LMFDB - Embedded newform 349.2.a.a.1.4

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:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5x^{10} - x^{9} + 35x^{8} - 24x^{7} - 80x^{6} + 66x^{5} + 77x^{4} - 56x^{3} - 31x^{2} + 15x + 4 $ x^11 - 5x^10 - x^9 + 35x^8 - 24x^7 - 80x^6 + 66x^5 + 77x^4 - 56x^3 - 31x^2 + 15*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.31062$ 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)

$f(q)$	$=$	$q-1.31062 q^{2} +0.477277 q^{3} -0.282282 q^{4} -1.24067 q^{5} -0.625527 q^{6} +0.925788 q^{7} +2.99120 q^{8} -2.77221 q^{9} +O(q^{10})$	\(q-1.31062 q^{2} +0.477277 q^{3} -0.282282 q^{4} -1.24067 q^{5} -0.625527 q^{6} +0.925788 q^{7} +2.99120 q^{8} -2.77221 q^{9} +1.62604 q^{10} +0.851211 q^{11} -0.134727 q^{12} -1.57978 q^{13} -1.21335 q^{14} -0.592142 q^{15} -3.35575 q^{16} -5.42322 q^{17} +3.63330 q^{18} -1.01090 q^{19} +0.350218 q^{20} +0.441857 q^{21} -1.11561 q^{22} -4.56462 q^{23} +1.42763 q^{24} -3.46074 q^{25} +2.07048 q^{26} -2.75494 q^{27} -0.261333 q^{28} -5.24388 q^{29} +0.776072 q^{30} +3.41301 q^{31} -1.58429 q^{32} +0.406263 q^{33} +7.10776 q^{34} -1.14860 q^{35} +0.782544 q^{36} +3.76104 q^{37} +1.32490 q^{38} -0.753991 q^{39} -3.71109 q^{40} -2.05269 q^{41} -0.579105 q^{42} +4.80546 q^{43} -0.240282 q^{44} +3.43939 q^{45} +5.98248 q^{46} -9.06805 q^{47} -1.60162 q^{48} -6.14292 q^{49} +4.53571 q^{50} -2.58837 q^{51} +0.445943 q^{52} -7.21290 q^{53} +3.61067 q^{54} -1.05607 q^{55} +2.76921 q^{56} -0.482478 q^{57} +6.87272 q^{58} +0.699390 q^{59} +0.167151 q^{60} -1.15525 q^{61} -4.47316 q^{62} -2.56648 q^{63} +8.78790 q^{64} +1.95998 q^{65} -0.532456 q^{66} +9.21165 q^{67} +1.53088 q^{68} -2.17859 q^{69} +1.50537 q^{70} +8.09760 q^{71} -8.29222 q^{72} +11.2366 q^{73} -4.92928 q^{74} -1.65173 q^{75} +0.285358 q^{76} +0.788041 q^{77} +0.988194 q^{78} -8.12424 q^{79} +4.16338 q^{80} +7.00175 q^{81} +2.69029 q^{82} +0.642902 q^{83} -0.124728 q^{84} +6.72841 q^{85} -6.29812 q^{86} -2.50278 q^{87} +2.54614 q^{88} +10.1840 q^{89} -4.50773 q^{90} -1.46254 q^{91} +1.28851 q^{92} +1.62895 q^{93} +11.8847 q^{94} +1.25419 q^{95} -0.756144 q^{96} +6.83867 q^{97} +8.05101 q^{98} -2.35973 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * 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 $

$2$	−1.31062	−0.926746	−0.463373	−	0.886163i	$-0.653361\pi$
$2$	−1.31062	−0.926746	−0.463373	+	0.886163i	$0.653361\pi$
$3$	0.477277	0.275556	0.137778	−	0.990463i	$-0.456004\pi$
$3$	0.477277	0.275556	0.137778	+	0.990463i	$0.456004\pi$
$4$	−0.282282	−0.141141
$5$	−1.24067	−0.554844	−0.277422	−	0.960748i	$-0.589480\pi$
$5$	−1.24067	−0.554844	−0.277422	+	0.960748i	$0.589480\pi$
$6$	−0.625527	−0.255370
$7$	0.925788	0.349915	0.174957	−	0.984576i	$-0.444021\pi$
$7$	0.925788	0.349915	0.174957	+	0.984576i	$0.444021\pi$
$8$	2.99120	1.05755
$9$	−2.77221	−0.924069
$10$	1.62604	0.514200
$11$	0.851211	0.256650	0.128325	−	0.991732i	$-0.459040\pi$
$11$	0.851211	0.256650	0.128325	+	0.991732i	$0.459040\pi$
$12$	−0.134727	−0.0388922
$13$	−1.57978	−0.438152	−0.219076	−	0.975708i	$-0.570304\pi$
$13$	−1.57978	−0.438152	−0.219076	+	0.975708i	$0.570304\pi$
$14$	−1.21335	−0.324282
$15$	−0.592142	−0.152890
$16$	−3.35575	−0.838938
$17$	−5.42322	−1.31532	−0.657661	−	0.753314i	$-0.728454\pi$
$17$	−5.42322	−1.31532	−0.657661	+	0.753314i	$0.728454\pi$
$18$	3.63330	0.856378
$19$	−1.01090	−0.231916	−0.115958	−	0.993254i	$-0.536994\pi$
$19$	−1.01090	−0.231916	−0.115958	+	0.993254i	$0.536994\pi$
$20$	0.350218	0.0783112
$21$	0.441857	0.0964211
$22$	−1.11561	−0.237849
$23$	−4.56462	−0.951790	−0.475895	−	0.879502i	$-0.657876\pi$
$23$	−4.56462	−0.951790	−0.475895	+	0.879502i	$0.657876\pi$
$24$	1.42763	0.291414
$25$	−3.46074	−0.692148
$26$	2.07048	0.406055
$27$	−2.75494	−0.530188
$28$	−0.261333	−0.0493873
$29$	−5.24388	−0.973764	−0.486882	−	0.873468i	$-0.661866\pi$
$29$	−5.24388	−0.973764	−0.486882	+	0.873468i	$0.661866\pi$
$30$	0.776072	0.141691
$31$	3.41301	0.612996	0.306498	−	0.951871i	$-0.400843\pi$
$31$	3.41301	0.612996	0.306498	+	0.951871i	$0.400843\pi$
$32$	−1.58429	−0.280065
$33$	0.406263	0.0707213
$34$	7.10776	1.21897
$35$	−1.14860	−0.194148
$36$	0.782544	0.130424
$37$	3.76104	0.618310	0.309155	−	0.951012i	$-0.399954\pi$
$37$	3.76104	0.618310	0.309155	+	0.951012i	$0.399954\pi$
$38$	1.32490	0.214927
$39$	−0.753991	−0.120735
$40$	−3.71109	−0.586774
$41$	−2.05269	−0.320576	−0.160288	−	0.987070i	$-0.551242\pi$
$41$	−2.05269	−0.320576	−0.160288	+	0.987070i	$0.551242\pi$
$42$	−0.579105	−0.0893579
$43$	4.80546	0.732825	0.366413	−	0.930452i	$-0.380586\pi$
$43$	4.80546	0.732825	0.366413	+	0.930452i	$0.380586\pi$
$44$	−0.240282	−0.0362238
$45$	3.43939	0.512714
$46$	5.98248	0.882068
$47$	−9.06805	−1.32271	−0.661356	−	0.750072i	$-0.730019\pi$
$47$	−9.06805	−1.32271	−0.661356	+	0.750072i	$0.730019\pi$
$48$	−1.60162	−0.231174
$49$	−6.14292	−0.877560
$50$	4.53571	0.641446
$51$	−2.58837	−0.362445
$52$	0.445943	0.0618411
$53$	−7.21290	−0.990768	−0.495384	−	0.868674i	$-0.664973\pi$
$53$	−7.21290	−0.990768	−0.495384	+	0.868674i	$0.664973\pi$
$54$	3.61067	0.491350
$55$	−1.05607	−0.142401
$56$	2.76921	0.370052
$57$	−0.482478	−0.0639057
$58$	6.87272	0.902432
$59$	0.699390	0.0910528	0.0455264	−	0.998963i	$-0.485503\pi$
$59$	0.699390	0.0910528	0.0455264	+	0.998963i	$0.485503\pi$
$60$	0.167151	0.0215791
$61$	−1.15525	−0.147914	−0.0739570	−	0.997261i	$-0.523563\pi$
$61$	−1.15525	−0.147914	−0.0739570	+	0.997261i	$0.523563\pi$
$62$	−4.47316	−0.568092
$63$	−2.56648	−0.323345
$64$	8.78790	1.09849
$65$	1.95998	0.243106
$66$	−0.532456	−0.0655408
$67$	9.21165	1.12538	0.562691	−	0.826667i	$-0.309766\pi$
$67$	9.21165	1.12538	0.562691	+	0.826667i	$0.309766\pi$
$68$	1.53088	0.185646
$69$	−2.17859	−0.262271
$70$	1.50537	0.179926
$71$	8.09760	0.961008	0.480504	−	0.876993i	$-0.340454\pi$
$71$	8.09760	0.961008	0.480504	+	0.876993i	$0.340454\pi$
$72$	−8.29222	−0.977248
