LMFDB - Embedded newform 403.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(1,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("403.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.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:	$3.21797120146$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.5748973.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 4x - 1 $ x^6 - x^5 - 6x^4 + 4x^3 + 8x^2 - 4x - 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			1.4
Root			$0.699790$ of defining polynomial
Character	$\chi$	$=$	403.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.482827 q^{2} -0.300210 q^{3} -1.76688 q^{4} +0.848172 q^{5} -0.144950 q^{6} -1.74674 q^{7} -1.81875 q^{8} -2.90987 q^{9} +O(q^{10})$	\(q+0.482827 q^{2} -0.300210 q^{3} -1.76688 q^{4} +0.848172 q^{5} -0.144950 q^{6} -1.74674 q^{7} -1.81875 q^{8} -2.90987 q^{9} +0.409520 q^{10} +0.172417 q^{11} +0.530435 q^{12} +1.00000 q^{13} -0.843372 q^{14} -0.254630 q^{15} +2.65561 q^{16} -7.81383 q^{17} -1.40497 q^{18} -7.12497 q^{19} -1.49862 q^{20} +0.524389 q^{21} +0.0832475 q^{22} +2.39809 q^{23} +0.546008 q^{24} -4.28060 q^{25} +0.482827 q^{26} +1.77420 q^{27} +3.08627 q^{28} +4.75312 q^{29} -0.122942 q^{30} +1.00000 q^{31} +4.91970 q^{32} -0.0517613 q^{33} -3.77273 q^{34} -1.48153 q^{35} +5.14139 q^{36} -0.630212 q^{37} -3.44013 q^{38} -0.300210 q^{39} -1.54261 q^{40} -5.65635 q^{41} +0.253189 q^{42} +1.81589 q^{43} -0.304640 q^{44} -2.46807 q^{45} +1.15786 q^{46} +1.80389 q^{47} -0.797243 q^{48} -3.94891 q^{49} -2.06679 q^{50} +2.34579 q^{51} -1.76688 q^{52} -1.19545 q^{53} +0.856634 q^{54} +0.146239 q^{55} +3.17688 q^{56} +2.13899 q^{57} +2.29494 q^{58} +9.16997 q^{59} +0.449900 q^{60} +12.0122 q^{61} +0.482827 q^{62} +5.08279 q^{63} -2.93586 q^{64} +0.848172 q^{65} -0.0249918 q^{66} -5.84643 q^{67} +13.8061 q^{68} -0.719930 q^{69} -0.715324 q^{70} +2.22849 q^{71} +5.29233 q^{72} -6.64115 q^{73} -0.304283 q^{74} +1.28508 q^{75} +12.5890 q^{76} -0.301167 q^{77} -0.144950 q^{78} -0.527743 q^{79} +2.25242 q^{80} +8.19699 q^{81} -2.73104 q^{82} +7.27854 q^{83} -0.926531 q^{84} -6.62747 q^{85} +0.876761 q^{86} -1.42694 q^{87} -0.313583 q^{88} -12.9621 q^{89} -1.19165 q^{90} -1.74674 q^{91} -4.23713 q^{92} -0.300210 q^{93} +0.870964 q^{94} -6.04320 q^{95} -1.47695 q^{96} +0.368869 q^{97} -1.90664 q^{98} -0.501711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9} - 8 q^{10} - 5 q^{11} - 13 q^{12} + 6 q^{13} - 17 q^{14} + 4 q^{15} + 14 q^{16} - 23 q^{17} + 9 q^{18} + 7 q^{19} - 10 q^{20} + 2 q^{21} + 2 q^{22} - 18 q^{23} - 13 q^{24} + 11 q^{25} - 2 q^{26} - 5 q^{27} - 25 q^{28} - 18 q^{29} + 25 q^{30} + 6 q^{31} + 2 q^{32} - 2 q^{33} - 16 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 8 q^{38} - 5 q^{39} - 29 q^{40} - 5 q^{41} + 31 q^{42} - 7 q^{43} + 30 q^{44} - 5 q^{45} + 19 q^{46} - 9 q^{47} - 19 q^{48} + 16 q^{49} + 29 q^{50} + 26 q^{51} + 6 q^{52} - 31 q^{53} - 4 q^{54} + 7 q^{55} + 8 q^{56} - 5 q^{57} + 35 q^{58} - q^{59} + 33 q^{60} - 15 q^{61} - 2 q^{62} + 11 q^{63} - 5 q^{64} - 9 q^{65} - 29 q^{66} - 28 q^{67} - 12 q^{68} + 5 q^{69} + 73 q^{70} + q^{71} + 45 q^{72} - 20 q^{73} + 4 q^{74} + q^{75} + 38 q^{76} - 29 q^{77} - 15 q^{79} + 7 q^{80} + 2 q^{81} + 36 q^{82} + q^{83} + 68 q^{84} + 29 q^{85} + 3 q^{86} + 10 q^{87} + 9 q^{88} - q^{89} - 32 q^{90} - 60 q^{92} - 5 q^{93} + 54 q^{94} - 13 q^{95} + 36 q^{96} - 5 q^{97} + 20 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9 - 8 * q^10 - 5 * q^11 - 13 * q^12 + 6 * q^13 - 17 * q^14 + 4 * q^15 + 14 * q^16 - 23 * q^17 + 9 * q^18 + 7 * q^19 - 10 * q^20 + 2 * q^21 + 2 * q^22 - 18 * q^23 - 13 * q^24 + 11 * q^25 - 2 * q^26 - 5 * q^27 - 25 * q^28 - 18 * q^29 + 25 * q^30 + 6 * q^31 + 2 * q^32 - 2 * q^33 - 16 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 8 * q^38 - 5 * q^39 - 29 * q^40 - 5 * q^41 + 31 * q^42 - 7 * q^43 + 30 * q^44 - 5 * q^45 + 19 * q^46 - 9 * q^47 - 19 * q^48 + 16 * q^49 + 29 * q^50 + 26 * q^51 + 6 * q^52 - 31 * q^53 - 4 * q^54 + 7 * q^55 + 8 * q^56 - 5 * q^57 + 35 * q^58 - q^59 + 33 * q^60 - 15 * q^61 - 2 * q^62 + 11 * q^63 - 5 * q^64 - 9 * q^65 - 29 * q^66 - 28 * q^67 - 12 * q^68 + 5 * q^69 + 73 * q^70 + q^71 + 45 * q^72 - 20 * q^73 + 4 * q^74 + q^75 + 38 * q^76 - 29 * q^77 - 15 * q^79 + 7 * q^80 + 2 * q^81 + 36 * q^82 + q^83 + 68 * q^84 + 29 * q^85 + 3 * q^86 + 10 * q^87 + 9 * q^88 - q^89 - 32 * q^90 - 60 * q^92 - 5 * q^93 + 54 * q^94 - 13 * q^95 + 36 * q^96 - 5 * q^97 + 20 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.482827	0.341410	0.170705	−	0.985322i	$-0.445395\pi$
$2$	0.482827	0.341410	0.170705	+	0.985322i	$0.445395\pi$
$3$	−0.300210	−0.173326	−0.0866632	−	0.996238i	$-0.527620\pi$
$3$	−0.300210	−0.173326	−0.0866632	+	0.996238i	$0.527620\pi$
$4$	−1.76688	−0.883439
$5$	0.848172	0.379314	0.189657	−	0.981850i	$-0.439262\pi$
$5$	0.848172	0.379314	0.189657	+	0.981850i	$0.439262\pi$
$6$	−0.144950	−0.0591754
$7$	−1.74674	−0.660205	−0.330102	−	0.943945i	$-0.607083\pi$
$7$	−1.74674	−0.660205	−0.330102	+	0.943945i	$0.607083\pi$
$8$	−1.81875	−0.643025
$9$	−2.90987	−0.969958
$10$	0.409520	0.129502
$11$	0.172417	0.0519857	0.0259928	−	0.999662i	$-0.491725\pi$
$11$	0.172417	0.0519857	0.0259928	+	0.999662i	$0.491725\pi$
$12$	0.530435	0.153123
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.843372	−0.225401
$15$	−0.254630	−0.0657451
$16$	2.65561	0.663904
$17$	−7.81383	−1.89513	−0.947566	−	0.319561i	$-0.896464\pi$
$17$	−7.81383	−1.89513	−0.947566	+	0.319561i	$0.896464\pi$
$18$	−1.40497	−0.331154
$19$	−7.12497	−1.63458	−0.817291	−	0.576226i	$-0.804525\pi$
$19$	−7.12497	−1.63458	−0.817291	+	0.576226i	$0.804525\pi$
$20$	−1.49862	−0.335101
$21$	0.524389	0.114431
$22$	0.0832475	0.0177484
$23$	2.39809	0.500036	0.250018	−	0.968241i	$-0.419564\pi$
$23$	2.39809	0.500036	0.250018	+	0.968241i	$0.419564\pi$
$24$	0.546008	0.111453
$25$	−4.28060	−0.856121
$26$	0.482827	0.0946902
$27$	1.77420	0.341446
$28$	3.08627	0.583251
$29$	4.75312	0.882632	0.441316	−	0.897352i	$-0.354512\pi$
$29$	4.75312	0.882632	0.441316	+	0.897352i	$0.354512\pi$
$30$	−0.122942	−0.0224461
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	4.91970	0.869689
$33$	−0.0517613	−0.00901049
$34$	−3.77273	−0.647017
