LMFDB - Embedded newform 349.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 $ x^17 - 5x^16 - 14x^15 + 102x^14 + 26x^13 - 792x^12 + 474x^11 + 2887x^10 - 3021x^9 - 4835x^8 + 6673x^7 + 2880x^6 - 5373x^5 - 164x^4 + 1075x^3 + 75x^2 - 41x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$1.43824$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.43824 q^{2} +3.12218 q^{3} +0.0685351 q^{4} +1.24047 q^{5} +4.49045 q^{6} -3.90458 q^{7} -2.77791 q^{8} +6.74802 q^{9} +O(q^{10})$	\(q+1.43824 q^{2} +3.12218 q^{3} +0.0685351 q^{4} +1.24047 q^{5} +4.49045 q^{6} -3.90458 q^{7} -2.77791 q^{8} +6.74802 q^{9} +1.78410 q^{10} +0.242218 q^{11} +0.213979 q^{12} +0.00614827 q^{13} -5.61573 q^{14} +3.87298 q^{15} -4.13237 q^{16} +2.54150 q^{17} +9.70527 q^{18} +3.13813 q^{19} +0.0850160 q^{20} -12.1908 q^{21} +0.348367 q^{22} -6.93361 q^{23} -8.67314 q^{24} -3.46123 q^{25} +0.00884270 q^{26} +11.7020 q^{27} -0.267601 q^{28} -3.69353 q^{29} +5.57028 q^{30} +0.958271 q^{31} -0.387524 q^{32} +0.756248 q^{33} +3.65529 q^{34} -4.84353 q^{35} +0.462476 q^{36} -4.87150 q^{37} +4.51339 q^{38} +0.0191960 q^{39} -3.44592 q^{40} -6.50157 q^{41} -17.5333 q^{42} +7.11406 q^{43} +0.0166004 q^{44} +8.37074 q^{45} -9.97219 q^{46} +9.65096 q^{47} -12.9020 q^{48} +8.24577 q^{49} -4.97808 q^{50} +7.93502 q^{51} +0.000421373 q^{52} -12.0075 q^{53} +16.8303 q^{54} +0.300465 q^{55} +10.8466 q^{56} +9.79783 q^{57} -5.31219 q^{58} +7.44292 q^{59} +0.265435 q^{60} +8.25740 q^{61} +1.37822 q^{62} -26.3482 q^{63} +7.70739 q^{64} +0.00762677 q^{65} +1.08767 q^{66} +13.5161 q^{67} +0.174182 q^{68} -21.6480 q^{69} -6.96616 q^{70} +10.4311 q^{71} -18.7454 q^{72} -9.64166 q^{73} -7.00639 q^{74} -10.8066 q^{75} +0.215072 q^{76} -0.945760 q^{77} +0.0276085 q^{78} -2.14854 q^{79} -5.12610 q^{80} +16.2917 q^{81} -9.35082 q^{82} -3.48055 q^{83} -0.835499 q^{84} +3.15266 q^{85} +10.2317 q^{86} -11.5319 q^{87} -0.672859 q^{88} +10.5268 q^{89} +12.0391 q^{90} -0.0240064 q^{91} -0.475196 q^{92} +2.99189 q^{93} +13.8804 q^{94} +3.89277 q^{95} -1.20992 q^{96} +1.33111 q^{97} +11.8594 q^{98} +1.63449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * 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 $

$2$	1.43824	1.01699	0.508495	−	0.861065i	$-0.330202\pi$
$2$	1.43824	1.01699	0.508495	+	0.861065i	$0.330202\pi$
$3$	3.12218	1.80259	0.901296	−	0.433203i	$-0.142617\pi$
$3$	3.12218	1.80259	0.901296	+	0.433203i	$0.142617\pi$
$4$	0.0685351	0.0342676
$5$	1.24047	0.554756	0.277378	−	0.960761i	$-0.410534\pi$
$5$	1.24047	0.554756	0.277378	+	0.960761i	$0.410534\pi$
$6$	4.49045	1.83322
$7$	−3.90458	−1.47579	−0.737897	−	0.674913i	$-0.764181\pi$
$7$	−3.90458	−1.47579	−0.737897	+	0.674913i	$0.764181\pi$
$8$	−2.77791	−0.982140
$9$	6.74802	2.24934
$10$	1.78410	0.564181
$11$	0.242218	0.0730314	0.0365157	−	0.999333i	$-0.488374\pi$
$11$	0.242218	0.0730314	0.0365157	+	0.999333i	$0.488374\pi$
$12$	0.213979	0.0617704
$13$	0.00614827	0.00170522	0.000852612	−	1.00000i	$-0.499729\pi$
$13$	0.00614827	0.00170522	0.000852612		1.00000i	$0.499729\pi$
$14$	−5.61573	−1.50087
$15$	3.87298	1.00000
$16$	−4.13237	−1.03309
$17$	2.54150	0.616404	0.308202	−	0.951321i	$-0.400273\pi$
$17$	2.54150	0.616404	0.308202	+	0.951321i	$0.400273\pi$
$18$	9.70527	2.28755
$19$	3.13813	0.719937	0.359969	−	0.932964i	$-0.382787\pi$
$19$	3.13813	0.719937	0.359969	+	0.932964i	$0.382787\pi$
$20$	0.0850160	0.0190102
$21$	−12.1908	−2.66025
$22$	0.348367	0.0742722
$23$	−6.93361	−1.44576	−0.722878	−	0.690975i	$-0.757181\pi$
$23$	−6.93361	−1.44576	−0.722878	+	0.690975i	$0.757181\pi$
$24$	−8.67314	−1.77040
$25$	−3.46123	−0.692245
$26$	0.00884270	0.00173420
$27$	11.7020	2.25205
$28$	−0.267601	−0.0505719
$29$	−3.69353	−0.685872	−0.342936	−	0.939359i	$-0.611421\pi$
$29$	−3.69353	−0.685872	−0.342936	+	0.939359i	$0.611421\pi$
$30$	5.57028	1.01699
$31$	0.958271	0.172110	0.0860552	−	0.996290i	$-0.472574\pi$
$31$	0.958271	0.172110	0.0860552	+	0.996290i	$0.472574\pi$
$32$	−0.387524	−0.0685053
$33$	0.756248	0.131646
$34$	3.65529	0.626876
$35$	−4.84353	−0.818706
$36$	0.462476	0.0770794
$37$	−4.87150	−0.800870	−0.400435	−	0.916325i	$-0.631141\pi$
$37$	−4.87150	−0.800870	−0.400435	+	0.916325i	$0.631141\pi$
$38$	4.51339	0.732169
$39$	0.0191960	0.00307382
$40$	−3.44592	−0.544848
$41$	−6.50157	−1.01538	−0.507688	−	0.861541i	$-0.669500\pi$
$41$	−6.50157	−1.01538	−0.507688	+	0.861541i	$0.669500\pi$
$42$	−17.5333	−2.70545
$43$	7.11406	1.08488	0.542442	−	0.840093i	$-0.317500\pi$
$43$	7.11406	1.08488	0.542442	+	0.840093i	$0.317500\pi$
$44$	0.0166004	0.00250261
$45$	8.37074	1.24784
$46$	−9.97219	−1.47032
$47$	9.65096	1.40774	0.703869	−	0.710330i	$-0.251454\pi$
$47$	9.65096	1.40774	0.703869	+	0.710330i	$0.251454\pi$
$48$	−12.9020	−1.86225
$49$	8.24577	1.17797
$50$	−4.97808	−0.704006
$51$	7.93502	1.11113
$52$	0.000421373 0	5.84339e−5 0
$53$	−12.0075	−1.64936	−0.824678	−	0.565602i	$-0.808644\pi$
$53$	−12.0075	−1.64936	−0.824678	+	0.565602i	$0.808644\pi$
$54$	16.8303	2.29031
$55$	0.300465	0.0405147
$56$	10.8466	1.44944
$57$	9.79783	1.29775
$58$	−5.31219	−0.697524
$59$	7.44292	0.968985	0.484493	−	0.874795i	$-0.339004\pi$
$59$	7.44292	0.968985	0.484493	+	0.874795i	$0.339004\pi$
$60$	0.265435	0.0342676
$61$	8.25740	1.05725	0.528626	−	0.848855i	$-0.322707\pi$
$61$	8.25740	1.05725	0.528626	+	0.848855i	$0.322707\pi$
$62$	1.37822	0.175035
$63$	−26.3482	−3.31956
$64$	7.70739	0.963424
$65$	0.00762677	0.000945984 0
$66$	1.08767	0.133882
$67$	13.5161	1.65125	0.825627	−	0.564217i	$-0.190822\pi$
$67$	13.5161	1.65125	0.825627	+	0.564217i	$0.190822\pi$
$68$	0.174182	0.0211227
$69$	−21.6480	−2.60611
$70$	−6.96616	−0.832616
