−25.6752	−1.04906	−0.524529	+	0.851392i	$0.675759\pi$
$600$	−11.7845	−0.481099
$601$	−32.1909	−1.31309	−0.656547	−	0.754285i	$-0.727984\pi$
$601$	−32.1909	−1.31309	−0.656547	+	0.754285i	$0.727984\pi$
$602$	−6.93900	−0.282813
$603$	9.15883	0.372977
$604$	0.231914	0.00943645
$605$	0	0
$606$	−13.4819	−0.547664
$607$	−20.0000	−0.811775	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000	−0.811775	−0.405887	+	0.913923i	$0.633038\pi$
$608$	30.7138	1.24561
$609$	7.40581	0.300099
$610$	0	0
$611$	0	0
$612$	2.71379	0.109699
$613$	−18.5023	−0.747302	−0.373651	−	0.927569i	$-0.621894\pi$
$613$	−18.5023	−0.747302	−0.373651	+	0.927569i	$0.621894\pi$
$614$	37.6775	1.52054
$615$	0	0
$616$	−2.93900	−0.118416
$617$	15.4491	0.621957	0.310978	−	0.950417i	$-0.399343\pi$
$617$	15.4491	0.621957	0.310978	+	0.950417i	$0.399343\pi$
$618$	−2.39612	−0.0963863
$619$	−25.1594	−1.01124	−0.505621	−	0.862756i	$-0.668737\pi$
$619$	−25.1594	−1.01124	−0.505621	+	0.862756i	$0.668737\pi$
$620$	0	0
$621$	0.225209	0.00903734
$622$	−3.64742	−0.146248
$623$	0.670251	0.0268530
$624$	0	0
$625$	25.0000	1.00000
$626$	39.7995	1.59071
$627$	−5.87800	−0.234745
$628$	59.0267	2.35542
$629$	3.25129	0.129637
$630$	0	0
$631$	−1.67324	−0.0666104	−0.0333052	−	0.999445i	$-0.510603\pi$
$631$	−1.67324	−0.0666104	−0.0333052	+	0.999445i	$0.510603\pi$
$632$	−12.0790	−0.480479
$633$	15.4765	0.615136
$634$	41.2476	1.63815
$635$	0	0
$636$	31.6069	1.25329
$637$	0	0
$638$	20.7506	0.821525
$639$	−2.44504	−0.0967244
$640$	0	0
$641$	11.2459	0.444187	0.222093	−	0.975025i	$-0.428711\pi$
$641$	11.2459	0.444187	0.222093	+	0.975025i	$0.428711\pi$
$642$	−44.3575	−1.75065
$643$	−43.6775	−1.72247	−0.861237	−	0.508203i	$-0.830310\pi$
$643$	−43.6775	−1.72247	−0.861237	+	0.508203i	$0.830310\pi$
$644$	−0.686645	−0.0270576
$645$	0	0
$646$	−9.42758	−0.370923
$647$	−19.9430	−0.784042	−0.392021	−	0.919956i	$-0.628224\pi$
$647$	−19.9430	−0.784042	−0.392021	+	0.919956i	$0.628224\pi$
$648$	−2.35690	−0.0925876
$649$	−8.98792	−0.352807
$650$	0	0
$651$	−0.396125	−0.0155253
$652$	49.0146	1.91956
$653$	−31.9928	−1.25198	−0.625988	−	0.779833i	$-0.715304\pi$
$653$	−31.9928	−1.25198	−0.625988	+	0.779833i	$0.715304\pi$
$654$	5.19806	0.203260
$655$	0	0
$656$	2.81163	0.109776
$657$	−6.93362	−0.270506
$658$	19.7995	0.771867
$659$	43.9821	1.71330	0.856649	−	0.515900i	$-0.172542\pi$
$659$	43.9821	1.71330	0.856649	+	0.515900i	$0.172542\pi$
$660$	0	0
$661$	36.4784	1.41885	0.709423	−	0.704783i	$-0.248956\pi$
$661$	36.4784	1.41885	0.709423	+	0.704783i	$0.248956\pi$