$35$	−1.48153	−0.250425
$36$	5.14139	0.856899
$37$	−0.630212	−0.103606	−0.0518031	−	0.998657i	$-0.516497\pi$
$37$	−0.630212	−0.103606	−0.0518031	+	0.998657i	$0.516497\pi$
$38$	−3.44013	−0.558063
$39$	−0.300210	−0.0480721
$40$	−1.54261	−0.243908
$41$	−5.65635	−0.883374	−0.441687	−	0.897169i	$-0.645620\pi$
$41$	−5.65635	−0.883374	−0.441687	+	0.897169i	$0.645620\pi$
$42$	0.253189	0.0390679
$43$	1.81589	0.276921	0.138460	−	0.990368i	$-0.455785\pi$
$43$	1.81589	0.276921	0.138460	+	0.990368i	$0.455785\pi$
$44$	−0.304640	−0.0459262
$45$	−2.46807	−0.367919
$46$	1.15786	0.170717
$47$	1.80389	0.263124	0.131562	−	0.991308i	$-0.458001\pi$
$47$	1.80389	0.263124	0.131562	+	0.991308i	$0.458001\pi$
$48$	−0.797243	−0.115072
$49$	−3.94891	−0.564130
$50$	−2.06679	−0.292288
$51$	2.34579	0.328476
$52$	−1.76688	−0.245022
$53$	−1.19545	−0.164208	−0.0821042	−	0.996624i	$-0.526164\pi$
$53$	−1.19545	−0.164208	−0.0821042	+	0.996624i	$0.526164\pi$
$54$	0.856634	0.116573
$55$	0.146239	0.0197189
$56$	3.17688	0.424528
$57$	2.13899	0.283316
$58$	2.29494	0.301340
$59$	9.16997	1.19383	0.596914	−	0.802305i	$-0.296393\pi$
$59$	9.16997	1.19383	0.596914	+	0.802305i	$0.296393\pi$
$60$	0.449900	0.0580818
$61$	12.0122	1.53800	0.769001	−	0.639248i	$-0.220754\pi$
$61$	12.0122	1.53800	0.769001	+	0.639248i	$0.220754\pi$
$62$	0.482827	0.0613191
$63$	5.08279	0.640371
$64$	−2.93586	−0.366983
$65$	0.848172	0.105203
$66$	−0.0249918	−0.00307627
$67$	−5.84643	−0.714256	−0.357128	−	0.934056i	$-0.616244\pi$
$67$	−5.84643	−0.714256	−0.357128	+	0.934056i	$0.616244\pi$
$68$	13.8061	1.67423
$69$	−0.719930	−0.0866694
$70$	−0.715324	−0.0854976
$71$	2.22849	0.264473	0.132236	−	0.991218i	$-0.457784\pi$
$71$	2.22849	0.264473	0.132236	+	0.991218i	$0.457784\pi$
$72$	5.29233	0.623708
$73$	−6.64115	−0.777288	−0.388644	−	0.921388i	$-0.627056\pi$
$73$	−6.64115	−0.777288	−0.388644	+	0.921388i	$0.627056\pi$
$74$	−0.304283	−0.0353722
$75$	1.28508	0.148388
$76$	12.5890	1.44405
$77$	−0.301167	−0.0343212
$78$	−0.144950	−0.0164123
$79$	−0.527743	−0.0593757	−0.0296879	−	0.999559i	$-0.509451\pi$
$79$	−0.527743	−0.0593757	−0.0296879	+	0.999559i	$0.509451\pi$
$80$	2.25242	0.251828
$81$	8.19699	0.910776
$82$	−2.73104	−0.301593
$83$	7.27854	0.798924	0.399462	−	0.916750i	$-0.369197\pi$
$83$	7.27854	0.798924	0.399462	+	0.916750i	$0.369197\pi$
$84$	−0.926531	−0.101093
$85$	−6.62747	−0.718850
$86$	0.876761	0.0945436
$87$	−1.42694	−0.152984
$88$	−0.313583	−0.0334281
$89$	−12.9621	−1.37398	−0.686989	−	0.726668i	$-0.741068\pi$
$89$	−12.9621	−1.37398	−0.686989	+	0.726668i	$0.741068\pi$
$90$	−1.19165	−0.125611
$91$	−1.74674	−0.183108
$92$	−4.23713	−0.441751
$93$	−0.300210	−0.0311304
$94$	0.870964	0.0898331
$95$	−6.04320	−0.620019
$96$	−1.47695	−0.150740
$97$	0.368869	0.0374529	0.0187265	−	0.999825i	$-0.494039\pi$
$97$	0.368869	0.0374529	0.0187265	+	0.999825i	$0.494039\pi$
$98$	−1.90664	−0.192600
$99$	−0.501711	−0.0504239
$100$	7.56331	0.756331
$101$	−8.82133	−0.877755	−0.438878	−	0.898547i	$-0.644624\pi$
$101$	−8.82133	−0.877755	−0.438878	+	0.898547i	$0.644624\pi$
$102$	1.13261	0.112145
$103$	10.8093	1.06507	0.532535	−	0.846408i	$-0.321240\pi$
$103$	10.8093	1.06507	0.532535	+	0.846408i	$0.321240\pi$
$104$	−1.81875	−0.178343
$105$	0.444772	0.0434053
$106$	−0.577198	−0.0560624
$107$	−4.55472	−0.440321	−0.220160	−	0.975464i	$-0.570658\pi$
$107$	−4.55472	−0.440321	−0.220160	+	0.975464i	$0.570658\pi$
$108$	−3.13480	−0.301647
$109$	16.4271	1.57343	0.786717	−	0.617314i	$-0.211779\pi$
$109$	16.4271	1.57343	0.786717	+	0.617314i	$0.211779\pi$
$110$	0.0706082	0.00673223
$111$	0.189196	0.0179577
$112$	−4.63866	−0.438312
$113$	−4.47812	−0.421267	−0.210633	−	0.977565i	$-0.567553\pi$
$113$	−4.47812	−0.421267	−0.210633	+	0.977565i	$0.567553\pi$
$114$	1.03276	0.0967271
$115$	2.03399	0.189671
$116$	−8.39818	−0.779752
$117$	−2.90987	−0.269018
$118$	4.42751	0.407585
$119$	13.6487	1.25117
$120$	0.463108	0.0422758
$121$	−10.9703	−0.997297
$122$	5.79981	0.525090
$123$	1.69809	0.153112
$124$	−1.76688	−0.158670
$125$	−7.87155	−0.704053
$126$	2.45411	0.218629
$127$	6.43512	0.571025	0.285512	−	0.958375i	$-0.407836\pi$
$127$	6.43512	0.571025	0.285512	+	0.958375i	$0.407836\pi$
$128$	−11.2569	−0.994981
$129$	−0.545149	−0.0479977
$130$	0.409520	0.0359173
$131$	−12.3895	−1.08247	−0.541236	−	0.840871i	$-0.682043\pi$
$131$	−12.3895	−1.08247	−0.541236	+	0.840871i	$0.682043\pi$
$132$	0.0914560	0.00796022
$133$	12.4455	1.07916
$134$	−2.82282	−0.243854
$135$	1.50483	0.129515
$136$	14.2114	1.21862
$137$	−18.7925	−1.60555	−0.802776	−	0.596281i	$-0.796645\pi$
$137$	−18.7925	−1.60555	−0.802776	+	0.596281i	$0.796645\pi$
$138$	−0.347602	−0.0295898
$139$	8.03922	0.681878	0.340939	−	0.940085i	$-0.389255\pi$
$139$	8.03922	0.681878	0.340939	+	0.940085i	$0.389255\pi$
$140$	2.61769	0.221235
$141$	−0.541545	−0.0456063
$142$	1.07597	0.0902937
$143$	0.172417	0.0144182
$144$	−7.72750	−0.643959
$145$	4.03146	0.334795
$146$	−3.20653	−0.265374
$147$	1.18550	0.0977786
$148$	1.11351	0.0915298
$149$	−2.89530	−0.237192	−0.118596	−	0.992943i	$-0.537839\pi$
$149$	−2.89530	−0.237192	−0.118596	+	0.992943i	$0.537839\pi$
$150$	0.620472	0.0506613
$151$	−9.56165	−0.778116	−0.389058	−	0.921213i	$-0.627199\pi$
$151$	−9.56165	−0.778116	−0.389058	+	0.921213i	$0.627199\pi$
$152$	12.9586	1.05108
$153$	22.7372	1.83820
$154$	−0.145412	−0.0117176
$155$	0.848172	0.0681268
$156$	0.530435	0.0424688
$157$	−20.4859	−1.63496	−0.817478	−	0.575960i	$-0.804629\pi$
$157$	−20.4859	−1.63496	−0.817478	+	0.575960i	$0.804629\pi$
$158$	−0.254809	−0.0202715
$159$	0.358888	0.0284617
$160$	4.17275	0.329885
$161$	−4.18883	−0.330126
$162$	3.95773	0.310948
$163$	10.3574	0.811258	0.405629	−	0.914038i	$-0.367052\pi$
$163$	10.3574	0.811258	0.405629	+	0.914038i	$0.367052\pi$
$164$	9.99408	0.780407
$165$	−0.0439025	−0.00341780
$166$	3.51428	0.272761
$167$	0.842674	0.0652081	0.0326040	−	0.999468i	$-0.489620\pi$
$167$	0.842674	0.0652081	0.0326040	+	0.999468i	$0.489620\pi$
$168$	−0.953732	−0.0735820
$169$	1.00000	0.0769231
$170$	−3.19992	−0.245423
$171$	20.7328	1.58547
$172$	−3.20846	−0.244643
$173$	−5.84433	−0.444336	−0.222168	−	0.975008i	$-0.571313\pi$
$173$	−5.84433	−0.444336	−0.222168	+	0.975008i	$0.571313\pi$