$71$	10.4311	1.23794	0.618970	−	0.785414i	$-0.287550\pi$
$71$	10.4311	1.23794	0.618970	+	0.785414i	$0.287550\pi$
$72$	−18.7454	−2.20917
$73$	−9.64166	−1.12847	−0.564236	−	0.825614i	$-0.690829\pi$
$73$	−9.64166	−1.12847	−0.564236	+	0.825614i	$0.690829\pi$
$74$	−7.00639	−0.814476
$75$	−10.8066	−1.24784
$76$	0.215072	0.0246705
$77$	−0.945760	−0.107779
$78$	0.0276085	0.00312605
$79$	−2.14854	−0.241730	−0.120865	−	0.992669i	$-0.538567\pi$
$79$	−2.14854	−0.241730	−0.120865	+	0.992669i	$0.538567\pi$
$80$	−5.12610	−0.573115
$81$	16.2917	1.81019
$82$	−9.35082	−1.03263
$83$	−3.48055	−0.382040	−0.191020	−	0.981586i	$-0.561180\pi$
$83$	−3.48055	−0.382040	−0.191020	+	0.981586i	$0.561180\pi$
$84$	−0.835499	−0.0911604
$85$	3.15266	0.341954
$86$	10.2317	1.10332
$87$	−11.5319	−1.23635
$88$	−0.672859	−0.0717271
$89$	10.5268	1.11584	0.557919	−	0.829896i	$-0.311600\pi$
$89$	10.5268	1.11584	0.557919	+	0.829896i	$0.311600\pi$
$90$	12.0391	1.26904
$91$	−0.0240064	−0.00251656
$92$	−0.475196	−0.0495426
$93$	2.99189	0.310245
$94$	13.8804	1.43165
$95$	3.89277	0.399390
$96$	−1.20992	−0.123487
$97$	1.33111	0.135153	0.0675767	−	0.997714i	$-0.478473\pi$
$97$	1.33111	0.135153	0.0675767	+	0.997714i	$0.478473\pi$
$98$	11.8594	1.19798
$99$	1.63449	0.164272
$100$	−0.237216	−0.0237216
$101$	16.8190	1.67355	0.836777	−	0.547543i	$-0.184437\pi$
$101$	16.8190	1.67355	0.836777	+	0.547543i	$0.184437\pi$
$102$	11.4125	1.13000
$103$	13.8594	1.36561	0.682806	−	0.730600i	$-0.260760\pi$
$103$	13.8594	1.36561	0.682806	+	0.730600i	$0.260760\pi$
$104$	−0.0170794	−0.00167477
$105$	−15.1224	−1.47579
$106$	−17.2697	−1.67738
$107$	−18.6337	−1.80139	−0.900693	−	0.434455i	$-0.856941\pi$
$107$	−18.6337	−1.80139	−0.900693	+	0.434455i	$0.856941\pi$
$108$	0.801998	0.0771723
$109$	−2.24403	−0.214939	−0.107470	−	0.994208i	$-0.534275\pi$
$109$	−2.24403	−0.214939	−0.107470	+	0.994208i	$0.534275\pi$
$110$	0.432140	0.0412030
$111$	−15.2097	−1.44364
$112$	16.1352	1.52463
$113$	−11.8346	−1.11331	−0.556653	−	0.830745i	$-0.687915\pi$
$113$	−11.8346	−1.11331	−0.556653	+	0.830745i	$0.687915\pi$
$114$	14.0916	1.31980
$115$	−8.60095	−0.802043
$116$	−0.253137	−0.0235032
$117$	0.0414887	0.00383563
$118$	10.7047	0.985448
$119$	−9.92349	−0.909685
$120$	−10.7588	−0.982140
$121$	−10.9413	−0.994666
$122$	11.8761	1.07521
$123$	−20.2991	−1.83031
$124$	0.0656752	0.00589781
$125$	−10.4959	−0.938784
$126$	−37.8950	−3.37596
$127$	−15.5890	−1.38330	−0.691650	−	0.722233i	$-0.743116\pi$
$127$	−15.5890	−1.38330	−0.691650	+	0.722233i	$0.743116\pi$
$128$	11.8601	1.04830
$129$	22.2114	1.95560
$130$	0.0109691	0.000962056 0
$131$	7.37396	0.644266	0.322133	−	0.946694i	$-0.395600\pi$
$131$	7.37396	0.644266	0.322133	+	0.946694i	$0.395600\pi$
$132$	0.0518295	0.00451118
$133$	−12.2531	−1.06248
$134$	19.4394	1.67931
$135$	14.5160	1.24934
$136$	−7.06006	−0.605395
$137$	16.5250	1.41183	0.705914	−	0.708297i	$-0.250536\pi$
$137$	16.5250	1.41183	0.705914	+	0.708297i	$0.250536\pi$
$138$	−31.1350	−2.65039
$139$	0.966790	0.0820020	0.0410010	−	0.999159i	$-0.486945\pi$
$139$	0.966790	0.0820020	0.0410010	+	0.999159i	$0.486945\pi$
$140$	−0.331952	−0.0280551
$141$	30.1321	2.53758
$142$	15.0024	1.25897
$143$	0.00148922	0.000124535 0
$144$	−27.8853	−2.32378
$145$	−4.58173	−0.380492
$146$	−13.8670	−1.14764
$147$	25.7448	2.12340
$148$	−0.333869	−0.0274438
$149$	−6.78714	−0.556024	−0.278012	−	0.960578i	$-0.589676\pi$
$149$	−6.78714	−0.556024	−0.278012	+	0.960578i	$0.589676\pi$
$150$	−15.5425	−1.26904
$151$	−18.2679	−1.48662	−0.743312	−	0.668945i	$-0.766746\pi$
$151$	−18.2679	−1.48662	−0.743312	+	0.668945i	$0.766746\pi$
$152$	−8.71746	−0.707079
$153$	17.1501	1.38650
$154$	−1.36023	−0.109610
$155$	1.18871	0.0954794
$156$	0.00131560	0.000105332 0
$157$	17.5851	1.40345	0.701723	−	0.712450i	$-0.252414\pi$
$157$	17.5851	1.40345	0.701723	+	0.712450i	$0.252414\pi$
$158$	−3.09012	−0.245837
$159$	−37.4896	−2.97312
$160$	−0.480714	−0.0380037
$161$	27.0728	2.13364
$162$	23.4314	1.84094
$163$	−19.5654	−1.53248	−0.766239	−	0.642555i	$-0.777874\pi$
$163$	−19.5654	−1.53248	−0.766239	+	0.642555i	$0.777874\pi$
$164$	−0.445586	−0.0347944
$165$	0.938105	0.0730314
$166$	−5.00587	−0.388531
$167$	17.5498	1.35805	0.679023	−	0.734117i	$-0.262404\pi$
$167$	17.5498	1.35805	0.679023	+	0.734117i	$0.262404\pi$
$168$	33.8650	2.61274
$169$	−13.0000	−0.999997
$170$	4.53428	0.347764
$171$	21.1762	1.61938
$172$	0.487563	0.0371763
$173$	−11.5374	−0.877175	−0.438588	−	0.898688i	$-0.644521\pi$
$173$	−11.5374	−0.877175	−0.438588	+	0.898688i	$0.644521\pi$
$174$	−16.5856	−1.25735
$175$	13.5146	1.02161
$176$	−1.00093	−0.0754483
$177$	23.2381	1.74669
$178$	15.1401	1.13480
$179$	21.9381	1.63973	0.819867	−	0.572554i	$-0.194047\pi$
$179$	21.9381	1.63973	0.819867	+	0.572554i	$0.194047\pi$
$180$	0.573689	0.0427603
$181$	−0.727217	−0.0540536	−0.0270268	−	0.999635i	$-0.508604\pi$
$181$	−0.727217	−0.0540536	−0.0270268	+	0.999635i	$0.508604\pi$
$182$	−0.0345270	−0.00255931
$183$	25.7811	1.90579
$184$	19.2609	1.41994
$185$	−6.04296	−0.444288
$186$	4.30306	0.315516
$187$	0.615596	0.0450168
$188$	0.661430	0.0482397
$189$	−45.6914	−3.32356
$190$	5.59874	0.406175
$191$	1.72297	0.124670	0.0623349	−	0.998055i	$-0.480145\pi$
$191$	1.72297	0.124670	0.0623349	+	0.998055i	$0.480145\pi$
$192$	24.0639	1.73666
$193$	−11.8778	−0.854985	−0.427492	−	0.904019i	$-0.640603\pi$
$193$	−11.8778	−0.854985	−0.427492	+	0.904019i	$0.640603\pi$
$194$	1.91445	0.137450
$195$	0.0238122	0.00170522
$196$	0.565125	0.0403661
$197$	0.0188266	0.00134134	0.000670670	−	1.00000i	$-0.499787\pi$
$197$	0.0188266	0.00134134	0.000670670		1.00000i	$0.499787\pi$
$198$	2.35079	0.167063