$662$	−40.9952	−1.59332
$663$	0	0
$664$	−20.2500	−0.785851
$665$	0	0
$666$	−8.20775	−0.318044
$667$	1.66786	0.0645797
$668$	70.9831	2.74642
$669$	6.17629	0.238789
$670$	0	0
$671$	−10.4397	−0.403019
$672$	−6.51573	−0.251350
$673$	12.8858	0.496710	0.248355	−	0.968669i	$-0.420110\pi$
$673$	12.8858	0.496710	0.248355	+	0.968669i	$0.420110\pi$
$674$	−71.5997	−2.75792
$675$	5.00000	0.192450
$676$	0	0
$677$	17.8431	0.685765	0.342883	−	0.939378i	$-0.388597\pi$
$677$	17.8431	0.685765	0.342883	+	0.939378i	$0.388597\pi$
$678$	29.3153	1.12585
$679$	8.31767	0.319203
$680$	0	0
$681$	23.6582	0.906583
$682$	−1.10992	−0.0425009
$683$	31.8431	1.21844	0.609221	−	0.793001i	$-0.291482\pi$
$683$	31.8431	1.21844	0.609221	+	0.793001i	$0.291482\pi$
$684$	14.3720	0.549526
$685$	0	0
$686$	−2.24698	−0.0857901
$687$	18.3961	0.701856
$688$	−2.47650	−0.0944157
$689$	0	0
$690$	0	0
$691$	−41.7405	−1.58788	−0.793941	−	0.607995i	$-0.791974\pi$
$691$	−41.7405	−1.58788	−0.793941	+	0.607995i	$0.791974\pi$
$692$	5.05562	0.192186
$693$	1.24698	0.0473688
$694$	69.6413	2.64355
$695$	0	0
$696$	−17.4547	−0.661620
$697$	−3.12067	−0.118204
$698$	67.6969	2.56237
$699$	−25.7778	−0.975005
$700$	−15.2446	−0.576191
$701$	42.0743	1.58912	0.794561	−	0.607184i	$-0.207701\pi$
$701$	42.0743	1.58912	0.794561	+	0.607184i	$0.207701\pi$
$702$	0	0
$703$	17.2185	0.649408
$704$	−16.2567	−0.612696
$705$	0	0
$706$	−37.6775	−1.41801
$707$	−6.00000	−0.225653
$708$	21.9758	0.825903
$709$	12.4131	0.466184	0.233092	−	0.972455i	$-0.425116\pi$
$709$	12.4131	0.466184	0.233092	+	0.972455i	$0.425116\pi$
$710$	0	0
$711$	5.12498	0.192202
$712$	−1.57971	−0.0592022
$713$	−0.0892109	−0.00334098
$714$	2.00000	0.0748481
$715$	0	0
$716$	−29.0291	−1.08487
$717$	5.28382	0.197328
$718$	−20.8974	−0.779883
$719$	−27.6474	−1.03107	−0.515537	−	0.856867i	$-0.672408\pi$
$719$	−27.6474	−1.03107	−0.515537	+	0.856867i	$0.672408\pi$
$720$	0	0
$721$	−1.06638	−0.0397139
$722$	−7.23490	−0.269255
$723$	22.8418	0.849494
$724$	80.4650	2.99046
$725$	37.0291	1.37522
$726$	−21.2228	−0.787653
$727$	16.0108	0.593806	0.296903	−	0.954908i	$-0.404046\pi$
$727$	16.0108	0.593806	0.296903	+	0.954908i	$0.404046\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	2.74871	0.101665
$732$	25.5254	0.943447
$733$	46.1038	1.70288	0.851441	−	0.524450i	$-0.175729\pi$
$733$	46.1038	1.70288	0.851441	+	0.524450i	$0.175729\pi$
$734$	−28.5918	−1.05534
$735$	0	0
$736$	−1.46740	−0.0540892
$737$	11.4209	0.420693
$738$	7.87800	0.289993