$174$	−0.688963	−0.0522302
$175$	7.47709	0.565215
$176$	0.457873	0.0345135
$177$	−2.75292	−0.206922
$178$	−6.25844	−0.469090
$179$	−22.3606	−1.67131	−0.835653	−	0.549258i	$-0.814911\pi$
$179$	−22.3606	−1.67131	−0.835653	+	0.549258i	$0.814911\pi$
$180$	4.36078	0.325034
$181$	−1.17586	−0.0874012	−0.0437006	−	0.999045i	$-0.513915\pi$
$181$	−1.17586	−0.0874012	−0.0437006	+	0.999045i	$0.513915\pi$
$182$	−0.843372	−0.0625149
$183$	−3.60618	−0.266576
$184$	−4.36152	−0.321536
$185$	−0.534528	−0.0392993
$186$	−0.144950	−0.0106282
$187$	−1.34724	−0.0985196
$188$	−3.18724	−0.232454
$189$	−3.09907	−0.225424
$190$	−2.91782	−0.211681
$191$	−25.1648	−1.82086	−0.910431	−	0.413662i	$-0.864250\pi$
$191$	−25.1648	−1.82086	−0.910431	+	0.413662i	$0.864250\pi$
$192$	0.881376	0.0636078
$193$	−4.55946	−0.328197	−0.164099	−	0.986444i	$-0.552471\pi$
$193$	−4.55946	−0.328197	−0.164099	+	0.986444i	$0.552471\pi$
$194$	0.178100	0.0127868
$195$	−0.254630	−0.0182344
$196$	6.97724	0.498374
$197$	−13.9405	−0.993220	−0.496610	−	0.867974i	$-0.665422\pi$
$197$	−13.9405	−0.993220	−0.496610	+	0.867974i	$0.665422\pi$
$198$	−0.242240	−0.0172152
$199$	−19.5841	−1.38828	−0.694141	−	0.719839i	$-0.744216\pi$
$199$	−19.5841	−1.38828	−0.694141	+	0.719839i	$0.744216\pi$
$200$	7.78535	0.550508
$201$	1.75516	0.123799
$202$	−4.25918	−0.299675
$203$	−8.30245	−0.582718
$204$	−4.14473	−0.290189
$205$	−4.79756	−0.335076
$206$	5.21901	0.363626
$207$	−6.97813	−0.485014
$208$	2.65561	0.184134
$209$	−1.22847	−0.0849748
$210$	0.214748	0.0148190
$211$	26.0696	1.79470	0.897352	−	0.441315i	$-0.145488\pi$
$211$	26.0696	1.79470	0.897352	+	0.441315i	$0.145488\pi$
$212$	2.11222	0.145068
$213$	−0.669015	−0.0458401
$214$	−2.19914	−0.150330
$215$	1.54019	0.105040
$216$	−3.22684	−0.219558
$217$	−1.74674	−0.118576
$218$	7.93146	0.537186
$219$	1.99374	0.134725
$220$	−0.258387	−0.0174204
$221$	−7.81383	−0.525615
$222$	0.0913490	0.00613094
$223$	−25.0024	−1.67428	−0.837142	−	0.546985i	$-0.815775\pi$
$223$	−25.0024	−1.67428	−0.837142	+	0.546985i	$0.815775\pi$
$224$	−8.59343	−0.574173
$225$	12.4560	0.830401
$226$	−2.16216	−0.143825
$227$	20.9389	1.38976	0.694882	−	0.719124i	$-0.255457\pi$
$227$	20.9389	1.38976	0.694882	+	0.719124i	$0.255457\pi$
$228$	−3.77933	−0.250293
$229$	2.42980	0.160566	0.0802828	−	0.996772i	$-0.474418\pi$
$229$	2.42980	0.160566	0.0802828	+	0.996772i	$0.474418\pi$
$230$	0.982065	0.0647555
$231$	0.0904135	0.00594877
$232$	−8.64474	−0.567555
$233$	−1.36125	−0.0891786	−0.0445893	−	0.999005i	$-0.514198\pi$
$233$	−1.36125	−0.0891786	−0.0445893	+	0.999005i	$0.514198\pi$
$234$	−1.40497	−0.0918455
$235$	1.53000	0.0998065
$236$	−16.2022	−1.05467
$237$	0.158434	0.0102914
$238$	6.58996	0.427164
$239$	20.7779	1.34401	0.672006	−	0.740545i	$-0.265433\pi$
$239$	20.7779	1.34401	0.672006	+	0.740545i	$0.265433\pi$
$240$	−0.676199	−0.0436484
$241$	19.0861	1.22945	0.614723	−	0.788743i	$-0.289268\pi$
$241$	19.0861	1.22945	0.614723	+	0.788743i	$0.289268\pi$
$242$	−5.29674	−0.340488
$243$	−7.78343	−0.499308
$244$	−21.2241	−1.35873
$245$	−3.34935	−0.213982
$246$	0.819886	0.0522740
$247$	−7.12497	−0.453351
$248$	−1.81875	−0.115491
$249$	−2.18509	−0.138475
$250$	−3.80060	−0.240371
$251$	−9.92063	−0.626185	−0.313092	−	0.949723i	$-0.601365\pi$
$251$	−9.92063	−0.626185	−0.313092	+	0.949723i	$0.601365\pi$
$252$	−8.98066	−0.565729
$253$	0.413471	0.0259947
$254$	3.10705	0.194954
$255$	1.98963	0.124596
$256$	0.436580	0.0272862
$257$	−14.1407	−0.882074	−0.441037	−	0.897489i	$-0.645389\pi$
$257$	−14.1407	−0.882074	−0.441037	+	0.897489i	$0.645389\pi$
$258$	−0.263213	−0.0163869
$259$	1.10081	0.0684013
$260$	−1.49862	−0.0929402
$261$	−13.8310	−0.856116
$262$	−5.98196	−0.369567
$263$	0.451850	0.0278622	0.0139311	−	0.999903i	$-0.495565\pi$
$263$	0.451850	0.0278622	0.0139311	+	0.999903i	$0.495565\pi$
$264$	0.0941409	0.00579397
$265$	−1.01395	−0.0622865
$266$	6.00900	0.368436
$267$	3.89135	0.238147
$268$	10.3299	0.631001
$269$	−0.0631497	−0.00385031	−0.00192515	−	0.999998i	$-0.500613\pi$
$269$	−0.0631497	−0.00385031	−0.00192515	+	0.999998i	$0.500613\pi$
$270$	0.726573	0.0442178
$271$	29.8153	1.81115	0.905575	−	0.424187i	$-0.139440\pi$
$271$	29.8153	1.81115	0.905575	+	0.424187i	$0.139440\pi$
$272$	−20.7505	−1.25818
$273$	0.524389	0.0317374
$274$	−9.07353	−0.548152
$275$	−0.738049	−0.0445060
$276$	1.27203	0.0765672
$277$	13.8071	0.829588	0.414794	−	0.909915i	$-0.363854\pi$
$277$	13.8071	0.829588	0.414794	+	0.909915i	$0.363854\pi$
$278$	3.88155	0.232800
$279$	−2.90987	−0.174210
$280$	2.69454	0.161030
$281$	2.53623	0.151299	0.0756493	−	0.997134i	$-0.475897\pi$
$281$	2.53623	0.151299	0.0756493	+	0.997134i	$0.475897\pi$
$282$	−0.261472	−0.0155705
$283$	−12.5971	−0.748821	−0.374410	−	0.927263i	$-0.622155\pi$
$283$	−12.5971	−0.748821	−0.374410	+	0.927263i	$0.622155\pi$
$284$	−3.93746	−0.233646
$285$	1.81423	0.107466
$286$	0.0832475	0.00492253
$287$	9.88016	0.583208
$288$	−14.3157	−0.843562
$289$	44.0559	2.59152
$290$	1.94650	0.114302
$291$	−0.110738	−0.00649159
$292$	11.7341	0.686686
$293$	−17.6688	−1.03222	−0.516110	−	0.856522i	$-0.672620\pi$
$293$	−17.6688	−1.03222	−0.516110	+	0.856522i	$0.672620\pi$
$294$	0.572393	0.0333826
$295$	7.77771	0.452836
$296$	1.14620	0.0666214
$297$	0.305903	0.0177503
$298$	−1.39793	−0.0809798
$299$	2.39809	0.138685
$300$	−2.27058	−0.131092
$301$	−3.17188	−0.182824
$302$	−4.61662	−0.265657
$303$	2.64825	0.152138
$304$	−18.9212	−1.08520
$305$	10.1884	0.583386
$306$	10.9782	0.627579
$307$	11.7570	0.671010	0.335505	−	0.942038i	$-0.391093\pi$
$307$	11.7570	0.671010	0.335505	+	0.942038i	$0.391093\pi$
$308$	0.532126	0.0303207
$309$	−3.24505	−0.184605
$310$	0.409520	0.0232592
$311$	16.4836	0.934698	0.467349	−	0.884073i	$-0.345209\pi$
$311$	16.4836	0.934698	0.467349	+	0.884073i	$0.345209\pi$
$312$	0.546008	0.0309116
$313$	−27.1494	−1.53458	−0.767288	−	0.641302i	$-0.778394\pi$
$313$	−27.1494	−1.53458	−0.767288	+	0.641302i	$0.778394\pi$
$314$	−9.89117	−0.558191
$315$	4.31107	0.242902
$316$	0.932458	0.0524548
$317$	23.1731	1.30153	0.650766	−	0.759278i	$-0.274448\pi$
$317$	23.1731	1.30153	0.650766	+	0.759278i	$0.274448\pi$
$318$	0.173281	0.00971710
$319$	0.819518	0.0458842
$320$	−2.49012	−0.139202
$321$	1.36737	0.0763193