$199$	15.5547	1.10264	0.551321	−	0.834293i	$-0.314124\pi$
$199$	15.5547	1.10264	0.551321	+	0.834293i	$0.314124\pi$
$200$	9.61498	0.679882
$201$	42.1997	2.97654
$202$	24.1898	1.70199
$203$	14.4217	1.01221
$204$	0.543828	0.0380755
$205$	−8.06503	−0.563286
$206$	19.9332	1.38881
$207$	−46.7881	−3.25200
$208$	−0.0254070	−0.00176166
$209$	0.760112	0.0525780
$210$	−21.7496	−1.50087
$211$	−5.15620	−0.354968	−0.177484	−	0.984124i	$-0.556796\pi$
$211$	−5.15620	−0.354968	−0.177484	+	0.984124i	$0.556796\pi$
$212$	−0.822935	−0.0565194
$213$	32.5677	2.23150
$214$	−26.7997	−1.83199
$215$	8.82480	0.601846
$216$	−32.5071	−2.21183
$217$	−3.74165	−0.254000
$218$	−3.22745	−0.218591
$219$	−30.1030	−2.03417
$220$	0.0205924	0.00138834
$221$	0.0156258	0.00105111
$222$	−21.8752	−1.46817
$223$	26.1315	1.74990	0.874948	−	0.484218i	$-0.160896\pi$
$223$	26.1315	1.74990	0.874948	+	0.484218i	$0.160896\pi$
$224$	1.51312	0.101100
$225$	−23.3564	−1.55709
$226$	−17.0210	−1.13222
$227$	2.39866	0.159204	0.0796022	−	0.996827i	$-0.474635\pi$
$227$	2.39866	0.159204	0.0796022	+	0.996827i	$0.474635\pi$
$228$	0.671495	0.0444709
$229$	−11.3237	−0.748292	−0.374146	−	0.927370i	$-0.622064\pi$
$229$	−11.3237	−0.748292	−0.374146	+	0.927370i	$0.622064\pi$
$230$	−12.3702	−0.815669
$231$	−2.95283	−0.194282
$232$	10.2603	0.673622
$233$	0.628701	0.0411876	0.0205938	−	0.999788i	$-0.493444\pi$
$233$	0.628701	0.0411876	0.0205938	+	0.999788i	$0.493444\pi$
$234$	0.0596707	0.00390079
$235$	11.9718	0.780952
$236$	0.510101	0.0332048
$237$	−6.70814	−0.435740
$238$	−14.2724	−0.925140
$239$	−8.05140	−0.520802	−0.260401	−	0.965501i	$-0.583855\pi$
$239$	−8.05140	−0.520802	−0.260401	+	0.965501i	$0.583855\pi$
$240$	−16.0046	−1.03309
$241$	13.4074	0.863645	0.431822	−	0.901959i	$-0.357871\pi$
$241$	13.4074	0.863645	0.431822	+	0.901959i	$0.357871\pi$
$242$	−15.7363	−1.01157
$243$	15.7597	1.01098
$244$	0.565922	0.0362295
$245$	10.2287	0.653485
$246$	−29.1950	−1.86140
$247$	0.0192941	0.00122765
$248$	−2.66199	−0.169037
$249$	−10.8669	−0.688663
$250$	−15.0957	−0.954733
$251$	−10.7976	−0.681536	−0.340768	−	0.940147i	$-0.610687\pi$
$251$	−10.7976	−0.681536	−0.340768	+	0.940147i	$0.610687\pi$
$252$	−1.80578	−0.113753
$253$	−1.67944	−0.105586
$254$	−22.4207	−1.40680
$255$	9.84318	0.616404
$256$	1.64293	0.102683
$257$	17.1390	1.06910	0.534551	−	0.845136i	$-0.320481\pi$
$257$	17.1390	1.06910	0.534551	+	0.845136i	$0.320481\pi$
$258$	31.9453	1.98883
$259$	19.0212	1.18192
$260$	0.000522702 0	3.24166e−5 0
$261$	−24.9240	−1.54276
$262$	10.6055	0.655211
$263$	19.6483	1.21156	0.605782	−	0.795631i	$-0.292860\pi$
$263$	19.6483	1.21156	0.605782	+	0.795631i	$0.292860\pi$
$264$	−2.10079	−0.129295
$265$	−14.8950	−0.914991
$266$	−17.6229	−1.08053
$267$	32.8666	2.01140
$268$	0.926327	0.0565844
$269$	−23.1942	−1.41418	−0.707089	−	0.707125i	$-0.749992\pi$
$269$	−23.1942	−1.41418	−0.707089	+	0.707125i	$0.749992\pi$
$270$	20.8775	1.27057
$271$	−2.53864	−0.154212	−0.0771058	−	0.997023i	$-0.524568\pi$
$271$	−2.53864	−0.154212	−0.0771058	+	0.997023i	$0.524568\pi$
$272$	−10.5024	−0.636803
$273$	−0.0749525	−0.00453633
$274$	23.7670	1.43581
$275$	−0.838371	−0.0505556
$276$	−1.48365	−0.0893051
$277$	−30.1802	−1.81335	−0.906677	−	0.421826i	$-0.861389\pi$
$277$	−30.1802	−1.81335	−0.906677	+	0.421826i	$0.861389\pi$
$278$	1.39048	0.0833952
$279$	6.46643	0.387135
$280$	13.4549	0.804084
$281$	3.35421	0.200095	0.100048	−	0.994983i	$-0.468100\pi$
$281$	3.35421	0.200095	0.100048	+	0.994983i	$0.468100\pi$
$282$	43.3371	2.58069
$283$	−24.0175	−1.42769	−0.713845	−	0.700303i	$-0.753048\pi$
$283$	−24.0175	−1.42769	−0.713845	+	0.700303i	$0.753048\pi$
$284$	0.714895	0.0424212
$285$	12.1539	0.719937
$286$	0.00214186	0.000126651 0
$287$	25.3859	1.49848
$288$	−2.61502	−0.154092
$289$	−10.5408	−0.620046
$290$	−6.58963	−0.386956
$291$	4.15596	0.243627
$292$	−0.660792	−0.0386700
$293$	−21.3044	−1.24461	−0.622307	−	0.782773i	$-0.713804\pi$
$293$	−21.3044	−1.24461	−0.622307	+	0.782773i	$0.713804\pi$
$294$	37.0272	2.15947
$295$	9.23274	0.537551
$296$	13.5326	0.786566
$297$	2.83443	0.164470
$298$	−9.76154	−0.565471
$299$	−0.0426297	−0.00246534
$300$	−0.740630	−0.0427603
$301$	−27.7774	−1.60106
$302$	−26.2737	−1.51188
$303$	52.5120	3.01674
$304$	−12.9679	−0.743762
$305$	10.2431	0.586517
$306$	24.6659	1.41006
$307$	−30.5054	−1.74104	−0.870519	−	0.492135i	$-0.836217\pi$
$307$	−30.5054	−1.74104	−0.870519	+	0.492135i	$0.836217\pi$
$308$	−0.0648178	−0.00369333
$309$	43.2717	2.46164
$310$	1.70965	0.0971015
$311$	−19.4729	−1.10421	−0.552104	−	0.833775i	$-0.686175\pi$
$311$	−19.4729	−1.10421	−0.552104	+	0.833775i	$0.686175\pi$
$312$	−0.0533249	−0.00301893
$313$	−3.72145	−0.210349	−0.105174	−	0.994454i	$-0.533540\pi$
$313$	−3.72145	−0.210349	−0.105174	+	0.994454i	$0.533540\pi$
$314$	25.2916	1.42729
$315$	−32.6842	−1.84155
$316$	−0.147251	−0.00828349
$317$	3.92854	0.220649	0.110324	−	0.993896i	$-0.464811\pi$
$317$	3.92854	0.220649	0.110324	+	0.993896i	$0.464811\pi$
$318$	−53.9190	−3.02363
$319$	−0.894639	−0.0500902
$320$	9.56081	0.534466
$321$	−58.1778	−3.24717
$322$	38.9373	2.16989
$323$	7.97556	0.443772
$324$	1.11655	0.0620308
$325$	−0.0212806	−0.00118043
$326$	−28.1397	−1.55851
$327$	−7.00627	−0.387448
$328$	18.0608	0.997240
$329$	−37.6830	−2.07753
$330$	1.34922	0.0742722
$331$	5.95865	0.327517	0.163759	−	0.986500i	$-0.447638\pi$
$331$	5.95865	0.327517	0.163759	+	0.986500i	$0.447638\pi$
$332$	−0.238540	−0.0130916
$333$	−32.8730	−1.80143
$334$	25.2408	1.38112
$335$	16.7664	0.916044
$336$	50.3770	2.74829
$337$	−14.3795	−0.783302	−0.391651	−	0.920114i	$-0.628096\pi$
$337$	−14.3795	−0.783302	−0.391651	+	0.920114i	$0.628096\pi$