$739$	2.81641	0.103603	0.0518017	−	0.998657i	$-0.483504\pi$
$739$	2.81641	0.103603	0.0518017	+	0.998657i	$0.483504\pi$
$740$	0	0
$741$	0	0
$742$	23.2935	0.855131
$743$	32.6872	1.19918	0.599589	−	0.800308i	$-0.295331\pi$
$743$	32.6872	1.19918	0.599589	+	0.800308i	$0.295331\pi$
$744$	0.933624	0.0342283
$745$	0	0
$746$	−7.54825	−0.276361
$747$	8.59179	0.314357
$748$	3.38404	0.123733
$749$	−19.7409	−0.721318
$750$	0	0
$751$	19.2577	0.702725	0.351362	−	0.936240i	$-0.385719\pi$
$751$	19.2577	0.702725	0.351362	+	0.936240i	$0.385719\pi$
$752$	7.06638	0.257684
$753$	17.2862	0.629944
$754$	0	0
$755$	0	0
$756$	−3.04892	−0.110888
$757$	5.95885	0.216578	0.108289	−	0.994119i	$-0.465463\pi$
$757$	5.95885	0.216578	0.108289	+	0.994119i	$0.465463\pi$
$758$	39.2325	1.42499
$759$	0.280831	0.0101935
$760$	0	0
$761$	3.95167	0.143248	0.0716240	−	0.997432i	$-0.477182\pi$
$761$	3.95167	0.143248	0.0716240	+	0.997432i	$0.477182\pi$
$762$	−21.8049	−0.789909
$763$	2.31336	0.0837491
$764$	47.2693	1.71014
$765$	0	0
$766$	−16.5133	−0.596651
$767$	0	0
$768$	10.4668	0.377689
$769$	10.4263	0.375980	0.187990	−	0.982171i	$-0.439803\pi$
$769$	10.4263	0.375980	0.187990	+	0.982171i	$0.439803\pi$
$770$	0	0
$771$	6.76809	0.243747
$772$	−40.2620	−1.44906
$773$	2.28488	0.0821814	0.0410907	−	0.999155i	$-0.486917\pi$
$773$	2.28488	0.0821814	0.0410907	+	0.999155i	$0.486917\pi$
$774$	−6.93900	−0.249417
$775$	−1.98062	−0.0711461
$776$	−19.6039	−0.703738
$777$	−3.65279	−0.131043
$778$	63.0471	2.26035
$779$	−16.5267	−0.592132
$780$	0	0
$781$	−3.04892	−0.109099
$782$	0.450419	0.0161069
$783$	7.40581	0.264662
$784$	−0.801938	−0.0286406
$785$	0	0
$786$	−32.0737	−1.14403
$787$	−27.4383	−0.978071	−0.489036	−	0.872264i	$-0.662651\pi$
$787$	−27.4383	−0.978071	−0.489036	+	0.872264i	$0.662651\pi$
$788$	14.2064	0.506083
$789$	−5.71678	−0.203523
$790$	0	0
$791$	13.0465	0.463881
$792$	−2.93900	−0.104433
$793$	0	0
$794$	77.4529	2.74870
$795$	0	0
$796$	−63.7512	−2.25960
$797$	27.5314	0.975212	0.487606	−	0.873064i	$-0.337870\pi$
$797$	27.5314	0.975212	0.487606	+	0.873064i	$0.337870\pi$
$798$	10.5918	0.374945
$799$	−7.84309	−0.277468
$800$	−32.5786	−1.15183
$801$	0.670251	0.0236822
$802$	40.8364	1.44198
$803$	−8.64609	−0.305114
$804$	−27.9245	−0.984822
$805$	0	0
$806$	0	0
$807$	−2.15213	−0.0757585
$808$	14.1414	0.497492
$809$	−15.7071	−0.552232	−0.276116	−	0.961124i	$-0.589047\pi$
$809$	−15.7071	−0.552232	−0.276116	+	0.961124i	$0.589047\pi$
$810$	0	0
$811$	5.78017	0.202969	0.101485	−	0.994837i	$-0.467641\pi$