$322$	−2.02248	−0.112708
$323$	55.6733	3.09775
$324$	−14.4831	−0.804615
$325$	−4.28060	−0.237445
$326$	5.00086	0.276972
$327$	−4.93159	−0.272718
$328$	10.2875	0.568032
$329$	−3.15091	−0.173715
$330$	−0.0211973	−0.00116687
$331$	−3.68237	−0.202402	−0.101201	−	0.994866i	$-0.532268\pi$
$331$	−3.68237	−0.202402	−0.101201	+	0.994866i	$0.532268\pi$
$332$	−12.8603	−0.705800
$333$	1.83384	0.100494
$334$	0.406866	0.0222627
$335$	−4.95878	−0.270927
$336$	1.39257	0.0759711
$337$	0.610718	0.0332679	0.0166340	−	0.999862i	$-0.494705\pi$
$337$	0.610718	0.0332679	0.0166340	+	0.999862i	$0.494705\pi$
$338$	0.482827	0.0262623
$339$	1.34438	0.0730166
$340$	11.7099	0.635060
$341$	0.172417	0.00933690
$342$	10.0103	0.541297
$343$	19.1249	1.03265
$344$	−3.30265	−0.178067
$345$	−0.610625	−0.0328749
$346$	−2.82180	−0.151701
$347$	−34.3743	−1.84531	−0.922654	−	0.385630i	$-0.873984\pi$
$347$	−34.3743	−1.84531	−0.922654	+	0.385630i	$0.873984\pi$
$348$	2.52122	0.135152
$349$	−0.794547	−0.0425311	−0.0212656	−	0.999774i	$-0.506770\pi$
$349$	−0.794547	−0.0425311	−0.0212656	+	0.999774i	$0.506770\pi$
$350$	3.61014	0.192970
$351$	1.77420	0.0947000
$352$	0.848240	0.0452113
$353$	−13.4134	−0.713924	−0.356962	−	0.934119i	$-0.616188\pi$
$353$	−13.4134	−0.713924	−0.356962	+	0.934119i	$0.616188\pi$
$354$	−1.32918	−0.0706453
$355$	1.89014	0.100318
$356$	22.9024	1.21383
$357$	−4.09748	−0.216862
$358$	−10.7963	−0.570601
$359$	−12.5532	−0.662534	−0.331267	−	0.943537i	$-0.607476\pi$
$359$	−12.5532	−0.662534	−0.331267	+	0.943537i	$0.607476\pi$
$360$	4.48881	0.236581
$361$	31.7653	1.67186
$362$	−0.567739	−0.0298397
$363$	3.29339	0.172858
$364$	3.08627	0.161765
$365$	−5.63284	−0.294836
$366$	−1.74116	−0.0910119
$367$	−29.2060	−1.52454	−0.762272	−	0.647257i	$-0.775916\pi$
$367$	−29.2060	−1.52454	−0.762272	+	0.647257i	$0.775916\pi$
$368$	6.36839	0.331975
$369$	16.4593	0.856835
$370$	−0.258085	−0.0134172
$371$	2.08815	0.108411
$372$	0.530435	0.0275018
$373$	−0.683653	−0.0353982	−0.0176991	−	0.999843i	$-0.505634\pi$
$373$	−0.683653	−0.0353982	−0.0176991	+	0.999843i	$0.505634\pi$
$374$	−0.650482	−0.0336356
$375$	2.36312	0.122031
$376$	−3.28082	−0.169195
$377$	4.75312	0.244798
$378$	−1.49631	−0.0769621
$379$	33.9242	1.74257	0.871284	−	0.490779i	$-0.163288\pi$
$379$	33.9242	1.74257	0.871284	+	0.490779i	$0.163288\pi$
$380$	10.6776	0.547749
$381$	−1.93189	−0.0989737
$382$	−12.1502	−0.621661
$383$	14.9792	0.765403	0.382702	−	0.923872i	$-0.374994\pi$
$383$	14.9792	0.765403	0.382702	+	0.923872i	$0.374994\pi$
$384$	3.37944	0.172456
$385$	−0.255441	−0.0130185
$386$	−2.20143	−0.112050
$387$	−5.28401	−0.268601
$388$	−0.651746	−0.0330874
$389$	−32.8943	−1.66781	−0.833903	−	0.551911i	$-0.813899\pi$
$389$	−32.8943	−1.66781	−0.833903	+	0.551911i	$0.813899\pi$
$390$	−0.122942	−0.00622542
$391$	−18.7382	−0.947633
$392$	7.18208	0.362750
$393$	3.71944	0.187621
$394$	−6.73086	−0.339096
$395$	−0.447617	−0.0225220
$396$	0.886463	0.0445464
$397$	35.6692	1.79019	0.895093	−	0.445879i	$-0.147109\pi$
$397$	35.6692	1.79019	0.895093	+	0.445879i	$0.147109\pi$
$398$	−9.45575	−0.473974
$399$	−3.73625	−0.187047
$400$	−11.3676	−0.568382
$401$	18.7092	0.934295	0.467147	−	0.884180i	$-0.345282\pi$
$401$	18.7092	0.934295	0.467147	+	0.884180i	$0.345282\pi$
$402$	0.847438	0.0422664
$403$	1.00000	0.0498135
$404$	15.5862	0.775443
$405$	6.95245	0.345470
$406$	−4.00865	−0.198946
$407$	−0.108659	−0.00538604
$408$	−4.26641	−0.211219
$409$	−6.75543	−0.334035	−0.167017	−	0.985954i	$-0.553414\pi$
$409$	−6.75543	−0.334035	−0.167017	+	0.985954i	$0.553414\pi$
$410$	−2.31639	−0.114398
$411$	5.64170	0.278285
$412$	−19.0987	−0.940924
$413$	−16.0175	−0.788171
$414$	−3.36923	−0.165589
$415$	6.17345	0.303043
$416$	4.91970	0.241208
$417$	−2.41346	−0.118188
$418$	−0.593137	−0.0290113
$419$	−1.17977	−0.0576358	−0.0288179	−	0.999585i	$-0.509174\pi$
$419$	−1.17977	−0.0576358	−0.0288179	+	0.999585i	$0.509174\pi$
$420$	−0.785857	−0.0383459
$421$	18.9358	0.922875	0.461437	−	0.887173i	$-0.347334\pi$
$421$	18.9358	0.922875	0.461437	+	0.887173i	$0.347334\pi$
$422$	12.5871	0.612730
$423$	−5.24908	−0.255219
$424$	2.17423	0.105590
$425$	33.4479	1.62246
$426$	−0.323018	−0.0156503
$427$	−20.9821	−1.01540
$428$	8.04763	0.388997
$429$	−0.0517613	−0.00249906
$430$	0.743644	0.0358617
$431$	29.1549	1.40434	0.702171	−	0.712008i	$-0.252214\pi$
$431$	29.1549	1.40434	0.702171	+	0.712008i	$0.252214\pi$
$432$	4.71160	0.226687
$433$	−11.9053	−0.572132	−0.286066	−	0.958210i	$-0.592348\pi$
$433$	−11.9053	−0.572132	−0.286066	+	0.958210i	$0.592348\pi$
$434$	−0.843372	−0.0404832
$435$	−1.21029	−0.0580288
$436$	−29.0247	−1.39003
$437$	−17.0863	−0.817349
$438$	0.962632	0.0459963
$439$	18.5713	0.886361	0.443180	−	0.896432i	$-0.353850\pi$
$439$	18.5713	0.886361	0.443180	+	0.896432i	$0.353850\pi$
$440$	−0.265973	−0.0126797
$441$	11.4908	0.547182
$442$	−3.77273	−0.179450
$443$	20.7364	0.985216	0.492608	−	0.870251i	$-0.336044\pi$
$443$	20.7364	0.985216	0.492608	+	0.870251i	$0.336044\pi$
$444$	−0.334286	−0.0158645
$445$	−10.9941	−0.521169
$446$	−12.0718	−0.571618
$447$	0.869198	0.0411117
$448$	5.12818	0.242284
$449$	21.5943	1.01910	0.509549	−	0.860441i	$-0.329812\pi$
$449$	21.5943	1.01910	0.509549	+	0.860441i	$0.329812\pi$
$450$	6.01410	0.283508
$451$	−0.975251	−0.0459228
$452$	7.91230	0.372163
$453$	2.87050	0.134868
$454$	10.1099	0.474479
$455$	−1.48153	−0.0694554
$456$	−3.89029	−0.182180
$457$	3.58158	0.167539	0.0837695	−	0.996485i	$-0.473304\pi$
$457$	3.58158	0.167539	0.0837695	+	0.996485i	$0.473304\pi$
$458$	1.17317	0.0548188
$459$	−13.8633	−0.647085
$460$	−3.59381	−0.167562
$461$	−35.3277	−1.64537	−0.822687	−	0.568495i	$-0.807526\pi$
$461$	−35.3277	−1.64537	−0.822687	+	0.568495i	$0.807526\pi$
$462$	0.0436541	0.00203097
$463$	15.4893	0.719849	0.359924	−	0.932981i	$-0.382802\pi$
$463$	15.4893	0.719849	0.359924	+	0.932981i	$0.382802\pi$
$464$	12.6225	0.585983
$465$	−0.254630	−0.0118082
$466$	−0.657249	−0.0304465
$467$	−12.7713	−0.590984	−0.295492	−	0.955345i	$-0.595484\pi$
$467$	−12.7713	−0.590984	−0.295492	+	0.955345i	$0.595484\pi$
$468$	5.14139	0.237661
$469$	10.2122	0.471555
$470$	0.738727	0.0340750
$471$	6.15009	0.283381
$472$	−16.6779	−0.767662
$473$	0.313090	0.0143959
$474$	0.0764962	0.00351359