$73$	11.2366	1.31514	0.657571	−	0.753392i	$-0.271584\pi$
$73$	11.2366	1.31514	0.657571	+	0.753392i	$0.271584\pi$
$74$	−4.92928	−0.573017
$75$	−1.65173	−0.190725
$76$	0.285358	0.0327328
$77$	0.788041	0.0898056
$78$	0.988194	0.111891
$79$	−8.12424	−0.914048	−0.457024	−	0.889454i	$-0.651085\pi$
$79$	−8.12424	−0.914048	−0.457024	+	0.889454i	$0.651085\pi$
$80$	4.16338	0.465480
$81$	7.00175	0.777973
$82$	2.69029	0.297092
$83$	0.642902	0.0705677	0.0352838	−	0.999377i	$-0.488766\pi$
$83$	0.642902	0.0705677	0.0352838	+	0.999377i	$0.488766\pi$
$84$	−0.124728	−0.0136090
$85$	6.72841	0.729799
$86$	−6.29812	−0.679143
$87$	−2.50278	−0.268326
$88$	2.54614	0.271420
$89$	10.1840	1.07950	0.539751	−	0.841825i	$-0.318518\pi$
$89$	10.1840	1.07950	0.539751	+	0.841825i	$0.318518\pi$
$90$	−4.50773	−0.475156
$91$	−1.46254	−0.153316
$92$	1.28851	0.134337
$93$	1.62895	0.168914
$94$	11.8847	1.22582
$95$	1.25419	0.128677
$96$	−0.756144	−0.0771736
$97$	6.83867	0.694361	0.347181	−	0.937798i	$-0.387139\pi$
$97$	6.83867	0.694361	0.347181	+	0.937798i	$0.387139\pi$
$98$	8.05101	0.813275
$99$	−2.35973	−0.237162
$100$	0.976905	0.0976905
$101$	2.46764	0.245539	0.122769	−	0.992435i	$-0.460822\pi$
$101$	2.46764	0.245539	0.122769	+	0.992435i	$0.460822\pi$
$102$	3.39237	0.335894
$103$	3.16683	0.312037	0.156019	−	0.987754i	$-0.450134\pi$
$103$	3.16683	0.312037	0.156019	+	0.987754i	$0.450134\pi$
$104$	−4.72543	−0.463366
$105$	−0.548198	−0.0534986
$106$	9.45336	0.918191
$107$	−7.27047	−0.702863	−0.351432	−	0.936214i	$-0.614305\pi$
$107$	−7.27047	−0.702863	−0.351432	+	0.936214i	$0.614305\pi$
$108$	0.777669	0.0748313
$109$	2.72473	0.260981	0.130491	−	0.991450i	$-0.458345\pi$
$109$	2.72473	0.260981	0.130491	+	0.991450i	$0.458345\pi$
$110$	1.38411	0.131969
$111$	1.79505	0.170379
$112$	−3.10672	−0.293557
$113$	3.37070	0.317089	0.158544	−	0.987352i	$-0.449320\pi$
$113$	3.37070	0.317089	0.158544	+	0.987352i	$0.449320\pi$
$114$	0.632344	0.0592244
$115$	5.66319	0.528095
$116$	1.48025	0.137438
$117$	4.37947	0.404882
$118$	−0.916633	−0.0843829
$119$	−5.02075	−0.460251
$120$	−1.77121	−0.161689
$121$	−10.2754	−0.934131
$122$	1.51408	0.137079
$123$	−0.979699	−0.0883365
$124$	−0.963432	−0.0865188
$125$	10.4970	0.938878
$126$	3.36367	0.299659
$127$	12.6062	1.11862	0.559308	−	0.828960i	$-0.311067\pi$
$127$	12.6062	1.11862	0.559308	+	0.828960i	$0.311067\pi$
$128$	−8.34900	−0.737954
$129$	2.29353	0.201934
$130$	−2.56879	−0.225297
$131$	−12.5469	−1.09623	−0.548113	−	0.836404i	$-0.684654\pi$
$131$	−12.5469	−1.09623	−0.548113	+	0.836404i	$0.684654\pi$
$132$	−0.114681	−0.00998168
$133$	−0.935876	−0.0811508
$134$	−12.0730	−1.04294
$135$	3.41797	0.294172
$136$	−16.2219	−1.39102
$137$	−13.9567	−1.19240	−0.596202	−	0.802834i	$-0.703324\pi$
$137$	−13.9567	−1.19240	−0.596202	+	0.802834i	$0.703324\pi$
$138$	2.85530	0.243059
$139$	−17.4095	−1.47665	−0.738327	−	0.674443i	$-0.764384\pi$
$139$	−17.4095	−1.47665	−0.738327	+	0.674443i	$0.764384\pi$
$140$	0.324228	0.0274023
$141$	−4.32797	−0.364481
$142$	−10.6129	−0.890611
$143$	−1.34472	−0.112452
$144$	9.30284	0.775237
$145$	6.50592	0.540287
$146$	−14.7269	−1.21880
$147$	−2.93187	−0.241817
$148$	−1.06167	−0.0872689
$149$	−19.9652	−1.63561	−0.817806	−	0.575493i	$-0.804810\pi$
$149$	−19.9652	−1.63561	−0.817806	+	0.575493i	$0.804810\pi$
$150$	2.16479	0.176754
$151$	3.21698	0.261794	0.130897	−	0.991396i	$-0.458214\pi$
$151$	3.21698	0.261794	0.130897	+	0.991396i	$0.458214\pi$
$152$	−3.02379	−0.245262
$153$	15.0343	1.21545
$154$	−1.03282	−0.0832270
$155$	−4.23442	−0.340117
$156$	0.212838	0.0170407
$157$	8.74768	0.698141	0.349070	−	0.937097i	$-0.386497\pi$
$157$	8.74768	0.698141	0.349070	+	0.937097i	$0.386497\pi$
$158$	10.6478	0.847091
$159$	−3.44255	−0.273012
$160$	1.96558	0.155393
$161$	−4.22587	−0.333045
$162$	−9.17662	−0.720983
$163$	−13.0527	−1.02237	−0.511183	−	0.859472i	$-0.670792\pi$
$163$	−13.0527	−1.02237	−0.511183	+	0.859472i	$0.670792\pi$
$164$	0.579436	0.0452464
$165$	−0.504038	−0.0392393
$166$	−0.842599	−0.0653983
$167$	−14.4710	−1.11980	−0.559899	−	0.828561i	$-0.689160\pi$
$167$	−14.4710	−1.11980	−0.559899	+	0.828561i	$0.689160\pi$
$168$	1.32168	0.101970
$169$	−10.5043	−0.808023
$170$	−8.81838	−0.676339
$171$	2.80242	0.214306
$172$	−1.35649	−0.103432
$173$	16.1495	1.22783	0.613913	−	0.789374i	$-0.289595\pi$
$173$	16.1495	1.22783	0.613913	+	0.789374i	$0.289595\pi$
$174$	3.28019	0.248670
$175$	−3.20391	−0.242193
$176$	−2.85645	−0.215313
$177$	0.333802	0.0250901
$178$	−13.3473	−1.00042
$179$	3.04532	0.227618	0.113809	−	0.993503i	$-0.463695\pi$
$179$	3.04532	0.227618	0.113809	+	0.993503i	$0.463695\pi$
$180$	−0.970878	−0.0723650
$181$	4.13495	0.307349	0.153674	−	0.988122i	$-0.450889\pi$
$181$	4.13495	0.307349	0.153674	+	0.988122i	$0.450889\pi$
$182$	1.91683	0.142085
$183$	−0.551372	−0.0407586
$184$	−13.6537	−1.00656
$185$	−4.66620	−0.343066
$186$	−2.13493	−0.156541
$187$	−4.61630	−0.337577
$188$	2.55975	0.186689
$189$	−2.55049	−0.185521
$190$	−1.64376	−0.119251
$191$	−0.0576067	−0.00416828	−0.00208414	−	0.999998i	$-0.500663\pi$
$191$	−0.0576067	−0.00416828	−0.00208414	+	0.999998i	$0.500663\pi$
$192$	4.19426	0.302695
$193$	3.45684	0.248829	0.124414	−	0.992230i	$-0.460295\pi$
$193$	3.45684	0.248829	0.124414	+	0.992230i	$0.460295\pi$
$194$	−8.96287	−0.643497
$195$	0.935453	0.0669892
$196$	1.73403	0.123860
$197$	21.4684	1.52956	0.764780	−	0.644292i	$-0.222848\pi$
$197$	21.4684	1.52956	0.764780	+	0.644292i	$0.222848\pi$
$198$	3.09271	0.219789
$199$	−4.56012	−0.323258	−0.161629	−	0.986852i	$-0.551675\pi$
$199$	−4.56012	−0.323258	−0.161629	+	0.986852i	$0.551675\pi$
$200$	−10.3518	−0.731980
$201$	4.39651	0.310106
$202$	−3.23413	−0.227552
$203$	−4.85472	−0.340735
$204$	0.730651	0.0511558
$205$	2.54670	0.177869
$206$	−4.15050	−0.289179
$207$	12.6541	0.879519
$208$	5.30134	0.367582
$209$	−0.860487	−0.0595211
$210$	0.718478	0.0495797
$211$	−25.4847	−1.75444	−0.877221	−	0.480087i	$-0.840605\pi$
$211$	−25.4847	−1.75444	−0.877221	+	0.480087i	$0.840605\pi$