$338$	−18.6971	−1.01699
$339$	−36.9498	−2.00684
$340$	0.216068	0.0117179
$341$	0.232110	0.0125695
$342$	30.4564	1.64690
$343$	−4.86422	−0.262643
$344$	−19.7622	−1.06551
$345$	−26.8537	−1.44576
$346$	−16.5936	−0.892078
$347$	−4.58702	−0.246244	−0.123122	−	0.992392i	$-0.539291\pi$
$347$	−4.58702	−0.246244	−0.123122	+	0.992392i	$0.539291\pi$
$348$	−0.790339	−0.0423666
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	19.4373	1.03897
$351$	0.0719471	0.00384025
$352$	−0.0938653	−0.00500304
$353$	13.1206	0.698338	0.349169	−	0.937060i	$-0.386464\pi$
$353$	13.1206	0.698338	0.349169	+	0.937060i	$0.386464\pi$
$354$	33.4220	1.77636
$355$	12.9395	0.686755
$356$	0.721455	0.0382370
$357$	−30.9829	−1.63979
$358$	31.5523	1.66759
$359$	19.0141	1.00352	0.501762	−	0.865006i	$-0.332685\pi$
$359$	19.0141	1.00352	0.501762	+	0.865006i	$0.332685\pi$
$360$	−23.2532	−1.22555
$361$	−9.15211	−0.481690
$362$	−1.04591	−0.0549719
$363$	−34.1608	−1.79298
$364$	−0.00164528	−8.62364e−5 0
$365$	−11.9602	−0.626027
$366$	37.0794	1.93817
$367$	−19.3252	−1.00877	−0.504384	−	0.863480i	$-0.668280\pi$
$367$	−19.3252	−1.00877	−0.504384	+	0.863480i	$0.668280\pi$
$368$	28.6523	1.49360
$369$	−43.8727	−2.28392
$370$	−8.69124	−0.451836
$371$	46.8843	2.43411
$372$	0.205050	0.0106313
$373$	−0.725592	−0.0375698	−0.0187849	−	0.999824i	$-0.505980\pi$
$373$	−0.725592	−0.0375698	−0.0187849	+	0.999824i	$0.505980\pi$
$374$	0.885375	0.0457817
$375$	−32.7702	−1.69225
$376$	−26.8095	−1.38260
$377$	−0.0227088	−0.00116957
$378$	−65.7152	−3.38003
$379$	−31.7729	−1.63206	−0.816031	−	0.578008i	$-0.803830\pi$
$379$	−31.7729	−1.63206	−0.816031	+	0.578008i	$0.803830\pi$
$380$	0.266792	0.0136861
$381$	−48.6717	−2.49353
$382$	2.47805	0.126788
$383$	−8.33629	−0.425964	−0.212982	−	0.977056i	$-0.568318\pi$
$383$	−8.33629	−0.425964	−0.212982	+	0.977056i	$0.568318\pi$
$384$	37.0295	1.88965
$385$	−1.17319	−0.0597913
$386$	−17.0832	−0.869511
$387$	48.0058	2.44027
$388$	0.0912276	0.00463138
$389$	−1.89814	−0.0962396	−0.0481198	−	0.998842i	$-0.515323\pi$
$389$	−1.89814	−0.0962396	−0.0481198	+	0.998842i	$0.515323\pi$
$390$	0.0342476	0.00173419
$391$	−17.6218	−0.891170
$392$	−22.9060	−1.15693
$393$	23.0228	1.16135
$394$	0.0270772	0.00136413
$395$	−2.66521	−0.134101
$396$	0.112020	0.00562922
$397$	2.37213	0.119054	0.0595269	−	0.998227i	$-0.481041\pi$
$397$	2.37213	0.119054	0.0595269	+	0.998227i	$0.481041\pi$
$398$	22.3714	1.12138
$399$	−38.2564	−1.91522
$400$	14.3031	0.715154
$401$	27.2740	1.36200	0.680999	−	0.732284i	$-0.261546\pi$
$401$	27.2740	1.36200	0.680999	+	0.732284i	$0.261546\pi$
$402$	60.6933	3.02711
$403$	0.00589171	0.000293487 0
$404$	1.15269	0.0573486
$405$	20.2094	1.00421
$406$	20.7419	1.02940
$407$	−1.17996	−0.0584886
$408$	−22.0428	−1.09128
$409$	7.68799	0.380147	0.190073	−	0.981770i	$-0.439127\pi$
$409$	7.68799	0.380147	0.190073	+	0.981770i	$0.439127\pi$
$410$	−11.5994	−0.572856
$411$	51.5941	2.54495
$412$	0.949859	0.0467962
$413$	−29.0615	−1.43002
$414$	−67.2925	−3.30725
$415$	−4.31753	−0.211939
$416$	−0.00238261	−0.000116817 0
$417$	3.01849	0.147816
$418$	1.09322	0.0534713
$419$	34.0550	1.66370	0.831848	−	0.555004i	$-0.187283\pi$
$419$	34.0550	1.66370	0.831848	+	0.555004i	$0.187283\pi$
$420$	−1.03641	−0.0505718
$421$	18.4462	0.899015	0.449507	−	0.893277i	$-0.351600\pi$
$421$	18.4462	0.899015	0.449507	+	0.893277i	$0.351600\pi$
$422$	−7.41586	−0.360998
$423$	65.1249	3.16648
$424$	33.3558	1.61990
$425$	−8.79670	−0.426703
$426$	46.8402	2.26941
$427$	−32.2417	−1.56029
$428$	−1.27706	−0.0617291
$429$	0.00464962	0.000224486 0
$430$	12.6922	0.612071
$431$	36.4762	1.75700	0.878498	−	0.477747i	$-0.158546\pi$
$431$	36.4762	1.75700	0.878498	+	0.477747i	$0.158546\pi$
$432$	−48.3570	−2.32658
$433$	25.9924	1.24912	0.624558	−	0.780978i	$-0.285279\pi$
$433$	25.9924	1.24912	0.624558	+	0.780978i	$0.285279\pi$
$434$	−5.38139	−0.258315
$435$	−14.3050	−0.685872
$436$	−0.153795	−0.00736544
$437$	−21.7586	−1.04085
$438$	−43.2954	−2.06873
$439$	−27.8024	−1.32693	−0.663467	−	0.748205i	$-0.730916\pi$
$439$	−27.8024	−1.32693	−0.663467	+	0.748205i	$0.730916\pi$
$440$	−0.834664	−0.0397910
$441$	55.6426	2.64965
$442$	0.0224737	0.00106896
$443$	−9.30882	−0.442276	−0.221138	−	0.975243i	$-0.570977\pi$
$443$	−9.30882	−0.442276	−0.221138	+	0.975243i	$0.570977\pi$
$444$	−1.04240	−0.0494701
$445$	13.0582	0.619018
$446$	37.5834	1.77963
$447$	−21.1907	−1.00228
$448$	−30.0942	−1.42182
$449$	−4.61569	−0.217828	−0.108914	−	0.994051i	$-0.534737\pi$
$449$	−4.61569	−0.217828	−0.108914	+	0.994051i	$0.534737\pi$
$450$	−33.5921	−1.58355
$451$	−1.57480	−0.0741543
$452$	−0.811087	−0.0381503
$453$	−57.0358	−2.67978
$454$	3.44984	0.161909
$455$	−0.0297794	−0.00139608
$456$	−27.2175	−1.27458
$457$	17.0322	0.796733	0.398366	−	0.917226i	$-0.369577\pi$
$457$	17.0322	0.796733	0.398366	+	0.917226i	$0.369577\pi$
$458$	−16.2862	−0.761005
$459$	29.7406	1.38817
$460$	−0.589467	−0.0274841
$461$	−16.3292	−0.760525	−0.380262	−	0.924879i	$-0.624166\pi$
$461$	−16.3292	−0.760525	−0.380262	+	0.924879i	$0.624166\pi$
$462$	−4.24688	−0.197583
$463$	2.42257	0.112586	0.0562931	−	0.998414i	$-0.482072\pi$
$463$	2.42257	0.112586	0.0562931	+	0.998414i	$0.482072\pi$
$464$	15.2631	0.708570
$465$	3.71137	0.172110
$466$	0.904223	0.0418873
$467$	0.757172	0.0350377	0.0175189	−	0.999847i	$-0.494423\pi$
$467$	0.757172	0.0350377	0.0175189	+	0.999847i	$0.494423\pi$
$468$	0.00284343	0.000131438 0
$469$	−52.7747	−2.43691
$470$	17.2183	0.794220
$471$	54.9040	2.52984
$472$	−20.6758	−0.951679
$473$	1.72315	0.0792306
$474$	−9.64791	−0.443143
$475$	−10.8618	−0.498373
$476$	−0.680108	−0.0311727