$475$	30.4992	1.39940
$476$	−24.1156	−1.10534
$477$	3.47862	0.159275
$478$	10.0321	0.458860
$479$	12.1752	0.556299	0.278150	−	0.960538i	$-0.410279\pi$
$479$	12.1752	0.556299	0.278150	+	0.960538i	$0.410279\pi$
$480$	−1.25270	−0.0571778
$481$	−0.630212	−0.0287352
$482$	9.21530	0.419745
$483$	1.25753	0.0572196
$484$	19.3831	0.881052
$485$	0.312864	0.0142064
$486$	−3.75805	−0.170469
$487$	18.5771	0.841808	0.420904	−	0.907105i	$-0.361713\pi$
$487$	18.5771	0.841808	0.420904	+	0.907105i	$0.361713\pi$
$488$	−21.8472	−0.988974
$489$	−3.10941	−0.140612
$490$	−1.61716	−0.0730557
$491$	22.6700	1.02308	0.511540	−	0.859259i	$-0.329075\pi$
$491$	22.6700	1.02308	0.511540	+	0.859259i	$0.329075\pi$
$492$	−3.00033	−0.135265
$493$	−37.1401	−1.67270
$494$	−3.44013	−0.154779
$495$	−0.425537	−0.0191265
$496$	2.65561	0.119241
$497$	−3.89258	−0.174606
$498$	−1.05502	−0.0472766
$499$	−27.0742	−1.21201	−0.606003	−	0.795462i	$-0.707228\pi$
$499$	−27.0742	−1.21201	−0.606003	+	0.795462i	$0.707228\pi$
$500$	13.9081	0.621987
$501$	−0.252979	−0.0113023
$502$	−4.78995	−0.213786
$503$	−10.1571	−0.452882	−0.226441	−	0.974025i	$-0.572709\pi$
$503$	−10.1571	−0.452882	−0.226441	+	0.974025i	$0.572709\pi$
$504$	−9.24432	−0.411775
$505$	−7.48200	−0.332945
$506$	0.199635	0.00887485
$507$	−0.300210	−0.0133328
$508$	−11.3701	−0.504466
$509$	11.3725	0.504076	0.252038	−	0.967717i	$-0.418899\pi$
$509$	11.3725	0.504076	0.252038	+	0.967717i	$0.418899\pi$
$510$	0.960649	0.0425382
$511$	11.6003	0.513169
$512$	22.7246	1.00430
$513$	−12.6412	−0.558121
$514$	−6.82752	−0.301149
$515$	9.16812	0.403996
$516$	0.963212	0.0424030
$517$	0.311020	0.0136787
$518$	0.531503	0.0233529
$519$	1.75453	0.0770152
$520$	−1.54261	−0.0676480
$521$	41.1410	1.80242	0.901210	−	0.433382i	$-0.142680\pi$
$521$	41.1410	1.80242	0.901210	+	0.433382i	$0.142680\pi$
$522$	−6.67797	−0.292287
$523$	24.7940	1.08417	0.542083	−	0.840325i	$-0.317636\pi$
$523$	24.7940	1.08417	0.542083	+	0.840325i	$0.317636\pi$
$524$	21.8907	0.956298
$525$	−2.24470	−0.0979667
$526$	0.218165	0.00951245
$527$	−7.81383	−0.340376
$528$	−0.137458	−0.00598210
$529$	−17.2492	−0.749964
$530$	−0.489563	−0.0212653
$531$	−26.6834	−1.15796
$532$	−21.9896	−0.953370
$533$	−5.65635	−0.245004
$534$	1.87885	0.0813058
$535$	−3.86318	−0.167020
$536$	10.6332	0.459285
$537$	6.71287	0.289682
$538$	−0.0304904	−0.00131453
$539$	−0.680859	−0.0293267
$540$	−2.65885	−0.114419
$541$	1.40582	0.0604409	0.0302204	−	0.999543i	$-0.490379\pi$
$541$	1.40582	0.0604409	0.0302204	+	0.999543i	$0.490379\pi$
$542$	14.3956	0.618345
$543$	0.353006	0.0151489
$544$	−38.4417	−1.64817
$545$	13.9330	0.596825
$546$	0.253189	0.0108355
$547$	−13.2873	−0.568126	−0.284063	−	0.958806i	$-0.591682\pi$
$547$	−13.2873	−0.568126	−0.284063	+	0.958806i	$0.591682\pi$
$548$	33.2041	1.41841
$549$	−34.9539	−1.49180
$550$	−0.356350	−0.0151948
$551$	−33.8659	−1.44273
$552$	1.30937	0.0557306
$553$	0.921829	0.0392001
$554$	6.66644	0.283230
$555$	0.160471	0.00681161
$556$	−14.2043	−0.602398
$557$	−20.1892	−0.855444	−0.427722	−	0.903910i	$-0.640684\pi$
$557$	−20.1892	−0.855444	−0.427722	+	0.903910i	$0.640684\pi$
$558$	−1.40497	−0.0594769
$559$	1.81589	0.0768040
$560$	−3.93438	−0.166258
$561$	0.404454	0.0170761
$562$	1.22456	0.0516549
$563$	−41.0121	−1.72846	−0.864228	−	0.503100i	$-0.832193\pi$
$563$	−41.0121	−1.72846	−0.864228	+	0.503100i	$0.832193\pi$
$564$	0.956844	0.0402904
$565$	−3.79822	−0.159792
$566$	−6.08223	−0.255655
$567$	−14.3180	−0.601299
$568$	−4.05306	−0.170063
$569$	−19.6986	−0.825809	−0.412904	−	0.910774i	$-0.635486\pi$
$569$	−19.6986	−0.825809	−0.412904	+	0.910774i	$0.635486\pi$
$570$	0.875960	0.0366899
$571$	−11.9584	−0.500445	−0.250223	−	0.968188i	$-0.580504\pi$
$571$	−11.9584	−0.500445	−0.250223	+	0.968188i	$0.580504\pi$
$572$	−0.304640	−0.0127376
$573$	7.55473	0.315604
$574$	4.77041	0.199113
$575$	−10.2653	−0.428091
$576$	8.54299	0.355958
$577$	−35.3881	−1.47322	−0.736612	−	0.676315i	$-0.763576\pi$
$577$	−35.3881	−1.47322	−0.736612	+	0.676315i	$0.763576\pi$
$578$	21.2714	0.884772
$579$	1.36880	0.0568852
$580$	−7.12310	−0.295771
$581$	−12.7137	−0.527453
$582$	−0.0534674	−0.00221629
$583$	−0.206117	−0.00853648
$584$	12.0786	0.499816
$585$	−2.46807	−0.102042
$586$	−8.53096	−0.352411
$587$	−12.2163	−0.504222	−0.252111	−	0.967698i	$-0.581125\pi$
$587$	−12.2163	−0.504222	−0.252111	+	0.967698i	$0.581125\pi$
$588$	−2.09464	−0.0863814
$589$	−7.12497	−0.293579
$590$	3.75529	0.154603
$591$	4.18509	0.172151
$592$	−1.67360	−0.0687845
$593$	−40.2153	−1.65144	−0.825722	−	0.564077i	$-0.809232\pi$
$593$	−40.2153	−1.65144	−0.825722	+	0.564077i	$0.809232\pi$
$594$	0.147698	0.00606013
$595$	11.5764	0.474588
$596$	5.11564	0.209545
$597$	5.87936	0.240626
$598$	1.15786	0.0473485
$599$	25.1290	1.02674	0.513371	−	0.858167i	$-0.328396\pi$
$599$	25.1290	1.02674	0.513371	+	0.858167i	$0.328396\pi$
$600$	−2.33724	−0.0954175
$601$	−37.4928	−1.52936	−0.764681	−	0.644409i	$-0.777103\pi$
$601$	−37.4928	−1.52936	−0.764681	+	0.644409i	$0.777103\pi$
$602$	−1.53147	−0.0624181
$603$	17.0124	0.692798
$604$	16.8943	0.687418
$605$	−9.30467	−0.378289
$606$	1.27865	0.0519416
$607$	27.6061	1.12050	0.560249	−	0.828324i	$-0.310705\pi$
$607$	27.6061	1.12050	0.560249	+	0.828324i	$0.310705\pi$
$608$	−35.0528	−1.42158
$609$	2.49248	0.101000
$610$	4.91923	0.199174
$611$	1.80389	0.0729774
$612$	−40.1739	−1.62394
$613$	17.2168	0.695381	0.347690	−	0.937609i	$-0.386966\pi$
$613$	17.2168	0.695381	0.347690	+	0.937609i	$0.386966\pi$
$614$	5.67662	0.229090
$615$	1.44028	0.0580775
$616$	0.547748	0.0220694
$617$	−30.9354	−1.24541	−0.622706	−	0.782456i	$-0.713967\pi$
$617$	−30.9354	−1.24541	−0.622706	+	0.782456i	$0.713967\pi$
$618$	−1.56680	−0.0630259
$619$	−26.4991	−1.06509	−0.532544	−	0.846402i	$-0.678764\pi$
$619$	−26.4991	−1.06509	−0.532544	+	0.846402i	$0.678764\pi$
$620$	−1.49862	−0.0601859
$621$	4.25470	0.170735
$622$	7.95872	0.319116
$623$	22.6414	0.907107
$624$	−0.797243	−0.0319152
$625$	14.7266	0.589064
$626$	−13.1085	−0.523920
$627$	0.368798	0.0147284
$628$	36.1962	1.44438
$629$	4.92437	0.196347
$630$	2.08150	0.0829291
$631$	16.3209	0.649726	0.324863	−	0.945761i	$-0.394682\pi$
$631$	16.3209	0.649726	0.324863	+	0.945761i	$0.394682\pi$