$212$	2.03607	0.139838
$213$	3.86479	0.264811
$214$	9.52881	0.651376
$215$	−5.96198	−0.406604
$216$	−8.24057	−0.560700
$217$	3.15973	0.214496
$218$	−3.57107	−0.241864
$219$	5.36296	0.362395
$220$	0.298110	0.0200986
$221$	8.56748	0.576311
$222$	−2.35263	−0.157898
$223$	28.0657	1.87942	0.939710	−	0.341973i	$-0.111095\pi$
$223$	28.0657	1.87942	0.939710	+	0.341973i	$0.111095\pi$
$224$	−1.46671	−0.0979990
$225$	9.59389	0.639593
$226$	−4.41770	−0.293861
$227$	−4.83817	−0.321121	−0.160560	−	0.987026i	$-0.551330\pi$
$227$	−4.83817	−0.321121	−0.160560	+	0.987026i	$0.551330\pi$
$228$	0.136195	0.00901971
$229$	−10.6743	−0.705379	−0.352689	−	0.935740i	$-0.614733\pi$
$229$	−10.6743	−0.705379	−0.352689	+	0.935740i	$0.614733\pi$
$230$	−7.42227	−0.489410
$231$	0.376113	0.0247464
$232$	−15.6855	−1.02980
$233$	−2.81756	−0.184585	−0.0922923	−	0.995732i	$-0.529419\pi$
$233$	−2.81756	−0.184585	−0.0922923	+	0.995732i	$0.529419\pi$
$234$	−5.73981	−0.375223
$235$	11.2505	0.733899
$236$	−0.197425	−0.0128513
$237$	−3.87751	−0.251871
$238$	6.58028	0.426536
$239$	−9.28748	−0.600757	−0.300379	−	0.953820i	$-0.597113\pi$
$239$	−9.28748	−0.600757	−0.300379	+	0.953820i	$0.597113\pi$
$240$	1.98708	0.128266
$241$	−4.08390	−0.263067	−0.131533	−	0.991312i	$-0.541990\pi$
$241$	−4.08390	−0.263067	−0.131533	+	0.991312i	$0.541990\pi$
$242$	13.4672	0.865703
$243$	11.6066	0.744563
$244$	0.326105	0.0208767
$245$	7.62133	0.486909
$246$	1.28401	0.0818655
$247$	1.59699	0.101614
$248$	10.2090	0.648272
$249$	0.306842	0.0194453
$250$	−13.7575	−0.870102
$251$	−12.9653	−0.818362	−0.409181	−	0.912453i	$-0.634186\pi$
$251$	−12.9653	−0.818362	−0.409181	+	0.912453i	$0.634186\pi$
$252$	0.724470	0.0456373
$253$	−3.88546	−0.244277
$254$	−16.5219	−1.03667
$255$	3.21131	0.201100
$256$	−6.63346	−0.414591
$257$	0.709544	0.0442601	0.0221301	−	0.999755i	$-0.492955\pi$
$257$	0.709544	0.0442601	0.0221301	+	0.999755i	$0.492955\pi$
$258$	−3.00594	−0.187142
$259$	3.48192	0.216356
$260$	−0.553267	−0.0343122
$261$	14.5371	0.899825
$262$	16.4442	1.01592
$263$	15.0849	0.930172	0.465086	−	0.885266i	$-0.346023\pi$
$263$	15.0849	0.930172	0.465086	+	0.885266i	$0.346023\pi$
$264$	1.21521	0.0747912
$265$	8.94882	0.549722
$266$	1.22658	0.0752062
$267$	4.86058	0.297463
$268$	−2.60028	−0.158838
$269$	−19.4709	−1.18716	−0.593582	−	0.804773i	$-0.702287\pi$
$269$	−19.4709	−1.18716	−0.593582	+	0.804773i	$0.702287\pi$
$270$	−4.47965	−0.272623
$271$	10.6193	0.645077	0.322539	−	0.946556i	$-0.395464\pi$
$271$	10.6193	0.645077	0.322539	+	0.946556i	$0.395464\pi$
$272$	18.1990	1.10347
$273$	−0.698036	−0.0422470
$274$	18.2919	1.10506
$275$	−2.94582	−0.177640
$276$	0.614976	0.0370172
$277$	1.53181	0.0920373	0.0460187	−	0.998941i	$-0.485347\pi$
$277$	1.53181	0.0920373	0.0460187	+	0.998941i	$0.485347\pi$
$278$	22.8172	1.36848
$279$	−9.46158	−0.566450
$280$	−3.43568	−0.205321
$281$	31.8226	1.89838	0.949188	−	0.314708i	$-0.101907\pi$
$281$	31.8226	1.89838	0.949188	+	0.314708i	$0.101907\pi$
$282$	5.67231	0.337781
$283$	4.20004	0.249666	0.124833	−	0.992178i	$-0.460160\pi$
$283$	4.20004	0.249666	0.124833	+	0.992178i	$0.460160\pi$
$284$	−2.28580	−0.135638
$285$	0.598595	0.0354577
$286$	1.76242	0.104214
$287$	−1.90035	−0.112174
$288$	4.39198	0.258800
$289$	12.4113	0.730075
$290$	−8.52677	−0.500709
$291$	3.26393	0.191335
$292$	−3.17188	−0.185620
$293$	5.38429	0.314554	0.157277	−	0.987555i	$-0.449728\pi$
$293$	5.38429	0.314554	0.157277	+	0.987555i	$0.449728\pi$
$294$	3.84256	0.224103
$295$	−0.867711	−0.0505201
$296$	11.2500	0.653893
$297$	−2.34504	−0.136073
$298$	26.1667	1.51580
$299$	7.21109	0.417028
$300$	0.466254	0.0269192
$301$	4.44883	0.256427
$302$	−4.21623	−0.242617
$303$	1.17774	0.0676597
$304$	3.39232	0.194563
$305$	1.43328	0.0820692
$306$	−19.7042	−1.12641
$307$	−14.4006	−0.821883	−0.410942	−	0.911662i	$-0.634800\pi$
$307$	−14.4006	−0.821883	−0.410942	+	0.911662i	$0.634800\pi$
$308$	−0.222450	−0.0126752
$309$	1.51145	0.0859836
$310$	5.54971	0.315202
$311$	3.41701	0.193761	0.0968805	−	0.995296i	$-0.469114\pi$
$311$	3.41701	0.193761	0.0968805	+	0.995296i	$0.469114\pi$
$312$	−2.25534	−0.127683
$313$	−21.6027	−1.22106	−0.610530	−	0.791993i	$-0.709043\pi$
$313$	−21.6027	−1.22106	−0.610530	+	0.791993i	$0.709043\pi$
$314$	−11.4649	−0.647000
$315$	3.18415	0.179406
$316$	2.29333	0.129010
$317$	−1.13242	−0.0636033	−0.0318016	−	0.999494i	$-0.510124\pi$
$317$	−1.13242	−0.0636033	−0.0318016	+	0.999494i	$0.510124\pi$
$318$	4.51187	0.253013
$319$	−4.46365	−0.249916
$320$	−10.9029	−0.609489
$321$	−3.47003	−0.193678
$322$	5.53850	0.308649
$323$	5.48231	0.305044
$324$	−1.97647	−0.109804
$325$	5.46720	0.303266
$326$	17.1071	0.947473
$327$	1.30045	0.0719149
$328$	−6.13999	−0.339024
$329$	−8.39509	−0.462836
$330$	0.660601	0.0363649
$331$	−15.4818	−0.850958	−0.425479	−	0.904968i	$-0.639894\pi$
$331$	−15.4818	−0.850958	−0.425479	+	0.904968i	$0.639894\pi$
$332$	−0.181480	−0.00995999
$333$	−10.4264	−0.571361
$334$	18.9659	1.03777
$335$	−11.4286	−0.624412
$336$	−1.48276	−0.0808913
$337$	21.0873	1.14870	0.574348	−	0.818611i	$-0.305256\pi$
$337$	21.0873	1.14870	0.574348	+	0.818611i	$0.305256\pi$
$338$	13.7671	0.748833
$339$	1.60876	0.0873756
$340$	−1.89931	−0.103005
$341$	2.90520	0.157325
$342$	−3.67290	−0.198607
$343$	−12.1676	−0.656986
$344$	14.3741	0.774998
$345$	2.70291	0.145520
$346$	−21.1659	−1.13788
$347$	−27.8963	−1.49755	−0.748777	−	0.662822i	$-0.769359\pi$
$347$	−27.8963	−1.49755	−0.748777	+	0.662822i	$0.769359\pi$
$348$	0.706490	0.0378718
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	4.19910	0.224451
$351$	4.35219	0.232303
$352$	−1.34856	−0.0718787
$353$	8.33251	0.443495	0.221747	−	0.975104i	$-0.428824\pi$
$353$	8.33251	0.443495	0.221747	+	0.975104i	$0.428824\pi$
$354$	−0.437487	−0.0232522
$355$	−10.0464	−0.533209
$356$	−2.87476	−0.152362
$357$	−2.39628	−0.126825
$358$	−3.99125	−0.210944
$359$	−11.3580	−0.599450	−0.299725	−	0.954026i	$-0.596895\pi$