$477$	−81.0268	−3.70996
$478$	−11.5799	−0.529650
$479$	17.3476	0.792631	0.396315	−	0.918114i	$-0.370289\pi$
$479$	17.3476	0.792631	0.396315	+	0.918114i	$0.370289\pi$
$480$	−1.50088	−0.0685053
$481$	−0.0299513	−0.00136566
$482$	19.2830	0.878318
$483$	84.5263	3.84608
$484$	−0.749865	−0.0340848
$485$	1.65120	0.0749773
$486$	22.6662	1.02816
$487$	−12.1597	−0.551007	−0.275504	−	0.961300i	$-0.588845\pi$
$487$	−12.1597	−0.551007	−0.275504	+	0.961300i	$0.588845\pi$
$488$	−22.9383	−1.03837
$489$	−61.0867	−2.76243
$490$	14.7113	0.664587
$491$	23.2518	1.04934	0.524670	−	0.851306i	$-0.324189\pi$
$491$	23.2518	1.04934	0.524670	+	0.851306i	$0.324189\pi$
$492$	−1.39120	−0.0627202
$493$	−9.38711	−0.422774
$494$	0.0277496	0.00124851
$495$	2.02754	0.0911312
$496$	−3.95993	−0.177806
$497$	−40.7290	−1.82694
$498$	−15.6292	−0.700363
$499$	23.4866	1.05141	0.525703	−	0.850668i	$-0.323802\pi$
$499$	23.4866	1.05141	0.525703	+	0.850668i	$0.323802\pi$
$500$	−0.719339	−0.0321698
$501$	54.7937	2.44800
$502$	−15.5295	−0.693115
$503$	10.2392	0.456545	0.228273	−	0.973597i	$-0.426692\pi$
$503$	10.2392	0.456545	0.228273	+	0.973597i	$0.426692\pi$
$504$	73.1930	3.26027
$505$	20.8635	0.928415
$506$	−2.41544	−0.107380
$507$	−40.5882	−1.80259
$508$	−1.06839	−0.0474023
$509$	21.4394	0.950286	0.475143	−	0.879909i	$-0.342396\pi$
$509$	21.4394	0.950286	0.475143	+	0.879909i	$0.342396\pi$
$510$	14.1569	0.626876
$511$	37.6467	1.66539
$512$	−21.3573	−0.943870
$513$	36.7224	1.62134
$514$	24.6500	1.08726
$515$	17.1923	0.757582
$516$	1.52226	0.0670138
$517$	2.33764	0.102809
$518$	27.3570	1.20200
$519$	−36.0220	−1.58119
$520$	−0.0211865	−0.000929089 0
$521$	−6.42180	−0.281344	−0.140672	−	0.990056i	$-0.544926\pi$
$521$	−6.42180	−0.281344	−0.140672	+	0.990056i	$0.544926\pi$
$522$	−35.8467	−1.56897
$523$	−10.7510	−0.470108	−0.235054	−	0.971982i	$-0.575527\pi$
$523$	−10.7510	−0.470108	−0.235054	+	0.971982i	$0.575527\pi$
$524$	0.505375	0.0220774
$525$	42.1952	1.84155
$526$	28.2589	1.23215
$527$	2.43544	0.106090
$528$	−3.12510	−0.136002
$529$	25.0749	1.09021
$530$	−21.4226	−0.930537
$531$	50.2249	2.17958
$532$	−0.839768	−0.0364086
$533$	−0.0399735	−0.00173144
$534$	47.2700	2.04557
$535$	−23.1146	−0.999331
$536$	−37.5465	−1.62176
$537$	68.4949	2.95577
$538$	−33.3589	−1.43820
$539$	1.99727	0.0860286
$540$	0.994857	0.0428118
$541$	26.5244	1.14037	0.570187	−	0.821515i	$-0.306871\pi$
$541$	26.5244	1.14037	0.570187	+	0.821515i	$0.306871\pi$
$542$	−3.65118	−0.156832
$543$	−2.27050	−0.0974366
$544$	−0.984893	−0.0422269
$545$	−2.78366	−0.119239
$546$	−0.107800	−0.00461340
$547$	18.6856	0.798936	0.399468	−	0.916747i	$-0.369195\pi$
$547$	18.6856	0.798936	0.399468	+	0.916747i	$0.369195\pi$
$548$	1.13254	0.0483799
$549$	55.7211	2.37812
$550$	−1.20578	−0.0514146
$551$	−11.5908	−0.493785
$552$	60.1362	2.55956
$553$	8.38916	0.356743
$554$	−43.4064	−1.84416
$555$	−18.8672	−0.800870
$556$	0.0662590	0.00281001
$557$	−15.1056	−0.640045	−0.320023	−	0.947410i	$-0.603691\pi$
$557$	−15.1056	−0.640045	−0.320023	+	0.947410i	$0.603691\pi$
$558$	9.30028	0.393712
$559$	0.0437392	0.00184997
$560$	20.0153	0.845800
$561$	1.92200	0.0811470
$562$	4.82415	0.203495
$563$	−33.5805	−1.41525	−0.707624	−	0.706589i	$-0.750233\pi$
$563$	−33.5805	−1.41525	−0.707624	+	0.706589i	$0.750233\pi$
$564$	2.06510	0.0869566
$565$	−14.6805	−0.617614
$566$	−34.5429	−1.45195
$567$	−63.6123	−2.67147
$568$	−28.9766	−1.21583
$569$	−23.6925	−0.993243	−0.496621	−	0.867967i	$-0.665426\pi$
$569$	−23.6925	−0.993243	−0.496621	+	0.867967i	$0.665426\pi$
$570$	17.4803	0.732169
$571$	−29.7823	−1.24635	−0.623175	−	0.782082i	$-0.714158\pi$
$571$	−29.7823	−1.24635	−0.623175	+	0.782082i	$0.714158\pi$
$572$	0.000102064 0	4.26751e−6 0
$573$	5.37943	0.224729
$574$	36.5111	1.52394
$575$	23.9988	1.00082
$576$	52.0096	2.16707
$577$	35.6487	1.48407	0.742037	−	0.670358i	$-0.233860\pi$
$577$	35.6487	1.48407	0.742037	+	0.670358i	$0.233860\pi$
$578$	−15.1602	−0.630580
$579$	−37.0847	−1.54119
$580$	−0.314009	−0.0130385
$581$	13.5901	0.563813
$582$	5.97727	0.247766
$583$	−2.90843	−0.120455
$584$	26.7837	1.10832
$585$	0.0514656	0.00212784
$586$	−30.6408	−1.26576
$587$	17.6585	0.728845	0.364423	−	0.931234i	$-0.381266\pi$
$587$	17.6585	0.728845	0.364423	+	0.931234i	$0.381266\pi$
$588$	1.76442	0.0727636
$589$	3.00718	0.123909
$590$	13.2789	0.546684
$591$	0.0587801	0.00241789
$592$	20.1309	0.827373
$593$	−17.5752	−0.721728	−0.360864	−	0.932618i	$-0.617518\pi$
$593$	−17.5752	−0.721728	−0.360864	+	0.932618i	$0.617518\pi$
$594$	4.07659	0.167265
$595$	−12.3098	−0.504654
$596$	−0.465157	−0.0190536
$597$	48.5646	1.98761
$598$	−0.0613118	−0.00250722
$599$	−9.96036	−0.406969	−0.203485	−	0.979078i	$-0.565227\pi$
$599$	−9.96036	−0.406969	−0.203485	+	0.979078i	$0.565227\pi$
$600$	30.0197	1.22555
$601$	−1.33278	−0.0543653	−0.0271827	−	0.999630i	$-0.508654\pi$
$601$	−1.33278	−0.0543653	−0.0271827	+	0.999630i	$0.508654\pi$
$602$	−39.9506	−1.62827
$603$	91.2068	3.71423
$604$	−1.25199	−0.0509429
$605$	−13.5724	−0.551798
$606$	75.5249	3.06799
$607$	12.4399	0.504918	0.252459	−	0.967608i	$-0.418761\pi$
$607$	12.4399	0.504918	0.252459	+	0.967608i	$0.418761\pi$
$608$	−1.21610	−0.0493195
$609$	45.0272	1.82459
$610$	14.7320	0.596482
$611$	0.0593368	0.00240051
$612$	1.17538	0.0475120
$613$	−6.78060	−0.273866	−0.136933	−	0.990580i	$-0.543724\pi$
$613$	−6.78060	−0.273866	−0.136933	+	0.990580i	$0.543724\pi$
$614$	−43.8742	−1.77062
$615$	−25.1805	−1.01537
$616$	2.62724	0.105854
$617$	38.8297	1.56323	0.781613	−	0.623764i	$-0.214397\pi$
$617$	38.8297	1.56323	0.781613	+	0.623764i	$0.214397\pi$
$618$	62.2351	2.50346