$811$	5.78017	0.202969	0.101485	+	0.994837i	$0.467641\pi$
$812$	−22.5797	−0.792393
$813$	10.0435	0.352242
$814$	−10.2349	−0.358733
$815$	0	0
$816$	0.713792	0.0249877
$817$	14.5569	0.509281
$818$	8.29350	0.289976
$819$	0	0
$820$	0	0
$821$	33.9377	1.18443	0.592216	−	0.805779i	$-0.298253\pi$
$821$	33.9377	1.18443	0.592216	+	0.805779i	$0.298253\pi$
$822$	−31.0954	−1.08458
$823$	−5.85325	−0.204031	−0.102016	−	0.994783i	$-0.532529\pi$
$823$	−5.85325	−0.204031	−0.102016	+	0.994783i	$0.532529\pi$
$824$	2.51334	0.0875562
$825$	6.23490	0.217071
$826$	16.1957	0.563519
$827$	−26.3376	−0.915849	−0.457925	−	0.888991i	$-0.651407\pi$
$827$	−26.3376	−0.915849	−0.457925	+	0.888991i	$0.651407\pi$
$828$	−0.686645	−0.0238626
$829$	26.2258	0.910860	0.455430	−	0.890272i	$-0.349486\pi$
$829$	26.2258	0.910860	0.455430	+	0.890272i	$0.349486\pi$
$830$	0	0
$831$	−22.6746	−0.786572
$832$	0	0
$833$	0.890084	0.0308396
$834$	39.7754	1.37731
$835$	0	0
$836$	17.9215	0.619830
$837$	−0.396125	−0.0136921
$838$	−32.0194	−1.10609
$839$	23.9711	0.827573	0.413786	−	0.910374i	$-0.364206\pi$
$839$	23.9711	0.827573	0.413786	+	0.910374i	$0.364206\pi$
$840$	0	0
$841$	25.8461	0.891244
$842$	−61.8732	−2.13229
$843$	16.6112	0.572119
$844$	−47.1866	−1.62423
$845$	0	0
$846$	19.7995	0.680722
$847$	−9.44504	−0.324535
$848$	8.31336	0.285482
$849$	33.4470	1.14790
$850$	10.0000	0.342997
$851$	−0.822643	−0.0281998
$852$	7.45473	0.255395
$853$	−12.2849	−0.420626	−0.210313	−	0.977634i	$-0.567448\pi$
$853$	−12.2849	−0.420626	−0.210313	+	0.977634i	$0.567448\pi$
$854$	18.8116	0.643721
$855$	0	0
$856$	46.5273	1.59027
$857$	10.8116	0.369318	0.184659	−	0.982803i	$-0.440882\pi$
$857$	10.8116	0.369318	0.184659	+	0.982803i	$0.440882\pi$
$858$	0	0
$859$	14.4698	0.493703	0.246852	−	0.969053i	$-0.420604\pi$
$859$	14.4698	0.493703	0.246852	+	0.969053i	$0.420604\pi$
$860$	0	0
$861$	3.50604	0.119486
$862$	56.4446	1.92251
$863$	11.9849	0.407972	0.203986	−	0.978974i	$-0.434610\pi$
$863$	11.9849	0.407972	0.203986	+	0.978974i	$0.434610\pi$
$864$	−6.51573	−0.221670
$865$	0	0
$866$	−29.9758	−1.01862
$867$	16.2078	0.550444
$868$	1.20775	0.0409937
$869$	6.39075	0.216791
$870$	0	0
$871$	0	0
$872$	−5.45234	−0.184639
$873$	8.31767	0.281510
$874$	2.38537	0.0806864
$875$	0	0
$876$	21.1400	0.714256
$877$	−45.0417	−1.52095	−0.760476	−	0.649366i	$-0.775034\pi$
$877$	−45.0417	−1.52095	−0.760476	+	0.649366i	$0.775034\pi$
$878$	68.1124	2.29868
$879$	−19.3599	−0.652993
$880$	0	0
$881$	12.4370	0.419013	0.209507	−	0.977807i	$-0.432814\pi$