$359$	−11.3580	−0.599450	−0.299725	+	0.954026i	$0.596895\pi$
$360$	10.2879	0.542220
$361$	−17.9781	−0.946215
$362$	−5.41934	−0.284834
$363$	−4.90423	−0.257405
$364$	0.412848	0.0216391
$365$	−13.9409	−0.729699
$366$	0.722637	0.0377729
$367$	−4.60632	−0.240448	−0.120224	−	0.992747i	$-0.538361\pi$
$367$	−4.60632	−0.240448	−0.120224	+	0.992747i	$0.538361\pi$
$368$	15.3177	0.798493
$369$	5.69047	0.296234
$370$	6.11560	0.317935
$371$	−6.67762	−0.346685
$372$	−0.459824	−0.0238407
$373$	23.8736	1.23613	0.618064	−	0.786128i	$-0.287917\pi$
$373$	23.8736	1.23613	0.618064	+	0.786128i	$0.287917\pi$
$374$	6.05021	0.312849
$375$	5.00996	0.258713
$376$	−27.1243	−1.39883
$377$	8.28417	0.426656
$378$	3.34272	0.171931
$379$	11.2135	0.575999	0.288000	−	0.957631i	$-0.407010\pi$
$379$	11.2135	0.575999	0.288000	+	0.957631i	$0.407010\pi$
$380$	−0.354035	−0.0181616
$381$	6.01663	0.308241
$382$	0.0755004	0.00386294
$383$	32.0195	1.63612	0.818060	−	0.575132i	$-0.195049\pi$
$383$	32.0195	1.63612	0.818060	+	0.575132i	$0.195049\pi$
$384$	−3.98478	−0.203348
$385$	−0.977698	−0.0498281
$386$	−4.53059	−0.230601
$387$	−13.3217	−0.677181
$388$	−1.93043	−0.0980028
$389$	36.0281	1.82670	0.913350	−	0.407176i	$-0.133486\pi$
$389$	36.0281	1.82670	0.913350	+	0.407176i	$0.133486\pi$
$390$	−1.22602	−0.0620820
$391$	24.7549	1.25191
$392$	−18.3747	−0.928062
$393$	−5.98833	−0.302071
$394$	−28.1368	−1.41751
$395$	10.0795	0.507154
$396$	0.666110	0.0334733
$397$	11.2182	0.563026	0.281513	−	0.959557i	$-0.409164\pi$
$397$	11.2182	0.563026	0.281513	+	0.959557i	$0.409164\pi$
$398$	5.97657	0.299578
$399$	−0.446672	−0.0223616
$400$	11.6134	0.580670
$401$	7.69533	0.384286	0.192143	−	0.981367i	$-0.438456\pi$
$401$	7.69533	0.384286	0.192143	+	0.981367i	$0.438456\pi$
$402$	−5.76214	−0.287389
$403$	−5.39181	−0.268585
$404$	−0.696569	−0.0346556
$405$	−8.68686	−0.431653
$406$	6.36268	0.315775
$407$	3.20144	0.158689
$408$	−7.74234	−0.383303
$409$	−9.07611	−0.448785	−0.224392	−	0.974499i	$-0.572040\pi$
$409$	−9.07611	−0.448785	−0.224392	+	0.974499i	$0.572040\pi$
$410$	−3.33775	−0.164840
$411$	−6.66122	−0.328574
$412$	−0.893939	−0.0440412
$413$	0.647487	0.0318607
$414$	−16.5847	−0.815092
$415$	−0.797629	−0.0391540
$416$	2.50282	0.122711
$417$	−8.30914	−0.406900
$418$	1.12777	0.0551610
$419$	−34.2198	−1.67175	−0.835873	−	0.548923i	$-0.815038\pi$
$419$	−34.2198	−1.67175	−0.835873	+	0.548923i	$0.815038\pi$
$420$	0.154746	0.00755085
$421$	−32.3357	−1.57594	−0.787972	−	0.615711i	$-0.788869\pi$
$421$	−32.3357	−1.57594	−0.787972	+	0.615711i	$0.788869\pi$
$422$	33.4007	1.62592
$423$	25.1385	1.22228
$424$	−21.5752	−1.04779
$425$	18.7683	0.910398
$426$	−5.06527	−0.245413
$427$	−1.06951	−0.0517573
$428$	2.05232	0.0992028
$429$	−0.641805	−0.0309867
$430$	7.81388	0.376819
$431$	2.33919	0.112675	0.0563375	−	0.998412i	$-0.482058\pi$
$431$	2.33919	0.112675	0.0563375	+	0.998412i	$0.482058\pi$
$432$	9.24490	0.444795
$433$	−8.90432	−0.427914	−0.213957	−	0.976843i	$-0.568635\pi$
$433$	−8.90432	−0.427914	−0.213957	+	0.976843i	$0.568635\pi$
$434$	−4.14119	−0.198784
$435$	3.10512	0.148879
$436$	−0.769141	−0.0368352
$437$	4.61437	0.220735
$438$	−7.02879	−0.335848
$439$	25.1961	1.20255	0.601273	−	0.799044i	$-0.294661\pi$
$439$	25.1961	1.20255	0.601273	+	0.799044i	$0.294661\pi$
$440$	−3.15892	−0.150596
$441$	17.0294	0.810926
$442$	−11.2287	−0.534094
$443$	−32.1155	−1.52585	−0.762926	−	0.646486i	$-0.776238\pi$
$443$	−32.1155	−1.52585	−0.762926	+	0.646486i	$0.776238\pi$
$444$	−0.506711	−0.0240475
$445$	−12.6350	−0.598955
$446$	−36.7834	−1.74175
$447$	−9.52892	−0.450703
$448$	8.13573	0.384377
$449$	27.3493	1.29069	0.645346	−	0.763890i	$-0.276713\pi$
$449$	27.3493	1.29069	0.645346	+	0.763890i	$0.276713\pi$
$450$	−12.5739	−0.592740
$451$	−1.74727	−0.0822757
$452$	−0.951488	−0.0447542
$453$	1.53539	0.0721389
$454$	6.34099	0.297597
$455$	1.81453	0.0850663
$456$	−1.44319	−0.0675834
$457$	−21.6953	−1.01486	−0.507432	−	0.861692i	$-0.669405\pi$
$457$	−21.6953	−1.01486	−0.507432	+	0.861692i	$0.669405\pi$
$458$	13.9899	0.653707
$459$	14.9406	0.697369
$460$	−1.59861	−0.0745358
$461$	−27.8453	−1.29689	−0.648443	−	0.761263i	$-0.724580\pi$
$461$	−27.8453	−1.29689	−0.648443	+	0.761263i	$0.724580\pi$
$462$	−0.492941	−0.0229337
$463$	−25.9139	−1.20432	−0.602160	−	0.798375i	$-0.705693\pi$
$463$	−25.9139	−1.20432	−0.602160	+	0.798375i	$0.705693\pi$
$464$	17.5972	0.816928
$465$	−2.02099	−0.0937212
$466$	3.69275	0.171063
$467$	−14.7224	−0.681271	−0.340635	−	0.940196i	$-0.610642\pi$
$467$	−14.7224	−0.681271	−0.340635	+	0.940196i	$0.610642\pi$
$468$	−1.23625	−0.0571455
$469$	8.52804	0.393788
$470$	−14.7450	−0.680138
$471$	4.17506	0.192377
$472$	2.09201	0.0962928
$473$	4.09046	0.188080
$474$	5.08193	0.233421
$475$	3.49845	0.160520
$476$	1.41727	0.0649603
$477$	19.9957	0.915538
$478$	12.1723	0.556750
$479$	17.8519	0.815676	0.407838	−	0.913054i	$-0.366283\pi$
$479$	17.8519	0.815676	0.407838	+	0.913054i	$0.366283\pi$
$480$	0.938124	0.0428193
$481$	−5.94160	−0.270914
$482$	5.35243	0.243796
$483$	−2.01691	−0.0917726
$484$	2.90057	0.131844
$485$	−8.48452	−0.385262
$486$	−15.2118	−0.690021
$487$	−13.5238	−0.612822	−0.306411	−	0.951899i	$-0.599128\pi$
$487$	−13.5238	−0.612822	−0.306411	+	0.951899i	$0.599128\pi$
$488$	−3.45557	−0.156426
$489$	−6.22974	−0.281719
$490$	−9.98864	−0.451241
$491$	0.544455	0.0245709	0.0122855	−	0.999925i	$-0.496089\pi$
$491$	0.544455	0.0245709	0.0122855	+	0.999925i	$0.496089\pi$
$492$	0.276551	0.0124679
$493$	28.4387	1.28081
$494$	−2.09305	−0.0941706
$495$	2.92765	0.131588
$496$	−11.4532	−0.514265
$497$	7.49666	0.336271
$498$	−0.402153	−0.0180209
$499$	−5.19958	−0.232765	−0.116382	−	0.993204i	$-0.537130\pi$
$499$	−5.19958	−0.232765	−0.116382	+	0.993204i	$0.537130\pi$
$500$	−2.96311	−0.132514
$501$	−6.90666	−0.308567
$502$	16.9925	0.758415
$503$	20.8000	0.927428	0.463714	−	0.885985i	$-0.346516\pi$
$503$	20.8000	0.927428	0.463714	+	0.885985i	$0.346516\pi$