$619$	−10.4018	−0.418085	−0.209042	−	0.977907i	$-0.567035\pi$
$619$	−10.4018	−0.418085	−0.209042	+	0.977907i	$0.567035\pi$
$620$	0.0814683	0.00327185
$621$	−81.1370	−3.25592
$622$	−28.0067	−1.12297
$623$	−41.1027	−1.64675
$624$	−0.0793252	−0.00317555
$625$	4.28622	0.171449
$626$	−5.35233	−0.213922
$627$	2.37321	0.0947768
$628$	1.20520	0.0480927
$629$	−12.3809	−0.493659
$630$	−47.0078	−1.87284
$631$	−20.9669	−0.834679	−0.417339	−	0.908751i	$-0.637037\pi$
$631$	−20.9669	−0.834679	−0.417339	+	0.908751i	$0.637037\pi$
$632$	5.96845	0.237412
$633$	−16.0986	−0.639862
$634$	5.65018	0.224397
$635$	−19.3377	−0.767395
$636$	−2.56935	−0.101882
$637$	0.0506973	0.00200870
$638$	−1.28671	−0.0509412
$639$	70.3891	2.78455
$640$	14.7122	0.581550
$641$	−0.677343	−0.0267534	−0.0133767	−	0.999911i	$-0.504258\pi$
$641$	−0.677343	−0.0267534	−0.0133767	+	0.999911i	$0.504258\pi$
$642$	−83.6736	−3.30233
$643$	2.21239	0.0872483	0.0436241	−	0.999048i	$-0.486110\pi$
$643$	2.21239	0.0872483	0.0436241	+	0.999048i	$0.486110\pi$
$644$	1.85544	0.0731146
$645$	27.5526	1.08488
$646$	11.4708	0.451312
$647$	−39.0523	−1.53530	−0.767652	−	0.640867i	$-0.778575\pi$
$647$	−39.0523	−1.53530	−0.767652	+	0.640867i	$0.778575\pi$
$648$	−45.2569	−1.77786
$649$	1.80281	0.0707664
$650$	−0.0306066	−0.00120049
$651$	−11.6821	−0.457858
$652$	−1.34092	−0.0525143
$653$	−17.5097	−0.685208	−0.342604	−	0.939480i	$-0.611309\pi$
$653$	−17.5097	−0.685208	−0.342604	+	0.939480i	$0.611309\pi$
$654$	−10.0767	−0.394030
$655$	9.14720	0.357411
$656$	26.8669	1.04898
$657$	−65.0621	−2.53832
$658$	−54.1972	−2.11283
$659$	39.4914	1.53837	0.769183	−	0.639028i	$-0.220663\pi$
$659$	39.4914	1.53837	0.769183	+	0.639028i	$0.220663\pi$
$660$	0.0642932	0.00250261
$661$	13.6709	0.531735	0.265868	−	0.964010i	$-0.414342\pi$
$661$	13.6709	0.531735	0.265868	+	0.964010i	$0.414342\pi$
$662$	8.56997	0.333081
$663$	0.0487867	0.00189472
$664$	9.66866	0.375217
$665$	−15.1997	−0.589417
$666$	−47.2792	−1.83203
$667$	25.6095	0.991604
$668$	1.20278	0.0465369
$669$	81.5873	3.15435
$670$	24.1140	0.931607
$671$	2.00009	0.0772126
$672$	4.72424	0.182242
$673$	−12.3890	−0.477561	−0.238781	−	0.971074i	$-0.576748\pi$
$673$	−12.3890	−0.477561	−0.238781	+	0.971074i	$0.576748\pi$
$674$	−20.6812	−0.796610
$675$	−40.5033	−1.55897
$676$	−0.890954	−0.0342675
$677$	36.0772	1.38656	0.693280	−	0.720668i	$-0.256165\pi$
$677$	36.0772	1.38656	0.693280	+	0.720668i	$0.256165\pi$
$678$	−53.1427	−2.04093
$679$	−5.19742	−0.199459
$680$	−8.75781	−0.335847
$681$	7.48904	0.286981
$682$	0.333830	0.0127830
$683$	−39.5602	−1.51373	−0.756864	−	0.653572i	$-0.773270\pi$
$683$	−39.5602	−1.51373	−0.756864	+	0.653572i	$0.773270\pi$
$684$	1.45131	0.0554923
$685$	20.4989	0.783221
$686$	−6.99592	−0.267105
$687$	−35.3547	−1.34886
$688$	−29.3979	−1.12079
$689$	−0.0738254	−0.00281252
$690$	−38.6221	−1.47032
$691$	−26.1999	−0.996691	−0.498345	−	0.866979i	$-0.666059\pi$
$691$	−26.1999	−0.996691	−0.498345	+	0.866979i	$0.666059\pi$
$692$	−0.790720	−0.0300587
$693$	−6.38200	−0.242432
$694$	−6.59724	−0.250428
$695$	1.19928	0.0454912
$696$	32.0345	1.21427
$697$	−16.5237	−0.625881
$698$	1.43824	0.0544382
$699$	1.96292	0.0742444
$700$	0.926228	0.0350081
$701$	−39.4020	−1.48819	−0.744096	−	0.668072i	$-0.767120\pi$
$701$	−39.4020	−1.48819	−0.744096	+	0.668072i	$0.767120\pi$
$702$	0.103477	0.00390550
$703$	−15.2874	−0.576576
$704$	1.86687	0.0703602
$705$	37.3780	1.40774
$706$	18.8705	0.710202
$707$	−65.6713	−2.46982
$708$	1.59263	0.0598547
$709$	−26.8634	−1.00887	−0.504437	−	0.863448i	$-0.668300\pi$
$709$	−26.8634	−1.00887	−0.504437	+	0.863448i	$0.668300\pi$
$710$	18.6101	0.698423
$711$	−14.4984	−0.543732
$712$	−29.2425	−1.09591
$713$	−6.64427	−0.248830
$714$	−44.5609	−1.66765
$715$	0.00184734	6.90866e−5 0
$716$	1.50353	0.0561897
$717$	−25.1379	−0.938794
$718$	27.3468	1.02057
$719$	23.3194	0.869668	0.434834	−	0.900511i	$-0.356807\pi$
$719$	23.3194	0.869668	0.434834	+	0.900511i	$0.356807\pi$
$720$	−34.5910	−1.28913
$721$	−54.1154	−2.01536
$722$	−13.1629	−0.489874
$723$	41.8602	1.55680
$724$	−0.0498399	−0.00185228
$725$	12.7842	0.474791
$726$	−49.1315	−1.82344
$727$	17.8489	0.661979	0.330989	−	0.943634i	$-0.392618\pi$
$727$	17.8489	0.661979	0.330989	+	0.943634i	$0.392618\pi$
$728$	0.0666878	0.00247161
$729$	0.329450	0.0122019
$730$	−17.2017	−0.636663
$731$	18.0804	0.668727
$732$	1.76691	0.0653069
$733$	28.0345	1.03548	0.517739	−	0.855539i	$-0.326774\pi$
$733$	28.0345	1.03548	0.517739	+	0.855539i	$0.326774\pi$
$734$	−27.7943	−1.02591
$735$	31.9357	1.17797
$736$	2.68694	0.0990420
$737$	3.27384	0.120593
$738$	−63.0995	−2.32273
$739$	5.76405	0.212034	0.106017	−	0.994364i	$-0.466190\pi$
$739$	5.76405	0.212034	0.106017	+	0.994364i	$0.466190\pi$
$740$	−0.414155	−0.0152247
$741$	0.0602397	0.00221296
$742$	67.4309	2.47546
$743$	4.11462	0.150951	0.0754753	−	0.997148i	$-0.475953\pi$
$743$	4.11462	0.150951	0.0754753	+	0.997148i	$0.475953\pi$
$744$	−8.31122	−0.304704
$745$	−8.41926	−0.308458
$746$	−1.04358	−0.0382080
$747$	−23.4868	−0.859338
$748$	0.0421900	0.00154262
$749$	72.7568	2.65848
$750$	−47.1314	−1.72100
$751$	46.8632	1.71006	0.855031	−	0.518577i	$-0.173538\pi$
$751$	46.8632	1.71006	0.855031	+	0.518577i	$0.173538\pi$
$752$	−39.8814	−1.45432
$753$	−33.7120	−1.22853
$754$	−0.0326608	−0.00118944
$755$	−22.6609	−0.824714
$756$	−3.13147	−0.113890
$757$	38.4751	1.39840	0.699200	−	0.714926i	$-0.253539\pi$
$757$	38.4751	1.39840	0.699200	+	0.714926i	$0.253539\pi$
$758$	−45.6970	−1.65979
$759$	−5.24353	−0.190328
$760$	−10.8138	−0.392257
$761$	−38.1196	−1.38183	−0.690917	−	0.722934i	$-0.742793\pi$
$761$	−38.1196	−1.38183	−0.690917	+	0.722934i	$0.742793\pi$