$881$	12.4370	0.419013	0.209507	+	0.977807i	$0.432814\pi$
$882$	−2.24698	−0.0756597
$883$	−32.5198	−1.09438	−0.547189	−	0.837009i	$-0.684302\pi$
$883$	−32.5198	−1.09438	−0.547189	+	0.837009i	$0.684302\pi$
$884$	0	0
$885$	0	0
$886$	80.6661	2.71003
$887$	−10.5724	−0.354987	−0.177494	−	0.984122i	$-0.556799\pi$
$887$	−10.5724	−0.354987	−0.177494	+	0.984122i	$0.556799\pi$
$888$	8.60925	0.288908
$889$	−9.70410	−0.325465
$890$	0	0
$891$	1.24698	0.0417754
$892$	−18.8310	−0.630509
$893$	−41.5362	−1.38995
$894$	10.4209	0.348526
$895$	0	0
$896$	16.2620	0.543277
$897$	0	0
$898$	1.56166	0.0521134
$899$	−2.93362	−0.0978418
$900$	−15.2446	−0.508153
$901$	−9.22713	−0.307400
$902$	9.82371	0.327094
$903$	−3.08815	−0.102767
$904$	−30.7493	−1.02271
$905$	0	0
$906$	0.170915	0.00567828
$907$	48.8450	1.62187	0.810936	−	0.585135i	$-0.198959\pi$
$907$	48.8450	1.62187	0.810936	+	0.585135i	$0.198959\pi$
$908$	−72.1318	−2.39378
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−36.0200	−1.19339	−0.596697	−	0.802466i	$-0.703521\pi$
$911$	−36.0200	−1.19339	−0.596697	+	0.802466i	$0.703521\pi$
$912$	3.78017	0.125174
$913$	10.7138	0.354575
$914$	22.8213	0.754862
$915$	0	0
$916$	−56.0883	−1.85321
$917$	−14.2741	−0.471373
$918$	2.00000	0.0660098
$919$	15.0261	0.495665	0.247832	−	0.968803i	$-0.420282\pi$
$919$	15.0261	0.495665	0.247832	+	0.968803i	$0.420282\pi$
$920$	0	0
$921$	16.7681	0.552527
$922$	65.5314	2.15816
$923$	0	0
$924$	−3.80194	−0.125075
$925$	−18.2640	−0.600515
$926$	37.1390	1.22046
$927$	−1.06638	−0.0350244
$928$	−48.2543	−1.58402
$929$	16.2440	0.532948	0.266474	−	0.963842i	$-0.414141\pi$
$929$	16.2440	0.532948	0.266474	+	0.963842i	$0.414141\pi$
$930$	0	0
$931$	4.71379	0.154488
$932$	78.5943	2.57444
$933$	−1.62325	−0.0531429
$934$	−14.6160	−0.478249
$935$	0	0
$936$	0	0
$937$	5.40342	0.176522	0.0882610	−	0.996097i	$-0.471869\pi$
$937$	5.40342	0.176522	0.0882610	+	0.996097i	$0.471869\pi$
$938$	−20.5797	−0.671951
$939$	17.7125	0.578024
$940$	0	0
$941$	38.6327	1.25939	0.629695	−	0.776843i	$-0.283180\pi$
$941$	38.6327	1.25939	0.629695	+	0.776843i	$0.283180\pi$
$942$	43.5013	1.41735
$943$	0.789593	0.0257127
$944$	5.78017	0.188128
$945$	0	0
$946$	−8.65279	−0.281327
$947$	−23.0696	−0.749662	−0.374831	−	0.927093i	$-0.622299\pi$
$947$	−23.0696	−0.749662	−0.374831	+	0.927093i	$0.622299\pi$
$948$	−15.6256	−0.507497
$949$	0	0
$950$	52.9590	1.71822
$951$	18.3569	0.595263
$952$	−2.09783	−0.0679912
$953$	17.7205	0.574023	0.287012	−	0.957927i	$-0.407338\pi$