$504$	−7.67684	−0.341954
$505$	−3.06152	−0.136236
$506$	5.09235	0.226383
$507$	−5.01346	−0.222655
$508$	−3.55849	−0.157883
$509$	−11.4697	−0.508386	−0.254193	−	0.967153i	$-0.581810\pi$
$509$	−11.4697	−0.508386	−0.254193	+	0.967153i	$0.581810\pi$
$510$	−4.20880	−0.186369
$511$	10.4027	0.460188
$512$	25.3919	1.12218
$513$	2.78496	0.122959
$514$	−0.929941	−0.0410179
$515$	−3.92899	−0.173132
$516$	−0.647423	−0.0285012
$517$	−7.71883	−0.339474
$518$	−4.56347	−0.200507
$519$	7.70779	0.338334
$520$	5.86269	0.257096
$521$	−0.0386001	−0.00169110	−0.000845550	−	1.00000i	$-0.500269\pi$
$521$	−0.0386001	−0.00169110	−0.000845550		1.00000i	$0.500269\pi$
$522$	−19.0526	−0.833910
$523$	−6.37551	−0.278782	−0.139391	−	0.990237i	$-0.544514\pi$
$523$	−6.37551	−0.278782	−0.139391	+	0.990237i	$0.544514\pi$
$524$	3.54176	0.154722
$525$	−1.52915	−0.0667377
$526$	−19.7705	−0.862033
$527$	−18.5095	−0.806287
$528$	−1.36332	−0.0593308
$529$	−2.16421	−0.0940962
$530$	−11.7285	−0.509453
$531$	−1.93885	−0.0841391
$532$	0.264181	0.0114537
$533$	3.24279	0.140461
$534$	−6.37036	−0.275673
$535$	9.02025	0.389979
$536$	27.5539	1.19015
$537$	1.45346	0.0627214
$538$	25.5190	1.10020
$539$	−5.22892	−0.225226
$540$	−0.964830	−0.0415197
$541$	−8.54443	−0.367354	−0.183677	−	0.982987i	$-0.558800\pi$
$541$	−8.54443	−0.367354	−0.183677	+	0.982987i	$0.558800\pi$
$542$	−13.9179	−0.597823
$543$	1.97352	0.0846917
$544$	8.59194	0.368376
$545$	−3.38048	−0.144804
$546$	0.914858	0.0391523
$547$	15.7722	0.674370	0.337185	−	0.941438i	$-0.390525\pi$
$547$	15.7722	0.674370	0.337185	+	0.941438i	$0.390525\pi$
$548$	3.93973	0.168297
$549$	3.20258	0.136683
$550$	3.86084	0.164627
$551$	5.30102	0.225831
$552$	−6.51659	−0.277364
$553$	−7.52132	−0.319839
$554$	−2.00761	−0.0852953
$555$	−2.22707	−0.0945337
$556$	4.91438	0.208416
$557$	−15.8985	−0.673643	−0.336821	−	0.941569i	$-0.609352\pi$
$557$	−15.8985	−0.673643	−0.336821	+	0.941569i	$0.609352\pi$
$558$	12.4005	0.524956
$559$	−7.59156	−0.321089
$560$	3.85440	0.162878
$561$	−2.20325	−0.0930214
$562$	−41.7072	−1.75931
$563$	29.8773	1.25918	0.629590	−	0.776928i	$-0.283223\pi$
$563$	29.8773	1.25918	0.629590	+	0.776928i	$0.283223\pi$
$564$	1.22171	0.0514432
$565$	−4.18192	−0.175935
$566$	−5.50464	−0.231377
$567$	6.48214	0.272224
$568$	24.2215	1.01631
$569$	35.7171	1.49734	0.748669	−	0.662943i	$-0.230693\pi$
$569$	35.7171	1.49734	0.748669	+	0.662943i	$0.230693\pi$
$570$	−0.784529	−0.0328603
$571$	−18.1699	−0.760388	−0.380194	−	0.924907i	$-0.624143\pi$
$571$	−18.1699	−0.760388	−0.380194	+	0.924907i	$0.624143\pi$
$572$	0.379591	0.0158715
$573$	−0.0274944	−0.00114859
$574$	2.49063	0.103957
$575$	15.7970	0.658780
$576$	−24.3619	−1.01508
$577$	−19.8439	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$577$	−19.8439	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$578$	−16.2664	−0.676594
$579$	1.64987	0.0685662
$580$	−1.83650	−0.0762566
$581$	0.595191	0.0246927
$582$	−4.27777	−0.177319
$583$	−6.13970	−0.254281
$584$	33.6108	1.39083
$585$	−5.43347	−0.224646
$586$	−7.05675	−0.291512
$587$	34.9103	1.44090	0.720450	−	0.693507i	$-0.243935\pi$
$587$	34.9103	1.44090	0.720450	+	0.693507i	$0.243935\pi$
$588$	0.827614	0.0341302
$589$	−3.45021	−0.142163
$590$	1.13724	0.0468193
$591$	10.2464	0.421479
$592$	−12.6211	−0.518724
$593$	−32.0421	−1.31581	−0.657906	−	0.753100i	$-0.728557\pi$
$593$	−32.0421	−1.31581	−0.657906	+	0.753100i	$0.728557\pi$
$594$	3.07344	0.126105
$595$	6.22908	0.255368
$596$	5.63581	0.230852
$597$	−2.17644	−0.0890757
$598$	−9.45098	−0.386479
$599$	−29.3227	−1.19809	−0.599047	−	0.800714i	$-0.704454\pi$
$599$	−29.3227	−1.19809	−0.599047	+	0.800714i	$0.704454\pi$
$600$	−4.94065	−0.201701
$601$	−19.7060	−0.803827	−0.401913	−	0.915678i	$-0.631655\pi$
$601$	−19.7060	−0.803827	−0.401913	+	0.915678i	$0.631655\pi$
$602$	−5.83072	−0.237642
$603$	−25.5366	−1.03993
$604$	−0.908096	−0.0369499
$605$	12.7484	0.518297
$606$	−1.54357	−0.0627033
$607$	−41.2151	−1.67287	−0.836434	−	0.548067i	$-0.815364\pi$
$607$	−41.2151	−1.67287	−0.836434	+	0.548067i	$0.815364\pi$
$608$	1.60155	0.0649515
$609$	−2.31704	−0.0938914
$610$	−1.87848	−0.0760573
$611$	14.3255	0.579548
$612$	−4.24390	−0.171550
$613$	19.5450	0.789415	0.394708	−	0.918807i	$-0.370846\pi$
$613$	19.5450	0.789415	0.394708	+	0.918807i	$0.370846\pi$
$614$	18.8736	0.761677
$615$	1.21548	0.0490130
$616$	2.35719	0.0949738
$617$	−28.5545	−1.14956	−0.574780	−	0.818308i	$-0.694912\pi$
$617$	−28.5545	−1.14956	−0.574780	+	0.818308i	$0.694912\pi$
$618$	−1.98094	−0.0796850
$619$	−22.4829	−0.903663	−0.451831	−	0.892103i	$-0.649229\pi$
$619$	−22.4829	−0.903663	−0.451831	+	0.892103i	$0.649229\pi$
$620$	1.19530	0.0480044
$621$	12.5753	0.504628
$622$	−4.47840	−0.179567
$623$	9.42822	0.377734
$624$	2.53021	0.101289
$625$	4.28043	0.171217
$626$	28.3129	1.13161
$627$	−0.410690	−0.0164014
$628$	−2.46931	−0.0985363
$629$	−20.3969	−0.813278
$630$	−4.17320	−0.166264
$631$	−35.4143	−1.40982	−0.704910	−	0.709297i	$-0.749012\pi$
$631$	−35.4143	−1.40982	−0.704910	+	0.709297i	$0.749012\pi$
$632$	−24.3012	−0.966650
$633$	−12.1633	−0.483446
$634$	1.48418	0.0589441
$635$	−15.6401	−0.620658
$636$	0.971769	0.0385332
$637$	9.70444	0.384504
$638$	5.85014	0.231609
$639$	−22.4482	−0.888038
$640$	10.3583	0.409450
$641$	11.6308	0.459390	0.229695	−	0.973263i	$-0.426227\pi$
$641$	11.6308	0.459390	0.229695	+	0.973263i	$0.426227\pi$
$642$	4.54788	0.179490
$643$	−15.6166	−0.615857	−0.307928	−	0.951410i	$-0.599636\pi$
$643$	−15.6166	−0.615857	−0.307928	+	0.951410i	$0.599636\pi$
$644$	1.19289	0.0470063
$645$	−2.84551	−0.112042
$646$	−7.18522	−0.282699
$647$	29.4432	1.15753	0.578766	−	0.815494i	$-0.303534\pi$
$647$	29.4432	1.15753	0.578766	+	0.815494i	$0.303534\pi$
$648$	20.9436	0.822744
$649$	0.595329	0.0233687
$650$	−7.16541	−0.281050
$651$	1.50806	0.0591057
$652$	3.68454	0.144298
$653$	−40.5911	−1.58845	−0.794227	−	0.607621i	$-0.792124\pi$
$653$	−40.5911	−1.58845	−0.794227	+	0.607621i	$0.792124\pi$