$762$	−70.0016	−2.53589
$763$	8.76200	0.317206
$764$	0.118084	0.00427213
$765$	21.2742	0.769171
$766$	−11.9896	−0.433201
$767$	0.0457611	0.00165234
$768$	5.12954	0.185096
$769$	10.8303	0.390552	0.195276	−	0.980748i	$-0.437440\pi$
$769$	10.8303	0.390552	0.195276	+	0.980748i	$0.437440\pi$
$770$	−1.68733	−0.0608071
$771$	53.5111	1.92715
$772$	−0.814049	−0.0292982
$773$	13.6162	0.489741	0.244870	−	0.969556i	$-0.421255\pi$
$773$	13.6162	0.489741	0.244870	+	0.969556i	$0.421255\pi$
$774$	69.0439	2.48173
$775$	−3.31679	−0.119143
$776$	−3.69770	−0.132740
$777$	59.3876	2.13052
$778$	−2.72998	−0.0978747
$779$	−20.4028	−0.731006
$780$	0.00163197	5.84339e−5 0
$781$	2.52659	0.0904085
$782$	−25.3443	−0.906311
$783$	−43.2217	−1.54462
$784$	−34.0746	−1.21695
$785$	21.8139	0.778571
$786$	33.1124	1.18108
$787$	41.9290	1.49461	0.747303	−	0.664483i	$-0.231348\pi$
$787$	41.9290	1.49461	0.747303	+	0.664483i	$0.231348\pi$
$788$	0.00129028	4.59645e−5 0
$789$	61.3454	2.18396
$790$	−3.83321	−0.136379
$791$	46.2092	1.64301
$792$	−4.54047	−0.161339
$793$	0.0507688	0.00180285
$794$	3.41169	0.121076
$795$	−46.5048	−1.64936
$796$	1.06604	0.0377849
$797$	22.1422	0.784317	0.392158	−	0.919898i	$-0.371729\pi$
$797$	22.1422	0.784317	0.392158	+	0.919898i	$0.371729\pi$
$798$	−55.0219	−1.94776
$799$	24.5279	0.867735
$800$	1.34131	0.0474225
$801$	71.0350	2.50990
$802$	39.2265	1.38514
$803$	−2.33538	−0.0824138
$804$	2.89216	0.101999
$805$	33.5831	1.18365
$806$	0.00847369	0.000298473 0
$807$	−72.4166	−2.54919
$808$	−46.7217	−1.64366
$809$	−21.8812	−0.769304	−0.384652	−	0.923062i	$-0.625678\pi$
$809$	−21.8812	−0.769304	−0.384652	+	0.923062i	$0.625678\pi$
$810$	29.0660	1.02128
$811$	27.6057	0.969369	0.484684	−	0.874689i	$-0.338934\pi$
$811$	27.6057	0.969369	0.484684	+	0.874689i	$0.338934\pi$
$812$	0.988393	0.0346858
$813$	−7.92610	−0.277981
$814$	−1.69707	−0.0594823
$815$	−24.2703	−0.850152
$816$	−32.7905	−1.14790
$817$	22.3249	0.781048
$818$	11.0572	0.386605
$819$	−0.161996	−0.00566060
$820$	−0.552738	−0.0193024
$821$	−9.43541	−0.329298	−0.164649	−	0.986352i	$-0.552649\pi$
$821$	−9.43541	−0.329298	−0.164649	+	0.986352i	$0.552649\pi$
$822$	74.2048	2.58819
$823$	−51.1925	−1.78446	−0.892230	−	0.451581i	$-0.850860\pi$
$823$	−51.1925	−1.78446	−0.892230	+	0.451581i	$0.850860\pi$
$824$	−38.5003	−1.34122
$825$	−2.61755	−0.0911312
$826$	−41.7974	−1.45432
$827$	3.42623	0.119142	0.0595708	−	0.998224i	$-0.481027\pi$
$827$	3.42623	0.119142	0.0595708	+	0.998224i	$0.481027\pi$
$828$	−3.20663	−0.111438
$829$	−5.88629	−0.204439	−0.102220	−	0.994762i	$-0.532594\pi$
$829$	−5.88629	−0.204439	−0.102220	+	0.994762i	$0.532594\pi$
$830$	−6.20965	−0.215540
$831$	−94.2281	−3.26874
$832$	0.0473872	0.00164285
$833$	20.9566	0.726104
$834$	4.34132	0.150328
$835$	21.7701	0.753384
$836$	0.0520944	0.00180172
$837$	11.2137	0.387601
$838$	48.9793	1.69196
$839$	6.95110	0.239979	0.119989	−	0.992775i	$-0.461714\pi$
$839$	6.95110	0.239979	0.119989	+	0.992775i	$0.461714\pi$
$840$	42.0086	1.44944
$841$	−15.3578	−0.529580
$842$	26.5301	0.914289
$843$	10.4724	0.360690
$844$	−0.353381	−0.0121639
$845$	−16.1261	−0.554755
$846$	93.6652	3.22028
$847$	42.7213	1.46792
$848$	49.6195	1.70394
$849$	−74.9869	−2.57354
$850$	−12.6518	−0.433952
$851$	33.7771	1.15786
$852$	2.23203	0.0764681
$853$	15.4340	0.528449	0.264224	−	0.964461i	$-0.414884\pi$
$853$	15.4340	0.528449	0.264224	+	0.964461i	$0.414884\pi$
$854$	−46.3713	−1.58679
$855$	26.2685	0.898364
$856$	51.7627	1.76921
$857$	−40.1179	−1.37040	−0.685201	−	0.728354i	$-0.740286\pi$
$857$	−40.1179	−1.37040	−0.685201	+	0.728354i	$0.740286\pi$
$858$	0.00668727	0.000228300 0
$859$	−9.32183	−0.318057	−0.159028	−	0.987274i	$-0.550836\pi$
$859$	−9.32183	−0.318057	−0.159028	+	0.987274i	$0.550836\pi$
$860$	0.604809	0.0206238
$861$	79.2595	2.70116
$862$	52.4615	1.78685
$863$	−25.7034	−0.874955	−0.437477	−	0.899229i	$-0.644128\pi$
$863$	−25.7034	−0.874955	−0.437477	+	0.899229i	$0.644128\pi$
$864$	−4.53481	−0.154277
$865$	−14.3119	−0.486619
$866$	37.3833	1.27034
$867$	−32.9103	−1.11769
$868$	−0.256434	−0.00870395
$869$	−0.520415	−0.0176539
$870$	−20.5740	−0.697524
$871$	0.0831006	0.00281576
$872$	6.23372	0.211100
$873$	8.98234	0.304006
$874$	−31.2941	−1.05854
$875$	40.9822	1.38545
$876$	−2.06311	−0.0697062
$877$	9.94741	0.335900	0.167950	−	0.985795i	$-0.446285\pi$
$877$	9.94741	0.335900	0.167950	+	0.985795i	$0.446285\pi$
$878$	−39.9865	−1.34948
$879$	−66.5161	−2.24353
$880$	−1.24163	−0.0418554
$881$	−14.3690	−0.484103	−0.242052	−	0.970263i	$-0.577820\pi$
$881$	−14.3690	−0.484103	−0.242052	+	0.970263i	$0.577820\pi$
$882$	80.0275	2.69466
$883$	18.9719	0.638454	0.319227	−	0.947678i	$-0.396577\pi$
$883$	18.9719	0.638454	0.319227	+	0.947678i	$0.396577\pi$
$884$	0.00107092	3.60189e−5 0
$885$	28.8263	0.968985
$886$	−13.3883	−0.449790
$887$	−1.76313	−0.0592002	−0.0296001	−	0.999562i	$-0.509423\pi$
$887$	−1.76313	−0.0592002	−0.0296001	+	0.999562i	$0.509423\pi$
$888$	42.2512	1.41786
$889$	60.8686	2.04147
$890$	18.7808	0.629535
$891$	3.94614	0.132201
$892$	1.79093	0.0599646
$893$	30.2860	1.01348
$894$	−30.4773	−1.01931
$895$	27.2137	0.909653
$896$	−46.3089	−1.54707
$897$	−0.133098	−0.00444400
$898$	−6.63847	−0.221529
$899$	−3.53940	−0.118046
$900$	−1.60074	−0.0533578
$901$	−30.5170	−1.01667
$902$	−2.26494	−0.0754141
$903$	−86.7262	−2.88607
$904$	32.8755	1.09342
$905$	−0.902093	−0.0299866
$906$	−82.0312	−2.72530
$907$	28.2859	0.939218	0.469609	−	0.882875i	$-0.344395\pi$
$907$	28.2859	0.939218	0.469609	+	0.882875i	$0.344395\pi$
$908$	0.164392	0.00545555
$909$	113.495	3.76439
$910$	−0.0428299	−0.00141980
$911$	41.2999	1.36833	0.684164	−	0.729329i	$-0.260167\pi$