$953$	17.7205	0.574023	0.287012	+	0.957927i	$0.407338\pi$
$954$	23.2935	0.754155
$955$	0	0
$956$	−16.1099	−0.521032
$957$	9.23490	0.298522
$958$	39.5013	1.27623
$959$	−13.8388	−0.446877
$960$	0	0
$961$	−30.8431	−0.994938
$962$	0	0
$963$	−19.7409	−0.636143
$964$	−69.6426	−2.24304
$965$	0	0
$966$	−0.506041	−0.0162816
$967$	48.5623	1.56166	0.780828	−	0.624746i	$-0.214797\pi$
$967$	48.5623	1.56166	0.780828	+	0.624746i	$0.214797\pi$
$968$	22.2610	0.715495
$969$	−4.19567	−0.134784
$970$	0	0
$971$	−28.9530	−0.929146	−0.464573	−	0.885535i	$-0.653792\pi$
$971$	−28.9530	−0.929146	−0.464573	+	0.885535i	$0.653792\pi$
$972$	−3.04892	−0.0977941
$973$	17.7017	0.567491
$974$	−88.2307	−2.82709
$975$	0	0
$976$	6.71379	0.214903
$977$	35.4922	1.13549	0.567747	−	0.823203i	$-0.307815\pi$
$977$	35.4922	1.13549	0.567747	+	0.823203i	$0.307815\pi$
$978$	36.1226	1.15507
$979$	0.835790	0.0267120
$980$	0	0
$981$	2.31336	0.0738598
$982$	−35.7767	−1.14168
$983$	−9.68830	−0.309009	−0.154504	−	0.987992i	$-0.549378\pi$
$983$	−9.68830	−0.309009	−0.154504	+	0.987992i	$0.549378\pi$
$984$	−8.26337	−0.263427
$985$	0	0
$986$	14.8116	0.471698
$987$	8.81163	0.280477
$988$	0	0
$989$	−0.695479	−0.0221150
$990$	0	0
$991$	−7.96748	−0.253095	−0.126548	−	0.991961i	$-0.540390\pi$
$991$	−7.96748	−0.253095	−0.126548	+	0.991961i	$0.540390\pi$
$992$	2.58104	0.0819481
$993$	−18.2446	−0.578974
$994$	5.49396	0.174258
$995$	0	0
$996$	−26.1957	−0.830042
$997$	3.96508	0.125575	0.0627877	−	0.998027i	$-0.480001\pi$
$997$	3.96508	0.125575	0.0627877	+	0.998027i	$0.480001\pi$
$998$	−45.6480	−1.44496
$999$	−3.65279	−0.115569

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.g.1.1	✓	3
13.12	even	2		3549.2.a.r.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.g.1.1	✓	3	1.1	even	1	trivial
3549.2.a.r.1.3	yes	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24698 q^{2} -1.00000 q^{3} +3.04892 q^{4} +2.24698 q^{6} +1.00000 q^{7} -2.35690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.24698 q^{2} -1.00000 q^{3} +3.04892 q^{4} +2.24698 q^{6} +1.00000 q^{7} -2.35690 q^{8} +1.00000 q^{9} +1.24698 q^{11} -3.04892 q^{12} -2.24698 q^{14} -0.801938 q^{16} +0.890084 q^{17} -2.24698 q^{18} +4.71379 q^{19} -1.00000 q^{21} -2.80194 q^{22} -0.225209 q^{23} +2.35690 q^{24} -5.00000 q^{25} -1.00000 q^{27} +3.04892 q^{28} -7.40581 q^{29} +0.396125 q^{31} +6.51573 q^{32} -1.24698 q^{33} -2.00000 q^{34} +3.04892 q^{36} +3.65279 q^{37} -10.5918 q^{38} -3.50604 q^{41} +2.24698 q^{42} +3.08815 q^{43} +3.80194 q^{44} +0.506041 