$654$	−1.70439	−0.0666469
$655$	15.5665	0.608234
$656$	6.88831	0.268943
$657$	−31.1501	−1.21528
$658$	11.0028	0.428932
$659$	−2.33252	−0.0908620	−0.0454310	−	0.998967i	$-0.514466\pi$
$659$	−2.33252	−0.0908620	−0.0454310	+	0.998967i	$0.514466\pi$
$660$	0.142281	0.00553827
$661$	12.0911	0.470290	0.235145	−	0.971960i	$-0.424443\pi$
$661$	12.0911	0.470290	0.235145	+	0.971960i	$0.424443\pi$
$662$	20.2908	0.788623
$663$	4.08906	0.158806
$664$	1.92305	0.0746287
$665$	1.16111	0.0450260
$666$	13.6650	0.529507
$667$	23.9363	0.926819
$668$	4.08490	0.158049
$669$	13.3951	0.517885
$670$	14.9785	0.578671
$671$	−0.983358	−0.0379621
$672$	−0.700029	−0.0270042
$673$	−26.5147	−1.02206	−0.511032	−	0.859561i	$-0.670737\pi$
$673$	−26.5147	−1.02206	−0.511032	+	0.859561i	$0.670737\pi$
$674$	−27.6373	−1.06455
$675$	9.53413	0.366969
$676$	2.96517	0.114045
$677$	28.1038	1.08012	0.540058	−	0.841628i	$-0.318402\pi$
$677$	28.1038	1.08012	0.540058	+	0.841628i	$0.318402\pi$
$678$	−2.10846	−0.0809751
$679$	6.33115	0.242967
$680$	20.1260	0.771798
$681$	−2.30915	−0.0884867
$682$	−3.80760	−0.145801
$683$	−25.3080	−0.968384	−0.484192	−	0.874962i	$-0.660886\pi$
$683$	−25.3080	−0.968384	−0.484192	+	0.874962i	$0.660886\pi$
$684$	−0.791071	−0.0302474
$685$	17.3157	0.661598
$686$	15.9470	0.608859
$687$	−5.09460	−0.194371
$688$	−16.1259	−0.614795
$689$	11.3948	0.434107
$690$	−3.54248	−0.134860
$691$	2.40279	0.0914065	0.0457033	−	0.998955i	$-0.485447\pi$
$691$	2.40279	0.0914065	0.0457033	+	0.998955i	$0.485447\pi$
$692$	−4.55872	−0.173297
$693$	−2.18461	−0.0829866
$694$	36.5614	1.38785
$695$	21.5994	0.819312
$696$	−7.48632	−0.283768
$697$	11.1322	0.421661
$698$	1.31062	0.0496076
$699$	−1.34476	−0.0508634
$700$	0.904406	0.0341833
$701$	17.9318	0.677275	0.338637	−	0.940917i	$-0.390034\pi$
$701$	17.9318	0.677275	0.338637	+	0.940917i	$0.390034\pi$
$702$	−5.70406	−0.215286
$703$	−3.80202	−0.143396
$704$	7.48036	0.281927
$705$	5.36958	0.202230
$706$	−10.9207	−0.411007
$707$	2.28451	0.0859177
$708$	−0.0942264	−0.00354124
$709$	16.0184	0.601584	0.300792	−	0.953690i	$-0.402749\pi$
$709$	16.0184	0.601584	0.300792	+	0.953690i	$0.402749\pi$
$710$	13.1670	0.494150
$711$	22.5221	0.844644
$712$	30.4624	1.14163
$713$	−15.5791	−0.583443
$714$	3.14061	0.117534
$715$	1.66836	0.0623930
$716$	−0.859639	−0.0321262
$717$	−4.43270	−0.165542
$718$	14.8859	0.555538
$719$	−28.3945	−1.05893	−0.529467	−	0.848330i	$-0.677608\pi$
$719$	−28.3945	−1.05893	−0.529467	+	0.848330i	$0.677608\pi$
$720$	−11.5417	−0.430135
$721$	2.93181	0.109186
$722$	23.5624	0.876902
$723$	−1.94915	−0.0724896
$724$	−1.16722	−0.0433795
$725$	18.1477	0.673989
$726$	6.42756	0.238549
$727$	16.5101	0.612327	0.306164	−	0.951979i	$-0.400955\pi$
$727$	16.5101	0.612327	0.306164	+	0.951979i	$0.400955\pi$
$728$	−4.37474	−0.162139
$729$	−15.4657	−0.572804
$730$	18.2712	0.676246
$731$	−26.0610	−0.963902
$732$	0.155642	0.00575270
$733$	−37.8700	−1.39876	−0.699380	−	0.714750i	$-0.746540\pi$
$733$	−37.8700	−1.39876	−0.699380	+	0.714750i	$0.746540\pi$
$734$	6.03713	0.222834
$735$	3.63748	0.134170
$736$	7.23168	0.266563
$737$	7.84106	0.288829
$738$	−7.45803	−0.274534
$739$	−21.2052	−0.780046	−0.390023	−	0.920805i	$-0.627533\pi$
$739$	−21.2052	−0.780046	−0.390023	+	0.920805i	$0.627533\pi$
$740$	1.31718	0.0484206
$741$	0.762207	0.0280004
$742$	8.75180	0.321289
$743$	1.51397	0.0555423	0.0277711	−	0.999614i	$-0.491159\pi$
$743$	1.51397	0.0555423	0.0277711	+	0.999614i	$0.491159\pi$
$744$	4.87252	0.178635
$745$	24.7702	0.907510
$746$	−31.2892	−1.14558
$747$	−1.78226	−0.0652094
$748$	1.30310	0.0476460
$749$	−6.73091	−0.245942
$750$	−6.56614	−0.239762
$751$	−15.5043	−0.565761	−0.282881	−	0.959155i	$-0.591290\pi$
$751$	−15.5043	−0.565761	−0.282881	+	0.959155i	$0.591290\pi$
$752$	30.4302	1.10967
$753$	−6.18803	−0.225504
$754$	−10.8574	−0.395402
$755$	−3.99121	−0.145255
$756$	0.719957	0.0261846
$757$	22.2273	0.807866	0.403933	−	0.914789i	$-0.367643\pi$
$757$	22.2273	0.807866	0.403933	+	0.914789i	$0.367643\pi$
$758$	−14.6966	−0.533805
$759$	−1.85444	−0.0673118
$760$	3.75153	0.136082
$761$	44.8324	1.62517	0.812587	−	0.582840i	$-0.198058\pi$
$761$	44.8324	1.62517	0.812587	+	0.582840i	$0.198058\pi$
$762$	−7.88550	−0.285662
$763$	2.52252	0.0913212
$764$	0.0162613	0.000588315 0
$765$	−18.6526	−0.674385
$766$	−41.9653	−1.51627
$767$	−1.10488	−0.0398949
$768$	−3.16599	−0.114243
$769$	34.2475	1.23500	0.617498	−	0.786572i	$-0.288146\pi$
$769$	34.2475	1.23500	0.617498	+	0.786572i	$0.288146\pi$
$770$	1.28139	0.0461780
$771$	0.338649	0.0121961
$772$	−0.975803	−0.0351199
$773$	−8.47206	−0.304719	−0.152359	−	0.988325i	$-0.548687\pi$
$773$	−8.47206	−0.304719	−0.152359	+	0.988325i	$0.548687\pi$
$774$	17.4597	0.627575
$775$	−11.8116	−0.424284
$776$	20.4558	0.734321
$777$	1.66184	0.0596181
$778$	−47.2191	−1.69289
$779$	2.07505	0.0743465
$780$	−0.264061	−0.00945492
$781$	6.89276	0.246643
$782$	−32.4443	−1.16020
$783$	14.4466	0.516278
$784$	20.6141	0.736218
$785$	−10.8530	−0.387359
$786$	7.84841	0.279944
$787$	27.5049	0.980443	0.490222	−	0.871598i	$-0.336916\pi$
$787$	27.5049	0.980443	0.490222	+	0.871598i	$0.336916\pi$
$788$	−6.06014	−0.215883
$789$	7.19965	0.256314
$790$	−13.2104	−0.470003
$791$	3.12055	0.110954
$792$	−7.05843	−0.250810
$793$	1.82503	0.0648088
$794$	−14.7028	−0.521783
$795$	4.27106	0.151479
$796$	1.28724	0.0456250
$797$	−31.2201	−1.10587	−0.552936	−	0.833224i	$-0.686493\pi$
$797$	−31.2201	−1.10587	−0.552936	+	0.833224i	$0.686493\pi$
$798$	0.585416	0.0207235
$799$	49.1780	1.73979
$800$	5.48281	0.193847
$801$	−28.2321	−0.997534
$802$	−10.0856	−0.356136
$803$	9.56470	0.337531
$804$	−1.24105	−0.0437686
$805$	5.24291	0.184788
$806$	7.06659	0.248910
$807$	−9.29302	−0.327130
$808$	7.38119	0.259669
$809$	−22.2973	−0.783932	−0.391966	−	0.919980i	$-0.628205\pi$
$809$	−22.2973	−0.783932	−0.391966	+	0.919980i	$0.628205\pi$
$810$	11.3851	0.400033
$811$	45.7585	1.60680	0.803399	−	0.595441i	$-0.203023\pi$