$911$	41.2999	1.36833	0.684164	+	0.729329i	$0.260167\pi$
$912$	−40.4883	−1.34070
$913$	−0.843052	−0.0279009
$914$	24.4964	0.810269
$915$	31.9808	1.05725
$916$	−0.776072	−0.0256421
$917$	−28.7922	−0.950803
$918$	42.7741	1.41176
$919$	−32.2404	−1.06351	−0.531756	−	0.846898i	$-0.678468\pi$
$919$	−32.2404	−1.06351	−0.531756	+	0.846898i	$0.678468\pi$
$920$	23.8927	0.787718
$921$	−95.2435	−3.13838
$922$	−23.4853	−0.773446
$923$	0.0641331	0.00211097
$924$	−0.202373	−0.00665758
$925$	16.8614	0.554398
$926$	3.48423	0.114499
$927$	93.5238	3.07172
$928$	1.43133	0.0469858
$929$	14.8529	0.487309	0.243654	−	0.969862i	$-0.421654\pi$
$929$	14.8529	0.487309	0.243654	+	0.969862i	$0.421654\pi$
$930$	5.33784	0.175035
$931$	25.8763	0.848063
$932$	0.0430881	0.00141140
$933$	−60.7980	−1.99044
$934$	1.08900	0.0356330
$935$	0.763631	0.0249734
$936$	−0.115252	−0.00376712
$937$	−30.0342	−0.981173	−0.490587	−	0.871392i	$-0.663217\pi$
$937$	−30.0342	−0.981173	−0.490587	+	0.871392i	$0.663217\pi$
$938$	−75.9027	−2.47831
$939$	−11.6190	−0.379173
$940$	0.820486	0.0267613
$941$	1.78902	0.0583203	0.0291602	−	0.999575i	$-0.490717\pi$
$941$	1.78902	0.0583203	0.0291602	+	0.999575i	$0.490717\pi$
$942$	78.9651	2.57282
$943$	45.0794	1.46799
$944$	−30.7569	−1.00105
$945$	−56.6790	−1.84377
$946$	2.47831	0.0805767
$947$	23.0841	0.750132	0.375066	−	0.926998i	$-0.377620\pi$
$947$	23.0841	0.750132	0.375066	+	0.926998i	$0.377620\pi$
$948$	−0.459743	−0.0149318
$949$	−0.0592796	−0.00192430
$950$	−15.6219	−0.506840
$951$	12.2656	0.397740
$952$	27.5666	0.893438
$953$	5.05262	0.163670	0.0818352	−	0.996646i	$-0.473922\pi$
$953$	5.05262	0.163670	0.0818352	+	0.996646i	$0.473922\pi$
$954$	−116.536	−3.77299
$955$	2.13730	0.0691614
$956$	−0.551804	−0.0178466
$957$	−2.79323	−0.0902922
$958$	24.9500	0.806097
$959$	−64.5233	−2.08357
$960$	29.8506	0.963424
$961$	−30.0817	−0.970378
$962$	−0.0430772	−0.00138886
$963$	−125.741	−4.05193
$964$	0.918876	0.0295950
$965$	−14.7341	−0.474308
$966$	121.569	3.91142
$967$	13.5834	0.436812	0.218406	−	0.975858i	$-0.429914\pi$
$967$	13.5834	0.436812	0.218406	+	0.975858i	$0.429914\pi$
$968$	30.3940	0.976901
$969$	24.9012	0.799940
$970$	2.37483	0.0762511
$971$	−40.6576	−1.30476	−0.652382	−	0.757890i	$-0.726230\pi$
$971$	−40.6576	−1.30476	−0.652382	+	0.757890i	$0.726230\pi$
$972$	1.08009	0.0346439
$973$	−3.77491	−0.121018
$974$	−17.4885	−0.560369
$975$	−0.0664418	−0.00212784
$976$	−34.1227	−1.09224
$977$	17.5282	0.560776	0.280388	−	0.959887i	$-0.409537\pi$
$977$	17.5282	0.560776	0.280388	+	0.959887i	$0.409537\pi$
$978$	−87.8573	−2.80937
$979$	2.54978	0.0814912
$980$	0.701022	0.0223933
$981$	−15.1428	−0.483471
$982$	33.4417	1.06717
$983$	43.4453	1.38569	0.692845	−	0.721086i	$-0.256357\pi$
$983$	43.4453	1.38569	0.692845	+	0.721086i	$0.256357\pi$
$984$	56.3891	1.79762
$985$	0.0233539	0.000744118 0
$986$	−13.5009	−0.429957
$987$	−117.653	−3.74494
$988$	0.00132232	4.20687e−5 0
$989$	−49.3261	−1.56848
$990$	2.91609	0.0926795
$991$	9.35248	0.297091	0.148546	−	0.988906i	$-0.452541\pi$
$991$	9.35248	0.297091	0.148546	+	0.988906i	$0.452541\pi$
$992$	−0.371353	−0.0117905
$993$	18.6040	0.590380
$994$	−58.5781	−1.85798
$995$	19.2952	0.611698
$996$	−0.744765	−0.0235988
$997$	4.86390	0.154041	0.0770206	−	0.997030i	$-0.475459\pi$
$997$	4.86390	0.154041	0.0770206	+	0.997030i	$0.475459\pi$
$998$	33.7794	1.06927
$999$	−57.0063	−1.80360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.12	✓	17
3.2	odd	2		3141.2.a.e.1.6		17
4.3	odd	2		5584.2.a.m.1.1		17
5.4	even	2		8725.2.a.m.1.6		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.12	✓	17	1.1	even	1	trivial
3141.2.a.e.1.6		17	3.2	odd	2
5584.2.a.m.1.1		17	4.3	odd	2
8725.2.a.m.1.6		17	5.4	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q+1.43824 q^{2} +3.12218 q^{3} +0.0685351 q^{4} +1.24047 q^{5} +4.49045 q^{6} -3.90458 q^{7} -2.77791 q^{8} +6.74802 q^{9} +O(q^{10})\)	\(q+1.43824 q^{2} +3.12218 q^{3} +0.0685351 q^{4} +1.24047 q^{5} +4.49045 q^{6} -3.90458 q^{7} -2.77791 q^{8} +6.74802 q^{9} +1.78410 q^{10} +0.242218 q^{11} +0.213979 q^{12} +0.00614827 q^{13} -5.61573 q^{14} +3.87298 q^{15} -4.13237 q^{16} +2.54150 q^{17} +9.70527 q^{18} +3.13813 q^{19} +0.0850160 q^{20} -12.1908 q^{21} +0.348367 q^{22} -6.93361 q^{23} -8.67314 q^{24} -3.46123 q^{25} +0.00884270 q^{26} +11.7020 q^{27} -0.267601 q^{28} -3.69353 q^{29} +5.57028 q^{30} +0.958271 q^{31} -0.387524 q^{32} +0.756248 q^{33} +3.65529 q^{34} -4.84353 q^{35} +0.462476 q^{36} -4.87150 q^{37} +4.51339 q^{38} +0.0191960 q^{39} -3.44592 q^{40} -6.50157 q^{41} -17.5333 q^{42} +7.11406 q^{43} +0.0166004 q^{44} +8.37074 q^{45} -9.97219 q^{46} +9.65096 q^{47} -12.9020 q^{48} +8.24577 q^{49} -4.97808 q^{50} +7.93502 q^{51} +0.000421373 q^{52} -12.0075 q^{53} +16.8303 q^{54} +0.300465 q^{55} +10.8466 q^{56} +9.79783 q^{57} -5.31219 q^{58} +7.44292 q^{59} +0.265435 q^{60} +8.25740 q^{61} +1.37822 q^{62} -26.3482 q^{63} +7.70739 q^{64} +0.00762677 q^{65} +1.08767 q^{66} +13.5161 q^{67} +0.174182 q^{68} -21.6480 q^{69} -6.96616 q^{70} +10.4311 q^{71} -18.7454 q^{72} -9.64166 q^{73} -7.00639 q^{74} -10.8066 q^{75} +0.215072 q^{76} -0.945760 q^{77} +0.0276085 q^{78} -2.14854 q^{79} -5.12610 q^{80} +16.2917 q^{81} -9.35082 q^{82} -3.48055 q^{83} -0.835499 q^{84} +3.15266 q^{85} +10.2317 q^{86} -11.5319 q^{87} -0.672859 q^{88} +10.5268 q^{89} +12.0391 q^{90} -0.0240064 q^{91} -0.475196 q^{92} +2.99189 q^{93} +13.8804 q^{94} +3.89277 q^{95} -1.20992 q^{96} +1.33111 q^{97} +11.8594 q^{98} +1.63449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * q^99

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