$632$	0.959833	0.0381801
$633$	−7.82636	−0.311070
$634$	11.1886	0.444356
$635$	5.45809	0.216598
$636$	−0.634111	−0.0251441
$637$	−3.94891	−0.156461
$638$	0.395686	0.0156653
$639$	−6.48462	−0.256527
$640$	−9.54780	−0.377410
$641$	13.8537	0.547187	0.273594	−	0.961845i	$-0.411788\pi$
$641$	13.8537	0.547187	0.273594	+	0.961845i	$0.411788\pi$
$642$	0.660204	0.0260562
$643$	−45.4581	−1.79269	−0.896346	−	0.443356i	$-0.853788\pi$
$643$	−45.4581	−1.79269	−0.896346	+	0.443356i	$0.853788\pi$
$644$	7.40115	0.291646
$645$	−0.462380	−0.0182062
$646$	26.8806	1.05760
$647$	−25.7784	−1.01345	−0.506727	−	0.862107i	$-0.669145\pi$
$647$	−25.7784	−1.01345	−0.506727	+	0.862107i	$0.669145\pi$
$648$	−14.9083	−0.585652
$649$	1.58106	0.0620619
$650$	−2.06679	−0.0810662
$651$	0.524389	0.0205524
$652$	−18.3003	−0.716697
$653$	−28.8461	−1.12883	−0.564417	−	0.825490i	$-0.690899\pi$
$653$	−28.8461	−1.12883	−0.564417	+	0.825490i	$0.690899\pi$
$654$	−2.38111	−0.0931086
$655$	−10.5084	−0.410597
$656$	−15.0211	−0.586475
$657$	19.3249	0.753936
$658$	−1.52135	−0.0593083
$659$	6.13123	0.238839	0.119419	−	0.992844i	$-0.461897\pi$
$659$	6.13123	0.238839	0.119419	+	0.992844i	$0.461897\pi$
$660$	0.0775704	0.00301942
$661$	9.46628	0.368196	0.184098	−	0.982908i	$-0.441064\pi$
$661$	9.46628	0.368196	0.184098	+	0.982908i	$0.441064\pi$
$662$	−1.77795	−0.0691020
$663$	2.34579	0.0911030
$664$	−13.2378	−0.513728
$665$	10.5559	0.409340
$666$	0.885426	0.0343096
$667$	11.3984	0.441348
$668$	−1.48890	−0.0576074
$669$	7.50598	0.290198
$670$	−2.39423	−0.0924973
$671$	2.07110	0.0799540
$672$	2.57984	0.0995193
$673$	25.2526	0.973416	0.486708	−	0.873565i	$-0.338198\pi$
$673$	25.2526	0.973416	0.486708	+	0.873565i	$0.338198\pi$
$674$	0.294871	0.0113580
$675$	−7.59467	−0.292319
$676$	−1.76688	−0.0679568
$677$	−7.53287	−0.289512	−0.144756	−	0.989467i	$-0.546240\pi$
$677$	−7.53287	−0.289512	−0.144756	+	0.989467i	$0.546240\pi$
$678$	0.649102	0.0249286
$679$	−0.644317	−0.0247266
$680$	12.0537	0.462239
$681$	−6.28607	−0.240883
$682$	0.0832475	0.00318771
$683$	−31.5199	−1.20607	−0.603037	−	0.797713i	$-0.706043\pi$
$683$	−31.5199	−1.20607	−0.603037	+	0.797713i	$0.706043\pi$
$684$	−36.6323	−1.40067
$685$	−15.9393	−0.609008
$686$	9.23400	0.352556
$687$	−0.729451	−0.0278303
$688$	4.82231	0.183849
$689$	−1.19545	−0.0455432
$690$	−0.294826	−0.0112238
$691$	−12.6388	−0.480801	−0.240401	−	0.970674i	$-0.577279\pi$
$691$	−12.6388	−0.480801	−0.240401	+	0.970674i	$0.577279\pi$
$692$	10.3262	0.392544
$693$	0.876358	0.0332901
$694$	−16.5968	−0.630007
$695$	6.81864	0.258646
$696$	2.59524	0.0983723
$697$	44.1978	1.67411
$698$	−0.383629	−0.0145206
$699$	0.408662	0.0154570
$700$	−13.2111	−0.499333
$701$	7.70250	0.290919	0.145460	−	0.989364i	$-0.453534\pi$
$701$	7.70250	0.290919	0.145460	+	0.989364i	$0.453534\pi$
$702$	0.856634	0.0323316
$703$	4.49024	0.169353
$704$	−0.506192	−0.0190778
$705$	−0.459323	−0.0172991
$706$	−6.47636	−0.243741
$707$	15.4085	0.579498
$708$	4.86407	0.182803
$709$	24.9575	0.937298	0.468649	−	0.883384i	$-0.344741\pi$
$709$	24.9575	0.937298	0.468649	+	0.883384i	$0.344741\pi$
$710$	0.912611	0.0342497
$711$	1.53567	0.0575920
$712$	23.5748	0.883503
$713$	2.39809	0.0898091
$714$	−1.97837	−0.0740388
$715$	0.146239	0.00546903
$716$	39.5084	1.47650
$717$	−6.23775	−0.232953
$718$	−6.06104	−0.226196
$719$	−1.16871	−0.0435854	−0.0217927	−	0.999763i	$-0.506937\pi$
$719$	−1.16871	−0.0435854	−0.0217927	+	0.999763i	$0.506937\pi$
$720$	−6.55425	−0.244262
$721$	−18.8810	−0.703164
$722$	15.3371	0.570789
$723$	−5.72985	−0.213096
$724$	2.07761	0.0772137
$725$	−20.3462	−0.755640
$726$	1.59014	0.0590155
$727$	25.2048	0.934796	0.467398	−	0.884047i	$-0.345192\pi$
$727$	25.2048	0.934796	0.467398	+	0.884047i	$0.345192\pi$
$728$	3.17688	0.117743
$729$	−22.2543	−0.824233
$730$	−2.71969	−0.100660
$731$	−14.1891	−0.524801
$732$	6.37168	0.235504
$733$	−8.03218	−0.296675	−0.148338	−	0.988937i	$-0.547392\pi$
$733$	−8.03218	−0.296675	−0.148338	+	0.988937i	$0.547392\pi$
$734$	−14.1015	−0.520495
$735$	1.00551	0.0370888
$736$	11.7979	0.434876
$737$	−1.00802	−0.0371310
$738$	7.94698	0.292532
$739$	3.29736	0.121295	0.0606477	−	0.998159i	$-0.480683\pi$
$739$	3.29736	0.121295	0.0606477	+	0.998159i	$0.480683\pi$
$740$	0.944446	0.0347185
$741$	2.13899	0.0785778
$742$	1.00821	0.0370127
$743$	−7.63134	−0.279967	−0.139983	−	0.990154i	$-0.544705\pi$
$743$	−7.63134	−0.279967	−0.139983	+	0.990154i	$0.544705\pi$
$744$	0.546008	0.0200176
$745$	−2.45571	−0.0899703
$746$	−0.330086	−0.0120853
$747$	−21.1796	−0.774922
$748$	2.38040	0.0870361
$749$	7.95589	0.290702
$750$	1.14098	0.0416626
$751$	27.7614	1.01303	0.506513	−	0.862232i	$-0.330934\pi$
$751$	27.7614	1.01303	0.506513	+	0.862232i	$0.330934\pi$
$752$	4.79042	0.174689
$753$	2.97828	0.108534
$754$	2.29494	0.0835766
$755$	−8.10992	−0.295150
$756$	5.47568	0.199149
$757$	−33.7745	−1.22755	−0.613777	−	0.789479i	$-0.710351\pi$
$757$	−33.7745	−1.22755	−0.613777	+	0.789479i	$0.710351\pi$
$758$	16.3795	0.594931
$759$	−0.124128	−0.00450557
$760$	10.9911	0.398688
$761$	41.8501	1.51706	0.758532	−	0.651636i	$-0.225917\pi$
$761$	41.8501	1.51706	0.758532	+	0.651636i	$0.225917\pi$
$762$	−0.932769	−0.0337907
$763$	−28.6939	−1.03879
$764$	44.4631	1.60862
$765$	19.2851	0.697254
$766$	7.23238	0.261316
$767$	9.16997	0.331108
$768$	−0.131066	−0.00472943
$769$	1.68878	0.0608990	0.0304495	−	0.999536i	$-0.490306\pi$
$769$	1.68878	0.0608990	0.0304495	+	0.999536i	$0.490306\pi$
$770$	−0.123334	−0.00444465
$771$	4.24519	0.152887
$772$	8.05601	0.289942
$773$	38.2742	1.37663	0.688314	−	0.725413i	$-0.258351\pi$
$773$	38.2742	1.37663	0.688314	+	0.725413i	$0.258351\pi$
$774$	−2.55126	−0.0917033
$775$	−4.28060	−0.153764
$776$	−0.670880	−0.0240832
$777$	−0.330476	−0.0118558
$778$	−15.8822	−0.569406
$779$	40.3014	1.44395
$780$	0.449900	0.0161090
$781$	0.384229	0.0137488
$782$	−9.04733	−0.323532
$783$	8.43301	0.301371
$784$	−10.4868	−0.374528
$785$	−17.3756	−0.620162
$786$	1.79585	0.0640557
$787$	−7.90010	−0.281608	−0.140804	−	0.990037i	$-0.544969\pi$
$787$	−7.90010	−0.281608	−0.140804	+	0.990037i	$0.544969\pi$
$788$	24.6312	0.877450
$789$	−0.135650	−0.00482926
$790$	−0.216121	−0.00768926
$791$	7.82211	0.278122
$792$	0.912488	0.0324238