$811$	45.7585	1.60680	0.803399	+	0.595441i	$0.203023\pi$
$812$	1.37040	0.0480916
$813$	5.06835	0.177755
$814$	−4.19586	−0.147065
$815$	16.1941	0.567253
$816$	8.68594	0.304069
$817$	−4.85782	−0.169954
$818$	11.8953	0.415910
$819$	4.05446	0.141674
$820$	−0.718888	−0.0251047
$821$	31.9610	1.11545	0.557723	−	0.830027i	$-0.311675\pi$
$821$	31.9610	1.11545	0.557723	+	0.830027i	$0.311675\pi$
$822$	8.73031	0.304505
$823$	46.6783	1.62710	0.813552	−	0.581492i	$-0.197531\pi$
$823$	46.6783	1.62710	0.813552	+	0.581492i	$0.197531\pi$
$824$	9.47262	0.329994
$825$	−1.40597	−0.0489496
$826$	−0.848607	−0.0295268
$827$	−27.4837	−0.955702	−0.477851	−	0.878441i	$-0.658584\pi$
$827$	−27.4837	−0.955702	−0.477851	+	0.878441i	$0.658584\pi$
$828$	−3.57202	−0.124136
$829$	−8.38516	−0.291229	−0.145614	−	0.989341i	$-0.546516\pi$
$829$	−8.38516	−0.291229	−0.145614	+	0.989341i	$0.546516\pi$
$830$	1.04539	0.0362859
$831$	0.731095	0.0253614
$832$	−13.8829	−0.481304
$833$	33.3144	1.15427
$834$	10.8901	0.377094
$835$	17.9537	0.621313
$836$	0.242900	0.00840087
$837$	−9.40265	−0.325003
$838$	44.8491	1.54928
$839$	−18.0620	−0.623569	−0.311785	−	0.950153i	$-0.600927\pi$
$839$	−18.0620	−0.623569	−0.311785	+	0.950153i	$0.600927\pi$
$840$	−1.63977	−0.0565774
$841$	−1.50172	−0.0517834
$842$	42.3797	1.46050
$843$	15.1882	0.523109
$844$	7.19388	0.247624
$845$	13.0324	0.448327
$846$	−32.9470	−1.13274
$847$	−9.51288	−0.326866
$848$	24.2047	0.831194
$849$	2.00458	0.0687970
$850$	−24.5981	−0.843709
$851$	−17.1677	−0.588502
$852$	−1.09096	−0.0373757
$853$	−3.08006	−0.105459	−0.0527295	−	0.998609i	$-0.516792\pi$
$853$	−3.08006	−0.105459	−0.0527295	+	0.998609i	$0.516792\pi$
$854$	1.40172	0.0479659
$855$	−3.47687	−0.118906
$856$	−21.7474	−0.743312
$857$	26.4632	0.903966	0.451983	−	0.892027i	$-0.350717\pi$
$857$	26.4632	0.903966	0.451983	+	0.892027i	$0.350717\pi$
$858$	0.841161	0.0287168
$859$	−8.94787	−0.305297	−0.152649	−	0.988281i	$-0.548780\pi$
$859$	−8.94787	−0.305297	−0.152649	+	0.988281i	$0.548780\pi$
$860$	1.68296	0.0573884
$861$	−0.906993	−0.0309102
$862$	−3.06579	−0.104421
$863$	−2.84904	−0.0969824	−0.0484912	−	0.998824i	$-0.515441\pi$
$863$	−2.84904	−0.0969824	−0.0484912	+	0.998824i	$0.515441\pi$
$864$	4.36462	0.148487
$865$	−20.0362	−0.681252
$866$	11.6702	0.396568
$867$	5.92361	0.201176
$868$	−0.891934	−0.0302742
$869$	−6.91544	−0.234590
$870$	−4.06963	−0.137973
$871$	−14.5524	−0.493088
$872$	8.15019	0.276000
$873$	−18.9582	−0.641638
$874$	−6.04767	−0.204565
$875$	9.71797	0.328527
$876$	−1.51387	−0.0511488
$877$	−40.1179	−1.35469	−0.677343	−	0.735668i	$-0.736869\pi$
$877$	−40.1179	−1.35469	−0.677343	+	0.735668i	$0.736869\pi$
$878$	−33.0225	−1.11445
$879$	2.56980	0.0866771
$880$	3.54391	0.119465
$881$	−54.1837	−1.82549	−0.912747	−	0.408525i	$-0.866043\pi$
$881$	−54.1837	−1.82549	−0.912747	+	0.408525i	$0.866043\pi$
$882$	−22.3191	−0.751522
$883$	31.8455	1.07169	0.535844	−	0.844317i	$-0.319994\pi$
$883$	31.8455	1.07169	0.535844	+	0.844317i	$0.319994\pi$
$884$	−2.41844	−0.0813410
$885$	−0.414138	−0.0139211
$886$	42.0911	1.41408
$887$	41.1909	1.38305	0.691527	−	0.722350i	$-0.256938\pi$
$887$	41.1909	1.38305	0.691527	+	0.722350i	$0.256938\pi$
$888$	5.36936	0.180184
$889$	11.6706	0.391421
$890$	16.5596	0.555079
$891$	5.95997	0.199667
$892$	−7.92244	−0.265263
$893$	9.16687	0.306758
$894$	12.4888	0.417687
$895$	−3.77823	−0.126292
$896$	−7.72940	−0.258221
$897$	3.44168	0.114915
$898$	−35.8445	−1.19615
$899$	−17.8974	−0.596913
$900$	−2.70818	−0.0902727
$901$	39.1171	1.30318
$902$	2.29000	0.0762487
$903$	2.12332	0.0706598
$904$	10.0824	0.335337
$905$	−5.13011	−0.170531
$906$	−2.01231	−0.0668545
$907$	−11.4484	−0.380137	−0.190068	−	0.981771i	$-0.560871\pi$
$907$	−11.4484	−0.380137	−0.190068	+	0.981771i	$0.560871\pi$
$908$	1.36573	0.0453233
$909$	−6.84080	−0.226895
$910$	−2.37815	−0.0788349
$911$	−29.1575	−0.966032	−0.483016	−	0.875611i	$-0.660459\pi$
$911$	−29.1575	−0.966032	−0.483016	+	0.875611i	$0.660459\pi$
$912$	1.61908	0.0536130
$913$	0.547246	0.0181112
$914$	28.4343	0.940522
$915$	0.684069	0.0226146
$916$	3.01317	0.0995578
$917$	−11.6157	−0.383586
$918$	−19.5814	−0.646284
$919$	45.1302	1.48871	0.744354	−	0.667785i	$-0.232758\pi$
$919$	45.1302	1.48871	0.744354	+	0.667785i	$0.232758\pi$
$920$	16.9397	0.558486
$921$	−6.87305	−0.226475
$922$	36.4946	1.20188
$923$	−12.7924	−0.421067
$924$	−0.106170	−0.00349274
$925$	−13.0160	−0.427962
$926$	33.9632	1.11610
$927$	−8.77911	−0.288344
$928$	8.30782	0.272717
$929$	0.458441	0.0150410	0.00752049	−	0.999972i	$-0.497606\pi$
$929$	0.458441	0.0150410	0.00752049	+	0.999972i	$0.497606\pi$
$930$	2.64874	0.0868558
$931$	6.20986	0.203520
$932$	0.795347	0.0260525
$933$	1.63086	0.0533919
$934$	19.2954	0.631365
$935$	5.72730	0.187303
$936$	13.0999	0.428183
$937$	−0.0852524	−0.00278507	−0.00139254	−	0.999999i	$-0.500443\pi$
$937$	−0.0852524	−0.00278507	−0.00139254	+	0.999999i	$0.500443\pi$
$938$	−11.1770	−0.364942
$939$	−10.3105	−0.336470
$940$	−3.17580	−0.103583
$941$	−43.8558	−1.42966	−0.714829	−	0.699300i	$-0.753495\pi$
$941$	−43.8558	−1.42966	−0.714829	+	0.699300i	$0.753495\pi$
$942$	−5.47191	−0.178284
$943$	9.36974	0.305121
$944$	−2.34698	−0.0763877
$945$	3.16431	0.102935
$946$	−5.36103	−0.174302
$947$	−7.43315	−0.241545	−0.120773	−	0.992680i	$-0.538537\pi$
$947$	−7.43315	−0.241545	−0.120773	+	0.992680i	$0.538537\pi$
$948$	1.09455	0.0355494
$949$	−17.7513	−0.576232
$950$	−4.58513	−0.148761
$951$	−0.540480	−0.0175263
$952$	−15.0180	−0.486738
$953$	−36.3525	−1.17757	−0.588786	−	0.808289i	$-0.700394\pi$
$953$	−36.3525	−1.17757	−0.588786	+	0.808289i	$0.700394\pi$
$954$	−26.2067	−0.848472
$955$	0.0714709	0.00231274
$956$	2.62169	0.0847914
$957$	−2.13040	−0.0688659
$958$	−23.3971	−0.755925
$959$	−12.9210	−0.417240
$960$	−5.20369	−0.167948
$961$	−19.3513	−0.624236
$962$	7.78716	0.251068
$963$	20.1553	0.649494
$964$	1.15281	0.0371295
$965$	−4.28879	−0.138061
$966$	2.64340	0.0850499