q^{46} -8.81163 q^{47} +0.801938 q^{48} +1.00000 q^{49} +11.2349 q^{50} -0.890084 q^{51} -10.3666 q^{53} +2.24698 q^{54} -2.35690 q^{56} -4.71379 q^{57} +16.6407 q^{58} -7.20775 q^{59} -8.37196 q^{61} -0.890084 q^{62} +1.00000 q^{63} -13.0368 q^{64} +2.80194 q^{66} +9.15883 q^{67} +2.71379 q^{68} +0.225209 q^{69} -2.44504 q^{71} -2.35690 q^{72} -6.93362 q^{73} -8.20775 q^{74} +5.00000 q^{75} +14.3720 q^{76} +1.24698 q^{77} +5.12498 q^{79} +1.00000 q^{81} +7.87800 q^{82} +8.59179 q^{83} -3.04892 q^{84} -6.93900 q^{86} +7.40581 q^{87} -2.93900 q^{88} +0.670251 q^{89} -0.686645 q^{92} -0.396125 q^{93} +19.7995 q^{94} -6.51573 q^{96} +8.31767 q^{97} -2.24698 q^{98} +1.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 3 q^{3} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 2 q^{2} - 3 q^{3} + 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - q^{11} - 2 q^{14} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 6 q^{19} - 3 q^{21} - 4 q^{22} + q^{23} + 3 q^{24} - 15 q^{25} - 3 q^{27} - 9 q^{29} + 10 q^{31} + 7 q^{32} + q^{33} - 6 q^{34} - 7 q^{37} - 4 q^{38} - 20 q^{41} + 2 q^{42} + 13 q^{43} + 7 q^{44} + 11 q^{46} - 2 q^{48} + 3 q^{49} + 10 q^{50} - 2 q^{51} - 5 q^{53} + 2 q^{54} - 3 q^{56} - 6 q^{57} + 13 q^{58} - 4 q^{59} + 4 q^{61} - 2 q^{62} + 3 q^{63} - 11 q^{64} + 4 q^{66} + 19 q^{67} - q^{69} - 7 q^{71} - 3 q^{72} - 14 q^{73} - 7 q^{74} + 15 q^{75} + 14 q^{76} - q^{77} - 9 q^{79} + 3 q^{81} + 4 q^{82} - 2 q^{83} - 11 q^{86} + 9 q^{87} + q^{88} - 10 q^{93} + 14 q^{94} - 7 q^{96} + 8 q^{97} - 2 q^{98} - q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 3 * q^3 + 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - q^11 - 2 * q^14 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 6 * q^19 - 3 * q^21 - 4 * q^22 + q^23 + 3 * q^24 - 15 * q^25 - 3 * q^27 - 9 * q^29 + 10 * q^31 + 7 * q^32 + q^33 - 6 * q^34 - 7 * q^37 - 4 * q^38 - 20 * q^41 + 2 * q^42 + 13 * q^43 + 7 * q^44 + 11 * q^46 - 2 * q^48 + 3 * q^49 + 10 * q^50 - 2 * q^51 - 5 * q^53 + 2 * q^54 - 3 * q^56 - 6 * q^57 + 13 * q^58 - 4 * q^59 + 4 * q^61 - 2 * q^62 + 3 * q^63 - 11 * q^64 + 4 * q^66 + 19 * q^67 - q^69 - 7 * q^71 - 3 * q^72 - 14 * q^73 - 7 * q^74 + 15 * q^75 + 14 * q^76 - q^77 - 9 * q^79 + 3 * q^81 + 4 * q^82 - 2 * q^83 - 11 * q^86 + 9 * q^87 + q^88 - 10 * q^93 + 14 * q^94 - 7 * q^96 + 8 * q^97 - 2 * q^98 - q^99

Introduction

L-functions

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Database

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