$793$	12.0122	0.426565
$794$	17.2221	0.611188
$795$	0.304398	0.0107959
$796$	34.6028	1.22646
$797$	−31.1460	−1.10325	−0.551625	−	0.834092i	$-0.685992\pi$
$797$	−31.1460	−1.10325	−0.551625	+	0.834092i	$0.685992\pi$
$798$	−1.80396	−0.0638597
$799$	−14.0952	−0.498654
$800$	−21.0593	−0.744559
$801$	37.7180	1.33270
$802$	9.03332	0.318978
$803$	−1.14505	−0.0404078
$804$	−3.10115	−0.109369
$805$	−3.55285	−0.125221
$806$	0.482827	0.0170069
$807$	0.0189582	0.000667360 0
$808$	16.0438	0.564419
$809$	19.2376	0.676358	0.338179	−	0.941082i	$-0.390189\pi$
$809$	19.2376	0.676358	0.338179	+	0.941082i	$0.390189\pi$
$810$	3.35683	0.117947
$811$	8.38444	0.294417	0.147209	−	0.989105i	$-0.452971\pi$
$811$	8.38444	0.294417	0.147209	+	0.989105i	$0.452971\pi$
$812$	14.6694	0.514796
$813$	−8.95085	−0.313920
$814$	−0.0524636	−0.00183885
$815$	8.78490	0.307721
$816$	6.22952	0.218077
$817$	−12.9382	−0.452649
$818$	−3.26170	−0.114043
$819$	5.08279	0.177607
$820$	8.47670	0.296019
$821$	19.9624	0.696691	0.348346	−	0.937366i	$-0.386744\pi$
$821$	19.9624	0.696691	0.348346	+	0.937366i	$0.386744\pi$
$822$	2.72397	0.0950092
$823$	−29.0804	−1.01368	−0.506840	−	0.862040i	$-0.669186\pi$
$823$	−29.0804	−1.01368	−0.506840	+	0.862040i	$0.669186\pi$
$824$	−19.6594	−0.684867
$825$	0.221570	0.00771407
$826$	−7.73369	−0.269090
$827$	16.7954	0.584032	0.292016	−	0.956413i	$-0.405674\pi$
$827$	16.7954	0.584032	0.292016	+	0.956413i	$0.405674\pi$
$828$	12.3295	0.428480
$829$	−15.6959	−0.545142	−0.272571	−	0.962136i	$-0.587874\pi$
$829$	−15.6959	−0.545142	−0.272571	+	0.962136i	$0.587874\pi$
$830$	2.98071	0.103462
$831$	−4.14503	−0.143790
$832$	−2.93586	−0.101783
$833$	30.8561	1.06910
$834$	−1.16528	−0.0403504
$835$	0.714733	0.0247343
$836$	2.17055	0.0750700
$837$	1.77420	0.0613255
$838$	−0.569627	−0.0196774
$839$	−36.4473	−1.25830	−0.629150	−	0.777284i	$-0.716597\pi$
$839$	−36.4473	−1.25830	−0.629150	+	0.777284i	$0.716597\pi$
$840$	−0.808928	−0.0279107
$841$	−6.40784	−0.220960
$842$	9.14272	0.315079
$843$	−0.761401	−0.0262241
$844$	−46.0618	−1.58551
$845$	0.848172	0.0291780
$846$	−2.53440	−0.0871344
$847$	19.1622	0.658420
$848$	−3.17467	−0.109019
$849$	3.78178	0.129790
$850$	16.1495	0.553925
$851$	−1.51130	−0.0518068
$852$	1.18207	0.0404970
$853$	−56.3291	−1.92867	−0.964336	−	0.264679i	$-0.914734\pi$
$853$	−56.3291	−1.92867	−0.964336	+	0.264679i	$0.914734\pi$
$854$	−10.1307	−0.346667
$855$	17.5850	0.601393
$856$	8.28389	0.283138
$857$	20.1096	0.686929	0.343465	−	0.939166i	$-0.388399\pi$
$857$	20.1096	0.686929	0.343465	+	0.939166i	$0.388399\pi$
$858$	−0.0249918	−0.000853205 0
$859$	22.4894	0.767329	0.383664	−	0.923473i	$-0.374662\pi$
$859$	22.4894	0.767329	0.383664	+	0.923473i	$0.374662\pi$
$860$	−2.72132	−0.0927963
$861$	−2.96613	−0.101085
$862$	14.0768	0.479457
$863$	−51.3272	−1.74720	−0.873599	−	0.486647i	$-0.838220\pi$
$863$	−51.3272	−1.74720	−0.873599	+	0.486647i	$0.838220\pi$
$864$	8.72856	0.296952
$865$	−4.95699	−0.168543
$866$	−5.74820	−0.195332
$867$	−13.2260	−0.449179
$868$	3.08627	0.104755
$869$	−0.0909918	−0.00308669
$870$	−0.584359	−0.0198116
$871$	−5.84643	−0.198099
$872$	−29.8768	−1.01176
$873$	−1.07336	−0.0363278
$874$	−8.24973	−0.279051
$875$	13.7495	0.464819
$876$	−3.52270	−0.119021
$877$	−38.2648	−1.29211	−0.646055	−	0.763291i	$-0.723582\pi$
$877$	−38.2648	−1.29211	−0.646055	+	0.763291i	$0.723582\pi$
$878$	8.96674	0.302613
$879$	5.30434	0.178911
$880$	0.388355	0.0130914
$881$	30.2398	1.01881	0.509403	−	0.860528i	$-0.329866\pi$
$881$	30.2398	1.01881	0.509403	+	0.860528i	$0.329866\pi$
$882$	5.54808	0.186814
$883$	4.67446	0.157308	0.0786541	−	0.996902i	$-0.474938\pi$
$883$	4.67446	0.157308	0.0786541	+	0.996902i	$0.474938\pi$
$884$	13.8061	0.464349
$885$	−2.33495	−0.0784884
$886$	10.0121	0.336363
$887$	−22.4333	−0.753235	−0.376618	−	0.926369i	$-0.622913\pi$
$887$	−22.4333	−0.753235	−0.376618	+	0.926369i	$0.622913\pi$
$888$	−0.344100	−0.0115473
$889$	−11.2405	−0.376993
$890$	−5.30824	−0.177932
$891$	1.41330	0.0473473
$892$	44.1762	1.47913
$893$	−12.8526	−0.430097
$894$	0.419672	0.0140359
$895$	−18.9656	−0.633950
$896$	19.6629	0.656891
$897$	−0.719930	−0.0240378
$898$	10.4263	0.347931
$899$	4.75312	0.158525
$900$	−22.0083	−0.733609
$901$	9.34108	0.311196
$902$	−0.470877	−0.0156785
$903$	0.952232	0.0316883
$904$	8.14459	0.270885
$905$	−0.997334	−0.0331525
$906$	1.38596	0.0460453
$907$	−15.9983	−0.531214	−0.265607	−	0.964081i	$-0.585572\pi$
$907$	−15.9983	−0.531214	−0.265607	+	0.964081i	$0.585572\pi$
$908$	−36.9965	−1.22777
$909$	25.6690	0.851386
$910$	−0.715324	−0.0237128
$911$	33.8374	1.12108	0.560541	−	0.828127i	$-0.310593\pi$
$911$	33.8374	1.12108	0.560541	+	0.828127i	$0.310593\pi$
$912$	5.68033	0.188095
$913$	1.25494	0.0415326
$914$	1.72928	0.0571996
$915$	−3.05866	−0.101116
$916$	−4.29316	−0.141850
$917$	21.6411	0.714653
$918$	−6.69359	−0.220921
$919$	9.19972	0.303471	0.151735	−	0.988421i	$-0.451514\pi$
$919$	9.19972	0.303471	0.151735	+	0.988421i	$0.451514\pi$
$920$	−3.69932	−0.121963
$921$	−3.52958	−0.116304
$922$	−17.0572	−0.561748
$923$	2.22849	0.0733515
$924$	−0.159750	−0.00525537
$925$	2.69769	0.0886994
$926$	7.47865	0.245764
$927$	−31.4536	−1.03307
$928$	23.3839	0.767616
$929$	38.0189	1.24736	0.623679	−	0.781680i	$-0.285637\pi$
$929$	38.0189	1.24736	0.623679	+	0.781680i	$0.285637\pi$
$930$	−0.122942	−0.00403143
$931$	28.1359	0.922116
$932$	2.40517	0.0787839
$933$	−4.94854	−0.162008
$934$	−6.16632	−0.201768
$935$	−1.14269	−0.0373699
$936$	5.29233	0.172985
$937$	−12.8024	−0.418236	−0.209118	−	0.977890i	$-0.567059\pi$
$937$	−12.8024	−0.418236	−0.209118	+	0.977890i	$0.567059\pi$
$938$	4.93072	0.160994
$939$	8.15054	0.265983
$940$	−2.70333	−0.0881729
$941$	19.0245	0.620181	0.310090	−	0.950707i	$-0.399641\pi$
$941$	19.0245	0.620181	0.310090	+	0.950707i	$0.399641\pi$
$942$	2.96943	0.0967493
$943$	−13.5644	−0.441718
$944$	24.3519	0.792587
$945$	−2.62854	−0.0855065
$946$	0.151168	0.00491491
$947$	−2.15887	−0.0701539	−0.0350770	−	0.999385i	$-0.511168\pi$
$947$	−2.15887	−0.0701539	−0.0350770	+	0.999385i	$0.511168\pi$
$948$	−0.279933	−0.00909181
$949$	−6.64115	−0.215581
$950$	14.7258	0.477769
$951$	−6.95681	−0.225590
$952$	−24.8236	−0.804537
$953$	18.2117	0.589936	0.294968	−	0.955507i	$-0.404691\pi$