$967$	32.6754	1.05077	0.525384	−	0.850865i	$-0.323922\pi$
$967$	32.6754	1.05077	0.525384	+	0.850865i	$0.323922\pi$
$968$	−30.7359	−0.987889
$969$	2.61658	0.0840567
$970$	11.1200	0.357040
$971$	−46.5886	−1.49510	−0.747549	−	0.664207i	$-0.768770\pi$
$971$	−46.5886	−1.49510	−0.747549	+	0.664207i	$0.768770\pi$
$972$	−3.27633	−0.105088
$973$	−16.1175	−0.516703
$974$	17.7245	0.567931
$975$	2.60937	0.0835666
$976$	3.87672	0.124091
$977$	−1.63717	−0.0523776	−0.0261888	−	0.999657i	$-0.508337\pi$
$977$	−1.63717	−0.0523776	−0.0261888	+	0.999657i	$0.508337\pi$
$978$	8.16481	0.261082
$979$	8.66873	0.277054
$980$	−2.15136	−0.0687227
$981$	−7.55350	−0.241165
$982$	−0.713573	−0.0227710
$983$	−45.2803	−1.44422	−0.722109	−	0.691779i	$-0.756827\pi$
$983$	−45.2803	−1.44422	−0.722109	+	0.691779i	$0.756827\pi$
$984$	−2.93047	−0.0934201
$985$	−26.6352	−0.848667
$986$	−37.2722	−1.18699
$987$	−4.00678	−0.127537
$988$	−0.450802	−0.0143419
$989$	−21.9351	−0.697496
$990$	−3.83703	−0.121949
$991$	−18.8343	−0.598292	−0.299146	−	0.954207i	$-0.596702\pi$
$991$	−18.8343	−0.598292	−0.299146	+	0.954207i	$0.596702\pi$
$992$	−5.40720	−0.171679
$993$	−7.38911	−0.234486
$994$	−9.82525	−0.311638
$995$	5.65760	0.179358
$996$	−0.0866160	−0.00274453
$997$	25.8592	0.818968	0.409484	−	0.912317i	$-0.365709\pi$
$997$	25.8592	0.818968	0.409484	+	0.912317i	$0.365709\pi$
$998$	6.81465	0.215714
$999$	−10.3614	−0.327821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.a.1.4	✓	11
3.2	odd	2		3141.2.a.b.1.8		11
4.3	odd	2		5584.2.a.j.1.3		11
5.4	even	2		8725.2.a.l.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.a.1.4	✓	11	1.1	even	1	trivial
3141.2.a.b.1.8		11	3.2	odd	2
5584.2.a.j.1.3		11	4.3	odd	2
8725.2.a.l.1.8		11	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)

\(f(q)\)	\(=\)	\(q-1.31062 q^{2} +0.477277 q^{3} -0.282282 q^{4} -1.24067 q^{5} -0.625527 q^{6} +0.925788 q^{7} +2.99120 q^{8} -2.77221 q^{9} +O(q^{10})\)	\(q-1.31062 q^{2} +0.477277 q^{3} -0.282282 q^{4} -1.24067 q^{5} -0.625527 q^{6} +0.925788 q^{7} +2.99120 q^{8} -2.77221 q^{9} +1.62604 q^{10} +0.851211 q^{11} -0.134727 q^{12} -1.57978 q^{13} -1.21335 q^{14} -0.592142 q^{15} -3.35575 q^{16} -5.42322 q^{17} +3.63330 q^{18} -1.01090 q^{19} +0.350218 q^{20} +0.441857 q^{21} -1.11561 q^{22} -4.56462 q^{23} +1.42763 q^{24} -3.46074 q^{25} +2.07048 q^{26} -2.75494 q^{27} -0.261333 q^{28} -5.24388 q^{29} +0.776072 q^{30} +3.41301 q^{31} -1.58429 q^{32} +0.406263 q^{33} +7.10776 q^{34} -1.14860 q^{35} +0.782544 q^{36} +3.76104 q^{37} +1.32490 q^{38} -0.753991 q^{39} -3.71109 q^{40} -2.05269 q^{41} -0.579105 q^{42} +4.80546 q^{43} -0.240282 q^{44} +3.43939 q^{45} +5.98248 q^{46} -9.06805 q^{47} -1.60162 q^{48} -6.14292 q^{49} +4.53571 q^{50} -2.58837 q^{51} +0.445943 q^{52} -7.21290 q^{53} +3.61067 q^{54} -1.05607 q^{55} +2.76921 q^{56} -0.482478 q^{57} +6.87272 q^{58} +0.699390 q^{59} +0.167151 q^{60} -1.15525 q^{61} -4.47316 q^{62} -2.56648 q^{63} +8.78790 q^{64} +1.95998 q^{65} -0.532456 q^{66} +9.21165 q^{67} +1.53088 q^{68} -2.17859 q^{69} +1.50537 q^{70} +8.09760 q^{71} -8.29222 q^{72} +11.2366 q^{73} -4.92928 q^{74} -1.65173 q^{75} +0.285358 q^{76} +0.788041 q^{77} +0.988194 q^{78} -8.12424 q^{79} +4.16338 q^{80} +7.00175 q^{81} +2.69029 q^{82} +0.642902 q^{83} -0.124728 q^{84} +6.72841 q^{85} -6.29812 q^{86} -2.50278 q^{87} +2.54614 q^{88} +10.1840 q^{89} -4.50773 q^{90} -1.46254 q^{91} +1.28851 q^{92} +1.62895 q^{93} +11.8847 q^{94} +1.25419 q^{95} -0.756144 q^{96} +6.83867 q^{97} +8.05101 q^{98} -2.35973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9	\( 11 q - 5 q^{2} - 6 q^{3} + 5 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} - 15 q^{8} + 3 q^{9} + 2 q^{10} - 31 q^{11} - 4 q^{13} - 7 q^{14} - 12 q^{15} + 5 q^{16} - q^{17} - 17 q^{19} - 10 q^{20} - 15 q^{21} + 17 q^{22} - 24 q^{23} - 3 q^{24} + 10 q^{25} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 17 q^{29} + 9 q^{30} - 10 q^{31} - 5 q^{32} + 11 q^{33} + 2 q^{34} - 28 q^{35} - 4 q^{36} - q^{37} + 2 q^{38} + 8 q^{39} + 21 q^{40} - 15 q^{41} + 30 q^{42} - 5 q^{43} - 24 q^{44} - 3 q^{45} + 23 q^{46} + 4 q^{47} + 29 q^{48} + 14 q^{49} - 3 q^{50} - 19 q^{51} + 25 q^{52} - 3 q^{53} + 28 q^{54} + 24 q^{55} + 8 q^{56} + 11 q^{57} + 8 q^{58} - 52 q^{59} + 21 q^{60} + 42 q^{62} + 35 q^{63} + 5 q^{64} - 3 q^{65} + 30 q^{66} - 23 q^{67} + 15 q^{68} + 25 q^{69} + 27 q^{70} - 30 q^{71} + 23 q^{72} + 12 q^{73} + 30 q^{74} + 34 q^{75} + 2 q^{76} + 6 q^{77} + 41 q^{78} + 11 q^{79} + 18 q^{80} + 7 q^{81} + 46 q^{82} - 13 q^{83} + 23 q^{84} + 19 q^{85} - 21 q^{86} + 35 q^{87} + 80 q^{88} - 19 q^{89} + 38 q^{90} - 30 q^{91} + q^{92} + 13 q^{93} - 2 q^{94} - 7 q^{95} + 13 q^{96} + 26 q^{97} + 35 q^{98} - 41 q^{99}+O(q^{100}) \) 11 * q - 5 * q^2 - 6 * q^3 + 5 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 - 15 * q^8 + 3 * q^9 + 2 * q^10 - 31 * q^11 - 4 * q^13 - 7 * q^14 - 12 * q^15 + 5 * q^16 - q^17 - 17 * q^19 - 10 * q^20 - 15 * q^21 + 17 * q^22 - 24 * q^23 - 3 * q^24 + 10 * q^25 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 17 * q^29 + 9 * q^30 - 10 * q^31 - 5 * q^32 + 11 * q^33 + 2 * q^34 - 28 * q^35 - 4 * q^36 - q^37 + 2 * q^38 + 8 * q^39 + 21 * q^40 - 15 * q^41 + 30 * q^42 - 5 * q^43 - 24 * q^44 - 3 * q^45 + 23 * q^46 + 4 * q^47 + 29 * q^48 + 14 * q^49 - 3 * q^50 - 19 * q^51 + 25 * q^52 - 3 * q^53 + 28 * q^54 + 24 * q^55 + 8 * q^56 + 11 * q^57 + 8 * q^58 - 52 * q^59 + 21 * q^60 + 42 * q^62 + 35 * q^63 + 5 * q^64 - 3 * q^65 + 30 * q^66 - 23 * q^67 + 15 * q^68 + 25 * q^69 + 27 * q^70 - 30 * q^71 + 23 * q^72 + 12 * q^73 + 30 * q^74 + 34 * q^75 + 2 * q^76 + 6 * q^77 + 41 * q^78 + 11 * q^79 + 18 * q^80 + 7 * q^81 + 46 * q^82 - 13 * q^83 + 23 * q^84 + 19 * q^85 - 21 * q^86 + 35 * q^87 + 80 * q^88 - 19 * q^89 + 38 * q^90 - 30 * q^91 + q^92 + 13 * q^93 - 2 * q^94 - 7 * q^95 + 13 * q^96 + 26 * q^97 + 35 * q^98 - 41 * q^99

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