$953$	18.2117	0.589936	0.294968	+	0.955507i	$0.404691\pi$
$954$	1.67957	0.0543782
$955$	−21.3441	−0.690678
$956$	−36.7121	−1.18735
$957$	−0.246028	−0.00795295
$958$	5.87851	0.189926
$959$	32.8256	1.05999
$960$	0.747558	0.0241273
$961$	1.00000	0.0322581
$962$	−0.304283	−0.00981049
$963$	13.2536	0.427093
$964$	−33.7229	−1.08614
$965$	−3.86720	−0.124490
$966$	0.607169	0.0195353
$967$	17.9039	0.575751	0.287876	−	0.957668i	$-0.407051\pi$
$967$	17.9039	0.575751	0.287876	+	0.957668i	$0.407051\pi$
$968$	19.9522	0.641288
$969$	−16.7137	−0.536921
$970$	0.151059	0.00485022
$971$	−2.17673	−0.0698546	−0.0349273	−	0.999390i	$-0.511120\pi$
$971$	−2.17673	−0.0698546	−0.0349273	+	0.999390i	$0.511120\pi$
$972$	13.7524	0.441108
$973$	−14.0424	−0.450179
$974$	8.96952	0.287402
$975$	1.28508	0.0411555
$976$	31.8997	1.02109
$977$	24.3730	0.779762	0.389881	−	0.920865i	$-0.372516\pi$
$977$	24.3730	0.779762	0.389881	+	0.920865i	$0.372516\pi$
$978$	−1.50131	−0.0480065
$979$	−2.23488	−0.0714271
$980$	5.91790	0.189040
$981$	−47.8009	−1.52616
$982$	10.9457	0.349290
$983$	0.0380046	0.00121216	0.000606080	−	1.00000i	$-0.499807\pi$
$983$	0.0380046	0.00121216	0.000606080		1.00000i	$0.499807\pi$
$984$	−3.08841	−0.0984550
$985$	−11.8239	−0.376742
$986$	−17.9322	−0.571078
$987$	0.945937	0.0301095
$988$	12.5890	0.400508
$989$	4.35466	0.138470
$990$	−0.205461	−0.00652998
$991$	−6.63973	−0.210918	−0.105459	−	0.994424i	$-0.533631\pi$
$991$	−6.63973	−0.210918	−0.105459	+	0.994424i	$0.533631\pi$
$992$	4.91970	0.156201
$993$	1.10549	0.0350816
$994$	−1.87944	−0.0596123
$995$	−16.6107	−0.526595
$996$	3.86079	0.122334
$997$	30.6435	0.970490	0.485245	−	0.874378i	$-0.338730\pi$
$997$	30.6435	0.970490	0.485245	+	0.874378i	$0.338730\pi$
$998$	−13.0721	−0.413791
$999$	−1.11813	−0.0353759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.b.1.4	✓	6
3.2	odd	2		3627.2.a.m.1.3		6
4.3	odd	2		6448.2.a.y.1.3		6
13.12	even	2		5239.2.a.g.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.b.1.4	✓	6	1.1	even	1	trivial
3627.2.a.m.1.3		6	3.2	odd	2
5239.2.a.g.1.3		6	13.12	even	2
6448.2.a.y.1.3		6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.a (trivial)

\(f(q)\)	\(=\)	\(q+0.482827 q^{2} -0.300210 q^{3} -1.76688 q^{4} +0.848172 q^{5} -0.144950 q^{6} -1.74674 q^{7} -1.81875 q^{8} -2.90987 q^{9} +O(q^{10})\)	\(q+0.482827 q^{2} -0.300210 q^{3} -1.76688 q^{4} +0.848172 q^{5} -0.144950 q^{6} -1.74674 q^{7} -1.81875 q^{8} -2.90987 q^{9} +0.409520 q^{10} +0.172417 q^{11} +0.530435 q^{12} +1.00000 q^{13} -0.843372 q^{14} -0.254630 q^{15} +2.65561 q^{16} -7.81383 q^{17} -1.40497 q^{18} -7.12497 q^{19} -1.49862 q^{20} +0.524389 q^{21} +0.0832475 q^{22} +2.39809 q^{23} +0.546008 q^{24} -4.28060 q^{25} +0.482827 q^{26} +1.77420 q^{27} +3.08627 q^{28} +4.75312 q^{29} -0.122942 q^{30} +1.00000 q^{31} +4.91970 q^{32} -0.0517613 q^{33} -3.77273 q^{34} -1.48153 q^{35} +5.14139 q^{36} -0.630212 q^{37} -3.44013 q^{38} -0.300210 q^{39} -1.54261 q^{40} -5.65635 q^{41} +0.253189 q^{42} +1.81589 q^{43} -0.304640 q^{44} -2.46807 q^{45} +1.15786 q^{46} +1.80389 q^{47} -0.797243 q^{48} -3.94891 q^{49} -2.06679 q^{50} +2.34579 q^{51} -1.76688 q^{52} -1.19545 q^{53} +0.856634 q^{54} +0.146239 q^{55} +3.17688 q^{56} +2.13899 q^{57} +2.29494 q^{58} +9.16997 q^{59} +0.449900 q^{60} +12.0122 q^{61} +0.482827 q^{62} +5.08279 q^{63} -2.93586 q^{64} +0.848172 q^{65} -0.0249918 q^{66} -5.84643 q^{67} +13.8061 q^{68} -0.719930 q^{69} -0.715324 q^{70} +2.22849 q^{71} +5.29233 q^{72} -6.64115 q^{73} -0.304283 q^{74} +1.28508 q^{75} +12.5890 q^{76} -0.301167 q^{77} -0.144950 q^{78} -0.527743 q^{79} +2.25242 q^{80} +8.19699 q^{81} -2.73104 q^{82} +7.27854 q^{83} -0.926531 q^{84} -6.62747 q^{85} +0.876761 q^{86} -1.42694 q^{87} -0.313583 q^{88} -12.9621 q^{89} -1.19165 q^{90} -1.74674 q^{91} -4.23713 q^{92} -0.300210 q^{93} +0.870964 q^{94} -6.04320 q^{95} -1.47695 q^{96} +0.368869 q^{97} -1.90664 q^{98} -0.501711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9	\( 6 q - 2 q^{2} - 5 q^{3} + 6 q^{4} - 9 q^{5} - 3 q^{8} - q^{9} - 8 q^{10} - 5 q^{11} - 13 q^{12} + 6 q^{13} - 17 q^{14} + 4 q^{15} + 14 q^{16} - 23 q^{17} + 9 q^{18} + 7 q^{19} - 10 q^{20} + 2 q^{21} + 2 q^{22} - 18 q^{23} - 13 q^{24} + 11 q^{25} - 2 q^{26} - 5 q^{27} - 25 q^{28} - 18 q^{29} + 25 q^{30} + 6 q^{31} + 2 q^{32} - 2 q^{33} - 16 q^{34} - q^{35} - 2 q^{36} - 13 q^{37} - 8 q^{38} - 5 q^{39} - 29 q^{40} - 5 q^{41} + 31 q^{42} - 7 q^{43} + 30 q^{44} - 5 q^{45} + 19 q^{46} - 9 q^{47} - 19 q^{48} + 16 q^{49} + 29 q^{50} + 26 q^{51} + 6 q^{52} - 31 q^{53} - 4 q^{54} + 7 q^{55} + 8 q^{56} - 5 q^{57} + 35 q^{58} - q^{59} + 33 q^{60} - 15 q^{61} - 2 q^{62} + 11 q^{63} - 5 q^{64} - 9 q^{65} - 29 q^{66} - 28 q^{67} - 12 q^{68} + 5 q^{69} + 73 q^{70} + q^{71} + 45 q^{72} - 20 q^{73} + 4 q^{74} + q^{75} + 38 q^{76} - 29 q^{77} - 15 q^{79} + 7 q^{80} + 2 q^{81} + 36 q^{82} + q^{83} + 68 q^{84} + 29 q^{85} + 3 q^{86} + 10 q^{87} + 9 q^{88} - q^{89} - 32 q^{90} - 60 q^{92} - 5 q^{93} + 54 q^{94} - 13 q^{95} + 36 q^{96} - 5 q^{97} + 20 q^{98} - 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 + 6 * q^4 - 9 * q^5 - 3 * q^8 - q^9 - 8 * q^10 - 5 * q^11 - 13 * q^12 + 6 * q^13 - 17 * q^14 + 4 * q^15 + 14 * q^16 - 23 * q^17 + 9 * q^18 + 7 * q^19 - 10 * q^20 + 2 * q^21 + 2 * q^22 - 18 * q^23 - 13 * q^24 + 11 * q^25 - 2 * q^26 - 5 * q^27 - 25 * q^28 - 18 * q^29 + 25 * q^30 + 6 * q^31 + 2 * q^32 - 2 * q^33 - 16 * q^34 - q^35 - 2 * q^36 - 13 * q^37 - 8 * q^38 - 5 * q^39 - 29 * q^40 - 5 * q^41 + 31 * q^42 - 7 * q^43 + 30 * q^44 - 5 * q^45 + 19 * q^46 - 9 * q^47 - 19 * q^48 + 16 * q^49 + 29 * q^50 + 26 * q^51 + 6 * q^52 - 31 * q^53 - 4 * q^54 + 7 * q^55 + 8 * q^56 - 5 * q^57 + 35 * q^58 - q^59 + 33 * q^60 - 15 * q^61 - 2 * q^62 + 11 * q^63 - 5 * q^64 - 9 * q^65 - 29 * q^66 - 28 * q^67 - 12 * q^68 + 5 * q^69 + 73 * q^70 + q^71 + 45 * q^72 - 20 * q^73 + 4 * q^74 + q^75 + 38 * q^76 - 29 * q^77 - 15 * q^79 + 7 * q^80 + 2 * q^81 + 36 * q^82 + q^83 + 68 * q^84 + 29 * q^85 + 3 * q^86 + 10 * q^87 + 9 * q^88 - q^89 - 32 * q^90 - 60 * q^92 - 5 * q^93 + 54 * q^94 - 13 * q^95 + 36 * q^96 - 5 * q^97 + 20 * q^98 - 15 * q^99

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